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### CIS Department Talk - May 27, 2010

The Department of Computer and Information Science Present

 Speaker:Xing de Jia, Texas State Univeristy Topic: Additive Bases and Distributed Networks Date: May 27, 2010, at 5:00PM Place:Lincoln Center Campus, Lowenstein, Room 812

Abstract:

Additive bases in number theory can be used in the construction of distributed networks. Efficiency of certain networks relies on the choice of the additive bases involved in the construction of the networks. Here I mainly focus on the properties of certain additive bases. Let A be a set of integers. Let hA denote the set of all sums of h elements in A. A is called an asymptotic basis of order h if the union of all iA for i=1,2,...,h contains all large integers. A is called an exact asymptotic basis of order h if hA contains all large integers. It is clear that an asymptotic basis of order \$h\$ may not be an exact asymptotic basis of any order. However, when an asymptotic basis of order h is actually an exact asymptotic basis, the exact order might increase. Given positive integers h and k. Define G_k(h)=max_{A, g^*(A)\le h}\max_{Fin I_k(A)}g^*(A-F), where the first maximum is taken over all asymptotic bases of order at most h, and I_k(A)=\F is a subset of A with |F|=k, and \$A-F\$ is an asymptotic basis}. We shall discuss how to calculate the exact values of G_{k}(h) for small h and k. We shall also discuss some computations involved in constructing "efficient'' asymptotic bases to provide lower bounds for G_{k}(h) as h or k approaches infinity.

Bio:
Dr. Xing de Jia received his Ph.D. in Mathematics from The City University of New York, New York, USA, in 1990 and his B.S. degree in mathematics from Qufu Normal University, China, in 1982. He is a Professor of Mathematics at Texas State University, San Marcos, Texas. He has been an Instructor of Mathematics at Fordham University. He and collaborators have appeared in more than 30 peer reviewed papers including the Journal of Interconnection Networks, In Number Theory, Congressus Numerantium, and J. Number Theory to name a few.