Related papers: Reducibility of rational functions in several vari…

In this paper, we lay the foundations of the theory of slice regular functions in several variables ranging in any real alternative $^*$-algebra, including quaternions, octonions and Clifford algebras. This theory is an extension of the…

We investigate semiconjugate rational functions, that is rational functions $A,$ $B$ related by the functional equation $A\circ X=X\circ B$, where $X$ is a rational function of degree at least two. We show that if $A$ and $B$ is a pair of…

Optimization methods have been broadly applied to two classes of objects viz. (i) modeling and description of data and (ii) the determination of the stationary points of functions. Here, a theoretical basis is developed that optimizes an…

Adopting the approach of [7] we study rational function carrying invariant line fields on the Julia set. In particular, we show that under certain weak conditions all possible measurable invariant line fields of a rational function on its…

Complex functions have multiple uses in various fields of study, so analyze their characteristics it is of extensive interest to other sciences. This work begins with a particular class of rational functions of a complex variable; over this…

We study how the field of definition of a rational function changes under iteration. We provide a complete classification of polynomials with the property that the field of definition of one of their iterates drops in degree (over a given…

The necessary and sufficient conditions for differentiability of a function of several real variables stated and proved and its ramifications discussed.

We state and prove a Lemma in 1 variable Calculus, that justifies some arguments previously used to ilustrate non-uniqueness of some generalized physical quantities.

We study the rational approximation properties of special manifolds defined by a set of polynomials with rational coefficients. Mostly we will assume the case of all polynomials to depend on only one variable. In this case the manifold can…

This paper focuses on the problem of reconstructing a vector of rational functions given some evaluations, or more generally given their remainders modulo different polynomials. The special case of rational functions sharing the same…

We obtain explicit upper bounds for the number of irreducible factors for a class of compositions of polynomials in several variables over a given field. In particular, some irreducibility criteria are given for this class of compositions…

Let K be a non-archimedean field, and let f in K(z) be a rational function of degree d>1. If f has potentially good reduction, we give an upper bound, depending only on d, for the minimal degree of an extension L/K such that f is conjugate…

We contribute a new algebraic method for computing the orthogonal projections of a point onto a rational algebraic surface embedded in the three dimensional projective space. This problem is first turned into the computation of the finite…

We consider the connection of functional decompositions of rational functions over the real and complex numbers, and a question about curves on a Riemann sphere which are invariant under a rational function.

For a rational function of several variables with nonnegative imaginary part on the upper poly-half-plane, the matrix representations are obtained.

Under certain conditions, we obtain sharp bounds on some functionals defined in the coefficient space of starlike functions. It has been found that the functionals are closely associated with certain coefficient problems, which are of…

By studying the spectral aspects of the fractional part function in a well-known separable Hilbert space, we show, among other things, a rational approximation of the Riemann zeta function and its derivatives valid on every vertical line in…

In this work we prove the Stepanov differentiation theorem for multiple-valued functions. This theorem is proved in the wide generality of metric-space-multiple-valued functions without relying on a Lipschitz extension result. General…

The integration by parts recurrence relations allow to reduce some Feynman integrals to more simple ones (with some lines missing). Nevertheless the possibility of such reduction for the given particular integral was unclear. The recently…

Let f be a G-function (in the sense of Siegel), and x be an algebraic number; assume that the value f(x) is a real number. As a special case of a more general result, we show that f(x) can be written as g(1), where g is a G-function with…