OPTIMAL QUADRATURE OF THE SOBOLEV CLASS W_1~r(R) DEFINED ON WHOLE REAL AXIS

ＯＰＴＩＭＡＬＱＵＡＤＲＡＴＵＲＥＯＦＴＨＥＳＯＢＯＬＥＶＣＬＡＳＳＷ_１~ｒ（Ｒ）ＤＥＦＩＮＥＤＯＮＷＨＯＬＥＲＥＡＬＡＸＩＳ（房艮孙，刘永平）￥ＦａｎｇＧｅｎｓｕｎ；ＬｉｕＹｏｎｇｐｉｎｇ（Ｄｅｐｔ．ｏｆＭａｔｈ．，ＢｅｉｊｉｎｇＮｏｒｍａｌＵｎｉ...     

Burghelea-Friedlander-Kappeler's gluing formula for the zeta-determinant and its applications to the adiabatic decompositions of the zeta-determinant and the analytic torsion

The gluing formula of the zeta-determinant of a Laplacian given by Burghelea, Friedlander and Kappeler contains an unknown constant. In this paper we compute this constant to complete the formula under an assumption that the product structure is given near the boundary. As applications of this result, we prove the adiabatic decomposition theorems of the zeta-determinant of a Laplacian with respect to the Dirichlet and Neumann boundary conditions and of the analytic torsion with respect to the absolute and relative boundary conditions.

     

Synthesis and properties of soluble trifluoromethyl‐substituted polyimides containing laterally attached p‐Terphenyls

A new fluorinated diamine monomer, 2′,5′‐bis(4‐amino‐2‐trifluoromethylphenoxy)‐p‐terphenyl, was synthesized from the chloro‐displacement of 2‐chloro‐5‐nitrobenzotrifluoride with the potassium phenolate of 2,5‐diphenylhydroquinone, followed by hydrazine palladium‐catalyzed reduction. A series of trifluoromethyl‐substituted polyimides containing flexible ether linkages and laterally attached side rods were synthesized from the diamine with various aromatic dianhydrides via a conventional two‐step process. The inherent viscosities of the poly(amic acid) precursors were 0.84–1.26 dL/g. All the polyimides afforded flexible and tough films. The use of 4,4′‐oxydiphthalic anhydride and 2,2′‐bis(3,4‐dicarboxyphenyl)hexafluoropropane dianhydride produced essentially colorless polyimide films. Most of the polyimides revealed an excellent solubility in many organic solvents. The glass‐transition temperatures of these polyimides were recorded between 254 and 299 °C by differential scanning calorimetry, and the softening temperatures of the polymer films stayed in the range of 253–300 °C according to thermomechanical analysis. The polyimides did not show significant decomposition before 500 °C in air or under nitrogen. These polyimides also showed low dielectric constants (2.83–3.34 at 1 MHz) and low moisture absorption (0.4–2.2%). For a comparative study, a series of analogous polyimides based on the nonfluorinated diamine 2′,5′‐bis(4‐aminophenoxy)‐p‐terphenyl were also prepared and characterized. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 1255–1271, 2004     

An integration by parts formula in submanifolds of positive codimension

We prove a general integration by parts formula for first‐order differential operators on submanifolds of arbitrary codimension of a given Riemannian manifold. The differential operators in question are assumed to satisfy a suitable tangentiality condition. Several particular cases, particularly relevant to applications to PDE arising in mathematical physics are discussed. Copyright © 2004 John Wiley & Sons, Ltd.     

实二次代数整数环上的单位格的类数

用邻格方法及Siegelmass公式证明了实二次代数域Q(√d)上单位格种gen(In)n≥4)的类数h(In)=3当且仅当Q(√3):n=4;Q(√5);n=6;Q(√3);n=4;Q(√17):n=4.     

Time changes of symmetric Markov processes and a Feynman-Kac formula

We prove a Feynman-Kac formula in the context of symmetric Markov processes and Dirichlet spaces. This result is used to characterize the Dirichlet space of the time change of an arbitrary symmetric Markov process, completing work of Silverstein and Fukushima.     

The Median Formula and Related Inequalities in n—simplex

5l.TheMedianFormulaAseveryoneknows:in6ABC,letal=BC,a2=CA,a3=AB,;)11,)n2,n13aremedian1inesseparatelyonthethreeedgesBC,CA,AB,tI1entheequalityistrueasfollowsTheequality(l)iscalledmedianformulaofQABC,andwecanobtainfrom(l)Inthispaper,wesha1lextendtheequality(l)and(2)to,l-simplexin)l-EuclideanspaceH.Itisobtainedthemedianformulaof)I-simplex,andusingthisformula.wegetsomein-equalities.Themedianformulaofn-simp1exisobtainedasfollows:TheoremlFork=1,2,--',It 1andl相似文献   

球面折射物象公式的几种推导方法

分别从光线方程，程函方程，折射定射的矢量表示，哈密顿混合特征函数和球面折射矩阵出发导出近轴光线条件下球折射的物象公式。     

泡沫硅橡胶冲击压缩性实验研究

 采用锰铜计技术，通过测量冲击波压力获得材料雨贡纽数据的技术路线，给出了初始密度为0.92 g/cm³的泡沫硅橡胶在6~33 GPa范围内的雨贡纽关系，精度优于国内外相关工作。对本实验锰铜计的典型信号作了较为详细的分析，通过数值模拟很好地重现了该非常规信号。此外，采用先前Wu等建立的疏松材料雨贡纽模型进行了预估计算，预估结果与实验结果符合很好，表明该模型不但适用于金属、岩石矿物等，亦可广泛应用于高聚物疏松材料的冲击压缩性研究。     

Numerical solution of fractional order differential equations by extrapolation

We present an extrapolation type algorithm for the numerical solution of fractional order differential equations. It is based on the new result that the sequence of approximate solutions of these equations, computed by means of a recently published algorithm by Diethelm [6], possesses an asymptotic expansion with respect to the stepsize. From this we conclude that the application of extrapolation is justified, and we obtain a very efficient differential equation solver with practically no additional numerical costs. This is also illustrated by a number of numerical examples. This revised version was published online in August 2006 with corrections to the Cover Date.