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 differ...
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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.
In this note it is proved that the integral arithmetic mean of a convex function is a schur-convex function. Applications to schur-convexity of logarithmic mean and gamma functions are given.
In this note it is proved that the integral arithmetic mean of a convex function is a schur-convex function. Applications to schur-convexity of logarithmic mean and gamma functions are given.
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 ...
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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.
The positive dependence of a subclass of multivariate exponential distributions is examined. This class is characterized by an index vector k and a parameter vector lambda, which are used as an ordering to yield degre...
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The positive dependence of a subclass of multivariate exponential distributions is examined. This class is characterized by an index vector k and a parameter vector lambda, which are used as an ordering to yield degrees of positive dependence. The results presented have a direct implication on the reliability function of a system and the survival probability function of a shock model, and consequently on the optimal assembly of systems.
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 ...
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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.
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...
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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 area-ratio function is not concave in their respective domain.
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...
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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 current results in the literature could be improved. (C) 2013 Elsevier B.V. All rights reserved.
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...
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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 probabili...
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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.
The strong schur-convexity of the integral mean as well as of the left and right gaps in the Hermite-Hadamard inequality for strongly convexfunctions are proved. An useful characterization of strongly schurconvex fu...
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The strong schur-convexity of the integral mean as well as of the left and right gaps in the Hermite-Hadamard inequality for strongly convexfunctions are proved. An useful characterization of strongly schurconvexfunctions 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.
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