Summary– We generalize the sum of remainders map by replacing set summation indices with an arbitrary finite nonempty positive integers. The iteration this produces interesting dynamical behavior, which we explore. In particular, discuss existence nonzero fixed points and some their properties.

We define two functions which determine the properties and the representation of the mean value of a function on a ball and on its associated sphere. Using these two functions, we obtain Pizzetti’s formula in R as well as a similar formula for the mean value of a function on the ball associated to the sphere. We also give the expressions of the remainders in these two formulas, using the surfac...

We continue the study of quantum electrodynamics on a three dimensional torus as the limit of a lattice gauge theory. In this paper we give a preliminary treatment of the renormalization group flow. We study the propagators which arise under multiple block spin averaging, both in global and local versions. We also study low order perturbation theory. However we do not control remainders. This i...

It is shown that a real Hankel matrix admits an approximate block diagonalization in which the successive transformation matrices are upper triangular Toeplitz matrices. The structure of this factorization was first fully discussed in [1]. This approach is extended to obtain the quotients and the remainders appearing in the Euclidean algorithm applied to two polynomials u(x) and v(x) of degree ...

In the present work the approach density matrix deformation earlier developed by the author to study a quantum theory of the Early Universe (Planck’s scales) is applied to study a quantum theory of black holes. On this basis the author investigates the information paradox problem, entropy of the black hole remainders after evaporation, and consistency with the holographic principle. The possibi...

We define two functions which determine the properties and the representation of the mean value of a function on a ball and on its associated sphere. Using these two functions, we obtain Pizzetti’s formula in R as well as a similar formula for the mean value of a function on the ball associated to the sphere. We also give the expressions of the remainders in these two formulas, using the surfac...

Abstract. Taylor expansions of analytic functions are considered with respect to several points, allowing confluence of any of them. Cauchy-type formulas are given for coefficients and remainders in the expansions, and the regions of convergence are indicated. It is explained how these expansions can be used in deriving uniform asymptotic expansions of integrals. The method is also used for obt...