Modeling Optical Response of Thin Films: Choice of the Refractive Index Dispersion Law

Determination of the so-called optical constants (complex refractive index N, which is usually a function of the wavelength, and physical thickness D) of thin films from experimental data is a typical inverse non-linear problem. It is still a challenge to the scientific community because of the complexity of the problem and its basic and technological significance in optics. Usually, solutions are looked for models with 3-10 parameters. Best estimates of these parameters are obtained by minimization procedures. Herein, we discuss the choice of orthogonal polynomials for the dispersion law of the thin film refractive index. We show the advantage of their use, compared to the Selmeier, Lorentz or Cauchy models.

An Intelligent System for Investigations and Provision of Safety for Complex Constructions

Methodology of computer-aided investigation and provision of safety for complex constructions and a prototype of the intelligent applied system, which implements it, are considered. The methodology is determined by the model of the object under scrutiny, by the structure and functions of investigation of safety as well as by a set of research methods. The methods are based on the technologies of object-oriented databases, expert systems and on the mathematical modeling. The intelligent system’s prototype represents component software, which provides for support of decision making in the process of safety investigations and investigation of the cause of failure. Support of decision making is executed by analogy, by determined search for the precedents (cases) with respect to predicted (on the stage of design) and observed (on the stage of exploitation) parameters of the damage, destruction and malfunction of a complex hazardous construction.

A Cauchy Integral Related to a Robot-safety Device System

We introduce a robot-safety device system attended by two different repairmen. The twin system is characterized by the natural feature of cold standby and by an admissible “risky” state. In order to analyse the random behaviour of the entire system (robot, safety device, repair facility) we employ a stochastic process endowed with probability measures satisfying general Hokstad-type differential equations. The solution procedure is based on the theory of sectionally holomorphic functions, characterized by a Cauchy-type integral defined as a Cauchy principal value in double sense. An application of the Sokhotski-Plemelj formulae determines the long-run availability of the robot-safety device. Finally, we consider the particular but important case of deterministic repair.