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Let X be a normed space, V be an open convex subset of X and let be a given function. A function is called -midconvex if By the result of Tabor and Tabor, we know that under respective conditions on , if f is -midconvex and locally bounded above at a point then there exists a continuous function such that In this paper we determine the smallest function satisfying the above inequality. The required conditions on are such that the functions , satisfy them. As the main tool we use de Rham theorem. [ABSTRACT FROM AUTHOR]

This paper focuses on the issue of description of the set of parametric perturbation which preserves the spectrum of a discrete linear time varying system. We prove that all perturbations with the Lyapunov exponent lower then a regularity coefficient are characterized with this feature. Moreover, in case of a diagonal system, the perturbations with Lyapunov exponent equal to the regularity coefficient also reveal this feature. [ABSTRACT FROM AUTHOR]

This paper is concerned with asymptotic behaviour of solutions of perturbed dynamic systems on time scales. A time scale version of the Hartman-Wintner theorem is established for a class of time scales. [ABSTRACT FROM AUTHOR]

In this paper, we consider geometric aspects of a rational, planar system of difference equations defined on the open first quadrant and whose behaviour is governed by four independent, non-negative parameters. This system, indexed as (23, 23) in the notation of Ladas (Open problems and conjectures, J. Differential Equ. Appl. 15(3) 2009, pp. 303–323), is one of the 200 systems from Ladas about which little is known. Using geometric techniques, we answer several questions concerning the behaviour of this system. [ABSTRACT FROM AUTHOR]

We present a nonlinear method to approximate solutions of a Burgers–Huxley equation with generalized advection factor and logistic reaction. The equation under investigation possesses travelling-wave solutions that are temporally and spatially monotone functions; the travelling-wave fronts considered are bounded and connect asymptotically the stationary solutions of the model. For the linear regime, the method is consistent of first order in time and second order in space. In the nonlinear scenario, we investigate conditions under which bounded initial profiles evolve into bounded new approximations. The main results report on parametric conditions that guarantee the boundedness, the positivity and the monotonicity preservation of the method. As a consequence, our recursive method is capable of preserving the temporal and the spatial monotonicity of the solutions. We provide simulations that show that, indeed, our technique preserves the positivity, the boundedness and the temporal and spatial monotonicity of solutions. [ABSTRACT FROM PUBLISHER]

We consider the quadratic family of complex maps given by, wherecis the centre of a hyperbolic component in the Mandelbrot set. Then, we introduce a singular perturbation on the corresponding bounded super-attracting cycle by adding one pole to each point in the cycle. Whenc = − 1, the Julia set ofq− 1is the well-known basilica and the perturbed map is given by, whereare integers, and λ is a complex parameter such that λ is very small. We focus on the topological characteristics of the Julia and Fatou sets offλthat arise when the parameter λ becomes non-zero. We give sufficient conditions on the order of the poles so that for small λ, the Julia sets consist of the union of homeomorphic copies of the unperturbed Julia set, countably many Cantor sets of concentric closed curves, and Cantor sets of point components that accumulate on them. [ABSTRACT FROM AUTHOR]

The analytic information theory of discrete distributions was initiated in 1998 by C. Knessl, P. Jacquet and S. Szpankowski who addressed the precise evaluation of the Renyi and Shannon entropies of the Poisson, Pascal (or negative binomial) and binomial distributions. They were able to derive various asymptotic approximations and, at times, lower and upper bounds for these quantities. Here, we extend these investigations in a twofold way. First, we consider a much larger class of distributions, the Rakhmanov distributions , where denote the sequences of discrete hypergeometric-type polynomials that are orthogonal with respect to the weight function ω(x) of Poisson, Pascal, binomial and hypergeometric types, i.e. the polynomials of Charlier, Meixner, Kravchuk and Hahn. Second, we obtain the explicit expressions for the relative Fisher information of these four families of Rakhmanov distributions with respect to their respective weight functions. [ABSTRACT FROM AUTHOR]

We analyze the Hermite polynomials Hn(x) and their zeros asymptotically, as n → ∞ We obtain asymptotic approximations from the differential-difference equation which they satisfy, using the ray method. We give numerical examples showing the accuracy of our formulas. [ABSTRACT FROM AUTHOR]