Covering collections and a challenge problem of Serre

Covering Collections and a Challenge Problem of Serre

We answer a challenge of Serre by showing that every rational point on the projective curve X + Y 4 = 17Z is of the form (±1,±2, 1) or (±2,±1, 1). Our approach builds on recent ideas from both Nils Bruin and the authors on the application of covering collections and Chabauty arguments to curves of high rank. This is the only value of c ≤ 81 for which the Fermat quartic X+Y 4 = cZ cannot be solv...

Covering Colle tions and a Challenge Problem of SerreE

Descent and Covering Collections

We explain several approaches that allow to prove that a given curve over Q has no rational points.

General form of a cooperative gradual maximal covering location problem

Cooperative and gradual covering are two new methods for developing covering location models. In this paper, a cooperative maximal covering location–allocation model is developed (CMCLAP). In addition, both cooperative and gradual covering concepts are applied to the maximal covering location simultaneously (CGMCLP). Then, we develop an integrated form of a cooperative gradual maximal covering ...

A cross entropy algorithm for continuous covering location problem

Covering problem tries to locate the least number of facilities and each demand has at least one facility located within a specific distance.This paper considers a cross entropy algorithm for solving the mixed integer nonlinear programming (MINLP) for covering location model.The model is solved to determine the best covering value.Also, this paper proposes aCross Entropy (CE) algorithm consider...