...\gamma$ is the [[Euler constant]], $\gamma \approx 0.577$. Obtained by P. Dirichlet in 1849; he noted that this sum is equal to the number of points $(x,y)$ wi
951 bytes (154 words) - 08:27, 30 December 2015
$#C+1 = 120 : ~/encyclopedia/old_files/data/D032/D.0302810 Dirichlet character
In other words, a Dirichlet character $ \mathop{\rm mod} k $
10 KB (1,462 words) - 11:49, 26 March 2023
''Voronoi tesselation, Dirichlet–Voronoi tesselation, Dirichlet–Voronoi decomposition, Thiessen tesselation''
...is also called the Dirichlet–Voronoi tiling. The straight-line dual of the Dirichlet tesselation is the [[Delaunay triangulation|Delaunay triangulation]].
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...a Dirichlet algebra if $A + \overline{A}$ is uniformly dense in $C ( X )$. Dirichlet algebras were introduced by A.M. Gleason [[#References|[a4]]].
...ine{\mathbf D }$. The algebra $A ( \mathbf{D} )$ is a typical example of a Dirichlet algebra on the unit circle $\partial \mathbf{D}$. For $A ( \mathbf{D} )$, t
7 KB (1,114 words) - 19:36, 23 December 2023
$#C+1 = 13 : ~/encyclopedia/old_files/data/D032/D.0302880 Dirichlet kernel
It was shown by P.G.L. Dirichlet [[#References|[1]]] that the partial sum $ S _ {n} $
3 KB (508 words) - 23:39, 29 December 2021
-
783 bytes (125 words) - 21:31, 18 November 2017
$#C+1 = 131 : ~/encyclopedia/old_files/data/D032/D.0302920 Dirichlet series
one obtains the so-called ordinary Dirichlet series
11 KB (1,638 words) - 11:32, 16 April 2023
...Dirichlet polynomials are partial sums of corresponding [[Dirichlet series|Dirichlet series]].
...Dirichlet $L$-function]]), as well as their powers, can be approximated by Dirichlet polynomials, mostly with $\lambda _ { m } = \operatorname { log } m$. For e
5 KB (706 words) - 17:03, 1 July 2020
$#C+1 = 104 : ~/encyclopedia/old_files/data/D110/D.1100210 Dirichlet process
...tained in the collection of normal distributions. The large support of the Dirichlet process accounts for its use in non-parametric Bayesian analysis. General r
11 KB (1,528 words) - 19:35, 5 June 2020
$#C+1 = 38 : ~/encyclopedia/old_files/data/D032/D.0302870 Dirichlet integral
A functional connected with the solution of the [[Dirichlet problem]] for the Laplace equation by the variational method. Let $ \Omeg
4 KB (557 words) - 10:41, 20 January 2024
...Dirichlet boundary value problem (cf. also [[Dirichlet boundary conditions|Dirichlet boundary conditions]]):
...is bounded and the boundary $\partial \Omega$ is sufficiently regular, the Dirichlet Laplacian has a discrete spectrum of infinitely many positive eigenvalues w
12 KB (1,753 words) - 10:12, 16 March 2023
$#C+1 = 16 : ~/encyclopedia/old_files/data/D032/D.0302840 Dirichlet distribution
...e Dirichlet distribution: the [[Beta-distribution|beta-distribution]]. The Dirichlet distribution plays an important role in the theory of order statistics. For
2 KB (306 words) - 08:57, 8 April 2023
$#C+1 = 12 : ~/encyclopedia/old_files/data/D032/D.0302900 Dirichlet principle
...nals in certain classes of functions. In the narrow sense of the term, the Dirichlet principle reduces the first boundary value problem
6 KB (847 words) - 19:35, 5 June 2020
''Dirichlet–Laplace operator''
...$C _ { 0 } ^ { \infty } ( \Omega )$) is given by the [[Dirichlet integral|Dirichlet integral]]
4 KB (579 words) - 19:34, 7 February 2024
A name referring to several theorems associated with Peter Gustav Lejeune Dirichlet (1805-1859).
===Dirichlet's theorem in the theory of Diophantine approximations===
7 KB (1,065 words) - 14:05, 17 March 2020
...s) \ge 1$, then $A$ is a regular set of prime ideals and $a$ is called its Dirichlet density. Here, $N(\mathfrak{p})$ is the norm of $\mathfrak{p}$, i.e. the nu
i) The set of all prime ideals of $K$ is regular with Dirichlet density $1$.
2 KB (310 words) - 09:04, 26 November 2023
$#C+1 = 151 : ~/encyclopedia/old_files/data/D032/D.0302910 Dirichlet problem
...this task were studied as early as 1840 by C.F. Gauss, and then by P.G.L. Dirichlet [[#References|[1]]].
17 KB (2,472 words) - 08:26, 21 March 2022
The Dirichlet convolution of two [[arithmetic function]]s $f(n)$ and $g(n)$ is defined as
...over the positive divisors $d$ of $n$. General background material on the Dirichlet convolution can be found in, e.g., [[#References|[a1]]], [[#References|[a6]
4 KB (627 words) - 09:28, 19 March 2023
$#C+1 = 21 : ~/encyclopedia/old_files/data/D032/D.0302950 Dirichlet variational problem
The problem of finding the minimum of the [[Dirichlet integral|Dirichlet integral]]
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#REDIRECT [[Dirichlet L-function]]
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$#C+1 = 4 : ~/encyclopedia/old_files/data/D032/D.0302800 Dirichlet box principle
elements comprises at least one set with at least two elements. Dirichlet's box principle can be formulated in a most popular manner as follows: If
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''Dirichlet conditions, Dirichlet data, boundary conditions of the first kind''
are called Dirichlet boundary conditions.
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''Dirichlet principal character''
...erve to define the concepts of primitive and imprimitive characters (cf. [[Dirichlet character]]).
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#REDIRECT [[Dirichlet series]]
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#REDIRECT [[Dirichlet L-function]]
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#REDIRECT [[Dirichlet L-function]]
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...ependent functions with zero mathematical expectations; [[Dirichlet series|Dirichlet series]] with exponents that are independent over the field of rational num
452 bytes (57 words) - 17:11, 7 February 2011
''Voronoi tesselation, Dirichlet–Voronoi tesselation, Dirichlet–Voronoi decomposition, Thiessen tesselation''
...is also called the Dirichlet–Voronoi tiling. The straight-line dual of the Dirichlet tesselation is the [[Delaunay triangulation|Delaunay triangulation]].
509 bytes (70 words) - 19:53, 29 April 2014
$#C+1 = 21 : ~/encyclopedia/old_files/data/D032/D.0302950 Dirichlet variational problem
The problem of finding the minimum of the [[Dirichlet integral|Dirichlet integral]]
3 KB (503 words) - 17:53, 6 January 2024
...s) \ge 1$, then $A$ is a regular set of prime ideals and $a$ is called its Dirichlet density. Here, $N(\mathfrak{p})$ is the norm of $\mathfrak{p}$, i.e. the nu
i) The set of all prime ideals of $K$ is regular with Dirichlet density $1$.
2 KB (310 words) - 09:04, 26 November 2023
$#C+1 = 13 : ~/encyclopedia/old_files/data/D032/D.0302880 Dirichlet kernel
It was shown by P.G.L. Dirichlet [[#References|[1]]] that the partial sum $ S _ {n} $
3 KB (508 words) - 23:39, 29 December 2021
...inuous function of the parameters $\alpha>0$ and $\beta>0$. Used by P.G.L.
Dirichlet in his studies on the attraction of ellipsoids [[#References|[1]]]. The int
<table><TR><TD valign="top">[1]</TD> <TD valign="top"> P.G.L.
Dirichlet, "Werke" , '''1''' , Chelsea, reprint (1969)</TD></TR><TR><TD valign="to
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.... It follows from Dirichlet's "box" principle (cf. [[Dirichlet principle|Dirichlet principle]]) that the following always holds:
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$#C+1 = 27 : ~/encyclopedia/old_files/data/D032/D.0302930 Dirichlet series for an analytic almost\AAhperiodic function
...erent almost-periodic functions in the same strip correspond two different Dirichlet series. In the case of a $ 2 \pi $-
3 KB (422 words) - 19:35, 5 June 2020
...emann zeta function]] which may be used to exhibit properties of various [[Dirichlet L-function]]s.
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$#C+1 = 12 : ~/encyclopedia/old_files/data/D032/D.0302900 Dirichlet principle
...nals in certain classes of functions. In the narrow sense of the term, the Dirichlet principle reduces the first boundary value problem
6 KB (847 words) - 19:35, 5 June 2020
...a_n$ are real numbers and $b_n$ are complex numbers, established by P.G.L. Dirichlet and published posthumously in {{Cite|Di}}. If a sequence of real numbers $a
|valign="top"|{{Ref|Di}}|| P.G.L. Dirichlet, "Démonstration d’un théorème d’Abel", ''J. de Math. (2)'' , '''7'''
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...ue problem|First boundary value problem]]; [[Dirichlet boundary conditions|Dirichlet boundary conditions]]; [[Third boundary value problem|Third boundary value
885 bytes (129 words) - 07:13, 23 August 2014
A name referring to several theorems associated with Peter Gustav Lejeune Dirichlet (1805-1859).
===Dirichlet's theorem in the theory of Diophantine approximations===
7 KB (1,065 words) - 14:05, 17 March 2020
$#C+1 = 38 : ~/encyclopedia/old_files/data/D032/D.0302870 Dirichlet integral
A functional connected with the solution of the [[Dirichlet problem]] for the Laplace equation by the variational method. Let $ \Omeg
4 KB (557 words) - 10:41, 20 January 2024