Related papers: Application of difference sequences theory
The differential transform method is used to find numerical approximation of solution to a class of certain nonlinear differential algebraic equations. The method is based on Taylor's theorem. Coefficients of the Taylor series are…
This article presents a reformulation of the Theory of Functional Connections: a general methodology for functional interpolation that can embed a set of user-specified linear constraints. The reformulation presented in this paper exploits…
The differential constraints are applied to obtain explicit solutions of nonlinear diffusion equations. Certain linear determining equations with parameters are used to find such differential constraints. They generalize the determining…
Let $A\subset \N_{+}$ and by $P_{A}(n)$ denotes the number of partitions of an integer $n$ into parts from the set $A$. The aim of this paper is to prove several result concerning the existence of integer solutions of Diophantine equations…
The metric Bezout Theorem proved in an earlier paper can be extended to a derivative version that compares derivatives of the algebraic distance of a point $\theta$ to two properly intersecting cycles in projective space with the…
The rules of d-separation provide a framework for deriving conditional independence facts from model structure. However, this theory only applies to simple directed graphical models. We introduce relational d-separation, a theory for…
Shnirelman's theorem is applied to solving Diophantine equations, and also discussing of the problems of a representation of Gaussian integers by a sum of odd Gaussian primes.
We develop machinery to explicitly determine, in many instances, when the difference $x^2-y^n$ is divisible only by powers of a given fixed prime. This combines a wide variety of techniques from Diophantine approximation (bounds for linear…
In this paper we present the theory of lacunary trigonometric sums and lacunary sums of dilated functions, from the origins of the subject up to recent developments. We describe the connections with mathematical topics such as…
Finding integer solutions to norm form equations is a classical Diophantine problem. Using the units of the associated coefficient ring, we can produce sequences of solutions to these equations. It is known that these solutions can be…
The techniques of dispersion relations match very well with those of effective field theory. I describe the techniques for using dispersion relations effectively, and give some pedagogical examples to illustrate the range of applications.
In 1996 N. Chevallier proved a beautiful lemma which connects Diophantine approximation and multidimensional generalizations of the famous Three Distance Theorem. Using this lemma we show how known results about multidimensional three…
A class of Laplace transforms is examined to show that particular cases of this class are associated with production-destruction and reaction-diffusion problems in physics, study of differences of independently distributed random variables…
We study approximation of non-autonomous linear differential equations with variable delay over infinite intervals. We use piecewise constant argument to obtain a corresponding discrete difference equation. The study of numerical…
We state some elementary problems concerning the relation between difference calculus and differential calculus, and we try to convince the reader that, in spite of the simplicity of the statements, a solution of these problems would be a…
We study correlations of multiplicative functions taken along deterministic sequences and sequences that satisfy certain linear independence assumptions. The results obtained extend recent results of Tao and Ter\"av\"ainen and results of…
We introduce the notion of Differential Sequences of ordinary differential equations. This is motivated by related studies based on evolution partial differential equations. We discuss the Riccati Sequence in terms of symmetry analysis,…
We study a general class of recurrence relations that appear in the application of a matrix diagonalization procedure. We find general closed formula and determine analytical properties of the solutions. We finally apply these findings in…
The work relates to a new way for analysis of one-dimensional stochastic systems, based on consideration of its higher order difference structure. From this point of view, the deterministic and random processes are analyzed. A new numerical…
A new definition of a fractional derivative has recently been developed, making use of a fractional Dirac delta function as its integral kernel. This derivative allows for the definition of a distributional fractional derivative, and as…