We derive new representations of the efficient score for coarse data problems based on Neumann series expansion. The representations can be applied to both ignorable and nonignorable coarse data. An approximation to the new representation may be used for computing locally efficient scores in such problems. We show that many of the successive approximation approaches to the computation of the lo...

We compare the effectiveness of solving Dirichlet–Neumann problems via the Craig–Sulem (CS) expansion, the Ablowitz-Fokas-Musslimani (AFM) implicit formulation, the dual AFM formulation (AFM∗), a boundary integral collocation method (BIM), and the transformed field expansion (TFE) method. The first three methods involve highly ill-conditioned intermediate calculations that we show can be overco...

In this paper, we are concerned with the error analysis for the finite element solution of the two-dimensional exterior Neumann boundary value problem in acoustics. In particular, we establish an explicit priori error estimates in H and Lnorms including both the effect of the truncation of the DtN mapping and that of the numerical discretization. To apply the finite element method (FEM) to the ...

Questions of flux regulation in biological cells raise a renewed interest in the narrow escape problem. The determination of a higher order asymptotic expansion of the narrow escape time depends on determining the singularity behavior of the Neumann Green's function for the Laplacian in a three-dimensional (3D) domain with a Dirac mass on the boundary. In addition to the usual 3D Coulomb singul...

Conformal deformations of hyperbolic surfaces with conical singularities are shown to be real-analytic. The first nontrivial term in the power series expansion around a cusped surface is shown to be a multiple of the Eisenstein series E2.

In this paper we introduce some new subclasses of the class σ of bi-univalent functions and obtain bounds for the initial coefficients of the Taylor series expansion of functions from the considered classes.

Using binomial coefficients a general series expansion formula is established for the integral