This paper leverages pseudorandom properties of the Legendre symbol to reduce the number of random bits in an RIP matrix with Bernoulli entries. In this regard, the Legendre symbol is not special our main result naturally generalizes to any small-bias sample space. We also conjecture that no ...
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If we denote by \( \varvec{A}^\alpha \) the contravariant basis vectors such that \( \varvec{A}^\alpha \cdot \varvec{A}_\beta = \delta ^\alpha _\beta \) (Kronecker symbol), then the surface gradient operator \( \nabla _s \) can be expressed by $$\begin{aligned} \nabla ...
1 Legendre-Fenchel transforms in a nutshell 2 Hugo Touchette School of Mathematical Sciences, Queen Mary, University of London, London E1 4NS, UK 3 Started: July 11, 2005; last compiled: August 14, 2007 4 The aim of this report is to list and explain the basic properties of the Legendre...
When non-PV work is involved in a thermodynamic system, 2k can be much larger than 4 and the larger number of thermodynamic potentials increases nomenclature problems because each new thermodynamic potential that is defined by a Legendre transform needs a symbol and a name. Callen discussed this ...
Legendre symbolIn an earlier paper Hubert, Mauduit and S谩rkzyintroduced pseudorandom measures for pseudorandomness of binary lattices, and they gave constructions for binary lattices with strong pseudorandom properties. They gave nearly optimal upper bounds for the pseudorandom measures of the lattices...
The main purpose of this article is using the elementary methods and the properties of the character sums to study the calculating problem of the number of the solutions for one kind congruence equation modulo (an odd prime) and give some interesting identities and asymptotic formulas for it....
The main purpose of this article is using the elementary methods and the properties of the quadratic residue modulo an odd prime to study the calculating problem of the fourth power mean of one kind two-term exponential sums and give an interesting calculating formula for it.Jingzhe Wang...
The main purpose of this article is using the elementary methods and the properties of the character sums of the polynomials to study the calculating problem of one kind sixth power mean of the two-term exponential sums weighted by Legendre's symbol modulo $ p $, an odd prime, and give ...
Motivated by the work initiated by Chapman ['Determinants of Legendre symbol matrices', Acta Arith. 115 (2004), 231鈥 244], we investigate some arithmetical properties of generalised Legendre matrices over finite fields. For example, letting $a_1,\\ldots ,a_{(q-1)/2}...