Mathematical models of innovation diffusion with stage structure

Mathematical models with stage structures are proposed to describe the process of awareness, evaluation and decision-making. First, a system of ordinary differential equations is presented that incorporates the awareness stage and the decision-making stage. If the adoption rate is bilinear and imitations are dominant, we find a threshold above which innovation diffusion is successful. Further, if the adoption rate has a higher nonlinearity, it is shown that there exist bistable equilibria and a region such that an innovation diffusion is successful inside and is unsuccessful outside. Secondly, a model with a time delay is proposed that includes an evaluation stage of a product. It is proved that the system exhibits stability switches. The bifurcation direction of equilibria is also discussed.     

An Analytic Zariski Structure Over a Field

Following the introduction and preliminary investigations of analytic Zariski structures in Peatfield and Zilber (Ann pure Appl Logic 132:125–180, 2005) an example of an analytic Zariski structure extending an algebraically closed field is provided. The example is constructed using Hrushovski’s method of free amalgamation, and a topology is introduced in which we can verify the analytic Zariski axioms.     

冈村枝管藻孢子体的形态和超微结构

从日本冲绳采回枝管藻，用毛细管将成熟多室孢子囊挑出，在试验室条件下培养，可长成孢子体．用光学显微镜和透射电子显微镜观察发现：孢子释放后形成盘状体附着在基质上，念珠状同化丝从盘状体中间分生．同化丝可从中间部位产生分支，多室孢子囊位于部分同化丝的近端部；同化丝大量产生后基部细胞平行排列，中空，形成假薄壁组织，而后孢子体进入伸长生长阶段；在每个盘状体细胞和同化丝细胞中都有多个色素体和线粒体，蛋白核突出于色素体其他部分，类脂体存在于类囊体中；在同化丝的细胞壁上存在缺口；对同化纤毛而言，色素体和线粒体数量少，紧贴细胞膜，质壁分离严重，在细胞壁上存在“通道”．     

基于几何不变量的蛋白质三维分子结构比对

为了解决蛋白质三维结构比对需要处理大量的旋转、平移变换，直接用动态规划将变得十分繁琐这一问题，在保留蛋白质空间结构属性特征的基础上，对蛋白质三维数据进行了预先的处理．通过计算蛋白质结构在旋转和平移下的几何不变量，将蛋白质的三维结构坐标变换为具有旋转、平移不变性的一维序列．进一步给出了“距离”以及“相似得分”的定义．在此基础上采用动态规划方法给出了新的蛋白质结构比对算法．对专家分类的蛋白质结构数据库进行测试，结果显示准确、快速．     

Poly(L‐lysine) and clay nanocomposite with desired matrix secondary structure: Effects of polypeptide molecular weight

Nanocomposites (NC) were formed using cationic poly(L ‐lysine) (PLL), a semicrystalline polypeptide, that was reinforced by sodium montmorillonite (MMT) clay via solution intercalation technique. By varying solution conditions such as pH, temperature, and polypeptide concentration in the presence of clay platelets, the secondary structure of PLL was controllably altered into α‐helical, β‐sheet, and random coil. The high molecular weight polypeptide shows a strong propensity to fold into the β‐sheet structure when cast as films, irrespective of the initial secondary structure in solution. Nanocomposite local morphology confirms intercalated MMT platelets with PLL over a wide range of compositions. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 239–252, 2007.     

Crystal structure and magnetic properties of two new cobalt selenite halides: Co5(SeO3)4X2 (X=Cl, Br)

Two new isostructural cobalt selenite halides Co₅(SeO₃)₄Cl₂ and Co₅(SeO₃)₄Br₂ have been synthesized. They crystallize in the triclinic system space group P−1 with the following lattice parameters for Co₅(SeO₃)₄Cl₂: a=6.4935(8) Å, b=7.7288(8) Å, c=7.7443(10) Å, α=66.051(11)°, β=73.610(11)°, γ=81.268(9)°, and Z=1. The crystal structures were solved from single-crystal X-ray data, R1=3.73 and 4.03 for Co₅(SeO₃)₄Cl₂ and Co₅(SeO₃)₄Br₂, respectively. The new compounds are isostructural to Ni₅(SeO₃)₄Br₂.Magnetic susceptibility measurements on oriented single-crystalline samples show anisotropic response in a broad temperature range. The anisotropic susceptibility is quantitatively interpreted within the zero-field splitting schemes for Co²⁺ and Ni²⁺ ions. Sharp low-temperature susceptibility features, at T_N=18 and 20 K for Co₅(SeO₃)₄Cl₂ and Co₅(SeO₃)₄Br₂, respectively, are ascribed to antiferromagnetic ordering in a minority magnetic subsystem. In isostructural Ni₅(SeO₃)₄Br₂ magnetically ordered subsystem represents a majority fraction (T_N=46 K). Nevertheless, anisotropic susceptibility of Ni₅(SeO₃)₄Br₂ is dominated at low temperatures by a minority fraction, subject to single-ion anisotropy effects and increasing population of S_z=0 (singlet) ground state of octahedrally coordinated Ni²⁺.     

Comparative analysis of heterogeneous solid and soft materials by adsorption, NMR and thermally stimulated depolarisation current methods

Structural characterisation of such bio-objects as fibrinogen solution, yeast cells, wheat seeds and bone tissues has been done using two versions of cryoporometry based on the integral Gibbs-Thomson (IGT) equation for freezing point depression of pore liquids and the measurements by ¹H NMR spectroscopy (180-200 < T < 273 K) and the thermally stimulated depolarisation current (TSDC) method (90 < T < 273 K) of structured water. The IGT equation was solved using a self-consisting regularization procedure including the maximum entropy principle applied to the distribution function of pore size (PSD). Both methods give clear pictures of changes in the structural characteristics caused, e.g., by hydration and swelling of wheat seeds and yeast cells, coagulation and interaction of fibrinogen with solid nanoparticles in the aqueous media, and the human bone tissue disease.     

Influence of organic modifiers on morphology and crystallization of poly(ϵ‐caprolactone)/synthetic clay intercalated nanocomposites

ε‐caprolactone was polymerized in the presence of neat montmorillonite or organomontmorillonites to obtain a variety of poly(ε‐caprolactone) (PCL)‐based systems loaded with 10 wt % of the silicates. The materials were thoroughly investigated by different X‐ray scattering techniques to determine factors affecting structure of the systems. For one of the nanocomposites it was found that varying the temperature in the range corresponding to crystallization of PCL causes reversible changes in the interlayer distance of the organoclay. Extensive experimental and literature studies on this phenomenon provided clues indicating that this effect might be a result of two‐dimensional ordering of PCL chains inside the galleries of the silicate. Small angle X‐ray scattering and wide angle X‐ray scattering investigation of filaments oriented above melting point of PCL revealed that polymer lamellae were oriented perpendicularly to particles of unmodified silicate, while in PCL/organoclay systems they were found parallel to clay tactoids. Calorimetric and microscopic studies shown that clay particles are effective nucleating agents. In the nanocomposites, PCL crystallized 20‐fold faster than in the neat polymer. The crystallization rate in nanocomposites was also significantly higher than in microcomposite. Further research provided an insight how the presence of the filler affects crystalline fraction and spherulitic structure of the polymer matrix in the investigated systems. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2350–2367, 2007     

A Tin(IV) Porphyrin with Two Axial Organometallic NCN‐Pincer Platinum Units

A tin(IV) porphyrin was combined with two axial NCN‐pincer platinum(II) fragments by utilizing the oxophilicity of the apical positions on the tin atom and the acidic nature of the NCN‐pincer platinum derived benzoic acid. The solid‐state structure determined by X‐ray crystallography revealed some close contacts between the pincer complexes and the meso‐p‐tolyl subsitutents of the porphyrin. It was shown by ¹H NMR spectroscopy that these close contacts were not present in solution and that this compound can potentially act as a novel building block for supramolecular architectures.     

Application of N,N‐bis(diphenylphosphino)aniline palladium(II) complexes as pre‐catalysts in Heck coupling reactions

Palladium(II) complexes with N,N‐bis(diphenylphosphino)aniline ligands catalyse the Heck reaction between styrene and aryl bromides, affording stilbenes in good yield. The structures of two of the complexes used as pre‐catalysts have been determined by single‐crystal X‐ray diffraction. Copyright © 2007 John Wiley & Sons, Ltd.