A statement about the [[distribution of prime numbers]] in an [[arithmetic progression]]. It is known that in t
...'Surveys in number theory: Papers from the millennial conference on number theory''. (Natick, MA: A K Peters, 2002) pp. 75–108. {{ISBN|1-56881-162-4}}. {{Z
1 KB (250 words) - 19:33, 6 December 2023
...om number of new particles at the end of their life time. If $G(t)$ is the distribution function of the life times of the individual particles, if $h(s)$ is the ge
|valign="top"|{{Ref|BH}}|| R. Bellman, T.E. Harris, "On the theory of age-dependent stochastic branching processes" ''Proc. Nat. Acad. Sci. U
1 KB (204 words) - 19:33, 28 October 2014
...istribution of prime numbers in arithmetic progressions (cf. also [[Number theory]]; [[Prime number]]; [[Dirichlet theorem]]). Let $\pi(x;q,a)$ denote the nu
where $\mathrm{li}$ is the [[logarithmic integral]] (cf. also [[Distribution of prime numbers]]) and $\phi$ is the Euler totient function (cf. [[Totient
4 KB (622 words) - 16:31, 23 December 2014
to an arithmetic progression and are a powerful tool in analytic number theory [[#References|[2]]]–[[#References|[4]]].
The distribution of the non-trivial zeros, and of the values of $ L ( s , \chi ) $
15 KB (2,181 words) - 11:50, 26 March 2023
A [[Markov process|Markov process]] with finite or countable state space. The theory of Markov chains was created by [[Markov, Andrei Andreevich|A.A. Markov]] w
and the initial distribution $ {\mathsf P} \{ \xi ( 0) = i \} $
12 KB (1,726 words) - 08:04, 14 January 2024
be mutually independent random variables with a normal distribution, and let $ {\mathsf E} X _ {1i} = \mu _ {1} $,
have a standard normal distribution, while $ S _ {1} ^ {2} / \sigma _ {1} ^ {2} $
7 KB (881 words) - 10:27, 16 July 2021
$#C+1 = 79 : ~/encyclopedia/old_files/data/R081/R.0801180 Reliability theory
...ost, etc.) are random. Other widely used methods are those of optimization theory, mathematical logic, etc.
16 KB (2,542 words) - 08:10, 6 June 2020
...n of ideas and methods from the theory of random processes, especially the theory of point processes.
...form a more general concept; here, stochastic geometry is linked with the theory of random sets (see [[#References|[1]]]).
7 KB (1,051 words) - 09:27, 22 August 2014
...s a starting point for further mathematical research. Nowadays (2000), the theory of pricing of so-called derivative contracts and related subjects has grown
...sset at time $t$; $N ( . )$ is the cumulative [[Normal distribution|normal distribution]] function; $r$ is the interest rate; and $\sigma$ is a parameter known as
8 KB (1,291 words) - 18:53, 7 February 2024
conditional probability distribution which assigns a probability to
to sample from a distribution on the state space, which is the
16 KB (2,671 words) - 20:19, 12 March 2016
This function occurs in number theory as the limit
...imilar results have been exploited in the study of irregularities in the [[distribution of prime numbers]]; see [[#References|[a2]]], [[#References|[a3]]].
2 KB (243 words) - 15:57, 22 September 2017
tend to a proper limit distribution $ F $
...probability theory and its applications"|"An introduction to probability theory and its applications"]], '''2''', Wiley (1971) pp. Sect. IX.9</TD></TR></t
2 KB (273 words) - 16:15, 13 January 2021
and the distribution of the sequence $ \{ \tau _ {j} ^ {e} , \nu _ {j} ^ {e} \} \in G _ {S}
is related to the distribution of $ e ( t) $
8 KB (1,152 words) - 19:56, 18 January 2024
[[Category:Distribution theory]]
is, by definition, that of its probability distribution
8 KB (1,162 words) - 19:58, 19 January 2024
relative to the distribution $ d \sigma ( t) $.
...le><TR><TD valign="top">[1]</TD> <TD valign="top"> V.L. Goncharov, "The theory of interpolation and approximation of functions" , Moscow (1954) (In Russ
2 KB (334 words) - 20:15, 10 January 2024
...ite number of integro-differential evolution equations for the sequence of distribution (correlation) functions describing all possible states of a many-particle s
...imes \mathbf{R} ^ { \nu }$, $\nu \geq 1$ (cf. also [[Distribution function|Distribution function]]). The BBGKY hierarchy for classical systems reads as follows:
10 KB (1,427 words) - 07:38, 7 February 2024
with distribution function
of the probability distribution of $ \mu (t) $
4 KB (535 words) - 06:29, 30 May 2020
A tensor defining the distribution of internal stresses in a body under strain. The stress tensor is a symmetr
...p">[1]</TD> <TD valign="top"> L.D. Landau, E.M. Lifshitz, "Elasticity theory" , Pergamon (1959) (Translated from Russian)</TD></TR></table>
2 KB (313 words) - 19:53, 22 January 2016
The periodic distribution functions
arises; the game then continues, at random, in accordance with the distribution $ F ( \cdot \mid x _ {1} , s ^ {( x _ {1} ) } \dots x _ {k-1} , s ^ {( x
4 KB (716 words) - 19:39, 16 January 2024
...of radiation transfer. The solution of the kinetic equation determines the distribution function of the dynamical states of a single particle, which usually depend
...orm. A method has been developed for obtaining the kinetic equation of gas theory taking into account the correlation between the dynamical states of the mol
6 KB (882 words) - 13:51, 20 April 2014