在模情况时二面体群$D_{2p}$作用下的transfer理想

In this paper, we determine the structures of the transfer ideal and its radical ideal for the ring of polynomials F p[x, y] under the action of dihedral group D2 p in the modular case. We mainly use Transfer variety, p order elements, and Hilbert’s Nullstellensatz Theorem.     

Analysis of polar peptides using a silica hydride column and high aqueous content mobile phases

The retention behavior of a set of polar peptides separated on a silica hydride stationary phase was examined with a capillary HPLC system coupled to ESI‐MS detection. The mobile phases consisted of formic acid or acetic acid/acetonitrile/water mixtures with the acetonitrile content ranging from 5 to 80% v/v. The effects on peptide retention of these two acidic buffer additives and their concentrations in the mobile phase were systematically investigated. Strong retention of the peptides on the silica hydride phase was observed with relatively high‐organic low‐aqueous mobile phases (i.e. under aqueous normal‐phase conditions). However, when low concentrations of acetic acid were employed as the buffer additive, strong retention of the peptides was also observed even when high aqueous content mobile phases were employed. This unique feature of the stationary phase therefore provides an opportunity for chromatographic analysis of polar peptides with water‐rich eluents, a feature usually not feasible with traditional RP sorbents, and thus under conditions more compatible with analytical green chemistry criteria. In addition, both isocratic and gradient elution procedures can be employed to optimize peptide separations with excellent reproducibility and resolution under these high aqueous mobile phase conditions with this silica hydride stationary phase.     

Simultaneous separation of hydrophobic and polar bases using a silica hydride stationary phase

In this study, the retention behavior of selected hydrophobic and polar bases on a minimally modified silica hydride phase was investigated. From these results and the associated retention plots, significant differences in the chromatographic dependencies of these two classes of basic compounds were evident. The polar bases exhibited strong retention with mobile phases of high organic solvent content, but displayed weak retention with mobile phases of high water content. In contrast, the hydrophobic bases showed “U‐shape” retention dependencies, indicative of the interplay of both RP and normal‐phase retention characteristics. These studies have demonstrated that hydrophobic and polar bases can be simultaneously separated on the same column either under typical RP‐like or aqueous normal‐phase‐like conditions, respectively, with distinctive selectivity. Finally, the effects of temperature on the RP and aqueous normal phase modality of separations with these analytes were investigated, where discrete changes in retention behavior were also observed.     

Separation of 1,3‐dimethylamylamine and other polar compounds in a dietary supplement formulation using aqueous normal phase chromatography with MS

Five ingredients (caffeine, l ‐arginine, creatine, β‐alanine, and 1,3‐dimethylamylamine) from a workout supplement were separated by HPLC with UV detection and LC–MS using an analytical column based on silica hydride operating in aqueous normal phase mode. While RP methods were observed to be inadequate for the analysis due to low retention, aqueous normal phase chromatography was able to readily retain and resolve the analytes. After method development on the HPLC–UV system, the conditions were successfully transferred to an LC–MS system for analysis. Based on calibration curve data, estimates of 63.5, 380.3, and 13.1 mg/serving (5.50 g) were obtained for creatine, l ‐arginine, and 1,3‐dimethylamylamine, respectively. Standard addition data results were compared to those of the calibration curve study, and the two values differed by less than 1% in the case of creatine. The conditions are suitable for further development as a reliable means of quantitating the analytes in workout supplement formulations.     

Factoriality for the reductive Zassenhaus variety and quantum enveloping algebra

Let U(g)$U(\mathfrak{g})$ be the enveloping algebra of a finite dimensional reductive Lie algebra g$\mathfrak{g}$ over an algebraically closed field of prime characteristic. Let _U?,P(s:)$U_{?,P}(\mathfrak{s}:)$ be the simply connected quantum enveloping algebra at the root of unity ?  , of a complex semi-simple finite dimensional Lie algebra s:$\mathfrak{s}:$. We show, by similar proofs, that the centers of both are factorial. While the first result was established by R. Tange [32] (by different methods), the second one confirms a conjecture in [4]. We also provide a general criterion for the factoriality of the centers of enveloping algebras in prime characteristic.     

条件风险下的两基金分离定理

鉴于条件风险价值CVaR具有风险度量的合理性以及两基金分离定理对证券投资的重要意义,以CVaR作为风险度量研究两基金分离定理.在组合收益率服从正态分布的假设下,分别就投资组合含有或没有无风险资产的情形提出并证明了两基金分离定理;放开方差-协方差矩阵为非奇异这一通常假设,证明了CVaR风险度量下的两基金分离定理依然成立.     

Bifurcation analysis of a diffusive predator–prey system with a herd behavior and quadratic mortality

In this paper, a diffusive predator–prey system, in which the prey species exhibits herd behavior and the predator species with quadratic mortality, has been studied. The stability of positive constant equilibrium, Hopf bifurcations, and diffusion‐driven Turing instability are investigated under the Neumann boundary condition. The explicit condition for the occurrence of the diffusion‐driven Turing instability is derived, which is determined by the relationship of the diffusion rates of two species. The formulas determining the direction and the stability of Hopf bifurcations depending on the parameters of the system are derived. Finally, numerical simulations are carried out to verify and extend the theoretical results and show the existence of spatially homogeneous periodic solutions and nonconstant steady states. Copyright © 2014 John Wiley & Sons, Ltd.     

涉及复代数超曲面的全纯映射正规族

本文研究了涉及固定超曲面的全纯映照的正规性问题。利用Aladro 和Krantz对全纯映射族正规性的刻画和Shirosahi建立的一系列涉及一些特殊复代数超曲面的Picard 型定理,得到了全纯映射族的一些正规定则。