In this paper it is shown that, given n ∈ Z ≥3 and a, b, c ∈ Q × , there exists a polynomial d(t) ∈ Q[t] such that the curves over Q(t) given by y 2 = x n + ad(t) resp. y 2 = x n + bd(t) and y 2 = x n + cd(t) all have a Jacobian with positive Mordell-Weil rank over Q(t). Extensions of this result to sets of four curves are discussed, as well as the problem of demanding in addition that d(t) is ...

Let be a surface with a symplectic form, let φ be a symplectomorphism of , and let Y be the mapping torus of φ. We show that the dimensions of moduli spaces of embedded pseudoholomorphic curves in R×Y , with cylindrical ends asymptotic to periodic orbits of φ or multiple covers thereof, are bounded from above by an additive relative index. We deduce some compactness results for these moduli spa...

in this note we review a simple criterion, due to ekedahl, for superspecial curves defined over finite fields.using this we generalize and give some simple proofs for some well-known superspecial curves.

In this paper, we look at long geometric progressions on diferent model of elliptic curves, namely Weierstrass curves, Edwards and twisted Edwards curves, Huf curves and general quartics curves. By a geometric progression on an elliptic curve, we mean the existence of rational points on the curve whose x-coordinate (or y-coordinate) are in geometric progression. We fnd infnite families of twist...

Braid monodromy is an important tool for computing invariants of curves and surfaces. In this paper, the rectangular braid diagram (RBD) method is proposed to compute the braid monodromy of a completely reducible n-gonal curve, i.e. the curves in the form (y−y1(x))...(y−yn(x)) = 0 where n ∈ Z+ and yi ∈ C[x]. Also, an algorithm is presented to compute the Alexander polynomial of these curve comp...

Let X be a smooth algebraic curve. Suppose that there exists a triple covering f : X → Y where Y is a smooth algebraic curve. In this paper, we investigate the existence of morphisms from X to the projective line P which do not factor through the covering f . For this purpose, we generalize the classical results of Maroni concerning base-point-free pencils on trigonal curves to the case of trip...

Let E denote an elliptic curve over Q and Y E (7) the modular curve classifying the elliptic curves E over Q such that the representations of Gal(Q/Q) in the 7-torsion points of E and of E are symplectically isomorphic. In case E is given by a Weierstraß equation such that the c 4 invariant is a square, we exhibit here nontrivial points of Y E (7)(Q). From this we deduce an infinite family of c...

A mathematical model for receptive field of retinal ganglion cell is proposed. This model includes the effect of the non-classical receptive field, which is resulted from the cross-inhabitation between the amacrine cells. This model also concerns the nonlinear effect of the photoreceptors so that unifies the X and Y ganglion cells. The null-test response of the X cell, the on-off response of th...

Approximately 75% of installed offshore wind turbines (OWTs) are supported by monopiles, a foundation whose design is dominated by lateral loading. Monopiles are typically designed using the p-y method which models soil-pile resistance using decoupled, nonlinear elastic Winkler springs. Because cyclic soil behavior is difficult to predict, the cyclic py method accounts for cyclic soil-pile inte...

THEOREM 1. Let the region R of the extended (x, y)-plane be bounded by a finite number of mutually disjoint Jordan curves Co, G., C2, • • • , Cn. Let the function u(x, y) be harmonic in R, continuous in the corresponding closed region, equal to zero on Co and to unity on G, C2, • • • , Cn. Denote by Ro the region bounded by Co containing the curves Ci, C2, • • • , Cn in its interior; define non...