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1
Content available Complex Fibonacci (c, p) : numbers
Prasad Bandhu
Mathematica Applicanda
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2022
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Vol. 50, no. 2
235-247
EN
In this paper a new complex Fibonacci Q_{p,c} matrix for complex Fibonacci (c,p)-numbers, where p is a positive integer and c is a non-zero complex number, is introduced. Thereby, we discuss various properties of Q_{p,c} matrix, coding and decoding method followed from the Q_{p,c} matrix.
PL
W artykule przedstawiono nową macierz zespoloną Fibonacciego oznaczaną Qp,c dla liczb zespolonych Fibonacciego (c, p), gdzie p jest liczbą całkowitą dodatnią, a c jest niezerową liczbą zespoloną. Omówiono różne własności macierzy Qp,c, oraz sposób kodowania i dekodowania wynikający z macierzy Qp,c.
2
Content available A coding theoretical interpretation of Gaussian-Pell polynomials
Prasad Bandhu
Mathematica Applicanda
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2022
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Vol. 50, no. 1
129--138
EN
In this paper, we establish a new result followed from Gaussian Pell polynomials matrix, Qn(x)P(x) (cf. Serpil and Sinan (2018)) whose elements are Gaussian Pell polynomials and we develop new coding and decoding method follow from Gaussian Pell polynomials matrix, Qn(x)P(x). The correction ability of this method is 93:33%.
PL
W artykule z wykorzystaniem macierzy wielomianów Gaussa Pella, Qn(x)P(x) (v. Serpil and Sinan (2018)), opracowano nową metodę kodowania. Ta metoda wynika z własności tej macierzy. Uzyskany kod daje możliwość korekcji na poziomie 93:33% .
3
Content available A new geometric approach for sensitivity analysis in linear programming
Kaci Mustapha, Radjef Sonia
Mathematica Applicanda
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2021
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Vol. 49, no. 2
145--157
EN
The article presents a geometric method of sensitivity analysis in linear programming, which is a computationally practical way to study the behavior of an optimal solution to a linear programming problem. In this approach, we improve the implementation of the constraints, and then we formulate the problem of linear programming geometrically. In this way, we obtain a new, equivalent geometrical formulation of the problem for the sensitivity analysis using the concepts of affine geometry. It consists in entering the objective function coefficient vector in the polar coordinates and determining all angles for which the solution remains unchanged. The method is presented in detail and illustrated by a numerical example.
PL
W niniejszym artykule przedstawiamy nowe podejście geometryczne do analizy wrażliwości w programowaniu liniowym, które jest praktyczne obliczeniowo. Pozwala analizować zachowania optymalnego rozwi¡zania problemu programowania liniowego przy zmianach danych zadania. Najpierw ustalamy dopuszczalną dziedzinę (naprawiamy ograniczenia liniowe). Następnie geometrycznie formułujemy problem programowania liniowego. Nast¦pnie podajemy nowe równoważne sformułowanie geometryczne problemu analizy wrażliwości przy użyciu pojęć geometrii afinicznej. Piszemy wektor współczynników funkcji celu we współrzędnych biegunowych i wyznaczamy wszystkie kąty, dla których rozwiązanie pozostaje niezmienione. Proponowane podejście zostało szczegółowo przedstawione i zilustrowane przykładem liczbowym.
4
Content available A geometric approach to structural model matching by output feedback in linear impulsive systems
Zattoni E.
International Journal of Applied Mathematics and Computer Science
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2018
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Vol. 28, no. 1
25--38
EN
This paper provides a complete characterization of solvability of the problem of structural model matching by output feedback in linear impulsive systems with nonuniformly spaced state jumps. Namely, given a linear impulsive plant and a linear impulsive model, both subject to sequences of state jumps which are assumed to be simultaneous and measurable, the problem consists in finding a linear impulsive compensator that achieves exact matching between the respective forced responses of the linear impulsive plant and of the linear impulsive model, by means of a dynamic feedback of the plant output, for all the admissible input functions and for all the admissible sequences of jump times. The solution of the stated problem is achieved by reducing it to an equivalent problem of structural disturbance decoupling by dynamic feedforward. Indeed, this latter problem is formulated for the so-called extended linear impulsive system, which consists of a suitable connection between the given plant and a modified model. A necessary and sufficient condition for the solution of the structural disturbance decoupling problem is first shown. The proof of sufficiency is constructive, since it is based on the synthesis of the compensator that solves the problem. The proof of necessity is based on the definition and the geometric properties of the unobservable subspace of a linear impulsive system subject to unequally spaced state jumps. Finally, the equivalence between the two structural problems is formally established and proven.
5
Content available remote Redundancy relations for fault diagnosis in nonlinear uncertain systems
Shumsky A.
International Journal of Applied Mathematics and Computer Science
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2007
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Vol. 17, no 4
477-489
EN
The problem of fault detection and isolation in nonlinear uncertain systems is studied within the scope of the analytical redundancy concept. The problem solution involves checking the redundancy relations existing among measured system inputs and outputs. A novel method is proposed for constructing redundancy relations based on system models described by differential equations whose right-hand sides are polynomials. The method involves a nonlinear transformation of the initial system model into a strict feedback form. Algebraic and geometric tools are used for this transformation. The features of the method are made particular for uncertain systems with a linear structure.
6
Content available remote Nonlinear diagnostic filter design: Algebraic and geometric points of view
Shumsky A., Zhirabok A.
International Journal of Applied Mathematics and Computer Science
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2006
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Vol. 16, no 1
115-127
EN
The problem of diagnostic filter design is studied. Algebraic and geometric approaches to solving this problem are investigated. Some relations between these approaches are established. New definitions of fault detectability and isolability are formulated. On the basis of these definitions, a procedure for diagnostic filter design is given in both algebraic and geometric terms.
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