For each integer n > 1 we construct a closed unknotted PL curve Kn in R 3 having less than 33n edges with the property that any PL triangluated disk spanning the curve contains at least 2 n triangles.

let $e$ be an elliptic curve over $bbb{q}$ with the given weierstrass equation $ y^2=x^3+ax+b$. if $d$ is a squarefree integer, then let $e^{(d)}$ denote the $d$-quadratic twist of $e$ that is given by $e^{(d)}: y^2=x^3+ad^2x+bd^3$. let $e^{(d)}(bbb{q})$ be the group of $bbb{q}$-rational points of $e^{(d)}$. it is conjectured by j. silverman that there are infinitely many primes $p$ for which $...

In [14] Matsuda and Yorozu.explained that there is no special Bertrand curves in Eⁿ and they new kind of Bertrand curves called (1,3)-type Bertrand curves Euclidean space. In this paper , by using the similar methods given by Matsuda and Yorozu [14], we obtain that bitorsion of the quaternionic curve is not equal to zero in semi-Euclidean space E4^2. Obtain (N,B2) type quaternionic Bertrand cur...

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...

Let C be a curve of genus 2 and ψ1 : C −→ E1 a map of degree n, from C to an elliptic curve E1, both curves defined over C. This map induces a degree n map φ1 : P 1 −→ P 1 which we call a Frey-Kani covering. We determine all possible ramifications for φ1. If ψ1 : C −→ E1 is maximal then there exists a maximal map ψ2 : C −→ E2, of degree n, to some elliptic curve E2 such that there is an isogeny...

Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive...

In this paper, we present a new and more general version of polygonal approximation problem (GPA). Given an N−vertex polygonal curve P in the n-dimensional space <n, we approximate P by finding another M−vertex polygonal curve Ṗ , such that the vertices of Ṗ are an ordered subsequence of the curve points along P . The definition of the classical polygonal approximation problem (PA) demands the ...

We propose an adaptive geometry compression method based on 4-point interpolatory subdivision schemes. It can work on digital curves of arbitrary dimensions. With the geometry compression method, a digital curve is adaptively compressed into several segments with different compression levels. Each segment is a 4-point subdivision curve with a subdivision step. In the meantime, we provide high-s...

LetX denote the rational curve with n+1 nodes obtained from the Riemann sphere by identifying 0 with∞ and ζj with −ζj for j = 0, 1, . . . , n−1, where ζ is a primitive (2n)th root of unity. We show that if n is even, then X has no smooth Weierstrass points, while if n is odd, then X has 2n smooth Weierstrass points. C. Widland [14] showed that the rational curve with three nodes obtained from P...

In this present paper, rectifying curves are re-characterized in a shorter and simpler way using harmonic curvatures some relations between focal found terms of their curvature functions $n-$dimensional Euclidean space. Then, Salkowski curve, which is the curve given space investigated. Finally, figures related to theory case $n=3$.