Let $E$ be an elliptic curve over $Bbb{Q}$ with the given Weierstrass equation $ y^2=x^3+ax+b$. If $D$ is a squarefree integer, then let $E^{(D)}$ denote the $D$-quadratic twist of $E$ that is given by $E^{(D)}: y^2=x^3+aD^2x+bD^3$. Let $E^{(D)}(Bbb{Q})$ be the group of $Bbb{Q}$-rational points of $E^{(D)}$. It is conjectured by J. Silverman that there are infinitely many primes $p$ for which $...

DEFINITION 1.1. Let D ⊂ R be a domain, i.e., an open connected set. (i) A time-dependent vector field on D is a pair consisting of a domain V ⊂ D × R together with a continuous map F : V → R. (ii) The time-dependent vector field F is said to be autonomous (or one simply omits the adjective time-dependent) if V = D × R and for each x ∈ D, F (x, ·) is constant. That is to say, a vector field on D...

In this paper identities related to derivations on semiprime rings and standard operator algebras are investigated. We prove the following result which generalizes a classical result of Chernoff. Let X be a real or complex Banach space, let L(X) be the algebra of all bounded linear operators of X into itself and let A(X) ⊆ L(X) be a standard operator algebra. Suppose there exists a linear mappi...

background: 49, xxxxy syndrome is a rare sex chromosomal disorder, occurring in 1 per 85,000-100,000 male births. the classical phenotype is ambiguous genitalia, facial dysmorphism, mental retardation and a combination of cardiac, skeletal and other malformations. case: a two month-old boy with intrauterine growth restriction (iugr) and low birth weight, facial dysmorphism, clinodactyly in feet...

The purpose of this paper is to extend recent results [2] and [10] for the stochastic heat equation wave given by|?2u(t,x)?t2=?2u(t,x)?x2+?(u(t,x))W?(t,x)+b(u(t,x)),x?D??D,t>0,u(0,x)=u0(x),??tu(0,x)=v0(x),x?D, where W? space-time white noise, ? a real-valued globally Lipschitz function but b assumed be only locally continuous. Three types domain conditions are studied: D=[0,1] with homogeneous ...

i n m a n u f a c t u r i n g a c t i v i t i e s, i s s u e s s u c h a s t h e i n t e n s i t y o f c o m p e t i t i o n, r i s i n g a n d c h a n g i n g c u s t o m e r e x p e c t a t i o n s, a n d e v e r-i n c r e a s i n g t e c h n o l o g i c a l d e v e l o p m e n t s, i n t e n s i f y m a n u f a c t u r e r c o m m i t m e n t t o e l i m i n a t e d e f e c t s i n i t s p r...

Given a system (V, f, d) on a finite set V consisting of two set functions f : 2 → R and d : 2 → R, we consider the problem of finding a set R ⊆ V of minimum cardinality such that f(X) ≥ d(X) for all X ⊆ V − R, where the problem can be regarded as a natural generalization of the source location problems and the external network problems in (undirected) graphs and hypergraphs. We give a structur...

In this paper we prove the following result. Let R be a 6−torsion free semiprime ∗−ring and let D : R → R be an additive mapping satisfying the relation D(xyx) = D(x)y∗x∗ + xD(y)x∗ + xyD(x), for all pairs x, y ∈ R. In this case D is a Jordan ∗−derivation. Mathematics Subject Classification: 16W10, 39B05

A m i t r a z, a n i ns e c t i c i d e /a ca ri c i de of the f o r m a m i d i n e p e st i c i d e s group, is a ? 2 a d r e n e r g i c ag on i st a nd of t he a m i d i ne c h e m i ca l f a m il y generally us e d to c o n t r ol animal e c top a r a s i t e s. Poisoning due to am i t r a z i s r a r e and character...

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