Related papers: An Introduction to Finite Fibonomial Calculus

In this short note we use ideas from systems theory to define a functional calculus for infinitesimal generators of strongly continuous semigroups on a Hilbert space. Among others, we show how this leads to new proofs of (known) results in…

In this present investigation, we introduce the new class R of bi-univalent functions defined by using the Tremblay fractional derivative operator. Additionally, we use the Faber polynomial expansions and Fibonacci numbers to derive bounds…

In this paper, a new axiomatization for unbounded functional calculi is proposed and the associated theory is elaborated comprising, among others, uniqueness and compatibility results and extension theorems of algebraic and topological…

We present a new formula for umbral operators that yields three main insights. First, it makes explicit a connection between umbral calculus and iteration theory. Second, it leads naturally to a definition of fractional exponents of umbral…

This is an expository survey on the theory of Bernstein-Sato polynomials with special emphasis in its recent developments and its importance in commutative algebra.

We give direct and inverse theorems for the weighted approximation of functions with endpoint singularities by combinations of Bernstein operators.

We prove some results on the border of Ramsey theory (finite partition calculus) and model theory. Also a beginning of classification theory of finite models in undertaken.

Let us denote ${\cal V}$, the finite dimensional vector spaces of functions of the form $\psi(x) = p_n(x) + f(x) p_m(x)$ where $p_n(x)$ and $p_m(x)$ are arbitrary polynomials of degree at most $n$ and $m$ in the variable $x$ while $f(x)$…

We define the notion of circular words, then consider on such words a constraint derived from the Fibonacci condition. We give several results on the structure of these circular words, then mention possible applications to various…

We retrace the recent history of the Umbral Calculus. After studying the classic results concerning polynomial sequences of binomial type, we generalize to a certain type of logarithmic series. Finally, we demonstrate numerous typical…

Fibonomial coefficients count the number of specific finite birth self-similar subposets of an infinite non-tree poset naturally related to the Fibonacci tree of rabbits growth process.

It is a common knowledge that the integer functions definable in simply typed lambda-calculus are exactly the extended polynomials. This is indeed the case when one interprets integers over the type (p->p)->p->p where p is a base type…

In these notes we will survey recent results on various finitary approximation properties of infinite groups. We will discuss various restrictions on groups that are approximated for example by finite solvable groups or finite-dimensional…

Probabilistic operational semantics for a nondeterministic extension of pure lambda calculus is studied. In this semantics, a term evaluates to a (finite or infinite) distribution of values. Small-step and big-step semantics are both…

We survey the theory and applications of Goodwillie's calculus of homotopy functors and related topics.

This is an exposition of some basic ideas in the realm of Global Inverse Function theorems. We address ourselves mainly to readers who are interested in the applications to Differential Equations. But we do not deal with those applications…

This is the English translation of my old paper 'Definici\'on y estudio de una funci\'on indefinidamente diferenciable de soporte compacto', Rev. Real Acad. Ciencias 76 (1982) 21-38. In it a function (essentially Fabius function) is defined…

An algorithm for computing power conjugate presentations for finite soluble quotients of predetermined structure of finitely presented groups is described. Practical aspects of an implementation are discussed.

We simplify the proof of some widely used theoretical theorems, extending their applicability, while correcting some erroneous results. We also generalize key results and present new results that contribute to the development of the theory.…

An important class of fractional differential and integral operators is given by the theory of fractional calculus with respect to functions, sometimes called $\Psi$-fractional calculus. The operational calculus approach has proved useful…