Related papers: Siegel measures
The paper presents a new formula for the fractional integration, which generalizes the Riemann-Liouville and Hadamard fractional integrals into a single form, which when a parameter fixed at different values, produces the above integrals as…
This paper lays the foundations for a nonlinear theory of differential geometry that is developed in a subsequent paper which is based on Colombeau algebras of tensor distributions on manifolds. We adopt a new approach and construct a…
In this paper we extend some results of Norman and Oort and of de Jong, and give an explicit description of the geometry of the Siegel modular threefold with paramodular level structure. We also discuss advantages and restrictions of three…
In the paper we prove integral formulae for a Riemannian manifold endowed with $k>2$ orthogonal complementary distributions, which generalize well-known formula for $k=2$ and give applications to splitting and isometric immersions of…
We obtain the integral formulae for computing the tetrads and metric components in Riemann normal coordinates and Fermi coordinate system of an observer in arbitrary motion. Our approach admits essential enlarging the range of validity of…
It is the purpose of this article to outline a course that can be given to engineers looking for an understandable mathematical description of the foundations of distribution theory and the necessary functional analytic methods. Arguably,…
The aim of these notes is to present an accessible overview of some topics in classical algebraic geometry which have applications to aspects of discrete integrable systems. Precisely, we focus on surface theory on the algebraic geometry…
Visual insights into a wide variety of statistical methods, for both didactic and data analytic purposes, can often be achieved through geometric diagrams and geometrically based statistical graphs. This paper extols and illustrates the…
The present thesis represents developments in two main directions related to the simple Lie algebras. The first one is devoted to the representation theory of the simple Lie algebras. Specifically, we present recent results, which include…
We employ methods of geometry and generalized convergence to construct a geometric measure that serves as an alternative to the integer-dimension Hausdorff measure. This construction prioritizes integration, yields the Area Formula as a…
This is a collection of articles, written as sections, on arithmetic properties of differential equations, holomorphic foliations, Gauss-Manin connections and Hodge loci. Each section is independent from the others and it has its own…
The goal is to review the notion of a complete Segal space and how certain categorical notions behave in this context. In particular, we study functoriality in complete Segal spaces via fibrations. Then we use it to define limits and…
We study an $\ell$-adic Galois analogue of the distribution formulas for polylogarithms with special emphasis on path dependency and arithmetic behaviors. As a goal, we obtain a notion of certain universal Kummer-Heisenberg measures that…
The paper gives the main lines of a general theory for physical measurements.
A natural extension of Riemannian geometry to a much wider context is presented on the basis of the iterated differential form formalism developed in math.DG/0605113 and an application to general relativity is given.
In this paper we consider a random partition of the plane into cells, the partition being based on the nodes and links of a {\it random planar geometric graph}. The resulting structure generalises the \emph{random \tes}\ hitherto studied in…
We study global properties of Dirichlet forms such as uniqueness of the Dirichlet extension, stochastic completeness and recurrence. We characterize these properties by means of vanishing of a boundary term in Green's formula for functions…
The existence of kinematic formulas for area measures with respect to any connected, closed subgroup of the orthogonal group acting transitively on the unit sphere is established. In particular, the kinematic operator for area measures is…
We will present several examples in which ideas from ergodic theory can be useful to study some problems in arithmetic and algebraic geometry.
Gauge theory on the q-deformed two-dimensional Euclidean plane R^2_q is studied using two different approaches. We first formulate the theory using the natural algebraic structures on R^2_q, such as a covariant differential calculus, a…