Geometric Phase in a Time-Dependent System with Laguerre Polynomial State

By using of the invariant theory, we have studied the geometric phase in a time-dependent system with Laguerre polynomial state, the dynamical and geometric phases are given, respectively. The Aharonov-Anandan phase is also obtained under the cyclical evolution.     

Structure and optical properties of nanostructured zinc oxide films with different growth temperatures

ZnO films were prepared by pulsed laser deposition (PLD) on glass substrate with temperature ranging from room temperature (RT) to 500 °C. All the films formed the hexagonal wurtzite structure and showed the c-axis (0 0 2) preferred orientation. The films deposited at 200 °C showed the narrowest full width at half maximum of both X-ray diffraction (XRD) and rocking curve, largest height grain size, smallest macrostress and least point defects. Meanwhile, it was found that the films deposited at 350 °C displayed the most intense diffraction peak in XRD and a strong UV emission while it showed the most intense defect-related green emission, fastest growth rate and larger macrostress. In addition, the cross section images showed all films grew with a columnar form along (0 0 2) orientation.     

Interactions of solitary waves under the conditions of the (3 + 1)-dimensional Kadomtsev-Petviashvilli equation

Using an extended mapping method with a linear variable separation process, a new family of the exact solutions of the (3 + 1)-dimensional Kadomtsev-Petviashvilli (KP) equation was derived. By applying the solitary wave solutions, this paper studied some newly localized excitations and the interactions of various solitary waves under the conditions of the (3 + 1)-dimensional KP equation.     

Exact solutions and conservation laws of (2 + 1)-dimensional Boiti-Leon-Pempinelli equation

In this paper, we obtain the symmetry group theorem by using the modified CK’s direct method, and some new exact solutions of (2 + 1)-dimensional BLP equation. Also we derive the corresponding Lie algebra and the conservation laws of BLP equation.     

Blow-up of periodic solutions to reducible quasilinear hyperbolic systems

Under general assumption, we prove that the smooth solution to reducible quasilinear hyperbolic system with periodic initial data in general develop singularities in finite time, provided that the total variation on one period of the initial data is small.     

Symmetry reductions and exact solutions to the systems of carbon nanotubes conveying fluid

In this paper, the systems of carbon nanotubes (CNTs) conveying fluid are considered by the combination of Lie symmetry analysis and the dynamical system method. All of the geometric vector fields of the three systems are obtained, then the symmetry reductions and exact solutions to the systems are investigated by the dynamical system and the power series method. Especially, the convergence of the power series solution to the nonlinear system is shown under the condition which is easily satisfied generally.     

The recursion operator method for generalized symmetries and Bäcklund transformations of the Burgers’ equations

In this paper, the generalized symmetries of the second-order Burgers’ equation are obtained through the symmetry transformation method. The Bäcklund transformations (BTs) of the two equations are constructed by the recursion operator method. Then, the infinite number of exact solutions to these equations are investigated in terms of the generalized symmetries and Bäcklund transformations. Furthermore, the Bäcklund transformations and conservation law of the general Burgers’ equations are discussed.     

Low-temperature heat capacities and thermodynamic properties of n-undecylammonium bromide monohydrate C11H28BrNO(s)

Crystal structure of n-undecylammonium bromide monohydrate was determined by X-ray crystallography. Low-temperature heat capacities of the compound were measured by a precision automated adiabatic calorimeter over the temperature range from 78 to 390?K. Two solid–solid phase transitions were observed for the title compound. The temperatures, molar enthalpies, and entropies of the phase transitions were derived based on the analysis of heat–capacity curve. Two polynomial equations of heat capacities as a function of temperature were fitted by least-squares method. Based on the two polynomial equations, smoothed heat capacities and thermodynamic functions of the compound relative to the standard reference temperature 298.15?K were calculated and tabulated at 5 K intervals.     

Effect of concentration of the Er3+ ion on electromagnetically induced transparency in Er3+:YAG crystal

We studied the effect of Er³⁺ concentration on electromagnetically induced transparency in two types of three-level schemes—the ladder and the Λ models in Er³⁺:YAG. The numerical calculations show that, under the same intensities of the probe and the coupling fields, the absorption and the dispersion were dramatically changed with Er³⁺ concentration.     

Development of three novel benzothiazole-based ratiometric fluorescent chemosensor for detecting of hydrazine in serum and gas phase via ESIPT process and different recognition sites

In this article, we have successfully designed and synthesized three novel ratiometric fluorescent probes BTP-LA, BTP-LB and BTP-LN for detection of hydrazine based on benzothiazole-derived fluorophores and different recognition sites. The probes BTP-LA, BTP-LB and BTP-LN displays a good fluorescence ratio emission signals, high selectivity and large emission shifts (>100 nm) toward hydrazine. The three probes BTP-LA, BTP-LB and BTP-LN can be used not only to detect hydrazine in serum, but also to detect gaseous hydrazine in air. More importantly, compared with probes BTP-LB and BTP-LN, BTP-LA has lower saturation concentration (200 µM) and detection limits (1.22 × 10^?7 M) to hydrazine.