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1
Content available Decomposition method and its application to the extremal problems
100%
Górecki H. , Zaczyk M.
Archives of Control Sciences
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2016
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tom 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.
2
Necessary and sufficient conditions for oscillations of delay partial difference equations
100%
Zhang B. , Liu S.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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1995
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tom 15
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nr 2
213-219
EN
This paper is concerned with the delay partial difference equation (1) $A_{m+1,n}+A_{m,n+1}-A_{m,n} + Σ_{i=1}^u p_i A_{m-k_i, n-l_i} = 0$ where $p_i$ are real numbers, $k_i$ and $l_i$ are nonnegative integers, u is a positive integer. Sufficient and necessary conditions for all solutions of (1) to be oscillatory are obtained.
3
Content available Generalized characteristic singular integral equation with Hilbert kernel
100%
Karczmarek P.
Opuscula Mathematica
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2008
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tom 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.
4
Content available Analytic solutions of transcendental equations with application to automatics
100%
Górecki H. , Zaczyk M.
Archives of Control Sciences
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2016
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tom 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.
5
Content available A new method for estimating fault location in radial medium voltage distribution network only using measurements at feeder beginning
88%
Ngoc-Hung T.
Archives of Electrical Engineering
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2023
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tom 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.
6
Content available remote Universal characteristic equations and qualitative conclusions about frequency spectra
75%
Zoriy L.
Vibrations in Physical Systems
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2000
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tom Vol. 19
315--316
7
Content available remote Asymptotic Properties of the Factors of Words Over a Finite Alphabet
75%
Tomescu I.
Fundamenta Informaticae
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2005
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tom 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.
8
Content available Characteristic equations of the standard and descriptor linear electrical circuits
75%
Kaczorek T.
Poznan University of Technology Academic Journals. Electrical Engineering
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2017
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tom 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.
9
Content available Characteristic equations of the standard and descriptor linear electrical circuits of integer and fractional orders
75%
Kaczorek T.
Acta Mechanica et Automatica
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2018
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tom 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.
10
Content available Fourth order computational spline method for two-parameter singularly perturbed boundary value problem
63%
Kambampati S. , Emineni S. P. , Reddy M. C. K. , Kolloju P.
International Journal of Applied Mechanics and Engineering
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2023
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tom 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.
11
Circuit synthesis using admittance network modification and GA in MATLAB
63%
Slezak J. , Sotner R.
Elektronika : konstrukcje, technologie, zastosowania
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2009
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tom 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.
12
Content available Cayley-Hamilton theorem for Drazin inverse matrix and standard inverse matrices
63%
Kaczorek T.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2016
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tom 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.
13
Content available remote An asymptotic expansion for the distribution of the supremum of a random walk
63%
Sgibnev M. S.
Studia Mathematica
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2000
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tom 140
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nr 1
41-55
EN
Let ${S_n}$ be a random walk drifting to -∞. We obtain an asymptotic expansion for the distribution of the supremum of ${S_n}$ which takes into account the influence of the roots of the equation $1-∫_ℝe^{sx}F(dx)=0,F$ being the underlying distribution. An estimate, of considerable generality, is given for the remainder term by means of submultiplicative weight functions. A similar problem for the stationary distribution of an oscillating random walk is also considered. The proofs rely on two general theorems for Laplace transforms.
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