id int32 0 100k | text stringlengths 21 3.54k | source stringlengths 1 124 | similarity float32 0.78 0.88 |
|---|---|---|---|
30,600 | The factorial number system is a mixed radix notation for numbers in which the place values of each digit are factorials.Factorials are used extensively in probability theory, for instance in the Poisson distribution and in the probabilities of random permutations. In computer science, beyond appearing in the analysis ... | Factorial function | 0.804893 |
30,601 | by all positive integers up to n {\displaystyle n} , described more precisely for prime factors by Legendre's formula. It follows that arbitrarily large prime numbers can be found as the prime factors of the numbers n ! ± 1 {\displaystyle n!\pm 1} , leading to a proof of Euclid's theorem that the number of primes is in... | Factorial function | 0.804893 |
30,602 | coming from the n {\displaystyle n} th derivative of x n {\displaystyle x^{n}} . This usage of factorials in power series connects back to analytic combinatorics through the exponential generating function, which for a combinatorial class with n i {\displaystyle n_{i}} elements of size i {\displaystyle i} is defined as... | Factorial function | 0.804893 |
30,603 | In calculus, factorials occur in Faà di Bruno's formula for chaining higher derivatives. In mathematical analysis, factorials frequently appear in the denominators of power series, most notably in the series for the exponential function, and in the coefficients of other Taylor series (in particular those of the trigono... | Factorial function | 0.804893 |
30,604 | In algebra, the factorials arise through the binomial theorem, which uses binomial coefficients to expand powers of sums. They also occur in the coefficients used to relate certain families of polynomials to each other, for instance in Newton's identities for symmetric polynomials. Their use in counting permutations ca... | Factorial function | 0.804893 |
30,605 | The power series for the exponential function, with the reciprocals of factorials for its coefficients, was first formulated in 1676 by Isaac Newton in a letter to Gottfried Wilhelm Leibniz. Other important works of early European mathematics on factorials include extensive coverage in a 1685 treatise by John Wallis, a... | Factorial function | 0.804893 |
30,606 | 1040) was the first to formulate Wilson's theorem connecting the factorials with the prime numbers. In Europe, although Greek mathematics included some combinatorics, and Plato famously used 5,040 (a factorial) as the population of an ideal community, in part because of its divisibility properties, there is no direct e... | Factorial function | 0.804893 |
30,607 | In mathematical analysis, factorials are used in power series for the exponential function and other functions, and they also have applications in algebra, number theory, probability theory, and computer science. Much of the mathematics of the factorial function was developed beginning in the late 18th and early 19th c... | Factorial function | 0.804893 |
30,608 | Many oligopeptides that possess an N-Formylmethionine N-terminal residue such as the prototypical tripeptide N-Formylmethionine-leucyl-phenylalanine (i.e. FMLP), are products of the protein synthesis conducted by bacteria. They stimulate granulocytes to migrate directionally (see chemotaxis) and become active in engulf... | Formyl peptide receptor 2 | 0.80489 |
30,609 | This follows from the classical theorem that there is only one Archimedean complete ordered field, along with the fact that all the axioms of an Archimedean complete ordered field are expressible in second-order logic. This shows that the second-order theory of the real numbers cannot be reduced to a first-order theory... | Henkin semantics | 0.80489 |
30,610 | That theorem implies that there is some countably infinite subset of the real numbers, whose members we will call internal numbers, and some countably infinite collection of sets of internal numbers, whose members we will call "internal sets", such that the domain consisting of internal numbers and internal sets satisf... | Henkin semantics | 0.80489 |
30,611 | This reduction can be attempted in a one-sorted theory by adding unary predicates that tell whether an element is a number or a set, and taking the domain to be the union of the set of real numbers and the power set of the real numbers. But notice that the domain was asserted to include all sets of real numbers. That r... | Henkin semantics | 0.80489 |
30,612 | A large number of tutorials are published on a dedicated website. They describe the statistical and machine learning methods and their implementation with Tanagra on real case studies. The use of other free data mining tools on the same problems is also widely described. The comparison of the tools enables readers to u... | Tanagra (machine learning) | 0.80489 |
30,613 | This makes it is easy to export the outputs in order to visualize the results in a browser. It is also possible to copy the result tables to a spreadsheet. Tanagra makes a good compromise between statistical approaches (e.g. parametric and nonparametric statistical tests), multivariate analysis methods (e.g. factor ana... | Tanagra (machine learning) | 0.80489 |
30,614 | Tanagra works similarly to current data mining tools. The user can design visually a data mining process in a diagram. Each node is a statistical or machine learning technique, the connection between two nodes represents the data transfer. But unlike the majority of tools which are based on the workflow paradigm, Tanag... | Tanagra (machine learning) | 0.80489 |
30,615 | Tanagra is a free suite of machine learning software for research and academic purposes developed by Ricco Rakotomalala at the Lumière University Lyon 2, France. Tanagra supports several standard data mining tasks such as: Visualization, Descriptive statistics, Instance selection, feature selection, feature constructio... | Tanagra (machine learning) | 0.80489 |
30,616 | The historical application of biotechnology throughout time is provided below in chronological order. These discoveries, inventions and modifications are evidence of the application of biotechnology since before the common era and describe notable events in the research, development and regulation of biotechnology. | Timeline of biotechnology | 0.804889 |
30,617 | Cellular bioengineers report the development of nonreplicating bacterial 'cyborg cells' (similar to artificial cells) using a novel approach, assembling a synthetic hydrogel polymer network as an artificial cytoskeleton inside the bacteria. The cells can resist stressors that would kill natural cells and e.g. invade ca... | Timeline of biotechnology | 0.804889 |
30,618 | Artificial intelligence in healthcare Diagnostic microbiology Gene therapy#2020s List of emerging technologies#Medical Regeneration in humans Timeline of human vaccines Timeline of medicine and medical technology#2000–2022 Timeline of senescence research == References == | Timeline of biotechnology | 0.804889 |
30,619 | The paper's senior author cautions that the two neutralizing systems they demonstrated in cage trials "should not be used with a false sense of security for field-implemented gene drives".28 September – Biotechnologists report the genetically engineered refinement and mechanical description of synergistic enzymes – PET... | Timeline of biotechnology | 0.804889 |
30,620 | They used inverse statistical physics to learn the patterns of amino acid conservation and co-evolution to identify design-rules. 8 September – Scientists report that suppressing activin type 2 receptors-signalling proteins myostatin and activin A via activin A/myostatin inhibitor ACVR2B – tested preliminarily in human... | Timeline of biotechnology | 0.804889 |
30,621 | Their technology could be used in molecular biology and in medical applications such as for better targeting of virus RNA or human RNA. Targeting human RNA after it has been transcribed from DNA, rather than DNA, would allow for more temporary effects than permanent changes to human genomes. The technology is made avai... | Timeline of biotechnology | 0.804889 |
30,622 | Lukyanovich publish clear images of 50 nanometer diameter tubes made of carbon, in the Soviet Journal of Physical Chemistry. 1953 – James D. Watson and Francis Crick describe the structure of DNA. 1958 – The term bionics is coined by Jack E. Steele. | Timeline of biotechnology | 0.804889 |
30,623 | 1919 – Károly Ereky, a Hungarian agricultural engineer, first uses the word biotechnology. 1928 – Alexander Fleming notices that a certain mould could stop the duplication of bacteria, leading to the first antibiotic: penicillin. 1933 – Hybrid corn is commercialized. 1942 – Penicillin is mass-produced in microbes for t... | Timeline of biotechnology | 0.804889 |
30,624 | 1663 – First recorded description of living cells by Robert Hooke. 1677 – Antonie van Leeuwenhoek discovers and describes bacteria and protozoa. 1798 – Edward Jenner uses first viral vaccine to inoculate a child from smallpox. 1802 – The first recorded use of the word biology. | Timeline of biotechnology | 0.804889 |
30,625 | Bioengineers report the development of a viable CRISPR-Cas gene-editing system, "CasMINI", that is about twice as compact as the commonly used Cas9 and Cas12a. Media outlets report that the world's first cultured coffee product has been created, still awaiting regulatory approval for near-term commercialization. It was... | Timeline of biotechnology | 0.804889 |
30,626 | 0 Researchers partially restore eyesight of a patient with Retinitis pigmentosa using eye-injected viral vectors for genes encoding the light-sensing channelrhodopsin protein ChrimsonR found in glowing algae, and light stimulation of them via engineered goggles that transform visual information of the environment. 0 Sc... | Timeline of biotechnology | 0.804889 |
30,627 | 0A novel synthetic biology-based process for recycling of plastics mixtures is presented. 0Emulate researchers assess advantages of using liver-chips predicting drug-induced liver injury which could reduce the high costs and time needed in drug development workflows/pipelines, sometimes described as the pharmaceutical ... | Timeline of biotechnology | 0.804889 |
30,628 | Researchers report the controlled growth of diverse foods in the dark via solar energy and electrocatalysis-based artificial photosynthesis as a potential way to increase energy efficiency of food production and reduce its environmental impacts. 0News outlets report about the development of algae biopanels by a company... | Timeline of biotechnology | 0.804889 |
30,629 | He then points out that Darwin dismissed the need to explain the origin of the 'simple' light-sensitive spot, summarizes the modern understanding of the biochemistry of vision and claims that many other evolutionary explanations face a similar challenge. Behe next introduces and defines the concept of irreducible compl... | Darwin's Black Box | 0.804889 |
30,630 | Behe suggests that such a paradigm shift in biology (and particularly in evolution) is imminent due to recent discoveries (circa 1996) in biochemistry. Behe acknowledges acceptance of the theory of evolution by "the great majority" of scientists, and he states that "most (though not all) do so based on authority." Behe... | Darwin's Black Box | 0.804889 |
30,631 | The "black box" in the title refers to the conceptual tool in which, for one reason or another, the internal workings of a device are taken for granted, so that its function may be discussed. The philosophical tool is commonly used in scientific discourse, and Behe notes that understandings of cellular structure and ot... | Darwin's Black Box | 0.804889 |
30,632 | Darwin's Black Box: The Biochemical Challenge to Evolution (1996; second edition 2006) is a book by Michael J. Behe, a professor of biochemistry at Lehigh University in Pennsylvania and a senior fellow of the Discovery Institute's Center for Science and Culture. In the book Behe presents his notion of irreducible compl... | Darwin's Black Box | 0.804889 |
30,633 | Darwin's Black Box was not well received by the scientific community, which rejected Behe's premises and arguments. Kenneth Miller described Behe's argument as an updated version of the argument from design with reference to biochemistry (which was echoed by other reviewers), and also cites areas in biochemistry and th... | Darwin's Black Box | 0.804889 |
30,634 | The application and interpretation of water footprints may sometimes be used to promote industrial activities that lead to facile criticism of certain products. For example, the 140 litres required for coffee production for one cup might be of no harm to water resources if its cultivation occurs mainly in humid areas, ... | Water usage | 0.804887 |
30,635 | KPTI fixes these leaks by separating user-space and kernel-space page tables entirely. One set of page tables includes both kernel-space and user-space addresses same as before, but it is only used when the system is running in kernel mode. The second set of page tables for use in user mode contains a copy of user-spac... | Kernel page-table isolation | 0.804882 |
30,636 | In 1934, Popper published Zur Kritik der Ungenauigkeitsrelationen (Critique of the Uncertainty Relations) in Naturwissenschaften, and in the same year Logik der Forschung (translated and updated by the author as The Logic of Scientific Discovery in 1959), outlining his arguments for the statistical interpretation. In 1... | Uncertainty Principle | 0.804882 |
30,637 | Karl Popper approached the problem of indeterminacy as a logician and metaphysical realist. He disagreed with the application of the uncertainty relations to individual particles rather than to ensembles of identically prepared particles, referring to them as "statistical scatter relations". In this statistical interpr... | Uncertainty Principle | 0.804882 |
30,638 | In probability theory, the matrix geometric method is a method for the analysis of quasi-birth–death processes, continuous-time Markov chain whose transition rate matrices with a repetitive block structure. The method was developed "largely by Marcel F. Neuts and his students starting around 1975." | Matrix geometric method | 0.80488 |
30,639 | variable . vector . vector calculus . | Glossary of calculus | 0.80488 |
30,640 | trigonometric integral . trigonometric substitution . trigonometry . triple integral . | Glossary of calculus | 0.80488 |
30,641 | table of integrals . Taylor series . Taylor's theorem . tangent . | Glossary of calculus | 0.80488 |
30,642 | sine wave . slope field . squeeze theorem . | Glossary of calculus | 0.80488 |
30,643 | Riemann integral . related rates . removable discontinuity . Rolle's theorem . root test . | Glossary of calculus | 0.80488 |
30,644 | quadratic function In algebra, a quadratic function, a quadratic polynomial, a polynomial of degree 2, or simply a quadratic, is a polynomial function with one or more variables in which the highest-degree term is of the second degree. For example, a quadratic function in three variables x, y, and z contains exclusivel... | Glossary of calculus | 0.80488 |
30,645 | nonstandard calculus . notation for differentiation . numerical integration . | Glossary of calculus | 0.80488 |
30,646 | Using the fundamental theorem of calculus often requires finding an antiderivative. For this and other reasons, integration by substitution is an important tool in mathematics. It is the counterpart to the chain rule for differentiation. | Glossary of calculus | 0.80488 |
30,647 | . integrand The function to be integrated in an integral. integration by parts In calculus, and more generally in mathematical analysis, integration by parts or partial integration is a process that finds the integral of a product of functions in terms of the integral of their derivative and antiderivative. | Glossary of calculus | 0.80488 |
30,648 | integral An integral assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data. Integration is one of the two main operations of calculus, with its inverse operation, differentiation, being the other. | Glossary of calculus | 0.80488 |
30,649 | {\displaystyle {\boldsymbol {v}}=\lim _{{\Delta t}\to 0}{\frac {\Delta {\boldsymbol {x}}}{\Delta t}}={\frac {d{\boldsymbol {x}}}{d{\mathit {t}}}}.} From this derivative equation, in the one-dimensional case it can be seen that the area under a velocity vs. time (v vs. t graph) is the displacement, x. In calculus terms,... | Glossary of calculus | 0.80488 |
30,650 | inflection point In differential calculus, an inflection point, point of inflection, flex, or inflection (British English: inflexion) is a point on a continuous plane curve at which the curve changes from being concave (concave downward) to convex (concave upward), or vice versa. instantaneous rate of change The deriva... | Glossary of calculus | 0.80488 |
30,651 | The implicit function theorem provides conditions under which some kinds of relations define an implicit function, namely relations defined as the indicator function of the zero set of some continuously differentiable multivariate function. improper fraction Common fractions can be classified as either proper or improp... | Glossary of calculus | 0.80488 |
30,652 | A first order differential equation is said to be homogeneous if it may be written f ( x , y ) d y = g ( x , y ) d x , {\displaystyle f(x,y)dy=g(x,y)dx,} where f and g are homogeneous functions of the same degree of x and y. In this case, the change of variable y = ux leads to an equation of the form d x x = h ( u ) d ... | Glossary of calculus | 0.80488 |
30,653 | As defined in set theory, the maximum and minimum of a set are the greatest and least elements in the set, respectively. Unbounded infinite sets, such as the set of real numbers, have no minimum or maximum. golden spiral In geometry, a golden spiral is a logarithmic spiral whose growth factor is φ, the golden ratio. | Glossary of calculus | 0.80488 |
30,654 | That is, there exist numbers c and d in such that: f ( c ) ≥ f ( x ) ≥ f ( d ) for all x ∈ . {\displaystyle f(c)\geq f(x)\geq f(d)\quad {\text{for all }}x\in .} A related theorem is the boundedness theorem which states that a continuous function f in the closed interval is bounded on that interval. That is, there ex... | Glossary of calculus | 0.80488 |
30,655 | For real numbers c and d, a function of the form f ( x ) = a b c x + d {\displaystyle f(x)=ab^{cx+d}} is also an exponential function, as it can be rewritten as a b c x + d = ( a b d ) ( b c ) x . {\displaystyle ab^{cx+d}=\left(ab^{d}\right)\left(b^{c}\right)^{x}.} extreme value theorem States that if a real-valued fun... | Glossary of calculus | 0.80488 |
30,656 | It is the most basic explicit method for numerical integration of ordinary differential equations and is the simplest Runge–Kutta method. The Euler method is named after Leonhard Euler, who treated it in his book Institutionum calculi integralis (published 1768–1870). exponential function In mathematics, an exponential... | Glossary of calculus | 0.80488 |
30,657 | }}={\frac {1}{1}}+{\frac {1}{1}}+{\frac {1}{1\cdot 2}}+{\frac {1}{1\cdot 2\cdot 3}}+\cdots } elliptic integral In integral calculus, elliptic integrals originally arose in connection with the problem of giving the arc length of an ellipse. They were first studied by Giulio Fagnano and Leonhard Euler (c. 1750). | Glossary of calculus | 0.80488 |
30,658 | It is one of the two traditional divisions of calculus, the other being integral calculus, the study of the area beneath a curve. differential equation Is a mathematical equation that relates some function with its derivatives. In applications, the functions usually represent physical quantities, the derivatives repres... | Glossary of calculus | 0.80488 |
30,659 | Using calculus, it is possible to relate the infinitely small changes of various variables to each other mathematically using derivatives. If y is a function of x, then the differential dy of y is related to dx by the formula d y = d y d x d x , {\displaystyle dy={\frac {dy}{dx}}\,dx,} where dy/dx denotes the derivativ... | Glossary of calculus | 0.80488 |
30,660 | differential (infinitesimal) The term differential is used in calculus to refer to an infinitesimal (infinitely small) change in some varying quantity. For example, if x is a variable, then a change in the value of x is often denoted Δx (pronounced delta x). The differential dx represents an infinitely small change in ... | Glossary of calculus | 0.80488 |
30,661 | Derivatives are a fundamental tool of calculus. For example, the derivative of the position of a moving object with respect to time is the object's velocity: this measures how quickly the position of the object changes when time advances. derivative test A derivative test uses the derivatives of a function to locate th... | Glossary of calculus | 0.80488 |
30,662 | Here input is an equation. In digital geometry it is a method of drawing a curve pixel by pixel. Here input is an array (digital image). | Glossary of calculus | 0.80488 |
30,663 | critical point A critical point or stationary point of a differentiable function of a real or complex variable is any value in its domain where its derivative is 0. curve A curve (also called a curved line in older texts) is, generally speaking, an object similar to a line but that need not be straight. curve sketching... | Glossary of calculus | 0.80488 |
30,664 | Cramer's rule In linear algebra, Cramer's rule is an explicit formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever the system has a unique solution. It expresses the solution in terms of the determinants of the (square) coefficient matrix and of matrices obtained f... | Glossary of calculus | 0.80488 |
30,665 | calculus (From Latin calculus, literally 'small pebble', used for counting and calculations, as on an abacus) is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations. Cavalieri's principle Cavalieri's princi... | Glossary of calculus | 0.80488 |
30,666 | . {\displaystyle {\binom {n}{k}}={\frac {n!}{k!(n-k)!}}.} binomial theorem (or binomial expansion) Describes the algebraic expansion of powers of a binomial. | Glossary of calculus | 0.80488 |
30,667 | binomial coefficient Any of the positive integers that occurs as a coefficient in the binomial theorem is a binomial coefficient. Commonly, a binomial coefficient is indexed by a pair of integers n ≥ k ≥ 0 and is written ( n k ) . {\displaystyle {\tbinom {n}{k}}.} It is the coefficient of the xk term in the polynomial ... | Glossary of calculus | 0.80488 |
30,668 | function composition Is an operation that takes two functions f and g and produces a function h such that h(x) = g(f(x)). In this operation, the function g is applied to the result of applying the function f to x. That is, the functions f: X → Y and g: Y → Z are composed to yield a function that maps x in X to g(f(x)) ... | Glossary of calculus | 0.80488 |
30,669 | Fractional calculus Is a branch of mathematical analysis that studies the several different possibilities of defining real number powers or complex number powers of the differentiation operator D D f ( x ) = d d x f ( x ) {\displaystyle Df(x)={\dfrac {d}{dx}}f(x)} , and of the integration operator J J f ( x ) = ∫ 0 x f... | Glossary of calculus | 0.80488 |
30,670 | Faà di Bruno's formula Is an identity in mathematics generalizing the chain rule to higher derivatives, named after Francesco Faà di Bruno (1855, 1857), though he was not the first to state or prove the formula. In 1800, more than 50 years before Faà di Bruno, the French mathematician Louis François Antoine Arbogast st... | Glossary of calculus | 0.80488 |
30,671 | (2003). Numerical Methods for Ordinary Differential Equations. New York: John Wiley & Sons. | Glossary of calculus | 0.80488 |
30,672 | Apostol, T (1967), Calculus, Vol. 1 (2nd ed. ), Jon Wiley & Sons. Arbogast, L. F. A. | Glossary of calculus | 0.80488 |
30,673 | Some sources include the requirement that the curve may not cross the line infinitely often, but this is unusual for modern authors. In projective geometry and related contexts, an asymptote of a curve is a line which is tangent to the curve at a point at infinity. automatic differentiation In mathematics and computer ... | Glossary of calculus | 0.80488 |
30,674 | antiderivative An antiderivative, primitive function, primitive integral or indefinite integral of a function f is a differentiable function F whose derivative is equal to the original function f. This can be stated symbolically as F ′ = f {\displaystyle F'=f} . The process of solving for antiderivatives is called anti... | Glossary of calculus | 0.80488 |
30,675 | product rule . proper fraction . proper rational function . Pythagorean theorem . Pythagorean trigonometric identity . | Glossary of calculus | 0.80488 |
30,676 | Pappus's centroid theorem (Also known as the Guldinus theorem, Pappus–Guldinus theorem or Pappus's theorem) is either of two related theorems dealing with the surface areas and volumes of surfaces and solids of revolution. parabola Is a plane curve that is mirror-symmetrical and is approximately U-shaped. It fits sever... | Glossary of calculus | 0.80488 |
30,677 | Most of the terms listed in Wikipedia glossaries are already defined and explained within Wikipedia itself. However, glossaries like this one are useful for looking up, comparing and reviewing large numbers of terms together. You can help enhance this page by adding new terms or writing definitions for existing ones. T... | Glossary of calculus | 0.80488 |
30,678 | linear combination In mathematics, a linear combination is an expression constructed from a set of terms by multiplying each term by a constant and adding the results (e.g. a linear combination of x and y would be any expression of the form ax + by, where a and b are constants). The concept of linear combinations is ce... | Glossary of calculus | 0.80488 |
30,679 | Application (or repeated application) of the rule often converts an indeterminate form to an expression that can be evaluated by substitution, allowing easier evaluation of the limit. The rule is named after the 17th-century French mathematician Guillaume de l'Hôpital. Although the contribution of the rule is often att... | Glossary of calculus | 0.80488 |
30,680 | natural logarithm The natural logarithm of a number is its logarithm to the base of the mathematical constant e, where e is an irrational and transcendental number approximately equal to 2.718281828459. The natural logarithm of x is generally written as ln x, loge x, or sometimes, if the base e is implicit, simply log ... | Glossary of calculus | 0.80488 |
30,681 | mean value theorem . monotonic function . multiple integral . Multiplicative calculus . multivariable calculus . | Glossary of calculus | 0.80488 |
30,682 | . intermediate value theorem In mathematical analysis, the intermediate value theorem states that if a continuous function, f, with an interval, , as its domain, takes values f(a) and f(b) at each end of the interval, then it also takes any value between f(a) and f(b) at some point within the interval. This has two imp... | Glossary of calculus | 0.80488 |
30,683 | dot product In mathematics, the dot product or scalar product is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors) and returns a single number. In Euclidean geometry, the dot product of the Cartesian coordinates of two vectors is widely used and often called "the" inne... | Glossary of calculus | 0.80488 |
30,684 | disc integration Also known in integral calculus as the disc method, is a means of calculating the volume of a solid of revolution of a solid-state material when integrating along an axis "parallel" to the axis of revolution. divergent series Is an infinite series that is not convergent, meaning that the infinite seque... | Glossary of calculus | 0.80488 |
30,685 | differential operator . differential of a function In calculus, the differential represents the principal part of the change in a function y = f(x) with respect to changes in the independent variable. The differential dy is defined by d y = f ′ ( x ) d x , {\displaystyle dy=f'(x)\,dx,} where f ′ ( x ) {\displaystyle f'... | Glossary of calculus | 0.80488 |
30,686 | Hairer, Ernst; Nørsett, Syvert Paul; Wanner, Gerhard (1993). Solving ordinary differential equations I: Nonstiff problems. Berlin, New York: Springer-Verlag. | Glossary of calculus | 0.80488 |
30,687 | This implies the existence of antiderivatives for continuous functions. Conversely, the second part of the theorem, sometimes called the second fundamental theorem of calculus, states that the integral of a function f over some interval can be computed by using any one, say F, of its infinitely many antiderivatives. Th... | Glossary of calculus | 0.80488 |
30,688 | The center can be found using the Floyd–Warshall algorithm. Another algorithm has been proposed based on matrix calculus.The concept of the center of a graph is related to the closeness centrality measure in social network analysis, which is the reciprocal of the mean of the distances d(A,B). == References == | Graph center | 0.804879 |
30,689 | Huang took this technology and started a new business, RayBiotech, Inc., the first to successfully commercialize a planar antibody array. In the last ten years, the sensitivity of the method was improved by an optimization of the surface chemistry as well as dedicated protocols for their chemical labeling. Currently, t... | Antibody matrix | 0.804877 |
30,690 | In mathematics, the Hasse invariant (or Hasse–Witt invariant) of a quadratic form Q over a field K takes values in the Brauer group Br(K). The name "Hasse–Witt" comes from Helmut Hasse and Ernst Witt. The quadratic form Q may be taken as a diagonal form Σ aixi2.Its invariant is then defined as the product of the classe... | Hasse invariant of a quadratic form | 0.804876 |
30,691 | Moreover, Gödel's second incompleteness theorem shows that the consistency of sufficiently strong recursively enumerable theories of arithmetic can be tested in a particular way. Such a theory is consistent if and only if it does not prove a particular sentence, called the Gödel sentence of the theory, which is a forma... | Logically consistent | 0.804875 |
30,692 | It is both consistent and complete. Gödel's incompleteness theorems show that any sufficiently strong recursively enumerable theory of arithmetic cannot be both complete and consistent. Gödel's theorem applies to the theories of Peano arithmetic (PA) and primitive recursive arithmetic (PRA), but not to Presburger arith... | Logically consistent | 0.804875 |
30,693 | In mathematics, a formal sum, formal series, or formal linear combination may be: In group theory, an element of a free abelian group, a sum of finitely many elements from a given basis set multiplied by integer coefficients. In linear algebra, an element of a vector space, a sum of finitely many elements from a given ... | Formal sum | 0.804875 |
30,694 | Many operations in automatic theorem provers require search in huge collections of terms and clauses. Such operations typically fall into the following scheme. Given a collection S {\displaystyle S} of terms (clauses) and a query term (clause) q {\displaystyle q} , find in S {\displaystyle S} some/all terms t {\display... | Term indexing | 0.804874 |
30,695 | In computer science, a term index is a data structure to facilitate fast lookup of terms and clauses in a logic program, deductive database, or automated theorem prover. | Term indexing | 0.804874 |
30,696 | 2D chemical structure drawing (includes stereochemical recognition) Scientific publishing / reporting tools 3D ViewIt Input and visualization of 3D structures Portal with useful links for user community 3D presentations and 3D modeling, plus calculation of bond lengths, angles, etc. Build databases with structures and ... | ChemWindow | 0.804873 |
30,697 | The International Conference on Functional Programming (ICFP) is an annual academic conference in the field of computer science sponsored by the ACM SIGPLAN, in association with IFIP Working Group 2.8 (Functional Programming). The conference focuses on functional programming and related areas of programming languages, ... | Workshop on Generic Programming | 0.804873 |
30,698 | The strong nuclear force is believed to emerge from the strong interaction described by quantum chromodynamics (QCD), but QCD is non-perturbative in the low-energy regime relevant to nuclear physics. This makes the direct use of QCD for the description of the inter-nucleon interactions very difficult (see lattice QCD),... | Ab initio methods (nuclear physics) | 0.804871 |
30,699 | In nuclear physics, ab initio methods seek to describe the atomic nucleus from the bottom up by solving the non-relativistic Schrödinger equation for all constituent nucleons and the forces between them. This is done either exactly for very light nuclei (up to four nucleons) or by employing certain well-controlled appr... | Ab initio methods (nuclear physics) | 0.804871 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.