Related papers: Discrete $d$-dimensional moduli of smoothness

The purpose of this paper is twofold: 1) Applications of Gallagher's larger sieve modulo prime squares do not work. In some relevant cases we can transform the residue class information modulo $p^2$ to more suitable residue information…

Let $\Q=[0,1)^d$ denote the unit cube in $d$-dimensional Euclidean space \Rd and let \T be a discrete subset of \Rd. We show that the exponentials $e_t(x):=exp(i2\pi tx)$, $t\in\T$ form an othonormal basis for $L^2(\Q)$ if and only if the…

Let $(\lambda_f(n))_{n\geqslant1}$ be the Hecke eigenvalues of a holomorphic cusp form $f$. We prove that the exponent of distribution of $\lambda_f*1$ in arithmetic progressions is as large as $\frac{1}{2}+\frac{1}{46}$ when the modulus…

In this paper we give an effective criterion as to when a prime number p is the order of an automorphism of a smooth cubic hypersurface of P^{n+1}, for a fixed n > 1. We also provide a computational method to classify all such hypersurfaces…

Discrete Morse theory emerged as an essential tool for computational geometry and topology. Its core structures are discrete gradient fields, defined as acyclic matchings on a complex $C$, from which topological and geometrical informations…

Let ${\cal D}^k$ be the space of $k$-th order linear differential operators on ${\bf R}$: $A=a_k(x)\frac{d^k}{dx^k}+\cdots+a_0(x)$. We study a natural 1-parameter family of $\Diff(\bf R)$- (and $\Vect(\bf R)$)-modules on ${\cal D}^k$. (To…

An efficient integral equation based solver is constructed for the electrostatic problem on domains with cuboidal inclusions. It can be used to compute the polarizability of a dielectric cube in a dielectric background medium at virtually…

We prove that $\delta$-invariants of smooth cubic surfaces are at least $\frac{6}{5}$.

In this paper, we show that the \alpha_{m,2}-invariant of a smooth cubic surface with Eckardt points is strictly bigger than 2/3. This can be used to simplify Tian's original proof of the existence of Kaehler-Einstein metrics on such…

We study the moduli space of stable sheaves of Euler characteristic 1, supported on curves of arithmetic genus 2 contained in a smooth quadric surface. We show that this moduli space is rational. We give a classification of the stable…

Recently Jeong and Kim [Phys. Rev. E {\bf 66}, 051605 (2002)] investigated the scaling properties of equilibrium self-flattening surfaces subject to a restricted curvature constraint. In one dimension (1D), they found numerically that the…

We show that isotropic positive definite functions on the $d$-dimensional sphere which are $2k$ times differentiable at zero have $2k+[(d-1)/2]$ continuous derivatives on $(0,\pi)$. This result is analogous to the result for radial positive…

We show that the moduli space of degree $e$ maps from smooth genus $g \ge 1$ curves to an arbitrary low degree smooth hypersurface is singular when $e$ is large compared to $g$. We also give a lower bound for the dimension of the singular…

The goal of this paper is to construct a compactification of the moduli space of degree $d \ge 5$ surfaces in $\mathbb{P}^3$, i.e. a parameter space whose interior points correspond to (equivalence classes of) smooth surfaces in…

As a continuation of the authors and Wakatsuki's previous paper [5], we study relations among Dirichlet series whose coefficients are class numbers of binary cubic forms. We show that for any integral models of the space of binary cubic…

In this paper we show that the moduli space of nodal cubic surfaces is isomorphic to a quotient of a 4-dimensional complex ball by an arithmetic subgroup of the unitary group. This complex ball uniformization uses the periods of certain K3…

Motivated by asymptotic phenomena of moduli spaces of higher rank stable sheaves on algebraic surfaces, we study the Picard number of the moduli space of one-dimensional stable sheaves supported in a sufficiently positive divisor class on a…

This note investigates the regularity of zero-extensions of $L^p$ functions from bounded domains. Simple examples show the possibility of a loss in smoothness and our goal is to quantify this loss more generally. For the unit cube…

We study the moduli space of stable sheaves of Euler characteristic 1 supported on curves of arithmetic genus 3 contained in a smooth quadric surface. We show that this moduli space is rational. We compute its Betti numbers by studying the…

We study smoothness of densities for the solutions of SDEs whose coefficients are smooth and nondegenerate only on an open domain $D$. We prove that a smooth density exists on $D$ and give upper bounds for this density. Under some…