Simplicial normalization in the entire cyclic cohomology of Banach algebras

We show that the entire cyclic cohomology of Banach algebras defined by Connes has the simplicial normalization property. A key tool in the proof is the notion and properties of supertraces on the Cuntz algebraQ A. As an example of further applications of this technique, we give a proof of the homotopy invariance of entire cyclic cohomology.Address after 1st October 1995: Department of Mathematics, University of Exeter, North Park Road, Exeter EX4 4QE, U.K.     

激光脉冲能量对激光烧蚀保护气体电离的影响

用Ar气作保护气体 ,气压保持在一个标准大气压 ,用Nd :YAG脉冲激光烧蚀Al靶获得等离子体。利用时空分辨技术 ,采集了激光脉冲能量在 5 2 ,92 ,115和 14 5mJ情况下等离子体辐射的时空分辨谱。详细描述了 115mJ时等离子体的辐射特征 ,简要分析了其他脉冲能量下Ar的特征辐射规律。根据这些脉冲能量下Ar 特征谱线的分布规律 ,简要论述了Ar气体电离与激光脉冲能量的关系。讨论了环境气体电离机制 ,并对结果进行了简单解释。结果发现 ,在本实验采用的能量范围内 ,较高的脉冲能量更容易使环境气体电离 ,产生较强的Ar 离子辐射 ,且Ar 辐射持续时间较长。     

Variational Inequalities and Applications to a Continuum Model of Transportation Network with Capacity Constraints

A continuum model of transportation network is considered in presence of capacity constraints on the flow. The equilibrium conditions are expressed in terms of a Variational Inequality for which an existence theorem is provided.     

Vertex function and coupling constant for the virtual decay of7Li

The alpha-triton relative wave function with various nucleon exchange contributions and their asymptotic normalization are considered in the framework of the generator coordinate method (GCM). The asymptotic normalization of relative wave function provide the estimate of the coupling constant. The relative wave function is also used to obtain⁷Li-α-t vertex function in the virtual decay of⁷Li. The extrapolation of vertex function for negative values ofq ² up to the alpha-triton pole provide the vertex constant, which is compared with the experimentally determined estimates 0.67 FM and 0.72 FM. Our calculated value is 0.656 FM which is in close agreement with the above estimates.     

Elastic charge density representation of the interaction via the nematic director field

The interaction between particle-like sources of the nematic director distortions (e.g., colloids, point defects, macromolecules in nematic emulsions) allows for a useful analogy with the electrostatic multipole interaction between charged bodies. In this paper we develop this analogy to the level corresponding to the charge density and consider the general status of the pairwise approach to the nematic emulsions with finite-size colloids. It is shown that the elastic analog of the surface electric charge density is represented by the two transverse director components on the surface imposing the director distortions. The elastic multipoles of a particle are expressed as integrals over the charge density distribution on this surface. Because of the difference between the scalar electrostatics and vector nematostatics, the number of elastic multipoles of each order is doubled compared to that in the electrostatics: there are two elastic charges, two vectors of dipole moments, two quadrupolar tensors, and so on. The two-component elastic charge is expressed via the vector of external mechanical torque applied on the particle. As a result, the elastic Coulomb-like coupling between two particles is found to be proportional to the scalar product of the two external torques and does not directly depend on the particles' form and anchoring. The real-space Green function method is used to develop the pairwise approach to nematic emulsions and determine its form and restrictions. The pairwise potentials are obtained in the familiar form, but, in contrast to the electrostatics, they describe the interaction between pairs (dyads) of the elastic multipole moments. The multipole moments are shown to be uniquely determined by the single-particle director field, unperturbed by other particles. The pairwise approximation is applicable only in the leading order in the small ratio particle size-to-interparticle distance as the next order contains irreducible three-body terms.     

Continuum theory of dislocations revisited

The paper continues the discussion of continuum theory of dislocations suggested by Berdichevsky and Sedov (PMM 31(6): 981–1000, 1967). The major new points are: the choice of energy, the variational form of the governing dynamical equations, the variational principle for the final plastic state.     

Homogeneous monotropic elastic rods: Normal uniform configurations and universal solutions

A number of simple solutions are obtained which are universal for an homogeneous monotropic elastic rod whose theory is based on a Cosserat-type model.

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Sommario Si ottengono alcune soluzioni semplici che sono universali per una trave omogenea monotropica la cui teoria è basata su un modello alla Cosserat.

     

An atomistic-based continuum theory for carbon nanotubes: analysis of fracture nucleation

Carbon nanotubes (CNTs) display unique properties and have many potential applications. Prior theoretical studies on CNTs are based on atomistic models such as empirical potential molecular dynamics (MD), tight-binding methods, or first-principles calculations. Here we develop an atomistic-based continuum theory for CNTs. The interatomic potential is directly incorporated into the continuum analysis through constitutive models. Such an approach involves no additional parameter fitting beyond those introduced in the interatomic potential. The atomistic-based continuum theory is then applied to study fracture nucleation in CNTs by modelling it as a bifurcation problem. The results agree well with the MD simulations.     

基于长短时记忆神经网络的能谱核素识别方法

针对新兴的能谱核素识别方法在混合放射性核素的噪声环境中存在识别速度慢、准确率较低等问题,提出了基于长短时记忆神经网络（LSTM）的能谱核素识别方法。实验使用溴化镧（LaBr₃）晶体探测器,分别对环境中⁶⁰Co、¹³⁷Cs放射性源分组测量得到能谱数据集,首先使用数据平滑方法和归一化方法进行数据预处理,然后将能谱数据按时间序列分组以获得可用的输入序列数组,最后训练LSTM模型得到预测结果。通过基于BP神经网络和卷积神经网络（CNN）的两个能谱识别模型进行对比,得到在测试集中平均识别率分别为83.45%和86.21%,而LSTM能谱识别模型平均识别率为93.04%,实验结果表明,该能谱模型在核素识别效果中表现较好,可用于快速的能谱核素识别设备上。