We prove that a form of finite Galois descent obstruction is the only obstruction to the existence of integral points on integral models of twists of modular curves over function fields.

a back propagation artificial neural network (bpann) is a well-known learning algorithmpredicated on a gradient descent method that minimizes the square error involving the networkoutput and the goal of output values. in this study, 261 gps/leveling and 8869 gravity intensityvalues of iran were selected, then the geoid with three methods “ellipsoidal stokes integral”,“bpann”, and “collocation” ...

In this paper , we first extend and analyze the steepest descent method for solving optimal control problem for systems governed by Volterra integral equations . Then, we present some hybrid methods based on the extended steepest descent and two-step Newton methods, to solve the problem. The global convergence results are also established using some mild assumptions and conditions. Numerical re...

A Back Propagation Artificial Neural Network (BPANN) is a well-known learning algorithmpredicated on a gradient descent method that minimizes the square error involving the networkoutput and the goal of output values. In this study, 261 GPS/Leveling and 8869 gravity intensityvalues of Iran were selected, then the geoid with three methods “ellipsoidal stokes integral”,“BPANN”, and “collocation” ...

The method of descent is a technique developed by Fermat for proving certain equations have no (or few) integral solutions. The idea is to show that if there is an integral solution to an equation then there is another integral solution which is smaller in some way. Repeating this process and comparing the sizes of the successive solutions leads to an infinitely decreasing sequence a1 > a2 > a3...

Let R be an integral domain of finite type over Z and let f : X → SpecR be a smooth projective morphism of relative dimension d ≥ 1. We investigate, for a vector bundle E on the total space X , under what arithmetical properties of a sequence (pn, en)n∈N, consisting of closed points pn in SpecR and Frobenius descent data Epn ∼= F n(F) on the closed fibers Xpn , the bundle E0 on the generic fibe...

We study a new obstruction to the existence of integral and rational points for algebraic varieties over function fields, the differential descent obstruction. We prove that that is the only obstruction to the existence of integral points in affine varieties in characteristic zero and also, in most cases, for rational points on curves in arbitrary characteristic.

In this paper we study the geometric properties, existence, regularity and related issues for a family of surfaces which are boundaries of sets minimizing certain integral norms. These surfaces can be interpreted as a non-infinitesimal version of classical minimal surfaces. Our work is motivated by the structure of interphases that arise in classical phase field models when very long space corr...

This paper deals with a new accelerated path integral method, which iteratively searches optimal controls with a small number of iterations. This study is based on the recent observations that a path integral method for reinforcement learning can be interpreted as gradient descent. This observation also applies to an iterative path integral method for optimal control, which sets a convincing ar...