Hamiltonian and long paths in bipartite graphs with connectivity

Let G be a graph, $\nu (G)$ the order of G, $\kappa (G)$ the connectivity of G and k a positive integer such that $k\le (\nu (G)?2)/2$. Then G is said to be k-extendable if it has a matching of size k and every matching of size k extends to a perfect matching of G. A Hamiltonian path of a graph G is a spanning path of G. A bipartite graph G with vertex sets $V_1$ and $V_2$ is defined to be Hamiltonian-laceable if such that $|V_1|=|V_2|$ and for every pair of vertices $p\in V_1$ and $q\in V_2$, there exists a Hamiltonian path in G with endpoints p and q, or $|V_1|=|V_2|+1$ and for every pair of vertices $p,q\in V_1,p\ne q$, there exists a Hamiltonian path in G with endpoints p and q. Let G be a bipartite graph with bipartition $(X,Y)$. Define $bn(G)$ to be a maximum integer such that $0\le bn(G)<min\{|X|,|Y|\}$ and (1) for each non-empty subset S of X, if $|S|\le |X|?bn(G)$, then $|N(S)|\ge |S|+bn(G)$, and if $|X|?bn(G)<|S|\le |X|$, then $N(S)=Y$; and (2) for each non-empty subset S of Y, if $|S|\le |Y|?bn(G)$, then $|N(S)|\ge |S|+bn(G)$, and if $|Y|?bn(G)<|S|\le |Y|$, then $N(S)=X$; and (3) $bn(G)=0$ if there is no non-negative integer satisfying (1) and (2).Let G be a bipartite graph with bipartition $(X,Y)$ such that $|X|=|Y|$ and $bn(G)>0$. In this paper, we show that if $\nu (G)\le 2\kappa (G)+4bn(G)?4$, then G is Hamiltonian-laceable; or if $\nu (G)>6bn(G)?2$, then for every pair of vertices $x\in X$ and $y\in Y$, there is an $(x,y)$-path P in G with $|V(P)|\ge 6bn(G)?2$. We show some of its corollaries in k-extendable, bipartite graphs and a conjecture in k-extendable graphs.     

复合材料失效判据有效性验证方法研究

为系统地验证复合材料失效判据计算精度和有效性范围,给出了4种材料体系、6种铺层形式的层合板在单轴、双轴载荷下的失效试验数据,用以评估复合材料失效判据在单向层合板失效包线、多向层合板初始失效包线、多向层合板最终失效包线、层合板变形及层合板的破坏特性等五个方面的预测能力。并根据验证方法和有效性评估策略对失效判据计算精度进行量化考核,给出了失效判据在五个层面上的计算精度。     

Discovering DNA methylation patterns for long non-coding RNAs associated with cancer subtypes

Despite growing evidence demonstrates that the long non-coding ribonucleic acids (lncRNAs) are critical modulators for cancers, the knowledge about the DNA methylation patterns of lncRNAs is quite limited. We develop a systematic analysis pipeline to discover DNA methylation patterns for lncRNAs across multiple cancer subtypes from probe, gene and network levels. By using The Cancer Genome Atlas (TCGA) breast cancer methylation data, the pipeline discovers various DNA methylation patterns for lncRNAs across four major subtypes such as luminal A, luminal B, her2-enriched as well as basal-like. On the probe and gene level, we find that both differentially methylated probes and lncRNAs are subtype specific, while the lncRNAs are not as specific as probes. On the network level, the pipeline constructs differential co-methylation lncRNA network for each subtype. Then, it identifies both subtype specific and common lncRNA modules by simultaneously analyzing multiple networks. We show that the lncRNAs in subtype specific and common modules differ greatly in terms of topological structure, sequence conservation as well as expression. Furthermore, the subtype specific lncRNA modules serve as biomarkers to improve significantly the accuracy of breast cancer subtypes prediction. Finally, the common lncRNA modules associate with survival time of patients, which is critical for cancer therapy.     

Teflon Magnetic Stirring Capsules (TMSC) as a Practical and Reusable Delivery System for Sensitive Reagents and Catalysts

The development of a user-friendly reusable laboratory equipment for the delivery of sensitive reagents and catalysts is described. The tightness of these Teflon Magnetic Stirring Capsules (TMSC) is ensured by the magnetic force and release of the reagent inside the solution is triggered by adjusting the stirring rate so that the centrifuge force exceeds the magnetic force. They can be loaded with several chemicals at the same time and do operate across a broad range of temperatures. The inertness of Teflon facilitates reaction purification.     

Remarkably improved cycling stability of 3D porous Cu–Sn anode for lithium-ion full cells by adjusting working voltage range

Numerous studies confirm that three dimensional porous Cu–Sn (3DP Cu–Sn) anode possesses good application prospect in light of its desirable electrochemical performance on lithium ion half cells, but there are a few related systematic researches on lithium ion full cells until now, which is indispensable before its commercialization. Herein, the effects of galvanostatic charge-discharge voltage range on the cycling stability of 3DP Cu–Sn anode for lithium ion full cells are investigated systematically. The results show that the suitable charge-discharge voltage range plays a key role in improving the reversible capacity and cycling stability of the 3DP Cu–Sn||LiCoO₂ full cell, which is closely related to maintaining the electrode structure stable by controlling the amount of Li⁺ extracted and inserted. Especially, in the voltage range of 1.2–3.9 ​V, the full cell exhibits remarkably improved electrochemical properties with the high initial reversible capacity of 2.71 ​mAh cm⁻² and 71.95% capacity retention upon 80 cycles. We believe that this work can provide a significant reference for the practical application of porous Sn-based anodes.     

长链支化聚丙烯的非线性流变行为

通过大幅振荡剪切试验方法, 研究了长链支化聚丙烯的非线性流变学行为, 揭示了长链支化结构与非线性黏弹响应的关系. 利用傅里叶变换流变学方法得到试样的三次倍频相对振幅I_3/1与应变的标度关系, 用于界定线性聚丙烯和长链支化聚丙烯非线性流变行为的差异, 并定义了非线性系数来量度长链支化程度. 在高应变下, I_3/1与应变的变化关系可以进一步描述长链支化在非线性流场下的特性, 并得到了长链支化程度与其非线性响应之间的变化关系. 通过应力波的Lissajous曲线分解, 发现了环内和环间黏弹性的差异, 长链支化结构在大应变流场下的非线性黏弹性响应弱于线性结构, 支化程度越高非线性响应越弱.     

High‐temperature superconductivity and long‐range order in strongly correlated electronic systems

A selective review of the question of how repulsive electron correlations might give rise to off‐diagonal long‐range order (ODLRO) in high‐temperature superconductors is presented. The article makes detailed explanations of the relevance to superconductivity of reduced electronic density matrices and how these can be used to understand whether ODLRO might arise from Coulombic repulsions in strongly correlated electronic systems. Time‐reversed electron pairs on alternant Cuprate and the iron‐based pnictide and chalcogenide lattices may have a weak long‐range attractive tail and much stronger short‐range repulsive Coulomb interaction. The long‐range attractive tail may find its origin in one of the many suggested proposals for high‐T_c superconductivity and thus has an uncertain origin. A phenomenological Hamiltonian is invoked whose model parameters are obtained by fitting to experimental data. A detailed summary is given of the arguments that such interacting electrons can cooperate to produce a superconducting state in which time‐reversed pairs of electrons effectively avoid the repulsive hard‐core of the Coulomb interaction but reside on average in the attractive well of the long‐range potential. Thus, the pairing of electrons itself provides an enhanced screening mechanism. The alternant lattice structure is the key to achieving robust high‐temperature superconductivity with dx²‐y² or sign alternating s‐wave or s± condensate symmetries in cuprates and iron‐based compounds. Some attention is also given to the question first raised by Leggett as to where the Coulombic energy is saved in the superconducting transition in cuprates. A mean‐field‐type model in which the condensate density serves as an order parameter is discussed. Many of the observed trends in the thermal properties of cuprate superconductors are reproduced giving strong support for the proposed model for high‐temperature superconductivity in such strongly correlated electronic systems. © 2015 Wiley Periodicals, Inc.     

Continuous fast focusing in a trapezoidal void channel based on bidirectional isotachophoresis in a wide pH range

This study concentrates on development of instrumentation for focusing and separation of analytes in continuous flow. It is based on bidirectional ITP working in wide pH range with separation space of closed void channel of trapezoidal shape and continuous supply of sample. The novel instrumentation is working with electrolyte system formulated previously and on the contrary to devices currently available, it allows preparative separation and concentration of cationic, anionic, and amphoteric analytes simultaneously and in wide pH range. The formation of sharp edges at zone boundaries as well as low conductivity zones are avoided in suggested system and thus, local overheating is eliminated allowing for high current densities at initial stages of focusing. This results in high focusing speed and reduction of analysis time, which is particularly advantageous for separations performed in continuous flow systems. The closed void channel is designed to avoid basic obstacles related to liquid leakage, bubbles formation, contacts with electrodes, channel height and complicated assembling. The performance of designed instrumentation and focusing dynamics were tested by using colored low molecular mass pH indicators for local pH determination, focusing pattern, and completion. In addition, feasibility and separation efficiency were demonstrated by focusing of cytochrome C and myoglobin. The collection of fractions at instrument output allows for subsequent analysis and identification of sample components that are concentrated and conveniently in form of solution for further processing. Since the instrumentation operates with commercially available simple defined buffers and compounds without need of carrier ampholytes background, it is economically favorable.