In this paper we discuss various aspects of non-compact models of CFT of the type: ∏NL j=1{N = 2 Liouville theory}j ⊗ ∏NM i=1{N = 2 minimal model}i and ∏NL j=1{SL(2;R)/U(1) supercoset}j⊗ ∏NM i=1 {N = 2 minimal model}i. These models are related to each other by T-duality. Such string vacua are expected to describe non-compact Calabi-Yau compactifications, typically ALE fibrations over (weighted)...

-This paper introduces general discrete linear Harniltonian eigenvalue problems and characterizes the eigenvalues. Assumptions are given, among them the new notion of strict controllability of a discrete system, that imply isolatedness and lower boundedness of the eigenvalues. Due to the quite general assumptions, discrete Sturrn-Liouville eigenvalue problems of higher order are included in the...

The measure algebras of the title are those which are also hypergroups with some regularity conditions, Examples include the convolutions associated with Jacobi polynomial series and Fourier Bessel series, It is shown here that there is a one-to-one correspondence between these hypergroups and a class of Sturm-Liouville problems which have the characters of the hypergroup as eigenfunctions, The...

It is well known that the two spectra {λn} and {μn} uniquely determine the potential function q (r) in a Sturm-Liouville equation defined on the unit interval having the singularity type ( ) 2 1 2 r r + +   (where  is a integer) at the point zero. In this work, we give the solution of the inverse problem on two partially noncoincide spectra for the Sturm-Liouville equation with the peculiari...

We study infinite linear independence of polyadic numbers $$

In this study, we obtained a system of eigenfunctions and eigenvalues for the mixed homogeneous Sturm-Liouville problem second-order differential equation containing fractional derivative operator. The differentiation operator was considered according to two definitions: Gerasimov-Caputo Riemann-Liouville-Visualizations eigenfunctions, biorthogonal system, distribution on real axis were present...

We first verify the global well-posedness of impulsive reaction-diffusion equations on infinite lattices. Then we establish that generated process by solution operators has a pullback attractor and family Borel invariant probability measures. Furthermore, formulate definition statistical for addressed system prove existence. Our results show satisfies merely Liouville type theorem piecewise, eq...

We describe a self-consistent canonical quantization of Liouville theory in terms of canonical free fields. In order to keep the non-linear Liouville dynamics, we use the solution of the Liouville equation as a canonical transformation. This also defines a Liouville vertex operator. We show, in particular, that a canonical quantized conformal and local quantum Liouville theory has a quantum gro...

Abstract: In this paper, we present a novel method for computation of eigenvalues and eigenfunctions for a class of singular Sturm-Liouville boundary value problems using modified Adomian decomposition method. The proposed method can be applied to any type of regular as well as singular Sturm-Liouville problems. This current method is capable of finding any n-th eigenvalues and eigenfunctions o...