Absolute Lax 2-categories

We have introduced, in a previous paper, the fundamental lax 2-category of a ‘directed space’ . Here we show that, when has a -topology, this structure can be embedded into a larger one, with the same objects (the points of ), the same arrows (the directed paths) and the same cells (based on directed homotopies of paths), but a larger system of comparison cells. The new comparison cells are absolute, in the sense that they only depend on the arrows themselves rather than on their syntactic expression, as in the usual settings of lax or weak structures. It follows that, in the original structure, all the diagrams of comparison cells commute, even if not constructed in a natural way and even if the composed cells need not stay within the old system.Work supported by MIUR Research Projects.     

Surplus analysis for a class of Coxian interclaim time distributions with applications to mixed Erlang claim amounts

Gerber-Shiu analysis with the generalized penalty function proposed by Cheung et al. (in press-a) is considered in the Sparre Andersen risk model with a K_n family distribution for the interclaim time. A defective renewal equation and its solution for the present Gerber-Shiu function are derived, and their forms are natural for analysis which jointly involves the time of ruin and the surplus immediately prior to ruin. The results are then used to find explicit expressions for various defective joint and marginal densities, including those involving the claim causing ruin and the last interclaim time before ruin. The case with mixed Erlang claim amounts is considered in some detail.     

Intermittency for stochastic partial differential equations driven by strongly inhomogeneous space–time white noises

In this paper, the main topic is to investigate the intermittent property of the one-dimensional stochastic heat equation driven by an inhomogeneous Brownian sheet, which is a noise deduced from the study of the catalytic super-Brownian motion. Under some proper conditions on the catalytic measure of the inhomogeneous Brownian sheet, we show that the solution is weakly full intermittent based on the estimates of moments of the solution. In particular, it is proved that the second moment of the solution grows at the exponential rate. The novelty is that the catalytic measure relative to the inhomogeneous noise is not required to be absolutely continuous with respect to the Lebesgue measure on $\mathbb{R}$.     

Jumping Platonic Solids on a Vibrating Plate

The mechanical excitation of solid bodies by a vibrating plate is not only an interesting fundamental problem, but also has relevance in many mechanical systems, for example, in the preparation of granular gases in microgravity. Herein, the energy input by an oscillating plate is numerically investigated as a function of the excitation parameters for selected Platonic solids and their behavior compared to that of a jumping sphere. The most important additional features, not relevant for spheres, are the excitation of body rotations and a permanent energy exchange between the rotational and translational degrees of freedom during the collisions with the plate. The distribution of kinetic energies is analyzed by a numerical simulation of the dynamics, using structures which emulate the mechanical behavior of regular polyhedra.     

YVO_4:Eu~(3+)纳米晶的水热合成与发光特性

采用水热法在不同温度下制备了系列YVO4:Eu3+纳米晶。利用X射线衍射、电镜和荧光光谱对前驱体和系列样品的结构、形貌和发光性能进行了研究。XRD研究结果表明:合成的样品均为四方相YVO4,纳米晶的一次性粒径分布在13~44 nm。发射光谱和激发光谱的研究表明:特征发射峰来自于5D0-7FJ跃迁,激发带主要来自于Eu-O和V-O的电荷迁移带,发射强度和激发强度随样品结晶度的提高而增强。对样品5D0-7F2跃迁中来自于不同态的发射峰的相对强度进行了比较和讨论。     

Label-free imaging of arterial cells and extracellular matrix using a multimodal CARS microscope

A multimodal nonlinear optical imaging system that integrates coherent anti-Stokes Raman scattering (CARS), sum-frequency generation (SFG), and two-photon excitation fluorescence (TPEF) on the same platform was developed and applied to visualize single cells and extracellular matrix in fresh carotid arteries. CARS signals arising from CH₂-rich membranes allowed visualization of endothelial cells and smooth muscle cells of the arterial wall. Additionally, CARS microscopy allowed vibrational imaging of elastin and collagen fibrils which are also rich in CH₂ bonds. The extracellular matrix organization was further confirmed by TPEF signals arising from elastin’s autofluorescence and SFG signals arising from collagen fibrils’ non-centrosymmetric structure. Label-free imaging of significant components of arterial tissues suggests the potential application of multimodal nonlinear optical microscopy to monitor onset and progression of arterial diseases.     

GEOMETRIC INEQUALITIES FOR CERTAIN SUBMANIFOLDS IN A PINCHED RIEMANNIAN MANIFOLD

This article gives some geometric inequalities for a submanifold with parallel second fundamental form in a pinched Riemannian manifold and the distribution for the square norm of its second fundamental form.     

Symbolic powers,Serre conditions and Cohen-Macaulay Rees algebras

Summary LetR be a Cohen-Macaulay ring andI an unmixed ideal of heightg which is generically a complete intersection and satisfiesI ⁽ⁿ⁾=Iⁿ for alln≥1. Under what conditions will the Rees algebra be Cohen-Macaulay or have good depth? A series of partial answers to this question is given, relating the Serre condition (S _r ) of the associated graded ring to the depth of the Rees algebra. A useful device in arguments of this nature is the canonical module of the Rees algebra. By making use of the technique of the fundamental divisor, it is shown that the canonical module has the expected form: ω _R[It] ≅(t(1−t) ^g−2). The third author was partially supported by the NSF This article was processed by the author using theLaTex style filecljour1 from Springer-Verlag.