Related papers: On transcendental numbers
In this paper we discuss some non-trivial relations for ordered exponentials on smooth Riemannian manifolds. As an example of application, we study a dependence of the four-dimensional quantum Yang-Mills effective action on the background…
In the paper, the authors establish three kinds of double inequalities for the trigamma function in terms of the exponential function to powers of the digamma function. These newly established inequalities extend some known results. The…
We review recent progress in the fractional Calder\'on problem, where one tries to determine an unknown coefficient in a fractional Schr\"odinger equation from exterior measurements of solutions. This equation enjoys remarkable uniqueness…
Over the past two decades, the field of high-dimensional statistics has experienced substantial progress, driven largely by technological advances that have dramatically reduced the cost and effort for data collection and storage across a…
There are many striking phenomena which are attributed to ``quantum coherence''. It is natural to wonder if there are new quantum coherence effects waiting to be discovered which could lead to interesting results and perhaps even practical…
This article discusses some important applications of the quadratic function with the aim of highlighting the importance of cuadr\'aticas.- forms are also intended to show how a simple function covers virtually all areas of knowledge are…
In this short paper I consider relation between measurements, numbers and p-adic mathematical physics. p-Adic numbers are not result of measurements, but nevertheless they play significant role in description of some systems and phenomena.…
For a transcendental entire function, a partial affirmative answer to Baker's question on the boundedness of its Fatou components is given. In addition, we have addressed Wang's question on Fej\'er gaps. Certain results about functions with…
The purpose of this paper is to combine classical methods from transcendental number theory with the technique of restriction to real scalars. We develop a conceptual approach relating transcendence properties of algebraic groups to results…
In this thesis we examined mathematical properties of Fibonacci numbers and applications of this numbers in the nature,geometry and economy.We obtained Golden section and proved some mathematical identities using Golden section. Infinity of…
Notions of (pointwise) tangential dimension are considered, for measures of R^n. Under regularity conditions (volume doubling), the upper resp. lower dimension at a point x of a measure can be defined as the supremum, resp. infimum, of…
This paper deals with the study of the zeros of the big $q$-Bessel functions. In particular, we prove a new orthogonality relations for this functions similar to the one for the classical Bessel functions. Also we give some applications…
In this paper we prove a functional transcendence statement for the j-function which is an analogue of the Ax-Schanuel theorem for the exponential function. It asserts, roughly, that atypical algebraic relations among functions and their…
The review of modern study of algebraic, geometric and differential properties of quaternionic (Q) numbers with their applications. Traditional and "tensor" formulation of Q-units with their possible representations are discussed and groups…
Feynman amplitudes in perturbation theory form the basis for most predictions in particle collider experiments. The mathematical quantities which occur as amplitudes include values of the Riemann zeta function and relate to fundamental…
We introduced a new continued fraction expansions in our previous paper. For these expansions, we show formulae of probability about incomplete quotients. Furthermore, we prove the existence of invariant measures with respect to the…
The discovery of the infinite integer leads to a partition between finite and infinite numbers. Construction of an infinitesimal and infinitary number system, the Gossamer numbers. Du Bois-Reymond's much-greater-than relations and…
We investigate the question: what structures of numbers (as physical quantities) are suitable to be used in special relativity? The answer to this question depends strongly on the auxiliary assumptions we add to the basic assumptions of…
We discuss the possibility that "quintessential effects", recently displayed by large scale observations, may be consistently described in the context of the low-energy string effective action, and we suggest a possible approach to the…
Students of quantum mechanics encounter discrete quantum numbers in a somewhat incoherent and bewildering number of ways. For each physical system studied, quantum numbers seem to be introduced in its own specific way, some enumerating from…