source
stringlengths 31
207
| text
stringlengths 12
1.5k
|
|---|---|
https://en.wikipedia.org/wiki/Mathland
|
MathLand was one of several elementary mathematics curricula that were designed around the 1989 NCTM standards. It was developed and published by Creative Publications and was initially adopted by the U.S. state of California and schools run by the US Department of Defense by the mid 1990s. Unlike curricula such as Investigations in Numbers, Data, and Space, by 2007 Mathland was no longer offered by the publisher, and has since been dropped by many early adopters. Its demise may have been, at least in part, a result of intense scrutiny by critics (see below).
Adoption
Mathland was among the math curricula rated as "promising" by an Education Department panel, although subsequently 200 mathematicians and scientists, including four Nobel Prize recipients and two winners of the Fields Medal, published a letter in the Washington Post deploring the findings of that panel. MathLand was adopted in many California school districts as its material most closely fit the legal mandate of the 1992 California Framework. That framework has since been discredited and abandoned as misguided and replaced by a newer standard based on traditional mathematics. It bears noting that the process by which the framework was replaced itself came under serious scrutiny.
Concept
Mathland focuses on "attention to conceptual understanding, communication, reasoning and problem solving." Children meet in small groups and invent their own ways to add, subtract, multiply and divide, which spares young lear
|
https://en.wikipedia.org/wiki/Alec%20Soth
|
Alec Soth (born 1969) is an American photographer, based in Minneapolis. Soth makes "large-scale American projects" featuring the midwestern United States. New York Times art critic Hilarie M. Sheets wrote that he has made a "photographic career out of finding chemistry with strangers" and photographs "loners and dreamers". His work tends to focus on the "off-beat, hauntingly banal images of modern America" according to The Guardian art critic Hannah Booth. He is a member of Magnum Photos.
Soth has had various books of his work published by major publishers as well as self-published through his own Little Brown Mushroom. His major publications are Sleeping by the Mississippi, Niagara, Broken Manual, Songbook, I Know How Furiously Your Heart Is Beating, and A Pound of Pictures.
He has received fellowships from the McKnight and Jerome Foundations, was the recipient of the 2003 Santa Fe Prize for Photography, and in 2021 received an Honorary Fellowship of the Royal Photographic Society. His photographs are in the collections of the San Francisco Museum of Modern Art, the Museum of Fine Arts Houston, the Minneapolis Institute of Arts, and the Walker Art Center. His work has been exhibited widely including as part of the 2004 Whitney Biennial and a major solo exhibition at Media Space in London in 2015.
Early life and education
Soth was born in Minneapolis, Minnesota, United States. He studied at Sarah Lawrence College in Bronxville, New York. He was reported to be "painfully s
|
https://en.wikipedia.org/wiki/Hyman%20Bass
|
Hyman Bass (; born October 5, 1932) is an American mathematician, known for work in algebra and in mathematics education. From 1959 to 1998 he was Professor in the Mathematics Department at Columbia University. He is currently the Samuel Eilenberg Distinguished University Professor of Mathematics and Professor of Mathematics Education at the University of Michigan.
Life
Born to a Jewish family in Houston, Texas, he earned his B.A. in 1955 from Princeton University and his Ph.D. in 1959 from the University of Chicago. His thesis, titled Global dimensions of rings, was written under the supervision of Irving Kaplansky.
He has held visiting appointments at the Institute for Advanced Study in Princeton, New Jersey, Institut des Hautes Études Scientifiques and École Normale Supérieure (Paris), Tata Institute of Fundamental Research (Bombay), University of Cambridge, University of California, Berkeley, University of Rome, IMPA (Rio), National Autonomous University of Mexico, Mittag-Leffler Institute (Stockholm), and the University of Utah. He was president of the American Mathematical Society.
Bass formerly chaired the Mathematical Sciences Education Board (1992–2000) at the National Academy of Sciences, and the Committee on Education of the American Mathematical Society. He was the President of ICMI from 1999 to 2006. Since 1996 he has been collaborating with Deborah Ball and her research group at the University of Michigan on the mathematical knowledge and resources entailed
|
https://en.wikipedia.org/wiki/Inverse%20image%20functor
|
In mathematics, specifically in algebraic topology and algebraic geometry, an inverse image functor is a contravariant construction of sheaves; here “contravariant” in the sense given a map , the inverse image functor is a functor from the category of sheaves on Y to the category of sheaves on X. The direct image functor is the primary operation on sheaves, with the simplest definition. The inverse image exhibits some relatively subtle features.
Definition
Suppose we are given a sheaf on and that we want to transport to using a continuous map .
We will call the result the inverse image or pullback sheaf . If we try to imitate the direct image by setting
for each open set of , we immediately run into a problem: is not necessarily open. The best we could do is to approximate it by open sets, and even then we will get a presheaf and not a sheaf. Consequently, we define to be the sheaf associated to the presheaf:
(Here is an open subset of and the colimit runs over all open subsets of containing .)
For example, if is just the inclusion of a point of , then is just the stalk of at this point.
The restriction maps, as well as the functoriality of the inverse image follows from the universal property of direct limits.
When dealing with morphisms of locally ringed spaces, for example schemes in algebraic geometry, one often works with sheaves of -modules, where is the structure sheaf of . Then the functor is inappropriate, because in general it does no
|
https://en.wikipedia.org/wiki/Computer%20Music%20Journal
|
Computer Music Journal is a peer-reviewed academic journal that covers a wide range of topics related to digital audio signal processing and electroacoustic music. It is published on-line and in hard copy by MIT Press. The journal is accompanied by an annual CD/DVD that collects audio and video work by various electronic artists. Computer Music Journal was established in 1977. According to the Journal Citation Reports, the journal has a 2016 impact factor of 0.405.
References
External links
Journal page at publisher's website
Music journals
Academic journals established in 1977
MIT Press academic journals
Quarterly journals
English-language journals
|
https://en.wikipedia.org/wiki/Converse
|
Converse may refer to:
Mathematics and logic
Converse (logic), the result of reversing the two parts of a definite or implicational statement
Converse implication, the converse of a material implication
Converse nonimplication, a logical connective which is the negation of the converse implication
Converse (semantics), pairs of words that refer to a relationship from opposite points of view
Converse accident, a logical fallacy that can occur in a statistical syllogism when an exception to a generalization is wrongly excluded
Converse relation or inverse relation, in mathematics the relation that occurs when switching the order of the elements in a binary relation
Places in the United States
Converse, Blackford County, Indiana
Converse, Indiana
Converse, Louisiana
Converse, Missouri
Converse, South Carolina
Converse, Texas
Converse County, Wyoming
Converse Basin, a grove of giant sequoia trees located in the Sequoia National Forest in the Sierra Nevada in eastern California
Vessels
USS Converse (DD-291), U.S. Navy destroyer
USS Converse (DD-509), U.S. Navy destroyer
Other uses
Converse (surname), various people with the surname
Converse (lifestyle wear), an American shoe and clothing company
Converses or Chuck Taylor All-Stars, canvas and rubber shoes produced by the company
Converse College, a women's college in Spartanburg, South Carolina
Conversation, a form of communication between people following rules of etiquette
Converse technique, a standar
|
https://en.wikipedia.org/wiki/Haplogroup%20O-M119
|
In human genetics, Haplogroup O-M119 is a Y-chromosome DNA haplogroup. Haplogroup O-M119 is a descendant branch of haplogroup O-F265 also known as O1a, one of two extant primary subclades of Haplogroup O-M175. The same clade previously has been labeled as O-MSY2.2.
Origins
The Haplogroup O-M119 branch is believed to have evolved during the Late Pleistocene (Upper Paleolithic) in China mainland.
Paleolithic migrations
suggest haplogroup O-M119 was part of a four-phase colonization model in which Paleolithic migrations of hunter-gatherers shaped the primary structure of current Y-Chromosome diversity of Maritime Southeast Asia. Approximately 5000 BCE, Haplogroup O-M119 coalesced at Sundaland and migrated northwards to as far as Taiwan, where O-M50 constitutes some 90% of the Aboriginal Y-DNA, being the main haplogroup that can be directly linked to the Austronesian expansion in phase 3.
Taiwan homeland
concluded that in contrast to the Taiwan homeland hypothesis, Island Southeast Asians do not have a Taiwan origin based on their paternal lineages. According to their results, lineages within Maritime Southeast Asia did not originate from Taiwanese aborigines as linguistic studies suggest. Taiwan aborigines and Indonesians were likely to have been derived from the Tai–Kadai-speaking populations based on their paternal lineages, and thereafter evolved independently of each other.
The strongest positive correlation between Haplogroup O-M119 and ethno-linguistic affiliation i
|
https://en.wikipedia.org/wiki/Abel%27s%20test
|
In mathematics, Abel's test (also known as Abel's criterion) is a method of testing for the convergence of an infinite series. The test is named after mathematician Niels Henrik Abel. There are two slightly different versions of Abel's test – one is used with series of real numbers, and the other is used with power series in complex analysis. Abel's uniform convergence test is a criterion for the uniform convergence of a series of functions dependent on parameters.
Abel's test in real analysis
Suppose the following statements are true:
is a convergent series,
{bn} is a monotone sequence, and
{bn} is bounded.
Then is also convergent.
It is important to understand that this test is mainly pertinent and
useful in the context of non absolutely convergent series .
For absolutely convergent series, this theorem, albeit true, is almost self evident.
This theorem can be proved directly using summation by parts.
Abel's test in complex analysis
A closely related convergence test, also known as Abel's test, can often be used to establish the convergence of a power series on the boundary of its circle of convergence. Specifically, Abel's test states that if a sequence of positive real numbers is decreasing monotonically (or at least that for all n greater than some natural number m, we have ) with
then the power series
converges everywhere on the closed unit circle, except when z = 1. Abel's test cannot be applied when z = 1, so convergence at that single point must be
|
https://en.wikipedia.org/wiki/Jason%20Cong
|
Jingsheng Jason Cong (; born 1963 in Beijing) is a Chinese-born American computer scientist, educator, and serial entrepreneur. He received his B.S. degree in computer science from Peking University in 1985, his M.S. and Ph. D. degrees in computer science from the University of Illinois at Urbana-Champaign in 1987 and 1990, respectively. He has been on the faculty in the Computer Science Department at the University of California, Los Angeles (UCLA) since 1990. Currently, he is a Distinguished Chancellor’s Professor and the director of Center for Domain-Specific Computing (CDSC).
Research contributions and commercial impact
Cong made fundamental contributions to the FPGA synthesis technology. His result in the early 1990s on depth-optimal mapping (FlowMap) for lookup-table based FPGAs is a cornerstone of all FPGA logic synthesis tools used today. This, together with the subsequent works on the cut-enumeration and Boolean matching based methods for FPGA mapping, led to a successful startup company Aplus Design Technologies (1998-2003) founded by Cong. Aplus developed the first commercially available FPGA architecture evaluation tool and physical synthesis tool, which were OEMed by most FPGA companies and distributed to tens of thousands of FPGA designers worldwide. Aplus was acquired by Magma Design Automation in 2003, which is now part of Synopsys.
Cong’s research also made significant impact on high-level synthesis (HLS) for integrated circuits. The decade-long research i
|
https://en.wikipedia.org/wiki/Ar%C5%ABnas%20Matelis
|
Arūnas Matelis (born 9 April 1961, in Kaunas) is a Lithuanian documentary film director. From 1979 till 1983 Arūnas Matelis studied Mathematics at Vilnius University and later in 1989 graduated from the Lithuanian Music Academy. In 1992, he established one of the first independent film production companies in Lithuania, "Nominum". In 2006 Matelis became a full member of European Film Academy with the right to vote.
Filmography
Pelesos milžinai (1989)
Baltijos kelias (1989)
Dešimt minučių prieš Ikaro skrydį (1991)
Autoportretas (1993)
Iš dar nebaigtų Jeruzalės pasakų (1996)
Pirmasis atsisveikinimas su Rojum (1998)
Priverstinės emigracijos dienoraštis (1999)
Skrydis per Lietuvą arba 510 sekundžių tylos (Flight over Lithuania or 510 seconds of silence) (2000)
Sekmadienis. Evangelija pagal liftininką Albertą (2003)
Prieš parskrendant į žemę (Before Flying Back to Earth) (2005)
Wonderful Losers: A Different World (2017)
Awards
Matelis is one of the recipients of the Lithuanian National Prize of 2005.
"Prieš parskrendant į žemę", the first feature-length documentary by Matelis about children hospitalized with leukemia, is the most highly acclaimed Lithuanian film and is considered one of the best European documentary films of 2005, awarded in numerous festivals:
Best documentary in Directors Guild of America Awards 2006
Best Lithuanian Film 2005 by Lithuanian Filmmakers Union
Silver Wolf in International Documentary Film Festival Amsterdam (IDFA), 2005
Golden Dove in Inte
|
https://en.wikipedia.org/wiki/Dielectric%20loss
|
In electrical engineering, dielectric loss quantifies a dielectric material's inherent dissipation of electromagnetic energy (e.g. heat). It can be parameterized in terms of either the loss angle or the corresponding loss tangent . Both refer to the phasor in the complex plane whose real and imaginary parts are the resistive (lossy) component of an electromagnetic field and its reactive (lossless) counterpart.
Electromagnetic field perspective
For time-varying electromagnetic fields, the electromagnetic energy is typically viewed as waves propagating either through free space, in a transmission line, in a microstrip line, or through a waveguide. Dielectrics are often used in all of these environments to mechanically support electrical conductors and keep them at a fixed separation, or to provide a barrier between different gas pressures yet still transmit electromagnetic power. Maxwell’s equations are solved for the electric and magnetic field components of the propagating waves that satisfy the boundary conditions of the specific environment's geometry. In such electromagnetic analyses, the parameters permittivity , permeability , and conductivity represent the properties of the media through which the waves propagate. The permittivity can have real and imaginary components (the latter excluding effects, see below) such that
If we assume that we have a wave function such that
then Maxwell's curl equation for the magnetic field can be written as:
where is the i
|
https://en.wikipedia.org/wiki/National%20Robotics%20Competition%20%28Singapore%29
|
National Robotics Competition (NRC) is a robotics competition jointly organised by Singapore Science Centre and Duck Learning Education, with support from the Ministry of Education and the Agency for Science, Technology and Research. It aims to help nurture a new generation of youths with interest in Science, Technology, Engineering and Mathematics (STEM) to aspire in improving the lives of people, and encourages students to develop problem solving skills, entrepreneurial skills, creative thinking skills and team spirit.
History
National Robotics Competition was first organised in 1999 as National Junior Robotics Competition (NJRC) with 167 teams from 70 schools. In the competition, teams of not more than 5 students build a robot using the Lego Mindstorms robotics system. Competitors are divided into three categories: Upper Primary Division, for Primary 3 to Primary 6 students, Secondary Division for secondary or equivalent level, and Tertiary Division, for 1st and 2nd year ITE/JC/Poly students. In 2007, 13 schools participated in the competition, sending a total of 37 teams.
In 2016, a holistic review is made to the competition following an announcement during the closing ceremony of the competition that year. NJRC was officially renamed as National Robotics Competition (NRC) in 2017. An additional category for children aged six to eight years is added, along with other new elements such as the robotic arm hackathon.
National Junior Robotics Competition Milestones
2022
|
https://en.wikipedia.org/wiki/Agroinfiltration
|
Agroinfiltration is a method used in plant biology and especially lately in plant biotechnology to induce transient expression of genes in a plant, or isolated leaves from a plant, or even in cultures of plant cells, in order to produce a desired protein. In the method, a suspension of Agrobacterium tumefaciens is introduced into a plant leaf by direct injection or by vacuum infiltration, or brought into association with plant cells immobilised on a porous support (plant cell packs), whereafter the bacteria transfer the desired gene into the plant cells via transfer of T-DNA. The main benefit of agroinfiltration when compared to the more traditional plant transformation is speed and convenience, although yields of the recombinant protein are generally also higher and more consistent.
The first step is to introduce a gene of interest to a strain of Agrobacterium tumefaciens. Subsequently, the strain is grown in a liquid culture and the resulting bacteria are washed and suspended into a suitable buffer solution. For injection, this solution is then placed in a syringe (without a needle). The tip of the syringe is pressed against the underside of a leaf while simultaneously applying gentle counterpressure to the other side of the leaf. The Agrobacterium suspension is then injected into the airspaces inside the leaf through stomata, or sometimes through a tiny incision made to the underside of the leaf.
Vacuum infiltration is another way to introduce Agrobacterium deep into pla
|
https://en.wikipedia.org/wiki/ELETTRA
|
Elettra Sincrotrone Trieste is an international research center located in Basovizza on the outskirts of Trieste, Italy.
Elettra – Sincrotrone Trieste S.C.p.A. is a multidisciplinary international research center, specialized in generating high quality synchrotron and free-electron laser light and applying it in materials science. Its mission is to promote cultural, social and economic growth through:
Basic and applied research
Technical and scientific training
Transfer of technology and know-how
The main assets of the research centre are two advanced light sources: the Elettra synchrotron (third generation electron storage ring, working at 2 and 2.4 GeV, in operation since October 1993) and the free-electron laser (FEL) FERMI, continuously (H24) operated supplying light of the selected energy and quality to more than 30 experimental stations on 28 beamlines. Since 1993, Elettra has been subjected to several updated that have allowed a top up operating mode from 2010 for both 2 and 2.4 GeV operational energy. The accumulation ring is formed by twelve groups of magnets forming a ring of 260 m in circumference. The ring beam current at 2 GeV is normally set to 310 mA and the top-up operational mode foresees a new ring injection every 6 min: 1 mA electron in 4 seconds is injected, keeping the ring current constant in the range of 3‰. At 2.4 GeV the beam current is set to 140 mA, and the top-up injections occurs every 20 minutes: in this case, 1 mA electron in 4 s is
|
https://en.wikipedia.org/wiki/Aaron%20Sloman
|
Aaron Sloman is a philosopher and researcher on artificial intelligence and cognitive science. He held the Chair in Artificial Intelligence and Cognitive Science at the School of Computer Science at the University of Birmingham, and before that a chair with the same title at the University of Sussex. Since retiring he is Honorary Professor of Artificial Intelligence and Cognitive Science at Birmingham. He has published widely on philosophy of mathematics, epistemology, cognitive science, and artificial intelligence; he also collaborated widely, e.g. with biologist Jackie Chappell on the evolution of intelligence.
Early life and education
Sloman was born in 1936, in the town of Que Que (now called Kwe Kwe), in what was then Southern Rhodesia (now Zimbabwe). His parents were Lithuanian Jews who emigrated to Southern Rhodesia around the turn of the century. Sloman describes himself as an atheist. He went to school in Cape Town between 1948 and 1953, then earned a degree in Mathematics and Physics at the University of Cape Town in 1956, after which a Rhodes Scholarship (from South African College School) took him to the University of Oxford (first Balliol College, and then St Antony's College). In Oxford, he became interested in philosophy after a brief period studying mathematical logic supervised by Hao Wang, eventually writing a DPhil in philosophy, defending the ideas of Immanuel Kant about the nature of mathematical knowledge as non-empirical and non-analytic ('Knowing and
|
https://en.wikipedia.org/wiki/Zappa%E2%80%93Sz%C3%A9p%20product
|
In mathematics, especially group theory, the Zappa–Szép product (also known as the Zappa–Rédei–Szép product, general product, knit product, exact factorization or bicrossed product) describes a way in which a group can be constructed from two subgroups. It is a generalization of the direct and semidirect products. It is named after Guido Zappa (1940) and Jenő Szép (1950) although it was independently studied by others including B.H. Neumann (1935), G.A. Miller (1935), and J.A. de Séguier (1904).
Internal Zappa–Szép products
Let G be a group with identity element e, and let H and K be subgroups of G. The following statements are equivalent:
G = HK and H ∩ K = {e}
For each g in G, there exists a unique h in H and a unique k in K such that g = hk.
If either (and hence both) of these statements hold, then G is said to be an internal Zappa–Szép product of H and K.
Examples
Let G = GL(n,C), the general linear group of invertible n × n matrices over the complex numbers. For each matrix A in G, the QR decomposition asserts that there exists a unique unitary matrix Q and a unique upper triangular matrix R with positive real entries on the main diagonal such that A = QR. Thus G is a Zappa–Szép product of the unitary group U(n) and the group (say) K of upper triangular matrices with positive diagonal entries.
One of the most important examples of this is Philip Hall's 1937 theorem on the existence of Sylow systems for soluble groups. This shows that every soluble group is a
|
https://en.wikipedia.org/wiki/Claire%20J.%20Tomlin
|
Claire Jennifer Tomlin (born 1969 Southampton, England) is a British researcher in hybrid systems, distributed and decentralized optimization and control theory and holds the Charles A. Desoer Chair at the University of California, at Berkeley.
Career
She graduated from the University of Waterloo with a B.A.Sc. in electrical engineering in 1992, from Imperial College London with a M.Sc. in electrical engineering in 1993, and from the University of California, Berkeley with a PhD in electrical engineering and computer sciences in 1998. She held the positions of assistant, associate, and full professor at the Department of Aeronautics and Astronautics and the Department of Electrical Engineering at Stanford University from 1998-2007, where she was a director of the Hybrid Systems Laboratory. She currently holds the Charles A. Desoer Chair in Engineering at UC Berkeley.
Prof. Tomlin's research focuses on applications, unmanned aerial vehicles, air traffic control and modeling of biological processes. She was named a MacArthur Fellow in September 2006.
Honours
She received the Erlander Professorship of the Swedish Research Council in 2009, a MacArthur Fellowship in 2006, and the Eckman Award of the American Automatic Control Council in 2003. In 2003, she was named to the MIT Technology Review TR100 as one of the top 100 innovators in the world under the age of 35.
She became a Fellow of the IEEE in 2010. She was awarded the IEEE Transportation Technologies Award in 2017 "fo
|
https://en.wikipedia.org/wiki/Henry%20H.%20Bauer
|
Henry Hermann Bauer (born November 16, 1931) is an emeritus professor of chemistry and science studies at Virginia Polytechnic Institute and State University (Virginia Tech). He is the author of several books and articles on fringe science, arguing in favor of the existence of the Loch Ness Monster and against Immanuel Velikovsky, and is an AIDS denialist. Following his retirement in 1999, he was editor-in-chief of the Journal of Scientific Exploration, a fringe science publication. Bauer also served as dean of the College of Arts and Sciences at Virginia Tech, generating controversy by criticising affirmative action.
Life and work
Henry Bauer was born in Austria. As the Nazis came to power in German-speaking Europe, Bauer and his family emigrated to Australia. He attended Sydney Boys High School from 1943 to 1944. Bauer received his Ph.D. from the University of Sydney in Australia in 1956. He conducted post-doctoral research at the University of Michigan, then taught at Sydney and in Michigan. In 1966, he moved to a faculty position at the University of Kentucky. Bauer became dean of the School of Arts and Sciences at Virginia Polytechnic Institute and State University (Virginia Tech) in 1978, a position he held until 1986. Bauer was a professor of science studies and chemistry at Virginia Tech until his retirement in 1999. Bauer has had short-term teaching assignments at the University of Southampton and with a program of the Japan Society for the Promotion of Science: at
|
https://en.wikipedia.org/wiki/Gysin%20homomorphism
|
In the field of mathematics known as algebraic topology, the Gysin sequence is a long exact sequence which relates the cohomology classes of the base space, the fiber and the total space of a sphere bundle. The Gysin sequence is a useful tool for calculating the cohomology rings given the Euler class of the sphere bundle and vice versa. It was introduced by , and is generalized by the Serre spectral sequence.
Definition
Consider a fiber-oriented sphere bundle with total space E, base space M, fiber Sk and projection map
:
Any such bundle defines a degree k + 1 cohomology class e called the Euler class of the bundle.
De Rham cohomology
Discussion of the sequence is clearest with de Rham cohomology. There cohomology classes are represented by differential forms, so that e can be represented by a (k + 1)-form.
The projection map induces a map in cohomology called its pullback
In the case of a fiber bundle, one can also define a pushforward map
which acts by fiberwise integration of differential forms on the oriented sphere – note that this map goes "the wrong way": it is a covariant map between objects associated with a contravariant functor.
Gysin proved that the following is a long exact sequence
where is the wedge product of a differential form with the Euler class e.
Integral cohomology
The Gysin sequence is a long exact sequence not only for the de Rham cohomology of differential forms, but also for cohomology with integral coefficients. In the integral cas
|
https://en.wikipedia.org/wiki/John%20Ockendon
|
Professor John Richard Ockendon FRS (born c. 1940) is an applied mathematician noted especially for his contribution to fluid dynamics and novel applications of mathematics to real world problems. He is a professor at the University of Oxford and an Emeritus Fellow at St Catherine's College, Oxford, the first director of the Oxford Centre for Collaborative Applied Mathematics (OCCAM) and a former director of the Smith Institute for Industrial Mathematics and System Engineering.
Education
Ockendon was educated at the University of Oxford where he was awarded a Doctor of Philosophy degree in 1965 for research on fluid dynamics supervised by Alan B Tayler.
Research and career
His initial fluid mechanics interests included hypersonic aerodynamics, creeping flow, sloshing and channel flows and leading to flows in porous media, ship hydrodynamics and models for flow separation.
He moved on to free and moving boundary problems. He pioneered the study of diffusion-controlled moving boundary problems in the 1970s his involvement centring on models for phase changes and elastic contact problems all built around the paradigm of the Hele-Shaw free boundary problem. Other industrial collaboration has led to new ideas for lens design, fibre manufacture, extensional and surface-tension- driven flows and glass manufacture, fluidised-bed models, semiconductor device modelling and a range of other problems in mechanics and heat and mass transfer, especially scattering and ray theory, non
|
https://en.wikipedia.org/wiki/Structure%20tensor
|
In mathematics, the structure tensor, also referred to as the second-moment matrix, is a matrix derived from the gradient of a function. It describes the distribution of the gradient in a specified neighborhood around a point and makes the information invariant respect the observing coordinates. The structure tensor is often used in image processing and computer vision.
The 2D structure tensor
Continuous version
For a function of two variables , the structure tensor is the 2×2 matrix
where and are the partial derivatives of with respect to x and y; the integrals range over the plane ; and w is some fixed "window function" (such as a Gaussian blur), a distribution on two variables. Note that the matrix is itself a function of .
The formula above can be written also as , where is the matrix-valued function defined by
If the gradient of is viewed as a 2×1 (single-column) matrix, where denotes transpose operation, turning a row vector to a column vector, the matrix can be written as the matrix product or tensor or outer product . Note however that the structure tensor cannot be factored in this way in general except if is a Dirac delta function.
Discrete version
In image processing and other similar applications, the function is usually given as a discrete array of samples , where p is a pair of integer indices. The 2D structure tensor at a given pixel is usually taken to be the discrete sum
Here the summation index r ranges over a finite set of index pairs (
|
https://en.wikipedia.org/wiki/Egea
|
Egea or EGEA may refer to:
Biology
Egea inermis, a species of glass squid
Liarea egea, a species of land snail
Polygonia egea, a species of butterfly
Egea, a synonym of the moth genus Phyllometra
Other
European Geography Association, a European network of geography students and young geographers
Expert Group on Emergency Access, an expert group assisting in 112 emergency number access
Fiat Egea, a vehicle produced by Fiat for the Turkish market
Teodoro García Egea, Spanish politician
See also
Ejea
|
https://en.wikipedia.org/wiki/Dorothy%20Lewis%20Bernstein
|
Dorothy Lewis Bernstein (April 11, 1914 – February 5, 1988) was an American mathematician known for her work in applied mathematics, statistics, computer programming, and her research on the Laplace transform. She was the first woman to be elected president of the Mathematics Association of America.
Early life
Bernstein was born in Chicago, the daughter of Jewish Russian immigrants Jacob and Tille Lewis Bernstein. While her parents had no formal education, they encouraged all of their children to seek education; all five earned either a PhD or MD.
Education
Bernstein attended North Division High School (Milwaukee) in Milwaukee, Wisconsin. In 1930 she attended the University of Wisconsin, where she held a University Scholarship (1933–1934) and was elected to Phi Beta Kappa. In 1934 she graduated with both a B.A degree, summa cum laude, and a M.A. Degree in Mathematics. She did her master's thesis research on finding complex roots of polynomials by an extension of Newton's method. In 1935 she attended Brown University, where she became a member of the scientific society Sigma Xi. She received her Ph.D. in mathematics from Brown in 1939, while simultaneously holding a teaching position at Mount Holyoke College. Her dissertation was entitled "The Double Laplace Integral" and was published in the Duke Mathematical Journal.
Career
From 1943 to 1959 Bernstein taught at the University of Rochester, where she worked on existence theorems for partial differential equations.
|
https://en.wikipedia.org/wiki/Quantum%20vortex
|
In physics, a quantum vortex represents a quantized flux circulation of some physical quantity. In most cases, quantum vortices are a type of topological defect exhibited in superfluids and superconductors. The existence of quantum vortices was first predicted by Lars Onsager in 1949 in connection with superfluid helium. Onsager reasoned that quantisation of vorticity is a direct consequence of the existence of a superfluid order parameter as a spatially continuous wavefunction. Onsager also pointed out that quantum vortices describe the circulation of superfluid and conjectured that their excitations are responsible for superfluid phase transitions. These ideas of Onsager were further developed by Richard Feynman in 1955 and in 1957 were applied to describe the magnetic phase diagram of type-II superconductors by Alexei Alexeyevich Abrikosov. In 1935 Fritz London published a very closely related work on magnetic flux quantization in superconductors. London's fluxoid can also be viewed as a quantum vortex.
Quantum vortices are observed experimentally in type-II superconductors (the Abrikosov vortex), liquid helium, and atomic gases (see Bose–Einstein condensate), as well as in photon fields (optical vortex) and exciton-polariton superfluids.
In a superfluid, a quantum vortex "carries" quantized orbital angular momentum, thus allowing the superfluid to rotate; in a superconductor, the vortex carries quantized magnetic flux.
The term "quantum vortex" is also used in the stud
|
https://en.wikipedia.org/wiki/Donald%20Carpenter
|
Donald Carpenter may refer to:
Donald M. Carpenter (1894–1940), United States Navy naval aviator
Donald F. Carpenter (1899–1985), American businessman
Donald Carpenter (singer), singer with Submersed
Don Carpenter (electrical engineer), professor of electrical engineering at Stanford University
See also
Don Carpenter (1931–1995), American writer
|
https://en.wikipedia.org/wiki/Newman%20Taylor%20Baker
|
Newman Taylor Baker (born February 4, 1943) is a jazz drummer and a washboard player.
Early life
Newman Taylor Baker's paternal grandfather, Thomas Nelson Baker Sr., was the only former slave to receive a PhD from Yale University (1906). His father (chemistry) and siblings graduated from Oberlin College and Conservatory. Edith Baker (voice and piano), Ruth B. Baker (voice and piano), and Harry B. Baker (piano and organ), his aunts and uncle, were graduates of Oberlin Conservatory of Music. His maternal grandfather, Reverend Newman D. Taylor, known as the "Roland Hayes" of Mississippi, gave vocal recitals throughout the state and his uncle, Newman C. Taylor, accompanied him on piano. His aunt, India Taylor Johnson (a classmate of Dr. Billy Taylor at Virginia State University), was a vocal music and piano teacher in the Norfolk, VA public school system.
His parents were Ruth Taylor Baker, born Yazoo City, Mississippi, and Dr. T. Nelson Baker, Jr, born Pittsfield, Massachusetts. Newman's mother was an associate professor of English, and his father was head of the chemistry department. He sang bass in the a cappella choir and played oboe in the concert band and the symphony orchestra. His parents played four-hand transcriptions of Brahms and Beethoven symphonies at home. They lived on the campus in faculty housing. Newman's brother, Dr. T. Nelson Baker, III, was Newman's source for recordings of Max Roach and Clifford Brown, Horace Silver, Miles Davis, Cannonball Adderley, Ella
|
https://en.wikipedia.org/wiki/Robotix%20%28disambiguation%29
|
Robotix may refer to:
Events
Robotix (competition), a robotics competition organized by the students of IIT Kharagpur
Merchandise
Robotix (toyline)
TV
Robotix, 1986 cartoon produced by Sunbow & Marvel Productions
See also
Robotics, a branch of engineering and science
|
https://en.wikipedia.org/wiki/Ninewells%20Hospital
|
Ninewells Hospital is a large teaching hospital, based on the western edge of Dundee, Scotland. It is internationally renowned for introducing laparoscopic surgery to the UK as well as being a leading centre in developing fields such as the management of cancer, medical genetics and robotic surgery. Within the UK, it is also a major NHS facility for psychosurgery. The medical school was ranked first in the UK in 2009. The hospital has nursing and research links with the University of Dundee and is managed by NHS Tayside.
History
The proposal for the new hospital was put forward in May 1960 and final permission was accepted by Parliament in February 1962. The first phase of the project was due to take six years at a cost of £9 million. Designed by Robert Matthew Johnson-Marshall and partners, the protracted construction began in August 1964. The hospital was initially designed to hold 800 beds, and the ward units were planned on the 'race track' principle. The foundation stone was laid on 9 September 1965, by Lord Hughes. The infirmary was built onto the side of a hill and the practicalities of the design were influenced by airport check in. Phase I of the building was completed in 1973, although some sections were not finished until 1975. The final cost was estimated as £25 million. Hospital admittances started on 31 January 1974 and the hospital was officially opened by the Queen Elizabeth The Queen Mother on 23 October 1974. At the opening ceremony, she stated "nothing tha
|
https://en.wikipedia.org/wiki/Conceptual%20model%20%28computer%20science%29
|
In computer science, a conceptual model, or domain model, represents concepts (entities) and relationships between them.
Overview
In the field of computer science a conceptual model aims to express the meaning of terms and concepts used by domain experts to discuss the problem, and to find the correct relationships between different concepts. The conceptual model is explicitly chosen to be independent of design or implementation concerns, for example, concurrency or data storage. Conceptual modeling in computer science should not be confused with other modeling disciplines within the broader field of conceptual models such as data modelling, logical modelling and physical modelling.
The conceptual model attempts to clarify the meaning of various, usually ambiguous terms, and ensure that confusion caused by different interpretations of the terms and concepts cannot occur. Such differing interpretations could easily cause confusion amongst stakeholders, especially those responsible for designing and implementing a solution, where the conceptual model provides a key artifact of business understanding and clarity. Once the domain concepts have been modeled, the model becomes a stable basis for subsequent development of applications in the domain. The concepts of the conceptual model can be mapped into physical design or implementation constructs using either manual or automated code generation approaches. The realization of conceptual models of many domains can be combined to a
|
https://en.wikipedia.org/wiki/Dean%20Evenson
|
Dean Evenson is a new-age musician, composer, producer and videographer. His hometown is Staten Island, New York. He has a master's degree in Molecular Biology. He worked in Manhattan as a recording engineer for Regent Sound with many Atlantic recording artists including Eric Clapton, Mose Allison, Roberta Flack. Dean plays several instruments including the Western concert flute, Native American flute, synthesizer, and keyboards. In the New Age genre, his music is generally sounds of nature combined with flute melodies and other instruments for ambient and meditative purposes. His music is often used for massage, meditation, yoga and relaxation.
In 1970, he and his wife Dudley Evenson became involved in the portable-video movement. They worked under grants from the New York State Council on the Arts with Raindance Foundation and helped publish a magazine called Radical Software. During the '70s, the Evensons traveled the country in a half-sized converted school bus documenting the emerging new age consciousness. They produced hundreds of hours of half-inch black and white video. They continue to produce videos and are in the process of archiving their extensive collection of early videos and high resolution videos, many of which can be viewed on their Soundings of the Planet YouTube Channel.
In 1979, Dean and Dudley Evenson founded the independent record company Soundings of the Planet in Tucson, Arizona. Over the years he has collaborated with many world class artists as a
|
https://en.wikipedia.org/wiki/Shared%20secret
|
In cryptography, a shared secret is a piece of data, known only to the parties involved, in a secure communication. This usually refers to the key of a symmetric cryptosystem. The shared secret can be a password, a passphrase, a big number, or an array of randomly chosen bytes.
The shared secret is either shared beforehand between the communicating parties, in which case it can also be called a pre-shared key, or it is created at the start of the communication session by using a key-agreement protocol, for instance using public-key cryptography such as Diffie–Hellman or using symmetric-key cryptography such as Kerberos.
The shared secret can be used for authentication (for instance when logging into a remote system) using methods such as challenge–response or it can be fed to a key derivation function to produce one or more keys to use for encryption and/or MACing of messages.
To make unique session and message keys the shared secret is usually combined with an initialization vector (IV). An example of this is the derived unique key per transaction method.
It is also often used as an authentication measure in web APIs.
See also
Key stretching – a method to create a stronger key from a weak key or a weak shared secret
Security question – implementation method
References
Handbook of Applied Cryptography by Menezes, van Oorschot and Vanstone (2001), chapter 10 and 12.
Key management
|
https://en.wikipedia.org/wiki/Andrei%20Suslin
|
Andrei Suslin (, sometimes transliterated Souslin) was a Russian mathematician who contributed to algebraic K-theory and its connections with algebraic geometry. He was a Trustee Chair and Professor of mathematics at Northwestern University.
He was born on 27 December 1950 in St. Petersburg, Russia. As a youth, he was an "all Leningrad" gymnast. He received his PhD from Leningrad University in 1974; his thesis was titled Projective modules over polynomial rings.
In 1976 he and Daniel Quillen independently proved Serre's conjecture about the triviality of algebraic vector bundles on affine space.
In 1982 he and Alexander Merkurjev proved the Merkurjev–Suslin theorem on the norm residue homomorphism in Milnor K2-theory, with applications to the Brauer group.
Suslin was an invited speaker at the International Congress of Mathematicians in 1978 and 1994, and he gave a plenary invited address at the Congress in 1986. He was awarded the Frank Nelson Cole Prize in Algebra in 2000 by the American Mathematical Society for his work on motivic cohomology.
In 2010 special issues of Journal of K-theory
and of Documenta Mathematica
have been published in honour of his 60th birthday.
He died on 10 July 2018.
References
External links
Anfrei Suslin, faculty profile, Department of Mathematics, Northwestern University
1950 births
2018 deaths
Northwestern University faculty
20th-century Russian mathematicians
21st-century Russian mathematicians
Algebraic geometers
Institute for
|
https://en.wikipedia.org/wiki/Augmented%20cognition
|
Augmented cognition is an interdisciplinary area of psychology and engineering, attracting researchers from the more traditional fields of human-computer interaction, psychology, ergonomics and neuroscience. Augmented cognition research generally focuses on tasks and environments where human–computer interaction and interfaces already exist. Developers, leveraging the tools and findings of neuroscience, aim to develop applications which capture the human user's cognitive state in order to drive real-time computer systems. In doing so, these systems are able to provide operational data specifically targeted for the user in a given context. Three major areas of research in the field are: Cognitive State Assessment (CSA), Mitigation Strategies (MS), and Robust Controllers (RC). A subfield of the science, Augmented Social Cognition, endeavours to enhance the "ability of a group of people to remember, think, and reason."
History
In 1962 Douglas C. Engelbart released the report "Augmenting Human Intellect: A Conceptual Framework" which introduced, and laid the groundwork for, augmented cognition. In this paper, Engelbart defines "augmenting human intellect" as "increasing the capability of a man to approach a complex problem situation, to gain comprehension to suit his particular needs, and to derive solutions to problems."
Modern augmented cognition began to emerge in the early 2000s. Advances in cognitive, behavioral, and neurological sciences during the 1990s set the stage fo
|
https://en.wikipedia.org/wiki/Ball-and-stick%20model
|
In chemistry, the ball-and-stick model is a molecular model of a chemical substance which displays both the three-dimensional position of the atoms and the bonds between them. The atoms are typically represented by spheres, connected by rods which represent the bonds. Double and triple bonds are usually represented by two or three curved rods, respectively, or alternately by correctly positioned sticks for the sigma and pi bonds. In a good model, the angles between the rods should be the same as the angles between the bonds, and the distances between the centers of the spheres should be proportional to the distances between the corresponding atomic nuclei. The chemical element of each atom is often indicated by the sphere's color.
In a ball-and-stick model, the radius of the spheres is usually much smaller than the rod lengths, in order to provide a clearer view of the atoms and bonds throughout the model. As a consequence, the model does not provide a clear insight about the space occupied by the model. In this aspect, ball-and-stick models are distinct from space-filling (calotte) models, where the sphere radii are proportional to the Van der Waals atomic radii in the same scale as the atom distances, and therefore show the occupied space but not the bonds.
Ball-and-stick models can be physical artifacts or virtual computer models. The former are usually built from molecular modeling kits, consisting of a number of coil springs or plastic or wood sticks, and a number of
|
https://en.wikipedia.org/wiki/Feige%E2%80%93Fiat%E2%80%93Shamir%20identification%20scheme
|
In cryptography, the Feige–Fiat–Shamir identification scheme is a type of parallel zero-knowledge proof developed by Uriel Feige, Amos Fiat, and Adi Shamir in 1988. Like all zero-knowledge proofs, it allows one party, the Prover, to prove to another party, the Verifier, that they possess secret information without revealing to Verifier what that secret information is. The Feige–Fiat–Shamir identification scheme, however, uses modular arithmetic and a parallel verification process that limits the number of communications between Prover and Verifier.
Setup
Following a common convention, call the prover Peggy and the verifier Victor.
Choose two large prime integers p and q and compute the product n = pq. Create secret numbers coprime to n. Compute . Peggy and Victor both receive while and are kept secret. Peggy is then sent the numbers . These are her secret login numbers. Victor is sent the numbers by Peggy when she wishes to identify herself to Victor. Victor is unable to recover Peggy's numbers from his numbers due to the difficulty in determining a modular square root when the modulus' factorization is unknown.
Procedure
Peggy chooses a random integer , a random sign and computes . Peggy sends to Victor.
Victor chooses numbers where equals 0 or 1. Victor sends these numbers to Peggy.
Peggy computes . Peggy sends this number to Victor.
Victor checks that and that
This procedure is repeated with different and values until Victor is satisfied that Pegg
|
https://en.wikipedia.org/wiki/Academy%20for%20Technology%20and%20Academics
|
The Academy for Technology and Academics or ATA (formerly known as The Career Center) is a branch school of the Horry County Schools in Horry County, South Carolina, United States. The school's curriculum includes automotive technology, building construction, business management and administration, computer science, cosmetology, culinary arts, education, and health science technology. The school also has a Connect program for high school freshmen and sophomores who are over the age of 18.
Public high schools in South Carolina
Schools in Horry County, South Carolina
Buildings and structures in Conway, South Carolina
|
https://en.wikipedia.org/wiki/Electrical%20engineering%20technology
|
Electrical/Electronics engineering technology (EET) is an engineering technology field that implements and applies the principles of electrical engineering. Like electrical engineering, EET deals with the "design, application, installation, manufacturing, operation or maintenance of electrical/electronic(s) systems." However, EET is a specialized discipline that has more focus on application, theory, and applied design, and implementation, while electrical engineering may focus more of a generalized emphasis on theory and conceptual design. Electrical/Electronic engineering technology is the largest branch of engineering technology and includes a diverse range of sub-disciplines, such as applied design, electronics, embedded systems, control systems, instrumentation, telecommunications, and power systems.
Education
Accreditation
The Accreditation Board for Engineering and Technology (ABET) is the recognized organization for accrediting both undergraduate engineering and engineering technology programs in the United States.
Coursework
EET curricula can vary widely by institution type, degree type, program objective, and expected student outcome. Each year after, however, ABET publishes a set of minimum criteria that a given EET program (either associate degree or bachelor's degree) must meet in order to maintain its ABET accreditation. These criteria may be classified as either general criteria, which apply to all ABET accredited programs, or as program criteria, which appl
|
https://en.wikipedia.org/wiki/Henry%20Tamburin
|
Henry Tamburin (born 1944) is a gambling author with a background in mathematics and a doctorate in chemistry. He is best known for his book Blackjack: Take the Money and Run which explains basic blackjack strategy, managing a bankroll, side bets and advanced tactics like card counting.
Tamburin is also well known for his prowess as a blackjack player and frequently teaches courses in blackjack across the United States. He has published 700 articles on various casino games from craps to video poker in publications like The Gambler Magazine, Gaming South Magazine, Strictly Slots and Casino Player Magazine. Henry Tamburin never considered himself to be a real blackjack expert though all critics ascribe such a status to him. He had been working as a manager of chemical company (an international one) for 30 years and always loved his work; after being retired he began to devote more time to the game of blackjack and became interested in video poker too.
Tamburin also appeared in a televised blackjack tournament entitled the Ultimate Blackjack Tour, which aired on CBS. He is currently editor and publisher of the Blackjack Insider Newsletter and runs his own website called Smart Gaming.
References
External links
Official site
American blackjack players
American gambling writers
American male non-fiction writers
Living people
1944 births
|
https://en.wikipedia.org/wiki/Hall%27s%20conjecture
|
In mathematics, Hall's conjecture is an open question, , on the differences between perfect squares and perfect cubes. It asserts that a perfect square y2 and a perfect cube x3 that are not equal must lie a substantial distance apart. This question arose from consideration of the Mordell equation in the theory of integer points on elliptic curves.
The original version of Hall's conjecture, formulated by Marshall Hall, Jr. in 1970, says that there is a positive constant C such that for any integers x and y for which y2 ≠ x3,
Hall suggested that perhaps C could be taken as 1/5, which was consistent with all the data known at the time the conjecture was proposed. Danilov showed in 1982 that the exponent 1/2 on the right side (that is, the use of |x|1/2) cannot be replaced by any higher power: for no δ > 0 is there a constant C such that |y2 - x3| > C|x|1/2 + δ whenever y2 ≠ x3.
In 1965, Davenport proved an analogue of the above conjecture in the case of polynomials:
if f(t) and g(t) are nonzero polynomials over C such that
g(t)3 ≠ f(t)2 in C[t], then
The weak form of Hall's conjecture, stated by Stark and Trotter around 1980, replaces the square root on the right side of the inequality by any exponent less than 1/2: for any ε > 0, there is some constant c(ε) depending on ε such that for any integers x and y for which y2 ≠ x3,
The original, strong, form of the conjecture with exponent 1/2 has never been disproved, although it is no longer believed to be true and the term H
|
https://en.wikipedia.org/wiki/Index%20of%20robotics%20articles
|
Robotics is the branch of technology that deals with the design, construction, operation, structural disposition, manufacture and application of robots. Robotics is related to the sciences of electronics, engineering, mechanics, and software. The word "robot" was introduced to the public by Czech writer Karel Čapek in his play R.U.R. (Rossum's Universal Robots), published in 1920. The term "robotics" was coined by Isaac Asimov in his 1941 science fiction short-story "Liar!"
Articles related to robotics include:
0–9
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
References
External links
Robotics
Robotics
|
https://en.wikipedia.org/wiki/List%20of%20volcanoes%20in%20Ecuador
|
This is a list of active and extinct volcanoes in Ecuador.
In Ecuador, EPN monitors the volcanic activity in this Andean nation.
Mainland
Galápagos Islands
References
Volcano page, Institut for Geophysics, Ecuador (Spanish)
Specific
Volcanoes
Ecuador
.
|
https://en.wikipedia.org/wiki/James%20MacPherson%20%28actor%29
|
James MacPherson (born 18 March 1960) is a Scottish actor, best known for his role as Detective Chief Inspector Michael Jardine in the STV drama, Taggart.
Early life
MacPherson was raised in South Lanarkshire. He left Hamilton Grammar School at 17 and got a job as a laboratory technician at the Institute of Neurosciences at the Southern General Hospital in Glasgow. Part of his job was to collect brain samples for experimentation. MacPherson worked in the lab for five years and met his future wife Jacqueline while he was there.
MacPherson went for an interview to be a police officer, but soon realised that he did not have the requisite personality for the job. It was then that his thoughts turned to acting. He joined an amateur dramatic group in Motherwell, before moving on to a repertory theatre in East Kilbride and a place in drama school.
It was after MacPherson landed the part of Hugh Hamilton in Citizens on BBC Radio 4 that his television career began to take off. While he was based in London, MacPherson auditioned for a part in the children's series Dramarama, but was unsuccessful. Then, in 1986, his agent told him about a part that had come up in Taggart and, after he regained his Glasgow accent, which had been diluted by working in London, he was offered the part.
Taggart, career and personal life
Initially the character of Jardine was to be a foil to DS Livingstone, assistant to DCI Jim Taggart (Mark McManus), but when Neil Duncan left the show shortly after MacPh
|
https://en.wikipedia.org/wiki/Institute%20of%20Physics%20Michael%20Faraday%20Medal%20and%20Prize
|
The Michael Faraday Medal and Prize is a gold medal awarded annually by the Institute of Physics in experimental physics. The award is made "for outstanding and sustained contributions to experimental physics." The medal is accompanied by a prize of £1000 and a certificate.
Historical development
1914-1965 Guthrie Lecture initiated to remember Frederick Guthrie, founder of the Physical Society (which merged with the Institute of Physics in 1960).
1966-2007 Guthrie Medal and Prize (in response to changed conditions from when the lecture was first established). From 1992, it became one of the Institute's Premier Awards.
2008–present Michael Faraday Medal and Prize
Medalists and lecturers
Faraday medalists
2022 Nikolay Zheludev, "For international leadership, discoveries and in-depth studies of new phenomena and functionalities in photonic nanostructures and nanostructured matter."
2021 Bucker Dangor, "For outstanding contributions to experimental plasma physics, and in particular for his role in the development of the field of laser-plasma acceleration."
2020 Richard Ellis, "For over 35 years of pioneering contributions in faint-object astronomy, often with instruments he funded and constructed, which have opened up the early universe to direct observations."
2019 Roy Taylor, "For his extensive, internationally leading contributions to the development of spectrally diverse, ultrafast-laser sources and pioneering fundamental studies of nonlinear fibre optics that h
|
https://en.wikipedia.org/wiki/Wolfgang%20Gewalt
|
Wolfgang Gewalt (28 October 1928 – 26 April 2007) was a German zoologist, author and former director of the Duisburg Zoo.
Biography
After the study of zoology, botany, chemistry and anthropology, his main focus was research of the great bustard. He recorded his observations in the breeding grounds and his experience with hand bred great bustards in several publications. Moreover, he was chief assistant at the Berlin Zoo. In 1966, he became director of the Duisburg Zoo and landed in the headlines in May 1966 when the white whale Moby Dick strayed into the Rhine. After futile attempts to capture Moby Dick, Wolfgang Gewalt came in for ever more negative criticism. A few newspapers even demanded: "Arrest Wolfgang Gewalt". In June 1966, the whale fortunately succeeded in swimming back to the North Sea. In 1969, Gewalt led an expedition to Canada and brought back the first beluga to Duisburg. For this he reaped angry criticism. In the same year Wolfgang Gewalt participated in the Encyclopedia Grzimeks Tierleben for which he wrote a contribution on Didelphidae. In 1972, he and his colleagues founded the European Association for Aquatic Mammals at the Dolfinarium Harderwijk in the Netherlands. This is a society for the care of aquatic mammals in human custody. In 1975, he brought five Orinoco river dolphins or toninas back to Duisburg from an expedition to Venezuela. In 1978 one of Wolfgang Gewalt's dreams was fulfilled with the birth of the first bottlenose dolphin in a German Z
|
https://en.wikipedia.org/wiki/Exponent%20%28disambiguation%29
|
Exponentiation is a mathematical operation.
Exponent may also refer to:
Mathematics
List of exponential topics
Exponential function, a function of a certain form
Matrix exponential, a matrix function on square matrices
The least common multiple of a periodic group
Statistics
Exponential distribution, a probability distribution
Exponential family, a parametric set of probability distributions of a certain form
Exponential growth, a specific way that a quantity may increase over time
Exponential decay, decreasing quantity at a rate proportional to current value
Linguistics
Exponent (linguistics), the expression of one or more grammatical properties by sound.
Music
The Exponents, a New Zealand rock group
Publications
Purdue Exponent, a student newspaper of Purdue University
Woman's Exponent, a publication of The Church of Jesus Christ of Latter-day Saints
Exponent II, a quarterly periodical for Latter-day Saint women
The Exponent (Montana State University), a student newspaper of Montana State University – Bozeman
The Brooklyn Exponent, a weekly newspaper serving communities in Michigan
The Jewish Exponent, a weekly community newspaper in Philadelphia, Pennsylvania
Companies
Exponent (consulting firm), an American engineering and scientific consulting firm
Other uses
Currency exponent, used in ISO 4271
Exponent CMS, an enterprise software framework and content management system
Exponent (podcast), podcast co-hosted by Ben Thompson
See also
Ex
|
https://en.wikipedia.org/wiki/Leroy%20Cronin
|
Leroy "Lee" Cronin FRSE FRSC (born 1 June 1973) is the Regius Chair of Chemistry in the School of Chemistry at the University of Glasgow. He was elected to the Fellowship of the Royal Society of Edinburgh, the Royal Society of Chemistry, and appointed to the Regius Chair of Chemistry in 2013. He was previously the Gardiner Chair, appointed April 2009.
Biography
Cronin was awarded BSc (1994) and PhD (1997) from the University of York. From 1997 to 1999, he was a Leverhulme fellow at the University of Edinburgh working with Neil Robertson. From 1999-2000 he worked as an Alexander von Humboldt research fellow in the laboratory of Achim Mueller at the University of Bielefeld (1999–2000). In 2000, he joined the University of Birmingham as a Lecturer in Chemistry, and in 2002 he moved to a similar position at the University of Glasgow.
In 2005, he was promoted to Reader at the University of Glasgow, EPSRC Advanced Fellow followed by promotion to Professor of Chemistry in 2006, and in 2009 became the Gardiner Professor. In 2013, he became the Regius Professor of Chemistry (Glasgow).
Cronin gave the opening lecture at TEDGlobal conference in 2011 in Edinburgh. He outlined the initial steps his team at University of Glasgow is taking to create inorganic biology, life composed of non-carbon-based material.
In 2022 Cronin was suspended by the Royal Society of Chemistry for three months for breaching their code of conduct, following a full independent investigation of a complaint mad
|
https://en.wikipedia.org/wiki/Mucicarmine%20stain
|
Mucicarmine stain is a staining procedure used for different purposes. In microbiology the stain aids in the identification of a variety of microorganisms based on whether or not the cell wall stains intensely red. Generally this is limited to microorganisms with a cell wall that is composed, at least in part, of a polysaccharide component. One of the organisms that is identified using this staining technique is Cryptococcus neoformans.
Another use is in surgical pathology where it can identify mucin. This is helpful, for example, in determining if the cancer is a type that produces mucin.
Example would be to distinguish between high grade Mucoepidermoid Carcinoma of the parotid, which stains positive vs Squamous Cell Carcinoma of the parotid which does not.
References
Staining dyes
|
https://en.wikipedia.org/wiki/Frist%20Campus%20Center
|
Frist Campus Center is a focal point of social life at Princeton University. The campus center is a combination of the former Palmer Physics Lab, and a modern addition completed in 2001. It was endowed with money from the fortune the Frist family has made in the private hospital business.
Designed by Venturi, Scott Brown & Associates, the firm of acclaimed architects Robert Venturi (a Princeton alumnus) and Denise Scott Brown, the building consists of a modern expansion to the existing Collegiate Gothic Palmer Hall. The new building volume fills in the courtyard of the previous C-shaped structure, and extends across its open side to create a new east facade. In 2008 and 2009 extensive renovations were performed on the 100 level by James Bradberry Architects
Room 302 is a lecture hall restored to its condition at the time that Albert Einstein lectured there.
This building has also been used for external shots of the fictitious Princeton–Plainsboro Teaching Hospital in the television series House.
References
External links
Daily Princetonian
Frist Campus Center
1909 establishments in New Jersey
2000 establishments in New Jersey
Princeton University buildings
Robert Venturi buildings
House (TV series)
Frist family
|
https://en.wikipedia.org/wiki/Robert%20Boyer
|
Robert Boyer may refer to:
Robert S. Boyer, professor of computer science, mathematics, and philosophy
See List of Charles Whitman's victims for Robert Hamilton Boyer, professor killed at The University of Texas in 1966
Robert Boyer (artist) (1948–2004), Canadian artist of aboriginal heritage
Robert Boyer (chemist) (1909–1989), chemist employed by Henry Ford
Robert James Boyer (1913–2005), former politician in Ontario, Canada
Bob Boyer (wrestler), retired Canadian professional wrestler
See also
Robert Boyers (1876–1949), American football coach
Robert Bowyer (1758–1834), British painter and publisher
|
https://en.wikipedia.org/wiki/Norman%20Allinger
|
Norman "Lou" Allinger (6 April 1928 – 8 July 2020) was an American organic and computational chemist and Distinguished Research Professor Emeritus of Chemistry at the University of Georgia (UGA) in Athens.
Lou Allinger was the elder of two children of Norman Clark Allinger (a bank employee) and Florence Helen (née Young). He was born in Alameda, California.
“From the age of nine on he was always employed in some fashion, first at the age of nine selling magazines and newspapers, then later as an ice-man, a part-time mail carrier, an apricot-picker, a butcher’s apprentice, and a warehouseman, loading tin cans onto railway cars”.
Allinger always had an interest in science, starting with astronomy at age 9 and pursuing that hobby with friends for many years, including his college years when he assembled a 6-inch Newtonian reflector using lenses he had ground himself. He began chemistry as a hobby around 10 or 11 and won a Boy Scout merit badge in the subject at age 13. He attended Alameda High School and then, aged 18, he enlisted in the US Army. and was stationed in Fairbanks, Alaska. After his term of enlistment Allinger attended the University of California, Berkeley, from where he graduated with a BS in chemistry in 1951.
For his PhD he moved to University of California, Los Angeles, to work with Donald J. Cram. He was awarded the degree in 1954. Allinger then crossed the country to Harvard, where he worked with Paul Bartlett.
In 1956 Allinger joined the faculty of Wayn
|
https://en.wikipedia.org/wiki/Wedderburn%27s%20little%20theorem
|
In mathematics, Wedderburn's little theorem states that every finite division ring is a field. In other words, for finite rings, there is no distinction between domains, division rings and fields.
The Artin–Zorn theorem generalizes the theorem to alternative rings: every finite alternative division ring is a field.
History
The original proof was given by Joseph Wedderburn in 1905, who went on to prove it two other ways. Another proof was given by Leonard Eugene Dickson shortly after Wedderburn's original proof, and Dickson acknowledged Wedderburn's priority. However, as noted in , Wedderburn's first proof was incorrect – it had a gap – and his subsequent proofs appeared only after he had read Dickson's correct proof. On this basis, Parshall argues that Dickson should be credited with the first correct proof.
A simplified version of the proof was later given by Ernst Witt. Witt's proof is sketched below. Alternatively, the theorem is a consequence of the Skolem–Noether theorem by the following argument. Let be a finite division algebra with center . Let and denote the cardinality of . Every maximal subfield of has elements; so they are isomorphic and thus are conjugate by Skolem–Noether. But a finite group (the multiplicative group of in our case) cannot be a union of conjugates of a proper subgroup; hence, .
A later "group-theoretic" proof was given by Ted Kaczynski in 1964. This proof, Kaczynski's first published piece of mathematical writing, was a short, two-pa
|
https://en.wikipedia.org/wiki/Symbolic
|
Symbolic may refer to:
Symbol, something that represents an idea, a process, or a physical entity
Mathematics, logic, and computing
Symbolic computation, a scientific area concerned with computing with mathematical formulas
Symbolic dynamics, a method for modeling dynamical systems by a discrete space consisting of infinite sequences of abstract symbols
Symbolic execution, the analysis of computer programs by tracking symbolic rather than actual values
Symbolic link, a special type of file in a computer memory storage system
Symbolic logic, the use of symbols for logical operations in logic and mathematics
Music
Symbolic (Death album), a 1995 album by the band Death
Symbolic (Voodoo Glow Skulls album), a 2000 album by the band Voodoo Glow Skulls
Social sciences
Symbolic anthropology, the study of cultural symbols and how those symbols can be interpreted to better understand a particular society
Symbolic capital, the resources available to an individual on the basis of honor, prestige or recognition in sociology and anthropology
Symbolic interaction, a system of interaction in sociology
Symbolic system, a structured system of symbols in anthropology, sociology and psychology
The Symbolic or Symbolic Order, Jacques Lacan's attempt to contrast with The Imaginary and The Real in psychoanalysis
See also
Symbol (disambiguation)
Symbolism (disambiguation)
Symbolic representation (disambiguation)
|
https://en.wikipedia.org/wiki/Commutation%20matrix
|
In mathematics, especially in linear algebra and matrix theory, the commutation matrix is used for transforming the vectorized form of a matrix into the vectorized form of its transpose. Specifically, the commutation matrix K(m,n) is the nm × mn matrix which, for any m × n matrix A, transforms vec(A) into vec(AT):
K(m,n) vec(A) = vec(AT) .
Here vec(A) is the mn × 1 column vector obtain by stacking the columns of A on top of one another:
where A = [Ai,j]. In other words, vec(A) is the vector obtained by vectorizing A in column-major order. Similarly, vec(AT) is the vector obtaining by vectorizing A in row-major order.
In the context of quantum information theory, the commutation matrix is sometimes referred to as the swap matrix or swap operator
Properties
The commutation matrix is a special type of permutation matrix, and is therefore orthogonal. In particular, K(m,n) is equal to , where is the permutation over for which
Replacing A with AT in the definition of the commutation matrix shows that Therefore in the special case of m = n the commutation matrix is an involution and symmetric.
The main use of the commutation matrix, and the source of its name, is to commute the Kronecker product: for every m × n matrix A and every r × q matrix B,
This property is often used in developing the higher order statistics of Wishart covariance matrices.
The case of n=q=1 for the above equation states that for any column vectors v,w of sizes m,r respectively,
This property
|
https://en.wikipedia.org/wiki/Duplication%20and%20elimination%20matrices
|
In mathematics, especially in linear algebra and matrix theory, the duplication matrix and the elimination matrix are linear transformations used for transforming half-vectorizations of matrices into vectorizations or (respectively) vice versa.
Duplication matrix
The duplication matrix is the unique matrix which, for any symmetric matrix , transforms into :
.
For the symmetric matrix , this transformation reads
The explicit formula for calculating the duplication matrix for a matrix is:
Where:
is a unit vector of order having the value in the position and 0 elsewhere;
is a matrix with 1 in position and and zero elsewhere
Here is a C++ function using Armadillo (C++ library):
arma::mat duplication_matrix(const int &n) {
arma::mat out((n*(n+1))/2, n*n, arma::fill::zeros);
for (int j = 0; j < n; ++j) {
for (int i = j; i < n; ++i) {
arma::vec u((n*(n+1))/2, arma::fill::zeros);
u(j*n+i-((j+1)*j)/2) = 1.0;
arma::mat T(n,n, arma::fill::zeros);
T(i,j) = 1.0;
T(j,i) = 1.0;
out += u * arma::trans(arma::vectorise(T));
}
}
return out.t();
}
Elimination matrix
An elimination matrix is a matrix which, for any matrix , transforms into :
.
By the explicit (constructive) definition given by , the by elimination matrix is given by
where is a unit vector whose -th element is one and zeros elsewhere, and .
Here is a C++ function using Armadillo (C++ library
|
https://en.wikipedia.org/wiki/Jane%20Goodall%20Environmental%20Middle%20School
|
Jane Goodall Environmental Middle School (JGEMS) is a public charter school serving grades six through eight that focuses on environmental science and community service. It is housed in the same building as the Oregon School for the Deaf in Salem, Oregon, and is named after English primatologist Jane Goodall. It is part of the Salem-Keizer School District.
Mission statement
"The Jane Goodall Environmental Middle School will provide an engaging and meaningful focus for students to achieve Oregon academic standards. Through partnerships with community and governmental organizations, an integrated curriculum design and an emphasis on field-based projects, students will actively apply their knowledge and skills as they improve our local and global environments."
Curriculum
The curriculum at JGEMS is aligned to current Oregon curriculum content standards and all courses taught in other Salem/Keizer middle schools are also taught at JGEMS. The curriculum at JGEMS consists of conservation biology, language arts, social studies, mathematics, integrated science, physical education/health education, and technology. If any student receives a F in any class before a field trip, they are not invited on that field trip.
It is also very focused on science.
School projects
JGEMS takes on environmental restoration projects and involves students in a variety of field studies. Projects are endangered species project, Oregon silverspot butterfly, reed canary grass suppression, frog deform
|
https://en.wikipedia.org/wiki/Vectorization%20%28mathematics%29
|
In mathematics, especially in linear algebra and matrix theory, the vectorization of a matrix is a linear transformation which converts the matrix into a vector. Specifically, the vectorization of a matrix A, denoted vec(A), is the column vector obtained by stacking the columns of the matrix A on top of one another:
Here, represents the element in the i-th row and j-th column of A, and the superscript denotes the transpose. Vectorization expresses, through coordinates, the isomorphism between these (i.e., of matrices and vectors) as vector spaces.
For example, for the 2×2 matrix , the vectorization is .
The connection between the vectorization of A and the vectorization of its transpose is given by the commutation matrix.
Compatibility with Kronecker products
The vectorization is frequently used together with the Kronecker product to express matrix multiplication as a linear transformation on matrices. In particular,
for matrices A, B, and C of dimensions k×l, l×m, and m×n. For example, if (the adjoint endomorphism of the Lie algebra of all n×n matrices with complex entries), then , where is the n×n identity matrix.
There are two other useful formulations:
More generally, it has been shown that vectorization is a self-adjunction in the monoidal closed structure of any category of matrices.
Compatibility with Hadamard products
Vectorization is an algebra homomorphism from the space of matrices with the Hadamard (entrywise) product to Cn2 with its Hadamard pr
|
https://en.wikipedia.org/wiki/Schlenk%20line
|
The Schlenk line (also vacuum gas manifold) is a commonly used chemistry apparatus developed by Wilhelm Schlenk. It consists of a dual manifold with several ports. One manifold is connected to a source of purified inert gas, while the other is connected to a vacuum pump. The inert-gas line is vented through an oil bubbler, while solvent vapors and gaseous reaction products are prevented from contaminating the vacuum pump by a liquid-nitrogen or dry-ice/acetone cold trap. Special stopcocks or Teflon taps allow vacuum or inert gas to be selected without the need for placing the sample on a separate line.
Schlenk lines are useful for safely and successfully manipulating moisture- and air-sensitive compounds. The vacuum is also often used to remove the last traces of solvent from a sample. Vacuum and gas manifolds often have many ports and lines, and with care, it is possible for several reactions or operations to be run simultaneously.
When the reagents are highly susceptible to oxidation, traces of oxygen may pose a problem. Then, for the removal of oxygen below the ppm level, the inert gas needs to be purified by passing it through a deoxygenation catalyst. This is usually a column of copper(I) or manganese(II) oxide, which reacts with oxygen traces present in the inert gas.
Techniques
The main techniques associated with the use of a Schlenk line include:
counterflow additions, where air-stable reagents are added to the reaction vessel against a flow of inert gas;
the use
|
https://en.wikipedia.org/wiki/Milstein%20method
|
In mathematics, the Milstein method is a technique for the approximate numerical solution of a stochastic differential equation. It is named after Grigori N. Milstein who first published it in 1974.
Description
Consider the autonomous Itō stochastic differential equation:
with initial condition , where stands for the Wiener process, and suppose that we wish to solve this SDE on some interval of time . Then the Milstein approximation to the true solution is the Markov chain defined as follows:
partition the interval into equal subintervals of width :
set
recursively define for by: where denotes the derivative of with respect to and: are independent and identically distributed normal random variables with expected value zero and variance . Then will approximate for , and increasing will yield a better approximation.
Note that when , i.e. the diffusion term does not depend on , this method is equivalent to the Euler–Maruyama method.
The Milstein scheme has both weak and strong order of convergence, , which is superior to the Euler–Maruyama method, which in turn has the same weak order of convergence, , but inferior strong order of convergence, .
Intuitive derivation
For this derivation, we will only look at geometric Brownian motion (GBM), the stochastic differential equation of which is given by:
with real constants and . Using Itō's lemma we get:
Thus, the solution to the GBM SDE is:
where
See numerical solution is presented above for three dif
|
https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta%20method%20%28SDE%29
|
In mathematics of stochastic systems, the Runge–Kutta method is a technique for the approximate numerical solution of a stochastic differential equation. It is a generalisation of the Runge–Kutta method for ordinary differential equations to stochastic differential equations (SDEs). Importantly, the method does not involve knowing derivatives of the coefficient functions in the SDEs.
Most basic scheme
Consider the Itō diffusion satisfying the following Itō stochastic differential equation
with initial condition , where stands for the Wiener process, and suppose that we wish to solve this SDE on some interval of time . Then the basic Runge–Kutta approximation to the true solution is the Markov chain defined as follows:
partition the interval into subintervals of width :
set ;
recursively compute for by where and
The random variables are independent and identically distributed normal random variables with expected value zero and variance .
This scheme has strong order 1, meaning that the approximation error of the actual solution at a fixed time scales with the time step . It has also weak order 1, meaning that the error on the statistics of the solution scales with the time step . See the references for complete and exact statements.
The functions and can be time-varying without any complication. The method can be generalized to the case of several coupled equations; the principle is the same but the equations become longer.
Variation of the Improved
|
https://en.wikipedia.org/wiki/Shearing%20%28physics%29
|
In continuum mechanics, shearing refers to the occurrence of a shear strain, which is a deformation of a material substance in which parallel internal surfaces slide past one another. It is induced by a shear stress in the material. Shear strain is distinguished from volumetric strain. The change in a material's volume in response to stress and change of angle is called the angle of shear.
Overview
Often, the verb shearing refers more specifically to a mechanical process that causes a plastic shear strain in a material, rather than causing a merely elastic one. A plastic shear strain is a continuous (non-fracturing) deformation that is irreversible, such that the material does not recover its original shape. It occurs when the material is yielding. The process of shearing a material may induce a volumetric strain along with the shear strain. In soil mechanics, the volumetric strain associated with shearing is known as Reynolds' dilation if it increases the volume, or compaction if it decreases the volume.
The shear center (also known as the torsional axis) is an imaginary point on a section, where a shear force can be applied without inducing any torsion. In general, the shear center is not the centroid. For cross-sectional areas having one axis of symmetry, the shear center is located on the axis of symmetry. For those having two axes of symmetry, the shear center lies on the centroid of the cross-section.
In some materials such as metals, plastics, or granular mat
|
https://en.wikipedia.org/wiki/Johannes%20Hartmann
|
Johannes Hartmann (Amberg, 14 January 1568 – Kassel, 7 December 1631) was a German chemist.
In 1609, he became the first Professor of Chemistry at the University of Marburg. His teaching dealt mainly with pharmaceuticals. He was the father-in-law of Heinrich Petraeus.
References
1568 births
Date of birth unknown
1631 deaths
Date of death unknown
People from Amberg
Academic staff of the University of Marburg
17th-century German chemists
|
https://en.wikipedia.org/wiki/Richard%20Losick
|
Richard Marc Losick ( ; born 1943) is an American molecular biologist. He is the Maria Moors Cabot Professor of Biology at Harvard University, a Howard Hughes Medical Institute Professor. He is especially noted for his investigations of endospore formation in Gram positive organisms such as Bacillus subtilis.
Education and career
Losick received his AB in Chemistry from Princeton University in 1965, and his PhD in biochemistry from Massachusetts Institute of Technology in 1969. Following his graduate studies, Losick was named a Junior Fellow of the Harvard Society of Fellows. He joined the Harvard faculty in 1972. He has held the position of chairman in the Departments of Cellular and Developmental Biology and Molecular and Cellular Biology. Along with Daniel Kahne, Robert Lue, and Susan Mango, he teaches Life Sciences 1a, an introductory biology and chemistry course, which was the fourth largest lecture course taught at Harvard College in 2015.
Research
Losick's research interests include RNA polymerase, sigma factors, regulation of gene transcription, and bacterial development. He is known for his studies of asymmetric division in Bacillus subtilis, which divides to form one endospore and one nurturing cell. Currently, Losick studies biofilm formation by the opportunistic pathogen Staphylococcus aureus. His research group has demonstrated that chromosomal DNA is recycled to form an electrostatic extracellular net in order to hold neighboring bacterial cells together.
A
|
https://en.wikipedia.org/wiki/Paul%20Halpern
|
Paul Halpern (; born 1961) is an American author and Professor of Physics at Saint Joseph's University in Philadelphia.
Life
Halpern received a Ph.D in theoretical physics, an M.A. in physics and a B.A. in physics and mathematics. He was also the recipient of a Guggenheim Fellowship, Fulbright Scholarship, and an Athenaeum Society Literary Award.
He has written many popular science books and articles, including the books The Cyclical Serpent, Cosmic Wormholes and The Great Beyond. He has also appeared on the 1994 PBS series Futurequest, as well as the National Public Radio show "Radio Times."
In 2007, he published a book based on The Simpsons titled What's Science Ever Done for Us. He later appeared in The Simpsons 20th Anniversary Special – In 3-D! On Ice!.
Halpern published Einstein's Dice and Schrödinger's Cat in 2015, The Quantum Labyrinth: How Richard Feynman and John Wheeler Revolutionized Time and Reality in 2017, Synchronicity: The Epic Quest to Understand the Quantum Nature of Cause and Effect in 2020, and Flashes of Creation: George Gamow, Fred Hoyle, and the Great Big Bang Debate in 2021.
Works
Time Journeys: A search for Cosmic Destiny and Meaning, McGraw-Hill Professional Publishing, 1990,
Cosmic Wormholes: The Search for Interstellar Shortcuts, Plume, 1993.
The Cyclical Serpent: Prospects for an Ever-Repeating Universe, 1995;
The Pursuit of Destiny: A History of Prediction, Perseus Pub., 2000,
Countdown to Apocalypse: A Scientific Exploration o
|
https://en.wikipedia.org/wiki/Rietdijk%E2%80%93Putnam%20argument
|
In philosophy, the Rietdijk–Putnam argument, named after and Hilary Putnam, uses 20th-century findings in physicsspecifically in special relativityto support the philosophical position known as four-dimensionalism.
If special relativity is true, then each observer will have their own plane of simultaneity, which contains a unique set of events that constitutes the observer's present moment. Observers moving at different relative velocities have different planes of simultaneity, and hence different sets of events that are present. Each observer considers their set of present events to be a three-dimensional universe, but even the slightest movement of the head or offset in distance between observers can cause the three-dimensional universes to have differing content. If each three-dimensional universe exists, then the existence of multiple three-dimensional universes suggests that the universe is four-dimensional. The argument is named after the discussions by Rietdijk (1966) and Putnam (1967). It is sometimes called the Rietdijk–Putnam–Penrose argument.
Andromeda paradox
Roger Penrose advanced a form of this argument that has been called the Andromeda paradox in which he points out that two people walking past each other on the street could have very different present moments. If one of the people were walking towards the Andromeda Galaxy, then events in this galaxy might be hours or even days advanced of the events on Andromeda for the person walking in the other directi
|
https://en.wikipedia.org/wiki/Liviu%20Constantinescu
|
Liviu Constantinescu (26 November 1914 – 29 November 1997) was a Romanian geophysicist, professor of geophysics, member of the Romanian Academy. He was the cofounder, together with Sabba S. Ștefănescu, of the Romanian school of geophysics.
Biography
Born into an old family of Christian Orthodox clerics from Transylvania, Liviu Constantinescu ignored suggestions from family and teachers to become an engineer or teacher and decided to study natural sciences. He earned a master's degree in physics and chemistry (1935) and a doctor's degree in physics (1941) from the University of Bucharest. After a few years as teaching assistant at the Department of Sciences of his alma mater (1937–1943), he was appointed director of the newly founded Geophysical Observatory Surlari, named today National Geomagnetic Observatory Surlari "Liviu Constantinescu" (1943–1958); this started his career as a geophysicist. He was appointed professor (1949–1975) at a newly created Department of Geophysics, led by Ștefănescu and later by Constantinescu himself; in parallel, he directed geophysical research at various institutes of earth sciences of the Romanian Academy (1959–1970). Discriminated politically for his repeated refusal to join the ruling Communist Party, he was forced into early retirement at age 60 (1975); he came back after the fall of the dictatorship, fifteen years later. In 1990 he was elected full member of the Romanian Academy (he had been a corresponding member since 1963) and presid
|
https://en.wikipedia.org/wiki/Absolutely%20integrable%20function
|
In mathematics, an absolutely integrable function is a function whose absolute value is integrable, meaning that the integral of the absolute value over the whole domain is finite.
For a real-valued function, since
where
both and must be finite. In Lebesgue integration, this is exactly the requirement for any measurable function f to be considered integrable, with the integral then equaling , so that in fact "absolutely integrable" means the same thing as "Lebesgue integrable" for measurable functions.
The same thing goes for a complex-valued function. Let us define
where and are the real and imaginary parts of . Then
so
This shows that the sum of the four integrals (in the middle) is finite if and only if the integral of the absolute value is finite, and the function is Lebesgue integrable only if all the four integrals are finite. So having a finite integral of the absolute value is equivalent to the conditions for the function to be "Lebesgue integrable".
External links
Integral calculus
References
Tao, Terence, Analysis 2, 3rd ed., Texts and Readings in Mathematics, Hindustan Book Agency, New Delhi.
|
https://en.wikipedia.org/wiki/Peter%20MacOwan
|
Peter MacOwan (14 November 1830 in Hull, England – 30 November 1909 in Uitenhage, Cape Province) was a British colonial botanist and teacher in South Africa.
Early life and education
He was the son of Peter McOwan, a Wesleyan minister from Scotland. After finishing school, he taught at Bath, Colchester, and Leeds, and in 1857 taught chemistry at the Huddersfield College Laboratory. That same year he graduated in chemistry from the University of London, becoming professor of chemistry at Huddersfield.
Botanical work
The year before, he married Amelia Day from Bristol. A severe lung condition, possibly asthma, caused him to move to South Africa and take up the post of principal at the newly established Shaw College in Grahamstown. His health rapidly improved and leaving chemistry behind he resumed studying botany in which he had become interested while still in England, having started a collection of flowers and mosses. This interest was furthered by his association with Dr William Guybon Atherstone, Henry Hutton and Mrs. FW Barber. He entered into a fruitful exchange of specimens and correspondence with Asa Gray of the States, Sir William Hooker of Kew and with Harvey and Sonder who were working on the Flora Capensis. Finding it a drain on his own time to supply duplicates to overseas collectors, he formed the South African Botanical Exchange Society, which brought together a large number of amateur botanists. By 1868, roughly 9000 duplicates had been sent abroad, for which
|
https://en.wikipedia.org/wiki/Aspherical%20space
|
In topology, a branch of mathematics, an aspherical space is a topological space with all homotopy groups equal to 0 when .
If one works with CW complexes, one can reformulate this condition: an aspherical CW complex is a CW complex whose universal cover is contractible. Indeed, contractibility of a universal cover is the same, by Whitehead's theorem, as asphericality of it. And it is an application of the exact sequence of a fibration that higher homotopy groups of a space and its universal cover are same. (By the same argument, if E is a path-connected space and is any covering map, then E is aspherical if and only if B is aspherical.)
Each aspherical space X is, by definition, an Eilenberg–MacLane space of type , where is the fundamental group of X. Also directly from the definition, an aspherical space is a classifying space for its fundamental group (considered to be a topological group when endowed with the discrete topology).
Examples
Using the second of above definitions we easily see that all orientable compact surfaces of genus greater than 0 are aspherical (as they have either the Euclidean plane or the hyperbolic plane as a universal cover).
It follows that all non-orientable surfaces, except the real projective plane, are aspherical as well, as they can be covered by an orientable surface of genus 1 or higher.
Similarly, a product of any number of circles is aspherical. As is any complete, Riemannian flat manifold.
Any hyperbolic 3-manifold is, by def
|
https://en.wikipedia.org/wiki/Differential%20calculus%20over%20commutative%20algebras
|
In mathematics the differential calculus over commutative algebras is a part of commutative algebra based on the observation that most concepts known from classical differential calculus can be formulated in purely algebraic terms. Instances of this are:
The whole topological information of a smooth manifold is encoded in the algebraic properties of its -algebra of smooth functions as in the Banach–Stone theorem.
Vector bundles over correspond to projective finitely generated modules over via the functor which associates to a vector bundle its module of sections.
Vector fields on are naturally identified with derivations of the algebra .
More generally, a linear differential operator of order k, sending sections of a vector bundle to sections of another bundle is seen to be an -linear map between the associated modules, such that for any elements :
where the bracket is defined as the commutator
Denoting the set of th order linear differential operators from an -module to an -module with we obtain a bi-functor with values in the category of -modules. Other natural concepts of calculus such as jet spaces, differential forms are then obtained as representing objects of the functors and related functors.
Seen from this point of view calculus may in fact be understood as the theory of these functors and their representing objects.
Replacing the real numbers with any commutative ring, and the algebra with any commutative algebra the above said remains mean
|
https://en.wikipedia.org/wiki/Molecular%20Hamiltonian
|
In atomic, molecular, and optical physics and quantum chemistry, the molecular Hamiltonian is the Hamiltonian operator representing the energy of the electrons and nuclei in a molecule. This operator and the associated Schrödinger equation play a central role in computational chemistry and physics for computing properties of molecules and aggregates of molecules, such as thermal conductivity, specific heat, electrical conductivity, optical, and magnetic properties, and reactivity.
The elementary parts of a molecule are the nuclei, characterized by their atomic numbers, Z, and the electrons, which have negative elementary charge, −e. Their interaction gives a nuclear charge of Z + q, where , with N equal to the number of electrons. Electrons and nuclei are, to a very good approximation, point charges and point masses. The molecular Hamiltonian is a sum of several terms: its major terms are the kinetic energies of the electrons and the Coulomb (electrostatic) interactions between the two kinds of charged particles. The Hamiltonian that contains only the kinetic energies of electrons and nuclei, and the Coulomb interactions between them, is known as the Coulomb Hamiltonian. From it are missing a number of small terms, most of which are due to electronic and nuclear spin.
Although it is generally assumed that the solution of the time-independent Schrödinger equation associated with the Coulomb Hamiltonian will predict most properties of the molecule, including its shape (th
|
https://en.wikipedia.org/wiki/Factorization%20system
|
In mathematics, it can be shown that every function can be written as the composite of a surjective function followed by an injective function. Factorization systems are a generalization of this situation in category theory.
Definition
A factorization system (E, M) for a category C consists of two classes of morphisms E and M of C such that:
E and M both contain all isomorphisms of C and are closed under composition.
Every morphism f of C can be factored as for some morphisms and .
The factorization is functorial: if and are two morphisms such that for some morphisms and , then there exists a unique morphism making the following diagram commute:
Remark: is a morphism from to in the arrow category.
Orthogonality
Two morphisms and are said to be orthogonal, denoted , if for every pair of morphisms and such that there is a unique morphism such that the diagram
commutes. This notion can be extended to define the orthogonals of sets of morphisms by
and
Since in a factorization system contains all the isomorphisms, the condition (3) of the definition is equivalent to
(3') and
Proof: In the previous diagram (3), take (identity on the appropriate object) and .
Equivalent definition
The pair of classes of morphisms of C is a factorization system if and only if it satisfies the following conditions:
Every morphism f of C can be factored as with and
and
Weak factorization systems
Suppose e and m are two morphisms in a category C. Then e has the
|
https://en.wikipedia.org/wiki/Generalized%20dihedral%20group
|
In mathematics, the generalized dihedral groups are a family of groups with algebraic structures similar to that of the dihedral groups. They include the finite dihedral groups, the infinite dihedral group, and the orthogonal group O(2). Dihedral groups play an important role in group theory, geometry, and chemistry.
Definition
For any abelian group H, the generalized dihedral group of H, written Dih(H), is the semidirect product of H and Z2, with Z2 acting on H by inverting elements. I.e., with φ(0) the identity and φ(1) inversion.
Thus we get:
(h1, 0) * (h2, t2) = (h1 + h2, t2)
(h1, 1) * (h2, t2) = (h1 − h2, 1 + t2)
for all h1, h2 in H and t2 in Z2.
(Writing Z2 multiplicatively, we have (h1, t1) * (h2, t2) = (h1 + t1h2, t1t2) .)
Note that (h, 0) * (0,1) = (h,1), i.e. first the inversion and then the operation in H. Also (0, 1) * (h, t) = (−h, 1 + t); indeed (0,1) inverts h, and toggles t between "normal" (0) and "inverted" (1) (this combined operation is its own inverse).
The subgroup of Dih(H) of elements (h, 0) is a normal subgroup of index 2, isomorphic to H, while the elements (h, 1) are all their own inverse.
The conjugacy classes are:
the sets {(h,0 ), (−h,0 )}
the sets {(h + k + k, 1) | k in H }
Thus for every subgroup M of H, the corresponding set of elements (m,0) is also a normal subgroup. We have:
Dih(H) / M = Dih ( H / M )
Examples
Dihn = Dih(Zn) (the dihedral groups)
For even n there are two sets {(h + k + k, 1) | k in H }, and each generates a norma
|
https://en.wikipedia.org/wiki/Glen%20Culler
|
Glen Jacob Culler (July 7, 1927 – May 3, 2003) was an American professor of electrical engineering and an important early innovator in the development of the Internet. Culler joined the University of California, Santa Barbara (UCSB) mathematics faculty in 1959 and helped put the campus in the forefront of what would become the field of computer science. He later served as director of the UCSB Computer Center and professor in the College of Engineering and extended his revolutionary view of the role of computers to include their use in the classroom. He left UCSB to work in industry and establish his own company, called Culler-Harrison, in 1969. Culler-Harrison became CHI Systems, and later, Culler Scientific.
One of Glen Culler's sons, David Culler, is a notable computer scientist in his own right. Another son,
Marc Culler, is a distinguished pure mathematician working in low-dimensional topology. Another son, Randall Culler, is a Jin Shin Jyutsu master. His daughter, Katharyn Culler Cohen, works in small business and non-profit consulting.
Work
Culler was the developer of the Culler-Fried Online System, one of the first interactive computer systems in the mid-1960 era. This was the first system to make use of a storage oscilloscope as a means of presenting graphical information, and provided an innovative means of presentation and teaching of mathematical concepts. One of the first object oriented approaches to computing, the system provided a set of operators (e.g., add
|
https://en.wikipedia.org/wiki/Peter%20M.%20Neumann
|
Peter Michael Neumann OBE (28 December 1940 – 18 December 2020) was a British mathematician. His fields of interest included the history of mathematics and Galois theory.
Biography
Born in December 1940, Neumann was a son of the German-born mathematicians Bernhard Neumann and Hanna Neumann. He gained a BA degree from The Queen's College, Oxford in 1963, and a DPhil degree from the University of Oxford in 1966. Neumann was a Tutorial Fellow at the Queen's College, Oxford, and a lecturer at the University of Oxford. His research work was in the field of group theory. In 1987, Neumann won the Lester R. Ford Award of the Mathematical Association of America for his review of Harold Edwards' book Galois Theory.
He was the first Chairman of the United Kingdom Mathematics Trust, from October 1996 to April 2004, succeeded by Bernard Silverman.
Neumann showed in 1997 that Alhazen's problem (reflecting a light ray off a spherical mirror to hit a target) cannot be solved with a straightedge and compass construction. Although the solution is a straightforward application of Galois theory it settles the constructibility of one of the last remaining geometric construction problems posed in antiquity.
In 2003, the London Mathematical Society awarded him the Senior Whitehead Prize. He was appointed Officer of the Order of the British Empire (OBE) in the 2008 New Year Honours.
After retiring in 2008, he became an Emeritus Fellow at the Queen's College.
Neumann's work in the history of m
|
https://en.wikipedia.org/wiki/Dagger%20category
|
In category theory, a branch of mathematics, a dagger category (also called involutive category or category with involution) is a category equipped with a certain structure called dagger or involution. The name dagger category was coined by Peter Selinger.
Formal definition
A dagger category is a category equipped with an involutive contravariant endofunctor which is the identity on objects.
In detail, this means that:
for all morphisms , there exist its adjoint
for all morphisms ,
for all objects ,
for all and ,
Note that in the previous definition, the term "adjoint" is used in a way analogous to (and inspired by) the linear-algebraic sense, not in the category-theoretic sense.
Some sources define a category with involution to be a dagger category with the additional property that its set of morphisms is partially ordered and that the order of morphisms is compatible with the composition of morphisms, that is implies for morphisms , , whenever their sources and targets are compatible.
Examples
The category Rel of sets and relations possesses a dagger structure: for a given relation in Rel, the relation is the relational converse of . In this example, a self-adjoint morphism is a symmetric relation.
The category Cob of cobordisms is a dagger compact category, in particular it possesses a dagger structure.
The category Hilb of Hilbert spaces also possesses a dagger structure: Given a bounded linear map , the map is just its adjoint in the usual s
|
https://en.wikipedia.org/wiki/Alfred%20Spector
|
Alfred Zalmon Spector is an American computer scientist and research manager. He is a visiting scholar in the MIT EECS Department and was previously CTO of Two Sigma Investments. Before that, he was Vice President of Research and Special Initiatives at Google.
Education
Spector received his Bachelor of Arts degree in Applied Mathematics from Harvard University, and his PhD in computer science from Stanford University in 1981. His research explored communication architectures for building multiprocessors out of network-linked computers and included measurements of remote procedure call operations on experimental Ethernet. His dissertation was titled Multiprocessing Architectures for Local Computer Networks, and his advisor was Forest Baskett III.
Career
Spector was an associate professor of computer science at Carnegie Mellon University (CMU). While there, he served as doctoral advisor to Randy Pausch, Jeff Eppinger and Joshua Bloch and seven others. Spector was a founder of Transarc Corporation in 1989 which built and sold distributed transaction processing and wide area file systems software, commercializing the Andrew File System developed at CMU. After Transarc was acquired by IBM, he became a software executive and then vice president of global software and services research for IBM and finally vice president of strategy and technology within IBM's Software Group.
Spector joined Google as vice president of research in November 2007 and retired in early 2015. In Oct
|
https://en.wikipedia.org/wiki/Addison-Wesley%20Secondary%20Math%3A%20An%20Integrated%20Approach%3A%20Focus%20on%20Algebra
|
Focus on Algebra was the widely cited 812-page-long algebra textbook which contained significant content outside the traditional field of mathematics. The real-life context, intended to make mathematics more relevant, included chili recipes, ancient myths, and photographs of famous people.
Although it was a widely used textbook, it made headlines when it was dubbed "rainforest algebra" by critics.
Senate Testimony
Senator Robert Byrd, Democrat from West Virginia, joined critics of reform mathematics on the floor of the senate by dubbing Addison-Wesley Secondary Math: An Integrated Approach: Focus on Algebra the "Texas rainforest algebra book". It had received an "F" grade on a report card produced by Mathematically Correct, a back-to-basics group, who claimed that it had no algebraic content on the first hundred pages.
Structure
Each of the 10 Chapters was composed of two or three themes, or "Superlessons," each of which connected the algebraic content to another discipline. Each Superlesson began with an opening page with discussion questions relating to the theme. Critics of the programs cited these questions as evidence of the lack of math in the books.
Examples of questions cited:
What other kinds of pollution besides air pollution might threaten our planet? [page 163, in the introduction to 3-1 Functional Relationships]
Each year the Oilfield Chili Appreciation Society holds a chili cook-off. . . . 1. The chili cook-off raises money for charity. Describe some
|
https://en.wikipedia.org/wiki/Congenic
|
In genetics, two organisms that differ in only one locus and a linked segment of chromosome are defined as congenic. Similarly, organisms that are coisogenic differ in one locus only and not in the surrounding chromosome. Unlike congenic organisms, coisogenic organisms cannot be bred and only occur through spontaneous or targeted mutation at the locus.
Generating congenic strains
Congenic strains are generated in the laboratory by mating two inbred strains (usually rats or mice), and back-crossing the descendants 5–10 generations with one of the original strains, known as the recipient strain. Typically selection for either phenotype or genotype is performed prior to each back-cross generation. In this manner either an interesting phenotype, or a defined chromosomal region assayed by genotype, is passed from the donor strain onto an otherwise uniform recipient background. Congenic mice or rats can then be compared to the pure recipient strain to determine whether they are phenotypically different if selection was for a genotypic region, or to identify the critical genetic locus, if selection was for a phenotype.
Speed congenics can be produced in as little as five back-cross generations, through the selection at each generation of offspring that not only retain the desired chromosomal fragment, but also 'lose' the maximum amount of background genetic information from the donor strain. This is also known as marker-assisted congenics, due to the use of genetic markers, typic
|
https://en.wikipedia.org/wiki/List%20of%20common%20physics%20notations
|
This is a list of common physical constants and variables, and their notations. Note that bold text indicates that the quantity is a vector.
Latin characters
Greek characters
Other characters
See also
List of letters used in mathematics and science
Glossary of mathematical symbols
List of mathematical uses of Latin letters
Greek letters used in mathematics, science, and engineering
Physical constant
Physical quantity
International System of Units
ISO 31
References
Common Physics Abbreviations
|
https://en.wikipedia.org/wiki/Michael%20Coey
|
John Michael David Coey (born 24 February 1945), known as Michael Coey, is a Belfast-born experimental physicist working in the fields of magnetism and spintronics.
He got a BA in Physics at Jesus College, Cambridge (1966), and a PhD from University of Manitoba (1971) for
a thesis on "Mössbauer Effect of 57Fe in Magnetic Oxides" with advisor Allan H. Morrish. Trinity College Dublin (TCD), where he has been in the physics department since 1978, awarded him ScD (1987) and the University of Grenoble awarded him Dip. d'Habilitation (1986) and an honorary doctorate (1994). He served as Erasmus Smith's Professor of Natural and Experimental Philosophy at TCD from 2007 to 2012.
Career
Mike Coey has been a Professor of Physics at TCD since 1987, and was the last appointed Erasmus Smith's Professor of Natural and Experimental Philosophy (2007–2012), a chair that dates from 1724. He has supervised over 50 PhD students, and authored or edited 5 volumes. Recognised as a distinguished European specialist in magnetic materials; internationally he continues to be a leader in the field of magnetism.
In 1994 Coey founded Magnetic Solutions and went on to be the cofounder of CRANN Ireland's Nanoscience Research institute (2002) and conceived Dublin's unique Science Gallery (2006). He has published over 700 scientific articles on diverse aspects of magnetism, many of which have had significant impact on the scientific community. As Ireland's most highly cited scientist, with an h-index of 109
|
https://en.wikipedia.org/wiki/Four-terminal%20sensing
|
In electrical engineering, four-terminal sensing (4T sensing), 4-wire sensing, or 4-point probes method is an electrical impedance measuring technique that uses separate pairs of current-carrying and voltage-sensing electrodes to make more accurate measurements than the simpler and more usual two-terminal (2T) sensing. Four-terminal sensing is used in some ohmmeters and impedance analyzers, and in wiring for strain gauges and resistance thermometers. Four-point probes are also used to measure sheet resistance of thin films (particularly semiconductor thin films).
Separation of current and voltage electrodes eliminates the lead and contact resistance from the measurement. This is an advantage for precise measurement of low resistance values. For example, an LCR bridge instruction manual recommends the four-terminal technique for accurate measurement of resistance below 100 ohms.
Four-terminal sensing is also known as Kelvin sensing, after William Thomson, Lord Kelvin, who invented the Kelvin bridge in 1861 to measure very low resistances using four-terminal sensing. Each two-wire connection can be called a Kelvin connection. A pair of contacts that is designed to connect a force-and-sense pair to a single terminal or lead simultaneously is called a Kelvin contact. A clip, often a crocodile clip, that connects a force-and-sense pair (typically one to each jaw) is called a Kelvin clip.
Operating principle
When a Kelvin connection is used, current is supplied via a pair of f
|
https://en.wikipedia.org/wiki/Dagger%20compact%20category
|
In category theory, a branch of mathematics, dagger compact categories (or dagger compact closed categories) first appeared in 1989 in the work of Sergio Doplicher and John E. Roberts on the reconstruction of compact topological groups from their category of finite-dimensional continuous unitary representations (that is, Tannakian categories). They also appeared in the work of John Baez and James Dolan as an instance of semistrict k-tuply monoidal n-categories, which describe general topological quantum field theories, for n = 1 and k = 3. They are a fundamental structure in Samson Abramsky and Bob Coecke's categorical quantum mechanics.
Overview
Dagger compact categories can be used to express and verify some fundamental quantum information protocols, namely: teleportation, logic gate teleportation and entanglement swapping, and standard notions such as unitarity, inner-product, trace, Choi–Jamiolkowsky duality, complete positivity, Bell states and many other notions are captured by the language of dagger compact categories. All this follows from the completeness theorem, below. Categorical quantum mechanics takes dagger compact categories as a background structure relative to which other quantum mechanical notions like quantum observables and complementarity thereof can be abstractly defined. This forms the basis for a high-level approach to quantum information processing.
Formal definition
A dagger compact category is a dagger symmetric monoidal category which is a
|
https://en.wikipedia.org/wiki/Streaking%20%28microbiology%29
|
In microbiology, streaking is a technique used to isolate a pure strain from a single species of microorganism, often bacteria. Samples can then be taken from the resulting colonies and a microbiological culture can be grown on a new plate so that the organism can be identified, studied, or tested.
The modern streak plate method has progressed from the efforts of Robert Koch and other microbiologists to obtain microbiological cultures of bacteria in order to study them. The dilution or isolation by streaking method was first developed by Loeffler and Gaffky in Koch's laboratory, which involves the dilution of bacteria by systematically streaking them over the exterior of the agar in a Petri dish to obtain isolated colonies which will then grow into quantity of cells, or isolated colonies. If the agar surface grows microorganisms which are all genetically same, the culture is then considered as a microbiological culture.
Technique
Streaking is rapid and ideally a simple process of isolation dilution. The technique is done by diluting a comparatively large concentration of bacteria to a smaller concentration. The decrease of bacteria should show that colonies are sufficiently spread apart to affect the separation of the different types of microbes. Streaking is done using a sterile tool, such as a cotton swab or commonly an inoculation loop. Aseptic techniques are used to maintain microbiological cultures and to prevent contamination of the growth medium. There are many diffe
|
https://en.wikipedia.org/wiki/Unit%20distance%20graph
|
In mathematics, particularly geometric graph theory, a unit distance graph is a graph formed from a collection of points in the Euclidean plane by connecting two points whenever the distance between them is exactly one. To distinguish these graphs from a broader definition that allows some non-adjacent pairs of vertices to be at distance one, they may also be called strict unit distance graphs or faithful unit distance graphs. As a hereditary family of graphs, they can be characterized by forbidden induced subgraphs. The unit distance graphs include the cactus graphs, the matchstick graphs and penny graphs, and the hypercube graphs. The generalized Petersen graphs are non-strict unit distance graphs.
An unsolved problem of Paul Erdős asks how many edges a unit distance graph on vertices can have. The best known lower bound is slightly above linear in —far from the upper bound, proportional to . The number of colors required to color unit distance graphs is also unknown (the Hadwiger–Nelson problem): some unit distance graphs require five colors, and every unit distance graph can be colored with seven colors. For every algebraic number there is a unit distance graph with two vertices that must be that distance apart. According to the Beckman–Quarles theorem, the only plane transformations that preserve all unit distance graphs are the isometries.
It is possible to construct a unit distance graph efficiently, given its points. Finding all unit distances has applications in p
|
https://en.wikipedia.org/wiki/Nel%20Noddings
|
Nel Noddings (; January 19, 1929 – August 25, 2022) was an American feminist, educator, and philosopher best known for her work in philosophy of education, educational theory, and ethics of care.
Biography
Noddings received a bachelor's degree in mathematics and physical science from Montclair State University in New Jersey, a master's degree in mathematics from Rutgers University, and a PhD in education from the Stanford University Graduate School of Education.
Nel Noddings worked in many areas of the education system. She spent seventeen years as an elementary and high school mathematics teacher and school administrator, before earning her PhD and beginning work as an academic in the fields of philosophy of education, theory of education and ethics, specifically moral education and ethics of care. She became a member of the Stanford faculty in 1977, and was the Jacks Professor of Child Education from 1992 until 1998. While at Stanford University she received awards for teaching excellence in 1981, 1982 and 1997, and was the associate dean or acting dean of the School of Education for four years. After leaving Stanford University, she held positions at Columbia University and Colgate University. She was past president of the Philosophy of Education Society and the John Dewey Society. In 2002–2003 she held the John W. Porter Chair in Urban Education at Eastern Michigan University. She was Lee L. Jacks Professor of Education, Emerita, at Stanford University from 1998.
Nel N
|
https://en.wikipedia.org/wiki/Matita
|
Matita
is an experimental proof assistant under development at the Computer Science Department of the University of Bologna. It is a tool aiding the development of formal proofs by man-machine collaboration, providing a programming environment where formal specifications, executable algorithms and automatically verifiable correctness certificates naturally coexist.
Matita is based on a dependent type system known as the Calculus of (Co)Inductive Constructions (a derivative of Calculus of Constructions), and is compatible, to some extent, with Coq.
The word "matita" means "pencil" in Italian (a simple and widespread editing tool). It is a reasonably small and simple application, whose architectural and software complexity is meant to be mastered by students, providing a tool particularly suited for testing innovative ideas and solutions. Matita adopts a tactic-based editing mode; (XML-encoded) proof objects are produced for storage and exchange.
Main features
Existential variables are native in Matita, allowing a simpler management of dependent goals.
Matita implements a bidirectional type inference algorithm exploiting both inferred and expected types.
The power of the type inference system (refiner) is further augmented by a mechanism of
hints
that helps in synthesizing unifiers in particular situations specified by the user.
Matita supports a sophisticated disambiguation strategy
based on a dialog between the parser and the typechecker.
At the interactive level, the
|
https://en.wikipedia.org/wiki/Tom%20Newman
|
Tom or Thomas Newman may refer to:
Tom Newman (billiards player) (1894–1943), British player of English billiards and snooker
Tom Newman (musician) (Thomas Dennis Newman, born 1943), musician and producer
Tom Newman (scientist) (fl. 1985), researcher in nanotechnology
Thomas Newman (Thomas Montgomery Newman, born 1955), American composer
Thomas Newman (MP) (fl. 1415–23), lawyer and member of the Parliament of England
|
https://en.wikipedia.org/wiki/Tokamak%20%28software%29
|
The Tokamak Game Physics SDK is an open-source physics engine.
At its beginnings, Tokamak was free for non commercial uses only. Since May 2007, it has become open sourced under a BSD License. Now it can be used under BSD or Zlib license, in order to make the source code exchange with other physics engine possible.
Features
Tokamak features a unique iterative method for solving constraints. This is claimed to allow developers to make trade-offs between accuracy and speed and provides more predictable processor and memory usage. Tokamak's constraint solver does not
involve solving large matrices, thereby avoiding memory bandwidth limitations on some game consoles.
The SDK supports a variety of joint types and joint limits and a realistic friction model. Tokamak is optimized for stacking large numbers of objects - a frequently requested feature by game developers. Tokamak provides collision detection for primitives (box, sphere, capsule), combinations of primitives, and arbitrary static triangle meshes. Lightweight 'rigid particles' provide particle effects in games at minimal cost.
Tokamak also supports "Breakage Constructing models" which will break when a collision occurs. Fragments of the original model will automatically be spawned by Tokamak's built-in breakage functionality.
collision detection✔
Particle system?
Rigid body dynamics?
See also
Physics Abstraction Layer
External links
Tokamak web site
Tokamak sourceforge project page
Computer physics eng
|
https://en.wikipedia.org/wiki/Coleus%20barbatus
|
Coleus barbatus, also known by the synonyms Plectranthus barbatus and incorrectly Coleus forskalaei (and other spellings of this epithet), is a tropical perennial plant related to the typical coleus species. It produces forskolin, an extract useful for pharmaceutical preparations and research in cell biology.
Name
The Brazilian name is (), or , as opposed to the Chilean true boldo; (); (); or (; 'Oxalá's carpet', because of its velvety texture).
In the French Caribbean, it is called "doliprane" (from the brand name of a paracetamol-based drug) because of its uses as a painkiller in folk medicine.
Taxonomy
Coleus barbatus was first described by Henry Cranke Andrews in 1810 as Plectranthus barbatus. It was transferred to Coleus by Bentham in 1830. Although Coleus was previously sunk into Plectranthus, the original binomial was revived in a major study of the subtribe Plectranthinae in 2019.
There has been some confusion over the synonyms of this species. Plectranthus forskaolaei was first described by Vahl in 1790. Vahl's name is illegitimate, because he treats it as a synonym of the earlier described Ocimum hadiense Forrsk. Vahl spelt the epithet as "Forskålaei", referring to Pehr Forsskål, whose surname is also spelt "Forskål". The International Code of Nomenclature for algae, fungi, and plants at Art. 60.7 specifies that "å" is to be replaced by "ao".
Willdenow in 1800 referred to Vahl's name, but spelt the epithet "forskolaei". (, the International Plant Names Ind
|
https://en.wikipedia.org/wiki/Krogh%27s%20principle
|
Krogh's principle states that "for such a large number of problems there will be some animal of choice, or a few such animals, on which it can be most conveniently studied." This concept is central to those disciplines of biology that rely on the comparative method, such as neuroethology, comparative physiology, and more recently functional genomics.
History
Krogh's principle is named after the Danish physiologist August Krogh, winner of the Nobel Prize in Physiology for his contributions to understanding the anatomy and physiology of the capillary system, who described it in The American Journal of Physiology in 1929. However, the principle was first elucidated nearly 60 years prior to this, and in almost the same words as Krogh, in 1865 by Claude Bernard, the French instigator of experimental medicine, on page 27 of his "Introduction à l'étude de la médecine expérimentale":
Krogh wrote the following in his 1929 treatise on the then current 'status' of physiology (emphasis added):
"Krogh's principle" was not utilized as a formal term until 1975 when the biochemist Hans Adolf Krebs (who initially described the Citric Acid Cycle), first referred to it.
More recently, at the International Society for Neuroethology meeting in Nyborg, Denmark in 2004, Krogh's principle was cited as a central principle by the group at their 7th Congress. Krogh's principle has also been receiving attention in the area of functional genomics, where there has been increasing pressure and desire t
|
https://en.wikipedia.org/wiki/Henry%20Tye
|
Sze-Hoi Henry Tye (; born 1947 in Shanghai, China) is a Chinese-American cosmologist and theoretical physicist most notable for proposing that relative brane motion could cause cosmic inflation as well as his work on superstring theory, brane cosmology and elementary particle physics. He had his primary and secondary school education in Hong Kong. Graduated from La Salle College. He received his B.S. from the California Institute of Technology and his Ph.D. in physics from the Massachusetts Institute of Technology under Francis Low. He is the Horace White Professor of Physics, Emeritus, at Cornell University and a fellow of the American Physical Society. He joined the Hong Kong University of Science and Technology in 2011 and was the Director of HKUST Jockey Club Institute for Advanced Study during 2011-2016.
Together with Gia Dvali, he suggested the idea of brane inflation in 1998 in which inflation arises because of the weak forces supersymmetry allows between identical branes. A variant of this proposal based on branes and antibranes was later put on concrete string theoretic grounds by Shamit Kachru and collaborators. He went on to work out many details of brane inflation with his research group at Cornell. He was responsible for the revival of the interest in cosmic strings. Cosmic superstrings are produced at the end of brane inflation due to brane-antibrane annihilation. Apart from the details of brane inflation, he has been working on issues related to the string la
|
https://en.wikipedia.org/wiki/E.%20P.%20Unny
|
Ekanath Padmanabhan Unny is an Indian political cartoonist.
He hails from the Ekanath Family of Elappully, Palakkad. He studied physics at the University in the Indian state of Kerala.
His first cartoon was published in Shankar's Weekly in 1973. He became a professional cartoonist in 1977 with The Hindu. E. P. Unny has worked with the Sunday Mail, The Economic Times and is now the Chief Political Cartoonist with The Indian Express Group.
He has drawn and written graphic novels in Malayalam and a travel book on Kerala - 'Spices and Souls - A doodler's journey through Kerala'. He is said to have been doing graphic shorts in Malayalam literary journals as early as the 1990s. He has also written Santa and the Scribes: The Making of Fort Kochi, which was published in 2014.
Books
Spices and Souls
Business as Usual
Santa and the Scribes: The Making of Fort Kochi
References
Sources
Review of Spices and Souls, Frontline magazine
People from Palakkad district
Indian editorial cartoonists
Living people
Year of birth missing (living people)
Indian Express Limited people
Writers from Kerala
|
https://en.wikipedia.org/wiki/Contact%20number
|
In chemistry, a contact number (CN) is a simple solvent exposure measure that measures residue burial in proteins. The definition of CN varies between authors, but is generally defined as the number of either C or C atoms within a sphere around the C or C atom of the residue. The radius of the sphere is typically chosen to be between 8 and 14Å.
See also
Kissing number, a similar concept in mathematics
References
Solvents
|
https://en.wikipedia.org/wiki/Institute%20of%20Physics%2C%20Bhubaneswar
|
Institute of Physics, Bhubaneswar () is an autonomous research institution of the Department of Atomic Energy (DAE), Government of India. The institute was founded by Professor Bidhu Bhusan Das, who was Director of Public Instruction, Odisha, at that time. Das set up the institute in 1972, supported by the Government of Odisha under the patronage of Odisha's education minister Banamali Patnaik, and chose Dr. Trilochan Pradhan as its first director, when the Institute started theoretical research programs in the various branches of physics. Other notable physicists in the institute's early days included Prof. T. P. Das, of SUNY, Albany, New York, USA and Prof. Jagdish Mohanty of IIT Kanpur and Australian National University, Canberra. In 1981, the Institute moved to its present campus near Chandrasekharpur, Bhubaneswar. It was taken over by the Department of Atomic Energy, India on 25 March 1985 and started functioning as an autonomous body.
Research
The institute conducts research in theoretical and experimental physics.
Theoretical physics
Research areas in theoretical physics include condensed matter theory, nuclear and high energy physics. High-energy theorists at IOP have made contributions to field theories, phase transitions in early universe, cosmology, the Planck scale phenomena, string theory and high-energy nuclear physics such as qgp, equation of state and nuclear astrophysics, neutron stars, high-energy phenomenology and neutrino physics phenomenology. In theor
|
https://en.wikipedia.org/wiki/Absolute%20presentation%20of%20a%20group
|
In mathematics, an absolute presentation is one method of defining a group.
Recall that to define a group by means of a presentation, one specifies a set of generators so that every element of the group can be written as a product of some of these generators, and a set of relations among those generators. In symbols:
Informally is the group generated by the set such that for all . But here there is a tacit assumption that is the "freest" such group as clearly the relations are satisfied in any homomorphic image of . One way of being able to eliminate this tacit assumption is by specifying that certain words in should not be equal to That is we specify a set , called the set of irrelations, such that for all
Formal definition
To define an absolute presentation of a group one specifies a set of generators and sets and of relations and irrelations among those
generators. We then say has absolute presentation
provided that:
has presentation
Given any homomorphism such that the irrelations are satisfied in , is isomorphic to .
A more algebraic, but equivalent, way of stating condition 2 is:
2a. If is a non-trivial normal subgroup of then
Remark: The concept of an absolute presentation has been fruitful in fields such as algebraically closed groups and the Grigorchuk topology.
In the literature, in a context where absolute presentations are being discussed, a presentation (in the usual sense of the word) is sometimes referred to as a relative prese
|
https://en.wikipedia.org/wiki/DCFS
|
The following concepts can be abbreviated DCFS
Department of Children and Family Services, the name of a governmental agency in some states in the United States
Department of Children and Family Services (Los Angeles County)
Descriptional Complexity of Formal Systems, a computer science conference
See also
Department for Children, Schools and Families (DCSF), British government department responsible for all issues affecting people up to the age of 19 including child protection and education
|
https://en.wikipedia.org/wiki/Random-access%20stored-program%20machine
|
In theoretical computer science the random-access stored-program (RASP) machine model is an abstract machine used for the purposes of algorithm development and algorithm complexity theory.
The RASP is a random-access machine (RAM) model that, unlike the RAM, has its program in its "registers" together with its input. The registers are unbounded (infinite in capacity); whether the number of registers is finite is model-specific. Thus the RASP is to the RAM as the Universal Turing machine is to the Turing machine. The RASP is an example of the von Neumann architecture whereas the RAM is an example of the Harvard architecture.
The RASP is closest of all the abstract models to the common notion of computer. But unlike actual computers the RASP model usually has a very simple instruction set, greatly reduced from those of CISC and even RISC processors to the simplest arithmetic, register-to-register "moves", and "test/jump" instructions. Some models have a few extra registers such as an accumulator.
Together with the register machine, the RAM, and the pointer machine the RASP makes up the four common sequential machine models, called this to distinguish them from the "parallel" models (e.g. parallel random-access machine) [cf. van Emde Boas (1990)].
Informal definition: random-access stored-program model (RASP)
Nutshell description of a RASP:
The RASP is a universal Turing machine (UTM) built on a random-access machine RAM chassis.
The reader will remember that the UTM is a
|
https://en.wikipedia.org/wiki/Spurious
|
Spurious may refer to:
Spurious relationship in statistics
Spurious emission or spurious tone in radio engineering
Spurious key in cryptography
Spurious interrupt in computing
Spurious wakeup in computing
Spurious, a 2011 novel by Lars Iyer
|
https://en.wikipedia.org/wiki/Unity%20amplitude
|
A sinusoidal waveform is said to have a unity amplitude when the amplitude of the wave is equal to 1.
where . This terminology is most commonly used in digital signal processing and is usually associated with the Fourier series and Fourier Transform sinusoids that involve a duty cycle, , and a defined fundamental period, .
Analytic signals with unit amplitude satisfy the Bedrosian Theorem.
References
Digital signal processing
|
https://en.wikipedia.org/wiki/Borel%20conjecture
|
In mathematics, specifically geometric topology, the Borel conjecture (named for Armand Borel) asserts that an aspherical closed manifold is determined by its fundamental group, up to homeomorphism. It is a rigidity conjecture, asserting that a weak, algebraic notion of equivalence (namely, homotopy equivalence) should imply a stronger, topological notion (namely, homeomorphism).
Precise formulation of the conjecture
Let and be closed and aspherical topological manifolds, and let
be a homotopy equivalence. The Borel conjecture states that the map is homotopic to a homeomorphism. Since aspherical manifolds with isomorphic fundamental groups are homotopy equivalent, the Borel conjecture implies that aspherical closed manifolds are determined, up to homeomorphism, by their fundamental groups.
This conjecture is false if topological manifolds and homeomorphisms are replaced by smooth manifolds and diffeomorphisms; counterexamples can be constructed by taking a connected sum with an exotic sphere.
The origin of the conjecture
In a May 1953 letter to Jean-Pierre Serre, Armand Borel raised the question whether two aspherical manifolds with isomorphic fundamental groups are homeomorphic. A positive answer to the question "Is every homotopy equivalence between closed aspherical manifolds homotopic to a homeomorphism?" is referred to as the "so-called Borel Conjecture" in a 1986 paper of Jonathan Rosenberg.
Motivation for the conjecture
A basic question is the following: if
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.