相关论文: Fuchsian differential equation for the perimeter g…
In this work we define a unified generating functions for 9 different kinds of set partitions including cyclically ordered set partitions. Such generating function depends on 4 parameters. We consider property of this function and provide…
When studying boundary value problems for some partial differential equations arising in applied mathematics, we often have to study the solution of a system of partial differential equations satisfied by hypergeometric functions and find…
Starting with a quaternion difference equation with boundary conditions, a parameterized sequence which is complete in finite dimensional quaternion Hilbert space is derived. By employing the parameterized sequence as the kernel of discrete…
We consider finite approximations of a fractal generated by an iterated function system of affine transformations on $\mathbb{R}^d$ as a discrete set of data points. Considering a signal supported on this finite approximation, we propose a…
We propose a resolution for the fermion doubling problem in discrete field theories based on the fuzzy sphere and its Cartesian products.
We construct generating trees with one, two, and three labels for some classes of permutations avoiding generalized patterns of length 3 and 4. These trees are built by adding at each level an entry to the right end of the permutation,…
Using a general $q$-series expansion, we derive some nontrivial $q$-formulas involving many infinite products. A multitude of Hecke--type series identities are derived. Some general formulas for sums of any number of squares are given. A…
Let $F_g(t)$ be the generating function of intersection numbers on the moduli spaces $\bar{\mathcal{M}}_{g,n}$ of complex curves of genus $g$. As by-product of a complete solution of all non-planar correlation functions of the renormalised…
We consider Problem 6.94 posed in the book Concrete Mathematics by Graham, Knuth, and Patashnik, and solve it by using bivariate exponential generating functions. The family of recurrence relations considered in the problem contains many…
The generating function method that we had developing has various applications in physics and not only interress undergraduate students but also physicists. We solve simply difficult problems or unsolved commonly used in quantum, nuclear…
Computational mathematics plays an increasingly important role in computational fluid dynamics (CFD). The aeronautics and aerospace re- search community is working on next generation of CFD capacity that is accurate, automatic, and fast. A…
In their study of cyclic pattern containment, Domagalski et al. conjecture differential equations for the generating functions of circular permutations avoiding consecutive patterns of length 3. In this note, we prove and significantly…
We show that for every second order Fuchsian linear differential equation $E$ with $n$ singularities of which $n-3$ are apparent there exists a hypergeometric equation $H$ and a linear differential operator with polynomial coefficients…
In this paper, we present a probabilistic extension of the Fubini polynomials and numbers associated with a random variable satisfying some appropriate moment conditions. We obtain the exponential generating function and an integral…
A generating function for the Wigner's $D$-matrix elements of $SU(3)$ is derived. From this an explicit expression for the individual matrix elements is obtained in a closed form.
The main aim of this paper is to provide a novel approach to deriving identities for the Bernstein polynomials using functional equations. We derive various functional equations and differential equations using generating functions.…
A recursive method is given for finding generating functions which enumerate rooted hypermaps by number of vertices, edges and faces for any given number of darts. It makes use of matrix-integral expressions arising from the study of…
We present a short, direct proof of the fact that the generating function of all permutations of a fixed length $n\geq 4$ is divisible by $(1+z)^m$, where $m=\lfloor (n-2)/2 \rfloor$.
The main aim of this paper is to provide a unified approach to deriving identities for the Bernstein polynomials using a novel generating function. We derive various functional equations and differential equations using this generating…
This work presents a generative adversarial architecture for generating three-dimensional shapes based on signed distance representations. While the deep generation of shapes has been mostly tackled by voxel and surface point cloud…