On the Behaviour of Solutions of a Class of Third Order Difference Equations

In this paper, the structure of the solution space of y n +3 + ry n +2 + qy n +1 + py n =0, n S 0, is studied, keeping oscillatory/nonoscillatory behaviour of solutions of the equation in view, where p , q and r are constants. Some of these results are generalized partially to hold for y n +3 + r n y n +2 + q n y n +1 + p n y n =0, n S 0, where { p n }, { q n } and { r n } are sequences of real numbers.     

Global periodicity and complete integrability of discrete dynamical systems

Consider the discrete dynamical system generated by a map F. It is said that it is globally periodic if there exists a natural number p such that F ^p (x)=x for all x in the phase space. On the other hand, it is called completely integrable if it has as many functionally independent first integrals as the dimension of the phase space. In this paper, we relate both concepts. We also give a large list of globally periodic dynamical systems together with a complete set of their first integrals, emphasizing the ones coming from difference equations.     

A generalization of Baer’s Lemma

There is a classical result known as Baer’s Lemma that states that an R-module E is injective if it is injective for R. This means that if a map from a submodule of R, that is, from a left ideal L of R to E can always be extended to R, then a map to E from a submodule A of any R-module B can be extended to B; in other words, E is injective. In this paper, we generalize this result to the category q _ω consisting of the representations of an infinite line quiver. This generalization of Baer’s Lemma is useful in proving that torsion free covers exist for q _ω.      

金银三层纳米管局域表面等离激元共振特性研究

相对于单一金属纳米材料,二金属复合纳米材料具有更大的潜在应用价值.基于时域有限差分方法,研究了SiO₂-Ag-Au和SiO₂-Au-Ag二金属三层纳米管的消光光谱,并对其局域表面等离激元共振(Localized Surface Plasmon Resonance,LSPR)特性进行了分析.研究发现,内核尺寸变大将导致上述两种金属纳米管LSPR峰红移;内层金属及外层金属壳层厚度增大均会导致其LSPR峰蓝移.银壳厚度变化对纳米管LSPR的调制作用大于金壳厚度变化造成的影响.上述现象可以利用等离激元杂化理论及自由电子和振荡电子变化的竞争机制进行分析.     

Monitoring Photoinduced Interparticle Chemical Communication In Situ

Monitoring interparticle chemical communication plays a critical role in the nanomaterial synthesis as this communication controls the final structure and stability of global nanoparticles (NPs). Yet most ensemble analytical techniques, which could only reveal average macroscopic information, are unable to elucidate NP-to-NP interactions. Herein, we employ stochastic collision electrochemistry to track the morphology transformation of Ag NPs in photochemical process at the single NP level. By further statistical analysis of time-resolved current transients, we quantitatively determine the dynamic chemical potential difference and interparticle communication between populations of large and small Ag NPs. The high sensitivity of stochastic collision electrochemistry enables the in situ investigation of chemical communication-dependent transformation kinetics of NPs in photochemical process, shedding light on designing nanomaterials.     

Effect of CyDye minimum labeling in differential gel electrophoresis on the reliability of protein identification

Differential 2-DE (DIGE) is a widely applied tool for the quantitative analysis of differentially represented proteins. The method involves covalent minimal labeling of proteins prior to their electrophoretic separation using CyDye DIGE Fluor minimal dyes. This methodology creates two different species per protein, the labeled (approx. 1-2%) and unlabeled (approx. 98-99%) ones, which differ in their molecular masses by 434-464 Da, depending on the attached dye. DIGE followed by automated spot picking according to the CyDye coordinates misses in many instances the exact positions where the maximum amounts of the considered proteins are located. This fact leads to a loss in sensitivity of the subsequent MALDI-MS analyses and results in a reduced reliability of protein identification and sequence coverage. In this paper, the migration differences of labeled and unlabeled species are quantified together with the impact of this effect on the certainty of protein identification and sequence coverage investigating proteins up to 90 kDa.