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1,500 | The journal was established in 1923 as the Journal of Scientific Instruments. The first issue was introduced by J. J. Thomson, then president of the Institute of Physics, who stated that no publication existed at that time in the English language specially devoted to scientific instruments. The idea for the journal was... | Measurement Science and Technology | 0.838883 |
1,501 | Measurement Science and Technology is a monthly peer-reviewed scientific journal, published by IOP Publishing, covering the areas of measurement, instrumentation, and sensor technology in the sciences. The editor-in-chief is Andrew Yacoot (National Physical Laboratory). | Measurement Science and Technology | 0.838883 |
1,502 | In physics, angular velocity (symbol ω or ω → {\displaystyle {\vec {\omega }}} , the lowercase Greek letter omega), also known as angular frequency vector, is a pseudovector representation of how the angular position or orientation of an object changes with time, i.e. how quickly an object rotates (spins or revolves) a... | Rotation velocity | 0.838881 |
1,503 | In mathematics, analytic geometry (also called Cartesian geometry) describes every point in two-dimensional space by means of two coordinates. Two perpendicular coordinate axes are given which cross each other at the origin. They are usually labeled x and y. Relative to these axes, the position of any point in two-dime... | Plane coordinates | 0.838873 |
1,504 | A reordering of the rows and columns of such a matrix can assemble all the ones into a rectangular part of the matrix.Let h be the vector of all ones. Then if v is an arbitrary logical vector, the relation R = v hT has constant rows determined by v. In the calculus of relations such an R is called a vector. A particula... | Binary matrix | 0.838839 |
1,505 | A logical matrix may represent an adjacency matrix in graph theory: non-symmetric matrices correspond to directed graphs, symmetric matrices to ordinary graphs, and a 1 on the diagonal corresponds to a loop at the corresponding vertex. The biadjacency matrix of a simple, undirected bipartite graph is a (0, 1)-matrix, a... | Binary matrix | 0.838839 |
1,506 | A permutation matrix is a (0, 1)-matrix, all of whose columns and rows each have exactly one nonzero element. A Costas array is a special case of a permutation matrix. An incidence matrix in combinatorics and finite geometry has ones to indicate incidence between points (or vertices) and lines of a geometry, blocks of ... | Binary matrix | 0.838839 |
1,507 | A major branch of virology is virus classification. It is artificial in that it is not based on evolutionary phylogenetics but it is based shared or distinguishing properties of viruses. It seeks to describe the diversity of viruses by naming and grouping them on the basis of similarities. In 1962, André Lwoff, Robert ... | Molecular virology | 0.838838 |
1,508 | Reverse genetics is a powerful research method in virology. In this procedure complimentary DNA (cDNA) copies of virus genomes called "infectious clones" are used to produce genetically modified viruses that can be then tested for changes in say, virulence or transmissibility. | Molecular virology | 0.838838 |
1,509 | Reassortment is the switching of genes from different parents and it is particularly useful when studying the genetics of viruses that have segmented genomes (fragmented into two or more nucleic acid molecules) such as influenza viruses and rotaviruses. The genes that encode properties such as serotype can be identifie... | Molecular virology | 0.838838 |
1,510 | The methods for separating viral nucleic acids (RNA and DNA) and proteins, which are now the mainstay of virology, did not exist. Now there are many methods for observing the structure and functions of viruses and their component parts. Thousands of different viruses are now known about and virologists often specialize... | Molecular virology | 0.838838 |
1,511 | Virology is the scientific study of biological viruses. It is a subfield of microbiology that focuses on their detection, structure, classification and evolution, their methods of infection and exploitation of host cells for reproduction, their interaction with host organism physiology and immunity, the diseases they c... | Molecular virology | 0.838838 |
1,512 | Scientific calculators are used widely in situations that require quick access to certain mathematical functions, especially those that were once looked up in mathematical tables, such as trigonometric functions or logarithms. They are also used for calculations of very large or very small numbers, as in some aspects o... | Scientific calculator | 0.838817 |
1,513 | The GRE subject test in mathematics is a standardized test in the United States created by the Educational Testing Service (ETS), and is designed to assess a candidate's potential for graduate or post-graduate study in the field of mathematics. It contains questions from many fields of mathematics; about 50% of the que... | GRE Mathematics Test | 0.838772 |
1,514 | {\displaystyle L(R)=\{x\mid \exists yR(x,y)\}.\,} This definition may be generalized to n-ary relations using any suitable encoding which allows multiple strings to be compressed into one string (for instance by listing them consecutively with a delimiter). More formally, a relation R can be viewed as a search problem,... | Search problem | 0.838772 |
1,515 | Macro-level quantum entanglement has been proposed, but it is so far out of the realm of current physics that nobody believes it. The space tunnels also lead to the discovery of the Fallers, an alien race who refused to establish communications and immediately launched a war, which they are winning. No Faller has been ... | Probability Moon | 0.838736 |
1,516 | Kirkus Reviews wrote that the book is "twisty and compelling, brimful of ideas with Kress’s usual life-sized characters", and called it a "top-notch work from a major talent". Roland Green of Booklist wrote that "Kress' characterizations are as sound as ever, but many will be agreeably surprised at her proficiency with... | Probability Moon | 0.838736 |
1,517 | In general relativity, the laws of physics can be expressed in a generally covariant form. In other words, the description of the world as given by the laws of physics does not depend on our choice of coordinate systems. However, it is often useful to fix upon a particular coordinate system, in order to solve actual pr... | Coordinate condition | 0.838734 |
1,518 | An example of an under-determinative condition is the algebraic statement that the determinant of the metric tensor is −1, which still leaves considerable gauge freedom. This condition would have to be supplemented by other conditions in order to remove the ambiguity in the metric tensor. An example of an over-determin... | Coordinate condition | 0.838734 |
1,519 | As it passes through the point where the tangent line and the curve meet, called the point of tangency, the tangent line is "going in the same direction" as the curve, and is thus the best straight-line approximation to the curve at that point. Similarly, the tangent plane to a surface at a given point is the plane tha... | Coordinate geometry | 0.838701 |
1,520 | In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point. Informally, it is a line through a pair of infinitely close points on the curve. More precisely, a straight line is said to be a tangent of a curve y = f(x) at a point x ... | Coordinate geometry | 0.838701 |
1,521 | However, although Apollonius came close to developing analytic geometry, he did not manage to do so since he did not take into account negative magnitudes and in every case the coordinate system was superimposed upon a given curve a posteriori instead of a priori. That is, equations were determined by curves, but curve... | Coordinate geometry | 0.838701 |
1,522 | The Greek mathematician Menaechmus solved problems and proved theorems by using a method that had a strong resemblance to the use of coordinates and it has sometimes been maintained that he had introduced analytic geometry.Apollonius of Perga, in On Determinate Section, dealt with problems in a manner that may be calle... | Coordinate geometry | 0.838701 |
1,523 | Lines in a Cartesian plane, or more generally, in affine coordinates, can be described algebraically by linear equations. In two dimensions, the equation for non-vertical lines is often given in the slope-intercept form: where: m is the slope or gradient of the line. b is the y-intercept of the line. x is the independe... | Coordinate geometry | 0.838701 |
1,524 | It is the foundation of most modern fields of geometry, including algebraic, differential, discrete and computational geometry. Usually the Cartesian coordinate system is applied to manipulate equations for planes, straight lines, and circles, often in two and sometimes three dimensions. Geometrically, one studies the ... | Coordinate geometry | 0.838701 |
1,525 | In mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry. Analytic geometry is used in physics and engineering, and also in aviation, rocketry, space science, and spaceflight. | Coordinate geometry | 0.838701 |
1,526 | Some aspects of brane physics have been applied to cosmology. For example, brane gas cosmology attempts to explain why there are three dimensions of space using topological and thermodynamic considerations. According to this idea it would be since three is the largest number of spatial dimensions in which strings can g... | N-dimensional space | 0.838675 |
1,527 | In 1921, Kaluza–Klein theory presented 5D including an extra dimension of space. At the level of quantum field theory, Kaluza–Klein theory unifies gravity with gauge interactions, based on the realization that gravity propagating in small, compact extra dimensions is equivalent to gauge interactions at long distances. ... | N-dimensional space | 0.838675 |
1,528 | In physics, three dimensions of space and one of time is the accepted norm. However, there are theories that attempt to unify the four fundamental forces by introducing extra dimensions/hyperspace. Most notably, superstring theory requires 10 spacetime dimensions, and originates from a more fundamental 11-dimensional t... | N-dimensional space | 0.838675 |
1,529 | ": 290 Davis Baird has argued that the major change associated with Floris Cohen's identification of a "fourth big scientific revolution" after World War II is the development of scientific instrumentation, not only in chemistry but across the sciences. In chemistry, the introduction of new instrumentation in the 1940s... | Measuring instrument | 0.838636 |
1,530 | For example, they could be used to identify and destroy cancer cells. Molecular nanotechnology is a speculative subfield of nanotechnology regarding the possibility of engineering molecular assemblers, biological machines which could re-order matter at a molecular or atomic scale. Nanomedicine would make use of these n... | Molecular machinery | 0.838625 |
1,531 | AMMs have been pivotal in the design of several stimuli-responsive smart materials, such as 2D and 3D self-assembled materials and nanoparticle-based systems, for versatile applications ranging from 3D printing to drug delivery.AMMs are gradually moving from the conventional solution-phase chemistry to surfaces and int... | Molecular machinery | 0.838625 |
1,532 | Chemical energy (or "chemical fuels") was an attractive option at the beginning, given the broad array of reversible chemical reactions (heavily based on acid-base chemistry) to switch molecules between different states. However, this comes with the issue of practically regulating the delivery of the chemical fuel and ... | Molecular machinery | 0.838625 |
1,533 | The first example of an artificial molecular machine (AMM) was reported in 1994, featuring a rotaxane with a ring and two different possible binding sites. In 2016 the Nobel Prize in Chemistry was awarded to Jean-Pierre Sauvage, Sir J. Fraser Stoddart, and Bernard L. Feringa for the design and synthesis of molecular ma... | Molecular machinery | 0.838625 |
1,534 | AMMs have diversified rapidly over the past few decades and their design principles, properties, and characterization methods have been outlined better. A major starting point for the design of AMMs is to exploit the existing modes of motion in molecules, such as rotation about single bonds or cis-trans isomerization. ... | Molecular machinery | 0.838625 |
1,535 | However, the most crucial aspect of the process is that the reference gene must be stable.The selection of these reference genes was traditionally carried out in molecular biology using qualitative or semi-quantitative studies such as the visual examination of RNA gels, northern blot densitometry or semi-quantitative P... | Real-time polymerase chain reaction | 0.838617 |
1,536 | The first was in the January 1984 issue of Acorn User magazine, and Banthorpe followed this with a three-dimensional version in the May 1984 issue. Susan Stepney, Professor of Computer Science at the University of York, followed this up in 1988 with Life on the Line, a program that generated one-dimensional cellular au... | Conway game | 0.838602 |
1,537 | However, in isotropic rules, the positions of neighbour cells relative to each other may be taken into account in determining a cell's future state—not just the total number of those neighbours. Some variations on the Game of Life modify the geometry of the universe as well as the rule. The above variations can be thou... | Conway game | 0.838602 |
1,538 | Ranging is technique that measures distance or slant range from the observer to a target, especially a far and moving target. Active methods use unilateral transmission and passive reflection. Active rangefinding methods include laser (lidar), radar, sonar, and ultrasonic rangefinding. Other devices which measure dista... | Length measurement | 0.838575 |
1,539 | Three-dimensional space has a number of topological properties that distinguish it from spaces of other dimension numbers. For example, at least three dimensions are required to tie a knot in a piece of string.In differential geometry the generic three-dimensional spaces are 3-manifolds, which locally resemble R 3 {\di... | Spatial geometry | 0.838528 |
1,540 | The fundamental theorem of line integrals, says that a line integral through a gradient field can be evaluated by evaluating the original scalar field at the endpoints of the curve. Let φ: U ⊆ R n → R {\displaystyle \varphi :U\subseteq \mathbb {R} ^{n}\to \mathbb {R} } . Then φ ( q ) − φ ( p ) = ∫ γ ∇ φ ( r ) ⋅ d r . ... | Spatial geometry | 0.838528 |
1,541 | Suppose V is a subset of R n {\displaystyle \mathbb {R} ^{n}} (in the case of n = 3, V represents a volume in 3D space) which is compact and has a piecewise smooth boundary S (also indicated with ∂V = S ). If F is a continuously differentiable vector field defined on a neighborhood of V, then the divergence theorem say... | Spatial geometry | 0.838528 |
1,542 | Experimental physics is a branch of physics that is concerned with data acquisition, data-acquisition methods, and the detailed conceptualization (beyond simple thought experiments) and realization of laboratory experiments. It is often contrasted with theoretical physics, which is more concerned with predicting and ex... | Experimental Physics | 0.838525 |
1,543 | LIGO, the Laser Interferometer Gravitational-Wave Observatory, is a large-scale physics experiment and observatory to detect cosmic gravitational waves and to develop gravitational-wave observations as an astronomical tool. Currently two LIGO observatories exist: LIGO Livingston Observatory in Livingston, Louisiana, an... | Experimental Physics | 0.838525 |
1,544 | Some examples of prominent experimental physics projects are: Relativistic Heavy Ion Collider which collides heavy ions such as gold ions (it is the first heavy ion collider) and protons, it is located at Brookhaven National Laboratory, on Long Island, USA. HERA, which collides electrons or positrons and protons, and i... | Experimental Physics | 0.838525 |
1,545 | See the timelines below for listings of physics experiments. Timeline of atomic and subatomic physics Timeline of classical mechanics Timeline of electromagnetism and classical optics Timeline of gravitational physics and relativity Timeline of nuclear fusion Timeline of particle discoveries Timeline of particle physic... | Experimental Physics | 0.838525 |
1,546 | Phase 1 ended in July 2006. HPF Phase 2 (HPF2) applies the Rosetta v4.8x software in higher resolution, "full atom refinement" mode, concentrating on cancer biomarkers (proteins found at dramatically increased levels in cancer tissues), human secreted proteins and malaria. Phase 1 ran on two volunteer computing grids: ... | Human Proteome Folding Project | 0.838522 |
1,547 | The Human Proteome Folding Project (HPF) is a collaborative effort between New York University (Bonneau Lab), the Institute for Systems Biology (ISB) and the University of Washington (Baker Lab), using the Rosetta software developed by the Rosetta Commons. The project is managed by the Bonneau lab. HPF Phase 1 applied ... | Human Proteome Folding Project | 0.838522 |
1,548 | The question about how many vertices/watchmen/guards were needed, was posed to Chvátal by Victor Klee in 1973. Chvátal proved it shortly thereafter. Chvátal's proof was later simplified by Steve Fisk, via a 3-coloring argument. Chvátal has a more geometrical approach, whereas Fisk uses well-known results from Graph the... | Art gallery problem | 0.83852 |
1,549 | Chvátal's upper bound remains valid if the restriction to guards at corners is loosened to guards at any point not exterior to the polygon. There are a number of other generalizations and specializations of the original art-gallery theorem. For instance, for orthogonal polygons, those whose edges/walls meet at right an... | Art gallery problem | 0.83852 |
1,550 | Chvátal's art gallery theorem, named after Václav Chvátal, gives an upper bound on the minimal number of guards. It states: | Art gallery problem | 0.83852 |
1,551 | The art gallery problem or museum problem is a well-studied visibility problem in computational geometry. It originates from the following real-world problem: In the geometric version of the problem, the layout of the art gallery is represented by a simple polygon and each guard is represented by a point in the polygon... | Art gallery problem | 0.83852 |
1,552 | To illustrate the proof, we consider the polygon below. The first step is to triangulate the polygon (see Figure 1). Then, one applies a proper 3 {\displaystyle 3} -colouring (Figure 2) and observes that there are 4 {\displaystyle 4} red, 4 {\displaystyle 4} blue and 6 {\displaystyle 6} green vertices. The colour with ... | Art gallery problem | 0.83852 |
1,553 | Let ri be a rotamer at residue position i in the protein chain, and E(ri) the potential energy between the internal atoms of the rotamer. Let E(ri, rj) be the potential energy between ri and rotamer rj at residue position j. Then, we define the optimization problem as one of finding the conformation of minimum energy (... | Protein Design | 0.838477 |
1,554 | Furthermore, even if amino acid side-chain conformations are limited to a few rotamers (see Structural flexibility), this results in an exponential number of conformations for each sequence. Thus, in our 100 residue protein, and assuming that each amino acid has exactly 10 rotamers, a search algorithm that searches thi... | Protein Design | 0.838477 |
1,555 | When the first proteins were rationally designed during the 1970s and 1980s, the sequence for these was optimized manually based on analyses of other known proteins, the sequence composition, amino acid charges, and the geometry of the desired structure. The first designed proteins are attributed to Bernd Gutte, who de... | Protein Design | 0.838477 |
1,556 | Hence, it is also termed inverse folding. Protein design is then an optimization problem: using some scoring criteria, an optimized sequence that will fold to the desired structure is chosen. | Protein Design | 0.838477 |
1,557 | Recently, several alternatives based on message-passing algorithms have been designed specifically for the optimization of the LP relaxation of the protein design problem. These algorithms can approximate both the dual or the primal instances of the integer programming, but in order to maintain guarantees on optimality... | Protein Design | 0.838477 |
1,558 | ILP solvers depend on linear programming (LP) algorithms, such as the Simplex or barrier-based methods to perform the LP relaxation at each branch. These LP algorithms were developed as general-purpose optimization methods and are not optimized for the protein design problem (Equation (1)). In consequence, the LP relax... | Protein Design | 0.838477 |
1,559 | Thus, these algorithms provide a good perspective on the different kinds of algorithms available for protein design. In 2020 scientists reported the development of an AI-based process using genome databases for evolution-based designing of novel proteins. They used deep learning to identify design-rules. In 2022, a stu... | Protein Design | 0.838477 |
1,560 | Although these algorithms address only the most basic formulation of the protein design problem, Equation (1), when the optimization goal changes because designers introduce improvements and extensions to the protein design model, such as improvements to the structural flexibility allowed (e.g., protein backbone flexib... | Protein Design | 0.838477 |
1,561 | Several algorithms have been developed specifically for the protein design problem. These algorithms can be divided into two broad classes: exact algorithms, such as dead-end elimination, that lack runtime guarantees but guarantee the quality of the solution; and heuristic algorithms, such as Monte Carlo, that are fast... | Protein Design | 0.838477 |
1,562 | Molecular mechanics force-fields, which have been used mostly in molecular dynamics simulations, are optimized for the simulation of single sequences, but protein design searches through many conformations of many sequences. Thus, molecular mechanics force-fields must be tailored for protein design. In practice, protei... | Protein Design | 0.838477 |
1,563 | Statistical potentials, in contrast to physics-based potentials, have the advantage of being fast to compute, of accounting implicitly of complex effects and being less sensitive to small changes in the protein structure. These energy functions are based on deriving energy values from frequency of appearance on a struc... | Protein Design | 0.838477 |
1,564 | The trend has been toward using more physics-based potential energy functions.Physics-based energy functions, such as AMBER and CHARMM, are typically derived from quantum mechanical simulations, and experimental data from thermodynamics, crystallography, and spectroscopy. These energy functions typically simplify physi... | Protein Design | 0.838477 |
1,565 | The most accurate energy functions are those based on quantum mechanical simulations. However, such simulations are too slow and typically impractical for protein design. Instead, many protein design algorithms use either physics-based energy functions adapted from molecular mechanics simulation programs, knowledge bas... | Protein Design | 0.838477 |
1,566 | Suppose the winning-sets are all of size k (i.e., the game-hypergraph is k-uniform). In a Maker-Breaker game, the Erdos-Selfridge theorem implies that Breaker wins if the number of winning-sets is less than 2 k − 1 {\displaystyle 2^{k-1}} . By the above conjecture, we would expect the same to hold in the corresponding ... | Picker-Chooser game | 0.838466 |
1,567 | Introduced in 1962, Petri nets were an early attempt to codify the rules of concurrent execution. Dataflow theory later built upon these, and Dataflow architectures were created to physically implement the ideas of dataflow theory. Beginning in the late 1970s, process calculi such as Calculus of Communicating Systems (... | Concurrent algorithm | 0.838456 |
1,568 | One of the earliest applications of PairWise to problems in bioinformatics was by Ewan Birney. Frameshifting refers to the phenomena where in one DNA strands, there are more than one translation frame. For normal Protein-DNA alignment tools, they first choose one of three frames to translate the DNA into a protein sequ... | Pairwise Algorithm | 0.838443 |
1,569 | In theoretical computer science, nondeterministic constraint logic is a combinatorial system in which an orientation is given to the edges of a weighted undirected graph, subject to certain constraints. One can change this orientation by steps in which a single edge is reversed, subject to the same constraints. The con... | Constraint logic problem | 0.838436 |
1,570 | In practice, in bialgebras, this map is required to be the identity, which can be obtained by normalizing the counit by dividing by dimension ( ϵ := 1 n tr {\displaystyle \epsilon :=\textstyle {\frac {1}{n}}\operatorname {tr} } ), so in these cases the normalizing constant corresponds to dimension. Alternatively, it ma... | Vector space dimension | 0.838421 |
1,571 | Firstly, it allows for a definition of a notion of dimension when one has a trace but no natural sense of basis. For example, one may have an algebra A {\displaystyle A} with maps η: K → A {\displaystyle \eta :K\to A} (the inclusion of scalars, called the unit) and a map ϵ: A → K {\displaystyle \epsilon :A\to K} (corre... | Vector space dimension | 0.838421 |
1,572 | Translating back to the lattice world by using the theorem above and using a lattice-theoretical analogue of the V(R) construction, called the dimension monoid, introduced by Wehrung in 1998, yields the following result. Theorem (Wehrung 2004). There exists a distributive (∨,0,1)-semilattice of cardinality ℵ1 that is n... | Congruence lattice problem | 0.838416 |
1,573 | Theorem (Wehrung 1999). Let R be a von Neumann regular ring. Then the (∨,0)-semilattices Idc R and Conc L(R) are both isomorphic to the maximal semilattice quotient of V(R). | Congruence lattice problem | 0.838416 |
1,574 | The proof of the negative solution for CLP shows that the problem of representing distributive semilattices by compact congruences of lattices already appears for congruence lattices of semilattices. The question whether the structure of partially ordered set would cause similar problems is answered by the following re... | Congruence lattice problem | 0.838416 |
1,575 | Theorem. Every distributive (∨,0)-semilattice of cardinality at most ℵ1 is isomorphic to (1) Conc L, for some locally finite, relatively complemented modular lattice L (Tůma 1998 and Grätzer, Lakser, and Wehrung 2000). (2) The semilattice of finitely generated two-sided ideals of some (not necessarily unital) von Neuma... | Congruence lattice problem | 0.838416 |
1,576 | It should be observed that while the transition homomorphisms used in the Ershov-Pudlák Theorem are (∨,0)-embeddings, the transition homomorphisms used in the result above are not necessarily one-to-one, for example when one tries to represent the three-element chain. Practically this does not cause much trouble, and m... | Congruence lattice problem | 0.838416 |
1,577 | Furthermore, it follows from deep 1998 results of universal algebra by Kearnes and Szendrei in so-called commutator theory of varieties that the result above can be extended from the variety of all lattices to any variety V {\displaystyle {\mathcal {V}}} such that all Con A, for A ∈ V {\displaystyle A\in {\mathcal {V}}... | Congruence lattice problem | 0.838416 |
1,578 | The problem remained open until it was recently solved in the negative by Tůma and Wehrung.Theorem (Tůma and Wehrung 2006). There exists a diagram D of finite Boolean (∨,0)-semilattices and (∨,0,1)-embeddings, indexed by a finite partially ordered set, that cannot be lifted, with respect to the Conc functor, by any dia... | Congruence lattice problem | 0.838416 |
1,579 | Theorem (Pudlák 1985). There exists a direct limits preserving functor Φ, from the category of all distributive lattices with zero and 0-lattice embeddings to the category of all lattices with zero and 0-lattice embeddings, such that ConcΦ is naturally equivalent to the identity. Furthermore, Φ(S) is a finite atomistic... | Congruence lattice problem | 0.838416 |
1,580 | The approach of CLP suggested by Pudlák in his 1985 paper is different. It is based on the following result, Fact 4, p. 100 in Pudlák's 1985 paper, obtained earlier by Yuri L. Ershov as the main theorem in Section 3 of the Introduction of his 1977 monograph.Theorem (Ershov 1977, Pudlák 1985). Every distributive (∨,0)-s... | Congruence lattice problem | 0.838416 |
1,581 | Comparing with classical mechanics, which gives accurate results dealing with macroscopic objects moving much slower than the speed of light, total momentum of the two colliding bodies is frame-dependent. In the center of momentum frame, according to classical mechanics, This agrees with the relativistic calculation u ... | Elastic interaction | 0.838393 |
1,582 | In physics, an elastic collision is an encounter (collision) between two bodies in which the total kinetic energy of the two bodies remains the same. In an ideal, perfectly elastic collision, there is no net conversion of kinetic energy into other forms such as heat, noise, or potential energy. During the collision of ... | Elastic interaction | 0.838393 |
1,583 | A general form triangle has six main characteristics (see picture): three linear (side lengths a, b, c) and three angular (α, β, γ). The classical plane trigonometry problem is to specify three of the six characteristics and determine the other three. A triangle can be uniquely determined in this sense when given any o... | Solution of triangles | 0.838382 |
1,584 | Solution of triangles (Latin: solutio triangulorum) is the main trigonometric problem of finding the characteristics of a triangle (angles and lengths of sides), when some of these are known. The triangle can be located on a plane or on a sphere. Applications requiring triangle solutions include geodesy, astronomy, con... | Solution of triangles | 0.838382 |
1,585 | Spherical geometry differs from planar Euclidean geometry, so the solution of spherical triangles is built on different rules. For example, the sum of the three angles α + β + γ depends on the size of the triangle. | Solution of triangles | 0.838382 |
1,586 | The Krull dimension of a commutative ring is the maximal length of chains of prime ideals in it, a chain of length n being a sequence P 0 ⊊ P 1 ⊊ ⋯ ⊊ P n {\displaystyle {\mathcal {P}}_{0}\subsetneq {\mathcal {P}}_{1}\subsetneq \cdots \subsetneq {\mathcal {P}}_{n}} of prime ideals related by inclusion. It is strongly re... | High-dimensional space | 0.83838 |
1,587 | In biology, there is generally no well established theory of measurement. However, the importance of the theoretical context is emphasized. Moreover, the theoretical context stemming from the theory of evolution leads to articulate the theory of measurement and historicity as a fundamental notion. Among the most develo... | Theory of measurement | 0.838357 |
1,588 | Many people measure their height in feet and inches and their weight in stone and pounds, to give just a few examples. Imperial units are used in many other places, for example, in many Commonwealth countries that are considered metricated, land area is measured in acres and floor space in square feet, particularly for... | Theory of measurement | 0.838357 |
1,589 | Information theory recognises that all data are inexact and statistical in nature. Thus the definition of measurement is: "A set of observations that reduce uncertainty where the result is expressed as a quantity." This definition is implied in what scientists actually do when they measure something and report both the... | Theory of measurement | 0.838357 |
1,590 | In quantum mechanics, a measurement is an action that determines a particular property (position, momentum, energy, etc.) of a quantum system. Quantum measurements are always statistical samples from a probability distribution; the distribution for many quantum phenomena is discrete. : 197 Quantum measurements alter qu... | Theory of measurement | 0.838357 |
1,591 | However, in other fields such as statistics as well as the social and behavioural sciences, measurements can have multiple levels, which would include nominal, ordinal, interval and ratio scales.Measurement is a cornerstone of trade, science, technology and quantitative research in many disciplines. Historically, many ... | Theory of measurement | 0.838357 |
1,592 | Pascal's work on this problem began an important correspondence between him and fellow mathematician Pierre de Fermat (1601-1665). Communicating through letters, the two continued to exchange their ideas and thoughts. These interactions led to the conception of basic probability theory. To this day, many gamblers still... | Poker probability | 0.838344 |
1,593 | His work from 1550, titled Liber de Ludo Aleae, discussed the concepts of probability and how they were directly related to gambling. However, his work did not receive any immediate recognition since it was not published until after his death. Blaise Pascal (1623-1662) also contributed to probability theory. | Poker probability | 0.838344 |
1,594 | Probability and gambling have been ideas since long before the invention of poker. The development of probability theory in the late 1400s was attributed to gambling; when playing a game with high stakes, players wanted to know what the chance of winning would be. In 1494, Fra Luca Paccioli released his work Summa de a... | Poker probability | 0.838344 |
1,595 | The cumulative probability is determined by adding one hand's probability with the probabilities of all hands above it. The Odds are defined as the ratio of the number of ways not to draw the hand, to the number of ways to draw it. In statistics, this is called odds against. | Poker probability | 0.838344 |
1,596 | The second-level codes are a single letter from the Latin alphabet. These represent specific areas covered by the first-level discipline. The second-level codes vary from discipline to discipline. For example, for differential geometry, the top-level code is 53, and the second-level codes are: A for classical different... | Mathematics Subject Classification | 0.838341 |
1,597 | For physics papers the Physics and Astronomy Classification Scheme (PACS) is often used. Due to the large overlap between mathematics and physics research it is quite common to see both PACS and MSC codes on research papers, particularly for multidisciplinary journals and repositories such as the arXiv. The ACM Computi... | Mathematics Subject Classification | 0.838341 |
1,598 | At the top level, 64 mathematical disciplines are labeled with a unique two-digit number. In addition to the typical areas of mathematical research, there are top-level categories for "History and Biography", "Mathematics Education", and for the overlap with different sciences. Physics (i.e. mathematical physics) is pa... | Mathematics Subject Classification | 0.838341 |
1,599 | The MSC is a hierarchical scheme, with three levels of structure. A classification can be two, three or five digits long, depending on how many levels of the classification scheme are used. The first level is represented by a two-digit number, the second by a letter, and the third by another two-digit number. For examp... | Mathematics Subject Classification | 0.838341 |
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