The Xedni Calculus and the Elliptic Curve Discrete Logarithm Problem

Let be an elliptic curve defined over a finite field, and let be two points on E. The Elliptic Curve Discrete Logarithm Problem (ECDLP) asks that an integer m be found so that S=mT in . In this note we give a new algorithm, termed the Xedni Calculus, which might be used to solve the ECDLP. As remarked by Neal Koblitz, the Xedni method is also applicable to the classical discrete logarithm problem for and to the integer factorization problem.     

Regularity of solutions of divergence form elliptic equations

The aim of this paper is to study local regularity in the Morrey spaces of the first derivatives of the solutions of an elliptic second order equation in divergence form

where is assumed to be in some spaces and the coefficients belong to the space

     

Nonsymmetric systems and area integral estimates

Even though the Dirichlet problem on Lipschitz domains is not always solvable for nonsymmetric strongly elliptic systems, so that many results and techniques from the symmetric systems are unavailable, there are some similarities with the symmetric systems. We show that the nontangential maximal function and the square function of a solution are equivalent and that there is a Fatou theorem for these solutions.

     

Computing the -Selmer group of an elliptic curve

In this paper we explain how to bound the -Selmer group of an elliptic curve over a number field . Our method is an algorithm which is relatively simple to implement, although it requires data such as units and class groups from number fields of degree at most . Our method is practical for , but for larger values of it becomes impractical with current computing power. In the examples we have calculated, our method produces exactly the -Selmer group of the curve, and so one can use the method to find the Mordell-Weil rank of the curve when the usual method of -descent fails.

     

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通过求解椭圆积分,计算了EAST极向场系统的磁场分布,从而计算出极向场线圈在等离子体放电过程中的热负荷。并根据磁体运行的热工水力条件估算出极向场线圈在等离子体放电过程中的最高温升。     

Computing the rank of elliptic curves over real quadratic number fields of class number 1

In this paper we describe an algorithm for computing the rank of an elliptic curve defined over a real quadratic field of class number one. This algorithm extends the one originally described by Birch and Swinnerton-Dyer for curves over . Several examples are included.

     

基于椭圆形光强分布光栅投影的三维面形测量方法

基于椭圆形光强分布光栅投影测量物体三维面形的方法,将椭圆形光强分布光栅投影到被测物体表面,用摄像机获取变形条纹图,通过系统参量和条纹图携带的相位信息求解出物体的三维面形.推导出通过椭圆形光强分布光栅条纹求解相位的计算公式并对提出方法作了计算机仿真.实验结果表明该方法可以比较准确地测量物体的三维面形,在噪音较大的情况下测量结果仍具有较高准确度.     

A Meyers type regularity result for approximations of second order elliptic operators by P1 finite elements

We prove a Meyers type regularity estimate for approximate solutions of second order elliptic equations obtained by P1 finite elements. The proofs rely on interpolation results for Sobolev spaces on graphs. Estimates for second order elliptic operators on rather general graphs are also obtained.