Related papers: Novel Approach to Infinite Products Using Multipli…
We consider analytic functions of the Riemann zeta type, for which, if $s$ is a zero, so is $1-s$. We use infinite product representations of these functions, assuming their zeros to be of first order. We use exponential factors to…
The rearrangement inequality states that the sum of products of permutations of 2 sequences of real numbers are maximized when the terms are similarly ordered and minimized when the terms are ordered in opposite order. We show that similar…
Construal of observable facts or events, that is, the manner in which we understand reality, is based not only on mathematical formulas of a theory suggested as a reasonable explanation for physical phenomena (like general relativity or…
We prove two-sided inequalities between the integral moduli of smoothness of a function on $\mathbb{R}^d/\mathbb{T}^d$ and the weighted tail-type integrals of its Fourier transform/series. Sharpness of obtained results in particular is…
We take a unifying and new approach toward polynomial and trigonometric approximation in an arbitrary number of variables, resulting in a precise and general ready-to-use tool that anyone can easily apply in new situations of interest. The…
The global additive and multiplicative properties of Laplace type operators acting on irreducible rank 1 symmetric spaces are considered. The explicit form of the zeta function on product spaces and of the multiplicative anomaly is derived.
We present a novel linear $\lambda$-calculus for Classical Multiplicative Exponential Linear Logic (\MELL) along the lines of the propositions-as-types paradigm. Starting from the standard term assignment for Intuitionistic Multiplicative…
We prove upper and lower bounds for certain sums of products of fractional parts by using majoring and minorizing functions from Fourier analysis. In special cases the upper bounds are sharp if there exist counterexamples to the Littlewood…
We look at non-classical negations and their corresponding adjustment connectives from a modal viewpoint, over complete distributive lattices, and apply a very general mechanism in order to offer adequate analytic proof systems to logics…
The main goal of this paper is to give a modular type representation for the infinite product $(1-x)(1-xq)(1-xq^2)(1-xq^3)...$. It is shown that this representation essentially contains the well-known modular formulae either for Dedekind's…
A zero-finding technique for solving nonlinear equations more efficiently than they usually are with traditional iterative methods in which the order of convergence is improved is presented. The key idea in deriving this procedure is to…
By means of a variational approach we find new series representations both for well known mathematical constants, such as $\pi$ and the Catalan constant, and for mathematical functions, such as the Riemann zeta function. The series that we…
We develop an analog of Jones' planar calculus for II_1-factor bimodules with arbitrary left and right von Neumann dimension. We generalize to bimodules Burns' results on rotations and extremality for infinite index subfactors. These…
We introduce a notion of real-valued reward testing for probabilistic processes by extending the traditional nonnegative-reward testing with negative rewards. In this richer testing framework, the may and must preorders turn out to be…
In this work we derive and evaluate some infinite integrals involving the product of a generalized logarithm and polynomial functions in the denominator. These integrals are expressed in terms of finite series involving the Hurwitz-Lerch…
Reverse Mathematics is a program in the foundations of mathematics which provides an elegant classification of theorems of ordinary mathematics based on computability. Our aim is to provide an alternative classification of theorems based on…
It is shown how Dedekind cuts can be used to introduce the extended real numbers along with sound arithmetic laws via one simple rule for the addition of sets. The crucial idea is that the use of the lower and the upper part of the cuts,…
Shimura reciprocity law allows us to verify that a modular function is a class invariant. Here we present a new method based on Shimura reciprocity that allows us not only to verify but to find new class invariants from a modular function…
This paper is concerned with the study of the fractional finite sums theory. We present the classes of functions for which it is possible to characterize the constant related to the derivative of fractional sums (denominated by essence of a…
By some hypergeometric summation theorems, the authors establish a series of new infinite summation formulas involving generalized harmonic numbers related to Riemann-Zeta function, with three different patterns.