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Strong schur-convexity of the Integral Mean

RESULTS IN MATHEMATICS 2023年第2期78卷 1-12页

作者： Adamek, Miroslaw Bakula, Milica Klaricic Nikodem, Kazimierz Univ Bielsko Biala Dept Math Ul Willowa 2 PL-43309 Bielsko Biala Poland Univ Split Fac Sci Rudera Boskovica 33 Split 21000 Croatia

The strong schur-convexity of the integral mean as well as of the left and right gaps in the Hermite-Hadamard inequality for strongly convex functions are proved. An useful characterization of strongly schur convex functions F : I-n -> R by partial derivatives is given. As an application, a result on the strong schur-concavity of the integral mean of the digamma function is obtained.

关键词： schur-convex functions strongly schur-convex functions strongly convex functions

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New Versions of Uniformly convex functions via Quadratic Complete Homogeneous Symmetric Polynomials

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MEDITERRANEAN JOURNAL OF MATHEMATICS 2023年第5期20卷 279-279页

作者： Lachescu, Geanina Maria Malin, Maria Roventa, Ionel Univ Craiova Dept Math AI Cuza St 13 Craiova 200585 Romania

We introduce new versions of uniformly convex functions, namely h(d) strongly (weaker) convex functions. Based on the positivity of complete homogeneous symmetric polynomials with even degree, recently studied in Roventa and Temereanc (Mediterr J Math 16:1- 16, 2019), Rovent,a et al. (A note on weighted Ingham's inequality for families of exponentials with no gap, In: 24th ICSTCC, pp 43-48, 2020;Weighted Ingham's type inequalities via the positivity of quadratic polynomials, submitted), and Tao (https://***/2017/ 08/06/schur-convexity-and-positive-definiteness-of-the-even-degree-complete-homogeneous-symmetric-polynomials/), we introduce stronger and weaker versions of uniformly convexity. In this context, we recover well-known type inequalities such as: Jensen's, Hardy-Littlewood- Polya's and Popoviciu's inequalities. Some final remarks related to Sherman's and Ingham's type inequalities are also discussed.

关键词： & nbsp Complete homogeneous symmetric polynomials uniformly convex functions h(d) strongly convex function schur-convex functions majorization theory

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On the Design of Amplify-and-Forward MIMO-OFDM Relay Systems With QoS Requirements Specified as schur-convex functions of the MSEs

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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY 2013年第4期62卷 1871-1877页

作者： Sanguinetti, Luca D'Amico, Antonio A. Rong, Yue Univ Pisa Dept Informat Engn I-56126 Pisa Italy Curtin Univ Technol Dept Elect & Comp Engn Bentley WA 6102 Australia

In this paper, we focus on the design of linear and nonlinear architectures in amplify-and-forward multiple-input-multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) relay networks in which different types of services are supported. The goal is to jointly optimize the processing matrices to minimize the total power consumption while satisfying the quality-of-service (QoS) requirements of each service specified as schur-convex functions of the mean square errors (MSEs) over all assigned subcarriers. It turns out that the optimal solution leads to the diagonalization of the source-relay-destination channel up to a unitary matrix, depending on the specific schur-convex function.

关键词： Amplify-and-forward multiple-input multiple-output (MIMO) nonregenerative relay orthogonal frequency-division multiplexing (OFDM) power minimization quality-of-service (QoS) requirements schur-convex functions transceiver design

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OPTIMIZATION RESULTS FOR A GENERALIZED COUPON COLLECTOR PROBLEM

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JOURNAL OF APPLIED PROBABILITY 2016年第2期53卷 622-629页

作者： Anceaume, Emmanuelle Busnel, Yann Schulte-Geers, Ernst Sericola, Bruno CNRS Campus Beaulieu F-35042 Rennes France Ensai Campus Ker LannBP 37203 F-35172 Bruz France BSI Godesberger Allee 185-189 D-53175 Bonn Germany Inria Campus Beaulieu F-35042 Rennes France

In this paper we study a generalized coupon collector problem, which consists of analyzing the time needed to collect a given number of distinct coupons that are drawn from a set of coupons with an arbitrary probability distribution. We suppose that a special coupon called the null coupon can be drawn but never belongs to any collection. In this context, we prove that the almost uniform distribution, for which all the nonnull coupons have the same drawing probability, is the distribution which stochastically minimizes the time needed to collect a fixed number of distinct coupons. Moreover, we show that in a given closed subset of probability distributions, the distribution with all its entries, but one, equal to the smallest possible value is the one which stochastically maximizes the time needed to collect a fixed number of distinct coupons.

关键词： Coupon collector problem optimization schur-convex functions

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New bounds of degree-based topological indices for some classes of c-cyclic graphs

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DISCRETE APPLIED MATHEMATICS 2015年 184卷 62-75页

作者： Bianchi, Monica Cornaro, Alessandra Palacios, Jose Luis Torriero, Anna Catholic Univ Dept Math & Econometr Milan Italy Univ New Mexico Dept Elect & Comp Engn Albuquerque NM 87131 USA

Making use of a majorization technique for a suitable class of graphs, we derive upper and lower bounds for some topological indices depending on the degree sequence over all vertices, namely the first general Zagreb index and the first multiplicative Zagreb index. Specifically, after characterizing c-cyclic graphs (0 <= c <= 6) as those whose degree sequence belongs to particular subsets of R-n, we identify the maximal and minimal vectors of these subsets with respect to the majorization order. This technique allows us to determine lower and upper bounds of the above indices recovering some existing results in the literature as well as obtaining new ones. (C) 2015 Published by Elsevier B.V.

关键词： Majorization schur-convex functions c-cyclic graphs Zagreb indices

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A majorization method for localizing graph topological indices

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DISCRETE APPLIED MATHEMATICS 2013年第16-17期161卷 2731-2739页

作者： Bianchi, Monica Cornaro, Alessandra Torriero, Anna Univ Cattolica Sacro Cuore Dept Math & Econometr I-20123 Milan Italy

This paper presents a unified approach for localizing some relevant graph topological indices via majorization techniques. Using this method, we derive old and new bounds. Numerical examples are provided showing how c... 详细信息

关键词： Majorization schur-convex functions Graphs Topological indices

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Bounds for the Kirchhoff index via majorization techniques

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JOURNAL OF MATHEMATICAL CHEMISTRY 2013年第2期51卷 569-587页

作者： Bianchi, Monica Cornaro, Alessandra Luis Palacios, Jose Torriero, Anna Catholic Univ Dept Math & Econometr Milan Italy Univ Simon Bolivar Dept Sci Comp & Stat Caracas Venezuela

Using a majorization technique that identifies the maximal and minimal vectors of a variety of subsets of R-n, we find upper and lower bounds for the Kirchhoff index K(G) of an arbitrary simple connected graph G that improve those existing in the literature. Specifically we show that K(G) >= n/d1 [1/1 + sigma/root n-1 + (n-2)(2)/n - 1 - sigma/root n-1], where d(1) is the largest degree among all vertices in G, sigma(2) = 2/n Sigma((i,j)is an element of E) 1/d(i)d(j) = (2/n) R-1(G), and R-1(G) is the general Randic index of G for alpha = -1. Also we show that K(G) <= n/d(n) (n - k - 2/1 - lambda(2) + k/2 + 1/theta), where d(n) is the smallest degree, lambda(2) is the second eigenvalue of the transition probability of the random walk on G, k = [lambda(2)(n - 1) + 1/lambda(2) + 1] and theta = lambda(2) (n - k - 2) - k + 2.

关键词： Majorization schur-convex functions Graphs Kirchhoff index

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NON-convexITY OF THE DIMENSION FUNCTION FOR SIERPINSKI PEDAL TRIANGLES

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FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY 2010年第2期18卷 191-195页

作者： Ding, Jiu Tang, Yifa Univ So Mississippi Dept Math Hattiesburg MS 39406 USA Chinese Acad Sci State Key Lab Sci & Engn Comp Acad Math & Syst Sci Beijing 100190 Peoples R China

We disprove the conjecture of the paper by Zhang et al.(1) on the schur-convexity of the dimension function for the family of Sierpinski pedal triangles. We also show that this function is not convex and the related a... 详细信息

关键词： Sierpinski Pedal Triangles Sierpinski Triangle Moran Equation Fractal Dimension schur-convex functions convex functions

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On the minimization of multinomial tails and the Gupta-Nagel conjecture

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JOURNAL OF MULTIVARIATE ANALYSIS 2005年第1期94卷 70-108页

作者： Gastaldi, T Univ Roma La Sapienza Dipartimento Stat Probabil & Stat Applicate I-00185 Rome Italy

This paper is primarily concerned with the open problem of minimizing the lower tail of the multmomial distribution. During the study of that specific problem, we have developed an approach which reveals itself useful for solving a general class of problems involving multinomial probabilities. Concerning the main problem, we provide a self-contained proof that the minimum of the multinomial lower tail is reached, as conjectured by Gupta and Nagel (Sankhya Ser. B 29 (1967) 1) (within the framework of subset-selection problems) at the equal probability configuration, i.e., when the cell probabilities are equal to one another. We also point out some novel inequalities and general properties involving multinomial probabilities and multinomial coefficients. © 2004 Elsevier Inc. All rights reserved.

关键词： multinomial distribution lower tail best selection subset selection indifference-zone selection multinomial coefficients partitions of integer pascal triangle schur-convex functions

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Algebraic theory of optimal filterbanks

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2003年第2期51卷 442-457页

作者： Jahromi, OS Francis, BA Kwong, RH Univ Toronto Dept Elect & Comp Engn Toronto ON M5S 3G4 Canada

We introduce an optimality theory for finite impulse response (FIR) filterbanks using a general algebraic point of view. We consider an admissible set L of FIR filterbanks and use scalability as the main notion based on which performance of the elements in L are compared. We show that quantification of scalability leads naturally to a partial ordering on the set L. An optimal solution is, therefore, represented by the greatest element in L. It turns out that a greatest element does not necessarily exist in L. Hence, one has to settle with one of the maximal elements that exist in L. We provide a systematic way of finding a maximal element by embedding the partial ordering at hand in a total ordering. This is done by using a special class of order-preserving functions known as schur-convex. There is, however, a price to pay for achieving a total ordering: There are infinitely many possible choices for schur-convex functions, and the optimal solution specified in L depends on this (subjective) choice. An interesting aspect of the presented algebraic theory is that the connection between several concepts, namely, principal component filterbanks (PCFBs), filterbanks with maximum coding gain, and filterbanks with good scalability, is clearly revealed. We show that these are simply associated with different extremal elements of the partial ordering induced on L by scalability.

关键词： compression applications filterbanks majorization theory multiresolution coding multiscale representation optimal filtering partial ordering principal component filterbank progressive transmission quadrature mirror filters scalability schur-convex functions subband coding successively refinable coding

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