The exact solution and integrable properties to the variable-coefficient modified Korteweg-de Vries equation

In this paper, a variable-coefficient modified Korteweg-de Vries (vc-mKdV) equation is investigated. With the help of symbolic computation, the N-soliton solution is derived through the Hirota method. Then the bilinear Bäcklund transformations and Lax pairs are presented. At last, we show some interactions of solitary waves.     

Nuclear fusion rate for ddμ muonic molecule

A variational approach using a new wave function to ddμ muonic molecular ion is proposed. This approach requires four terms in the total three‐body wave function. The formation and fusion take place by the reason of the existence of the both Coulomb potential and nuclear absorption. The nuclear fusion rates and eigenvalues related to such levels below dμ(1s) + d threshold are calculated with a good accuracy and a short computation time. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

螺旋波激发等离子体源的原理和应用

介绍了一种低气压，高密度等离子体源－螺旋波激发等离子体源，讲述了它的结构位形，该离子源在实际中的应用以及目前研究状况。     

Simultaneous determination of docosahexaenoic acid and eicosapentaenoic acid in common seafood using ultrasonic cell crusher extraction combined with gas chromatography

An effective method for the simultaneous determination of docosahexaenoic acid and eicosapentaenoic acid in common seafood by gas chromatography was developed and validated. Total docosahexaenoic acid and eicosapentaenoic acid were extracted from seafood by ultrasonic cell crusher assisted extraction and methyl esterified for gas chromatography analysis in the presence of the internal standard. The linearity was good (r > 0.999) in 9.59 ∼ 479.5 μg/mL for docosahexaenoic acid and 9.56 ∼ 477.8 μg/mL for eicosapentaenoic acid. The intrarun and interrun precisions were both within 4.8 and 6.1% for the two analytes, while the accuracy was less than 5.8%. The developed method was applied for determination of docosahexaenoic acid and eicosapentaenoic acid in six kinds of seafood. The result showed the content of docosahexaenoic acid and eicosapentaenoic acid was all higher than 1 mg/g in yellow croaker, hairtail, venerupis philippinarum, mussel, and oyster. Our work may be helpful for dietary optimization and production of docosahexaenoic acid and eicosapentaenoic acid.     

From exaptation to radical niche construction in biological and technological complex systems

Biological adaptation assumes the evolution of structures toward better functions. Yet, the roots of adaptive trajectories usually entail subverted—perverted—structures, derived from a different function: what Gould and Vrba called “exaptation.” Generally, this derivation is regarded as contingent or serendipitous, but it also may have regularities, if not rules, in both biological evolution and technological innovation. On the basis of biological examples and examples from the history of technology, the authors demonstrate the centrality of exaptation for a modern understanding of niche, selection, and environment. In some cases, biological understanding illuminates technical exaptation. Thus, the driver of exaptation is not simply chance matching of function and form; it depends on particular, permissive contexts. © 2013 Wiley Periodicals, Inc. Complexity 18: 7–14, 2013     

晃荡

本文列举了诸多工程领域中的液体共振运动现象,详细探讨了船舱中伴有剧烈流动的晃荡问题.描述了基于理论分析的非线性多模态方法,该方法便于波动稳定性分区、多分支解和物理稳定性的研究.强调了方形舱、垂向圆柱舱以及球形舱内伴有旋转和混沌(不规则波动)的三维流动的重要性.晃荡引起的砰击涉及到各种各样的内流条件,这些条件随液体深度与舱体长度之比而变化.针对棱柱状LNG舱,讨论了许多与流体力学和热力学参数、影响砰击载荷效应的水弹性以及模型实验缩尺比的物理现象.     

A proof of Price's Law on Schwarzschild black hole manifolds for all angular momenta

Price's Law states that linear perturbations of a Schwarzschild black hole fall off as t−2?−3 for t→∞ provided the initial data decay sufficiently fast at spatial infinity. Moreover, if the perturbations are initially static (i.e., their time derivative is zero), then the decay is predicted to be t−2?−4. We give a proof of t−2?−2 decay for general data in the form of weighted L¹ to L^∞ bounds for solutions of the Regge–Wheeler equation. For initially static perturbations we obtain t−2?−3. The proof is based on an integral representation of the solution which follows from self-adjoint spectral theory. We apply two different perturbative arguments in order to construct the corresponding spectral measure and the decay bounds are obtained by appropriate oscillatory integral estimates.     

Bäcklund transformations and abundant exact explicit solutions of the Sharma-Tasso-Olver equation

By using an extension of the homogeneous balance method and Maple, the Bäcklund transformations for the Sharma-Tasso-Olver equation are derived. The connections between the Sharma-Tasso-Olver equation and some linear partial differential equations are found. With the aid of the transformations given here and the computer program Maple 12, abundant exact explicit special solutions to the Sharma-Tasso-Olver equation are constructed. In addition to all known solutions re-deriving in a systematic way, several entirely new and more general exact explicit solitary wave solutions can also be obtained. These solutions include (a) the algebraic solitary wave solution of rational function, (b) single-soliton solutions, (c) double-soliton solutions, (d) N-soliton solutions, (e) singular traveling solutions, (f) the periodic wave solutions of trigonometric function type, and (g) many non-traveling solutions. By using the Airy’s function and the Bäcklund transformations obtained here, the exact explicit solution of the initial value problem for the STO equation is presented. The variety of the structure of the solutions for the Sharma-Tasso-Olver equation is illustrated.     

Solitary wave solutions and kink wave solutions for a generalized KDV-mKDV equation

Bifurcation method of dynamical systems is employed to investigate solitary wave solutions and kink wave solutions of the generalized KDV-mKDV equation. Under some parameter conditions, their explicit expressions are obtained.