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BEHAVIOR OF SOLUTIONS OF A RATIONAL THIRD ORDER DIFFERENCE EQUATION
ABO-ZEID, R. The Korean Society for Computational and Applied M 2020 Journal of applied mathematics & informatics Vol.38 No.1
In this paper, we solve the difference equation $x_{n+1}={\frac{x_nx_{n-2}}{ax_n-bx_{n-2}}}$, n = 0, 1, …, where a and b are positive real numbers and the initial values x<sub>-2</sub>, x<sub>-1</sub> and x<sub>0</sub> are real numbers. We also find invariant sets and discuss the global behavior of the solutions of aforementioned equation.
Behavior of Solutions of a Fourth Order Difference Equation
Abo-Zeid, Raafat Department of Mathematics 2016 Kyungpook mathematical journal Vol.56 No.2
In this paper, we introduce an explicit formula for the solutions and discuss the global behavior of solutions of the difference equation $$x_{n+1}={\frac{ax_{n-3}}{b-cx_{n-1}x_{n-3}}}$$, $n=0,1,{\ldots}$ where a, b, c are positive real numbers and the initial conditions $x_{-3}$, $x_{-2}$, $x_{-1}$, $x_0$ are real numbers.
Abo-Zeid Salim Maha Ahmed,Bakrey Sherine,Elbadrawy Rania Elmohamady 대한마취통증의학회 2023 Korean Journal of Anesthesiology Vol.76 No.4
Background: The shivering effect after spinal anesthesia in total knee arthroplasty (TKA) is challenging for anesthesiologists. This study aimed to compare two administration routes of dexmedetomidine as a post-neuraxial shivering prevention measure and an adjunctive analgesic and sedative agent.Methods: Fifty-six patients were randomly allocated into two equal groups. The intravenous dexmedetomidine (IV dex) group received an IV infusion of 0.5 µg/kg dexmedetomidine diluted in 20 ml saline and an adductor canal block (ACB) consisting of 20 ml of 0.25% levobupivacaine and 1 ml saline. The adductor canal block dexmedetomidine (ACB dex) group received a 20 ml IV infusion of saline and an ACB consisting of 20 ml 0.25% levobupivacaine and 1 ml of 0.5 µg/kg dexmedetomidine.Results: The incidence of shivering 1 h post spinal anesthesia was equal in both groups (50%); however, the shivering grade was significantly lower in the IV dex group 1 h postoperatively. The onset of sensory block was significantly later in the IV dex group (22.14 ± 2.52 min) than in the ACB dex group (12 ± 3.31 min). Postoperative analgesic duration (h) was significantly longer in the ACB dex group (12.28 ± 4.47) compared to the IV dex group (9.28 ± 1.90). The sedation scores were also significantly higher in the IV dex group in the preoperative, intraoperative, and immediate postoperative periods.Conclusions: While perineural ACB dexmedetomidine had similar intraoperative anti-shivering with less sedative effects as IV dexmedetomidine, it was associated with both less shivering control and superior analgesia post-TKA under spinal anesthesia.
GLOBAL ASYMPTOTIC STABILITY OF A SECOND ORDER RATIONAL DIFFERENCE EQUATION
Abo-Zeid, R. The Korean Society for Computational and Applied M 2010 Journal of applied mathematics & informatics Vol.28 No.3
The aim of this paper is to investigate the global stability, periodic nature, oscillation and the boundedness of solutions of the difference equation $x_{n+1}\;=\;\frac{A+Bx_{n-1}}{C+Dx_n^2}$, n = 0, 1, 2, ... where A, B are nonnegative real numbers and C, D > 0.
BEHAVIOR OF SOLUTIONS OF A RATIONAL THIRD ORDER DIFFERENCE EQUATION
R. Abo-Zeid 한국전산응용수학회 2020 Journal of applied mathematics & informatics Vol.38 No.1
In this paper, we solve the difference equation x_{n+1}={x_nx_{n-2}}/{ax_{n}-bx_{n-2}}, n=0,1,..., where a and b are positive real numbers and the initial values x_{-2}, x_{-1} and x_{0} are real numbers. We also find invariant sets nd discuss the global behavior of the solutions of aforementioned equation.
GLOBAL ASYMPTOTIC STABILITY OF A SECOND ORDER RATIONAL DIFFERENCE EQUATION
R. Abo-Zeid 한국전산응용수학회 2010 Journal of applied mathematics & informatics Vol.28 No.3
The aim of this paper is to investigate the global stability, pe-riodic nature, oscillation and the boundedness of solutions of the difference equation [수식]where A, B are nonnegative real numbers and C,D >0.
Dynamical Behavior of a Third-Order Difference Equation with Arbitrary Powers
Gumus, Mehmet,Abo-Zeid, Raafat,Ocalan, Ozkan Department of Mathematics 2017 Kyungpook mathematical journal Vol.57 No.2
The aim of this paper is to investigate the dynamical behavior of the difference equation $$x_{n+1}={\frac{{\alpha}x_n}{{\beta}+{\gamma}x^p_{n-1}x^q_{n-2}}},\;n=0,1,{\ldots}$$, where the parameters ${\alpha}$, ${\beta}$, ${\gamma}$, p, q are non-negative numbers and the initial values $x_{-2}$, $x_{-1}$, $x_0$ are positive numbers. Also, some numerical examples are given to verify our theoretical results.
ON A HIGHER-ORDER RATIONAL DIFFERENCE EQUATION
BELHANNACHE, FARIDA,TOUAFEK, NOURESSADAT,ABO-ZEID, RAAFAT The Korean Society for Computational and Applied M 2016 Journal of applied mathematics & informatics Vol.34 No.5
In this paper, we investigate the global behavior of the solutions of the difference equation $x_{n+1}=\frac{A+Bx_{n-2k-1}}{C+D\prod_{i=l}^{k}x_{n-2i}^{m_i}}$, n=0, 1, ..., with non-negative initial conditions, the parameters A, B are non-negative real numbers, C, D are positive real numbers, k, l are fixed non-negative integers such that l ≤ k, and m<sub>i</sub>, i=l, k are positive integers.
On a Higher-Order Rational Difference Equation
Farida Belhannache,Nouressadat Touafek,Raafat Abo-Zeid 한국전산응용수학회 2016 Journal of applied mathematics & informatics Vol.34 No.5
In this paper, we investigate the global behavior of the solutions of the difference equation \begin{equation*} x_{n+1}=\frac{A+B x_{n-2k-1}}{C+D \prod^{k}_{i=l}x_{n-2i}^{m_{i}}},\text{ }n=0,1,..., \end{equation*}% with non-negative initial conditions, the parameters $A,$ $B$ are non-negative real numbers, $C$, $D$ are positive real numbers, $k,$ $l$ are fixed non-negative integers such that $l\leq k$, and $m_{i}, i=\overline{l,k}$ are positive integers.