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AN EXTREMAL PROBLEM FOR UNIVALENT FUNCTIONS [PDF]
Analele Universităţii Constantin Brâncuşi din Târgu Jiu : Seria Economie, 2010 Let S be the class of functions f(z)=z+a2z 2 …, f(0)=0, f′(0)=1 which are regular and univalent in the unit disk |z| x the equation φ′( x)=0 does not have real roots. Since S is a compact class, there exists x .
Miodrag IOVANOV
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Extremality of Koebe’s Function
AxiomsThe remarkable Koebe function is the (unique) extremal of many important distortion functionals in geometric function theory. This paper provides a complete characterization of such functionals.
Samuel L. Krushkal
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On the existence of an extremal function for the Delsarte extremal problem
Analysis MathematicaAbstract In the general setting of a locally compact Abelian group G, the Delsarte extremal problem asks for the supremum of integrals over the collection of continuous positive definite functions $$f \colon G \to \mathbb{R}$$ f :
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On the Existence of an Extremal Function in the Delsarte Extremal Problem [PDF]
Mediterranean Journal of Mathematics, 2020 AbstractThis paper is concerned with a Delsarte-type extremal problem. Denote by$${\mathcal {P}}(G)$$P(G)the set of positive definite continuous functions on a locally compact abelian groupG. We consider the function class, which was originally introduced by Gorbachev,$$\begin{aligned}&{\mathcal {G}}(W, Q)_G = \left\{ f \in {\mathcal {P}}(G) \cap L^
Marcell Gaál, Zsuzsanna Nagy-Csiha
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A Functional Extremal Criterion [PDF]
Journal of Mathematical Sciences, 2004 Let \({\mathcal N}=\{(t_k, X_k):\, k\geq 1\}\) be a point process with time space \([0, \infty)\) and state space \([0, \infty)^d\), where \(\{t_k\}\) are distinct nonrandom time points monotonically increasing to \(\infty\). \(\{X_k\}\) are independent and identically distributed random vectors on a given probability space with values in \([0,\infty ...
Jordanova, P. K., Pancheva, E. I.
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On the extremal function for graph minors [PDF]
Journal of Graph Theory, 2022 AbstractFor a graph , let , where means that is a minor of . We show that if has average degree , then where is an explicitly defined constant. This bound matches a corresponding lower bound shown to hold for almost all such by Norin, Reed, Wood and the first author.
Andrew Thomason 0001, Matthew Wales
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Approximation of Minimal Functions by Extreme Functions [PDF]
SIAM Journal on Optimization, 2018 In a recent paper, Basu, Hildebrand, and Molinaro established that the set of continuous minimal functions for the 1-dimensional Gomory-Johnson infinite group relaxation possesses a dense subset of extreme functions. The $n$-dimensional version of this result was left as an open question.
Teresa M. Lebair, Amitabh Basu
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On an Optimal Quadrature Formula in a Hilbert Space of Periodic Functions
Algorithms, 2022 The present work is devoted to the construction of optimal quadrature formulas for the approximate calculation of the integrals ∫02πeiωxφ(x)dx in the Sobolev space H˜2m.
Kholmat Shadimetov +2 more
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Construction of optimal interpolation formula exact for trigonometric functions by Sobolev’s method
Vestnik KRAUNC: Fiziko-Matematičeskie Nauki, 2022 The paper is devoted to derivation of the optimal interpolation formula in W2(0,2)(0,1) Hilbert space by Sobolev’s method. Here the interpolation formula consists of a linear combination ΣNβ=0Cβφ(xβ) of the given values of a function φ from the space ...
Shadimetov, Kh.M. +2 more
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Entropy of an extremal electrically charged thin shell and the extremal black hole
Physics Letters B, 2015 There is a debate as to what is the value of the entropy S of extremal black holes. There are approaches that yield zero entropy S=0, while there are others that yield the Bekenstein–Hawking entropy S=A+/4, in Planck units.
José P.S. Lemos +2 more
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