相关论文: Determination of accessory parameters in a system …
We study the structure of analytic continuation of solutions of an even rank system of linear ordinary differential equations of Okubo normal form (ONF). We develop an adjustment of the method by using the Euler integral for evaluating the…
We study the accessory parameter problem for four-punctured spheres from the point of view of modular forms. The value of the accessory parameter giving the uniformization is characterized as the unique zero of a system of equations. This…
By applying an hyperbolic deformation to the uniformization problem for the infinite strip, we give a method for computing the accessory parameter for the torus with one source as an expansion in the modular parameter q. At O(q^0) we obtain…
Using the Observable form of Maxwell's equations, we reveal that effective parameters at materials boundaries emerge naturally as anisotropic transfer functions. The complexity of the boundary dictates the order of these functions.…
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated…
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated…
The relationship between various methods to calculate the physical degrees of freedom for gauge invariant systems of a general form is established. The set of hidden parameters caused for the superfluous degrees of freedom is revealed.
A general sufficient condition for the convergence of subsequences of solutions of non-autonomous, nonlinear difference equations and systems is obtained. For higher order equations the delay sizes and patterns play essential roles in…
In the paper a new sufficient condition for the Aubin property to a class of parameterized variational systems is derived. In these systems the constraints depend both on the parameter as well as on the decision variable itself and they…
The paper deals with a new sharp criterion ensuring the Aubin property of solution maps to a class of parameterized variational systems. This class includes parameter-dependent variational inequalities with non-polyhedral constraint sets…
We present infinitely many solutions of the general Heun equation in terms of generalized hypergeometric functions. Each solution assumes that two restrictions are imposed on the involved parameters: a characteristic exponent of one of the…
Pseudo-differential operator equations with parameter are studied. Uniform separability properties and resolvent estimates are obtained in terms of fractional derivatives. Moreover, maximal regularity properties of the pseudo-differential…
Parameter estimation-based observer (PEBO) is a recently developed constructive tool to design state observers for nonlinear systems. It reformulates the state estimation problem as one of online parameter identification, effectively…
We construct the fundamental solution of second order parabolic equations in non-divergence form under the assumption that the coefficients are of Dini mean oscillation in the spatial variables. We also prove that the fundamental solution…
A singularly perturbed linear system of second order ordinary differential equations of reaction-diffusion type with given boundary conditions is considered. The leading term of each equation is multiplied by a small positive parameter.…
We consider the uniqueness of solutions of ordinary differential equations where the coefficients may have singularities. We derive upper bounds on the the order of singularities of the coefficients and provide examples to illustrate the…
In this paper, we consider the problem of local parameter identifiability of a parameter function in a system of ordinary differential equations. Previously, in this problem, the case where the dimensions of a parameter and a solution of a…
In this paper we construct explicit connection coefficients and monodromy representations for the canonical solution matrices of Okubo systems ${\rm II}^*$, ${\rm III}^*$, ${\rm IV}$ and ${\rm IV}^*$ of ordinary differential equations in…
In this thesis we introduce the concept of a guided dynamical system, and exploit this idea to solve various problems in functional equations and PDE's. Our main results are 1) a necessary and sufficient condition for unique-solvability of…
In this work we propose a new kind of parameterized outer estimate of the united solution set to an interval parametric linear system. The new method has several advantages compared to the methods obtaining parameterized solutions…