Abundant explicit exact solutions to the generalized nonlinear Schrödinger equation with parabolic law and dual‐power law nonlinearities

This paper is concerned with the generalized nonlinear Schrödinger equation with parabolic law and dual‐power law. Abundant explicit and exact solutions of the generalized nonlinear Schrödinger equation with parabolic law and dual‐power law are derived uniformly by using the first integral method. These exact solutions are include that of extended hyperbolic function solutions, periodic wave solutions of triangle functions type, exponential form solution, and complex hyperbolic trigonometric function solutions and so on. The results obtained confirm that the first integral method is an efficient technique for analytic treatment of a wide variety of nonlinear systems of partial DEs. Copyright © 2014 John Wiley & Sons, Ltd.     

Kinetics of radical‐molecule reactions in aqueous solution: A benchmark study of the performance of density functional methods

The performance of 18 density functional approximations has been tested for a very challenging task, the calculations of rate constants for radical‐molecule reactions in aqueous solution. Despite of the many difficulties involved in such an enterprise, six of them provide high quality results, and are recommended to that purpose. They are LC‐ωPBE, M06‐2X, BMK, B2PLYP, M05‐2X, and MN12SX, in that order. This trend was obtained using experimental data as reference. The other relevant aspects used in this benchmark are: (i) the SMD model for mimicking the solvent; (ii) the conventional transition state, the zero‐curvature tunneling correction, and the limit imposed by diffusion for the calculation of the rate constants. Even though changing any of these aspects might alter the trend in performance, at least, when using them, the aforementioned functionals can be successfully used to obtain high quality kinetic data for the kind of reactions investigated in this work. © 2014 Wiley Periodicals, Inc.     

有限长密绕圆柱形螺线管自感系数的精确表达式

对于有限长密绕圆柱形螺线管,首先用贝塞尔函数展开法推导出自感系数的积分形式的表达式,然后用直接积分的方法得出两个级数形式的自感系数表达式,最后对这两个表达式作了简要的分析与比较.     

Analytical Solitary Wave Solutions to a （3＋1）-Dimensional Gross-Pitaevskii Equation with Variable Coefficients

A （3＋1）-dimensional Gross-Pitaevskii （GP） equation with time variable coefficients is considered, and is transformed into a standard nonlinear Schrodinger （NLS） equation. Exact solutions of the （3＋1）D GP equation are constructed via those of the NLS equation. By applying specific time-modulated nonlinearities, dispersions, and potentials, the dynamics of the solutions can be controlled. Solitary and periodic wave solutions with snaking and breathing behavior are reported.     

A unified approach to fuzzy modelling and robust synchronization of different hyperchaotic systems

In this paper, a Takagi Sugeno （T-S） fuzzy model-based method is proposed to deal with the problem of synchronization of two identical or different hyperchaotic systems. The T S fuzzy models with a small number of fuzzy IF-THEN rules are employed to represent many typical hyperchaotic systems exactly. The benefit of employing the T-S fuzzy models lies in mathematical simplicity of analysis. Based on the T-S fuzzy hyperchaotic models, two fuzzy controllers arc designed via parallel distributed compensation （PDC） and exact linearization （EL） techniques to synchronize two identical hyperchaotic systems with uncertain parameters and two different hyperchaotic systems, respectively. The sufficient conditions for the robust synchronization of two identical hyperchaotic systems with uncertain parameters and the asymptotic synchronization of two different hyperchaotic systems are derived by applying the Lyapunov stability theory. This method is a universal one of synchronizing two identical or different hyperchaotic systems. Numerical examples are given to demonstrate the validity of the proposed fuzzy model and hyperchaotic synchronization scheme.     

Systematics on fission fragment mass distribution of neutron induced 235U fission

Based on the neutron induced fission fragment mass distribution data up to neutron energy 20 MeV measured with the double kinetic energy method (KEM) and the radio active method (RAM), the systematics of fission fragment mass distribution was investigated by using 5 Gaussian model and the systematics parameters were obtained by fitting the experimental data. With the systematics, the yields of any mass A and at any energy in the region from 0 to 20 MeV of neutron energy can be calculated. The calculated results could well reproduce the experimental data measured with KEM, but show some systematical deviation from the data measured by RAM, which reflects some systematical deviations between the two kinds of measured data.The error of systematics yield was calculated in an exact error transformation way, including from the error of the experimental yield data to the error of the discrete parameters, then to the systematics parameters,and at last to the yield calculated with systematics.     

The ε c -Product of a Schwartz b-Space by a Quotient Banach Space and Applications

We define the -product of a -space by a quotient Banach space. We give conditions under which this -product will be monic. Finally, we define the _c -product of a Schwartz b-space by a quotient Banach space and we give some examples of applications.     

Strong conjugation actions induced by flags of exact Borel subalgebras

Let A be a quasi-hereditary algebra with a strong exact Borel subalgebra. It is proved that for any standard semisimple subalgebra T there exists an exact Borel subalgebra B of A such that T is a maximal semisimple subalgebra of B. It is shown that the maximal length of flags of exact Borel subalgebras of A is the difference of the radium and the rank of Grothendic group of A plus 2. The number of conjugation-classes of exact Borel subalgebras is 1 if and only if A is basic; the number is 2 if and only if A is semisimple. For all other cases, this number is 0 or no less than 3. Furthermore, it is shown that all the exact Borel subalgebras are idempotent-conjugate to each other, that is, for any exact Borel subalgebras B and C of A, there exists an idempotent e of A, and an invertible element u of A, such that eBe = u^-1eCeu.