二元序列的自相关函数和游程的一些结果

给出了二元周期序列的自相关性质与其游程性质之间的关系,作为一个应用,我们给出了周期为1 2的零自相关窗大于等于6的所有序列.     

Undecidability of the Real-Algebraic Structure of Scott's Model

We show that true first-order arithmetic of the positive integers is interpretable over the real-algebraic structure of Scott's topological model for intuitionistic analysis. From this the undecidability of the structure follows.     

REMARKS ON THE PAPER “ON HERMITE-FEJER INTERPOLATION IN A JORDAN DOMAIN”

本文改进了复域中用Ｈｅｒｍｉｔｅ－Ｆｅｊｅｒ插值一致逼近与平均逼近［１］的边界条件且简化了证明过程     

Existence of an Angular Density of Roots of Entire Functions of Order Zero

We obtain sufficient conditions for the set of roots of an entire function of order zero of strongly regular growth to possess an angular density.     

An Approximate Distribution for the Maximum Order Complexity

In this paper we give an approximate probability distribution for the maximum order complexity of a random binary sequence. This enables the development of statistical tests based on maximum order complexity for the testing of a binary sequence generator. These tests are analogous to those based on linear complexity.     

关于亚纯函数导数亏量和的Ozawa问题

设σλ表示所有限级λ的亚纯函数构成的集合,R.Nevanlinna显示,当λ是正的非整数时,κ(λ)>0,其中设f为有限级λ的亚纯函数,Ozawa证明了存在正常数d=d(λ),满足1/2(5-(21~(1/2))≤d≤1/4,使我们曾将d的范围精确为1/4≤d≤4/13。本文中,我们得到一个更精确、更广泛的结论:设f是有限级λ的亚纯函数,则对任何自然数n,存在仅与n,λ有关的正常数d,满足2n(n+1)/(4n~2+7n+2)≤d≤4n(n+1)/(4n~2+6n+1+(16n~4+56n~3+60n~2+20n+1)~(1/2))使得     

Thin films of metal-organic compounds and metal nanoparticle-embedded polymers for nonlinear optical applications

Thin films based on two very different metal-organic systems are developed and some nonlinear optical applications are explored. A family of zinc complexes which form perfectly polar assemblies in their crystalline state are found to organize as uniaxially oriented crystallites in vapor deposited thin films on glass substrate. Optical second harmonic generation from these films is investigated. A simple protocol is developed for thein-situ fabrication of highly monodisperse silver nanoparticles in a polymer film matrix. The methodology can be used to produce free-standing films. Optical limiting capability of the nanoparticle-embedded polymer film is demonstrated     

A study of NMR parameters of cyclobutenones and benzocyclobutenones

An NMR study of ketones 5–12 was undertaken to gain insight into the low electrophilicity of the carbonyl moiety of butenones 9–11. Initial IR studies on compounds 9–12 indicated that there is relatively strong double bond character (and hence low electrophilicity) in the carbonyl of saturated and unsaturated cyclobutyl ketones. The ¹³C chemical shifts confirm that the carbonyl moiety is highly conjugated with the fused benzene ring in 9, and with the olefinic linkage in 10 and 11. Partial positive charge is distributed away from the carbonyl carbon, which is also expected to lower the electrophilicity of the carbonyl carbon atoms of 9–11. One‐bond carbon–proton coupling constants (¹J_CH) depend directly on carbon hybridization. In the four‐membered ring ketones 9–12 the experimental values are larger than in cyclobutane, probably as a result of the additional strain of the extra trigonal centers in the ring. A similar trend is seen in the case of the olefinic CH in 10 and 11 (ca 175 Hz), for which the coupling constant is larger than for the corresponding carbon in cyclobutene. ¹J_CC values between the ring carbon atoms of the cyclobutenones are some 20% lower than in the models—a bigger difference than in cyclobutanes, again indicative of the increased ring strain. The very low 42.4 Hz coupling between C‐1 and C‐2 in 9 might well indicate a measure of bond localization. ²J_CC and ³J_CC values are also discussed. Copyright © 2003 John Wiley & Sons, Ltd.     

A Uniqueness Result for a Model for Mixtures in the Absence of External Forces and Interaction Momentum

We consider a continuum model describing steady flows of a miscible mixture of two fluids. The densities ϱ _i of the fluids and their velocity fields u ⁽ⁱ⁾ are prescribed at infinity: ϱ _i |_∞ = ϱ _i∞ > 0, u ⁽ⁱ⁾|∞ = 0. Neglecting the convective terms, we have proved earlier that weak solutions to such a reduced system exist. Here we establish a uniqueness type result: in the absence of the external forces and interaction terms, there is only one such solution, namely ϱ _i ≡ ϱ _i∞, u ⁽ⁱ⁾ ≡ 0, i = 1, 2. This work was supported by the SFB 611 at the University of Bonn and the European HYKE network (contract no. HPRN-CT-2002-00282). The third author was also supported by the project CSF 201/03/0934, and by MSM 0021620839.