THE GLOBAL THEOREM OF A.N.BERLINSKII

ＳｏｃａｌｔｈｅＢｅｒｌｉｎｓｋｉｔｈｅｏｒｅｍｆｏｒｐｌａｎａｒｑｕａｄｒａｔｉｃＳｙｓｔｅｍ（ＱＳ）ｉｓ：ＴｈｅｏｒｅｍＡ［１］ＳｕｐｐｏｓｅｔｈａｔａＱＳｈａｓ４ｆｉｎｉｔｅｃｒｉｔｉｃａｌｐｏｉｎｔｓ（ＣＰｓ），Ｉｆｔｈｅｑｕａｄｒｉｌａ...     

Weak singularities may help periodic solutions to exist

In a periodically forced semilinear differential equation with a singular nonlinearity, a weak force condition enables the achievement of new existence criteria through a basic application of Schauder's fixed point theorem. The originality of the arguments relies in that, contrary to the customary situation in the available references, a weak singularity facilitates the arguments of the proofs.     

B（X）上保点谱的可加映射和初等算子

记Ｘ为复数域上无限维Ｂａｎａｃｈ空间，Ｈ为无限维复可分Ｈｉｌｅｒｔ空间。本文给出Ｂ（Ｘ）上保持点谱的满射可加射具有的形式，以及Ｂ（Ｈ）上某些初等算子保点谱的充要条件。     

二阶Melnikov函数及其应用

在Ｍｅｌｎｉｋｏｖ函数的种种应用中，目前常见到的仅是一阶形式。本文具体推导了二阶Ｍｅｌｎｉｋｏｖ函数的分析表达，提出了临界情况下考察双曲鞍点的稳定流形与不稳定流形相对位置的二阶判据，并成功地用于环面ｖａｎｄｅｒＰｏｌ方程的研究中。     

THE BLOW-UP PROPERLIES OF SOLUTIONS TO SEMILINEAR HEAT EQUATIONS WITH NEUMANN BOUNDARY CONDITIONS

1IntroductionInthispaper,weconsidertheinitial-boundaryvalueproblem,where"o(x)isnon-negativesmoothfunctionsatisfying"o.(0)=0,"o.(1)=1'Whenconsideringtheblow-upofsolution,thefollowingproblemarisenaturally:Doesblow-upoccur?Howdoesthesolutionapproachtheblow-uptime'!Andwilersisthehotspotlocated(blow-upset)?WelookattheheatequationwithanonlillearboundaryconditiollHerefiisaboundeddomaininR",p>1isarealnumber.IthasbeenknownforalongtimethattheDroblelil(1.1).(1.2)withAL(~,0)--'no(x)doesnothaveaglobals…     

COMPUTATION OF HOPF BRANCHES BIFURCATING FROM A HOPF/PITCHFORK POINT FOR PROBLEMS WITH Z_2-SYMMETRY

1.IntroductionThispaperisdevotedtothecalculatiollofT,ranchesofHopfpointswhichemallatefromacertaillsingularPointofatwopar:lmeterII()nlinearsystemwhereXisarealHillersspac(},Aabifllrcationparallleter,oranadditionalcontrolparameter,alldgisasnlootllmapping.\Nreassllllle(HI)gisA--synlnletric:thereexistsalillearoperators:X-Xsatisfying(I:identicaloperatorillX)Itiswellknottrnthat(1.2)irldllcestilesplittillgl)Th.firstauthorhasbeedsupportedbyar(>searchgralltoftileV'Olkswagen-StiftungWesaythatxiss…     

Statistical mechanics of warm and cold unfolding in proteins

We present a statistical mechanics treatment of the stability of globular proteins which takes explicitly into account the coupling between the protein and water degrees of freedom. This allows us to describe both the cold and the warm unfolding, thus qualitatively reproducing the known thermodynamics of proteins. Received: 19 March 1998 / Revised and Accepted: 25 May 1998     

一种非刚性医学图像点匹配方法

提出了一种非刚性点匹配的算法并把其运用于医学图像配准．该算法采用信号滤波的方法来获得点集间的匹配信息，并运用松弛标记法将各点邻域关系对模糊的匹配信息进行迭代获得明确的匹配关系．在此基础上，利用高斯径向基函数来描述点模式间的弹性形变，在基本的迭代框架下实现问题的求解．实验结果显示在形变程度为5％、出格点比率50％和噪声标准差为5％的情况下该算法的匹配误差能控制在0．13以下，表明了该算法的鲁棒性和有效性，较好地解决了医学非刚性形变的点匹配问题．     

Living anionic polymerization of N‐methoxymethyl‐N‐isopropylacrylamide: Synthesis of well‐defined poly(N‐isopropylacrylamide) having various stereoregularity

Anionic polymerization of N‐methoxymethyl‐N‐isopropylacrylamide ( 1 ) was carried out with 1,1‐diphenyl‐3‐methylpentyllithium and diphenylmethyllithium, ‐potassium, and ‐cesium in THF at ?78 °C for 2 h in the presence of Et₂Zn. The poly( 1 )s were quantitatively obtained and possessed the predicted molecular weights based on the feed molar ratios between monomer to initiators and narrow molecular weight distributions (M_w/M_n = 1.1). The living character of propagating carbanion of poly( 1 ) either at 0 or ?78 °C was confirmed by the quantitative efficiency of the sequential block copolymerization using N,N‐diethylacrylamide as a second monomer. The methoxymethyl group of the resulting poly( 1 ) was completely removed to give a well‐defined poly(N‐isopropylacrylamide), poly(NIPAM), via the acidic hydrolysis. The racemo diad contents in the poly(NIPAM)s could be widely changed from 15 to 83% by choosing the initiator systems for 1 . The poly(NIPAM)s obtained with Li⁺/Et₂Zn initiator system possessed syndiotactic‐rich configurations (r = 75–83%), while either atactic (r = 50%) or isotactic poly(NIPAM) (r = 15–22%) was generated with K⁺/Et₂Zn or Li⁺/LiCl initiator system, respectively. Atactic and syndiotactic poly(NIPAM)s (42 < r < 83%) were water‐soluble, whereas isotactic‐rich one (r < 31%) was insoluble in water. The cloud points of the aqueous solution of poly(NIPAM)s increased from 32 to 37 °C with the r‐contents. These indicated the significant effect of stereoregularity of the poly(NIPAM) on the water‐solubility and the cloud point in water © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 4832–4845, 2006     

Thermodynamic and surface properties of Sb-Sn and In-Sn liquid alloys

The thermodynamic properties of Sb-Sn and In-Sn liquid alloys have been studied using the quasi-chemical model for compound forming binary alloys and that for simple regular alloys. The concentration fluctuation S _cc(0) and the Warren-Cowley short-range order parameter (α ₁) were determined for the whole concentration range at a temperature of 770 K. The surface tensions of these liquid alloys were determined for the whole concentration range by using energetics determined from thermodynamic calculations. In all calculations, In-Sn manifested properties very close to alloys of ideal mixing, while Sb-Sn showed properties that are asymmetric about equiatomic composition. Our results suggest that a weak complex of the form SbSn₂ could be present in the Sb-Sn alloy at a temperature of about 770 K.