Related papers: Generator functions and their applications
The algebra of symmetric functions contains several interesting families of symmetric functions indexed by integer partitions or skew partitions. Given a sequence $\{u_n\}$ of symmetric functions taken from one of these families such that…
We utilize undetermined coefficient method and an iterative method to construct the series solutions of the 3D Cauchy problem for a class of incompressible Navier-Stokes and Euler Equations. Then we can turn the Navier-Stokes Equations…
This paper examines the coefficient problems for the class of semigroup generators, a topic in complex dynamics that has recently been studied in context of geometric function theory. Further, sharp bounds of coefficient functional such as…
Numerical solvers of the incompressible Navier-Stokes equations have reproduced turbulence phenomena such as the law of the wall, the dependence of turbulence intensities on the Reynolds number, and experimentally observed properties of…
Euler-Leray data functions of first and second order are defined by first and second order derivatives of the nonlinear spatial part of the incompressible Euler equation operator in Leray projection form applied to Cauchy data. The…
This work introduces an explicit expression for the generation function for the reduction of an $n$-gon to an $(n-k)$-gon. A novel recursive relation of generation function is formulated based on Feynman Parametrization in projective space,…
We describe generating functions for several important families of classical symmetric functions and shifted Schur functions. The approach is originated from vertex operator realization of symmetric functions and offers a unified method to…
Many combinatorial generating functions can be expressed as combinations of symmetric functions, or extracted as sub-series and specializations from such combinations. Gessel has outlined a large class of symmetric functions for which the…
Certain classical generating functions for elements of reflection groups can be expressed using fundamental invariants called exponents. We give new analogues of such generating functions that accommodate orbits of reflecting hyperplanes…
In the context of phase-space quantization, matrix elements and observables result from integration of c-number functions over phase space, with Wigner functions serving as the quasi-probability measure. The complete sets of Wigner…
The interrelation between analytic functions and real-valued functions is formulated in the work. It is shown such an interrelation realizes nonlinear representations for real-valued functions that allows to develop new methods of…
We consider the Cauchy problem in the band $\mathbb{C}^{n}\times[0, T], n>1,T>0$, for a system of nonlinear differential equations structurally similar to the classical Navier-Stokes equations for an incompressible fluid. The main…
In this paper we generalize and specialize generating functions for classical orthogonal polynomials, namely Jacobi, Gegenbauer, Chebyshev and Legendre polynomials. We derive a generalization of the generating function for Gegenbauer…
We introduce a generating function associated to the homogeneous generators of a graded algebra that measures how far is this algebra from being finitely generated. For the case of some algebras of Frobenius endomorphisms we describe this…
We introduce a generating function approach to the affine Brauer and Kauffman categories and show how it allows one to efficiently recover important sets of relations in these categories. We use this formalism to deduce restrictions on…
We introduce two families of generators (functions) $\mathcal{G}$ that consist of entire and meromorphic functions enjoying a certain periodicity property and contain the classical Gaussian and hyperbolic secant generators. Sharp results…
For an arbitrary solution to the KdV hierarchy, the generating series of logarithmic derivatives of the tau-function of the solution can be expressed by the basic matrix resolvent via algebraic manipulations. Based on this we develop in…
We prove several claims made by Kontsevich about the orbifold Euler characteristic of the three types of graph homology introduced by him. For this purpose, first we develop a simplified version of the Feynman diagram method, which requires…
We find the exponential generating function for permutations with all valleys even and all peaks odd, and use it to determine the asymptotics for its coefficients, answering a question posed by Liviu Nicolaescu. The generating function can…
We establish the membership criteria in terms of Hadamard product for a normalized analytic function to be in the class of infinitesimal generators. Furthermore, the embedding of various subclasses of normalized univalent functions in the…