Canonical maps to twisted rings

If A is a strongly noetherian graded algebra generated in degree one, then there is a canonically constructed graded ring homomorphism from A to a twisted homogeneous coordinate ring , which is surjective in large degree. This result is a key step in the study of projectively simple rings. The proof relies on some results concerning the growth of graded rings which are of independent interest. D. Rogalski was partially supported by NSF grant DMS-0202479. J. J. Zhang was partially supported by NSF grant DMS-0245420 and Leverhulme Research Interchange Grant F/00158/X (UK).     

Increasing the polynomial reproduction of a quasi-interpolation operator

Quasi-interpolation is an important tool, used both in theory and in practice, for the approximation of smooth functions from univariate or multivariate spaces which contain , the d-variate polynomials of degree ≤m. In particular, the reproduction of Π_m leads to an approximation order of m+1. Prominent examples include Lagrange and Bernstein type approximations by polynomials, the orthogonal projection onto Π_m for some inner product, finite element methods of precision m, and multivariate spline approximations based on macroelements or the translates of a single spline.For such a quasi-interpolation operator L which reproduces and any r≥0, we give an explicit construction of a quasi-interpolant which reproduces Π_m+r, together with an integral error formula which involves only the (m+r+1)th derivative of the function approximated. The operator is defined on functions with r additional orders of smoothness than those on which L is defined. This very general construction holds in all dimensions d. A number of representative examples are considered.     

Finding transition states using reduced potential-energy surfaces

 We propose a method to locate saddle points that is based on the interplay between the driving coordinate and the restricted quasi-Newton algorithm. The method locates the transition state using a reduced potential-energy surface. The reduced potential-energy surface is characterized by the set of driving coordinates. The proposed algorithm starts at a point on the surface that is slightly perturbed from either reactant or product and, in principle, converges to the transition state. Finally we give a special type of update Hessian matrix formula that should be applied in optimizations carried out on reduced potential-energy surfaces. Received: 29 September 2000 / Accepted: 3 January 2001 / Published online: 3 April 2001     

Preparation and Characterization of Al8.31Si1.91Mg3.78O20/Al4.8Si1.2O9.6/Mg2.0Al4.02Si4.98O18 Multiphase Material

A two-step sintering method was used to prepare Al8.31Si1.91Mg3.78O20 (corundum solid solution)/Al4.8Si1.2O9.6 (mullite solid solution)/Mg2.0Al4.02Si4.98O18 (cordierite solid solution) multiphase material, for the purposes of making these three crystal structures have point defects which could help the particles diffuse and transfer at high temperature, accelerate the sintering efficiently and enhance the material strength as well as the bulk density. The impacts of different formulas on the structure and properties of the multiphase material were investigated. With XRD and SEM analyses, for each sample, the crystal structure and microstructure were characterized, the crystalline phase content and cell parameters were determined with Rietveld Quantification software, and the properties were tested. The comparative optimal formula determined was calcinated chamotte of 80wt% and calcinated sludge of 20wt%; and its corresponding bending strength and retention rate of bending strength after a thermal shock were 29.74 MPa and 80.15%, respectively.     

Visual detection of melamine in milk products by label-free gold nanoparticles

A simple, rapid, field-portable colorimetric method for the detection of melamine based on melamine-induced color change of label-free gold nanoparticles (Au NPs) was developed in this study. Melamine can induced the aggregation of Au NPs and results in the color change from wine-red to purple, which provided a platform for rapid and field-portable colorimetric detection of melamine. The proposed method can be used to detect melamine in liquid milk and infant formula with a detection limit of 1.0 and 4.2 ppm, respectively, within 30 min by naked eyes observation without the aid of any advanced instrument and the need of any complex pretreatment, and detect as low as 0.15 ppm of melamine in liquid milk and 2.5 ppm of melamine in infant formula with UV-vis-spectroscopy. The proposed method is promising for on-site screening of melamine adulterant in milk products.     

Orthokinetic Aggregation in Two Dimensions of Monodisperse and Bidisperse Colloidal Systems

Orthokinetic aggregation of colloids trapped at the air–liquid interface was studied by direct imaging in a couette cell. This method allowed us to follow the temporal evolution of both the cluster-mass distribution and the cluster structure at a shear rate where Brownian aggregation is suppressed. The interactions between the monodisperse latex particles floating at the air–liquid interface were controlled either by varying the electrolyte concentration or by creating a bidisperse system through the addition of small particles. The results show that the clusters in all of the systems are characterized by a high fractal dimension, indicating that the clusters are rearranged and densified by the shear. Kinetic analysis suggests that aggregation of monodisperse systems mainly proceeds through homogeneous aggregation, i.e., large clusters sticking to other large clusters. The bidisperse system, finally, with a size ratio around 10, favored a more heterogeneous aggregation among small and large clusters throughout the aggregation process; a slightly lower fractal dimension was observed compared to the strongly aggregated monodisperse system.     

Adjacency matrices of probe interval graphs

In this paper we obtain several characterizations of the adjacency matrix of a probe interval graph. In course of this study we describe an easy method of obtaining interval representation of an interval bigraph from its adjacency matrix. Finally, we note that if we add a loop at every probe vertex of a probe interval graph, then the Ferrers dimension of the corresponding symmetric bipartite graph is at most 3.     

Bi-Sobolev mappings with differential matrices in Orlicz Zygmund classes

Bi-Sobolev mappings have been defined as those homeomorphisms such that f and f−1 belong to . We deduce regularity properties of the distortion of f from the regularity of the differential matrix Df−1 and conversely.     

特征函数的性质

得到了特征函数、条件特征函数的一致可微性和条件特征函数的反演公式.