A procedure to obtain differentiation matrices with application to solve boundary value problems and to find limit-cycles of nonautonomous dynamical systems is extended straightforwardly to yield new differentiation matrices useful to obtain derivatives of complex rational functions. Such matrices can be used to obtain numerical solutions of some singular differential problems defined in the co...

s. m. shah

-Crossing-over data from a homozygous III-IV translocation in Drosphila melanogaster indicate that the spindle fibre interferes with crossing-over in its immediate neighborhood. Acknowledgments.-The writer is grateful to Professor T. Dobzhansky who suggested the study here reported and furnished the original stock carrying the translocation studied. Professor A. H. Sturtevant has made many help...

Let f and g be two nonconstant meromorphic functions defined in the open complex plane C. If for some a ∈ C∪ {∞}, f − a and g − a have the same set of zeros with the same multiplicities, we say that f and g share the value a CM (counting multiplicities), and if we do not consider the multiplicities, then f and g are said to share the value a IM (ignoring multiplicities). We denote by T(r) the m...

Laplace operators perturbed by meromorphic potential on the Riemann and separated type Klein surfaces are constructed and their indices are calculated by two different ways. The topological expressions for the indices are obtained from the study of spectral properties of the operators. Analytical expressions are provided by the Heat Kernel approach in terms of the functional integrals. As a res...

Let M be a Riemannian manifold. For p ∈ M , the tensor algebra of the negative part of the (complex) affinization of the tangent space of M at p has a natural structure of a meromorphic open-string vertex algebra. These meromorphic open-string vertex algebras form a vector bundle over M with a connection. We construct a sheaf V of meromorphic open-string vertex algebras on the sheaf of parallel...

Abstract. We obtain growth comparison results of logarithmic differences, difference quotients and logarithmic derivatives for finite order meromorphic functions. Our results are both generalizations and extensions of previous results. We construct examples showing that the results obtained are best possible in certain sense. Our findings show that there are marked differences between the growt...

The aim of the present paper is to study the relations between the prime distribution and the zero distribution for generalized zeta functions which are expressed by an Euler products and are analytically continued as meromorphic functions of finite order. In this paper, we give an inequality between the order of the zeta function as a meromorphic function and the growth of the multiplicity in ...