Genus 2 curves with simple but not absolutely simple jacobians can be used to construct pairing-based cryptosystems more efficient than for a generic genus 2 curve. We show that there is a full analogy between methods for constructing ordinary pairing-friendly elliptic curves and simple abelian varieties, which are iogenous over some extension to a product of elliptic curves. We extend the noti...

Because of their applicability for ordering distributions within general classes of utility and social welfare functions, tests for stochastic and Lorenz dominance have attracted considerable attention in the literature. To date the focus has been on sampling theory tests, with some tests having a null hypothesis that X dominates Y (say), and others having a null hypothesis that Y does not domi...

We prove new patchworking theorems for singular algebraic curves, which state the following. Given a complex toric threefold Y which is fibred over C with a reduced reducible zero fiber Y0 and other fibers Yt smooth, and given a curve C0 ⊂ Y0, the theorems provide sufficient conditions for the existence of one-parametric family of curves Ct ⊂ Yt, which induces an equisingular deformation for so...

M e t h o d s Data sources: PubMed (to December 2005) and reference lists. Study selection and assessment: Prospective cohort studies that reported all-cause mortality in adults by level of alcohol intake and separately for men and women. 34 studies met the selection criteria and provided 56 dose-response curves: 37 curves in men (n = 705 596 participants and 78 592 deaths) and 19 curves in wom...

The variational derivative of a functional J[y] can be defined as δJ/δy = F y (x, y, y ′)− d dx F y ′ (x, y, y ′) [1, pp. 27–29]. Euler's equation essentially states that the variational derivative of the functional must vanish at an extremum. This is analogous to the well-known result from calculus that the derivative of a function must vanish at an extremum. In this section, we consider a sim...

K e y w o r d s B l e n d i n g curves, Ordinary differential equation (ODE), Separation techniques, Fundamental solutions, Finite element method, Computer geometric aided design. We thank the reviewer for one's valuable comments and suggestions on this manuscript. *Author to whom all correspondence should be addressed. 0895-7177/05/$ see front matter @ 2005 Elsevier Ltd. All rights reserved. T...

The map x y p x y x of the plane is area preserving and has the remarkable property that in numerical studies it shows exact integrability The plane is a union of smooth disjoint invariant curves of the map However the integral has not explicitly been known In the current paper we will show that the map does not have an algebraic integral i e there is no non constant function F x y such that F ...

This paper sets new software speed records for high-security Diffie-Hellman computations, specifically 251-bit elliptic-curve variablebase-point scalar multiplication. In one second of computation on a $200 Core 2 Quad Q6600 CPU, this paper’s software performs 30000 251-bit scalar multiplications on the binary Edwards curve d(x + x + y + y) = (x + x)(y + y) over the field F2[t]/(t 251 + t + t +...

Given two finite covers $$p: X \rightarrow S$$ and $$q: Y of a connected, oriented, closed surface S genus at least 2, we attempt to characterize the equivalence p q in terms which curves lift simple curves. Using Teichmüller theory complex curves, show that regular are equivalent if for any curve $$\gamma \subset , $$ lifts on only it does Y. When abelian, also give characterization powers

This paper presents an algorithm to compute the bisector curve of two planar paramet-ric curves. We reduce the problem of computing a bisector curve to that of intersecting two developable surfaces. Given an input curve C (t) = (x(t); y(t)), the corresponding developable surface D C(t) is constructed symbolically as the envelope surface of a one-parameter family of tangent planes of the parabol...