相关论文: Characterizing Volume Forms

In a previous work (arXiv:2505.05574), a summation formula for harmonic Maass forms of polynomial growth was established. In this note, we use the theory of $L$-series of harmonic Maass forms to state and prove a summation formula for such…

The advent of high resolution imaging has made data on surface shape widespread. Methods for the analysis of shape based on landmarks are well established but high resolution data require a functional approach. The starting point is a…

In this paper, we introduce the notion of Maass-Jacobi forms and investigate some properties of these new automorphic forms. We also characterize these automorphic forms in several ways.

This thesis presents L\"uscher's $\mu$- and $F$-term corrections to volume dependence of non-diagonal finite volume form factors in the scaling Lee-Yang model. An explicit calculation proves the suspected relation that the $\mu$-terms known…

This report discusses the foundations of the VO approach. Then, it explores multiple directions and argues about structure and applications.

This paper extends our earlier results to higher dimensions using a different approach, based on the rigidity of complex structures on certain domains.

Formalism of differential forms is developed for a variety of Quantum and noncommutative situations.

A introduction into density-functional theory and electronic structure methods is given, that aims at providing an intuitive understanding of the underlying concepts for the novice as well as an entry point towards the more advanced…

This paper is an extended abstract of the dissertation presented by the author for the doctoral degree in physics and mathematics (in Russia). The main characteristic studied in the dissertation is combinatorial complexity, which is a…

Accurate volume estimation of objects from visual data is a long-standing challenge in computer vision with significant applications in robotics, logistics, and smart health. Existing methods often rely on complex 3D reconstruction…

Integral representations are obtained of positive additive functionals on finite products of the space of continuous functions (or of bounded Borel functions) on a compact Hausdorff space. These are shown to yield characterizations of the…

Characteristic modes of a spherical shell are found analytically as spherical harmonics normalized to radiate unitary power and to fulfill specific boundary conditions. The presented closed-form formulas lead to a proposal of precise…

We formulate a notion of modular form on the double half-plane for half-integral weights and explain its relationship to the usual notion of modular form. The construction we provide is compatible with certain physical considerations due to…

We characterize the generating function of the number of representations described in the title in terms of the theory of modular forms. Appealing to this characterization we obtain explicit formulas for the representation numbers as…

An overview of some of the recent developments in the theory of valuations on convex sets and its generalizations to manifolds is given. The exposition is focused towards applications to integral geometry; several of such applications are…

We prove convergence results for `increasing' sequences of sectorial forms. We treat both the case of closed forms and the case of non-closable forms.

We give divisibility results for the (global) characteristic varieties of hypersurface complements expressed in terms of the local characteristic varieties at points along one of the irreducible components of the hypersurface. As an…

We present here a large collection of harmonic and quadratic harmonic sums, that can be useful in applied questions, e.g., probabilistic ones. We find closed-form formulae, that we were not able to locate in the literature.

In this paper we give a method, based on the characteristic function of a set, to solve some difficult problems of set theory in undergraduate research.

We present a general form of attribute exploration, a knowledge completion algorithm from Formal Concept Analysis. The aim of our presentation is not only to extend the applicability of attribute exploration by a general description. It may…