Variability in penetration, development, and reproduction of two resistance-breaking field pathotypes (pt.) of Meloidogyne arenaria, M. incognita, and a population of mixed Meloidogyne spp. virulent to grape hosts were compared on two resistant Vitis rootstocks 'Freedom' and 'Harmony' in separate tests. 'Cabernet Sauvignon' was included as a susceptible host to all four nematode populations. Se...

The aim of this paper is to find the class of continuous pointwise transformations (as general as possible) in the framework of which Kummer’s transformation z(t) = g(t)y(h(t)) represents the most general pointwise transformation converting every linear homogeneous differential equation of the nth order into an equation of the same type. Further, some forms of these equations having certain sub...

We construct an invariant JM of integral homology spheres M with values in a completion Ẑ[q] of the polynomial ring Z[q] such that the evaluation at each root of unity ζ gives the the SU(2) Witten-ReshetikhinTuraev invariant τζ(M) of M at ζ. Thus JM unifies all the SU(2) WittenReshetikhin-Turaev invariants of M . As a consequence, τζ(M) is an algebraic integer. Moreover, it follows that τζ(M) a...

Recently, an infinite hierarchy of languages accepted by stateless deterministic pushdown automata has been established based on the number of pushdown symbols. However, the witness language for the nth level of the hierarchy is over an input alphabet with 2(n−1) elements. In this paper, we improve this result by showing that a binary alphabet is sufficient to establish this hierarchy. As a con...

The purpose of this paper is to describe subgroups of a Chevalley group G of type B l , C l or F 4 , generated by a pair of unipotent short root subgroups. In fact we do somewhat more: namely, we classify orbits of a Chevalley group acting by simultaneous conjugation on pairs of unipotent short root subgroups. In the sequel of this paper we consider analogous problems for the case of the Cheval...

This paper presents a short survey of convergence results and properties of the Lebesgue function kmn(x) for (0, 1 , . . . , m) Hermite-Fejer interpolation based on the zeros of the nth Chebyshev polynomial of the first kind. The limiting behaviour as n -*• oo of the Lebesgue constant Amn = max{Xm n(x) : — 1 < x < 1} for even m is then studied, and new results are obtained for the asymptotic ex...

Abstract. We prove the main conjecture from [DSZ2] concerning the metric dependence and asymptotic minimization of the expected number N crit N,h of critical points of random holomorphic sections of the Nth tensor power of a positive line bundle. The first nontopological term in the asymptotic expansion of N crit N,h is the the Calabi functional multiplied by the constant β2(m) which depends on...

This work presents the nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (nth-CASAM-N), which enables most efficient computation of exactly determined expressions arbitrarily high-order sensitivities generic nonlinear system responses with respect to model parameters, uncertain boundaries, and internal interfaces in model’s phase space. The mathematical fram...

INTRODUCTION Let p denote a prime, n a natural number, Fin) the nth Fibonacci number. Consider the equation: F(n) = px, (*) In [3], J. H. E. Cohn proved that for p = 2, the only solutions of (*) are (i) n = 3, x = 1 and (ii) n = 6, x = 4. In [8], R. Steiner proved that for p = 3, the only solution of (*) is n 4, a: = 1. Call a solution of (*) trivial if x = 1 . In this article, we solve O ) for...