We systematically investigate the farthest distance function, farthest points, Klee sets, and Chebyshev centers, with respect to Bregman distances induced by Legendre functions. These objects are of considerable interest in Information Geometry and Machine Learning; when the Legendre function is specialized to the energy, one obtains classical notions from Approximation Theory and Convex Analys...

This paper studies the optimal investment problem of utility maximization with taxes, dividends and transaction costs under the constant elasticity of variance (CEV) model. The Hamilton-Jacobi-Bellman (HJB) equation associated with the optimization problem is established via stochastic control approach. Applying power transform and variable change technique, we obtain explicit solutions for the...

Abstract Sequences of consecutive Legendre and Jacobi symbols as pseudorandom bit generators were proposed for cryptographic use in 1988. Major interest has been shown towards functions (PRF) recently, based on the power residue symbols, due to their efficiency multi-party setting. The security these PRFs is not known be reducible standard assumptions. In this work, we show that key-recovery at...

Variance components of the covariance function coefficients in a random regression test-day model were estimated by Legendre polynomials up to a fifth order for first-parity records of Dutch dairy cows using Gibbs sampling. Two Legendre polynomials of equal order were used to model the random part of the lactation curve, one for the genetic component and one for permanent environment. Test-day ...

We derive the Legendre series expansion for insolation distribution on rapidly rotating planets as a function of sine latitude and planet's obliquity. give an explicit formula coefficients this it depends obliquity approximate convergence rate. determine optimal truncation use in climate models compare approximation to other approximations literature.