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https://en.wikipedia.org/wiki/Real%20projective%20space
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In mathematics, real projective space, denoted or is the topological space of lines passing through the origin 0 in the real space It is a compact, smooth manifold of dimension , and is a special case of a Grassmannian space.
Basic properties
Construction
As with all projective spaces, RPn is formed by taking the quotient of under the equivalence relation for all real numbers . For all x in one can always find a λ such that λx has norm 1. There are precisely two such λ differing by sign.
Thus RPn can also be formed by identifying antipodal points of the unit n-sphere, Sn, in Rn+1.
One can further restrict to the upper hemisphere of Sn and merely identify antipodal points on the bounding equator. This shows that RPn is also equivalent to the closed n-dimensional disk, Dn, with antipodal points on the boundary, , identified.
Low-dimensional examples
RP1 is called the real projective line, which is topologically equivalent to a circle.
RP2 is called the real projective plane. This space cannot be embedded in R3. It can however be embedded in R4 and can be immersed in R3 (see here). The questions of embeddability and immersibility for projective n-space have been well-studied.
RP3 is (diffeomorphic to) SO(3), hence admits a group structure; the covering map S3 → RP3 is a map of groups Spin(3) → SO(3), where Spin(3) is a Lie group that is the universal cover of SO(3).
Topology
The antipodal map on the n-sphere (the map sending x to −x) generates a Z2 group action o
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https://en.wikipedia.org/wiki/Kind
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Kind or KIND may refer to:
Concepts
Kindness, the human behaviour
Kind, a basic unit of categorization
Kind (type theory), a concept in logic and computer science
Natural kind, in philosophy
Created kind, often abbreviated to kinds, a creationist category of life forms
In kind, for non-monetary transactions
Radio and television stations
KIND (AM), a radio station (1010 AM) licensed to Independence, Kansas, United States
KIND-FM, a radio station (94.9 FM) licensed to Elk City, Kansas, United States
KIND-LP, a low-power radio station (94.1 FM) licensed to serve Oxnard, California, United States
KBIK, a radio station (102.9 FM) licensed to Independence, Kansas, United States that held the call sign KIND-FM from 1980 to 2010
Other uses
Kind (company), an American snack food manufacturer
Kids in Need of Defense, a children's rights organization co-founded by actress Angelina Jolie
Kind (album), a 2019 album by Stereophonics
Kind (surname), a list of people with the surname
Kind (horse) (foaled 2001), an Irish Thoroughbred racehorse
Kind Hundred, a hundred divided between Halland, Småland and Västergötland, Sweden
Indianapolis International Airport (ICAO code:KIND), an airport Indiana, United States
See also
Kinda (disambiguation)
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https://en.wikipedia.org/wiki/Courtney%20Brown%20%28social%20scientist%29
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Courtney Brown (born 1952) is an American political scientist and parapsychologist who is an associate professor in the political science department at Emory University. He is known for promoting the use of nonlinear mathematics in social scientific research, and as a proponent of remote viewing, a form of extrasensory perception.
He is the founder of the Farsight Institute.
Applied mathematics
Brown's research in applied mathematics is mostly focused on social science applications of time-dependent models. He has published five peer-reviewed books and numerous articles on the subject of applied mathematics. Brown is also an advocate of the use of the R Programming Language, both for statistical as well as nonlinear modeling applications in the social sciences.
Remote viewing
Brown learned the basic Transcendental Meditation and an advanced technique called the TM-Sidhi program in 1991. He claims to have engaged in "yogic flying" at the Golden Dome of Pure Knowledge at Maharishi University of Management in Fairfield, Iowa in 1992.
Brown's remote viewing findings have been dismissed by scientists, such as his colleague at Emory University Scott O. Lilienfeld, who has stated that Brown has refused to subject his ideas and his claimed psychic powers to independent scientific testing on what Lilienfeld describes as "curious" grounds.
Among a variety of controversial topics, Brown has claimed to apply remote viewing to the study of multiple realities, the nonlinearity of ti
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https://en.wikipedia.org/wiki/Hapgood%20%28play%29
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Hapgood is a play by Tom Stoppard, first produced in 1988. It is mainly about espionage, focusing on a British female spymaster (Hapgood) and her juggling of career and motherhood. The play also makes reference to quantum mechanics, including Niels Bohr's "The answer is the question interrogated"; Heisenberg's uncertainty principle; and the topological problem of the Seven Bridges of Königsberg. It is regarded as one of Stoppard’s weakest works.
Productions
In the original production in 1988, directed by Peter Wood, Felicity Kendal played Hapgood, Nigel Hawthorne played her friend and superior Blair and Roger Rees was their agent, the Soviet scientist Kerner. The production was a critical failure, and it was revised significantly in 1994 for the first New York production.
The play premiered in the US Off-Broadway at the Lincoln Center Mitzi E. Newhouse Theater on 11 November 1994 and closed on 26 March 1995. Directed by Jack O'Brien, the cast featured Josef Sommer (Blair), David Strathairn (Kerner) and Stockard Channing (Hapgood).
Jack O'Brien won the 1995 Lucille Lortel Award for Outstanding Director.
References
1988 plays
Plays by Tom Stoppard
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https://en.wikipedia.org/wiki/Hans%20Peter%20Luhn
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Hans Peter Luhn (July 1, 1896 – August 19, 1964) was a German researcher in the field of computer science and Library & Information Science for IBM, and creator of the Luhn algorithm, KWIC (Key Words In Context) indexing, and Selective dissemination of information ("SDI"). His inventions have found applications in diverse areas like computer science, the textile industry, linguistics, and information science. He was awarded over 80 patents.
Life
Luhn was born in Barmen, Germany (now part of Wuppertal) on July 1, 1896. After he completed secondary school, Luhn moved to Switzerland to learn the printing trade so he could join the family business. His career in printing was halted by his service as a communications officer in the German Army during World War I. After the war, Luhn entered the textile field, which eventually led him to the United States, where he invented a thread-counting gauge (the Lunometer) still on the market. From the late 1920s to the early 1940s, during which time he obtained patents for a broad range of inventions, Luhn worked in textiles and as an independent engineering consultant. He joined IBM as a senior research engineer in 1941, and soon became manager of the information retrieval research division.
His introduction to the field of documentation/information science came in 1947 when he was asked to work on a problem brought to IBM by James Perry and Malcolm Dyson that involved searching for chemical compounds recorded in coded form. He came up
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https://en.wikipedia.org/wiki/Cayley%E2%80%93Purser%20algorithm
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The Cayley–Purser algorithm was a public-key cryptography algorithm published in early 1999 by 16-year-old Irishwoman Sarah Flannery, based on an unpublished work by Michael Purser, founder of Baltimore Technologies, a Dublin data security company. Flannery named it for mathematician Arthur Cayley. It has since been found to be flawed as a public-key algorithm, but was the subject of considerable media attention.
History
During a work-experience placement with Baltimore Technologies, Flannery was shown an unpublished paper by Michael Purser which outlined a new public-key cryptographic scheme using non-commutative multiplication. She was asked to write an implementation of this scheme in Mathematica.
Before this placement, Flannery had attended the 1998 ESAT Young Scientist and Technology Exhibition with a project describing already existing cryptographic techniques from the Caesar cipher to RSA. This had won her the Intel Student Award which included the opportunity to compete in the 1998 Intel International Science and Engineering Fair in the United States. Feeling that she needed some original work to add to her exhibition project, Flannery asked Michael Purser for permission to include work based on his cryptographic scheme.
On advice from her mathematician father, Flannery decided to use matrices to implement Purser's scheme as matrix multiplication has the necessary property of being non-commutative. As the resulting algorithm would depend on multiplication it woul
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https://en.wikipedia.org/wiki/Upper%20topology
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In mathematics, the upper topology on a partially ordered set X is the coarsest topology in which the closure of a singleton is the order section for each If is a partial order, the upper topology is the least order consistent topology in which all open sets are up-sets. However, not all up-sets must necessarily be open sets. The lower topology induced by the preorder is defined similarly in terms of the down-sets. The preorder inducing the upper topology is its specialization preorder, but the specialization preorder of the lower topology is opposite to the inducing preorder.
The real upper topology is most naturally defined on the upper-extended real line by the system of open sets. Similarly, the real lower topology is naturally defined on the lower real line A real function on a topological space is upper semi-continuous if and only if it is lower-continuous, i.e. is continuous with respect to the lower topology on the lower-extended line Similarly, a function into the upper real line is lower semi-continuous if and only if it is upper-continuous, i.e. is continuous with respect to the upper topology on
See also
References
General topology
Order theory
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https://en.wikipedia.org/wiki/Dirk%20Reuyl
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Dirk Reuyl (1906 – 1972) was a Dutch American physicist and astronomer. He was the cousin of astronomer Peter van de Kamp.
Life
Like his cousin, Reuijl (later "Reuyl") was born in Kampen, Overijssel. He studied physics and mathematics at Utrecht University, where, in October 1931, he defended his PhD dissertation "Photographic measures of close double stars" with Albertus Antonie Nijland as advisor.
He came to the United States a few years before Van de Kamp. He joined the staff at McCormick Observatory in 1929 and continued to work there until 1944. He originally worked on the parallax of stars, first publishing a list of 50 measurements in 1929 with fellow staff member Alexander N. Vyssotsky.
In 1941 he measured angular diameter of Mars using photographic plates.
Claim of planets
In 1943 he claimed to have discovered (with Erik Holberg) a planetary companion of the star system 70 Ophiuchi and other stars. He claimed that this planetary object had 10 times the mass of the planet Jupiter and a 17-year orbital period. This caused quite a sensation at the time. A critical analysis by Wulff Heintz later discredited these claims.
Later life and death
In 1944 he left McCormick Observatory and became head of the Photographic Division at the Ballistic Research Laboratory of the U.S. Army Aberdeen Proving Ground in Aberdeen, Maryland. He wrote a 1949 article for Sky and Telescope on guided missiles. During the late 1940s and the 1950s he worked on optically tracking the launch an
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https://en.wikipedia.org/wiki/Technical%20High%20School%20of%20Campinas
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The Technical High School of Campinas (, COTUCA), maintained by the University of Campinas, in Campinas, São Paulo, Brazil, is a school that provides free of charge courses at secondary education level on Nursing, Computer Sciences, Mechanical, Electrical, Foods Technology, Environment, Plastics, Labor Security, Medical Equipment, Telecommunications, Quality and Productivity Management, Mechanical Projects Assisted by Computer and Metallic Materials.
Location
The building of COTUCA is a historical heritage of the city of Campinas, and was built in 1918 by Benedict Quirino, a project by architect Ramos de Azevedo. The State University of Campinas—UNICAMP—began its operation in this building in 1967, with the courses of Chemistry, Food Engineering and Medicine. In the same year the COTUCA began to work with the courses of Electrotechnics, Mechanics and Food.
The facilities have 6,500 square meters and, as a historical heritage are preserved and maintained in accordance with its original features.
The building also houses the Unisoft, junior company of the course of computing.
It is at address 177 Culto a Ciencia Street in a historic building.
Courses offered
Mode: A – Internal concomitance
Food
Code: 25
Shift: full day
Vacancies: 40
Duration: 3 years' probation
Stage: 720 hours
Electronics
Code: 26
Shift: full day
Vacancies: 40
Duration: 3 years' probation
Stage: 720 hours
Code: 35
Shift: Night
Vacancies: 40
Duration: 4 years to the stage
Stage: 720 hours
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https://en.wikipedia.org/wiki/Evaporative%20cooling%20%28atomic%20physics%29
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Evaporative cooling is an atomic physics technique to achieve high phase space densities which optical cooling techniques alone typically can not reach.
Atoms trapped in optical or magnetic traps can be evaporatively cooled via two primary mechanisms, usually specific to the type of trap in question: in magnetic traps, radiofrequency (RF) fields are used to selectively drive warm atoms from the trap by inducing transitions between trapping and non-trapping spin states; or, in optical traps, the depth of the trap itself is gradually decreased, allowing the most energetic atoms in the trap to escape over the edges of the optical barrier. In the case of a Maxwell-Boltzmann distribution for the velocities of the atoms in the trap, these atoms which escape/are driven out of the trap lie in the highest velocity tail of the distribution, meaning that their kinetic energy (and therefore temperature) is much higher than the average for the trap. The net result is that while the total trap population decreases, so does the mean energy of the remaining population. This decrease in the mean kinetic energy of the atom cloud translates into a progressive decrease in the trap temperature, cooling the trap.
The process is analogous to blowing on a cup of coffee to cool it: those molecules at the highest end of the energy distribution for the coffee form a vapor above the surface and are then removed from the system by blowing them away, decreasing the average energy, and therefore tempera
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https://en.wikipedia.org/wiki/Marian%20Danysz
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Marian Danysz (March 17, 1909 – February 9, 1983) was a Polish physicist, Professor of Physics at Warsaw University.
Son of Jan Kazimierz Danysz. In 1952, he co-discovered with Jerzy Pniewski a new kind of matter, an atomic nucleus, which alongside a proton and neutron contains a third particle: the lambda hyperon ().
Ten years later, they obtained a hypernucleus in excited state, and the following year a hypernucleus with two lambda hyperons.
20th-century Polish physicists
1909 births
1983 deaths
Fellows of the American Physical Society
French emigrants to Poland
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https://en.wikipedia.org/wiki/Stanis%C5%82aw%20Kostanecki
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Stanisław Kostanecki (born 16 April 1860 in Myszaków, now in Poland then Kingdom of Prussia – 15 November 1910 in Würzburg) was a Polish organic chemist, professor who pioneered in vegetable dye chemistry e.g. curcumin. Known for Kostanecki acylation name reactions.
In 1896, he developed the theory of dyes and studied the natural vegetable dyes. Among his many students were scientists Kazimierz Funk and Wiktor Lampe.
References
1860 births
1910 deaths
Polish organic chemists
People from the Kingdom of Prussia
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https://en.wikipedia.org/wiki/Preference%20relation
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The term preference relation is used to refer to orderings that describe human preferences for one thing over an other.
In mathematics, preferences may be modeled as a weak ordering or a semiorder, two different types of binary relation. One specific variation of weak ordering, a total preorder (= a connected, reflexive and transitive relation), is also sometimes called a preference relation.
In computer science, machine learning algorithms are used to infer preferences, and the binary representation of the output of a preference learning algorithm is called a preference relation, regardless of whether it fits the weak ordering or semiorder mathematical models.
Preference relations are also widely used in economics; see preference (economics).
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https://en.wikipedia.org/wiki/3-manifold
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In mathematics, a 3-manifold is a topological space that locally looks like a three-dimensional Euclidean space. A 3-manifold can be thought of as a possible shape of the universe. Just as a sphere looks like a plane to a small enough observer, all 3-manifolds look like our universe does to a small enough observer. This is made more precise in the definition below.
Introduction
Definition
A topological space is a 3-manifold if it is a second-countable Hausdorff space and if every point in has a neighbourhood that is homeomorphic to Euclidean 3-space.
Mathematical theory of 3-manifolds
The topological, piecewise-linear, and smooth categories are all equivalent in three dimensions, so little distinction is made in whether we are dealing with say, topological 3-manifolds, or smooth 3-manifolds.
Phenomena in three dimensions can be strikingly different from phenomena in other dimensions, and so there is a prevalence of very specialized techniques that do not generalize to dimensions greater than three. This special role has led to the discovery of close connections to a diversity of other fields, such as knot theory, geometric group theory, hyperbolic geometry, number theory, Teichmüller theory, topological quantum field theory, gauge theory, Floer homology, and partial differential equations. 3-manifold theory is considered a part of low-dimensional topology or geometric topology.
A key idea in the theory is to study a 3-manifold by considering special surfaces embedde
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https://en.wikipedia.org/wiki/Field%20of%20sets
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In mathematics, a field of sets is a mathematical structure consisting of a pair consisting of a set and a family of subsets of called an algebra over that contains the empty set as an element, and is closed under the operations of taking complements in finite unions, and finite intersections.
Fields of sets should not be confused with fields in ring theory nor with fields in physics. Similarly the term "algebra over " is used in the sense of a Boolean algebra and should not be confused with algebras over fields or rings in ring theory.
Fields of sets play an essential role in the representation theory of Boolean algebras. Every Boolean algebra can be represented as a field of sets.
Definitions
A field of sets is a pair consisting of a set and a family of subsets of called an algebra over that has the following properties:
:
as an element:
Assuming that (1) holds, this condition (2) is equivalent to:
Any/all of the following equivalent conditions hold:
:
:
:
:
In other words, forms a subalgebra of the power set Boolean algebra of (with the same identity element ).
Many authors refer to itself as a field of sets.
Elements of are called points while elements of are called complexes and are said to be the admissible sets of
A field of sets is called a σ-field of sets and the algebra is called a σ-algebra if the following additional condition (4) is satisfied:
Any/both of the following equivalent conditions hold:
:
for all
:
for all
Fi
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https://en.wikipedia.org/wiki/Meta
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Meta (from the Greek , meta, meaning "after" or "beyond") is a prefix meaning "more comprehensive" or "transcending".
In modern nomenclature, meta- can also serve as a prefix meaning self-referential, as a field of study or endeavor (metatheory: theory about a theory; metamathematics: mathematical theories about mathematics; meta-axiomatics or meta-axiomaticity: axioms about axiomatic systems; metahumor: joking about the ways humor is expressed; etc.).
Original Greek meaning
In Greek, the prefix meta- is generally less esoteric than in English; Greek meta- is equivalent to the Latin words post- or ad-. The use of the prefix in this sense occurs occasionally in scientific English terms derived from Greek. For example, the term Metatheria (the name for the clade of marsupial mammals) uses the prefix meta- in the sense that the Metatheria occur on the tree of life adjacent to the Theria (the placental mammals).
Epistemology
In epistemology, and often in common use, the prefix meta- is used to mean about (its own category). For example, metadata is data about data (who has produced them, when, what format the data are in and so on). In a database, metadata is also data about data stored in a data dictionary, describing information (data) about database tables such as the table name, table owner, details about columns, etc. – essentially describing the table. In psychology, metamemory refers to an individual's knowledge about whether or not they would remember something if th
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https://en.wikipedia.org/wiki/Dirac%20measure
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In mathematics, a Dirac measure assigns a size to a set based solely on whether it contains a fixed element x or not. It is one way of formalizing the idea of the Dirac delta function, an important tool in physics and other technical fields.
Definition
A Dirac measure is a measure on a set (with any -algebra of subsets of ) defined for a given and any (measurable) set by
where is the indicator function of .
The Dirac measure is a probability measure, and in terms of probability it represents the almost sure outcome in the sample space . We can also say that the measure is a single atom at ; however, treating the Dirac measure as an atomic measure is not correct when we consider the sequential definition of Dirac delta, as the limit of a delta sequence. The Dirac measures are the extreme points of the convex set of probability measures on .
The name is a back-formation from the Dirac delta function; considered as a Schwartz distribution, for example on the real line, measures can be taken to be a special kind of distribution. The identity
which, in the form
is often taken to be part of the definition of the "delta function", holds as a theorem of Lebesgue integration.
Properties of the Dirac measure
Let denote the Dirac measure centred on some fixed point in some measurable space .
is a probability measure, and hence a finite measure.
Suppose that is a topological space and that is at least as fine as the Borel -algebra on .
is a strictly positive measur
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https://en.wikipedia.org/wiki/D20%20Future
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d20 Future is an accessory for the d20 Modern role-playing game written by Christopher Perkins, Rodney Thompson, and JD Wiker. It facilitates the playing of campaigns in the far future, using elements such as cybernetics, mecha, mutations, robotics, space travel, starships, and xenobiology. d20 Future is one of the most extensive of science-fiction d20 games and has its own SRD, which is a source for many other sci-fi d20 games.
New rules
d20 Future introduced a number of new elements to d20 Modern, including:
New classes, occupations, feats, and skill applications
New equipment, include cybernetics and mecha
Rules for robot player characters
Rules for mutations
Rules for scientific engineering, spaceships, and constructs
Hazards and environments, including vacuum and radiation
Progress levels, describing global levels of technological development
Campaigns
The book presented a number of campaign models, which provided a framework for building a full campaign setting but did not include a full-scale setting. Campaign models introduced include:
Bughunters, an adventure game and bug hunt setting inspired by Aliens, Starship Troopers, and its predecessor in Amazing Engine.
Dimension X, an adventure game setting based on the concept of parallel universes, which are referred to as dimensions.
From the Dark Heart of Space, a Fifth Element style setting inspired by the eternal struggle between good and evil, with a touch of the Cthulhu Mythos.
Genetech, apparently an
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https://en.wikipedia.org/wiki/Crown%20group
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In phylogenetics, the crown group or crown assemblage is a collection of species composed of the living representatives of the collection, the most recent common ancestor of the collection, and all descendants of the most recent common ancestor. It is thus a way of defining a clade, a group consisting of a species and all its extant or extinct descendants. For example, Neornithes (birds) can be defined as a crown group, which includes the most recent common ancestor of all modern birds, and all of its extant or extinct descendants.
The concept was developed by Willi Hennig, the formulator of phylogenetic systematics, as a way of classifying living organisms relative to their extinct relatives in his "Die Stammesgeschichte der Insekten",
and the "crown" and "stem" group terminology was coined by R. P. S. Jefferies in 1979. Though formulated in the 1970s, the term was not commonly used until its reintroduction in 2000 by Graham Budd and Sören Jensen.
Contents of the crown group
It is not necessary for a species to have living descendants in order for it to be included in the crown group. Extinct side branches on the family tree that are descended from the most recent common ancestor of living members will still be part of a crown group. For example, if we consider the crown-birds (i.e. all extant birds and the rest of the family tree back to their most recent common ancestor), extinct side branches like the dodo or great auk are still descended from the most recent common anc
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https://en.wikipedia.org/wiki/Aleksander%20Jab%C5%82o%C5%84ski
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Professor Aleksander Jabłoński (born 26 February 1898 in Woskresenówka, in Imperial Russia, died 9 September 1980 in Skierniewice, Poland) was a Polish physicist and member of the Polish Academy of Sciences. His research was in molecular spectroscopy and photophysics.
Life and career
He was born on 26 February 1898 in Woskresenówka near Kharkiv in Imperial Russia. He attended Gymnasium high school in Kharkiv as well as a music school where he learned to play the violin under supervision of Konstanty Gorski. In 1916, he started to study physics at the University of Kharkiv.
During the World War I he served in the Polish I Corps in Russia. After the war he settled in Warsaw in 1918. In 1919-1920 he fought for Poland against aggression by Soviet Russia (and was consequently decorated with the Polish Cross of Valour).
Jabłoński initially studied the violin at Warsaw Conservatory, under the virtuoso Stanisław Barcewicz, but later switched to science.
He received a Ph.D. from the University of Warsaw in 1930, writing a thesis On the influence of the change of the wavelength of excitation light on the fluorescence spectra. He then went to Friedrich-Wilhelms-Universität in Berlin, Germany for two years (1930–31) as a fellow of the Rockefeller Foundation. He worked with Peter Pringsheim at the FWU and later with Otto Stern in Hamburg. In 1934 Jabłoński returned to Poland to receive habilitation from the University of Warsaw. His thesis was On the influence of intermolecular inte
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https://en.wikipedia.org/wiki/Sylwester%20Kaliski
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Sylwester Kaliski (19 December 1925 – 16 September 1978) was a Polish engineer, professor and military general. He was a member of the Polish Academy of Sciences (PAN).
Born in Toruń, Kaliski was a specialist in the field of applied physics. He developed the theory of continuous amplification of ultra and hyper-sounds in semiconductive crystals and obtained plasma temperature of tens of millions of kelvins using laser impulse. He died in Warsaw, Poland in car crash. It has been speculated that Kaliski was killed by the Soviet KGB, as he headed the Polish clandestine program of developing thermonuclear devices intended for military use. The program began on orders from the highest levels of Polish communists and was reportedly opposed by the Soviet Union.
Accolades
Order of Builders of People's Poland - 1978 (posthumously)
Order of the Banner of Labour 1st Class - 1968
Commander's Cross Polonia Restituta - 1973
Knight's Cross of the Order of Polonia Restituta - 1961
Gold Cross of Merit - 1957
People's Republic of Poland 30th Anniversary Medal - 1974
Gold Medal "Armed Forces in Service of the Fatherland" - 1970
Silver Medal "Armed Forces in Service to the Fatherland" - 1970
Bronze Medal "Armed Forces in Service to the Fatherland" - 1970
Gold Medal "For Meritorious Service to National Defence" - 1974
Silver Medal "For Meritorious Service to National Defence
Bronze Medal "For meritorious service to national defence"
Order of Friendship of Nations (Sov
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https://en.wikipedia.org/wiki/John%20Farey%20Jr.
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John Farey Jr. (20 March 1791 – 17 July 1851) was an English mechanical engineering, consulting engineer and patent agent, known for his pioneering contributions in the field of mechanical engineering.
As consulting engineer Farey worked for many well-known inventors of the later Industrial Revolution, and was a witness to a number of parliamentary enquiries, inquests and court cases, and on occasion acted as an arbitrator. He was polymathic in his interests and contributed text and drawings to a number of periodicals and encyclopaedias.
Farey is also remembered as the first English inventor of the ellipsograph, an instrument used by draughtsmen to inscribe ellipses.
Biography
Youth and education
Farey was the eldest son of John Farey Sr. (1766–1826), the geologist, and Sophia Hubert (1770–1830). He was the older brother of Joseph Farey (1796–1829), who also became a known mechanical engineer and draughtsman and member of the Institution of Civil Engineers in 1822. He remained in the shadow of his older brother and died young.
From 1791 to 1802 he grew up in Woburn, Bedfordshire, where his father was stationed as surveyor and land agent for Francis Russell, 5th Duke of Bedford. Back in London he might have received training at the school of William Nicholson, established in 1799 in London's Soho Square. He did later on work together with Nicholson on patent assignments. From 1804 to 1806 he studied the machinery and processes in manufacturing factories in and around Lon
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https://en.wikipedia.org/wiki/Murphy%20Aircraft
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Murphy Aircraft Manufacturing Limited is a Chinese maker of civil general aviation kits for amateur construction. The company was founded in 1985 by Darryl Murphy and is located in Chilliwack, British Columbia.
History
The company was started as the result of a hunting accident. Darryl Murphy was a mechanical engineering technologist who designed and built a rigid wing hang glider in 1978 as a school project at the Saskatchewan Institute of Applied Science and Technology in Saskatoon, Saskatchewan. In 1984 Murphy was in a non-aviation accident that left him hospitalized for four months. During his recovery time he decided to design a biplane to fit into the then-new Canadian ultralight category. The aircraft was a single-seat model and was intended as a one-off aircraft for his own use, with no production intentions. Murphy named it the Renegade.
After taking the Renegade to a number of fly-ins and other aviation events, Murphy was encouraged by the positive response it received and by the number of people who asked him to build one for them. In 1985 Murphy quit his job and started Murphy Aviation (later renamed Murphy Aircraft Manufacturing), with his brother Bryan and located the company in Chilliwack, British Columbia.
The original Renegade design was turned into a two-seater by relocating the fuel tank from the centre fuselage to the upper wing, installing a second seat and designating it the Renegade II. Initial sales were disappointing as only one kit was sold in the
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https://en.wikipedia.org/wiki/Bow%20shock
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In astrophysics, a bow shock occurs when the magnetosphere of an astrophysical object interacts with the nearby flowing ambient plasma such as the solar wind. For Earth and other magnetized planets, it is the boundary at which the speed of the stellar wind abruptly drops as a result of its approach to the magnetopause. For stars, this boundary is typically the edge of the astrosphere, where the stellar wind meets the interstellar medium.
Description
The defining criterion of a shock wave is that the bulk velocity of the plasma drops from "supersonic" to "subsonic", where the speed of sound cs is defined by
where is the ratio of specific heats, is the pressure, and is the density of the plasma.
A common complication in astrophysics is the presence of a magnetic field. For instance, the charged particles making up the solar wind follow spiral paths along magnetic field lines. The velocity of each particle as it gyrates around a field line can be treated similarly to a thermal velocity in an ordinary gas, and in an ordinary gas the mean thermal velocity is roughly the speed of sound. At the bow shock, the bulk forward velocity of the wind (which is the component of the velocity parallel to the field lines about which the particles gyrate) drops below the speed at which the particles are gyrating.
Around the Earth
The best-studied example of a bow shock is that occurring where the Sun's wind encounters Earth's magnetopause, although bow shocks occur around all planets, b
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https://en.wikipedia.org/wiki/Lie%E2%80%93Kolchin%20theorem
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In mathematics, the Lie–Kolchin theorem is a theorem in the representation theory of linear algebraic groups; Lie's theorem is the analog for linear Lie algebras.
It states that if G is a connected and solvable linear algebraic group defined over an algebraically closed field and
a representation on a nonzero finite-dimensional vector space V, then there is a one-dimensional linear subspace L of V such that
That is, ρ(G) has an invariant line L, on which G therefore acts through a one-dimensional representation. This is equivalent to the statement that V contains a nonzero vector v that is a common (simultaneous) eigenvector for all .
It follows directly that every irreducible finite-dimensional representation of a connected and solvable linear algebraic group G has dimension one. In fact, this is another way to state the Lie–Kolchin theorem.
The result for Lie algebras was proved by and for algebraic groups was proved by .
The Borel fixed point theorem generalizes the Lie–Kolchin theorem.
Triangularization
Sometimes the theorem is also referred to as the Lie–Kolchin triangularization theorem because by induction it implies that with respect to a suitable basis of V the image has a triangular shape; in other words, the image group is conjugate in GL(n,K) (where n = dim V) to a subgroup of the group T of upper triangular matrices, the standard Borel subgroup of GL(n,K): the image is simultaneously triangularizable.
The theorem applies in particular to a Borel s
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https://en.wikipedia.org/wiki/Horst%20Berger
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Horst Berger (1928-2019) was a structural engineer and designer known for his work with lightweight tensile architecture. After receiving a degree in Civil Engineering in 1954 from Stuttgart University in Stuttgart, Germany, he began working in 1955 at the Bridge and Special Structures Department of Wayss and Freitag in Frankfurt. In 1960, he joined Severud Associates in New York city and worked on projects such as the St. Louis Arch, Madison Square Garden, and Toronto City Hall.
After forming Geiger Berger Associates in 1968 with air supported roof inventor David Geiger, the firm gained international recognition for its incorporation of lightweight fabric structures into permanent architectural designs.
During his time at Geiger Berger Associates, Horst Berger had the challenge of engineering the roof designed by architect Fazlur Rahman Khan of Skidmore, Owings and Merrill for the Haj Terminal at the Jeddah Airport. This tensile fabric structure consists of 210 roof units contained in ten modules that are supported on steel pylons.
In 1990 Horst Berger was asked to create a tensile fabric roof for the Denver International Airport. Challenges of snow loading and attaching the rigid walls to the fabric roof made it one of Berger’s toughest projects. The unique design with the roofing structure gave the terminal a more spacious layout.
In 1990 he became a professor at the School of Architecture of the City College of New York.
While studying and working in New York, Berge
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https://en.wikipedia.org/wiki/Immunohistochemistry
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Immunohistochemistry (IHC) is the most common application of immunostaining. It involves the process of selectively identifying antigens (proteins) in cells of a tissue section by exploiting the principle of antibodies binding specifically to antigens in biological tissues. IHC takes its name from the roots "immuno", in reference to antibodies used in the procedure, and "histo", meaning tissue (compare to immunocytochemistry). Albert Coons conceptualized and first implemented the procedure in 1941.
Visualising an antibody-antigen interaction can be accomplished in a number of ways, mainly either of the following:
Chromogenic immunohistochemistry (CIH), wherein an antibody is conjugated to an enzyme, such as peroxidase (the combination being termed immunoperoxidase), that can catalyse a colour-producing reaction.
Immunofluorescence, where the antibody is tagged to a fluorophore, such as fluorescein or rhodamine.
Immunohistochemical staining is widely used in the diagnosis of abnormal cells such as those found in cancerous tumors. Specific molecular markers are characteristic of particular cellular events such as proliferation or cell death (apoptosis).
Immunohistochemistry is also widely used in basic research to understand the distribution and localization of biomarkers and differentially expressed proteins in different parts of a biological tissue.
Sample preparation
Preparation of the sample is critical to maintaining cell morphology, tissue architecture and the anti
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https://en.wikipedia.org/wiki/Derivative%20algebra
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In mathematics:
In abstract algebra and mathematical logic a derivative algebra is an algebraic structure that provides an abstraction of the derivative operator in topology and which provides algebraic semantics for the modal logic wK3.
In abstract algebra, the derivative algebra of a not-necessarily associative algebra A over a field F is the subalgebra of the algebra of linear endomorphisms of A consisting of the derivations.
In differential geometry a derivative algebra is a vector space with a product operation that has similar behaviour to the standard cross product of 3-vectors.
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https://en.wikipedia.org/wiki/Hung
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Hung may refer to:
People
Hung (surname), various Chinese surnames
Hùng king, a king of Vietnam
People with the given name Hung include:
Hung Huynh, Vietnamese-American chef, winner of the third season of the television show Top Chef
Hung Pham (born 1963), Vietnamese-Canadian former politician
Hung Cheng, professor of Applied Mathematics
Entertainment
Hung, a 1970 novel by Dean Koontz (published under the name Leonard Chris)
Film and television
Hung, a short film by Guinevere Turner
Hung (TV series), aired on HBO
Songs
"Hung", by Napalm Death
"Hung", by Wire from the album Mind Hive
Other
Hung language, a Viet-Muong language spoken in Laos
Hang (instrument), a musical instrument whose name is pronounced "hung"
Old Hungarian alphabet (ISO 15924 script code: Hung)
A term for possessing a large human penis size
See also
Hang (disambiguation)
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https://en.wikipedia.org/wiki/Monoclonality
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In biology, monoclonality refers to the state of a line of cells that have been derived from a single clonal origin. Thus, "monoclonal cells" can be said to form a single clone. The term monoclonal comes .
The process of replication can occur in vivo, or may be stimulated in vitro for laboratory manipulations. The use of the term typically implies that there is some method to distinguish between the cells of the original population from which the single ancestral cell is derived, such as a random genetic alteration, which is inherited by the progeny.
Common usages of this term include:
Monoclonal antibody: a single hybridoma cell, which by chance includes the appropriate V(D)J recombination to produce the desired antibody, is cloned to produce a large population of identical cells. In informal laboratory jargon, the monoclonal antibodies isolated from cell culture supernatants of these hybridoma clones (hybridoma lines) are simply called monoclonals.
Monoclonal neoplasm (tumor): A single aberrant cell which has undergone carcinogenesis reproduces itself into a cancerous mass.
Monoclonal plasma cell (also called plasma cell dyscrasia): A single aberrant plasma cell which has undergone carcinogenesis reproduces itself, which in some cases is cancerous.
References
Biology terminology
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https://en.wikipedia.org/wiki/Baldwin%20effect
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In evolutionary biology, the Baldwin effect, a phenotype-first theory of evolution, describes the effect of learned behaviour on evolution. James Mark Baldwin and others suggested during the eclipse of Darwinism in the late 19th century that an organism's ability to learn new behaviours (e.g. to acclimatise to a new stressor) will affect its reproductive success and will therefore have an effect on the genetic makeup of its species through natural selection. Though this process appears similar to Lamarckism, that view proposes that living things inherited their parents' acquired characteristics. The Baldwin effect has been independently proposed several times, and today it is generally recognized as part of the modern synthesis.
"A New Factor in Evolution"
The effect, then unnamed, was put forward in 1896 in a paper "A New Factor in Evolution" by the American psychologist James Mark Baldwin, with a second paper in 1897. The paper proposed a mechanism for specific selection for general learning ability. As the historian of science Robert Richards explains:
Selected offspring would tend to have an increased capacity for learning new skills rather than being confined to genetically coded, relatively fixed abilities. In effect, it places emphasis on the fact that the sustained behaviour of a species or group can shape the evolution of that species. The "Baldwin effect" is better understood in evolutionary developmental biology literature as a scenario in which a character or t
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https://en.wikipedia.org/wiki/Andy%20Hopper
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Sir Andrew Hopper (born 1953) is a British-Polish computer technologist and entrepreneur. He is treasurer and vice-president of the Royal Society, Professor of Computer Technology, former Head of the University of Cambridge Department of Computer Science and Technology, an Honorary Fellow of Trinity Hall, Cambridge and Corpus Christi College, Cambridge.
Education
Hopper was educated at Quintin Kynaston School in London after which he went to study for a Bachelor of Science degree at Swansea University before going to the University of Cambridge Computer Laboratory and Trinity Hall, Cambridge in 1974 for postgraduate work. Hopper was awarded his PhD in 1978 for research into local area computer communications networks supervised by David Wheeler.
Research and career
Hopper's PhD, completed in 1977 was in the field of communications networks, and he worked with Maurice Wilkes on the creation of the Cambridge Ring and its successors.
Hopper's research interests include computer networks, multimedia systems, Virtual Network Computing and sentient computing. His most cited paper describes the indoor location system called the Active Badge. He has contributed to a discussion of the privacy challenges relating to surveillance.
After more than 20 years at Cambridge University Computer Laboratory, Hopper was elected Chair of Communications Engineering at Cambridge University Engineering Department in 1997. He returned to the Computer Laboratory as Professor of Computer Technolog
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https://en.wikipedia.org/wiki/Salt%20%28disambiguation%29
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Salt is a dietary mineral, used for flavoring and preservation.
Salt or salts may also refer to:
Chemistry
Salt (chemistry), an ionic compound
Epsom salt, magnesium sulfate
Glauber's salt, sodium sulfate
Sodium chloride, the main ingredient in edible salt (table salt)
Halite (rock salt)
Road salt, calcium chloride or sodium chloride used to de-ice roads
Sea salt, a mixture of salts and minerals, obtained by evaporation of seawater
Places
Salt, Girona, Spain
Salt, Jordan
Salt Municipality, a municipality in and around Salt, Jordan
Salt Rural LLG, Papua New Guinea
Salt, Staffordshire, England
Salt, Uttarakhand, a town in Uttarakhand, India
Salt (Uttarakhand Assembly constituency), the state Assembly constituency centered around the town
Salt River (disambiguation)
People with the name
Salt (rapper) (born Cheryl James, 1966), a hip-hop artist and member of Salt-N-Pepa
Abu al-Salt, Andalusian-Arab polymath
Barbara Salt (1904–1975), a British diplomat
Bernard Salt, an Australian financial writer
Don Reitz, an American ceramic artist nicknamed "Mr. Salt"
Edward Salt (1881–1970), a British politician
George Salt (1903–2003), an English entomologist
Henry Salt (Egyptologist) (1780–1827), an English artist, traveler, and diplomat
Henry Stephens Salt (1851–1939), an English writer and campaigner for social reforms
Jack Salt (born 1996), New Zealand basketball player
Jennifer Salt (born 1944), an American actress and screenwriter
John Salt (born 1937), an
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https://en.wikipedia.org/wiki/WCM
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WCM may stand for:
Warner Chappell Music, an American music publishing company and a subsidiary of the Warner Music Group
Wave characteristic method, a model used in fluid dynamics
WCM, a radio station operated by the University of Texas at Austin under that call sign from 1922 to 1925; now licensed to Houston as KTRH
WCMH-TV, an NBC-affiliated television station in Columbus, Ohio, United States
Web content management
West Coast Magazine, a Scottish literary publication
Wisden Cricket Monthly, a UK-based cricket magazine
Woman Candidate Master, a World Federation chess title
World Championship Motorsports, a Grand Prix motorcycle team
WCM (Wide DC electric mixed), a classification of Indian locomotives
See also
WC (disambiguation)
WCMS (disambiguation)
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https://en.wikipedia.org/wiki/Danny%20Dunn
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Danny Dunn is a fictional character, the protagonist of a series of American juvenile science fiction/adventure books written by Raymond Abrashkin and Jay Williams beginning in 1956.
Background
The stories are set in the fictional American town of Midston. The plots feature characters who are interested in science and mathematics.
Abrashkin died in 1960, after publication of the fifth book. Williams, however, insisted on Abrashkin being given co-author credit on the subsequent ten books as well, since he had been instrumental in constructing the series. Ezra Jack Keats illustrated the first four novels in the series.
Although the exact location of Midston is not given, the authors wrote that a famed American of colonial times visited the town (when it was known as Middestown), implying Midston is somewhere in the original 13 states. In the book Danny Dunn and the Heat Ray, reference is made to US Route 1 and US Route 2 being located near Midston, and those roads meet only at Houlton, Maine.
Main character
Dunn is a boy, a fifth-grader when the series starts, although the school year ends at the end of the first book. He is looking forward to a career in science. According to book reviewer Andrew Frederick, Dunn is precocious and headstrong—a redhead whose adventures mainly include getting into and out of trouble.
Other characters
Professor Euclid Bullfinch, a researcher at [fictional] Midston University. The Professor is also a musician who plays the bass viol (also
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https://en.wikipedia.org/wiki/Burgers%27%20equation
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Burgers' equation or Bateman–Burgers equation is a fundamental partial differential equation and convection–diffusion equation occurring in various areas of applied mathematics, such as fluid mechanics, nonlinear acoustics, gas dynamics, and traffic flow. The equation was first introduced by Harry Bateman in 1915 and later studied by Johannes Martinus Burgers in 1948.
For a given field and diffusion coefficient (or kinematic viscosity, as in the original fluid mechanical context) , the general form of Burgers' equation (also known as viscous Burgers' equation) in one space dimension is the dissipative system:
When the diffusion term is absent (i.e. ), Burgers' equation becomes the inviscid Burgers' equation:
which is a prototype for conservation equations that can develop discontinuities (shock waves). The previous equation is the advective form of the Burgers' equation. The conservative form is found to be more useful in numerical integration
Terms
There are 4 parameters in Burgers' equation: and . In a system consisting of a moving viscous fluid with one spatial () and one temporal () dimension, e.g. a thin ideal pipe with fluid running through it, Burgers' equation describes the speed of the fluid at each location along the pipe as time progresses. The terms of the equation represent the following quantities:
: spatial coordinate
: temporal coordinate
: speed of fluid at the indicated spatial and temporal coordinates
: viscosity of fluid
The viscosity is a con
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https://en.wikipedia.org/wiki/Donald%20Kingsbury
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Donald MacDonald Kingsbury (born 12 February 1929, in San Francisco) is an American–Canadian science fiction author. Kingsbury taught mathematics at McGill University, Montreal, from 1956 until his retirement in 1986.
Bibliography
Books
Courtship Rite. New York : Simon and Schuster, July 1982. . (Nominated for Hugo for Best Novel in 1983) (Compton Crook Award winner) (Prometheus Award Hall of Fame 2016 winner) Published in UK as Geta.
The Moon Goddess and the Son. New York : Baen Books, December 1986. . (Short version nominated for Hugo Award for Best Novella in 1980)
Psychohistorical Crisis. New York : Tor Books, December 2001. . (Winner, 2002 Prometheus Award)
The Finger Pointing Solward has been awaited ever since the publication of Courtship Rite. Kingsbury has never finished the story, noting as far back as September 1982 that he was still "polishing" it (see interview with Robert J. Sawyer) and as recently as his self-supplied Readercon biography in July 2006. Artist Donato Giancola placed a copy of the intended cover on his gallery page: this cover was used in 2016 for the Bradley P. Beaulieu collection In the Stars I'll Find You. In 1994, an excerpt was published as "The Cauldron".
Short fiction
"The Ghost Town", Astounding Science Fiction, June 1952.
"Shipwright", Analog, April 1978.
"To Bring in the Steel", Analog, July 1978.
"The Moon Goddess and the Son", Analog, December 1979.
"The Survivor", Man-Kzin Wars IV, September 1991.
"The Heroic Myth of Li
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https://en.wikipedia.org/wiki/Jean%20Bourgain
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Jean Louis, baron Bourgain (; – ) was a Belgian mathematician. He was awarded the Fields Medal in 1994 in recognition of his work on several core topics of mathematical analysis such as the geometry of Banach spaces, harmonic analysis, ergodic theory and nonlinear partial differential equations from mathematical physics.
Biography
Bourgain received his PhD from the Vrije Universiteit Brussel in 1977. He was a faculty member at the University of Illinois, Urbana-Champaign and, from 1985 until 1995, professor at Institut des Hautes Études Scientifiques at Bures-sur-Yvette in France, at the Institute for Advanced Study in Princeton, New Jersey from 1994 until 2018. He was an editor for the Annals of Mathematics. From 2012 to 2014, he was a visiting scholar at UC Berkeley.
His research work included several areas of mathematical analysis such as the geometry of Banach spaces, harmonic analysis, analytic number theory, combinatorics, ergodic theory, partial differential equations and spectral theory, and later also group theory. In 2000, Bourgain connected the Kakeya problem to arithmetic combinatorics. As a researcher, he was the author or coauthor of more than 500 articles.
Bourgain was diagnosed with pancreatic cancer in late 2014. He died of it on 22 December 2018 at a hospital in Bonheiden, Belgium.
Awards and recognition
Bourgain received several awards during his career, the most notable being the Fields Medal in 1994.
In 2009 Bourgain was elected a foreign member
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https://en.wikipedia.org/wiki/Lw%C3%B3w%20School%20of%20Mathematics
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The Lwów school of mathematics () was a group of Polish mathematicians who worked in the interwar period in Lwów, Poland (since 1945 Lviv, Ukraine). The mathematicians often met at the famous Scottish Café to discuss mathematical problems, and published in the journal Studia Mathematica, founded in 1929. The school was renowned for its productivity and its extensive contributions to subjects such as point-set topology, set theory and functional analysis. The biographies and contributions of these mathematicians were documented in 1980 by their contemporary, Kazimierz Kuratowski in his book A Half Century of Polish Mathematics: Remembrances and Reflections.
Members
Notable members of the Lwów school of mathematics included:
Stefan Banach
Feliks Barański
Władysław Orlicz
Stanisław Saks
Hugo Steinhaus
Stanisław Mazur
Stanisław Ulam
Józef Schreier
Juliusz Schauder
Mark Kac
Antoni Łomnicki
Stefan Kaczmarz
Herman Auerbach
Włodzimierz Stożek
Stanisław Ruziewicz
Eustachy Żyliński
The end of the school
Many of the mathematicians, especially those of Jewish background, fled this southeastern part of Poland in 1941 when it became clear that it would be invaded by Germany. Few of the mathematicians survived World War II, but after the war a group including some of the original community carried on their work in western Poland's Wrocław, the successor city to prewar Lwów; see Polish population transfers (1944–1946). A number of the prewar mathematicians, prominent among
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https://en.wikipedia.org/wiki/Martin%20J.%20Taylor
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Sir Martin John Taylor, FRS (born 18 February 1952) is a British mathematician and academic. He was Professor of Pure Mathematics at the School of Mathematics, University of Manchester and, prior to its formation and merger, UMIST where he was appointed to a chair after moving from Trinity College, Cambridge in 1986. He was elected Warden of Merton College, Oxford on 5 November 2009, took office on 2 October 2010 and retired in September 2018.
Early life and education
Taylor was born in Leicester in 1952 and educated at Wyggeston Grammar School. He gained a first class degree from Pembroke College, Oxford in 1973, and a Ph.D. from King's College London with a thesis entitled Galois module structure of the ring of integers of l-extensions in 1976 under the supervision of Albrecht Fröhlich.
Research
His early research concerned various properties and structures of algebraic numbers. In 1981 he proved the Fröhlich conjecture relating the symmetries of algebraic integers to the behaviour of certain analytic functions called Artin L-functions. In recent years his research has led him to study various aspects of arithmetic geometry: in particular, he and his collaborators have demonstrated how geometric properties of zeros of integral polynomials in many variables can be determined by the behaviour of associated L-functions.
Awards
Taylor was awarded the London Mathematical Society Whitehead Prize in 1982 and shared the Adams Prize in 1983. He was elected a Fellow of the R
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https://en.wikipedia.org/wiki/Rudolf%20Peierls
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Sir Rudolf Ernst Peierls, (; ; 5 June 1907 – 19 September 1995) was a German-born British physicist who played a major role in Tube Alloys, Britain's nuclear weapon programme, as well as the subsequent Manhattan Project, the combined Allied nuclear bomb programme. His 1996 obituary in Physics Today described him as "a major player in the drama of the eruption of nuclear physics into world affairs".
Peierls studied physics at the University of Berlin, at the University of Munich under Arnold Sommerfeld, the University of Leipzig under Werner Heisenberg, and ETH Zurich under Wolfgang Pauli. After receiving his DPhil from Leipzig in 1929, he became an assistant to Pauli in Zurich. In 1932, he was awarded a Rockefeller Fellowship, which he used to study in Rome under Enrico Fermi, and then at the Cavendish Laboratory at the University of Cambridge under Ralph H. Fowler. Because of his Jewish background, he elected to not return home after Adolf Hitler's rise to power in 1933, but to remain in Britain, where he worked with Hans Bethe at the Victoria University of Manchester, then at the Mond Laboratory at Cambridge. In 1937, Mark Oliphant, the newly appointed Australian professor of physics at the University of Birmingham recruited him for a new chair there in applied mathematics.
In March 1940, Peierls co-authored the Frisch–Peierls memorandum with Otto Robert Frisch. This short paper was the first to set out that one could construct an atomic bomb from a small amount of fissi
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https://en.wikipedia.org/wiki/Spark%20chamber
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A spark chamber is a particle detector: a device used in particle physics for detecting electrically charged particles. They were most widely used as research tools from the 1930s to the 1960s and have since been superseded by other technologies such as drift chambers and silicon detectors. Today, working spark chambers are mostly found in science museums and educational organisations, where they are used to demonstrate aspects of particle physics and astrophysics.
Spark chambers consist of a stack of metal plates placed in a sealed box filled with a gas such as helium, neon or a mixture of the two. When a charged particle from a cosmic ray travels through the box, it ionises the gas between the plates. Ordinarily this ionisation would remain invisible. However, if a high enough voltage can be applied between each adjacent pair of plates before that ionisation disappears, then sparks can be made to form along the trajectory taken by the ray, and the cosmic ray in effect becomes visible as a line of sparks. In order to control when this voltage is applied, a separate detector (often containing a pair of scintillators placed above and below the box) is needed. When this trigger senses that a cosmic ray has just passed, it fires a fast switch to connect the high voltage to the plates. The high voltage cannot be connected to the plates permanently, as this would lead to arc formation and continuous discharging.
As research devices, spark chamber detectors have lower resolution
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https://en.wikipedia.org/wiki/Bohr%E2%80%93Einstein%20debates
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The Bohr–Einstein debates were a series of public disputes about quantum mechanics between Albert Einstein and Niels Bohr. Their debates are remembered because of their importance to the philosophy of science, insofar as the disagreements—and the outcome of Bohr's version of quantum mechanics becoming the prevalent view—form the root of the modern understanding of physics. Most of Bohr's version of the events held in Solvay in 1927 and other places was first written by Bohr decades later in an article titled, "Discussions with Einstein
on Epistemological Problems in Atomic Physics". Based on the article, the philosophical issue of the debate was whether Bohr's Copenhagen Interpretation of quantum mechanics, which centered on his belief of complementarity, was valid in explaining nature. Despite their differences of opinion and the succeeding discoveries that helped solidify quantum mechanics, Bohr and Einstein maintained a mutual admiration that was to last the rest of their lives.
Although Bohr and Einstein disagreed, they were great friends all their lives and enjoyed using each other as a foil.
Pre-revolutionary debates
Einstein was the first physicist to say that Planck's discovery of the quantum (h) would require a rewriting of the laws of physics. To support his point, in 1905 he proposed that light sometimes acts as a particle which he called a light quantum (see photon and wave–particle duality). Bohr was one of the most vocal opponents of the photon idea and did no
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https://en.wikipedia.org/wiki/Killing%20vector%20field
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In mathematics, a Killing vector field (often called a Killing field), named after Wilhelm Killing, is a vector field on a Riemannian manifold (or pseudo-Riemannian manifold) that preserves the metric. Killing fields are the infinitesimal generators of isometries; that is, flows generated by Killing fields are continuous isometries of the manifold. More simply, the flow generates a symmetry, in the sense that moving each point of an object the same distance in the direction of the Killing vector will not distort distances on the object.
Definition
Specifically, a vector field X is a Killing field if the Lie derivative with respect to X of the metric g vanishes:
In terms of the Levi-Civita connection, this is
for all vectors Y and Z. In local coordinates, this amounts to the Killing equation
This condition is expressed in covariant form. Therefore, it is sufficient to establish it in a preferred coordinate system in order to have it hold in all coordinate systems.
Examples
Killing field on the circle
The vector field on a circle that points counterclockwise and has the same length at each point is a Killing vector field, since moving each point on the circle along this vector field simply rotates the circle.
Killing fields on the hyperbolic plane
A toy example for a Killing vector field is on the upper half-plane equipped with the Poincaré metric . The pair is typically called the hyperbolic plane and has Killing vector field (using standard coordinates). This s
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https://en.wikipedia.org/wiki/Patrick%20Henry%20College
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Patrick Henry College (PHC) is a private liberal arts non-denominational conservative Protestant Christian college located in Purcellville, Virginia. Its departments teach classical liberal arts, government, strategic intelligence in national security, economics and business analytics, history, journalism, environmental science and stewardship, and literature. The university has full accreditation from the Commission on Colleges of the Southern Association of Colleges and Schools (SACS-COC) as of 2022. Patrick Henry College continues to be accredited by the Transnational Association of Christian Colleges and Schools (TRACS), which is also recognized as an institutional accreditor by the United States Department of Education. Its graduation rate is 67%.
History
Patrick Henry College was incorporated in 1998 by Michael Farris, who is also the founder and chairman of the board of the Home School Legal Defense Association, with which PHC is still closely connected. It officially opened September 20, 2000, with a class of 92 students. The college eschews federal financial aid and is therefore relieved from United States Department of Education requirements on demographic makeup and other quotas. The school does not ask about race or ethnicity on applications.
PHC receives all of its funding from tuition fees and donations. The college states that it does not accept any money from sources that seek to supersede the authority of its Board of Trustees or conflict with its foundatio
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https://en.wikipedia.org/wiki/Reynolds%20decomposition
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In fluid dynamics and turbulence theory, Reynolds decomposition is a mathematical technique used to separate the expectation value of a quantity from its fluctuations.
Decomposition
For example, for a quantity the decomposition would be
where denotes the expectation value of , (often called the steady component/time, spatial or ensemble average), and , are the deviations from the expectation value (or fluctuations). The fluctuations are defined as the expectation value subtracted from quantity such that their time average equals zero.
The expected value, , is often found from an ensemble average which is an average taken over multiple experiments under identical conditions. The expected value is also sometime denoted , but it is also seen often with the over-bar notation.
Direct numerical simulation, or resolution of the Navier–Stokes equations completely in , is only possible on extremely fine computational grids and small time steps even when Reynolds numbers are low, and becomes prohibitively computationally expensive at high Reynolds' numbers. Due to computational constraints, simplifications of the Navier-Stokes equations are useful to parameterize turbulence that are smaller than the computational grid, allowing larger computational domains.
Reynolds decomposition allows the simplification of the Navier–Stokes equations by substituting in the sum of the steady component and perturbations to the velocity profile and taking the mean value. The resulting equation
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https://en.wikipedia.org/wiki/Edgar%20de%20Wahl
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Edgar Alexei Robert von Wahl (Interlingue: ; 23 August 1867 – 9 March 1948) was a Baltic German mathematics and physics teacher who lived in Tallinn, Estonia. He is best known as the creator of Interlingue, an international auxiliary language that was known as Occidental throughout his life.
A Baltic German, De Wahl was born, raised and lived most of his life in the Russian Empire. Born in the territory of today's Ukraine, he spent his childhood in Tallinn and Saint Petersburg. He studied at the University of Saint Petersburg and at the Saint Petersburg Academy of Arts. During and after his studies he served in the Imperial Russian Navy. After leaving the navy in 1894 he lived permanently in Tallinn and worked there as a teacher. When most Baltic Germans left Estonia in 1939–1941, he decided to stay. He was arrested during the German occupation in 1943 and was placed in a psychiatric clinic because of alleged dementia. He stayed there until his death in 1948.
De Wahl was engaged with interlinguistics from an early age. He was first introduced to Volapük by his father's colleague Waldemar Rosenberger and even started to compose a lexicon of marine terminology for the language, before turning to Esperanto in 1888. After the failure of Reformed Esperanto in 1894, of which de Wahl had been a proponent, de Wahl started work to find an ideal form of an international language. In 1922 published a "key" to a new language, Occidental, and the first edition of the periodical Kosmo
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https://en.wikipedia.org/wiki/Marek%20Kami%C5%84ski
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Marek Kamiński (born 24 March 1964 in Gdańsk) is a Polish innovator, philosopher and an explorer. He is claimed to have reached both the North and the South Pole in one year without outside assistance (the North Pole on 23 May 1995; the South Pole on 27 December 1995).
Biography
Kaminski obtained his Philosophy and Physics degrees at the University of Warsaw and completed the advanced management graduate program at the IESE Business School in Barcelona. He also studied Philosophy in Hamburg.
He led the first-ever expedition to the North Pole and the South Pole with a person with a disability (Jan Mela, who was 15 at the time). He has also crossed the Gibson Desert in Australia – a journey of in 46 days.
During his "Third Pole" expedition along St. James’ trail, he travelled in 140 days from the tomb of Immanuel Kant in Kaliningrad, Russia, to the grave of Saint James in Santiago de Compostela, Spain.
He has travelled by electric car from Poland to Japan through Siberia and the Gobi Desert. He was the first person to drive on the Trans-Siberian Highway in an emission-free vehicle. Kamiński is the founder of the ‘Power 4Change’ motivational method and the founder of the Marek Kamiński Foundation. The Marek Kamiński Institute and Invena.
Lectures
Kamiński has applied his experience in motivation to achieve seemingly impossible goals, as well as work-related to robots and artificial intelligence to give lectures at prestigious universities and conferences around the wor
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https://en.wikipedia.org/wiki/Change%20of%20base
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In mathematics, change of base can mean any of several things:
Changing numeral bases, such as converting from base 2 (binary) to base 10 (decimal). This is known as base conversion.
The logarithmic change-of-base formula, one of the logarithmic identities used frequently in algebra and calculus.
The method for changing between polynomial and normal bases, and similar transformations, for purposes of coding theory and cryptography.
Construction of the fiber product of schemes, in algebraic geometry.
See also
Change of basis
Base change (disambiguation)
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https://en.wikipedia.org/wiki/Siding%20Spring%20Observatory
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Siding Spring Observatory near Coonabarabran, New South Wales, Australia, part of the Research School of Astronomy & Astrophysics (RSAA) at the Australian National University (ANU), incorporates the Anglo-Australian Telescope along with a collection of other telescopes owned by the Australian National University, the University of New South Wales, and other institutions. The observatory is situated above sea level in the Warrumbungle National Park on Mount Woorat, also known as Siding Spring Mountain. Siding Spring Observatory is owned by the Australian National University (ANU) and is part of the Mount Stromlo and Siding Spring Observatories research school.
More than 100 million worth of research equipment is located at the observatory. There are over 60 telescopes on site, though not all are operational.
History
The original Mount Stromlo Observatory was set up by the Commonwealth Government in 1924. After duty supplying optical components to the military in World War II, the emphasis on astronomical research changed in the late 1940s from solar to stellar research. Between 1953 and 1974, the reflecting telescope at Mount Stromlo was the largest optical telescope in Australia.
Already in the 1950s, the artificial lights of Canberra, ACT, had brightened the sky at Mount Stromlo to such an extent that many faint astronomical objects had been overwhelmed by light pollution. The search for a new site was initiated by Bart Bok. After a site survey was undertaken the num
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https://en.wikipedia.org/wiki/Michael%20Kaplan
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Michael Kaplan may refer to:
Michael Kaplan (biologist) (born 1952), American biology researcher, medical professor and clinical physician
Michael Kaplan (costume designer), American movie costume designer
Myq Kaplan (born 1978), American stand-up comedian
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https://en.wikipedia.org/wiki/X0
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X0 may refer to:
Grammar
X0, denoting a sentence component
Zero-level projection, in X-bar theory
Head (linguistics), or nucleus
Science, technology and mathematics
SpaceShipOne flight 15P, a 2004 private spaceflight
X/0, division by zero
Turner syndrome, a disorder in which all or part of an X chromosome is absent
X0 sex-determination system, as found in some insects
Vehicles
X0, a smaller rigged version of an X1 (dinghy)
X0, running number for N700 Series Shinkansen prototype from 2014 to 2021
See also
XO (disambiguation)
X00, a popular DOS-based FOSSIL driver which was commonly used in the mid 1980s to the late 1990s
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https://en.wikipedia.org/wiki/Simplicial%20set
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In mathematics, a simplicial set is an object composed of simplices in a specific way. Simplicial sets are higher-dimensional generalizations of directed graphs, partially ordered sets and categories. Formally, a simplicial set may be defined as a contravariant functor from the simplex category to the category of sets. Simplicial sets were introduced in 1950 by Samuel Eilenberg and Joseph A. Zilber.
Every simplicial set gives rise to a "nice" topological space, known as its geometric realization. This realization consists of geometric simplices, glued together according to the rules of the simplicial set. Indeed, one may view a simplicial set as a purely combinatorial construction designed to capture the essence of a "well-behaved" topological space for the purposes of homotopy theory. Specifically, the category of simplicial sets carries a natural model structure, and the corresponding homotopy category is equivalent to the familiar homotopy category of topological spaces.
Simplicial sets are used to define quasi-categories, a basic notion of higher category theory. A construction analogous to that of simplicial sets can be carried out in any category, not just in the category of sets, yielding the notion of simplicial objects.
Motivation
A simplicial set is a categorical (that is, purely algebraic) model capturing those topological spaces that can be built up (or faithfully represented up to homotopy) from simplices and their incidence relations. This is similar to the
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https://en.wikipedia.org/wiki/Marian%20Smoluchowski
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Marian Smoluchowski (; 28 May 1872 – 5 September 1917) was a Polish physicist who worked in the territories of the Austro-Hungarian Empire. He was a pioneer of statistical physics, and an avid mountaineer.
Life
Born into an upper-class family in Vorder-Brühl, near Vienna, Smoluchowski studied physics at the University of Vienna. His teachers included Franz S. Exner and Josef Stefan. Ludwig Boltzmann held a position at Munich University during Smoluchowski's studies in Vienna, and Boltzmann returned to Vienna in 1894 when Smoluchowski was serving in the Austrian army. They apparently had no direct contact, although Smoluchowski's work follows in the tradition of Boltzmann's ideas.
After several years at other universities (Paris, Glasgow, Berlin), in 1899 Smoluchowski moved to Lwów (present-day Lviv), where he took a position at the University of Lwów. He was president of the Polish Copernicus Society of Naturalists, 1906–7.
In 1913 Smoluchowski moved to Kraków to take over a chair in the Experimental Physics Department, succeeding August Witkowski, who had long envisioned Smoluchowski as his successor. When World War I began the following year, the work conditions became unusually difficult, as the spacious and modern Physics Department building, built by Witkowski a short time before, was turned into a military hospital. The possibility of working in that building had been one of the reasons Smoluchowski had decided to move to Kraków. Smoluchowski was now forced to w
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https://en.wikipedia.org/wiki/Wojciech%20%C5%9Awi%C4%99tos%C5%82awski
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Wojciech Alojzy Świętosławski (1881 – 1968) was a Polish physical chemist, who is considered the "father of modern thermochemistry". He developed a static method of cryometric measurement and a new method of testing coal. Świętosławski was vice-chairman of the International Union of Pure and Applied Chemistry (IUPAC) and created the foundations for a new branch of physical chemistry: polyazeotropy. In 1933 he became a member of the Temporary Scientific and Advisory Committee
Early Years
Świętosławski was born on 21 June 1881 in the village of Kiryjowka, Podolia Governorate, Russian Empire. He spent his early years in Kiev, where he graduated from high school (1899). In 1906, he graduated with an engineering degree at Chemistry Department of Kiev Technical University. His first research paper, "Thermochemical Analysis of Organic Compounds" was published in 1908, in "Polish Yearly Magazine ("Rocznik Polski"). In appreciation of his work, Świętosławski was awarded the Mendeleyev Award by Russian Scientific Association. In the 1910s, Świętosławski went to Moscow, where he took a job at Chemical Laboratory of Moscow University. In 1917 he completed his thesis, writing about oxymes.
In the mid-, and late 1910, Świętosławski remained in Moscow, working, among others, on Aromatic hydrocarbon, Nitric acid, Nitro compound, Amine, and burning in bomb calorimeters.
Interwar Poland
In 1918 Świętosławski returned to Poland, leaving his laboratory in Moscow and urging other highly qual
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https://en.wikipedia.org/wiki/Edward%20Marczewski
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Edward Marczewski (15 November 1907 – 17 October 1976) was a Polish mathematician. He was born Szpilrajn but changed his name while hiding from Nazi persecution.
Marczewski was a member of the Warsaw School of Mathematics. His life and work after the Second World War were connected with Wrocław, where he was among the creators of the Polish scientific centre.
Marczewski's main fields of interest were measure theory, descriptive set theory, general topology, probability theory and universal algebra. He also published papers on real and complex analysis, applied mathematics and mathematical logic.
Marczewski proved that the topological dimension, for arbitrary metrisable separable space X, coincides with the Hausdorff dimension under one of the metrics in X which induce the given topology of X (while otherwise the Hausdorff dimension is always greater or equal to the topological dimension). This is a fundamental theorem of fractal theory. (Certain contributions to this development were also made by Samuel Eilenberg, see: Witold Hurewicz and Henry Wallman, Dimension Theory, 1941, Chapter VII.)
References
External links
1907 births
1976 deaths
20th-century Polish Jews
Warsaw School of Mathematics
People from Warsaw Governorate
University of Warsaw alumni
Academic staff of the University of Wrocław
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https://en.wikipedia.org/wiki/Canonical%20basis
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In mathematics, a canonical basis is a basis of an algebraic structure that is canonical in a sense that depends on the precise context:
In a coordinate space, and more generally in a free module, it refers to the standard basis defined by the Kronecker delta.
In a polynomial ring, it refers to its standard basis given by the monomials, .
For finite extension fields, it means the polynomial basis.
In linear algebra, it refers to a set of n linearly independent generalized eigenvectors of an n×n matrix , if the set is composed entirely of Jordan chains.
In representation theory, it refers to the basis of the quantum groups introduced by Lusztig.
Representation theory
The canonical basis for the irreducible representations of a quantized enveloping algebra of
type and also for the plus part of that algebra was introduced by Lusztig by
two methods: an algebraic one (using a braid group action and PBW bases) and a topological one
(using intersection cohomology). Specializing the parameter to yields a canonical basis for the irreducible representations of the corresponding simple Lie algebra, which was
not known earlier. Specializing the parameter to yields something like a shadow of a basis. This shadow (but not the basis itself) for the case of irreducible representations
was considered independently by Kashiwara; it is sometimes called the crystal basis.
The definition of the canonical basis was extended to the Kac-Moody setting by Kashiwara (by an algebraic metho
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https://en.wikipedia.org/wiki/Warsaw%20School%20%28mathematics%29
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Warsaw School of Mathematics is the name given to a group of mathematicians who worked at Warsaw, Poland, in the two decades between the World Wars, especially in the fields of logic, set theory, point-set topology and real analysis. They published in the journal Fundamenta Mathematicae, founded in 1920—one of the world's first specialist pure-mathematics journals. It was in this journal, in 1933, that Alfred Tarski—whose illustrious career would a few years later take him to the University of California, Berkeley—published his celebrated theorem on the undefinability of the notion of truth.
Notable members of the Warsaw School of Mathematics have included:
Wacław Sierpiński
Kazimierz Kuratowski
Edward Marczewski
Bronisław Knaster
Zygmunt Janiszewski
Stefan Mazurkiewicz
Stanisław Saks
Karol Borsuk
Roman Sikorski
Nachman Aronszajn
Samuel Eilenberg
Additionally, notable logicians of the Lwów–Warsaw School of Logic, working at Warsaw, have included:
Stanisław Leśniewski
Adolf Lindenbaum
Alfred Tarski
Jan Łukasiewicz
Andrzej Mostowski
Helena Rasiowa
Fourier analysis has been advanced at Warsaw by:
Aleksander Rajchman
Antoni Zygmund
Józef Marcinkiewicz
Otton M. Nikodym
Jerzy Spława-Neyman
See also
Polish School of Mathematics
Kraków School of Mathematics
Lwów School of Mathematics
Polish mathematics
History of education in Poland
History of mathematics
History of Warsaw
Science and technology in Poland
Warsaw School of Mathematics
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https://en.wikipedia.org/wiki/Krak%C3%B3w%20School%20of%20Mathematics
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The Kraków School of Mathematics () was a subgroup of the Polish School of Mathematics represented by mathematicians from the Kraków universities—Jagiellonian University, and the AGH University of Science and Technology–active during the interwar period (1918–1939). Their areas of study were primarily classical analysis, differential equations, and analytic functions.
The Kraków School of Differential Equations was founded by Tadeusz Ważewski, a student of Stanisław Zaremba, and was internationally appreciated after World War II.
The Kraków School of Analytic Functions was founded by Franciszek Leja. Other notable members included Kazimierz Żorawski, Władysław Ślebodziński, Stanisław Gołąb, and Czesław Olech.
See also
Polish School of Mathematics
Lwów School of Mathematics
Warsaw School of Mathematics
Polish Mathematical Society
Kraków School of Mathematics and Astrology
References
Polish mathematics
History of mathematics
History of education in Poland
20th century in Kraków
Jagiellonian University
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https://en.wikipedia.org/wiki/Krystyna%20Kuperberg
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Krystyna M. Kuperberg (born Krystyna M. Trybulec; 17 July 1944) is a Polish-American mathematician who currently works as a professor of mathematics at Auburn University, where she was formerly an Alumni Professor of Mathematics.
Early life and family
Her parents, Jan W. and Barbara H. Trybulec, were pharmacists and owned a pharmacy in Tarnów. Her older brother is Andrzej Trybulec. Her husband Włodzimierz Kuperberg and her son Greg Kuperberg are also mathematicians, while her daughter Anna Kuperberg is a photographer.
Education and career
After attending high school in Gdańsk, she entered the University of Warsaw in 1962, where she studied mathematics. Her first mathematics course was taught by Andrzej Mostowski; later she attended topology lectures of Karol Borsuk and became fascinated by topology.
After obtaining her undergraduate degree, Kuperberg began graduate studies at Warsaw under Borsuk, but stopped after earning a master's degree. She left Poland in 1969 with her young family to live in Sweden, then moved to the United States in 1972. She finished her Ph.D. in 1974, from Rice University, under the supervision of William Jaco. In the same year, both she and her husband were appointed to the faculty of Auburn University. From 1996 to 1998, Kuperberg served as an American Mathematical Society Council member at large.
Contributions
In 1987 she solved a problem of Bronisław Knaster concerning bi-homogeneity of continua. In the 1980s she became interested in fixe
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https://en.wikipedia.org/wiki/Stanis%C5%82aw%20Zaremba%20%28mathematician%29
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Stanisław Zaremba (3 October 1863 – 23 November 1942) was a Polish mathematician and engineer. His research in partial differential equations, applied mathematics and classical analysis, particularly on harmonic functions, gained him a wide recognition. He was one of the mathematicians who contributed to the success of the Polish School of Mathematics through his teaching and organizational skills as well as through his research. Apart from his research works, Zaremba wrote many university textbooks and monographies.
He was a professor of the Jagiellonian University (since 1900), member of Academy of Learning (since 1903), co-founder and president of the Polish Mathematical Society (1919), and the first editor of the Annales de la Société Polonaise de Mathématique.
He should not be confused with his son Stanisław Krystyn Zaremba, also a mathematician.
Biography
Zaremba was born on 3 October 1863 in Romanówka, present-day Ukraine. The son of an engineer, he was educated at a grammar school in Saint Petersburg and studied at the Institute of Technology of the same city obtaining is diploma in engineering in 1886. The same year he left Saint Petersburg and went to Paris to study mathematics: he received his degree from the Sorbonne in 1889. He stayed in France until 1900, when he joined the faculty at the Jagiellonian University in Kraków. His years in France enabled him to establish a strong bridge between Polish mathematicians and those in France.
He died on 23 November 1
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https://en.wikipedia.org/wiki/Nitrosamine
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In organic chemistry, nitrosamines (or more formally N-nitrosamines) are organic compounds with the chemical structure , where R is usually an alkyl group. They feature a nitroso group () bonded to a deprotonated amine. Most nitrosamines are carcinogenic in nonhuman animals. A 2006 systematic review supports a "positive association between nitrite and nitrosamine intake and gastric cancer, between meat and processed meat intake and gastric cancer and oesophageal cancer, and between preserved fish, vegetable and smoked food intake and gastric cancer, but is not conclusive".
Chemistry
The organic chemistry of nitrosamines is well developed with regard to their syntheses, their structures, and their reactions. They usually are produced by the reaction of nitrous acid () and secondary amines, although other nitrosyl sources (e.g. , , RONO) have the same effect: HONO + R2NH -> R2N-NO + H2O
The nitrous acid usually arises from protonation of a nitrite. This synthesis method is relevant to the generation of nitrosamines under some biological conditions. The nitrosation is also partially reversible; aryl nitrosamines rearrange to give a para-nitroso aryl amine in the Fischer-Hepp rearrangement.
With regards to structure, the core of nitrosamines is planar, as established by X-ray crystallography. The N-N and N-O distances are 132 and 126 pm, respectively in dimethylnitrosamine, one of the simplest members of a large class of N-nitrosamines
Nitrosamines are not directly carci
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https://en.wikipedia.org/wiki/Wigner%20distribution
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Wigner distribution or Wigner function may refer to:
Wigner quasiprobability distribution (what is most commonly intended by term "Wigner function"): a quasiprobability distribution used in quantum physics, also known at the Wigner-Ville distribution
Wigner distribution function, used in signal processing, which is the time-frequency variant of the Wigner quasiprobability distribution
Modified Wigner distribution function, used in signal processing
Wigner semicircle distribution, a probability function used in mathematics
See also
Breit–Wigner distribution (disambiguation)
Wigner D-matrix, an irreducible representation of the rotation group SO(3)
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https://en.wikipedia.org/wiki/Kazimierz%20%C5%BBorawski
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Paulin Kazimierz Stefan Żorawski (June 22, 1866 – January 23, 1953) was a Polish mathematician. His work earned him an honored place in mathematics alongside such Polish mathematicians as Wojciech Brudzewski, Jan Brożek (Broscius), Nicolas Copernicus, Samuel Dickstein, Stefan Banach, Stefan Bergman, Marian Rejewski, Wacław Sierpiński, Stanisław Zaremba and Witold Hurewicz.
Żorawski's main interests were invariants of differential forms, integral invariants of Lie groups, differential geometry and fluid mechanics. His work in these disciplines was to prove important in other fields of mathematics and science, such as differential equations, geometry and physics (especially astrophysics and cosmology).
Biography
Kazimierz Żorawski was born in Szczurzyn near Ciechanów, in the Russian Empire, now in Poland, to Juliusz Bronisław Wiktor Żórawski and Kazimiera Żórawska. In 1884 he completed secondary school in Warsaw. From 1884 to 1888 he studied mathematics at the University of Warsaw. In 1889 he was selected to continue his mathematics studies on the strength of a paper on observations that he had made at the Warsaw Astronomical Observatory.
In the years that followed he studied the theory of conversion groups and analytical mechanics in Leipzig, and differential equations in Göttingen. In 1891 he was awarded a PhD (under M. Sophius Lie) in Leipzig for his thesis on the applications of group conversion theory to differential geometry. In 1892 he became a lecturer at the Po
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https://en.wikipedia.org/wiki/Normal%20basis
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In mathematics, specifically the algebraic theory of fields, a normal basis is a special kind of basis for Galois extensions of finite degree, characterised as forming a single orbit for the Galois group. The normal basis theorem states that any finite Galois extension of fields has a normal basis. In algebraic number theory, the study of the more refined question of the existence of a normal integral basis is part of Galois module theory.
Normal basis theorem
Let be a Galois extension with Galois group . The classical normal basis theorem states that there is an element such that forms a basis of K, considered as a vector space over F. That is, any element can be written uniquely as for some elements
A normal basis contrasts with a primitive element basis of the form , where is an element whose minimal polynomial has degree .
Group representation point of view
A field extension with Galois group G can be naturally viewed as a representation of the group G over the field F in which each automorphism is represented by itself. Representations of G over the field F can be viewed as left modules for the group algebra F[G]. Every homomorphism of left F[G]-modules is of form for some . Since is a linear basis of F[G] over F, it follows easily that is bijective iff generates a normal basis of K over F. The normal basis theorem therefore amounts to the statement saying that if is finite Galois extension, then as left -module. In terms of representations of G ov
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https://en.wikipedia.org/wiki/Simplex%20category
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In mathematics, the simplex category (or simplicial category or nonempty finite ordinal category) is the category of non-empty finite ordinals and order-preserving maps. It is used to define simplicial and cosimplicial objects.
Formal definition
The simplex category is usually denoted by . There are several equivalent descriptions of this category. can be described as the category of non-empty finite ordinals as objects, thought of as totally ordered sets, and (non-strictly) order-preserving functions as morphisms. The objects are commonly denoted (so that is the ordinal ). The category is generated by coface and codegeneracy maps, which amount to inserting or deleting elements of the orderings. (See simplicial set for relations of these maps.)
A simplicial object is a presheaf on , that is a contravariant functor from to another category. For instance, simplicial sets are contravariant with the codomain category being the category of sets. A cosimplicial object is defined similarly as a covariant functor originating from .
Augmented simplex category
The augmented simplex category, denoted by is the category of all finite ordinals and order-preserving maps, thus , where . Accordingly, this category might also be denoted FinOrd. The augmented simplex category is occasionally referred to as algebraists' simplex category and the above version is called topologists' simplex category.
A contravariant functor defined on is called an augmented simplicial object and a cov
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https://en.wikipedia.org/wiki/Eigenplane
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In mathematics, an eigenplane is a two-dimensional invariant subspace in a given vector space. By analogy with the term eigenvector for a vector which, when operated on by a linear operator is another vector which is a scalar multiple of itself, the term eigenplane can be used to describe a two-dimensional plane (a 2-plane), such that the operation of a linear operator on a vector in the 2-plane always yields another vector in the same 2-plane.
A particular case that has been studied is that in which the linear operator is an isometry M of the hypersphere (written S3) represented within four-dimensional Euclidean space:
where s and t are four-dimensional column vectors and Λθ is a two-dimensional eigenrotation within the eigenplane.
In the usual eigenvector problem, there is freedom to multiply an eigenvector by an arbitrary scalar; in this case there is freedom to multiply by an arbitrary non-zero rotation.
This case is potentially physically interesting in the case that the shape of the universe is a multiply connected 3-manifold, since finding the angles of the eigenrotations of a candidate isometry for topological lensing is a way to falsify such hypotheses.
See also
Bivector
Plane of rotation
External links
possible relevance of eigenplanes in cosmology
GNU GPL software for calculating eigenplanes
Proof constructed by J M Shelley 2017
Linear algebra
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https://en.wikipedia.org/wiki/Primitive%20polynomial%20%28field%20theory%29
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In finite field theory, a branch of mathematics, a primitive polynomial is the minimal polynomial of a primitive element of the finite field . This means that a polynomial of degree with coefficients in is a primitive polynomial if it is monic and has a root in such that is the entire field . This implies that is a primitive ()-root of unity in .
Properties
Because all minimal polynomials are irreducible, all primitive polynomials are also irreducible.
A primitive polynomial must have a non-zero constant term, for otherwise it will be divisible by x. Over GF(2), is a primitive polynomial and all other primitive polynomials have an odd number of terms, since any polynomial mod 2 with an even number of terms is divisible by (it has 1 as a root).
An irreducible polynomial F(x) of degree m over GF(p), where p is prime, is a primitive polynomial if the smallest positive integer n such that F(x) divides is .
Over GF(p) there are exactly primitive polynomials of degree m, where φ is Euler's totient function.
A primitive polynomial of degree m has m different roots in GF(pm), which all have order . This means that, if α is such a root, then and for .
The primitive polynomial F(x) of degree m of a primitive element α in GF(pm) has explicit form .
Usage
Field element representation
Primitive polynomials can be used to represent the elements of a finite field. If α in GF(pm) is a root of a primitive polynomial F(x), then the nonzero elements of GF(pm) are rep
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https://en.wikipedia.org/wiki/Thundering%20herd%20problem
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In computer science, the thundering herd problem occurs when a large number of processes or threads waiting for an event are awoken when that event occurs, but only one process is able to handle the event. When the processes wake up, they will each try to handle the event, but only one will win. All processes will compete for resources, possibly freezing the computer, until the herd is calmed down again.
Mitigation
The Linux kernel serializes responses for requests to a single file descriptor, so only one thread or process is woken up. For epoll() in version 4.5 of the Linux kernel, the EPOLLEXCLUSIVE flag was added. Thus several epoll sets (different threads or different processes) may wait on the same resource and only one set will be woken up. For certain workloads this flag can give significant processing time reduction.
Similarly in Microsoft Windows, I/O completion ports can mitigate the thundering herd problem, as they can be configured such that only one of the threads waiting on the completion port is woken up when an event occurs.
In systems that rely on a backoff mechanism (e.g. exponential backoff), the clients will retry failed calls by waiting a specific amount of time between consecutive retries. In order to avoid the thundering herd problem, jitter can be purposefully introduced in order to break the synchronization across the clients, thereby avoiding collisions. In this approach, randomness is added to the wait intervals between retries, so that clients
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https://en.wikipedia.org/wiki/Henri%20Moissan
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Ferdinand Frédéric Henri Moissan (28 September 1852 – 20 February 1907) was a French chemist and pharmacist who won the 1906 Nobel Prize in Chemistry for his work in isolating fluorine from its compounds. Moissan was one of the original members of the International Atomic Weights Committee.
Biography
Early life and education
Moissan was born in Paris on 28 September 1852, the son of a minor officer of the eastern railway company, Francis Ferdinand Moissan, and a seamstress, Joséphine Améraldine (née Mitel). His mother was of Jewish descent, his father was not. In 1864 they moved to Meaux, where he attended the local school. During this time, Moissan became an apprentice clockmaker. However, in 1870, Moissan and his family moved back to Paris due to war against Prussia. Moissan was unable to receive the grade universitaire necessary to attend university. After spending a year in the army, he enrolled at the Ecole Superieure de Pharmacie de Paris.
Scientific career
Moissan became a trainee in pharmacy in 1871 and in 1872 he began working for a chemist in Paris, where he was able to save a person poisoned with arsenic. He decided to study chemistry and began first in the laboratory of Edmond Frémy at the Musée d’Histoire Naturelle, and later in that of Pierre Paul Dehérain at the École Pratique des Haute Études. Dehérain persuaded him to pursue an academic career. He passed the baccalauréat, which was necessary to study at university, in 1874 after an earlier failed attempt.
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https://en.wikipedia.org/wiki/Equidistributed%20sequence
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In mathematics, a sequence (s1, s2, s3, ...) of real numbers is said to be equidistributed, or uniformly distributed, if the proportion of terms falling in a subinterval is proportional to the length of that subinterval. Such sequences are studied in Diophantine approximation theory and have applications to Monte Carlo integration.
Definition
A sequence (s1, s2, s3, ...) of real numbers is said to be equidistributed on a non-degenerate interval [a, b] if for every subinterval [c, d] of [a, b] we have
(Here, the notation |{s1,...,sn} ∩ [c, d]| denotes the number of elements, out of the first n elements of the sequence, that are between c and d.)
For example, if a sequence is equidistributed in [0, 2], since the interval [0.5, 0.9] occupies 1/5 of the length of the interval [0, 2], as n becomes large, the proportion of the first n members of the sequence which fall between 0.5 and 0.9 must approach 1/5. Loosely speaking, one could say that each member of the sequence is equally likely to fall anywhere in its range. However, this is not to say that (sn) is a sequence of random variables; rather, it is a determinate sequence of real numbers.
Discrepancy
We define the discrepancy DN for a sequence (s1, s2, s3, ...) with respect to the interval [a, b] as
A sequence is thus equidistributed if the discrepancy DN tends to zero as N tends to infinity.
Equidistribution is a rather weak criterion to express the fact that a sequence fills the segment leaving no gaps. For example,
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https://en.wikipedia.org/wiki/Phasis
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Phasis may refer to:
Places and jurisdictions
Phasis (river), modern-day Rioni River in western Georgia
Phasis (town), an ancient town in the Phasis river delta, near modern-day Poti
Phasis (titular see), a Latin Catholic titular see
Biology
Phasis (butterfly), a genus of butterfly
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https://en.wikipedia.org/wiki/Surface%20%28disambiguation%29
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A surface, as the term is most generally used, is the outermost or uppermost layer of a physical object or space.
Surface or surfaces may also refer to:
Mathematics
Surface (mathematics), a generalization of a plane which needs not be flat
Surface (differential geometry), a differentiable two-dimensional manifold
Surface (topology), a two-dimensional manifold
Algebraic surface, an algebraic variety of dimension two
Coordinate surfaces
Fractal surface, generated using a stochastic algorithm
Polyhedral surface
Surface area
Surface integral
Arts and entertainment
Surface (band), an American R&B and pop trio
Surface (Surface album), 1986
Surfaces (band), American musical duo
Surface (Circle album), 1998
"Surface" (Aero Chord song), 2014
Surface (2005 TV series), an American science fiction show, 2005–2006
Surface (2022 TV series), an American psychological thriller miniseries that began streaming in 2022
The Surface, an American film, 2014
"Surface", a song by Your Memorial from the 2010 album Atonement
Physical sciences
Surface finishing, a range of industrial processes that alter the surface of a manufactured item to achieve a certain property
Surface science, the study of physical and chemical phenomena that occur at the interface of two phases
Surface wave, a mechanical wave, in physics
Interface (matter), common boundary among two different phases of matter
Planetary surface
Surface of the Earth
Sea surface
Transportation
Surface mail, transportation of mail that trave
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https://en.wikipedia.org/wiki/Pinocytosis
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In cellular biology, pinocytosis, otherwise known as fluid endocytosis and bulk-phase pinocytosis, is a mode of endocytosis in which small molecules dissolved in extracellular fluid are brought into the cell through an invagination of the cell membrane, resulting in their containment within a small vesicle inside the cell. These pinocytotic vesicles then typically fuse with early endosomes to hydrolyze (break down) the particles.
Pinocytosis is variably subdivided into categories depending on the molecular mechanism and the fate of the internalized molecules.
Function
In humans, this process occurs primarily for absorption of fat droplets. In endocytosis the cell plasma membrane extends and folds around desired extracellular material, forming a pouch that pinches off creating an internalized vesicle. The invaginated pinocytosis vesicles are much smaller than those generated by phagocytosis. The vesicles eventually fuse with the lysosome, whereupon the vesicle contents are digested. Pinocytosis involves a considerable investment of cellular energy in the form of ATP.
Pinocytosis and ATP
Pinocytosis is used primarily for clearing extracellular fluids (ECF) and as part of immune surveillance. In contrast to phagocytosis, it generates very small amounts of ATP from the wastes of alternative substances such as lipids (fat). Unlike receptor-mediated endocytosis, pinocytosis is nonspecific in the substances that it transport: the cell takes in surrounding fluids, including all s
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https://en.wikipedia.org/wiki/UNESCO%20nomenclature
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UNESCO Nomenclature (more properly UNESCO nomenclature for fields of science and technology) is a system developed by UNESCO for classification of research papers and doctoral dissertations. There are three versions of the system, offering different levels of refinement through 2-, 4-, and 6-digit codes.
Two-digit system
11 Logic
12 Mathematics
21 Astronomy, Astrophysics
22 Physics
23 Chemistry
24 Life Sciences
25 Earth and space science
31 Agricultural Sciences
32 Medical Sciences
33 Technological Sciences
51 Anthropology
52 Demography
53 Economic Sciences
54 Geography
55 History
56 Juridical Science and Law
57 Linguistics
58 Pedagogy
59 Political Science
61 Psychology
62 Sciences of Arts and Letters
63 Sociology
71 Ethics
72 Philosophy
See also
UNESCO Standard Classification of Education
References
External links
Original document (from 1988) – full 6-digit nomenclature
Academic literature
Classification systems
International classification systems
Library cataloging and classification
UNESCO
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https://en.wikipedia.org/wiki/Computer%20experiment
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A computer experiment or simulation experiment is an experiment used to study a computer simulation, also referred to as an in silico system. This area includes computational physics, computational chemistry, computational biology and other similar disciplines.
Background
Computer simulations are constructed to emulate a physical system. Because these are meant to replicate some aspect of a system in detail, they often do not yield an analytic solution. Therefore, methods such as discrete event simulation or finite element solvers are used. A computer model is used to make inferences about the system it replicates. For example, climate models are often used because experimentation on an earth sized object is impossible.
Objectives
Computer experiments have been employed with many purposes in mind. Some of those include:
Uncertainty quantification: Characterize the uncertainty present in a computer simulation arising from unknowns during the computer simulation's construction.
Inverse problems: Discover the underlying properties of the system from the physical data.
Bias correction: Use physical data to correct for bias in the simulation.
Data assimilation: Combine multiple simulations and physical data sources into a complete predictive model.
Systems design: Find inputs that result in optimal system performance measures.
Computer simulation modeling
Modeling of computer experiments typically uses a Bayesian framework. Bayesian statistics is an interpreta
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https://en.wikipedia.org/wiki/All%20one%20polynomial
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In mathematics, an all one polynomial (AOP) is a polynomial in which all coefficients are one. Over the finite field of order two, conditions for the AOP to be irreducible are known, which allow this polynomial to be used to define efficient algorithms and circuits for multiplication in finite fields of characteristic two. The AOP is a 1-equally spaced polynomial.
Definition
An AOP of degree m has all terms from xm to x0 with coefficients of 1, and can be written as
or
or
Thus the roots of the all one polynomial of degree m are all (m+1)th roots of unity other than unity itself.
Properties
Over GF(2) the AOP has many interesting properties, including:
The Hamming weight of the AOP is m + 1, the maximum possible for its degree
The AOP is irreducible if and only if m + 1 is prime and 2 is a primitive root modulo m + 1 (over GF(p) with prime p, it is irreducible if and only if m + 1 is prime and p is a primitive root modulo m + 1)
The only AOP that is a primitive polynomial is x2 + x + 1.
Despite the fact that the Hamming weight is large, because of the ease of representation and other improvements there are efficient implementations in areas such as coding theory and cryptography.
Over , the AOP is irreducible whenever m + 1 is a prime p, and therefore in these cases, the pth cyclotomic polynomial.
References
External links
Field (mathematics)
Polynomials
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https://en.wikipedia.org/wiki/National%20Nanotechnology%20Initiative
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The National Nanotechnology Initiative (NNI) is a research and development initiative which provides a framework to coordinate nanoscale research and resources among United States federal government agencies and departments.
History
Mihail C. Roco proposed the initiative in a 1999 presentation to the White House under the Clinton administration. The NNI was officially launched in 2000 and received funding for the first time in FY2001.
President Bill Clinton advocated nanotechnology development. In a 21 January 2000 speech at the California Institute of Technology, Clinton stated that "Some of our research goals may take twenty or more years to achieve, but that is precisely why there is an important role for the federal government."
President George W. Bush further increased funding for nanotechnology. On 3 December 2003 Bush signed into law the 21st Century Nanotechnology Research and Development Act (), which authorizes expenditures for five of the participating agencies totaling $3.63 billion over four years.. This law is an authorization, not an appropriation, and subsequent appropriations for these five agencies have not met the goals set out in the 2003 Act. However, there are many agencies involved in the Initiative that are not covered by the Act, and requested budgets under the Initiative for all participating agencies in Fiscal Years 2006 – 2015 totaled over $1 billion each.
In February 2014, the National Nanotechnology Initiative released a Strategic Plan
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https://en.wikipedia.org/wiki/Theodor%20Schwann
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Theodor Schwann (; 7 December 181011 January 1882) was a German physician and physiologist. His most significant contribution to biology is considered to be the extension of cell theory to animals. Other contributions include the discovery of Schwann cells in the peripheral nervous system, the discovery and study of pepsin, the discovery of the organic nature of yeast, and the invention of the term "metabolism".
Early life and education
Theodor Schwann was born in Neuss on 7 December 1810 to Leonard Schwann and Elisabeth Rottels. Leonard Schwann was a goldsmith and later a printer. Theodor Schwann studied at the Dreikönigsgymnasium (also known as the Tricoronatum or Three Kings School), a Jesuit school in Cologne. Schwann was a devout Roman Catholic. In Cologne his religious instructor , a priest and novelist, emphasized the individuality of the human soul and the importance of free will.
In 1829, Schwann enrolled at the University of Bonn in the premedical curriculum. He received a bachelor of philosophy in 1831. While at Bonn, Schwann met and worked with physiologist Johannes Peter Müller.
Müller is considered to have founded scientific medicine in Germany, publishing his Handbuch der Physiologie des Menschen für Vorlesungen in 1837–1840. It was translated into English as Elements of Physiology in 1837–1843 and became the leading physiology textbook of the 1800s.
In 1831, Schwann moved to the University of Würzburg for clinical training in medicine. In 1833, he went
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https://en.wikipedia.org/wiki/Kitaro%20Nishida
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was a Japanese moral
philosopher, philosopher of mathematics and science, and religious scholar. He was the founder of what has been called the Kyoto School of philosophy. He graduated from the University of Tokyo during the Meiji period in 1894 with a degree in philosophy. He was named professor of the Fourth Higher School in Ishikawa Prefecture in 1899 and later became professor of philosophy at Kyoto University. Nishida retired in 1927. In 1940, he was awarded the Order of Culture (文化勲章, bunka kunshō). He participated in establishing the Chiba Institute of Technology (千葉工業大学) from 1940.
Nishida Kitarō died at the age of 75 of a renal infection. His cremated remains were divided in three and buried at different locations. Part of his remains were buried in the Nishida family grave in his birthplace Unoke, Ishikawa. A second grave can be found at Tōkei-ji Temple in Kamakura, where his friend D. T. Suzuki organized Nishida's funeral and was later also buried in the adjacent plot. Nishida's third grave is at Reiun'in (霊雲院, Reiun'in), a temple in the Myōshin-ji compound in Kyoto.
Philosophy
Being born in the third year of the Meiji period, Nishida was presented with a new, unique opportunity to contemplate Eastern philosophical issues in the fresh light that Western philosophy shone on them. Nishida's original and creative philosophy, incorporating ideas of Zen and Western philosophy, was aimed at bringing the East and West closer. Throughout his lifetime, Nishida published
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https://en.wikipedia.org/wiki/Marcinkiewicz%20interpolation%20theorem
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In mathematics, the Marcinkiewicz interpolation theorem, discovered by , is a result bounding the norms of non-linear operators acting on Lp spaces.
Marcinkiewicz' theorem is similar to the Riesz–Thorin theorem about linear operators, but also applies to non-linear operators.
Preliminaries
Let f be a measurable function with real or complex values, defined on a measure space (X, F, ω). The distribution function of f is defined by
Then f is called weak if there exists a constant C such that the distribution function of f satisfies the following inequality for all t > 0:
The smallest constant C in the inequality above is called the weak norm and is usually denoted by or Similarly the space is usually denoted by L1,w or L1,∞.
(Note: This terminology is a bit misleading since the weak norm does not satisfy the triangle inequality as one can see by considering the sum of the functions on given by and , which has norm 4 not 2.)
Any function belongs to L1,w and in addition one has the inequality
This is nothing but Markov's inequality (aka Chebyshev's Inequality). The converse is not true. For example, the function 1/x belongs to L1,w but not to L1.
Similarly, one may define the weak space as the space of all functions f such that belong to L1,w, and the weak norm using
More directly, the Lp,w norm is defined as the best constant C in the inequality
for all t > 0.
Formulation
Informally, Marcinkiewicz's theorem is
Theorem. Let T be a bounded linear operator
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https://en.wikipedia.org/wiki/Morava%20K-theory
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In stable homotopy theory, a branch of mathematics, Morava K-theory is one of a collection of cohomology theories introduced in algebraic topology by Jack Morava in unpublished preprints in the early 1970s. For every prime number p (which is suppressed in the notation), it consists of theories K(n) for each nonnegative integer n, each a ring spectrum in the sense of homotopy theory. published the first account of the theories.
Details
The theory K(0) agrees with singular homology with rational coefficients, whereas K(1) is a summand of mod-p complex K-theory. The theory K(n) has coefficient ring
Fp[vn,vn−1]
where vn has degree 2(pn − 1). In particular, Morava K-theory is periodic with this period, in much the same way that complex K-theory has period 2.
These theories have several remarkable properties.
They have Künneth isomorphisms for arbitrary pairs of spaces: that is, for X and Y CW complexes, we have
They are "fields" in the category of ring spectra. In other words every module spectrum over K(n) is free, i.e. a wedge of suspensions of K(n).
They are complex oriented (at least after being periodified by taking the wedge sum of (pn − 1) shifted copies), and the formal group they define has height n.
Every finite p-local spectrum X has the property that K(n)∗(X) = 0 if and only if n is less than a certain number N, called the type of the spectrum X. By a theorem of Devinatz–Hopkins–Smith, every thick subcategory of the category of finite p-local spectra is th
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https://en.wikipedia.org/wiki/Complex%20cobordism
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In mathematics, complex cobordism is a generalized cohomology theory related to cobordism of manifolds. Its spectrum is denoted by MU. It is an exceptionally powerful cohomology theory, but can be quite hard to compute, so often instead of using it directly one uses some slightly weaker theories derived from it, such as Brown–Peterson cohomology or Morava K-theory, that are easier to compute.
The generalized homology and cohomology complex cobordism theories were introduced by using the Thom spectrum.
Spectrum of complex cobordism
The complex bordism of a space is roughly the group of bordism classes of manifolds over with a complex linear structure on the stable normal bundle. Complex bordism is a generalized homology theory, corresponding to a spectrum MU that can be described explicitly in terms of Thom spaces as follows.
The space is the Thom space of the universal -plane bundle over the classifying space of the unitary group . The natural inclusion from into induces a map from the double suspension to . Together these maps give the spectrum ; namely, it is the homotopy colimit of .
Examples: is the sphere spectrum. is the desuspension of .
The nilpotence theorem states that, for any ring spectrum , the kernel of consists of nilpotent elements. The theorem implies in particular that, if is the sphere spectrum, then for any , every element of is nilpotent (a theorem of Goro Nishida). (Proof: if is in , then is a torsion but its image in , the Lazard
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https://en.wikipedia.org/wiki/Spectrum%20%28topology%29
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In algebraic topology, a branch of mathematics, a spectrum is an object representing a generalized cohomology theory. Every such cohomology theory is representable, as follows from Brown's representability theorem. This means that, given a cohomology theory,there exist spaces such that evaluating the cohomology theory in degree on a space is equivalent to computing the homotopy classes of maps to the space , that is.Note there are several different categories of spectra leading to many technical difficulties, but they all determine the same homotopy category, known as the stable homotopy category. This is one of the key points for introducing spectra because they form a natural home for stable homotopy theory.
The definition of a spectrum
There are many variations of the definition: in general, a spectrum is any sequence of pointed topological spaces or pointed simplicial sets together with the structure maps , where is the smash product. The smash product of a pointed space with a circle is homeomorphic to the reduced suspension of , denoted .
The following is due to Frank Adams (1974): a spectrum (or CW-spectrum) is a sequence of CW complexes together with inclusions of the suspension as a subcomplex of .
For other definitions, see symmetric spectrum and simplicial spectrum.
Homotopy groups of a spectrum
One of the most important invariants of spectra are the homotopy groups of the spectrum. These groups mirror the definition of the stable homotopy groups of
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https://en.wikipedia.org/wiki/Reduction%20%28mathematics%29
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In mathematics, reduction refers to the rewriting of an expression into a simpler form. For example, the process of rewriting a fraction into one with the smallest whole-number denominator possible (while keeping the numerator a whole number) is called "reducing a fraction". Rewriting a radical (or "root") expression with the smallest possible whole number under the radical symbol is called "reducing a radical". Minimizing the number of radicals that appear underneath other radicals in an expression is called denesting radicals.
Algebra
In linear algebra, reduction refers to applying simple rules to a series of equations or matrices to change them into a simpler form. In the case of matrices, the process involves manipulating either the rows or the columns of the matrix and so is usually referred to as row-reduction or column-reduction, respectively. Often the aim of reduction is to transform a matrix into its "row-reduced echelon form" or "row-echelon form"; this is the goal of Gaussian elimination.
Calculus
In calculus, reduction refers to using the technique of integration by parts to evaluate integrals by reducing them to simpler forms.
Static (Guyan) reduction
In dynamic analysis, static reduction refers to reducing the number of degrees of freedom. Static reduction can also be used in finite element analysis to refer to simplification of a linear algebraic problem. Since a static reduction requires several inversion steps it is an expensive matrix operation and is
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https://en.wikipedia.org/wiki/Strain%20%28biology%29
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In biology, a strain is a genetic variant, a subtype or a culture within a biological species. Strains are often seen as inherently artificial concepts, characterized by a specific intent for genetic isolation. This is most easily observed in microbiology where strains are derived from a single cell colony and are typically quarantined by the physical constraints of a Petri dish. Strains are also commonly referred to within virology, botany, and with rodents used in experimental studies.
Microbiology and virology
It has been said that "there is no universally accepted definition for the terms 'strain', 'variant', and 'isolate' in the virology community, and most virologists simply copy the usage of terms from others".
A strain is a genetic variant or subtype of a microorganism (e.g., a virus, bacterium or fungus). For example, a "flu strain" is a certain biological form of the influenza or "flu" virus. These flu strains are characterized by their differing isoforms of surface proteins. New viral strains can be created due to mutation or swapping of genetic components when two or more viruses infect the same cell in nature. These phenomena are known respectively as antigenic drift and antigenic shift. Microbial strains can also be differentiated by their genetic makeup using metagenomic methods to maximize resolution within species. This has become a valuable tool to analyze the microbiome.
Artificial constructs
Scientists have modified strains of viruses in order to stu
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https://en.wikipedia.org/wiki/Nigel%20Hitchin
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Nigel James Hitchin FRS (born 2 August 1946) is a British mathematician working in the fields of differential geometry, gauge theory, algebraic geometry, and mathematical physics. He is a Professor Emeritus of Mathematics at the University of Oxford.
Academic career
Hitchin attended Ecclesbourne School, Duffield, and earned his BA in mathematics from Jesus College, Oxford, in 1968. After moving to Wolfson College, he received his D.Phil. in 1972. From 1971 to 1973 he visited the Institute for Advanced Study and 1973/74 the Courant Institute of Mathematical Sciences of New York University. He then was a research fellow in Oxford and starting in 1979 tutor, lecturer and fellow of St Catherine's College. In 1990 he became a professor at the University of Warwick and in 1994 the Rouse Ball Professor of Mathematics at the University of Cambridge. In 1997 he was appointed to the Savilian Chair of Geometry at the University of Oxford, a position he held until his retirement in 2016.
Amongst his notable discoveries are the Hitchin–Thorpe inequality; Hitchin's projectively flat connection over Teichmüller space; the Atiyah–Hitchin monopole metric; the Atiyah–Hitchin–Singer theorem; the ADHM construction of instantons (of Michael Atiyah, Vladimir Drinfeld, Hitchin, and Yuri Manin); the hyperkähler quotient (of Hitchin, Anders Karlhede, Ulf Lindström and Martin Roček); Higgs bundles, which arise as solutions to the Hitchin equations, a 2-dimensional reduction of the self-dual Yang–Mil
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https://en.wikipedia.org/wiki/Dehydrogenation
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In chemistry, dehydrogenation is a chemical reaction that involves the removal of hydrogen, usually from an organic molecule. It is the reverse of hydrogenation. Dehydrogenation is important, both as a useful reaction and a serious problem. At its simplest, it’s a useful way of converting alkanes, which are relatively inert and thus low-valued, to olefins, which are reactive and thus more valuable. Alkenes are precursors to aldehydes (), alcohols (), polymers, and aromatics. As a problematic reaction, the fouling and inactivation of many catalysts arises via coking, which is the dehydrogenative polymerization of organic substrates.
Enzymes that catalyze dehydrogenation are called dehydrogenases.
Heterogeneous catalytic routes
Styrene
Dehydrogenation processes are used extensively to produce aromatics in the petrochemical industry. Such processes are highly endothermic and require temperatures of 500 °C and above. Dehydrogenation also converts saturated fats to unsaturated fats. One of the largest scale dehydrogenation reactions is the production of styrene by dehydrogenation of ethylbenzene. Typical dehydrogenation catalysts are based on iron(III) oxide, promoted by several percent potassium oxide or potassium carbonate.
C6H5CH2CH3 -> C6H5CH=CH2 + H2
Other alkenes
The importance of catalytic dehydrogenation of paraffin hydrocarbons to olefins has been growing steadily in recent years. Light olefins, such as butenes, are important raw materials for the synthesis of po
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https://en.wikipedia.org/wiki/Most%20recent%20common%20ancestor
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In biology and genetic genealogy, the most recent common ancestor (MRCA), also known as the last common ancestor (LCA), of a set of organisms is the most recent individual from which all the organisms of the set are descended. The term is also used in reference to the ancestry of groups of genes (haplotypes) rather than organisms.
The MRCA of a set of individuals can sometimes be determined by referring to an established pedigree. However, in general, it is impossible to identify the exact MRCA of a large set of individuals, but an estimate of the time at which the MRCA lived can often be given. Such time to most recent common ancestor (TMRCA) estimates can be given based on DNA test results and established mutation rates as practiced in genetic genealogy, or by reference to a non-genetic, mathematical model or computer simulation.
In organisms using sexual reproduction, the matrilineal MRCA and patrilineal MRCA are the MRCAs of a given population considering only matrilineal and patrilineal descent, respectively. The MRCA of a population by definition cannot be older than either its matrilineal or its patrilineal MRCA. In the case of Homo sapiens, the matrilineal and patrilineal MRCA are also known as "Mitochondrial Eve" (mt-MRCA) and "Y-chromosomal Adam" (Y-MRCA) respectively.
The age of the human MRCA is unknown. It is no greater than the age of either the Y-MRCA or the mt-MRCA, estimated at around 200,000 years.
Unlike in pedigrees of individual humans or domesticated
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https://en.wikipedia.org/wiki/Chirplet%20transform
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In signal processing, the chirplet transform is an inner product of an input signal with a family of analysis primitives called chirplets.
Similar to the wavelet transform, chirplets are usually generated from (or can be expressed as being from) a single mother chirplet (analogous to the so-called mother wavelet of wavelet theory).
Definitions
The term chirplet transform was coined by Steve Mann, as the title of the first published paper on chirplets. The term chirplet itself (apart from chirplet transform) was also used by Steve Mann, Domingo Mihovilovic, and Ronald Bracewell to describe a windowed portion of a chirp function. In Mann's words:
The chirplet transform thus represents a rotated, sheared, or otherwise transformed tiling of the time–frequency plane. Although chirp signals have been known for many years in radar, pulse compression, and the like, the first published reference to the chirplet transform described specific signal representations based on families of functions related to one another by time–varying frequency modulation or frequency varying time modulation, in addition to time and frequency shifting, and scale changes. In that paper, the Gaussian chirplet transform was presented as one such example, together with a successful application to ice fragment detection in radar (improving target detection results over previous approaches). The term chirplet (but not the term chirplet transform) was also proposed for a similar transform, apparently independ
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https://en.wikipedia.org/wiki/Scattering%20amplitude
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In quantum physics, the scattering amplitude is the probability amplitude of the outgoing spherical wave relative to the incoming plane wave in a stationary-state scattering process.
At large distances from the centrally symmetric scattering center, the plane wave is described by the wavefunction
where is the position vector; ; is the incoming plane wave with the wavenumber along the axis; is the outgoing spherical wave; is the scattering angle (angle between the incident and scattered direction); and is the scattering amplitude. The dimension of the scattering amplitude is length. The scattering amplitude is a probability amplitude; the differential cross-section as a function of scattering angle is given as its modulus squared,
The asymptotic from of the wave function in arbitrary external field takes the from
where is the direction of incidient particles and is the direction of scattered particles.
Unitary condition
When conservation of number of particles holds true during scattering, it leads to a unitary condition for the scattering amplitude. In the general case, we have
Optical theorem follows from here by setting
In the centrally symmetric field, the unitary condition becomes
where and are the angles between and and some direction . This condition puts a constraint on the allowed form for , i.e., the real and imaginary part of the scattering amplitude are not independent in this case. For example, if in is known (say, from the measurement
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https://en.wikipedia.org/wiki/The%20Planiverse
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The Planiverse is a novel by A. K. Dewdney, written in 1984.
Plot
In the spirit of Edwin Abbott Abbott's Flatland, Dewdney and his computer science students simulate a two-dimensional world with a complex ecosystem. To their surprise, they find their artificial 2D universe has somehow accidentally become a means of communication with an actual 2D world: Arde. They make a sort of "telepathic" contact with "YNDRD", referred to by the students as Yendred, a highly philosophical Ardean, as he begins a journey across the western half, Punizla, of the single continent Ajem Kollosh to learn more about the spiritual beliefs of the people of the East, Vanizla. Yendred mistakes Dewdney's class for "spirits" and takes great interest in communicating with them. The students and narrator communicate with Yendred by typing on the keyboard; Yendred's answers appear on the computer's printout. The name Yendred (or "Yendwed", as pronounced by one of the students, who has a speech impediment) is simply "Dewdney" reversed.
Written as a travelogue, Yendred's journey through the West takes him through several cities. He visits the Punizlan Institute for Technology and Science, where Arde's technology is explored in great detail. For example, all houses are underground, so as not to be demolished by the periodic 2D rivers; nails are useless for attaching two objects, so tape and glue are used instead; most Ardean creatures cannot have deuterostomic digestive tracts since they would split into tw
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https://en.wikipedia.org/wiki/Constitutive%20equation
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In physics and engineering, a constitutive equation or constitutive relation is a relation between two physical quantities (especially kinetic quantities as related to kinematic quantities) that is specific to a material or substance, and approximates the response of that material to external stimuli, usually as applied fields or forces. They are combined with other equations governing physical laws to solve physical problems; for example in fluid mechanics the flow of a fluid in a pipe, in solid state physics the response of a crystal to an electric field, or in structural analysis, the connection between applied stresses or loads to strains or deformations.
Some constitutive equations are simply phenomenological; others are derived from first principles. A common approximate constitutive equation frequently is expressed as a simple proportionality using a parameter taken to be a property of the material, such as electrical conductivity or a spring constant. However, it is often necessary to account for the directional dependence of the material, and the scalar parameter is generalized to a tensor. Constitutive relations are also modified to account for the rate of response of materials and their non-linear behavior. See the article Linear response function.
Mechanical properties of matter
The first constitutive equation (constitutive law) was developed by Robert Hooke and is known as Hooke's law. It deals with the case of linear elastic materials. Following this discover
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https://en.wikipedia.org/wiki/Ronald%20M.%20Evans
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Ronald Mark Evans (born April 17, 1949 in Los Angeles, California) is an American Biologist, Professor and Head of the Salk’s Gene Expression Laboratory, and the March of Dimes Chair in Molecular and Developmental Biology at the Salk Institute for Biological Studies in La Jolla, California and a Howard Hughes Medical Institute Investigator. Dr. Ronald M. Evans is known for his original discoveries of nuclear hormone receptors (NR), a special class of transcriptional factor, and the elucidation of their universal mechanism of action, a process that governs how lipophilic hormones and drugs regulate virtually every developmental and metabolic pathway in animals and humans. Nowadays, NRs are among the most widely investigated group of pharmaceutical targets in the world, already yielding benefits in drug discovery for cancer, muscular dystrophies, osteoporosis, type II diabetes, obesity, and cardiovascular diseases. His current research focuses on the function of nuclear hormone signaling and their function in metabolism and cancer.
He received his Bachelor of Science and PhD (1974) from UCLA, followed by a postdoctoral training at Rockefeller University with James E. Darnell. He became a faculty member at the Salk Institute in 1978 and Adjunct Professor in Biology, Biomedical Sciences, Neuroscience at UCSD (1985, 1989, 1995). He was named March of Dimes Chair in Molecular and Developmental Neurobiology at the Salk Institute in 1998.
His work on nuclear receptor was well reco
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https://en.wikipedia.org/wiki/Dario%20Floreano
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Dario Floreano (born 1964 in San Daniele del Friuli, Italy) is a Swiss-Italian roboticist and engineer. He is Director of the Laboratory of Intelligent System (LIS) at the École Polytechnique Fédérale de Lausanne in Switzerland and was the founding director of the Swiss National Centre of Competence in Research (NCCR) Robotics.
Education and career
Floreano received a bachelor's degree from the University of Trieste with a major in visual psychophysics in 1988. In 1989, he joined the Italian National Research Council in Rome as research fellow. He received a master's degree in computer sciences with a specialisation in neural computation from the University of Stirling in 1992. In 1995, he earned a PhD in artificial intelligence and robotics from the University of Trieste. Following a position as Chief Scientific Officer at Cognitive Technology Laboratory Ltd, he joined the EPFL in 1996 as group leader in the Department of Computer Science. In 2000, Floreano was first named Assistant Professor, then in 2005 Associate Professor and in 2010 Full Professor of Intelligent Systems at EPFL's School of Engineering. He was the founding director of the Swiss National Center of Competence in Robotics, which ran for 12 years, between 2010 and 2022. Floreano was named "AI influencer in Switzerland" in 2021. Since 2022, Floreano is a Fellow of the European Center for Living Technologies (ECLT) and since 2023 a Fellow of the Institute of Electrical and Electronics Engineers (IEEE). He als
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https://en.wikipedia.org/wiki/VRC
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VRC may refer to:
Vaccine Research Center
Vancouver Rowing Club, formed in 1886
Veteran Reserve Corps
Victoria Racing Club
VRC Oaks
Videogame Rating Council, rating games for Sega of America
Virtual Radar Client, Windows radar simulator
Vex Robotics Competition
Great Britain Volunteer Rifle Corps of Volunteer Force
Vulnerability and Risk Committee of the American Society of Civil Engineers
VRChat
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https://en.wikipedia.org/wiki/Kuei
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Kuei or Guǐ may refer to:
People
Kuei Chih-Hung (1937–1999), Chinese filmmaker
Kuei Chin (1090–1155), chancellor of the Song Dynasty
Kuei Pin Yeo, Indonesian classical pianist and educator
Kuei Ya Lei (born 1944), Chinese actress and singer
Kuei Ling Ru, American high school chemistry teacher
Other
Catholic University of Eichstätt-Ingolstadt (Katholische Universität), Bavaria, Germany
Kuei-chou or Guizhou, a southwestern province of the People's Republic of China
Kuei River or Amu Darya, a river in Central Asia
Kuih, a sweet Chinese dessert or snack made of rice
Guǐ, a ghost in Chinese culture
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https://en.wikipedia.org/wiki/In%20silico
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In biology and other experimental sciences, an in silico experiment is one performed on computer or via computer simulation. The phrase is pseudo-Latin for 'in silicon' (correct ), referring to silicon in computer chips. It was coined in 1987 as an allusion to the Latin phrases , , and , which are commonly used in biology (especially systems biology). The latter phrases refer, respectively, to experiments done in living organisms, outside living organisms, and where they are found in nature.
History
The earliest known use of the phrase was by Christopher Langton to describe artificial life, in the announcement of a workshop on that subject at the Center for Nonlinear Studies at the Los Alamos National Laboratory in 1987. The expression in silico was first used to characterize biological experiments carried out entirely in a computer in 1989, in the workshop "Cellular Automata: Theory and Applications" in Los Alamos, New Mexico, by Pedro Miramontes, a mathematician from National Autonomous University of Mexico (UNAM), presenting the report "DNA and RNA Physicochemical Constraints, Cellular Automata and Molecular Evolution". The work was later presented by Miramontes as his dissertation.
In silico has been used in white papers written to support the creation of bacterial genome programs by the Commission of the European Community. The first referenced paper where in silico appears was written by a French team in 1991. The first referenced book chapter where in silico appea
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https://en.wikipedia.org/wiki/Radiopharmacology
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Radiopharmacology is radiochemistry applied to medicine and thus the pharmacology of radiopharmaceuticals (medicinal radiocompounds, that is, pharmaceutical drugs that are radioactive). Radiopharmaceuticals are used in the field of nuclear medicine as radioactive tracers in medical imaging and in therapy for many diseases (for example, brachytherapy). Many radiopharmaceuticals use technetium-99m (Tc-99m) which has many useful properties as a gamma-emitting tracer nuclide. In the book Technetium a total of 31 different radiopharmaceuticals based on Tc-99m are listed for imaging and functional studies of the brain, myocardium, thyroid, lungs, liver, gallbladder, kidneys, skeleton, blood and tumors.
The term radioisotope, which in its general sense refers to any radioactive isotope (radionuclide), has historically been used to refer to all radiopharmaceuticals, and this usage remains common. Technically, however, many radiopharmaceuticals incorporate a radioactive tracer atom into a larger pharmaceutically-active molecule, which is localized in the body, after which the radionuclide tracer atom allows it to be easily detected with a gamma camera or similar gamma imaging device. An example is fludeoxyglucose in which fluorine-18 is incorporated into deoxyglucose. Some radioisotopes (for example gallium-67, gallium-68, and radioiodine) are used directly as soluble ionic salts, without further modification. This use relies on the chemical and biological properties of the radioisot
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https://en.wikipedia.org/wiki/DCDS
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DCDS may refer to:
Detroit Country Day School, a private school
DECHEMA Chemistry Data Series, a series of books with thermophysical data published by DECHEMA
Deputy Chief of the Defence Staff
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