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Matrix methods in evaluation of integrals

Wituła Roman, Słota Damian, Matlak Jarosław, Różański Michał

Journal of Applied Mathematics and Computational Mechanics

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2020

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Vol. 19, nr 1

103--112

EN

The method of evaluating the integrals through use of the matrix inversion, presented here, was introduced by J.W. Rogers and then generalized by Matlak, Słota and Wituła. This method is still developed and one of its other possible applications is presented in this paper. This application concerns a new way of evaluating the integral ʃ sec2n+1 xdx on the basis of the discussed method. Additionally, many other applications of the obtained original recursive formula for this type of integral are given here. Some of them are used to generate the interesting identities for inverses of the central binomial coefficients and the trigonometric limits. The historical view is also presented as well as the connections between the received and previously known identities.

2

Metodologia macierzy satysfakcja-lojalność i oczekiwania-satysfakcja wykorzystywanych w badaniach zadowolenia klienta

Biesok G., Wyród-Wróbel J.

Zeszyty Naukowe. Organizacja i Zarządzanie / Politechnika Śląska

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2018

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z. 131

27--37

PL

Artykuł prezentuje metodologię konstruowania macierzy satysfakcja-lojalność i oczekiwania-satysfakcja, możliwości wnioskowania z ich pomocą, ich zastosowanie w badaniach satysfakcji klienta i wynikające z tego korzyści. Opracowanie przedstawia zasady tworzenia macierzy, ilustruje ich użycie, pokazuje zaproponowane przez autorów wskaźniki parametryzujące macierz oraz wnioski, jakie można wysnuć na podstawie analizy macierzy. W podsumowaniu wskazuje na zalety i wady związane z wykorzystaniem prezentowanych metod.

EN

The article presents the methodology of constructing the satisfaction-loyalty and expectation-satisfaction matrices and their application in customer satisfaction surveys. It presents the principles of matrix creation, illustrates their use, shows the indicators proposed by the authors, parameterizing the matrix. The paper shows what conclusions can be derived from the matrix analysis and summarizes the advantages and disadvantages of using the presented methods.

3

Analysis of risk and failure scenarios in water supply system

Boryczko K., Rak J., Tchórzewska-Cieślak B.

Journal of Polish Safety and Reliability Association

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2014

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Vol. 5, No. 2

11--18

EN

Water supply system is complicated technical system which belongs to underground urban infrastructure. Its accurate functioning determines everyday live stability of citizens. Risk analysis is a key phase of the process of water supply safety management. The aim of this paper is to present new propose of methods for risk of the first type (associated with quantity of supplied water) and the risk of the second type (associated with quality of supplied water) analyses in water supply system. The paper contains the description of matrix methods for risk analyses and methods describing cause-and-effect relationship of failure events (fault tree analysis).

4

Natural frequency analysis of piezoelectric rods and their assemblies by compliance method

Cupiał P.

Vibrations in Physical Systems

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2012

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Vol. 25

109--116

EN

The vibrations of one-dimensional structures that consist of several interconnected members are conveniently analysed by matrix methods that include: the compliance (receptance) method, the mobility approach, dynamic stiffness method or the transfer matrix method. The paper presents the generalization of the classical receptance method to the coupled electromechanical vibrations of piezoelectric rods. Several compliance matrices are derived for piezoelectric rods undergoing longitudinal vibrations. These matrices can then be used in the derivation of the characteristic equations of rods with different boundary conditions as well as piezoelectric rod assemblies. The approach is illustrated by deriving the characteristic equation for a single piezoelectric rod with one end fixed and a spring and capacitor attached to its other end, as well as a two-rod assembly.

5

Matrix method for estimating the risk of failure in the collective water supply system using fuzzy logic

Tchórzewska-Cieślak B.

Environment Protection Engineering

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2011

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Vol. 37, nr 3

111-118

EN

Collective water supply system (CWSS) belongs to the so called critical infrastructure with a priority importance for urban agglomerations. The draft of European standard Security of drinking water supply. Guidelines for risk and crisis management defines the concept of risk in CWSS and principles of management and protection in crisis situations. In the paper, a method for estimating the risk of failure in CWSS, based on the assumptions of classical matrix methods while information from the system operation is inaccurate, was proposed. The proposed method is based on fuzzy logic, which allows one to incorporate incomplete data and develop a risk evaluation system.