Mathematical Sciences
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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 ... 
Existence of Approximate Solution to Abstract Nonlocal Cauchy Problem
(1992)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 righthand side of the nonlocal condition belongs to a locally ... 
Lyapunov Stability Theory for Dynamic Systems on Time Scales
(1992)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 ... 
On Modulated Random Measures
(1991)In this paper the author introduces the notion of a modulated marked random measure, Zξ on the class of locally compact and σcompact spaces with countable bases. As special cases, are marked processes modulated by ξ are ... 
Monotone iterations for differential equations with a parameter
(1997)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. 
On a multilevel controlled bulk queueing system MX/Gr,R/1
(1992)The authors introduce and study a class of bulk queueing systems with a compound Poisson input modulated by a semiMarkov process, multilevel control service time and a queue length dependent service delay discipline. ... 
Extremal Solutions to a Class of Multivalued Integral Equations in Banach Space
(1992)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 ... 
Generalized Two Point Boundary Value Problems. Existence and Uniqueness
(1992)An algorithm is presented for finding the pseudoinverse 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 ... 
On Solvability of Mixed Monotone Operator Equations with Applications to Mixed Quasimonotone Differential Systems Involving Discontinuities
(1992)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 ... 
A First Passage Problem and its Applications to the Analysis of a Class of Stochastic Models
(1992)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 ... 
A positive solution for singular discrete boundary value problems with signchanging nonlinearities
(20050302)This paper presents new existence results for the singular discrete boundary value problem  Δ²u(k  1) = g(k, u(k)) + λh(k,u(k)), k ∈ [1,T], u(0) = 0 = u(T + 1). In particular, our nonlinearity may be singular in its ... 
Generalized flow invariance for differential inclusions
(20050512)We introduce a generalized notion of invariance for differential inclusions, using a proximal aiming condition in terms of proximal normals. A set of sufficient conditions for the weak and strong invariance in the generalized ... 
A nonmarkovian queueing system with a variable number of channels
(2003)In this paper we study a queueing model of type GI/M/m̃a/∞ with m parallel channels, sonic of which may suspend their service at specified random moments of time. Whether or not this phenomenon occurs depends on the queue ... 
Unique Solution to Periodic Boundary Value Problems
(1991)Existence of unique solution to periodic boundary value problems of differential equations with continuous or discontinuous righthand side is considered by utilizing the method of lower and upper solutions and the monotone ... 
Error Bounds for Two Even Degree Tridiagonal Splines
(1990)We study a C(¹) parabolic and a C(²) quartic spline which are determined by solution of a tridiagonal matrix and which interpolate subinterval midpoints. In contrast to the cubic C(²) spline, both of these algorithms ... 
Strong Maximum Principles for Parabolic Nonlinear Problems With Nonlocal Inequalities Together With Integrals
(1990)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 ... 
Asymptotic Optimality of Experimental Designs in Estimating a Product of Means
(1990)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 ... 
Existence and Uniqueness of Solutions of Nonlocal Problems for Hyperbolic Equation uxt=F(x, t, u, ux)
(1990)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 ...