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On the Qualitative Theory of the Nonlinear Parabolic pLaplacian Type ReactionDiffusion Equations
(201811)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 pLaplacian type ... 
Fluctuation Analysis in Stochastic System with Parallel Queues
(201807)In this dissertation, We analyze a complex queueing system with a single server operating in three different modes and, dependent on circumstances, servicing two different queues simultaneously. There are different switching ... 
Time Sensitive Functionals of Marked Random Measures in Real Time
(201810)In this dissertation, we study marked random measures that model stochastic networks (under attacks), status of queueing systems during vacation modes, responses to cancer treatments (such as chemotherapy and radiation), ... 
Boundary Value Problems in a Multidimensional Box for Higher Order Linear and QuasiLinear Hyperbolic Equations
(201805)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) ... 
Lower Order Perturbations of Critical Fractional Laplacian Equations
(201807)We give suffcient conditions for the existence of nontrivial solutions to a class of critical nonlocal problems of the BrezisNirenberg type. Our result extends some results in the literature for ... 
On the Qualitative Theory of the Nonlinear Degenerate Second Order Parabolic Equations Modeling ReactionDiffusionConvection Processes
(201805)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 reactiondiffusionconvection processes arising in many areas of science and ... 
The Capacitated Transfer Point Covering Problem (TPCP): Expanding Delivery Network Coverage with Minimal Resources
(201805)Retail delivery services have begun using unmanned systems in attempts to reduce the time from a customer’s order to when the product arrives at its intended destination. Utilizing these systems are beneficial to both ... 
Parametric and NonParametric Regression Models with Applications to Climate Change
(201712)In this dissertation we have studied the climate factors that contribute to climate change using univariate and multivariate parametric methods as well as nonparametric models. In this study, we have three major ... 
On Logconcavity of Multivariate Discrete Distributions
(201712)The contribution of this dissertation to the literature is twofold. First, we use a geometric perspective to present all possible subdivisions of R³ into tetrahedra with disjoint interiors and adopt a combinatorial ... 
SturmLiouville Equations with Singular Endpoints of Poincaré Rank Zero and One
(201705)In this dissertation, my objective is to study, for x ∊ (0, ∞), the equations (1) (xy′)′ + (‐v²/x + λ x)y = 0, with a view to obtaining representations of solutions near the singular endpoints, connection formulas for ... 
On the Classification of the Second Minimal Orbits of the Continuous Endomorphisms on the Real Line and Universality in Chaos
(201704)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 ... 
New Bounds for the koutofn Type Probabilities and Their Applications
(201704)The contribution of the shape information of the underlying distribution in probability bounding problem is investigated and an efficient linear programming based bounding methodology, which takes advantage of the advanced ... 
InitialBoundary and Nonlocal Boundary Value Problems for Higher Order Nonlinear Hyperbolic Equations with Two Independent Variables
(201705)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 ... 
Discrete and Continuous Operational Calculus in Stochastic Games
(201612)First, we consider a class of antagonistic stochastic games between two players A and B. The game is specified in terms of two "hostile" stochastic processes representing mutual attacks upon random times exerting casualties ... 
On the Inverse Multiphase Stefan Problem
(201507)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, ... 
Random Walks on Random Lattices and Their Applications
(201505)This work studies a class of continuoustime, multidimensional random walk processes with mutually dependent random step sizes and their exits from hyperrectangles. Fluctuations of the process about the critical boundary ...