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1
Content available Applications of the fractional Sturm-Liouville difference problem to the fractional diffusion difference equation
Malinowska Agnieszka B., Odzijewicz Tatiana, Poskrobko Anna
International Journal of Applied Mathematics and Computer Science
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2023
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Vol. 33, no. 3
349--359
EN
This paper deals with homogeneous and non-homogeneous fractional diffusion difference equations. The fractional operators in space and time are defined in the sense of Grünwald and Letnikov. Applying results on the existence of eigenvalues and corresponding eigenfunctions of the Sturm-Liouville problem, we show that solutions of fractional diffusion difference equations exist and are given by a finite series.
2
Content available remote Mathematical modeling and creation of algorithms for analyzing the ranges of the amplitude-frequency response of a vibrating rotary crusher in the software Mathcad
Honcharuk Inna, Kupchuk Ihor, Yaropud Vitalii, Kravets Ruslan, Burlaka Serhiy, Hraniak Valerii, Poberezhets Julia, Rutkevych Volodymyr
Przegląd Elektrotechniczny
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2022
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R. 98, nr 9
14--20
EN
The article is devoted to the study of motion laws for rotary vibration crusher. Kinematic and dynamic analysis was performed. Differential equations of rotor motion are solved and analyzed, frequency response and energy consumption graphs in MathCad 15.0 software environment are presented. Verification of the mathematical model was carried out by comparing the results of experimental research with theoretical research. It was proved that the proposed mathematical models are adequate (discrepancy are 7.2 to 12.1%).
PL
Artykuł poświęcony jest badaniu praw ruchu obrotowego kruszarki wibracyjnej. Przeprowadzono analizę kinematyczną i dynamiczną. Równania różniczkowe ruchu wirnika są rozwiązywane i analizowane, prezentowane są wykresy odpowiedzi częstotliwościowej i zużycia energii w środowisku oprogramowania MathCad 15.0. Weryfikację modelu matematycznego przeprowadzono poprzez porównanie wyników badań eksperymentalnych z badaniami teoretycznymi. Wykazano, że zaproponowane modele matematyczne są adekwatne (rozbieżność wynosi od 7,2 do 12,1%).
3
Content available remote Fourth order qualitative inspection of nonlinear neutral delay difference equation
Jesinthaangel R., Jawahar G. Gomathi, Aruna K.
Przegląd Elektrotechniczny
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2022
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R. 98, nr 7
66--69
EN
This paper aim is to investigate the nonlinear neutral fourth order difference equation in the form. We establish some conditions to assure that all solutions to this equation are oscillatory or nonoscillatory. We derived this using summation averaging technique and comparison principle. The main outcomes are illustrated using examples.
PL
W artykule badano nieliniowe równanie różnicowe czwartego rzędu. Ustalamy pewne warunki, aby zapewnić, że wszystkie rozwiązania tego równania są oscylacyjne lub nieoscylacyjne. Wyprowadziliśmy to za pomocą techniki uśredniania sumowania i zasady porównania. Główne wyniki zilustrowano na przykładach.
4
Content available remote Mathematical modeling and optimal control of the impact of rumors on the banking crisis
Tadmon Calvin, Njike-Tchaptchet Eric Rostand
Demonstratio Mathematica
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2022
|
Vol. 55, nr 1
90--118
EN
The bank run phenomenon, mostly due to rumor spread about the financial health of given financial institutions, is prejudicious to the stability of financial systems. In this paper, by using the epidemiological approach, we propose a nonlinear model for describing the impact of rumor on the banking crisis spread. We establish conditions under which the crisis dies out or remains permanent. We also solve an optimal control problem focusing on the minimization, at the lowest cost, of the number of stressed banks, as well as the number of banks undergoing the restructuring process. Numerical simulations are performed to illustrate theoretical results obtained.
5
Content available Construction of algebraic and difference equations with a prescribed solution space
Moysis L., Karampetakis N. P.
International Journal of Applied Mathematics and Computer Science
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2017
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Vol. 27, no. 1
19--32
EN
This paper studies the solution space of systems of algebraic and difference equations, given as auto-regressive (AR) representations A(σ) β (k) = 0, where σ denotes the shift forward operator and A(σ) is a regular polynomial matrix. The solution space of such systems consists of forward and backward propagating solutions, over a finite time horizon. This solution space can be constructed from knowledge of the finite and infinite elementary divisor structure of A(σ) . This work deals with the inverse problem of constructing a family of polynomial matrices A(σ) such that the system A(σ) β (k) = 0 satisfies some given forward and backward behavior. Initially, the connection between the backward behavior of an AR representation and the forward behavior of its dual system is showcased. This result is used to construct a system satisfying a certain backward behavior. By combining this result with the method provided by Gohberg et al. (2009) for constructing a system with a forward behavior, an algorithm is proposed for computing a system satisfying the prescribed forward and backward behavior.
6
Content available Rozwiązanie liniowego równania różnicowego w przestrzeni wyników generowanej przez ciągi dwustronne
Wysocki H.
Zeszyty Naukowe Akademii Marynarki Wojennej
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2010
|
R. 51 nr 3 (182)
85-101
PL
W pracy rozważa się zagadnienie początkowe dla liniowego równania różnicowego o stałych współczynnikach określonego w przestrzeni ciągów dwustronnych C (Z) . Problem ten przedstawiono w ujęciu nieklasycznego rachunku operatorów Bittnera. Wykorzystując model nabla tego rachunku z pochodną rozumianą jako różnica wsteczna, rozpatrywane zagadnienie rozwiązano w tzw. przestrzeni wyników. Wyniki powstają przez dzielenie elementów przestrzeni C (Z) przez injekcyjne endomorfizmy tej przestrzeni. Przedstawione rozważania dają początek nabla-rachunkowi, który może być konkurencyjny w stosunku do rachunku opartego na dwustronnym przekształceniu.
EN
The paper analyses the initial value problem for a linear difference equation with constant coefficients, defined in the space of two-sided sequences. The above problem has been C (Z) presented using the non-classical Bittner operational calculus approach. Using the -model of that calculus with its derivative understood as a backward difference, the issue in question has been solved in a so-called results' space. The results are obtained by dividing the elements of the C (Z) space by the injective endomorphisms of that space. The described analysis gives rise to a nabla-calculus that can be considered competitive to the calculus based on the bilateral -transform.
7
Content available remote Oscillation criteria for higher order neutral difference equations with oscillating coefficient
Migda M.
Fasciculi Mathematici
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2010
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Nr 44
85-93
EN
In this paper sufficient conditions for oscillation of all bounded solutions of the equation ...[wzór] where m ≥ 2, (pn) is an oscillatory sequence of real numbers, limn→∞ pn = 0, τ and σ are positive integers, f : N×R×R → R are established.
8
Content available remote On the solutions of the recursive sequence xx+1 = ...[wzór]
Karatas R.
Fasciculi Mathematici
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2010
|
Nr 45
37-45
EN
In this paper we study the solutions of the difference equation x + ...[wzór] for n = 0,1,2, ... where a, x-(2k+1), x-(2k), x-(2k-1), ..., x0 are the real numbers such that x0x-(k+1) ≠ a, x-1x-(k+2) ≠ a, x-2x-(k+3) ≠ a. ..., x-kx-(2k+1) ≠ a and k is a natural number.
9
Content available remote On the solutions of the difference equation xn+1 = max ...[wzór]
Yalcinkaya Ç., Kurbanli A. S.
Fasciculi Mathematici
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2010
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Nr 43
165-169
EN
We study the solutions of the following difference equation ...[wzór] where initial conditions x-1and x0 are nonzero real numbers. In most of the cases we determine the solutions in function of the initial conditions x-1 and x0.
10
Content available remote On the solutions of a rational system of difference equations
Elsayed E. M.
Fasciculi Mathematici
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2010
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Nr 45
25-36
EN
In this paper we deal with the solutions of the system of the difference equations xn+1 = ...[wzór], yn+1 = ...[wzór], with a nonzero real numbers initial conditions.
11
Content available remote On connections between oscillatory solutions of functional, difference and differential equations
Nowakowska W., Werbowski J.
Fasciculi Mathematici
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2010
|
Nr 44
95-106
EN
The paper contains connections between oscillation of solutions of iterative functional equations, difference equations and differential equations with advanced or delayed arguments. New oscillatory criteria for these equations are given.
12
Content available remote On asymptotically periodic solutions of linear discrete Volterra equations
Győri I., Reynolds D. W.
Fasciculi Mathematici
|
2010
|
Nr 44
53-67
EN
We show that a class of linear nonconvolution discrete Volterra equations has asymptotically periodic solutions. We also examine an example for which the calculations can be done explicitly. The results are established using theorems on the boundedness and convergence to a finite limit of solutions of linear discrete Volterra equations.
13
Content available remote On a linear difference equation with several infinite lags
Čermák J.
Fasciculi Mathematici
|
2010
|
Nr 44
19-28
EN
This paper deals with asymptotic properties of the solutions of a variable order linear difference equation. As the main result, we derive the effective asymptotic estimate valid for all solutions of this equation. Moreover, we are going to discuss some consequences of this theoretical result, especially with respect to the numerical analysis of the multi-pantograph differential equation.
14
Content available remote On a class of rational difference equations
Atasever N., Yalcinkaya I.
Fasciculi Mathematici
|
2010
|
Nr 43
13-18
EN
In this paper we study the behavior of the positive solutions of the following nonlinear difference equation ...[wzór], n = 0, 1, 2, ... where the initial values ...[wzór] and k = 0, 1, 2, . . ..
15
Content available remote Further instances of periodicity in May's host parasitoid equation
Sizer W. S.
Fasciculi Mathematici
|
2010
|
Nr 44
115-121
EN
May’s host parasitoid equation is the difference equation (1) ...[wzór] We show that for each &slpha; there is a number k such that, whenever n > k, equation (1) has a one cycle periodic solution of period n. We also give some results on two cycle periodic solutions.
16
Content available remote Boundedness of solutions of nonlinear three-dimensional difference systems with delays
Schmeidel E.
Fasciculi Mathematici
|
2010
|
Nr 44
107-113
EN
In this paper three-dimensional nonlinear difference system with delays ...[wzór] is investigated. The classification of nonoscillatory solutions of the considered system are presented. Next, the sufficient conditions under which nonoscillatory solution of considered system is bounded or is unbounded are given. Key words: difference equation, nonlinear system, nonoscillatory, bounded, unbounded solution.
17
Content available remote Analysis of a stochastic difference equation: exit times and invariant distributions
Högnäs G., Jung B.
Fasciculi Mathematici
|
2010
|
Nr 44
69-74
EN
The mean return time of a discrete Markov chain to a point x is the reciprocal of the invariant probability π(x). We revisit this classical theme to investigate certain exit times for stochastic difference equations of autoregressive type. More specifically, we will discuss the asymptotics, as 0, of the first time that the n-dimensional process ...[wzór] (where ξ1, ξ2, . . . is a sequence of i.i.d. random n-vectors) leaves a given neighborhood of the fixed point of the contraction f.
18
Content available remote On the solution of the recursive sequence
Elabbasy E.M., Elsayed E.M.
Fasciculi Mathematici
|
2009
|
Nr 41
55-63
EN
We obtain in this paper the solution of the following recursive sequence where the initial conditions x-2, x-1are arbitrary non zero real numbers.
19
Content available remote On the dynamics of the difference equation xn+1 = ...[wzór]
Yalçinkaya ĺ., Çinar C.
Fasciculi Mathematici
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2009
|
Nr 42
141-148
EN
This paper studies the global behavior of the difference equation xn+1 = ...[wzór], n = 0, 1, 2, ... with non-negative parameters and non-negative initial conditions where k is an odd number.
20
Content available remote On the difference equation xn+1 = α + ...[wzór]
Yalçinkaya ĺ.
Fasciculi Mathematici
|
2009
|
Nr 42
133-139
EN
In this paper, we investigate the global behavior of the difference equation of order three xn+1 = α + ...[wzór], n = 0, 1,… where the parameters α, k ∈ (0, ∞) and the initial values x-2, x-1 and x0 are arbitrary positive real numbers.
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