DSpace Collection: 2012 Volume 21
http://hdl.handle.net/10525/2105
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Existence Theorems for Non-Cooperative Elliptic Systems
http://hdl.handle.net/10525/2158
Title: Existence Theorems for Non-Cooperative Elliptic Systems<br/><br/>Authors: Boyadzhiev, G.<br/><br/>Abstract: Existence of classical C2()TC() solutions of non-cooperative weakly coupled systems of elliptic second-order PDE is proved via the method of sub- and super-solutions.<br/><br/>Description: 2010 Mathematics Subject Classification: 35J65, 35K60, 35B05, 35R05.Oscillation Properties of Some Functional Fourth Order Ordinary Differential Equations
http://hdl.handle.net/10525/2157
Title: Oscillation Properties of Some Functional Fourth Order Ordinary Differential Equations<br/><br/>Authors: Petrova, Zornitza<br/><br/>Abstract: In this paper are considered oscillation properties of some classes of functional ordinary differential equations, namely equations of the typeziv(t) + mz′′(t) + g(z(t), z′(t), z′′(t), z′′′(t)) +nXi=1_i(t)z(t − i) = f(t),where m > 0 is constant, f(t) 2 C([T,1);R), T _ 0 is a large enough constant, g(z, _, _, _) 2 C(R4;R), _i(t) 2 C([0,1); [0,1)), 8 i = 1, n, n 2 N and {i}n i=1 are nonnegative constants. As a main result of this work we derive a sufficient condition for the distribution of the zeros of the above equations. Furthermore we discuss the complexity of the oscillation behavior of such equations and its relation to some properties of the corresponding solutions. Finally, we comment the oscillation behavior of a neutral fourth order ordinary differential equation, which appears in two papers of Ladas and Stavroulakis, as well as in a paper of Grammatikopoulos et al.<br/><br/>Description: 2010 Mathematics Subject Classification: 34A30, 34A40, 34C10.Best Approximation and Moduli of Smoothness
http://hdl.handle.net/10525/2156
Title: Best Approximation and Moduli of Smoothness<br/><br/>Authors: Dimova Zapryanova, Teodora<br/><br/>Abstract: The aim of this note is to present moduli of smoothness which are introduced by different schools of approximation for characterization of the best algebraic approximation. We observe that Potapov’s generalized moduli are equivalent to the error in approximation by the algebraic version of the trigonometric Jackson integrals in uniform norm and in weighted integral metric.<br/><br/>Description: 2010 Mathematics Subject Classification: 41A25, 41A10.Canonically Conjugate Variables for the μCH Equation
http://hdl.handle.net/10525/2155
Title: Canonically Conjugate Variables for the μCH Equation<br/><br/>Authors: Christov, Ognyan<br/><br/>Abstract: We consider the μCH equation which arises as an asymptotic rotator equation in a liquid crystal with a preferred direction if one takes into account the reciprocal action of dipoles on themselves. This equation is closely related to the periodic Camassa–Holm and the Hunter-Saxton equations. The μCH equation is also integrable and bi-Hamiltonian, that is, it is Hamiltonian with respect to two compatible Poisson brackets. We give a set of conjugated variables for both brackets.<br/><br/>Description: 2010 Mathematics Subject Classification: 35Q35, 37K10.Hyperbolic Fibrations and PDE
http://hdl.handle.net/10525/2154
Title: Hyperbolic Fibrations and PDE<br/><br/>Authors: Dimiev, Stancho<br/><br/>Abstract: In this note we try to distinguish the hyperbolic fibrations from the Euclidean one with the help of the invariant action of partial differential operators on the fibration. Two examples are given.<br/><br/>Description: 2010 Mathematics Subject Classification: 35L10, 35L90.Hyperbolic Double-Complex Laplace Operator
http://hdl.handle.net/10525/2153
Title: Hyperbolic Double-Complex Laplace Operator<br/><br/>Authors: N. Apostolova, Lilia<br/><br/>Abstract: In this paper is introduced the hyperbolic double-complex Laplace operator. The hyperbolic decomplexification of the hyperbolic doublecomplex Laplace operator and its characteristic set is found. The exponential eigenfunctions of the zero eigenvalue of the hyperbolic double-complex Laplace operator are found as well.<br/><br/>Description: 2010 Mathematics Subject Classification: 35G35, 32A30, 30G35.On Modified Method of Simplest Equation for Obtaining Exact Solutions of Nonlinear PDEs: Case of Elliptic Simplest Equation
http://hdl.handle.net/10525/2152
Title: On Modified Method of Simplest Equation for Obtaining Exact Solutions of Nonlinear PDEs: Case of Elliptic Simplest Equation<br/><br/>Authors: K. Vitanov, Nikolay<br/><br/>Abstract: The modified method of simplest equation is useful tool for obtaining exact and approximate solutions of nonlinear PDEs. These so- lutions are constructed on the basis of solutions of more simple equations called simplest equations. In this paper we study the role of the simplest equation for the application of the modified method of simplest equation. As simplest equation we discuss the elliptic equation.<br/><br/>Description: 2010 Mathematics Subject Classification: 74J30, 34L30.Interior Boundaries for Degenerate Elliptic Equations of Second Order Some Theory and Numerical Observations
http://hdl.handle.net/10525/2151
Title: Interior Boundaries for Degenerate Elliptic Equations of Second Order Some Theory and Numerical Observations<br/><br/>Authors: Chobanov, G.; Kutev, N.<br/><br/>Abstract: For boundary value problems for degenerate-elliptic equations of second order in ⊂ Rn there are cases when a closed surface exists, dividing into two subdomains in such a manner that two new correct boundary value problems can be formulated without introducing new boundary conditions. Such surfaces are called interior boundaries. Some theoretical results regarding the connections between the solutions of the original problem and the two new problems are given. Some numerical experiments using the finite elements method are carried out trying to visualize the effects of the presence of such interior boundary when n = 2. Also some more precise study of the solutions in the case n = 2 is presented.<br/><br/>Description: 2010 Mathematics Subject Classification: Primary 35J70; Secondary 35J15, 35D05.New Hardy-Type Inequalities with Singular Weights
http://hdl.handle.net/10525/2150
Title: New Hardy-Type Inequalities with Singular Weights<br/><br/>Authors: Fabricant, Alexander; Kutev, Nikolai; Rangelov, Tsviatko<br/><br/>Abstract: We prove a new Hardy–type inequality with weights that are possibly singular at internal point and on the boundary of the domain. As an illustration some applications and examples are given.<br/><br/>Description: 2010 Mathematics Subject Classification: 26D10.On the 3-Wave Equations with Constant Boundary Conditions
http://hdl.handle.net/10525/2149
Title: On the 3-Wave Equations with Constant Boundary Conditions<br/><br/>Authors: Gerdjikov, V. S.; Grahovski, G. G.<br/><br/>Abstract: The inverse scattering transform for a special case of the 3- wave resonant interaction equations with non-vanishing boundary conditions is studied. The Jost solutions and the fundamental analytic solutions (FAS) for the associated spectral problem are constructed. The inverse scattering problem for the Lax operator is formulated as a Riemann-Hilbert problem on a Riemannian surface. The spectral properties of the Lax operator are formulated.<br/><br/>Description: 2010 Mathematics Subject Classification: 37K40, 35Q15, 35Q51, 37K15.Riemann-Hilbert Problems with Canonical Normalization and Families of Commuting Operators
http://hdl.handle.net/10525/2148
Title: Riemann-Hilbert Problems with Canonical Normalization and Families of Commuting Operators<br/><br/>Authors: Gerdjikov, V. S.<br/><br/>Abstract: We start with a Riemann-Hilbert Problems (RHP) with canon- ical normalization whose sewing functions depends on several additional vari- ables. Using Zakharov-Shabat theorem we are able to construct a family of ordinary differential operators for which the solution of the RHP is a common fundamental analytic solution. This family of operators obviously commute. Thus we are able to construct new classes of integrable nonlinear evolution equations.<br/><br/>Description: 2010 Mathematics Subject Classification: 35Q15, 31A25, 37K10, 35Q58.An Invariant Theory of Surfaces in the Four-Dimensional Euclidean or Minkowski Space
http://hdl.handle.net/10525/2147
Title: An Invariant Theory of Surfaces in the Four-Dimensional Euclidean or Minkowski Space<br/><br/>Authors: Ganchev, Georgi; Milousheva, Velichka<br/><br/>Abstract: The present article is a survey of some of our recent results on the theory of two-dimensional surfaces in the four-dimensional Euclidean or Minkowski space. We present our approach to the theory of surfaces in Euclidean or Minkowski 4-space, which is based on the introduction of an invariant linear map of Weingarten-type in the tangent plane at any point of the surface under consideration. This invariant map allows us to introduce principal lines and an invariant moving frame field at each point of the surface. Writing derivative formulas of Frenet-type for this frame field, we obtain a system of invariant functions, which determine the surface up to a motion.We formulate the fundamental theorems for the general classes of surfaces in Euclidean or Minkowski 4-space in terms of the invariant functions.We show that the basic geometric classes of surfaces, determined by conditions on their invariants, can be interpreted in terms of the properties of two geometric figures: the tangent indicatrix and the normal curvature ellipse.We apply our theory to some special classes of surfaces in Euclidean or Minkowski 4-space.<br/><br/>Description: 2010 Mathematics Subject Classification: 53A07, 53A35, 53A10.Polyharmonic Hardy Spaces on the Klein-Dirac Quadric with Application to Polyharmonic Interpolation and Cubature Formulas
http://hdl.handle.net/10525/2146
Title: Polyharmonic Hardy Spaces on the Klein-Dirac Quadric with Application to Polyharmonic Interpolation and Cubature Formulas<br/><br/>Authors: Kounchev, Ognyan; Render, Hermann<br/><br/>Abstract: In the present paper we introduce a new concept of Hardy type space naturally defined on the Klein-Dirac quadric. We study different properties of the functions belonging to these spaces, in particular boundary value problems. We apply these new spaces to polyharmonic interpolation and to interpolatory cubature formulas.<br/><br/>Description: 2010 Mathematics Subject Classification: Primary 65D30, 32A35, Secondary 41A55.Closed Form Solutions of Integrable Nonlinear Evolution Equations
http://hdl.handle.net/10525/2145
Title: Closed Form Solutions of Integrable Nonlinear Evolution Equations<br/><br/>Authors: van der Mee, Cornelis<br/><br/>Abstract: In this article we obtain closed form solutions of integrable nonlinear evolution equations associated with the nonsymmetricmatrix Zakharov- Shabat system by means of the inverse scattering transform. These solutions are parametrized by triplets of matrices. Alternatively, the time evolution of the Marchenko integral kernels and direct substitution are employed in deriving these solutions.<br/><br/>Description: 2010 Mathematics Subject Classification: 35Q55.On the Holomorphic Extension of Solutions of Elliptic Pseudodifferential Equations
http://hdl.handle.net/10525/2144
Title: On the Holomorphic Extension of Solutions of Elliptic Pseudodifferential Equations<br/><br/>Authors: Cappiello, Marco; Nicola, Fabio<br/><br/>Abstract: We derive analytic estimates and holomorphic extensions for the solutions of a class of elliptic pseudodifferential equations on Rd.<br/><br/>Description: 2010 Mathematics Subject Classification: 35B65, 35S05, 35A20.Windowed-Wigner Representations, Interferences and Operators
http://hdl.handle.net/10525/2143
Title: Windowed-Wigner Representations, Interferences and Operators<br/><br/>Authors: Boggiatto, Paolo; Carypis, Evanthia; Oliaro, Alessandro<br/><br/>Abstract: “Windowed-Wigner” representations, denoted by Wig and Wig_ , were introduced in [2] in connection with uncertainty principles and interferences problems. In this paper we present a more precise analysis of their behavior obtaining an estimate of the L2-norm of interferences of couples of “model” signals. We further define a suitable functional framework for the associated operators and show that they form a class of pseudodifferential operators which define a natural “path” between the multiplication, Weyl and Fourier multipliers operators.<br/><br/>Description: 2010 Mathematics Subject Classification: 42B10, 47A07, 35S05.