Linear Differential Equations on Some Classes of Weighted Function Spaces

Some weighted-type classes of holomorphic function spaces were introduced in the current study. Moreover, as an application of the new defined classes, the specific growth of certain entire-solutions of a linear-type differential equation by the use of concerned coefficients of certain analytic-type functions, that is the equation h(k)+Kk−1(υ)h(k−1)+…+K1(υ)h′+K0(υ)h=0, will be discussed in this current research, whereas the considered coefficients K0(υ),…,Kk−1(υ) are holomorphic in the disc ΓR={υ∈C:|υ|<R},0<R≤∞. In addition, some non-trivial specific examples are illustrated to clear the roles of the obtained results with some sharpness sense. Hence, the obtained results are strengthen to some previous interesting results from the literature.

BOUNDARY-VALUE PROBLEM FOR A TWO-DIMENSIONAL SECOND ORDER-TYPE EQUATION WITH DISCRETE ADDITIVE AND MULTIPLICATIVE DERIVATIVES

The present paper is concerned with the study of solutions to the boundary-value problem for a two-dimensional second order-type differential equation with a discrete additive derivative for one argument and a discrete multiplicative derivative for another argument. We will determine the general solution of the considered equation, containing some derived sequences. Further, these unknown sequences are determined using an assigned boundary condition.

Surface Diffusion by Means of Stochastic Wave Functions. The Ballistic Regime

Stochastic wave function formalism is briefly introduced and applied to study the dynamics of open quantum systems; in particular, the diffusion of Xe atoms adsorbed on a Pt(111) surface. By starting from a Lindblad functional and within the microscopic Caldeira–Leggett model for linear dissipation, a stochastic differential equation (Ito^-type differential equation) is straightforwardly obtained. The so-called intermediate scattering function within the ballistic regime is obtained, which is observable in Helium spin echo experiments. An ideal two-dimensional gas has been observed in this regime, leading to this function behaving as a Gaussian function. The influence of surface–adsorbate interaction is also analyzed by using the potential of two interactions describing flat and corrugated surfaces. Very low surface coverages are considered and, therefore, the adsorbate–adsorbate interaction is safely neglected. Good agreement is observed when our numerical results are compared with the corresponding experimental results and previous standard Langevin simulations.

Observing the epidemiological SIR model on COVID-19 pandemic data

This article shows that in the period January 22-June 04, 2020, the combined data set of cumulative recoveries and deaths from the current coronavirus COVID-19 pandemic falls on the Kermack and McKendrick approximated solution of the epidemiological {\sir} contagious disease model. Then, as an original contribution of this work, based on the knowledge of the infectious period of any epidemic, a methodology is presented that helps to find numerical solutions of the full {\sir} model that falls on the observed data of the epidemic in case it could be described by the {\sir} model. The methodology is first illustrated by finding a solution of the {\sir} model that falls on the epidemic data of the Bombay plague of 1905-06 analyzed by Kermack and McKendrick. After that, the methodology is applied on analyzing the previously considered coronavirus COVID-19 pandemic data set. Moreover, since the Kermack and McKendrick approximated solution of the {\sir} model comes from solving a Riccati type differential equation, commonly found when studying (in introductory physics courses) the vertical motion of objects on a resistive medium, enough details are given in the article so the epidemiological {\sir} model can be used as an additional example for enhancing and enriching the undergraduate curriculum Physics courses for Biology, Life Sciences, Medicine and/or Computational Modeling.