This paper proposes statistical analysis of phase-only correlation functions based on linear statistics and directional statistics. We derive the expectation and variance of the phase-only correlation functions assuming phase-spectrum differences of two input signals to be probability variables. We first assume linear probability distributions for the phasespectrum differences. We next assume c...

Let f(z) = P n a(n)n e(nz) ∈ Sk(N,χ) be a cusp form for Γ0(N), weight k > 4 and character χ. Let q(x) = x + sx+ t ∈ Z[x] be a quadratic polynomial. It is shown that

We consider polynomial differential systems in the plane with Liouvillian first integrals. It is shown that all such systems have Darbouxian integrating factors, and that the search for such integrals can be reduced to a search for the invariant algebraic curves of the system and their ‘degenerate’ counterparts.

RC6 has been submitted as a candidate for the Advanced Encryption Standard (AES). Two important features of RC6 that were absent from its predecessor RC5 are a quadratic function and a fixed rotation. By examining simplified variants that omit these features we clarify their essential contribution to the overall security of RC6.

In 2011 ISO standardized [2] a family of deterministic pseudorandom bit generators MQ—DRBG, based on multivariate quadratic functions satisfying certain properties. The security of the generator could be described in terms of complexity of solving the corresponding system of multivariate quadratic equations. In our previous article [1] we proposed two different techniques for constructing syste...

Let q : Ĉ → Ĉ be any quadratic polynomial and r : C2 ∗ C3 → PSL(2,C) be any faithful discrete representation of the free product of finite cyclic groups C2 and C3 (of orders 2 and 3) having connected regular set. We show how the actions of q and r can be combined, using quasiconformal surgery, to construct a 2 : 2 holomorphic correspondence z → w, defined by an algebraic relation p(z,w) = 0.

The topic of our research is unconstrained 0-1 quadratic programming. We find some properties of the Boolean Quadric Polytope, which is obtained from the standard linearization of the given 0-1 quadratic function. By using a result obtained by Deza and Laurent on a class of hypermetric inequalities for the Cut Polytope, we find a necessary and sufficient condition for a class of inequalities to...

The principal topic of this article is to extend Shanks' infrastructure ideas in real quadratic number elds to the case of real quadratic congruence function elds. In this view, this paper is intended as a \low-brow" approach to the theory of ideals and operations in the ideal class group. We summarize some basic properties of ideals and provide elementary proofs of the main results. For the pu...

Variational theories of double-porosity models can be derived by homogenization of high-contrast periodic media (see [12]). Typically, we have one or more strong phases (i.e., uniformly elliptic energies on periodic connected domains) and a weak phase with a small ellipticity constant, coupled with some lower-order term. In the simplest case of quadratic energies, this amounts to considering en...

D.H. Lehmer found a quadratic polynomial such that 326 is a primitive root for the first 206 primes represented by this polynomial. It is shown that this is related to the class number one problem and prime producing quadratics. More impressive examples in the same spirit are given using recent results on prime producing quadratics. Y. Gallot holds the current record in which 206 is being repla...