On Sobolev infinitesimal rigidity of linear hyperbolic actions on the 2-torus*

Let A be a symmetric hyperbolic matrix in SL(2, ℤ) and Γ the subgroup of SL(2, ℤ) generated by A. We aim to study the infinitesimal rigidity of the standard action of Γ on the torus . More precisely, we will consider the Sobolev W^s–infinitesimal rigidity of this action (that is to determine if the cohomology space H¹(Γ,W^s (T M)) is trivial or not), and show that it is W^s–infinitesimally rigid only if 0 ≤ s < 1. A consequence will be that this action is not C^∞–infinitesimally rigid. *I would like to thank A. El Kacimi for introducing me this problem about which we had many fruitful discussions.     

Dynamic Behavior of Rigid–Plastic Sector Plates

The paper studies the dynamic behavior of perfect rigid-plastic plates in the form of a sector with hinged or clamped sides under short-term intensive loads. Two dynamic deformation mechanisms are demonstrated. The dynamic equation is derived for each of the mechanisms. The realization conditions for the mechanisms are analyzed. Analytical expressions are derived for the ultimate (high) loads and the maximum residual deflection. Numerical examples are given     

Equivalence Bimodule Between Non-Commutative Tori

The non-commutative torus C ^*(ⁿ,) is realized as the C*-algebra of sections of a locally trivial C*-algebra bundle over S with fibres isomorphic to C ^*n/S, ₁) for a totally skew multiplier ₁ on ⁿ/S. D. Poguntke [9] proved that A is stably isomorphic to C(S) C(^*( Zⁿ/S, ₁) C(S) A M_kl( C) for a simple non-commutative torus A and an integer kl. It is well-known that a stable isomorphism of two separable C*-algebras is equivalent to the existence of equivalence bimodule between them. We construct an A-C(S) A-equivalence bimodule.     

Distribution of Cardinalities of Row Spaces of Boolean Matrices of Order n

Let R(A) denote the row space of a Boolean matrix A of order n. We show that if n 7, then the cardinality |R(A)| (2^n–1 - 2^n–5, 2^n–1 - 2^n–6) U (2^n–1 - 2^n–6, 2^n–1). This result confirms a conjecture in [1].AMS Subject Classification (1991): 05B20 06E05 15A36Support partially by the Postdoctoral Science Foundation of China.Dedicated to Professor Chao Ko on the occasion of his 90th birthday     

Completeness in the set of wavelets

We study the completeness properties of the set of wavelets in . It is well-known that this set is not closed in the unit ball of . However, if one considers the metric inherited as a subspace (in the Fourier transform side) of , we do obtain a complete metric space.

     

A bracket power characterization of analytic spread one ideals

The main theorem characterizes, in terms of bracket powers, analytic spread one ideals in local rings. Specifically, let be regular nonunits in a local (Noetherian) ring and assume that , the integral closure of , where . Then the main result shows that for all but finitely many units in that are non-congruent modulo and for all large integers and it holds that for and not divisible by , where is the -th bracket power of . And, conversely, if there exist positive integers , , and such that has a basis such that , then has analytic spread one.

     

用等效网络方法求均匀弹簧纵振动的本征频率

利用机电类比方法导出了均匀质量弹簧在几种特定边界条件下的本征频率方程,并给出了相应的本征频率公式。体现了等效网络理论分析机械振动问题的优越性。     

Mie理论在生物组织散射特性分析中的应用

根据等效颗粒散射模型，运用经典的Mie理论，对生物组织的散射相函数、各向异性因子及散射系数进行了数值计算.计算结果表明：可见光照射生物组织时，各向异性因子、散射系数随等效颗粒直径增大而增大；等效颗粒直径较小时，各向异性因子、散射系数随入射光波长增大而单调减小；随着等效颗粒直径增大，各向异性因子、散射系数随入射光波长变化不再具有单调性.上述计算结果可合理解释公布的实验结果. 关键词： 生物组织 散射 Mie理论 等效颗粒     

Valence band and band gap photoemission study of (1 1 1) In2O3 epitaxial films under interactions with oxygen, water and carbon monoxide

Synchrotron radiation ultraviolet photoemission experiments at photon energies of 150 and 49 eV were performed on an epitaxial layer of (1 1 1) In₂O₃ with good crystallinity as established by a standard scanning probe and diffraction methods. Valence band (VB) and band gap photoemission spectra were monitored under separate oxygen, water and carbon monoxide exposures (100 L) at different activation temperatures within the range utilized for chemiresistive gas sensors (160-450 °C). Large changes in photoemission response within the whole VB were observed for all gases. Regular shifts of the valence band edge relative to the Fermi energy were found under gas exposures on two kinds of surface (partially reduced or partially oxidized), and are interpreted as changes of surface potential. Treatments in oxygen resulted in upward band bending (∼0.5 eV at T = 320 °C). Regardless of activation temperature, treatments in water resulted in downward band bending, but with small changes (<0.1 eV). Reduction properties of carbon monoxide were observed only at high temperatures of T ? 370 °C. At temperatures of 160 and 250 °C unusual “oxidizing” behavior of CO was observed with upward band bending of ∼0.7 eV (160 °C). Oxidizing and reducing effects of the gas interactions with the (1 1 1) In₂O₃ surface in all cases were accompanied by a corresponding behavior, i.e., a decrease or increase in photoemission response from so-called defect states in the band gap near the top of the valence band. The increases of photoemission within a band gap with maxima at binding energies (BE) of 0.4 (O₂-induced peak) and 1.0 eV (CO-induced peak) were, respectively, found for interactions with O₂ and CO for low temperatures (T = 160 and 250 °C). These responses were ascribed to acceptor-like electronic levels of O₂ and CO chemisorption states, respectively. A definite split of the top VB peak (BE ∼ 4.0 eV) was found under CO dosing at 160 °C. Established knowledge of the CO interaction with the (1 1 1) In₂O₃ surface explains earlier revealed acceptor-like behavior of In₂O₃ film conductivity during CO detection at operational temperatures lower than 250 °C through the formation of acceptor-like electronic levels of adsorbed CO molecules.     

探寻等价无穷小关系的几种方法

介绍利用导数建立等价无穷小关系的三个方法，并举例说明．