— For given positive integers a, b, q we investigate the density of solutions (x, y) ∈ Z to congruences ax+ by ≡ 0 mod q.

Quadratic programming (QP) is an optimization problem wherein one minimizes (or maximizes) a quadratic function of a finite number of decision variable subject to a finite number of linear inequality and/ or equality constraints. In this paper, a quadratic programming problem (FFQP) is considered in which all cost coefficients, constraints coefficients, and right hand side are characterized by ...

We propose a quartic function to represent a family of continuous quality loss functions. Depending on the choice of its parameters the shape of this function within the specification limits can be either symmetric or asymmetric, and it can be either similar to the ubiquitous quadratic loss function or somewhat closer to the conventional step function. We examine this family of loss functions i...

In the present paper we outline the stochastic limit approach to superfluidity. The Hamiltonian describing the interaction between the Bose condensate and the normal phase is introduced. Sufficient in the stochastic limit condition of superfluidity is proposed. Existence of superfluidity in the stochastic limit of this system is proved and the non– linear (quadratic) equation of motion describi...

Intended for mathematical physicists interested in applications of the division algebras to physics, this article highlights some of their more elegant properties with connections to the theories of Galois fields and quadratic residues.

Let A„{a, b) = {ban+(a-l)/b)2+4an with n > 1 and ¿>|a-l . If W is a finite set of primes such that for each n > 1 there exists some q £W for which the Legendre symbol {A„{a, b)/q) ^ -1 , we call <£ a quadratic residue cover (QRC) for the quadratic fields K„{a, b) = Q{^jA„{a, b)). It is shown how the existence of a QRC for any a, b can be used to determine lower bounds on the class number of K„{...

We consider the problem of admissible quadratic estimation of a linear function of μ and σ in n dimensional normal model N(Kμ, σIn) under quadratic risk function. After reducing this problem to admissible estimation of a linear function of two quadratic forms, the set of admissible estimators are characterized by giving formulae on the boundary of the set D ⊂ R of components of the two quadrati...