Smooth functions and local extreme values

Smooth functions and local extreme values

Given a sample of n observations y1, . . . , yn at time points t1, . . . , tn we consider the problem of specifying a function f̃ such that f̃ • is smooth, • fits the data in the sense that the residuals yi − f̃(ti) satisfy the multiresolution criterion

Extreme Values of Zeta and L-functions

On Factorizations of Smooth Nonnegative Matrix-values Functions and on Smooth Functions with Values in Polyhedra

We discuss the possibility to represent smooth nonnegative matrix-valued functions as finite linear combinations of fixed matrices with positive real-valued coefficients whose square roots are Lipschitz continuous. This issue is reduced to a similar problem for smooth functions with values in a polyhedron. 1. Motivation One of the main goals of the article is to understand what kind of optimal ...

Extreme values of Artin L-functions and class numbers

Assuming the GRH and Artin conjecture for Artin L-functions, we prove that there exists a totally real number field of any fixed degree (> 1) with an arbitrarily large discriminant whose normal closure has the full symmetric group as Galois group and whose class number is essentially as large as possible. One ingredient is an unconditional construction of totally real fields with small regulato...

Chemical Trees with Extreme Values of Zagreb Indices and Coindices

We give sharp upper bounds on the Zagreb indices and lower bounds on the Zagreb coindices of chemical trees and characterize the case of equality for each of these topological invariants.