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19,300 | The closing of atoms into rings may lock particular atoms with distinct substitution by functional groups such that the result is stereochemistry and chirality of the compound, including some manifestations that are unique to rings (e.g., configurational isomers). | Cyclic molecule | 0.811583 |
19,301 | Because of the unique shapes, reactivities, properties, and bioactivities that they engender, cyclic compounds are the largest majority of all molecules involved in the biochemistry, structure, and function of living organisms, and in the man-made molecules (e.g., drugs, herbicides, etc.) through which man attempts to ... | Cyclic molecule | 0.811583 |
19,302 | A variety of further synthetic procedures are particularly useful in opening carbocyclic and other rings, generally which contain a double bound or other functional group "handle" to facilitate chemistry; these are termed ring-opening reactions. Examples include: ring opening metathesis, which can also be used to accom... | Cyclic molecule | 0.811583 |
19,303 | Nuclear Medicine and Biology is a peer-reviewed medical journal published by Elsevier that covers research on all aspects of nuclear medicine, including radiopharmacology, radiopharmacy and clinical studies of targeted radiotracers. It is the official journal of the Society of Radiopharmaceutical Sciences. According to... | Nuclear Medicine and Biology | 0.811582 |
19,304 | IAPR Conferences: The International Conference on Pattern Recognition2014—Stockholm, Sweden 2016—Santiago, Chile 2018—Beijing, China 2020—Milan, Italy 2022—Montreal, Canada The International Conference on Pattern Recognition in Bioinformatics The International Conference on Pattern Recognition and Image Analysis The In... | International Association for Pattern Recognition | 0.81158 |
19,305 | The International Association for Pattern Recognition (IAPR), founded in 1978 by Purdue University computer scientist King-Sun Fu, is an international association of non-profit, scientific, or professional organizations (being national, multi-national, or international in scope) concerned with pattern recognition, comp... | International Association for Pattern Recognition | 0.81158 |
19,306 | Given a bounded lattice A with largest and smallest elements 1 and 0, and a binary operation →, these together form a Heyting algebra if and only if the following hold: a → a = 1 {\displaystyle a\to a=1} a ∧ ( a → b ) = a ∧ b {\displaystyle a\wedge (a\to b)=a\wedge b} b ∧ ( a → b ) = b {\displaystyle b\wedge (a\to b)=b... | Relative pseudo-complement | 0.811573 |
19,307 | Given a set A with three binary operations →, ∧ and ∨, and two distinguished elements ⊥ {\displaystyle \bot } and ⊤ {\displaystyle \top } , then A is a Heyting algebra for these operations (and the relation ≤ defined by the condition that a ≤ b {\displaystyle a\leq b} when a→b = ⊤ {\displaystyle \top } ) if and only if... | Relative pseudo-complement | 0.811573 |
19,308 | This characterization of Heyting algebras makes the proof of the basic facts concerning the relationship between intuitionist propositional calculus and Heyting algebras immediate. (For these facts, see the sections "Provable identities" and "Universal constructions".) One should think of the element ⊤ {\displaystyle \... | Relative pseudo-complement | 0.811573 |
19,309 | MODUS-PONENS follows from the fact that if a formula ⊤→F is provably true, where ⊤ is provably true, then F is provably true (by application of the rule of inference modus ponens). Finally, EQUIV results from the fact that if F→G and G→F are both provably true, then F and G are provable from each other (by application ... | Relative pseudo-complement | 0.811573 |
19,310 | Verify that H0, together with these operations, is a Heyting algebra. We do this using the axiom-like definition of Heyting algebras. H0 satisfies conditions THEN-1 through FALSE because all formulas of the given forms are axioms of intuitionist logic. | Relative pseudo-complement | 0.811573 |
19,311 | In fact, ∼ is the relation of (intuitionist) logical equivalence.) Let H0 be the quotient set L/∼. This will be the desired Heyting algebra. | Relative pseudo-complement | 0.811573 |
19,312 | The metaimplication 2 ⇒ 1 in the section "Provable identities" is proved by showing that the result of the following construction is itself a Heyting algebra: Consider the set L of propositional formulas in the variables A1, A2,..., An. Endow L with a preorder ≼ by defining F≼G if G is an (intuitionist) logical consequ... | Relative pseudo-complement | 0.811573 |
19,313 | A complete Heyting algebra is a Heyting algebra that is a complete lattice. A subalgebra of a Heyting algebra H is a subset H1 of H containing 0 and 1 and closed under the operations ∧, ∨ and →. It follows that it is also closed under ¬. A subalgebra is made into a Heyting algebra by the induced operations. | Relative pseudo-complement | 0.811573 |
19,314 | In any Heyting algebra, one defines the pseudo-complement ¬a of any element a by setting ¬a = (a→0). By definition, a ∧ ¬ a = 0 {\displaystyle a\wedge \lnot a=0} , and ¬a is the largest element having this property. However, it is not in general true that a ∨ ¬ a = 1 {\displaystyle a\vee \lnot a=1} , thus ¬ is only a p... | Relative pseudo-complement | 0.811573 |
19,315 | A Heyting algebra H is a bounded lattice such that for all a and b in H there is a greatest element x of H such that a ∧ x ≤ b . {\displaystyle a\wedge x\leq b.} This element is the relative pseudo-complement of a with respect to b, and is denoted a→b. We write 1 and 0 for the largest and the smallest element of H, res... | Relative pseudo-complement | 0.811573 |
19,316 | Some quantum chemistry software uses sets of Slater-type functions (STF) analogous to Slater type orbitals, but with variable exponents chosen to minimize the total molecular energy (rather than by Slater's rules as above). The fact that products of two STOs on distinct atoms are more difficult to express than those of... | Slater orbital | 0.811571 |
19,317 | Biological oceanography is similar to marine biology, but is different because of the perspective used to study the ocean. Biological oceanography takes a bottom-up approach (in terms of the food web), while marine biology studies the ocean from a top-down perspective. Biological oceanography mainly focuses on the ecos... | Biological oceanography | 0.81157 |
19,318 | The ocean makes the earth habitable through regulation of the Earth's climate and processes such as primary production which provide oxygen as a byproduct. Biology is central to facilitating some of these processes but with climate change and human impacts, the ocean environment is constantly changing and so calls for ... | Biological oceanography | 0.81157 |
19,319 | Oceans occupy about 71% of the Earth's surface. Whilst the average depth of the oceans is about 3800 m, the deepest parts are almost 11000 m. The marine environment has a total volume (approximately 1370 x 106 km3) that is 300 times larger for life than the volume of land and freshwater combined. It is thought that the... | Biological oceanography | 0.81157 |
19,320 | Captain James Cook’s voyages were responsible for the extensive data collection on geography, geology, biota, currents, tides, and water temperatures of the Atlantic and Pacific oceans in the 1760s and 1770s. In 1820, Alexander Marcet noted the varying chemical composition of seawater in the different oceans. | Biological oceanography | 0.81157 |
19,321 | Biological oceanography is the study of how organisms affect and are affected by the physics, chemistry, and geology of the oceanographic system. Biological oceanography may also be referred to as ocean ecology, in which the root word of ecology is Oikos (oικoσ), meaning ‘house’ or ‘habitat’ in Greek. With that in mind... | Biological oceanography | 0.81157 |
19,322 | In the Dungeons & Dragons role-playing game, game mechanics and dice rolls determine much of what happens. These mechanics include: Ability scores, the most basic statistics of a character, which influence all other statistics Armor class, how well-protected a character is against physical attack Hit points, how much p... | Ability score | 0.81157 |
19,323 | In AD&D, ability scores were "determined by rolling three 6-sided dice and adding up their values". This had a significant impact on character creations as "certain classes could only be taken up by characters with the right combination of statistics. As a result, players often" re-rolled characters until they ended up... | Ability score | 0.81157 |
19,324 | All player characters have six basic statistics: Strength (STR): Strength is a measure of muscle, endurance and stamina combined; a high strength score indicates superiority in all these attributes. Strength affects the ability of characters to lift and carry weights, melee attack rolls, damage rolls (for both melee an... | Ability score | 0.81157 |
19,325 | Topology Analysis analyzes the topology of a network to identify relevant participates and substructures that may be of biological significance. The term encompasses an entire class of techniques such as network motif search, centrality analysis, topological clustering, and shortest paths. These are but a few examples,... | Biological network inference | 0.81157 |
19,326 | Topological Clustering or Topological Data Analysis (TDA) provides a general framework to analyze high dimensional, incomplete, and noisy data in a way that reduces dimensional and gives a robustness to noise. The idea that is that the shape of data sets contains relevant information. When this information is a homolog... | Biological network inference | 0.81157 |
19,327 | The shortest path problem is a common problem in graph theory that tries to find the path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized. This method can be used to determine the network diameter or redundancy in a network. there are many algorithms for... | Biological network inference | 0.81157 |
19,328 | Such algorithms are typically based on linearity, independence or normality assumptions, which must be verified on a case-by-case basis. Clustering or some form of statistical classification is typically employed to perform an initial organization of the high-throughput mRNA expression values derived from microarray ex... | Biological network inference | 0.81157 |
19,329 | Genes are the nodes and the edges are directed. A gene serves as the source of a direct regulatory edge to a target gene by producing an RNA or protein molecule that functions as a transcriptional activator or inhibitor of the target gene. If the gene is an activator, then it is the source of a positive regulatory conn... | Biological network inference | 0.81157 |
19,330 | For our purposes, network analysis is closely related to graph theory. By measuring the attributes in the previous section we can utilize many different techniques to create accurate inferences based on biological data. | Biological network inference | 0.81157 |
19,331 | Cluster analysis groups objects (nodes) such that objects in the same cluster are more similar to each other than to those in other clusters. This can be used to perform pattern recognition, image analysis, information retrieval, statistical data analysis, and so much more. It has applications in Plant and animal ecolo... | Biological network inference | 0.81157 |
19,332 | Biological network inference is the process of making inferences and predictions about biological networks. By using these networks to analyze patterns in biological systems, such as food-webs, we can visualize the nature and strength of these interactions between species, DNA, proteins, and more. The analysis of biolo... | Biological network inference | 0.81157 |
19,333 | A network's diameter is the maximum number of steps separating any two nodes and can be used to determine the How connected a graph is, in topology analysis, and clustering analysis. | Biological network inference | 0.81157 |
19,334 | Briefly, methods using high-throughput data for inference of regulatory networks rely on searching for patterns of partial correlation or conditional probabilities that indicate causal influence. Such patterns of partial correlations found in the high-throughput data, possibly combined with other supplemental data on t... | Biological network inference | 0.81157 |
19,335 | Systems biology, in this sense, is still in its infancy. There is great interest in network medicine for the modelling biological systems. This article focuses on inference of biological network structure using the growing sets of high-throughput expression data for genes, proteins, and metabolites. | Biological network inference | 0.81157 |
19,336 | A gene regulatory network is a set of molecular regulators that interact with each other and with other substances in the cell. The regulator can be DNA, RNA, protein and complexes of these. Gene regulatory networks can be modeled in numerous ways including; Coupled ordinary differential equations, Boolean networks, Co... | Biological network inference | 0.81157 |
19,337 | Such variation can lead to statistical confounding. Accordingly, more sophisticated statistical techniques must be applied to analyse such datasets. (very important in the biology of cancer) | Biological network inference | 0.81157 |
19,338 | One of the most intensely studied networks in biology, Protein-protein interaction networks (PINs) visualize the physical relationships between proteins inside a cell. in a PIN, proteins are the nodes and their interactions are the undirected edges. PINs can be discovered with a variety of methods including; Two-hybrid... | Biological network inference | 0.81157 |
19,339 | Perlin Noise is not suited for simulation because it is not divergence-free. Noises based on lattices, such as simulation noise and Perlin noise, are often calculated at different frequencies and summed together to form band-limited fractal signals. Other approaches developed later that use vector calculus identities t... | Simulation noise | 0.811568 |
19,340 | Several techniques can be used by that system to extend KB by means of valid inferences. An additional requirement is that the conclusions the system arrives at are relevant to its task. Additionally, the term 'inference' has also been applied to the process of generating predictions from trained neural networks. In th... | Inference procedure | 0.811566 |
19,341 | AI systems first provided automated logical inference and these were once extremely popular research topics, leading to industrial applications under the form of expert systems and later business rule engines. More recent work on automated theorem proving has had a stronger basis in formal logic. An inference system's ... | Inference procedure | 0.811566 |
19,342 | Prolog (for "Programming in Logic") is a programming language based on a subset of predicate calculus. Its main job is to check whether a certain proposition can be inferred from a KB (knowledge base) using an algorithm called backward chaining. Let us return to our Socrates syllogism. We enter into our Knowledge Base ... | Inference procedure | 0.811566 |
19,343 | Human inference (i.e. how humans draw conclusions) is traditionally studied within the fields of logic, argumentation studies, and cognitive psychology; artificial intelligence researchers develop automated inference systems to emulate human inference. Statistical inference uses mathematics to draw conclusions in the p... | Inference procedure | 0.811566 |
19,344 | The Gyroelongated square pyramid represents the capped square antiprismatic molecular geometry: | Gyroelongated square pyramid | 0.811566 |
19,345 | In geometry, the gyroelongated square pyramid is one of the Johnson solids (J10). As its name suggests, it can be constructed by taking a square pyramid and "gyroelongating" it, which in this case involves joining a square antiprism to its base. A Johnson solid is one of 92 strictly convex polyhedra that is composed of... | Gyroelongated square pyramid | 0.811566 |
19,346 | From examples given in the Arithmetica, it is clear that Diophantus was aware of the theorem. This book was translated in 1621 into Latin by Bachet (Claude Gaspard Bachet de Méziriac), who stated the theorem in the notes of his translation. But the theorem was not proved until 1770 by Lagrange.Adrien-Marie Legendre ext... | Four square theorem | 0.811565 |
19,347 | Lagrange's four-square theorem can be refined in various ways. For example, Zhi-Wei Sun proved that each natural number can be written as a sum of four squares with some requirements on the choice of these four numbers. One may also wonder whether it is necessary to use the entire set of square integers to write each n... | Four square theorem | 0.811565 |
19,348 | The United States Air Force developed its own set of MOS based upon their dynamical weather model by 1983.Model output statistics differ from the perfect prog technique, which assumes that the output of numerical weather prediction guidance is perfect. MOS can correct for local effects that cannot be resolved by the mo... | Atmospheric modelling | 0.811556 |
19,349 | It is a model system that like WRF can be run in many configurations, including at high resolution with the non-hydrostatic Arome physics or at lower resolutions with hydrostatic physics based on the ALADIN physical schemes. It has mostly been used in Europe and the Arctic for climate studies including 3km downscaling ... | Atmospheric modelling | 0.811556 |
19,350 | Different models use different solution methods. Global models often use spectral methods for the horizontal dimensions and finite-difference methods for the vertical dimension, while regional models usually use finite-difference methods in all three dimensions. For specific locations, model output statistics use clima... | Atmospheric modelling | 0.811556 |
19,351 | Forecasts are computed using mathematical equations for the physics and dynamics of the atmosphere. These equations are nonlinear and are impossible to solve exactly. Therefore, numerical methods obtain approximate solutions. | Atmospheric modelling | 0.811556 |
19,352 | Because forecast models based upon the equations for atmospheric dynamics do not perfectly determine weather conditions near the ground, statistical corrections were developed to attempt to resolve this problem. Statistical models were created based upon the three-dimensional fields produced by numerical weather models... | Atmospheric modelling | 0.811556 |
19,353 | The Engelbert–Schmidt zero–one law is a theorem that gives a mathematical criterion for an event associated with a continuous, non-decreasing additive functional of Brownian motion to have probability either 0 or 1, without the possibility of an intermediate value. This zero-one law is used in the study of questions of... | Engelbert–Schmidt zero–one law | 0.811553 |
19,354 | Let F {\displaystyle {\mathcal {F}}} be a σ-algebra and let F = ( F t ) t ≥ 0 {\displaystyle F=({\mathcal {F}}_{t})_{t\geq 0}} be an increasing family of sub-σ-algebras of F {\displaystyle {\mathcal {F}}} . Let ( W , F ) {\displaystyle (W,F)} be a Wiener process on the probability space ( Ω , F , P ) {\displaystyle (\O... | Engelbert–Schmidt zero–one law | 0.811553 |
19,355 | The PRIDE (PRoteomics IDEntifications database) is a public data repository of mass spectrometry (MS) based proteomics data, and is maintained by the European Bioinformatics Institute as part of the Proteomics Team.Originally designed by Lennart Martens in 2003 during a stay at the European Bioinformatics Institute as ... | Proteomics Identifications Database | 0.811553 |
19,356 | Since detailed proteomics data currently cannot be curated from the existing literature, the source of PRIDE data is solely submissions by academic researchers. PRIDE is a standards-compliant public repository, meaning that its own XML-based data exchange format for submissions, PRIDE XML, was built around the Proteomi... | Proteomics Identifications Database | 0.811552 |
19,357 | Using the principal value of the complex logarithm, The decimal expansion of is given by A049006: i i = {\displaystyle i^{i}=} 0.2078795763507619085469556198349787700338778416317696080751358830554198772854821397886002778654260353...Because of the equivalence, we can use the Gelfond-Schneider theorem to prove that the r... | Gelfond's constant | 0.811551 |
19,358 | The decimal expansion of πe is given by A059850: π e = {\displaystyle \pi ^{e}=} 22.4591577183610454734271522045437350275893151339966922492030025540669260403991179123185197527271430315...It is not known whether or not this number is transcendental. Note that, by Gelfond-Schneider theorem, we can only infer definitively... | Gelfond's constant | 0.811551 |
19,359 | In mathematics, Gelfond's constant, named after Aleksandr Gelfond, is eπ, that is, e raised to the power π. Like both e and π, this constant is a transcendental number. This was first established by Gelfond and may now be considered as an application of the Gelfond–Schneider theorem, noting that where i is the imaginar... | Gelfond's constant | 0.811551 |
19,360 | In geometry and combinatorics, an arrangement of hyperplanes is an arrangement of a finite set A of hyperplanes in a linear, affine, or projective space S. Questions about a hyperplane arrangement A generally concern geometrical, topological, or other properties of the complement, M(A), which is the set that remains wh... | Hyperplane arrangement | 0.811548 |
19,361 | These questions can be answered just from the intersection semilattice. For instance, two basic theorems, from Zaslavsky (1975), are that the number of regions of an affine arrangement equals (−1)npA(−1) and the number of bounded regions equals (−1)npA(1). Similarly, the number of k-dimensional faces or bounded faces c... | Hyperplane arrangement | 0.811548 |
19,362 | Speculative execution is an optimization technique where a computer system performs some task that may not be needed. Work is done before it is known whether it is actually needed, so as to prevent a delay that would have to be incurred by doing the work after it is known that it is needed. If it turns out the work was... | Speculative execution | 0.811545 |
19,363 | For example, aqueous sodium chloride may be written as . to show the dissociation. An aromatic "one and a half" bond may be indicated with :; see § Aromaticity below. Single bonds adjacent to double bonds may be represented using / or \ to indicate stereochemical configuration; see § Stereochemistry below. | Simplified Molecular Input Line Entry Specification | 0.811541 |
19,364 | Scaling horizontally (out/in) means adding more nodes to (or removing nodes from) a system, such as adding a new computer to a distributed software application. An example might involve scaling out from one web server to three. High-performance computing applications, such as seismic analysis and biotechnology, scale w... | Scalability | 0.811539 |
19,365 | Many organic compounds—two examples are ethanol and insulin—are manufactured industrially using organisms such as bacteria and yeast. Typically, the DNA of an organism is altered to express compounds not ordinarily produced by the organism. Many such biotechnology-engineered compounds did not previously exist in nature... | Organic chemicals | 0.811534 |
19,366 | These instantons are indeed found in lattice calculations. The first computations performed with instantons used the dilute gas approximation. The results obtained did not solve the infrared problem of QCD, making many physicists turn away from instanton physics. | Partially conserved axial vector current | 0.81153 |
19,367 | However, even after the development of QCD string models continued to play a role in the physics of strong interactions. These models are called non-fundamental strings or QCD strings, since they should be derived from QCD, as they are, in certain approximations such as the strong coupling limit of lattice QCD. The mod... | Partially conserved axial vector current | 0.81153 |
19,368 | Another important class of problems occurs in enclosed spaces specified by boundary conditions, for which the solutions represent standing waves, or harmonics, analogous to the harmonics of musical instruments. The two-way wave equation – describing a standing wave field – is the simplest example of a second-order hype... | Wave Equation | 0.811526 |
19,369 | In other words, this term shows how the displacement's changes are squashed up in a tiny surrounding area.The equation states that at any given instance, at any given point, the way the displacement accelerates is proportional to the way the displacement's changes are squashed up in the surrounding area. Or, in even si... | Wave Equation | 0.811526 |
19,370 | In terms of finding a solution, this causality property means that for any given point on the line being considered, the only area that needs to be considered is the area encompassing all the points that could causally affect the point being considered. Denote the area that causally affects point (xi, ti) as RC. Suppos... | Wave Equation | 0.811526 |
19,371 | This property is called the superposition principle in physics. The wave equation alone does not specify a physical solution; a unique solution is usually obtained by setting a problem with further conditions, such as initial conditions, which prescribe the amplitude and phase of the wave. | Wave Equation | 0.811526 |
19,372 | The answer sheet had room for 115 answers; however, no test had more than 95 questions. 1–100 were standard multiple-choice bubbles and 101–115 were for 'relationship analysis questions', which were only used for the chemistry exam. The biology test was the only test to use answers 96–100; questions 1–60 were common to... | SAT Subject Tests | 0.811523 |
19,373 | Prior to the first administration of the new SAT Reasoning Test (which included the writing section) in March 2005, some highly selective colleges required applicants to take three SAT Subject Tests, including the writing test and two other tests of the applicant's choosing, in addition to the SAT. However, when writin... | SAT Subject Tests | 0.811523 |
19,374 | As a consequence of Lagrange's theorem, the order of a (mod n) always divides φ(n). If the order of a is actually equal to φ(n), and therefore as large as possible, then a is called a primitive root modulo n. This means that the group U(n) is cyclic and the residue class of a generates it. The order of a (mod n) also d... | Multiplicative order | 0.81152 |
19,375 | In number theory, given a positive integer n and an integer a coprime to n, the multiplicative order of a modulo n is the smallest positive integer k such that a k ≡ 1 ( mod n ) {\textstyle a^{k}\ \equiv \ 1{\pmod {n}}} .In other words, the multiplicative order of a modulo n is the order of a in the multiplicative grou... | Multiplicative order | 0.81152 |
19,376 | In nuclear physics, atoms decay or react where the atom's nucleus splits, producing several atoms. In nuclear computation, a computational thread splits into several processing threads. | Nuclear computation | 0.81152 |
19,377 | In nuclear physics, atoms may react together to fuse where several atomic nuclei may fuse into one nucleus. In nuclear computation, several computational threads fuse into one processing thread. | Nuclear computation | 0.81152 |
19,378 | However, there are examples where A ⊗ k B {\displaystyle A\otimes _{k}B} is a domain but A and B are not linearly disjoint: for example, A = B = k(t), the field of rational functions over k. One also has: A, B are linearly disjoint over k if and only if subfields of Ω {\displaystyle \Omega } generated by A , B {\displa... | Linearly disjoint | 0.81152 |
19,379 | In mathematics, algebras A, B over a field k inside some field extension Ω {\displaystyle \Omega } of k are said to be linearly disjoint over k if the following equivalent conditions are met: (i) The map A ⊗ k B → A B {\displaystyle A\otimes _{k}B\to AB} induced by ( x , y ) ↦ x y {\displaystyle (x,y)\mapsto xy} is inj... | Linearly disjoint | 0.81152 |
19,380 | For linear forms ax + by the only invariants are constants. The algebra of covariants is generated by the form itself of degree 1 and order 1. | Binary quantic | 0.811515 |
19,381 | Brouwer & Popoviciu (2010a) showed that the algebra of invariants of a degree 9 form is generated by 92 invariants. Cröni, Hagedorn, and Brouwer computed 476 covariants, and Lercier & Olive showed that this list is complete. | Binary quantic | 0.811515 |
19,382 | The algebra of invariants of the cubic form ax3 + 3bx2y + 3cxy2 + dy3 is a polynomial algebra in 1 variable generated by the discriminant D = 3b2c2 + 6abcd − 4b3d − 4c3a − a2d2 of degree 4. The algebra of covariants is generated by the discriminant, the form itself (degree 1, order 3), the Hessian H (degree 2, order 2)... | Binary quantic | 0.811515 |
19,383 | More generally a covariant is a polynomial in a0, ..., an, x, y that is invariant, so an invariant is a special case of a covariant where the variables x and y do not occur. More generally still, a simultaneous invariant is a polynomial in the coefficients of several different forms in x and y. In terms of representati... | Binary quantic | 0.811515 |
19,384 | Similarly it can be shown that the slope of the moment diagram at a given point is equal to the magnitude of the shear diagram at that distance. The relationship between distributed shear force and bending moment is: d M d x = Q {\displaystyle {\frac {dM}{dx}}=Q} A direct result of this is that at every point the shear... | Shear and moment diagram | 0.811515 |
19,385 | Since this method can easily become unnecessarily complicated with relatively simple problems, it can be quite helpful to understand different relations between the loading, shear, and moment diagram. The first of these is the relationship between a distributed load on the loading diagram and the shear diagram. Since a... | Shear and moment diagram | 0.811515 |
19,386 | Major contributions of supramolecular chemistry have been devoted to recognition and sensing of anions. Ion pairing is the most important driving force for anion complexation, but selectivity e.g. within the halide series has been achieved, mostly by hydrogen bonds contributions. | Salt bridge (protein and supramolecular) | 0.811513 |
19,387 | BIND was the first database of its kind to contain info on biomolecular interactions, reactions and pathways in one schema. It is also the first to base its ontology on chemistry which allows 3D representation of molecular interactions. The underlying chemistry allows molecular interactions to be described down to the ... | Biomolecular Object Network Databank | 0.811512 |
19,388 | The Biomolecular Object Network Databank is a bioinformatics databank containing information on small molecule structures and interactions. The databank integrates a number of existing databases to provide a comprehensive overview of the information currently available for a given molecule. | Biomolecular Object Network Databank | 0.811512 |
19,389 | The absolute square of a complex number is always a nonnegative real number, that is zero if and only if the complex number is zero. It is easier to compute than the absolute value (no square root), and is a smooth real-valued function. Because of these two properties, the absolute square is often preferred to the abso... | Square function | 0.811511 |
19,390 | No square root can be taken of a negative number within the system of real numbers, because squares of all real numbers are non-negative. The lack of real square roots for the negative numbers can be used to expand the real number system to the complex numbers, by postulating the imaginary unit i, which is one of the s... | Square function | 0.811511 |
19,391 | Squares are ubiquitous in algebra, more generally, in almost every branch of mathematics, and also in physics where many units are defined using squares and inverse squares: see below. Least squares is the standard method used with overdetermined systems. Squaring is used in statistics and probability theory in determi... | Square function | 0.811511 |
19,392 | Let X be a topological space and let T: X → X be a continuous function. Let Inv(T) denote the set of all Borel probability measures on X that are invariant under T, i.e., for every Borel-measurable subset A of X, μ(T−1(A)) = μ(A). (Note that, by the Krylov-Bogolyubov theorem, if X is compact and metrizable, Inv(T) is n... | Maximising measure | 0.811503 |
19,393 | Thus the K-trivials are far from random. This is why these sets are studied in the field of algorithmic randomness, which is a subfield of Computability theory and related to algorithmic information theory in computer science. At the same time, K-trivial sets are close to computable. For instance, they are all superlow... | K-trivial set | 0.811503 |
19,394 | In mathematics, a set of natural numbers is called a K-trivial set if its initial segments viewed as binary strings are easy to describe: the prefix-free Kolmogorov complexity is as low as possible, close to that of a computable set. Solovay proved in 1975 that a set can be K-trivial without being computable. The Schno... | K-trivial set | 0.811503 |
19,395 | It can be shown that if X is a compact space, then Inv(T) is also compact with respect to the topology of weak convergence of measures. Hence, in this case, each continuous function f: X → R has at least one maximising measure. If T is a continuous map of a compact metric space X into itself and E is a topological vect... | Maximising measure | 0.811503 |
19,396 | In particular, in extant works attributed to Archimedes, the moment is pointed out in phrasings like: "Commensurable magnitudes (σύμμετρα μεγέθεα) are equally balanced (ἰσορροπέοντι) if their distances are inversely proportional (ἀντιπεπονθότως) to their weights (βάρεσιν). "Moreover, in extant texts such as The Metho... | Moment (physics) | 0.811503 |
19,397 | In works believed to stem from Ancient Greece, the concept of a moment is alluded to by the word ῥοπή (rhopḗ, lit. "inclination") and composites like ἰσόρροπα (isorropa, lit. "of equal inclinations"). The context of these works is mechanics and geometry involving the lever. | Moment (physics) | 0.811503 |
19,398 | In physics, a moment is a mathematical expression involving the product of a distance and physical quantity. Moments are usually defined with respect to a fixed reference point and refer to physical quantities located some distance from the reference point. In this way, the moment accounts for the quantity's location o... | Moment (physics) | 0.811503 |
19,399 | The Jeffreys–Lindley paradox shows how different interpretations, applied to the same data set, can lead to different conclusions about the 'statistical significance' of a result.As William Feller noted: There is no place in our system for speculations concerning the probability that the sun will rise tomorrow. Before ... | Frequency probability | 0.811502 |
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