Related papers: Generalised Potential Functions in Differential Ge…
Generalized tensor analysis in the sense of Colombeau's construction is employed to introduce a nonlinear distributional pseudo-Riemannian geometry. In particular, after deriving several characterizations of invertibility in the algebra of…
In physics geometrical connections are the mean to create models with local symmetries (gauge connections), as well as general diffeomorphisms invariance (affine connections). Here we study the irreducible tensor decomposition of…
We consider the problem of uniform interpolation of functions with values in a complex inner product space of finite dimension. This problem can be casted within a modified weighted pluripotential theoretic framework. Indeed, in the…
Convexity and convex functions play an important role in theoretical physics. To initiate a study of the possible uses of convex functions in General Relativity, we discuss the consequences of a spacetime $(M,g_{\mu \nu})$ or an initial…
Convexity and convex functions play an important role in theoretical physics. To initiate a study of the possible uses of convex functions in General Relativity, we discuss the consequences of a spacetime $(M,g_{\mu \nu})$ or an initial…
In this work, generalized hypergeometric functions for bicomplex argument is introduced and its convergence criteria is derived. Furthermore, integral representation of this function has been established. Moreover, quadratic transformation,…
We derive transformation formulas for the generalized polarization tensors under rigid motions and scaling in three dimensions, and use them to construct an infinite number of invariants under those transformations. These invariants can be…
Information geometry provides differential geometric concepts like a Riemannian metric, connections and covariant derivatives on spaces of probability distributions. We discuss here how these concepts apply to quantum field theories in the…
We derive self-reciprocity properties for a number of polyomino generating functions, including several families of column-convex polygons, three-choice polygons and staircase polygons with a staircase hole. In so doing, we establish a…
We generate random functions locally via a novel generalization of Dyson Brownian motion, such that the functions are in a desired differentiability class, while ensuring that the Hessian is a member of the Gaussian orthogonal ensemble…
Several integrals involving powers and ordinary hypergeometric functions are rederived by means of a generalized hypergeometric function of two variables (Appell's function) recovering some well-known expressions as particular cases. Simple…
In this paper we investigate the shape invariance property of a potential in one dimension. We show that a simple ansatz allows us to reconstruct all the known shape invariant potentials in one dimension. This ansatz can be easily extended…
A 4-dimensional Riemannian manifold equipped with an additional tensor structure, whose fourth power is the identity, is considered. This structure has a circulant matrix with respect to some basis, i.e. the structure is circulant, and it…
We study arithmetic distribution relations and the inverse function theorem in algebraic and arithmetic geometry, with an emphasis on versions that can be applied uniformly across families of varieties and maps. In particular, we prove two…
We investigate geometric properties of a class of trace functions expressed in terms of the deformed logarithmic and exponential functions. These trace functions and their properties may be of independent interest. We use them in particular…
Co lombeau's construction of generalized functions (in its special variant) is extended to a theory of generalized sections of vector bundles. As particular cases, generalized tensor analysis and exterior algebra are studied. A point value…
Based on Colombeau's theory of algebras of generalized functions we introduce the concepts of generalized functions taking values in differentiable manifolds as well as of generalized vector bundle homomorphisms. We study their basic…
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.
We study the arithmetic property which allows to sharpen number-theoretic estimates. Previous results on this property are, as a rule, quantitive. The application of our general qualitive theorems to generalized hypergeometric functions…
The problem of constructing a quantum theory of gravity has been tackled with very different strategies, most of which relying on the interplay between ideas from physics and from advanced mathematics. On the mathematical side, a central…