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https://en.wikipedia.org/wiki/Howard%20Georgi
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Howard Mason Georgi III (born January 6, 1947) is an American theoretical physicist and the Mallinckrodt Professor of Physics and Harvard College Professor at Harvard University. He is also director of undergraduate studies in physics. He was co-master and then faculty dean of Leverett House with his wife, Ann Blake Georgi, from 1998 to 2018. His early work was in Grand Unification and gauge coupling unification within SU(5) and SO(10) groups (see Georgi–Glashow model).
Education
Georgi graduated from Pingry School in 1964, graduated from Harvard College in 1967 and obtained his Ph.D. from Yale University in 1971. He was junior fellow in the Harvard Society of Fellows from 1973–76 and a senior fellow from 1982-1998.
Career
In early 1974 Georgi (with Sheldon Glashow) published the first grand unified theory (GUT), the Minimal SU(5) Georgi–Glashow model. Georgi independently (alongside
Harald Fritzsch and Peter Minkowski) published a minimal SO(10) GUT model in 1974.
Georgi proposed an SU(5) GUT model with softly broken supersymmetry with Savas Dimopoulos in 1981. This paper is one of the foundational works for the supersymmetric Standard Model (MSSM). After the measurements of the three Standard Model gauge couplings at LEP I in 1991, it was shown that particle content of the MSSM, in contrast to the Standard Model alone, led to precision gauge coupling unification.
He has since worked on several different areas of physics including composite Higgs models, heavy quark e
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https://en.wikipedia.org/wiki/TERON%20%28Tillage%20erosion%29
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TERON is a foundation dedicated to the assessment of tillage related erosion in Europe.
See also
Conservation biology
Environmental protection
Habitat conservation
Natural environment
Natural resource
Sustainability
Tillage erosion
External links
http://www.ex.ac.uk/~yszhang/teron/
https://web.archive.org/web/20060603160639/http://www.fi.cnr.it/irpi/teron.htm
Agricultural organizations
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https://en.wikipedia.org/wiki/Paul%20Zamecnik
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Paul Charles Zamecnik (November 22, 1912 – October 27, 2009) was an American scientist who played a central role in the early history of molecular biology. He was a professor of medicine at Harvard Medical School and a senior scientist at Massachusetts General Hospital. Zamecnik pioneered the in vitro synthesis of proteins and helped elucidate the way cells generate proteins. With Mahlon Hoagland he co-discovered transfer RNA (tRNA). Through his later work, he is credited as the inventor of antisense therapeutics. Throughout his career, Zamecnik earned over a dozen US patents for his therapeutic techniques. Up until his death in 2009 he maintained a lab at MGH where he studied the application of synthetic oligonucleotides (antisense hybrids) for chemotherapeutic treatment of drug resistant and XDR tuberculosis in his later years.
Education and research
Paul Zamecnik was born in Cleveland, Ohio to John Charles Zamecnik (1879-1930) and Mary Gertrude Mccarthy (1883-1937). John's first cousin was the composer John Stepan Zamecnik. Paul's paternal grandparents Jan Nepomucký Zámečník (1842-1915) and Konstancie Hrubecká (1843-1924) were Czech immigrants from Budičovice and Skály respectively. His mother's parents were Irish immigrants. He attended Dartmouth College, majored in chemistry and zoology, and received his AB degree in 1933. He then attended Harvard Medical School and received his MD degree in 1936. Between 1936 and 1939, he worked at Collis P. Huntington Memorial Hos
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https://en.wikipedia.org/wiki/Marv%20Kaisersatt
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Marvin Robert Kaisersatt is an American woodcarver. He was born in Montgomery, Minnesota February 1, 1939 to Bessie and Benjamin Kaisersatt.
Career
After high school in Montgomery, MN, Kaisersatt graduated from St. John's University in Collegeville, MN, with a degree in Mathematics. He then joined the US Army and spent time overseas before leaving the military early to teach math at Escuela San Antonio Abad in Humaca, Puerto Rico. He then moved to Monticello, MN, where he continued to teach before moving to Faribault in 1976, where he taught math until his retirement in 1995.
He began wood carving seriously in 1976 during a teacher's strike. A caricature carver, he specializes in carving multi-figure scenes from a single block of basswood. Pieces take on a sculptural quality through the interplay of mass and space. The carvings are finished with sealer but not varnished and presented either without color or with a hand-painted, detailed, watercolor finish and then waxed.
Kaisersatt has taught classes (held through Whillock Studios and CCA) focusing on design, clay modeling, and carving technique. He is a founding member of the Caricature Carvers of America, dedicated to promoting caricature carving. His favorite caricaturist is Al Hirschfeld. Cartooning and caricatures are prominent in Kaisersatt's designs and story lines. His book, Creating Caricature Heads in Wood and on Paper, explains carving caricature heads and describes a detailed design procedure. Kaisersatt has a
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https://en.wikipedia.org/wiki/Dante%20Lauretta
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Dante S. Lauretta (born 1970) is a professor of planetary science and cosmochemistry at the University of Arizona's Lunar and Planetary Laboratory. He is the principal investigator on NASA's OSIRIS-REx mission.
Education
Lauretta grew up in Arizona and received a B.S. in physics and mathematics and a B.A. in Oriental Studies with focus in Japanese from the University of Arizona in 1993 and a Ph.D. in Earth and planetary sciences from Washington University in St. Louis in 1997. He was a postdoctoral research associate in the Department of Geological Sciences at Arizona State University from 1997 through 1999. He was an Associate Research Scientist in the Department of Chemistry and Biochemistry at Arizona State University from 1999 through 2001. He was hired onto the faculty at the University of Arizona in 2001.
Work
His research focuses on the chemistry and mineralogy of asteroids and comets as determined by in situ laboratory analyses and spacecraft observations. This work is important for constraining the chemistry of the solar nebula, understanding the origin of complex organic molecules in the early Solar System, and constraining the initial chemical inventories of the terrestrial planets. He is an expert in the analysis of extraterrestrial materials. In particular, he uses inductively coupled plasma mass spectrometry (ICP-MS), scanning electron microscopy (SEM), transmission electron microscopy (TEM), electron microprobe analysis (EPMA), and X-ray diffraction (XRD) to
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https://en.wikipedia.org/wiki/Ted%20Gold
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Theodore "Ted" Gold (December 13, 1947 – March 6, 1970) was a member of Weather Underground who died in the 1970 Greenwich Village townhouse explosion.
Early years and education
Gold, a red diaper baby, was the son of Hyman Gold, a prominent Jewish physician and of a mathematics instructor at Columbia University who had both been part of the Old Left. His mother was a statistician who taught at Columbia. His parents lived in an upper-middle-class high-rise apartment on Manhattan's Upper West Side.
While Gold's father had gone to medical school, Gold's parents had experienced economic hardship. But Gold considered his parents affluent and upper-middle-class. In 1958, before he reached the age of 11, Gold had attended his first civil-rights demonstration in Washington, D.C. As a boy, he had gone to summer camp with other red-diaper babies at Camp Kinderland (Yiddish for "Children's Land") in upstate New York. From 1959 to 1961 Gold attended Joan of Arc Junior High School (JHS 118) on 93rd Street between Amsterdam Avenue and Columbus Avenue.
Gold attended Stuyvesant High School, an elite public high school in Manhattan, where he was a member of the school's cross-country track team, the Stamp Club, and the History and Folklore Society.
Arriving at Columbia University in Fall 1964, Gold immediately became involved in campus Civil Rights Movement activity. He organized fund-raising activities for the Student Nonviolent Coordinating Committee (SNCC) Selma Project with Friends
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https://en.wikipedia.org/wiki/Parallelizable%20manifold
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In mathematics, a differentiable manifold of dimension n is called parallelizable if there exist smooth vector fields
on the manifold, such that at every point of the tangent vectors
provide a basis of the tangent space at . Equivalently, the tangent bundle is a trivial bundle, so that the associated principal bundle of linear frames has a global section on
A particular choice of such a basis of vector fields on is called a parallelization (or an absolute parallelism) of .
Examples
An example with is the circle: we can take V1 to be the unit tangent vector field, say pointing in the anti-clockwise direction. The torus of dimension is also parallelizable, as can be seen by expressing it as a cartesian product of circles. For example, take and construct a torus from a square of graph paper with opposite edges glued together, to get an idea of the two tangent directions at each point. More generally, every Lie group G is parallelizable, since a basis for the tangent space at the identity element can be moved around by the action of the translation group of G on G (every translation is a diffeomorphism and therefore these translations induce linear isomorphisms between tangent spaces of points in G).
A classical problem was to determine which of the spheres Sn are parallelizable. The zero-dimensional case S0 is trivially parallelizable. The case S1 is the circle, which is parallelizable as has already been explained. The hairy ball theorem shows that S2 is not paral
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https://en.wikipedia.org/wiki/Stunted%20projective%20space
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In mathematics, a stunted projective space is a construction on a projective space of importance in homotopy theory, introduced by . Part of a conventional projective space is collapsed down to a point.
More concretely, in a real projective space, complex projective space or quaternionic projective space
KPn,
where K stands for the real numbers, complex numbers or quaternions, one can find (in many ways) copies of
KPm,
where m < n. The corresponding stunted projective space is then
KPn,m = KPn/KPm,
where the notation implies that the KPm has been identified to a point. This makes a topological space that is no longer a manifold. The importance of this construction was realised when it was shown that real stunted projective spaces arose as Spanier–Whitehead duals of spaces of Ioan James, so-called quasi-projective spaces, constructed from Stiefel manifolds. Their properties were therefore linked to the construction of frame fields on spheres.
In this way the vector fields on spheres question was reduced to a question on stunted projective spaces: for RPn,m, is there a degree one mapping on the 'next cell up' (of the first dimension not collapsed in the 'stunting') that extends to the whole space? Frank Adams showed that this could not happen, completing the proof.
In later developments spaces KP∞,m and stunted lens spaces have also been used.
References
Homotopy theory
Differential topology
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https://en.wikipedia.org/wiki/Spanier%E2%80%93Whitehead%20duality
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In mathematics, Spanier–Whitehead duality is a duality theory in homotopy theory, based on a geometrical idea that a topological space X may be considered as dual to its complement in the n-sphere, where n is large enough. Its origins lie in Alexander duality theory, in homology theory, concerning complements in manifolds. The theory is also referred to as S-duality, but this can now cause possible confusion with the S-duality of string theory. It is named for Edwin Spanier and J. H. C. Whitehead, who developed it in papers from 1955.
The basic point is that sphere complements determine the homology, but not the homotopy type, in general. What is determined, however, is the stable homotopy type, which was conceived as a first approximation to homotopy type. Thus Spanier–Whitehead duality fits into stable homotopy theory.
Statement
Let X be a compact neighborhood retract in . Then and are dual objects in the category of pointed spectra with the smash product as a monoidal structure. Here is the union of and a point, and are reduced and unreduced suspensions respectively.
Taking homology and cohomology with respect to an Eilenberg–MacLane spectrum recovers Alexander duality formally.
References
Homotopy theory
Duality theories
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https://en.wikipedia.org/wiki/Hermitian%20function
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In mathematical analysis, a Hermitian function is a complex function with the property that its complex conjugate is equal to the original function with the variable changed in sign:
(where the indicates the complex conjugate) for all in the domain of . In physics, this property is referred to as PT symmetry.
This definition extends also to functions of two or more variables, e.g., in the case that is a function of two variables it is Hermitian if
for all pairs in the domain of .
From this definition it follows immediately that: is a Hermitian function if and only if
the real part of is an even function,
the imaginary part of is an odd function.
Motivation
Hermitian functions appear frequently in mathematics, physics, and signal processing. For example, the following two statements follow from basic properties of the Fourier transform:
The function is real-valued if and only if the Fourier transform of is Hermitian.
The function is Hermitian if and only if the Fourier transform of is real-valued.
Since the Fourier transform of a real signal is guaranteed to be Hermitian, it can be compressed using the Hermitian even/odd symmetry. This, for example, allows the discrete Fourier transform of a signal (which is in general complex) to be stored in the same space as the original real signal.
If f is Hermitian, then .
Where the is cross-correlation, and is convolution.
If both f and g are Hermitian, then .
See also
Types of functions
Ca
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https://en.wikipedia.org/wiki/Alexander%20duality
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In mathematics, Alexander duality refers to a duality theory initiated by a result of J. W. Alexander in 1915, and subsequently further developed, particularly by Pavel Alexandrov and Lev Pontryagin. It applies to the homology theory properties of the complement of a subspace X in Euclidean space, a sphere, or other manifold. It is generalized by Spanier–Whitehead duality.
General statement for spheres
Let be a compact, locally contractible subspace of the sphere of dimension n. Let be the complement of in . Then if stands for reduced homology or reduced cohomology, with coefficients in a given abelian group, there is an isomorphism
for all . Note that we can drop local contractibility as part of the hypothesis if we use Čech cohomology, which is designed to deal with local pathologies.
Applications
This is useful for computing the cohomology of knot and link complements in . Recall that a knot is an embedding and a link is a disjoint union of knots, such as the Borromean rings. Then, if we write the link/knot as , we have
,
giving a method for computing the cohomology groups. Then, it is possible to differentiate between different links using the Massey products.
For example, for the Borromean rings , the homology groups are
Alexander duality for constructible sheaves
For smooth manifolds, Alexander duality is a formal consequence of Verdier duality for sheaves of abelian groups. More precisely, if we let denote a smooth manifold and we let be a closed subspac
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https://en.wikipedia.org/wiki/Chemism
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Chemism refers to forces of attraction or adhesion between entities. It has uses in chemistry and philosophy.
Chemistry
In the past, chemism referred to intramolecular forces between atoms, or more generally, any forces acting on atoms and molecules. It is now typically superseded by more precise terms such as hydrogen interaction.
Philosophy
The concept of chemism has been referred to in many of the various disciplines that constitute philosophical practice. Some of the include:
The use of the term in philosophy references the activities of chemism in chemistry.
Chemism is a term in Hegelian philosophy that stands for the "mutual attraction, interpenetration, and neutralisation of independent individuals which unite to form a whole." Hegel posits that the concept of "Objectivity" contains the "three forms of Mechanism, Chemism , and Teleology":
"The object of mechanical type is the immediate and undifferentiated object. No doubt it contains difference, but the different pieces stand, as it were, without affinity to each other, and their connection is only extraneous. In chemism, on the contrary, the object exhibits an essential tendency to differentiation, in such a way that the objects are what they are only by their relation to each other: this tendency to difference constitutes their quality. The third type of objectivity, the teleological relation, is the unity of mechanism and chemism. Design, like the mechanical object, is a self-contained totality, enriched howe
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https://en.wikipedia.org/wiki/Reduced%20homology
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In mathematics, reduced homology is a minor modification made to homology theory in algebraic topology, motivated by the intuition that all of the homology groups of a single point should be equal to zero. This modification allows more concise statements to be made (as in Alexander duality) and eliminates many exceptional cases (as in the homology groups of spheres).
If P is a single-point space, then with the usual definitions the integral homology group
H0(P)
is isomorphic to (an infinite cyclic group), while for i ≥ 1 we have
Hi(P) = {0}.
More generally if X is a simplicial complex or finite CW complex, then the group H0(X) is the free abelian group with the connected components of X as generators. The reduced homology should replace this group, of rank r say, by one of rank r − 1. Otherwise the homology groups should remain unchanged. An ad hoc way to do this is to think of a 0-th homology class not as a formal sum of connected components, but as such a formal sum where the coefficients add up to zero.
In the usual definition of homology of a space X, we consider the chain complex
and define the homology groups by .
To define reduced homology, we start with the augmented chain complex
where . Now we define the reduced homology groups by
for positive n and .
One can show that ; evidently for all positive n.
Armed with this modified complex, the standard ways to obtain homology with coefficients by applying the tensor product, or reduced cohomology group
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https://en.wikipedia.org/wiki/Sensory%20threshold
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In psychophysics, sensory threshold is the weakest stimulus that an organism can sense. Unless otherwise indicated, it is usually defined as the weakest stimulus that can be detected half the time, for example, as indicated by a point on a probability curve. Methods have been developed to measure thresholds in any of the senses.
Several different sensory thresholds have been defined;
Absolute threshold: the lowest level at which a stimulus can be detected.
Recognition threshold: the level at which a stimulus can not only be detected but also recognized.
Differential threshold: the level at which an increase in a detected stimulus can be perceived.
Terminal threshold: the level beyond which any increase to a stimulus no longer changes the perceived intensity.
History
The first systematic studies to determine sensory thresholds were conducted by Ernst Heinrich Weber, a physiologist and pioneer of experimental psychology at the Leipzig University. His experiments were intended to determine the absolute and difference, or differential, thresholds. Weber was able to define absolute and difference threshold statistically, which led to the establishment of Weber's Law and the concept of just noticeable difference to describe threshold perception of stimuli.
Following Weber's work, Gustav Fechner, a pioneer of psychophysics, studied the relationship between the physical intensity of a stimulus and the psychologically perceived intensity of the stimulus. Comparing the measured int
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https://en.wikipedia.org/wiki/Nasrin%20Soltankhah
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Nasrin Soltankhah () is an Iranian politician who was a Vice President under Mahmoud Ahmadinejad from 2009 to 2013.
Education
Soltankhan received a Bachelor of Science in Mathematics (1976), a Master of Science in Mathematics (1978), and a PhD in Mathematics (1994) from Sharif University of Technology.
Career
Cabinet position
Soltankhan was appointed to the Iranian Cabinet on September 25, 2005 by President Mahmoud Ahmadinejad. She was also president of Iran's National Elites Foundation.
Center for Women and Family Affairs
Soltankhan's portfolio includes both the position as head of the Center for Women and Family Affairs (formerly called the Center for Women's Participation, or CWP) and also the position of advisor to the President on issues pertaining to women.
Soltankhan has mentioned three main points for women-related policies which the center will be focusing on. These are, “upholding human dignity of women regardless of their gender,“ “capitalizing on women’s potentials in managerial and decision-making arenas,“ and “emphasizing on women’s key role in families.“ Soltankhah has also stated that the center is engaged in directing women’s capabilities into different social and cultural fields as well as generating jobs for them.
Political affiliation
Soltankhan is a member of the political organization called the Alliance of Builders of Islamic Iran.
City Council of Tehran
Apart from her work in the executive branch of the Iranian government, Nasrin Soltankhan wa
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https://en.wikipedia.org/wiki/Institut%20d%27Astrophysique%20de%20Paris
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The Institut d'Astrophysique de Paris (translated: Paris Institute of Astrophysics) is a research institute in Paris, France. The Institute is part of the Sorbonne University and is associated with the CNRS Centre national de la recherche scientifique. It is located at 98bis, Boulevard Arago Il in the 14th arrondissement of Paris, adjacent to the Paris Observatory.
History
The IAP was created in 1936 by the French ministry of education under Jean Zay, initially for the purpose of processing data received from the Observatory of Haute-Provence, which was created at the same time. Construction of the building started on 6 January 1938. On 15 June 1939, Henri Mineur became the institute's first director. IAP scientists were at first located in Paris Observatory, then in the École normale supérieure de Paris before arriving in the current building in 1944 which was finally completed in 1952.
Current research
The IAP includes 160 researchers, engineers, technicians, and administrators and regularly welcomes many visitors and students.
The main areas of research at the IAP are:
General relativity and cosmology
Cosmological structure formation
High-energy astrophysics
Origin and evolution of galaxies
Stellar structure
Exoplanets
The IAP is one of five laboratories of AERA, the European association for research in astronomy. The laboratory is situated at the interface between two disciplines, astrophysics and theoretical physics. The International Astronomical Union has
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https://en.wikipedia.org/wiki/Carbon%E2%80%93hydrogen%20bond
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In chemistry, the carbon-hydrogen bond ( bond) is a chemical bond between carbon and hydrogen atoms that can be found in many organic compounds. This bond is a covalent, single bond, meaning that carbon shares its outer valence electrons with up to four hydrogens. This completes both of their outer shells, making them stable.
Carbon–hydrogen bonds have a bond length of about 1.09 Å (1.09 × 10−10 m) and a bond energy of about 413 kJ/mol (see table below). Using Pauling's scale—C (2.55) and H (2.2)—the electronegativity difference between these two atoms is 0.35. Because of this small difference in electronegativities, the bond is generally regarded as being non-polar. In structural formulas of molecules, the hydrogen atoms are often omitted. Compound classes consisting solely of bonds and bonds are alkanes, alkenes, alkynes, and aromatic hydrocarbons. Collectively they are known as hydrocarbons.
In October 2016, astronomers reported that the very basic chemical ingredients of life—the carbon-hydrogen molecule (CH, or methylidyne radical), the carbon-hydrogen positive ion () and the carbon ion ()—are the result, in large part, of ultraviolet light from stars, rather than in other ways, such as the result of turbulent events related to supernovae and young stars, as thought earlier.
Bond length
The length of the carbon-hydrogen bond varies slightly with the hybridisation of the carbon atom. A bond between a hydrogen atom and an sp2 hybridised carbon atom is about 0.6% sh
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https://en.wikipedia.org/wiki/Rog-2000
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Rog-2000 (pronounced "Rahj-two-thousand", and sometimes spelled "ROG 2000") is a fictional robot that was the first professional creation of comic book artist-writer John Byrne. Rog-2000 serves as the mascot of Byrne Robotics.
Publication history
The character began life during Byrne's fan-artist days in the 1970s, as a spot illustration for Roger Stern and Bob Layton's fanzine CPL (Contemporary Pictorial Literature). Layton gave the character a name (riffing on the amount of "Rogers" – specifically Roger Stern and Roger Slifer – who contributed to CPL), and he and Stern began using him as a magazine mascot, with Byrne supplying additional art. A Rog-2000 story, "The Coming of the Gang", appeared in CPL #11 (1974), written by Stern with art by Byrne and Layton, and featuring caricatures of "the CPL Gang", including Byrne and fellow CPL contributor Duffy Vohland.
On the strength of that fan piece, Charlton Comics writer Nicola Cuti contacted Byrne about drawing the character for professional comic books. During this same period, the CPL Gang was producing the officially sanctioned fanzine Charlton Bullseye. Written by Cuti, "Rog-2000" became one of several alternating backup features in the Charlton Comics superhero series E-Man, starting with the eight-page "That Was No Lady" in issue #6 (Jan. 1975). This marked the color-comics debut of future industry star Byrne, who'd previously drawn a two-page story for Skywald Publications' black-and-white horror-comics magazine Nigh
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https://en.wikipedia.org/wiki/OGF
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OGF can refer to:
Open Gaming Foundation for role-playing games
Open Grid Forum for grid computing
Ordinary generating function in mathematics
Opioid growth factor, an alternative name for met-enkephalin
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https://en.wikipedia.org/wiki/Menadione
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Menadione is a natural organic compound with the formula C6H4(CO)2C2H(CH3). It is an analog of 1,4-naphthoquinone with a methyl group in the 2-position. It is sometimes called vitamin K3. Use is allowed as a nutritional supplement in animal feed because of its vitamin K activity.
Biochemistry
Menadione is converted to vitamin K2 (specifically, MK-4) by the prenyltransferase action of vertebrate UBIAD1. This reaction requires the hydroquinone (reduced) form of K3, menadiol, produced by NQO1.
Menadione is also a circulating form of vitamin K, produced in small amounts (1–5%) after intestinal absorption of K1 and K2. This circulation explains the uneven tissue distribution of MK-4, especially since menadione can penetrate the blood–brain barrier. The cleavage enzyme is yet to be identified. As K3 is known to be toxic in large amounts, researchers speculate that the cleavage process is closely regulated.
Terminology
The compound is variously known as vitamin K3 and provitamin K3. Proponents of the latter name generally argue that the compound is not a real vitamin due to its artificial status (prior to its identification as a circulating intermediate) and its lack of a 3-methyl side chain preventing it from exert all the functions (specifically, it cannot act as a cofactor for GGCX in vitro) of the K vitamins.
Uses
It is an intermediate in the chemical synthesis of vitamin K by first reduction to the diol menadiol, which is susceptible to coupling to the phytol. It is a use
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https://en.wikipedia.org/wiki/Council%20for%20Responsible%20Genetics
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The Council for Responsible Genetics (CRG) was a nonprofit NGO with a focus on biotechnology.
History
The Council for Responsible Genetics was founded in 1983 in Cambridge, Massachusetts.
An early voice concerned about the social and ethical implications of modern genetic technologies, CRG organized a 1985 Congressional Briefing and a 1986 panel of the American Association for the Advancement of Science, both focusing on the potential dangers of genetically engineered biological weapons. Francis Boyle was asked to draft legislation setting limits on the use of genetic engineering, leading to the Biological Weapons Anti-Terrorism Act of 1989.
CRG was the first organization to advance a comprehensive, scientifically based position against human germline engineering. It was also the first to compile documented cases of genetic discrimination, laying the intellectual groundwork for the Genetic Information Nondiscrimination Act of 2008 (GINA).
The organization created both a Genetic Bill of Rights and a Citizen's Guide to Genetically Modified Food. Also notable are CRG's support for the "Safe Seeds Campaign" (for avoiding gene flow from genetically engineered to non-GE seed) and the organization of a US conference on Forensic DNA Databanks and Racial Disparities in the Criminal Justice System. In 2010 CRG led a successful campaign to roll back a controversial student genetic testing program at the University of California, Berkeley. In 2011, CRG led a campaign to successful
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https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93Szekeres%20theorem
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In mathematics, the Erdős–Szekeres theorem asserts that, given r, s, any sequence of distinct real numbers with length at least (r − 1)(s − 1) + 1 contains a monotonically increasing subsequence of length r or a monotonically decreasing subsequence of length s. The proof appeared in the same 1935 paper that mentions the Happy Ending problem.
It is a finitary result that makes precise one of the corollaries of Ramsey's theorem. While Ramsey's theorem makes it easy to prove that every infinite sequence of distinct real numbers contains a monotonically increasing infinite subsequence or a monotonically decreasing infinite subsequence, the result proved by Paul Erdős and George Szekeres goes further.
Example
For r = 3 and s = 2, the formula tells us that any permutation of three numbers has an increasing subsequence of length three or a decreasing subsequence of length two. Among the six permutations of the numbers 1,2,3:
1,2,3 has an increasing subsequence consisting of all three numbers
1,3,2 has a decreasing subsequence 3,2
2,1,3 has a decreasing subsequence 2,1
2,3,1 has two decreasing subsequences, 2,1 and 3,1
3,1,2 has two decreasing subsequences, 3,1 and 3,2
3,2,1 has three decreasing length-2 subsequences, 3,2, 3,1, and 2,1.
Alternative interpretations
Geometric interpretation
One can interpret the positions of the numbers in a sequence as x-coordinates of points in the Euclidean plane, and the numbers themselves as y-coordinates; conversely, for any point s
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https://en.wikipedia.org/wiki/Amy%20B.%20Smith
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Amy Smith (born November 4, 1962) is an American inventor, educator, and founder of the MIT D-Lab and senior lecturer of mechanical engineering at MIT.
Early life and education
Smith was born in Lexington, Massachusetts. Her father, Arthur Smith, was an electrical engineering professor at MIT.
Arthur Smith took his family to India for a year when Amy was growing up while he worked at a university there. "I think that set a lot of things in motion for her. It's very different from growing up in a Boston suburb", he said.
Smith says that being exposed to severe poverty as a child made her want to do something to help kids around the world. "Living in India is something that stayed with me—I could put faces on the kids who had so little money."
Smith received her bachelor's degree in mechanical engineering from MIT in 1984. Smith returned to MIT after the Peace Corps to get her master's degree in mechanical engineering.
Peace Corps service
Smith joined the Peace Corps serving four years as a volunteer in Botswana.
During her Peace Corps service she was struck by the fact that "the most needy are often the least empowered to invent solutions to their problems."
While she was serving in the middle of the Kalahari Desert, she decided what she wanted to do with the rest of her life. "At one point I had sort of an epiphany, sitting at my desk looking out over the bush, when I realized I wanted to do engineering for developing countries", Smith said. "In Botswana, I was teaching a
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https://en.wikipedia.org/wiki/Urca%20process
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In astroparticle physics, an Urca process is a reaction which emits a neutrino and which is assumed to take part in cooling processes in neutron stars and white dwarfs. The process was first discussed by George Gamow and Mário Schenberg while they were visiting a casino named Cassino da Urca in Urca, Rio de Janeiro. As Gamow recounts in his autobiography, the name was chosen in part to commemorate the gambling establishment where the two physicists had first met, and "partially because the Urca Process results in a rapid disappearance of thermal energy from the interior of a star, similar to the rapid disappearance of money from the pockets of the gamblers on the Casino de Urca." In Gamow's South Russian dialect, urca () can also mean a robber or gangster.
The direct Urca processes are the simplest neutrino-emitting processes and are thought to be central in the cooling of neutron stars. They have the general form
{|
| B || || || → || B || + || || + || ,
|------------------------------------------
| B || + || || → || B || + ||,
|}
where B and B are baryons, is a lepton, and (and ) are (anti-)neutrinos. The baryons can be nucleons (free or bound), hyperons like , and , or members of the isobar. The lepton is either an electron or a muon.
The Urca process is especially important in the cooling of white dwarfs, where a lepton (usually an electron) is absorbed by the nucleus of an ion and then convectively carried away
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https://en.wikipedia.org/wiki/Cartan%20formula
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In mathematics, Cartan formula can mean:
one in differential geometry: , where , and are Lie derivative, exterior derivative, and interior product, respectively, acting on differential forms. See interior product for the detail. It is also called the Cartan homotopy formula or Cartan magic formula. This formula is named after Élie Cartan.
one in algebraic topology, which is one of the five axioms of Steenrod algebra. It reads:
.
See Steenrod algebra for the detail. The name derives from Henri Cartan, son of Élie.
Footnotes
See also
List of things named after Élie Cartan
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https://en.wikipedia.org/wiki/Vlastimil%20Pt%C3%A1k
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Vlastimil Pták (; November 8, 1925 in Prague – May 5 1999) was a Czech mathematician, who worked in functional analysis, theoretical numerical analysis, and linear algebra. Notable early work include generalizations of the open mapping theorem .
During 1945–49 Vlastimil Pták studied mathematics and physics at the Charles University in Prague. Later, he worked at the university and since 1952 in Mathematical Institute of Czechoslovak Academy of Sciences. In 1965 he was named professor at the Charles University. He has published more than 160 mathematical research papers. He had three Ph.D. students, Nicholas Young, Michal Zajac and Miroslav Engliš.
Selected publications
Completeness and the open mapping theorem. Bull. Soc. Math. France 86 1958 41–74. Text online
On complete topological linear spaces. Czechoslovak Math. J. 3(78), (1953). 301–364.
On matrices with non-positive off-diagonal elements and positive principal minors. (with Miroslav Fiedler) Czechoslovak Math. J. 12 (87) 1962 382–400.
References
External links
Short obituary
Short biography (in Czech)
Overview of Pták's work
Seventy years of Professor Vlastimil Pták: Biography and interview (PDF or Postscript file, requires subscription)
Czechoslovak mathematicians
1999 deaths
1925 births
20th-century Czech mathematicians
Charles University alumni
Academic staff of Charles University
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https://en.wikipedia.org/wiki/Complete%20intersection
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In mathematics, an algebraic variety V in projective space is a complete intersection if the ideal of V is generated by exactly codim V elements. That is, if V has dimension m and lies in projective space Pn, there should exist n − m homogeneous polynomials:
in the homogeneous coordinates Xj, which generate all other homogeneous polynomials that vanish on V.
Geometrically, each Fi defines a hypersurface; the intersection of these hypersurfaces should be V. The intersection of hypersurfaces will always have dimension at least m, assuming that the field of scalars is an algebraically closed field such as the complex numbers. The question is essentially, can we get the dimension down to m, with no extra points in the intersection? This condition is fairly hard to check as soon as the codimension . When then V is automatically a hypersurface and there is nothing to prove.
Examples
Easy examples of complete intersections are given by hypersurfaces which are defined by the vanishing locus of a single polynomial. For example,
gives an example of a quintic threefold. It can be difficult to find explicit examples of complete intersections of higher dimensional varieties using two or more explicit examples (bestiary), but, there is an explicit example of a 3-fold of type given by
Non-examples
Twisted cubic
One method for constructing local complete intersections is to take a projective complete intersection variety and embed it into a higher dimensional projective space. A
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https://en.wikipedia.org/wiki/James%20Irvine%20%28educator%29
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James Irvine (1793–1835) was an educator and Presbyterian minister who served as the second president of Ohio University, located in Athens, Ohio, from 1822 to 1824.
Irvine, a native of Washington County, New York, graduated from Union College, and was hired as a professor of mathematics at Ohio University in 1821. He became president of the university in 1822, and served only a year before taking a leave of absence due to poor health. Irvine never returned from his leave and resigned in 1824. He was pastor at West Hebron, New York, 1824–1831, and of the Second Presbyterian Church of New York City, 1831–1835. He died in New York City, November 25, 1835.
External links
Ohio University profile
Ohio University
Ohio University faculty
Presidents of Ohio University
1793 births
1835 deaths
People from Washington County, New York
People from Hebron, New York
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https://en.wikipedia.org/wiki/Altitude%20%28disambiguation%29
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Altitude is the height of an object over a datum.
It may also refer to:
Science and mathematics
Altitude (astronomy), one of the angular coordinates of the horizontal coordinate system
Altitude (triangle), in geometry, a line passing through one vertex of a triangle and perpendicular to the opposite side
Music
Altitude (ALT album), the collaborative album released by Andy White, Tim Finn and Liam O'Moanlai under the name ALT
Altitude (Autumn album), the album by Dutch rockband Autumn
Altitude (Yellow Second album), the album by pop punk band Yellow Second
Altitude (Joe Morris album), the album by jazz guitarist Joe Morris
Other uses
Altitude (building), a proposed skyscraper in Sri Lanka
Altitude (film), a 2010 Canadian horror film directed by Kaare Andrews
Altitude (computer game), a 2D aerial combat game released in 2009
Altitude (G.I. Joe), a fictional character in the G.I. Joe universe
Altitude Sports and Entertainment, a regional sports network in Colorado
See also
Altitude Film Entertainment, a British film production and distribution company
Major Altitude, a fictional character in the G.I. Joe universe
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https://en.wikipedia.org/wiki/Grassmann%20number
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In mathematical physics, a Grassmann number, named after Hermann Grassmann (also called an anticommuting number or supernumber), is an element of the exterior algebra over the complex numbers. The special case of a 1-dimensional algebra is known as a dual number. Grassmann numbers saw an early use in physics to express a path integral representation for fermionic fields, although they are now widely used as a foundation for superspace, on which supersymmetry is constructed.
Informal discussion
Grassmann numbers are generated by anti-commuting elements or objects. The idea of anti-commuting objects arises in multiple areas of mathematics: they are typically seen in differential geometry, where the differential forms are anti-commuting. Differential forms are normally defined in terms of derivatives on a manifold; however, one can contemplate the situation where one "forgets" or "ignores" the existence of any underlying manifold, and "forgets" or "ignores" that the forms were defined as derivatives, and instead, simply contemplate a situation where one has objects that anti-commute, and have no other pre-defined or pre-supposed properties. Such objects form an algebra, and specifically the Grassmann algebra or exterior algebra.
The Grassmann numbers are elements of that algebra. The appellation of "number" is justified by the fact that they behave not unlike "ordinary" numbers: they can be added, multiplied and divided: they behave almost like a field. More can be done: one
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https://en.wikipedia.org/wiki/Adjunction%20formula
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In mathematics, especially in algebraic geometry and the theory of complex manifolds, the adjunction formula relates the canonical bundle of a variety and a hypersurface inside that variety. It is often used to deduce facts about varieties embedded in well-behaved spaces such as projective space or to prove theorems by induction.
Adjunction for smooth varieties
Formula for a smooth subvariety
Let X be a smooth algebraic variety or smooth complex manifold and Y be a smooth subvariety of X. Denote the inclusion map by i and the ideal sheaf of Y in X by . The conormal exact sequence for i is
where Ω denotes a cotangent bundle. The determinant of this exact sequence is a natural isomorphism
where denotes the dual of a line bundle.
The particular case of a smooth divisor
Suppose that D is a smooth divisor on X. Its normal bundle extends to a line bundle on X, and the ideal sheaf of D corresponds to its dual . The conormal bundle is , which, combined with the formula above, gives
In terms of canonical classes, this says that
Both of these two formulas are called the adjunction formula.
Examples
Degree d hypersurfaces
Given a smooth degree hypersurface we can compute its canonical and anti-canonical bundles using the adjunction formula. This reads aswhich is isomorphic to .
Complete intersections
For a smooth complete intersection of degrees , the conormal bundle is isomorphic to , so the determinant bundle is and its dual is , showingThis generalizes in the sam
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https://en.wikipedia.org/wiki/Canadian%20Society%20for%20Civil%20Engineering
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The Canadian Society for Civil Engineering (CSCE) (French: Société canadienne de génie civil) was founded in 1887 as the Canadian Society of Civil Engineers, renamed in 1918 as the Engineering Institute of Canada (EIC), and re-established in June 1972 as a member society of the EIC under the slightly different but current name. It promotes advances in the field of civil engineering including geotechnical engineering, structural engineering, hydrotechnical engineering, environmental engineering, transportation engineering and surveying and geomatics engineering. Members who are professional civil engineers are usually categorized and may use the post nominals as associates (AMCSCE), members (MCSCE) or fellows (FCSCE). The grade of "Fellow" is achieved through election by one's peers within the CSCE.
There are also student chapters of the Canadian Society for Civil Engineering at many universities throughout the country including the University of Toronto, University of Waterloo, McGill University and the University of British Columbia.
In the year 2019, the CSCE named its best paper award in construction after Osama Moselhi. Moselhi Best Paper Award is offered every two years in the construction specialty conference.
References
External links
Professional associations based in Canada
Civil engineering professional associations
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https://en.wikipedia.org/wiki/Rotation%20system
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In combinatorial mathematics, rotation systems (also called combinatorial embeddings or combinatorial maps) encode embeddings of graphs onto orientable surfaces by describing the circular ordering of a graph's edges around each vertex.
A more formal definition of a rotation system involves pairs of permutations; such a pair is sufficient to determine a multigraph, a surface, and a 2-cell embedding of the multigraph onto the surface.
Every rotation scheme defines a unique 2-cell embedding of a connected multigraph on a closed oriented surface (up to orientation-preserving topological equivalence). Conversely, any embedding of a connected multigraph G on an oriented closed surface defines a unique rotation system having G as its underlying multigraph. This fundamental equivalence between rotation systems and 2-cell-embeddings was first settled in a dual form by Lothar Heffter in the 1890s and extensively used by Ringel during the 1950s. Independently, Edmonds gave the primal form of the theorem and the details of his study have been popularized by Youngs. The generalization to multigraphs was presented by Gross and Alpert.
Rotation systems are related to, but not the same as, the rotation maps used by Reingold et al. (2002) to define the zig-zag product of graphs. A rotation system specifies a circular ordering of the edges around each vertex, while a rotation map specifies a (non-circular) permutation of the edges at each vertex. In addition, rotation systems can be defined
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https://en.wikipedia.org/wiki/Ryogo%20Kubo
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was a Japanese mathematical physicist, best known for his works in statistical physics and non-equilibrium statistical mechanics.
Work
In the early 1950s, Kubo transformed research into the linear response properties of near-equilibrium condensed-matter systems, in particular the understanding of electron transport and conductivity, through the Kubo formalism, a Green's function approach to linear response theory for quantum systems. In 1977 Ryogo Kubo was awarded the Boltzmann Medal for his contributions to the theory of non-equilibrium statistical mechanics, and to the theory of fluctuation phenomena. He is cited particularly for his work in the establishment of the basic relations between transport coefficients and equilibrium time correlation functions: relations with which his name is generally associated.
Publications
Books available in English
Statistical mechanics : an advanced course with problems and solutions / Ryogo Kubo, in cooperation with Hiroshi Ichimura, Tsunemaru Usui, Natsuki Hashitsume (1965, 7th edit.1988)
Many-body theory : lectures / edited by Ryōgo Kubo (1966)
Dynamical processes in solid state optics / edited by Ryōgo Kubo and Hiroshi Kamimura(1967)
Thermodynamics : an advanced course with problems and solutions / Kubo Ryogo (1968)
Statistical physics of charged particle systems / edited by Ryogo Kubo and Taro Kihara (1969)
Solid state physics / edited by Ryogo Kubo and Takeo Nagamiya ; translator, Scripta-Technica, Inc. ; editor of English ed., Rob
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https://en.wikipedia.org/wiki/Concept%20drift
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In predictive analytics, data science, machine learning and related fields, concept drift or drift is an evolution of data that invalidates the data model. It happens when the statistical properties of the target variable, which the model is trying to predict, change over time in unforeseen ways. This causes problems because the predictions become less accurate as time passes. Drift detection and drift adaptation are of paramount importance in the fields that involve dynamically changing data and data models.
Predictive model decay
In machine learning and predictive analytics this drift phenomenon is called concept drift. In machine learning, a common element of a data model are the statistical properties, such as probability distribution of the actual data. If they deviate from the statistical properties of the training data set, then the learned predictions may become invalid, if the drift is not addressed.
Data configuration decay
Another important area is software engineering, where three types of data drift affecting data fidelity may be recognized. Changes in the software environment ("infrastructure drift") may invalidate software infrastructure configuration. "Structural drift" happens when the data schema changes, which may invalidate databases. "Semantic drift" is changes in the meaning of data while the structure does not change. In many cases this may happen in complicated applications when many independent developers introduce changes without proper awareness o
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https://en.wikipedia.org/wiki/Wetted%20area
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In fluid dynamics, the wetted area is the surface area that interacts with the working fluid or gas.
In maritime use, the wetted area is the area of the watercrafts hull which is immersed in water. This has a direct relationship on the overall hydrodynamic drag of the ship or submarine.
In aeronautics, the wetted area is the area which is in contact with the external airflow. This has a direct relationship on the overall aerodynamic drag of the aircraft. See also: Wetted aspect ratio.
In motorsport, such as Formula One, the term wetted surfaces is used to refer to the bodywork, wings and the radiator, which are in direct contact with the airflow, similarly to the term's use in aeronautics.
References
Intake Aerodynamics (October 1999) by Seddon and Goldsmith, Blackwell Science and the AIAA Educational Series; 2nd edition
Naval architecture
Aerodynamics
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https://en.wikipedia.org/wiki/Folch%20solution
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A Folch solution is a solution containing chloroform and methanol, usually in a 2:1 (vol/vol) ratio. One of its uses is in separating polar from nonpolar compounds, for example separating nonpolar lipids from polar proteins and carbohydrates in blood serum.
References
Reagents for organic chemistry
Solutions
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https://en.wikipedia.org/wiki/The%20Journal%20of%20Physical%20Chemistry%20A
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The Journal of Physical Chemistry A is a scientific journal which reports research on the chemistry of molecules - including their dynamics, spectroscopy, kinetics, structure, bonding, and quantum chemistry. It is published weekly by the American Chemical Society.
Before 1997 the title was simply Journal of Physical Chemistry. Owing to the ever-growing amount of research in the area, in 1997 the journal was split into Journal of Physical Chemistry A (molecular theoretical and experimental physical chemistry) and The Journal of Physical Chemistry B (solid state, soft matter, liquids, etc.). Beginning in 2007, the latter underwent a further split, with The Journal of Physical Chemistry C now being dedicated to nanotechnology, molecular electronics, and related subjects.
According to the Journal Citation Reports, the journal had an impact factor of 2.944 for 2021.
Editors-in-chief
1896–1932 Wilder Dwight Bancroft, Joseph E. Trevor
1933–1951 S. C. Lind
1952–1964 William A. Noyes
1965–1969 F. T. Wall
1970–1980 Bryce Crawford
1980–2004 Mostafa El-Sayed
2005–2019 George C. Schatz
2020–present Joan-Emma Shea
Popular culture
Sheldon Cooper, a fictional physicist from the television series The Big Bang Theory, appeared on the cover of a fictional issue of the journal.
See also
The Journal of Physical Chemistry B
The Journal of Physical Chemistry C
The Journal of Physical Chemistry Letters
Russian Journal of Physical Chemistry A
Russian Journal of Physical Chemistry B
Ex
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https://en.wikipedia.org/wiki/The%20Journal%20of%20Physical%20Chemistry%20B
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The Journal of Physical Chemistry B is a peer-reviewed scientific journal that covers research on several fields of material chemistry (macromolecules, soft matter, and surfactants) as well as statistical mechanics, thermodynamics, and biophysical chemistry. It has been published weekly since 1997 by the American Chemical Society. According to the Journal Citation Reports, the journal had an impact factor of 3.5 for 2023.
Due to the growing amount of research in the fields it covers, the journal was split into two at the beginning of 2007, with The Journal of Physical Chemistry C specializing in nanostructures, the structures and properties of surfaces and interfaces, electronics, and related topics.
List of editors-in-chief
The following persons have been editor-in-chief:
1997–2005 Mostafa El-Sayed
2005–2019 George C. Schatz
2020–Present Joan-Emma Shea
See also
The Journal of Physical Chemistry A
The Journal of Physical Chemistry C
The Journal of Physical Chemistry Letters
External links
References
American Chemical Society academic journals
Weekly journals
English-language journals
Academic journals established in 1997
Physical chemistry journals
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https://en.wikipedia.org/wiki/Pi%20Tau%20Sigma
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Pi Tau Sigma () is an international honor society in the field of mechanical engineering, with most chapters established in the United States. It honors mechanical engineering students who have exemplified the "principles of scholarship, character and service..." in the mechanical engineering profession.
History
Pi Tau Sigma came into being on March 16, 1915, at the University of Illinois. A similar organization was formed November 15, 1915, at the University of Wisconsin. The two schools then met to join their societies, doing so in Chicago on March 12, 1916. To date, 167 chapters have been inducted into the organization throughout the United States, with 157 still active.
Membership
Both undergraduate and graduate students are eligible to join Pi Tau Sigma based on academic achievement. Juniors in the top 25% of their class and seniors in the top 35% of their class, based on grades, are invited to join. Membership fees are due at initiation, and membership lasts a lifetime.
Pi Tau Sigma members are chosen on a basis of sound engineering ability, scholarship, personality, and probable future success in their chosen field of mechanical engineering. There are three grades of membership: Honorary, Graduate, and Active. Honorary members are technical graduates actively engaged in engineering work, or members of mechanical engineering faculties. Graduate membership is conferred upon persons who would have been eligible had Pi Tau Sigma been established earlier in schools no
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https://en.wikipedia.org/wiki/Peetre%20theorem
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In mathematics, the (linear) Peetre theorem, named after Jaak Peetre, is a result of functional analysis that gives a characterisation of differential operators in terms of their effect on generalized function spaces, and without mentioning differentiation in explicit terms. The Peetre theorem is an example of a finite order theorem in which a function or a functor, defined in a very general way, can in fact be shown to be a polynomial because of some extraneous condition or symmetry imposed upon it.
This article treats two forms of the Peetre theorem. The first is the original version which, although quite useful in its own right, is actually too general for most applications.
The original Peetre theorem
Let M be a smooth manifold and let E and F be two vector bundles on M. Let
be the spaces of smooth sections of E and F. An operator
is a morphism of sheaves which is linear on sections such that the support of D is non-increasing: supp Ds ⊆ supp s for every smooth section s of E. The original Peetre theorem asserts that, for every point p in M, there is a neighborhood U of p and an integer k (depending on U) such that D is a differential operator of order k over U. This means that D factors through a linear mapping iD from the k-jet of sections of E into the space of smooth sections of F:
where
is the k-jet operator and
is a linear mapping of vector bundles.
Proof
The problem is invariant under local diffeomorphism, so it is sufficient to prove it when M is
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https://en.wikipedia.org/wiki/Polyhedral%20skeletal%20electron%20pair%20theory
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In chemistry the polyhedral skeletal electron pair theory (PSEPT) provides electron counting rules useful for predicting the structures of clusters such as borane and carborane clusters. The electron counting rules were originally formulated by Kenneth Wade, and were further developed by others including Michael Mingos; they are sometimes known as Wade's rules or the Wade–Mingos rules. The rules are based on a molecular orbital treatment of the bonding. These rules have been extended and unified in the form of the Jemmis mno rules.
Predicting structures of cluster compounds
Different rules (4n, 5n, or 6n) are invoked depending on the number of electrons per vertex.
The 4n rules are reasonably accurate in predicting the structures of clusters having about 4 electrons per vertex, as is the case for many boranes and carboranes. For such clusters, the structures are based on deltahedra, which are polyhedra in which every face is triangular. The 4n clusters are classified as closo-, nido-, arachno- or hypho-, based on whether they represent a complete (closo-) deltahedron, or a deltahedron that is missing one (nido-), two (arachno-) or three (hypho-) vertices.
However, hypho clusters are relatively uncommon due to the fact that the electron count is high enough to start to fill antibonding orbitals and destabilize the 4n structure. If the electron count is close to 5 electrons per vertex, the structure often changes to one governed by the 5n rules, which are based on 3-conne
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https://en.wikipedia.org/wiki/Lamina
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Lamina may refer to:
People
Saa Emerson Lamina, Sierra Leonean politician
Tamba Lamina, Sierra Leonean politician and diplimat
Science and technology
Planar lamina, a two-dimensional planar closed surface with mass and density, in mathematics
Laminar flow, (or streamline flow) occurs when a fluid flows in parallel layers, with no disruption between the layers
Lamina (algae), a structure in seaweeds
Lamina (anatomy), with several meanings
Lamina (leaf), the flat part of a leaf, an organ of a plant
Lamina, the largest petal of a floret in an aster family flowerhead: see
Lamina (spider), a genus in the family Toxopidae
Lamina (neuropil), the most peripheral neuropil of the insect visual system
Nuclear lamina, another structure of a living cell
Basal lamina, a structure of a living cell
Lamina propria, the connective part of the mucous
Lamina of the vertebral arch
Lamination (geology), a layering structure in sedimentary rocks usually less than 1 cm in thickness
Laminae, a part of the horse hoof
Laminae, another name for the core lamiids, a clade in botany
See also
Lamia, a creature from Greek mythology.
Lamia (Basque mythology), a creature from Basque mythology
Lamina cribrosa (disambiguation)
Laminar (disambiguation)
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https://en.wikipedia.org/wiki/Planar%20lamina
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In mathematics, a planar lamina (or plane lamina) is a figure representing a thin, usually uniform, flat layer of the solid. It serves also as an idealized model of a planar cross section of a solid body in integration.
Planar laminas can be used to determine moments of inertia, or center of mass of flat figures, as well as an aid in corresponding calculations for 3D bodies.
Definition
Basically, a planar lamina is defined as a figure (a closed set) of a finite area in a plane, with some mass .
This is useful in calculating moments of inertia or center of mass for a constant density, because the mass of a lamina is proportional to its area. In a case of a variable density, given by some (non-negative) surface density function the mass of the planar lamina is a planar integral of over the figure:
Properties
The center of mass of the lamina is at the point
where is the moment of the entire lamina about the y-axis and is the moment of the entire lamina about the x-axis:
with summation and integration taken over a planar domain .
Example
Find the center of mass of a lamina with edges given by the lines and where the density is given as .
For this the mass must be found as well as the moments and .
Mass is which can be equivalently expressed as an iterated integral:
The inner integral is:
Plugging this into the outer integral results in:
Similarly are calculated both moments:
with the inner integral:
which makes:
and
Finally, the center of mass is
R
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https://en.wikipedia.org/wiki/Chromosomal%20polymorphism
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In genetics, chromosomal polymorphism is a condition where one species contains members with varying chromosome counts or shapes. Polymorphism is a general concept in biology where more than one version of a trait is present in a population.
In some cases of differing counts, the difference in chromosome counts is the result of a single chromosome undergoing fission, where it splits into two smaller chromosomes, or two undergoing fusion, where two chromosomes join to form one.
This condition has been detected in many species. Trichomycterus davisi, for example, is an extreme case where the polymorphism was present within a single chimeric individual.
It has also been studied in alfalfa, shrews, Brazilian rodents, and an enormous variety of other animals and plants. In one instance it has been found in a human.
Another process resulting in differing chromosomal counts is polyploidy. This results in cells which contain multiple copies of complete chromosome sets.
Possessing chromosomes of varying shapes is generally the result of a chromosomal translocation or chromosomal inversion.
In a translocation, genetic material is transferred from one chromosome to another, either symmetrically or asymmetrically (a Robertsonian translocation).
In an inversion, a segment of a chromosome is flipped end-for-end.
Implications for speciation
All forms of chromosomal polymorphism can be viewed as a step towards speciation. Polymorphisms will generally result in a level of reduced fer
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https://en.wikipedia.org/wiki/Order%20dimension
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In mathematics, the dimension of a partially ordered set (poset) is the smallest number of total orders the intersection of which gives rise to the partial order.
This concept is also sometimes called the order dimension or the Dushnik–Miller dimension of the partial order.
first studied order dimension; for a more detailed treatment of this subject than provided here, see .
Formal definition
The dimension of a finite poset P is the least integer t for which there exists a family
of linear extensions of P so that, for every x and y in P, x precedes y in P if and only if it precedes y in all of the linear extensions. That is,
An alternative definition of order dimension is the minimal number of total orders such that P embeds into their product with componentwise ordering i.e. if and only if for all i (, ).
Realizers
A family of linear orders on X is called a realizer of a poset P = (X, <P) if
,
which is to say that for any x and y in X,
x <P y precisely when x <1 y, x <2 y, ..., and x <t y.
Thus, an equivalent definition of the dimension of a poset P is "the least cardinality of a realizer of P."
It can be shown that any nonempty family R of linear extensions is a realizer of a finite partially ordered set P if and only if, for every critical pair (x,y) of P, y <i x for some order
<i in R.
Example
Let n be a positive integer, and let P be the partial order on the elements ai and bi (for 1 ≤ i ≤ n) in which ai ≤ bj whenever i ≠ j, but no other pairs are comparab
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https://en.wikipedia.org/wiki/Eilenberg%E2%80%93Steenrod%20axioms
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In mathematics, specifically in algebraic topology, the Eilenberg–Steenrod axioms are properties that homology theories of topological spaces have in common. The quintessential example of a homology theory satisfying the axioms is singular homology, developed by Samuel Eilenberg and Norman Steenrod.
One can define a homology theory as a sequence of functors satisfying the Eilenberg–Steenrod axioms. The axiomatic approach, which was developed in 1945, allows one to prove results, such as the Mayer–Vietoris sequence, that are common to all homology theories satisfying the axioms.
If one omits the dimension axiom (described below), then the remaining axioms define what is called an extraordinary homology theory. Extraordinary cohomology theories first arose in K-theory and cobordism.
Formal definition
The Eilenberg–Steenrod axioms apply to a sequence of functors from the category of pairs of topological spaces to the category of abelian groups, together with a natural transformation called the boundary map (here is a shorthand for . The axioms are:
Homotopy: Homotopic maps induce the same map in homology. That is, if is homotopic to , then their induced homomorphisms are the same.
Excision: If is a pair and U is a subset of A such that the closure of U is contained in the interior of A, then the inclusion map induces an isomorphism in homology.
Dimension: Let P be the one-point space; then for all .
Additivity: If , the disjoint union of a family of topologica
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https://en.wikipedia.org/wiki/%E2%89%A4
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≤ may refer to:
Inequality (mathematics), relation between values; a ≤ b means "a is less than or equal to b"
Subgroup, a subset of a given group in group theory; H ≤ G is read as "H is a subgroup of G"
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https://en.wikipedia.org/wiki/Allette%20Brooks
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Allette Brooks is an American folk singer-songwriter from Long Beach, California. She graduated from Stanford University, majoring in human biology. Her song "Silicon Valley Rebel", about a feminist Web designer who "comes in to work every day in her bike shorts and political T-shirts", was featured in "Silicon Valley USA", a BBC radio documentary. She also teaches Forrest yoga and Restorative Yoga.
Discography
Privilege (1996)
Silicon Valley Rebel (1999)
Swim With Me (2001)
Blaze (2008)
References
External links
Official Website
Songwriters from California
American folk musicians
Musicians from Long Beach, California
Stanford University alumni
American women singers
Living people
Writers from Long Beach, California
Singers from California
Year of birth missing (living people)
21st-century American women
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https://en.wikipedia.org/wiki/Phil%20Moorby
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Phil Moorby () was a British engineer and computer scientist. Moorby was born and brought up in Birmingham, England, and studied Mathematics at Southampton University, England. Moorby received his master's degree in computer science from Manchester University, England, in 1974. He moved to the United States in 1983.
While working in Gateway Design Automation, in 1984 he invented the Verilog hardware description language, and developed the first and industry standard simulator Verilog-XL. In 1990 Gateway was purchased by Cadence Design Systems.
In 1997, Moorby joined startup company SynaPix, where he worked on match moving and video tracking algorithms for automatically extracting 3D models from video frames, using techniques such as optical flow, motion field and point clouds.
Moorby joined Co-Design Automation in 1999, and in 2002 he joined Synopsys to work on SystemVerilog verification language.
On October 10, 2005, Moorby became the recipient of the 2005 Phil Kaufman Award for his contributions to the EDA industry, specifically for development and popularization of Verilog, one of the world's most popular tools of electronic design automation.
In April 2016, Moorby was made a Fellow of the Computer History Museum, "for his invention and promotion of the Verilog hardware description language."
Philip Raymond Moorby passed away on September 15, 2022 at the age of 69 in Rockport, MA.
References
American computer scientists
Electronic design automation people
People as
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https://en.wikipedia.org/wiki/Mark%20Erelli
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Mark Erelli (born June 20, 1974) is an American singer/songwriter, multi-instrumentalist, and touring folk musician from Reading, Massachusetts who earned a master's degree in evolutionary biology from the University of Massachusetts Amherst before pursuing a career in music. Erelli has released nine solo albums and three collaborative albums. His self-titled debut album was released in 1999, the same year that he won the Kerrville Folk Festival's New Folk Award. His first recording for the Signature Sounds label, Compass & Companion, spent ten weeks in the Top Ten on the Americana Chart. Erelli has worked as a side musician for singer songwriters Lori McKenna and Josh Ritter. He has performed at various music festivals and shared the stage with John Hiatt, Dave Alvin, and Gillian Welch. Erelli's song “People Look Around”, which he co-wrote with Catie Curtis, was the Grand Prize winner at the 2005 International Songwriting Competition. His songs have been recorded by Ellis Paul, Vance Gilbert, Antje Duvekot, and Red Molly.
Early life and education
Erelli was born in Boston and grew up in the town of Reading, Massachusetts. Erelli performed in numerous high school musicals and founded the band, Freddie and Slip. Later he was a member of the band Organic Ice Cube and wrote his first song "Hell In the Sky" as a member of the band Dead Flowers (Greg Pothier, Scott Collins, Brian Moynihan, Kevin Larimore, Kris Tuscano, Chris Kerrigan Borning). Erelli was introduced to
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https://en.wikipedia.org/wiki/Jerry%20Hobbs
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Jerry R. Hobbs (born January 25, 1942) is an American researcher in the fields of computational linguistics, discourse analysis, and artificial intelligence.
Education
Hobbs earned his doctor's degree from New York University in 1974 in computer science and has taught at Yale University and the City University of New York.
Career
From 1977 to 2002 he was with the Artificial Intelligence Center at SRI International, Menlo Park, California, where he was a principal scientist and program director of the Natural Language Program. He has written numerous papers in the areas of parsing, syntax, semantic interpretation, information extraction, knowledge representation, encoding commonsense knowledge, discourse analysis, the structure of conversation, and the Semantic Web.
He is the author of the book Literature and Cognition, and was also editor of the book Formal Theories of the Commonsense World. He led SRI's text-understanding research, and directed the development of the abduction-based TACITUS system for text understanding, and the FASTUS system for rapid extraction of information from text based on finite-state automata. The latter system constituted the basis for an SRI spinoff, Discern Communications. In September 2002 he took a position as senior computer scientist and research professor at the Information Sciences Institute, University of Southern California. He has been a consulting professor with the Linguistics Department and the Symbolic Systems Program at Stanford
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https://en.wikipedia.org/wiki/Weierstrass%20point
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In mathematics, a Weierstrass point on a nonsingular algebraic curve defined over the complex numbers is a point such that there are more functions on , with their poles restricted to only, than would be predicted by the Riemann–Roch theorem.
The concept is named after Karl Weierstrass.
Consider the vector spaces
where is the space of meromorphic functions on whose order at is at least and with no other poles. We know three things: the dimension is at least 1, because of the constant functions on ; it is non-decreasing; and from the Riemann–Roch theorem the dimension eventually increments by exactly 1 as we move to the right. In fact if is the genus of , the dimension from the -th term is known to be
for
Our knowledge of the sequence is therefore
What we know about the ? entries is that they can increment by at most 1 each time (this is a simple argument: has dimension as most 1 because if and have the same order of pole at , then will have a pole of lower order if the constant is chosen to cancel the leading term). There are question marks here, so the cases or need no further discussion and do not give rise to Weierstrass points.
Assume therefore . There will be steps up, and steps where there is no increment. A non-Weierstrass point of occurs whenever the increments are all as far to the right as possible: i.e. the sequence looks like
Any other case is a Weierstrass point. A Weierstrass gap for is a value of such that no function on has ex
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https://en.wikipedia.org/wiki/Chennai%20Mathematical%20Institute
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Chennai Mathematical Institute (CMI) is a higher education and research institute in Chennai, India. It was founded in 1989 by the SPIC Science Foundation, and offers undergraduate and postgraduate programmes in physics, mathematics and computer science. CMI is noted for its research in algebraic geometry, in particular in the area of moduli of bundles.
CMI was at first located in T. Nagar in the heart of Chennai in an office complex. It moved to a new campus in Siruseri in October 2005.
In December 2006, CMI was recognized as a university under Section 3 of the University Grants Commission (UGC) Act 1956, making it a deemed university. Until then, the teaching program was offered in association with Bhoj Open University, as it offered more flexibility.
History
CMI began as the School of Mathematics, SPIC Science Foundation, in 1989. The SPIC Science Foundation was set up in 1986 by Southern Petrochemical Industries Corporation (SPIC) Ltd., one of the major industrial houses in India, to foster the growth of science and technology in the country.
In 1996, the School of Mathematics became an independent institution and changed its name to SPIC Mathematical Institute. In 1998, in order to better reflect the emerging role of the institute, it was renamed the Chennai Mathematical Institute (CMI).
From its inception, the institute has had a Ph.D. programme in Mathematics and Computer Science. In the initial years, the Ph.D. programme was affiliated to the BITS, Pilani and t
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https://en.wikipedia.org/wiki/Substring%20index
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In computer science, a substring index is a data structure which gives substring search in a text or text collection in sublinear time. If you have a document of length , or a set of documents of total length , you can locate all occurrences of a pattern in time. (See Big O notation.)
The phrase full-text index is also often used for an index of all substrings of a text. But this is ambiguous, as it is also used for regular word indexes such as inverted files and document retrieval. See full text search.
Substring indexes include:
Suffix tree
Suffix array
N-gram index, an inverted file for all N-grams of the text
Compressed suffix array
FM-index
LZ-index
References
Algorithms on strings
String data structures
Database index techniques
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https://en.wikipedia.org/wiki/Azumaya%20algebra
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In mathematics, an Azumaya algebra is a generalization of central simple algebras to -algebras where need not be a field. Such a notion was introduced in a 1951 paper of Goro Azumaya, for the case where is a commutative local ring. The notion was developed further in ring theory, and in algebraic geometry, where Alexander Grothendieck made it the basis for his geometric theory of the Brauer group in Bourbaki seminars from 1964–65. There are now several points of access to the basic definitions.
Over a ring
An Azumaya algebra
over a commutative ring is an -algebra obeying any of the following equivalent conditions:
There exists an -algebra such that the tensor product of -algebras is Morita equivalent to .
The -algebra is Morita equivalent to , where is the opposite algebra of .
The center of is , and is separable.
is finitely generated, faithful, and projective as an -module, and the tensor product is isomorphic to via the map sending to the endomorphism of .
Examples over a field
Over a field , Azumaya algebras are completely classified by the Artin–Wedderburn theorem since they are the same as central simple algebras. These are algebras isomorphic to the matrix ring for some division algebra over whose center is just . For example, quaternion algebras provide examples of central simple algebras.
Examples over local rings
Given a local commutative ring , an -algebra is Azumaya if and only if is free of positive finite rank as an -module, and t
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https://en.wikipedia.org/wiki/Inverted%20index
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In computer science, an inverted index (also referred to as a postings list, postings file, or inverted file) is a database index storing a mapping from content, such as words or numbers, to its locations in a table, or in a document or a set of documents (named in contrast to a forward index, which maps from documents to content). The purpose of an inverted index is to allow fast full-text searches, at a cost of increased processing when a document is added to the database. The inverted file may be the database file itself, rather than its index. It is the most popular data structure used in document retrieval systems, used on a large scale for example in search engines. Additionally, several significant general-purpose mainframe-based database management systems have used inverted list architectures, including ADABAS, DATACOM/DB, and Model 204.
There are two main variants of inverted indexes: A record-level inverted index (or inverted file index or just inverted file) contains a list of references to documents for each word. A word-level inverted index (or full inverted index or inverted list) additionally contains the positions of each word within a document. The latter form offers more functionality (like phrase searches), but needs more processing power and space to be created.
Applications
The inverted index data structure is a central component of a typical search engine indexing algorithm. A goal of a search engine implementation is to optimize the speed of the que
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https://en.wikipedia.org/wiki/Left-right%20planarity%20test
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In graph theory, a branch of mathematics, the left-right planarity test
or de Fraysseix–Rosenstiehl planarity criterion is a characterization of planar graphs based on the properties of the depth-first search trees, published by and used by them with Patrice Ossona de Mendez to develop a linear time planarity testing algorithm. In a 2003 experimental comparison of six planarity testing algorithms, this was one of the fastest algorithms tested.
T-alike and T-opposite edges
For any depth-first search of a graph G, the edges
encountered when discovering a vertex for the first time define a depth-first search tree T of G. This is a Trémaux tree, meaning that the remaining edges (the cotree) each connect a pair of vertices that are related to each other as an ancestor and descendant in T. Three types of patterns can be used to define two relations between pairs of cotree edges, named the T-alike and T-opposite relations.
In the following figures, simple circle nodes represent vertices, double circle nodes represent subtrees, twisted segments represent tree paths, and curved arcs represent cotree edges. The root of each tree is shown at the bottom of the figure. In the first figure, the edges labeled and are T-alike, meaning that, at the endpoints nearest the root of the tree, they will both be on the same side of the tree in every planar drawing. In the next two figures, the edges with the same labels are T-opposite, meaning that they will be on different sides of the tree in
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https://en.wikipedia.org/wiki/Instantaneous%20phase%20and%20frequency
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Instantaneous phase and frequency are important concepts in signal processing that occur in the context of the representation and analysis of time-varying functions. The instantaneous phase (also known as local phase or simply phase) of a complex-valued function s(t), is the real-valued function:
where arg is the complex argument function.
The instantaneous frequency is the temporal rate of change of the instantaneous phase.
And for a real-valued function s(t), it is determined from the function's analytic representation, sa(t):
where represents the Hilbert transform of s(t).
When φ(t) is constrained to its principal value, either the interval or , it is called wrapped phase. Otherwise it is called unwrapped phase, which is a continuous function of argument t, assuming sa(t) is a continuous function of t. Unless otherwise indicated, the continuous form should be inferred.
Examples
Example 1
where ω > 0.
In this simple sinusoidal example, the constant θ is also commonly referred to as phase or phase offset. φ(t) is a function of time; θ is not. In the next example, we also see that the phase offset of a real-valued sinusoid is ambiguous unless a reference (sin or cos) is specified. φ(t) is unambiguously defined.
Example 2
where ω > 0.
In both examples the local maxima of s(t) correspond to φ(t) = 2N for integer values of N. This has applications in the field of computer vision.
Formulations
Instantaneous angular frequency is defined as:
and instantaneous (ordina
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https://en.wikipedia.org/wiki/Scheinerman%27s%20conjecture
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In mathematics, Scheinerman's conjecture, now a theorem, states that every planar graph is the intersection graph of a set of line segments in the plane. This conjecture was formulated by E. R. Scheinerman in his Ph.D. thesis (1984), following earlier results that every planar graph could be represented as the intersection graph of a set of simple curves in the plane . It was proven by .
For instance, the graph G shown below to the left may be represented as the intersection graph of the set of segments shown below to the right. Here, vertices of G are represented by straight line segments and edges of G are represented by intersection points.
Scheinerman also conjectured that segments with only three directions would be sufficient to represent 3-colorable graphs, and conjectured that analogously every planar graph could be represented using four directions. If a graph is represented with segments having only k directions
and no two segments belong to the same line, then the graph can be colored using k colors, one color for each direction. Therefore, if every planar graph can be represented in this way with only four directions,
then the four color theorem follows.
and proved that every bipartite planar graph can be represented as an intersection graph of horizontal and vertical line segments; for this result see also . proved that every triangle-free planar graph can be represented as an intersection graph of line segments having only three directions; this resu
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https://en.wikipedia.org/wiki/Whitney%27s%20planarity%20criterion
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In mathematics, Whitney's planarity criterion is a matroid-theoretic characterization of planar graphs, named after Hassler Whitney. It states that a graph G is planar if and only if its graphic matroid is also cographic (that is, it is the dual matroid of another graphic matroid).
In purely graph-theoretic terms, this criterion can be stated as follows: There must be another (dual) graph G'=(V',E') and a bijective correspondence between the edges E' and the edges E of the original graph G, such that a subset T of E forms a spanning tree of G if and only if the edges corresponding to the complementary subset E-T form a spanning tree of G'.
Algebraic duals
An equivalent form of Whitney's criterion is that a graph G is planar if and only if it has a dual graph whose graphic matroid is dual to the graphic matroid of G.
A graph whose graphic matroid is dual to the graphic matroid of G is known as an algebraic dual of G. Thus, Whitney's planarity criterion can be expressed succinctly as: a graph is planar if and only if it has an algebraic dual.
Topological duals
If a graph is embedded into a topological surface such as the plane, in such a way that every face of the embedding is a topological disk, then the dual graph of the embedding is defined as the graph (or in some cases multigraph) H that has a vertex for every face of the embedding, and an edge for every adjacency between a pair of faces.
According to Whitney's criterion, the following conditions are equivalent:
The su
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https://en.wikipedia.org/wiki/Vittorio%20Fossombroni
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Vittorio Fossombroni (15 September 175413 April 1844) was an Italian statesman, mathematician, economist and a distinguished drainage engineer.
Biography
Fossombroni was born at Arezzo. He was educated at the University of Pisa, where he devoted himself particularly to mathematics and hydraulics. He obtained an official appointment in Tuscany in 1782, and twelve years later was entrusted by the grand duke with the direction of the works for the drainage of the marshy Valdichiana, one of the four valleys around Arezzo, on which subject he had published a treatise in 1789.
In 1796 he was made minister for foreign affairs, but on the French occupation of Tuscany in 1799 he fled to Sicily. On the erection of the grand duchy into the ephemeral Kingdom of Etruria, under the queen-regent Maria Louise, he was, appointed president of the commission of finance. In 1809 he went to Paris as one of the senators for Tuscany to pay homage to Napoleon.
On the restoration of the Grand Duke Ferdinand III in 1814, he was made president of the legislative commission and was appointed prime minister, a position he retained under the Grand Duke Leopold II. He was an important representative of the Italian School of virtual work laws. When he was prime minister, he pursued a policy of laissez-faire and international free trade.
According to Luigi Villaris, writing in the Encyclopædia Britannica Eleventh Edition: "His administration, which was only terminated by his death, greatly contributed to
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https://en.wikipedia.org/wiki/Operad
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In mathematics, an operad is a structure that consists of abstract operations, each one having a fixed finite number of inputs (arguments) and one output, as well as a specification of how to compose these operations. Given an operad , one defines an algebra over to be a set together with concrete operations on this set which behave just like the abstract operations of . For instance, there is a Lie operad such that the algebras over are precisely the Lie algebras; in a sense abstractly encodes the operations that are common to all Lie algebras. An operad is to its algebras as a group is to its group representations.
History
Operads originate in algebraic topology; they were introduced to characterize iterated loop spaces by J. Michael Boardman and Rainer M. Vogt in 1968 and by J. Peter May in 1972.
Martin Markl, Steve Shnider, and Jim Stasheff write in their book on operads:
"The name operad and the formal definition appear first in the early 1970's in J. Peter May's "The Geometry of Iterated Loop Spaces", but a year or more earlier, Boardman and Vogt described the same concept under the name categories of operators in standard form, inspired by PROPs and PACTs of Adams and Mac Lane. In fact, there is an abundance of prehistory. Weibel [Wei] points out that the concept first arose a century ago in A.N. Whitehead's "A Treatise on Universal Algebra", published in 1898."
The word "operad" was created by May as a portmanteau of "operations" and "monad" (and also becau
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https://en.wikipedia.org/wiki/Klein%20paradox
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In 1929, physicist Oskar Klein obtained a surprising result by applying the Dirac equation to the familiar problem of electron scattering from a potential barrier. In nonrelativistic quantum mechanics, electron tunneling into a barrier is observed, with exponential damping. However, Klein's result showed that if the potential is at least of the order of the electron mass, , the barrier is nearly transparent. Moreover, as the potential approaches infinity, the reflection diminishes and the electron is always transmitted.
The immediate application of the paradox was to Rutherford's proton–electron model for neutral particles within the nucleus, before the discovery of the neutron. The paradox presented a quantum mechanical objection to the notion of an electron confined within a nucleus. This clear and precise paradox suggested that an electron could not be confined within a nucleus by any potential well. The meaning of this paradox was intensely debated at the time.
Massless particles
Consider a massless relativistic particle approaching a potential step of height with energy and momentum .
The particle's wave function, , follows the time-independent Dirac equation:
And is the Pauli matrix:
Assuming the particle is propagating from the left, we obtain two solutions — one before the step, in region (1) and one under the potential, in region (2):
where the coefficients , and are complex numbers.
Both the incoming and transmitted wave functions are associated wit
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https://en.wikipedia.org/wiki/Trimethylsilyldiazomethane
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Trimethylsilyldiazomethane is the organosilicon compound with the formula (CH3)3SiCHN2. It is classified as a diazo compound. Trimethylsilyldiazomethane is a commercially available reagent used in organic chemistry as a methylating agent and as a source of CH2 group. Its behavior is akin to the less convenient reagent diazomethane.
Preparation
Trimethylsilyldiazomethane can be prepared by treating (trimethylsilyl)methylmagnesium chloride with diphenyl phosphorazidate. The 13C-labeled reagent is also known.
Uses
It is a less explosive alternative to diazomethane for the methylation of carboxylic acids. It also reacts with alcohols to give methyl ethers, where diazomethane may not.
It has also been employed widely in tandem with GC-MS for the analysis of various carboxylic compounds which are ubiquitous in nature. The fact that the reaction is rapid and occurs readily makes it attractive. However, it can form artifacts which complicate spectral interpretation. Such artifacts are usually the trimethylsilylmethyl esters, RCO2CH2SiMe3, formed when insufficient methanol is present. Acid-catalysed methanolysis is necessary to achieve near-quantitative yields of the desired methyl esters, RCO2Me.
The compound is a reagent in the Doyle-Kirmse reaction with allyl sulfides and allyl amines.
Trimethylsilyldiazomethyllithium
Trimethylsilyldiazomethane is deprotonated by butyllithium:
(CH3)3SiCHN2 + BuLi → (CH3)3SiCLiN2 + BuH
The lithio compound is versatile. From it can b
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https://en.wikipedia.org/wiki/Boolean%20expression
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In computer science, a Boolean expression is an expression used in programming languages that produces a Boolean value when evaluated. A Boolean value is either true or false. A Boolean expression may be composed of a combination of the Boolean constants true or false, Boolean-typed variables, Boolean-valued operators, and Boolean-valued functions.
Boolean expressions correspond to propositional formulas in logic and are a special case of Boolean circuits.
Boolean operators
Most programming languages have the Boolean operators OR, AND and NOT; in C and some languages inspired by it, these are represented by "||" (double pipe character), "&&" (double ampersand) and "!" (exclamation point) respectively, while the corresponding bitwise operations are represented by "|", "&" and "~" (tilde). In the mathematical literature the symbols used are often "+" (plus), "·" (dot) and overbar, or "∨" (vel), "∧" (et) and "¬" (not) or "′" (prime).
Some languages, e.g., Perl and Ruby, have two sets of Boolean operators, with identical functions but different precedence. Typically these languages use and, or and not for the lower precedence operators.
Some programming languages derived from PL/I have a bit string type and use BIT(1) rather than a separate Boolean type. In those languages the same operators serve for Boolean operations and bitwise operations. The languages represent OR, AND, NOT and EXCLUSIVE OR by "|", "&", "¬" (infix) and "¬" (prefix).
Short-circuit operators
Some progr
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https://en.wikipedia.org/wiki/Join%20%28topology%29
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In topology, a field of mathematics, the join of two topological spaces and , often denoted by or , is a topological space formed by taking the disjoint union of the two spaces, and attaching line segments joining every point in to every point in . The join of a space with itself is denoted by . The join is defined in slightly different ways in different contexts
Geometric sets
If and are subsets of the Euclidean space , then:,that is, the set of all line-segments between a point in and a point in .
Some authors restrict the definition to subsets that are joinable: any two different line-segments, connecting a point of A to a point of B, meet in at most a common endpoint (that is, they do not intersect in their interior). Every two subsets can be made "joinable". For example, if is in and is in , then and are joinable in . The figure above shows an example for m=n=1, where and are line-segments.
Examples
The join of two simplices is a simplex: the join of an n-dimensional and an m-dimensional simplex is an (m+n+1)-dimensional simplex. Some special cases are:
The join of two disjoint points is an interval (m=n=0).
The join of a point and an interval is a triangle (m=0, n=1).
The join of two line segments is homeomorphic to a solid tetrahedron or disphenoid, illustrated in the figure above right (m=n=1).
The join of a point and an (n-1)-dimensional simplex is an n-dimensional simplex.
The join of a point and a polygon (or any polytope) is a pyramid, li
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https://en.wikipedia.org/wiki/Pl%C3%BCcker%20formula
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In mathematics, a Plücker formula, named after Julius Plücker, is one of a family of formulae, of a type first developed by Plücker in the 1830s, that relate certain numeric invariants of algebraic curves to corresponding invariants of their dual curves. The invariant called the genus, common to both the curve and its dual, is connected to the other invariants by similar formulae. These formulae, and the fact that each of the invariants must be a positive integer, place quite strict limitations on their possible values.
Plücker invariants and basic equations
A curve in this context is defined by a non-degenerate algebraic equation in the complex projective plane. Lines in this plane correspond to points in the dual projective plane and the lines tangent to a given algebraic curve C correspond to points in an algebraic curve C* called the dual curve. In the correspondence between the projective plane and its dual, points on C correspond to lines tangent C*, so the dual of C* can be identified with C.
The first two invariants covered by the Plücker formulas are the degree d of the curve C and the degree d*, classically called the class of C. Geometrically, d is the number of times a given line intersects C with multiplicities properly counted. (This includes complex points and points at infinity since the curves are taken to be subsets of the complex projective plane.) Similarly, d* is the number of tangents to C that are lines through a given point on the plane; so for exa
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https://en.wikipedia.org/wiki/PDG
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PDG may refer to:
Gabonese Democratic Party (Parti démocratique gabonais), the ruling party of Gabon
Democratic Party of Guinea or Parti démocratique de Guinée
Minangkabau International Airport, Padang, Indonesia IATA airport code
Particle Data Group, international group of particle physicists
Program dependence graph, in computer science, a diagram to clarify dependencies
Patrouille des Glaciers, skiing competition organised by the Swiss military
Permanent downhole gauge, pressure or temperature gauge in an oil or gas well
Padgate railway station, England (station code)
PDG S.A., Brazilian real estate company
Président-directeur général, a combination of chairman and CEO in France
Phänomenologie des Geistes (Phenomenology of Spirit) by Hegel
Public Data Group, for accessibility of official UK data
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https://en.wikipedia.org/wiki/Outbreeding%20depression
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In biology, outbreeding depression happens when crosses between two genetically distant groups or populations result in a reduction of fitness. The concept is in contrast to inbreeding depression, although the two effects can occur simultaneously. Outbreeding depression is a risk that sometimes limits the potential for genetic rescue or augmentations. It is considered postzygotic response because outbreeding depression is noted usually in the performance of the progeny.
Outbreeding depression manifests in two ways:
Generating intermediate genotypes that are less fit than either parental form. For example, selection in one population might favor a large body size, whereas in another population small body size might be more advantageous, while individuals with intermediate body sizes are comparatively disadvantaged in both populations. As another example, in the Tatra Mountains, the introduction of ibex from the Middle East resulted in hybrids which produced calves at the coldest time of the year.
Breakdown of biochemical or physiological compatibility. Within isolated breeding populations, alleles are selected in the context of the local genetic background. Because the same alleles may have rather different effects in different genetic backgrounds, this can result in different locally coadapted gene complexes. Outcrossing between individuals with differently adapted gene complexes can result in disruption of this selective advantage, resulting in a loss of fitness.
Mecha
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https://en.wikipedia.org/wiki/Vector%20bundles%20on%20algebraic%20curves
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In mathematics, vector bundles on algebraic curves may be studied as holomorphic vector bundles on compact Riemann surfaces, which is the classical approach, or as locally free sheaves on algebraic curves C in a more general, algebraic setting (which can for example admit singular points).
Some foundational results on classification were known in the 1950s. The result of , that holomorphic vector bundles on the Riemann sphere are sums of line bundles, is now often called the Birkhoff–Grothendieck theorem, since it is implicit in much earlier work of on the Riemann–Hilbert problem.
gave the classification of vector bundles on elliptic curves.
The Riemann–Roch theorem for vector bundles was proved by , before the 'vector bundle' concept had really any official status. Although, associated ruled surfaces were classical objects. See Hirzebruch–Riemann–Roch theorem for his result. He was seeking a generalization of the Jacobian variety, by passing from holomorphic line bundles to higher rank. This idea would prove fruitful, in terms of moduli spaces of vector bundles. following on the work in the 1960s on geometric invariant theory.
See also
Hitchin system
References
Also in Collected Works vol. I
Algebraic curves
Vector bundles
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https://en.wikipedia.org/wiki/Viktor%20Arnar%20Ing%C3%B3lfsson
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Viktor Arnar Ingólfsson (born 12 April 1955, in Akureyri) is an Icelandic writer of crime fiction. He has a B.Sc. degree in civil engineering and, in addition to having a successful career as a writer, he continues to work full-time at the Public Roads Administration in Iceland.
Viktor Arnar has twice been the Icelandic nominee for the Glass Key award, which is awarded by Skandinaviska Kriminalselskapet (Crime Writers of Scandinavia). Three of his five novels have been translated into German, and Flateyjargáta was published in English as The Flatey Enigma in February 2012. His novel Afturelding was the basis of the Icelandic television series Mannaveiðar, english title I Hunt Men (2008). His novel Flateyjargáta was the basis of the Icelandic television series Flateyjargátan, english title The Flatey Enigma (2018).
Bibliography
Dauðasök (1978)
Heitur snjór (1982)
Engin spor (1998) (English translation by Björg Árnardóttir & Andrew Cauthery, House of Evidence, 2012)
Leyndardómar Reykjavíkur 2000 (2000) (one chapter)
Flateyjargáta (2003) (English translation by Brian FitzGibbon, The Flatey Enigma, 2012)
Afturelding (2005) (English translation by Björg Árnardóttir & Andrew Cauthery, Daybreak, 2013)
Sólstjakar (2009) (English translation by Björg Árnardóttir & Andrew Cauthery, Sun On Fire, 2014)
References
External links
Viktor Arnar Ingólfsson's official website's English language page
Ingólfsson's biography at the Reykjavík City Library web
Interview
1955 births
Living p
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https://en.wikipedia.org/wiki/Opposite%20ring
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In mathematics, specifically abstract algebra, the opposite of a ring is another ring with the same elements and addition operation, but with the multiplication performed in the reverse order. More explicitly, the opposite of a ring is the ring whose multiplication ∗ is defined by for all in R. The opposite ring can be used to define multimodules, a generalization of bimodules. They also help clarify the relationship between left and right modules (see ).
Monoids, groups, rings, and algebras can all be viewed as categories with a single object. The construction of the opposite category generalizes the opposite group, opposite ring, etc.
Relation to automorphisms and antiautomorphisms
In this section the symbol for multiplication in the opposite ring is changed from asterisk to diamond, to avoid confusion with some unary operation.
A ring having isomorphic opposite ring is called a self-opposite ring, which name indicates that is essentially the same as .
All commutative rings are self-opposite.
Let us define the antiisomorphism
, where for .
It is indeed an antiisomorphism, since .
The antiisomorphism can be defined generally for semigroups, monoids, groups, rings, rngs, algebras. In case of rings (and rngs) we obtain the general equivalence.
A ring is self-opposite if and only if it has at least one antiautomorphism.
Proof:
: Let be self-opposite. If is an isomorphism, then , being a composition of antiisomorphism and isomorphism, is an antiisomorphism from
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https://en.wikipedia.org/wiki/Quasi-Lie%20algebra
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In mathematics, a quasi-Lie algebra in abstract algebra is just like a Lie algebra, but with the usual axiom
replaced by
(anti-symmetry).
In characteristic other than 2, these are equivalent (in the presence of bilinearity), so this distinction doesn't arise when considering real or complex Lie algebras. It can however become important, when considering Lie algebras over the integers.
In a quasi-Lie algebra,
Therefore, the bracket of any element with itself is 2-torsion, if it does not actually vanish.
See also
Whitehead product
References
Lie algebras
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https://en.wikipedia.org/wiki/Far-infrared%20laser
|
Far-infrared laser or terahertz laser (FIR laser, THz laser) is a laser with output wavelength in between 30-1000 µm (frequency 0.3-10 THz), in the far infrared or terahertz frequency band of the electromagnetic spectrum.
FIR lasers have application in terahertz spectroscopy, terahertz imaging as well in fusion plasma physics diagnostics. They can be used to detect explosives and chemical warfare agents, by the means of infrared spectroscopy or to evaluate the plasma densities by the means of interferometry techniques.
FIR lasers typically consist of a long (1–3 meters) waveguide filled with gaseous organic molecules, optically pumped or via HV discharge. They are highly inefficient, often require helium cooling, high magnetic fields, and/or are only line tunable. Efforts to develop smaller solid-state alternatives are under way.
The p-Ge (p-type germanium) laser is a tunable, solid state, far infrared laser which has existed for over 25 years. It operates in crossed electric and magnetic fields at liquid helium temperatures. Wavelength selection can be achieved by changing the applied electric/magnetic fields or through the introduction of intracavity elements.
Quantum cascade laser (QCL) is a construction of such alternative. It is a solid-state semiconductor laser that can operate continuously with output power of over 100 mW and wavelength of 9.5 µm. A prototype was already demonstrated. and potential use shown.
A molecular FIR laser optically pumped by a QCL has bee
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https://en.wikipedia.org/wiki/Whitehead%20product
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In mathematics, the Whitehead product is a graded quasi-Lie algebra structure on the homotopy groups of a space. It was defined by J. H. C. Whitehead in .
The relevant MSC code is: 55Q15, Whitehead products and generalizations.
Definition
Given elements , the Whitehead bracket
is defined as follows:
The product can be obtained by attaching a -cell to the wedge sum
;
the attaching map is a map
Represent and by maps
and
then compose their wedge with the attaching map, as
The homotopy class of the resulting map does not depend on the choices of representatives, and thus one obtains a well-defined element of
Grading
Note that there is a shift of 1 in the grading (compared to the indexing of homotopy groups), so has degree ; equivalently, (setting L to be the graded quasi-Lie algebra). Thus acts on each graded component.
Properties
The Whitehead product satisfies the following properties:
Bilinearity.
Graded Symmetry.
Graded Jacobi identity.
Sometimes the homotopy groups of a space, together with the Whitehead product operation are called a graded quasi-Lie algebra; this is proven in via the Massey triple product.
Relation to the action of
If , then the Whitehead bracket is related to the usual action of on by
where denotes the conjugation of by .
For , this reduces to
which is the usual commutator in . This can also be seen by observing that the -cell of the torus is attached along the commutator in the -skeleton .
Whitehead products
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https://en.wikipedia.org/wiki/Stacking%20%28chemistry%29
|
In chemistry, pi stacking (also called π–π stacking) refers to the presumptive attractive, noncovalent pi interactions (orbital overlap) between the pi bonds of aromatic rings. However this is a misleading description of the phenomena since direct stacking of aromatic rings (the "sandwich interaction") is electrostatically repulsive. What is more commonly observed (see figure to the right) is either a staggered stacking (parallel displaced) or pi-teeing (perpendicular T-shaped) interaction both of which are electrostatic attractive For example, the most commonly observed interactions between aromatic rings of amino acid residues in proteins is a staggered stacked followed by a perpendicular orientation. Sandwiched orientations are relatively rare.
Pi stacking is repulsive as it places carbon atoms with partial negative charges from one ring on top of other partial negatively charged carbon atoms from the second ring and hydrogen atoms with partial positive charges on top of other hydrogen atoms that likewise carry partial positive charges. In staggered stacking, one of the two aromatic rings is offset sideways so that the carbon atoms with partial negative charge in the first ring are placed above hydrogen atoms with partial positive charge in the second ring so that the electrostatic interactions become attractive. Likewise, pi-teeing interactions in which the two rings are oriented perpendicular to either other is electrostatically attractive as it places partial positiv
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https://en.wikipedia.org/wiki/The%20Magic%20Hour%20%28talk%20show%29
|
The Magic Hour is an American talk show hosted by basketball player Earvin "Magic" Johnson. The series aired in syndication from June to September 1998.
Synopsis
Soon after its debut, the series was panned by critics citing Johnson's apparent nervousness as a host, his overly complimentary tone with his celebrity guests, and lack of chemistry with his sidekick, comedian Craig Shoemaker. Before Shoemaker was chosen, the role was offered to Stephen Colbert and Jimmy Kimmel. Both rejected the role as they didn't think the character would work. The series was quickly retooled with Shoemaker being relieved of his 'sidekick' responsibilities and relegated to the supporting cast after the third episode. Comedian Steve White (who had been part of the supporting cast) became the new sidekick for a period of time. Radio personality and UPN Sports host Kenny Sargent was considered for Johnson’s new Ed McMahon styled side man, but finally comedian and actor Tommy Davidson was brought in as the new sidekick and Johnson interacted more with the show band leader Sheila E. Jimmy Hodson was the show's announcer and a comedy cast member. The format of the show was also changed to include more interview time with celebrity guests.
Howard Stern appearance
One vocal critic of The Magic Hour was Howard Stern. Stern would regularly mock Johnson's diction and hosting abilities on his popular morning show. In an attempt to confront Stern (and to boost ratings), Stern was booked to appear on
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https://en.wikipedia.org/wiki/B%C3%A9zout%20domain
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In mathematics, a Bézout domain is a form of a Prüfer domain. It is an integral domain in which the sum of two principal ideals is again a principal ideal. This means that for every pair of elements a Bézout identity holds, and that every finitely generated ideal is principal. Any principal ideal domain (PID) is a Bézout domain, but a Bézout domain need not be a Noetherian ring, so it could have non-finitely generated ideals (which obviously excludes being a PID); if so, it is not a unique factorization domain (UFD), but still is a GCD domain. The theory of Bézout domains retains many of the properties of PIDs, without requiring the Noetherian property. Bézout domains are named after the French mathematician Étienne Bézout.
Examples
All PIDs are Bézout domains.
Examples of Bézout domains that are not PIDs include the ring of entire functions (functions holomorphic on the whole complex plane) and the ring of all algebraic integers. In case of entire functions, the only irreducible elements are functions associated to a polynomial function of degree 1, so an element has a factorization only if it has finitely many zeroes. In the case of the algebraic integers there are no irreducible elements at all, since for any algebraic integer its square root (for instance) is also an algebraic integer. This shows in both cases that the ring is not a UFD, and so certainly not a PID.
Valuation rings are Bézout domains. Any non-Noetherian valuation ring is an example of a non-noetheria
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https://en.wikipedia.org/wiki/Holomorphic%20functional%20calculus
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In mathematics, holomorphic functional calculus is functional calculus with holomorphic functions. That is to say, given a holomorphic function f of a complex argument z and an operator T, the aim is to construct an operator, f(T), which naturally extends the function f from complex argument to operator argument. More precisely, the functional calculus defines a continuous algebra homomorphism from the holomorphic functions on a neighbourhood of the spectrum of T to the bounded operators.
This article will discuss the case where T is a bounded linear operator on some Banach space. In particular, T can be a square matrix with complex entries, a case which will be used to illustrate functional calculus and provide some heuristic insights for the assumptions involved in the general construction.
Motivation
Need for a general functional calculus
In this section T will be assumed to be a n × n matrix with complex entries.
If a given function f is of certain special type, there are natural ways of defining f(T). For instance, if
is a complex polynomial, one can simply substitute T for z and define
where T0 = I, the identity matrix. This is the polynomial functional calculus. It is a homomorphism from the ring of polynomials to the ring of n × n matrices.
Extending slightly from the polynomials, if f : C → C is holomorphic everywhere, i.e. an entire function, with MacLaurin series
mimicking the polynomial case suggests we define
Since the MacLaurin series converges every
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https://en.wikipedia.org/wiki/Coframe
|
In mathematics, a coframe or coframe field on a smooth manifold is a system of one-forms or covectors which form a basis of the cotangent bundle at every point. In the exterior algebra of , one has a natural map from , given by . If is dimensional a coframe is given by a section of such that . The inverse image under of the complement of the zero section of forms a principal bundle over , which is called the coframe bundle.
References
See also
Frame fields in general relativity
Moving frame
Differential geometry
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https://en.wikipedia.org/wiki/Daniel%20P.%20Friedman
|
Daniel Paul Friedman (born 1944) is a professor of Computer Science at Indiana University in Bloomington, Indiana. His research focuses on programming languages, and he is a prominent author in the field.
With David Wise, Friedman wrote a highly influential paper on lazy programming, specifically on lazy streams (ICALP 1976). The paper, entitled "Cons should not evaluate its arguments," is one of the first publications pushing for the exploration of a programming style with potentially infinite data structures and a form of programming that employs no computational effects (though programs may diverge). Over the 1970s, Friedman and Wise explored the topic in depth and also considered extensions to the world of parallel computing.
In the 1980s, Friedman turned to the study of the Scheme programming language. He explored the use of macros for defining programming languages; with Eugene Kohlbecker, Matthias Felleisen, and Bruce Duba, he co-introduced the notion of hygienic macros in a 1986 LFP paper that is still widely cited today. With Christopher T. Haynes and Mitchell Wand, he simultaneously studied the nature of continuation objects, their uses, and the possibilities of constraining them. Following that, Friedman and Felleisen introduced a lambda calculus with continuations and control operators. Their work has spawned work on semantics, connections between classical logic and computation, and practical extensions of continuations.
Friedman is also a prolific textbook
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https://en.wikipedia.org/wiki/CR%20manifold
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In mathematics, a CR manifold, or Cauchy–Riemann manifold, is a differentiable manifold together with a geometric structure modeled on that of a real hypersurface in a complex vector space, or more generally modeled on an edge of a wedge.
Formally, a CR manifold is a differentiable manifold M together with a preferred complex distribution L, or in other words a complex subbundle of the complexified tangent bundle such that
(L is formally integrable)
.
The subbundle L is called a CR structure on the manifold M.
The abbreviation CR stands for "Cauchy–Riemann" or "Complex-Real".
Introduction and motivation
The notion of a CR structure attempts to describe intrinsically the property of being a hypersurface (or certain real submanifolds of higher codimension) in complex space by studying the properties of holomorphic vector fields which are tangent to the hypersurface.
Suppose for instance that M is the hypersurface of given by the equation
where z and w are the usual complex coordinates on . The holomorphic tangent bundle of consists of all linear combinations of the vectors
The distribution L on M consists of all combinations of these vectors which are tangent to M. The tangent vectors must annihilate the defining equation for M, so L consists of complex scalar multiples of
In particular, L consists of the holomorphic vector fields which annihilate F. Note that L gives a CR structure on M, for [L,L] = 0 (since L is one-dimensional) and since ∂/∂z and ∂/∂w are lin
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https://en.wikipedia.org/wiki/Barry%20Simon
|
Barry Martin Simon (born 16 April 1946) is an American mathematical physicist and was the IBM professor of Mathematics and Theoretical Physics at Caltech, known for his prolific contributions in spectral theory, functional analysis, and nonrelativistic quantum mechanics (particularly Schrödinger operators), including the connections to atomic and molecular physics. He has authored more than 400 publications on mathematics and physics.
His work has focused on broad areas of mathematical physics and analysis covering: quantum field theory, statistical mechanics, Brownian motion, random matrix theory, general nonrelativistic quantum mechanics (including N-body systems and resonances), nonrelativistic quantum mechanics in electric and magnetic fields, the semi-classical limit, the singular continuous spectrum, random and ergodic Schrödinger operators, orthogonal polynomials, and non-selfadjoint spectral theory.
Early life
Barry Simon's mother was a school teacher, his father was an accountant. Simon attended James Madison High School in Brooklyn.
Career
During his high school years, Simon started attending college courses for highly gifted pupils at Columbia University. In 1962, Simon won a MAA mathematics competition. The New York Times reported that in order to receive full credits for a faultless test result he had to make a submission with MAA. In this submission he proved that one of the problems posed in the test was ambiguous.
In 1962, Simon entered Harvard with a st
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https://en.wikipedia.org/wiki/Nakai%20conjecture
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In mathematics, the Nakai conjecture is an unproven characterization of smooth algebraic varieties, conjectured by Japanese mathematician Yoshikazu Nakai in 1961.
It states that if V is a complex algebraic variety, such that its ring of differential operators is generated by the derivations it contains, then V is a smooth variety. The converse statement, that smooth algebraic varieties have rings of differential operators that are generated by their derivations, is a result of Alexander Grothendieck.
The Nakai conjecture is known to be true for algebraic curves and Stanley–Reisner rings. A proof of the conjecture would also establish the Zariski–Lipman conjecture, for a complex variety V with coordinate ring R. This conjecture states that if the derivations of R are a free module over R, then V is smooth.
References
Algebraic geometry
Singularity theory
Conjectures
Unsolved problems in geometry
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https://en.wikipedia.org/wiki/Ehud%20Hrushovski
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Ehud Hrushovski (; born 30 September 1959) is a mathematical logician. He is a Merton Professor of Mathematical Logic at the University of Oxford and a Fellow of Merton College, Oxford. He was also Professor of Mathematics at the Hebrew University of Jerusalem.
Early life and education
Hrushovski's father, Benjamin Harshav (Hebrew: בנימין הרשב, né Hruszowski; 1928–2015), was a literary theorist, a Yiddish and Hebrew poet and a translator, professor at Yale University and Tel Aviv University in comparative literature. Ehud Hrushovski earned his PhD from the University of California, Berkeley in 1986 under Leo Harrington; his dissertation was titled Contributions to Stable Model Theory. He was a professor of mathematics at the Massachusetts Institute of Technology until 1994, when he became a professor at the Hebrew University of Jerusalem. Hrushovski moved in 2017 to the University of Oxford, where he is the Merton Professor of Mathematical Logic.
Career
Hrushovski is well known for several fundamental contributions to model theory, in particular in the branch that has become known as geometric model theory, and its applications. His PhD thesis revolutionized stable model theory (a part of model theory arising from the stability theory introduced by Saharon Shelah). Shortly afterwards he found counterexamples to the Trichotomy Conjecture of Boris Zilber and his method of proof has become well known as Hrushovski constructions and found many other applications since.
One of
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https://en.wikipedia.org/wiki/Zariski%20geometry
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In mathematics, a Zariski geometry consists of an abstract structure introduced by Ehud Hrushovski and Boris Zilber, in order to give a characterisation of the Zariski topology on an algebraic curve, and all its powers. The Zariski topology on a product of algebraic varieties is very rarely the product topology, but richer in closed sets defined by equations that mix two sets of variables. The result described gives that a very definite meaning, applying to projective curves and compact Riemann surfaces in particular.
Definition
A Zariski geometry consists of a set X and a topological structure on each of the sets
X, X2, X3, ...
satisfying certain axioms.
(N) Each of the Xn is a Noetherian topological space, of dimension at most n.
Some standard terminology for Noetherian spaces will now be assumed.
(A) In each Xn, the subsets defined by equality in an n-tuple are closed. The mappings
Xm → Xn
defined by projecting out certain coordinates and setting others as constants are all continuous.
(B) For a projection
p: Xm → Xn
and an irreducible closed subset Y of Xm, p(Y) lies between its closure Z and Z \ where is a proper closed subset of Z. (This is quantifier elimination, at an abstract level.)
(C) X is irreducible.
(D) There is a uniform bound on the number of elements of a fiber in a projection of any closed set in Xm, other than the cases where the fiber is X.
(E) A closed irreducible subset of Xm, of dimension r, when intersected with a diagonal subset in
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https://en.wikipedia.org/wiki/Steve%20Ciarcia
|
Steve Ciarcia is an embedded control systems engineer. He became popular through his Ciarcia's Circuit Cellar column in BYTE magazine, and later through the Circuit Cellar magazine that he published. He is also the author of Build Your Own Z80 Computer, edited in 1981 and Take My Computer...Please!, published in 1978. He has also compiled seven volumes of his hardware project articles that appeared in BYTE magazine.
In 1982 and 1983, he published a series of articles on building the MPX-16, a 16-bit single-board computer that was hardware-compatible with the IBM PC.
In December 2009, Steve Ciarcia announced that for the American market a strategic cooperation would be entered between Elektor and his Circuit Cellar magazine. In November 2012, Steve Ciarcia announced that he was quitting Circuit Cellar and Elektor would take it over.
In October 2014, Ciarcia purchased Circuit Cellar, audioXpress, Voice Coil, Loudspeaker Industry Sourcebook, and their respective websites, newsletters, and products from Netherlands-based Elektor International Media. The aforementioned magazines will continue to be published by Ciarcia's US-based team.
In July 2016, Steve Ciarcia sold the company to long time employee KC Prescott operating under the company name KCK Media Corp.
References
External links
Circuit Cellar magazine
Index on Steve Ciarcia's articles in BYTE
American magazine editors
American technology writers
Control theorists
Living people
Year of birth missing (living peopl
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https://en.wikipedia.org/wiki/Genetics%20and%20archaeogenetics%20of%20South%20Asia
|
Genetics and archaeogenetics of South Asia is the study of the genetics and archaeogenetics of the ethnic groups of South Asia. It aims at uncovering these groups' genetic histories. The geographic position of the Indian subcontinent makes its biodiversity important for the study of the early dispersal of anatomically modern humans across Asia.
Based on mitochondrial DNA (mtDNA) variations, genetic unity across various South Asian subpopulations have shown that most of the ancestral nodes of the phylogenetic tree of all the mtDNA types originated in the subcontinent. Conclusions of studies based on Y chromosome variation and autosomal DNA variation have been varied.
Modern South Asians are descendants of a combination of an indigenous South Asian component (termed Ancient Ancestral South Indians, short "AASI"), closest to Southern Indian tribal groups and distantly related to the Andamanese peoples, as well as to East Asian people and Aboriginal Australians, and later-arriving West-Eurasian (Western steppe herders/West Asian-related) and additional East/Southeast Asian components respectively.
The AASI type ancestry is found at the highest levels among certain Southern Indian tribal groups, such as the Paniya or Irula, and is generally found throughout all South Asian ethnic groups in varying degrees. The AASI ancestry is hypothesized to be the ancestry of the very first hunter gatherers and peoples of the Indian subcontinent, before the later groups arrived. Using a proxy
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https://en.wikipedia.org/wiki/Theta%20divisor
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In mathematics, the theta divisor Θ is the divisor in the sense of algebraic geometry defined on an abelian variety A over the complex numbers (and principally polarized) by the zero locus of the associated Riemann theta-function. It is therefore an algebraic subvariety of A of dimension dim A − 1.
Classical theory
Classical results of Bernhard Riemann describe Θ in another way, in the case that A is the Jacobian variety J of an algebraic curve (compact Riemann surface) C. There is, for a choice of base point P on C, a standard mapping of C to J, by means of the interpretation of J as the linear equivalence classes of divisors on C of degree 0. That is, Q on C maps to the class of Q − P. Then since J is an algebraic group, C may be added to itself k times on J, giving rise to subvarieties Wk.
If g is the genus of C, Riemann proved that Θ is a translate on J of Wg − 1. He also described which points on Wg − 1 are non-singular: they correspond to the effective divisors D of degree g − 1 with no associated meromorphic functions other than constants. In more classical language, these D do not move in a linear system of divisors on C, in the sense that they do not dominate the polar divisor of a non constant function.
Riemann further proved the Riemann singularity theorem, identifying the multiplicity of a point p = class(D) on Wg − 1 as the number of linearly independent meromorphic functions with pole divisor dominated by D, or equivalently as h0(O(D)), the number of linearl
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https://en.wikipedia.org/wiki/Polarizable%20vacuum
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In theoretical physics, particularly fringe physics, polarizable vacuum (PV) and its associated theory refers to proposals by Harold Puthoff, Robert H. Dicke, and others to develop an analogue of general relativity to describe gravity and its relationship to electromagnetism.
Description
In essence, Dicke and Puthoff proposed that the presence of mass alters the electric permittivity and the magnetic permeability of flat spacetime, εo and μo respectively by multiplying them by a scalar function, K:
arguing that this will affect the lengths of rulers made of ordinary matter, so that in the presence of a gravitational field the spacetime metric of Minkowski spacetime is replaced by
where is the so-called "dielectric constant of the vacuum". This is a "diagonal" metric given in terms of a Cartesian chart and having the same stratified conformally flat form in the Watt-Misner theory of gravitation. However, according to Dicke and Puthoff, κ must satisfy a field equation which differs from the field equation of the Watt-Misner theory. In the case of a static spherically symmetric vacuum, this yields the asymptotically flat solution
The resulting Lorentzian spacetime happens to agree with the analogous solution in the Watt-Misner theory, and it has the same weak-field limit, and the same far-field, as the Schwarzschild vacuum solution in general relativity, and it satisfies three of the four classical tests of relativistic gravitation (redshift, deflection of light, prece
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https://en.wikipedia.org/wiki/List%20of%20Lund%20University%20people
|
This is a list of notable people affiliated with Lund University, either as students or as researchers and academic teachers (or both). Lund University, located in the town of Lund in Skåne, Sweden, was founded in 1666.
Nobel laureates affiliated with Lund University
Manne Siegbahn (1886-1978), Physics 1924; professor at Uppsala University (B.A. 1908, Ph.D. 1911)
Bertil Ohlin (1899-1979), Economics 1977; professor at the Stockholm School of Economics; leader of the liberal Liberal People's Party, 1944-1967 (B.A. 1917)
Sune Bergström (1916-2004), Medicine 1982 (Professor 1947-1958)
Arvid Carlsson (1923-2018), Medicine 2000 (M.D. 1951, Assistant Professor 1951-1959)
Government, politics and civil service
Gbehzohngar Milton Findley (1960–), Liberian politician and businessman, former Senate Pro-tempore, and former Minister of Foreign Affairs
Peter Estenberg (1686–1740), Greek scholar, professor, and advisor to King Stanislaw (Stanisław Leszczyński) of Poland in the early 18th century
Lars von Engeström (1751–1826), statesman and diplomat, first Prime Minister for Foreign Affairs 1809–1824, Chancellor of Lund University 1810–1824
Arvid Posse (1820–1901), Prime Minister of Sweden 1880–1883 (B.A. 1840)
Östen Undén (1886–1974), Rector Magnificus of Uppsala University and politician; Minister for Foreign Affairs 1924-26, 1945-62 (B.A. 1905, LL.B. 1910, LL.D. 1912)
Ernst Wigforss (1881–1977), linguist and politician, Swedish Minister of Finance (Ph.D. 1913)
Per Edvin Sköld (1891–19
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https://en.wikipedia.org/wiki/Poromechanics
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Poromechanics is a branch of physics and specifically continuum mechanics and acoustics that studies the behaviour of fluid-saturated porous media. A porous medium or a porous material is a solid referred to as matrix) permeated by an interconnected network of pores (voids) filled with a fluid (liquid or gas). Usually both solid matrix and the pore network, or pore space, are assumed to be continuous, so as to form two interpenetrating continua such as in a sponge. Natural substances including rocks, soils, biological tissues including heart and cancellous bone, and man-made materials such as foams and ceramics can be considered as porous media. Porous media whose solid matrix is elastic and the fluid is viscous are called poroelastic. A poroelastic medium is characterised by its porosity, permeability as well as the properties of its constituents (solid matrix and fluid).
The concept of a porous medium originally emerged in soil mechanics, and in particular in the works of Karl von Terzaghi, the father of soil mechanics. However a more general concept of a poroelastic medium, independent of its nature or application, is usually attributed to Maurice Anthony Biot (1905–1985), a Belgian-American engineer. In a series of papers published between 1935 and 1962 Biot developed the theory of dynamic poroelasticity (now known as Biot theory) which gives a complete and general description of the mechanical behaviour of a poroelastic medium. Biot's equations of the linear theory of
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https://en.wikipedia.org/wiki/Threading%20%28protein%20sequence%29
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In molecular biology, protein threading, also known as fold recognition, is a method of protein modeling which is used to model those proteins which have the same fold as proteins of known structures, but do not have homologous proteins with known structure.
It differs from the homology modeling method of structure prediction as it (protein threading) is used for proteins which do not have their homologous protein structures deposited in the Protein Data Bank (PDB), whereas homology modeling is used for those proteins which do. Threading works by using statistical knowledge of the relationship between the structures deposited in the PDB and the sequence of the protein which one wishes to model.
The prediction is made by "threading" (i.e. placing, aligning) each amino acid in the target sequence to a position in the template structure, and evaluating how well the target fits the template. After the best-fit template is selected, the structural model of the sequence is built based on the alignment with the chosen template. Protein threading is based on two basic observations: that the number of different folds in nature is fairly small (approximately 1300); and that 90% of the new structures submitted to the PDB in the past three years have similar structural folds to ones already in the PDB.
Classification of protein structure
The Structural Classification of Proteins (SCOP) database provides a detailed and comprehensive description of the structural and evolutionary relatio
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https://en.wikipedia.org/wiki/Grothendieck%E2%80%93Katz%20p-curvature%20conjecture
|
In mathematics, the Grothendieck–Katz p-curvature conjecture is a local-global principle for linear ordinary differential equations, related to differential Galois theory and in a loose sense analogous to the result in the Chebotarev density theorem considered as the polynomial case. It is a conjecture of Alexander Grothendieck from the late 1960s, and apparently not published by him in any form.
The general case remains unsolved, despite recent progress; it has been linked to geometric investigations involving algebraic foliations.
Formulation
In a simplest possible statement the conjecture can be stated in its essentials for a vector system written as
for a vector v of size n, and an n×n matrix A of algebraic functions with algebraic number coefficients. The question is to give a criterion for when there is a full set of algebraic function solutions, meaning a fundamental matrix (i.e. n vector solutions put into a block matrix). For example, a classical question was for the hypergeometric equation: when does it have a pair of algebraic solutions, in terms of its parameters? The answer is known classically as Schwarz's list. In monodromy terms, the question is of identifying the cases of finite monodromy group.
By reformulation and passing to a larger system, the essential case is for rational functions in A and rational number coefficients. Then a necessary condition is that for almost all prime numbers p, the system defined by reduction modulo p should also have a full
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https://en.wikipedia.org/wiki/Ethyl
|
Ethyl may refer to:
Arts and entertainment
Cold Ethyl, a Swedish rock band
Ethyl Sinclair, a character in the Dinosaurs television show
Science and technology
Ethyl group, an organic chemistry moiety
Ethyl alcohol (or ethanol)
Ethyl Corporation, a fuel additive company
Tetraethyllead-treated gasoline
See also
Ethel (disambiguation)
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https://en.wikipedia.org/wiki/Systems%20biomedicine
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Systems biomedicine, also called systems biomedical science, is the application of systems biology to the understanding and modulation of developmental and pathological processes in humans, and in animal and cellular models. Whereas systems biology aims at modeling exhaustive networks of interactions (with the long-term goal of, for example, creating a comprehensive computational model of the cell), mainly at intra-cellular level, systems biomedicine emphasizes the multilevel, hierarchical nature of the models (molecule, organelle, cell, tissue, organ, individual/genotype, environmental factor, population, ecosystem) by discovering and selecting the key factors at each level and integrating them into models that reveal the global, emergent behavior of the biological process under consideration.
Such an approach will be favorable when the execution of all the experiments necessary to establish exhaustive models is limited by time and expense (e.g., in animal models) or basic ethics (e.g., human experimentation).
In the year of 1992, a paper on system biomedicine by Kamada T. was published (Nov.-Dec.), and an article on systems medicine and pharmacology by Zeng B.J. was also published (April) in the same time period.
In 2009, the first collective book on systems biomedicine was edited by Edison T. Liu and Douglas A. Lauffenburger.
In October 2008, one of the first research groups uniquely devoted to systems biomedicine was established at the European Institute of Oncology. O
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https://en.wikipedia.org/wiki/Mass%20flow%20%28life%20sciences%29
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In the life sciences, mass flow, also known as mass transfer and bulk flow, is the movement of fluids down a pressure or temperature gradient. As such, mass flow is a subject of study in both fluid dynamics and biology. Examples of mass flow include blood circulation and transport of water in vascular plant tissues. Mass flow is not to be confused with diffusion which depends on concentration gradients within a medium rather than pressure gradients of the medium itself.
Plant biology
In general, bulk flow in plant biology typically refers to the movement of water from the soil up through the plant to the leaf tissue through xylem, but can also be applied to the transport of larger solutes (e.g. sucrose) through the phloem.
Xylem
According to cohesion-tension theory, water transport in xylem relies upon the cohesion of water molecules to each other and adhesion to the vessel's wall via hydrogen bonding combined with the high water pressure of the plant's substrate and low pressure of the extreme tissues (usually leaves).
As in blood circulation in animals, (gas) embolisms may form within one or more xylem vessels of a plant. If an air bubble forms, the upward flow of xylem water will stop because the pressure difference in the vessel cannot be transmitted. Once these embolisms are nucleated , the remaining water in the capillaries begins to turn to water vapor. When these bubbles form rapidly by cavitation, the "snapping" sound can be used to measure the rate of cavitation
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https://en.wikipedia.org/wiki/Principal%20ideal%20theorem
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In mathematics, the principal ideal theorem of class field theory, a branch of algebraic number theory, says that extending ideals gives a mapping on the class group of an algebraic number field to the class group of its Hilbert class field, which sends all ideal classes to the class of a principal ideal. The phenomenon has also been called principalization, or sometimes capitulation.
Formal statement
For any algebraic number field K and any ideal I of the ring of integers of K, if L is the Hilbert class field of K, then
is a principal ideal αOL, for OL the ring of integers of L and some element α in it.
History
The principal ideal theorem was conjectured by , and was the last remaining aspect of his program on class fields to be completed, in 1929.
reduced the principal ideal theorem to a question about finite abelian groups: he showed that it would follow if the transfer from a finite group to its derived subgroup is trivial. This result was proved by Philipp Furtwängler (1929).
References
Ideals (ring theory)
Group theory
Homological algebra
Theorems in algebraic number theory
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https://en.wikipedia.org/wiki/Alexander%20Tropsha
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Alexander Tropsha is a chemist and professor at the University of North Carolina - Chapel Hill. Tropsha is Associate Dean for Pharmacoinformatics and Data Science at the UNC Eshelman School of Pharmacy. His primary fields of research are cheminformatics and quantitative structure-activity relationship (QSAR) modeling in the context of drug discovery. As of 2015, Tropsha has been an associate editor of the American Chemical Society’s Journal of Chemical Information and Modeling.
Background
In 1982, Tropsha earned his master's degree chemistry from Moscow State University. Tropsha continued his studies under Lev S. Yaguzhinski earning his PhD in biochemistry and pharmacology in 1986.
Tropsha immigrated to the United States in 1989 where he began his career in academics as an assistant professor and director of the Laboratory for Molecular Modeling at the University of North Carolina - Chapel Hill in 1991. Tropsha became a professor in 2004, and, in 2008, he became the K.H. Lee Distinguished Professor at the UNC Eshelman School of Pharmacy.
Research
Research in his laboratory includes the development and application of k-nearest neighbor pattern recognition methods to the field of QSARs and application of the Delaunay tessellation technique to protein structure analysis. His recent work focuses on methods of rigorous validation of QSAR models and the development of best-practice QSAR workflows. Tropsha's group has also raised concerns over the utility of structural alerts in
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