A standard technique for solving the recursion xn+1 = g (xn) where g : C→ C is a complex function is to first find a fairly simple function g : C→ C and a bijection f : C→ C such that g = f◦g◦f−1 where ◦ is the composition of functions. Then xn = g (x0) = (f ◦ g ◦ f−1) (x0) where g and g are the n-fold composition of functions and g is fairly easy to compute. With this motivation we find all pa...

0. Introduction Our object is to study domains which are the region of negative definiteness of an operator-valued Hermitian form defined on a space of operators and to investigate the biholomorphic linear fractional transformations between them. This is a unified setting in which to consider operator balls, operator half-planes, strictly J-contractive operators, strictly J-dissipative operator...

These notes supplement the discussion of linear fractional mappings presented in a beginning graduate course in complex analysis. The goal is to prove that a mapping of the Riemann sphere to itself is a rotation if and only if the corresponding map induced on the plane by stereographic projection is a linear fractional whose (two-by-two) coefficient matrix is unitary. 1. Spheres, points, and su...

In this paper, a nonlinear modelling framework is presented that combines symbolic modelling and linear fractional transformation (LFT) techniques to obtain a nonlinear symbolic LFT representation. This modelling approach presents three clear advantages: (i) it provides a unifying framework for the different models that stem from the same nonlinear system, (ii) it allows for a highly structured...

Explicit invariant measures are derived for a family of finite-toone, ergodic transformations of the unit interval having indifferent periodic orbits. Examples of interesting, non-trivial maps of [0, 1] for which one can readily compute an invariant measure absolutely continuous to Lebesgue measure are not easy to come by. The familiar examples are the Gauss map, the backward continued fraction...

If g, g are complex rational functions, we say that g ∼ g if g = ( ax+b cx+d )−1 ◦ g ◦ (ax+b cx+d ) , where ∣∣∣∣ a b c d ∣∣∣∣ 6= 0. For practical purposes, the general problem of finding a collection of rational invariants that are sufficient to partition ∼ into equivalency classes may be intractable for arbitrary degree rational functions. In this paper, we first outline a simple and naive met...

in this article we implement an operational matrix of fractional integration for legendre polynomials. we proposed an algorithm to obtain an approximation solution for fractional differential equations, described in riemann-liouville sense, based on shifted legendre polynomials. this method was applied to solve linear multi-order fractional differential equation with initial conditions, and the...

Symbol-pair code is a new coding framework which is proposed to correct errors in the symbolpair read channel. In particular, maximum distance separable (MDS) symbol-pair codes are a kind of symbol-pair codes with the best possible error-correction capability. Employing cyclic and constacyclic codes, we construct three new classes of MDS symbol-pair codes with minimum pairdistance five or six. ...

For a subgroup of PGL(2,q) we show how some irreducible polynomials over Fq arise from the field invariant rational functions. The proofs rely on combining two actions PGL(2,F), one projective line F and other function F(x). functions in F(x) are used to that regular patterns exist factorization certain into polynomials. We use results about group orbit polynomial, whose included.

in this paper, we study the classical sensitivity analysis when the right - hand – side vector, and the coefficients of the objective function are allowed to vary.