Related papers: Generalized QCD$_2$ via the Bilocal Method
The coupled nonlocal NLS equation is studied by virtue of the $2\times2$ Dbar-problem. Two spectral transform matrices are introduced to define two associated Dbar-problems. The relations between the coupled nonlocal NLS potential and the…
This paper presents a novel variant of the Broyden quasi-Newton secant-type method aimed at solving constrained mixed generalized equations, which can include functions that are not necessarily differentiable. The proposed method integrates…
Let $k$ be a field of characteristic $\neq 2$. We survey a general method of the field intersection problem of generic polynomials via formal Tschirnhausen transformation. We announce some of our recent results of cubic, quartic and quintic…
We obtain the estimate of difference between binomial and generalized binomial distributions in $\chi^2$ metric and in several other related metrics
The aim of this paper is to present an efficient numerical procedure to approximate the generalized Abel's integral equations of the first and second kinds. For this reason, the Taylor polynomials and the collocation method are applied.…
We use decoupling theory to estimate the number of solutions for quadratic and cubic Parsell--Vinogradov systems in two dimensions.
We extend the Newton's method and show the extended Newton's method leads to the binomial expansion of Newton's method that the convergences become the quadratic and linearly. In case of the quadratic convergence, we give the convergence…
The Hirota bilinear difference equation is generalized to discrete space of arbitrary dimension. Solutions to the nonlinear difference equations can be obtained via B\"acklund transformation of the corresponding linear problems.
We use ideas from our previous work to obtain some theorems that will allow us to obtain the integer solution of a quadratic polynomial in two variables that represents a natural number
In this article we give, for the fist time the solution of the general difference equation of 2-degree. We also give as application the expansion of a continued fraction into series, which was first proved, found in the past by the author.
A combinatorial methods are used to investigate some properties of certain generalized Stirling numbers, including explicit formula and recurrence relations. Furthermore, an expression of these numbers with symmetric function is deduced.
Quantile regression is often used when a comprehensive relationship between a response variable and one or more explanatory variables is desired. The traditional frequentists' approach to quantile regression has been well developed around…
Using a common technique for approximating distributions [generalized functions], we are able to use standard Monte Carlo methods to compute QFT quantities in Minkowski spacetime, under phase transitions, or when dealing with coalescing…
In this short paper we present an algorithm for finding a solution to a generalized Sudoku.
We describe a simple algorithm for computing the canonical basis of any finite-dimensional $U_{q}(sp_{2n})$-module.
We introduce a $q$-deformation of the Pythagoras equation $a^2 + b^2 = c^2$, which is a polynomial version of it different from the standard one. We construct a polynomial analogue, or ``$q$-analogue'', of every primitive Pythagorean…
A general formula is presented for any order derivative of Chebyshev polynomials instead of the existing recursive relationship. Hence, the Chebyshev finite difference method is made applicable not only to second order problems but also to…
We prove a series of Stephan's conjectures concerning Pascal triangle modulo 2 and give a polynomial generalization.
We propose a natural family of higher-order partial differential equations generalizing the second-order Klein-Gordon equation. We characterize the associated model by means of a generalized action for a scalar field, containing…
The infinite-dimensional family of exact solutions of the Klein--Gordon equation is constructed by the hypercomplex method.