Related papers: A combinatorial integration on the Cantor dust

We provide formulas for computing the cocycles on a 3-point Witt algebra Der(R), using an isomorphism between two 3-point algebras Der(R) and Der(S), where the cocycle is already defined. These cocycles can be used to construct universal…

Several new formulas are developed that enable the evaluation of a family of definite integrals containing the product of two Whittaker W-functions. The integration is performed with respect to the second index, and the first index is…

A product of cochains in a polyhedral complex is constructed. The multiplication algorithm depends on the choice of a parameter. The parameter is a linear functional on the ambient space. Cocycles form a subring of the ring of cochains,…

We prove a compact embedding theorem in a class of spaces of piecewise H1 functions subordinated to a class of shape regular, but not necessarily quasi-uniform triangulations of a polygonal domain. This result generalizes the…

Building on recent progress in constructing derivations on Fourier algebras, we provide the first examples of locally compact groups whose Fourier algebras support non-zero, alternating 2-cocycles; this is the first step in a larger…

The present article studies combinatorial tilings of Euclidean or spherical spaces by polytopes, serving two main purposes: first, to survey some of the main developments in combinatorial space tiling; and second, to highlight some new and…

Two components of spherically symmetric, inhomogeneous dust penetrating each other are introduced as a generalization of the well-known Tolman-Bondi dust solution. The field equations of this model are formulated and general properties are…

This paper explores generalized slice monogenic functions by introducing their operator symbols, representation formula, and integral formula. The study extends the Teodorescu transform to a broader class of theorems and inferences,…

We provide a combinatorial formula for the structure constants of spin Hall--Littlewood functions. This is achieved by representing these functions and the structure constants as the partition function of a lattice model and applying the…

We investigate topology change in (1+1) dimensions by analyzing the scalar-curvature action $1/2 \int R dV$ at the points of metric-degeneration that (with minor exceptions) any nontrivial Lorentzian cobordism necessarily possesses. In two…

We generalize the definition of convolution of vectors and tensors on the 2-sphere, and prove that it commutes with differential operators. Moreover, vectors and tensors that are normal/tangent to the spherical surface remain so after the…

In this paper, we are concerned with the effective elastic property of a two-phase high-contrast periodic composite with densely packed inclusions. The equations of linear elasticity are assumed. We first give a novel proof of the…

A formula for the interior epsilon-neighborhood of the classical von Koch snowflake curve is computed in detail. This function of epsilon is shown to match quite closely with earlier predictions of what it should be, but is also much more…

The implementation of a new particle module describing the physics of dust grains coupled to the gas via drag forces is the subject of this work. The proposed particle-gas hybrid scheme has been designed to work in Cartesian as well as in…

We study the unwheeled rational Kontsevich integral of torus knots. We give a precise formula for these invariants up to loop degree 3 and show that they appear as colorings of simple diagrams. We show that they behave under cyclic branched…

In this paper, general quaternionic structure are developed for the local fractional Moisil-Teodorescu operator in Cantor-type cylindrical and spherical coordinate systems. Two examples for the Helmholtz equation with local fractional…

We study the strongly singular volume integral equation that describes the scattering of time-harmonic electromagnetic waves by a penetrable obstacle. We consider the case of a cylindrical obstacle and fields invariant along the axis of the…

We study quasi-Monte Carlo (QMC) integration over the multi-dimensional unit cube in several weighted function spaces with different smoothness classes. We consider approximating the integral of a function by the median of several integral…

In this note, we study a concatenation of quasi-Monte Carlo and plain Monte Carlo rules for high-dimensional numerical integration in weighted function spaces. In particular, we consider approximating the integral of periodic functions…

In this paper we take up again the deformation theory for $K$-linear pseudofunctors initiated in a previous work (Adv. Math. 182 (2004) 204-277). We start by introducing a notion of a 2-cosemisimplicial object in an arbitrary 2-category and…