Related papers: Combinatorial Approach to Boson Anti-Normal Orderi…
In this paper, we explore the merits of various algorithms for polynomial optimization problems, focusing on alternatives to sum of squares programming. While we refer to advantages and disadvantages of Quantifier Elimination, Reformulation…
Generalizations of Bell polynomials, Bell numbers, and Stirling numbers of the second kind have been introduced and their generating functions were evaluated.
Using a supersymmetry formalism, we reduce exactly the problem of electron motion in an external potential to a new supermatrix model valid at all distances. All approximate nonlinear sigma models obtained previously for disordered systems…
This paper introduces an alternative form of the derivation of Spivey's Bell number formula which involves the $q$-Boson operators $a$ and $a^{\dagger}$. Furthermore, a similar formula for the case of the $(q,r)$-Dowling polynomials is…
The q-fermion numbers emerging from the q-fermion oscillator algebra are used to reproduce the q-fermionic Stirling and Bell numbers. New recurrence relations for the expansion coefficients in the 'anti-normal ordering' of the q-fermion…
An analytical solution to the Hill problem Hamiltonian expanded about the libration points has been obtained by means of perturbation techniques. In order to compute the higher orders of the perturbation solution that are needed to capture…
We study set partitions with $r$ distinguished elements and block sizes found in an arbitrary index set $S$. The enumeration of these $(S,r)$-partitions leads to the introduction of $(S,r)$-Stirling numbers, an extremely wide-ranging…
Set partitions and permutations with restrictions on the size of the blocks and cycles are important combinatorial sequences. Counting these objects lead to the sequences generalizing the classical Stirling and Bell numbers. The main focus…
We present a new approach to solving polynomial ordinary differential equations by transforming them to linear functional equations and then solving the linear functional equations. We will focus most of our attention upon the first-order…
The normal ordering formulae for powers of the boson number operator $\hat{n}$ are extended to deformed bosons. It is found that for the `M-type' deformed bosons, which satisfy $a a^{\dagger} - q a^{\dagger} a = 1$, the extension involves a…
We obtain some recurrence relationships among the partition vectors of the partial exponential Bell polynomials. On using such results, the $n$-th Adomian polynomial for any nonlinear operator can be expressed explicitly in terms of the…
In some previous works, two of the authors have introduced a strategy to develop high-order numerical methods for systems of balance laws that preserve all the stationary solutions of the system. The key ingredient of these methods is a…
The powers of matrices with Stirling number-coefficients are investigated. It is revealed that the elements of these matrices have a number of properties of the ordinary Stirling numbers. Moreover, "higher order" Bell, Fubini and Eulerian…
We introduce new refinements of the Bell, factorial, and unsigned Stirling numbers of the first and second kind that unite the derangement, involution, associated factorial, associated Bell, incomplete Stirling, restricted factorial,…
We systematically introduce the idea of applying differential operator method to find a particular solution of an ordinary nonhomogeneous linear differential equation with constant coefficients when the nonhomogeneous term is a polynomial…
This paper extends the model reduction method by the operator projection to the one-dimensional special relativistic Boltzmann equation. The derivation of arbitrary order globally hyperbolic moment system is built on our careful study of…
In this paper, we introduce a class of new generalized super Bell polynomials on a superspace, explore their properties, and show that they are a natural and effective tool to systematically investigate integrability of supersymmetric…
We present a new technique for putting general boson fields into ant-Wick ordered form. The anti-Wick map associates an operator with a given function of complex variables, and we show that it may be realized as composition of a mapping to…
It is remarkable that, in recent years, intensive studies have been done for degenerate versions of many special polynomials and numbers and have yielded many interesting results. The aim of this paper is to study the generalized degenerate…
We propose and study a novel stochastic inertial primal-dual approach to solve composite optimization problems. These latter problems arise naturally when learning with penalized regularization schemes. Our analysis provide convergence…