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On Soft $\Gamma $-Hyperideals over Left Almost $\Gamma $-Semihypergroups
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Naveed Yaqoob, Muhammad Aslam, Faisal
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Volume 4, Issue 1, 2012
pp.
1 - 12
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Received
18 September 2011,
Accepted
17 January 2012
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Abstract.
n this paper, the concept of soft LA-$\Gamma $-semihypergroup is introduced and some of the properties of soft $\Gamma $-hyperideals are provided.
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Keywords.
Soft sets; Soft LA-$\Gamma $-semihypergroups; Soft $\Gamma $-hyperideals; Soft bi-$\Gamma $-hyperideals.
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Growth and Oscillation of Solutions of some Higher Order Linear Differential Equations with Transcendental Meromorphic Coefficients
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Benharrat Belaidi, Abdallah El Farissi
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Volume 3, Issue 3, 2011
pp.
50 - 65
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Received
15 September 2011,
Accepted
05 December 2011
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Abstract.
In this paper, we investigate the growth and the complex oscillation of the differential equation \begin{equation*} f^{\left( k\right) }+A_{k-1}f^{\left( k-1\right) }+...+A_{0}f=F,\ \ \end{equation*} where $A_{j}$ $\left( j=0,1,...,k-1\right) ,$ $F\not\equiv 0$ are finite order transcendental meromorphic functions having only finitely many poles and there exists $s\in \left\{ 0,1,...,k-1\right\} $ such that the order of \ $A_{s}$ is larger than that of $A_{j}$ $(j=0,1,...$ $,s-1,s+1,...,k-1)$. Some precise estimates of the order of growth and the exponent of convergence of the zero-sequence of solutions are obtained for the above equation.
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Keywords.
Linear differential equations; Order of growth; Exponent of convergence of distinct zeros.
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Existence and Uniqueness of Weak Solution for Weighted p-Laplacian Dirichlet Problem
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S.A. Khafagy
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Volume 3, Issue 3, 2011
pp.
41 - 49
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Received
14 September 2011,
Accepted
04 December 2011
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Abstract.
This paper deals with the equation $-\Delta _{P,p}u+\lambda a(x)|u|^{p-2}u=f(x,u)$ in bounded domain $\Omega \in \Re ^{N}$ with Dirichlet boundary value condition. The existence and uniqueness results are obtained by Browder Theorem.
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Keywords.
Weak solutions; Weighted $p$-Laplacian.
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Approximation of Accessible Diffeomorphisms by Stable Non Uniformly Hyperbolic Systems
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Alireza Zamani Bahabadi
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Volume 3, Issue 3, 2011
pp.
36 - 40
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Received
30 July 2011,
Accepted
01 December 2011
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Abstract.
In this paper, we show that every accessible diffeomorphism can be approximated by stable non uniformly hyperbolic diffeomorphisms. As a corollary we show that every partial hyperbolic diffeomorphism can be approximated by stable non uniformly hyperbolic ones.
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Keywords.
Non-uniform hyperbolic; Accessible diffeomorphism; Lyapunov exponent; Dominated splitting.
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Some Characterizations of Bertrand Offsets of Timelike Ruled Surfaces
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Mehmet Önder
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Volume 3, Issue 3, 2011
pp.
21 - 35
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Received
12 September 2011,
Accepted
30 November 2011
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Abstract.
In this paper, we study Bertrand offsets of timelike ruled surface by considering dual geodesic trihedron (dual Darboux frame) of the timelike ruled surfaces. We give the relationships between invariants of a timelike ruled surface and its Bertrand offset. Furthermore, we obtain conditions for these surface offsets to be developable.
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Keywords.
Timelike ruled surface; Bertrand offset; Dual geodesic trihedron.
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An iterative scheme for a class of fractional optimal control problems
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Akbar H. Borzabadi, Mohammad Heidari
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Volume 3, Issue 3, 2011
pp.
13 - 20
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Received
02 February 2011,
Accepted
20 October 2011
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Abstract.
This paper presents a hybrid scheme based on Dinkelbach approach and wavelet collocation method to extract approximate solutions of fractional optimal control problems (FOCP)'s. First Dinkelbach approach is considered to linearize the problem, then it is tried by combination of collocation wavelet approach and a numerical scheme of solving nonlinear equations, an iterative approach be proposed to obtain approximate optimal trajectory and control functions. Finally, numerical examples are listed to show the efficiency of the given approach.
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Keywords.
Optimal control; Fractional programming; Haar wavelet; Nonlinear programming.
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Analytic Approximations for Fractional-Order Hyperchaotic System
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Mohamed S. Mohamed, Hossam A. Ghany
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Volume 3, Issue 3, 2011
pp.
1 - 12
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Received
25 June 2011,
Accepted
19 October 2011
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Abstract.
In this paper, the numerical analytic solution for the fractional order hyperchaotic system is obtained the step homotopy analysis method (SHAM). The fractional derivatives are describing by Caputo's sense. Exact and/or approximate analytical solutions of these equations are obtained. An analytical form of the solution within each time interval is given which is not possible using standard numerical method.
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Keywords.
Homotopy analysis method; Hyperchaotic system; Fractional-order hyperchaotic system; Caputo's fractional derivative.
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A Hybrid Iterative Scheme for Optimal Control Problems Based on L-M and Penalty Techniques
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Akbar H. Borzabadi, Safie Ghasemi, Omid S. Fard
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Volume 3, Issue 2, 2011
pp.
53 - 65
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Received
12 May 2011,
Accepted
01 October 2011
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Abstract.
This paper presents an investigation on applying the methods of solving nonlinear least square problems (NLSP)'s for detecting approximate solutions of optimal control problems (OCP)'s under an iterative hybrid process. Levenberg-Marquardt method as a successful classic approach is applied for solving the created NLSP's. Results of implementing the proposed algorithm for solving some linear and nonlinear OCP's are given.
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Keywords.
Nonlinear least square problem; Optimal control; Penalty method; Approximation.
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The Asymptotic Average Shadowing Property and Strong Ergodicity
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Ali Barzanouni, Bahman Honary
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Volume 3, Issue 2, 2011
pp.
47 - 52
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Received
28 March 2011,
Accepted
14 July 2011
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Abstract.
Let $X$ be a compact metric space and $f:X\rightarrow X$ be a continuous map. We prove that if $f$ has asymptotic average shadowing property and the minimal points of $f$ are dense in $X$, then $f$ is weakly mixing and totally strongly ergodic. As a corollary we obtain that if $f$ is distal, then $f$ does not have the asymptotic average-shadowing property.
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Keywords.
Asymptotic average shadowing property; Topological ergodic; Strongly ergodic; Minimal point; Distal map.
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Linear Control Differential Inclusions with Fuzzy Right-Hand Side and some Optimal Problems
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Andrej V. Plotnikov, Tatyana A. Komleva, Irina V. Molchanyuk
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Volume 3, Issue 2, 2011
pp.
34 - 46
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Received
11 April 2011,
Accepted
21 June 2011
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Abstract.
In this article we consider the some properties of the fuzzy R-solution of the control linear fuzzy differential inclusions and research the optimal time problems for it.
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Keywords.
Fuzzy differential inclusion; Control system; Optimal control; Optimal time problems.
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