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7,800 | In physics, electromagnetism is an interaction that occurs between particles with electric charge via electromagnetic fields. The electromagnetic force is one of the four fundamental forces of nature. It is the dominant force in the interactions of atoms and molecules. Electromagnetism can be thought of as a combinatio... | Applied electromagnetics | 0.822307 |
7,801 | Theorem 1 Let X 1 , X 2 , ⋯ , X n {\displaystyle X_{1},X_{2},\cdots ,X_{n}} be identically distributed non-negative random variables with absolutely continuous distribution function F {\displaystyle F} . Then E ( N ) ≤ n F ( t ) , {\displaystyle E(N)\leq nF(t),} (2)where t := t ( n , s ) {\displaystyle t:=t(n,s)} solv... | BRS-inequality | 0.822301 |
7,802 | Depending on the type of the distributions F k {\displaystyle F_{k}} , refinements of Theorem 2 can be of true interest. We just mention one of them. Let A {\displaystyle A} be the random set of those variables one can sum up to yield the maximum random number N {\displaystyle N} , that is, # A = N {\displaystyle \... | BRS-inequality | 0.822301 |
7,803 | , X n {\displaystyle X_{1},X_{2},...,X_{n}} that one can sum up without exceeding s {\displaystyle s} . Now, to obtain N {\displaystyle N} one may think of looking at the list of all observations, first select the smallest one, then add the second smallest, then the third and so on, as long as the accumulated sum does... | BRS-inequality | 0.822301 |
7,804 | Theorem 2. Let X 1 , X 2 , ⋯ , X n {\displaystyle X_{1},X_{2},\cdots ,X_{n}} be positive random variables that are jointly distributed such that X k {\displaystyle X_{k}} has an absolutely continuous distribution function F k , k = 1 , 2 , ⋯ , n . {\displaystyle F_{k},~k=1,2,\cdots ,n.} . | BRS-inequality | 0.822301 |
7,805 | The first version of the BRS-inequality (Theorem 1) was proved in Lemma 4.1 of F. Thomas Bruss and James B. Robertson (1991). This paper proves moreover that the upper bound is asymptotically tight if the random variables are independent of each other. The generalisation to arbitrary continuous distributions (Theorem 2... | BRS-inequality | 0.822301 |
7,806 | The so-called residual s − S A {\displaystyle s-S_{A}} is by definition always non-negative, and one has: Theorem 3. Let X 1 , X 2 , ⋯ , X n {\displaystyle X_{1},X_{2},\cdots ,X_{n}} be jointly continuously distributed with marginal distribution functions F k , k = 1 , 2 , ⋯ , n {\displaystyle F_{k},k=1,2,\cdots ,n} ,... | BRS-inequality | 0.822301 |
7,807 | The BRS-inequality is a versatile tool since it applies to many types of problems, and since the computation of the BRS-equation is often not very involved. Also, and in particular, one notes that the maximum number N {\displaystyle N} always dominates the maximum number of selections under any additional constraint, ... | BRS-inequality | 0.822301 |
7,808 | Learning can happen either through autonomous self-exploration or through guidance from a human teacher, like for example in robot learning by imitation. Robot learning can be closely related to adaptive control, reinforcement learning as well as developmental robotics which considers the problem of autonomous lifelong... | Robot learning | 0.8223 |
7,809 | Robot learning is a research field at the intersection of machine learning and robotics. It studies techniques allowing a robot to acquire novel skills or adapt to its environment through learning algorithms. The embodiment of the robot, situated in a physical embedding, provides at the same time specific difficulties ... | Robot learning | 0.8223 |
7,810 | Maya Cakmak, assistant professor of computer science and engineering at the University of Washington, is trying to create a robot that learns by imitating - a technique called "programming by demonstration". A researcher shows it a cleaning technique for the robot's vision system and it generalizes the cleaning motion ... | Robot learning | 0.8223 |
7,811 | There are several broadly recognized algorithmic techniques that offer a proven method or process for designing and constructing algorithms. Different techniques may be used depending on the objective, which may include searching, sorting, mathematical optimization, constraint satisfaction, categorization, analysis, an... | Algorithmic technique | 0.822296 |
7,812 | Graph traversal is a technique for finding solutions to problems that can be represented as graphs. This approach is broad, and includes depth-first search, breadth-first search, tree traversal, and many specific variations that may include local optimizations and excluding search spaces that can be determined to be no... | Algorithmic technique | 0.822296 |
7,813 | Dynamic programming is a systematic technique in which a complex problem is decomposed recursively into smaller, overlapping subproblems for solution. Dynamic programming stores the results of the overlapping sub-problems locally using an optimization technique called memoization. | Algorithmic technique | 0.822296 |
7,814 | Mathematical optimization is a technique that can be used to calculate a mathematical optimum by minimizing or maximizing a function. | Algorithmic technique | 0.822296 |
7,815 | Learning techniques employ statistical methods to perform categorization and analysis without explicit programming. Supervised learning, unsupervised learning, reinforcement learning, and deep learning techniques are included in this category. | Algorithmic technique | 0.822296 |
7,816 | In mathematics and computer science, an algorithmic technique is a general approach for implementing a process or computation. | Algorithmic technique | 0.822296 |
7,817 | Number fields share a great deal of similarity with another class of fields much used in algebraic geometry known as function fields of algebraic curves over finite fields. An example is Kp(T). They are similar in many respects, for example in that number rings are one-dimensional regular rings, as are the coordinate r... | Algebraic number fields | 0.822289 |
7,818 | The real numbers, R {\displaystyle \mathbb {R} } , and the complex numbers, C {\displaystyle \mathbb {C} } , are fields which have infinite dimension as Q {\displaystyle \mathbb {Q} } -vector spaces, hence, they are not number fields. This follows from the uncountability of R {\displaystyle \mathbb {R} } and C {\displa... | Algebraic number fields | 0.822289 |
7,819 | This enables the use of group cohomology for the Galois group Gal(K), also known as Galois cohomology, which in the first place measures the failure of exactness of taking Gal(K)-invariants, but offers deeper insights (and questions) as well. For example, the Galois group G of a field extension L / K acts on L×, the no... | Algebraic number fields | 0.822289 |
7,820 | The fundamental theorem of Galois theory links fields in between K {\displaystyle K} and its algebraic closure and closed subgroups of Gal(K). For example, the abelianization (the biggest abelian quotient) Gab of G corresponds to a field referred to as the maximal abelian extension Kab (called so since any further exte... | Algebraic number fields | 0.822289 |
7,821 | Generally in abstract algebra, field extensions K / L can be studied by examining the Galois group Gal(K / L), consisting of field automorphisms of K {\displaystyle K} leaving L {\displaystyle L} elementwise fixed. As an example, the Galois group G a l ( Q ( ζ n ) / Q ) {\displaystyle \mathrm {Gal} (\mathbb {Q} (\zeta ... | Algebraic number fields | 0.822289 |
7,822 | Much of the significance of the discriminant lies in the fact that ramified ultrametric places are all places obtained from factorizations in Q p {\displaystyle \mathbb {Q} _{p}} where p divides the discriminant. This is even true of the polynomial discriminant; however the converse is also true, that if a prime p divi... | Algebraic number fields | 0.822289 |
7,823 | A steep rise in abstraction was seen mid 20th century. In practice, however, these developments led to a sharp divergence from physics, particularly from 1950 to 1983. Later this was criticised, for example by Vladimir Arnold, as too much Hilbert, not enough Poincaré. The point does not yet seem to be settled, in that ... | Abstract mathematics | 0.822288 |
7,824 | The study of numbers, called algebra at the beginning undergraduate level, extends to abstract algebra at a more advanced level; and the study of functions, called calculus at the college freshman level becomes mathematical analysis and functional analysis at a more advanced level. Each of these branches of more abstra... | Abstract mathematics | 0.822288 |
7,825 | Category theory is one area of mathematics dedicated to exploring this commonality of structure as it plays out in some areas of math.Generality's impact on intuition is both dependent on the subject and a matter of personal preference or learning style. Often generality is seen as a hindrance to intuition, although it... | Abstract mathematics | 0.822288 |
7,826 | One central concept in pure mathematics is the idea of generality; pure mathematics often exhibits a trend towards increased generality. Uses and advantages of generality include the following: Generalizing theorems or mathematical structures can lead to deeper understanding of the original theorems or structures Gener... | Abstract mathematics | 0.822288 |
7,827 | McDonnell Genome Institute's Outreach Department was established in 2003 in response to the National Human Genome Research Institute's Minority Action Plan. Since its inception, Outreach has conducted activities that serve to educate K-12 students and the community at large regarding genomics and the role the McDonnell... | McDonnell Genome Institute | 0.822285 |
7,828 | McDonnell Genome Institute (The Elizabeth H. and James S. McDonnell III Genome Institute) at Washington University in St. Louis, Missouri, is one of three NIH funded large-scale sequencing centers in the United States. Affiliated with Washington University School of Medicine and the Alvin J. Siteman Cancer Center, the ... | McDonnell Genome Institute | 0.822285 |
7,829 | A closely related formulation of classical mechanics is Hamiltonian mechanics. The Hamiltonian is defined by H = ∑ i = 1 n q ˙ i ∂ L ∂ q ˙ i − L {\displaystyle H=\sum _{i=1}^{n}{\dot {q}}_{i}{\frac {\partial L}{\partial {\dot {q}}_{i}}}-L\,} and can be obtained by performing a Legendre transformation on the Lagrangian,... | Lagrange equation | 0.822284 |
7,830 | The velocity of each particle is how fast the particle moves along its path of motion, and is the time derivative of its position, thusIn Newtonian mechanics, the equations of motion are given by Newton's laws. The second law "net force equals mass times acceleration",applies to each particle. For an N particle system ... | Lagrange equation | 0.822284 |
7,831 | Some of the better-known named charts are: Some specific charts have become well known by effectively explaining a phenomenon or idea. An Allele chart is a chart originating from the study of genetics to show the interaction of two data points in a grid. A Gantt chart helps in scheduling complex projects. The Nolan cha... | Graphical methods | 0.822279 |
7,832 | {\displaystyle A\mathrel {{\underline {\delta }}_{\Phi }} B\Leftrightarrow A\mathrel {\mathop {\ll } _{\Phi }} E1,B\mathrel {\mathop {\ll } _{\Phi }} E2,\ {\mbox{for some}}\ E1,E2\subset X\ {\mbox{(See Fig. 6).}}} Theorem 6 Any two sets descriptively far from each other belong to disjoint descriptive δ Φ {\displaystyle... | Near sets | 0.822278 |
7,833 | Consequently, Φ ( x ) ∈ Q ( cl Φ ( A ) ) {\displaystyle \Phi (x)\in {\mathcal {Q}}({\mbox{cl}}_{\Phi }(A))} . Hence, cl ( A ) ⊆ cl Φ ( A ) {\displaystyle {\mbox{cl}}(A)\subseteq {\mbox{cl}}_{\Phi }(A)} In a proximal relator space, EF-proximity δ {\displaystyle \delta } leads to the following results for descriptive pro... | Near sets | 0.822278 |
7,834 | That is, x ∈ X {\displaystyle x\in X} is in the descriptive closure of A {\displaystyle A} , provided the closure of Φ ( x ) {\displaystyle \Phi (x)} and the closure of Q ( cl ( A ) ) {\displaystyle {\mathcal {Q}}({\mbox{cl}}(A))} have at least one element in common. Theorem 2 The descriptive closure of any set A {\dis... | Near sets | 0.822278 |
7,835 | He introduced the concept of nearness of pairs of sets at the ICM in Rome in 1908. This concept is useful in simplifying teaching calculus and advanced calculus. For example, the passage from an intuitive definition of continuity of a function at a point to its rigorous epsilon-delta definition is sometime difficult fo... | Near sets | 0.822278 |
7,836 | Relations with the same formal properties as similarity relations of sensations considered by Poincaré are nowadays, after Zeeman, called tolerance relations. A tolerance τ {\displaystyle \tau } on a set O {\displaystyle O} is a relation τ ⊆ O × O {\displaystyle \tau \subseteq O\times O} that is reflexive and symmetric... | Near sets | 0.822278 |
7,837 | In this context, a space is a set with some added structure. With a proximity space X {\displaystyle X} , the structure of X {\displaystyle X} is induced by the EF-proximity relation δ {\displaystyle \delta } . In a proximity space X {\displaystyle X} , the closure of A {\displaystyle A} in X {\displaystyle X} coincide... | Near sets | 0.822278 |
7,838 | In 2006, a formal approach to the descriptive nearness of objects was considered by J. Peters, A. Skowron and J. Stepaniuk in the context of proximity spaces. In 2007, descriptively near sets were introduced by J. Peters followed by the introduction of tolerance near sets. Recently, the study of descriptively near sets... | Near sets | 0.822278 |
7,839 | The 1893 and 1895 articles on continua (Pt. 1, ch. II) as well as representative spaces and geometry (Pt. | Near sets | 0.822278 |
7,840 | Fechner's sensation sensitivity experiments and a framework for the study of resemblance in representative spaces as models of what he termed physical continua. The elements of a physical continuum (pc) are sets of sensations. The notion of a pc and various representative spaces (tactile, visual, motor spaces) were int... | Near sets | 0.822278 |
7,841 | From the beginning, descriptively near sets have proved to be useful in applications of topology, and visual pattern recognition , spanning a broad spectrum of applications that include camouflage detection, micropaleontology, handwriting forgery detection, biomedical image analysis, content-based image retrieval, popu... | Near sets | 0.822278 |
7,842 | Near set theory provides a formal basis for the observation, comparison, and classification of elements in sets based on their closeness, either spatially or descriptively. Near sets offer a framework for solving problems based on human perception that arise in areas such as image processing, computer vision as well as... | Near sets | 0.822278 |
7,843 | A common usage of mixed-precision arithmetic is for operating on inaccurate numbers with a small width and expanding them to a larger, more accurate representation. For example, two half-precision or bfloat16 (16-bit) floating-point numbers may be multiplied together to result in a more accurate single-precision (32-bi... | Mixed-precision arithmetic | 0.822276 |
7,844 | A motor is an actuator, converting electrical energy in to rotational mechanical energy. A motor requiring a DC power supply for operation is termed a DC motor. DC motors are widely used in control applications like robotics, tape drives, machines and many more. Separately excited DC motors are suitable for control app... | Armature Controlled DC Motor | 0.822274 |
7,845 | {\displaystyle \dim X=\operatorname {Ind} X=\operatorname {ind} X.} Such spaces are exactly the separable and metrizable X (see Urysohn's metrization theorem). | Inductive dimension | 0.822267 |
7,846 | The Nöbeling–Pontryagin theorem then states that such spaces with finite dimension are characterised up to homeomorphism as the subspaces of the Euclidean spaces, with their usual topology. The Menger–Nöbeling theorem (1932) states that if X {\displaystyle X} is compact metric separable and of dimension n {\displaystyl... | Inductive dimension | 0.822267 |
7,847 | Let dim {\displaystyle \dim } be the Lebesgue covering dimension. For any topological space X, we have dim X = 0 {\displaystyle \dim X=0} if and only if Ind X = 0. {\displaystyle \operatorname {Ind} X=0.} Urysohn's theorem states that when X is a normal space with a countable base, then dim X = Ind X = ind X ... | Inductive dimension | 0.822267 |
7,848 | In the mathematical field of topology, the inductive dimension of a topological space X is either of two values, the small inductive dimension ind(X) or the large inductive dimension Ind(X). These are based on the observation that, in n-dimensional Euclidean space Rn, (n − 1)-dimensional spheres (that is, the boundarie... | Inductive dimension | 0.822267 |
7,849 | In mathematics, a semigroup with two elements is a semigroup for which the cardinality of the underlying set is two. There are exactly five nonisomorphic semigroups having two elements: O2, the null semigroup of order two, LO2, the left zero semigroup of order two, RO2, the right zero semigroup of order two, ({0,1}, ∧)... | Semigroup with two elements | 0.822261 |
7,850 | The order induced is a linear order, and so it is in fact a lattice and it is also a distributive and complemented lattice, i.e. it is actually the two-element Boolean algebra. The two binary operations defined by matrices in a blue background are associative and pairing either with A creates a semigroup isomorphic to ... | Semigroup with two elements | 0.82226 |
7,851 | The Institute of Problems of Chemical Physics (IPCP) (Russian: Институт проблем химической физики РАН) of the Russian Academy of Sciences (RAS) consists of 10 scientific departments and about 100 laboratories each one held by an independent research groups. IPCP was established in 1956 as branch of the Moscow Institute... | Institute of Problems of Chemical Physics | 0.822256 |
7,852 | Solid-state physics is the study of rigid matter, or solids, through methods such as solid-state chemistry, quantum mechanics, crystallography, electromagnetism, and metallurgy. It is the largest branch of condensed matter physics. Solid-state physics studies how the large-scale properties of solid materials result fro... | Crystal physics | 0.822253 |
7,853 | In the ostensibly covariant (relativistically invariant) Dirac equation, and in natural units, this becomes: ( − i γ μ ∂ μ + m ) ψ = 0 {\displaystyle (-i\gamma ^{\mu }\partial _{\mu }+m)\psi =0} where the "mass" parameter m is now simply a constant associated with the quantum described by the wave function ψ. In the St... | Units of mass | 0.822252 |
7,854 | This difference in elapsed time is a form of curvature called gravitational time dilation. Other forms of curvature have been measured using the Gravity Probe B satellite. Quantum mass manifests itself as a difference between an object's quantum frequency and its wave number. The quantum mass of a particle is proportio... | Units of mass | 0.822252 |
7,855 | Chevalley (1955) showed that the points of the (split) algebraic group E8 (see above) over a finite field with q elements form a finite Chevalley group, generally written E8(q), which is simple for any q, and constitutes one of the infinite families addressed by the classification of finite simple groups. Its number of... | E8 (mathematics) | 0.822251 |
7,856 | The Lie algebra E8 contains as subalgebras all the exceptional Lie algebras as well as many other important Lie algebras in mathematics and physics. The height of the Lie algebra on the diagram approximately corresponds to the rank of the algebra. A line from an algebra down to a lower algebra indicates that the lower ... | E8 (mathematics) | 0.822251 |
7,857 | In 1982, Michael Freedman used the E8 lattice to construct an example of a topological 4-manifold, the E8 manifold, which has no smooth structure. Antony Garrett Lisi's incomplete "An Exceptionally Simple Theory of Everything" attempts to describe all known fundamental interactions in physics as part of the E8 Lie alge... | E8 (mathematics) | 0.822251 |
7,858 | Wilhelm Killing (1888a, 1888b, 1889, 1890) discovered the complex Lie algebra E8 during his classification of simple compact Lie algebras, though he did not prove its existence, which was first shown by Élie Cartan. Cartan determined that a complex simple Lie algebra of type E8 admits three real forms. Each of them giv... | E8 (mathematics) | 0.822251 |
7,859 | Since the adjoint representation can be described by the roots together with the generators in the Cartan subalgebra, we may see that decomposition by looking at these. In this description, (3,1) consists of the roots (0,0,0,0,0,0,1,−1), (0,0,0,0,0,0,−1,1) and the Cartan generator corresponding to the last dimension; (... | E8 (mathematics) | 0.822251 |
7,860 | The smaller exceptional groups E7 and E6 sit inside E8. In the compact group, both E7×SU(2)/(−1,−1) and E6×SU(3)/(Z/3Z) are maximal subgroups of E8. The 248-dimensional adjoint representation of E8 may be considered in terms of its restricted representation to the first of these subgroups. It transforms under E7×SU(2) ... | E8 (mathematics) | 0.822251 |
7,861 | The Weyl group of E8, which is the group of symmetries of the maximal torus which are induced by conjugations in the whole group, has order 214 35 52 7 = 696729600. The compact group E8 is unique among simple compact Lie groups in that its non-trivial representation of smallest dimension is the adjoint representation (... | E8 (mathematics) | 0.822251 |
7,862 | The E8 Lie group has applications in theoretical physics and especially in string theory and supergravity. E8×E8 is the gauge group of one of the two types of heterotic string and is one of two anomaly-free gauge groups that can be coupled to the N = 1 supergravity in ten dimensions. E8 is the U-duality group of superg... | E8 (mathematics) | 0.822251 |
7,863 | The Electronic Journal of Probability is a peer-reviewed open access scientific journal published by the Institute of Mathematical Statistics and the Bernoulli Society. It covers all aspects of probability theory and the current editor-in-chief is Bénédicte Haas (Université Sorbonne Paris Nord). Electronic Communicatio... | Electronic Journal of Probability | 0.822234 |
7,864 | In mathematics, a collapsing algebra is a type of Boolean algebra sometimes used in forcing to reduce ("collapse") the size of cardinals. The posets used to generate collapsing algebras were introduced by Azriel Lévy in 1963.The collapsing algebra of λω is a complete Boolean algebra with at least λ elements but generat... | Collapsing algebra | 0.822231 |
7,865 | In number theory, the unit function is a completely multiplicative function on the positive integers defined as: ε ( n ) = { 1 , if n = 1 0 , if n ≠ 1 {\displaystyle \varepsilon (n)={\begin{cases}1,&{\mbox{if }}n=1\\0,&{\mbox{if }}n\neq 1\end{cases}}} It is called the unit function because it is the identity element fo... | Unit function | 0.822221 |
7,866 | Hard disk recorders typically allow some limited editing capabilities, allowing highlight reels to be edited together in the middle of a game. Several character generators allowing scores and statistics to be shown on screen. | Electronic field production | 0.822211 |
7,867 | Minimal caps Macbeath regions Approximations (approximations of convex bodies see properties of definition 1) Economic cap covering theorem (see relation from properties of definition 1 to floating bodies) == References == | Random polytope | 0.82221 |
7,868 | The Oncologic Drugs Advisory Committee (ODAC) receives requests for technical and clinical evaluation of new drugs by the U.S. Food and Drug Administration (FDA). The committee, consisting of members from academic and clinical oncology biostatistics, the general public, and the pharmaceutical industry, makes non-bindin... | Oncology Drug Advisory Committee | 0.822208 |
7,869 | The number of sequenced genomes is continuously growing "simply scaling up established bioinformatics pipelines will not be sufficient for leveraging the full potential of such rich genomic data sets". Pangenome graphs are emerging data structures designed to represent pangenomes and to efficiently map reads to them. T... | Pangenomics | 0.822204 |
7,870 | In the fields of molecular biology and genetics, a pan-genome (pangenome or supragenome) is the entire set of genes from all strains within a clade. More generally, it is the union of all the genomes of a clade. The pan-genome can be broken down into a "core pangenome" that contains genes present in all individuals, a ... | Pangenomics | 0.822204 |
7,871 | : Appendix D The European Commission published in 2021 a request for regulation and standardization of electric road systems. Shortly afterward, a working group of the French Ministry of Ecology recommended adopting a European electric road standard formulated with Sweden, Germany, Italy, the Netherlands, Spain, Poland... | Electric transportation technology | 0.822185 |
7,872 | Ammonia added to water functions as Arrhenius base: it increases the concentration of the anion hydroxide. Conversely, using a solvent system definition of acidity and basicity, water added to liquid ammonia functions as an acid, because it increases the concentration of the cation ammonium. The carbonyl group (C=O), w... | Alternative biochemistries | 0.822182 |
7,873 | Special sciences are those sciences other than fundamental physics. In this view, chemistry, biology, and neuroscience—indeed, all sciences except fundamental physics—are special sciences. The status of the special sciences, and their relation to physics, is unresolved in the philosophy of science. Jerry Fodor, for ins... | Special sciences | 0.822182 |
7,874 | The drawbacks of persistent programming languages include: While they are powerful, it is easy to make programming errors that damage the database. It is harder to do automatic high-level optimization. They do not support declarative querying well. | Persistent programming language | 0.822176 |
7,875 | In physics-related problems, Monte Carlo methods are useful for simulating systems with many coupled degrees of freedom, such as fluids, disordered materials, strongly coupled solids, and cellular structures (see cellular Potts model, interacting particle systems, McKean–Vlasov processes, kinetic models of gases). Othe... | Monte-Carlo methods | 0.822162 |
7,876 | Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be deterministic in principle. They are often used in physical and mathematical probl... | Monte-Carlo methods | 0.822162 |
7,877 | The central idea is to design a judicious Markov chain model with a prescribed stationary probability distribution. That is, in the limit, the samples being generated by the MCMC method will be samples from the desired (target) distribution. By the ergodic theorem, the stationary distribution is approximated by the emp... | Monte-Carlo methods | 0.822161 |
7,878 | In experimental particle physics, Monte Carlo methods are used for designing detectors, understanding their behavior and comparing experimental data to theory. In astrophysics, they are used in such diverse manners as to model both galaxy evolution and microwave radiation transmission through a rough planetary surface.... | Monte-Carlo methods | 0.822161 |
7,879 | Monte Carlo methods are very important in computational physics, physical chemistry, and related applied fields, and have diverse applications from complicated quantum chromodynamics calculations to designing heat shields and aerodynamic forms as well as in modeling radiation transport for radiation dosimetry calculati... | Monte-Carlo methods | 0.822161 |
7,880 | For example, if binary tree sort is implemented with a self-balancing BST, we have a very simple-to-describe yet asymptotically optimal O ( n log n ) {\displaystyle O(n\log n)} sorting algorithm. Similarly, many algorithms in computational geometry exploit variations on self-balancing BSTs to solve problems such as t... | Balanced binary search tree | 0.822159 |
7,881 | If a scholar has several versions of a manuscript but no known original, then established methods of textual criticism can be used to seek to reconstruct the original text as closely as possible. The same methods can be used to reconstruct intermediate versions, or recensions, of a document's transcription history, dep... | Stemmatics | 0.822158 |
7,882 | In the subject area of control theory, an internal model is a process that simulates the response of the system in order to estimate the outcome of a system disturbance. The internal model principle was first articulated in 1976 by B. A. Francis and W. M. Wonham as an explicit formulation of the Conant and Ashby good r... | Internal model (motor control) | 0.822154 |
7,883 | The Trans-Proteomic Pipeline (TPP) is an open-source data analysis software for proteomics developed at the Institute for Systems Biology (ISB) by the Ruedi Aebersold group under the Seattle Proteome Center. The TPP includes PeptideProphet, ProteinProphet, ASAPRatio, XPRESS and Libra. | Trans-Proteomic Pipeline | 0.822144 |
7,884 | By adding several dipole sections on the same plane, the bending radial effect of the beam increases. In accelerator physics, dipole magnets are used to realize bends in the design trajectory (or 'orbit') of the particles, as in circular accelerators. Other uses include: Injection of particles into the accelerator Ejec... | Bending magnets | 0.822142 |
7,885 | "On Physical Lines of Force" is a four-part paper written by James Clerk Maxwell, published in 1861. In it, Maxwell derived the equations of electromagnetism in conjunction with a "sea" of "molecular vortices" which he used to model Faraday's lines of force. Maxwell had studied and commented on the field of electricity... | On physical lines of force | 0.822141 |
7,886 | The transport of Ca2+ through the cytoplasm to the coccolith vesicle (CV) is the dominant cost associated with calcification. (B) represents metabolic processes include the synthesis of coccolith-associated polysaccharides (CAPs – gray rectangles) by the Golgi complex (white rectangles) that regulate the nucleation and... | Protist shell | 0.822137 |
7,887 | Coccolithophores and foraminifera also have hard protective shells, but the shells are made of calcium carbonate. These shells can help with buoyancy, allowing the organisms to float in the water column and move around more easily. In addition to protection and support, protist shells also serve scientists as a means o... | Protist shell | 0.822137 |
7,888 | First-order resolution Automated theorem proving ACL2 theorem prover E equational theorem prover Gandalf theorem prover HOL theorem prover Isabelle theorem prover LCF theorem prover Otter theorem prover Paradox theorem prover Vampire theorem prover Interactive proof system Mizar system QED project Coq | List of mathematical logic topics | 0.822128 |
7,889 | Entscheidungsproblem Decision problem Decidability (logic) Church-Turing thesis Computable function Algorithm Recursion Primitive recursive function Mu operator Ackermann function Turing machine Halting problem Computability theory, computation Herbrand Universe Markov algorithm Lambda calculus Church-Rosser theorem Ca... | List of mathematical logic topics | 0.822128 |
7,890 | Algebra of sets Axiom of choice Axiom of countable choice Axiom of dependent choice Zorn's lemma Boolean algebra (structure) Boolean-valued model Burali-Forti paradox Cantor's back-and-forth method Cantor's diagonal argument Cantor's first uncountability proof Cantor's theorem Cantor–Bernstein–Schroeder theorem Cardina... | List of mathematical logic topics | 0.822128 |
7,891 | Nonconstructive proof Existence theorem Intuitionistic logic Intuitionistic type theory Type theory Lambda calculus Church–Rosser theorem Simply typed lambda calculus Typed lambda calculus Curry–Howard isomorphism Calculus of constructions Constructivist analysis Lambda cube System F Introduction to topos theory LF (lo... | List of mathematical logic topics | 0.822128 |
7,892 | Metamathematics Cut-elimination Tarski's undefinability theorem Diagonal lemma Provability logic Interpretability logic Sequent Sequent calculus Analytic proof Structural proof theory Self-verifying theories Substructural logics Structural rule Weakening Contraction Linear logic Intuitionistic linear logic Proof net Af... | List of mathematical logic topics | 0.822128 |
7,893 | Finite model theory Descriptive complexity theory Model checking Trakhtenbrot's theorem Computable model theory Tarski's exponential function problem Undecidable problem Institutional model theory Institution (computer science) Non-standard analysis Non-standard calculus Hyperinteger Hyperreal number Transfer principle... | List of mathematical logic topics | 0.822128 |
7,894 | Peano axioms Giuseppe Peano Mathematical induction Structural induction Recursive definition Naive set theory Element (mathematics) Ur-element Singleton (mathematics) Simple theorems in the algebra of sets Algebra of sets Power set Empty set Non-empty set Empty function Universe (mathematics) Axiomatization Axiomatic s... | List of mathematical logic topics | 0.822128 |
7,895 | Kripke semantics Sahlqvist formula Interior algebra | List of mathematical logic topics | 0.822128 |
7,896 | In 2004/5, Plus attracted over 1.3 million website visits (more than 31 million hits). The website won the Webby award in 2001 for the best Science site on the Internet. The Motivate video-conferencing project links university mathematicians and scientists to primary and secondary schools in areas of the UK from Jersey... | Millennium Mathematics Project | 0.822122 |
7,897 | Roark's Formulas for Stress and Strain is a mechanical engineering design book written by Richard G. Budynas and Ali M. Sadegh. It was first published in 1938 and the most current ninth edition was published in March 2020. | Roark's Formulas for Stress and Strain | 0.82212 |
7,898 | Warren C. Young is professor emeritus in the department of mechanical engineering at the University of Wisconsin, Madison, where he was on the faculty for over 40 years. Dr. Young has also taught as a visiting professor at Bengal Engineering College in Calcutta, India, and served as chief of the Energy Manpower and Tra... | Roark's Formulas for Stress and Strain | 0.82212 |
7,899 | Richard G. Budynas is professor of mechanical engineering at Rochester Institute of Technology. He is author of a newly revised McGraw-Hill textbook, Applied Strength and Applied Stress Analysis, 2nd Edition. Ali M. Sadegh is a professor and the Founder and Director of the Center for Advanced Engineering Design at The ... | Roark's Formulas for Stress and Strain | 0.82212 |
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