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Full-Text Articles in Physical Sciences and Mathematics
A Center Of A Polytope: An Expository Review And A Parallel Implementation, S. K. Sen, Hongwei Du, Donald W. Fausett
A Center Of A Polytope: An Expository Review And A Parallel Implementation, S. K. Sen, Hongwei Du, Donald W. Fausett
Mathematics and System Engineering Faculty Publications
The solution space of the rectangular linear system Ax = b, subject to x ≥ 0, is called a polytope. An attempt is made to provide a deeper geometric insight, with numerical examples, into the condensed paper by Lord, et al. [1], that presents an algorithm to compute a center of a polytope. The algorithm is readily adopted for either sequential or parallel computer implementation. The computed center provides an initial feasible solution (interior point) of a linear programming problem. © 1993, Hindawi Publishing Corporation. All rights reserved.
A Queueing System With A Fixed Accumulation Level, Random Server Capacity And Capacity Dependent Service Time, Jewgeni H. Dshalalow, Lotfi Tadj
A Queueing System With A Fixed Accumulation Level, Random Server Capacity And Capacity Dependent Service Time, Jewgeni H. Dshalalow, Lotfi Tadj
Mathematics and System Engineering Faculty Publications
This paper introduces a bulk queueing system with a single server processing groups of customers of a variable size. If upon completion of service the queueing level is at least r the server takes a batch of size r and processes it a random time arbitrarily distributed. If the queueing level is less than r the server idles until the queue accumulates r customers in total. Then the server capacity is generated by a random number equals the batch size taken for service which lasts an arbitrarily distributed time dependent on the batch size. The objective of the paper is …
On A Single-Server Queue With Fixed Accumulation Level, State Dependent Service, And Semi-Markov Modulated Input Flow, Gary Russell, Jewgeni H. Dshalalow
On A Single-Server Queue With Fixed Accumulation Level, State Dependent Service, And Semi-Markov Modulated Input Flow, Gary Russell, Jewgeni H. Dshalalow
Mathematics and System Engineering Faculty Publications
The authors study the queueing process in a single-server queueing system with state dependent service and with the input modulated by a semi-Markov process embedded in the queueing process. It is also assumed that the server capacity is r≥1 and that any service act will not begin until the queue accumulates at least r units. In this model, therefore, idle periods also depend upon the queue length. The authors establish an ergodicity criterion for the queueing process and evaluate explicitly its stationary distribution and other characteristics of the system, such as the mean service cycle, intensity of the system, intensity …
Generalized Two Point Boundary Value Problems. Existence And Uniqueness, K. N. Murty, Seenith Sivasundaram
Generalized Two Point Boundary Value Problems. Existence And Uniqueness, K. N. Murty, Seenith Sivasundaram
Mathematics and System Engineering Faculty Publications
An algorithm is presented for finding the pseudo-inverse of a rectangular matrix. Using this algorithm as a tool, existence and uniqueness of solutions to two point boundary value problems associated with general first order matrix differential equations are established.
Extremal Solutions To A Class Of Multivalued Integral Equations In Banach Space, Sergiu Aizicovici, Nikolaos S. Papageorgiou
Extremal Solutions To A Class Of Multivalued Integral Equations In Banach Space, Sergiu Aizicovici, Nikolaos S. Papageorgiou
Mathematics and System Engineering Faculty Publications
We consider a nonlinear Volterra integral inclusion in a Banach space. We establish the existence of extremal integral solutions, and we show that they are dense in the solution set of the original equation. As an important application, we obtain a “bang-bang” theorem for a class of nonlinear, infinite dimensional control systems.
Lyapunov Stability Theory For Dynamic Systems On Time Scales, Billur Kaymakçalan
Lyapunov Stability Theory For Dynamic Systems On Time Scales, Billur Kaymakçalan
Mathematics and System Engineering Faculty Publications
By use of the necessary calculus and the fundamental existence theory for dynamic systems on time scales, in this paper, we develop Lyapunov’s second method in the framework of general comparison principle so that one can cover and include several stability results for both types of equations at the same time.
Existence Of A Solution Of A Fourier Nonlocal Quasilinear Parabolic Problem, Ludwik Byszewski
Existence Of A Solution Of A Fourier Nonlocal Quasilinear Parabolic Problem, Ludwik Byszewski
Mathematics and System Engineering Faculty Publications
The aim of this paper is to give a theorem about the existence of a classical solution of a Fourier third nonlocal quasilinear parabolic problem. To prove this theorem, Schauder’s theorem is used. The paper is a continuation of papers [l]-[8] and the generalizations of some results from [9]-[11]. The theorem established in this paper can be applied to describe some phenomena in the theories of diffusion and heat conduction with better effects than the analogous classical theorem about the existence of a solution of the Fourier third quasilinear parabolic problem.
A First Passage Problem And Its Applications To The Analysis Of A Class Of Stochastic Models, Lev M. Abolnikov, Jewgeni H. Dshalalow
A First Passage Problem And Its Applications To The Analysis Of A Class Of Stochastic Models, Lev M. Abolnikov, Jewgeni H. Dshalalow
Mathematics and System Engineering Faculty Publications
A problem of the first passage of a cumulative random process with generally distributed discrete or continuous increments over a fixed level is considered in the article as an essential part of the analysis of a class of stochastic models (bulk queueing systems, inventory control and dam models). Using direct probability methods the authors find various characteristics of this problem: the magnitude of the first excess of the process over a fixed level, the shortage before the first excess, the levels of the first and pre-first excesses, the index of the first excess and others. The results obtained are illustrated …
On A Multilevel Controlled Bulk Queueing System Mx/Gr,R/1, Lev M. Abolnikov, Jewgeni H. Dshalalow
On A Multilevel Controlled Bulk Queueing System Mx/Gr,R/1, Lev M. Abolnikov, Jewgeni H. Dshalalow
Mathematics and System Engineering Faculty Publications
The authors introduce and study a class of bulk queueing systems with a compound Poisson input modulated by a semi-Markov process, multilevel control service time and a queue length dependent service delay discipline. According to this discipline, the server immediately starts the next service act if the queue length is not less than r; in this case all available units, or R (capacity of the server) of them, whichever is less, are taken for service. Otherwise, the server delays the service act until the number of units in the queue reaches or exceeds level r. The authors establish a necessary …
A First Passage Problem And Its Applications To The Analysis Of A Class Of Stochastic Models, Lev M. Abolnikov, Jewgeni H. Dshalalow
A First Passage Problem And Its Applications To The Analysis Of A Class Of Stochastic Models, Lev M. Abolnikov, Jewgeni H. Dshalalow
Mathematics and System Engineering Faculty Publications
A problem of the first passage of a cumulative random process with generally distributed discrete or continuous increments over a fixed level is considered in the article as an essential part of the analysis of a class of stochastic models (bulk queueing systems, inventory control and dam models). Using direct probability methods the authors find various characteristics of this problem: the magnitude of the first excess of the process over a fixed level, the shortage before the first excess, the levels of the first and pre-first excesses, the index of the first excess and others. The results obtained are illustrated …
On A First Passage Problem In General Queueing Systems With Multiple Vacations, Jewgeni H. Dshalalow
On A First Passage Problem In General Queueing Systems With Multiple Vacations, Jewgeni H. Dshalalow
Mathematics and System Engineering Faculty Publications
The author studies a generalized single-server queueing system with bulk arrivals and batch service, where the server takes vacations each time the queue level falls below r(≥1) in accordance with the multiple vacation discipline. The input to the system is assumed to be a compound Poisson process modulated by the system and the service is assumed to be state dependent. One of the essential part in the analysis of the system is the employment of new techniques related to the first excess level processes. A preliminary analysis of such processes and recent results of the author on modulated processes enabled …
Existence Of Approximate Solution To Abstract Nonlocal Cauchy Problem, Ludwik Byszewski
Existence Of Approximate Solution To Abstract Nonlocal Cauchy Problem, Ludwik Byszewski
Mathematics and System Engineering Faculty Publications
The aim of the paper is to prove a theorem about the existence of an approximate solution to an abstract nonlinear nonlocal Cauchy problem in a Banach space. The right-hand side of the nonlocal condition belongs to a locally closed subset of a Banach space. The paper is a continuation of papers [1], [2] and generalizes some results from [3].
On Solvability Of Mixed Monotone Operator Equations With Applications To Mixed Quasimonotone Differential Systems Involving Discontinuities, Seppo V. Heikkilä, Martti Kumpulainen, V. Lakshmikantham
On Solvability Of Mixed Monotone Operator Equations With Applications To Mixed Quasimonotone Differential Systems Involving Discontinuities, Seppo V. Heikkilä, Martti Kumpulainen, V. Lakshmikantham
Mathematics and System Engineering Faculty Publications
In this paper we shall first study solvability of mixed monotone systems of operator equations in an ordered normed space by using a generalized iteration method. The obtained results are then applied to prove existence of coupled extremal quasisolutions of the systems of first and second order mixed quasimonotone differential equations with discontinuous right hand sides. Most of the results deal with systems in a Banach space ordered by a regular order cone.