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Articles 31 - 60 of 64
Full-Text Articles in Applied Mathematics
On The Inverse Multiphase Stefan Problem, Bruno Giuseppe Poggi Cevallos
On The Inverse Multiphase Stefan Problem, Bruno Giuseppe Poggi Cevallos
Theses and Dissertations
We consider inverse multiphase Stefan problem, where information on the heat flux on the fixed boundary is missing and must be found along with the temperature and free boundaries. Optimal control framework is pursued, where boundary heat flux is the control, and optimality criteria consists of the minimization of the L₂-norm declination of the trace of the solution to the Stefan problem from the temperature measurement on the fixed boundary. State vector solves multiphase Stefan problem in a weak formulation, which is equivalent to Neumann problem for the quasilinear parabolic PDE with discontinuous coefficient. Full discretization through finite differences is …
Random Walks On Random Lattices And Their Applications, Ryan Tyler White
Random Walks On Random Lattices And Their Applications, Ryan Tyler White
Theses and Dissertations
This work studies a class of continuous-time, multidimensional random walk processes with mutually dependent random step sizes and their exits from hyperrectangles. Fluctuations of the process about the critical boundary are studied extensively by stochastic analysis and operational calculus. Further, information on the process can be ascertained only upon observations occurring according to a delayed renewal process, rather than in real time. Passage times are thus obscured and results are first derived pertaining to the pre-passage and post-passage observations. Two distinct strategies are developed to combat the crudeness of delayed observations in order to derive more refined information about the …
Phenotypic Variance Predicts Symbiont Population Densities In Corals: A Modeling Approach, Robert Van Woesik, Kazuyo Shiroma, Semen Koksal
Phenotypic Variance Predicts Symbiont Population Densities In Corals: A Modeling Approach, Robert Van Woesik, Kazuyo Shiroma, Semen Koksal
Ocean Engineering and Marine Sciences Faculty Publications
We test whether the phenotypic variance of symbionts (Symbiodinium) in corals is closely related with the capacity of corals to acclimatize to increasing seawater temperatures. Moreover, we assess whether more specialist symbionts will increase within coral hosts under ocean warming. The present study is only applicable to those corals that naturally have the capacity to support more than one type of Symbiodinium within the lifetime of a colony; for example, Montastraea annularis and Montastraea faveolata. Methodology/Principal Findings: The population dynamics of competing Symbiodinium symbiont populations were projected through time in coral hosts using a novel, discrete time optimal-resource model. Models …
Random Fixed Point Theory In Spaces With Two Metrics, Donal O'Regan, Naseer Shahzad, Ravi P. Agarwal
Random Fixed Point Theory In Spaces With Two Metrics, Donal O'Regan, Naseer Shahzad, Ravi P. Agarwal
Mathematics and System Engineering Faculty Publications
We present new random fixed point theorems in spaces with two metrics. Our results extend recent results of Tan and Yuan [10] and Xu [11].
On Intensities Of Modulated Cox Measures, Jewgeni H. Dshalalow
On Intensities Of Modulated Cox Measures, Jewgeni H. Dshalalow
Mathematics and System Engineering Faculty Publications
In this paper we introduce and study functionals of the intensities of random measures modulated by a stochastic process ξ, which occur in applications to stochastic models and telecommunications. Modulation of a random measure by ξ is specified for marked Cox measures. Particular cases of modulation by ξ as semi-Markov and semiregenerative processes enabled us to obtain explicit formulas for the named intensities. Examples in queueing (systems with state dependent parameters, Little's and Campbell's formulas) demonstrate the use of the results.
On The Level Crossing Of Multi-Dimensional Delayed Renewal Processes, Jewgeni H. Dshalalow
On The Level Crossing Of Multi-Dimensional Delayed Renewal Processes, Jewgeni H. Dshalalow
Mathematics and System Engineering Faculty Publications
The paper studies the behavior of an (l+3)th-dimensional, delayed renewal process with dependent components, the first three (called active) of which are to cross one of their respective thresholds. More specifically, the crossing takes place when at least one of the active components reaches or exceeds its assigned level. The values of the other two active components, as well as the rest of the components (passive), are to be registered. The analysis yields the joint functional of the crossing level and other characteristics (some of which can be interpreted as the first passage time) in a closed form, refining earlier …
Monotone Iterations For Differential Equations With A Parameter, Tadeusz Jankowski, V. Lakshmikantham
Monotone Iterations For Differential Equations With A Parameter, Tadeusz Jankowski, V. Lakshmikantham
Mathematics and System Engineering Faculty Publications
Consider the problem {y′(t)=f(t,y(t),λ),t∈J=[0,b],y(0)=k0,G(y,λ)=0. Employing the method of upper and lower solutions and the monotone iterative technique, existence of extremal solutions for the above equation are proved.
Exp For Windows, Version 4.0 A Software Review, Donn E. Miller-Harnish
Exp For Windows, Version 4.0 A Software Review, Donn E. Miller-Harnish
Mathematics and System Engineering Faculty Publications
No abstract provided.
Asymptotic Optimality Of Sequential Designs For Estimation, Kamel Rekab
Asymptotic Optimality Of Sequential Designs For Estimation, Kamel Rekab
Mathematics and System Engineering Faculty Publications
This paper is concerned with the problem of allocating a fixed number of trials between K independent populations from the exponential family, in order to estimate a linear combination of the means with squared error loss. Introducing independent conjugate priors, a batch sequential procedure is proposed and compared with the optimal. © 1995, Hindawi Publishing Corporation. All rights reserved.
Exp For Windows, Version 3.0 A Software Review, Donn E. Miller-Harnish
Exp For Windows, Version 3.0 A Software Review, Donn E. Miller-Harnish
Mathematics and System Engineering Faculty Publications
No abstract provided.
Optimality Conditions For Systems Driven By Nonlinear Evolution Equations, Nikolaos S. Papageorgiou
Optimality Conditions For Systems Driven By Nonlinear Evolution Equations, Nikolaos S. Papageorgiou
Mathematics and System Engineering Faculty Publications
Using the Dubovitskii-Milyutin theory we derive necessary and sufficient conditions for optimality for a class of Lagrange optimal control problems monitored by a nonlinear evolution equation and involving initial and/or terminal constraints. An example of a parabolic control system is also included.
Stability Of Conditionally Invariant Sets And Controlled Uncertain Dynamic Systems On Time Scales, V. Lakshmikantham
Stability Of Conditionally Invariant Sets And Controlled Uncertain Dynamic Systems On Time Scales, V. Lakshmikantham
Mathematics and System Engineering Faculty Publications
A basic feedback control problem is that of obtaining some desired stability property from a system which contains uncertainties due to unknown inputs into the system. Despite such imperfect knowledge in the selected mathematical model, we often seek to devise controllers that will steer the system in a certain required fashion. Various classes of controllers whose design is based on the method of Lyapunov are known for both discrete [4], [10], [15], and continuous [3–9], [11] models described by difference and differential equations, respectively. Recently, a theory for what is known as dynamic systems on time scales has been built …
Bulk Input Queues With Quorum And Multiple Vacations, Jay Yellen, Jewgeni H. Dshalalow
Bulk Input Queues With Quorum And Multiple Vacations, Jay Yellen, Jewgeni H. Dshalalow
Mathematics and System Engineering Faculty Publications
The authors study a single-server queueing system with bulk arrivals and batch service in accordance to the general quorum discipline: a batch taken for service is not less than r and not greater than R(≥r). 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. The analysis of the system is based on the theory of first excess processes developed by the first author. A preliminary analysis of such processes enabled the authors to obtain all major characteristics …
Extension Of The Method Of Quasilinearization For Stochastic Initial Value Problems, Naseer Shahzad, Farzana A. Mcrae
Extension Of The Method Of Quasilinearization For Stochastic Initial Value Problems, Naseer Shahzad, Farzana A. Mcrae
Mathematics and System Engineering Faculty Publications
In this paper we extend the method of quasilinearization to stochastic initial value problems. Further we prove that the iterates converge uniformly almost surely to the unique solution and the convergence is quadratic.
First Passage Processes In Queuing System Mx/Gr/1 With Service Delay Discipline, Lev M. Abolnikov, Jewgeni H. Dshalalow, Alexander M. Dukhovny
First Passage Processes In Queuing System Mx/Gr/1 With Service Delay Discipline, Lev M. Abolnikov, Jewgeni H. Dshalalow, Alexander M. Dukhovny
Mathematics and System Engineering Faculty Publications
This article deals with a general single-server bulk queueing system with a server waiting until the queue will reach level r before it starts processing customers. If at least r customers are available the server takes a batch of the fixed size r of units for service. The input stream is assumed to be a compound Poisson process modulated by a semi-Markov process and with a multilevel control of service time. The authors evaluate the steady state probabilities of the queueing processes with discrete and continuous time parameter preliminarily establishing necessary and sufficient conditions for the ergodicity of the processes. …
Existence Of Solutions For Second-Order Evolution Inclusions, Nikolaos S. Papageorgiou
Existence Of Solutions For Second-Order Evolution Inclusions, Nikolaos S. Papageorgiou
Mathematics and System Engineering Faculty Publications
In this paper we examine second-order nonlinear evolution inclusions and prove two existence theorems; one with a convex-valued orientor field and the other with a nonconvex-valued field. An example of a hyperbolic partial differential inclusion is also presented.
Quasilinearization For Some Nonlocal Problems, Yunfeng Yin
Quasilinearization For Some Nonlocal Problems, Yunfeng Yin
Mathematics and System Engineering Faculty Publications
The method of generalized quasilinearization [4] is applied to study semilinear parabolic equation ut – Lu = f{t,x,u) with nonlocal boundary conditions u(t,x)=∫Ωϕ(x,y)u(t,y)dy in this paper. The convexity of f in u is relaxed by requiring f(t,x,u) Muz to be convex for some M > 0. The quadratic convergence of monotone sequence is obtained.
Optimal Controllability Of Impulsive Control Systems, Farzana A. Mcrae
Optimal Controllability Of Impulsive Control Systems, Farzana A. Mcrae
Mathematics and System Engineering Faculty Publications
The problem of optimal controllability of a nonlinear impulsive control system is studied using the method of vector Lyapunov functions and the generalized comparison principle.
A Bulk Queueing System Under N-Policy With Bilevel Service Delay Discipline And Start-Up Time, David C.R. Muh
A Bulk Queueing System Under N-Policy With Bilevel Service Delay Discipline And Start-Up Time, David C.R. Muh
Mathematics and System Engineering Faculty Publications
The author studies the queueing process in a single-server, bulk arrival and batch service queueing system with a compound Poisson input, bilevel service delay discipline, start-up time, and a fixed accumulation level with control operating policy. It is assumed that when the queue length falls below a predefined level r (≥ 1), the system, with server capacity Λ, immediately stops service until the queue length reaches or exceeds the second predefined accumulation level N(≥ r). Two cases, with N ≦ R and N ≥ R, are studied. The author finds explicitly the probability generating function of the stationary distribution of …
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.
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 …
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].
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.