Existence Theorem of Global Solutions for Monge-Ampere Equation

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A residual method of finite differencing for the elliptic transport problem and its application to cavity flow

A residual method of finite differencing the governing differential equation for the elliptic transport problem is presented. The new finite differencing technique is applied to (1) the one-dimensional transport problem and (2) the cavity flow problem for numerical illustrations. The results indicate the validity of the residual method of finite differencing. The usual method of term-by-term finite differencing, and considerations such as central differencing, hybrid differencing and upwind differencing are not needed in the present residual method.     

On standardized models of isogenous elliptic curves

Let be isogenous elliptic curves over given by standardized Weierstrass models. We show that (in the obvious notation)

and, moreover, that there are integers such that

where .

     

On the -torsion of elliptic curves and elliptic surfaces in characteristic

We study the extension generated by the -coordinates of the -torsion points of an elliptic curve over a function field of characteristic . If is a non-isotrivial elliptic surface in characteristic with a -torsion section, then for 11$"> our results imply restrictions on the genus, the gonality, and the -rank of the base curve , whereas for such a surface can be constructed over any base curve . We also describe explicitly all occurring in the cases where the surface is rational or or the base curve is rational, elliptic or hyperelliptic.

     

Intermediate boundary corrections for split operator methods in three dimensions

This paper deals with the intermediate boundary corrections required by splittings of alternating direction methods for solving three space dimensional problems involving Laplace's equation or the heat conduction equation. In addition to considering the existing splittings of Douglas and D'Yakonov, a new splitting is introduced. The extensions of the results to multidimensional problems are briefly noted.     

Integer points on the curve

We completely solve diophantine equations of the form where is a positive integer, using a reduction to some quartic elliptic equations, which can be solved with well known methods.

     

Average size of -Selmer groups of elliptic curves, I

In this paper, we study a class of elliptic curves over with -torsion group , and prove that the average order of the -Selmer groups is bounded.

     

Cubic elliptic functions

The function