The ratio monotonicity of a polynomial is a stronger property than log-concavity. Let P (x) be a polynomial with nonnegative and nondecreasing coefficients. We prove the ratio monotone property of P (x+ 1), which leads to the log-concavity of P (x+ c) for any c ≥ 1 due to Llamas and Mart́ınez-Bernal. As a consequence, we obtain the ratio monotonicity of the Boros-Moll polynomials obtained by Che...

We study power expansions of the characteristic function of a linear operator A in a p|q-dimensional superspace V. We show that the traces of exterior powers of A satisfy universal recurrence relations of period q. " Underlying " recurrence relations hold in the Grothendieck ring of representations of GL(V). They are expressed by vanishing of certain Hankel determinants of order q + 1 in this r...

Since synonyms are important lexical knowledge, various methods have been proposed for automatic synonym acquisition. Whereas most of the methods are based on the distributional hypothesis and utilize contextual clues, little attention has been paid to what kind of contextual information is useful for the purpose. As one of the ways to augment contextual information, we propose the use of indir...

We modified the rational Jacobi elliptic functions method to construct some new exact solutions for nonlinear differential difference equations in mathematical physics via the lattice equation, the discrete nonlinear Schrodinger equation with a saturable nonlinearity, the discrete nonlinear Klein-Gordon equation, and the quintic discrete nonlinear Schrodinger equation. Some new types of the Jac...

Learning systems that express theories in rst-order logic must ensure that the theories are executable and, in particular, that they do not lead to innnite recursion. This paper presents a heuristic method for preventing innnite re-cursion in the (multi-clause) deenition of a recursive relation. The method has been implemented in the latest version of foil, but could also be used with any learn...

We report some observations concerning two well-known approaches to construction of quantum groups. Thus, starting from a bialgebra of inhomogeneous type and imposing quadratic, cubic or quartic commutation relations on a subset of its generators we come, in each case, to a q-deformed universal enveloping algebra of a certain simple Lie algebra. An interesting correlation between the order of i...

The hypergeometric function is shown to be logarithmically concave in integer values of one of its parameters. The methods used are probabilistic. THEOREM. Let m, and g be positive integers satisfying 3 <=i + <_ g, and let z be a negative real number. Then {2Fl[-m,i’g’z]} 2 > 2Fl[-m,i + 1;g;Z]EFl[-m,i1;g;z]. We first establish the following lemma concerning the evaluation of the generating func...

This work presents a difference geometric approach to the strongly normal Galois theory of difference equations. In this approach, a system of ordinary difference equations is encoded in a difference extension, and the Galois groups are group schemes of finite type over the constants. The Galois groups need neither be linear nor reduced. The main result is a characterization of the extensions t...

Global almost sure asymptotic stability of solutions of some nonlinear stochastic difference equations with cubic-type main part in their drift and diffusive part driven by square-integrable martingale differences is proven under appropriate conditions in R1. As an application of this result, the asymptotic stability of stochastic numerical methods, such as partially drift-implicit θ-methods wi...

Orthogonal systems of trigonometric polynomials of semi-integer degree with respect to a weight function w(x) on [0, 2π) have been considered firstly by Turetzkii in [Uchenye Zapiski, Vypusk 1(149) (1959), 31–55, (translation in English in East J. Approx. 11 (2005) 337–359)]. It is proved that such orthogonal trigonometric polynomials of semi-integer degree satisfy five-term recurrence relation...