A complete characterization of exponential stability for discrete dynamics

For a discrete dynamics defined by a sequence of bounded and not necessarily invertible linear operators, we give a complete characterization of exponential stability in terms of invertibility of a certain operator acting on suitable Banach sequence spaces. We connect the invertibility of this operator to the existence of a particular type of admissible exponents. For the bounded orbits, exponential stability results from a spectral property. Some adequate examples are presented to emphasize some significant qualitative differences between uniform and nonuniform behavior.Comment: The final version will be published in Journal of Difference Equations and Application

Asymptotic study of the Rayleigh equation

This paper provides an asymptotic treatment of the Cauchy problem for the Rayleigh equation µÿ + ?3/3 + ay – ? = 0 modelling a harmonic oscillator. The method of boundary layer functions and our version of the Tikhonov theorem are used. The models of asymptotic approximations are derive

Generalized evolution semigroups and general dichotomies

We introduce a special class of real semiflows, which is used to define a general type of evolution semigroups, associated to not necessarily exponentially bounded evolution families. Giving spectral characterizations of the corresponding generators, our results directly apply to a wide class of dichotomies, such as those with time-varying rate of change

STUDIES REGARDING THE EVOLUTION OF CLIMATE INDICES IN THE MATURATION PROCESS OF GRAPES IN DRĂGĂŞANI VINEYARD

      The Drăgăşani vineyard has a favorable climate to ensure the ripening of the grapes as well as the strings necessary for next year's fruit. Being located in the Getic plateau, the vineyard has a temperate Mediterranean climate with oceanic influence. The study was carried out at the Research and Development Station for viticulture and vinification Drăgăşani on Olt Hill in 2019. The objective of the study was to monitor the influence of the climatic profile on the physico-chemical parameters in the grape ripening process. For the evaluation of the area, the active and useful balance, the real insolation, the sum of precipitations, the heliothermal index, hydrothermal coefficient, the bioclimatic index of the vine and the oenoclimatic aptitude index during the vegetation and development period were calculated