概率统计教学的几点建议

概率统计是大学数学的基础课程之一,我们通过具体的例子分析了概率统计课程教学应该重视的几个问题,并提出了解决问题的建议．这对概率统计课程的教学有一定的借鉴意义．     

Quantum-Statistics Behavior of the Exciton-Biexciton System In GaAs/AlAs Type-II Superlattices

We have investigated the quantum-statistics behavior of the exciton-biexciton system from the photoluminescence properties in (GaAs) m /(AlAs) m type-II superlattices with m = 12 and 13 monolayers, where the lowest-energy type-II exciton consists of the n = 1 X electron of AlAs and n = 1 o heavy hole of GaAs. The long exciton lifetime of the order of w s due to the indirect transition nature enables us to obtain precisely the density relation between the exciton and biexciton from the line-shape analysis of time-resolved photoluminescence spectra. In a relatively low exciton-density region, the biexciton density obeys a well-known square law. At an exciton density around 1 2 10 10 cm m 2 , the biexciton density suddenly increases with a threshold-like nature. This behavior, which is realized at a bath temperature up to 8 K under an excitation power of the order of 100 mW/cm 2 , results from the characteristics of Bose-Einstein statistics of the exciton-biexciton system.     

Force microscopy analysis using chemometric tools

In this paper we report the first application of multivariate data analysis techniques to force spectrometry measurement sets to enable the physicochemical assignment of spatially ordered multi-component systems. Principal component analysis (PCA) and hierarchical clustering techniques were used to reveal hidden chemical information within force-distance curves generated by high spatial resolution force microscopy. Two experimental samples were analyzed: (i) a two-component system of cytochrome c proteins on a mica surface, and (ii) a three-component system of avidin protein islands positioned on a gold and glass surface. PCA and hierarchical clustering techniques were used to discriminate the different components of the two-component system, whereas hierarchical clustering was found to be superior for the three-component system. Results were in good agreement with the topography and prior knowledge of the surface patterns. This research represents a formative step towards the combination of force spectrometry with chemometric tools for the high resolution physicochemical investigation of complex biochemical systems.     

Application of the Doehlert experimental design to molecularly imprinted polymers: surface response optimization of specific template recognition as a function of the type and degree of cross-linking

We propose the use of Doehlert’s experimental design, a second-order uniform shell design, for the optimization of molecularly imprinted polymers (MIPs). We have chosen a simple model system where the influence of kind and degree of cross-linking on template recognition was studied using S-propranolol as the template. We found that Doehlert’s design allows—with very few experiments—one to screen the evolution of the binding capacity of a MIP as a function the different parameters, and thus appears to be a powerful means to screen for the best composition and synthesis method for MIPs. We believe that this chemometric tool can significantly accelerate the development of new MIPs as synthetic recognition elements, particularly in the context of a given application, and will be a versatile complement or alternative to first-order designs to fit complex processes. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Morphology and dynamics of a crack front propagating in a model disordered material

We present an experiment on the morphology and dynamics of a crack front propagating at the interface between an elastomer and a glass slide patterned with a prescribed distribution of defects. Regimes of high and low pinning strength are explored by changing the fracture energy contrast of the defects. We first analyze the roughness of crack fronts by measuring their typical amplitude in real and Fourier space. Irrespective of the pinning regime, no well defined self-affine behavior is found which may be explained by the emergence of an intermediate lengthscale between the defect size and the sample size. Then, we show that the dynamics at high fracture energy contrast results in rapid jumps alternating with periods of arrest. The distributions of speeds, displacements and waiting times are found to have an exponential decay which is directly related to the distribution of distances between defects along the direction of propagation.     

Porosity and effective mechanical properties of plasma-sprayed Ni-based alloy coatings

The aim of this paper was to address the relationship between the porosity and micro-mechanical properties of the Ni-based alloy coatings which were prepared by a novel plasma-spraying system. The porosity and the mechanical properties of the coatings varied through changing the spraying parameters. Experimental results showed that the measured data of porosity, Young’s modulus and micro-hardness of the coating exhibited high scattering and followed the Weibull distribution. From statistic trend, the micro-hardness and Young’s modulus of the coating decreased with increasing the porosity of the coating. Moreover, generally, with increasing the micro-hardness of the coating, Young’s modulus of the coating increased.     

Paradoxes and paradigms: influence of the power of z on the estimation of entropies of formation of aqueous anions using simple parameters

We continue our use of “simple” energetic patterns, where simple means the use of parameters derived only from the stoichiometry of these species in our studies of the entropy of formation (TΔ_f S ^o) of aqueous anions. Relationships between the entropy of formation and different parameters such as the number of oxygen atoms, the natural logarithm of the molecular weight and the total number of atoms are explored. The charge of the species, z− continues to be explicitly considered where we now explore various choices of p and use of z ^p as a parameter.     

Extreme value laws in dynamical systems under physical observables

Extreme value theory for chaotic deterministic dynamical systems is a rapidly expanding area of research. Given a system and a real function (observable) defined on its phase space, extreme value theory studies the limit probabilistic laws obeyed by large values attained by the observable along orbits of the system. Based on this theory, the so-called block maximum method is often used in applications for statistical prediction of large value occurrences. In this method, one performs statistical inference for the parameters of the Generalised Extreme Value (GEV) distribution, using maxima over blocks of regularly sampled observable values along an orbit of the system. The observables studied so far in the theory are expressed as functions of the distance with respect to a point, which is assumed to be a density point of the system’s invariant measure. However, at least with respect to the ambient (usually Euclidean) metric, this is not the structure of the observables typically encountered in physical applications, such as windspeed or vorticity in atmospheric models. In this paper we consider extreme value limit laws for observables which are not expressed as functions of the distance (in the ambient metric) from a density point of the dynamical system. In such cases, the limit laws are no longer determined by the functional form of the observable and the dimension of the invariant measure: they also depend on the specific geometry of the underlying attractor and of the observable’s level sets. We present a collection of analytical and numerical results, starting with a toral hyperbolic automorphism as a simple template to illustrate the main ideas. We then formulate our main results for a uniformly hyperbolic system, the solenoid map. We also discuss non-uniformly hyperbolic examples of maps (Hénon and Lozi maps) and of flows (the Lorenz63 and Lorenz84 models). Our purpose is to outline the main ideas and to highlight several serious problems found in the numerical estimation of the limit laws.     

Statistics of Polymer Solutions from Scaling Concepts for Geometry and Relativistic Self-Diffusion in Liquids

Basic results on conformational statistics of polymer solutions are derived from recent scaling concepts for geometry and a relativistic picture for Brownian self-diffusion in liquid media. Any chain conformation is interpreted as a geometrical state affected by its end-to-end dimension, which here denotes the mean deviation between geodesic paths diffusing in the relativistic liquid phase. Statistical polymer length distributions solve an ondulatory equation in non-Euclidean manifolds for coil extension and shape. When length scale is vanishing, the size scaling is found again in terms of parallelism angle rotations. The characteristic chain ratio identifies instead an average metric coefficient, originating topologically from rotational degrees of freedom internal to single molecules.     

协方差矩阵的齐性检验

基于ＰＰ技术、Ｂｏｏｔｓｔｒａｐ方法和数论方法,对于ｋ个总体协方差矩阵相等的检验,给出了ＰＰ型检验统计量,并讨论了它的渐近分布和Ｂｏｏｔｓｔｒａｐ逼近,最后给出了一些实际模拟结果。