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.     

Lemniscates and inequalities for the logarithmic capacities of continua

It is shown that if P(z) = z ⁿ + ? is a polynomial with connected lemniscate E(P) = {z: ¦P(z)¦ ≤ 1} and m critical points, then, for any n? m+1 points on the lemniscate E(P), there exists a continuum γ ? E(P) of logarithmic capacity cap γ ≤ 2^?1/n which contains these points and all zeros and critical points of the polynomial. As corollaries, estimates for continua of minimum capacity containing given points are obtained.     

关于艾森斯坦因判别法的间接应用

探讨了间接应用艾森斯坦因判别法判断整系数多项式在有理数域上不可约的两种途径.     

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。     

Minimum concave cost production system: A further generalization of multi-echelon model

We will consider a concave minimization problem associated with a series production system in which raw material is processed inm consecutive facilities. The products at some facility are either sent to the next facility or stocked in the warehouse. The amount of demand for the final products during periodi, i = 1,,n, are known in advance. Our problem is to minimize the sum of processing, holding and backlogging cost, all of which are assumed to be concave.The origin of this model is the classical economic lot size problem of Wagner and Whitin and was extensively studied by Zangwill. This model is very important from the theoretical as well as practical point of view and this is one of the very rare instances in which polynomial time algorithm has been constructed for concave minimization problems.The purpose of this paper is to extend the model further to the situation in which time lag is associated with processing at each facility. We will propose an efficient O(n ⁴ m) algorithm for this class of problems.     

On the average length of lexicographic paths

A bound is given for the average length of a lexicographic path, a definition that is motivated by degeneracies encountered when using the randomized simplex method.     

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。     

Hosoya polynomials of armchair open‐ended nanotubes

For a connected graph G we denote by d(G,k) the number of vertex pairs at distance k. The Hosoya polynomial of G is H(G,x) = ∑_k≥0 d(G,k)x^k. In this paper, analytical formulae for calculating the polynomials of armchair open‐ended nanotubes are given. Furthermore, the Wiener index, derived from the first derivative of the Hosoya polynomial in x = 1, and the hyper‐Wiener index, from one‐half of the second derivative of the Hosoya polynomial multiplied by x in x = 1, can be calculated. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

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.