Stabilization to a positive equilibrium for some reaction–diffusion systems

The aim of this paper is to study the asymptotic behavior of solutions for some reaction–diffusion systems in biology. First, we establish a Liouville type theorem for entire solutions of these reaction–diffusion systems. Based on this theorem, we derive the stabilization of the solutions of the reaction–diffusion system to the unique positive constant state, under the condition that this positive constant state is globally stable in the corresponding kinetic systems. Two specific examples about spreading phenomena from ecology and epidemiology are given to illustrate the application of this theory.     

Heteroleptic [Cu(NN)P2]+-type cuprous complexes and their structural modulation on phosphorescent color: Synthesis,structural characterization,properties, and theoretical calculations

Four new heteroleptic [Cu(NN)P₂]⁺-type cuprous complexes— 1 -TPP, 2 -POP, 3 -Xantphos, and 4 -DPPF—were designed and synthesized using a diimine ligand 2-(2′-pyridyl)benzoxazole (2-PBO) and different phosphine ligands (TPP, triphenylphosphine; POP, bis[2-(diphenylphosphino)phenyl]ether; Xantphos, 4,5-bis(diphenylphosphino)-9,9-dimethylxanthene; DPPF, 1,1′-bis(diphenylphosphino)-ferrocene). All complexes were characterized using single-crystal X-ray diffraction, spectroscopic analysis (infrared, UV–Vis.), elemental analysis, and photoluminescence (PL). Single-crystal X-ray diffraction revealed complexes 1 – 4 as isolated cation complex structures with a tetrahedral CuN₂P₂ coordination geometry and diverse P–Cu–P angles. Their UV–Vis. absorption spectra exhibited a blue-shift sequence in wavelength with an enlarged P–Cu–P angle from 4 to 2 then to 3 and then to 1 . The PL emission peaks of 1 – 3 also exhibited a similar blue-shift sequence ( 2 → 3 → 1 ). Their PL lifetime in microseconds (~7.5, 5.1, and 4.7 μs for 1 , 2 , and 3 , respectively) indicated that their PL behavior represents phosphorescence. Time-dependent density functional theory (TD-DFT) calculation and wavefunction analysis revealed that S₁ and T₁ states of 1 – 3 should be assigned as metal–ligand and ligand–ligand charge-transfer (ML + L'L)CT states. Their UV–Vis. absorption and phosphorescence should be attributed to the charge transfer from the P–Cu–P segment to the 2-PBO ligand. Therefore, as the P–Cu–P angle increased (lower HOMO), the energy of S₁ and T₁ states also increased, following the change of PL color.     

Patterning catalyst via inkjet printing to grow single-walled carbon nanotubes

We demonstrated a method to pattern catalyst via inkjet printing to grow SWNTs, using metal salt solutions as the inks and an ordinary office-use printer. We printed water solutions of cobalt acetate on hydrophilic Si substrates and grew high quality SWNT films.     

Convergence to equilibrium states for fluid models of many-server queues with abandonment

Fluid models, in particular their equilibrium states, have become an important tool for the study of many-server queues with general service and patience time distributions. However, it remains an open question whether the solution to a fluid model converges to the equilibrium state and under what condition. We show in this paper that the convergence holds under some conditions. Our method builds on the framework of measure-valued processes, which keeps track of the remaining patience and service times.     

Integral quantizations with two basic examples

The paper concerns integral quantization, a procedure based on operator-valued measure and resolution of the identity. We insist on covariance properties in the important case where group representation theory is involved. We also insist on the inherent probabilistic aspects of this classical–quantum map. The approach includes and generalizes coherent state quantization. Two applications based on group representation are carried out. The first one concerns the Weyl–Heisenberg group and the euclidean plane viewed as the corresponding phase space. We show that a world of quantizations exist, which yield the canonical commutation rule and the usual quantum spectrum of the harmonic oscillator. The second one concerns the affine group of the real line and gives rise to an interesting regularization of the dilation origin in the half-plane viewed as the corresponding phase space.     

光栅衍射实验中测量光栅常数的两种辅助方法

衍射光栅可以将不同波长的光在空间上分离开,在光谱分析领域中有广泛应用.利用光栅的衍射来测量光栅常数是大学物理实验中的一个典型实验,而本文介绍的正是光栅衍射实验中的两个有趣现象:一是旋转光栅时,谱线的偏转角存在一个最小值;二是光栅旋转到一定角度时,衍射光斑会逐渐消失在视野中.论文从理论上分析解释这两种现象,并设计出两种测量光栅常数的方法,在实验上进行验证.与传统的用最小偏转角测光栅常数的方法相比,本文重点分析了由判定最小偏转角位置偏差所带来的影响,并提出了对称旋转测量的方法来进一步减小误差.     

金属Al背电极二维AZO光栅的制备和陷光特性

研究了背电极金属Al膜上二维ZnO:Al光栅的制备及其反射光谱特性.在厚度为300 nm的Al膜上溅射80 nm ZnO:Al薄膜,旋涂AZ5206光刻胶,用波长为325 nm的激光进行光刻制作光栅掩模.采用溶脱-剥离法在Al衬底上制备周期(624~1250 nm)和槽深(100~300 nm)可独立调控的ZnO:Al二维光栅.表面形貌采用原子力显微镜和扫描电镜观察,反射光谱用带积分球的分光光度计测试,双向反射分布函数用散射仪测量.结果表明,300 nm Al膜上织构二维ZnO:Al光栅背电极结构,当光栅槽深为228 nm,周期从624 nm增加到986 nm时,背电极总反射率、漫反射率以及雾度均随光栅周期增大而显著增加,而当周期从986 nm增加到1250 nm时,总反射率、漫反射率以及雾度略有增加.双向反射分布函数测试结果进一步证实了上述实验结果,即随着周期增大,漫反射峰值越大,衍射峰个数也增多.提示背反电极上槽深为228 nm、周期为986 nm的二维ZnO:Al光栅具有较好的散射效果,其中漫反射占总反射的百分比为45%.     

Oscillation and non‐oscillation results for solutions of perturbed half‐linear equations

The purpose of this paper is to describe the oscillatory properties of second‐order Euler‐type half‐linear differential equations with perturbations in both terms. All but one perturbations in each term are considered to be given by finite sums of periodic continuous functions, while coefficients in the last perturbations are considered to be general continuous functions. Since the periodic behavior of the coefficients enables us to solve the oscillation and non‐oscillation of the considered equations, including the so‐called critical case, we determine the oscillatory properties of the equations with the last general perturbations. As the main result, we prove that the studied equations are conditionally oscillatory in the considered very general setting. The novelty of our results is illustrated by many examples, and we give concrete new corollaries as well. Note that the obtained results are new even in the case of linear equations.