Asymptotic Distribution of Nodes for Near-Optimal Polynomial Interpolation on Certain Curves in R 2

Let E\subset \Bbb R ^s be compact and let d _n ^E denote the dimension of the space of polynomials of degree at most n in s variables restricted to E . We introduce the notion of an asymptotic interpolation measure (AIM). Such a measure, if it exists , describes the asymptotic behavior of any scheme τ _n ={ \bf x _k,n } _k=1 ^dnE , n=1,2,\ldots , of nodes for multivariate polynomial interpolation for which the norms of the corresponding interpolation operators do not grow geometrically large with n . We demonstrate the existence of AIMs for the finite union of compact subsets of certain algebraic curves in R ² . It turns out that the theory of logarithmic potentials with external fields plays a useful role in the investigation. Furthermore, for the sets mentioned above, we give a computationally simple construction for ``good' interpolation schemes. November 9, 2000. Date revised: August 4, 2001. Date accepted: September 14, 2001.     

关于NF-环的构造

研究了无限的ＮＦ－环及有限的ＮＦ－环，并且给出了有限ＮＦ－环的构造．     

Factorisation in the ring of exponential polynomials

We study factorisation in the ring of exponential polynomials and provide a proof of Ritt's factorisation theorem in modern notation and so generalised as to deal with polynomial coefficients as well as with several variables. We do this in the more general context of a group ring of a divisible torsion-free ordered abelian group over a unique factorisation domain.

     

Supersemiprime Rings and Supersemiprime Radical

§1.　IntroductionInthisrecentyears,theprimeringswithspecialpropertieshavebeenstudiedsomeau-thors,forexample,N.T.Groenewaldintroducedthecompletelyprimeringsandthecompletelyrimeradicalin[1].D.HandelmanandJ.Lawrencediscussedthestronglyprimeringsandthestronglyprimeradicalin[2].S.Veldsmanstudiedthesuperprimeringsandthesuperprimeradicalin[3].ZhangXianjunintroducedtheAbsolutelysemiprimeringsandtheabsolutelysemiprimeradicalandsoon.Theaimofthispaperistostudythesemiprimeringswithspecialpropertiesan…     

用频域法实现圆环形目标物的计数

研究了用频域法实现圆环形目标物计数的方法。对空域中含有圆环形目标物的二值图像，经傅里叶变换后在频域内进行滤波，再经傅里叶反变换后取一阈值进行处理，则对应于圆环形目标物即变为一个实心体，然后对实心体进行计数即可实现对圆环形目标物的计数。对该方法进行了数学描述，并分别用模拟图像和实际图像进行了实验。结果表明，该方法消除噪声的效果好，对部分封闭圆的检测同样有效，且可用于目标物有粘连的情况。该方法对圆环形目标物的尺寸相差不大的情况更为有效。     

Exchange环的K0群的正向凸子群格

本文证明了：(1)Exchange环R的K0群的正向凸子群格同构于R的稳定余有限半本原理想格；(2)稳定有限、半本原的exchange环R是单的当且仅当它是K0-单的并且满足逼近弱s^*—可比性，推广了Goodearl，Ara等人的结果。     

Synthesis,characterization, and micellization of an epoxy‐based amphiphilic diblock copolymer of ϵ‐caprolactone and glycidyl methacrylate by enzymatic ring‐opening polymerization and atom transfer radical polymerization

Amphiphilic diblock copolymer polycaprolactone‐block‐poly(glycidyl methacrylate) (PCL‐b‐PGMA) was synthesized via enzymatic ring‐opening polymerization (eROP) and atom transfer radical polymerization (ATRP). Methanol first initiated eROP of ?‐caprolactone (?‐CL) in the presence of biocatalyst Novozyme‐435 under anhydrous conditions. The resulting monohydroxyl‐terminated polycaprolactone (PCL–OH) was subsequently converted to a bromine‐ended macroinitiator (PCL–Br) for ATRP by esterification with α‐bromopropionyl bromide. PCL‐b‐PGMA diblock copolymers were synthesized in a subsequent ATRP of glycidyl methacrylate (GMA). A kinetic analysis of ATRP indicated a living/controlled radical process. The macromolecular structures were characterized for PCL–OH, PCL–Br, and the block copolymers by means of nuclear magnetic resonance, gel permeation chromatography, and infrared spectroscopy. Differential scanning calorimetry and wide‐angle X‐ray diffraction analyses indicated that the copolymer composition (?‐CL/GMA) had a great influence on the thermal properties. The well‐defined, amphiphilic diblock copolymer PCL‐b‐PGMA self‐assembled into nanoscale micelles in aqueous solutions, as investigated by dynamic light scattering and transmission electron microscopy. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 5037–5049, 2007     

Syntheses and characterization of 16‐arm star and star diblock copolymer and AB8 9‐miktoarm star copolymer via NMRP and ROP from dendritic multifunctional macroinitiators

A dendritic macroinitiator having 16 TEMPO‐based alkoxyamines, Star‐16 , was prepared by the reaction of a dendritic macroinitiator having eight TEMPO‐based alkoxyamines, [G‐3]‐OH , with 4,4′‐bis(chlorocarbonyl)biphenyl. The nitroxide‐mediated radical polymerization (NMRP) of styrene (St) from Star‐16 gave 16‐arm star polymers with PDI of 1.19–1.47, and NMPR of 4‐vinylpyridine from the 16‐arm star polymer gave 16‐arm star diblock copolymers with PDI of 1.30–1.43. The ring‐opening polymerization of ε‐caprolactone from [G‐3]‐OH and the subsequent NMRP of St gave AB₈ 9‐miktoarm star copolymers with PDI of 1.30–1.38. The benzyl ether linkages of the 16‐arm star polymers and the AB₈ 9‐miktoarm star copolymers were cleaved by treating with Me₃SiI, and the resultant poly(St) arms were investigated by size exclusion chromatography (SEC). The SEC results showed PDIs of 1.23–1.28 and 1.18–1.22 for the star polymers and miktoarm stars copolymers, respectively, showing that they have well‐controlled poly(St) arms. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 1159–1169, 2007.     

Ring‐opening grafting polymerization of cyclic monomers onto human hair

Natural human hair was successfully modified by the graft polymerization of trimethylene carbonate, β‐propiolactone, ε‐caprolactone, glycidol, ε‐caprolactam, and 5,5‐dimethyl‐1,3‐dioxane‐2‐thione. In contrast, we could not modify natural human hair by the graft polymerization of oxetane under similar conditions. The model reaction suggested that the main initiating species in these polymerizations were the amino, thiol, and hydroxyl groups in hair, which could induce ring‐opening polymerization. Among the tested monomers, β‐propiolactone was most effective for hair modification with its graft polymer, whose concentration was as high as 0.5 g/g of hair though polymerization under mild conditions. The effects of the hair pretreatment and polymerization temperature on the weight ratio of the grafted polymers were also investigated. Hair modified by grafted polymers was characterized with scanning electron microscopy and Fourier transform infrared measurements. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 736–744, 2007     

关于Noetherian环上拓扑滤子交换性的一个注记

Let R be a ring with identity,and R-fil denote the set of all left topolo-gizing filters on R.In this paper,we give a sufficient condition for the commutativityof R-fil under the hypothesis of left Noetherianness,as well as some examples.