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Algebraic operations are understood as topologiztion of algebra. They become an example of simplest convergence space. In our article the convergence is a arbitrary multivalued appointment. The continuity of some mapping between two…

General Topology · Mathematics 2010-04-20 Gintaras Valiukevicius

We develop a theory of multiplicative functions (with values inside or on the unit circle) in arithmetic progressions analogous to the well-known theory of primes in arithmetic progressions.

Number Theory · Mathematics 2007-05-23 Antal Balog , Andrew Granville , K. Soundararajan

The necessary and sufficient conditions for differentiability of a function of several real variables stated and proved and its ramifications discussed.

Classical Analysis and ODEs · Mathematics 2007-05-23 R. P. Venkataraman

We prove a characterization of the dual mixed volume in terms of functional properties of the polynomial associated to it. To do this, we use tools from the theory of multilinear operators on spaces of continuos functions. Along the way we…

Functional Analysis · Mathematics 2014-08-29 Carlos H. Jiménez , Ignacio Villanueva

We give an elementary characterization of rational functions among meromorphic functions in the complex plane.

Complex Variables · Mathematics 2017-12-13 Bao Qin Li

We study the complexity of deterministic and probabilistic inversions of partial computable functions on the reals.

Logic · Mathematics 2026-01-14 George Barmpalias , Mingyang Wang , Xiaoyan Zhang

A formulation of linearized gravity which is manifestly invariant under electric-magnetic duality rotations in the internal space of the metric and its dual, and which contains both metrics as basic variables (rather than the corresponding…

High Energy Physics - Theory · Physics 2013-01-24 Claudio Bunster , Marc Henneaux , Sergio Hörtner

The partition function for unitary two matrix models is known to be a double KP tau-function, as well as providing solutions to the two dimensional Toda hierarchy. It is shown how it may also be viewed as a Borel sum regularization of…

Exactly Solvable and Integrable Systems · Physics 2023-08-02 J. Harnad , A. Yu. Orlov

We consider classes of non-manipulable social choice functions with range of cardinality at most two within a set of at least two alternatives. We provide the functional form for each of the classes we consider. This functional form is a…

Theoretical Economics · Economics 2024-02-28 Achille Basile , K. P. S. Bhaskara Rao , Surekha Rao

In this paper, on the basis of a specific question raised in [6], we further continue our investigations on the uniqueness of a meromorphic function with its higher derivatives sharing two sets and answer the question affirmatively.…

Complex Variables · Mathematics 2018-01-08 Abhijit Banerjee , Bikash Chakraborty

There are two definitions of the measurable functional on the topological vector space: as a linear and measurable real-valued function and as a pointwise limit of the sequence of the continious linear functionals. In general case they are…

Functional Analysis · Mathematics 2016-02-23 Denis Fufaev

We prove a closed formula for the derivative, of any order, of a implicit function, in terms of some binomial building blocks, and explain the combinatorics behind the coefficients appearing in the formula.

Combinatorics · Mathematics 2020-08-13 Shaul Zemel

Generalizing the well-known mean-value property of harmonic functions, we prove that a p-harmonic function of two variables satisfies, in a viscosity sense, two asymptotic formulas involving its local statistics. Moreover, we show that…

Analysis of PDEs · Mathematics 2011-08-10 David Hartenstine , Matthew Rudd

We give a weighted sum formula for the double polylogarithm in two variables, from which we can recover the classical weighted sum formulas for double zeta values, double $T$-values, and some double $L$-values. Also presented is a…

Number Theory · Mathematics 2024-10-01 Masanobu Kaneko , Hirofumi Tsumura

This paper provides an approach to establishing the calculus method from the concept of mean, i.e., average. This approach is from a statistics perspective and can help calculus learners understand calculus ideas and analyze a function…

History and Overview · Mathematics 2014-06-12 Samuel S. P. Shen , Dov Zazkis , Kimberly Leung , Chris Rasmussen

Double $L$-functions are the generalization of Dirichlet $L$-functions to two variable functions. We investigate the order estimation of double $L$-functions, and give upper bounds which are explicit in conductor aspect.

Number Theory · Mathematics 2023-12-05 Yuichiro Toma

In this article, a characterization of the class of Herglotz-Nevanlinna functions in $n$ variables is given in terms of an integral representation. Furthermore, alternative conditions on the measure appearing in this representation are…

Complex Variables · Mathematics 2019-09-24 Annemarie Luger , Mitja Nedic

The Simpson's formula is obtained by approximating the integral of a function on some interval by the integral of the quadratic polynomial determined by the function. However, a multidimensional analogue of the formula has not been given as…

Mathematical Physics · Physics 2015-05-14 Kazuyuki Fujii

We introduce a notion of resultant of two meromorphic functions on a compact Riemann surface and demonstrate its usefulness in several respects. For example, we exhibit several integral formulas for the resultant, relate it to potential…

Algebraic Geometry · Mathematics 2009-03-01 B. Gustafsson , V. Tkachev

The purpose of this paper is to show that functions that derivate the two-variable product function and one of the exponential, trigonometric or hyperbolic functions are also standard derivations. The more general problem considered is to…

Classical Analysis and ODEs · Mathematics 2019-04-30 Richárd Grünwald , Zsolt Páles