Let $E$ be an elliptic curve, with identity $O$, and let $C$ a cyclic subgroup of odd order $N$, over algebraically closed field $k$ $\operatorname{char} k \nmid N$. For $P \in C$, $s_P$ rational function divisor $N \cdot P - N O$. We ask whether the $N$ functions are linearly independent. generic $(E,C)$, we prove that answer is yes. bound number exceptional $(E,C)$ when prime by using geometr...

‎second derivative general linear methods (sglms) as an extension‎ ‎of general linear methods (glms) have been introduced to improve‎ ‎the stability and accuracy properties of glms‎. ‎the coefficients of‎ ‎sglms are given by six matrices‎, ‎instead of four matrices for‎ ‎glms‎, ‎which are obtained by solving nonlinear systems of order and‎ ‎usually runge--kutta stability conditions‎. ‎in this p...

in this paper, we investigate the existence of a positive solution of fully fuzzy linear equation systems. this paper mainly to discuss a new decomposition of a nonsingular fuzzy matrix, the symmetric times triangular (st) decomposition. by this decomposition, every nonsingular fuzzy matrix can be represented as a product of a fuzzy symmetric matrix s and a fuzzy triangular matrix t.