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...the study of many classes of partial and functional differential equations and has solved problems that had been left open by the previous classical metho
8 KB (1,236 words) - 17:03, 1 July 2020
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...s it is typical to assume that the solution of the original problem exists and has sufficiently many derivatives. Because of the absence of other assumpti
17 KB (2,540 words) - 19:55, 12 January 2024
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...f the original problem, but such a discretization is nevertheless implicit and is realized relative to a known model.
19 KB (2,657 words) - 14:54, 7 June 2020
...ue of its derivative, at a given point of the extremal. In the case of the functional
and let $ X ^{*} $
7 KB (975 words) - 22:37, 28 January 2020
...old_files/data/B017/B.0107380 Boundary value problem, partial differential equations
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11 KB (1,579 words) - 06:29, 30 May 2020
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...ly related to those of a [[Generalized derivative|generalized derivative]] and a [[Generalized function|generalized function]]. The concept of a generaliz
7 KB (1,006 words) - 19:41, 5 June 2020
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...terpolation|interpolation]] of functions. The interpolation of functionals and operators is also widely used in constructing numerical methods.
26 KB (3,882 words) - 22:13, 5 June 2020
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...tions. The best known of these are the [[Löwner equation|Löwner equation]] and the Löwner–Kufarev equation. In the discrete case — for lattice domain
8 KB (1,168 words) - 20:13, 12 January 2024
...rder in function spaces makes it possible to study within the framework of
functional analysis problems that are essentially connected with inequalities between
...opediaofmath.org/legacyimages/s/s084/s084260/s08426022.png" /> is a wedge,
and every wedge with vertex at the origin generates a quasi-order in <img align
43 KB (5,981 words) - 17:13, 2 May 2020
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a minimum of a functional, eigen values and eigen vectors of an equation $ A u = \lambda u $,
8 KB (1,124 words) - 11:46, 17 June 2020
$#C+1 = 202 : ~/encyclopedia/old_files/data/T093/T.0903900 Transport equations, numerical methods
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17 KB (2,415 words) - 09:04, 13 January 2024
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...mation is functionally parametrized by a pair of solutions of the equation and the transform vanishes if the solutions coincide.
14 KB (2,023 words) - 17:02, 1 July 2020
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...ad influences on many parts of mathematics and different areas of sciences and technology ([[#References|[a4]]], [[#References|[a7]]], [[#References|[a8]]
7 KB (1,001 words) - 16:57, 1 July 2020
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Iteration methods for the solution of non-linear equations.
20 KB (2,830 words) - 19:25, 9 January 2024
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...ight makes it possible to enlarge or restrict ordinary non-weighted normed and semi-normed function spaces consisting of functions with infinite ordinary
9 KB (1,435 words) - 08:13, 13 January 2024
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...tic aspects), depending on input functions or parameters, called controls, and usually subject to constraints. The sought controls, as well as the realiza
21 KB (3,161 words) - 08:04, 6 June 2020
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A system of ordinary differential equations in the numerical solution of which by explicit methods of Runge–Kutta or
30 KB (4,292 words) - 05:40, 24 February 2022
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...statistical models for vertical-heterogeneous random fields of turbulence and [[Internal waves|internal waves]] (cf. also [[Turbulence, mathematical prob
13 KB (1,880 words) - 08:03, 6 June 2020
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...respective boundary value problem. In direct methods, the extremum of the functional is found directly. The optimization methods thus employed are a development
23 KB (3,462 words) - 08:27, 6 June 2020
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defined and acting on a closed subset $ G $
15 KB (2,235 words) - 08:13, 6 June 2020
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...ing them, to an examination of simpler algebraic problems. The development and systematic use of operational calculus began with the work of O. Heaviside
12 KB (1,635 words) - 14:54, 7 June 2020
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is considered to be fixed for the given quadrature formula and is called the weight function; the function $ f ( x) $
11 KB (1,719 words) - 01:56, 4 January 2022
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...atics that are applied to find the extrema (maxima or minima) of functions and functionals.
22 KB (3,158 words) - 19:38, 5 June 2020
...everal classes of functions that arise in the solution of both theoretical and applied problems in various branches of mathematics.
...ons of mathematical physics, which arise when solving partial differential equations by the
7 KB (905 words) - 12:54, 1 May 2023
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...ymplectic manifolds, Hamiltonian vector fields, symplectic diffeomorphisms and Lagrangean submanifolds.
15 KB (2,211 words) - 07:18, 15 February 2024
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A branch of modern computational mathematics, devoted to the design and investigation of methods which allow one to find an approximate solution, w
20 KB (2,838 words) - 19:21, 13 January 2024
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and of the strain tensor $ \epsilon _ {ij} ( x, t) $,
28 KB (4,176 words) - 05:30, 19 March 2022
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...nti-holomorphic involution, cf. also [[Riemann surface|Riemann surface]]), and with the theory of multi-dimensional systems. The theory of operator vessel
24 KB (3,136 words) - 20:00, 24 November 2023
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and the law of motion of the dividing boundary $ \xi = \xi ( t) $(
12 KB (1,620 words) - 08:23, 6 June 2020
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and $ A _ {1} ( t) $,
32 KB (4,803 words) - 17:49, 6 January 2024
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...he relation between algebraic-topological properties of topological spaces and extremal properties of functions (functionals) on them. Morse theory is a b
21 KB (3,095 words) - 08:01, 6 June 2020
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...o that differing ages imply different reproduction and survival capacities and, also, different behaviours.
11 KB (1,634 words) - 13:07, 10 February 2024
...ce of the operations, a restricted number of digit places to form a number and a restricted storage capacity.
...e sequence of operations of the computer is independent of the input data, and is called non-linear otherwise.
10 KB (1,642 words) - 08:41, 29 August 2014
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...for solving a problem, the researcher concentrates on certain properties, and his choice of the algorithm depends on these, while the algorithm will also
12 KB (1,798 words) - 20:07, 12 January 2024
...the base of the cone and the part of the conical surface between the base and the vertex is called the lateral surface of the cone.
...rac{1}{3}\pi (R^2 + r^2 + Rr) h$, where $R$, $r$ are the radii of the base and $h$ is the height (the distance between the base); the area of the lateral
13 KB (2,188 words) - 13:05, 10 June 2016
...primary quantities and the corresponding experimental units of measurement and, associated with the choice of the primary units of measurement, the format
...he mass unit $M$; on the basis of the definition of force in terms of mass and acceleration, the dimension formula for the force $K$ has the form
16 KB (2,568 words) - 20:00, 4 January 2024
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...alls takes place in several channels simultaneously. The basic definitions and notations are as in [[Queue|Queue]].
18 KB (2,750 words) - 19:29, 16 January 2024
...ometry in the large]], and find wide and profound application in mechanics and physics [[#References|[4]]].
55 KB (7,564 words) - 16:56, 7 February 2011
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A branch of mathematics studying the theory and the methods of solution of multi-step problems of optimal control.
10 KB (1,500 words) - 16:50, 20 January 2024
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and a given "terminal" criterion
32 KB (4,621 words) - 08:04, 6 June 2020
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...onnection with work on the construction of atomic reactors, J. von Neumann and S. Ulam suggested using the apparatus of probability theory in the computer
24 KB (3,433 words) - 13:09, 13 January 2024
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and $ \mathfrak M _ {1} $,
38 KB (5,491 words) - 22:11, 5 June 2020
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...e manufacturing work-cell and expressing the relationship between discrete and continuous events by means of a unified auxiliary variable, as proposed in
12 KB (1,887 words) - 16:55, 1 July 2020
...t of convergence arises, for example, in the study of mathematical objects and their approximation by simpler objects. Thus, in order to calculate the are
...r ordinary and partial differential equations there are various convergent difference methods for their numerical solution, which are suitable for use in modern
22 KB (3,726 words) - 10:31, 2 September 2017
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...in applications of probability theory in various areas of natural science and technology, since these processes accurately describe many real phenomena a
24 KB (3,614 words) - 08:52, 21 January 2024
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...the influence of the ideas of Hilbert). One of the most generally followed and definitive approaches to the development of constructive mathematics on thi
20 KB (2,913 words) - 07:40, 14 August 2023
...timate the unknown values of these parameters from results of observations
and to test hypotheses concerning their values.
...://www.encyclopediaofmath.org/legacyimages/n/n067/n067230/n0672306.png" />
and <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/l
37 KB (5,331 words) - 17:14, 7 February 2011
...dy of certain algebraic objects, as is done in analytic geometry (with the difference that the transition from geometry to algebra in homology theory is irrevers
...e algebras, the theory of finite-dimensional algebras, the theory of rings and the theory of quadratic forms.
12 KB (1,885 words) - 23:48, 23 April 2017
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and let $ C _ {0} ^ \infty ( \Omega ) $
29 KB (4,077 words) - 04:02, 4 January 2022
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if and only if $ x = 0 $;
31 KB (4,586 words) - 18:43, 13 January 2024
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...as the geometry of the spectrum and its main parts, spectral multiplicity and the asymptotics of eigenvalues.
16 KB (2,424 words) - 08:22, 6 June 2020
...degrees of freedom. Quantum field theory unifies the description of fields and particles, which, in classical physics, appear as two distinct entities.
...d, as this is the only field having a clear content, both in the classical and the quantum case.
35 KB (5,270 words) - 23:26, 6 December 2016
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...ces|[2]]]; engineers had discovered the idea of a feedback law (see below) and found means for its realization.
43 KB (6,618 words) - 07:32, 26 March 2023
...diameter is greater than three and ten seventy-firsts and less than three and one seventh" is written as
...as intimately bound up with the general evolution of mathematical concepts and methods.
18 KB (2,697 words) - 13:11, 13 December 2013
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...ial differential equations, the calculus of variations, harmonic analysis, and fractals.
21 KB (3,319 words) - 17:46, 1 July 2020
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...pplications. Of particular significance is the connection with the science and practice of economics.
37 KB (5,562 words) - 11:11, 7 January 2024
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...' responses to the organization and its offerings by providing information and by supplying reasons for preferring a particular organization's offer.
28 KB (4,346 words) - 17:47, 1 July 2020
''a history of the mathematics preceding and relevant to Hilbert’s statement of his 2nd problem, initiating his progra
...had developed deductively a large part of analysis using the real numbers and their properties as a starting point.
189 KB (29,059 words) - 14:31, 19 March 2023