Let E/Q(t) be an elliptic curve and let t0∈Q a rational number for which the specialization Et0 is curve. Given subgroup M of E(Q(t)) with mild conditions coming from relatively large subset SM⊂Q, we provide algorithm that can show map σt0:E(Q(t))→Et0(Q) injective when restricted to M. The set SM effectively computable in certain cases, carry out this computation some explicit examples where E ...

P-V curve and V-Q curve (often term as Q-V curve) are widely used for planning and operation studies. The P-V curve and V-Q curve of an unbalanced three-phase system, unlike the balanced three-phase system, may not have similar loading margin (LM) and reactive power margin (RPM) on each phase. Therefore, DIgSILENT Programming Language (DPL) has been used to study the maximum loading point (MLP)...

When we have a singular Cab curve with many rational points, we had better to construct linear codes on its normalization rather than the original curve. The only obstacle to construct linear codes on the normalization is finding a basis of L(∞Q) having pairwise distinct pole orders at Q, where Q is the unique place of the Cab curve at infinity. We present an algorithm finding such a basis from...

with A,B ∈ k. Then the rational point that comes with the curve is O = (0: 1 : 0), in the projective model Y Z = X +AXZ +BZ. There is a group law on an elliptic curve, given as follows. Let P,Q be points on the curve. Draw the unique line through P and Q (the tangent at P if they are equal) and find the unique third point of intersection, R, with the curve; this exists by Bézout’s theorem. Now ...

We show that an Fq2-maximal curve of genus 1 6 (q − 3)q > 0 is either a non-reflexive space curve of degree q+1 whose tangent surface is also non-reflexive, or it is uniquely determined, up to isomorphism, by a plane model of Artin-Schreier type whenever q ≥ 27. MSC 2000: 11G20 (primary), 14G05, 14G10 (secondary)

this article presents an implementation of a reinforcement learning (rl) method for a snake like robot navigation. the paper starts with developing kinematics and dynamics model of a snake robot in serpentine locomotion followed by performing simulation and finishes with actual experimentation. first, gibbs-appell's method is used to obtain the robot dynamics. the robot is also modeled in simme...

Let F be the finite field of order q, q = p with p prime. It is commonly atribute to J.P. Serre the fact that any curve F-covered by the Hermitian curve Hq+1 : y = x + x is also F-maximal. Nevertheless, the converse is not true as the GiuliettiKorchmáros example shows provided that q > 8 and h ≡ 0 (mod 3). In this paper, we show that if an F-maximal curve X of genus g ≥ 2 where q = p is such th...

By the Mordell-Weil theorem the group of Q(z)-rational points of an elliptic curve is finitely generated. It is not known whether the rank of this group can get arbitrary large as the curve varies. Mestre and Nagao have constructed examples of elliptic curves E with rank at least 13. In this paper a method is explained for finding a 14th independent point on E, which is defined over k(z), with ...

For the integer D = pq of the product of two distinct odd primes, we construct an elliptic curve E2rD : y 2 = x3 − 2rDx over Q, where r is a parameter dependent on the classes of p and q modulo 8, and show, under Birch and Swinnerton-Dyer conjecture, that the elliptic curve has rank one and vp(x([k]Q)) 6= vq(x([k]Q)) for odd k and a generator Q of the free part of E2rD(Q). Thus we can get p or ...

Under the assumption that we have defining equations of an affine algebraic curve in special position with respect to a rational place Q, we propose an algorithm computing a basis of L(D) of a divisor D from an ideal basis of the ideal L(D +∞Q) of the affine coordinate ring L(∞Q) of the given algebraic curve, where L(D+∞Q) := S∞ i=1 L(D+ iQ). Elements in the basis produced by our algorithm have...