Iterative solutions to coupled Sylvester-transpose matrix equations

This note studies the iterative solutions to the coupled Sylvester-transpose matrix equation with a unique solution. By using the hierarchical identification principle, an iterative algorithm is presented for solving this class of coupled matrix equations. It is proved that the iterative solution consistently converges to the exact solution for any initial values. Meanwhile, sufficient conditions are derived to guarantee that the iterative solutions given by the proposed algorithm converge to the exact solution for any initial matrices. Finally, a numerical example is given to illustrate the efficiency of the proposed approach.     

大学物理中几个常见超越方程解的渐近表示

简要介绍了布尔曼一拉格朗日级数,并推出了几个常见超越方程的解的渐近表示.     

Re-entrant Photoinduced Morphological Transformation and Temperature-Dependent Kinetic Products of a Rectangular Amphiphilic Diarylethene Assembly

An amphiphilic rectangular-shaped photochromic diarylethene bearing two hydrophobic alkyl chains and two hydrophilic tri(ethylene glycol) chains was synthesized, and its photoinduced morphological transformation in water was investigated. Two unexpected phenomena were revealed in the course of the experiments: a re-entrant photoinduced macroscopic morphological transformation and temperature-dependent kinetic products of supramolecular assembly. When the pure closed-ring isomer was dispersed in water, a re-entrant photoinduced morphological transformation, that is, a photoinduced transition from the hydrated phase to the dehydrated phase and then back to the hydrated phase, was observed by optical microscopy upon irradiation with green light at 20 °C; this was interpreted by the V-shaped phase diagram of the LCST transition. The aqueous assembly of the pure closed-ring isomer was controlled by changing the temperature; specifically, rapid cooling to 15 and 5 °C gave J and H aggregates, respectively, as the kinetic products. The thermodynamic product at both temperatures was a mixture of mostly H aggregate with a small amount of J aggregate. This behavior was rationalized by the temperature-dependent potential energy surface of the supramolecular assembly.     

On the long-time limit of the Garvin–Alterman–Loewenthal solution for a buried blast load

The Garvin–Alterman–Loewenthal solution refers to the problem of a line blast load suddenly applied in the interior of an elastic half-space. It is expected that the long-time asymptotic limit of this solution should be equal to the solution of a related static problem. This expectation is justified here. First, the solution of the static problem is constructed. Then, the asymptotic limit of the transient problem is found, correcting previously published results.     

Thermophysical effects of carbon nanotubes on MHD flow over a stretching surface

This article is intended for investigating the effects of magnetohydrodynamics (MHD) and volume fraction of carbon nanotubes (CNTs) on the flow and heat transfer in two lateral directions over a stretching sheet. For this purpose, three types of base fluids specifically water, ethylene glycol and engine oil with single and multi-walled carbon nanotubes are used in the analysis. The convective boundary condition in the presence of CNTs is presented first time and not been explored so far. The transformed nonlinear differential equations are solved by the Runge–Kutta–Fehlberg method with a shooting technique. The dimensionless velocity and shear stress are obtained in both directions. The dimensionless heat transfer is determined on the surface. Three different models of thermal conductivity are comparable for both CNTs and it is found that the Xue [1] model gives the best approach to guess the superb thermal conductivity in comparison with the Maxwell [2] and Hamilton and Crosser [3] models. And finally, another finding suggests the engine oil provides the highest skin friction and heat transfer rates.     

Difficulties in the growth and characterization of non-linear optical materials: A case study of salts of amino acids

In the crystallographic literature, there is an ever-increasing number of publications on crystals that are referred to as ‘new non-linear optical materials’, many of them reporting salts of amino acids. However, the term NLO material is used improperly in most cases. In fact, the establishment of any crystal species as such a material requires several experimental and computational procedures, which are seldom satisfied when characterizing a supposedly new species. Here, some frequent hazards and problems are addressed and observations of papers reporting amino acid compounds as supposedly new NLO materials are made.     

具有非局部时滞的扩散Nicholson苍蝇方程的波前解

研究了具有非局部时滞的扩散Nicholson苍蝇方程,其中时滞由一个定义在所有过去时间和整个一维空间区域上的积分卷积表示.当时滞核是强生成核时,根据线性链式技巧和几何奇异扰动理论,获得了小时滞时波前解的存在性.     

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.