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Articles 31 - 60 of 75

Full-Text Articles in Applied Mathematics

Stability Analysis Of Neutral Functional Differential Equations Arising In Partial Element Equivalent Circuit Models, Howard Michael Allison Dec 2019

Stability Analysis Of Neutral Functional Differential Equations Arising In Partial Element Equivalent Circuit Models, Howard Michael Allison

Theses and Dissertations

Neutral Functional Differential Equations (NFDEs) arise in the study of the Partial Element Equivalent Circuit (PEEC) model with time delays. We present sufficient conditions for asymptotic stability and global stability in the delays of the PEEC NFDE’s, using Lyapunov-Razumikhin function methods.. We develop, for the first time, a standard mixing-type nonlinearity for the PEEC NFDEs. Introducing time invariant and time varying nonlinear perturbation to the PEEC NFDEs, we develop sufficient conditions for stability of the nonlinear perturbed PEEC NFDEs and convergence of the nonlinear system to the original stable linear autonomous system. We also develop sufficient conditions for stability and …


Computational Models For Biological Locomotion In Gels, Hashim Mohammed Alshehri Dec 2019

Computational Models For Biological Locomotion In Gels, Hashim Mohammed Alshehri

Theses and Dissertations

We investigated Low Reynold’s Number Locomotion in two-phase biological gels. The gel is composed of two materials: a viscous fluid solvent phase and a viscoelastic polymer network phase. A novel Two-phase Immersed Boundary Method (IBM) is developed to simulate the complicated interactions between an elastic boundary and a mixture of two fluids with very different physical properties. A further extension of the method is developed for the case where fluids satisfy partial-slip and free-slip conditions on the elastic boundary. Our major conclusions are summarized as following: (i) Our numerical scheme is proved to be robust and efficient. It can successfully …


Two-Point Boundary Value Problems For Higher Order Nonlinear Hyperbolic Equations, Audison Beaubrun May 2019

Two-Point Boundary Value Problems For Higher Order Nonlinear Hyperbolic Equations, Audison Beaubrun

Theses and Dissertations

Two–point boundary value problems in a multidimensional box for higher order nonlinear hyperbolic equations are considered. The concepts of a strongly isolated solution, and locally and globally strong well–posedness of a nonlinear boundary value problem are introduced. For general two–point boundary value problems and periodic problems there are established: (i) Necessary and sufficient conditions of locally and globally strong well–posedness; (ii) Unimprovable Sufficient conditions of solvability. For the Dirichlet and Periodic type problems for equations of even order there are established: (i) Effective sufficient conditions of solvability and locally strong well–posedness; (ii) Unimprovable sufficient conditions of solvability for the case, …


Qualitative Analysis Of The Nonlinear Double Degenerate Parabolic Equation Of Turbulent Filtration With Absorption, Adam Prinkey May 2019

Qualitative Analysis Of The Nonlinear Double Degenerate Parabolic Equation Of Turbulent Filtration With Absorption, Adam Prinkey

Theses and Dissertations

The goal of the dissertation is to pursue qualitative analysis of the mathematical model of turbulent polytropic filtration of a gas in a porous media with reaction or absorption described by the second order nonlinear double degenerate parabolic equation ∂u ∂t − ∂ ∂x F [ ∂u m ∂x ] + Q(u) = 0, (1) where F(y) = |y| p−1 y, Q(u) = buβ , m, p, β > 0, b ∈ R. In the absence of the reaction term there is a finite speed of propagation with an expanding interface in the case of slow diffusion (mp > 1), and infinite …


Generalized Random Measures On Topological Spaces, Ali Hussein Mahmood Al-Obaidi May 2019

Generalized Random Measures On Topological Spaces, Ali Hussein Mahmood Al-Obaidi

Theses and Dissertations

Our work deals with classes of random measures on -compact Hausdorff spaces perturbed by stochastic processes. We render a rigorous construction of the stochastic integral of functions of two variables and show that such an integral is a random measure. We establish a new Campbell-type formula that, along with a rigorous construction of modulation, leads to the intensity of a modulated random measure. We further introduce and study a marked Poisson random measure on a - compact Hausdorff space. The underlying parameters of this measure are changing in accordance with the evolution of a stochastic process. This generalized random measure …


On The Qualitative Theory Of The Nonlinear Parabolic P-Laplacian Type Reaction-Diffusion Equations, Roqia Abdullah Jeli Nov 2018

On The Qualitative Theory Of The Nonlinear Parabolic P-Laplacian Type Reaction-Diffusion Equations, Roqia Abdullah Jeli

Theses and Dissertations

This dissertation presents full classification of the evolution of the interfaces and asymptotics of the local solution near the interfaces and at infinity for the nonlinear second order parabolic p-Laplacian type reaction-diffusion equation of non-Newtonian elastic filtration ut − ( |ux| p−2 ux ) x +buβ = 0, p > 1, β > 0. (1) Nonlinear partial differential equation (1) is a key model example expressing competition between nonlinear diffusion with gradient dependent diffusivity in either slow (p > 2) or fast (1 < p < 2) regime and nonlinear state dependent reaction (b > 0) or absorption (b < 0) forces. If interface is finite, it may expand, shrink, or remain stationary as a result of the competition of the diffusion and reaction terms near the interface, expressed in terms of the parameters p, β,sign b, and asymptotics of the initial function near its support. In the fast diffusion regime strong domination of the diffusion causes infinite speed of propagation and interfaces are absent. In all cases with finite interfaces we prove the explicit formula for the interface and the local solution with accuracy up to constant coefficients. We prove explicit asymptotics of the local solution at infinity in all cases with infinite speed of propagation. The methods of the proof are generaliii ization of the methods developed in U.G. Abdulla & J. King, SIAM J. Math. Anal., 32, 2(2000), 235-260; U.G. Abdulla, Nonlinear Analysis, 50, 4(2002), 541-560 and based on rescaling laws for the nonlinear PDE and blow-up techniques for the identification of the asymptotics of the solution near the interfaces, construction of barriers using special comparison theorems in irregular domains with characteristic boundary curves.


Lower Order Perturbations Of Critical Fractional Laplacian Equations, Khalid Fanoukh Al Oweidi Jul 2018

Lower Order Perturbations Of Critical Fractional Laplacian Equations, Khalid Fanoukh Al Oweidi

Theses and Dissertations

We give sufficient conditions for the existence of nontrivial solutions to a class of critical nonlocal problems of the Brezis-Nirenberg type. Our result extends some results in the literature for the local case to the nonlocal setting. It also complements the known results for the nonlocal case.


On The Qualitative Theory Of The Nonlinear Degenerate Second Order Parabolic Equations Modeling Reaction-Diffusion-Convection Processes, Habeeb Abed Kadhim Aal-Rkhais May 2018

On The Qualitative Theory Of The Nonlinear Degenerate Second Order Parabolic Equations Modeling Reaction-Diffusion-Convection Processes, Habeeb Abed Kadhim Aal-Rkhais

Theses and Dissertations

We consider nonlinear second order degenerate or singular parabolic equation ut − a(um)xx + buβ + c(up)x = 0, a, m, β, p > 0, b, c ∈ R describing reaction-diffusion-convection processes arising in many areas of science and engineering, such as filtration of oil or gas in porous media, transport of thermal energy in plasma physics, flow of chemically reacting fluid, evolution of populations in mathematical biology etc. We apply the methods developed in U.G. Abdulla, Journal of Differential Equations, 164, 2(2000), 321-354 for the reaction-diffusion equation (c = 0) and prove the existence, uniqueness, boundary regularity and comparison theorems …


Boundary Value Problems In A Multidimensional Box For Higher Order Linear And Quasi-Linear Hyperbolic Equations, Noha Aljaber May 2018

Boundary Value Problems In A Multidimensional Box For Higher Order Linear And Quasi-Linear Hyperbolic Equations, Noha Aljaber

Theses and Dissertations

Boundary value problems in a multidimensional box for higher order linear hyperbolic equations are considered. The concept of associated problems are introduced. For general boundary value problems there are established: (i) Necessary and sufficient conditions for a linear problem to have the Fredholm property in two–dimensional case; (ii) Necessary and sufficient conditions of well–posedness in two–dimensional case; (iii) Unimprovable sufficient conditions for a linear problem to have the Fredholm property; (iv) Unimprovable sufficient conditions of well–posedness and α–well–posedness; (v) Effective sufficient conditions of unqie solvability of two–point, periodic and Dirichlet type problems. (iv) Unimprovable conditions of unique solvability of two …


Initial{Boundary And Nonlocal Boundary Value Problems For Higher Order Nonlinear Hyperbolic Equations With Two Independent Variables, Raja Ben-Rabha May 2017

Initial{Boundary And Nonlocal Boundary Value Problems For Higher Order Nonlinear Hyperbolic Equations With Two Independent Variables, Raja Ben-Rabha

Theses and Dissertations

Boundary value problems in a characteristic rectangle for nonlinear hyperbolic equations of higher order are considered. The concept of strong well–posedness of a boundary value problem is introduced. For initial–boundary value problems there are established: (i) Necessary and sufficient conditions of strong well–posedness; (ii) Unimprovable sufficient conditions of local and global solvability; (iii) Effective sufficient conditions of solvability of two–point, multi–point, periodic and Dirichlet type problems; (iv) Sharp a priori estimates of solutions of ill–posed initial–boundary value problems; (v) Unimprovable conditions guaranteeing unique solvability of ill–posed initial–boundary value problems. For nonlocal boundary value problems there are established: (i) Necessary and …


On The Classification Of The Second Minimal Orbits Of The Continuous Endomorphisms On The Real Line And Universality In Chaos, Naveed H. Iqbal Apr 2017

On The Classification Of The Second Minimal Orbits Of The Continuous Endomorphisms On The Real Line And Universality In Chaos, Naveed H. Iqbal

Theses and Dissertations

This dissertation presents full classification of second minimal odd periodic orbits of a continuous endomorphisms on the real line. A (2k + 1)-periodic orbit (k ≥ 3) is called second minimal for the map f , if 2k−1 is a minimal period of f in the Sharkovskii ordering. We prove that there are 4k−3 types of second minimal (2k+1)-orbits, each characterized with unique cyclic permutation and directed graph of transitions with accuracy up to inverses. The result is applied to the problem on the distribution of periodic windows within the chaotic regime of the bifurcation diagram of the one-parameter family …


On The Inverse Multiphase Stefan Problem, Bruno Giuseppe Poggi Cevallos Jul 2015

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 May 2015

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 Feb 2010

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 Jan 2003

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 Jan 1998

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 Jan 1997

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 Jan 1997

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 Jan 1996

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 Nov 1995

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.


Bulk Input Queues With Quorum And Multiple Vacations, Jay Yellen, Jewgeni H. Dshalalow Jan 1995

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 …


Exp For Windows, Version 3.0 A Software Review, Donn E. Miller-Harnish Jan 1995

Exp For Windows, Version 3.0 A Software Review, Donn E. Miller-Harnish

Mathematics and System Engineering Faculty Publications

No abstract provided.


Stability Of Conditionally Invariant Sets And Controlled Uncertain Dynamic Systems On Time Scales, V. Lakshmikantham Jan 1995

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 …


Extension Of The Method Of Quasilinearization For Stochastic Initial Value Problems, Naseer Shahzad, Farzana A. Mcrae Jan 1995

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.


Optimality Conditions For Systems Driven By Nonlinear Evolution Equations, Nikolaos S. Papageorgiou Jan 1995

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.


First Passage Processes In Queuing System Mx/Gr/1 With Service Delay Discipline, Lev M. Abolnikov, Jewgeni H. Dshalalow, Alexander M. Dukhovny Nov 1994

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 Jan 1994

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.


A Bulk Queueing System Under N-Policy With Bilevel Service Delay Discipline And Start-Up Time, David C.R. Muh Jan 1993

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 …


Optimal Controllability Of Impulsive Control Systems, Farzana A. Mcrae Jan 1993

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.


Quasilinearization For Some Nonlocal Problems, Yunfeng Yin Jan 1993

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.