scholarly journals Boundedness character of the recursive sequence xn=α+∏j=1kxn−jaj

2015 ◽  
Vol 50 ◽  
pp. 83-90 ◽  
Author(s):  
Stevo Stević ◽  
Mohammed A. Alghamdi ◽  
Abdullah Alotaibi
Keyword(s):  
Recursive Sequence ◽  
Boundedness Character

scholarly journals On the Dynamics of the Recursive Sequence

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Mehmet Gümüş ◽  
Özkan Öcalan ◽  
Nilüfer B. Felah
Keyword(s):  
Periodic Solution ◽  
Difference Equation ◽  
Periodic Solutions ◽  
Positive Solutions ◽  
Initial Conditions ◽  
Recursive Sequence ◽  
Boundedness Character ◽  
The Difference

We investigate the boundedness character, the oscillatory, and the periodic character of positive solutions of the difference equation , where , , and the initial conditions are arbitrary positive numbers. We investigate the boundedness character for . Also, we investigate the existence of a prime two periodic solution for is odd. Moreover, when is even, we prove that there are no prime two periodic solutions of the equation above.

scholarly journals On the Rational Recursive Sequence

2008 ◽  
Vol 2008 ◽  
pp. 1-15 ◽  
Author(s):  
E. M. E. Zayed ◽  
A. B. Shamardan ◽  
T. A. Nofal
Keyword(s):  
Difference Equation ◽  
Global Stability ◽  
Global Attractor ◽  
Positive Solutions ◽  
Initial Conditions ◽  
Positive Equilibrium ◽  
Real Numbers ◽  
Recursive Sequence ◽  
Boundedness Character ◽  
The Difference

We study the global stability, the periodic character, and the boundedness character of the positive solutions of the difference equation , , in the two cases: (i) ; (ii) , where the coefficients and, and the initial conditions are real numbers. We show that the positive equilibrium of this equation is a global attractor with a basin that depends on certain conditions posed on the coefficients of this equation.

A Buffer Pool Optimization Algorithm Based on Max-Heap

2014 ◽  
Vol 945-949 ◽  
pp. 2439-2442
Author(s):  
Xiao Mei Xiong
Keyword(s):  
Optimization Algorithm ◽  
Database Access ◽  
Buffer Pool ◽  
Operation Efficiency ◽  
Data Query ◽  
Recursive Sequence ◽  
Access Request

To reduce the number of requests to the database connection, this paper designed the max-heap in buffer pool. We use the buffer pool maintenance algorithm to manage SQL data query request when database access intensive. When we update the max-heap, the structure of the buffer pool will be updated and the heap will be balance through the heap of recursive sequence, it got good performance in database access request. Experiment results show that this algorithm can improve the operation efficiency of system effectively.

scholarly journals Some Identities Involving Fibonacci Polynomials and Fibonacci Numbers

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 334 ◽  
Author(s):  
Yuankui Ma ◽  
Wenpeng Zhang
Keyword(s):  
Power Series ◽  
Structural Properties ◽  
Fibonacci Numbers ◽  
Second Order ◽  
Fibonacci Polynomials ◽  
Recursive Sequence ◽  
Combinatorial Methods

The aim of this paper is to research the structural properties of the Fibonacci polynomials and Fibonacci numbers and obtain some identities. To achieve this purpose, we first introduce a new second-order nonlinear recursive sequence. Then, we obtain our main results by using this new sequence, the properties of the power series, and the combinatorial methods.

ASYMPTOTIC BEHAVIOR OF THE SOLUTIONS OF DIFFERENCE EQUATION SYSTEM OF EXPONENTIAL FORM

Fractals ◽  
2020 ◽  
Vol 28 (06) ◽  
pp. 2050118
Author(s):  
ABDUL KHALIQ ◽  
MUHAMMAD ZUBAIR ◽  
A. Q. KHAN
Keyword(s):  
Initial Conditions ◽  
Equation System ◽  
Global Behavior ◽  
Real Numbers ◽  
Positive Real ◽  
Exponential Form ◽  
Numerical Examples ◽  
Rational Difference Equations ◽  
Boundedness Character ◽  
Theoretical Results

In this paper, we study the boundedness character and persistence, local and global behavior, and rate of convergence of positive solutions of following system of rational difference equations [Formula: see text] wherein the parameters [Formula: see text] for [Formula: see text] and the initial conditions [Formula: see text] are positive real numbers. Some numerical examples are given to verify our theoretical results.

scholarly journals LOOK, KNAVE

2020 ◽  
pp. 1-8
Author(s):  
THOMAS MORRILL
Keyword(s):  
Existence And Uniqueness ◽  
Binary Sequences ◽  
The Other ◽  
Binary Expansion ◽  
Recursive Sequence ◽  
Limiting Behaviour

Abstract We examine a recursive sequence in which $s_n$ is a literal description of what the binary expansion of the previous term $s_{n-1}$ is not. By adapting a technique of Conway, we determine the limiting behaviour of $\{s_n\}$ and dynamics of a related self-map of $2^{\mathbb {N}}$ . Our main result is the existence and uniqueness of a pair of binary sequences, each the complement-description of the other. We also take every opportunity to make puns.

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