This paper is concerned with weak solution of a mixed boundary value problem for the biharmonic equation in the plane. Using Green’s formula, the problem is converted into a system of Fredholm integral equations for the unknown data on different part of the boundary. Existence and uniqueness of the solutions of the system of boundary integral equations are established in appropriate Sobolev spa...

The vibro-acoustic characteristics of cylindrical shell are widely studied because of its strong engineering application background, especially when the shell is immersed in infinite fluid field or partially immersed. In the present paper, the method for analyzing sound radiation of semi-submerged finite cylindrical shell with antisymmetric velocity distribution is first proposed. The orthogona...

It is shown that certain natural maps between the ideal, Gromov, and end boundaries of a complete CAT(0) space can fail to be either injective or surjective. Additionally the natural map from the Gromov boundary to the end boundary of a complete CAT(−1) space can fail to be either injective or surjective.

krein [1] mentioned that for each pd equation we have two extreme operators, one is the minimal in which solution and its derivatives on the boundary are zero, the other one is the maximal operator in which there is no prescribed boundary conditions. they claim it is not possible to have a related boundary value problem for an arbitrarily chosen operator in between. they have only considered lo...

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...