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Cayley's problem

Peter Petek (1990)

Aplikace matematiky

Newton's method for computation of a square root yields a difference equation which can be solved using the hyperbolic cotangent function. For the computation of the third root Newton's sequence presents a harder problem, which already Cayley was trying to solve. In the present paper two mutually inverse functions are defined in order to solve the difference equation, instead of the hyperbolic cotangent and its inverse. Several coefficients in the expansion around the fixed points are obtained,...

Characterizacion of the bivariate discrete distributions defined by a partial difference equations system.

Ramón Gutiérrez Jáimez, Miguel Angel Fajardo Caldera (1988)

Trabajos de Estadística

Conditions under which the solutions of a partial difference equations system can be probability functions are examined.When the coefficients of the system are polynomials then the partial difference equations system satisfied by generating functions associated to these distributions are easily obtained; they give useful recurrence relations for the moments. Three examples are given as well.

Characterization of functions whose forward differences are exponential polynomials

J. M. Almira (2017)

Commentationes Mathematicae Universitatis Carolinae

Given { h 1 , ⋯ , h t } a finite subset of ℝ d , we study the continuous complex valued functions and the Schwartz complex valued distributions f defined on ℝ d with the property that the forward differences Δ h k m k f are (in distributional sense) continuous exponential polynomials for some natural numbers m 1 , ⋯ , m t .

Cheeger inequalities for unbounded graph Laplacians

Frank Bauer, Matthias Keller, Radosław K. Wojciechowski (2015)

Journal of the European Mathematical Society

We use the concept of intrinsic metrics to give a new definition for an isoperimetric constant of a graph. We use this novel isoperimetric constant to prove a Cheeger-type estimate for the bottom of the spectrum which is nontrivial even if the vertex degrees are unbounded.

Classification of nonoscillatory solutions of higher order neutral type difference equations

Ethiraju Thandapani, P. Sundaram, John R. Graef, A. Miciano, Paul W. Spikes (1995)

Archivum Mathematicum

The authors consider the difference equation Δ m [ y n - p n y n - k ] + δ q n y σ ( n + m - 1 ) = 0 ( * ) where m ≥ 2 , δ = ± 1 , k ∈ N 0 = { 0 , 1 , 2 , ⋯ } , Δ y n = y n + 1 - y n , q n > 0 , and { σ ( n ) } is a sequence of integers with σ ( n ) ≤ n and lim n → ∞ σ ( n ) = ∞ . They obtain results on the classification of the set of nonoscillatory solutions of ( * ) and use a fixed point method to show the existence of solutions having certain types of asymptotic behavior. Examples illustrating the results are included.

Classification rationnelle et confluence des systèmes aux différences singuliers réguliers

Julien Roques (2006)

Annales de l’institut Fourier

En choisissant des “caractères” et des “logarithmes”, méromorphes sur ℂ , construits à l’aide de la fonction Gamma d’Euler, et en utilisant des séries de factorielles convergentes, nous sommes en mesure, dans une première partie, de donner une “forme normale” pour les solutions d’un système aux différences singulier régulier. Nous pouvons alors définir une matrice de connexion d’un tel système. Nous étudions ensuite, suivant une idée de G.D. Birkhoff, le lien de celles-ci avec le problème de la classification...

Currently displaying 181 – 200 of 1085