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1
Content available Fourth order computational spline method for two-parameter singularly perturbed boundary value problem
Kambampati Satyanarayana, Emineni Siva Prasad, Reddy M. Chenna Krishna, Kolloju Phaneendra
International Journal of Applied Mechanics and Engineering
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2023
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Vol. 28, no. 4
79--93
EN
The current research work considers a two-parameter singularly perturbed two-point boundary value problem. Here, we suggest a computational scheme derived by using an exponential spline for the numerical solution of the problem on a uniform mesh. The proposed numerical scheme is analyzed for convergence and an accuracy of O(h4) is achieved. Numerical experiments are considered to validate the efficiency of the spline method, and compared comparison with the existing method to prove the superiority of the proposed scheme.
2
Content available A new method for estimating fault location in radial medium voltage distribution network only using measurements at feeder beginning
Ngoc-Hung Truong
Archives of Electrical Engineering
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2023
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Vol. 72, nr 2
503--520
EN
This paper proposes a new fault location method in radial medium voltage distribution networks. The proposed method only uses the measurement data at the feeder beginning to approximate the characteristic equation showing the dependence between the positive-sequence voltage and phase angle at the monitoring point with the distance to the fault location for each fault type on each line segment. To determine these characteristic equation coefficients, the entire distribution network will be modeled and simulated by four types of faults at different locations along the lines to build the initial database. Based on this database, the mathematical functions in MATLAB software are applied to approximate these coefficients corresponding to each type of fault for each line segment in the network. Then, from the current and voltage measurement data at the feeder beginning, the algorithms of global search, comparison, and fault ranking are used to find out where the fault occurs on the distribution network. Two types of distribution network with and without branches are studied and simulated in this paper to verify and evaluate the effectiveness of the proposed method.
3
Content available Extremal values of differential equations with application to control systems
Górecki Henryk, Zaczyk Mieczysław
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2021
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Vol. 69, nr 1
art. no. e136041
EN
In the paper, maximal values xe(τ) of the solutions x(t) of the linear differential equations excited by the Dirac delta function are determined. The analytical solutions of the equations and also the maximal positive values of these solutions are obtained. The analytical formulae enable the design of the system with prescribed properties. The complementary case to the earlier paper is presented. In an earlier paper it was assumed that the roots si are different, and now we consider the case when s1=s2=...=sn.
4
Content available Characteristic equations of the standard and descriptor linear electrical circuits of integer and fractional orders
Kaczorek T.
Acta Mechanica et Automatica
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2018
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Vol. 12, no. 3
209--216
EN
The problem of calculation of the characteristic equations of the standard and descriptor linear electrical circuits of integer and fractional orders is addressed. It is shown that the characteristic equations of standard and descriptor linear electrical circuits are independent of the method used in their analysis: the state space method, the mesh method and the node method. The considerations are illustrated by examples of standard and fractional linear electrical circuits.
5
Content available Characteristic equations of the standard and descriptor linear electrical circuits
Kaczorek T.
Poznan University of Technology Academic Journals. Electrical Engineering
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2017
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No. 89
11--23
EN
The problem of calculation of the characteristic equations of the standard and descriptor linear electrical circuits is addressed. It is shown that the characteristic equation of the linear electrical circuit is independent of the method used for its analysis. The well-known three methods: the state space method, the mesh method and the node method are analyzed.
6
Content available Cayley-Hamilton theorem for Drazin inverse matrix and standard inverse matrices
Kaczorek T.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2016
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Vol. 64, nr 4
793--797
EN
The classical Cayley-Hamilton theorem is extended to Drazin inverse matrices and to standard inverse matrices. It is shown that knowing the characteristic polynomial of the singular matrix or nonsingular matrix, it is possible to write the analog Cayley-Hamilton equations for Drazin inverse matrix and for standard inverse matrices.
7
Content available Decomposition method and its application to the extremal problems
Górecki H., Zaczyk M.
Archives of Control Sciences
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2016
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Vol. 26, no. 1
49--67
EN
In the article solution of the problem of extremal value of x(τ) is presented, for the n-th order linear systems. The extremum of x(τ) is considered as a function of the roots s1, s2, ... sn of the characteristic equation. The obtained results give a possibility of decomposition of the whole n-th order system into a set of 2-nd order systems.
8
Content available Analytic solutions of transcendental equations with application to automatics
Górecki H., Zaczyk M.
Archives of Control Sciences
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2016
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Vol. 26, no. 4
497--513
EN
In the paper the extremal dynamic error x(τ) and the moment of time τ are considered. The extremal value of dynamic error gives information about accuracy of the system. The time τ gives information about velocity of transient. The analytical formulae enable design of the system with prescribed properties. These formulae are calculated due to the assumption that x(τ) is a function of the roots s1, ..., sn of the characteristic equation.
9
Circuit synthesis using admittance network modification and GA in MATLAB
Slezak J., Sotner R.
Elektronika : konstrukcje, technologie, zastosowania
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2009
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Vol. 50, nr 12
27-31
EN
The paper describes the method of circuit synthesis using the admittance network modification programmed in MATLAB. The principle of the described algorithm is based on the substitution of all the possible combinations of limit admittances values (zero, infinitive) to the characteristic equation of the input circuit structure. The method is in detail described, and an example of the synthesized circuit is presented.
PL
Artykuł opisuje metodę syntezy obwodów poprzez modyfikacje sieci admitancyjnych w środowisku Matlab. Zaproponowany algorytm jest oparty na analizie i podstawianiu wszystkich możliwych kombinacji wartości granicznych admitancji (zero, nieskończoność) w równaniu charakterystycznym struktury wyjściowej. Metoda ta została szczegółowo przedstawiona na praktycznym przykładzie syntezy obwodu.
10
Content available Generalized characteristic singular integral equation with Hilbert kernel
Karczmarek P.
Opuscula Mathematica
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2008
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Vol. 28, no. 3
287-294
EN
In this paper an explicit solution of a generalized singular integral equation with a Hilbert kernel depending on indices of characteristic operators is presented.
11
Content available remote Asymptotic Properties of the Factors of Words Over a Finite Alphabet
Tomescu I.
Fundamenta Informaticae
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2005
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Vol. 64, nr 1-4
463-470
EN
Let A be an alphabet of cardinality m, kn be a sequence of positive integers and w e A* (|w| = kkn). In this paper it is shown that if lim sup n→∞knn <1/lnm, then almost all words of length n over A contain the factor w, but if lim sup n→∞kn/lnn > 1/lnm, then this property is not true. Also, if lim inf...kn/lnn > 1/lnm , then almost all words of length n over A do not contain the factor w. Moreover, if lim...(ln n - knln m) = a e IR, then lim sup...|W(n,kn,w,A)|/m^n < 1-exp(-exp(a)) and liminf n→∞|W(n,kn,w,A)|/m^n >1-exp(-(1-1/m)exp(a)), where W(n,kn,w,A) denotes the set of words of length n over A containing the factor w of length kn.
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