The point source traveltime eld has an upwind singularity at the source point. Consequently, all formally high-order nite-diierence eikonal solvers exhibit rst-order convergence and relatively large errors. Adaptive upwind nite-diierence methods based on high-order Weighted Essentially NonOscillatory (WENO) Runge-Kutta diierence schemes for the paraxial eikonal equation overcome this diiculty. ...

The point-source traveltime field has an upwind singularity at the source point. Consequently, all formally high-order, finite-difference eikonal solvers exhibit firstorder convergence and relatively large errors. Adaptive upwind finite-difference methods based on high-order Weighted Essentially NonOscillatory (WENO) RungeKutta difference schemes for the paraxial eikonal equation overcome this ...

Let Σ be a weighted homogeneous (singular) subvariety of C . The main objective of this paper is to present an explicit formula for solving the ∂-equation λ = ∂g on the regular part of Σ, where λ is a ∂-closed (0, 1)-form with compact support. This formula will then be used to give Hölder estimates for the solution in case Σ is homogeneous (a cone) with an isolated singularity. Finally, a sligh...

Let (X, g) be a compact Riemannian stratified space with simple edge singularity. Thus a neighbourhood of the singular stratum is a bundle of truncated cones over a lower dimensional compact smooth manifold. We calculate the various polynomially weighted de Rham cohomology spaces of X , as well as the associated spaces of harmonic forms. In the unweighted case, this is closely related to recent...

We give formulas for the image Milnor number of a weighted-homogeneous map-germ $$({\mathbb {C}}^n,0)\rightarrow ({\mathbb {C}}^{n+1},0)$$ , $$n=4$$ and 5, in terms weights degrees. Our expressions are obtained by purely interpolative method, applied to result Ohmoto. use our approach recover $$n=2$$ 3 due Mond Ohmoto, respectively. For $$n\ge 6$$ method is valid as long certain multi-singulari...

Abstract The hybrid model is the Landau–Ginzburg-type theory that expected, via Landau–Ginzburg/ Calabi–Yau correspondence, to match Gromov–Witten of a complete intersection in weighted projective space. We prove wall-crossing formula exhibiting dependence genus-zero on its stability parameter, generalizing work [21] for quantum singularity and paralleling Ciocan-Fontanine–Kim [7] quasimaps. Th...

‎in this study‎, ‎properties of spectral characteristic are investigated for‎ ‎singular sturm-liouville operators in the case where an eigen‎ ‎parameter not only appears in the differential equation but is‎ ‎also linearly contained in the jump conditions‎. ‎also weyl function‎ ‎for considering operator has been defined and the theorems which‎ ‎related to uniqueness of solution of inverse proble...

in this paper, we investigate the canonical property of solutions of a system of differentialequations having a singularity and turning point of even order. first, by a replacement, we transform thesystem to the sturm-liouville equation with a turning point. using the asymptotic estimates for a specialfundamental system of solutions of sturm-liouville equation, we study the infinite product rep...

We study the problem -? u = f , where has a point-singularity. In particular, we are interested in ? x 0 Dirac delta with support but singularities of form ~ | ? ?s also considered. prove stability Galerkin projection on graded meshes weighted spaces, weights given by powers distance to . recover optimal rates convergence for finite element method these meshes. Our approach is general and holds...

Abstract In this article, we consider an infinite family of normal surface singularities with integral homology sphere link which is related to the space monomial curves a plane semigroup. These appear as special fibers equisingular families whose generic are complex branch, and in proof monodromy conjecture for these curves. To investigate whether singularity sphere, one can use characterizati...