Convergence of Riemannian Manifolds and Laplace Operators, II

We study spectral convergence of compact Riemannian manifolds or more generally certain Dirichlet spaces, obtaining some compactness results on harmonic functions and harmonic maps. Mathematics Subject Classifications (2000) 53C21, 58D17, 58J50. Atsushi Kasue: Partly supported by the Grant-in-Aid for Scientific Research (B) No. 15340053 of the Japan Society for the Promotion of Science.     

Fast computation of a rational point of a variety over a finite field

We exhibit a probabilistic algorithm which computes a rational point of an absolutely irreducible variety over a finite field defined by a reduced regular sequence. Its time-space complexity is roughly quadratic in the logarithm of the cardinality of the field and a geometric invariant of the input system. This invariant, called the degree, is bounded by the Bézout number of the system. Our algorithm works for fields of any characteristic, but requires the cardinality of the field to be greater than a quantity which is roughly the fourth power of the degree of the input variety.

     

激光对生物分子的共振激发作用

在生物分子的“谐”和“非谐”振子势模型的基础上，用量子力学讨论了激光对生物分子的共振激作用；并用之对激光的生物激活、诱变机理的“共振吸收”定性理论作一解析分析。     

Percolation in strongly correlated systems: The massless Gaussian field

We derive a number of new results for correlated nearest neighbor site percolation onZ ^d. We show in particular that in three dimensions the strongly correlated massless harmonic crystal, i.e., the Gaussian random field with mean zero and covariance –, has a nontrivial percolation behavior: sites on whichS _x h percolate if and only ifh _c . with0 _c < . This provides the first rigorous example of a percolation transition in a system with infinite susceptibility.     

STRUCTURING ＆ RHEOLOGY OF MOLTEN POLYMER／CLAY NANOCOMPOSITES

The evolution and the origin of “solid-like state” in molten polymer/clay nanocomposites are studied. Using polypropylene/clay hybrid (PPCH) with sufficient maleic anhydride modified PP (PP-MA) as compatibilizer, well exfoliation yet solid-like state was achieved after annealing in molten state. Comprehensive linear viscoelasticity and non-linear rheological behaviors together with WAXD and TEM are studied on PPCH at various dispersion stages focusing on time,temperature and deformation dependencies of the “solid-like” state in molten nanocomposites. Based on these, it is revealed that the solid-structure is developed gradually along with annealing through the stages of inter-layer expansion by PP-MA,the diffusion and association of exfoliated silicate platelets, the formation of band/chain structure and, finally, a percolated clay associated network, which is responsible for the melt rigidity or solid-like state. The network will be broken down by melt frozen/crystallization and weakened at large shear or strong flow and, even more surprisingly, may be disrupted by using trace amount of silane coupling agent which may block the edge interaction of platelets. The solid-like structure causes characteristic non-linear rheological behaviors, e.g. residual stress after step shear, abnormal huge stress overshoots in step flows and, most remarkably, the negative first normal stress functions in steady shear or step flows. The rheological and structural arguments challenge the existing models of strengthened entangled polymer network by tethered polymer chains connecting clay particles or by chains in confined melts or frictional interaction among tactoids. A scheme of percolated networking of associated clay platelets, which may in band form of edge connecting exfoliated platelets, is suggested to explain previous experimental results.     

Crystallization and second harmonic generation in thermally poled niobium borophosphate glasses

Crystallization of glasses with compositions (1−x)(0.95 NaPO₃+0.05 Na₂B₄O₇)+xNb₂O₅, x=0.4, 0.43, 0.45, 0.48 was investigated by differential scanning calorimetry and X-ray powder diffraction. Crystallization of two phases was observed in the glasses with x=0.43-0.48. First phase is a sodium niobate with the structure of tetragonal tungsten bronze () and second phase is Na₄Nb₈P₄O₃₂ (). The crystallization of sodium niobate is correlated with increasing of nonlinear optical efficiency reported for thermally poled glasses with x>0.4. The results of Raman spectroscopy show the formation of three-dimensional (3D) niobium oxide framework in the glasses with increase of niobium concentration. This framework is supposed to have tetragonal tungsten bronze structure and to be responsible for nonlinear optical properties of the glass. Second harmonic generation signals of as prepared and crystallized glass after thermal poling are compared. The nucleation and crystallization do not improve the NLO properties of the glasses under study.     

（H2O）^＋n（n=1,2）的几何结构优化和振动光谱分析

采用Ｈａｒｔｒｅｅ－Ｆｏｃｋ和ＭＰ２方法在多种水平下优化了（Ｈ２Ｏ）＾＋ｎ（ｎ ＝１，２）的几何结构，并进行了振动光谱分析。结果表明：对（Ｈ２Ｏ）＾＋采用ＭＰ２／６－３１１＋＋Ｇ（ｄ，ｐ）可得出最满意的结论。     

Second‐harmonic response of a series of chiral polyesters: A joint experimental and theoretical study

A series of polyesters with π‐conjugated donor–acceptor segments was synthesized by the condensation of azobenzene‐4,4′‐dicarbonylchloride with 1,4:3,6‐dianhydro‐D‐sorbitol ([α] = + 42.5°) and biphenolic chromophores, bis(4‐hydroxyphenylazo)‐2,2′‐dinitrodiphenylmethane and bis(4‐hydroxyphenylazo)‐2,2′‐dinitrodiphenylsulfone. The polymers were characterized by spectral methods (IR, ultraviolet–visible, and NMR), thermal methods (thermogravimetry and differential scanning calorimetry), wide‐angle X‐ray scattering, and polarimetry. The polymers containing isosorbide units were optically active and crystalline. They exhibited glass‐transition temperature values between 100 and 160 °C and were stable up to 400 °C. The second‐harmonic generation (SHG) efficiency of the polymers was experimentally verified by a powder‐reflection technique with 2‐methyl‐4‐nitroaniline as a reference. The SHG efficiencies of the polymers were compared to those of the chromophores and explained as a function of the percentage of chiral composition. The hyperpolarizability β values were also determined by a two‐level model solvatochromic method and computational methods. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 2868–2877, 2002     

Synthesis and Structure of the New Ammonium Indium Phosphate (NH4)In(OH)PO4

A new ammonium indium phosphate (NH₄)In(OH)PO₄ was prepared by hydrothermal reaction in the In₂O₃-NH₄H₂PO₄-NH₃/OH system (T=200°C, autogenous pressure, 7 days). The formula (NH₄)In(OH)PO₄ was determined on the basis of chemical and thermal analysis (TG/DSC), X-ray powder diffraction and IR-spectroscopy. (NH₄)In(OH)PO₄ crystallizes in the tetragonal system with space group P4₃2₁2 (No. 96); a=9.4232(1) Å, c=11.1766(1) Å, V=992.45(2) ų; Z=8. The crystal structure was refined by the Rietveld method (R_w=6.35%, R_p=5.10%). The second-harmonic generation study confirmed that structure of (NH₄)In(OH)PO₄ does not have a center of symmetry. The cis-InO₄(OH)₂ octahedra form helical chains, parallel to the c-axis. The In-O-In bonds are nearly equidistant. The chains are interconnected by phosphate tetrahedra and create tunnels containing the NH₄⁺ ions along the c-axis. (NH₄)In(OH)PO₄ is isostructural with RbIn(OH)PO₄.     

Second-order nonlinear optical properties of side-chain liquid crystalline polymers studied by second harmonic generation from thin films

The two independent elements of the second-order nonlinear optical susceptibility tensor of a range of contact poled, donor–acceptor substitued side-chain polymers are reported. The susceptibilities were measured by second harmonic generation from thin films, typically less than 0.5 μm thick, at a fundamental wavelength of 1064 nm. The largest value was χ = 2.64 pm/V which is three times greater than the χ value of KDP and was measured in a nitrobenzylidene side chain, polyhydroxystyrene polymer with an eleven unit alkyl chain spacer attaching the side group to the backbone. Typical susceptibility values obtained were χ～0.3 pm/V and X⁽²⁾₃₃～1 pm/V. The coherence lengths of the materials, which lay in the range 4–12 μm, were measured at 1064 nm by the maker fringe technique using thick, wedge-shaped samples.