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https://en.wikipedia.org/wiki/Generic%20polynomial
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In mathematics, a generic polynomial refers usually to a polynomial whose coefficients are indeterminates. For example, if , , and are indeterminates, the generic polynomial of degree two in is
However in Galois theory, a branch of algebra, and in this article, the term generic polynomial has a different, although related, meaning: a generic polynomial for a finite group G and a field F is a monic polynomial P with coefficients in the field of rational functions L = F(t1, ..., tn) in n indeterminates over F, such that the splitting field M of P has Galois group G over L, and such that every extension K/F with Galois group G can be obtained as the splitting field of a polynomial which is the specialization of P resulting from setting the n indeterminates to n elements of F. This is sometimes called F-generic or relative to the field F; a Q-generic polynomial, which is generic relative to the rational numbers is called simply generic.
The existence, and especially the construction, of a generic polynomial for a given Galois group provides a complete solution to the inverse Galois problem for that group. However, not all Galois groups have generic polynomials, a counterexample being the cyclic group of order eight.
Groups with generic polynomials
The symmetric group Sn. This is trivial, as
is a generic polynomial for Sn.
Cyclic groups Cn, where n is not divisible by eight. Lenstra showed that a cyclic group does not have a generic polynomial if n is divisible by eight
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https://en.wikipedia.org/wiki/Gesture%20recognition
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Gesture recognition is an area of research and development in computer science and language technology concerned with the recognition and interpretation of human gestures. A subdiscipline of computer vision, it employs mathematical algorithms to interpret gestures. Gestures can originate from any bodily motion or state, but commonly originate from the face or hand. One area of the field is emotion recognition derived from facial expressions and hand gestures. Users can make simple gestures to control or interact with devices without physically touching them. Many approaches have been made using cameras and computer vision algorithms to interpret sign language, however, the identification and recognition of posture, gait, proxemics, and human behaviors is also the subject of gesture recognition techniques. Gesture recognition is a path for computers to begin to better understand and interpret human body language, previously not possible through text or unenhanced graphical (GUI) user interfaces.
Overview
Gesture recognition has application in such areas as:
Automobiles
Consumer electronics
Transit
Gaming
Handheld devices
Defense
Home automation
Automated sign language translation
Gesture recognition can be conducted with techniques from computer vision and image processing.
The literature includes ongoing work in the computer vision field on capturing gestures or more general human pose and movements by cameras connected to a computer.
The term "gesture recognition" ha
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https://en.wikipedia.org/wiki/John%20Landen
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John Landen (23 January 1719 – 15 January 1790) was an English mathematician.
Life
He was born at Peakirk, near Peterborough in Northamptonshire, on 28 January 1719. He was brought up to the business of a surveyor, and acted as land agent to Earl Fitzwilliam, from 1762 to 1788.
Cultivating mathematics during his leisure hours, he became a contributor to the Ladies' Diary in 1744, published Mathematical Lucubrations in 1755, and from 1754 onwards communicated to the Royal Society valuable investigations on points connected with the fluxionary calculus.
His attempt to substitute for it a purely algebraic method, expounded in book i. of Residual Analysis was further prosecuted by Lagrange. Book ii. never appeared.
Landen's transformation, for expressing a hyperbolic arc in terms of two elliptic arcs, was inserted in the Philosophical Transactions for 1775, and specimens of its use were given in the first volume of his ‘Mathematical Memoirs (1780).
In a paper on rotary motion laid before the Royal Society on 17 March 1785 he obtained results differing from those of Euler and D'Alembert, and defending them in the second volume of Mathematical Memoirs prepared for the press during the intervals of a painful disease, and placed in his hands, printed, the day before his death at Milton, near Peterborough, the seat of the Earl Fitzwilliam on 15 January 1790.
In the same work he solved the problem of the spinning of a top, and explained Newton's error in calculating the effects of p
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https://en.wikipedia.org/wiki/H.%20T.%20Kung
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Hsiang-Tsung Kung (; born November 9, 1945) is a Taiwanese-born American computer scientist. He is the William H. Gates professor of computer science at Harvard University. His early research in parallel computing produced the systolic array in 1979, which has since become a core computational component of hardware accelerators for artificial intelligence, including Google's Tensor Processing Unit (TPU). Similarly, he proposed optimistic concurrency control in 1981, now a key principle in memory and database transaction systems, including MySQL, Apache CouchDB, Google's App Engine, and Ruby on Rails. He remains an active researcher, with ongoing contributions to computational complexity theory, hardware design, parallel computing, routing, wireless communication, signal processing, and artificial intelligence.
Kung is well-known as an influential mentor. His 1987 advice on Ph.D. research remains well cited. Throughout his career, he has been equally regarded for the role of his own research as for the legacy of his students, who have gone on to become pillars at Y Combinator, Google Brain, IBM, Intel, Akamai, MediaTek, Stanford, and MIT.
He was elected a member of the US National Academy of Engineering 1993 for introducing the idea of systolic computation, contributions to parallel computing, and applying complexity analysis to very-large-scale integrated (VLSI) computation. Kung is also a Guggenheim Fellow, member of the Academia Sinica in Taiwan, and president of the Taiw
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https://en.wikipedia.org/wiki/Christoffel%20symbols
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In mathematics and physics, the Christoffel symbols are an array of numbers describing a metric connection. The metric connection is a specialization of the affine connection to surfaces or other manifolds endowed with a metric, allowing distances to be measured on that surface. In differential geometry, an affine connection can be defined without reference to a metric, and many additional concepts follow: parallel transport, covariant derivatives, geodesics, etc. also do not require the concept of a metric. However, when a metric is available, these concepts can be directly tied to the "shape" of the manifold itself; that shape is determined by how the tangent space is attached to the cotangent space by the metric tensor. Abstractly, one would say that the manifold has an associated (orthonormal) frame bundle, with each "frame" being a possible choice of a coordinate frame. An invariant metric implies that the structure group of the frame bundle is the orthogonal group . As a result, such a manifold is necessarily a (pseudo-)Riemannian manifold. The Christoffel symbols provide a concrete representation of the connection of (pseudo-)Riemannian geometry in terms of coordinates on the manifold. Additional concepts, such as parallel transport, geodesics, etc. can then be expressed in terms of Christoffel symbols.
In general, there are an infinite number of metric connections for a given metric tensor; however, there is a unique connection that is free of torsion, the Levi-Civ
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https://en.wikipedia.org/wiki/Kuzyk%20quantum%20gap
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The Kuzyk quantum gap is a discrepancy between the maximum value of the nonlinear-optical susceptibility allowed by quantum mechanics and the highest values actually observed in real molecules. The highest possible value (in theory) is known as the Kuzyk limit, after its discoverer Professor Mark G. Kuzyk of Washington State University.
Background
In 2000, Professor Mark G. Kuzyk of Washington State University calculated the fundamental limit of the nonlinear-optical susceptibility of molecules. The nonlinear susceptibility is a measure of how strongly light interacts with matter. As such, these results can be used to predict the maximum attainable efficiency of various types of optical devices.
For example, Kuzyk's theory can be used to estimate how efficiently optical information can be manipulated in an optical fiber (based on the Kerr effect), which in turn is related to the amount of information that a fiber-optic system can handle. In effect, the speed limit of the internet is intimately linked to the Kuzyk limit.
One peculiar finding is that all molecules that have ever been measured appear to fall below the Kuzyk limit by about a factor of 30. This factor-of-thirty gap between the fundamental limit and the best molecules is called the Kuzyk quantum gap. Nobody understands the cause of this gap, but there is no reason to believe that it is of a fundamental nature. It is therefore likely that new approaches to synthetic chemistry may find ways to make better mo
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https://en.wikipedia.org/wiki/Lambda%20%28unit%29
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Lambda (written λ, in lowercase) is a non-SI unit of volume equal to 10−9 m3, 1 cubic millimetre (mm3) or 1 microlitre (μL). Introduced by the BIPM in 1880, the lambda has been used in chemistry and in law for measuring volume, but its use is not recommended.
This use of λ parallels the pre-SI use of μ on its own for a micrometre and γ for a microgram. Although the use of λ is deprecated, some clinical laboratories continue to use it. The standard abbreviation μL for a microlitre has the disadvantage that it can be misread as mL (a unit 1000 times larger). In pharmaceutical use, no abbreviation for a microlitre is considered safe. The recommended practice is to write "microlitre" in full.
References
Units of volume
Customary units of measurement
Typographical symbols
Non-SI metric units
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https://en.wikipedia.org/wiki/Human%20mitochondrial%20genetics
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Human mitochondrial genetics is the study of the genetics of human mitochondrial DNA (the DNA contained in human mitochondria). The human mitochondrial genome is the entirety of hereditary information contained in human mitochondria. Mitochondria are small structures in cells that generate energy for the cell to use, and are hence referred to as the "powerhouses" of the cell.
Mitochondrial DNA (mtDNA) is not transmitted through nuclear DNA (nDNA). In humans, as in most multicellular organisms, mitochondrial DNA is inherited only from the mother's ovum. There are theories, however, that paternal mtDNA transmission in humans can occur under certain circumstances.
Mitochondrial inheritance is therefore non-Mendelian, as Mendelian inheritance presumes that half the genetic material of a fertilized egg (zygote) derives from each parent.
Eighty percent of mitochondrial DNA codes for mitochondrial RNA, and therefore most mitochondrial DNA mutations lead to functional problems, which may be manifested as muscle disorders (myopathies).
Because they provide 30 molecules of ATP per glucose molecule in contrast to the 2 ATP molecules produced by glycolysis, mitochondria are essential to all higher organisms for sustaining life. The mitochondrial diseases are genetic disorders carried in mitochondrial DNA, or nuclear DNA coding for mitochondrial components. Slight problems with any one of the numerous enzymes used by the mitochondria can be devastating to the cell, and in turn, to th
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https://en.wikipedia.org/wiki/Thames%20Ironworks%20and%20Shipbuilding%20Company
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The Thames Ironworks and Shipbuilding Company, Limited was a shipyard and iron works straddling the mouth of Bow Creek at its confluence with the River Thames, at Leamouth Wharf (often referred to as Blackwall) on the west side and at Canning Town on the east side. Its main activity was shipbuilding, but it also diversified into civil engineering, marine engines, cranes, electrical engineering and motor cars.
The company notably produced iron work for Isambard Kingdom Brunel's Royal Albert Bridge over the Tamar in the 1850s, and the world's first all-iron warship, HMS Warrior, launched in 1860.
History
1837–46
The company originated in 1837 as the Ditchburn and Mare Shipbuilding Company, founded by shipwright Thomas J. Ditchburn and the engineer and naval architect Charles John Mare. Originally located at Deptford, after a fire destroyed their yard the company moved to Orchard Place in 1838, between the East India Dock Basin and Bow Creek. There they took over the premises of the defunct shipbuilders William and Benjamin Wallis.
The firm did well and within a few years occupied three sites covering an area of over .
Ditchburn and Mare were among the first builders of iron ships in the area; their partnership commenced with the construction of small paddle steamers of between 50 and 100 tons, before progressing to cross-Channel vessels and by 1840 were building ships of more than 300 tons. The company's early customers included the Iron Steamboat Company and the Blackwall
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https://en.wikipedia.org/wiki/Corwin%20Hansch
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Corwin Herman Hansch (October 6, 1918 – May 8, 2011) was a professor of chemistry at Pomona College in California. He became known as the 'father of computer-assisted molecule design.'
Education and career
Hansch was born on October 6, 1918, in Kenmare, North Dakota. He earned a BS from the University of Illinois in 1940 and a PhD from New York University in 1944. He briefly worked as a postdoc at the University of Illinois Chicago.
Hansch worked on the Manhattan Project at the University of Chicago and as a group leader at DuPont Nemours in Richland, Washington. In February 1946 he received an academic position at Pomona College, where he taught until 1988. Hansch completed sabbaticals at ETH Zurich with Vladimir Prelog and at University of Munich with Rolf Huisgen.
Hansch taught Organic Chemistry for many years at Pomona College, and was known for giving complex lectures without using notes. His course in Physical Bio-Organic Medicinal Chemistry was ground-breaking at an undergraduate level.
Hansch may be best known as the father of the concept of quantitative structure-activity relationship (QSAR), the quantitative correlation of the physicochemical properties of molecules with their biological activities.
He is also noted for the Hansch equation, which is used in
Multivariate Statistics - Multivariate statistics is a set of statistical tools to analyse data (e.g., chemical and biological) matrices using regression and/or pattern recognition techniques.
Hansch Analy
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https://en.wikipedia.org/wiki/Kjeldahl
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Kjeldahl may refer to:
Johan Kjeldahl (1849–1900), Danish chemist
Kjeldahl method, analytical chemistry method for determining total nitrogen
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https://en.wikipedia.org/wiki/%C4%BDudov%C3%ADt%20La%C4%8Dn%C3%BD
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Ľudovít Lačný (December 8, 1926 – December 25, 2019) was a Slovak chess problem composer and judge.
Lačný was born in Banská Štiavnica and studied mathematics, working as a teacher, and as a computer programmer.
In 1956 Lačný was appointed an International Judge of Chess Compositions and in 2005 was awarded the International Master for Chess Composition title. He is best known as the eponym of the Lacny cycle, according to the theme invented by him in 1949.
External links
Lacny's page on Juraj Lorinc's website
References
Chess composers
Slovak chess players
1926 births
2019 deaths
People from Banská Štiavnica
International Judges of Chess Compositions
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https://en.wikipedia.org/wiki/List%20of%20University%20of%20California%2C%20Los%20Angeles%20people
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This is a list of notable present and former faculty, staff, and students of the University of California, Los Angeles (UCLA).
Notable alumni
Nobel laureates
Ralph Bunche – recipient of the 1950 Nobel Peace Prize
Richard F. Heck – recipient of the 2010 Nobel Prize in Chemistry
Robert Bruce Merrifield – recipient of the 1984 Nobel Prize in Chemistry
Elinor Ostrom – recipient of the 2009 Nobel Memorial Prize in Economic Sciences
Ardem Patapoutian – recipient of the 2021 Nobel Prize in Medicine
Randy Schekman – recipient of the 2013 Nobel Prize in Medicine
Glenn T. Seaborg – recipient of the 1951 Nobel Prize in Chemistry
William F. Sharpe – recipient of the 1990 Nobel Memorial Prize in Economic Sciences
Andrea Ghez – recipient of the 2020 Nobel Prize in Physics
Academia, science and technology
Arts and literature
Amy Adler – artist
Luis Aguilar-Monsalve – writer and educator
Sara Kathryn Arledge – artist
Catherine Asaro – Nebula Award-winning science-fiction novelist
Glenna Avila – artist
James Robert Baker – novelist
Gary Baseman – artist
Edith Baumann – abstract artist
Rosa Beltrán – writer, lecturer and academic
Guy Bennett – writer, translator and educator
Susan Berman – author and screenwriter
Stan Bitters – sculptor
Justina Blakeney – designer and author
Slater Bradley – artist
JaNay Brown-Wood, children's book author
Kenneth Wayne Bushnell – artist and educator
Jan Butterfield – art writer and educator
Vija Celmins – artist
Judy Chica
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https://en.wikipedia.org/wiki/Philosophy%20of%20chemistry
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The philosophy of chemistry considers the methodology and underlying assumptions of the science of chemistry. It is explored by philosophers, chemists, and philosopher-chemist teams. For much of its history, philosophy of science has been dominated by the philosophy of physics, but the philosophical questions that arise from chemistry have received increasing attention since the latter part of the 20th century.
Foundations of chemistry
Major philosophical questions arise as soon as one attempts to define chemistry and what it studies. Atoms and molecules are often assumed to be the fundamental units of chemical theory, but traditional descriptions of molecular structure and chemical bonding fail to account for the properties of many substances, including metals and metal complexes and aromaticity.
Additionally, chemists frequently use non-existent chemical entities like resonance structures to explain the structure and reactions of different substances; these explanatory tools use the language and graphical representations of molecules to describe the behavior of chemicals and chemical reactions that in reality do not behave as straightforward molecules.
Some chemists and philosophers of chemistry prefer to think of substances, rather than microstructures, as the fundamental units of study in chemistry. There is not always a one-to-one correspondence between the two methods of classifying substances. For example, many rocks exist as mineral complexes composed of multi
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https://en.wikipedia.org/wiki/Pandiagonal%20magic%20cube
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In recreational mathematics, a pandiagonal magic cube is a magic cube with the additional property that all broken diagonals (parallel to exactly two of the three coordinate axes) have the same sum as each other. Pandiagonal magic cubes are extensions of diagonal magic cubes (in which only the unbroken diagonals need to have the same sum as the rows of the cube) and generalize pandiagonal magic squares to three dimensions.
In a pandiagonal magic cube, all 3m planar arrays must be panmagic squares. The 6 oblique squares are always magic. Several of them may be panmagic squares.
A proper pandiagonal magic cube has exactly 9m2 lines plus the 4 main space diagonals summing correctly (no broken space diagonals have the correct sum.)
The smallest pandiagonal magic cube has order 7.
See also
Magic cube classes
References
Hendricks, J.R; Magic Squares to Tesseracts by Computer, Self-published 1999.
Hendricks, J.R.; Perfect n-Dimensional Magic Hypercubes of Order 2n, Self-published 1999.
Harvey Heinz: All about magic cubes
Magic squares
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https://en.wikipedia.org/wiki/Geoinformatics
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Geoinformatics is a technical science primarily within the domain of Computer Science. It focuses on the programming of applications, spatial data structures, and the analysis of objects and space-time phenomena related to the surface and underneath of Earth and other celestial bodies. The field develops software and web services to model and analyse spatial data, serving the needs of geosciences and related scientific and engineering disciplines. The term is often used interchangeably with Geomatics, although the two have distinct focuses; Geomatics emphasizes acquiring spatial knowledge and leveraging information systems, not their development.
Overview
In a general sense, geoinformatics can be understood as "a variety of efforts to promote collaboration between computer scientists and geoscientists to solve complex scientific questions". More technically, geoinformatics has been described as "the science and technology dealing with the structure and character of spatial information, its capture, its classification and qualification, its storage, processing, portrayal and dissemination, including the infrastructure necessary to secure optimal use of this information" or "the art, science or technology dealing with the acquisition, storage, processing production, presentation and dissemination of geoinformation". Along with the thriving of data science and artificial intelligence since the 2010s, the field of geoinformatics has also incorporated the latest methodology and t
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https://en.wikipedia.org/wiki/2C-P
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2C-P is a relatively potent and long acting psychedelic phenethylamine of the 2C family.
Chemistry
2C-P is 2,5-dimethoxy-4-n-propylphenethylamine. The full name of the chemical is 2-(2,5-dimethoxy-4-propylphenyl)ethanamine. The hydrochloride salt is the most common form, normally found as a white powder, or white crystals.
Alexander Shulgin's 2C-P crude freebase (soluble in chloroform), after "removal of the solvent under vacuum," was an off-white colored oil which he distilled at 100–110 °C at (turning it "water white" in color), and it "spontaneously crystallized" upon cooling.
Effects
2C-P produces intense hallucinogenic, psychedelic, and entheogenic effects including open eye visualizations and closed-eye visualizations. It can have a very slow onset if ingested, and peak effects reportedly do not occur for 3 to 5 hours. The peak lasts for five to ten hours, with the overall experience lasting up to 20 hours.
Dose
In his book PiHKAL, Shulgin listed 2C-P's dosage range as 6–10 mg and wrote that while most reports with dosages between 6 and 12 mg were favorable, "there was one report of an experience in which a single dosage of 16 mg was clearly an overdose, with the entire experiment labeled a physical disaster, not to be repeated." He cautioned readers regarding dosing with 2C-P by commenting that "a consistent observation is that there may not be too much latitude in dosage between that which would be modest, or adequate, and that which would be excessive. The nee
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https://en.wikipedia.org/wiki/Midpoint%20method
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In numerical analysis, a branch of applied mathematics, the midpoint method is a one-step method for numerically solving the differential equation,
The explicit midpoint method is given by the formula
the implicit midpoint method by
for Here, is the step size — a small positive number, and is the computed approximate value of The explicit midpoint method is sometimes also known as the modified Euler method, the implicit method is the most simple collocation method, and, applied to Hamiltonian dynamics, a symplectic integrator. Note that the modified Euler method can refer to Heun's method, for further clarity see List of Runge–Kutta methods.
The name of the method comes from the fact that in the formula above, the function giving the slope of the solution is evaluated at the midpoint between at which the value of is known and at which the value of needs to be found.
A geometric interpretation may give a better intuitive understanding of the method (see figure at right). In the basic Euler's method, the tangent of the curve at is computed using . The next value is found where the tangent intersects the vertical line . However, if the second derivative is only positive between and , or only negative (as in the diagram), the curve will increasingly veer away from the tangent, leading to larger errors as increases. The diagram illustrates that the tangent at the midpoint (upper, green line segment) would most likely give a more accurate approximation of the
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https://en.wikipedia.org/wiki/Wallace%20Smith%20Broecker
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Wallace "Wally" Smith Broecker (November 29, 1931 – February 18, 2019) was an American geochemist. He was the Newberry Professor in the Department of Earth and Environmental Sciences at Columbia University, a scientist at Columbia's Lamont–Doherty Earth Observatory and a sustainability fellow at Arizona State University. He developed the idea of a global "conveyor belt" linking the circulation of the global ocean and made major contributions to the science of the carbon cycle and the use of chemical tracers and isotope dating in oceanography. Broecker popularized the term "global warming". He received the Crafoord Prize and the Vetlesen Prize.
Life
Born in Chicago in 1931, he attended Wheaton College and interacted with J. Laurence Kulp, Paul Gast and Karl Turekian. At Wheaton, he met his wife Grace Carder. Broecker then transferred to Columbia University, graduating in 1953 with a B.A. and a Ph.D. in 1958. At Columbia, he worked at the Lamont Geological Observatory with W. Maurice Ewing and Walter Bucher.
In 1975, Broecker popularized the term global warming when he published a paper titled: "Climatic Change: Are we on the Brink of a Pronounced Global Warming?"; the phrase had previously appeared in a 1957 newspaper report about Roger Revelle's research.
Broecker co-wrote an account of climate science with the science journalist, Robert Kunzig. This included a discussion of the work of Broecker's Columbia colleague Klaus Lackner in capturing from the atmosphere—which Br
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https://en.wikipedia.org/wiki/Representation%20theory%20of%20the%20Galilean%20group
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In nonrelativistic quantum mechanics, an account can be given of the existence of mass and spin (normally explained in Wigner's classification of relativistic mechanics) in terms of the representation theory of the Galilean group, which is the spacetime symmetry group of nonrelativistic quantum mechanics.
In dimensions, this is the subgroup of the affine group on (), whose linear part leaves invariant both the metric () and the (independent) dual metric (). A similar definition applies for dimensions.
We are interested in projective representations of this group, which are equivalent to unitary representations of the nontrivial central extension of the universal covering group of the Galilean group by the one-dimensional Lie group , cf. the article Galilean group for the central extension of its Lie algebra. The method of induced representations will be used to survey these.
We focus on the (centrally extended, Bargmann) Lie algebra here, because it is simpler to analyze and we can always extend the results to the full Lie group through the Frobenius theorem.
is the generator of time translations (Hamiltonian), Pi is the generator of translations (momentum operator), Ci is the generator of Galilean boosts, and Lij stands for a generator of rotations (angular momentum operator). The central charge is a Casimir invariant.
The mass-shell invariant
is an additional Casimir invariant.
In dimensions, a third Casimir invariant is , where
somewhat analogous to the Pau
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https://en.wikipedia.org/wiki/CCR%20and%20CAR%20algebras
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In mathematics and physics CCR algebras (after canonical commutation relations) and CAR algebras (after canonical anticommutation relations) arise from the quantum mechanical study of bosons and fermions respectively. They play a prominent role in quantum statistical mechanics and quantum field theory.
CCR and CAR as *-algebras
Let be a real vector space equipped with a nonsingular real antisymmetric bilinear form (i.e. a symplectic vector space). The unital *-algebra generated by elements of subject to the relations
for any in is called the canonical commutation relations (CCR) algebra. The uniqueness of the representations of this algebra when is finite dimensional is discussed in the Stone–von Neumann theorem.
If is equipped with a nonsingular real symmetric bilinear form instead, the unital *-algebra generated by the elements of subject to the relations
for any in is called the canonical anticommutation relations (CAR) algebra.
The C*-algebra of CCR
There is a distinct, but closely related meaning of CCR algebra, called the CCR C*-algebra. Let be a real symplectic vector space with nonsingular symplectic form . In the theory of operator algebras, the CCR algebra over is the unital C*-algebra generated by elements subject to
These are called the Weyl form of the canonical commutation relations and, in particular, they imply that each is unitary and . It is well known that the CCR algebra is a simple non-separable algebra and is unique up to isomorphi
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https://en.wikipedia.org/wiki/The%20Compendious%20Book%20on%20Calculation%20by%20Completion%20and%20Balancing
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The Compendious Book on Calculation by Completion and Balancing (, ; ), also known as al-Jabr (Arabic: ), is an Arabic mathematical treatise on algebra written in Baghdad around 820 CE by the Persian polymath Muḥammad ibn Mūsā al-Khwārizmī. It was a landmark work in the history of mathematics, establishing algebra as an independent discipline.
Al-Jabr provided an exhaustive account of solving for the positive roots of polynomial equations up to the second degree. It was the first text to teach elementary algebra, and the first to teach algebra for its own sake. It also introduced the fundamental concept of "reduction" and "balancing" (which the term al-jabr originally referred to), the transposition of subtracted terms to the other side of an equation, i.e. the cancellation of like terms on opposite sides of the equation. Mathematics historian Victor J. Katz regards Al-Jabr as the first true algebra text that is still extant. Translated into Latin by Robert of Chester in 1145, it was used until the sixteenth century as the principal mathematical textbook of European universities.
Several authors have also published texts under this name, including Abū Ḥanīfa al-Dīnawarī, Abū Kāmil Shujā ibn Aslam, Abū Muḥammad al-ʿAdlī, Abū Yūsuf al-Miṣṣīṣī, 'Abd al-Hamīd ibn Turk, Sind ibn ʿAlī, Sahl ibn Bišr, and Šarafaddīn al-Ṭūsī.
Legacy
R. Rashed and Angela Armstrong write:
J. J. O'Connor and E. F. Robertson wrote in the MacTutor History of Mathematics archive:
The book
The book was
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https://en.wikipedia.org/wiki/Katherine%20Igoe
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Katherine Igoe is an Irish actress.
Early life and training
A native of Abbeyleix, County Laois, Igoe first studied computer science at University College Dublin. Having decided on a career change, she moved to Edinburgh where she trained in acting at Queen Margaret College, now known as Queen Margaret University. She graduated in 1996.
Career
Igoe has appeared in a number of TV productions, such as I Fought The Law (2003), Down to Earth (2005) with Ricky Tomlinson and Taggart (1997). She also starred as Maire Brennan in TV3's first home-made drama, School Run, which was nominated for the Best Single Drama award in the IFTAs.
She has appeared extensively on stage in the UK in plays such as The Weir (2003), Daisy Pulls It Off (2002) and Babes in the Wood (2001). Igoe has also worked as a voice actor in BBC Radio productions of Resurrection by Leo Tolstoy (2006–07), The All-Colour Vegetarian Cookbook (2005), Hippomania (2004) and Parade's End (2003).
External links
References
Irish stage actresses
Alumni of Queen Margaret University
Living people
Irish radio actresses
Year of birth missing (living people)
Actors from County Laois
People from Abbeyleix
20th-century Irish actresses
21st-century Irish actresses
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https://en.wikipedia.org/wiki/Bradley%20Schaefer
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Bradley Elliott Schaefer is a professor of astronomy and astrophysics at Louisiana State University. He received his PhD from the Massachusetts Institute of Technology in 1983.
Early life
In addition to his academic pursuits, Schaefer is remembered at MIT as the founder of the annual MIT Mystery Hunt in 1981 during his graduate studies there. The tradition of the hunt continues today.
Scientific career
His research interests include the use of photometry of exploding objects to get results of interest for physical cosmology. He has also researched the dwarf planet Pluto with the aim of understanding the atmospheric variability of the system. Bradley has also studied KIC 8462852, a star with unusual within-day light fluctuations of about 20 percent, and found that the century-long light (1890 to 1989) from the star faded by about 20 percent as well, adding to its unusual luminosity.
Hipparchus's star catalog
In 2005, at a meeting of the American Astronomical Society in San Diego, California, Schaefer reported on a potential link between the long-lost star catalog of Hipparchus and a sculpture called The Farnese Atlas, created in the 2nd century, and thus a potential source for antique astronomy. Hipparchus is considered to be one of the greatest astronomers of ancient times, but most of his works are lost to history. The Farnese Atlas depicts Atlas, from Greek mythology, bearing the weight of the heavens upon his shoulders. The heavens are represented by a globe showin
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https://en.wikipedia.org/wiki/American%20Computer%20%26%20Robotics%20Museum
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The American Computer & Robotics Museum (ACRM), formerly known as the American Computer Museum, is a museum of the history of computing, communications, artificial intelligence and robotics that is located in Bozeman, Montana, United States.
The museum's mission is "... to explore the past and imagine the future of the Information Age through thought-provoking exhibits, innovative storytelling, and the bold exchange of ideas."
History of the museum
The American Computer & Robotics Museum was founded by George and Barbara Keremedjiev as a non-profit organization in May 1990 in Bozeman, Montana. It is likely the oldest extant museum dedicated to the history of computers in the world. The museum's artifacts trace over 4,000 years of computing history and information technology. George Keremedjiev passed away in November 2018, but his wife Barbara, the Museum Board, and the museum's Executive Director continue working toward his goals to "collect, preserve, interpret, and display the artifacts and history of the information age."
Exhibits on display
The museum has several permanent exhibits on display. The Benchmarks of the Information Age provides an overview of information technology from roughly 1860 B.C.E. with the development of ancient writing systems up to 1976 C.E. with the Apple I personal computer. Another significant exhibit is the NASA Apollo program, including NASA artifacts on loan from the National Air and Space Museum, such as an Apollo Guidance Computer and a
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https://en.wikipedia.org/wiki/Isolobal%20principle
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In organometallic chemistry, the isolobal principle (more formally known as the isolobal analogy) is a strategy used to relate the structure of organic and inorganic molecular fragments in order to predict bonding properties of organometallic compounds. Roald Hoffmann described molecular fragments as isolobal "if the number, symmetry properties, approximate energy and shape of the frontier orbitals and the number of electrons in them are similar – not identical, but similar." One can predict the bonding and reactivity of a lesser-known species from that of a better-known species if the two molecular fragments have similar frontier orbitals, the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). Isolobal compounds are analogues to isoelectronic compounds that share the same number of valence electrons and structure. A graphic representation of isolobal structures, with the isolobal pairs connected through a double-headed arrow with half an orbital below, is found in Figure 1.
For his work on the isolobal analogy, Hoffmann was awarded the Nobel Prize in Chemistry in 1981, which he shared with Kenichi Fukui. In his Nobel Prize lecture, Hoffmann stressed that the isolobal analogy is a useful, yet simple, model and thus is bound to fail in certain instances.
Construction of isolobal fragments
To begin to generate an isolobal fragment, the molecule needs to follow certain criteria. Molecules based around main group elements should satisf
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https://en.wikipedia.org/wiki/Don%20Zagier
|
Don Bernard Zagier (born 29 June 1951) is an American-German mathematician whose main area of work is number theory. He is currently one of the directors of the Max Planck Institute for Mathematics in Bonn, Germany. He was a professor at the Collège de France in Paris from 2006 to 2014. Since October 2014, he is also a Distinguished Staff Associate at the International Centre for Theoretical Physics (ICTP).
Background
Zagier was born in Heidelberg, West Germany. His mother was a psychiatrist, and his father was the dean of instruction at the American College of Switzerland. His father held five different citizenships, and he spent his youth living in many different countries. After finishing high school (at age 13) and attending Winchester College for a year, he studied for three years at MIT, completing his bachelor's and master's degrees and being named a Putnam Fellow in 1967 at the age of 16. He then wrote a doctoral dissertation on characteristic classes under Friedrich Hirzebruch at Bonn, receiving his PhD at 20. He received his Habilitation at the age of 23, and was named professor at the age of 24.
Work
Zagier collaborated with Hirzebruch in work on Hilbert modular surfaces. Hirzebruch and Zagier coauthored Intersection numbers of curves on Hilbert modular surfaces and modular forms of Nebentypus, where they proved that intersection numbers of algebraic cycles on a Hilbert modular surface occur as Fourier coefficients of a modular form. Stephen Kudla, John Millson
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https://en.wikipedia.org/wiki/Metagenomics
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Metagenomics is the study of genetic material recovered directly from environmental or clinical samples by a method called sequencing. The broad field may also be referred to as environmental genomics, ecogenomics, community genomics or microbiomics.
While traditional microbiology and microbial genome sequencing and genomics rely upon cultivated clonal cultures, early environmental gene sequencing cloned specific genes (often the 16S rRNA gene) to produce a profile of diversity in a natural sample. Such work revealed that the vast majority of microbial biodiversity had been missed by cultivation-based methods.
Because of its ability to reveal the previously hidden diversity of microscopic life, metagenomics offers a powerful way of understanding the microbial world that might revolutionize understanding of biology. As the price of DNA sequencing continues to fall, metagenomics now allows microbial ecology to be investigated at a much greater scale and detail than before. Recent studies use either "shotgun" or PCR directed sequencing to get largely unbiased samples of all genes from all the members of the sampled communities.
Etymology
The term "metagenomics" was first used by Jo Handelsman, Robert M. Goodman, Michelle R. Rondon, Jon Clardy, and Sean F. Brady, and first appeared in publication in 1998. The term metagenome referenced the idea that a collection of genes sequenced from the environment could be analyzed in a way analogous to the study of a single genome. In 200
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https://en.wikipedia.org/wiki/Computer%20ethics
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Computer ethics is a part of practical philosophy concerned with how computing professionals should make decisions regarding professional and social conduct.
Margaret Anne Pierce, a professor in the Department of Mathematics and Computers at Georgia Southern University has categorized the ethical decisions related to computer technology and usage into three primary influences:
The individual's own personal [ethical] code.
Any informal code of ethical conduct that exists in the work place.
Exposure to formal codes of ethics.
Foundation
Computer ethics was first coined by Walter Maner, a professor at Bowling Green State University. Maner noticed ethical concerns that were brought up during his Medical Ethics course at Old Dominion University became more complex and difficult when the use of technology and computers became involved. The conceptual foundations of computer ethics are investigated by information ethics, a branch of philosophical ethics promoted, among others, by Luciano Floridi.
History
The concept of computer ethics originated in the 1940s with MIT professor Norbert Wiener, the American mathematician and philosopher. While working on anti-aircraft artillery during World War II, Wiener and his fellow engineers developed a system of communication between the part of a cannon that tracked a warplane, the part that performed calculations to estimate a trajectory, and the part responsible for firing. Wiener termed the science of such information feedback systems,
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https://en.wikipedia.org/wiki/Dyson%20series
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In scattering theory, a part of mathematical physics, the Dyson series, formulated by Freeman Dyson, is a perturbative expansion of the time evolution operator in the interaction picture. Each term can be represented by a sum of Feynman diagrams.
This series diverges asymptotically, but in quantum electrodynamics (QED) at the second order the difference from experimental data is in the order of 10−10. This close agreement holds because the coupling constant (also known as the fine-structure constant) of QED is much less than 1.
Notice that in this article Planck units are used, so that ħ = 1 (where ħ is the reduced Planck constant).
The Dyson operator
Suppose that we have a Hamiltonian , which we split into a free part and an interacting part , i.e. .
We will work in the interaction picture here, that is,
where is time-independent and is the possibly time-dependent interacting part of the Schrödinger picture.
To avoid subscripts, stands for in what follows.
We choose units such that the reduced Planck constant is 1.
In the interaction picture, the evolution operator defined by the equation:
is called the Dyson operator.
We have a few properties:
Identity and normalization:
Composition:
Time Reversal:
Unitarity:
and from these is possible to derive the time evolution equation of the propagator:
We notice again that in the interaction picture the Hamiltonian is the same as the interaction potential .
This equation is not to be confused with the To
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https://en.wikipedia.org/wiki/Dendrogram
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A dendrogram is a diagram representing a tree. This diagrammatic representation is frequently used in different contexts:
in hierarchical clustering, it illustrates the arrangement of the clusters produced by the corresponding analyses.
in computational biology, it shows the clustering of genes or samples, sometimes in the margins of heatmaps.
in phylogenetics, it displays the evolutionary relationships among various biological taxa. In this case, the dendrogram is also called a phylogenetic tree.
The name dendrogram derives from the two ancient greek words (), meaning "tree", and (), meaning "drawing, mathematical figure".
Clustering example
For a clustering example, suppose that five taxa ( to ) have been clustered by UPGMA based on a matrix of genetic distances. The hierarchical clustering dendrogram would show a column of five nodes representing the initial data (here individual taxa), and the remaining nodes represent the clusters to which the data belong, with the arrows representing the distance (dissimilarity). The distance between merged clusters is monotone, increasing with the level of the merger: the height of each node in the plot is proportional to the value of the intergroup dissimilarity between its two daughters (the nodes on the right representing individual observations all plotted at zero height).
See also
Cladogram
Distance matrices in phylogeny
Hierarchical clustering
MEGA, a freeware for drawing dendrograms
yEd, a freeware for drawing an
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https://en.wikipedia.org/wiki/Microarchitecture
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In electronics, computer science and computer engineering, microarchitecture, also called computer organization and sometimes abbreviated as µarch or uarch, is the way a given instruction set architecture (ISA) is implemented in a particular processor. A given ISA may be implemented with different microarchitectures; implementations may vary due to different goals of a given design or due to shifts in technology.
Computer architecture is the combination of microarchitecture and instruction set architecture.
Relation to instruction set architecture
The ISA is roughly the same as the programming model of a processor as seen by an assembly language programmer or compiler writer. The ISA includes the instructions, execution model, processor registers, address and data formats among other things. The microarchitecture includes the constituent parts of the processor and how these interconnect and interoperate to implement the ISA.
The microarchitecture of a machine is usually represented as (more or less detailed) diagrams that describe the interconnections of the various microarchitectural elements of the machine, which may be anything from single gates and registers, to complete arithmetic logic units (ALUs) and even larger elements. These diagrams generally separate the datapath (where data is placed) and the control path (which can be said to steer the data).
The person designing a system usually draws the specific microarchitecture as a kind of data flow diagram. Like a
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https://en.wikipedia.org/wiki/Desulfobacteraceae
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The Desulfobacteraceae are a family of Thermodesulfobacteriota. They reduce sulfates to sulfides to obtain energy and are strictly anaerobic. They have a respiratory and fermentative type of metabolism. Some species are chemolithotrophic and use inorganic materials to obtain energy and use hydrogen as their electron donor.
Biology and biochemistry
Morphology
Desulfobacteraceae vary widely in shape and size across the family. Desulfofaba are straight or slightly curved rods that range in size from 0.8 to 2.1 x 3.2-6.1 μm. Those in the genus Desulfobacterium are spherical or oval shaped and somewhat smaller, ranging in size from 0.9 to 1.3 x 1.5-3.0 μm or 1.5-2.0 x 2.0-2.5 μm. They stain Gram-negative and are not known to produce spores. Some species contain a single polar flagellum used for motility.
Genus and species of Desulfobacteraceae may only be definitively distinguished by analysis of 16S rDNA sequences, but certain genera may be determined through physiological characteristics alone. Desulfofrigus displays an optimal growth rate at very low temperatures compared to other sulfate reducing bacteria. It is also unable to grow in the presence of propionate.
Metabolism
Most species of Desulfobacteraceae use sulfur compounds as their main energy source. The most common source used is sulfate which, through metabolic processes, is reduced to sulfide. In an environment with little or no sulfate, sulfite or elemental sulfur may also be used and reduced into sulfide. In r
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https://en.wikipedia.org/wiki/Bethe%20lattice
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In statistical mechanics and mathematics, the Bethe lattice (also called a regular tree) is an infinite connected cycle-free graph where all vertices have the same number of neighbors. The Bethe lattice was introduced into the physics literature by Hans Bethe in 1935. In such a graph, each node is connected to z neighbors; the number z is called either the coordination number or the degree, depending on the field.
Due to its distinctive topological structure, the statistical mechanics of lattice models on this graph are often easier to solve than on other lattices. The solutions are related to the often used Bethe ansatz for these systems.
Basic Properties
When working with the Bethe lattice, it is often convenient to mark a given vertex as the root, to be used as a reference point when considering local properties of the graph.
Sizes of layers
Once a vertex is marked as the root, we can group the other vertices into layers based on their distance from the root. The number of vertices at a distance from the root is , as each vertex other than the root is adjacent to vertices at a distance one greater from the root, and the root is adjacent to vertices at a distance 1.
In statistical mechanics
The Bethe lattice is of interest in statistical mechanics mainly because lattice models on the Bethe lattice are often easier to solve than on other lattices, such as the two-dimensional square lattice. This is because the lack of cycles removes some of the more complicated int
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https://en.wikipedia.org/wiki/Paul%20Horwich
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Paul Gordon Horwich (born 1947) is a British analytic philosopher at New York University, noted for his contributions to philosophy of science, philosophy of physics, the philosophy of language (especially truth and meaning) and the interpretation of Wittgenstein's later philosophy.
Education and career
Horwich read Physics at Oxford, graduating in 1968, and earned his PhD in Philosophy from Cornell University in 1975 with a thesis on The Metric and Topology of Time, under the direction of Richard Boyd. He began his academic career at MIT, where he taught from 1973 until 1994, when he took up a post at University College London. He returned to the U.S. in 2000, to take up a chair at the CUNY Graduate Center. He moved to NYU in 2005.
Philosophical work
In Truth (1990), Horwich presented a detailed defence of the minimalist variant of the deflationary theory of truth. He is opposed to appealing to reference and truth to explicate meaning, and so has defended a naturalistic use theory of meaning in his book Meaning. Other concepts he has advanced are a probabilistic account of scientific methodology and a unified explanation of temporally asymmetric phenomena.
In the context of philosophical speculations about time travel, Horwich coined the term autofanticide for a variant of the grandfather paradox, in which a person goes back in time and deliberately or inadvertently kills their infant self.
Books
Probability and Evidence (Cambridge University Press, 1982)
Asymmetries
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https://en.wikipedia.org/wiki/Field%20equation
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In theoretical physics and applied mathematics, a field equation is a partial differential equation which determines the dynamics of a physical field, specifically the time evolution and spatial distribution of the field. The solutions to the equation are mathematical functions which correspond directly to the field, as functions of time and space. Since the field equation is a partial differential equation, there are families of solutions which represent a variety of physical possibilities. Usually, there is not just a single equation, but a set of coupled equations which must be solved simultaneously. Field equations are not ordinary differential equations since a field depends on space and time, which requires at least two variables.
Whereas the "wave equation", the "diffusion equation", and the "continuity equation" all have standard forms (and various special cases or generalizations), there is no single, special equation referred to as "the field equation".
The topic broadly splits into equations of classical field theory and quantum field theory. Classical field equations describe many physical properties like temperature of a substance, velocity of a fluid, stresses in an elastic material, electric and magnetic fields from a current, etc. They also describe the fundamental forces of nature, like electromagnetism and gravity. In quantum field theory, particles or systems of "particles" like electrons and photons are associated with fields, allowing for infinite degre
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https://en.wikipedia.org/wiki/Wiedemann%E2%80%93Franz%20law
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In physics, the Wiedemann–Franz law states that the ratio of the electronic contribution of the thermal conductivity (κ) to the electrical conductivity (σ) of a metal is proportional to the temperature (T).
Theoretically, the proportionality constant L, known as the Lorenz number, is equal to
where kB is Boltzmann's constant and e is the elementary charge.
This empirical law is named after Gustav Wiedemann and Rudolph Franz, who in 1853 reported that κ/σ has approximately the same value for different metals at the same temperature. The proportionality of κ/σ with temperature was discovered by Ludvig Lorenz in 1872.
Derivation
Qualitatively, this relationship is based upon the fact that the heat and electrical transport both involve the free electrons in the metal.
The mathematical expression of the law can be derived as following. Electrical conduction of metals is a well-known phenomenon and is attributed to the free conduction electrons, which can be measured as sketched in the figure. The current density j is observed to be proportional to the applied electric field and follows Ohm's law where the prefactor is the specific electrical conductivity. Since the electric field and the current density are vectors Ohm's law is expressed here in bold face. The conductivity can in general be expressed as a tensor of the second rank (3×3 matrix). Here we restrict the discussion to isotropic, i.e. scalar conductivity. The specific resistivity is the inverse of the conduct
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https://en.wikipedia.org/wiki/Humin
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Humins are carbon-based macromolecular substances, that can be found in soil chemistry or as a by-product from saccharide-based biorefinery processes.
Humins in soil chemistry
Soil consists of both mineral (inorganic) and organic components. The organic components can be subdivided into fractions that are soluble, largely humic acids, and insoluble, the humins. Humins make up about 50% of the organic matter in soil.
Due to their very complex molecular structure, humic substances, including humin, do not correspond to pure substances but consist of a mixture of many compounds that remain very difficult to characterize even using modern analytical techniques.
Humins from biomass sources
Humins also produced during the dehydration of sugars, as occurs during the conversion of lignocellulosic biomass to smaller, higher value organic compounds such as 5-hydroxymethylfurfural (HMF). These humins can be in the form of either viscous liquids or solids depending on the process conditions used.
Humin structure and mechanism of formation
Both the structure of humins and the mechanism by which they are synthesized is at present not well defined as the formation and chemical properties of humins will change depending on the process conditions used. Generally, humins have a polymeric furanic-type structure, with hydroxyl, aldehyde and ketone functionalities. However, the structure is dependent on feedstock type (e.g. xylose or glucose) or concentration, reaction time, temperature, ca
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https://en.wikipedia.org/wiki/Weak%20derivative
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In mathematics, a weak derivative is a generalization of the concept of the derivative of a function (strong derivative) for functions not assumed differentiable, but only integrable, i.e., to lie in the Lp space .
The method of integration by parts holds that for differentiable functions and we have
A function u' being the weak derivative of u is essentially defined by the requirement that this equation must hold for all infinitely differentiable functions vanishing at the boundary points ().
Definition
Let be a function in the Lebesgue space . We say that in is a weak derivative of if
for all infinitely differentiable functions with .
Generalizing to dimensions, if and are in the space of locally integrable functions for some open set , and if is a multi-index, we say that is the -weak derivative of if
for all , that is, for all infinitely differentiable functions with compact support in . Here is defined as
If has a weak derivative, it is often written since weak derivatives are unique (at least, up to a set of measure zero, see below).
Examples
The absolute value function , which is not differentiable at has a weak derivative known as the sign function, and given by This is not the only weak derivative for u: any w that is equal to v almost everywhere is also a weak derivative for u. (In particular, the definition of v(0) above is superfluous and can be replaced with any desired real number r.) Usually, this is not a problem, since in t
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https://en.wikipedia.org/wiki/Science%20Museum%20of%20Minnesota
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The Science Museum of Minnesota is an American museum focused on topics in technology, natural history, physical science, and mathematics education. Founded in 1907 and located in Saint Paul, Minnesota, the 501(c)(3) nonprofit institution has 385 employees and is supported by volunteers.
History
The museum was established in 1906 through the efforts of a group of businessmen, led by Charles W. Ames, with the aim of promoting intellectual and scientific growth in St. Paul. Initially known as the St. Paul Institute of Science and Letters, it was initially housed at the St. Paul Auditorium on Fourth Street. A brief merger with the St. Paul School of Fine Arts (now the Minnesota Museum of American Art) occurred in 1909.
In 1927, the museum relocated to Merriam Mansion on Capitol Hill, which had previously been the residence of Col. John Merriam. This new location offered increased exhibit storage space. Due to the museum's continued growth, it moved to the St. Paul-Ramsey Arts and Sciences Center at 30 East Tenth Street in 1964.[3] In 1978, the museum expanded into a new area on Wabasha between 10th and Exchange via a skyway connection, allowing for additional exhibit space and the addition of an IMAX Dome (OMNIMAX) cinema.
In the early 1990s, plans for a new facility, to be located adjacent to the Mississippi River, were formed. With aid from public funding initiatives, the new museum broke ground on May 1, 1997, and opened on December 11, 1999. During the move, 1.75 milli
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https://en.wikipedia.org/wiki/Connected%20category
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In category theory, a branch of mathematics, a connected category is a category in which, for every two objects X and Y there is a finite sequence of objects
with morphisms
or
for each 0 ≤ i < n (both directions are allowed in the same sequence). Equivalently, a category J is connected if each functor from J to a discrete category is constant. In some cases it is convenient to not consider the empty category to be connected.
A stronger notion of connectivity would be to require at least one morphism f between any pair of objects X and Y. Any category with this property is connected in the above sense.
A small category is connected if and only if its underlying graph is weakly connected, meaning that it is connected if one disregard the direction of the arrows.
Each category J can be written as a disjoint union (or coproduct) of a collection of connected categories, which are called the connected components of J. Each connected component is a full subcategory of J.
References
Categories in category theory
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https://en.wikipedia.org/wiki/Lev%20Shestov
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Lev Isaakovich Shestov (; 31 January [O.S. 13 February] 1866 – 19 November 1938; born Yeguda Leib Shvartsman) was a Russian existentialist and religious philosopher. He is best known for his critiques of both philosophic rationalism and positivism. His work advocated a movement beyond reason and metaphysics, arguing that these are incapable of conclusively establishing truth about ultimate problems, including the nature of God or existence. Contemporary scholars have associated his work with the label "anti-philosophy."
Shestov wrote extensively on philosophers such as Nietzsche and Kierkegaard, as well as Russian writers such as Dostoyevsky, Tolstoy, and Chekhov. His published books include Apotheosis of Groundlessness (1905) and his magnum opus Athens and Jerusalem (1930-37). After emigrating to France in 1921, he befriended and influenced thinkers such as Edmund Husserl, Benjamin Fondane, Rachel Bespaloff, and Georges Bataille. He lived in Paris until his death in 1938.
Life
Shestov was born Yeguda Leib Shvartsman in Kiev into a Jewish family. He was a cousin of Nicholas Pritzker, a lawyer who emigrated to Chicago and became the patriarch of the Pritzker family that is prominent in business and politics. He obtained an education at various places, due to fractious clashes with authority. He went on to study law and mathematics at the Moscow State University but after a clash with the Inspector of Students he was told to return to Kiev, where he completed his studies.
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https://en.wikipedia.org/wiki/TRACE
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Transition Region and Coronal Explorer (TRACE, or Explorer 73, SMEX-4) was a NASA heliophysics and solar observatory designed to investigate the connections between fine-scale magnetic fields and the associated plasma structures on the Sun by providing high resolution images and observation of the solar photosphere, the transition region, and the solar corona. A main focus of the TRACE instrument is the fine structure of coronal loops low in the solar atmosphere. TRACE is the third spacecraft in the Small Explorer program, launched on 2 April 1998, and obtained its last science image on 21 June 2010, at 23:56 UTC.
Mission
The Transition Region and Coronal Explorer (TRACE) is a NASA small explorer mission designed to examine the three-dimensional magnetic structures which emerge through the Sun's photosphere (the visible surface of the Sun) and define both the geometry and dynamics of the upper solar atmosphere (the transition region and corona). Its primary science objectives are to: (1) follow the evolution of magnetic field structures from the solar interior to the corona; (2) investigate the mechanisms of the heating of the outer solar atmosphere; and, (3) determine the triggers and onset of solar flares and mass ejections. TRACE is a single-instrument, three-axis stabilized spacecraft. The spacecraft attitude control system (ACS) utilizes three magnetic-torquer coils, a digital Sun sensor, six coarse Sun sensors, a three-axis magnetometer, four reaction wheels, and thre
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https://en.wikipedia.org/wiki/David%20Todd%20Wilkinson
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David Todd Wilkinson (May 13, 1935 – September 5, 2002) was an American cosmologist, specializing in the study of the cosmic microwave background radiation (CMB).
Education
Wilkinson was born in Hillsdale, Michigan on May 13, 1935, and earned his Ph.D. in physics at the University of Michigan under the supervision of H. Richard Crane.
Research and career
Wilkinson was a Professor of Physics at Princeton University from 1965 until his retirement in 2002. He made fundamental contributions to many major cosmic microwave background experiments, including two NASA satellites: the Cosmic Background Explorer (COBE) and the Wilkinson Microwave Anisotropy Probe (WMAP), the latter of which was named in his honor after his death due to cancer on September 5, 2002.
Accolades
Princeton President's Award for Distinguished Teaching
Election to the National Academy of Sciences (1983)
James Craig Watson Medal (2001)
References
External links
John Mather and P. James E. Peebles, "David Todd Wilkinson", Biographical Memoirs of the National Academy of Sciences (2009)
1935 births
2002 deaths
20th-century American astronomers
American cosmologists
Princeton University faculty
Deaths from cancer in New Jersey
Members of the United States National Academy of Sciences
People from Hillsdale, Michigan
University of Michigan alumni
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https://en.wikipedia.org/wiki/Trunnion
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A trunnion () is a cylindrical protrusion used as a mounting or pivoting point. First associated with cannons, they are an important military development.
Alternatively, a trunnion is a shaft that positions and supports a tilting plate. This is a misnomer, as in reality it is a cradle for the true trunnion.
In mechanical engineering (see the trunnion bearing section below), it is one part of a rotating joint where a shaft (the trunnion) is inserted into (and turns inside) a full or partial cylinder.
Medieval history
In a cannon, the trunnions are two projections cast just forward of the center of mass of the cannon and fixed to a two-wheeled movable gun carriage. As they allowed the muzzle to be raised and lowered easily, the integral casting of trunnions is seen by military historians as one of the most important advances in early field artillery.
With the creation of larger and more powerful siege guns in the early 15th century, a new way of mounting them became necessary. Stouter gun carriages were created with reinforced wheels, axles, and “trails” which extended behind the gun. Guns were now as long as eight feet in length and they were capable of shooting iron projectiles weighing from twenty-five to fifty pounds. When discharged, these wrought iron balls were comparable in range and accuracy with stone-firing bombards.
Trunnions were mounted near the center of mass to allow the barrel to be elevated to any desired angle, without having to dismount it from the c
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https://en.wikipedia.org/wiki/Science%20of%20photography
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The science of photography is the use of chemistry and physics in all aspects of photography. This applies to the camera, its lenses, physical operation of the camera, electronic camera internals, and the process of developing film in order to take and develop pictures properly.
Optics
Camera obscura
The fundamental technology of most photography, whether digital or analog, is the camera obscura effect and its ability to transform of a three dimensional scene into a two dimensional image. At its most basic, a camera obscura consists of a darkened box, with a very small hole in one side, which projects an image from the outside world onto the opposite side. This form is often referred to as a pinhole camera.
When aided by a lens, the hole in the camera doesn't have to be tiny to create a sharp and distinct image, and the exposure time can be decreased, which allows cameras to be handheld.
Lenses
A photographic lens is usually composed of several lens elements, which combine to reduce the effects of chromatic aberration, coma, spherical aberration, and other aberrations. A simple example is the three-element Cooke triplet, still in use over a century after it was first designed, but many current photographic lenses are much more complex.
Using a smaller aperture can reduce most, but not all aberrations. They can also be reduced dramatically by using an aspheric element, but these are more complex to grind than spherical or cylindrical lenses. However, with modern manuf
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https://en.wikipedia.org/wiki/Pierre%20Lemonnier%20%28physicist%29
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Pierre Lemonnier (aka Petro Lemonnier) (28 June 1675 in Saint-Sever – 27 November 1757 in Saint-Germain-en-Laye) was a French astronomer, a professor of Physics and Philosophy at the Collège d'Harcourt (University of Paris), and a member of the French Academy of Sciences.
Lemonnier published the 6-volume Latin university textbook Cursus philosophicus ad scholarum usum accommodatus (Paris, 1750/1754) which consisted of the following volumes (generally consistent with the Ratio Studiorum):
Volume 1 - Logica
Volume 2 - Metaphysica
Volume 3 - Physica Generalis including mechanics and geometry
Volume 4 - Physica Particularis (Part I) including astronomy (Ptolemaic, Copernican, Tychonic), optics, chemistry, gravity, and Newtonian versus Cartesian dynamics
Volume 5 - Physica Particularis (Part II) including fluid mechanics, human anatomy, magnetism, and miscellaneous subjects (earthquakes, electricity, botany, metallurgy, etc. ...)
Volume 6 - Moralis including appendices on trigonometry and sundials
He was also the father of Pierre Charles Le Monnier and Louis-Guillaume Le Monnier.
See also
Johann Baptiste Horvath
Andreas Jaszlinszky
Edmond Pourchot
Philip of the Blessed Trinity
Charles Morton
References
1675 births
1757 deaths
Members of the French Academy of Sciences
18th-century writers in Latin
18th-century French male writers
18th-century French physicists
18th-century French astronomers
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https://en.wikipedia.org/wiki/Lewi%20Tonks
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Lewi Tonks (1897–1971) was an American quantum physicist noted for his discovery (with Marvin D. Girardeau) of the Tonks–Girardeau gas.
Tonks was employed by General Electric for most of his working life, researching microwaves and ferromagnetism. He worked under Irving Langmuir on plasma physics, with a special interest in ball lightning, nuclear fusion, tungsten filament light bulbs, and lasers.
Tonks advocated a logarithmic pressure scale for vacuum technology to replace the torr.
Tonks was notable for his high ethical standards and concern with social problems. Several times, he put up bail money for people who could not afford to do so. He provided career counselling for the poor, and after retiring from GE worked as a volunteer for the Schenectady Human Rights Commission. He also campaigned on Vietnam war issues. In 1934, he ran for the U.S. House of Representatives from New York's 30th congressional district as a member of the Socialist Party, earning 2.5% of the vote. He ran again in 1936, winning 1.9%.
Death and professional papers
In July 1971, Tonks died of a heart attack at the age of seventy-four. He left his wife Edna and three children, Mary Lew, Joan and Bruce L. Tonks.
After his death, his collected papers containing correspondence, both personal and professional, research notes, drafts of papers and completed research papers from 1930's to the 1960s passed to his wife. Shortly thereafter, the collection was deposited at the Niels Bohr Library of the
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https://en.wikipedia.org/wiki/Incomplete%20polylogarithm
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In mathematics, the Incomplete Polylogarithm function is related to the polylogarithm function. It is sometimes known as the incomplete Fermi–Dirac integral or the incomplete Bose–Einstein integral. It may be defined by:
Expanding about z=0 and integrating gives a series representation:
where Γ(s) is the gamma function and Γ(s,x) is the upper incomplete gamma function. Since Γ(s,0)=Γ(s), it follows that:
where Lis(.) is the polylogarithm function.
References
GNU Scientific Library - Reference Manual https://www.gnu.org/software/gsl/manual/gsl-ref.html#SEC117
Special functions
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https://en.wikipedia.org/wiki/Energy%20transformation
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Energy transformation, also known as energy conversion, is the process of changing energy from one form to another. In physics, energy is a quantity that provides the capacity to perform work or moving (e.g. lifting an object) or provides heat. In addition to being converted, according to the law of conservation of energy, energy is transferable to a different location or object, but it cannot be created or destroyed.
The energy in many of its forms may be used in natural processes, or to provide some service to society such as heating, refrigeration, lighting or performing mechanical work to operate machines. For example, to heat a home, the furnace burns fuel, whose chemical potential energy is converted into thermal energy, which is then transferred to the home's air to raise its temperature.
Limitations in the conversion of thermal energy
Conversions to thermal energy from other forms of energy may occur with 100% efficiency. Conversion among non-thermal forms of energy may occur with fairly high efficiency, though there is always some energy dissipated thermally due to friction and similar processes. Sometimes the efficiency is close to 100%, such as when potential energy is converted to kinetic energy as an object falls in a vacuum. This also applies to the opposite case; for example, an object in an elliptical orbit around another body converts its kinetic energy (speed) into gravitational potential energy (distance from the other object) as it moves away from its p
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https://en.wikipedia.org/wiki/Machinery%27s%20Handbook
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Machinery's Handbook for machine shop and drafting-room; a reference book on machine design and shop practice for the mechanical engineer, draftsman, toolmaker, and machinist (the full title of the 1st edition) is a classic reference work in mechanical engineering and practical workshop mechanics in one volume published by Industrial Press, New York, since 1914. The first edition was created by Erik Oberg (1881–1951) and Franklin D. Jones (1879–1967), who are still mentioned on the title page of the 29th edition (2012). Recent editions of the handbook contain chapters on mathematics, mechanics, materials, measuring, toolmaking, manufacturing, threading, gears, and machine elements, combined with excerpts from ANSI standards. The work is available in online and ebook form as well as print.
During the decades from World War I to World War II, these phrases could refer to either of two competing reference books: McGraw-Hill's American Machinists' Handbook or Industrial Press's Machinery's Handbook. The former book ceased publication after the 8th edition (1945). (One short-lived spin-off appeared in 1955.) The latter book, Machinery's Handbook, is still regularly revised and updated, and it continues to be a "bible of the metalworking industries" today.
Machinery's Handbook is apparently the direct inspiration for similar works in other countries, such as Sweden's Karlebo handbok (1st ed. 1936).
Machinery's Encyclopedia
In 1917, Oberg and Jones also published Machinery's E
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https://en.wikipedia.org/wiki/Fuzzball%20%28string%20theory%29
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Fuzzball theory, which is derived from superstring theory, is advanced by its proponents as a description of black holes that harmonizes quantum mechanics and Albert Einstein's general theory of relativity, which have long been incompatible. Fuzzball theory dispenses with the singularity at the heart of a black hole by positing that the entire region within the black hole's event horizon is actually an extended object: a ball of strings, which are advanced as the ultimate building blocks of matter and light. Under string theory, strings are bundles of energy vibrating in complex ways in both the three physical dimensions of space as well as in compact directions—extra dimensions interwoven in the quantum foam (see Fig. 2, below).
Fuzzball theory addresses two intractable problems that classic black hole theory poses for modern physics:
It dispenses with the gravitational singularity at the heart of the black hole, which is thought to be surrounded by an event horizon, the inside of which is detached from the space and time—spacetime—of the rest of the universe (see Conventional black hole theory holds that a singularity is a zero-dimensional, zero-volume point in which all of a black hole's mass exists at infinite density. Modern physics breaks down under such extremes because gravity would be so intense that spacetime itself breaks down catastrophically.
It resolves the black hole information paradox wherein conventional black hole theory holds that the quantum informat
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https://en.wikipedia.org/wiki/Riemann%E2%80%93Siegel%20theta%20function
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In mathematics, the Riemann–Siegel theta function is defined in terms of the gamma function as
for real values of t. Here the argument is chosen in such a way that a continuous function is obtained and holds, i.e., in the same way that the principal branch of the log-gamma function is defined.
It has an asymptotic expansion
which is not convergent, but whose first few terms give a good approximation for . Its Taylor-series at 0 which converges for is
where denotes the polygamma function of order .
The Riemann–Siegel theta function is of interest in studying the Riemann zeta function, since it can rotate the Riemann zeta function such that it becomes the totally real valued Z function on the critical line .
Curve discussion
The Riemann–Siegel theta function is an odd real analytic function for real values of with three roots at and . It is an increasing function for , and has local extrema at , with value . It has a single inflection point at with , which is the minimum of its derivative.
Theta as a function of a complex variable
We have an infinite series expression for the log-gamma function
where γ is Euler's constant. Substituting for z and taking the imaginary part termwise gives the following series for θ(t)
For values with imaginary part between −1 and 1, the arctangent function is holomorphic, and it is easily seen that the series converges uniformly on compact sets in the region with imaginary part between −1/2 and 1/2, leading to a holomorphic f
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https://en.wikipedia.org/wiki/Z%20function
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In mathematics, the Z function is a function used for studying the Riemann zeta function along the critical line where the argument is one-half. It is also called the Riemann–Siegel Z function, the Riemann–Siegel zeta function, the Hardy function, the Hardy Z function and the Hardy zeta function. It can be defined in terms of the Riemann–Siegel theta function and the Riemann zeta function by
It follows from the functional equation of the Riemann zeta function that the Z function is real for real values of t. It is an even function, and real analytic for real values. It follows from the fact that the Riemann-Siegel theta function and the Riemann zeta function are both holomorphic in the critical strip, where the imaginary part of t is between −1/2 and 1/2, that the Z function is holomorphic in the critical strip also. Moreover, the real zeros of Z(t) are precisely the zeros of the zeta function along the critical line, and complex zeros in the Z function critical strip correspond to zeros off the critical line of the Riemann zeta function in its critical strip.
The Riemann–Siegel formula
Calculation of the value of Z(t) for real t, and hence of the zeta function along the critical line, is greatly expedited by the Riemann–Siegel formula. This formula tells us
where the error term R(t) has a complex asymptotic expression in terms of the function
and its derivatives. If , and then
where the ellipsis indicates we may continue on to higher and increasingly complex term
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https://en.wikipedia.org/wiki/Wider%20than%20the%20Sky
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Wider than the Sky: The Phenomenal Gift of Consciousness is an English-language book on neuroscience by the neuroscientist Gerald M. Edelman. Yale University Press published the book in 2004. The book includes a glossary, a bibliographic note, and an index. The title alludes to an English-language poem written by Emily Dickinson in about 1862. In that poem, Dickinson describes the brain as "wider than the sky", "deeper than the sea", and "just the weight of God".
In the preface, Edelman describes, as follows, the purpose of the book.
The book's content is similar to the 2000 book Edelman co-authored: A Universe of Consciousness: How Matter Becomes Imagination. Both books put forward the theory of neuronal group selection, also known as neural Darwinism. Both books make a distinction between primary consciousness and higher-order consciousness.
Reviews
2004 non-fiction books
Biology books
Books about consciousness
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https://en.wikipedia.org/wiki/Megatrajectory
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In evolutionary biology, megatrajectories are the major evolutionary milestones and directions in the evolution of life.
Posited by A. H. Knoll and Richard K. Bambach in their 2000 collaboration, "Directionality in the History of Life," Knoll and Bamback argue that, in consideration of the problem of progress in evolutionary history, a middle road that encompasses both contingent and convergent features of biological evolution may be attainable through the idea of the megatrajectory:
We believe that six broad megatrajectories capture the essence of vectoral change in the history of life. The megatrajectories for a logical sequence dictated by the necessity for complexity level N to exist before N+1 can evolve...In the view offered here, each megatrajectory adds new and qualitatively distinct dimensions to the way life utilizes ecospace.
According to Knoll and Bambach, the six megatrajectories outlined by biological evolution thus far are:
the origin of life to the "Last Common Ancestor"
prokaryote diversification
unicellular eukaryote diversification
multicellular organisms
land organisms
appearance of intelligence and technology
Milan M. Ćirković and Robert Bradbury, have taken the megatrajectory concept one step further by theorizing that a seventh megatrajectory exists: postbiological evolution triggered by the emergence of artificial intelligence at least equivalent to the biologically-evolved one, as well as the invention of several key technologies of the similar l
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https://en.wikipedia.org/wiki/Fitting%20subgroup
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In mathematics, especially in the area of algebra known as group theory, the Fitting subgroup F of a finite group G, named after Hans Fitting, is the unique largest normal nilpotent subgroup of G. Intuitively, it represents the smallest subgroup which "controls" the structure of G when G is solvable. When G is not solvable, a similar role is played by the generalized Fitting subgroup F*, which is generated by the Fitting subgroup and the components of G.
For an arbitrary (not necessarily finite) group G, the Fitting subgroup is defined to be the subgroup generated by the nilpotent normal subgroups of G. For infinite groups, the Fitting subgroup is not always nilpotent.
The remainder of this article deals exclusively with finite groups.
The Fitting subgroup
The nilpotency of the Fitting subgroup of a finite group is guaranteed by Fitting's theorem which says that the product of a finite collection of normal nilpotent subgroups of G is again a normal nilpotent subgroup. It may also be explicitly constructed as the product of the p-cores of G over all of the primes p dividing the order of G.
If G is a finite non-trivial solvable group then the Fitting subgroup is always non-trivial, i.e. if G≠1 is finite solvable, then F(G)≠1. Similarly the Fitting subgroup of G/F(G) will be nontrivial if G is not itself nilpotent, giving rise to the concept of Fitting length. Since the Fitting subgroup of a finite solvable group contains its own centralizer, this gives a method of unde
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https://en.wikipedia.org/wiki/History%20of%20chemistry
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The history of chemistry represents a time span from ancient history to the present. By 1000 BC, civilizations used technologies that would eventually form the basis of the various branches of chemistry. Examples include the discovery of fire, extracting metals from ores, making pottery and glazes, fermenting beer and wine, extracting chemicals from plants for medicine and perfume, rendering fat into soap, making glass,
and making alloys like bronze.
The protoscience of chemistry, alchemy, was unsuccessful in explaining the nature of matter and its transformations. However, by performing experiments and recording the results, alchemists set the stage for modern chemistry.
The history of chemistry is intertwined with the history of thermodynamics, especially through the work of Willard Gibbs.
Ancient history
Early humans
Fire
Arguably the first chemical reaction used in a controlled manner was fire. However, for millennia fire was seen simply as a mystical force that could transform one substance into another (burning wood, or boiling water) while producing heat and light. Fire affected many aspects of early societies. These ranged from the simplest facets of everyday life, such as cooking and habitat heating and lighting, to more advanced uses, such as making pottery and bricks and melting of metals to make tools. It was fire that led to the discovery of glass and the purification of metals; this was followed by the rise of metallurgy.
Paint
A 100,000-year-old ochre
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https://en.wikipedia.org/wiki/PM3
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PM3 or PM-3 may be:
Pm3 (dentistry), dental nomenclature for premolar tooth
PM3 (chemistry), Computational chemistry
PM3 (project management, software development, CMMI), Project Management Maturity Model
Paper Mario 3, a 2007 Wii game
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https://en.wikipedia.org/wiki/Oscillon
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In physics, an oscillon is a soliton-like phenomenon that occurs in granular and other dissipative media. Oscillons in granular media result from vertically vibrating a plate with a layer of uniform particles placed freely on top. When the sinusoidal vibrations are of the correct amplitude and frequency and the layer of sufficient thickness, a localized wave, referred to as an oscillon, can be formed by locally disturbing the particles. This meta-stable state will remain for a long time (many hundreds of thousands of oscillations) in the absence of further perturbation. An oscillon changes form with each collision of the grain layer and the plate, switching between a peak that projects above the grain layer to a crater like depression with a small rim. This self-sustaining state was named by analogy with the soliton, which is a localized wave that maintains its integrity as it moves. Whereas solitons occur as travelling waves in a fluid or as electromagnetic waves in a waveguide, oscillons may be stationary.
Oscillons of opposite phase will attract over short distances and form 'bonded' pairs. Oscillons of like phase repel. Oscillons have been observed forming 'molecule' like structures and long chains. In comparison, solitons do not form bound states.
Stable interacting localized waves with subharmonic response were discovered and named oscillons at The University of Texas at Austin. Solitary bursts had been reported earlier in a quasi-two-dimensional grain layer at the
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https://en.wikipedia.org/wiki/Social%20computing
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Social computing is an area of computer science that is concerned with the intersection of social behavior and computational systems. It is based on creating or recreating social conventions and social contexts through the use of software and technology. Thus, blogs, email, instant messaging, social network services, wikis, social bookmarking and other instances of what is often called social software illustrate ideas from social computing.
History
Social computing begins with the observation that humans—and human behavior—are profoundly social. From birth, humans orient to one another, and as they grow, they develop abilities for interacting with each other. This ranges from expression and gesture to spoken and written language. As a consequence, people are remarkably sensitive to the behavior of those around them and make countless decisions that are shaped by their social context. Whether it is wrapping up a talk when the audience starts fidgeting, choosing the crowded restaurant over the nearly deserted one, or crossing the street against the light because everyone else is doing so, social information provides a basis for inferences, planning, and coordinating activity.
The premise of 'Social Computing' is that it is possible to design digital systems that support useful functionality by making socially produced information available to their users. This information may be provided directly, as when systems show the number of users who have rated a review as helpful or
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https://en.wikipedia.org/wiki/Constantin%20Le%20Paige
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Constantin Marie Le Paige (9 March 1852 – 26 January 1929) was a Belgian mathematician.
Born in Liège, Belgium, Le Paige began studying mathematics in 1869 at the University of Liège. After studying analysis under Professor Eugène Charles Catalan, Le Paige became a professor at the Université de Liège in 1882.
While interested in astronomy and the history of mathematics, Le Paige mainly worked on the theory of algebraic form, especially algebraic curves and surfaces and more particularly for his work on the construction of cubic surfaces. Le Paige remained at the university until his retirement in 1922.
External links
Le Paige biography at www-groups.dcs.st-and.ac.uk
1852 births
1929 deaths
19th-century Belgian mathematicians
20th-century Belgian mathematicians
20th-century Belgian astronomers
University of Liège alumni
Scientists from Liège
Academic staff of the University of Liège
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https://en.wikipedia.org/wiki/Mark%20Naimark
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Mark Aronovich Naimark (; 5 December 1909 – 30 December 1978) was a Soviet mathematician who made important contributions to functional analysis and mathematical physics.
Life
Naimark was born on 5 December 1909 in Odessa, part of modern-day Ukraine, but which was then part of the Russian Empire. His family was Jewish, his father Aron Iakovlevich Naimark a professional artist, and his mother was Zefir Moiseevna. He was four years old at the onset of World War I in 1914, and seven when the tumultuous Russian Revolution began in 1917. Showing an early talent for mathematics, Naimark enrolled in a technical college at the age of fifteen in 1924 soon after the Russian Civil War had ended. There he studied while working at a foundry until enrolling in the Physics and Mathematics faculty at Odessa Institute of National Education in 1929. He married his wife Larisa Petrovna Shcherbakova in 1932, with whom he had two sons.
In 1933, Naimark began graduate studies at Odessa State University in the Department of the Theory of Functions. He was supervised by the functional analyst Mark Krein, completing his candidate's dissertation in 1936. Krein was at the time still a young mathematician, only two years older than Naimark, but had already built a research group in functional analysis, and they worked together on some of Naimark's first works on symmetric and Hermitian forms. In 1938 Naimark began his doctoral studies at the Steklov Institute of Mathematics, where he developed his ren
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https://en.wikipedia.org/wiki/Fuchsian%20model
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In mathematics, a Fuchsian model is a representation of a hyperbolic Riemann surface R as a quotient of the upper half-plane H by a Fuchsian group. Every hyperbolic Riemann surface admits such a representation. The concept is named after Lazarus Fuchs.
A more precise definition
By the uniformization theorem, every Riemann surface is either elliptic, parabolic or hyperbolic. More precisely this theorem states that a Riemann surface which is not isomorphic to either the Riemann sphere (the elliptic case) or a quotient of the complex plane by a discrete subgroup (the parabolic case) must be a quotient of the hyperbolic plane by a subgroup acting properly discontinuously and freely.
In the Poincaré half-plane model for the hyperbolic plane the group of biholomorphic transformations is the group acting by homographies, and the uniformization theorem means that there exists a discrete, torsion-free subgroup such that the Riemann surface is isomorphic to . Such a group is called a Fuchsian group, and the isomorphism is called a Fuchsian model for .
Fuchsian models and Teichmüller space
Let be a closed hyperbolic surface and let be a Fuchsian group so that is a Fuchsian model for . Let
and endow this set with the topology of pointwise convergence (sometimes called "algebraic convergence"). In this particular case this topology can most easily be defined as follows: the group is finitely generated since it is isomorphic to the fundamental group of . Let be a gener
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https://en.wikipedia.org/wiki/Massively%20parallel%20quantum%20chemistry
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Massively Parallel Quantum Chemistry (MPQC) is an ab initio computational chemistry software program. Three features distinguish it from other quantum chemistry programs such as Gaussian and GAMESS: it is open-source, has an object-oriented design, and is created from the beginning as a parallel processing program. It is available in Ubuntu and Debian.
MPQC provides implementations for a number of important methods for calculating electronic structure, including Hartree–Fock, Møller–Plesset perturbation theory (including its explicitly correlated linear R12 versions), and density functional theory.
See also
List of quantum chemistry and solid state physics software
References
External links
MPQC Homepage
Computational chemistry software
Free software programmed in C++
Free chemistry software
Chemistry software for Linux
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https://en.wikipedia.org/wiki/Pariah%20%28video%20game%29
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Pariah is a first-person shooter video game developed by Digital Extremes. It was released in May 2005 for Microsoft Windows and Xbox. It uses a modified version of the Unreal Engine and the Havok physics engine. A PlayStation 2 version was also in development but cancelled.
Gameplay
Pariah features standard first-person shooter gameplay, largely influenced by the Unreal franchise, particularly Unreal 2 (whose game engine Pariah is based on). The single-player and multi-player game feature drivable vehicles that may be used in combat. The most remarkable feature is the use of collectible weapon energy cores with which to upgrade the player's weapons, giving them additional features and greater power. Each weapon in the game can be upgraded a total of three times.
Synopsis
Pariah notably omits to explain key background information about the plot and the in-game universe from the player, and thus much of the story progresses without any context or background for the player to identify with. Even at the end of the game, many key plot points remain largely unexplained, leaving it up to the player to conjecture as to what really happened.
Setting
The game takes place 30 years after mankind fought a devastating war against an enemy known as "The Shroud". Exactly who or what the Shroud are is never actually explained. At the end of the game they are shown to be hairless humans with corpse-white skin and highly advanced technology, although whether they are aliens, terrorists, mut
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https://en.wikipedia.org/wiki/Tokamak%20Fusion%20Test%20Reactor
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The Tokamak Fusion Test Reactor (TFTR) was an experimental tokamak built at Princeton Plasma Physics Laboratory (PPPL) circa 1980 and entering service in 1982. TFTR was designed with the explicit goal of reaching scientific breakeven, the point where the heat being released from the fusion reactions in the plasma is equal or greater than the heating being supplied to the plasma by external devices to warm it up.
The TFTR never achieved this goal, but it did produce major advances in confinement time and energy density. It was the world's first magnetic fusion device to perform extensive scientific experiments with plasmas composed of 50/50 deuterium/tritium (D-T), the fuel mix required for practical fusion power production, and also the first to produce more than 10 MW of fusion power. It set several records for power output, maximum temperature, and fusion triple product.
TFTR shut down in 1997 after fifteen years of operation. PPPL used the knowledge from TFTR to begin studying another approach, the spherical tokamak, in their National Spherical Torus Experiment. The Japanese JT-60 is very similar to the TFTR, both tracing their design to key innovations introduced by Shoichi Yoshikawa (1934-2010) during his time at PPPL in the 1970s.
General
In nuclear fusion, there are two types of reactors stable enough to conduct fusion: magnetic confinement reactors and inertial confinement reactors. The former method of fusion seeks to lengthen the time that ions spend close togeth
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https://en.wikipedia.org/wiki/Left%20recursion
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In the formal language theory of computer science, left recursion is a special case of recursion where a string is recognized as part of a language by the fact that it decomposes into a string from that same language (on the left) and a suffix (on the right). For instance, can be recognized as a sum because it can be broken into , also a sum, and , a suitable suffix.
In terms of context-free grammar, a nonterminal is left-recursive if the leftmost symbol in one of its productions is itself (in the case of direct left recursion) or can be made itself by some sequence of substitutions (in the case of indirect left recursion).
Non-technical Introduction
Formal language theory may come across as very difficult. Let's start off with a very simple example just to show the problem. If we take a look at the name of a former Dutch bank, VSB Bank, you will see something odd.
What do you think the B stands for? Bank. The same word again. How many banks are in this name?
Let's chop down the name in parts:
VSB Bank:
V = Verenigde (United)
S = Spaarbank (Savings Bank)
B = Bank
Bank.
Concluding: VSB Bank = Verenigde Spaarbank Bank Bank.
Now you see what a left recursive name abbreviation is all about. The remainder of this article is not using examples, but abstractions in the forms of symbols.
Definition
A grammar is left-recursive if and only if there exists a nonterminal symbol that can derive to a sentential form with itself as the leftmost symbol. Symbolically,
,
whe
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https://en.wikipedia.org/wiki/Darwin%27s%20Black%20Box
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Darwin's Black Box: The Biochemical Challenge to Evolution (1996; second edition 2006) is a book by Michael J. Behe, a professor of biochemistry at Lehigh University in Pennsylvania and a senior fellow of the Discovery Institute's Center for Science and Culture. In the book Behe presents his notion of irreducible complexity and argues that its presence in many biochemical systems therefore indicates that they must be the result of intelligent design rather than evolutionary processes. In 1993, Behe had written a chapter on blood clotting in Of Pandas and People, presenting essentially the same arguments but without the name "irreducible complexity," which he later presented in very similar terms in a chapter in Darwin's Black Box. Behe later agreed that he had written both and agreed to the similarities when he defended intelligent design at the Kitzmiller v. Dover Area School District trial.
The book has received highly critical reviews by many scientists, arguing that the assertions made by Behe fail with logical scrutiny and amount to pseudoscience. For example, in a review for Nature, Jerry Coyne panned the book for what he saw as usage of quote mining and spurious ad hominem attacks. The New York Times also, in a critique written by Richard Dawkins, condemned the book for having promoted discredited arguments. Despite this, the book has become a commercial success, and, as a bestseller, it received a mostly supportive review from Publishers Weekly, which described it as
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https://en.wikipedia.org/wiki/Computational%20economics
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Computational economics is an interdisciplinary research discipline that involves computer science, economics, and management science. This subject encompasses computational modeling of economic systems. Some of these areas are unique, while others established areas of economics by allowing robust data analytics and solutions of problems that would be arduous to research without computers and associated numerical methods.
Computational methods have been applied in various fields of economics research, including but not limiting to:
Econometrics: Non-parametric approaches, semi-parametric approaches, and machine learning.
Dynamic systems modeling: Optimization, dynamic stochastic general equilibrium modeling, and agent-based modeling.
History
Computational economics developed concurrently with the mathematization of the field. During the early 20th century, pioneers such as Jan Tinbergen and Ragnar Frisch advanced the computerization of economics and the growth of econometrics. As a result of advancements in Econometrics, regression models, hypothesis testing, and other computational statistical methods became widely adopted in economic research. On the theoretical front, complex macroeconomic models, including the real business cycle (RBC) model and dynamic stochastic general equilibrium (DSGE) models have propelled the development and application of numerical solution methods that rely heavily on computation. In the 21st century, the development of computational alg
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https://en.wikipedia.org/wiki/Texas%20A%26M%20University%20College%20of%20Geosciences
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The Texas A&M University College of Geosciences was an academic college of Texas A&M University in College Station, Texas. The college had six academic departments and programs, including Atmospheric Sciences, Geography, Geology & Geophysics, Oceanography, Environmental Programs in Geosciences, and the Water Management & Hydrological Science (WMHS) Program. In addition, the College hosted three Research Centers and Institutes: Geochemical & Environmental Research Group (GERG), Integrated Ocean Drilling Program (IODP), and Texas Sea Grant College Program.
In 2022, the College of Geosciences merged with the College of Liberal Arts and the College of Science, along with a few other programs, to form the College of Arts & Sciences.
Facilities
The College of Geosciences is located on the main campus of Texas A&M University in College Station, Texas.
The David G. Eller Oceanography & Meteorology Building (O&M Building) has a total of of office, classroom, laboratory and storage space and is home to the Departments of Atmospheric Sciences, Geography, and Oceanography. At 15 floors, it is the tallest building on campus, and hosts a Doppler weather radar System on the roof.
The Michel T. Halbouty Geosciences Building is named in honor of Distinguished Alumnus and successful oil and gas developer Michel T. Halbouty, class of 1930. It has a total of of office, classroom, laboratory and storage space, and is home to the Department of Geology & Geophysics.
IODP is located in Resea
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https://en.wikipedia.org/wiki/OLP%20%28disambiguation%29
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OLP may refer to:
One Liberty Plaza
Off-line programming (robotics)
Our Lady Peace, a Canadian alternative rock band
Our Lady of Peace (disambiguation)
OLP Guitars
Ontario Liberal Party, a provincial political party in Ontario, Canada
Royal Mail Online Postage, a service provided by Royal Mail in the UK
Ordinal linguistic personification, the sense that ordered sequences have personalities
Open License Program, a Microsoft volume license service
Oral lichen planus of the oral mucosa
Places
Old Loggers Path, Pennsylvania, USA
Olympic Dam Airport (IATA airport code: OLP) in South Australia
Olp, a village within Sort municipal term, Pallars Sobirà, Spain
See also
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https://en.wikipedia.org/wiki/Regular%20matrix
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Regular matrix may refer to:
Mathematics
Regular stochastic matrix, a stochastic matrix such that all the entries of some power of the matrix are positive
The opposite of irregular matrix, a matrix with a different number of entries in each row
Regular Hadamard matrix, a Hadamard matrix whose row and column sums are all equal
A regular element of a Lie algebra, when the Lie algebra is gln
Invertible matrix (this usage is rare)
Other uses
QS Regular Matrix, a quadraphonic sound system developed by Sansui Electric
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https://en.wikipedia.org/wiki/Muhammed%20Zafar%20Iqbal
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Muhammed Zafar Iqbal (; ; born 23 December 1952) is a Bangladeshi science fiction author, physicist, academic, activist and former professor of computer science and engineering and former head of the department of Electrical and Electronic Engineering at Shahjalal University of Science and Technology (SUST). He achieved his PhD from University of Washington. After working 18 years as a scientist at California Institute of Technology and Bell Communications Research, he returned to Bangladesh and joined Shahjalal University of Science and Technology as a professor of Computer Science and Engineering. He retired from his teaching profession in October 2018. He is considered one of Bangladesh's top science fiction writers.
Early life and education
Muhammed Zafar Iqbal was born on 23 December 1952 in Sylhet of the then East Pakistan. His father, Faizur Rahman Ahmed, was a police officer who was killed in the Liberation War of Bangladesh. His mother was Ayesha Akhter Khatun. He spent his childhood in different parts of Bangladesh because of the transferring nature of his father's job. His elder brother, Humayun Ahmed, was a prominent writer and filmmaker. His younger brother, Ahsan Habib, is a cartoonist who is serving as the editor of the satirical magazine, Unmad. He has three sisters - Sufia Haider, Momtaz Shahid and Rukhsana Ahmed.
Iqbal passed the SSC exam from Bogra Zilla School in 1968 and the HSC exam from Dhaka College in 1970. He earned his bachelor's and master's in
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https://en.wikipedia.org/wiki/Mediant%20%28mathematics%29
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In mathematics, the mediant of two fractions, generally made up of four positive integers
and is defined as
That is to say, the numerator and denominator of the mediant are the sums of the numerators and denominators of the given fractions, respectively. It is sometimes called the freshman sum, as it is a common mistake in the early stages of learning about addition of fractions.
Technically, this is a binary operation on valid fractions (nonzero denominator), considered as ordered pairs of appropriate integers, a priori disregarding the perspective on rational numbers as equivalence classes of fractions. For example, the mediant of the fractions 1/1 and 1/2 is 2/3. However, if the fraction 1/1 is replaced by the fraction 2/2, which is an equivalent fraction denoting the same rational number 1, the mediant of the fractions 2/2 and 1/2 is 3/4. For a stronger connection to rational numbers the fractions may be required to be reduced to lowest terms, thereby selecting unique representatives from the respective equivalence classes.
The Stern–Brocot tree provides an enumeration of all positive rational numbers via mediants in lowest terms, obtained purely by iterative computation of the mediant according to a simple algorithm.
Properties
The mediant inequality: An important property (also explaining its name) of the mediant is that it lies strictly between the two fractions of which it is the mediant: If and , then This property follows from the two relations and
Co
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https://en.wikipedia.org/wiki/Obaid%20Siddiqi
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Obaid Siddiqi FRS (7 January 1932 – 26 July 2013) was an Indian National Research Professor and the Founder-Director of the Tata Institute of Fundamental Research (TIFR) National Center for Biological Sciences. He made seminal contributions to the field of behavioural neurogenetics using the genetics and neurobiology of Drosophila.
Early life and education
Obaid Siddiqi was born in 1932 in Basti district of Uttar Pradesh. He received his early education at Aligarh Muslim University where he completed
his M.Sc. He completed his Ph.D. at the University of Glasgow, under the supervision of Guido Pontecorvo. He carried out his post doctoral research at the Cold Spring Harbor Laboratory, and University of Pennsylvania. He was invited by Homi Bhabha to set up the molecular biology unit at the Tata Institute of Fundamental Research (TIFR) in Bombay in 1962. Thirty years later, he became the founding director of the TIFR National Center for Biological Sciences in Bangalore, where he would continue his research into his final days of life.
Research
Siddiqi's studies in the field of neurogenetics unravelled the link between genes, behaviour and the brain. In the 1970s, his work with Seymour Benzer at Caltech led to the discovery of temperature-sensitive paralytic Drosophila mutants and the generation and transmission of neural signals. This heralded the dawn of the field of neurogenetics.
At TIFR, Siddiqi and his graduate student, Veronica Rodrigues, isolated and characterized the
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https://en.wikipedia.org/wiki/John%20Spinks%20%28academic%29
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John William Tranter Spinks, (1 January 1908 – 27 March 1997) was President of the University of Saskatchewan from 1960 to 1975.
Life
Born in Norfolk, England, John Spinks received a BSc (1928) and his doctor of philosophy degree (Ph.D.) in chemistry (1930) from King's College London.
Spinks emigrated to Canada in 1930 to join the chemistry faculty of the University of Saskatchewan as an assistant professor and was promoted to professor in 1938, head of the Department of Chemistry in 1948, and dean of the college of Graduate Studies in 1949. In 1960 he was appointed President and served in that capacity to 1975. During his tenure, the university grew from 4,500 to 13,500 full-time students.
Spinks spent the 1933-34 academic year at the University of Darmstadt, Germany, where he first met Dr. Gerhard Herzberg, whom helped emigrate to Canada.
In 1939 Spinks married Mary Strelioff.
During World War II, Spinks developed search and rescue procedures for missing aircraft and was appointed MBE. After the war, he pioneered the use of radioactive isotopes in agricultural and chemical research.
He died in Saskatoon in 1997.
The University of Saskatchewan open source computer labs were named the Spinks Labs.
Mattergy
In 1954 Spinks wrote: “Einstein could have simplified matters considerably by coining a word such as [the hybrid word] mattergy, matter and energy merely being different forms of mattergy, mattergy I and mattergy II.”
Honours
In 1970 he was appointed a Compani
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https://en.wikipedia.org/wiki/Developmental%20robotics
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Developmental robotics (DevRob), sometimes called epigenetic robotics, is a scientific field which aims at studying the developmental mechanisms, architectures and constraints that allow lifelong and open-ended learning of new skills and new knowledge in embodied machines. As in human children, learning is expected to be cumulative and of progressively increasing complexity, and to result from self-exploration of the world in combination with social interaction. The typical methodological approach consists in starting from theories of human and animal development elaborated in fields such as developmental psychology, neuroscience, developmental and evolutionary biology, and linguistics, then to formalize and implement them in robots, sometimes exploring extensions or variants of them. The experimentation of those models in robots allows researchers to confront them with reality, and as a consequence, developmental robotics also provides feedback and novel hypotheses on theories of human and animal development.
Developmental robotics is related to but differs from evolutionary robotics (ER). ER uses populations of robots that evolve over time, whereas DevRob is interested in how the organization of a single robot's control system develops through experience, over time.
DevRob is also related to work done in the domains of robotics and artificial life.
Background
Can a robot learn like a child? Can it learn a variety of new skills and new knowledge unspecified at design t
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https://en.wikipedia.org/wiki/Mathlete
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A mathlete is a person who competes in mathematics competitions at any level or any age. More specifically, a Mathlete is a student who participates in any of the MATHCOUNTS programs, as Mathlete is a registered trademark of the MATHCOUNTS Foundation in the United States. The term is a portmanteau of the words mathematics and athlete.
Top Mathletes from MATHCOUNTS often go on to compete in the AIME, USAMO, and ARML competitions in the United States. Those in other countries generally participate in national olympiads to qualify for the International Mathematical Olympiad.
Participants in World Math Day also are commonly referred to as mathletes.
Mathletic competitions
The Putnam Exam: The William Lowell Putnam Competition is the preeminent undergraduate level mathletic competition in the United States. Administered by the Mathematical Association of America, students compete as individuals and as teams (as chosen by their Institution) for scholarships and team prize money. The exam is administered on the first saturday in December.
Mathletic off-season training
The academic off-season (traditionally referred to as "summer") can be especially difficult on mathletes, though various training regimens have been proposed to keep mathletic ability at its peak. Publications such as the MAA's The American Mathematical Monthly and the AMS's Notices of the American Mathematical Society are widely read to maintain and hone mathematical ability. Some coaches suggest seeking research
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https://en.wikipedia.org/wiki/Unbounded%20operator
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In mathematics, more specifically functional analysis and operator theory, the notion of unbounded operator provides an abstract framework for dealing with differential operators, unbounded observables in quantum mechanics, and other cases.
The term "unbounded operator" can be misleading, since
"unbounded" should sometimes be understood as "not necessarily bounded";
"operator" should be understood as "linear operator" (as in the case of "bounded operator");
the domain of the operator is a linear subspace, not necessarily the whole space;
this linear subspace is not necessarily closed; often (but not always) it is assumed to be dense;
in the special case of a bounded operator, still, the domain is usually assumed to be the whole space.
In contrast to bounded operators, unbounded operators on a given space do not form an algebra, nor even a linear space, because each one is defined on its own domain.
The term "operator" often means "bounded linear operator", but in the context of this article it means "unbounded operator", with the reservations made above. The given space is assumed to be a Hilbert space. Some generalizations to Banach spaces and more general topological vector spaces are possible.
Short history
The theory of unbounded operators developed in the late 1920s and early 1930s as part of developing a rigorous mathematical framework for quantum mechanics. The theory's development is due to John von Neumann and Marshall Stone. Von Neumann introduced using gra
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https://en.wikipedia.org/wiki/Nonlinear%20Schr%C3%B6dinger%20equation
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In theoretical physics, the (one-dimensional) nonlinear Schrödinger equation (NLSE) is a nonlinear variation of the Schrödinger equation. It is a classical field equation whose principal applications are to the propagation of light in nonlinear optical fibers and planar waveguides and to Bose–Einstein condensates confined to highly anisotropic, cigar-shaped traps, in the mean-field regime. Additionally, the equation appears in the studies of small-amplitude gravity waves on the surface of deep inviscid (zero-viscosity) water; the Langmuir waves in hot plasmas; the propagation of plane-diffracted wave beams in the focusing regions of the ionosphere; the propagation of Davydov's alpha-helix solitons, which are responsible for energy transport along molecular chains; and many others. More generally, the NLSE appears as one of universal equations that describe the evolution of slowly varying packets
of quasi-monochromatic waves in weakly nonlinear media that have dispersion. Unlike the linear Schrödinger equation, the NLSE never describes the time evolution of a quantum state. The 1D NLSE is an example of an integrable model.
In quantum mechanics, the 1D NLSE is a special case of the classical nonlinear Schrödinger field, which in turn is a classical limit of a quantum Schrödinger field. Conversely, when the classical Schrödinger field is canonically quantized, it becomes a quantum field theory (which is linear, despite the fact that it is called ″quantum nonlinear Schrödinger
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https://en.wikipedia.org/wiki/Leo%20Yaffe
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Leo Yaffe, (July 6, 1916 – May 14, 1997) was a Canadian nuclear chemistry scientist and a proponent of the peaceful uses of nuclear power.
Born in Devils Lake, North Dakota, his family moved to Winnipeg in 1920. He studied at the University of Manitoba receiving a B.Sc.(Hons) in 1940, a M.Sc. in 1941, and was awarded an honorary D.Sc. in 1982. He received a Ph.D. in 1943 from McGill University.
In 1943, he was recruited by Atomic Energy of Canada Limited to work at the Manhattan Project's Montreal Laboratory, moving to the Chalk River Laboratories, on the banks of the Ottawa River, in Ontario, at the end of the war. He remained with the AECL until 1952.
In 1952, he moved to Montreal, where the J.S. Foster cyclotron had just been built at McGill University. In 1958 he became the Macdonald Professor of Chemistry.
From 1963 to 1965 he was director of research at the International Atomic Energy Agency in Vienna. Returning to McGill he was appointed head of the department of chemistry until 1972. In 1974 he was appointed vice-principal (administration) which he held until he retired in 1981. From 1981 to 1982, he was the president of the Chemical Institute of Canada.
He married Betty Workman and has two children: Carla Krasnick, and Mark Yaffe. Yaffe died in Montreal in 1997. The McGill University Archives holds a collection of his personal papers and photographs.
Honours
Fellow, Royal Society of Canada, 1959
Doctor of Letters, Trent University, 1980
Officer, Order of C
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https://en.wikipedia.org/wiki/String%20interning
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In computer science, string interning is a method of storing only one copy of each distinct string value, which must be immutable. Interning strings makes some string processing tasks more time- or space-efficient at the cost of requiring more time when the string is created or interned. The distinct values are stored in a string intern pool.
The single copy of each string is called its intern and is typically looked up by a method of the string class, for example String.intern() in Java. All compile-time constant strings in Java are automatically interned using this method.
String interning is supported by some modern object-oriented programming languages, including Java, Python, PHP (since 5.4), Lua
and .NET languages. Lisp, Scheme, Julia, Ruby and Smalltalk are among the languages with a symbol type that are basically interned strings. The library of the Standard ML of New Jersey contains an atom type that does the same thing. Objective-C's selectors, which are mainly used as method names, are interned strings.
Objects other than strings can be interned. For example, in Java, when primitive values are boxed into a wrapper object, certain values (any boolean, any byte, any char from 0 to 127, and any short or int between −128 and 127) are interned, and any two boxing conversions of one of these values are guaranteed to result in the same object.
History
Lisp introduced the notion of interned strings for its symbols. Historically, the data structure used as a string int
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https://en.wikipedia.org/wiki/Joseph%20Tilly
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Joseph Marie de Tilly (16 August 1837 – 4 August 1906) was a Belgian military man and mathematician.
He was born in Ypres, Belgium. In 1858, he became a teacher in mathematics at the regimental school. He began with studying geometry, particularly Euclid's fifth postulate and non-Euclidean geometry. He found similar results as Lobachevsky in 1860, but the Russian mathematician was already dead at that time. Tilly is more known for his work on non-Euclidean mechanics, as he was the one who invented it. He worked thus alone on this topic until a French mathematician, Jules Hoüel, showed interest in that field. Tilly also wrote on military science and history of mathematics. He died in München, Germany.
References
1837 births
1906 deaths
Belgian mathematicians
People from Ypres
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https://en.wikipedia.org/wiki/Forward%20genetics
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Forward genetics is a molecular genetics approach of determining the genetic basis responsible for a phenotype. Forward genetics provides an unbiased approach because it relies heavily on identifying the genes or genetic factors that cause a particular phenotype or trait of interest.
This was initially done by using naturally occurring mutations or inducing mutants with radiation, chemicals, or insertional mutagenesis (e.g. transposable elements). Subsequent breeding takes place, mutant individuals are isolated, and then the gene is mapped. Forward genetics can be thought of as a counter to reverse genetics, which determines the function of a gene by analyzing the phenotypic effects of altered DNA sequences. Mutant phenotypes are often observed long before having any idea which gene is responsible, which can lead to genes being named after their mutant phenotype (e.g. Drosophila rosy gene which is named after the eye colour in mutants).
Techniques used in Forward Genetics
Forward genetics provides researchers with the ability to identify genetic changes caused by mutations that are responsible for individual phenotypes in organisms. There are three major steps involved with the process of forward genetics which includes: making random mutations, selecting the phenotype or trait of interest, and identifying the gene and its function. Forward genetics involves the use of several mutagenesis processes to induce DNA mutations at random which may include:
Chemical mutagenesis
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https://en.wikipedia.org/wiki/Annales%20de%20l%27Institut%20Fourier
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The Annales de l'Institut Fourier is a French mathematical journal publishing papers in all fields of mathematics. It was established in 1949. The journal publishes one volume per year, consisting of six issues. The current editor-in-chief is Hervé Pajot. Articles are published either in English or in French.
The journal is indexed in Mathematical Reviews, Zentralblatt MATH and the Web of Science. According to the Journal Citation Reports, the journal had a 2008 impact factor of 0.804.
References
External links
Mathematics journals
Academic journals established in 1949
Multilingual journals
Bimonthly journals
Open access journals
1949 establishments in France
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https://en.wikipedia.org/wiki/Nirmal%20Kumar%20Ganguly
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Nirmal Kumar Ganguly (born 1941) is an Indian microbiologist specialising in tropical diseases, cardiovascular diseases, and diarrhea.
Education
Ganguly is a graduate of R. G. Kar Medical College, then affiliated with the University of Calcutta. He did his MD in Microbiology from Post Graduate Institute of Medical Education and Research where he also served as Acting Director.
Career
Ganguly has been Emeritus Professor of Post Graduate Institute of Medical Education and Research and was Director General, Indian Council of Medical Research, New Delhi (1998-2007). An elected fellow of the National Academy of Medical Sciences, he is currently President of the Jawaharlal Institute of Postgraduate Medical Education and Research.
Awards and honours
He was awarded the Padma Bhushan in 2009.
References
1941 births
Living people
Indian biochemists
Scientists from Kolkata
University of Calcutta alumni
Recipients of the Padma Bhushan in medicine
Date of birth missing (living people)
Fellows of the National Academy of Medical Sciences
20th-century Indian biologists
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https://en.wikipedia.org/wiki/Differential%20equation
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In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.
The study of differential equations consists mainly of the study of their solutions (the set of functions that satisfy each equation), and of the properties of their solutions. Only the simplest differential equations are soluble by explicit formulas; however, many properties of solutions of a given differential equation may be determined without computing them exactly.
Often when a closed-form expression for the solutions is not available, solutions may be approximated numerically using computers. The theory of dynamical systems puts emphasis on qualitative analysis of systems described by differential equations, while many numerical methods have been developed to determine solutions with a given degree of accuracy.
History
Differential equations came into existence with the invention of calculus by Newton and Leibniz. In Chapter 2 of his 1671 work Methodus fluxionum et Serierum Infinitarum, Isaac Newton listed three kinds of differential equations:
In all these cases, is an unknown function of (or of and
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https://en.wikipedia.org/wiki/Ashesh%20Prosad%20Mitra
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Ashesh Prosad Mitra FNA, FASc, FRS (21 February 1927 – 3 September 2007) was a physicist who headed the National Physics Laboratory in Delhi, India and was the Director General of the Council of Scientific and Industrial Research (CSIR). He is primarily known for his work on environmental physics.
Life
Mitra studied at the Bangabasi College, an affiliated college of the University of Calcutta. He completed his post graduation studies from the renowned Rajabazar Science College campus of same university.
He was the director of the National Physical Laboratory (NPL) from 1982 to 1986 and the Director General of the Council of Scientific and Industrial Research (CSIR) from 1986 to 1991.
He died at New Delhi in September 2007.
Research
Radio & Space Physics was his area of specialization. He performed major work in the field of earth's near-space environment, through group based and space techniques. He worked on cosmic radio noise for studying the upper atmosphere led to a series of discoveries in ionosphere, solar physics and cosmic rays.
Honours and awards
He was awarded the Shanti Swarup Bhatnagar Prize for Physical Science in 1968. The citation read:
Foreign Fellow of Bangladesh Academy of Sciences
Awarded the Padma Bhushan in 1987
Fellow of the Royal Society of London in 1988.
President of the International Union of Radio Sciences - URSI between 1984-1987
Member, General Committee of International Council of Scientific Unions between 1984-1988
Fellow - Indian National
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https://en.wikipedia.org/wiki/Autar%20Singh%20Paintal
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Autar Singh Paintal (24 September 1925 – 21 December 2004) was a medical scientist who made pioneering discoveries in the area of neurosciences and respiratory sciences. He is the first Indian Physiologist to become the Fellow of the Royal Society, London.
He was a merit student and did his post graduation in physiology from King George Medical College, Lucknow.
Paintal completed his PhD under the supervision of David Whitteridge at the University of Edinburgh.
His major contribution to the world of science is the development of a single-fiber technique for recording afferent impulses from individual sensory receptors. Paintal discovered several sensory receptors including atrial B receptors, pulmonary J-receptors, ventricular pressure receptors, stomach stretch receptors, and muscle pain receptors. They have set the beginning of new era in physiological understanding.
Paintal returned to India in 1953 and joined All India Institute of Medical Sciences, New Delhi. He later became Director of the Vallabhai Patel Chest Institute. He was also the first Principal of University College of Medical Sciences, Delhi. Paintal subsequently was elevated to Director General of the Indian Council of Medical Research and he was also the founder president of Society of Scientific Values.
Paintal had 3 children by his first wife Iris Paintal. His second daughter Priti Paintal is a music composer in the UK. His second wife Dr Ashima Anand-Paintal is also a scientist.
References
Extern
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https://en.wikipedia.org/wiki/Quantum%20correlation
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In quantum mechanics, quantum correlation is the expected value of the product of the alternative outcomes. In other words, it is the expected change in physical characteristics as one quantum system passes through an interaction site. In John Bell's 1964 paper that inspired the Bell test, it was assumed that the outcomes A and B could each only take one of two values, -1 or +1. It followed that the product, too, could only be -1 or +1, so that the average value of the product would be
where, for example, N++ is the number of simultaneous instances ("coincidences") of the outcome +1 on both sides of the experiment.
However, in actual experiments, detectors are not perfect and produce many null outcomes. The correlation can still be estimated using the sum of coincidences, since clearly zeros do not contribute to the average, but in practice, instead of dividing by Ntotal, it is customary to divide by
the total number of observed coincidences. The legitimacy of this method relies on the assumption that the observed coincidences constitute a fair sample of the emitted pairs.
Following local realist assumptions as in Bell's paper, the estimated quantum correlation converges after a sufficient number of trials to
where a and b are detector settings and λ is the hidden variable, drawn from a distribution ρ(λ).
The quantum correlation is the key statistic in the CHSH inequality and some of the other Bell inequalities, tests that open the way for experimental discrimination
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https://en.wikipedia.org/wiki/F%C3%B8lner%20sequence
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In mathematics, a Følner sequence for a group is a sequence of sets satisfying a particular condition. If a group has a Følner sequence with respect to its action on itself, the group is amenable. A more general notion of Følner nets can be defined analogously, and is suited for the study of uncountable groups. Følner sequences are named for Erling Følner.
Definition
Given a group that acts on a countable set , a Følner sequence for the action is a sequence of finite subsets of which exhaust and which "don't move too much" when acted on by any group element. Precisely,
For every , there exists some such that for all , and
for all group elements in .
Explanation of the notation used above:
is the result of the set being acted on the left by . It consists of elements of the form for all in .
is the symmetric difference operator, i.e., is the set of elements in exactly one of the sets and .
is the cardinality of a set .
Thus, what this definition says is that for any group element , the proportion of elements of that are moved away by goes to 0 as gets large.
In the setting of a locally compact group acting on a measure space there is a more general definition. Instead of being finite, the sets are required to have finite, non-zero measure, and so the Følner requirement will be that
,
analogously to the discrete case. The standard case is that of the group acting on itself by left translation, in which case the measure in question is normally assumed
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https://en.wikipedia.org/wiki/Stannate
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In chemistry, the term stannate or tinnate refers to compounds of tin (Sn). Stannic acid (Sn(OH)4), the formal precursor to stannates, does not exist and is actually a hydrate of SnO2. The term is also used in naming conventions as a suffix; for example the hexachlorostannate ion is .
In materials science, two kinds of tin oxyanions are distinguished:
orthostannates contain discrete units (e.g. K4SnO4) or have a spinel structure (e.g. Mg2SnO4)
metastannates with a stoichiometry MIISnO3, MSnO3 which may contain polymeric anions or may be sometimes better described as mixed oxides
These materials are semiconductors.
Examples
Barium stannate, BaSnO3 (a metastannate)
Cobalt stannate, Co2SnO4, primary constituent of the pigment cerulean blue
Dysprosium stannate, Dy2Sn2O7
Lead stannate, Pb2SnO4, "Type I" lead-tin yellow
Potassium stannate, formally potassium hexahydroxostannate(IV), formula K2Sn(OH)6
Sodium stannate, formally sodium hexahydroxostannate(IV), formula Na2Sn(OH)6
See also
Stannite
Silicate
References
Oxometallates
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https://en.wikipedia.org/wiki/Gonzalo%20Rodriguez-Pereyra
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Gonzalo Rodriguez-Pereyra (born 7 August 1969) is a philosopher. He is currently a lecturer at the University of Oxford, where he has the title of Professor of Metaphysics, and a Tutorial Fellow at Oriel College.
Rodriguez-Pereyra has previously been a Research Fellow at Churchill College, University of Cambridge, Lecturer at the University of Edinburgh, Lecturer at the University of Oxford and Tutorial Fellow at Hertford College, and Professor at the University of Nottingham and Universidad Torcuato Di Tella.
His interests are primarily in Metaphysics and the philosophy of Leibniz. His work on resemblance nominalism provides a response to that of David Malet Armstrong and grounds resemblance relations in the sort of modal realism expressed in On the Plurality of Worlds by David Lewis.
Selected publications
Books
Resemblance Nominalism: A Solution to the Problem of Universals. Oxford: Oxford University Press, 2002.
Real Metaphysics: Essays in honour of D. H. Mellor (co-edited with Hallvard Lillehammer). London: Routledge, 2003.
Leibniz's Principle of Identity of Indiscernibles. Oxford: Oxford University Press, 2014.
Articles
'Leibniz's argument for the Principle of Identity of Indiscernibles in Primary Truths', in M. Carrara, A.-M. Nunziante, and G. Tomasi (eds.) Individuals, Minds and Bodies: Themes from Leibniz, Stuttgart : Steiner, 2004, pp. 49–59.
'Truthmaking and the Slingshot', in U. Meixner (Ed.), Metaphysics in the Post-Metaphysical Age, Wien: Verlag Hölder-Pic
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https://en.wikipedia.org/wiki/Holonomic
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Holonomic (introduced by Heinrich Hertz in 1894 from the Greek ὅλος meaning whole, entire and νόμ-ος meaning law) may refer to:
Mathematics
Holonomic basis, a set of basis vector fields {ek} such that some coordinate system {xk} exists for which
Holonomic constraints, which are expressible as a function of the coordinates and time
Holonomic module in the theory of D-modules
Holonomic function, a smooth function that is a solution of a linear homogeneous differential equation with polynomial coefficients
Other uses
Holonomic brain theory, model of cognitive function as being guided by a matrix of neurological wave interference patterns
See also
Holonomy in differential geometry
Holon (disambiguation)
Nonholonomic system, in physics, a system whose state depends on the path taken in order to achieve it
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https://en.wikipedia.org/wiki/Spray%20%28mathematics%29
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In differential geometry, a spray is a vector field H on the tangent bundle TM that encodes a quasilinear second order system of ordinary differential equations on the base manifold M. Usually a spray is required to be homogeneous in the sense that its integral curves t→ΦHt(ξ)∈TM obey the rule ΦHt(λξ)=ΦHλt(ξ) in positive reparameterizations. If this requirement is dropped, H is called a semispray.
Sprays arise naturally in Riemannian and Finsler geometry as the geodesic sprays whose integral curves are precisely the tangent curves of locally length minimizing curves.
Semisprays arise naturally as the extremal curves of action integrals in Lagrangian mechanics. Generalizing all these examples, any (possibly nonlinear) connection on M induces a semispray H, and conversely, any semispray H induces a torsion-free nonlinear connection on M. If the original connection is torsion-free it coincides with the connection induced by H, and homogeneous torsion-free connections are in one-to-one correspondence with full sprays.
Formal definitions
Let M be a differentiable manifold and (TM,πTM,M) its tangent bundle. Then a vector field H on TM (that is, a section of the double tangent bundle TTM) is a semispray on M, if any of the three following equivalent conditions holds:
(πTM)*Hξ = ξ.
JH=V, where J is the tangent structure on TM and V is the canonical vector field on TM\0.
j∘H=H, where j:TTM→TTM is the canonical flip and H is seen as a mapping TM→TTM.
A semispray H on M is a (fu
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https://en.wikipedia.org/wiki/Dependency
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Dependency, dependent or depend may refer to:
Computer science
Dependency (computer science) or coupling, a state in which one object uses a function of another object
Data dependency, which describes a dependence relation between statements in a program
Dependence analysis, in compiler theory
Dependency (UML), a relationship between one element in the Unified Modeling Language
Dependency relation, a type of binary relation in mathematics and computer science.
Functional dependency, a relationship between database attributes allowing normalization.
Dependent type, in computer science and logic, a type that depends on a value
Hidden dependency, a relation in which a change in many areas of a program produces unexpected side-effects
Library dependency, a relationship described in and managed by a software dependency manager tool to mitigate dependency hell
Economics
Dependant (British English) (Dependent - American English), a person who depends on another as a primary source of income
Dependency ratio, in economics, the ratio of the economically dependent part of the economy to the productive part
Dependency theory, an economic worldview that posits that resources flow from poor states to wealthy states
Linguistics
Dependent and independent verb forms, distinct verb forms in Goidelic languages used with or without a preceding particle
Dependency grammar is based on the dependency relation between the lexemes of a sentence
Dependent clause
Mathematics
De
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https://en.wikipedia.org/wiki/Fulkerson%20Prize
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The Fulkerson Prize for outstanding papers in the area of discrete mathematics is sponsored jointly by the Mathematical Optimization Society (MOS) and the American Mathematical Society (AMS). Up to three awards of $1,500 each are presented at each (triennial) International Symposium of the MOS. Originally, the prizes were paid out of a memorial fund administered by the AMS that was established by friends of the late Delbert Ray Fulkerson to encourage mathematical excellence in the fields of research exemplified by his work. The prizes are now funded by an endowment administered by MPS.
Winners
Source: Mathematical Optimization Society
1979:
Richard M. Karp for classifying many important NP-complete problems.
Kenneth Appel and Wolfgang Haken for the four color theorem.
Paul Seymour for generalizing the max-flow min-cut theorem to matroids.
1982:
D.B. Judin, Arkadi Nemirovski, Leonid Khachiyan, Martin Grötschel, László Lovász and Alexander Schrijver for the ellipsoid method in linear programming and combinatorial optimization.
G. P. Egorychev and D. I. Falikman for proving van der Waerden's conjecture that the matrix with all entries equal has the smallest permanent of any doubly stochastic matrix.
1985:
Jozsef Beck for tight bounds on the discrepancy of arithmetic progressions.
H. W. Lenstra Jr. for using the geometry of numbers to solve integer programs with few variables in time polynomial in the number of constraints.
Eugene M. Luks for a polynomial time gr
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https://en.wikipedia.org/wiki/Theodorus%20Moretus
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Theodorus Moretus, also known as Theodor or Theodore Moretus (1602–1667) was a Flemish Jesuit priest who was also a mathematician, geometer, theologian and philosopher. He spent most of his working life in Prague and Breslau (now Wroclaw) where he taught philosophy, theology and mathematics. He published a number of treatises on these three subjects and also on physics and music theory.
Life
Theodorus Moretus was born in Antwerp, the son of Pieter Moretus and Henrica Plantin. Both his parents were from prominent printing families: his mother was a daughter of Christophe Plantin, the founder of the famous Plantin Press in Antwerp while his father was the brother of Jan Moretus who was initially an assistant of Plantin, married another Plantin daughter and, after taking over the Plantin Press from his father-in-law, steered the business to further success well into the 17th century. Theodorus Moretus' father was a diamond trader and cutter.
Moretus studied mathematics at the Jesuit school in Antwerp founded by François d'Aguilon. He was a student at this school for seven years. He joined the Jesuit order in Mechelen as a novice on 15 November 1618. He then studied at the University of Leuven. He took physics in 1622–1623 and studied theology from 1623 to 1627. In 1627–28 Moretus is mentioned as a teacher of syntax in Bruges. His title was Magister, which indicates he had not been formally ordained yet. His aptitude for science (particularly mathematics) was appreciated
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https://en.wikipedia.org/wiki/Lw%C3%B3w%E2%80%93Warsaw%20school
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The Lwów–Warsaw School () was an interdisciplinary school (mainly philosophy, logic and psychology) founded by Kazimierz Twardowski in 1895 in Lemberg, Austro-Hungary (; now Lviv, Ukraine).
Though its members represented a variety of disciplines, from mathematics through logic to psychology, the Lwów–Warsaw School is widely considered to have been a philosophical movement. It has produced some of the leading logicians of the twentieth century such as Jan Łukasiewicz, Stanisław Leśniewski, and Alfred Tarski, among others. Its members did not only contribute to the techniques of logic but also to various domains that belong to the philosophy of language.
History
Polish philosophy and the Lwów–Warsaw school were considerably influenced by Franz Brentano and his pupils Kazimierz Twardowski, Anton Marty, Alexius Meinong, and Edmund Husserl. Twardowski founded the philosophical school when he became the chair of the Lviv University.
Principal topics of interest to the Lwów–Warsaw school included formal ontology, mereology, and universal or categorial grammar.
The Lwów-Warsaw School began as a general philosophical school but steadily moved toward logic. The Lwów–Warsaw school of logic lay at the origin of Polish logic and was closely associated with or was part of the Warsaw School of Mathematics. According to Jan Woleński, a decisive factor in the school's development was the view that the future of the Polish school of mathematics depended on the research connected with the
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