Normal Bundles to Laufer Rational Curves in Local Calabi–Yau Threefolds

We prove a conjecture by F. Ferrari. Let X be the total space of a nonlinear deformation of a rank two holomorphic vector bundle on a smooth rational curve, such that X has trivial canonical bundle and has sections. Then the normal bundle to such sections is computed in terms of the rank of the Hessian of a suitably defined superpotential at its critical points.     

Algorithms for finding connected separators between antipodal points

A set (or a collection of sets) contained in the Euclidean space Rm is symmetric if it is invariant under the antipodal map. Given a symmetric unicoherent polyhedron X (like an n-dimensional cube or a sphere) and an odd real function f defined on vertices of a certain symmetric triangulation of X, we algorithmically construct a connected symmetric separator of X by choosing a subcollection of the triangulation. Each element of the subcollection contains the vertices v and u such that f(v)f(u)?0.     

第I种非对称三态叠加多模叠加态光场的高次和压缩——第一正交分量的N次方H压缩效应

构造了第孙中禹种强度不等的非对称三态叠加多模叠加态光场|ψ₁^(ABC)〉_q.利用多模压缩态理论研究了态|ψ₁^(ABC)〉_q第一正交分量高次和压缩.结果发现:①当构成态|ψ₁^(ABC)〉_q的三个多模相干态光场的强度不相等时,在一定条件下,态|ψ₁^(ABC)〉_q的第一正交分量可出现任意幂次的高次和压缩.②当上述的三个多模相干态光场强度相等时,态|ψ₁^(ABC)〉_q的第一正交分量的高次和压缩现象消失.在这种情况下,态|ψ₁^(ABC)〉_q的第一正交分量恒处于NH最小测不准态.     

Combinatorial Lie bialgebras of curves on surfaces

Goldman (Invent. Math. 85(2) (1986) 263) and Turaev (Ann. Sci. Ecole Norm. Sup. (4) 24 (6) (1991) 635) found a Lie bialgebra structure on the vector space generated by non-trivial free homotopy classes of curves on a surface. When the surface has non-empty boundary, this vector space has a basis of cyclic reduced words in the generators of the fundamental group and their inverses. We give a combinatorial algorithm to compute this Lie bialgebra on this vector space of cyclic words. Using this presentation, we prove a variant of Goldman's result relating the bracket to disjointness of curve representatives when one of the classes is simple. We exhibit some examples we found by programming the algorithm which answer negatively Turaev's question about the characterization of simple curves in terms of the cobracket. Further computations suggest an alternative characterization of simple curves in terms of the bracket of a curve and its inverse. Turaev's question is still open in genus zero.     

Likelihood and conditional likelihood inference for generalized additive mixed models for clustered data

Lin and Zhang (J. Roy. Statist. Soc. Ser. B 61 (1999) 381) proposed the generalized additive mixed model (GAMM) as a framework for analysis of correlated data, where normally distributed random effects are used to account for correlation in the data, and proposed to use double penalized quasi-likelihood (DPQL) to estimate the nonparametric functions in the model and marginal likelihood to estimate the smoothing parameters and variance components simultaneously. However, the normal distributional assumption for the random effects may not be realistic in many applications, and it is unclear how violation of this assumption affects ensuing inferences for GAMMs. For a particular class of GAMMs, we propose a conditional estimation procedure built on a conditional likelihood for the response given a sufficient statistic for the random effect, treating the random effect as a nuisance parameter, which thus should be robust to its distribution. In extensive simulation studies, we assess performance of this estimator under a range of conditions and use it as a basis for comparison to DPQL to evaluate the impact of violation of the normality assumption. The procedure is illustrated with application to data from the Multicenter AIDS Cohort Study (MACS).     

Infrared absorption and reflectivity of double perovskite Sr2FeWO6

In this work we present temperature dependent infrared reflectivity and absorption of Sr₂FeWO₆ between 700 and 17 K measured from 40 to 10000 cm⁻¹. The reflectivity spectra show well defined phonon bands peaking at 143, 227, 377 and 625 cm⁻¹ assigned to overlapping vibrational modes split from those active in cubic perovskite. We have also verified that this compound is structurally stable in the whole temperature range and that its optical gap at ∼750 cm⁻¹ (95 meV) undergoes only a minor high temperature decrease ascribed to new thermally accessible levels.     

F-H实验仪与光栅光谱仪连用观测253.7nm谱线

通过F-H实验仪和光栅光谱仪的连用，可实时观测汞原子从6s6s1So态激发到6s6sSP1态，退激时，辐射出能量为4．9eV的光量子，其波长为253．7nm．     

增长曲线模型中回归系数的广义根方估计

本文对增长曲线模型中的回归系数B提出了一种新的估计形式－广义根方估计的B（K），其中K＝diag(k1,k2,…，kp）并证明了通过广义根方偏参数ki(i=1,2,…，p）的适当选取可使得该估计在均方误差矩阵的意义下优于已有的LS估计和根方估计，及广义根方估计是可容许估计，本文还给出了选取广义根方偏参数的两种方法，算法及一个应用实例。     

甚高频等离子体增强化学气相沉积法沉积μc-Si∶H薄膜中氧污染的初步研究

对不同的本底真空条件下,采用甚高频等离子体增强化学气相沉积技术沉积的氢化微晶硅（μc_Si∶H）薄膜中的氧污染问题进行了比较研究.对不同氧污染条件下制备的薄膜样品的x射线光电子能谱与傅里叶变换红外吸收光谱测量结果表明：μc_Si∶H薄膜中,氧以Si—O，O—O和O—H三种不同的键合模式存在,不同的键合模式源自不同的物理机理.μc_Si∶H薄膜的Raman光谱、电导率与激活能的测量结果进一步显示：沉积过程中氧污染程度的不同,对μc_Si∶H薄膜的结构特性与电学特性产生显著影响；而不同氧污染对μc_Si∶H薄膜电学特性的影响不同于氢化非晶硅（a_Si:H）薄膜. 关键词： 氢化微晶硅薄膜 甚高频等离子体增强化学气相沉积 氧污染     

Inner Radius of Univalence for a Strongly Starlike Domain

 The inner radius of univalence of a domain D with Poincaré density ρ _D is the possible largest number σ such that the condition ∥ S _f ∥ _D  = sup _{w∈ D} ρ _D (w) ⁻²∥ S _f (z) ∥ ≤ σ implies univalence of f for a nonconstant meromorphic function f on D, where S _f is the Schwarzian derivative of f. In this note, we give a lower bound of the inner radius of univalence for strongly starlike domains of order α in terms of the order α. The author was partially supported by the Ministry of Education, Grant-in-Aid for Encouragement of Young Scientists, 11740088. A part of this work was carried out during his visit to the University of Helsinki under the exchange programme of scientists between the Academy of Finland and the JSPS. Received November 26, 2001; in revised form September 24, 2002 Published online May 9, 2003