Fano varieties with many selfmaps

We study global log canonical thresholds of anticanonically embedded quasismooth weighted Fano threefold hypersurfaces having terminal quotient singularities to prove the existence of a Kähler-Einstein metric on most of them, and to produce examples of Fano varieties with infinite discrete groups of birational automorphisms.     

Finite generation of canonical ring by analytic method

An overview of the analytic proof of the theorem on the finite generation of the canonical ring for the projective algebraic manifold of general type is given.     

Finiteness of polyhedral decompositions of cusped hyperbolic manifolds obtained by the Epstein-Penner's method

Epstein and Penner give a canonical method of decomposing a cusped hyperbolic manifold into ideal polyhedra. The decomposition depends on arbitrarily specified weights for the cusps. From the construction, it is rather obvious that there appear at most a finite number of decompositions if the given weights are slightly changed. However, since the space of weights is not compact, it is not clear whether the total number of such decompositions is finite. In this paper we prove that the number of polyhedral decompositions of a cusped hyperbolic manifold obtained by the Epstein-Penner's method is finite.

     

A Test of Multivariate Independence Based on a Single Factor Model

A test of the independence of two sets of variables is developed to have high power against a special family of dependence. In this each set of variables has the structure of a single factor model and the dependence is solely via the correlation γ between the underlying latent variables. This is a model with only one nonzero canonical correlation. It is shown that a test based on the maximum likelihood estimate of γ is appreciably more powerful than that based on r₁, the largest sample canonical correlation. If, however, the model is used, not just as a family of alternatives but as the basis for interpretation, and if substantial cross-correlation is present then the procedure is essentially equivalent to the use of r₁.     

Points of Bounded Height on Equivariant Compactifications of Vector Groups, I

We prove asymptotic formulas for the number of rational points of bounded height on certain equivariant compactifications of the affine plane.     

A processing method enabling the use of peak height for accurate and precise proton NMR quantitation

In NMR, peak area quantitation is the most common method used because the area under a peak or peak group is proportional to the number of nuclei at those frequencies. Peak height quantitation has not enjoyed as much utility because of poor precision and linearity as a result of inconsistent shapes and peak widths (measured at half height). By using a post‐acquisition processing method employing a Gaussian or line‐broadening (exponential decay) apodization (i.e. weighting function) to normalize the shape and width of the internal standard (ISTD) peak, the heights of an analyte calibration spectrum can be compared to the analyte peaks in a sample spectrum resulting in accurate and precise quantitative results. Peak height results compared favorably with ‘clean’ peak area results for several hundred illicit samples of methamphetamine HCl, cocaine HCl, and heroin HCl, of varying composition and purity. Using peak height and peak area results together can enhance the confidence in the reported purity value; a major advantage in high throughput, automated quantitative analyses. Published in 2009 by John Wiley & Sons, Ltd.     

固体浸没透镜飞行高度的气浮控制

采用固体浸没透镜的光存储方法是提高光存储密度的比较实用的近场光存储方法,而严格控制SIL下底面与光存储介质之间的亚波长级距离是此光存储系统正常工作的前提.本文采用电容法测量SIL的飞行高度,采用弹性悬臂将SIL加载在转盘表面上,转盘以不同速度转动时SIL将悬浮在不同的高度.计算机首先采集到SIL的飞行高度信息,再与设定的飞行高度作比较,根据比较结果调整转盘转速,从而达到调整SIL飞行高度的目的.采用此方法,可以动态地将SIL的下底面控制在距高速转动的转盘表面上150～600 nm范围内的一定高度上.     

An Entropy-Based Tool to Help the Interpretation of Common-Factor Spaces in Factor Analysis

This paper proposes a method for deriving interpretable common factors based on canonical correlation analysis applied to the vectors of common factors and manifest variables in the factor analysis model. First, an entropy-based method for measuring factor contributions is reviewed. Second, the entropy-based contribution measure of the common-factor vector is decomposed into those of canonical common factors, and it is also shown that the importance order of factors is that of their canonical correlation coefficients. Third, the method is applied to derive interpretable common factors. Numerical examples are provided to demonstrate the usefulness of the present approach.     

Singularity-free augmented Lagrangian algorithms for constrained multibody dynamics

After a general review of the methods currently available for the dynamics of constrained multibody systems in the context of numerical efficiency and ability to solve the differential equations of motion in singular positions, we examine the acceleration based augmented Lagrangian formulations, and propose a new one for holonomic and non-holonomic systems that is based on the canonical equations of Hamilton. This new one proves to be more stable and accurate that the acceleration based counterpart under repetitive singular positions. The proposed algorithms are numerically efficient, can use standard conditionally stable numerical integrators and do not fail in singular positions, as the classical formulations do. The reason for the numerical efficiency and better behavior under singularities relies on the fact that the leading matrix of the resultant system of ODEs is sparse, symmetric, positive definite, and its rank is independent of that of the Jacobian of the constraint equations. The latter fact makes the proposed method particularly suitable for singular configurations.     

Dispersion in retentive pillar array columns

The method of volume averaging is applied to estimate the Taylor–Aris dispersion tensor of solute advected in columns consisting of ordered pillar arrays with wall retention of the type used in chromatographic separation. The appropriate closure equations are derived and solved in a unit cell with periodic boundary conditions to obtain the dispersion tensor (or the reduced plate height) as a function of the Peclet number (reduced velocity); pillar pattern, shape and size; partition coefficient; and resistance to mass transfer. The contributions of the velocity profile, the wall adsorption, and the mass transfer resistance to the dispersion tensor are identified and delineated. The model is verified by comparing its predictions and obtaining favorable agreement with results of direct numerical simulations and with experimental data for columns containing ordered pillars. The model is then used to study the effect of pillars’ shape and pattern on the longitudinal dispersion coefficient (plate height).