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Articles 61 - 75 of 75
Full-Text Articles in Applied Mathematics
Uniqueness Criterion For Solution Of Abstract Nonlocal Cauchy Problem, Ludwik Byszewski
Uniqueness Criterion For Solution Of Abstract Nonlocal Cauchy Problem, Ludwik Byszewski
Mathematics and System Engineering Faculty Publications
The aim of the paper is to prove an uniqueness criterion for a solution of an abstract nonlocal Cauchy problem. A dissipative operator in the nonlocal problem and an arbitrary functional in the nonlocal condition are considered. The paper is a continuation of papers [l]-[3] and generalizes some results from [4].
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.
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.
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 …
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.
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 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.
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].
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 …
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.
Unique Solution To Periodic Boundary Value Problems, Yong Sun
Unique Solution To Periodic Boundary Value Problems, Yong Sun
Mathematics and System Engineering Faculty Publications
Existence of unique solution to periodic boundary value problems of differential equations with continuous or discontinuous right-hand side is considered by utilizing the method of lower and upper solutions and the monotone properties of the operator. This is subject to discussion in the present paper.
On Modulated Random Measures, Jewgeni H. Dshalalow
On Modulated Random Measures, Jewgeni H. Dshalalow
Mathematics and System Engineering Faculty Publications
In this paper the author introduces the notion of a modulated marked random measure, Zξ on the class of locally compact and σ-compact spaces with countable bases. As special cases, are marked processes modulated by ξ are considered where ξ is a semi-Markov or semi-regenerative process. For either case, the intensities k=limt→∞1tE[Zξ([0,t])] are evaluated in terms of parameters of ξ. Examples and applications to inventories, queueing processes and economics are discussed.
Strong Maximum Principles For Parabolic Nonlinear Problems With Nonlocal Inequalities Together With Integrals, Ludwik Byszewski
Strong Maximum Principles For Parabolic Nonlinear Problems With Nonlocal Inequalities Together With Integrals, Ludwik Byszewski
Mathematics and System Engineering Faculty Publications
In [4] and [5], the author studied strong maximum principles for nonlinear parabolic problems with initial and nonlocal inequalities, respectively. Our purpose here is to extend results in [4] and [5] to strong maximum principles for nonlinear parabolic problems with nonlocal inequalities together with integrals. The results obtained in this paper can be applied in the theories of diffusion and heat conduction, since considered here integrals in nonlocal inequalities can be interpreted as mean amounts of the diffused substance or mean temperatures of the investigated medium.
Existence And Uniqueness Of Solutions Of Nonlocal Problems For Hyperbolic Equation Uxt=F(X, T, U, Ux), L. Byszewski
Existence And Uniqueness Of Solutions Of Nonlocal Problems For Hyperbolic Equation Uxt=F(X, T, U, Ux), L. Byszewski
Mathematics and System Engineering Faculty Publications
The aim of the paper is to give two theorems about existence and uniqueness of continuous solutions for hyperbolic nonlinear differential problems with nonlocal conditions in bounded and unbounded domains. The results obtained in this paper can be applied in the theory of elasticity with better effect than analogous known results with classical initial conditions.
Asymptotic Optimality Of Experimental Designs In Estimating A Product Of Means, Kamel Rekab
Asymptotic Optimality Of Experimental Designs In Estimating A Product Of Means, Kamel Rekab
Mathematics and System Engineering Faculty Publications
In nonlinear estimation problems with linear models, one difficulty in obtaining optimal designs is their dependence on the true value of the unknown parameters. A Bayesian approach is adopted with the assumption the means are independent apriori and have conjuguate prior distributions. The problem of designing an exper- iment to estimate the product of the means of two normal populations is considered. The main results determine an asymptotic lower bound for the Bayes risk, and a necessary and sufficient condition for any sequential procedure to achieve the bound.