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17,200 | The labeling ( r , s ) {\displaystyle (r,s)} is a standard convention for primary operators of the c < 1 {\displaystyle c<1} minimal models. Furthermore, the critical three-state Potts model is symmetric not only under the Virasoro algebra, but also under an enlarged algebra called the W-algebra that includes the Viras... | Critical three-state Potts model | 0.813093 |
17,201 | The CIE's most recent model, CIECAM02 (CAM stands for "color appearance model"), is more theoretically sophisticated and computationally complex than earlier models. Its aims are to fix several of the problems with models such as CIELAB and CIELUV, and to explain not only responses in carefully controlled experimental ... | Color model | 0.813091 |
17,202 | HSL and HSV are both cylindrical geometries, with hue, their angular dimension, starting at the red primary at 0°, passing through the green primary at 120° and the blue primary at 240°, and then wrapping back to red at 360°. In each geometry, the central vertical axis comprises the neutral, achromatic, or gray colors,... | Color model | 0.813091 |
17,203 | The formulation of the theorem is also given in a Lisp-like syntax: Should the theorem prove to be true, it will be added to the knowledge basis of the system and can be used as a rewrite rule for future proofs. The proof itself is given in a quasi-natural language manner. The authors randomly choose typical mathematic... | Boyer-Moore theorem prover | 0.813089 |
17,204 | In 2005 Robert S. Boyer, Matt Kaufmann, and J Strother Moore received the ACM Software System Award for their work on the Nqthm theorem prover. | Boyer-Moore theorem prover | 0.813089 |
17,205 | Definitions are formed as totally recursive functions, the system makes extensive use of rewriting and an induction heuristic that is used when rewriting and something that they called symbolic evaluation fails. The system was built on top of Lisp and had some very basic knowledge in what was called "Ground-zero", the ... | Boyer-Moore theorem prover | 0.813089 |
17,206 | A Computational Logic Handbook, R.S. Boyer and J S. Moore, Academic Press (2nd Edition), 1997. The Boyer-Moore Theorem Prover and Its Interactive Enhancement, with M. Kaufmann and R. S. Boyer, Computers and Mathematics with Applications, 29(2), 1995, pp. 27–62. | Boyer-Moore theorem prover | 0.813089 |
17,207 | Many proofs have been done or confirmed with the system, particularly (1971) list concatenation (1973) insertion sort (1974) a binary adder (1976) an expression compiler for a stack machine (1978) uniqueness of prime factorizations (1983) invertibility of the RSA encryption algorithm (1984) unsolvability of the halting... | Boyer-Moore theorem prover | 0.813089 |
17,208 | In chemistry, delocalized electrons are electrons in a molecule, ion or solid metal that are not associated with a single atom or a covalent bond.The term delocalization is general and can have slightly different meanings in different fields: In organic chemistry, it refers to resonance in conjugated systems and aromat... | Electron delocalization | 0.813089 |
17,209 | Standard ab initio quantum chemistry methods lead to delocalized orbitals that, in general, extend over an entire molecule and have the symmetry of the molecule. Localized orbitals may then be found as linear combinations of the delocalized orbitals, given by an appropriate unitary transformation. In the methane molecu... | Electron delocalization | 0.813089 |
17,210 | There is also a simple geometric proof that G = SL2(Z) is not boundedly generated. It acts by Möbius transformations on the upper half-plane H, with the Poincaré metric. Any compactly supported 1-form α on a fundamental domain of G extends uniquely to a G-invariant 1-form on H. If z is in H and γ is the geodesic from z... | Boundedly generated group | 0.813085 |
17,211 | If n ≥ 3, the group SLn(Z) is boundedly generated by its elementary subgroups, formed by matrices differing from the identity matrix only in one off-diagonal entry. In 1984, Carter and Keller gave an elementary proof of this result, motivated by a question in algebraic K-theory. A free group on at least two generators ... | Boundedly generated group | 0.813085 |
17,212 | Several authors have stated in the mathematical literature that it is obvious that finitely generated free groups are not boundedly generated. This section contains various obvious and less obvious ways of proving this. Some of the methods, which touch on bounded cohomology, are important because they are geometric rat... | Boundedly generated group | 0.813085 |
17,213 | The Redlich–Kwong equation is consistent with the theorem of corresponding states. When the equation expressed in reduced form, an identical equation is obtained for all gases: P r = 3 T r V r − b ′ − 1 b ′ T r V r ( V r + b ′ ) {\displaystyle P_{\text{r}}={\frac {3T_{\text{r}}}{V_{\text{r}}-b'}}-{\frac {1}{b'{\sqrt {T... | Peng–Robinson equation of state | 0.813079 |
17,214 | Institutiones calculi integralis (Foundations of integral calculus) is a three-volume textbook written by Leonhard Euler and published in 1768. It was on the subject of integral calculus and contained many of Euler's discoveries about differential equations. | Institutiones calculi integralis | 0.813075 |
17,215 | In quantum field theory, a Bogoliubov transformation on the creation and annihilation operators (turning an occupied negative-energy electron state into an unoccupied positive energy positron state and an unoccupied negative-energy electron state into an occupied positive energy positron state) allows us to bypass the ... | Dirac's equation | 0.813074 |
17,216 | (1992). The Dirac Equation. Texts and Monographs in Physics. Springer. | Dirac's equation | 0.813074 |
17,217 | Principles of Quantum Mechanics (2nd ed.). Plenum. Thaller, B. | Dirac's equation | 0.813074 |
17,218 | Schiff, L.I. (1968). Quantum Mechanics (3rd ed.). | Dirac's equation | 0.813074 |
17,219 | Quantum Mechanics (6th ed.). Routledge. ISBN 978-1482299182. | Dirac's equation | 0.813074 |
17,220 | Quarks & Leptons: An Introductory Course in Modern Particle Physics. John Wiley & Sons. ISBN 9780471887416. | Dirac's equation | 0.813074 |
17,221 | Bjorken, J D; Drell, S (1964). Relativistic Quantum mechanics. New York, McGraw-Hill. Halzen, Francis; Martin, Alan (1984). | Dirac's equation | 0.813074 |
17,222 | Moreover, in the limit of zero mass, the Dirac equation reduces to the Weyl equation. Although Dirac did not at first fully appreciate the importance of his results, the entailed explanation of spin as a consequence of the union of quantum mechanics and relativity—and the eventual discovery of the positron—represents o... | Dirac's equation | 0.813074 |
17,223 | In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. In its free form, or including electromagnetic interactions, it describes all spin-1⁄2 massive particles, called "Dirac particles", such as electrons and quarks for which parity is a symmetry. It is ... | Dirac's equation | 0.813074 |
17,224 | The Meissel–Mertens constant (named after Ernst Meissel and Franz Mertens), also referred to as Mertens constant, Kronecker's constant, Hadamard–de la Vallée-Poussin constant or the prime reciprocal constant, is a mathematical constant in number theory, defined as the limiting difference between the harmonic series sum... | Mertens constant | 0.813071 |
17,225 | Hence, by the (CE) condition, X j ⪯ i X i {\displaystyle X_{j}\preceq _{i}X_{i}} . Since the preferences are monotonic, any such allocation is also PE, since monotonicity implies local nonsatiation. See fundamental theorems of welfare economics. | Efficient envy-free division | 0.813071 |
17,226 | Theorem 1 (Varian):: 68 If the preferences of all agents are convex and strongly monotone, then PEEF allocations exist. Proof: The proof relies on the existence of a competitive equilibrium with equal incomes. Assume that all resources in an economy are divided equally between the agents. | Efficient envy-free division | 0.813071 |
17,227 | Let Xk be an allocation in the k-replicated economy where all copies of the same agent receive the same bundle as the original agent in X. The allocation X is called sigma-optimal if for every k, the allocation Xk is Pareto-optimal. Lemma:: 528 An allocation is sigma-optimal, if-and-only-if it is a competitive equilibr... | Efficient envy-free division | 0.813071 |
17,228 | Polar Biology is a monthly peer-reviewed scientific journal covering the biology of the polar regions. It is published by Springer Science+Business Media. According to the Journal Citation Reports, the journal has a 2015 impact factor of 1.711. | Polar Biology | 0.81307 |
17,229 | Kozen, Dexter. "CS786 Spring 04, Introduction to Kleene Algebra". | Kleene algebra | 0.81307 |
17,230 | Zero is the smallest element: 0 ≤ a for all a in A. The sum a + b is the least upper bound of a and b: we have a ≤ a + b and b ≤ a + b and if x is an element of A with a ≤ x and b ≤ x, then a + b ≤ x. Similarly, a1 + ... + an is the least upper bound of the elements a1, ..., an. Multiplication and addition are monotoni... | Kleene algebra | 0.81307 |
17,231 | Various inequivalent definitions of Kleene algebras and related structures have been given in the literature. Here we will give the definition that seems to be the most common nowadays. A Kleene algebra is a set A together with two binary operations +: A × A → A and ·: A × A → A and one function *: A → A, written as a ... | Kleene algebra | 0.81307 |
17,232 | The MEME algorithm could be understood from two different perspectives. From a biological point of view, MEME identifies and characterizes shared motifs in a set of unaligned sequences. From the computer science aspect, MEME finds a set of non-overlapping, approximately matching substrings given a starting set of strin... | Multiple EM for Motif Elicitation | 0.813067 |
17,233 | Although the unphysical axes in the space of detailed configurations are a fundamental property of the physical model, there is no special set of directions "perpendicular" to them. Hence there is an enormous amount of freedom involved in taking a "cross section" representing each physical configuration by a particular... | Landau gauge | 0.813067 |
17,234 | In the physics of gauge theories, gauge fixing (also called choosing a gauge) denotes a mathematical procedure for coping with redundant degrees of freedom in field variables. By definition, a gauge theory represents each physically distinct configuration of the system as an equivalence class of detailed local field co... | Landau gauge | 0.813067 |
17,235 | Natural Language Engineering is a bimonthly peer-reviewed academic journal published by Cambridge University Press which covers research and software in natural language processing. Its aim is to "bridge the gap between traditional computational linguistics research and the implementation of practical applications with... | Natural Language Engineering | 0.81306 |
17,236 | Techniques have been developed for NIR spectroscopic imaging. Hyperspectral imaging has been applied for a wide range of uses, including the remote investigation of plants and soils. Data can be collected from instruments on airplanes, satellites or unmanned aerial systems to assess ground cover and soil chemistry. Rem... | Near infrared spectroscopy | 0.813059 |
17,237 | Near-infrared spectroscopy is used in astronomy for studying the atmospheres of cool stars where molecules can form. The vibrational and rotational signatures of molecules such as titanium oxide, cyanide, and carbon monoxide can be seen in this wavelength range and can give a clue towards the star's spectral type. It i... | Near infrared spectroscopy | 0.813059 |
17,238 | {\displaystyle h(K_{1},K_{2}):=\max \left\{\sup _{a\in K_{1}}\inf _{b\in K_{2}}d(a,b),\sup _{b\in K_{2}}\inf _{a\in K_{1}}d(a,b)\right\}.} ( K , h ) {\displaystyle ({\mathcal {K}},h)} is also а complete separable metric space. The corresponding open subsets generate a σ-algebra on K {\displaystyle {\mathcal {K}}} , the... | Random set theory | 0.813059 |
17,239 | The retrieved data may be stored in a file, printed, or viewed on the screen. A query language, like for example Structured Query Language (SQL), is used to prepare the queries. SQL is an American National Standards Institute (ANSI) standardized query language developed specifically to write database queries. Each data... | Data retrieval | 0.813053 |
17,240 | Data retrieval means obtaining data from a database management system (DBMS), like for example an object-oriented database (ODBMS). In this case, it is considered that data is represented in a structured way, and there is no ambiguity in data. In order to retrieve the desired data the user presents a set of criteria by... | Data retrieval | 0.813053 |
17,241 | Reports and queries are the two primary forms of the retrieved data from a database. There are some overlaps between them, but queries generally select a relatively small portion of the database, while reports show larger amounts of data. Queries also present the data in a standard format and usually display it on the ... | Data retrieval | 0.813053 |
17,242 | By the variational representation of chi-squared divergence, Plug in g = g ^ , P = μ θ ′ , Q = μ θ {\displaystyle g={\hat {g}},P=\mu _{\theta '},Q=\mu _{\theta }} , to obtain Switch the denominator and the left side, and take supremum over θ ′ {\displaystyle \theta '} to obtain the single-variate case. For the multivar... | Chapman–Robbins bound | 0.813053 |
17,243 | In statistics, the Chapman–Robbins bound or Hammersley–Chapman–Robbins bound is a lower bound on the variance of estimators of a deterministic parameter. It is a generalization of the Cramér–Rao bound; compared to the Cramér–Rao bound, it is both tighter and applicable to a wider range of problems. However, it is usual... | Chapman–Robbins bound | 0.813053 |
17,244 | This algorithm works because if the ray never crosses the polygon, then its crossing number is zero, which is even, and the point is outside. Every time the ray does cross the polygon, the crossing number alternates between even and odd, and the point at its tip alternates between outside and inside. In graph theory, a... | Zero is even | 0.813053 |
17,245 | The classic point in polygon test from computational geometry applies the above ideas. To determine if a point lies within a polygon, one casts a ray from infinity to the point and counts the number of times the ray crosses the edge of polygon. The crossing number is even if and only if the point is outside the polygon... | Zero is even | 0.813053 |
17,246 | With this definition, the evenness of zero is not a theorem but an axiom. Indeed, "zero is an even number" may be interpreted as one of the Peano axioms, of which the even natural numbers are a model. A similar construction extends the definition of parity to transfinite ordinal numbers: every limit ordinal is even, in... | Zero is even | 0.813053 |
17,247 | The fact that zero is even, together with the fact that even and odd numbers alternate, is enough to determine the parity of every other natural number. This idea can be formalized into a recursive definition of the set of even natural numbers: 0 is even. (n + 1) is even if and only if n is not even.This definition has... | Zero is even | 0.813053 |
17,248 | In abstract algebra, the even integers form various algebraic structures that require the inclusion of zero. The fact that the additive identity (zero) is even, together with the evenness of sums and additive inverses of even numbers and the associativity of addition, means that the even integers form a group. Moreover... | Zero is even | 0.813053 |
17,249 | Countless results in number theory invoke the fundamental theorem of arithmetic and the algebraic properties of even numbers, so the above choices have far-reaching consequences. For example, the fact that positive numbers have unique factorizations means that one can determine whether a number has an even or odd numbe... | Zero is even | 0.813053 |
17,250 | Zero belongs to neither list, hence the slower responses.Repeated experiments have shown a delay at zero for subjects with a variety of ages and national and linguistic backgrounds, confronted with number names in numeral form, spelled out, and spelled in a mirror image. Dehaene's group did find one differentiating fac... | Zero is even | 0.813053 |
17,251 | Applications of this recursion from graph theory to computational geometry rely on zero being even. Not only is 0 divisible by 2, it is divisible by every power of 2, which is relevant to the binary numeral system used by computers. In this sense, 0 is the "most even" number of all.Among the general public, the parity ... | Zero is even | 0.813053 |
17,252 | When cell biologists largely abandoned colloidal phase separation, it was left to relative outsiders - agricultural scientists and physicists - to make further progress in the study of phase separating biomolecules in cells. Beginning in the early 1970s, Harold M Farrell Jr. at the US Department of Agriculture develope... | Biomolecular condensate | 0.813052 |
17,253 | In biochemistry, biomolecular condensates are a class of membrane-less organelles and organelle subdomains, which carry out specialized functions within the cell. Unlike many organelles, biomolecular condensate composition is not controlled by a bounding membrane. Instead, condensates can form and maintain organization... | Biomolecular condensate | 0.813052 |
17,254 | Biomolecular condensates can be synthesized for a number of purposes. Synthetic biomolecular condensates are inspired by endogenous biomolecular condensates, such as nucleoli, P bodies, and stress granules, which are essential to normal cellular organization and function.Synthetic condensates are an important tool in s... | Biomolecular condensate | 0.813052 |
17,255 | Advances in confocal microscopy at the end of the 20th century identified proteins, RNA or carbohydrates localising to many non-membrane bound cellular compartments within the cytoplasm or nucleus which were variously referred to as 'puncta/dots', 'signalosomes', 'granules', 'bodies', 'assemblies', 'paraspeckles', 'pur... | Biomolecular condensate | 0.813052 |
17,256 | A number of experimental and computational methods have been developed to examine the physico-chemical properties and underlying molecular interactions of biomolecular condensates. Experimental approaches include phase separation assays using bright-field imaging or fluorescence microscopy, as well as fluorescence reco... | Biomolecular condensate | 0.813052 |
17,257 | WB Hardy linked formation of biological colloids with phase separation in his study of globulins, stating that: "The globulin is dispersed in the solvent as particles which are the colloid particles and which are so large as to form an internal phase", and further contributed to the basic physical description of oil-wa... | Biomolecular condensate | 0.813052 |
17,258 | The term "biomolecular condensate" directly addresses this challenge by making no assumption regarding either the physical mechanism through which assembly is achieved, nor the material state of the resulting assembly. Consequently, cellular bodies that form through liquid-liquid phase separation are a subset of biomol... | Biomolecular condensate | 0.813052 |
17,259 | In nine-dimensional geometry, a rectified 9-simplex is a convex uniform 9-polytope, being a rectification of the regular 9-simplex. These polytopes are part of a family of 271 uniform 9-polytopes with A9 symmetry. There are unique 4 degrees of rectifications. Vertices of the rectified 9-simplex are located at the edge-... | Trirectified 9-simplex | 0.813049 |
17,260 | This is less than O ( ϵ m ) − log 1 δ {\displaystyle O(\epsilon m)-\log {\frac {1}{\delta }}} if we set m ≥ a ( 1 ϵ log 1 δ + ( ( n ⋅ s i z e ( c ) ) α ) ϵ ) 1 1 − β ) {\displaystyle m\geq a\left({\frac {1}{\epsilon }}\log {\frac {1}{\delta }}+\left({\frac {(n\cdot size(c))^{\alpha })}{\epsilon }}\right)^{\frac {1}... | Occam learning | 0.813047 |
17,261 | This concludes the proof of the second theorem above. Using the second theorem, we can prove the first theorem. Since we have a ( α , β ) {\displaystyle (\alpha ,\beta )} -Occam algorithm, this means that any hypothesis output by L {\displaystyle L} can be represented by at most ( n ⋅ s i z e ( c ) ) α m β {\displaysty... | Occam learning | 0.813046 |
17,262 | Let 0 < ϵ , δ < 1 {\displaystyle 0<\epsilon ,\delta <1} . Let L {\displaystyle L} be an algorithm such that, given m {\displaystyle m} samples drawn from a fixed but unknown distribution D {\displaystyle {\mathcal {D}}} and labeled according to a concept c ∈ C {\displaystyle c\in {\mathcal {C}}} of length n {\displayst... | Occam learning | 0.813046 |
17,263 | Occam learnability implies PAC learnability, as the following theorem of Blumer, et al. shows: | Occam learning | 0.813046 |
17,264 | Elementary vector and tensor algebra in curvilinear coordinates is used in some of the older scientific literature in mechanics and physics and can be indispensable to understanding work from the early and mid 1900s, for example the text by Green and Zerna. Some useful relations in the algebra of vectors and second-ord... | Tensors in curvilinear coordinates | 0.813045 |
17,265 | Curvilinear coordinates can be formulated in tensor calculus, with important applications in physics and engineering, particularly for describing transportation of physical quantities and deformation of matter in fluid mechanics and continuum mechanics. | Tensors in curvilinear coordinates | 0.813045 |
17,266 | The divergence of a vector field ( v {\displaystyle \mathbf {v} } )is defined as In terms of components with respect to a curvilinear basis An alternative equation for the divergence of a vector field is frequently used. To derive this relation recall that Now, Noting that, due to the symmetry of g {\displaystyle {\bol... | Tensors in curvilinear coordinates | 0.813045 |
17,267 | Simmonds, in his book on tensor analysis, quotes Albert Einstein saying The magic of this theory will hardly fail to impose itself on anybody who has truly understood it; it represents a genuine triumph of the method of absolute differential calculus, founded by Gauss, Riemann, Ricci, and Levi-Civita. Vector and tensor... | Tensors in curvilinear coordinates | 0.813045 |
17,268 | If we wish to use curvilinear coordinates for vector calculus calculations, adjustments need to be made in the calculation of line, surface and volume integrals. For simplicity, we again restrict the discussion to three dimensions and orthogonal curvilinear coordinates. However, the same arguments apply for n {\display... | Tensors in curvilinear coordinates | 0.813045 |
17,269 | A similar process can be used to arrive at the gradient of a vector field f(x). The gradient is given by If we consider the gradient of the position vector field r(x) = x, then we can show that The vector field bi is tangent to the qi coordinate curve and forms a natural basis at each point on the curve. This basis, as... | Tensors in curvilinear coordinates | 0.813045 |
17,270 | In the field of hydrogeology, storage properties are physical properties that characterize the capacity of an aquifer to release groundwater. These properties are storativity (S), specific storage (Ss) and specific yield (Sy). According to Groundwater, by Freeze and Cherry (1979), specific storage, S s {\displaystyle S... | Specific storage | 0.813039 |
17,271 | As its name implies, the fundamental solution of the governing equations is used as the basis function in the MFS. To avoid singularity of the fundamental solution, the artificial boundary outside the physical domain is required and has been a major bottleneck for the wide use of the MFS, since such fictitious boundary... | Boundary knot method | 0.813038 |
17,272 | The map sending a finite-dimensional F-vector space to its dimension induces an isomorphism K 0 ( F ) ≅ Z {\displaystyle K_{0}(F)\cong \mathbf {Z} } for any field F. Next, K 1 ( F ) = F × , {\displaystyle K_{1}(F)=F^{\times },} the multiplicative group of F. The second K-group of a field is described in terms of genera... | K-group of a field | 0.813037 |
17,273 | In mathematics, especially in algebraic K-theory, the algebraic K-group of a field is important to compute. For a finite field, the complete calculation was given by Daniel Quillen. | K-group of a field | 0.813037 |
17,274 | The IEEE 754 standard requires the same rounding to be applied to all fundamental algebraic operations, including square root and conversions, when there is a numeric (non-NaN) result. It means that the results of IEEE 754 operations are completely determined in all bits of the result, except for the representation of ... | Floating-point format | 0.813036 |
17,275 | In probability theory, the Gillespie algorithm (or the Doob–Gillespie algorithm or Stochastic Simulation Algorithm, the SSA) generates a statistically correct trajectory (possible solution) of a stochastic equation system for which the reaction rates are known. It was created by Joseph L. Doob and others (circa 1945), ... | Gillespie algorithm | 0.813034 |
17,276 | Traditional continuous and deterministic biochemical rate equations do not accurately predict cellular reactions since they rely on bulk reactions that require the interactions of millions of molecules. They are typically modeled as a set of coupled ordinary differential equations. In contrast, the Gillespie algorithm ... | Gillespie algorithm | 0.813034 |
17,277 | The process that led to the algorithm recognizes several important steps. In 1931, Andrei Kolmogorov introduced the differential equations corresponding to the time-evolution of stochastic processes that proceed by jumps, today known as Kolmogorov equations (Markov jump process) (a simplified version is known as master... | Gillespie algorithm | 0.813034 |
17,278 | The Underground Area 2 (UA2) experiment was a high-energy physics experiment at the Proton-Antiproton Collider (SppS) — a modification of the Super Proton Synchrotron (SPS) — at CERN. The experiment ran from 1981 until 1990, and its main objective was to discover the W and Z bosons. UA2, together with the UA1 experimen... | UA2 experiment | 0.81303 |
17,279 | Around 1968 Sheldon Glashow, Steven Weinberg, and Abdus Salam came up with the electroweak theory, which unified electromagnetism and weak interactions, and for which they shared the 1979 Nobel Prize in Physics. The theory postulated the existence of W and Z bosons, and the pressure on the research community to prove t... | UA2 experiment | 0.81303 |
17,280 | The UA1 and the UA2 experiments had many things in common; they were both operating on the same accelerator and both had the same objective (to discover the W and Z bosons). The main difference was the detector design; UA1 was a multipurpose detector, while UA2 had a more limited scope. UA2 was optimized for the detect... | UA2 experiment | 0.81303 |
17,281 | In 2007, a similar Python project, namely PyCogent, was established.The initial scope of Biopython involved accessing, indexing and processing biological sequence files. While this is still a major focus, over the following years added modules have extended its functionality to cover additional areas of biology (see Ke... | Biopython | 0.813029 |
17,282 | Biopython development began in 1999 and it was first released in July 2000. It was developed during a similar time frame and with analogous goals to other projects that added bioinformatics capabilities to their respective programming languages, including BioPerl, BioRuby and BioJava. Early developers on the project in... | Biopython | 0.813029 |
17,283 | The Biopython project is an open-source collection of non-commercial Python tools for computational biology and bioinformatics, created by an international association of developers. It contains classes to represent biological sequences and sequence annotations, and it is able to read and write to a variety of file for... | Biopython | 0.813029 |
17,284 | The Bio.PopGen module adds support to Biopython for Genepop, a software package for statistical analysis of population genetics. This allows for analyses of Hardy–Weinberg equilibrium, linkage disequilibrium and other features of a population's allele frequencies. This module can also carry out population genetic simul... | Biopython | 0.813029 |
17,285 | In mathematics (specifically multivariable calculus), a multiple integral is a definite integral of a function of several real variables, for instance, f(x, y) or f(x, y, z). Integrals of a function of two variables over a region in R 2 {\displaystyle \mathbb {R} ^{2}} (the real-number plane) are called double integral... | Multiple integrals | 0.813029 |
17,286 | Triple integral was demonstrated by Fubini's theorem. Drichlet theorem and Liouville 's extension theorem on Triple integral. | Multiple integrals | 0.813028 |
17,287 | If D is normal with respect to the y-axis and f: D → R is a continuous function; then α(y) and β(y) (both of which are defined on the interval ) are the two functions that determine D. Again, by Fubini's theorem: ∬ D f ( x , y ) d x d y = ∫ a b d y ∫ α ( y ) β ( y ) f ( x , y ) d x . {\displaystyle \iint _{D}f(x,y)\,dx... | Multiple integrals | 0.813028 |
17,288 | In six-dimensional geometry, a rectified 6-simplex is a convex uniform 6-polytope, being a rectification of the regular 6-simplex. There are three unique degrees of rectifications, including the zeroth, the 6-simplex itself. Vertices of the rectified 6-simplex are located at the edge-centers of the 6-simplex. Vertices ... | Rectified 6-simplex | 0.813026 |
17,289 | It ranges from −j to +j in steps of one. This generates 2j + 1 different values of mj. The total angular momentum corresponds to the Casimir invariant of the Lie algebra so(3) of the three-dimensional rotation group. | Total angular momentum | 0.813025 |
17,290 | In quantum mechanics, the total angular momentum quantum number parametrises the total angular momentum of a given particle, by combining its orbital angular momentum and its intrinsic angular momentum (i.e., its spin). If s is the particle's spin angular momentum and ℓ its orbital angular momentum vector, the total an... | Total angular momentum | 0.813025 |
17,291 | Genitourinary Disorders 11. Geriatrics 12. Gynecology and Obstetrics 13. | Merck Manual | 0.813025 |
17,292 | The composition of the Earth's atmosphere changes as result of natural processes such as volcano emissions, lightning and bombardment by solar particles from corona. It has also been changed by human activity and some of these changes are harmful to human health, crops and ecosystems. Examples of problems which have be... | Atmospheric composition | 0.81302 |
17,293 | Atmospheric chemistry is a branch of atmospheric science in which the chemistry of the Earth's atmosphere and that of other planets is studied. It is a multidisciplinary approach of research and draws on environmental chemistry, physics, meteorology, computer modeling, oceanography, geology and volcanology and other di... | Atmospheric composition | 0.81302 |
17,294 | Observations, lab measurements, and modeling are the three central elements in atmospheric chemistry. Progress in atmospheric chemistry is often driven by the interactions between these components and they form an integrated whole. For example, observations may tell us that more of a chemical compound exists than previ... | Atmospheric composition | 0.81302 |
17,295 | Measurements made in the laboratory are essential to our understanding of the sources and sinks of pollutants and naturally occurring compounds. These experiments are performed in controlled environments that allow for the individual evaluation of specific chemical reactions or the assessment of properties of a particu... | Atmospheric composition | 0.81302 |
17,296 | In condensed-matter physics, the binary collision approximation (BCA) is a heuristic used to more efficiently simulate the penetration depth and defect production by energetic ions (with kinetic energies in the kilo-electronvolt (keV) range or higher) in solids. In the method, the ion is approximated to travel through ... | Binary collision approximation | 0.813016 |
17,297 | MARLOWE is a large code that can handle crystalline materials and support numerous different physics models. TRIDYN, newer versions known as SDTrimSP, is a BCA code capably of handling dynamic composition changes. DART, French code developed by the CEA (Commisariat à l'Energie Atomique) in Saclay. Differs from SRIM in ... | Binary collision approximation | 0.813016 |
17,298 | Rocket City Math League (RCML) is a student-run mathematics competition in the United States. Run by students at Virgil I. Grissom High School in Huntsville, Alabama, RCML gets its name from Huntsville's nickname as the "Rocket City". RCML was started in 2001 and has been annually sponsored by the Mu Alpha Theta Math H... | Rocket City Math League | 0.813015 |
17,299 | The Sommerfeld parameter η, named after Arnold Sommerfeld, is a dimensionless quantity used in nuclear astrophysics in the calculation of reaction rates between two nuclei and also appears in the definition of the astrophysical S-factor. It is defined as η = Z 1 Z 2 e 2 4 π ϵ 0 ℏ v = α Z 1 Z 2 μ c 2 2 E {\displaystyle ... | Sommerfeld parameter | 0.813013 |
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