Stability and square integrability of solutions of nonlinear fourth order differential equations |
| Author : Moussadek Remili, Mebrouk Rahmane |
| Abstract | Full Text |
Abstract :The aim of the present paper is to establish a new result, which guarantees the asymptotic stability of zero solution and square integrability of solutions and their derivatives to nonlinear differential equations of fourth order. |
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Redox reactions as experimental examples of ternary weak algebraic hyperstructures |
| Author : Bijan Davvaz, Violeta Leoreanu-Fotea, Feng Feng |
| Abstract | Full Text |
Abstract :A ternary hyperoperation on a set H is a 3-ary hyperoperation,
which associates a subset of H with any three elements of H. In this paper, we give examples of ternary hyperoperations associated withredox reactions. We observe that for Ag, Cu, Am and Au the ternary hyperoperations are weak associative and so their algebraic structures are Hv-semigroups. |
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Two extensions of the Dai-Liao method with sufficient descent property based on a penalization scheme |
| Author : Masoud Fatemi, Saman Babaie-Kafaki |
| Abstract | Full Text |
Abstract :To achieve the good features of the linear conjugate gradient algorithm in a recent extension of the Dai-Liao method, two adaptive choices for parameter of the extended method are proposed based on a penalization approach. It is shown that the suggested parameters guarantee the sufficient descent property independent to the line search and the objective function convexity. Furthermore, they ensure the global convergence of the related algorithm for uniformly convex objective functions. Using a set of unconstrained optimization test problems from the CUTEr library, effectiveness of the suggested choices are numerically compared with two other recently proposed adaptive choices. Results of comparisons show that one of the proposed choices is computationally promising in the sense of the Dolan-Moré performance profile. |
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