schurconvexity, schur geometrical convexity and schur harmonic convexityof a class of symmetric functions are investigated. As consequences some knowninequalities are generalized. In addition, a class of geometric in...
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schurconvexity, schur geometrical convexity and schur harmonic convexityof a class of symmetric functions are investigated. As consequences some knowninequalities are generalized. In addition, a class of geometric inequalities involvingn-dimensional simplex in n-dimensional Euclidean space En and several matrix inequalitiesare established to show the applications of our results.
Recently, there has been a lot of attention in the literature on a less well-known aspect of queueing theory, the theory of the constructions of queues. Such an interest originates mainly from optical packet switching...
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Recently, there has been a lot of attention in the literature on a less well-known aspect of queueing theory, the theory of the constructions of queues. Such an interest originates mainly from optical packet switching due to the lack of optical buffers. These constructions of optical queues are based on optical switches and fiber delay lines (SDL). Theoretical studies in the SDL constructions have been recently reported for the constructions of various types of optical queues, including output-buffered switches, first-in-first-out (FIFO) multiplexers, FIFO queues, last-in-first-out (LIFO) queues, priority queues, linear compressors, nonovertaking delay lines, and flexible delay lines. In this paper, we consider the constructions of optical 2-to-1 FIFO multiplexers with a limited number of recirculations through the fibers, which is a very important practical feasibility issue on the constructions of optical queues that has not been theoretically addressed before. Specifically, we consider the constructions of optical 2-to-1 FIFO multiplexers with buffer size at least 2(n)-1 by using a feedback system consisting of an (M + 2) x (M + 2) optical crossbar switch and M fiber delay lines under a simple packet routing policy and under the limitation that each packet can be recirculated through the M fibers at most k times. In one of our previous works, we have shown that this can be done by using n fibers with delays 1, 2, 2(2) ,..., 2(n-1) if there is no limitation on the number of recirculations through the fibers. The main idea in our constructions in this paper is to use extra fibers (other than the n fibers with delays 1, 2, 2(2) ,..., 2(n-1) with appropriately chosen delays to emulate the effective delays of the concatenations of some of the n fibers with delays 1, 2, 2(2) ,..., 2(n-1) so that the number of recirculations is reduced by so doing. It turns out that the number of fibers needed and their delays are determined based on a dynamic programming formulation ob
Consider the problem of partitioning n nonnegative numbers into p parts, where part i can be assigned n(i) numbers with n(i) lying in a given range. The goal is to maximize a schur convex function F whose ith argument...
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Consider the problem of partitioning n nonnegative numbers into p parts, where part i can be assigned n(i) numbers with n(i) lying in a given range. The goal is to maximize a schur convex function F whose ith argument is the sum of numbers assigned to part i. The shape of a partition is the vector consisting of the sizes of its parts, further, a shape (without referring to a particular partition) is a vector of nonnegative integers (n(1),..., n(p)) which sum to n. A partition is called size-consecutive if there is a ranking of the parts which is consistent with their sizes, and all elements in a higher-ranked part exceed all elements in the lower-ranked part. We demonstrate that one can restrict attention to size-consecutive partitions with shapes that are nonmajorized, we study these shapes, bound their numbers and develop algorithms to enumerate them. Our study extends the analysis of a previous paper by Hwang and Rothblum which discussed the above problem assuming the existence of a majorizing shape.
In this paper we obtain two means for divide differences using two majorization type results where one is related with schurconvexity. We examine their monotonicity property using exponentially convexfunctions.
In this paper we obtain two means for divide differences using two majorization type results where one is related with schurconvexity. We examine their monotonicity property using exponentially convexfunctions.
Designs most resistant to loss of varieties are found in certain settings. It is shown that a design is most resistant to loss of up to t – 2 varieties if and only if it is a t -design. When loss of both varieties an...
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Designs most resistant to loss of varieties are found in certain settings. It is shown that a design is most resistant to loss of up to t – 2 varieties if and only if it is a t -design. When loss of both varieties and the corresponding blocks is likely to occur, most resistant designs turn out to be nonbinary.
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