Temat: variable coefficients - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Time-optimal control of linear fractional systems with variable coefficients
Autorzy:: Matychyn, Ivan
Onyshchenko, Viktoriia
Powiązania:: https://bibliotekanauki.pl/articles/2055161.pdf
Data publikacji:: 2021
Wydawca:: Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:: fractional calculus
Riemann-Liouville derivative
variable coefficients
optimal control
rachunek ułamkowy
pochodna ułamkowa Riemanna-Liouville'a
współczynnik zmienny
sterowanie optymalne
Opis:: Linear systems described by fractional differential equations (FDEs) with variable coefficients involving Riemann–Liouville and Caputo derivatives are examined in the paper. For these systems, a solution of the initial-value problem is derived in terms of the generalized Peano–Baker series and a time-optimal control problem is formulated. The optimal control problem is treated from the convex-analytical viewpoint. Necessary and sufficient conditions for time-optimal control similar to that of Pontryagin’s maximum principle are obtained. Theoretical results are supported by examples.
Źródło:: International Journal of Applied Mathematics and Computer Science; 2021, 31, 3; 375--386
1641-876X
2083-8492
Pojawia się w:: International Journal of Applied Mathematics and Computer Science
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 2.

Tytuł:: Wear cumulating process for friction pair implemented by first order recurrences
Autorzy:: Wierzcholski, K.
Powiązania:: https://bibliotekanauki.pl/articles/245033.pdf
Data publikacji:: 2014
Wydawca:: Instytut Techniczny Wojsk Lotniczych
Tematy:: cumulative wear values
operation after finite and infinite time units
first order recurrence implementation
variable coefficients after experiments
Opis:: Wear determination engages a major part of our efforts in considered numerous tribology problems including animal teeth and joints, human joints, cams, piston, rings, tires, brakes, dirt seals, belts, shoes, fabrics, electrical contacts, tape and CD reader heads and others. At times it seems after numerous observation, that the rate of progress in the knowledge of wear is very slow. Modern design activities are mostly concern in the wear cumulative values determination rather than the wear values determination in successive time units of friction nods during the operation time. Therefore, presented paper determines in analytical way the cumulative wear values of friction nods after specified finite and infinite units of operation time. Therefore are considered the convergences and divergences of wear value cumulative processes for various friction nods. The kind of friction nods depends on type of wear process propagation. Such propagation is described in this paper by the recurrence first order equation. Mentioned equation is formulated with constant or variable parameters. This parameters are determined by virtue of experimental measurements and depend on: bearing materials properties, environmental conditions, roughness of cooperating surfaces, vibration effects, electrical conductivity of materials, hardness of materials, deformations mode of cooperating surfaces, temperature, air humidity, kind of the friction, sliding velocity, loading of the friction nod and others. The range of wearing influence components and devices is endless. Therefore, this paper presents the methods of solutions of numerous specific class of ordinary non-homogeneous recurrence equations of first order with variable coefficients occurring in hydrodynamic theory of bearing especially micro-bearing wear problems. The obtained solutions are examined by means of the UOS operator. The examples presented in this paper determine the abrasive wear cumulative values of micro-bearing system after the indicated time units of operating time. Moreover, after infinite time units of micro-bearing operation are considered the convergences and divergences of the obtained sums of cumulative wear process.
Źródło:: Journal of KONES; 2014, 21, 1; 287-294
1231-4005
2354-0133
Pojawia się w:: Journal of KONES
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 3.

Tytuł:: Wear process in successive time units described by first order recurrences
Autorzy:: Wierzcholski, K.
Powiązania:: https://bibliotekanauki.pl/articles/244485.pdf
Data publikacji:: 2014
Wydawca:: Instytut Techniczny Wojsk Lotniczych
Tematy:: wear determination during slide bearings operating process
first order recurrence equation
class of variable coefficients
Opis:: The numerous tribology problems occurring in power-train and transport industry lead to wear bearing determination solutions. Especially the project designer demand the more and more information referring the slide bearing wear anticipation in succeeding years of machine operations. In this paper a perspective will be provided on what is known about various types of influences which are caused wear effects. Some machinery eventually fails or becomes uneconomical to operate because of single causes for example types of wear, but most mechanical devices succumb to combinations of causes. A direct parallel is seems in the human machine. Therefore this paper presents the methods of solutions of some specific class of ordinary non-homogeneous recurrence equations of first order with variable coefficients occurring in hydrodynamic theory of bearing wear problems. The various coefficients occurring in considered recurrent equations are determined from experimental measurements where the influence of various operating parameters on the wear effects is taking into account. The influence of numerous operating parameters on the wear effects is experimentally determined in the case if mentioned parameters are independent as well if are mutually connected. Moreover in this paper the theorems will be presented of the existence, determination and an algorithm construction of discrete solutions of non-homogeneous, linear, first order recurrent equations with variable coefficients. The Lemmas and Theorem are formulated and proved by means of the Unified Operator of Summation (UOS operator) with a unitary translation operator, where the operator properties and features are taking into account. In the case of the space of solution functions, the above mentioned wear problems determination are attributed to practical applications related to the non-homogeneous, linear, first order differential equations. The examples presented in this paper for various variable coefficients i.e. for various operating conditions determine the wear values of micro- bearing system during the indicated time units of operating time.
Źródło:: Journal of KONES; 2014, 21, 3; 285-292
1231-4005
2354-0133
Pojawia się w:: Journal of KONES
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 4.

Tytuł:: Solutions of recurrences with variable coefficients for slide bearing wear determination
Autorzy:: Wierzcholski, K.
Powiązania:: https://bibliotekanauki.pl/articles/247289.pdf
Data publikacji:: 2013
Wydawca:: Instytut Techniczny Wojsk Lotniczych
Tematy:: wear anticipation after exploitation
slide bearings
recurrence equation
variable coefficients
Opis:: The numerous methods of numerical calculations occurring in power-train tribology and transport concerning wear bearing determination problems demand the more and more information referring the slide bearing wear anticipation in succeeding years of machine operations. Therefore this paper presents the methods of solutions of some specific class of ordinary non-homogeneous recurrence equations of second and higher order with variable coefficients occurring in hydrodynamic theory of bearing wear problems. Contrary to linear recurrence equations with constant coefficients, linear recurrence equations with variable coefficients rarely have analytical solutions.. Numerical solutions of such equations are always practicable. In numerous analytical methods of solutions of linear recurrence equations with variable coefficients there are usually three research directions. The first of them depend upon the successive determination of the linear independent particular solutions of the considered recurrence equation. The second direction to be characterized by the reduction of the order of recurrence equation to obtain an always solved, first order recurrence equation. The third direction of solutions of recurrence equations with variable coefficients, contains the methods of analytical solutions by means of a summation factor. The majority of the general methods of analytical solutions of linear recurrence equations with variable coefficients constitute an adaptation of the methods applied in solutions of suitable differential equations In final conclusions the application of presented theory in this paper contains the the examples referring the wear values determination of HDD bearing system in the indicated period of operating time.
Źródło:: Journal of KONES; 2013, 20, 3; 427-433
1231-4005
2354-0133
Pojawia się w:: Journal of KONES
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 5.

Tytuł:: Linearization of the product of orthogonal polynomials of a discrete variable
Autorzy:: Belmehdi, Saïd
Lewanowicz, Stanisław
Ronveaux, André
Powiązania:: https://bibliotekanauki.pl/articles/1339159.pdf
Data publikacji:: 1997
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: linearization coefficients
classical orthogonal polynomials of a discrete variable
recurrence relations
Opis:: Let {$P_k$} be any sequence of classical orthogonal polynomials of a discrete variable. We give explicitly a recurrence relation (in k) for the coefficients in $P_iP_j=\sum_kc(i,j,k)P_k$, in terms of the coefficients σ and τ of the Pearson equation satisfied by the weight function ϱ, and the coefficients of the three-term recurrence relation and of two structure relations obeyed by {$P_k$}.
Źródło:: Applicationes Mathematicae; 1996-1997, 24, 4; 445-455
1233-7234
Pojawia się w:: Applicationes Mathematicae
Dostawca treści:: Biblioteka Nauki

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