Rotation number values at a discontinuity

In the space of orientation-preserving circle maps that are not necessarily surjective nor injective, the rotation number does not vary continuously. Each map where one of these discontinuities occurs is itself discontinuous and we can consider the possible values of the rotation number when we modify this map only at its discontinuities. These values are always rational numbers that necessarily obey a certain arithmetic relation. In this paper we show that in several examples this relation totally characterizes the possible values of the rotation number on its discontinuities, but we also prove that in certain circumstances this relation is not sufficient for this characterization.     

有理数集的可列性和稠密性及其应用

介绍关于有理数集可列性和稠密性的一种证明方法，并借助实例说明这两种看似互斥的性质在实分析中的一些应用。     

Michael addition of nitroalkanes to nonactivated α,β-unsaturated δ-thiolactams: reactivity, diastereoselectivity, and comparison to α,β-unsaturated δ-lactams

Aliphatic nitrocompounds add to nonactivated α,β-unsaturated δ-thiolactams leading to 4-nitroalkyl functionalized δ-thiolactams in good yields. The addition is a stereocontrolled process with respect to substituents at C-6, and takes place producing trans 4,6-disubstituted adducts in most cases. Ease of the addition has been studied in relation to the structure of the δ-thiolactam acceptors, within the FMO-theory. Comparative study with analogous δ-lactams has shown the advantages of α,β-unsaturated δ-thiolactams in Michael addition and indicated high prospects of these compounds in the synthesis of 4-functionalized piperidine derivatives.     

Hash函数的设计与分析

数字签名系统中需用一个安全可靠且易实现的Hash函数.Hash函数有严格的要求, 其构造及性能分析难度都较大.本文构造了一个比较实用的Hash函数, 并对其性能作了较全面的分析.同时指出了Hash函数在票据防伪、防止非法修改应用软件中的应用.     

MULTIPLE LIMIT CYCLES AND GLOBAL STABILITY IN PREDATOR-PREY MODEL

1.IntroductionWeconsideranextensivesystemofthefamiliarLotka-Volterrasysteminwhichthepopulationshaveself-inhibit(i.e.,withtheadditionofdampingterm)thatcanbemodeledbytheequationswherexandyrepresentthepreydensityandpredatordensityrespectively.Thespecifi...     

Tautomerism of 3‐nitro‐1,2,4‐triazole‐5‐one radical anions

The non‐degenerate tautomers of 3‐nitro‐1,2,4‐triazole‐5‐one (NTO) radical anions were investigated for the first time by an ESR method during electrochemical reduction of NTO in an aprotic medium. Copyright © 2009 John Wiley & Sons, Ltd.     

Half plane Toeplitz operators with generating functions having homogeneous discontinuities

We consider Toeplitz operators over the discrete half plane with generating functions admitting discontinuities of special kind which we call homogenous ones. The main results are the criteria of invertibility and one‐sided invertibility of such operators. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Activated transport in the exciton condensate at balanced and imbalanced densities measured in drag and counter-flow configuration

We observe the total filling factor ν_T=1 exciton condensate in independently contacted bilayer two-dimensional electron systems in samples with minute tunnel coupling. At balanced electron densities in the layers, we find for both drag and counter-flow current configurations, thermally activated transport with a monotonic increase of the activation energy for d/ℓ_B<1.65 with activation energies up to 0.4 K. In the imbalanced system the activation energies show a striking asymmetry around the balance point, implying that the gap to charge excitations is considerably different in the separate layers that form the bilayer condensate. This indicates that the measured activation energy is neither the binding energy of the excitons, nor their condensation energy.     

An Improved Hybrid Method for Inverse Obstacle Scattering Problems

An improved hybrid method is introduced in this paper as a numerical method to reconstruct the scatterer by far-field pattern for just one incident direction with unknown physical properties of the scatterer. The improved hybrid method inherits the idea of the hybrid method by Kress and Serranho which is a combination of Newton and decomposition method, and it improves the hybrid method by introducing a general boundary condition. The numerical experiments show the feasibility of this method.     

One-Pot Synthesis of 3-Benzylflavones

The synthesis of 3-benzylflavone derivatives was efficiently performed in a one-pot method using substituted 2-hydroxy-acetophenone and appropriate benzaldehydes in the presence of pyrrolidine and ethanol. The distinct features of this methodology include simple procedure, easy purification, and good yields.