Compact finite difference scheme is applied for a partial integro-differential equation with a weakly singular kernel. The product trapezoidal method is applied for discretization of the integral term. The order of accuracy in space and time is , where . Stability and convergence in  norm are discussed through energy method. Numerical examples are provided to confirm the theoretical prediction ...

the aim of this paper is to study the high order difference scheme for the solution of a fractional partial differential equation (pde) in the electroanalytical chemistry. the space fractional derivative is described in the riemann-liouville sense. in the proposed scheme we discretize the space derivative with a fourth-order compact scheme and use the grunwald- letnikov discretization of the ri...

Let L be a positive line bundle over a projective complex manifold X , L its tensor power of order p, H(X,L) the space of holomorphic sections of L and Np the complex dimension of H(X,L). The determinant of a basis ofH(X,L), together with some given probability measure on a weighted compact set in X , induces naturally a βensemble, i.e., a random Np-point process on the compact set. Physically,...

We prove that every fragmentable linearly ordered compact space is almost totally disconnected. This combined with a result of Arvanitakis yields that every linearly ordered quasi Radon-Nikodým compact space is Radon-Nikodým, providing a new partial answer to the problem of continuous images of Radon-Nikodým compacta. It is an open problem posed by Namioka [8] whether the class of Radon-Nikodým...

We study two quantization schemes for compact symplectic manifolds with almost complex structures. The first of these is the Spinc quantization. We prove the analog of Kodaira vanishing for the Spinc Dirac operator, which shows that the index space of this operator provides an honest (not virtual) vector space semiclassically. We also introduce a new quantization scheme, based on a rescaled Lap...

we define a new type of spectrum, called δ-approximate spectrum, of an element a in a complex unital banach algebra a and show that the δ-approximate spectrum σ_δ (a) of a is compact. the relation between the δ-approximate spectrum and the usual spectrum is investigated. also an analogue of the classical gleason-kahane-zelazko theorem is established: for each ε>0, there is δ>0 such that if ϕ is...

Fix integers g ≥ 3 and r ≥ 2, with r ≥ 3 if g = 3. Given a compact connected Riemann surface X of genus g, letMDH(X) denote the corresponding SL(r, C) Deligne–Hitchin moduli space. We prove that the complex analytic space MDH(X) determines (up to an isomorphism) the unordered pair {X, X}, where X is the Riemann surface defined by the opposite almost complex structure on X .

In [Fuzzy Sets and Systems 27 (1988) 385-389], M. Grabiec in- troduced a notion of completeness for fuzzy metric spaces (in the sense of Kramosil and Michalek) that successfully used to obtain a fuzzy version of Ba- nachs contraction principle. According to the classical case, one can expect that a compact fuzzy metric space be complete in Grabiecs sense. We show here that this is not the case,...