周期激励Stuart-Landau方程的某些动力学行为

研究了周期激励Stuart-Landau方程的锁频周期解．利用奇异性理论分别研究了这些解关于外部激励振幅和频率的分岔行为．结果表明:关于外部激励振幅的普适开折具有余维3,在某些条件下,得到了转迁集及分岔图．另外还证明:关于频率的分岔问题具有无穷余维,因此该情形下的动力学分岔行为非常复杂．发现了一些新的动力学现象,它们是孙亮等所获结果的补充．     

钙离子调控微丝切割蛋白中A6亚基解折叠的单分子力谱研究

在生命活动中,金属离子扮演了非常重要的角色.微丝切割蛋白(adseverin)需要钙离子的活化才能行使其切割肌动蛋白微丝的功能.本文通过基于原子力显微镜的单分子力谱研究了微丝切割蛋白C端末的A6亚基在结合钙离子前后的力学解折叠机理.实验结果显示:在未结合钙离子时,A6的解折叠表现为两态过程;在结合钙离子后A6力学稳定性显著提高;同时,钙离子的结合使得A6解折叠过程中出现稳定的中间态.通过对中间态的链长的分析,我们推测了中间态对应着A6的N端部分解折叠.而这一部分的解折叠可以使得掩藏在该结构后的A5亚基中肌动蛋白微丝结合位点暴露,从而促使微丝切割蛋白执行功能.我们的实验结果为理解微丝切割蛋白的工作原理提供了新的实验证据.     

Homogenization of contact problem with Coulomb's friction on periodic cracks

We consider the elasticity problem in a domain with contact on multiple periodic open cracks. The contact is described by the Signorini and Coulomb‐friction conditions. The problem is nonlinear, the dissipative functional depends on the unknown solution, and the existence of the solution for fixed period of the structure is usually proven by the fix‐point argument in the Sobolev spaces with a little higher regularity, H^1+α. We rescaled norms, trace, jump, and Korn inequalities in fractional Sobolev spaces with positive and negative exponents, using the unfolding technique, introduced by Griso, Cioranescu, and Damlamian. Then we proved the existence and uniqueness of the solution for friction and period fixed. Then we proved the continuous dependency of the solution to the problem with Coulomb's friction on the given friction and then estimated the solution using fixed‐point theorem. However, we were not able to pass to the strong limit in the frictional dissipative term. For this reason, we regularized the problem by adding a fourth‐order term, which increased the regularity of the solution and allowed the passing to the limit. This can be interpreted as micro‐polar elasticity.     

Thermochemical, volumetric and spectroscopic properties of lysozyme–poly(ethylene) glycol system

Investigations of lysozyme–polyethylene glycol system were made by differential scanning calorimetry, fluorescence and density techniques. The values of unfolding enthalpies, ΔH_N^U, unfolding temperatures, T_m, excess molar heat capacities, ΔC_p, and apparent molar volumes, V_Φ , were determined as functions of PEG concentration. The three PEGs of average molecular mass (MW) 6000, 10000, 20000 were used as macromolecular crowding agents. The concentration of polymers was changed in the range 0–30% mass per volume (w/v). The values of ΔH_N^U remained constant with no dependence on PEG concentration, while PEG addition to buffered lysozyme solutions caused linear decrease of T_m. The values of ΔC_p and V_Φ of lysozyme dramatically changed in the range of 8–10% of PEG concentration. The fluorescence spectroscopy was used in order to investigate the polymer influence on possible solvent–lysozyme interactions. The electrical properties of polymer–water and polymer–buffer systems, the dielectric constants of solutions were determined with use of impedance spectroscopy.     

The singularities of null surfaces in Anti de Sitter 3-space

We study the geometric properties of degenerate surfaces, which are called AdS null surfaces, in Anti de Sitter 3-space from a contact viewpoint. These surfaces are associated to spacelike curves in Anti de Sitter 3-space. We define a map which is called the torus Gauss image. We also define two families of functions and use them to investigate the singularities of AdS null surfaces and torus Gauss images as applications of singularity theory of functions.     

Sur les notions de quasi-homogénéité de feuilletages holomorphes endimension deux

In this note, we recall the different notions of quasi-homogeneity for singular germs of holomorphic foliations in the plane presented in [6]. The classical notion of quasi-homogenity allude to those functions which belong to its own jacobian ideal. Given a foliation in the plane, asking that the equation of the separatrix set is a classical quasi-homogeneous function we obtain a natural generalization in the context of foliations. On the other hand, topological quasi-homogeneity is characterized by the fact that every topologically trivial deformation whose sepatrix family is analytically trivial is an analytically trivial deformation. We give an explicit example of a topological quasi-homogeneous foliation which is not quasi-homogeneous in the sense given above.

     

ANALYSIS OF STABILITY ON ELASTIC PLATES WITH INITIAL IMPERFECTIONS

ＡＮＡＬＹＳＩＳＯＦＳＴＡＢＩＬＩＴＹＯＮＥＬＡＳＴＩＣＰＬＡＴＥＳＷＩＴＨＩＮＩＴＩＡＬＩＭＰＥＲＦＥＣＴＩＯＮＳＸｕＫａｉｙｕ（徐凯宇）（ＲｅｃｅｉｔｅｄＯｃｔ．５，１９９４．ＣｏｍｍｕｎｉｃａｔｅｄＰａｉＬｉｚｈｏｕ）ＡＮＡＬＹＳＩＳＯＦＳＴＡ...     

Interface water-induced hydrophobic carbon chain unfolding in water

The folding and unfolding of the carbon chain, which is the basic constitutional unit of polymers,are important to the performance of the material. However, it is difficult to regulate conformational transition of the carbon chain, especially in an aqueous environment. In this paper, we propose a strategy to regulate the conformational transition of the carbon chain in water based on the all-atom molecular dynamics simulations. It is shown that the unfolded carbon chain will spontaneously collapse into the folded state, while the folded carbon chain will unfold with an external electric field. The regulation ability of the electric field is attributed to the electric field-induced redistribution of interface water molecules near the carbon chain. The demonstrated method of regulating conformational transition of the carbon chain in water in this study provides an insight into regulating hydrophobic molecules in water, and has great potential in drug molecule design and new polymer material development.     

Asymptotic analysis of an interior optimal control problem governed by Stokes equations

This article introduces an interior optimal control problem (OCP) in a two-dimensional domain with a highly oscillatory boundary governed by the stationary Stokes equations. We consider the periodic controls in the oscillating region of the domain and use the unfolding operators to characterize the optimal controls. We establish the convergences of optimal control, state, and pressure in a suitable space to the ones of the limit system in a fixed domain.     

Equivariant multiparameter bifurcation via singularity theory

The theoretical machinery from singularity theory introduced by Golubitsky, Stewart, and Schaeffer, to study equivariant bifurcation problems, is completed and expanded while generalized to the multiple parameter context. In this setting the finite determinacy theorems or normal forms, the stability of equivariant bifurcation problems, and the structural stability of the universal unfolding are discussed.