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A bucket queue can be used to maintain the vertices of an undirected graph, prioritized by their degrees, and repeatedly find and remove the vertex of minimum degree. This greedy algorithm can be used to calculate the degeneracy of a given graph, equal to the largest degree of any vertex at the time of its removal. The...
Bucket queue
0.812301
18,301
Language technology, often called human language technology (HLT), studies methods of how computer programs or electronic devices can analyze, produce, modify or respond to human texts and speech. Working with language technology often requires broad knowledge not only about linguistics but also about computer science....
Human Language Technology
0.8123
18,302
Every morphism in a concrete category whose underlying function is injective is a monomorphism; in other words, if morphisms are actually functions between sets, then any morphism which is a one-to-one function will necessarily be a monomorphism in the categorical sense. In the category of sets the converse also holds,...
Strong monomorphism
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In the context of abstract algebra or universal algebra, a monomorphism is an injective homomorphism. A monomorphism from X to Y is often denoted with the notation X ↪ Y {\displaystyle X\hookrightarrow Y} . In the more general setting of category theory, a monomorphism (also called a monic morphism or a mono) is a left...
Strong monomorphism
0.812295
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This is the case of space-filling curves and fractal curves. For ensuring more regularity, the function that defines a curve is often supposed to be differentiable, and the curve is then said to be a differentiable curve. A plane algebraic curve is the zero set of a polynomial in two indeterminates.
Closed curve
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This definition encompasses most curves that are studied in mathematics; notable exceptions are level curves (which are unions of curves and isolated points), and algebraic curves (see below). Level curves and algebraic curves are sometimes called implicit curves, since they are generally defined by implicit equations....
Closed curve
0.812292
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More generally, an algebraic curve is the zero set of a finite set of polynomials, which satisfies the further condition of being an algebraic variety of dimension one. If the coefficients of the polynomials belong to a field k, the curve is said to be defined over k. In the common case of a real algebraic curve, where...
Closed curve
0.812292
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The rate-constant of probability-decay in hydrogen is equal to the inverse of the Bohr radius, but since Bohr worked with circular orbits, not zero area ellipses, the fact that these two numbers exactly agree is considered a "coincidence". (However, many such coincidental agreements are found between the semiclassical ...
Bohr Model
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Nevertheless, in the modern fully quantum treatment in phase space, the proper deformation (careful full extension) of the semi-classical result adjusts the angular momentum value to the correct effective one. As a consequence, the physical ground state expression is obtained through a shift of the vanishing quantum an...
Bohr Model
0.812288
18,309
Most research telescopes have spectrographs. The measured spectra are used to determine the chemical composition and physical properties of astronomical objects (such as their temperature, density of elements in a star, velocity, black holes and more). An important use for spectroscopy is in biochemistry. Molecular sam...
Spectroscopic analysis
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As a result, these spectra can be used to detect, identify and quantify information about the atoms and molecules. Spectroscopy is also used in astronomy and remote sensing on Earth.
Spectroscopic analysis
0.812281
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Spectroscopic studies were central to the development of quantum mechanics, because the first useful atomic models described the spectra of Hydrogen which models include the Bohr model, the Schrödinger equation, and Matrix mechanics which all can produce the spectral lines of Hydrogen, therefore, providing the basis fo...
Spectroscopic analysis
0.812281
18,312
Most programming languages, even those with no explicit Boolean type, have support for Boolean algebraic operations such as conjunction (AND, &, *), disjunction (OR, |, +), equivalence (EQV, =, ==), exclusive or/non-equivalence (XOR, NEQV, ^, !=, ¬), and negation (NOT, ~, !, ¬). In some languages, like Ruby, Smalltalk,...
Boolean type
0.812281
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Subsumption architecture is a methodology for developing artificial intelligence that is heavily associated with behavior based robotics. This architecture is a way of decomposing complicated intelligent behavior into many "simple" behavior modules, which are in turn organized into layers. Each layer implements a parti...
Hierarchical control system
0.81228
18,314
A kinetic triangulation data structure is a kinetic data structure that maintains a triangulation of a set of moving points. Maintaining a kinetic triangulation is important for applications that involve motion planning, such as video games, virtual reality, dynamic simulations and robotics.
Kinetic triangulation
0.812278
18,315
The area of the winding step is dependent on the wire gauge and coil bobbin geometry. If the winding step cannot be executed properly then the self-guiding ability of the wire is lost and a wild winding is produced. Overall, the first intruding wire mainly determines the location and quality of the winding step.
Coil winding technology
0.812278
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Parameters such as inductance, Q factor, insulation strength, and strength of the desired magnetic field greatly influence the design of coil windings. Coil winding can be structured into several groups regarding the type and geometry of the wound coil. Mass production of electromagnetic coils relies on automated machi...
Coil winding technology
0.812278
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In electrical engineering, coil winding is the manufacture of electromagnetic coils. Coils are used as components of circuits, and to provide the magnetic field of motors, transformers, and generators, and in the manufacture of loudspeakers and microphones. The shape and dimensions of a winding are designed to fulfill ...
Coil winding technology
0.812278
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When winding toothed chains, the flyer winding technique, also a type of needle winding and chain winding can be used. A disadvantage when using the flyer winding technique is the fact that only one tooth at a time can be wound. So, toothed chains are developing as a result but due to the wiring topology most of the st...
Coil winding technology
0.812278
18,319
a) T-segments T-segments are preferably processed with the linear winding technique or the flyer-winding technique. For this, the winding supports are designed in a way that a mounting at the tooth back can be carried out. It is in particular the outer geometry that will serve as the contact surface of the adjacent too...
Coil winding technology
0.812278
18,320
For the reasons described above, it is therefore in practice impossible for the wire guide to determine a precise gradient according to the wire diameter. These unpredictable circumstances may be prevented or counteracted at the beginning of the winding by forcing the wire, meaning, every single winding of the first la...
Coil winding technology
0.812277
18,321
Wigner's original paper has provoked and inspired many responses across a wide range of disciplines. These include Richard Hamming in computer science, Arthur Lesk in molecular biology, Peter Norvig in data mining, Max Tegmark in physics, Ivor Grattan-Guinness in mathematics and Vela Velupillai in economics.
Wigner's Puzzle
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It would give us a deep sense of frustration in our search for what I called 'the ultimate truth'. The reason that such a situation is conceivable is that, fundamentally, we do not know why our theories work so well. Hence, their accuracy may not prove their truth and consistency. Indeed, it is this writer's belief tha...
Wigner's Puzzle
0.812277
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Whether humans checking the results of humans can be considered an objective basis for observation of the known (to humans) universe is an interesting question, one followed up in both cosmology and the philosophy of mathematics. Wigner also laid out the challenge of a cognitive approach to integrating the sciences: A ...
Wigner's Puzzle
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The equations also describe radio waves, discovered by David Edward Hughes in 1879, around the time of James Clerk Maxwell's death. Wigner sums up his argument by saying that "the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and that there is no rational explanatio...
Wigner's Puzzle
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A different response, advocated by physicist Max Tegmark, is that physics is so successfully described by mathematics because the physical world is completely mathematical, isomorphic to a mathematical structure, and that we are simply uncovering this bit by bit. The same interpretation had been advanced some years pre...
Wigner's Puzzle
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We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning. Wigner's work provided a fresh insight into both physics and the philosophy of mathematics, and ...
Wigner's Puzzle
0.812277
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The tables were turned by Michael Atiyah with his essay "The unreasonable effectiveness of physics in mathematics". He argued that the toolbox of physicist enables a practitioner like Edward Witten to go beyond standard mathematics, in particular the geometry of 4-manifolds. The tools of a physicist are cited as quantu...
Wigner's Puzzle
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Hamming's account does not reveal an awareness of the 20th century scholarly debate over just what Galileo did.The inverse square law of universal gravitation necessarily follows from the conservation of energy and of space having three dimensions. Measuring the exponent in the law of universal gravitation is more a te...
Wigner's Puzzle
0.812277
18,329
The belief that science is experimentally grounded is only partially true. Rather, our intellectual apparatus is such that much of what we see comes from the glasses we put on. Eddington went so far as to claim that a sufficiently wise mind could deduce all of physics, illustrating his point with the following joke: "S...
Wigner's Puzzle
0.812277
18,330
In the mathematical discipline of graph theory, a subset of vertices in a graph G is called dissociation if it induces a subgraph with maximum degree 1. The number of vertices in a maximum cardinality dissociation set in G is called the dissociation number of G, denoted by diss(G). The problem of computing diss(G) (dis...
Dissociation number
0.812271
18,331
In probability theory, a normalizing constant or normalizing factor is used to reduce any probability function to a probability density function with total probability of one. For example, a Gaussian function can be normalized into a probability density function, which gives the standard normal distribution. In Bayes' ...
Normalization constant
0.81227
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In probability theory, a normalizing constant is a constant by which an everywhere non-negative function must be multiplied so the area under its graph is 1, e.g., to make it a probability density function or a probability mass function.
Normalization constant
0.81227
18,333
In linguistics, statistical semantics applies the methods of statistics to the problem of determining the meaning of words or phrases, ideally through unsupervised learning, to a degree of precision at least sufficient for the purpose of information retrieval.
Statistical semantics
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Statistical semantics focuses on the meanings of common words and the relations between common words, unlike text mining, which tends to focus on whole documents, document collections, or named entities (names of people, places, and organizations). Statistical semantics is a subfield of computational semantics, which i...
Statistical semantics
0.812267
18,335
The algebra of invariants of a sextic form is generated by invariants of degree 2, 4, 6, 10, 15. The generators of degrees 2, 4, 6, 10 generate a polynomial ring, which contains the square of the generator of degree 15. (Schur 1968, II.9) The ring of covariants is generated by 26 covariants. The ring of invariants is c...
Invariants of a binary form
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Sylvester stated that the ring of invariants of binary decics is generated by 104 invariants the ring of covariants by 475 covariants; his list is to be correct for degrees up to 16 but wrong for higher degrees. Brouwer & Popoviciu (2010b) showed that the algebra of invariants of a degree 10 form is generated by 106 in...
Invariants of a binary form
0.812265
18,337
University presses are more prestigious than commercial press publication. The status of working papers and conference proceedings depends on the discipline; they are typically more important in the applied sciences. The value of publication as a preprint or scientific report on the web has in the past been low, but in...
Scientific information
0.812262
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As with much steroid chemistry, the Marker degradation relies heavily on kinetic control to degrade the sapogenin side chain while leaving similar functional groups on the steroid nucleus (relatively) unaffected. The first step is the reaction that led Marker to discover that the sapogenins had a ketone spiro acetal st...
Marker degradation
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The Marker degradation is a three-step synthetic route in steroid chemistry developed by American chemist Russell Earl Marker in 1938–1940. It is used for the production of cortisone and mammalian sex hormones (progesterone, estradiol, etc.) from plant steroids, and established Mexico as a world center for steroid prod...
Marker degradation
0.812261
18,340
Rosenkranz would have to virtually reinvent the production process for progesterone from diosgenin: he also established an Institute of Chemistry at the National Autonomous University of Mexico, where one of the first research students was Luis E. Miramontes, later to become a pivotal researcher at Syntex. Rosenkranz a...
Marker degradation
0.812261
18,341
and renamed Hormonosynth (later Diosynth).The difficulties in fine chemicals manufacture in Mexico were indeed considerable: there was a severe shortage of trained chemists and indeed no doctoral program in chemistry at any Mexican university. When Marker left Syntex, his associates found no instructions for the produc...
Marker degradation
0.812261
18,342
The company emerged from a University of Edinburgh project initiated in 1994 by Win Rampen and Stephen Salter with a focus on producing high-tech machines to generate renewable energy and reduce fuel consumption of vehicles. The UK Carbon Trust supported the research project splitting off into a fully operational compa...
Artemis Intelligent Power
0.812259
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In mathematics, an algebraic structure ( R , T ) {\displaystyle (R,T)} consisting of a non-empty set R {\displaystyle R} and a ternary mapping T: R 3 → R {\displaystyle T\colon R^{3}\to R\,} may be called a ternary system. A planar ternary ring (PTR) or ternary field is special type of ternary system used by Marshall H...
Ternary ring
0.812256
18,344
there is x ~ = X − 3 ∈ S ′ {\displaystyle {\tilde {x}}=X-{\sqrt {3}}\in S'} such that a ~ x ~ = b {\displaystyle {\tilde {a}}{\tilde {x}}=b} . Note that a = X + 3 {\displaystyle a=X+3} is still not a divisor of b = X 2 − 3 {\displaystyle b=X^{2}-3} , because of the same reason as for R ′ = Z {\displaystyle R'=\mathbb ...
Divisibility (ring theory)
0.812254
18,345
The Gibbs method formalism is a method used to analyze pressures and temperatures of zoned minerals and textural changes in metamorphic rocks by applying differential thermodynamic equations based on Duhem's Theorem. It attempts to simulate the garnet growth zoning numerically by solving a set of differential equations...
Pressure-temperature-time path
0.812251
18,346
Powerful techniques like mutagenesis and complementation were made possible in Arabidopsis thaliana via generation of T-DNA containing mutant lines, recombinant plasmids, techniques like transposon tagging etc. Availability of complete physical and genetic maps, RNAi vectors, and rapid transformation protocols are some...
Plant evolutionary developmental biology
0.812251
18,347
The first collection of Arabidopsis thaliana mutants were made around 1945. However it formally became established as a model organism only in 1998. The recent spurt in information on various plant-related processes has largely been a result of the revolution in molecular biology.
Plant evolutionary developmental biology
0.812251
18,348
In this sense it is plant evolutionary developmental biology (plant evo-devo). According to Zimmermann, diversity in plant evolution occurs though various developmental processes. Three very basic processes are heterochrony (changes in the timing of developmental processes), heterotopy (changes in the relative position...
Plant evolutionary developmental biology
0.812251
18,349
Molecular genetics confirmed these conclusions (see below). It has been proposed that the before the evolution of leaves, plants had the photosynthetic apparatus on the stems. Today's megaphyll leaves probably became commonplace some 360 mya, about 40 my after the simple leafless plants had colonized the land in the ea...
Plant evolutionary developmental biology
0.812251
18,350
Apart from EST and genome sequences, several other tools like PCR, yeast two-hybrid system, microarrays, RNA Interference, SAGE, QTL mapping etc. permit the rapid study of plant developmental patterns. Recently, cross-species hybridization has begun to be employed on microarray chips, to study the conservation and dive...
Plant evolutionary developmental biology
0.812251
18,351
Evolutionary developmental biology (evo-devo) is the study of developmental programs and patterns from an evolutionary perspective. It seeks to understand the various influences shaping the form and nature of life on the planet. Evo-devo arose as a separate branch of science rather recently. An early sign of this occur...
Plant evolutionary developmental biology
0.812251
18,352
In fact, it is simply the timing of the KNOX gene expression!" In fact there is evidence for this continuum already at the beginning of land plant evolution. Furthermore, studies in molecular genetics confirmed that compound leaves are intermediate between simple leaves and shoots, that is, they are partially homologou...
Plant evolutionary developmental biology
0.812251
18,353
The coming years should see a rapid development in comparative studies on leaf development, with many EST sequences involved in the process coming online. Molecular genetics has also shed light on the relation between radial symmetry (characteristic of stems) and dorsiventral symmetry (typical for leaves). James (2009)...
Plant evolutionary developmental biology
0.812251
18,354
In molecular biology, a library is a collection of DNA fragments that is stored and propagated in a population of micro-organisms through the process of molecular cloning. There are different types of DNA libraries, including cDNA libraries (formed from reverse-transcribed RNA), genomic libraries (formed from genomic D...
Library (biology)
0.81225
18,355
Kurt Mahler showed in 1968 that the number π 2 Y 0 ( 2 ) J 0 ( 2 ) − γ {\displaystyle {\frac {\pi }{2}}{\frac {Y_{0}(2)}{J_{0}(2)}}-\gamma } is transcendental (here, J α ( x ) {\displaystyle J_{\alpha }(x)} and Y α ( x ) {\displaystyle Y_{\alpha }(x)} are Bessel functions). In 2009 Alexander Aptekarev proved that at le...
Euler–Mascheroni constant
0.812248
18,356
The number γ has not been proved algebraic or transcendental. In fact, it is not even known whether γ is irrational. Using a continued fraction analysis, Papanikolaou showed in 1997 that if γ is rational, its denominator must be greater than 10244663. The ubiquity of γ revealed by the large number of equations below ma...
Euler–Mascheroni constant
0.812248
18,357
The constant eγ is important in number theory. Some authors denote this quantity simply as γ′. eγ equals the following limit, where pn is the nth prime number: This restates the third of Mertens' theorems. The numerical value of eγ is: Other infinite products relating to eγ include: These products result from the Barne...
Euler–Mascheroni constant
0.812248
18,358
In the mathematical theory of Riemannian geometry, there are two uses of the term Fermi coordinates. In one use they are local coordinates that are adapted to a geodesic. In a second, more general one, they are local coordinates that are adapted to any world line, even not geodesical.Take a future-directed timelike cur...
Fermi coordinates
0.812245
18,359
Optimization Programming Language (OPL) is an algebraic modeling language for mathematical optimization models, which makes the coding easier and shorter than with a general-purpose programming language. It is part of the CPLEX software package and therefore tailored for the IBM ILOG CPLEX and IBM ILOG CPLEX CP Optimiz...
Optimization Programming Language
0.812244
18,360
Named after Dutch physicist Johannes Diderik van der Waals, the van der Waals force plays a fundamental role in fields as diverse as supramolecular chemistry, structural biology, polymer science, nanotechnology, surface science, and condensed matter physics. It also underlies many properties of organic compounds and mo...
Van der Waals forces
0.812242
18,361
In molecular physics, the van der Waals force is a distance-dependent interaction between atoms or molecules. Unlike ionic or covalent bonds, these attractions do not result from a chemical electronic bond; they are comparatively weak and therefore more susceptible to disturbance. The van der Waals force quickly vanish...
Van der Waals forces
0.812242
18,362
A few gamma rays in astronomy are known to arise from gamma decay (see discussion of SN1987A), but most do not. Photons from astrophysical sources that carry energy in the gamma radiation range are often explicitly called gamma-radiation. In addition to nuclear emissions, they are often produced by sub-atomic particle ...
Γ radiation
0.812242
18,363
Understanding the interactions between organisms and their abiotic environment, and the resulting coupled evolution of the biosphere and geosphere is a central theme of research in biogeology. Biogeochemists contribute to this understanding by studying the transformations and transport of chemical substrates and produc...
Ocean biogeochemistry
0.81224
18,364
Moreover, for all sufficiently large x {\displaystyle x} , the interval {\displaystyle } contains many practical numbers.Let p ( x ) {\displaystyle p(x)} count how many practical numbers are at most x {\displaystyle x} . Margenstern (1991) conjectured that p ( x ) {\displaystyle p(x)} is asymptotic to c x / log ⁡ x {\...
Practical number
0.812237
18,365
One reason for interest in practical numbers is that many of their properties are similar to properties of the prime numbers. Indeed, theorems analogous to Goldbach's conjecture and the twin prime conjecture are known for practical numbers: every positive even integer is the sum of two practical numbers, and there exis...
Practical number
0.812237
18,366
In number theory, a practical number or panarithmic number is a positive integer n {\displaystyle n} such that all smaller positive integers can be represented as sums of distinct divisors of n {\displaystyle n} . For example, 12 is a practical number because all the numbers from 1 to 11 can be expressed as sums of its...
Practical number
0.812237
18,367
The following outline is provided as an overview of and topical guide to physiology: Physiology – scientific study of the normal function in living systems. A branch of biology, its focus is in how organisms, organ systems, organs, cells, and biomolecules carry out the chemical or physical functions that exist in a liv...
Outline of physiology
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18,368
Physiology can be described as all of the following: An academic discipline A branch of science A branch of biology
Outline of physiology
0.812237
18,369
Its algorithm was later converged into Christopher Watkin's Q-Learning algorithm. Although not as a functional computer, in examples of demonstration, MENACE has been used as a teaching aid for various neural network classes, including a public demonstration from University College London Researcher Matthew Scroggs. A ...
Matchbox Educable Noughts and Crosses Engine
0.812236
18,370
Donald Michie's MENACE proved that a computer could learn from failure and success to become good at a task. It used what would become core principles within the field of machine learning before they had been properly theorised. For example, the combination of how MENACE starts with equal numbers of types of beads in e...
Matchbox Educable Noughts and Crosses Engine
0.812236
18,371
Donald Michie (1923–2007) had been on the team decrypting the German Tunny Code during World War II. Fifteen years later, he wanted to further display his mathematical and computational prowess with an early convolutional neural network. Since computer equipment was not obtainable for such uses, and Michie did not have...
Matchbox Educable Noughts and Crosses Engine
0.812236
18,372
Each colour represented a move on a square on the game grid, and so matchboxes with arrangements where positions on the grid were already taken would not have beads for that position. Additionally, at the front of the tray were two extra pieces of card in a "V" shape, the point of the "V" pointing at the front of the m...
Matchbox Educable Noughts and Crosses Engine
0.812236
18,373
Following MENACE's maiden tournament against Michie, it demonstrated successful artificial intelligence in its strategy. Michie's essays on MENACE's weight initialisation and the BOXES algorithm used by MENACE became popular in the field of computer science research. Michie was honoured for his contribution to machine ...
Matchbox Educable Noughts and Crosses Engine
0.812236
18,374
The Matchbox Educable Noughts and Crosses Engine (sometimes called the Machine Educable Noughts and Crosses Engine or MENACE) was a mechanical computer made from 304 matchboxes designed and built by artificial intelligence researcher Donald Michie in 1961. It was designed to play human opponents in games of noughts and...
Matchbox Educable Noughts and Crosses Engine
0.812236
18,375
Other fields that use trigonometry or trigonometric functions include music theory, geodesy, audio synthesis, architecture, electronics, biology, medical imaging (CT scans and ultrasound), chemistry, number theory (and hence cryptology), seismology, meteorology, oceanography, image compression, phonetics, economics, el...
Triangle identities
0.812234
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In land surveying, trigonometry is used in the calculation of lengths, areas, and relative angles between objects.On a larger scale, trigonometry is used in geography to measure distances between landmarks.
Triangle identities
0.812234
18,377
It was found in this study that offenders are disproportionally low-income and black and the average person of genetic testing is wealthy and white. The results from the study had different results. In 2016, there was a survey called the National Crime Victimization Survey (NCVS) that was provided by the US Bureau of J...
Forensic science
0.81223
18,378
Whereas traditional bioinformatics is a wide subject it has a large focus on molecular biology, pharmaceutical bioinformatics more specifically targets chemical-biological interaction and exploratory focus of chemical and biological interactors using e.g. cheminformatics and chemometrics methods. Methods include, apart...
Pharmaceutical bioinformatics
0.812229
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There are many software tools for pharmaceutical bioinformatics. An example of an open source tool is the Bioclipse workbench.
Pharmaceutical bioinformatics
0.812229
18,380
Pharmaceutical bioinformatics is a research field related to bioinformatics but with the focus on studying biological and chemical processes in the pharmaceutical area; to understand how xenobiotics interact with the human body and the drug discovery process.
Pharmaceutical bioinformatics
0.812229
18,381
One of the major fields within pharmaceutical bioinformatics is the in silico metabolism prediction of drug candidates. This field is in turn divided into three tasks; Predicting the occurrence of an interaction between a compound and an enzyme, Predicting the location in the compound that takes part in the interaction...
Pharmaceutical bioinformatics
0.812229
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One conference specific to Pharmaceutical Bioinformatics is "International Conference on Pharmaceutical Bioinformatics" (ICPB) (http://www.icpb.net)
Pharmaceutical bioinformatics
0.812229
18,383
Chinese Chemistry Olympiad (Chinese: 中国化学奥林匹克竞赛) is an annual academic competition held by Chinese Chemical Society. CAS changed its official Chinese name in February 2014, though its English translation remains the same.The first CChO was held in 1984, 16 years after IChO. The event has been held every year since then...
Chinese Chemistry Olympiad
0.812227
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It is considered to be the most difficult Chemistry exam throughout the world, the difficulty of Final round is much harder than IChO. The difficulty of the preliminary round is often enough to surpass IChO, also. Its problems are often beyond the abilities of an overwhelming majority of undergraduates. (As a consequen...
Chinese Chemistry Olympiad
0.812227
18,385
Most relay logic diagrams are in "ladder logic" form. Systems using relay logic diagrams in other forms include the Vernam cipher machine, the many 20th century telephone exchanges that controlled their crossbar switches by relays, and the designs for the various electro-mechanical computers including the Harvard Mark ...
Relay logic
0.81222
18,386
(From elementary geometry, all triangles on a circle with 2 vertices on opposite ends of a diameter are right triangles.) The curves of constant τ {\displaystyle \tau } are non-intersecting circles of different radii that surround the foci but again are not concentric.
Bipolar coordinate system
0.812216
18,387
The classic applications of bipolar coordinates are in solving partial differential equations, e.g., Laplace's equation or the Helmholtz equation, for which bipolar coordinates allow a separation of variables. An example is the electric field surrounding two parallel cylindrical conductors with unequal diameters.
Bipolar coordinate system
0.812215
18,388
Vector space Linear combination Linear span Linear independence Scalar multiplication Basis Change of basis Hamel basis Cyclic decomposition theorem Dimension theorem for vector spaces Hamel dimension Examples of vector spaces Linear map Shear mapping or Galilean transformation Squeeze mapping or Lorentz transformation...
Outline of linear algebra
0.812214
18,389
Projective space Projective transformation Projective geometry Projective linear group Quadric and conic section
Outline of linear algebra
0.812214
18,390
Multilinear algebra Tensor Classical treatment of tensors Component-free treatment of tensors Gamas's Theorem Outer product Tensor algebra Exterior algebra Symmetric algebra Clifford algebra Geometric algebra
Outline of linear algebra
0.812214
18,391
Matrix decomposition Cholesky decomposition LU decomposition QR decomposition Polar decomposition Reducing subspace Spectral theorem Singular value decomposition Higher-order singular value decomposition Schur decomposition Schur complement Haynsworth inertia additivity formula
Outline of linear algebra
0.812214
18,392
Matrix Matrix addition Matrix multiplication Basis transformation matrix Characteristic polynomial Trace Eigenvalue, eigenvector and eigenspace Cayley–Hamilton theorem Spread of a matrix Jordan normal form Weyr canonical form Rank Matrix inversion, invertible matrix Pseudoinverse Adjugate Transpose Dot product Symmetri...
Outline of linear algebra
0.812214
18,393
Topological vector space Normed vector space Inner product space Euclidean space Orthogonality Orthogonal complement Orthogonal projection Orthogonal group Pseudo-Euclidean space Null vector Indefinite orthogonal group Orientation (geometry) Improper rotation Symplectic structure
Outline of linear algebra
0.812214
18,394
This is an outline of topics related to linear algebra, the branch of mathematics concerning linear equations and linear maps and their representations in vector spaces and through matrices.
Outline of linear algebra
0.812214
18,395
Affine space Affine transformation Affine group Affine geometry Affine coordinate system Flat (geometry) Cartesian coordinate system Euclidean group Poincaré group Galilean group
Outline of linear algebra
0.812214
18,396
In certain situations such a measure can be useful, but it is not an intercept point according to definition. Its value depends on the measurement conditions that need to be documented, whereas the IP according to definition is mostly unambiguous; although there is some dependency on frequency and tone spacing, dependi...
Fifth-order intercept point
0.812214
18,397
In the Analysis–Synthesis test, the individual has to learn and orally state the solutions to incomplete logic puzzles that mimic a miniature mathematics system. The test also contains some of the features involved in using symbolic formulations in other fields such as chemistry and logic. The individual has presented ...
Fluid and crystallized intelligence
0.812209
18,398
In the summer of 1995, the Resource Centre was established as part of the German Human Genome Project (DHGP) by Hans Lehrach (Max Planck Institute for Molecular Genetics (MPIMG), Berlin-Dahlem), Günther Zehetner (MPIMG, until July 2000 Scientific Director of the Berlin Resource Center) and Annemarie Poustka (German Can...
German Resource Center for Genome Research
0.812207
18,399
Experimental results done with the standardized materials were reported back by researchers and collected in the Primary Database. In January 1990 Zehetner was appointed as Associated Scientist at the ICRF under the then Director General Sir Walter Bodmer. In early 1995 the RLDB moved to Berlin to the Max Planck Instit...
German Resource Center for Genome Research
0.812207