In this paper we study boundary integral formulations of the interior and exterior Dirichlet problem for the bi{Laplacian in a plane domain with a piecewise smooth boundary having corner points. The mapping properties of single and double layer bihar-monic potentials, of the Calderon projections and the Poincar e-Steklov operators for such domains are analysed. We derive direct boundary integra...

The Barnes double gamma function G(z) is considered for large argument z. A new integral representation is obtained for log G(z). An asymptotic expansion in decreasing powers of z and uniformly valid for |Arg z|<? is derived from this integral. The expansion is accompanied by an error bound at any order of the approximation. Numerical experiments show that this bound is very accurate for real z...

The tracking of a given voltage in the traditional double closed-loop proportional integral control current power grid simulator has problems such as static difference, delay and oscillation. It is proposed that outer loop inner inverter side adopt quasi-proportional resonance respectively, topology adopts cascaded modular design to establish single-phase model. Compared with proportional-integ...

A nonlinear problem of mean-square approximation of a real nonnegative continuous function with respect to two variables by the modulus of double Fourier integral dependent on two real parameters with use of the smoothing functional is studied. Finding the optimal solutions of this problem is reduced to solution of the Hammerstein type two-dimensional nonlinear integral equation. The numerical ...

NEMO’s main task is the computation of current-voltage (I-V) characteristics for resonant tunneling diodes (RTDs). The primary model for high performance RTDs is the full band sp3s∗ tight binding simulation, which is based on a numerical double integral of energy and transverse momentum over a transport kernel at each bias point. A full charge self-consistent simulation invoking this model on a...

We describe how the matrix integral of Imbimbo and Mukhi arises from a limit of the FZZT partition function in the double-scaled c = 1 matrix model. We show a similar result for 0A and comment on subtleties in 0B.

We define Oseen single layer and double layer potentials and study their properties. Using the integral equation method we prove the existence and uniqueness of an L q-solution of the Robin problem for the Oseen system.

let  be a banach algebra. let  be linear mappings on . first we demonstrate a theorem concerning the continuity of double derivations; especially that all of -double derivations are continuous on semi-simple banach algebras, in certain case. afterwards we define a new vocabulary called “-higher double derivation” and present a relation between this subject and derivations and finally give some ...

We obtain the degree of approximation of functions belonging to class Lip(ψ(u,v);p), p > 1 using the Gauss Weierstrass integral of the double Fourier series of f(x,y).