Ab initio calculation at HF/6-31G* level of theory for geometry optimization and MP2/6-31G*//HF/6-31G* for a single point total energy calculation are reported for the important energyminimumconformations and transition-state geometries of of cyclodeca-1,2,3-triene (1). The mostfavorable conformation of 1 is a unsymmetrical twist-chair (1-TC) structure. Degenerateinterconversion of 1-TC with it...

We will assume that the twisted L-series are primitive (i.e. the corresponding twisted modular forms are newforms). There is no loss of generality in making this assumption: if this is not the case, then f would be a quadratic twist of a newform of smaller level, which we can choose instead. The question of efficiently computing the family of central values L(f,D, 1), for fundamental discrimina...

Let $A$ be an abelian variety over a number field $F$ and let $p$ prime. Cohen-Lenstra-Delaunay-style heuristics predict that the Tate-Shafarevich group of $A_s$ should contain element order for positive proportion quadratic twists $A$. We give general method to prove instances this conjecture by exploiting independent isogenies For each prime $p$, there is large class elliptic curves which our...

In EUROCRYPT 2009, Galbraith, Lin and Scott constructed an efficiently computable endomorphism for a large family of elliptic curves defined over finite fields of large characteristic. They demonstrated that the endomorphism can be used to accelerate scalar multiplication in the elliptic curve cryptosystem based on these curves. In this paper we extend the method to any genus 2 hyperelliptic cu...

How fast can we compute the value of an L-function at the center of the critical strip? We will divide this question into two separate questions while also making it more precise. Fix an elliptic curve E defined over Q and let L(E, s) be its L-series. For each fundamental discriminant D let L(E,D, s) be the L-series of the twist ED of E by the corresponding quadratic character; note that L(E, 1...

background: metastasis is one the most leading cause of death from cancer. the chemokine receptor of cxcr4 has an important role in cell migration and cancer metastasis. additionally, metastasis is always associated with the process of epithelial-mesenchymal transition (emt). in this study the correlation between expression of cxcr4 and emt-tfs has been examined. methods: the expression of cxcr...

For counting points of jacobians of genus 2 curves over a large prime field, the best known approach is essentially an extension of Schoof’s genus 1 algorithm. We propose various practical improvements to this method and illustrate them with a large scale computation: we counted hundreds of curves, until one was found that is suitable for cryptographic use, with a state-ofthe-art security level...

*Correspondence: [email protected] 2School of Mathematical Sciences, Soochow University, Suzhou, 215006, China Full list of author information is available at the end of the article Abstract The existence of infinity of subharmonics for Duffing equations with convex and oscillatory nonlinearities is shown. This result is a corollary of two theorems. These theorems, one for a weak sub-quadratic...

we used qcd factorization for the hadronic matrix elements to show that the existing data, in particular the branching ratios br ( ?j/?k) and br ( ?j/??), can be accounted for this approach. we analyzed the decay within the framework of qcd factorization. we have complete calculation of the relevant hard-scattering kernels for twist-2 and twist-3. we calculated this decays in a special scale ( ...

Large angle gluon radiations induced by multiple parton scatterings contribute to dijet production in deeply inelastic scattering off a large nucleus at the electron-ion collider. Within generalized high-twist approach scattering, contributions leading order and twist four perturbative QCD Bjorken momentum fraction ${x}_{B}$ can be expressed as convolution of amplitudes transverse dependent (TM...