一类泛函微分方程周期解的存在性与应用

本文给出了一类滞后型泛函微分方程有一个周期解的四个充分性定理，其结果明显地优于著名的Ｙｏｓｈｉｚａｗａ周期解定理，最后给出了应用实例。     

θ*r,s,t-图与唯一2-列表染色图的特征化

如果一个图G存在一个k-列表安排使得G具有一个唯一列表染色,则称 G是唯一列表可染色图,简称UkLC图．我们称图G具有M(k)性质当且仅当G不 是UkLC图．本文在借鉴θr,s,t-图概念的基础上引入θr,s,t-图的定义,并证明:除了 r=s=t=2以外,θr,s,t-图都是U2LC图．利用如上结果我们给出M．Mahdian and E．S．Mahmoodian对U2LC图所作特征化的一个简单证明．     

Synthesis of optically active poly(N‐propargylsulfamides) with helical conformation

A novel chiral N‐propargylsulfamide monomer ( 1a ) and its enantiomer ( 1b ) were synthesized and polymerized with (nbd)Rh⁺B^?(C₆H₅)₄ as a catalyst providing poly(1) (poly( 1a ) and poly( 1b )) in high yields (≥99%). Poly(1) could take stable helices in less polar solvents (chloroform and THF), demonstrated by strong circular dichroism signals and UV–vis absorption peaks at about 415 nm and the large specific rotations; but in more polar solvents including DMF and DMSO, poly(1) failed to form helix. Quantitative evaluation with anisotropy factor showed that the helical screw sense had a relatively high thermal stability. These results together with the IR spectra measured in solvents showed that hydrogen bonding between the neighboring sulfamide groups is one of the main driving forces for poly(1) to adopt stable helices. In addition, copolymerization of monomer 1a and monomer 2 was conducted, the solubility of poly(1) was improved drastically. However, the copolymerization had adverse effects on the formation of stable helices in the copolymers. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 500–508, 2007     

Cluster and periodic DFT calculations of adsorption and activation of CO2 on the Cu(hkl) surfaces

The adsorption behavior and thermal activation of carbon dioxide on the Cu(1 1 1), Cu(1 0 0), and Cu(1 1 0) surfaces have been investigated by means of density functional theory calculations and cluster models and periodic slabs. According to the cluster models, the optimized results indicate that the basis set of C and O atoms has a distinct effect on the adsorption energy, but an indistinct one on the equilibrium geometry. For the CO₂/Cu(hkl) adsorption systems studied here, the final structure of adsorbed CO₂ is near linear and the preferred modes for the adsorption of CO₂ onto the Cu(1 1 1), Cu(1 0 0), and Cu(1 1 0) surfaces are the side-on adsorption at the cross bridge site with an adsorption energy of 13.06 kJ/mol, the side-on adsorption at the short bridge site (13.54 kJ/mol), and the end-on adsorption on the on-top site with C–O bonds located along the short bridge site (26.01 kJ/mol), respectively. However, the calculated adsorption energies from periodic slabs are lower as compared to the experimental data as well as the cluster model data, indicating that the periodic slab approach of generalized gradient approximation in the density function theory may be not suitable to obtain quantitative information on the interaction of CO₂ with Cu(hkl) surfaces.     

关于李萨如图形讨论的小结

对《大学物理》和其它一些刊物上多年来关于李萨如图形的讨论作了归纳和分析。     

A study of electrostatic spring softening for dual-axis micromirror

Electrostatic spring softening is an important characteristic of electrostatically actuated dual-axis micromirror, since it lowers the resonant frequencies. This paper presents an approach based on approximating the electrostatic forces by the first-order Taylor's series expansion to investigate this characteristic. The dual-axis micromirror studied in this paper has three motion modes, two torsional (about x- and y-axis, respectively) and one translational (about z-axis). The stiffnesses of all these modes are softened by a DC bias voltage applied to the mirror plate. The resonant frequencies are lowered with the increment of the bias voltage. The relationship of the bias voltage and the resonant frequencies of all the motion modes is derived. The analytical results show that the resonant frequency curves are affected by the capacitor geometries, i.e. the gap between the mirror plate and the electrodes and the electrodes size. The lowering curves drop slowly when the bias voltage is small. While for large bias voltage, the lowering curves drop rapidly. The experiment results are consistent with those obtained by the analytical approach.     

Synthesis and application as polymer electrolyte of hyperbranched polyether made by cationic ring‐opening polymerization of 3‐{2‐[2‐(2‐hydroxyethoxy)ethoxy]ethoxymethyl}‐3′‐methyl‐oxetane

A novel cyclic ether monomer 3‐{2‐[2‐(2‐hydroxyethoxy)ethoxy]ethoxy‐methyl}‐3′‐methyloxetane (HEMO) was prepared from the reaction of 3‐hydroxymethyl‐3′‐methyloxetane tosylate with triethylene glycol. The corresponding hyperbranched polyether (PHEMO) was synthesized using BF₃·Et₂O as initiator through cationic ring‐opening polymerization. The evidence from ¹H and ¹³C NMR analyses revealed that the hyperbranched structure is constructed by the competition between two chain propagation mechanisms, i.e. active chain end and activated monomer mechanism. The terminal structure of PHEMO with a cyclic fragment was definitely detected by MALDI‐TOF measurement. A DSC test implied that the resulting polyether has excellent segment motion performance potentially beneficial for the ion transport of polymer electrolytes. Moreover, a TGA assay showed that this hyperbranched polymer possesses high thermostability as compared to its liquid counterpart. The ion conductivity was measured to reach 5.6 × 10^?5 S/cm at room temperature and 6.3 × 10^?4 S/cm at 80 °C after doped with LiTFSI at a ratio of Li:O = 0.05, presenting the promise to meet the practical requirement of lithium ion batteries for polymer electrolytes. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 3650–3665, 2006     

Double‐hydrophilic block copolymer for encapsulation and two‐way pH change‐induced release of metalloporphyrins

A double hydrophilic block copolymer composed of poly(acrylic acid) (PAA) and poly(4‐vinyl pyridine) (P4VP) was obtained through hydrolysis of diblock copolymer of poly(tert‐butyl acrylate) (PtBA) and P4VP synthesized using atom transfer radical polymerization. Water‐soluble micelles with PAA core and P4VP corona were observed at low (acidic) pH, while micelles with P4VP core and PAA corona were formed at high (basic) pH. Two metalloporphyrins, zinc tetraphenylporphyrin (ZnTPP) and cobalt tetraphenylporphyrin (CoTPP), were used as model compounds to investigate the encapsulation of hydrophobic molecules by both types of micelles. UV–vis spectroscopic measurements indicate that micelles with P4VP core are able to entrap more ZnTPP and CoTPP as a result of the axial coordination between the transition metals and the pyridine groups. The study found that metalloporphyrins encapsulated by the micelles with PAA core could be released on pH increase, while those entrapped by the micelles with P4VP core could be released on pH decrease. This behavior originates from the two‐way pH change‐induced disruption of PAA‐b‐P4VP micelles. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 1734–1744, 2006