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- ...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 w12 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. For2 KB (306 words) - 08:57, 8 April 2023
- $#C+1 = 12 : ~/encyclopedia/old_files/data/D032/D.0302900 Dirichlet principle ...nals in certain classes of functions. In the narrow sense of the term, the Dirichlet principle reduces the first boundary value problem6 KB (847 words) - 19:35, 5 June 2020
- ''Dirichlet–Laplace operator'' ...$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
- ...\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 $(x,y)$ wi951 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]].509 bytes (70 words) - 19:53, 29 April 2014
- ...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 $A ( \mathbf{D} )$, t7 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 series11 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 e5 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 r11 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 $ \Omeg4 KB (557 words) - 10:41, 20 January 2024
- $#C+1 = 182 : ~/encyclopedia/old_files/data/D032/D.0302890 Dirichlet \BMI L\EMI\AAhfunction, ''Dirichlet $ L $-15 KB (2,181 words) - 11:50, 26 March 2023
- ...)$, where $A ^ { - 1 }$ is the family of invertible elements of $A$. Hypo-Dirichlet algebras were introduced by J. Wermer [[#References|[a4]]]. ...roximation of functions of a complex variable]]). Then $R ( X )$ is a hypo-Dirichlet algebra [[#References|[a3]]].3 KB (474 words) - 19:56, 27 February 2021
Page text matches
- $#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: If928 bytes (141 words) - 19:35, 5 June 2020
- ''Dirichlet conditions, Dirichlet data, boundary conditions of the first kind'' are called Dirichlet boundary conditions.810 bytes (116 words) - 14:55, 16 October 2014
- ''Dirichlet principal character'' ...erve to define the concepts of primitive and imprimitive characters (cf. [[Dirichlet character]]).340 bytes (45 words) - 20:04, 9 January 2015
- #REDIRECT [[Dirichlet series]]30 bytes (3 words) - 08:27, 29 December 2015
- #REDIRECT [[Dirichlet L-function]]34 bytes (3 words) - 20:59, 9 January 2015
- #REDIRECT [[Dirichlet L-function]]34 bytes (3 words) - 20:35, 25 November 2017
- ...ependent functions with zero mathematical expectations; [[Dirichlet series|Dirichlet series]] with exponents that are independent over the field of rational num452 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="to799 bytes (121 words) - 14:14, 14 February 2020
- .... It follows from Dirichlet's "box" principle (cf. [[Dirichlet principle|Dirichlet principle]]) that the following always holds:2 KB (342 words) - 12:47, 20 December 2014
- $#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.722 bytes (101 words) - 09:28, 19 March 2023
- $#C+1 = 12 : ~/encyclopedia/old_files/data/D032/D.0302900 Dirichlet principle ...nals in certain classes of functions. In the narrow sense of the term, the Dirichlet principle reduces the first boundary value problem6 KB (847 words) - 19:35, 5 June 2020
- ...a_n$ 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'''730 bytes (127 words) - 19:46, 16 January 2016
- ...ue problem|First boundary value problem]]; [[Dirichlet boundary conditions|Dirichlet boundary conditions]]; [[Third boundary value problem|Third boundary value885 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 $ \Omeg4 KB (557 words) - 10:41, 20 January 2024