On vanishing sums of m \,m\,th roots of unity in finite fields

In an earlier work, the authors have determined all possible weights $n$ for which there exists a vanishing sum $\zeta_1+\cdots +\zeta_n=0$ of $m$th roots of unity $\zeta_i$ in characteristic 0. In this paper, the same problem is studied in finite fields of characteristic $p$. For given $m$ and $p$, results are obtained on integers $n_0$ such that all integers $n\geq n_0$ are in the ``weight set'' $W_p(m)$. The main result $(1.3)$ in this paper guarantees, under suitable conditions, the existence of solutions of $x_1^d+\cdots+x_n^d=0$ with all coordinates not equal to zero over a finite field

Adaptive schemes for location update generation in execution location-dependent continuous queries

Cataloged from PDF version of article.An important feature that is expected to be owned by today's mobile computing systems is the ability of processing location-dependent continuous queries on moving objects. The result of a location-dependent query depends on the current location of the mobile client which has generated the query as well as the locations of the moving objects on which the query has been issued. When a location-dependent query is specified to be continuous, the result of the query can continuously change. In order to provide accurate and timely query results to a client, the location of the client as well as the locations of moving objects in the system has to be closely monitored. Most of the location generation methods proposed in the literature aim to optimize utilization of the limited wireless bandwidth. The issues of correctness and timeliness of query results reported to clients have been largely ignored. In this paper, we propose an adaptive monitoring method (AMM) and a deadline-driven method (DDM) for managing the locations of moving objects. The aim of our methods is to generate location updates with the consideration of maintaining the correctness of query evaluation results without increasing location update workload. Extensive simulation experiments have been conducted to investigate the performance of the proposed methods as compared to a well-known location update generation method, the plain dead-reckoning (pdr). © 2005 Elsevier Inc. All rights reserved

An Inter-molecular Adaptive Collision Scheme for Chemical Reaction Optimization

Optimization techniques are frequently applied in science and engineering research and development. Evolutionary algorithms, as a kind of general-purpose metaheuristic, have been shown to be very effective in solving a wide range of optimization problems. A recently proposed chemical-reaction-inspired metaheuristic, Chemical Reaction Optimization (CRO), has been applied to solve many global optimization problems. However, the functionality of the inter-molecular ineffective collision operator in the canonical CRO design overlaps that of the on-wall ineffective collision operator, which can potential impair the overall performance. In this paper we propose a new inter-molecular ineffective collision operator for CRO for global optimization. To fully utilize our newly proposed operator, we also design a scheme to adapt the algorithm to optimization problems with different search space characteristics. We analyze the performance of our proposed algorithm with a number of widely used benchmark functions. The simulation results indicate that the new algorithm has superior performance over the canonical CRO