For any prime `, it is possible to construct global function fields whose Jacobians have high `-rank by moving to a sufficiently large constant field extension. This was investigated in some detail by Bauer et al. in [2]. The two main results of [2] are an upper bound on the size of the field of definition of the `-torsion J [`] of the Jacobian, and a lower bound on the increase in the base fie...

We give a solution to the weak Schottky problem for genus five Jacobians with vanishing theta null, answering question of Grushevsky and Salvati Manni. More precisely, we show that if principally polarized abelian variety dimension has null quadric tangent cone rank at most three, then it is in Jacobian locus, up extra irreducible components. employ degeneration argument, together study ramific...

In this article, we obtain an estimator of the regression parameters for generalized linear models, using the Jacobian technique. We restrict ourselves to the natural exponential family for the response variable and choose the conjugate prior for the natural parameter. Using the Jacobian of transformation, we obtain the posterior distribution for the canonical link function and thereby obtain t...

Let C be a smooth projective absolutely irreducible curve of genus g ≥ 2 over a number field K of degree d, and denote its Jacobian by J . Denote the Mordell–Weil rank of J(K) by r. We give an explicit and practical Chabauty-style criterion for showing that a given subset K ⊆ C(K) is in fact equal to C(K). This criterion is likely to be successful if r ≤ d(g − 1). We also show that the only sol...

a systematic way is presented for the construction of multi-step iterative method with frozen jacobian. the inclusion of an auxiliary function is discussed. the presented analysis shows that how to incorporate auxiliary function in a way that we can keep the order of convergence and computational cost of newton multi-step method. the auxiliary function provides us the way to overcome the singul...

Abstract We investigate the rank gain of elliptic curves, and more generally, Jacobian varieties, over non‐Galois extensions whose Galois closure has a group permutation‐isomorphic to prescribed G (in short, “ ‐extensions”). In particular, for alternating groups (an infinite family of) projective linear , we show that most curves (for example) infinitely many ‐extensions, conditional only on pa...

When a physical system is modeled by nonlinear function, the unknown parameters can be estimated fitting experimental observations least-squares approach. Newton's method and its variants are often used to solve problems of this type. In paper, we concerned with computation minimal-norm solution an underdetermined problem. We present Gauss-Newton type method, which relies on two relaxation ensu...

The motivation for this work comes from two problems– test algebraic independence of arithmetic circuits over a field of small characteristic, and generalize the structural property of algebraic dependence used by (Kumar, Saraf CCC’16) to arbitrary fields. It is known that in the case of zero, or large characteristic, using a classical criterion based on the Jacobian, we get a randomized poly-t...

The motivation for this work comes from two problems– test algebraic independence 5 of arithmetic circuits over a field of small characteristic, and generalize the structural property of 6 algebraic dependence used by (Kumar, Saraf, CCC’16) to arbitrary fields. 7 It is known that in the case of zero, or large characteristic, using a classical criterion based on 8 the Jacobian, we get a randomiz...