Journal "Research Bulletin of National Technical University of Ukraine "Kyiv Polytechnic Institute" (Naukovi visti) publishes original research results and practical developments from areas of technical, physical, mathematical, chemical and biological sciences.

# Improving Adequacy of Type-2 Fuzzy Models by Using Type-2 Fuzzy Sets

An information approach to fuzzy modeling was considered. The present paper formulates the task of developing a formal approach, which would enable analyzing fuzzy systems in terms of their capability to describe uncertainties of input information using interval membership functions. The discussed approach would allow to introduce the information factor for evaluating the quality of fuzzy models functioning using interval membership functions, and to increase the adequacy of the application area representation by a developed fuzzy model.

# Estimation of Generalized Linear Models Using Bayesian Approach in Actuarial Modeling

The article deals with Bayesian methodology for estimating unknown parameters of mathematical models and the method of analysis statistic data in insurance based on generalized linear models. These models are extension of linear regression when distribution of random variable can differ from normal. For estimating the parameters of proposed models classical and Bayesian approach were used. The main advantage of Bayesian approach is its ability to generate not only accurate estimates but probability distributions too.

# Performance Characteristics of Aluminum Thermosyphon for PVT Solar Collector

This article discusses the design of aluminum profile thermosyphons intended for use in PVT solar collectors. PVT solar collectors can simultaneously convert solar energy into electricity and heat, thus increasing the efficiency of solar power installation. The analysis of experimental studies of performance aluminum profile thermosyphons was presented.

# A Hundredth Anniversary of the Peek’s Law for Estimating the Corona Inception Electric Field

This article is dedicated to the memory of well-known electrical engineer Frank William Peek, Junior, who estimated the corona inception electric field on the surface of electrodes with a small radius of curvature which allows for corona discharge inception and also known as the “Peek’s law”. Analyzing Peek’s first publications dated 1911–1915, we have seen that he has elaborated and summarized the laws, which describe the phenomenon of corona discharge in gas on the wires of power transmission line.

# Dynamic Model Heat-Mass Exchange for the Water Cooler of the Industrial Air Conditioner

Mathematical modelling of processes heat-mass exchange for a water cooler, which is used in systems of an artificial microclimate for cooling and air unwatering, is observed. Based on the equations of material and thermal balance two equivalent models allowing to spend modelling of transients in a cooler on the basic channels of regulating and perturbation are gained. Sampling of dynamic model is defined by methods of a control system synthesis of the industrial air conditioner.

# Comparative Analysis of Average Risk Using the Recommended Limit Concentration of Gases Dissolved in Oil for Detecting Defects in Transformers 110 kV

The comparative analysis of values of average risk, which are accompanied by use of boundary values of concentration of the gases dissolved in oil recommended by known techniques, is presented in this article. For the solution of the given problem, expression for calculation of average risk taking into account laws of distributions of concentration of gases for defectless states and defective states, in conditions, when diagnostics is made on a complex of diagnostic parameters is offered.

# The Image Restoration Algorithms by Conventional Deconvolution

The modified conventional deconvolution method using discrete orthogonal transformations is proposed. The algorithms for method realization in Hadamard transformation field and in RTF basis are considered. RTF transformation is different from Fourier transformation and is the “calque” of difference methods. The main problem of algorithm realization – forming image degradation inverse matrix by symbolic method of any order of matrix forming – is solved. These algorithms for conventional deconvolution method significantly allow simplifying the computations independently of matrix order.

# Peculiarities of Sorbtion of Phosphates by Hydrous Oxides of the Elements of III and IV Groups

Binary mixtures containing hydrous oxides of titanium, aluminum, lanthanum, and cerium with various ratio of ingredients have been synthesized by means of co-precipitation method from water solutions. The physical and chemical properties of the target materials have been characterized by X-ray diffraction, scanning electron microscopy, IR spectroscopy, porosity studies and pH titration. The sorption affinity of binary mixtures towards phosphate ions has been studied.

# Limiting Characteristics of Coherent Spectrum Analyzer

The influence of the component dimensions and parameters of a coherent optical spectrum analyzer on its performance was studied. One of the criteria for evaluating the performance of this instrument are the spatial resolution and the spatial bandwidth product. The purpose of this article is to study the dependence of the limiting characteristics on the changing of the component parameters of the coherent spectrum analyzer.

# Metrological Analysis of Integrating Sphere Photometers for LED Luminous Flux Measurement

A comparative metrological analysis using mathematical models of three integrating sphere photometer schemes, for LED luminous flux measurement, was held. Each model takes into account the main design parameters of the photometer, typical values of which are used in the calculations.