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    Wyświetlanie 1-8 z 8
    Tytuł:
    Iterations of homographic functions and recurrence equations involving a homographic function
    Iteracje funkcji homograficznej i równanie rekurencyjne zadane funkcja homograficzna
    Autorzy:
    Górowski, Jan
    Łomnicki, Adam
    Powiązania:
    https://bibliotekanauki.pl/articles/1791020.pdf
    Data publikacji:
    2017-07-04
    Wydawca:
    Uniwersytet Pedagogiczny im. Komisji Edukacji Narodowej w Krakowie
    Tematy:
    Iterations of homographic functions
    recurrence equation
    periodic
    sequences
    Opis:
    The formulas for the m-th iterate $(m \in N)$ of an arbitrary homographicfunction H are determined and the necessary and sufficient conditions for a solution ofthe equation $y_{m+1} = H(y_m)$, $m \in N$ to be an infinite n-periodic sequence are given. Based on the results from this paper one can easily determine some particular solutionsof the Babbage functional equation.
    Źródło:
    Annales Universitatis Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia; 2015, 7; 27-33
    2080-9751
    2450-341X
    Pojawia się w:
    Annales Universitatis Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    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
    Artykuł
    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
    Artykuł
    Tytuł:
    Solutions of recurrence and summation equations and their applications in slide bearing wear calculations
    Autorzy:
    Wierzcholski, K.
    Powiązania:
    https://bibliotekanauki.pl/articles/246728.pdf
    Data publikacji:
    2012
    Wydawca:
    Instytut Techniczny Wojsk Lotniczych
    Tematy:
    wear prognosis
    HDD micro-bearings
    recurrence non-homogeneous equation
    Opis:
    The investigations under the paper include a derivation of a non-homogenous recurrence equation of the second and higher orders with variable coefficients, whose particular solutions, with the boundary conditions set and obtained from experimental measurements, will be the sequences of the wear value of the bearing in the successive years of operation. Owing to these investigations, it will be possible to predict for example the wear values of slide bearings. Moreover, this paper presents the some particular applications of recurrence equations with regard to the calculation prognosis of micro-bearing parameters such as friction forces, friction coefficients and wear. Recurrence equations are presented in a form of difference equations where the unknown functions occur as the main terms of the sequence of inquired values. In this paper, the properties of the particular values of recurrence equations are defined. Possibility of modulation and control of mentioned problem belong to the artificial intelligence of HDD microbearing. Presented problem describes not continuous relations hence determines the mathematical and numerical solutions in discrete spaces. Properly in the case of continuous functions, the mentioned recurrence equations have the same meaning as differential equations. Recurrent equations for discrete function correspond to differential equations for the continuous function. In final conclusions, the application of presented theory in this paper contains the numerical solutions referring the wear values of HDD bearing system in the indicated period of operating time.
    Źródło:
    Journal of KONES; 2012, 19, 2; 543-550
    1231-4005
    2354-0133
    Pojawia się w:
    Journal of KONES
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A note on the order of polynomial-like iterative equations
    Autorzy:
    Draga, Szymon
    Powiązania:
    https://bibliotekanauki.pl/articles/746204.pdf
    Data publikacji:
    2016
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    continuous solution
    iterate
    polynomial-like iterative equation
    recurrence relation
    Opis:
    We show that, under reasonable assumptions, two negative roots can be eliminated from the characteristic equation of a polynomial-like iterative equation. This result gives a new case where we may lower the order of such an equation.
    Źródło:
    Commentationes Mathematicae; 2016, 56, 2
    0373-8299
    Pojawia się w:
    Commentationes Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Comparison of properties of solutions of differential equations and recurrence equations with the same characteristic equation (on example of third order linear equations with constant coefficients)
    Autorzy:
    Mikołajski, J.
    Schmeidel, E.
    Powiązania:
    https://bibliotekanauki.pl/articles/255810.pdf
    Data publikacji:
    2006
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    differential equation
    recurrence
    linear
    third order
    oscillatory solution
    bounded solution
    Opis:
    Third order linear homogeneous differential and recurrence equations with constant coefficients are considered. We take the both equations with the same characteristic equation. We show that these equations (differential and recurrence) can have solutions with different properties concerning oscillation and boundedness. Especially the numbers of suitable types of solutions taken out from fundamental sets are presented. We give conditions under which the asymptotic properties considered are the same for the both equations.
    Źródło:
    Opuscula Mathematica; 2006, 26, 2; 343-349
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Differential and recurrence unified reynolds equations and mega algorithm for their numerical solutions
    Autorzy:
    Wierzcholski, K.
    Miszczak, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/242919.pdf
    Data publikacji:
    2012
    Wydawca:
    Instytut Techniczny Wojsk Lotniczych
    Tematy:
    partial differential form
    partial recurrence form
    unified Reynolds equation
    mega algorithm
    Opis:
    The objective of the research under the paper topic is an analytical, unified formulation of a new standardized view of general solution of hydrodynamic problem using algorithm to determine changes of the components of the velocity vector, the distributions of hydrodynamic pressure, load carrying capacity, of slide bearings with cooperating curvilinear, orthogonal surfaces that are lubricated with a various non-Newtonian lubricants. In this paper for non- Newtonian lubricants are questioning the hitherto prevailing assumptions using in hydrodynamic theory of lubrication such as constant value of lubricant viscosity and pressure in the thickness of lubricating gap i.e. in gap height direction. Finally, the non-homogeneous partial differential equation generated with variable coefficients that is the result of the various boundary conditions being imposed that are different for each problem solved is an equation that determines the distributions of hydrodynamic pressure values. This equation is to be written in the form of a unified non-homogenous partial recurrence equation with variable coefficients. The Authors foresee that a mega-algorithm will be developed for the solution of this equation in a numerical form. This equation in particular cases is an equivalent of modified Reynolds equations in the research that has been conducted so far concerning the hydrodynamic theory of lubrication.
    Źródło:
    Journal of KONES; 2012, 19, 4; 643-650
    1231-4005
    2354-0133
    Pojawia się w:
    Journal of KONES
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Związek rekurencyjny oraz zależności i równanie różniczkowe dla wielomianów Legendre’a
    Recurrence formula, differential properties and differential equation for Legendre polynomials
    Autorzy:
    Czajkowski, A. A.
    Powiązania:
    https://bibliotekanauki.pl/articles/136092.pdf
    Data publikacji:
    2014
    Wydawca:
    Wyższa Szkoła Techniczno-Ekonomiczna w Szczecinie
    Tematy:
    wielomiany Legendre'a
    związek rekurencyjny
    zależność różniczkowa
    równanie różniczkowe
    Legendre polynomials
    recurrence formula
    differential compound
    differential equation
    Opis:
    W pracy przedstawiono związek rekurencyjny, zależności różniczkowe i równanie różniczkowe dla wielomianów Legendre’a. Celem rozważań było przeprowadzenie dowodów omawianych własności. Materiał i metody: Materiał stanowiły wybrane zależności rekurencyjne i równanie różniczkowe uzyskane z literatury przedmiotu. W przeprowadzonych dowodach zastosowano metodę dedukcji. Wyniki: Pokazano dowód twierdzenia o funkcji tworzącej dla wielomianów Legendre’a stosując metodę residuum funkcji. Przeprowadzono dowód związku rekurencyjnego, czterech zależności różniczkowych oraz równania różniczkowego dla wielomianów Legendre’a. Wnioski: Pochodną wielomianu Legendre’a wyrażoną przez wielomiany Legendre’a można określić z równania (1–z2)P'n(z) = nPn-1(z) – nzPn(z) dla n = 1, 2, … . Wielomian Legendre’a u=Pn(z) jest całką szczególną równania [(1-z2)u']'+n(n+1)u =0 dla n = 0, 1, 2,
    Introduction and aim: The paper presents a recurrence formula, some differential compounds and differential equation for Legendre polynomials. The aim of the discussion was to give some proofs of presented dependences. Material and methods: Selected material based on a recurrence formula, some differential compounds and differential equation has been obtained from the right literature. In presented proofs of theorems was used a deduction method. Results: Has been shown some proof of the theorem of the generating function for Legendre polynomials by using the method of function residue. It has been done the proof of recurrence formula, some proofs of four differential compounds and differential equation for Legendre polynomials. Conclusions: Some derivative of Legendre polynomial expressed by Legendre polynomials can be determined from the equation (1–z2)P'n(z) = nPn-1(z) – nzPn(z) for n = 1, 2, … . Legendre polynomial u=Pn(z) is the particular integral solution of the equation [(1-z2)u']'+n(n+1)u =0 for n = 0, 1, 2, … .
    Źródło:
    Problemy Nauk Stosowanych; 2014, 2; 59-68
    2300-6110
    Pojawia się w:
    Problemy Nauk Stosowanych
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-8 z 8

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