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A solution is proposed for the problem of composition of ordinary generating functions. A new class of functions that provides a composition of ordinary generating functions is introduced; main theorems are presented; compositae are written…
The paper represents the method for construction of the families of particular solutions to some new classes of $(n+1)$ dimensional nonlinear Partial Differential Equations (PDE). Method is based on the specific link between algebraic…
In this work we deal with a symbolic approach to the general quadratic polynomial decomposition. By means of a symbolic implementation, we investigate some properties of the components sequences like orthogonality and symmetry. We present…
In this note, given a regular Courant algebroid, we compute its group of automorphisms relative to a dissection. We also propose an infinitesimal version and recover examples of the literature.
In this paper we present algorithms that compute certain local cohomology modules associated to a ring of polynomials containing the rational numbers. In particular we are able to compute the local cohomological dimension of algebraic…
The analysis of observable phenomena (for instance, in biology or physics) allows the detection of dynamical behaviors and, conversely, starting from a desired behavior allows the design of objects exhibiting that behavior in engineering.…
The paper addresses the calculation of correlation functions of permanental polynomials of matrices with random entries. By exploiting a convenient contour integral representation of the matrix permanent some explicit results are provided…
In this paper we study Appell polynomials by connecting them to random variables. This probabilistic approach yields, e.g., the mean value property which is fundamental in the sense that many other properties can be derived from it. We also…
Existing score-based methods for inverse problems often resort to approximate minimization of the KL divergence between the inversion distribution and the Bayesian posterior. Such an approximation leads to severe mode collapse and…
In this article, we give a geometric description for any invertible operator on a finite dimensional inner--product space. With the aid of such a description, we are able to decompose any given conformal transformation as a product of…
In this paper, we consider central complete and incomplete Bell polynomials which are generalizations of the recently introduced central Bell polynomials and central analogues for the complete and incomplete Bell polynomials. We investigate…
In this papier, by the classical umbral calculus method, we establish identities involving the Appell polynomials and extend some existing identities.
We describe a method for determining a complete set of integrals for a classical Hamiltonian that separates in orthogonal subgroup coordinates. As examples, we use it to determine complete sets of integrals, polynomial in the momenta, for…
In this paper, we propose a new method for localization of polynomial ideal, which we call "Local Primary Algorithm". For an ideal $I$ and a prime ideal $P$, our method computes a $P$-primary component of $I$ after checking if $P$ is…
An element of a group is \emph{reversible} if it is conjugate to its own inverse, and it is \emph{strongly reversible} if it is conjugate to its inverse by an involution. A group element is strongly reversible if and only if it can be…
The inversion of nabla Laplace transform, corresponding to a causal sequence, is considered. Two classical methods, i.e., residual calculation method and partial fraction method are developed to perform the inverse nabla Laplace transform.…
We give direct and inverse theorems for the weighted approximation of functions with inner singularities by combinations of Bernstein polynomials.
An effective method to obtain exact analytical solutions of equations describing the coherent dynamics of multilevel systems is presented. The method is based on the usage of orthogonal polynomials, integral transforms and their discrete…
In this article we give a totally new proof of the integral localization formula for equivariantly closed differential forms (Theorem 7.11 in [BGV]). We restate it here as Theorem 2. This localization formula is very well known, but the…
Through this paper we will modify some of the results of [1], [5], [15], [28], [29], [31], [32] and consequently give the modified results.