The distribution of descents in a xed conjugacy class of Sn is studied and it is shown that its moments have a remarkable property. This is proven two ways: one way via generating functions and another way via a combinatorial algorithm. This leads to an asymptotic normality theorem for the number of descents and major index in conjugacy classes of Sn with large cycles. 3

The scaling function of a one-dimensional Markov map is defined and studied. We prove that the scaling function of a non-critical geometrically finite one-dimensional map is Hölder continuous, while the scaling function of a critical geometrically finite one-dimensional map is discontinuous. We prove that scaling functions determine Lipschitz conjugacy classes, and moreover, that the scaling fu...

Conjugate gradient methods are a class of important methods for unconstrained optimization, especially when the dimension is large. This paper proposes a new conjugacy condition, which considers an inexact line search scheme but reduces to the old one if the line search is exact. Based on the new conjugacy condition, two nonlinear conjugate gradient methods are constructed. Convergence analysis...

We analyze a technique for unconstrained minimization without derivatives. This stems from two theorems proved by M. J. D. Powell. A particular version, which we consider in detail, is related to the Jacobi process for finding the eigensystem of a symmetric matrix, and the two processes, although different, help to illuminate one another. We study convergence of the search directions to mutual ...

If the permutation action ρI is transitive, all factors Xi are quasiisometric to each other, and the restricted quasi-actions Gi y Xi are quasi-conjugate (when identifying different stabilizers Gi by inner automorphisms of G). The main result of this note is that in this case any of the quasi-actions Gi y Xi determines ρ up to quasi-conjugacy, and moreover any quasi-conjugacy class may arise as...

Let [Formula: see text] be a prime and let the complex field. We explicitly classify finite solvable irreducible monomial subgroups of up to conjugacy. That is, we give complete irredundant list text]-conjugacy class representatives as generating sets matrices. Copious structural information about non-solvable is also proved, enabling classification all such groups bar one family. explain obsta...

This paper defines Artin groups with m-gon structure and proves that for m > 3 in this class the problems of equality conjugacy words are solvable.

Friedland and Milnor [FM] have shown that from a dynamical point of view the polynomial diffeomorphisms of C2 fall naturally into two classes. The first class consists of diffeomorphisms with simple dynamics. The diffeomorphisms in this class have periodic points of at most finitely many periods and topological entropy zero. The second class contains the well-known Henon map f(x, y) = (y, i-ax ...