...-definable functionals and ... Conversion.
Defining complete and observable chaos
For a continuous map f from a real compact interval I into itself, we consider the set C(f) of points (x,y) ∈ I² for which and . We prove that if C(f) has full Lebesgue measure then it is residual, but the converse may not hold. Also, if λ² denotes the Lebesgue measure on the square and Ch(f) is the set of points (x,y) ∈ C(f) for which neither x nor y are asymptotically periodic, we show that λ²(C(f)) > 0 need not imply λ²(Ch(f)) > 0. We use these results to propose some plausible definitions...
Definitionen der Bernoulli-Polynome mit Hilfe ihrer Multiplikationstheoreme.
Delay dynamic equations with stability.
Delay-dependent exponential stability for discrete-time BAM neural networks with time-varying delays.
Der Hauptsatz über Iteration im Ring der formalen Potenzreihen.
Determinant criteria of solvability
In the paper [3] the determinant criterion of solvability for the Kuczma equation [4] was given. This criterion appeared in the natural way as barycenter of some mass system. It turned out that determinants do appear in many different situations as solvability criteria. The present article is aimed to review the mostly classical results in the theory of functional equations from this point of view. We begin with classical results of the linear functional equations and the determinant equations solved...
Développements asymptotiques -Gevrey et séries -sommables
Nous donnons une version -analogue de l’asymptotique Gevrey et de la sommabilité de Borel, dues respectivement à G. Watson et E. Borel et systématiquement développées depuis une quinzaine d’années par J.-P. Ramis, Y. Sibuya, etc. Le but de ces auteurs était l’étude des équations différentielles dans le champ complexe. De même notre but est l’étude des équations aux -différences dans le champ complexe, dans la ligne de G.D. Birkhoff et W.J. Trjitzinsky.Plus précisément, nous introduisons une nouvelle...
Diamond- Jensen's inequality on time scales.
Die allgemeine Lösung einer zylindrischen Differentialgleichung vierter Ordnung nullten Parameterwertes
Die Heavisidefunktion als spezielle Lösung ihrer Funktionalgleichung.
Die linearadditiven Zweiindizesfunktionen.
Difference equations for functions analytic beyond several squares.
Difference equations of Volterra type and extension of Lyapunov's method.
Difference equations on discrete polynomial hypergroups.
Difference functions of periodic measurable functions
We investigate some problems of the following type: For which sets H is it true that if f is in a given class ℱ of periodic functions and the difference functions are in a given smaller class G for every h ∈ H then f itself must be in G? Denoting the class of counter-example sets by ℌ(ℱ,G), that is, , we try to characterize ℌ(ℱ,G) for some interesting classes of functions ℱ ⊃ G. We study classes of measurable functions on the circle group that are invariant for changes on null-sets (e.g. measurable...
Difference independence of the Riemann zeta function
Difference of Function on Vector Space over F
In [11], the definitions of forward difference, backward difference, and central difference as difference operations for functions on R were formalized. However, the definitions of forward difference, backward difference, and central difference for functions on vector spaces over F have not been formalized. In cryptology, these definitions are very important in evaluating the security of cryptographic systems [3], [10]. Differential cryptanalysis [4] that undertakes a general purpose attack against...
Difference operators from interpolating moving least squares and their deviation from optimality
We consider the classical Interpolating Moving Least Squares (IMLS) interpolant as defined by Lancaster and Šalkauskas [Math. Comp. 37 (1981) 141–158] and compute the first and second derivative of this interpolant at the nodes of a given grid with the help of a basic lemma on Shepard interpolants. We compare the difference formulae with those defining optimal finite difference methods and discuss their deviation from optimality.
Difference operators from interpolating moving least squares and their deviation from optimality
We consider the classical Interpolating Moving Least Squares (IMLS) interpolant as defined by Lancaster and Šalkauskas [Math. Comp.37 (1981) 141–158] and compute the first and second derivative of this interpolant at the nodes of a given grid with the help of a basic lemma on Shepard interpolants. We compare the difference formulae with those defining optimal finite difference methods and discuss their deviation from optimality.