...lead to abstract generalizations and analogues of ordinary analytic number theory, which may then be applied in a unified way to further enumeration question
iii) the total number of elements $a$ with $|a| < x$ is finite, for each $x > 0$.
24 KB (3,738 words) - 07:41, 7 February 2024
A branch of the theory of control systems that studies control systems subject to noise.
...er by an error-probability distribution or by restrictions on the possible number of elementary failures.
23 KB (3,205 words) - 08:10, 6 June 2020
...cations of the current version of $\hat { f }$ and update it to reduce the number of misclassifications.
...e attribute-value pairs, first-order predicate logic, neural networks, and probabilistic functions.
21 KB (3,152 words) - 17:43, 1 July 2020
...ses of the classification of the states of a Markov chain with a countable number of states (see [[Markov chain|Markov chain]]). Two states $ x $
...r for Feller processes in comparison to classical [[Ergodic theory|ergodic theory]]. The "most-regular" behaviour is found with irreducible (topologically-in
11 KB (1,576 words) - 19:38, 5 June 2020
...ion inequalities. They are often stated deterministically but usually have probabilistic interpretations. For example, suppose $ S $
...odd number, this can only increase our confidence that it contains an even number.
18 KB (2,717 words) - 20:14, 8 December 2023
...mathematical abstractions which, in contrast to the concepts of a natural number, a fraction or a geometric figure, have no fairly sound support in prescien
...f fundamental and independent object of study as the notion of quantity or number had played earlier. The study of variable quantities and functional depende
22 KB (3,256 words) - 21:54, 30 March 2012
....org/legacyimages/b/b110/b110100/b11010096.png" /> has been established by probabilistic arguments. Gluskin [[#References|[a21]]] describes his idea as follows: Con
...ehaviour" and solving several other major open problems in the asymptotic theory of finite-dimensional normed spaces. An example of this is Szarek's finite-
88 KB (12,202 words) - 17:19, 23 October 2017
also dedicated his book on the mathematical theory of the pendulum clock,
lumière'' published in 1690 and containing his theory of
16 KB (2,633 words) - 12:03, 1 November 2023
...f. [[Optimal control, mathematical theory of|Optimal control, mathematical theory of]]), consisting of a synthesis of an optimal control (a feedback synthesi
...he delay in the system (see [[#References|[4]]], [[#References|[5]]]). The theory of linear, quadratic problems of optimal control is also well-developed for
32 KB (4,621 words) - 08:04, 6 June 2020
...s, J. von Neumann and S. Ulam suggested using the apparatus of probability theory in the computer solution of applied problems. The Monte-Carlo method is nam
...achieved by a transformation of one or more independent values of a random number $ \alpha $,
24 KB (3,433 words) - 13:09, 13 January 2024
completed with a dissertation on probability theory as a basis for theoretical
his ''Ocherki po Teorii Statistiki (Topics in the Theory of Statistics)'' for
12 KB (1,787 words) - 07:49, 18 August 2023
dark ages of the theory of probability.
attempt using statistics on the relative number births of males and
10 KB (1,512 words) - 07:24, 25 March 2023
''of a finite number of variables''
...descent method]] the direction of descent may be determined randomly. The probabilistic characteristics of the stochastic parameters, in turn, may be changed from
13 KB (1,911 words) - 08:00, 6 June 2020
theory of the vibrating string, and with [[DAlembert|D'Alembert]]
$w(t)$ of individuals at time $t$ after birth, with the number of susceptibles
10 KB (1,551 words) - 07:42, 9 March 2024
The mathematical theory of stochastic processes regards the instantaneous state of the system in qu
...ore the study of one-dimensional processes occupies a central place in the theory of stochastic processes. The parameter $ t $
22 KB (3,177 words) - 20:25, 16 January 2024
De Finetti's theorem has been generalized in a number of ways, in particular:
...rsions of De Finetti's theorem have both been proved directly by a quantum probabilistic approach (a further confirmation of the fruitfulness of this approach for m
13 KB (1,888 words) - 11:23, 26 March 2023
...icit-function theorem in non-linear functional analysis and on the general theory of linear problems of corresponding type.
...ed) problems for non-linear parabolic, or hyperbolic, equations this local theory makes it possible to establish the solvability of the problem on a sufficie
30 KB (4,331 words) - 16:42, 20 January 2022
Jakob also cultivated the theory of series which were published in five
mathematical theory centered around the concept of probability the classical
16 KB (2,550 words) - 08:45, 25 March 2023
th [[Betti number|Betti number]] for Čech homology with $ \mathbf Z _ {2} $
Important is the following probabilistic definition:
24 KB (3,546 words) - 19:41, 1 May 2023
of one of the few treatises of probability theory in the 19th century. He
probability theory and political arithmetic.
11 KB (1,779 words) - 16:32, 4 March 2024