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Journal articles on the topic 'Convex domains'

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Author: Grafiati

Published: 4 June 2021

Last updated: 1 August 2024

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1

Nikolov, Nikolai, Peter Pflug, and W{\l}odzimierz Zwonek. "An example of a bounded $\mathsf C$-convex domain which is not biholomorphic to a convex domain." MATHEMATICA SCANDINAVICA 102, no. 1 (March 1, 2008): 149. http://dx.doi.org/10.7146/math.scand.a-15056.

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We show that the symmetrized bidisc is a $\mathsf C$-convex domain. This provides an example of a bounded $\mathsf C$-convex domain which cannot be exhausted by domains biholomorphic to convex domains.

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2

Pflug, Peter, and Włodzimierz Zwonek. "Regularity of complex geodesics and (non-)Gromov hyperbolicity of convex tube domains." Forum Mathematicum 30, no. 1 (January 1, 2018): 159–70. http://dx.doi.org/10.1515/forum-2016-0217.

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Abstract We deliver examples of non-Gromov hyperbolic tube domains with convex bases (equipped with the Kobayashi distance). This is shown by providing a criterion on non-Gromov hyperbolicity of (non-smooth) domains. The results show the similarity of geometry of the bases of non-Gromov hyperbolic tube domains with the geometry of non-Gromov hyperbolic convex domains. A connection between the Hilbert metric of a convex domain Ω in {\mathbb{R}^{n}} with the Kobayashi distance of the tube domain over the domain Ω is also shown. Moreover, continuity properties up to the boundary of complex geodesics in tube domains with a smooth convex bounded base are also studied in detail.

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3

Bourchtein, Ludmila, and Andrei Bourchtein. "Logarithmically Convex Reinhardt Domains." Ciência e Natura 25, no. 25 (December 9, 2003): 07. http://dx.doi.org/10.5902/2179460x27233.

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The domains of certain types, such as Reinhardt ones, are important in different problems of theory of functions of several complex variables. For instance, any power series of several complex variables converges in the complete logarithmically convex Reinhardt domain. In this article we prove the logarithmic convexity of complete convex Reinhardt domain.

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4

Nikolov, Nikolai, and Pascal J. Thomas. "Convex characterization of linearly convex domains." MATHEMATICA SCANDINAVICA 111, no. 2 (December 1, 2012): 179. http://dx.doi.org/10.7146/math.scand.a-15223.

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5

Herbig, A. K., and J. D. McNeal. "Convex Defining Functions for Convex Domains." Journal of Geometric Analysis 22, no. 2 (November 16, 2010): 433–54. http://dx.doi.org/10.1007/s12220-010-9202-8.

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6

Peters, H. J. M., and P. P. Wakker. "Convex functions on non-convex domains." Economics Letters 22, no. 2-3 (January 1986): 251–55. http://dx.doi.org/10.1016/0165-1765(86)90242-9.

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7

Filipsson, Lars. "ℂ-convexity in infinite-dimensional Banach spaces and applications to Kergin interpolation." International Journal of Mathematics and Mathematical Sciences 2006 (2006): 1–9. http://dx.doi.org/10.1155/ijmms/2006/80846.

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We investigate the concepts of linear convexity andℂ-convexity in complex Banach spaces. The main result is that anyℂ-convex domain is necessarily linearly convex. This is a complex version of the Hahn-Banach theorem, since it means the following: given aℂ-convex domainΩin the Banach spaceXand a pointp∉Ω, there is a complex hyperplane throughpthat does not intersectΩ. We also prove that linearly convex domains are holomorphically convex, and that Kergin interpolation can be performed on holomorphic mappings defined inℂ-convex domains.

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8

Graf, S. Yu. "Harmonic mappings onto R-convex domains." Issues of Analysis 26, no. 2 (June 2019): 37–50. http://dx.doi.org/10.15393/j3.art.2019.6190.

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9

Jacquet, David. "-convex domains with C2boundary." Complex Variables and Elliptic Equations 51, no. 4 (April 2006): 303–12. http://dx.doi.org/10.1080/17476930600585738.

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10

Joiţa, Cezar. "Traces of convex domains." Proceedings of the American Mathematical Society 131, no. 9 (April 21, 2003): 2721–25. http://dx.doi.org/10.1090/s0002-9939-03-07119-3.

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11

Arango, Juan, and Diego Mejía. "Hyperbolically convex constricted domains." Journal of Mathematical Analysis and Applications 366, no. 2 (June 2010): 636–45. http://dx.doi.org/10.1016/j.jmaa.2009.12.017.

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12

Zając, Sylwester, and Paweł Zapałowski. "Complex geodesics in convex domains and ℂ-convexity of semitube domains." Advances in Geometry 21, no. 2 (April 1, 2021): 149–62. http://dx.doi.org/10.1515/advgeom-2020-0009.

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Abstract In this paper the complex geodesics of a convex domain in ℂ n are studied. One of the main results provides a certain necessary condition for a holomorphic map to be a complex geodesic for a convex domain in ℂ n . The established condition is of geometric nature and it allows to find a formula for every complex geodesic. The ℂ-convexity of semitube domains is also discussed.

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13

Dovhopiatyi, Oleksandr, and Evgeny Sevost'yanov. "On the application of one modulus inequality to the mapping theory." Proceedings of the Institute of Applied Mathematics and Mechanics NAS of Ukraine 37 (January 23, 2024): 104–17. http://dx.doi.org/10.37069/1683-4720-2023-37-10.

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The authors study mappings that satisfy some estimate of the distortion of the modulus of families of paths. Under certain conditions on the domains between which the mappings act, we established that, these mappings are Hölder logarithmic continuous at the boundary points. It is known that, the Hölder continuity is established for many classes of mappings, say quasiconformal and quasiregular mappings. In this regard, it is possible to point to the classical distortion estimates by Martio-Rickman-Väisälä type, as well as the estimates related to the modern classes of mappings with finite distortion. In particular, V.I. Ryazanov together with R.R. Salimov and E.O. Sevost'yanov established local distortion estimates for plane and spatial mappings under FMO condition, or under the Lehto-type integral condition. Recently, the second co-author have obtained Hölder logarithmic continuity for the studied class at points of the unit sphere. This article considers the situation of similar mappings of different domains, not only the unit sphere. Namely, we consider mappings between quasiextremal distance domains (QED-domains) and convex domains. Note that, quasiextremal distance domains introduced by Gehring and Martio are structures in which the modulus of families of paths is metrically related to the diameter of sets. Also, convex domains are involved in the formulation of the main result; we consider mappings that surjectively act onto them. In addition, the article contains the formulations and proofs for some other results on this topic. We consider several more cases in detail, in particular when: 1) the definition domain is a domain with a locally quasiconformal boundary, and the image domain is a bounded convex domain; 2) the definition domain is a regular domain in the sense of prime ends, and the image domain is a bounded convex domain; 3) the mapping acts between the QED-domain and the bounded convex domain and has a fixed point. In all three cases, the mapping is Hölder logarithmic continuous; moreover, in case 2), which refers to prime ends, logarithmic continuity should also be understood in terms of prime ends.

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14

Groemer, H. "Stability Theorems for Convex Domains of Constant Width." Canadian Mathematical Bulletin 31, no. 3 (September 1, 1988): 328–37. http://dx.doi.org/10.4153/cmb-1988-048-3.

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AbstractIt is known that among all plane convex domains of given constant width Reuleaux triangles have minimal and circular discs have maximal area. Some estimates are given concerning the following associated stability problem: If K is a convex domain of constant width w and if the area of K differs at most ∊ from the area of a Reuleaux triangle or a circular disc of width w, how close (in terms of the Hausdorff distance) is K to a Reuleaux triangle or a circular disc? Another result concerns the deviation of a convex domain M of diameter d from a convex domain of constant width if the perimeter of M is close to πd.

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15

Abu-Muhanna, Yusuf, and Glenn Schober. "Harmonic Mappings onto Convex Domains." Canadian Journal of Mathematics 39, no. 6 (December 1, 1987): 1489–530. http://dx.doi.org/10.4153/cjm-1987-071-4.

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Let D be a simply-connected domain and w0 a fixed point of D. Denote by SD the set of all complex-valued, harmonic, orientation-preserving, univalent functions f from the open unit disk U onto D with f(0) = w0. Unlike conformai mappings, harmonic mappings are not essentially determined by their image domains. So, it is natural to study the set SD.In Section 2, we give some mapping theorems. We prove the existence, when D is convex and unbounded, of a univalent, harmonic solution f of the differential equationwhere a is analytic and |a| < 1, such that f(U) ⊂ D and

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16

Djuric, Nemanja, Mihajlo Grbovic, and Slobodan Vucetic. "Convex Kernelized Sorting." Proceedings of the AAAI Conference on Artificial Intelligence 26, no. 1 (September 20, 2021): 893–99. http://dx.doi.org/10.1609/aaai.v26i1.8314.

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Kernelized sorting is a method for aligning objects across two domains by considering within-domain similarity, without a need to specify a cross-domain similarity measure. In this paper we present the Convex Kernelized Sorting method where, unlike in the previous approaches, the cross-domain object matching is formulated as a convex optimization problem, leading to simpler optimization and global optimum solution. Our method outputs soft alignments between objects, which can be used to rank the best matches for each object, or to visualize the object matching and verify the correct choice of the kernel. It also allows for computing hard one-to-one alignments by solving the resulting Linear Assignment Problem. Experiments on a number of cross-domain matching tasks show the strength of the proposed method, which consistently achieves higher accuracy than the existing methods.

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17

Piper, Jim, and Erik Granum. "Computing distance transformations in convex and non-convex domains." Pattern Recognition 20, no. 6 (1987): 599–615. http://dx.doi.org/10.1016/0031-3203(87)90030-6.

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18

Burns, Keith. "Convex Supporting Domains on Surfaces." Bulletin of the London Mathematical Society 17, no. 3 (May 1985): 271–74. http://dx.doi.org/10.1112/blms/17.3.271.

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19

Jerison, David. "Harmonic measure in convex domains." Bulletin of the American Mathematical Society 21, no. 2 (October 1, 1989): 255–61. http://dx.doi.org/10.1090/s0273-0979-1989-15823-0.

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20

Adivar, Murat, and Shu-Cherng Fang. "Convex optimization on mixed domains." Journal of Industrial & Management Optimization 8, no. 1 (2012): 189–227. http://dx.doi.org/10.3934/jimo.2012.8.189.

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21

Väisälä, Jussi. "Quasihyperbolic geodesics in convex domains." Results in Mathematics 48, no. 1-2 (August 2005): 184–95. http://dx.doi.org/10.1007/bf03322906.

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22

Brudnyi, Yu. "Polynomial approximation in convex domains." Journal of Approximation Theory 236 (December 2018): 36–53. http://dx.doi.org/10.1016/j.jat.2018.08.001.

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23

Vâjâitu, Viorel. "Neighborhoods of Leviq-convex domains." Journal of Geometric Analysis 8, no. 1 (January 1998): 163–77. http://dx.doi.org/10.1007/bf02922113.

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24

Bland, J., and T. Duchamp. "Moduli for pointed convex domains." Inventiones mathematicae 104, no. 1 (December 1991): 61–112. http://dx.doi.org/10.1007/bf01245067.

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25

McNeal, Jeffery D. "Convex domains of finite type." Journal of Functional Analysis 108, no. 2 (September 1992): 361–73. http://dx.doi.org/10.1016/0022-1236(92)90029-i.

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26

Maz′ya, V. "Elliptic equations in convex domains." St. Petersburg Mathematical Journal 29, no. 1 (December 27, 2017): 155–64. http://dx.doi.org/10.1090/spmj/1486.

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27

Edigarian, Armen. "Kobayashi isometries in convex domains." Proceedings of the American Mathematical Society 147, no. 12 (July 1, 2019): 5257–61. http://dx.doi.org/10.1090/proc/14681.

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28

Shimizu, Satoru. "A Remark on Homogeneous Convex Domains." Nagoya Mathematical Journal 105 (March 1987): 1–7. http://dx.doi.org/10.1017/s0027763000000696.

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In this note, by a homogeneous convex domain in Rn we mean a convex domain Ω in Rn containing no complete straight lines on which the group G(Ω) of all affine transformations of Rn leaving Ω invariant acts transitively. Let Ω be a homogeneous convex domain. Then Ω admits a G(©)-invariant Riemannian metric which is called the canonical metric (see [11]). The domain Ω endowed with the canonical metric is a homogeneous Riemannian manifold and we denote by I(Ω) the group of all isometries of it. A homogeneous convex domain Ω is called reducible if there is a direct sum decomposition of thé ambient space Rn = Rn1 × Rn2, ni > 0, such that Ω = Ω1 × 02 with Ωi a homogeneous convex domain in Rni; and if there is no such decomposition, then Ω is called irreducible.

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29

Cavoretto, R., A. De Rossi, and E. Perracchione. "Partition of unity interpolation on multivariate convex domains." International Journal of Modeling, Simulation, and Scientific Computing 06, no. 04 (December 2015): 1550034. http://dx.doi.org/10.1142/s1793962315500348.

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In this paper, we present an algorithm for multivariate interpolation of scattered data sets lying in convex domains [Formula: see text], for any [Formula: see text]. To organize the points in a multidimensional space, we build a [Formula: see text]-tree space-partitioning data structure, which is used to efficiently apply a partition of unity interpolant. This global scheme is combined with local radial basis function (RBF) approximants and compactly supported weight functions. A detailed description of the algorithm for convex domains and a complexity analysis of the computational procedures are also considered. Several numerical experiments show the performances of the interpolation algorithm on various sets of Halton data points contained in [Formula: see text], where [Formula: see text] can be any convex domain, like a 2D polygon or a 3D polyhedron. Finally, an application to topographical data contained in a pentagonal domain is presented.

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30

YANG, YUNLONG, and DEYAN ZHANG. "DEFORMING A CONVEX DOMAIN INTO A DISK BY KLAIN’S CYCLIC REARRANGEMENT." Bulletin of the Australian Mathematical Society 97, no. 2 (February 20, 2018): 313–19. http://dx.doi.org/10.1017/s0004972717001113.

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For a convex domain, we use Klain’s cyclic rearrangement to obtain a sequence of convex domains with increasing area and the same perimeter which converges to a disk. As a byproduct, we give a proof of the classical isoperimetric inequality in the plane.

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31

Qian, Qi, Shenghuo Zhu, Jiasheng Tang, Rong Jin, Baigui Sun, and Hao Li. "Robust Optimization over Multiple Domains." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 4739–46. http://dx.doi.org/10.1609/aaai.v33i01.33014739.

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In this work, we study the problem of learning a single model for multiple domains. Unlike the conventional machine learning scenario where each domain can have the corresponding model, multiple domains (i.e., applications/users) may share the same machine learning model due to maintenance loads in cloud computing services. For example, a digit-recognition model should be applicable to hand-written digits, house numbers, car plates, etc. Therefore, an ideal model for cloud computing has to perform well at each applicable domain. To address this new challenge from cloud computing, we develop a framework of robust optimization over multiple domains. In lieu of minimizing the empirical risk, we aim to learn a model optimized to the adversarial distribution over multiple domains. Hence, we propose to learn the model and the adversarial distribution simultaneously with the stochastic algorithm for efficiency. Theoretically, we analyze the convergence rate for convex and non-convex models. To our best knowledge, we first study the convergence rate of learning a robust non-convex model with a practical algorithm. Furthermore, we demonstrate that the robustness of the framework and the convergence rate can be further enhanced by appropriate regularizers over the adversarial distribution. The empirical study on real-world fine-grained visual categorization and digits recognition tasks verifies the effectiveness and efficiency of the proposed framework.

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32

Liu, Taishun, and Guangbin Ren. "Growth theorem of convex mappings on bounded convex circular domains." Science in China Series A: Mathematics 41, no. 2 (February 1998): 123–30. http://dx.doi.org/10.1007/bf02897437.

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33

Pankratov, A., T. Romanova, and A. Kotelevskiy. "Layout problems for arc objects in convex domains." Journal of Mechanical Engineering 19, no. 3 (September 30, 2016): 43–60. http://dx.doi.org/10.15407/pmach2016.03.043.

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34

SINGH, I. V., B. K. MISHRA, and MOHIT PANT. "AN EFFICIENT PARTIAL DOMAIN ENRICHED ELEMENT-FREE GALERKIN METHOD CRITERION FOR CRACKS IN NONCONVEX DOMAINS." International Journal of Modeling, Simulation, and Scientific Computing 02, no. 03 (September 2011): 317–36. http://dx.doi.org/10.1142/s1793962311000475.

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In the present work, an efficient partial domain, intrinsic, enriched element-free Galerkin criterion has been extended to simulate the cracks lying in nonconvex domains. According to this criterion, only a part of the domain near the crack tip has been enriched. A linear ramp function has been used to avoid the sudden truncation of the enrichment effect. Some cases of cracks lying in convex as well as in nonconvex domains have been solved by both full and partial domain enrichment criteria under plane stress conditions. For the cracks lying in convex domain, the results obtained by full domain enrichment criterion are found in good agreement with those obtained by partial domain enrichment criterion, whereas for cracks lying in nonconvex domain, the results obtained by full domain enrichment criterion are found to be misleading. The partial domain enrichment not only accurately simulates the cracks in nonconvex domains but also reduces the computational cost of the method.

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35

Abate, Marco, and Roberto Tauraso. "The Lindelöf principle and angular derivatives in convex domains of finite type." Journal of the Australian Mathematical Society 73, no. 2 (October 2002): 221–50. http://dx.doi.org/10.1017/s1446788700008818.

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AbstractWe describe a generalization of the classical Julia-Wolff-Carathéodory theorem to a large class of bounded convex domains of finite type, including convex circular domains and convex domains with real analytic boundary. The main tools used in the proofs are several explicit estimates on the boundary behaviour of Kobayashi distance and metric, and a new Lindelöf principle.

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36

Nasibullin, Ramil' Gaisaevich. "Hardy type inequalities for one weight function and their applications." Izvestiya: Mathematics 87, no. 2 (2023): 362–88. http://dx.doi.org/10.4213/im9291e.

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New one-dimensional Hardy-type inequalities for a weight function of the form $x^\alpha(2-x)^\beta$ for positive and negative values of the parameters $\alpha$ and $\beta$ are put forward. In some cases, the constants in the resulting one-dimensional inequalities are sharp. We use one-dimensional inequalities with additional terms to establish multivariate inequalities with weight functions depending on the mean distance function or the distance function from the boundary of a domain. Spatial inequalities are proved in arbitrary domains, in Davies-regular domains, in domains satisfying the cone condition, in $\lambda$-close to convex domains, and in convex domains. The constant in the additional term in the spatial inequalities depends on the volume or the diameter of the domain. As a consequence of these multivariate inequalities, estimates for the first eigenvalue of the Laplacian under the Dirichlet boundary conditions in various classes of domains are established. We also use one-dimensional inequalities to obtain new classes of meromorphic univalent functions in simply connected domains. Namely, Nehari-Pokornii type sufficient conditions for univalence are obtained.

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37

SABER, SAYED. "The ∂ Cauchy-Problem on Weakly q-Convex Domains in CPn." Kragujevac Journal of Mathematics 44, no. 4 (December 2020): 581–91. http://dx.doi.org/10.46793/kgjmat2004.581s.

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Let D be a weakly q-convex domain in the complex projective space ℂPn. In this paper, the (weighted) ∂-Cauchy problem with support conditions in D is studied. Speciﬁcally, the modiﬁed weight function method is used to study the L2 existence theorem for the ∂-Neumann problem on D. The solutions are used to study function theory on weakly q-convex domains via the ∂-Cauchy problem.

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38

Range, R. "On ∂̅-problems on (pseudo)-convex domains." Banach Center Publications 31, no. 1 (1995): 311–20. http://dx.doi.org/10.4064/-31-1-311-320.

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39

R. Alcantud, José Carlos, and Jianming Zhan. "Convex rough sets on finite domains." Information Sciences 611 (September 2022): 81–94. http://dx.doi.org/10.1016/j.ins.2022.08.013.

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40

Kaljaj, David. "Quasiconformal harmonic functions between convex domains." Publications de l'Institut Mathematique 75, no. 89 (2004): 139–46. http://dx.doi.org/10.2298/pim0475139k.

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41

Kalaj, David. "Quasiconformal harmonic functions between convex domains." Publications de l'Institut Mathematique 76, no. 90 (2004): 3–20. http://dx.doi.org/10.2298/pim0476003k.

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42

Li, Jian-Lin. "Schwarz-Pick inequalities for convex domains." Kodai Mathematical Journal 30, no. 2 (June 2007): 252–62. http://dx.doi.org/10.2996/kmj/1183475516.

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43

Atıcı, Ferhan M., and Hatice Yaldız. "Convex Functions on Discrete Time Domains." Canadian Mathematical Bulletin 59, no. 2 (June 1, 2016): 225–33. http://dx.doi.org/10.4153/cmb-2015-065-6.

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AbstractIn this paper, we introduce the definition of a convex real valued function f defined on the set of integers, ℤ. We prove that f is convex on Z if and only if Δ2 f ≥ 0 on ℤ. As a first application of this new concept, we state and prove discrete Hermite–Hadamard inequality using the basics of discrete calculus (i.e., the calculus on Z). Second, we state and prove the discrete fractional Hermite–Hadamard inequality using the basics of discrete fractional calculus. We close the paper by defining the convexity of a real valued function on any time scale.

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44

Martio, Olli, and Jussi Vaisala. "Quasihyperbolic Geodesics in Convex Domains II." Pure and Applied Mathematics Quarterly 7, no. 2 (2011): 395–409. http://dx.doi.org/10.4310/pamq.2011.v7.n2.a7.

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45

Chavel, Isaac. "Heat Diffusion in Insulated Convex Domains." Journal of the London Mathematical Society s2-34, no. 3 (December 1986): 473–78. http://dx.doi.org/10.1112/jlms/s2-34.3.473.

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46

Peyerimhoff, Norbert. "Areas and Intersections in Convex Domains." American Mathematical Monthly 104, no. 8 (October 1997): 697. http://dx.doi.org/10.2307/2975231.

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47

Kot, Piotr. "Homogeneous polynomials on strictly convex domains." Proceedings of the American Mathematical Society 135, no. 12 (December 1, 2007): 3895–904. http://dx.doi.org/10.1090/s0002-9939-07-08939-3.

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48

Colbois, Bruno, and Patrick Verovic. "Hilbert Geometry for Strictly Convex Domains." Geometriae Dedicata 105, no. 1 (April 2004): 29–42. http://dx.doi.org/10.1023/b:geom.0000024687.23372.b0.

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49

Cieślak, W., S. Koshi, and J. Zajac. "On integral formulas for convex domains." Acta Mathematica Hungarica 62, no. 3-4 (September 1993): 277–83. http://dx.doi.org/10.1007/bf01874648.

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50

Jerison, David. "Prescribing harmonic measure on convex domains." Inventiones Mathematicae 105, no. 1 (December 1991): 375–400. http://dx.doi.org/10.1007/bf01232271.

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