相关论文: Characterizing Volume Forms

We consider integration of functions with values in a partially ordered vector space, and two notions of extension of the space of integrable functions. Applying both extensions to the space of real valued simple functions on a measure…

Version 3 of FORM is introduced. It contains many new features that are inspired by current developments in the methodology of computations in quantum field theory. A number of these features is discussed in combination with examples. In…

We develop the theory of motivic integration for formal schemes

We investigate functionals defined on manifolds through parameterizations. If they are to be meaningful, from a geometrical viewpoint, they ought to be invariant under reparameterizations. Standard, local, integral functionals with this…

Both a general and a diagonal u-invariant for forms of higher degree are defined, generalizing the u-invariant of quadratic forms. Both old and new results on these invariants are collected.

This paper can be considered as an extension to our paper [On symplectically harmonic forms on six-dimensional nilmanifolds, Comment. Math. Helv. 76 (2001), n 1, 89-109]. Also, it contains a brief survey of recent results on symplectically…

We have derived an analytical formulation for estimating the volume of geometries enclosed by implicitly defined surfaces. The novelty of this work is due to two aspects. First we provide a general analytical formulation for all…

Continuing the investigation started in a previous work, we consider form factors of integrable quantum field theories in finite volume, extending our investigation to matrix elements with disconnected pieces. Numerical verification of our…

We introduce volume forms on mapping stacks in derived algebraic geometry using a parametrized version of the Reidemeister-Turaev torsion. In the case of derived loop stacks we describe this volume form in terms of the Todd class. In the…

Although the characterization of ring derivations has an extensive literature, up to now, all of the characterizations have had the following form: additivity and another property imply that the function in question is a derivation. The aim…

Given an integer homology class of a finitely presentable group, the systolic volume quantifies how tight could be a geometric realization of this class. In this paper, we study various aspects of this numerical invariant showing that it is…

In this paper, new refinements for integral and sum forms of H\"older inequality are established. We note that many existing inequalities related to the H\"older inequality can be improved via obtained new inequalities in here, we show this…

In this thesis we investigate finite size effects in 1+1 dimensional integrable QFT. In particular we consider matrix elements of local operators (finite volume form factors) and vacuum expectation values and correlation functions at finite…

Some recent additions to FORM are discussed. In particular large file support and the tablebases are presented.

A new version of the Hadwiger theorem on convex functions is established and an explicit representation of functional intrinsic volumes is found using new functional Cauchy-Kubota formulas. In addition, connections between functional…

A multidimensional generalization of the Bernstein class of functions and the properties of functions of the introduced class are examined. In particular, a new proof of the integral representation of Bernstein functions of many variables…

A new characterization of harmonic functions is obtained. It is based on quadrature identities involving mean values over annular domains and over concentric spheres lying within these domains or on their boundaries. The analogous result…

Recently, we proposed a three-dimensional generalization of QRT maps. These novel maps can be associated with pairs of pencils of quadrics in $\mathbb P^3$. By construction, these maps have two rational integrals (parameters of both…

Estimating the coefficient functionals on various classes of holomorphic functions traditionally forms an important field of geometric complex analysis and its mathematical and physical applications. These coefficients reflect fundamental…

Summarization is one of the key features of human intelligence. It plays an important role in understanding and representation. With rapid and continual expansion of texts, pictures and videos in cyberspace, automatic summarization becomes…