Related papers: Jump formulas for singular integrals and layer pot…
We estimate fractional Sobolev and Besov norms of some singular integrals arising in the model problem for the Zakai equation with discontinuous signal and observation.
New invariants for 2-dimensional cell complexes are defined, which can be interpreted as curvature bounds. These invariants are proved to be rational and computable in a companion article. This document is a survey that collects theorems…
We study asymptotic jumping numbers for graded sequences of ideals, and show that every such invariant is computed by a suitable real valuation of the function field. We conjecture that every valuation that computes an asymptotic jumping…
We complete the proof of Oka's conjecture on the Alexander polynomial of an irreducible plane sextic. We also calculate the fundamental groups of irreducible sextics with a singular point adjacent to $J_{10}$.
We propose three kinds of explicit formulas for the elliptic lambda function by the elliptic modular function. Further, we derive incredible cubic identities as a corollary of our explicit formulas and evaluate some singular values of the…
In this paper, we give an explicit computable algorithm for the Zelevinsky-Aubert dual of irreducible representations of $p$-adic symplectic and odd special orthogonal groups. To do this, we establish explicit formulas for certain…
We show how to use the combinatorial notion of jump sets to parametrize the possible structures of the group of principal units of local fields, viewed as filtered modules. We establish a natural bijection between the set of jump sets and…
We establish the jump conditions for the wavefunction and its derivatives through the formal solutions of the wave equation. These conditions respond to the requirement of continuity of the perturbations at the position of the particle and…
We construct new spin singular integral equations for solving scattering problems for Maxwell's equations, both against perfect conductors and in media with piecewise constant permittivity, permeability and conductivity, improving and…
Potentials play an important role in solving boundary value problems for elliptic equations. In the middle of the last century, a potential theory was constructed for a two-dimensional elliptic equation with one singular coefficient. In the…
The double exponential formula was introduced for calculating definite integrals with singular point oscillation functions and Fourier-integrals. The double exponential transformation is not only useful for numerical computations but it is…
We show, in a borderline case which was not covered before, the validity of nonlinear Calder\'on-Zygmund estimates for a class of non-uniformly elliptic problems driven by double phase energies.
Computable and sharp error bounds are derived for asymptotic expansions for linear differential equations having a simple turning point. The expansions involve Airy functions and slowly varying coefficient functions. The sharpness of the…
We study the extended prepotentials for the S-duality class of quiver gauge theories, considering them as quasiclassical tau-functions, depending on gauge theory condensates and bare couplings. The residue formulas for the third derivatives…
The jump of the Milnor number of an isolated singularity $f_{0}$ is the minimal non-zero difference between the Milnor numbers of $f_{0}$ and one of its deformation $(f_{s}).$ In the case $f_{s}$ are non-degenerate singularities we call the…
We investigate some necessary and sufficient conditions for an exceptional divisor to contribute jumping numbers of an effective divisor on a variety of arbitrary dimension, inspired by the results for curves on surfaces by Smith and…
We prove a recent conjecture of Borot et al. that a particular universal closed algebraic formula recovers the correlation differentials of topological recursion after the swap of $x$ and $y$ in the input data. We also show that this…
We describe an algorithm that determines a set of unramified covers of a given hyperelliptic curve, with the property that any rational point will lift to one of the covers. In particular, if the algorithm returns an empty set, then the…
We prove the uniqueness of crepant resolutions for some quotient singularities and for some nilpotent orbits. The finiteness of non-isomorphic symplectic resolutions for 4-dimenensional symplectic singularities is proved. We also give an…
Some remarks on the jump condition appearing in Theorems 1.1 and 1.2 in the article [1] and their implications are given.