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23,000 | The Bohr–Van Leeuwen theorem proves that there cannot be any diamagnetism or paramagnetism in a purely classical system. The paramagnetic response has then two possible quantum origins, either coming from permanent magnetic moments of the ions or from the spatial motion of the conduction electrons inside the material. ... | Paramagnetism | 0.809079 |
23,001 | The journal was established in 2007 with Anatole Katok as the founding editor-in-chief. It covers the theory of dynamical systems with particular emphasis on the mutual interaction between dynamics and other major areas of mathematical research: number theory, symplectic geometry, differential geometry, rigidity, quant... | Journal of Modern Dynamics | 0.809077 |
23,002 | The Journal of Modern Dynamics is a peer-reviewed scientific journal of mathematics published by the American Institute of Mathematical Sciences with the support of the Anatole Katok Center for Dynamical Systems and Geometry (Pennsylvania State University). The editor-in-chief is Giovanni Forni (University of Maryland ... | Journal of Modern Dynamics | 0.809077 |
23,003 | SAM is distributed by Stanford University in an R-package.SAM identifies statistically significant genes by carrying out gene specific t-tests and computes a statistic dj for each gene j, which measures the strength of the relationship between gene expression and a response variable. This analysis uses non-parametric s... | Significance analysis of microarrays | 0.809076 |
23,004 | F a l s e d i s c o v e r y r a t e ( F D R ) = M e d i a n ( o r 90 t h p e r c e n t i l e ) o f # o f f a l s e l y c a l l e d g e n e s N u m b e r o f g e n e s c a l l e d s i g n i f i c a n t {\displaystyle \mathrm {False\ discovery\ rate\ (FDR)={\frac {Median\ (or\ 90^{th}\ percentile)\ of\ \#\ of\ falsely\ c... | Significance analysis of microarrays | 0.809076 |
23,005 | Some minor anomalies may be clues to more significant internal abnormalities. Birth defect is a widely used term for a congenital malformation, i.e. a congenital, physical anomaly that is recognizable at birth, and which is significant enough to be considered a problem. According to the Centers for Disease Control and ... | Congenital diseases | 0.80907 |
23,006 | In a similar way, the theory of special relativity posits that the thermal energy in all objects, including solids, contributes to their total masses, even though this energy is present as the kinetic and potential energies of the atoms in the object, and it (in a similar way to the gas) is not seen in the rest masses ... | Mass-energy equivalence | 0.809066 |
23,007 | The nonrelativistic kinetic energy formula did not always include the traditional factor of 1/2, since German polymath Gottfried Leibniz introduced kinetic energy without it, and the 1/2 is largely conventional in prerelativistic physics. By assuming that every particle has a mass that is the sum of the masses of the e... | Mass-energy equivalence | 0.809066 |
23,008 | CERN estimated in 2011 that over a billion times more energy is required to make and store antimatter than could be released in its annihilation.As most of the mass which comprises ordinary objects resides in protons and neutrons, converting all the energy of ordinary matter into more useful forms requires that the pro... | Mass-energy equivalence | 0.809066 |
23,009 | Magnetic separation techniques are also used in microbiology. In this case, binding molecules and antibodies are used in order to isolate specific viable organisms, nucleic acids, or antigens. This technology helps isolating bacterial species to identify and give diagnostics of genes targeting certain organisms. When m... | Magnetic separation | 0.809064 |
23,010 | Magnetic cell separation is on the rise. It is currently being used in clinical therapies, more specifically in cancers and hereditary diseases researches. Magnetic cell separation took a turn when, Zborowski, an Immunomagnetic Cell Separation (IMCS) pioneer, analyzed commercial magnetic cell separation. Zborowski unco... | Magnetic separation | 0.809064 |
23,011 | Short-circuiting can lead to errors in branch prediction on modern central processing units (CPUs), and dramatically reduce performance. A notable example is highly optimized ray with axis aligned box intersection code in ray tracing. Some compilers can detect such cases and emit faster code, but programming language s... | Short-circuiting operator | 0.809063 |
23,012 | Assign the test cases to testers, who manually follow the steps and record the results. Author a test report, detailing the findings of the testers. The report is used by managers to determine whether the software can be released, and if not, it is used by engineers to identify and correct the problems.A rigorous test ... | Manual testing | 0.809059 |
23,013 | Meyer described the Eiffel software development method, based on a small number of key ideas from software engineering and computer science, in Object-Oriented Software Construction. Essential to the quality focus of Eiffel is Meyer's reliability mechanism, Design by Contract, which is an integral part of both the meth... | Object oriented programming language | 0.809058 |
23,014 | Terminology invoking "objects" in the modern sense of object-oriented programming made its first appearance at MIT in the late 1950s and early 1960s. In the environment of the artificial intelligence group, as early as 1960, "object" could refer to identified items (LISP atoms) with properties (attributes);Alan Kay lat... | Object oriented programming language | 0.809057 |
23,015 | In mathematics, particularly in algebraic geometry, complex analysis and algebraic number theory, an abelian variety is a projective algebraic variety that is also an algebraic group, i.e., has a group law that can be defined by regular functions. Abelian varieties are at the same time among the most studied objects in... | Principal polarization | 0.809057 |
23,016 | Given a curve with equation defined over the number field, we can apply this map to the coefficients to get a curve defined over some finite field, where the choices of finite field correspond to the finite primes of the number field. Abelian varieties appear naturally as Jacobian varieties (the connected components of... | Principal polarization | 0.809057 |
23,017 | Such abelian varieties turn out to be exactly those complex tori that can be embedded into a complex projective space. Abelian varieties defined over algebraic number fields are a special case, which is important also from the viewpoint of number theory. | Principal polarization | 0.809057 |
23,018 | Since minimal evaluation is part of an operator's semantic definition and not an optional optimization, a number of coding idioms rely on it as a succinct conditional construct. Examples include: Perl idioms: POSIX shell idioms: This idiom presumes that echo cannot fail. | Short-circuit evaluation | 0.809057 |
23,019 | In graph theory, a distinguishing coloring or distinguishing labeling of a graph is an assignment of colors or labels to the vertices of the graph that destroys all of the nontrivial symmetries of the graph. The coloring does not need to be a proper coloring: adjacent vertices are allowed to be given the same color. Fo... | Distinguishing coloring | 0.809056 |
23,020 | A coloring of a given graph is distinguishing for that graph if and only if it is distinguishing for the complement graph. Therefore, every graph has the same distinguishing number as its complement.For every graph G, the distinguishing number of G is at most proportional to the logarithm of the number of automorphisms... | Distinguishing coloring | 0.809056 |
23,021 | Proceedings of the IEEE provides in-depth review, survey, and tutorial coverage of the technical developments in electronics, electrical and computer engineering, and computer science. Reviews critically examine a technology, tracing its progress from its inception to the present—and perhaps into the future. Surveys co... | Proceedings of the IEEE | 0.809055 |
23,022 | The Proceedings of the IEEE is a monthly peer-reviewed scientific journal published by the Institute of Electrical and Electronics Engineers (IEEE). The journal focuses on electrical engineering and computer science. According to the Journal Citation Reports, the journal has a 2017 impact factor of 9.107, ranking it si... | Proceedings of the IEEE | 0.809055 |
23,023 | Enantiomers behave identically in chemical reactions, except when reacted with chiral compounds or in the presence of chiral catalysts, such as most enzymes. For this latter reason, the two enantiomers of most chiral compounds usually have markedly different effects and roles in living organisms. In biochemistry and fo... | Chemical isomer | 0.809053 |
23,024 | In chemistry, isomers are molecules or polyatomic ions with identical molecular formula – that is, same number of atoms of each element – but distinct arrangements of atoms in space. Isomerism refers to the existence or possibility of isomers. Isomers do not necessarily share similar chemical or physical properties. | Chemical isomer | 0.809053 |
23,025 | More generally, atoms or atom groups that can form three or more non-equivalent single bonds (such as the transition metals in coordination compounds) may give rise to multiple stereoisomers when different atoms or groups are attached at those positions. The same is true if a center with six or more equivalent bonds ha... | Chemical isomer | 0.809053 |
23,026 | Large molecules may have isomers that differ by the topology of their overall arrangement in space, even if there is no specific geometric constraint that separate them. For example, long chains may be twisted to form topologically distinct knots, with interconversion prevented by bulky substituents or cycle closing (a... | Chemical isomer | 0.809053 |
23,027 | Mars Science Laboratory (MSL) is a robotic space probe mission to Mars launched by NASA on November 26, 2011, which successfully landed Curiosity, a Mars rover, in Gale Crater on August 6, 2012. The overall objectives include investigating Mars' habitability, studying its climate and geology, and collecting data for a ... | Mars Science Laboratory | 0.809053 |
23,028 | In medicinal chemistry and biochemistry, enantiomers are a special concern because they may possess distinct biological activity. Many preparative procedures afford a mixture of equal amounts of both enantiomeric forms. In some cases, the enantiomers are separated by chromatography using chiral stationary phases. | Chemical isomer | 0.809053 |
23,029 | Alpha Particle X-ray Spectrometer (APXS): This device can irradiate samples with alpha particles and map the spectra of X-rays that are re-emitted for determining the elemental composition of samples. CheMin: CheMin is short for 'Chemistry and Mineralogy', and it is an X-ray diffraction and X-ray fluorescence analyzer.... | Mars Science Laboratory | 0.809053 |
23,030 | The MSL mission has four scientific goals: Determine the landing site's habitability including the role of water, the study of the climate and the geology of Mars. It is also useful preparation for a future human mission to Mars. To contribute to these goals, MSL has eight main scientific objectives: Biological (1) Det... | Mars Science Laboratory | 0.809053 |
23,031 | Many other optimizations can be used to make chess-playing programs stronger. For example, transposition tables are used to record positions that have been previously evaluated, to save recalculation of them. Refutation tables record key moves that "refute" what appears to be a good move; these are typically tried firs... | Chess programming | 0.809048 |
23,032 | In seven-dimensional geometry, a hexicated 7-simplex is a convex uniform 7-polytope, including 6th-order truncations (hexication) from the regular 7-simplex. There are 20 unique hexications for the 7-simplex, including all permutations of truncations, cantellations, runcinations, sterications, and pentellations. The si... | Hexicated 7-simplex | 0.809047 |
23,033 | The main results are those of William Browder (1969), who reduced the problem from differential topology to stable homotopy theory and showed that the only possible dimensions are 2 k − 2 {\displaystyle 2^{k}-2} , and those of Michael A. Hill, Michael J. Hopkins, and Douglas C. Ravenel (2016), who showed that there wer... | Kervaire invariant problem | 0.809046 |
23,034 | The Kervaire invariant is the Arf invariant of the quadratic form determined by the framing on the middle-dimensional Z / 2 Z {\displaystyle \mathbb {Z} /2\mathbb {Z} } -coefficient homology group q: H 2 m + 1 ( M ; Z / 2 Z ) → Z / 2 Z , {\displaystyle q\colon H_{2m+1}(M;\mathbb {Z} /2\mathbb {Z} )\to \mathbb {Z} /2\ma... | Kervaire invariant problem | 0.809046 |
23,035 | Reviewer Darren Glass writes that different parts of the book are aimed at different audiences, resulting in "a wonderful book which can be appreciated on many levels" and providing an unusual level of depth for a popular mathematics book. Its first section, on symmetries of low-dimensional Euclidean spaces, is suitabl... | The Symmetries of Things | 0.809045 |
23,036 | LEGO is a proof assistant developed by Randy Pollack at the University of Edinburgh. It implements several type theories: the Edinburgh Logical Framework (LF), the Calculus of Constructions (CoC), the Generalized Calculus of Constructions (GCC) and the Unified Theory of Dependent Types (UTT). | LEGO (proof assistant) | 0.809036 |
23,037 | In molecular biology, proteins containing the carboxyl transferase domain include biotin-dependent carboxylases. This domain carries out the following reaction: transcarboxylation from biotin to an acceptor molecule. There are two recognised types of carboxyl transferase. | Carboxyl transferase domain | 0.809036 |
23,038 | Soil biology involves work in the following areas: Modelling of biological processes and population dynamics Soil biology, physics and chemistry: occurrence of physicochemical parameters and surface properties on biological processes and population behavior Population biology and molecular ecology: methodological devel... | Soil organisms | 0.809035 |
23,039 | The results are used to enable releases or to improve the MBS model, in case the results are insufficient. One of the most important benefits of the MBS process chain is the usability of the results to optimize the 3D CAD master model components. Due to the fact that the process chain enables the optimization of compon... | Multibody simulation | 0.809033 |
23,040 | Also, stories with a single source or without any context of previous research mean that the subject at hand is presented as more definitive and certain than it is in reality. There is often a "product over process" approach to science journalism that aids, too, in the downplaying of uncertainty. Finally, and most nota... | Uncertainty notation | 0.809032 |
23,041 | The simplest form is the standard deviation of a repeated observation. In metrology, physics, and engineering, the uncertainty or margin of error of a measurement, when explicitly stated, is given by a range of values likely to enclose the true value. This may be denoted by error bars on a graph, or by the following no... | Uncertainty notation | 0.809032 |
23,042 | In statistics and economics, second-order uncertainty is represented in probability density functions over (first-order) probabilities.Opinions in subjective logic carry this type of uncertainty. | Uncertainty notation | 0.809032 |
23,043 | The cosmic age problem is a historical problem in astronomy concerning the age of the universe. The problem was that at various times in the 20th century, the universe was estimated to be younger than the oldest observed stars. Estimates of the universe's age came from measurements of the current expansion rate of the ... | Cosmic age problem | 0.809031 |
23,044 | In a classical ideal gas with massive particles, the energy of the particles is distributed according to a Maxwell–Boltzmann distribution. This distribution is established as the particles collide with each other, exchanging energy (and momentum) in the process. In a photon gas, there will also be an equilibrium distri... | Photon gas | 0.809031 |
23,045 | In physics, a photon gas is a gas-like collection of photons, which has many of the same properties of a conventional gas like hydrogen or neon – including pressure, temperature, and entropy. The most common example of a photon gas in equilibrium is the black-body radiation. Photons are part of a family of particles kn... | Photon gas | 0.809031 |
23,046 | Because LFP cells lacks cobalt and nickel which are expensive and energy intensive to produce, it is more energetically efficient to mine. In general, in addition to promoting the growth of a single sector, a more integrated effort should be in place to reduce the lifecycle emission of EV batteries. A finite total supp... | Traction battery | 0.809031 |
23,047 | At a glance, as shown in the plot b and d, the direct recycling process is the most ideal process for recycling pouch cell batteries, while the hydrometallurgical process is most suitable for cylindrical type battery. However, with the error bars shown, the best approach cannot be picked with confidence. It is worth no... | Traction battery | 0.809031 |
23,048 | The recycling process, on the other hand, as suggested by Ciez and Whitacre emits a significant amount of GHG. As shown in the battery recycling emission plot a and c, the emission of the recycling process varies with the different recycling processes, different chemistry and different form factor. Thus, the net emissi... | Traction battery | 0.809031 |
23,049 | The range of a BEV depends on the number and type of batteries used. The weight and type of vehicle as well as terrain, weather, and the performance of the driver also have an impact, just as they do on the mileage of traditional vehicles. Electric vehicle conversion performance depends on a number of factors including... | Traction battery | 0.809031 |
23,050 | Although battery life span can be extended by enabling a second-life application, ultimately EV batteries need to be recycled. Recyclability is not currently an important design consideration for battery manufacturers, and in 2019 only 5% of electric vehicle batteries were recycled. BEV technologies lack an established... | Traction battery | 0.809031 |
23,051 | The Tesla Roadster (2008) and other cars produced by the company used a modified form of traditional lithium-ion "laptop battery" cells. Recent EVs are using new variations on lithium-ion chemistry that sacrifice specific energy and specific power to provide fire resistance, environmental friendliness, rapid charging (... | Traction battery | 0.80903 |
23,052 | Lithium-ion (and the mechanistically similar lithium polymer) batteries, were initially developed and commercialized for use in laptops and consumer electronics. With their high energy density and long cycle life they have become the leading battery type for use in EVs. The first commercialized lithium-ion chemistry wa... | Traction battery | 0.80903 |
23,053 | 3D molecular graphics Automatic Force Field generator for bioelements: H, C, N, O Building and editing chemical structures Library of building blocks Force fields: Assisted Model Building with Energy Refinement (AMBER) 94, 96, 99SB, 03; Optimized Potentials for Liquid Simulations (OPLS) Geometry optimizing Molecular dy... | Abalone (molecular mechanics) | 0.80903 |
23,054 | The International Conference on Logic for Programming, Artificial Intelligence and Reasoning (LPAR) is an academic conference aiming at discussing cutting-edge results in the fields of automated reasoning, computational logic, programming languages and their applications. It grew out of the Russian Conferences on Logic... | Logic for Programming, Artificial Intelligence and Reasoning | 0.80903 |
23,055 | Particle filters and Feynman-Kac particle methodologies find application in several contexts, as an effective mean for tackling noisy observations or strong nonlinearities, such as: Bayesian inference, machine learning, risk analysis and rare event sampling Bioinformatics Computational science Economics, financial math... | Sequential Monte Carlo methods | 0.809028 |
23,056 | In mathematics, a pseudo-finite field F is an infinite model of the first-order theory of finite fields. This is equivalent to the condition that F is quasi-finite (perfect with a unique extension of every positive degree) and pseudo algebraically closed (every absolutely irreducible variety over F has a point defined ... | Pseudofinite field | 0.809027 |
23,057 | In general relativity, geodesics in spacetime describe the motion of point particles under the influence of gravity alone. In particular, the path taken by a falling rock, an orbiting satellite, or the shape of a planetary orbit are all geodesics in curved spacetime. More generally, the topic of sub-Riemannian geometry... | Affine parameter | 0.809026 |
23,058 | Going the "long way round" on a great circle between two points on a sphere is a geodesic but not the shortest path between the points. The map t → t 2 {\displaystyle t\to t^{2}} from the unit interval on the real number line to itself gives the shortest path between 0 and 1, but is not a geodesic because the velocity ... | Affine parameter | 0.809026 |
23,059 | A locally shortest path between two given points in a curved space, assumed to be a Riemannian manifold, can be defined by using the equation for the length of a curve (a function f from an open interval of R to the space), and then minimizing this length between the points using the calculus of variations. This has so... | Affine parameter | 0.809026 |
23,060 | In molecular biology, the flagellar motor switch protein (Flig) is one of three proteins in certain bacteria coded for by the gene fliG. The other two proteins are FliN coded for by fliN, and FliM coded for by fliM. The protein complex regulates the direction of flagellar rotation and hence controls swimming behaviour.... | Flagellar motor switch protein | 0.809025 |
23,061 | Sylvester's law of inertia is also valid if A {\displaystyle A} and B {\displaystyle B} have complex entries. In this case, it is said that A {\displaystyle A} and B {\displaystyle B} are ∗ {\displaystyle *} -congruent if and only if there exists a non-singular complex matrix S {\displaystyle S} such that B = S A S ∗ {... | Sylvester's law of inertia | 0.809025 |
23,062 | Sylvester's law of inertia is a theorem in matrix algebra about certain properties of the coefficient matrix of a real quadratic form that remain invariant under a change of basis. Namely, if A {\displaystyle A} is the symmetric matrix that defines the quadratic form, and S {\displaystyle S} is any invertible matrix su... | Sylvester's law of inertia | 0.809025 |
23,063 | Drummond Geometry is a trading method consisting of a series of technical analysis tools invented by the Canadian trader Charles Drummond starting in the 1970s and continuing to the present (2021). The method establishes support and resistance areas in multiple time periods and uses these to determine high probability ... | Drummond Geometry | 0.809025 |
23,064 | Statistical studies show positive effectiveness of the predicted support and resistance levels established by Drummond Geometry. Individual traders have reported both better and worse results as the trading approach requires traders to recognize signals and take action on them, and that skill varies by individuals. A r... | Drummond Geometry | 0.809025 |
23,065 | Recent enhancements include the "EOTEM" or "Pipes" indicators which combine momentum indicators, and predicted resistance and support areas. The "Pipes" indicator includes elements from traditional Drummond Geometry as well (the trading bands and the "PL dot" moving average). | Drummond Geometry | 0.809025 |
23,066 | Indicators developed for the efficient application of P&L charting or Drummond geometry include the assemblage of several P&L lines and levels into groups that represent future support and resistance "zones," which are further classified into "nearby" and "further-out" support and resistance areas. Other indicators inc... | Drummond Geometry | 0.809025 |
23,067 | Literate programming was first introduced in 1984 by Donald Knuth, who intended it to create programs that were suitable literature for human beings. He implemented it at Stanford University as a part of his research on algorithms and digital typography. The implementation was called "WEB" since he believed that it was... | Literate Programming | 0.809021 |
23,068 | Axiom, which is evolved from scratchpad, a computer algebra system developed by IBM. It is now being developed by Tim Daly, one of the developers of scratchpad, Axiom is totally written as a literate program. | Literate Programming | 0.809021 |
23,069 | Literate programming is writing out the program logic in a human language with included (separated by a primitive markup) code snippets and macros. Macros in a literate source file are simply title-like or explanatory phrases in a human language that describe human abstractions created while solving the programming pro... | Literate Programming | 0.809021 |
23,070 | Literate programming is a programming paradigm introduced in 1984 by Donald Knuth in which a computer program is given as an explanation of how it works in a natural language, such as English, interspersed (embedded) with snippets of macros and traditional source code, from which compilable source code can be generated... | Literate Programming | 0.809021 |
23,071 | In physics, the Saha ionization equation is an expression that relates the ionization state of a gas in thermal equilibrium to the temperature and pressure. The equation is a result of combining ideas of quantum mechanics and statistical mechanics and is used to explain the spectral classification of stars. The express... | Saha ionisation equation | 0.809018 |
23,072 | SVE can also be implemented with a minimum of site disturbance, primarily involving well installation and minimal aboveground equipment. Depending on the nature of the contamination and the subsurface geology, SVE has the potential to treat large soil volumes at reasonable costs. The soil gas (vapor) that is extracted ... | Soil vapor extraction | 0.809015 |
23,073 | On selection as a remedy, implementation of SVE involves the following elements: system design, operation, optimization, performance assessment, and closure. Several guidance documents provide information on these implementation aspects. EPA and U.S. Army Corps of Engineers (USACE) guidance documents establish an overa... | Soil vapor extraction | 0.809015 |
23,074 | The Air Force Center for Engineering and the Environment (AFCEE) guidance presents actions and considerations for SVE system optimization, but has limited information related to approaches for SVE closure and meeting remediation goals. Guidance from the Pacific Northwest National Laboratory (PNNL) supplements these doc... | Soil vapor extraction | 0.809015 |
23,075 | In predicate calculus, a Henkin witness for a sentence ∃ x φ ( x ) {\displaystyle \exists x\,\varphi (x)} in a theory T is a term c such that T proves φ(c) (Hinman 2005:196). The use of such witnesses is a key technique in the proof of Gödel's completeness theorem presented by Leon Henkin in 1949. | Witness (mathematics) | 0.809009 |
23,076 | The American weaver Ada Dietz wrote a 1949 monograph Algebraic Expressions in Handwoven Textiles, defining weaving patterns based on the expansion of multivariate polynomials. The mathematician Daina Taimiņa demonstrated features of the hyperbolic plane by crocheting in 2001. | Mathematical art | 0.809005 |
23,077 | His works are visual representations of mathematical objects; The Eightfold Way is based on the projective special linear group PSL(2,7), a finite group of 168 elements. The sculptor Bathsheba Grossman similarly bases her work on mathematical structures. The artist Nelson Saiers incorporates mathematical concepts and t... | Mathematical art | 0.809005 |
23,078 | Other works by Robinson explore the topology of toruses. Genesis is based on Borromean rings – a set of three circles, no two of which link but in which the whole structure cannot be taken apart without breaking. The sculptor Helaman Ferguson creates complex surfaces and other topological objects. | Mathematical art | 0.809005 |
23,079 | Stewart Coffin makes polyhedral puzzles in rare and beautiful woods; George W. Hart works on the theory of polyhedra and sculpts objects inspired by them; Magnus Wenninger makes "especially beautiful" models of complex stellated polyhedra.The distorted perspectives of anamorphosis have been explored in art since the si... | Mathematical art | 0.809005 |
23,080 | Escher used irregular polygons when tiling the plane and often used reflections, glide reflections, and translations to obtain further patterns. Many of his works contain impossible constructions, made using geometrical objects which set up a contradiction between perspective projection and three dimensions, but are pl... | Mathematical art | 0.809005 |
23,081 | Man Ray admitted that the object's formula "meant nothing to me, but the forms themselves were as varied and authentic as any in nature." He used his photographs of the mathematical models as figures in his series he did on Shakespeare's plays, such as his 1934 painting Antony and Cleopatra. The art reporter Jonathan ... | Mathematical art | 0.809005 |
23,082 | Metzinger, in 1910, wrote that: " lays out a free, mobile perspective, from which that ingenious mathematician Maurice Princet has deduced a whole geometry". Later, Metzinger wrote in his memoirs: Maurice Princet joined us often ... it was as an artist that he conceptualized mathematics, as an aesthetician that he invo... | Mathematical art | 0.809005 |
23,083 | The mathematician and theoretical physicist Henri Poincaré's Science and Hypothesis was widely read by the Cubists, including Pablo Picasso and Jean Metzinger. Being thoroughly familiar with Bernhard Riemann's work on non-Euclidean geometry, Poincaré was more than aware that Euclidean geometry is just one of many possi... | Mathematical art | 0.809005 |
23,084 | Computer art often makes use of fractals including the Mandelbrot set, and sometimes explores other mathematical objects such as cellular automata. Controversially, the artist David Hockney has argued that artists from the Renaissance onwards made use of the camera lucida to draw precise representations of scenes; the ... | Mathematical art | 0.809005 |
23,085 | The engraver Albrecht Dürer made many references to mathematics in his work Melencolia I. In modern times, the graphic artist M. C. Escher made intensive use of tessellation and hyperbolic geometry, with the help of the mathematician H. S. M. Coxeter, while the De Stijl movement led by Theo van Doesburg and Piet Mondri... | Mathematical art | 0.809005 |
23,086 | As Douglas Hofstadter writes in his 1980 reflection on human thought, Gödel, Escher, Bach, by way of (among other things) the mathematics of art: "The difference between an Escher drawing and non-Euclidean geometry is that in the latter, comprehensible interpretations can be found for the undefined terms, resulting in ... | Mathematical art | 0.809005 |
23,087 | He developed a style that he described as the geometry of life and the geometry of all nature. Consisting of simple geometric shapes with detailed patterning and coloring, in works such as Angular I and Automnes, Palazuelo expressed himself in geometric transformations.The artist Adrian Gray practises stone balancing, ... | Mathematical art | 0.809005 |
23,088 | In mathematics, addition and multiplication of real numbers is associative. By contrast, in computer science, the addition and multiplication of floating point numbers is not associative, as rounding errors are introduced when dissimilar-sized values are joined together.To illustrate this, consider a floating point rep... | Left associative operator | 0.809004 |
23,089 | In single shot systems the component is held statically or rotated in the coil and the whole area to be treated is heated simultaneously for a pre-set time followed by either a flood quench or a drop quench system. Single shot is often used in cases where no other method will achieve the desired result for example for ... | Induction hardening | 0.809003 |
23,090 | A concept is defined as a proposition without a logical status in the K-Space. A central finding of C-K theory is that concepts are the necessary departure point of a design process. Without concepts, design reduces to standard optimization or problem-solving. Concepts assert the existence of an unknown object that pre... | C-K theory | 0.809001 |
23,091 | In cycloalkanes, the carbon atoms are sp3 hybridized, which would imply an ideal tetrahedral bond angle of 109° 28′ whenever possible. Owing to evident geometrical reasons, rings with 3, 4, and (to a small extent) also 5 atoms can only afford narrower angles; the consequent deviation from the ideal tetrahedral bond ang... | Cyclic hydrocarbons | 0.809001 |
23,092 | Besides this standard definition by the International Union of Pure and Applied Chemistry (IUPAC), in some authors' usage the term cycloalkane includes also those saturated hydrocarbons that are polycyclic. In any case, the general form of the chemical formula for cycloalkanes is CnH2(n+1−r), where n is the number of c... | Cyclic hydrocarbons | 0.809001 |
23,093 | In organic chemistry, the cycloalkanes (also called naphthenes, but distinct from naphthalene) are the monocyclic saturated hydrocarbons. In other words, a cycloalkane consists only of hydrogen and carbon atoms arranged in a structure containing a single ring (possibly with side chains), and all of the carbon-carbon bo... | Cyclic hydrocarbons | 0.809001 |
23,094 | In indefinite signature, the spin group Spin(p, q) is constructed through Clifford algebras in a similar way to standard spin groups. It is a double cover of SO0(p, q), the connected component of the identity of the indefinite orthogonal group SO(p, q). For p + q > 2, Spin(p, q) is connected; for (p, q) = (1, 1) there ... | Spin group | 0.809 |
23,095 | This has important applications in 4-manifold theory and Seiberg–Witten theory. In physics, the Spin group is appropriate for describing uncharged fermions, while the SpinC group is used to describe electrically charged fermions. In this case, the U(1) symmetry is specifically the gauge group of electromagnetism. | Spin group | 0.809 |
23,096 | The SpinC group is defined by the exact sequence 1 → Z 2 → Spin C ( n ) → SO ( n ) × U ( 1 ) → 1. {\displaystyle 1\to \mathrm {Z} _{2}\to \operatorname {Spin} ^{\mathbf {C} }(n)\to \operatorname {SO} (n)\times \operatorname {U} (1)\to 1.} It is a multiplicative subgroup of the complexification Cl ( V ) ⊗ C {\di... | Spin group | 0.809 |
23,097 | It is straightforward to see that the spinors anti-commute, and that the product of a spinor and anti-spinor is a scalar. The spinor space is defined as the exterior algebra ⋀ W {\displaystyle \textstyle {\bigwedge }W} . The (complexified) Clifford algebra acts naturally on this space; the (complexified) spin group cor... | Spin group | 0.809 |
23,098 | As a Lie group, Spin(n) therefore shares its dimension, n(n − 1)/2, and its Lie algebra with the special orthogonal group. For n > 2, Spin(n) is simply connected and so coincides with the universal cover of SO(n). The non-trivial element of the kernel is denoted −1, which should not be confused with the orthogonal tran... | Spin group | 0.809 |
23,099 | In graph theory, the matching polytope of a given graph is a geometric object representing the possible matchings in the graph. It is a convex polytope each of whose corners corresponds to a matching. It has great theoretical importance in the theory of matching. : 273–285 | Matching polytope | 0.809 |
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