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961.
Infinitely many homoclinic orbits for a class of second‐order damped differential equations
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We investigate the existence and multiplicity of homoclinic orbits for the second‐order damped differential equations For Equation 1 where L(t) and W(t,u) are neither autonomous nor periodic in t. Under certain assumptions on g, L, and W, we get infinitely many homoclinic orbits for superquadratic, subquadratic and concave–convex nonlinearities cases by using fountain theorem and dual fountain theorem in critical point theory. These results generalize and improve some existing results in the literature. Copyright © 2015 JohnWiley & Sons, Ltd. 相似文献
962.
Hassan A. Zedan M. Alghamdi Seham Sh. Tantawy 《Mathematical Methods in the Applied Sciences》2015,38(17):4357-4364
We study in this paper the Q‐symmetry and conditional Q‐symmetries of Drinfel'd–Sokolov–Wilson equations. The solutions which we obtain in this paper take the form of convergent power series with easily computable components. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
963.
A deductive approach to the solution of the problem of optimal pairs trading from the viewpoint of stochastic control with time‐dependent parameters
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K. Charalambous C. Sophocleous J. G. O'Hara P. G. L. Leach 《Mathematical Methods in the Applied Sciences》2015,38(17):4448-4460
In a fairly recent paper (2008 American Control Conference, June 11‐13, 1035‐1039), the problem of dealing with trading in optimal pairs was treated from the viewpoint of stochastic control. The analysis of the subsequent nonlinear evolution partial differential equation was based upon a succession of Ansätze, which can lead to a solution of the terminal‐value problem. Through an application of the Lie Theory of Continuous Groups to this equation, we show that the Ansätze are based upon the underlying symmetries of the equation (their (14)). We solve the problem in a more general context by allowing the parameters to be explicitly time dependent. The extension means thatmore realistic problems are amenable to the samemode of solution. Copyright © 2014 JohnWiley & Sons, Ltd. 相似文献
964.
On existence and multiplicity of similarity solutions to a nonlinear differential equation arising in magnetohydrodynamic Falkner–Skan flow for decelerated flows
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R. Naseri A. Malek R. A. Van Gorder 《Mathematical Methods in the Applied Sciences》2015,38(17):4272-4278
Previously, existence and uniqueness of a class of monotone similarity solutions for a nonlinear differential equation arising in magnetohydrodynamic Falkner–Skan flow were considered in the case of accelerating flows. It was shown that a solution satisfying certain monotonicity properties exists and is unique for the case of accelerated flows and some decelerated flows. In this paper, we show that solutions to the problem can exist for decelerated flows even when the monotonicity conditions do not hold. In particular, these types of solutions have nonmonotone second derivatives and are, hence, a distinct type of solution from those studied previously. By virtue of this result, the present paper demonstrates the existence of an important type of solution for decelerated flows. Importantly, we show that multiple solutions can exist for the case of strongly decelerated flows, and this occurs because of the fact that the solutions do not satisfy the aforementioned monotonicity requirements. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
965.
Fredholm boundary value problems for perturbed systems of dynamic equations on time scales
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Ravi P. Agarwal Martin Bohner Alexandr Boı̆chuk Olexandr Strakh 《Mathematical Methods in the Applied Sciences》2015,38(17):4178-4186
This paper offers conditions ensuring the existence of solutions of linear boundary value problems for systems of dynamic equations on time scales. Utilizing a method of Moore–Penrose pseudo‐inverse matrices leads to an analytical form of a criterion for the existence of solutions in a relevant space and, moreover, to the construction of a family of linearly independent solutions of such problems in a general case with the number of boundary conditions (defined by a linear vector functional) not coinciding with the number of unknowns of a system of dynamic equations. As an example of an application of the presented results, the problem of bifurcation of solutions of boundary value problems for systems of dynamic equations on time scales with a small parameter is considered. 相似文献
966.
Grooming uniform all‐to‐all traffic in optical (SONET) rings with grooming ratio C requires the determination of a decomposition of the complete graph into subgraphs each having at most C edges. The drop cost of such a grooming is the total number of vertices of nonzero degree in these subgraphs, and the grooming is optimal when the drop cost is minimum. The determination of optimal C‐groomings has been considered for , and completely solved for . For , it has been shown that the lower bound for the drop cost of an optimal C‐grooming can be attained for almost all orders with 5 exceptions and 308 possible exceptions. For , there are infinitely many unsettled orders; especially the case is far from complete. In this paper, we show that the lower bound for the drop cost of a 6‐grooming can be attained for almost all orders by reducing the 308 possible exceptions to 3, and that the lower bound for the drop cost of a 7‐grooming can be attained for almost all orders with seven exceptions and 16 possible exceptions. Moreover, for the unsettled orders, we give upper bounds for the minimum drop costs. 相似文献
967.
968.
The first total synthesis of the marine steroid alkaloid plakinamine B (1) was accomplished in seven steps starting from known aldehyde 3. Key steps in this synthesis are the attachment of a vinylpyridine side chain by an aldol reaction, a chemoselective reduction of a pyridinium salt to a vinyl tetrahydropyridine, and the introduction of the 3α-methylamino group under Mitsunobu conditions. Plakinamine B and some of its precursors with amino or pyridinium side chains show significant antimicrobial activities. 相似文献
969.
Substituent effects on the redox potentials of dihydroxybenzenes: theoretical and experimental study
Tao Liu Meng-Meng Liu Xiao-Wen Zheng Chong-Yang Du Xiang-Yang Cui Lu Wang Ling-Li Han Zhang-Yu Yu 《Tetrahedron》2014
The redox reactions of p-hydroquinone and pyrocatechol undergo a two-proton-two-electron process in aqueous solution. We calculated their redox potentials at the B3LYP/6-311+G(d,p) level, and verified the values by employing cyclic voltammetry experiments. Then we selected seven substituent groups (–F, –Cl, –OH, –COOH, –CN, –NH2, and –NO2 groups) to systematically investigate the substituent effect, including the sort, position, and number of the substituent, on the redox potentials of p-hydroquinone and pyrocatechol. The calculated results show that –NH2 and –OH groups can decrease the redox potentials, while –F, –Cl, –COOH, –CN, and –NO2 groups increase the potential values of p-hydroquinone and pyrocatechol. The calculations can accurately predict the substituent effects on the redox potentials of pyrocatechol and p-hydroquinone. We would expect that the accurate calculation results for the model systems could be applied in the prediction of electrode potentials of other molecules. 相似文献
970.
Qun Dang Zhibo Zhang Bingyu Tang Yang Song Ling Wu Tongqian Chen Stephane Bogen Vinay Girijavallabhan David B. Olsen Peter T. Meinke 《Tetrahedron letters》2014
To discover novel nucleosides as potential antiviral agents, 2′-spirolactam and 2′-spiropyrrolidine-containing nucleoside analogs were envisioned. Efficient synthetic routes were developed with an epoxide opening as the key step to establish the quaternary center at the 2′ position, leading to the design and synthesis of uridine analogs 8 and 21, prodrugs 13–16, and cytidine analog 11. 相似文献