Let E be an elliptic curve over the finite field F_{q}, P a point in E(F_{q}) of order n, and Q a point in the group generated by P. The discrete logarithm problem on E is to find the number k such that Q = kP. In this paper we reduce the discrete logarithm problem on E[n] to the discrete logarithm on the group F*_{q} , the multiplicative group of nonzero elements of Fq, in the case where n | q...

Let η be a line bundle on a smooth curve X with η^2=0 such that π_η, the double covering induced by η is an etale morphism. Assume also that X_η be the Prym-canonical model of X associated to K_X.η and Q is a rank 4 quadric containing X_η. After stablishing the projective normality of the prym-canonical models of curves X with Clifford index 2, we obtain in this paper a sufficient condition for...

Biochemical leaf photosynthesis models are evaluated by laboratory results andhave been widely used at field scale for quantification of plant production,biochemical cycles and land surface processes. It is a key issue to search forappropriate model structure and parameterization, which determine modeluncertainty. A leaf photosynthesis model that couples the Farquhar-vonCaemmerer-Berry (FvCB) f...

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 $...

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 $...

early screening of autism increases the chance of receiving timely intervention. using the parent report questionnaires is effective in screening autism. the q-chat is a new instrument that has shown several advantages than other screening tools. because there is no adequate tool for the early screening of autistic traits in iranian children, we aimed to investigate the adequacy of the persian ...