Biharmonic hypersurfaces with three distinct principal curvatures in spheres

We obtain a complete classification of proper biharmonic hypersurfaces with at most three distinct principal curvatures in sphere spaces with arbitrary dimension. Precisely, together with known results of Balmu?‐Montaldo‐Oniciuc, we prove that compact orientable proper biharmonic hypersurfaces with at most three distinct principal curvatures in sphere spaces are either the hypersphere or the Clifford hypersurface with and . Moreover, we also show that there does not exist proper biharmonic hypersurface with at most three distinct principal curvatures in hyperbolic spaces .     

Global exixtence and exponential decay estimates for a dampad quasilinear equation

We prove the existence and uniqueness of a global solution of a damped quasilineat hyperbolic equatiion. We apply a method based on a special integral inequality, to show that the solution decays exponentially, and to obtain precise estimates of the constants in estimates.     

Group Entwining Structures and Group Coalgebra Galois Extensions

Abstract

The notions of group coalgebra Galois extension and group entwining structure are defined. It is proved that any group coalgebra Galois extension induces a unique group-entwining map ψ = {ψ_{α, β}}_{α, β∈π} compatible with the right group coaction, generalizing the recent work of Brzeziński and Hajac [Brzeziński, T., Hajac, P. M. (1999). Coalgebra extensions and algebra coextensions of Galois type. Comm. Algebra 27:1347–1368].     

一般矩阵函数的不等式

本文研究一般矩阵函数不等式.运用一般矩阵函数的两个公式和lp-范数的性质,结出了两个矩阵运算的一般矩阵函数不等式.     

关于对数平均的上界和下界

利用广义对数平均，给出了对数平均的上界和下界控制     

非空交定理及其应用

本文得到了广义区间空间中几个参数型非空交定理，并用此结果证明了一些新型极大极小定理，截口定理，重合定理，以及变分不等式解的存在性定理。本文中的结果包含（１，３，５－１２，１４－１６）中相应结果。     

广义笛卡尔积图的连通度

本文定义了图G_1、G_2的广义笛卡尔积图G=G_1∫G_2,并且证明了它们的连通度具有关系k(G)≥k(G_1)+k(G_2)。这一结果是对文[1]中关于G_1与G_2直积的结果的推广。此外,本文还讨论了G=G_1∫G_2的直径及Hamilton性。最后,利用G=G_1∫G_2的结果对循环图的连通度进行了讨论。     

Nuclear dynamics in the vicinity of a crossing seam: Vibrational spectrum of HD2 revisited

So far, most studies of the geometric phase effect have presumed that the phase is path‐independent; hence, one must supply another restriction concerning the boundary condition on the nuclear wave functions when dealing with nonsymmetric isotopomers of X₃ systems. We report calculations of the vibrational spectra of HD₂ using a recently proposed generalized Born–Oppenheimer (GBO) formalism. The calculations demonstrate that there are significant differences between the results calculated from the present GBO method and those based on the preceding presumption. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 83: 279–285, 2001     

Petrographic, chemical and microprobe analysis of an oxidized iron nodule from Dahr Safra, NW Syria: Is it an iron ore, or a meteorite called shale-ball?

The iron nodule DS-S revealed the concentrations of Ni, Co, Ga, Ge, As, Sb, P, S, many trace and rare earth elements, Fe (> 93 wt.%), and 2 wt.% silicates. The plotting of Ga, Ge, Cr, Cu, As, Au, W, and Ir-concentrations vs. Ni/Co in the classes (groups) IIAB, IIIAB, IVA, ungrouped (ung), NBS 809B steel (st), and DS-S, confirmed the meteoritic origin for DS-S. Magnetite-hematite resulted from oxidation during the melting/solidification process of the original meteorite across the atmosphere. The silicates suggested the presence of Ca-rich plagioclase, and traces of opx, cpx, and/or olivine which explained the low concentrations of Ni-Co. The plotting of Ga/Ge vs. Ni/Co; Ni/Co, Ga vs. P; and Ni/Co, Ga/Ge vs. As revealed the affinity of the DS-S nodule with the ungrouped Bellsbank trio. The compositional homogeneity in the DS-S nodule was probably due to O-fugacity. The conformable REE-graphs, for chondrite and DS-S, and the presence of silicates with the same phases suggested a mesosideritic origin for DS-S.