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Journal articles on the topic 'Singular functions'

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Author: Grafiati

Published: 14 March 2023

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1

Gorkin, Pamela, and Raymond Mortini. "Universal Singular Inner Functions." Canadian Mathematical Bulletin 47, no. 1 (March 1, 2004): 17–21. http://dx.doi.org/10.4153/cmb-2004-003-0.

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AbstractWe show that there exists a singular inner function S which is universal for noneuclidean translates; that is one for which the set is locally uniformly dense in the set of all zero-free holomorphic functions in bounded by one.

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2

Ryabininf, A. A., V. D. Bystritskii, and V. A. Il'ichev. "Singular Strictly Monotone Functions." Mathematical Notes 76, no. 3/4 (September 2004): 407–19. http://dx.doi.org/10.1023/b:matn.0000043468.33152.2d.

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3

Giorgadze, G., V. Jikia, and G. Makatsaria. "Singular Generalized Analytic Functions." Journal of Mathematical Sciences 237, no. 1 (January 5, 2019): 30–109. http://dx.doi.org/10.1007/s10958-019-4143-7.

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4

Horvat, Lana, and Darko Žubrinić. "Maximally singular Sobolev functions." Journal of Mathematical Analysis and Applications 304, no. 2 (April 2005): 531–41. http://dx.doi.org/10.1016/j.jmaa.2004.09.047.

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5

Grossmann, Christian, Lars Ludwig, and Hans-Görg Roos. "Layer-adapted methods for a singularly perturbed singular problem." Computational Methods in Applied Mathematics 11, no. 2 (2011): 192–205. http://dx.doi.org/10.2478/cmam-2011-0010.

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Abstract In the present paper we analyze linear finite elements on a layer adapted mesh for a boundary value problem characterized by the overlapping of a boundary layer with a singularity. Moreover, we compare this approach numerically with the use of adapted basis functions, in our case modified Bessel functions. It turns out that as well adapted meshes as adapted basis functions are suitable where for our one-dimensional problem adapted bases work slightly better.

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6

Nakai, Mitsuru, Shigeo Segawa, and Toshimasa Tada. "Surfaces carrying no singular functions." Proceedings of the Japan Academy, Series A, Mathematical Sciences 85, no. 10 (December 2009): 163–66. http://dx.doi.org/10.3792/pjaa.85.163.

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7

Nakai, Mitsuru, and Shigeo Segawa. "Existence of singular harmonic functions." Kodai Mathematical Journal 33, no. 1 (March 2010): 99–115. http://dx.doi.org/10.2996/kmj/1270559160.

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8

Estrada, Ricardo, and S. A. Fulling. "How singular functions define distributions." Journal of Physics A: Mathematical and General 35, no. 13 (March 22, 2002): 3079–89. http://dx.doi.org/10.1088/0305-4470/35/13/304.

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9

Delaye, A. "Quadrature formulae for singular functions." International Journal of Computer Mathematics 23, no. 2 (January 1988): 167–76. http://dx.doi.org/10.1080/00207168808803615.

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10

Žubrinić, Darko. "Singular sets of Sobolev functions." Comptes Rendus Mathematique 334, no. 7 (January 2002): 539–44. http://dx.doi.org/10.1016/s1631-073x(02)02316-6.

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11

Vynnyshyn, Ya F. "Convolutions of Singular Distribution Functions." Ukrainian Mathematical Journal 56, no. 1 (January 2004): 148–52. http://dx.doi.org/10.1023/b:ukma.0000031709.03258.e4.

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12

Fulling, R. Estrada and S. A. "How singular functions define distributions." Journal of Physics A: Mathematical and General 38, no. 35 (August 16, 2005): 7785. http://dx.doi.org/10.1088/0305-4470/38/35/c01.

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13

Paradís, Jaume, Pelegrí Viader, and Lluís Bibiloni. "Riesz–Nágy singular functions revisited." Journal of Mathematical Analysis and Applications 329, no. 1 (May 2007): 592–602. http://dx.doi.org/10.1016/j.jmaa.2006.06.082.

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14

Liu, Chein-Shan. "Solving Third-Order Singularly Perturbed Problems: Exponentially and Polynomially Fitted Trial Functions." Journal of Mathematics Research 8, no. 2 (March 10, 2016): 16. http://dx.doi.org/10.5539/jmr.v8n2p16.

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For the third-order linearly singularly perturbed problems under four different types boundary conditions, we develop a weak-form integral equation method (WFIEM) to find the singular solution. In the WFIEM the exponentially and polynomially fitted trial functions are designed to satisfy the boundary conditions automatically, while the test functions satisfy the adjoint boundary conditions exactly. The WFIEM provides accurate and stable solutions to the highly singular third-order problems.

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15

Błocki, Zbigniew. "Singular sets of separately analytic functions." Annales Polonici Mathematici 56, no. 2 (1992): 219–25. http://dx.doi.org/10.4064/ap-56-2-219-225.

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16

Siciak, Józef. "Singular sets of separately analytic functions." Colloquium Mathematicum 60, no. 1 (1990): 281–90. http://dx.doi.org/10.4064/cm-60-61-1-281-290.

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17

Kim, Tae-Sik. "FRACTAL DIMENSION ESTIMATION OF SINGULAR FUNCTIONS." Honam Mathematical Journal 30, no. 1 (March 25, 2008): 137–46. http://dx.doi.org/10.5831/hmj.2008.30.1.137.

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18

Łysik, Grzegorz. "Generalized Taylor expansions of singular functions." Studia Mathematica 99, no. 3 (1991): 235–62. http://dx.doi.org/10.4064/sm-99-3-235-262.

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19

Rzaev, Rahim M. "Approximation of Functions by Singular Integrals." Pure and Applied Mathematics Journal 3, no. 6 (2014): 113. http://dx.doi.org/10.11648/j.pamj.20140306.11.

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20

Bernardi, Christine, and Yvon Maday. "Polynomial approximation of some singular functions." Applicable Analysis 42, no. 1-4 (December 1991): 1–32. http://dx.doi.org/10.1080/00036819108840031.

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21

Barma, M. "Singular scaling functions in clustering phenomena." European Physical Journal B 64, no. 3-4 (April 9, 2008): 387–93. http://dx.doi.org/10.1140/epjb/e2008-00118-9.

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22

Dickenstein, Alicia, Mirta Susana Iriondo, and Teresita Alejandra Rojas. "Integrating singular functions on the sphere." Journal of Mathematical Physics 38, no. 10 (October 1997): 5361–70. http://dx.doi.org/10.1063/1.531947.

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23

Bhattacharya, G. S., and B. K. Raghuprasad. "Dimensional characterization of singular fractal functions." Chaos, Solitons & Fractals 8, no. 6 (June 1997): 901–8. http://dx.doi.org/10.1016/s0960-0779(96)00161-0.

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24

Žubrinić, Darko. "Singular sets of Lebesgue integrable functions." Chaos, Solitons & Fractals 21, no. 5 (September 2004): 1281–87. http://dx.doi.org/10.1016/j.chaos.2003.12.080.

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25

Izawa, Takeshi, and Tatsuo Suwa. "Multiplicity of Functions On Singular Varieties." International Journal of Mathematics 14, no. 05 (July 2003): 541–58. http://dx.doi.org/10.1142/s0129167x03001910.

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Let V be a local complete intersection in a complex manifold W. For a function g on W, we set f = g|V and f′ = g|V′, where V′ denotes the non-singular part of V. For each compact connected component S of the union of the singular set of V and the critical set of f′, we define the virtual multiplicity [Formula: see text] of f at S as the residue of the localization by df′ of the Chern class of the virtual cotangent bundle of V. The multiplicity m(f, S) of f at S is then defined by [Formula: see text], where μ(V, S) is the (generalized) Milnor number of [2]. If S = {p} is an isolated point and if g is holomorphic, we give an explicit expression of [Formula: see text] as a Grothendieck residue on V. In the global situation, where we have a holomorphic map of V onto a Riemann surface, we prove a singular version of a formule of B. Iversen [13].

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26

BENELKOURCHI, SLIMANE. "APPROXIMATION OF WEAKLY SINGULAR PLURISUBHARMONIC FUNCTIONS." International Journal of Mathematics 22, no. 07 (July 2011): 937–46. http://dx.doi.org/10.1142/s0129167x11007094.

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In this paper we give some properties of the weighted energy class εχ and study the approximation in these classes. We prove that any function in εχ can be approximated by an increasing sequence of plurisubharmonic functions defined on larger domains and with finite χ-energy.

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27

Boc Thaler, Luka. "Entire functions with prescribed singular values." International Journal of Mathematics 31, no. 10 (August 5, 2020): 2050075. http://dx.doi.org/10.1142/s0129167x20500755.

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We introduce a new class of entire functions [Formula: see text] which consists of all [Formula: see text] for which there exists a sequence [Formula: see text] and a sequence [Formula: see text] satisfying [Formula: see text] for all [Formula: see text]. This new class is closed under the composition and it is dense in the space of all nonvanishing entire functions. We prove that every closed set [Formula: see text] containing the origin and at least one more point is the set of singular values of some locally univalent function in [Formula: see text], hence, this new class has nontrivial intersection with both the Speiser class and the Eremenko–Lyubich class of entire functions. As a consequence, we provide a new proof of an old result by Heins which states that every closed set [Formula: see text] is the set of singular values of some locally univalent entire function. The novelty of our construction is that these functions are obtained as a uniform limit of a sequence of entire functions, the process under which the set of singular values is not stable. Finally, we show that the class [Formula: see text] contains functions with an empty Fatou set and also functions whose Fatou set is nonempty.

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28

Cygan, Ewa, and Maciej P. Denkowski. "Singular points of weakly holomorphic functions." Bulletin des Sciences Mathématiques 140, no. 6 (September 2016): 657–74. http://dx.doi.org/10.1016/j.bulsci.2015.12.004.

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29

Ricci, Fulvio, and Elias M. Stein. "Multiparameter singular integrals and maximal functions." Annales de l’institut Fourier 42, no. 3 (1992): 637–70. http://dx.doi.org/10.5802/aif.1304.

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30

Campbell, S. L., and K. D. Yeomans. "Solving Singular Systems Using Orthogonal Functions." IEE Proceedings D Control Theory and Applications 137, no. 4 (1990): 222. http://dx.doi.org/10.1049/ip-d.1990.0027.

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31

Lapidot, E. "On Singular Generalized Absolutely Monotone Functions." Journal of Approximation Theory 79, no. 2 (November 1994): 199–221. http://dx.doi.org/10.1006/jath.1994.1125.

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32

Weiping, Li. "Singular connections and Riemann theta functions." Topology and its Applications 90, no. 1-3 (December 1998): 149–63. http://dx.doi.org/10.1016/s0166-8641(97)00182-x.

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33

Zubrinić, Darko. "Maximally singular functions in Besov spaces." Archiv der Mathematik 87, no. 2 (August 2006): 154–62. http://dx.doi.org/10.1007/s00013-006-1655-4.

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34

Girgensohn, Roland. "Constructing Singular Functions via Farey Fractions." Journal of Mathematical Analysis and Applications 203, no. 1 (October 1996): 127–41. http://dx.doi.org/10.1006/jmaa.1996.0370.

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35

Araujo, Vitor, and Luciana Salgado. "Infinitesimal Lyapunov functions for singular flows." Mathematische Zeitschrift 275, no. 3-4 (April 5, 2013): 863–97. http://dx.doi.org/10.1007/s00209-013-1163-8.

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36

Ishii, Noburo, and Maho Kobayashi. "Singular values of some modular functions." Ramanujan Journal 24, no. 1 (November 24, 2010): 67–83. http://dx.doi.org/10.1007/s11139-010-9249-y.

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37

Bateniparvar, O., N. Noormohammadi, and B. Boroomand. "Singular functions for heterogeneous composites with cracks and notches; the use of equilibrated singular basis functions." Computers & Mathematics with Applications 79, no. 5 (March 2020): 1461–82. http://dx.doi.org/10.1016/j.camwa.2019.09.008.

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38

Peller, V. V., and N. J. Young. "Superoptimal approximation by meromorphic functions." Mathematical Proceedings of the Cambridge Philosophical Society 119, no. 3 (April 1996): 497–511. http://dx.doi.org/10.1017/s0305004100074375.

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AbstractLet G be a matrix function of type m × n and suppose that G is expressible as the sum of an H∞ function and a continuous function on the unit circle. Suppose also that the (k – 1)th singular value of the Hankel operator with symbol G is greater than the kth singular value. Then there is a unique superoptimal approximant to G in : that is, there is a unique matrix function Q having at most k poles in the open unit disc which minimizes s∞(G – Q) or, in other words, which minimizes the sequencewith respect to the lexicographic ordering, whereand Sj(·) denotes the jth singular value of a matrix. This result is due to the present authors [PY1] in the case k = 0 (when the hypothesis on the Hankel singular values is vacuous) and to S. Treil[T2] in general. In this paper we give a proof of uniqueness by a diagonalization argument, a high level algorithm for the computation of the superoptimal approximant and a recursive parametrization of the set of all optimal solutions of a matrix Nehari—Takagi problem.

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39

Moyano-Fernández, J. J., and W. A. Zúňiga-Galindo. "Motivic zeta functions for curve singularities." Nagoya Mathematical Journal 198 (June 2010): 47–75. http://dx.doi.org/10.1017/s0027763000009934.

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AbstractLetXbe a complete, geometrically irreducible, singular, algebraic curve defined over a field of characteristicpbig enough. Given a local ringOp,x at a rational singular pointPofX, we attached a universal zeta function which is a rational function and admits a functional equation ifOp,x is Gorenstein. This universal zeta function specializes to other known zeta functions and Poincaré series attached to singular points of algebraic curves. In particular, for the local ring attached to a complex analytic function in two variables, our universal zeta function specializes to the generalized Poincaré series introduced by Campillo, Delgado, and Gusein-Zade.

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40

Moyano-Fernández, J. J., and W. A. Zúňiga-Galindo. "Motivic zeta functions for curve singularities." Nagoya Mathematical Journal 198 (June 2010): 47–75. http://dx.doi.org/10.1215/00277630-2009-007.

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AbstractLet X be a complete, geometrically irreducible, singular, algebraic curve defined over a field of characteristic p big enough. Given a local ring Op,x at a rational singular point P of X, we attached a universal zeta function which is a rational function and admits a functional equation if Op,x is Gorenstein. This universal zeta function specializes to other known zeta functions and Poincaré series attached to singular points of algebraic curves. In particular, for the local ring attached to a complex analytic function in two variables, our universal zeta function specializes to the generalized Poincaré series introduced by Campillo, Delgado, and Gusein-Zade.

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41

Faber, V., Thomas A. Manteuffel, Andrew B. White, and G. Milton Wing. "Asymptotic behavior of singular values and singular functions of certain convolution operators." Computers & Mathematics with Applications 12, no. 6 (June 1986): 733–47. http://dx.doi.org/10.1016/0898-1221(86)90058-1.

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42

CHO, KOJI, and ATSUSHI NAKAYASHIKI. "DIFFERENTIAL STRUCTURE OF ABELIAN FUNCTIONS." International Journal of Mathematics 19, no. 02 (February 2008): 145–71. http://dx.doi.org/10.1142/s0129167x08004595.

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The space of Abelian functions of a principally polarized abelian variety (J,Θ) is studied as a module over the ring [Formula: see text] of global holomorphic differential operators on J. We construct a [Formula: see text] free resolution in case Θ is non-singular. As an application, in the case of dimensions 2 and 3, we construct a new linear basis of the space of abelian functions which are singular only on Θ in terms of logarithmic derivatives of the higher-dimensional σ-function.

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43

Wu, Nan, and Zu-Xing Xuan. "On indirect singular points for meromorphic functions." Kodai Mathematical Journal 34, no. 1 (March 2011): 1–15. http://dx.doi.org/10.2996/kmj/1301576757.

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44

DING, Yong, Dashan FAN, and Yibiao PAN. "On Littlewood-Paley functions and singular integrals." Hokkaido Mathematical Journal 29, no. 3 (February 2000): 537–52. http://dx.doi.org/10.14492/hokmj/1350912990.

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45

Lewis, F., and B. Mertzios. "Analysis of singular systems using orthogonal functions." IEEE Transactions on Automatic Control 32, no. 6 (June 1987): 527–30. http://dx.doi.org/10.1109/tac.1987.1104649.

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46

Zelený, Miroslav. "On singular boundary points of complex functions." Mathematika 45, no. 1 (June 1998): 119–33. http://dx.doi.org/10.1112/s002557930001408x.

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47

Iula, Stefano, and Gabriele Mancini. "Extremal functions for singular Moser–Trudinger embeddings." Nonlinear Analysis 156 (June 2017): 215–48. http://dx.doi.org/10.1016/j.na.2017.02.029.

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48

Kovalevsky, Alexander A. "On -functions with a very singular behaviour." Nonlinear Analysis: Theory, Methods & Applications 85 (July 2013): 66–77. http://dx.doi.org/10.1016/j.na.2013.02.017.

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49

Mastroianni, G., and D. Occorsio. "Markov–Sonin Gaussian rule for singular functions." Journal of Computational and Applied Mathematics 169, no. 1 (August 2004): 197–212. http://dx.doi.org/10.1016/j.cam.2003.12.020.

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50

Díaz-García, José A., and Ramón Gutiérrez-Jáimez. "Functions of singular random matrices with applications." TEST 14, no. 2 (December 2005): 475–87. http://dx.doi.org/10.1007/bf02595414.

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