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....

In this article we have proposed an accurate finite difference method for approximate numerical solution of second order boundary value problem with Dirichlet boundary conditions. There are numerous numerical methods for solving these boundary value problems. Some these methods are more efficient and accurate than others with some advantages and disadvantages. The results in experiment on model...

We first study positivity in C*-modules using tripotents (= partial isometries) which are what we call open. This is then used to study ordered operator spaces via an ‘ordered noncommutative Shilov boundary’ which we introduce. This boundary satisfies the usual universal diagram/property of the noncommutative Shilov boundary, but with all the ‘arrows’ completely positive. Because of their indep...

The recent progress of physiological measurement allows us to observe membrane potential behaviors of extensive regions with higher spatial and temporal resolutions. Accordingly, a new theory has been expected with which we can analyze the spatiotemporal dynamics of the membrane potential with the cell-shape and the spatial distributions of electrical parameters taken into consideration quantit...

The differentiation matrix for a Daubechies-based wavelet basis defined on an interval will be constructed. It will be shown that the differentiation matrix based on the currently available boundary constructions does not maintain the superconvergence encountered under periodic boundary conditions. BJgy .. .. . .. .A0000 w__ •t!ar ~'..,-

Abstract. The problem of Rayleigh–Bénard convection with internal heat sources and a variable gravity field is treated. For the case of stress-free boundary conditions, it is proved that the principle of exchange of stabilities holds as long as the product of gravity field and the integral of the heat sources is nonnegative throughout the layer. The proof is based on the idea of a positive oper...

Wepresent first-principles simulations of single grain boundary reflectivity of electrons in noble metals, Cu and Ag. We examine twin and non-twin grain boundaries using nonequilibrium Green’s function and first principles methods. We also investigate the determinants of reflectivity in grain boundaries by modeling atomic vacancies, disorder, and orientation and find that both the change in gra...

In this article, we introduce and study local constant and our preferred local linear nonparametric regression estimators when it is appropriate to assess performance in terms of mean squared relative error of prediction. We give asymptotic results for both boundary and non-boundary cases. These are special cases of more general asymptotic results that we provide concerning the estimation of th...

We study an initial-boundary-value problem of a nonlinear Korteweg-de Vries equation posed on a finite interval (0, 2π). The whole system has Dirichlet boundary condition at the left end-point, and both of Dirichlet and Neumann homogeneous boundary conditions at the right end-point. It is known that the origin is not asymptotically stable for the linearized system around the origin. We prove th...

In this paper we study boundary element methods for initialNeumann problems for the heat equation. Error estimates for some fully discrete methods are established. Numerical examples are presented.