Results 51 to 60 of about 7,643 (187)

Sum and Shifted-Product Subsets of Product-Sets over Finite Rings [PDF]

The Electronic Journal of Combinatorics, 2012
For sufficiently large subsets $\mathcal{A}, \mathcal{B}, \mathcal{C}, \mathcal{D}$ of $\mathbb{F}_q$, Gyarmati and Sárközy (2008)  showed the solvability of the equations $a + b= c d$ and $a b + 1 = c d$ with $a \in \mathcal{A}$, $b \in\mathcal{B}$, $c \in \mathcal{C}$, $d \in \mathcal{D}$.
openaire   +2 more sources

A Few Finite Trigonometric Sums

Mathematics, 2017
Finite trigonometric sums occur in various branches of physics, mathematics, and their applications. These sums may contain various powers of one or more trigonometric functions. Sums with one trigonometric function are known; however, sums with products
Chandan Datta, Pankaj Agrawal
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On Some Formulas for the Lauricella Function

Mathematics, 2023
Lauricella, G. in 1893 defined four multidimensional hypergeometric functions FA, FB, FC and FD. These functions depended on three variables but were later generalized to many variables.
Ainur Ryskan, Tuhtasin Ergashev
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The large N limit of SU(N) integrals in lattice models

Nuclear Physics B, 2020
The standard U(N) and SU(N) integrals are calculated in the large N limit. Our main finding is that for an important class of integrals this limit is different for two groups. We describe the critical behaviour of SU(N) models and discuss implications of
O. Borisenko, V. Chelnokov, S. Voloshyn
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SOME IDENTITIES ON SUM OF FINITE PRODUCTS OF GEGENBAUER POLYNOMIALS

JP Journal of Algebra, Number Theory and Applications
Xuan Wang
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On the sum-of-products to product-of-sums transformation between analytical low-rank approximations in finite basis representation

The European Physical Journal Special Topics, 2023
The transfer of a hydrated proton between water molecules in aqueous solution is accompanied by the large-scale structural reorganization of the environment as the proton relocates, giving rise to the Grotthus mechanism.
Panadés-Barrueta, Ramón, Nadoveza, Natasa, Gatti, Fabien, Peláez, Daniel   +3 more
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An embedding of the universal Askey–Wilson algebra into Uq(sl2)⊗Uq(sl2)⊗Uq(sl2)

Nuclear Physics B, 2017
The Askey–Wilson algebras were used to interpret the algebraic structure hidden in the Racah–Wigner coefficients of the quantum algebra Uq(sl2). In this paper, we display an injection of a universal analog △q of Askey–Wilson algebras into Uq(sl2)⊗Uq(sl2)⊗
Hau-Wen Huang
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Representation by several orthogonal polynomials for sums of finite products of Chebyshev polynomials of the first, third and fourth kinds

Advances in Difference Equations, 2019
The classical linearization problem concerns with determining the coefficients in the expansion of the product of two polynomials in terms of any given sequence of polynomials.
Taekyun Kim, Dae San Kim, Dmitry V. Dolgy, Dojin Kim   +3 more
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On the few products, many sums problem [PDF]

Journal de Théorie des Nombres de Bordeaux, 2017
We prove new results on additive properties of finite sets $A$ with small multiplicative doubling $|AA|\leq M|A|$ in the category of real/complex sets as well as multiplicative subgroups in the prime residue field.
B. Murphy, M. Rudnev, I. Shkredov, Yu. N. Shteinikov   +3 more
semanticscholar   +1 more source

On multiple sum and product sets of finite sets of integers

Comptes Rendus. Mathématique, 2003
Let A⊂ℤ be a finite set of integers of cardinality |A|=N⩾2. Given a positive integer k, denote kA (resp. A(k)) the set of all sums (resp. products) of k elements of A. We prove that for all b>1, there exists k=k(b) such that max(|kA|,|A(k)|)>Nb. This answers affirmably questions raised in Erdős and Szemerédi (Stud. Pure Math., 1983, pp. 213–218),
Bourgain, Jean, Chang, Mei-Chu
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