The spectrum of the Schrödinger operator with a rapidly oscillating compactly supported potential

We study the effect of an eigenvalue appearing from the boundary of the essential spectrum of the Schrödinger operator perturbed by a rapidly oscillating compactly supported potential. We prove sufficient conditions for the existence and absence of such an eigenvalue and obtain the first few terms of its asymptotic expansion for the case where this eigenvalue exists.     

Sensing and fluorescence behaviors of complex formation between new lariat crown ethers bearing fluorescence sidearm and metal ions in methanol solution

Fluorescence spectroscopic properties of the complex formation between six new C-pivot16-crown-5 ethers bearing fluorescence side arms and metal ions are studied. Six new C-pivot 16-crown-5 ethers that carry fluorescence side arms were synthesized. The research also included the examination of different fluorescent behavior of the new lariat ethers in the presence of silver and sodium ions (Ag⁺ and Na⁺) in methanol. Because of the good fit of the cavity size of these 16-crown-5 ethers with the Ag⁺ and Na⁺ ions, remarkable change in fluorescent spectra were observed. The results showed that the new lariat crown ethers exhibited enhanced selectivity towards sodium ion, but silver ion show quenching abilities towards the ligands. Cooperative participations of the C-pivot side arm oxygen with the ring oxygen molecules in complexation was also confirmed by the single crystal X-ray crystallography of the complex, (C₂₇H₃₀O₇)·NaClO₄. The freezing of crown ring conformation and the diminishment of the chance of sidearm oscillation that occurred upon complexation with sodium ion are the main causes of fluorescent enhancement. The quenching caused by the addition of silver ion was found to explainable by the photo-induced electron transfer that results in the reduction of silver ions.     

使用超声研究关节软骨的深度依赖瞬态膨胀行为

关节软骨是覆盖关节表面的一层承载生物重量的组织，关节软骨在正常状态下，软骨蛋白多糖的弹性和胶原纤维的张力保持平衡。这种平衡的微小变化会引起关节软骨的退化。量化关节软骨，特别是在表层区域的膨胀影响，可以表征骨关节炎的退化变化。本文的主要目的是使用一种新的实时超声膨胀测量系统来研究在改变浸泡关节软骨的盐水浓度，以及改用胰岛素溶液时的关节软骨的深度依赖瞬态膨胀行为。     

经济学视野下的经济违法行为成因探析

从经济学的成本收益角度分析了经济违法行为存在的经济根源，在对违法成本和违法收益比较分析的基础上分析了影响经济违法行为的诸因素，并提出了相应的对策。     

An exact estimate of the boundary behavior of functions from hardy-sobolev classes in the critical case

In the critical case αp=n functions from the Hardy-Sobolev spacesH _α ^p (B ⁿ ) have a limit almost everywhere on the boundary along certain regions of exponential contact with the boundary. It is proved in the paper that the maximal operator associated with these regions is bounded as an operator fromH _α ^p (B ⁿ ) toL ^p (ϖB ⁿ ). Translated fromMatematicheskie Zametki, Vol. 62, No. 4, pp. 527–539, October, 1997. Translated by N. K. Kulman     

一个非线性规划问题的注记

给出了不可行稳定点的充要条件及不可行稳定点与Ｆｒｉｔｚ Ｊｏｈｎ稳定点之间的关系，还给出了奇民稳定点的必要条件。     

Global qualitative analysis of coupled three-level food chains

A coupled model for three-level food chain is considered, the coupling rule is discretized Laplacian diffusion type. The focus of this paper is on the global behavior of solutions. We will show that the differences of the same level population density approach zero as t→∞, provided that the coupling strength is sufficiently large.     

Thermal and X‐ray analysis of polymorphic crystals,melting, and crystalline transformation in poly(butylene adipate)

Polymorphic crystals and complex multiple melting behavior in an aliphatic biodegradable polyester, poly(butylene adipate) (PBA), were thoroughly examined by wide‐angle X‐ray diffraction (WAXD) and differential scanning calorimetry (DSC). Further clarification on mechanisms of multiple melting peaks related to polymorphic crystal forms in PBA was attempted. More stable α‐form crystal is normally favored for crystallization from melt at higher temperatures (31–35 °C), or upon slow cooling from the melt; while the β‐form is the favored species for crystallization at low temperatures (25–28 °C). We further proved that PBA crystallization could also result in all α‐form even at low temperatures (25–28 °C) if it crystallized with the presence of prior α‐form nuclei. PBA packed with both crystal forms could display as many as four melting peaks (P1 ? P4, in ascending temperature order). However, PBA initially containing only the α‐crystal exhibited dual melting peaks of P1 and P3, which are attributed to dual lamellar distributions of the α‐crystal. By contrast, PBA initially containing only the β‐crystal could also exhibit dual melting peaks (P2 and P4) upon scanning. While P2 is clearly associated with melting of the initial β‐crystal, the fourth melting peak (P4), appearing rather broad, was determined to be associated with superimposed thermal events of crystal transformation from β‐ to α‐crystal and final re‐melting of the new re‐organized α‐crystal. Crystal transformation from one to the other or vice versa, lamellae thickening, annealing at molten state, and influence on crystal polymorphism in PBA were analyzed. Relationships and mechanisms of dual peaks for isolate α‐ or β‐crystals in PBA are discussed. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 1662–1672, 2005     

随机环境中强下临界分枝过程中的极限定理

通过对随机环境中伴有独立同分布的繁衍概率母函数序列分枝过程分析,求得过程在可积的假设下,其存活概率确切的渐近行为,而且证明了在Zn＞0的条件下,Zn有非退化的极限分布.     

Large-time Behavior of Solutions to the Stokes Approximation Equations for Two Dimensional Compressible Flows

In this paper, we study the large time asymptotic behavior of solutions to both the Cauchy problem and the exterior problem of the Stokes approximation equations of two dimensional compressible flows.