DRUM Community: A. James Clark School of Engineering
http://hdl.handle.net/1903/1654
2015-05-30T07:21:16ZOn Number Of Partitions Of An Integer Into A Fixed Number Of Positive Integers
http://hdl.handle.net/1903/16351
Title: On Number Of Partitions Of An Integer Into A Fixed Number Of Positive Integers
Authors: Oruc, A. Yavuz
Abstract: This paper focuses on the number of partitions of a positive integer $n$ into $k$ positive summands, where $k$ is an integer between $1$ and $n$. Recently some upper bounds were reported for this number in [Merca14]. Here, it is shown that these bounds are not as tight as an earlier upper bound proved in [Andrews76-1] for $k\le 0.42n$. A new upper bound for the number of partitions of $n$ into $k$ summands is given, and shown to be tighter than the upper bound in [Merca14] when $k$ is between $O(\frac{\sqrt{n}}{\ln n})$ and $n-O(\frac{\sqrt{n}}{\ln n})$. It is further shown that the new upper bound is also tighter than two other upper bounds previously reported in~[Andrews76-1] and [Colman82]. A generalization of this upper bound to number of partitions of $n$ into at most $k$ summands is also presented.
Description: Submitted to Journal of Number Theory.2015-04-01T00:00:00ZAmbiguous Behavior of Logic Bistable Systems
http://hdl.handle.net/1903/16339
Title: Ambiguous Behavior of Logic Bistable Systems
Authors: Hurtado, Marco; Elliott, David L.
Abstract: The standard specification of logic bistable devices do not specify the behavior under conditions in which the input is logically undefined or in which certain kinds of multiple input changes occur. These conditions are unavoidable in logic synchronizers and arbiters. A general deterministic model of bistable devices is proposed, consisting of a non-liner differential system with some adequate properties. Analysis of this model shows that bistable devices can be driven into a logically undefined region by certain admissible inputs and can remain in this region for an unbounded length of time.1975-10-04T00:00:00ZInstances for the Generalized Regenerator Location Problem
http://hdl.handle.net/1903/16328
Title: Instances for the Generalized Regenerator Location Problem
Authors: Chen, Si; Ljubic, Ivana; Raghavan, S.2015-01-01T00:00:00ZA GENERAL FRAMEWORK FOR CONSENSUS NETWORKS
http://hdl.handle.net/1903/16324
Title: A GENERAL FRAMEWORK FOR CONSENSUS NETWORKS
Authors: Somarakis, Christoforos
Abstract: A new framework for the analysis of consensus networks is developed. The theory
consists of necessary and sufficient conditions and it is flexible enough to comprise a variety of
consensus systems. Under mild connectivity assumptions, the discussion ranges from linear, nonlinear, ordinary, functional and leader-follower models. The establishment of explicit estimates on
the rate of convergence is the central objective. Our work extends and unifies past related works in
the literature. Illustrative examples and simulations are presented to outline the theoretical results.2015-03-10T00:00:00Z