Canonical maps between semidirect products with applications to elasticity and superfluids

It is shown that two canonical maps arising in the Poisson bracket formulations of elasticity and superfluids are particular instances of general canonical maps between duals of semidirect product Lie algebras.     

叶轮机械设计自变数在内外环壁面上的限制条件及轴流式叶轮机械S1流面的翘曲

本文利用中心流面法的概念,指出叶轮机械的设计白变数在内、外环壁面上应有附加的限制条件,并导得其具体简明方程。同时,还定性地分析了S₁流面的翘曲情况。     

超导临界温度理论(Ⅰ)

本文求出了Eliashberg方程在T=T_c时的解,得到了下面的临界温度级数表示式: 其中α₀(μ^*),α₁(μ^*)等系数是μ^*的函数.此式表明,T_c不仅依赖于λ,〈ω²〉和μ^*,而且依赖于有效声子谱α²F(ω)的各级矩〈ω²n〉.这是区别于前人的T_c公式最重要的一点。这说明像McMillan以及Allen和Dynes的T_c公式不仅是近似的,而主要是他们没有能正确地概括出α²F(ω)对T_c的影响.     

On the generators of semisimple lie algebras

It will be shown that given any element X in a simple Lie algebra $\text{Q}$ over C, there exists a Y ∈ $\text{Q}$ such that the Lie algebra generated by X and Y is $\text{Q}$. The result is extended to the real semisimple Lie algebras. In some sense the main theorem of this paper can be regarded as an extension of Morozov-Jacobson theorem concerning three dimensional simple Lie algebras (see the remark at the end of Sec. 4). A new property of a special class of regular elements, known as the cyclic elements, is given.     

Selective transfer of energy through an alamethicin-doped artificial lipid membrane studied at discrete molecular level

In this study we present novel evidence that strengthens the paradigm of selective transfer of energy mediated by a random gating of ion channels. Specifically, we investigated the spectral response of a noisy artificial biomembrane whose electrical properties were largely dictated by embedded alamethicin oligomers. In this respect, we first evaluated experimentally the linear transfer function of the system via the white-noise analysis method. We prove that such a system displays specific ranges of frequency over which input signals pass preferentially, depending on their spectral content and the holding potential across the artificial bilayer which contains alamethicin. By employing voltage-driven periodic stimulation of alamethicin oligomers, we demonstrate that overall response of the system obeys qualitatively the predictions inferred from the transfer function analysis of it. These results emphasize the exquisite ability of excitable membranes to behave as band-limited filters and allow for maximal transfer of energy from an external stimulus over well-defined frequency ranges.     

Robust Contour Tracking Model Using a Variational Level-Set Algorithm

In this work, we provide a novel variational level-set based object contour tracking approach. Thus, a mathematically rigorous variant of the Chan-Vese algorithm for image segmentation via geometric active contour model is proposed here. With respect to the original contour detection algorithm, the level set function ?(t) defining the evolving contour S _t  = {x; ?(t, x) = 0} is iteratively computed from a nonlinear parabolic boundary value problem that is well posed in the space of functions with bounded variations. We provide a robust mathematical justification of the proposed level-set model.