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Journal articles on the topic 'Dirichlet'

Author: Grafiati

Published: 4 June 2021

Last updated: 8 March 2025

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1

Guo, Bao Zhu. "Further results for a one-dimensional linear thermoelastic equation with Dirichlet-Dirichlet boundary conditions." ANZIAM Journal 43, no. 3 (January 2002): 449–62. http://dx.doi.org/10.1017/s1446181100012621.

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AbstractWe show that a sequence of generalized eigenfunctions of a one-dimensional linear thermoelastic system with Dirichiet-Dirichlet boundary conditions forms a Riesz basis for the state Hilbert space. This develops a parallel result for the same system with Dirichlet-Neumann or Neumann-Dirichlet boundary conditions.

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2

Duan, Yu, and Hong Jian Luo. "The Calculation and Estimate of Interval-Valued and Fuzzy Dirichlet Series Coefficient." Applied Mechanics and Materials 325-326 (June 2013): 1515–18. http://dx.doi.org/10.4028/www.scientific.net/amm.325-326.1515.

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This article gives the definition of interval-valued Dirichlet series. Based on [1, , this article discusses some properties about the coefficient of interval-valued and fuzzy Dirichlet series. Ihe calculation of coefficient , of interval-valued Dirichlet series and the coefficient of fuzzy Dirichelt series are also discussed. Moreover, some relative theorems and properties are presented.

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3

Ma, Rong, Yulong Zhang, and Guohe Zhang. "On a Kind of Dirichlet Character Sums." Abstract and Applied Analysis 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/750964.

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Letp≥3be a prime and letχdenote the Dirichlet character modulop. For any primeqwithq<p, define the setEq,p=a∣1≤a,a-≤p,aa-≡1modp and a≡a-modq. In this paper, we study a kind of mean value of Dirichlet character sums∑a≤p a∈Eq,pχ(a), and use the properties of the DirichletL-functions and generalized Kloosterman sums to obtain an interesting estimate.

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4

Aron, Richard M., Frédéric Bayart, Paul M. Gauthier, Manuel Maestre, and Vassili Nestoridis. "Dirichlet approximation and universal Dirichlet series." Proceedings of the American Mathematical Society 145, no. 10 (June 8, 2017): 4449–64. http://dx.doi.org/10.1090/proc/13607.

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5

ZHANG, LILING. "SET OF EXTREMELY DIRICHLET NON-IMPROVABLE POINTS." Fractals 28, no. 02 (March 2020): 2050034. http://dx.doi.org/10.1142/s0218348x20500346.

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Let [Formula: see text] be the continued fraction expansion of [Formula: see text]. The growth rate of the product of the partial quotients [Formula: see text] is closely connected with the improvability of Dirichlet’s theorem in the sense that the faster [Formula: see text] grows, the less possibility the improvement of Dirichlet’s theorem has. In this paper, we study the size of the points for which [Formula: see text] grows in a given speed. We call the points of this type as extremely Dirichlet non-improvable points.

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6

Jespers, E., S. O. Juriaans, A. Kiefer, A. de A. e. Silva, and A. C. Souza Filho. "Dirichlet-Ford domains and Double Dirichlet domains." Bulletin of the Belgian Mathematical Society - Simon Stevin 23, no. 3 (September 2016): 465–79. http://dx.doi.org/10.36045/bbms/1473186517.

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7

Kassmann, Moritz. "On Dirichlet Forms and Semi-Dirichlet Forms." Jahresbericht der Deutschen Mathematiker-Vereinigung 117, no. 3 (February 20, 2015): 207–15. http://dx.doi.org/10.1365/s13291-015-0110-5.

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8

Harvey, F. Reese, and H. Blaine Lawson. "Dirichlet duality and the nonlinear Dirichlet problem." Communications on Pure and Applied Mathematics 62, no. 3 (March 2009): 396–443. http://dx.doi.org/10.1002/cpa.20265.

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9

Ceretkova, Sona, and Lubica Korenekova. "DIRICHLET’S PRINCIPLE AS AN ELEMENTARY MATHEMATICAL MODEL IN MATHEMATIC EDUCATION." Problems of Education in the 21st Century 31, no. 1 (July 5, 2011): 45–55. http://dx.doi.org/10.33225/pec/11.31.45.

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One important part of nowadays research in theory of mathematics education is focused on searching for some interesting and non-traditional mathematical topics and themes. The topic named the “Dirichlet’s Principle” is aimed to promote and exercise mathematical competencies by using quite simple mathematical rules. The rules were discovered and described in the 19th century by Johann Peter Gustav Lejeune Dirichlet (1805-1859). The article describes case studies as the results of qualitative research of mathematics’ lessons with the topic of Dirichlet’s principle at upper-secondary school and university. The elements of the history of mathematics concerning the topic and Dirichlet’s personality are also involved. Definitions, examples of exercises, tasks and problems are given in the article, too. Recommended methods of teaching with the focus on active methods, which support inquiry based learning, are described. Two case studies, one realized at secondary grammar school (17 year-old pupils) and one at university (student teachers) are described as examples of theoretical and methodological background implementation. The context of tasks and problems which are solved by using Dirichlet’s principle is set in real life situations. The topic content therefore helps to show the importance of mathematical knowledge for everyday life. Key words: case study, elementary mathematical model, Johann Peter Gustav Lejeune Dirichlet, problem solving.

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10

Huxley, M. N. "Dirichlet polynomials." Banach Center Publications 17, no. 1 (1985): 307–16. http://dx.doi.org/10.4064/-17-1-307-316.

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11

Li, Miao. "Dirichlet strings." Nuclear Physics B 420, no. 1-2 (May 1994): 339–62. http://dx.doi.org/10.1016/0550-3213(94)90385-9.

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12

Biroli, Marco, and N. Tchou. "Relaxation for Dirichlet Problems Involving a Dirichlet Form." Zeitschrift für Analysis und ihre Anwendungen 19, no. 1 (2000): 203–25. http://dx.doi.org/10.4171/zaa/946.

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13

Halls, P. J., M. Bulling, P. C. L. White, L. Garland, and S. Harris. "Dirichlet neighbours: revisiting Dirichlet tessellation for neighbourhood analysis." Computers, Environment and Urban Systems 25, no. 1 (January 2001): 105–17. http://dx.doi.org/10.1016/s0198-9715(00)00035-1.

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14

Biroli, Marco, and N. Tchou. "Asymptotic Behaviour of Relaxed Dirichiet Problems Involving a Dirichlet-Poincar Form." Zeitschrift für Analysis und ihre Anwendungen 16, no. 2 (1997): 281–309. http://dx.doi.org/10.4171/zaa/764.

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15

Onozuka, Tomokazu. "The multiple Dirichlet product and the multiple Dirichlet series." International Journal of Number Theory 13, no. 08 (August 2, 2017): 2181–93. http://dx.doi.org/10.1142/s1793042117501184.

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First, we define the multiple Dirichlet product and study the properties of it. From those properties, we obtain a zero-free region of a multiple Dirichlet series and a multiple Dirichlet series expression of the reciprocal of a multiple Dirichlet series.

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16

Ko, Chul-Ki. "DECOMPOSITION OF DIRICHLET FORMS ASSOCIATED TO UNBOUNDED DIRICHLET OPERATORS." Bulletin of the Korean Mathematical Society 46, no. 2 (March 31, 2009): 347–58. http://dx.doi.org/10.4134/bkms.2009.46.2.347.

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17

Jiarong, Yu. "The lower orders of Dirichlet and random Dirichlet series." Wuhan University Journal of Natural Sciences 1, no. 1 (March 1996): 1–8. http://dx.doi.org/10.1007/bf02827568.

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18

MARKO, FRANTIŠEK, and ŠTEFAN PORUBSKÝ. "A NOTE ON DENSITY AND THE DIRICHLET CONDITION." International Journal of Number Theory 08, no. 03 (April 7, 2012): 823–30. http://dx.doi.org/10.1142/s1793042112500479.

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Motivated by topological approaches to Euclid and Dirichlet's theorems on infinitude of primes, we introduce and study [Formula: see text]-coprime topologies on a commutative ring R with an identity and without zero divisors. For infinite semiprimitive commutative domain R of finite character (i.e. every nonzero element of R is contained in at most finitely many maximal ideals of R), we characterize its subsets A for which the Dirichlet condition, requiring the existence of infinitely many pairwise nonassociated elements from A in every open set in the invertible topology, is satisfied.

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19

Thankamani, Princy, Nicy Sebastian, and Hans J. Haubold. "On Complex Matrix-Variate Dirichlet Averages and Its Applications in Various Sub-Domains." Entropy 25, no. 11 (November 10, 2023): 1534. http://dx.doi.org/10.3390/e25111534.

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This paper is about Dirichlet averages in the matrix-variate case or averages of functions over the Dirichlet measure in the complex domain. The classical power mean contains the harmonic mean, arithmetic mean and geometric mean (Hardy, Littlewood and Polya), which is generalized to the y-mean by de Finetti and hypergeometric mean by Carlson; see the references herein. Carlson’s hypergeometric mean averages a scalar function over a real scalar variable type-1 Dirichlet measure, which is known in the current literature as the Dirichlet average of that function. The idea is examined when there is a type-1 or type-2 Dirichlet density in the complex domain. Averages of several functions are computed in such Dirichlet densities in the complex domain. Dirichlet measures are defined when the matrices are Hermitian positive definite. Some applications are also discussed.

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20

Letac, Gérard, and Mauro Piccioni. "Dirichlet Random Walks." Journal of Applied Probability 51, no. 4 (December 2014): 1081–99. http://dx.doi.org/10.1239/jap/1421763329.

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This paper provides tools for the study of the Dirichlet random walk in Rd. We compute explicitly, for a number of cases, the distribution of the random variable W using a form of Stieltjes transform of W instead of the Laplace transform, replacing the Bessel functions with hypergeometric functions. This enables us to simplify some existing results, in particular, some of the proofs by Le Caër (2010), (2011). We extend our results to the study of the limits of the Dirichlet random walk when the number of added terms goes to ∞, interpreting the results in terms of an integral by a Dirichlet process. We introduce the ideas of Dirichlet semigroups and Dirichlet infinite divisibility and characterize these infinite divisible distributions in the sense of Dirichlet when they are concentrated on the unit sphere of Rd.

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21

Letac, Gérard, and Mauro Piccioni. "Dirichlet Random Walks." Journal of Applied Probability 51, no. 04 (December 2014): 1081–99. http://dx.doi.org/10.1017/s0021900200011992.

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This paper provides tools for the study of the Dirichlet random walk inRd. We compute explicitly, for a number of cases, the distribution of the random variableWusing a form of Stieltjes transform ofWinstead of the Laplace transform, replacing the Bessel functions with hypergeometric functions. This enables us to simplify some existing results, in particular, some of the proofs by Le Caër (2010), (2011). We extend our results to the study of the limits of the Dirichlet random walk when the number of added terms goes to ∞, interpreting the results in terms of an integral by a Dirichlet process. We introduce the ideas of Dirichlet semigroups and Dirichlet infinite divisibility and characterize these infinite divisible distributions in the sense of Dirichlet when they are concentrated on the unit sphere ofRd.

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22

Hamahata, Yoshinori. "Dirichlet product and the multiple Dirichlet series over function fields." Glasnik Matematicki 55, no. 2 (December 23, 2020): 253–65. http://dx.doi.org/10.3336/gm.55.2.06.

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We define the Dirichlet product for multiple arithmetic functions over function fields and consider the ring of the multiple Dirichlet series over function fields. We apply our results to absolutely convergent multiple Dirichlet series and obtain some zero-free regions for them.

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23

Faires, Hafedh. "Dirichlet Brownian Motions." Open Journal of Statistics 04, no. 11 (2014): 902–11. http://dx.doi.org/10.4236/ojs.2014.411085.

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24

Geleta, Hunduma Legesse. "Dirichlet-Power Series." Journal of Analysis & Number Theory 5, no. 1 (January 1, 2017): 41–48. http://dx.doi.org/10.18576/jant/050107.

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25

Liu, Chunlei. "Dirichlet character sums." Acta Arithmetica 88, no. 4 (1999): 299–309. http://dx.doi.org/10.4064/aa-88-4-299-309.

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26

Teh, Yee Whye, Michael I. Jordan, Matthew J. Beal, and David M. Blei. "Hierarchical Dirichlet Processes." Journal of the American Statistical Association 101, no. 476 (December 1, 2006): 1566–81. http://dx.doi.org/10.1198/016214506000000302.

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27

Begehr, H., T. N. H. Vu, and Z. X. Zhang. "Polyharmonic dirichlet problems." Proceedings of the Steklov Institute of Mathematics 255, no. 1 (December 2006): 13–34. http://dx.doi.org/10.1134/s0081543806040031.

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28

Diniz, Marcio A., Jasper De Bock, and Arthur Van Camp. "Characterizing Dirichlet Priors." American Statistician 70, no. 1 (January 2, 2016): 9–17. http://dx.doi.org/10.1080/00031305.2015.1100137.

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29

ALBEVERIO, S., Ya BELOPOLSKAYA, and M. FELLER. "LÉVY–DIRICHLET FORMS." Infinite Dimensional Analysis, Quantum Probability and Related Topics 09, no. 03 (September 2006): 435–49. http://dx.doi.org/10.1142/s0219025706002470.

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30

Li, Songzi. "Matrix Dirichlet processes." Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 55, no. 2 (May 2019): 909–40. http://dx.doi.org/10.1214/18-aihp903.

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31

Joo, Weonyoung, Wonsung Lee, Sungrae Park, and Il-Chul Moon. "Dirichlet Variational Autoencoder." Pattern Recognition 107 (November 2020): 107514. http://dx.doi.org/10.1016/j.patcog.2020.107514.

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32

Orpel, Aleksandra. "Superlinear Dirichlet problems." Nonlinear Analysis: Theory, Methods & Applications 56, no. 6 (March 2004): 937–50. http://dx.doi.org/10.1016/j.na.2003.10.021.

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33

Danos, Vincent, and Ilias Garnier. "Dirichlet is Natural." Electronic Notes in Theoretical Computer Science 319 (December 2015): 137–64. http://dx.doi.org/10.1016/j.entcs.2015.12.010.

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34

Albeverio, S., and Yu G. Kondrat'ev. "Supersymmetric Dirichlet operators." Ukrainian Mathematical Journal 47, no. 5 (May 1995): 675–85. http://dx.doi.org/10.1007/bf01059040.

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35

Carroll, Sean M., and Mark Trodden. "Dirichlet topological defects." Physical Review D 57, no. 8 (April 15, 1998): 5189–94. http://dx.doi.org/10.1103/physrevd.57.5189.

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36

Schoenberg, F. P. "Inverting Dirichlet Tessellations." Computer Journal 46, no. 1 (January 1, 2003): 76–83. http://dx.doi.org/10.1093/comjnl/46.1.76.

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37

Ash, Peter F., and Ethan D. Bolker. "Generalized Dirichlet tessellations." Geometriae Dedicata 20, no. 2 (April 1986): 209–43. http://dx.doi.org/10.1007/bf00164401.

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38

Gushchin, A. K. "On Dirichlet problem." Theoretical and Mathematical Physics 218, no. 1 (January 2024): 51–67. http://dx.doi.org/10.1134/s0040577924010045.

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39

Allouche, J. P., M. Mendès France, and J. Peyrière. "Automatic Dirichlet Series." Journal of Number Theory 81, no. 2 (April 2000): 359–73. http://dx.doi.org/10.1006/jnth.1999.2487.

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40

Hu, Yi-Teng, and Murat Şat. "Trace Formulae for Second-Order Differential Pencils with a Frozen Argument." Mathematics 11, no. 18 (September 20, 2023): 3996. http://dx.doi.org/10.3390/math11183996.

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This paper deals with second-order differential pencils with a fixed frozen argument on a finite interval. We obtain the trace formulae under four boundary conditions: Dirichlet–Dirichlet, Neumann–Neumann, Dirichlet–Neumann, Neumann–Dirichlet. Although the boundary conditions and the corresponding asymptotic behaviour of the eigenvalues are different, the trace formulae have the same form which reveals the impact of the frozen argument.

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41

Loghin, Daniel. "Preconditioned Dirichlet-Dirichlet Methods for Optimal Control of Elliptic PDE." Analele Universitatii "Ovidius" Constanta - Seria Matematica 26, no. 2 (July 1, 2018): 175–92. http://dx.doi.org/10.2478/auom-2018-0024.

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Abstract The discretization of optimal control of elliptic partial differential equations problems yields optimality conditions in the form of large sparse linear systems with block structure. Correspondingly, when the solution method is a Dirichlet-Dirichlet non-overlapping domain decomposition method, we need to solve interface problems which inherit the block structure. It is therefore natural to consider block preconditioners acting on the interface variables for the acceleration of Krylov methods with substructuring preconditioners. In this paper we describe a generic technique which employs a preconditioner block structure based on the fractional Sobolev norms corresponding to the domains of the boundary operators arising in the matrix interface problem, some of which may include a dependence on the control regularization parameter. We illustrate our approach on standard linear elliptic control problems. We present analysis which shows that the resulting iterative method converges independently of the size of the problem. We include numerical results which indicate that performance is also independent of the control regularization parameter and exhibits only a mild dependence on the number of the subdomains.

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42

Syed, Shaheen, and Marco Spruit. "Exploring Symmetrical and Asymmetrical Dirichlet Priors for Latent Dirichlet Allocation." International Journal of Semantic Computing 12, no. 03 (September 2018): 399–423. http://dx.doi.org/10.1142/s1793351x18400184.

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Latent Dirichlet Allocation (LDA) has gained much attention from researchers and is increasingly being applied to uncover underlying semantic structures from a variety of corpora. However, nearly all researchers use symmetrical Dirichlet priors, often unaware of the underlying practical implications that they bear. This research is the first to explore symmetrical and asymmetrical Dirichlet priors on topic coherence and human topic ranking when uncovering latent semantic structures from scientific research articles. More specifically, we examine the practical effects of several classes of Dirichlet priors on 2000 LDA models created from abstract and full-text research articles. Our results show that symmetrical or asymmetrical priors on the document–topic distribution or the topic–word distribution for full-text data have little effect on topic coherence scores and human topic ranking. In contrast, asymmetrical priors on the document–topic distribution for abstract data show a significant increase in topic coherence scores and improved human topic ranking compared to a symmetrical prior. Symmetrical or asymmetrical priors on the topic–word distribution show no real benefits for both abstract and full-text data.

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43

Rane, V. V. "Dirichlet expression for L(1, χ) with general Dirichlet character." Proceedings - Mathematical Sciences 120, no. 1 (February 2010): 7–9. http://dx.doi.org/10.1007/s12044-010-0003-6.

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44

Harvey, F. Reese, and H. Blaine Lawson. "Dirichlet Duality and the Nonlinear Dirichlet Problem on Riemanninan Manifolds." Journal of Differential Geometry 88, no. 3 (July 2011): 395–482. http://dx.doi.org/10.4310/jdg/1321366356.

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45

Funakura, Takeo. "On Coefficients of Artin L Functions as Dirichlet Series." Canadian Mathematical Bulletin 33, no. 1 (March 1, 1990): 50–54. http://dx.doi.org/10.4153/cmb-1990-008-1.

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AbstractThe paper is motivated by a result of Ankeny [1] above Dirichlet L functions in 1952. We generalize this from Dirichlet L functions to Artin L functions of relative abelian extensions, by complementing the ingenious proof of Ankeny's theorem given by Iwasaki [4]. Moreover, we characterize Dirichlet L functions in the class of all Artin L functions in terms of coefficients as Dirichlet series.

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46

Xu, Hongyan, Guangsheng Chen, Hari Mohan Srivastava, Hong Li, Zuxing Xuan, and Yongqin Cui. "A Study of the Growth Results for the Hadamard Product of Several Dirichlet Series with Different Growth Indices." Mathematics 10, no. 13 (June 24, 2022): 2220. http://dx.doi.org/10.3390/math10132220.

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In this paper, our first purpose is to describe a class of phenomena involving the growth in the Hadamard–Kong product of several Dirichlet series with different growth indices. We prove that (i) the order of the Hadamard–Kong product series is determined by the growth in the Dirichlet series with smaller indices if these Dirichlet series have different growth indices; (ii) the q1-type of the Hadamard–Kong product series is equal to zero if p Dirichlet series are of qj-regular growth, and q1<q2<⋯<qp, qj∈N+, j=1,2,…,p. The second purpose is to reveal the properties of the growth in the Hadamard–Kong product series of two Dirichlet series—when one Dirichlet series is of finite order, the other is of logarithmic order, and two Dirichlet series are of finite logarithmic order—and obtain the growth relationships between the Hadamard–Kong product series and two Dirchlet series concerning the order, the logarithmic order, logarithmic type, etc. Finally, some examples are given to show that our results are best possible.

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47

Hu, Ze-Chun, and Wei Sun. "Balayage of Semi-Dirichlet Forms." Canadian Journal of Mathematics 64, no. 4 (August 1, 2012): 869–91. http://dx.doi.org/10.4153/cjm-2011-055-5.

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Abstract In this paper we study the balayage of semi-Dirichlet forms. We present new results on balayaged functions and balayagedmeasures of semi-Dirichlet forms. Some of the results are new even in the Dirichlet forms setting.

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48

Engelbert, Hans-Jürgen, and Jochen Wolf. "Dirichlet functions of reflected Brownian motion." Mathematica Bohemica 125, no. 2 (2000): 235–47. http://dx.doi.org/10.21136/mb.2000.125954.

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49

DJANKOVIĆ, GORAN. "THE RECIPROCITY LAW FOR THE TWISTED SECOND MOMENT OF DIRICHLET -FUNCTIONS OVER RATIONAL FUNCTION FIELDS." Bulletin of the Australian Mathematical Society 98, no. 3 (August 28, 2018): 383–88. http://dx.doi.org/10.1017/s0004972718000874.

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We prove the reciprocity law for the twisted second moments of Dirichlet $L$-functions over rational function fields, corresponding to two irreducible polynomials. This formula is the analogue of the formulas for Dirichlet $L$-functions over $\mathbb{Q}$ obtained by Conrey [‘The mean-square of Dirichlet $L$-functions’, arXiv:0708.2699 [math.NT] (2007)] and Young [‘The reciprocity law for the twisted second moment of Dirichlet $L$-functions’, Forum Math. 23(6) (2011), 1323–1337].

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50

Bloom, Walter R., and Herbert Heyer. "Non-symmetric translation invariant Dirichlet forms on hypergroups." Bulletin of the Australian Mathematical Society 36, no. 1 (August 1987): 61–72. http://dx.doi.org/10.1017/s0004972700026307.

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In this note translation-invariant Dirichlet forms on a commutative hypergroup are studied. The main theorem gives a characterisation of an invariant Dirichlet form in terms of the negative definite function associated with it. As an illustration constructions of potentials arising from invariant Dirichlet forms are given. The examples of one- and two-dimensional Jacobi hypergroups yield specifications of invariant Dirichlet forms, particularly in the case of Gelfand pairs of compact type.

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