Abstract The goal of this study is to analyse the eigenvalues and weak eigenfunctions a new type multi-interval Sturm-Liouville problem (MISLP) which differs from standard problems (SLPs) in that Strum-Liouville equation defined on finite number non-intersecting subintervals boundary conditions are set not only at endpoints but also internal points interaction. For self-adjoint treatment consid...

We introduced the continuous and discrete $p$-adic shearlet systems. We restrict ourselves to a brief description of the $p$-adic theory and shearlets in real case. Using the group $G_p$ consist of all $p$-adic numbers that all of its elements have a square root, we defined the continuous $p$-adic shearlet system associated with $L^2left(Q_p^{2}right)$. The discrete $p$-adic shearlet frames for...

In recent years, substantial progress in shape analysis has been achieved through methods that use the spectra and eigenfunctions of discrete Laplace operators. In this work, we study spectra and eigenfunctions of discrete differential operators that can serve as an alternative to the discrete Laplacians for applications in shape analysis. We construct such operators as the Hessians of surface ...

The goal of this work is to characterize all second order difference operators of several variables that have discrete orthogonal polynomials as eigenfunctions. Under some mild assumptions, we give a complete solution of the problem.

Shape invariance is an important ingredient of many exactly solvable quantum mechanics. Several examples of shape invariant “discrete quantum mechanical systems” are introduced and discussed in some detail. They arise in the problem of describing the equilibrium positions of Ruijsenaars-Schneider type systems, which are “discrete” counterparts of Calogero and Sutherland systems, the celebrated ...

Shape invariance is an important ingredient of many exactly solvable quantum mechanics. Several examples of shape invariant “discrete quantum mechanical systems” are introduced and discussed in some detail. They arise in the problem of describing the equilibrium positions of Ruijsenaars-Schneider type systems, which are “discrete” counterparts of Calogero and Sutherland systems, the celebrated ...

in this article, we propose an adaptive grid based on mesh equidistribution principle for two-parameter convection-diffusion boundary value problems with continuous and discontinuous data. a numerical algorithm based on an upwind finite difference operator and an appropriate adaptive grid is constructed. truncation errors are derived for both continuous and discontinuous problems. parameter uni...

Applications in which data take nonnegative values but have a substantial proportion of values at zero occur in many disciplines. The modeling of such “clumped-at-zero” or “zero-inflated” data is challenging. We survey models that have been proposed. We consider cases in which the response for the non-zero observations is continuous and in which it is discrete. For the continuous and then the d...

in this paper, we investigate some properties of eigenvalues and eigenfunctions of boundary value problems with separated boundary conditions. also, we obtain formal series solutions for some partial differential equations associated with the second order differential equation, and study necessary and sufficient conditions for the negative and positive eigenvalues of the boundary value problem....