Localization systems are usually used for detecting moving and offensive targets of enemy. The sound localization, however, is one of the main approaches in passive defense which has an impending role to aggression of enemy. This kind of localization method is carried out in a passive way, without emission of any signals and cannot be detected easily. The acoustic signals emitted by a sound sou...

In this paper we consider three-dimensional quantum q-oscillator field theory without spectral parameters. We construct an essentially big set of eigenstates of evolution with unity eigenvalue of discrete time evolution operator. All these eigenstates belong to a subspace of total Hilbert space where an action of evolution operator can be identified with quantized discrete BKP equations (synony...

This paper is devoted to the a priori and a posteriori error analysis of the hp-version of the discontinuous Galerkin nite element method for partial differential equations of hyperbolic and nearly-hyperbolic character. We consider second-order partial diierential equations with nonnegative characteristic form, a large class of equations which includes convection-dominated diiusion problems , d...

Deng’s lemma gives estimates on the behavior of solutions of ordinary differential equations in the neighborhood of a partially hyperbolic equilibrium. We prove a generalization in which “partially hyperbolic equilibrium” is replaced by “normally hyperbolic invariant manifold.” © 2007 Elsevier Inc. All rights reserved. MSC: 34E15; 34B15; 34C30

The Dirichlet problem and other nonclassical boundary value problems for linear hyperbolic equations with two independent variables have been the subject of various studies (see, e.g., [1]–[8], [10]–[16] and the references therein). However such problems for higher order nonlinear hyperbolic equations still remain unstudied. The present paper is an attempt to fulfill the existing gap. Let m and...

of the Dissertation Applications of the Seiberg-Witten equations to the Differential Geometry of non-compact Kähler manifolds by Ilya Elson Doctor of Philosophy in Mathematics Stony Brook University 2014 Soon after the introduction of the Seiberg-Witten equations, and their magnificent application to the differential topology of 4manifolds, LeBrun [LeB95a] used these equations to study differen...

For several hyperbolic knots, a relation between certain quantum invariants and the volume of their complements are discovered by R. Kashaev in [2]. In [6], it is shown that Kashaev’s invariants are specializations of the colored Jones polynomials. Kashaev used the saddle point method to obtain certain limit of invariants, and Y. Yokota proved that the equations to determine the saddle points c...

CONTENTS Introduction. 0. Pseudodifferential operators and linear PDE. §0.1 The Fourier integral representation and symbol classes §0.2 Schwartz kernels of pseudodifferential operators §0.3 Adjoints and products §0.4 Elliptic operators and parametrices §0.5 L 2 estimates §0.6 Gårding's inequality §0.7 The sharp Gårding inequality §0.8 Hyperbolic evolution equations §0.9 Egorov's theorem §0.10 M...

With the help of the generalized hyperbolic function, the subsidiary ordinary differential equation method is improved and proposed to construct exact traveling wave solutions of the nonlinear partial differential equations in a unified way. A class of nonlinear Schrödinger-type equations including the generalized Zakharov system, the Rangwala-Rao equation, and the Chen-Lee-Liu equation are inv...

We report a new type of Hamiltonian equations and maximum principle for the optimal control of a Goursat system when the underlying domain of 2-D "time" is not rectangular and has non-smooth boundary. The resulting Hamiltonian equations form a system of impulsive hyperbolic partial differential equations, with the impulses induced by the conditions on the costate at points of discontinuity on t...