相关论文: An example of algebraization of analysis and Fibon…
Primary definitions, notation and general observations of finite fibonomial operator calculus (ffoc) are presented. Kwasniewski's combinatorial interpretation of fibonomial coefficients by the use of fibonacci cobweb poset is given. Some…
This is an indicatory presentation of main definitions and theorems of fibonomial calculus which is a special case of psi-extented rota's finite operator calculus.
The explicite formulas for Mobius function and some other important elements of the incidence algebra of an arbitrary cobweb poset are delivered. For that to do one uses Kwasniewski's construction of his cobweb posets . The digraph…
The explicite formulas for m\"{o}biusien function and some other important elements of the incidence algebra are delivered. For that to do one uses kwa\'sniewski's construction of his fibonacci cobweb poset in the plane grid coordinate…
A calculus of sequences started by professor morgan ward constitutes the general scheme for extensions of classical operator calculus of the distinguished gian carlo rota considered by many afterwards and after ward morgan. Because of the…
The characterization of fibonacci cobweb poset as d.a.g. and o.d.a.g. is given. The dim 2 poset such that its hasse diagram coincide with digraf of fibonacci cobweb poset is constructed.
We introduce a natural partial order in structurally natural finite subsets of the cobweb prefabs sets recently constructed by the present author. Whitney numbers of the second kind of the corresponding subposet which constitute Stirling…
Cobweb posets uniquely represented by directed acyclic graphs are such a generalization of the Fibonacci tree that allows joint combinatorial interpretation for all of them under admissibility condition. This interpretation was derived in…
At the first part of the paper we show how specific umbral extensions of the Stirling numbers of the second kind result in new type of Dobinski-like formulas. In the second part among others one recovers how and why Ward solution of…
A wardian calculus of sequences started almost seventy years ago constitutes the general scheme for extensions of the classical umbral operator calculus considered by many afterwards . At the same time this calculus is an example of the…
In order to be able to use methods of Universal Algebra for investigating posets, we assign to every pseudocomplemented poset, to every relatively pseudocomplemented poset and to every sectionally pseudocomplemented poset a certain algebra…
Kwasniewski's cobweb posets uniquely represented by directed acyclic graphs are such a generalization of the Fibonacci tree that allows joint combinatorial interpretation for all of them under admissibility condition. This interpretation…
This note is a response to one of problems posed by A.K. Kwasniewski in one of his recent papers. Namely for the sequence of finite cobweb subposets, the looked for explicit formulas for corresponding sequence of characteristic polynomials…
The algebra of polynomials in operators that represent generalized coordinate and momentum and depend on the Planck constant is defined. The Planck constant is treated as the parameter taking values between zero and some nonvanishing $h_0$.…
We establish an operator--theoretic correspondence between periodic Bernoulli kernels and Hermite polynomials, framed through the umbral calculus and a quantum analogy. Starting from the analytic master function $F^\ast$, the periodic…
Generalized orthomodular posets were introduced recently by D. Fazio, A. Ledda and the first author of the present paper in order to establish a useful tool for studying the logic of quantum mechanics. They investigated structural…
In addition to the three standard operations on posets which are dual of poset or ordinal and cardinal sums of partial ordered sets one adds the natural join of posets. This is especially natural natural join operation for graded posets…
Composition operators with analytic symbols on some reproducing kernel Hilbert spaces of entire functions on a complex Hilbert space are studied. The questions of their boundedness, seminormality and positivity are investigated. It is…
A class of extended umbral calculi in operator form is presented. Extensions of all basic theorems of classical Finite Operator Calculus are shown to hold. The impossibility of straightforward extending of quantum q-plane formulation of the…
The $\psi$-operator for $(\phi, \Gamma)$-modules plays an important role in the study of Iwasawa theory via Fontaine's big rings. In this note, we prove several sharp estimates for the $\psi$-operator in the cyclotomic case. These estimates…