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Positive Constant (positive + constant)

Distribution by Scientific Domains
Mathematics and Statistics100%

Selected Abstracts

Scheduling parallel machines with inclusive processing set restrictions

NAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 4 2008
Jinwen Ou
Abstract We consider the problem of assigning a set of jobs to different parallel machines of the same processing speed, where each job is compatible to only a subset of those machines. The machines can be linearly ordered such that a higher-indexed machine can process all those jobs that a lower-indexed machine can process. The objective is to minimize the makespan of the schedule. This problem is motivated by industrial applications such as cargo handling by cranes with nonidentical weight capacities, computer processor scheduling with memory constraints, and grades of service provision by parallel servers. We develop an efficient algorithm for this problem with a worst-case performance ratio of + ,, where , is a positive constant which may be set arbitrarily close to zero. We also present a polynomial time approximation scheme for this problem, which answers an open question in the literature. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008 [source]

Efficient communication in unknown networks

NETWORKS: AN INTERNATIONAL JOURNAL, Issue 1 2001
Luisa Gargano
Abstract We consider the problem of disseminating messages in networks. We are interested in information dissemination algorithms in which machines operate independently without any knowledge of the network topology or size. Three communication tasks of increasing difficulty are studied. In blind broadcasting (BB), the goal is to communicate the source message to all nodes. In acknowledged blind broadcasting (ABB), the goal is to achieve BB and inform the source about it. Finally, in full synchronization (FS), all nodes must simultaneously enter the state terminated after receiving the source message. The algorithms should be efficient both in terms of the time required and the communication overhead they put on the network. We limit the latter by allowing every node to send a message to at most one neighbor in each round. We show that BB is achieved in time at most 2n in any n -node network and show networks in which time 2n , o(n) is needed. For ABB, we show algorithms working in time (2 + ,)n, for any fixed positive constant , and sufficiently large n. Thus, for both BB and ABB, our algorithms are close to optimal. Finally, we show a simple algorithm for FS working in time 3n and a more complicated algorithm which works in time 2.9n. The optimal time of full synchronization remains an open problem. © 2001 John Wiley & Sons, Inc. [source]

CONFIDENCE INTERVALS UTILIZING PRIOR INFORMATION IN THE BEHRENS,FISHER PROBLEM

AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, Issue 4 2008
Paul Kabaila
Summary Consider two independent random samples of size f,+ 1, one from an N (,1, ,21) distribution and the other from an N (,2, ,22) distribution, where ,21/,22, (0, ,). The Welch ,approximate degrees of freedom' (,approximate t -solution') confidence interval for ,1,,2 is commonly used when it cannot be guaranteed that ,21/,22= 1. Kabaila (2005, Comm. Statist. Theory and Methods,34, 291,302) multiplied the half-width of this interval by a positive constant so that the resulting interval, denoted by J0, has minimum coverage probability 1 ,,. Now suppose that we have uncertain prior information that ,21/,22= 1. We consider a broad class of confidence intervals for ,1,,2 with minimum coverage probability 1 ,,. This class includes the interval J0, which we use as the standard against which other members of will be judged. A confidence interval utilizes the prior information substantially better than J0 if (expected length of J)/(expected length of J0) is (a) substantially less than 1 (less than 0.96, say) for ,21/,22= 1, and (b) not too much larger than 1 for all other values of ,21/,22. For a given f, does there exist a confidence interval that satisfies these conditions? We focus on the question of whether condition (a) can be satisfied. For each given f, we compute a lower bound to the minimum over of (expected length of J)/(expected length of J0) when ,21/,22= 1. For 1 ,,= 0.95, this lower bound is not substantially less than 1. Thus, there does not exist any confidence interval belonging to that utilizes the prior information substantially better than J0. [source]

General energy decay estimates of Timoshenko systems with frictional versus viscoelastic damping

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 16 2009
Aissa Guesmia
Abstract In this paper we consider the following Timoshenko system: with Dirichlet boundary conditions and initial data where a, b, g and h are specific functions and ,1, ,2, k1, k2 and L are given positive constants. We establish a general stability estimate using the multiplier method and some properties of convex functions. Without imposing any growth condition on h at the origin, we show that the energy of the system is bounded above by a quantity, depending on g and h, which tends to zero as time goes to infinity. Our estimate allows us to consider a large class of functions h with general growth at the origin. We use some examples (known in the case of wave equations and Maxwell system) to show how to derive from our general estimate the polynomial, exponential or logarithmic decay. The results of this paper improve and generalize some existing results in the literature and generate some interesting open problems. Copyright © 2009 John Wiley & Sons, Ltd. [source]