The ring Z has many analogies with the ring Fp[T ], where Fp is a field of prime size p. For example, for nonzero m ∈ Z and nonzero M ∈ Fp[T ], the residue rings Z/(m) and Fp[T ]/M are both finite. The unit groups Z × = {±1} and Fp[T ]× = Fp are both finite. Every nonzero integer can be made positive after multiplication by a suitable unit, and every nonzero polynomial in Fp[T ] can be made mon...

Abstract A sequence is said to be k-automatic if the nth term of this sequence is generated by a finite state machine with n in base k as input. Regular sequences were first defined by Allouche and Shallit as a generalization of automatic sequences. Given a prime p and a polynomial f(x) ∈ Qp[x], we consider the sequence {vp(f(n))}n=0, where vp is the p-adic valuation. We show that this sequence...

introduction: almond (prunus amygdalus b.) is one of the most important crops consumed as a dry fruit and it is mainly adaptable to arid and semi-arid regions mostly suffering from salinity stress (8). soils with dry humidity regime are dominant in iran and in the world at large and mostly include regions with more evaporation than precipitation. this in turn leads to increased salinity of the ...

Lenstra Jr, H.W., On the inverse Fermat equation, Discrete Mathematics 106/107 (1992) 329-33 1. In this paper the equation x”” + y”” = z “n is solved in positive integers x, y, z, n. If the nth roots are taken to be positive real numbers, then all solutions are known to be trivial in a certain sense. A very short proof of this is provided. The argument extends to give a complete description of ...

In this paper, for any positive integer N we shall study the special values of multiple polylogarithms at Nth roots of unity, called multiple polylogarithmic values (MPVs) of level N . By standard conjectures linear relations exist only between MPVs of the same weight. LetMPVZ(w,N) be the Z-module spanned by MPVs of weight w and level N . Our main interest is to investigate for what w and N the...

RNAi constructs targeted to four different genes were examined to determine their efficacy to reduce galls formed by Meloidogyne incognita in soybean roots. These genes have high similarity with essential soybean cyst nematode (Heterodera glycines) and Caenorhabditis elegans genes. Transformed roots were challenged with M. incognita. Two constructs, targeted to genes encoding tyrosine phosphata...

* From the Department of Genetics (No. 512), University of Wisconsin. This project was supported in part by the Research Committee of the Graduate School from funds supplied by the Wisconsin Alumni Research Foundation. 1 Irwin, M. R., Cole, L. J., and Gordon, C. D., J. Exptl. Zool. 73, 285 (1936). 2 Miller, W. J., Physiol. Zool. (in press). 3 Irwin, M. R., and Cole, L. J., J. Exptl. Zool. 73, 8...