Numerical solutions of the Helmholtz equation with Robbins boundary conditions are researched using the quadratic spline collocation method. By reordering the unknowns, we obtain a 2×2 block linear system where the two diagonal sub-matrices are block tridiagonal. For the obtained linear system, we introduce a two-step preconditioner using the block polynomial preconditioner. Theoretical analysi...

We propose and analyse a hybrid numerical–asymptotic hp boundary element method (BEM) for time-harmonic scattering of an incident plane wave by an arbitrary collinear array of sound-soft twodimensional screens. Our method uses an approximation space enriched with oscillatory basis functions, chosen to capture the high-frequency asymptotics of the solution. We provide a rigorous frequencyexplici...

In this work we extend Brosamler’s formula (see [2]) and give a probabilistic solution of a non degenerate Poisson type equation with Neumann boundary condition in a bounded domain of the Euclidean space.

We review the explicit derivation of the Gauss-Bonet and Hirzebruch formulae by physical model and give a physical proof of the Lefschetz fixed-point formula by twisting boundary conditions for the path integral.

We analyze the use of a five-point difference formula for the discretization of the third derivative operator on nonuniform grids. The formula was derived so as to coincide with the standard five-point formula on regular grids and to lead to skew-symmetric schemes. It is shown that, under periodic boundary conditions, the formula is supraconvergent in the sense that, in spite of being inconsist...

This paper establishes an isomorphism between the Bar-Natan skein module of the solid torus with a particular boundary curve system and the homology of the (n, n) Springer variety. The results build on Khovanov’s work with crossingless matchings and the cohomology of the (n, n) Springer variety. We also give a formula for comultiplication in the Bar-Natan skein module for this specific three-ma...

This paper proposes to incorporate boundary curvature ratio, region homogeneity and boundary smoothness into a single new merging criterion to improve the oversegmentation of marker-controlled watershed segmentation algorithm. The result is a more refined segmentation result with smooth boundaries and regular shapes. To pursue a final segmentation result with higher inter-variance and lower int...

We use simple currents to construct symmetric special Frobenius algebras in modular tensor categories. We classify such simple current type algebras with the help of abelian group cohomology. We show that they lead to the modular invariant torus partition functions that have been studied by Kreuzer and Schellekens. We also classify boundary conditions in the associated conformal field theories ...

Singular boundary conditions are formulated for non-selfadjoint Sturm-Liouville problems which are limitcircle in a very general sense. The characteristic determinant is constructed and it is shown that it can be used to extend the Birkhoff theory for so called ‘Birkhoff regular boundary conditions’ to the singular case. This is illustrated for a class of singular Birkhoff-regular problems; in ...