Bilinear estimates and applications to 2d NLS

The three bilinearities for functions are sharply estimated in function spaces associated to the Schrödinger operator . These bilinear estimates imply local wellposedness results for Schrödinger equations with quadratic nonlinearity. Improved bounds on the growth of spatial Sobolev norms of finite energy global-in-time and blow-up solutions of the cubic nonlinear Schrödinger equation (and certain generalizations) are also obtained.

     

Uniqueness and asymptotic behaviour for solutions of semilinear problems with boundary blow-up

In this paper we prove uniqueness of positive solutions to logistic singular problems , , 1$">, 0$"> in , where the main feature is the fact that . More importantly, we provide exact asymptotic estimates describing, in the form of a two-term expansion, the blow-up rate for the solutions near . This expansion involves both the distance function and the mean curvature of .

     

功率超声对溶液性质的影响

本文研究了在功率超声作用下，电解质溶液，小分子溶液和大分子溶液的粘度，表面张力和电导率等物理化学性质的变化规律。实验结果表明，在超声波作用下，溶液的粘度和表面张力暂时下降，而电导率长期升高。     

Positive Solutions for Semipositone ( p,n − p ) Right Focal Boundary Value Problems

We consider the ( p , n m p ) right focal boundary value problem: $${\matrix{{(- 1)^{n - p} u^{(n)} \! = \lambda \;f(t, u), } \hfill & \ {{\rm for }\ 0 \lt t \lt 1, } \hfill \cr \quad \quad \,{u^{(i)} (0) = 0, } \hfill & {0 \le i \le p - 1, } \hfill \cr \quad \quad \,{u^{(i)} (1) = 0, } \hfill & {p \le i \le n - 1, } \hfill \cr}} $$ where 1 h p h n m 1 is fixed and u > 0. Using a fixed point theorem for operators on a cone, we develop criteria for the existence of positive solutions of the boundary value problem for u on a suitable interval.     

Effect of Fe-doping on the structural,morphological and optical properties of ZnO nanoparticles synthesized by solution combustion process

The effect of Fe-doping on the structural, morphological and optical properties of ZnO nanoparticles synthesized by simple solution combustion process are reported. The powder XRD pattern indicates that the Fe-doped ZnO samples exhibit primary and secondary phases. The primary phase indicates the hexagonal wurtzite structure with the average crystalline size of around 25–50 nm and the secondary phase is associated with the face centered cubic structure of magnetite iron oxide. The elemental composition of pure and Fe-doped samples are evaluvated by EDX. The results of FE-SEM and HR-TEM cleary show that particles morphology have changed with respect to the incorporation of doping agent and particles are in aggregating nature. The vibrational properties of the synthesized ZnO nanoparticles are investigated by Raman scattering technique and it exhibits that the influence of Fe-doping significantly modify the lattice vibrational characteristics in ZnO sites. The optical properties of the Fe-doped ZnO nanoparticles are carried out by UV–vis absorption and PL spectra. The results of PL spectra show the near-band edge related emission as well as strong blue emissions in the Fe-doped ZnO nanoparticles.     

Some Notes on Reaction Diffusion Systems with Nonlinear Boundary Conditions

This paper deals with the existence and nonexistence of global positive solution to a semilinear reaction-diffusion system with nonlinear boundary conditions.For the heat diffusion case,the necessary and sufficient conditions on the global existence of all positive solutions are obtained.For the general fast diffusion case,we get some conditions on the global existence and nonexistence of positive solutions.The results of this paper fill the some gaps which were left in this field.     

一类广义Lanchester模型的数值解及若干结论

本讨论了一类广义的Lanchester模型在一些限制条件下的近似解，并给出了若干结论。     

A Stress Stability Behavior and Development of an LC Assay Method for Anastrozole

This present work narrates the stress stability behavior and development of a liquid chromatographic method for the quantitative determination of anastrozole. Anastrozole is appropriately used when using substantial amounts of aromatizing steroids, or when one is prone to gynecomastia and using moderate amounts of such steroids. A chromatographic separation was achieved on a Hichrom RPB18 (250 × 4.6 mm, 5 μ) column using water and mixture of acetonitrile and methanol (1:1 ratio) as mobile phase. Forced degradation studies were performed on bulk samples of anastrozole using acid, base, hydrogen peroxide, heat and UV light. Degradation of the drug substance was observed in base hydrolysis. Degradation product formed under base hydrolysis was found to be Imp-C. The sample solution and mobile phase were found to be stable up to 48 h. The developed method was validated with respect to linearity, accuracy, precision, robustness and forced degradation studies prove the stability indicating power of the method.