矩阵系统扰动后的稳定性问题

本文证明：若矩阵系统是广义各态历经的，则系统是稳定的；若矩阵系统是善真的，则系统是条件稳定的。     

非线性动力系统的规范形和余维3退化分叉

本文里我们利用矩阵表示法计算了具有Z_(2~-)对称性时非线性动力系统的高阶规范形,求出了余维2退化和余维3退化情况下相应规范形的普适开折。最后利用所得到的规范形和普适开折讨论了非线性动力系统的余维3退化分叉。     

Buoyancy Sustained by Viscous Dissipation

The quasi-parallel regime of a Darcy–Boussinesq boundary-layer flow over a permeable vertical flat plate adjacent to a fluid saturated porous medium is considered. Quasi-parallel means here a plane flow with a constant transversal velocity v=–v ₀ directed perpendicularly towards the vertical surface, where a lateral suction with the same velocity –v ₀ is applied. The plate is held at a constant temperature T _w which coincides with the ambient temperature T of the fluid. The heat released by viscous dissipation induces a density gradient in the fluid. Thus, although T _w=T , a thermal convection occurs. The steady regime of this self-sustaining buoyant flow has been examined in detail. Wall jet-like profiles with a continuous but finite spectrum of the momentum flow have been found. These self-sustaining buoyant jets show a universal behavior, that is, there exist certain length, velocity and temperature scales such that the flow characteristics become independent of the (constant) material properties of the fluid and the porous medium as well.     

Dissecting Cooperative Communications in a Protein with a High‐Throughput Single‐Molecule Scalpel

Miscued communication often leads to misfolding and aggregation of the proteins involved in many diseases. Owing to the ensemble average property of conventional techniques, detailed communication diagrams are difficult to obtain. Mechanical unfolding affords an unprecedented perspective on cooperative transitions by observing a protein along a trajectory defined by two mutated cysteine residues. Nevertheless, this approach requires tedious sample preparation at the risk of altering native protein conformations. To address these issues, we applied click chemistry to tether a protein to the two dsDNA handles through primary amines in lysine residues as well as at the N terminus. As a proof of concept, we used laser tweezers to mechanically unfold and refold calmodulin along 36 trajectories, maximally allowed by this strategy in a single batch of protein preparation. Without a priori knowledge of the particular residues to which the double‐stranded DNA handles attach, we used hierarchical cluster analysis to identify 20 major trajectories, according to the size and the pattern of unfolding transitions. We dissected the cooperativity into all‐or‐none and partially cooperative events, which represent strong and weak high‐order interactions in proteins, respectively. Although the overall cooperativity is higher within the N or C lobe than that between the lobes, the all‐or‐none cooperativity is anisotropic among different the unfolding trajectories and becomes relatively more predominant when the size of the protein segments increases. The average cooperativity for all‐or‐none transitions falls within the expected range observed by ensemble techniques, which supports the hypothesis that unfolding of a free protein can be reconstituted from individual trajectories.     

The effect of disulfide bonds on protein folding,unfolding, and misfolding investigated by FT–Raman spectroscopy

Disulfide bond is relevant to many protein folding/unfolding functions and conformational diseases. To elucidate the effects of disulfide bonds on protein folding, unfolding, and misfolding, we performed Fourier transform–Raman measurements on serial chemical‐induced denaturations of bovine serum albumin (BSA). By directly monitoring Raman stretching at S–S (~507 cm⁻¹), S–H (~2566 cm⁻¹), amide I (1655 cm⁻¹ for α‐helix; 1667 cm⁻¹ for β‐sheet structure), and amide III (>1300 cm⁻¹ for α‐helix; 1246 cm⁻¹ for β‐sheet structure), the status of disulfide bonds and secondary structure of BSA at different states were elucidated. Both disulfide bonds and secondary structure (mostly in α‐helix) of BSA appeared relatively stable even when the protein was unfolded by urea solution. However, disulfide bonds were completely reduced and protein secondary structure changed from α‐helix to a relatively β‐sheet dominant when the protein was modified by the mixed solution of urea and dithiothreitol (urea/DTT). Adhering to these structural changes, the protein proceeded to different degrees of polymerization. BSA would aggregate into a high molecular mass (over 700 kDa) of protein ensemble when it was exposed to the mixed urea/DTT solution. An irreversible change in S–S/S–H conversion and secondary structure was responsible for protein misfolding. We demonstrate here that Fourier transform–Raman directly probe S–S/S–H conversion and secondary structural change of BSA at different states, and these results clearly indicate that disulfide bonds and secondary structure of BSA serve as concrete frameworks to stabilize protein structure. As the frameworks collapse, the protein undergoes an irreversible structural change and results in protein misfolding. Copyright © 2016 John Wiley & Sons, Ltd.     

Triple Systems are Eulerian

An Euler tour of a hypergraph (also called a rank‐2 universal cycle or 1‐overlap cycle in the context of designs) is a closed walk that traverses every edge exactly once. In this paper, using a graph‐theoretic approach, we prove that every triple system with at least two triples is eulerian, that is, it admits an Euler tour. Horan and Hurlbert have previously shown that for every admissible order >3, there exists a Steiner triple system with an Euler tour, while Dewar and Stevens have proved that every cyclic Steiner triple system of order >3 and every cyclic twofold triple system admits an Euler tour.     

经典N=2李共形超代数的导子和第二上同调群

研究了经典N=2李共形超代数的导子和第二上同调群的结构,并应用第二上同调群的结果确定了该李共形超代数的泛中心扩张.     

Universal mappings for certain classes of operators and polynomials between Banach spaces

A well‐known result of J. Lindenstrauss and A. Pełczyński (1968) gives the existence of a universal non‐weakly compact operator between Banach spaces. We show the existence of universal non‐Rosenthal, non‐limited, and non‐Grothendieck operators. We also prove that there does not exist a universal non‐Dunford–Pettis operator, but there is a universal class of non‐Dunford–Pettis operators. Moreover, we show that, for several classes of polynomials between Banach spaces, including the non‐weakly compact polynomials, there does not exist a universal polynomial.     

Optimal control problem in a domain with branched structure and homogenization

We consider a linear parabolic problem in a thick junction domain which is the union of a fixed domain and a collection of periodic branched trees of height of order 1 and small width connected on a part of the boundary. We consider a three‐branched structure, but the analysis can be extended to n‐branched structures. We use unfolding operator to study the asymptotic behavior of the solution of the problem. In the limit problem, we get a multi‐sheeted function in which each sheet is the limit of restriction of the solution to various branches of the domain. Homogenization of an optimal control problem posed on the above setting is also investigated. One of the novelty of the paper is the characterization of the optimal control via the appropriately defined unfolding operators. Finally, we obtain the limit of the optimal control problem. Copyright © 2016 John Wiley & Sons, Ltd.     

非确定结构系统区间分析的泛灰求解方法

工程中的不确定性问题可以用区间分析、概率理论或模糊理论来求解。采用泛灰区间分析法来处理结构静力分析和设计中的不确定性问题。将结构系统中的不确定性参数用区间数来表示，用有限元法建立系统的控制方程。该控制方程是线性区间方程组。然后，在概述泛灰数的概念及其运算规则的基础上，介绍了泛灰数与区间数的转化，利用泛灰数的可扩展性对区间进行分析，研究了泛灰线性方程求解，然后将它应用于结构静力分析和设计中的不确定性问题，泛灰数不仅具有区间分析的功能，而且能解决区间分析所不能解决的问题。文中给出了两个算例，列出了本文算法与其他算法的结果比较。