The Experts below are selected from a list of 315 Experts worldwide ranked by ideXlab platform
Stevo Stevic - One of the best experts on this subject based on the ideXlab platform.
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on the Difference Equation xn xn kb cxn 1 xn k
Applied Mathematics and Computation, 2012Co-Authors: Stevo StevicAbstract:Abstract We describe the behavior of well-defined solutions of the Difference Equation x n = x n - k b + cx n - 1 ⋯ x n - k , n ∈ N 0 , where k ∈ N , parameters b , c and the initial values x − k , … , x −1 are real numbers. These results, among others, improve and extend our results in [S. Stevic, More on a rational recurrence relation, Appl. Math. E-Notes 4 (2004) 80–85].
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on the Difference Equation xn xn 2 bn cnxn 1xn 2
Applied Mathematics and Computation, 2011Co-Authors: Stevo StevicAbstract:Abstract We prove that the Difference Equation x n = x n - 2 b n + c n x n - 1 x n - 2 , n ∈ N 0 , where ( b n ) n ∈ N 0 and ( c n ) n ∈ N 0 are sequences periodic with period two and the initial values x −2 , x −1 are real numbers, can be solved explicitly. Some applications of obtained formulae are given.
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on a nonlinear generalized max type Difference Equation
Journal of Mathematical Analysis and Applications, 2011Co-Authors: Stevo StevicAbstract:Abstract The boundedness character of positive solutions of the following max-type Difference Equation x n = max { A , x n − 1 p x n − k r } , n ∈ N 0 , where k ∈ N ∖ { 1 } , the parameters A and r are positive and p is a nonnegative real number is studied in this paper. Our main results considerably improve results appearing in the literature.
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global stability of a max type Difference Equation
Applied Mathematics and Computation, 2010Co-Authors: Stevo StevicAbstract:We show that every positive solution to the Difference Equationx"n=maxA"1x"n"-"p"""1^@a^"^1,A"2x"n"-"p"""2^@a^"^2,...,A"kx"n"-"p"""k^@a^"^k,n@?N"0,where p"i,i=1,...,k are natural numbers such that 1=0,@a"i@?(-1,1),i=1,...,k, converges to max"1"=<"i"=<"kA"i^1^@a^"^i^+^1. This result improves and complements the main result in our recent note: S. Stevic, Global stability of a Difference Equation with maximum, Appl. Math. Comput. 210 (2009) 525-529, since it also considers the case when @a"i@?(-1,0],i=1,...,k.
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on a generalized max type Difference Equation from automatic control theory
Nonlinear Analysis-theory Methods & Applications, 2010Co-Authors: Stevo StevicAbstract:Abstract This paper studies the boundedness character of positive solutions of the following generalization of a max-type Difference Equation from automatic control theory (see, Mishkis, (1977) [18] and Popov (1966) [21] ) x n + 1 = max { A , x n p x n − 1 q x n − 2 r } , n ∈ N 0 , where the parameters A , p , q and r are positive numbers. In the study of the Equation we also introduce a new method called Oachkatzlschwoif.
Cengiz Cinar - One of the best experts on this subject based on the ideXlab platform.
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on a max type Difference Equation
Advances in Difference Equations, 2010Co-Authors: Ali Gelisken, Cengiz Cinar, Ibrahim YalcinkayaAbstract:We prove that every positive solution of the max-type Difference Equation , converges to where are positive integers, , and .
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on positive solutions of a reciprocal Difference Equation with minimum
Journal of Applied Mathematics and Computing, 2005Co-Authors: Cengiz Cinar, Stevo Stevic, Ibrahim YalcinkayaAbstract:In this paper we consider positive solutions of the following Difference Equation $$x_{n + 1} = \min \left\{ {\frac{A}{{x_n }},\frac{B}{{x_{n - 2} }}} \right\}, A, B > 0.$$ We prove that every positive solution is eventually periodic. Also, we present here some results concerning positive solutions of the Difference Equation $$x_{n + 1} = \min \left\{ {\frac{A}{{x_n x_{n - 1} ...x_{n - k} }},\frac{B}{{x_{n - (k + 2)} ...x_{n - (2k + 2)} }}} \right\}, A, B > 0.$$
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On the Difference Equation xn+1=xn-1-1+xnxn-1
Applied Mathematics and Computation, 2004Co-Authors: Cengiz CinarAbstract:In this paper, we investigate the solutions of the Difference Equation x"n"+"1=x"n"-"1-1+x"nx"n"-"1, n=0,1,2,..., where x"-"1 and x"0 are the real numbers such that x"-"1x"0 1.
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on the positive solutions of the Difference Equation xn 1 xn 11 axnxn 1
Applied Mathematics and Computation, 2004Co-Authors: Cengiz CinarAbstract:The positive solutions of the Difference Equation x"n"+"1=x"n"-"11+ax"nx"n"-"1, n=0,1,2,..., are investigated, where x"-"1, x"0 and a are the nonnegative real numbers.
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On the solutions of the Difference Equation xn+1=xn-1-1+axnxn-1
Applied Mathematics and Computation, 2004Co-Authors: Cengiz CinarAbstract:We investigate the solutions of the Difference Equation x"n"+"1=x"n"-"1-1+ax"nx"n"-"1, n=0,1,2,..., where a>0, x"-"1 and x"0 are real numbers such that ax"-"1x"0 1.
A.h. Tewfik - One of the best experts on this subject based on the ideXlab platform.
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Modeling techniques for multiscale Difference Equation signal models
1996 IEEE International Conference on Acoustics Speech and Signal Processing Conference Proceedings, 1996Co-Authors: A.h. TewfikAbstract:In this paper, we describe novel encoding and decoding methods for multiscale Difference Equation (MSDE) signal models. Recently, MSDE signal models have been introduced to exploit self-similarities in signals. The encoding process for MSDE models requires an adaptive signal representation from the dictionary of translations and dilations of the signal to be modeled. Here, we propose a new iterative technique that tries to select an 'active' set under the modeling constraints so that the portion of the signal representation due to the 'inactive' set has small or zero norm. Using methods similar to 'line searches and backtracking' used for global non-linear optimization, this method yields the global minima for exact representation. The decoding process involves an eigenvector analysis of a particular matrix. We provide a fast algorithm to obtain the required eigenvector in O(N/sup 2/ log N) operations. We also provide a perturbation analysis of MSDE models that gives a bound on the reconstruction error due to errors in the MSDE coefficients.
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Multiscale Difference Equation signal models. I. Theory
IEEE Transactions on Signal Processing, 1995Co-Authors: A.h. TewfikAbstract:The paper studies multiscale Difference Equation models for l-D and M-D signals. In this modeling technique, the signal of interest is viewed as a solution to a multiscale Difference Equation (MSDE). The model completely characterizes the signal as well as a number of its higher derivatives. It provides a recursive signal interpolation scheme as a function of scale. It also leads naturally to multigrid signal filtering, detection and estimation algorithms. An MSDE model must be uniquely decodable, i.e., it must correspond to a unique signal. Therefore, one must guarantee that the modeling MSDE has a unique solution. The authors investigate the existence and uniqueness of L/sub 1/ and L/sub 2/ solutions-to multiscale Difference Equations. Using Fourier domain techniques, they derive conditions for the existence of L/sub 1/ solutions to an MSDE. They provide conditions under which the L/sub 1/ solution is unique (up to a multiplicative constant) and has compact support. They also derive sufficient, but not necessary, conditions for the existence of a unique L/sub 2/ solution to a subclass of MSDEs. The results extend known facts about the solutions of two-scale Difference Equations. The paper concludes with several examples of MSDE signal models that highlight the modeling advantages of MSDEs over two-scale Difference Equation models.
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Multiscale Difference Equation signal modeling and analysis techniques
Proceedings of ICASSP '94. IEEE International Conference on Acoustics Speech and Signal Processing, 1994Co-Authors: A.h. TewfikAbstract:A novel signal modeling technique in which an arbitrary sequence of data points is represented as samples of the solution to a multiscale Difference Equation is proposed. Such a model completely characterizes a number of higher derivatives of the signal as well as the signal itself. It provides a recursive signal interpolation mechanism as a function of scale. It also leads to multigrid type signal filtering, detection and estimation algorithms. The existence and uniqueness of L/sub 1/ and L/sub 2/ solutions to the multiscale Difference Equation are first investigated. The paper generalizes the results obtained for the two scale Difference Equation. Next, we provide conditions for the existence of unique solution to such an Equation. Finally, techniques for modeling an arbitrary set of data samples as samples of the solution to a multiscale Difference Equation are presented. Specifically, we describe the encoding and decoding steps in these techniques. We also prevent audio signal modeling examples to illustrate multiscale Difference Equation models.
Xianyi Li - One of the best experts on this subject based on the ideXlab platform.
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Dichotomy of a perturbed Lyness Difference Equation
Applied Mathematics and Computation, 2014Co-Authors: Guifeng Deng, Xianyi LiAbstract:Abstract We investigate in this paper the perturbed Lyness Difference Equation bx n + 2 x n = α + β x n + 1 + γ x n 2 , n = 0 , 1 , 2 , … , where α , β , b are arbitrary positive real numbers and γ ∈ [ 0 , ∞ ) and the initial values x 1 , x 0 > 0 , which is a generalization of the Lyness Difference Equation x n + 2 x n = a + x n + 1 extensively studied. It is known that for the Lyness Difference Equation, i.e., the perturbed Lyness Difference Equation with γ = 0 , all its solutions are periodic or strictly oscillatory. However, one here finds that this perturbed Lyness Difference Equation possesses the following dichotomy: for 0 γ b , all of its solutions are globally asymptotically stable; for γ ⩾ b , all the sequences generated by it converge to + ∞ . We hence find that there exists the essential Difference for the properties of solutions between the unperturbed Lyness Difference Equation and the perturbed Lyness Difference Equation.
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global behavior for a fourth order rational Difference Equation
Journal of Mathematical Analysis and Applications, 2005Co-Authors: Xianyi LiAbstract:In this paper, we use a method different from the known literature to investigate the global behavior of the following fourth-order rational Difference Equation: xn+1 = xn−1xn−2xn−3 + xn−1 + xn−2 + xn−3 + a xn−1xn−2 + xn−1xn−3 + xn−2xn−3 + 1 + a ,n = 0, 1, 2 ,...,
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qualitative properties for a fourth order rational Difference Equation
Journal of Mathematical Analysis and Applications, 2005Co-Authors: Xianyi LiAbstract:Abstract In this paper, we use a method different from the known literature to investigate the qualitative properties of the following fourth-order rational Difference Equation: x n + 1 = x n x n − 1 x n − 3 + x n + x n − 1 + x n − 3 + a x n x n − 1 + x n x n − 3 + x n − 1 x n − 3 + 1 + a , n = 0 , 1 , 2 , … , where a ∈ [ 0 , ∞ ) and the initial values x −3 , x −2 , x −1 , x 0 ∈ ( 0 , ∞ ) . The successive lengths of positive and negative semicycles of nontrivial solutions of the above Equation is found to periodically occur, that is, … , 3 + , 2 − , 1 + , 1 − , 3 + , 2 − , 1 + , 1 − , 3 + , 2 − , 1 + , 1 − , 3 + , 2 − , 1 + , 1 − , … , or, … , 2 + , 1 − , 1 + , 3 − , 2 + , 1 − , 1 + , 3 − , 2 + , 1 − , 1 + , 3 − , 2 + , 1 − , 1 + , 3 − , 2 + , 1 − , 1 + , 3 − , … . By using the rule, the positive equilibrium point of the Equation is verified to be globally asymptotically stable.
Ibrahim Yalcinkaya - One of the best experts on this subject based on the ideXlab platform.
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on a max type Difference Equation
Advances in Difference Equations, 2010Co-Authors: Ali Gelisken, Cengiz Cinar, Ibrahim YalcinkayaAbstract:We prove that every positive solution of the max-type Difference Equation , converges to where are positive integers, , and .
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on positive solutions of a reciprocal Difference Equation with minimum
Journal of Applied Mathematics and Computing, 2005Co-Authors: Cengiz Cinar, Stevo Stevic, Ibrahim YalcinkayaAbstract:In this paper we consider positive solutions of the following Difference Equation $$x_{n + 1} = \min \left\{ {\frac{A}{{x_n }},\frac{B}{{x_{n - 2} }}} \right\}, A, B > 0.$$ We prove that every positive solution is eventually periodic. Also, we present here some results concerning positive solutions of the Difference Equation $$x_{n + 1} = \min \left\{ {\frac{A}{{x_n x_{n - 1} ...x_{n - k} }},\frac{B}{{x_{n - (k + 2)} ...x_{n - (2k + 2)} }}} \right\}, A, B > 0.$$
