Finding any given 2‐factor in sparse pseudorandom graphs efficiently

Given an $n$‐vertex pseudorandom graph $G$ and an $n$‐vertex graph $H$ with maximum degree at most two, we wish to find a copy of $H$ in $G$, that is, an embedding $\phi :V\left(H\right)\to V\left(G\right)$ so that $\phi \left(u\right)\phi \left(v\right)\in E\left(G\right)$ for all $uv\in E\left(H\right)$. Particular instances of this problem include finding a triangle‐factor and finding a Hamilton cycle in $G$. Here, we provide a deterministic polynomial time algorithm that finds a given $H$ in any suitably pseudorandom graph $G$. The pseudorandom graphs we consider are $\left(p,\lambda \right)$‐bijumbled graphs of minimum degree which is a constant proportion of the average degree, that is, $\mathrm{\Omega }\left(pn\right)$. A $\left(p,\lambda \right)$‐bijumbled graph is characterised through the discrepancy property: $|e\left(A,B\right)?p|A||B||<\lambda \sqrt{|A||B|}$ for any two sets of vertices $A$ and $B$. Our condition $\lambda =O(p^{2}n/\log n)$ on bijumbledness is within a log factor from being tight and provides a positive answer to a recent question of Nenadov. We combine novel variants of the absorption‐reservoir method, a powerful tool from extremal graph theory and random graphs. Our approach builds on our previous work, incorporating the work of Nenadov, together with additional ideas and simplifications.     

Poly (Ethylene Glycol)‐Based Hydrogels as Self‐Inflating Tissue Expanders with Tunable Mechanical and Swelling Properties

Tissue expansion is used by plastic/reconstructive surgeons to grow additional skin/tissue for replacing or repairing lost or damaged soft tissues. Recently, hydrogels have been widely used for tissue expansion applications. Herein, a self‐inflating tissue expander blend composition from three different molecular weights (2, 6, and 10 kDa) of poly (ethylene glycol) diacrylate (PEGDA) hydrogel with tunable mechanical and swelling properties is presented. The in vitro results demonstrate that, of the eight studied compositions, P6 (PEGDA 6 kDa:10 kDa (50:50)) and P8 (PEGDA 6 kDa:10 kDa (35:65)) formulations provide a balance of mechanical property and swelling capability suitable for tissue expansion. Furthermore, these expanders can be compressed up to 60% of their original height and can be loaded and unloaded cyclically at least ten times with no permanent deformation. The in vivo results indicate that these two engineered blend compositions are capable to generate a swelling pressure sufficient to dilate the surrounding tissue while retaining their original shape. The histological analyses reveal the formation of fibrous capsule at the interface between the implant and the subcutaneous tissue with no signs of inflammation. Ultimately, controlling the PEGDA chain length shows potential for the development of self‐inflating tissue expanders with tunable mechanical and swelling properties.

     

用光纤传输激光的方法实现激光扫描雕刻

利用扩束镜和聚焦透镜的组合，把峰值功率高达二百多千瓦的调ＱＹＡＧ激光耦合到光纤中，并用双透镜将光纤输出端的出射激光聚焦，成功地应用在光纤传输激光雕刻机中。     

Total internal reflection–refraction beam expander

Beam expanders being used presently have complex structure and none is perfect. A novel beam expander is proposed first. The beam expander can magnify (or decrease) the diameter of incident laser beam according to the theory of total internal reflection–refraction (TIR-R) principle. The characteristic of the beam expander was studied by using ray-tracing method and computer simulation. The beam expander can propagate a parallel laser beam along the propagation axis and would not change the propagation direction of the beam. For a nonparallel beam the Lagrange invariant (the product of diameter and divergence angle) is not constant. This beam expander would be an effective device in some applications.     

带膨胀机的CO_2跨(超)临界逆循环的热力学分析

ＣＯ２是一种安全可靠的自然工质,可望在空调和热泵系统中得到应用。根据热力学第二定律,本文提出比较各类循环的统一方法一当量温度法。本文对带膨胀机的ＣＯ２跨临界循环及其系统进行分析和研究。结果显示该循环具有较高的用能效率,在技术上是可行的．     

Group representations that resist random sampling

We show that there exists a family of groups G_n and nontrivial irreducible representations ρ_n such that, for any constant t, the average of ρ_n over t uniformly random elements has operator norm 1 with probability approaching 1 as . More quantitatively, we show that there exist families of finite groups for which random elements are required to bound the norm of a typical representation below 1. This settles a conjecture of A. Wigderson. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 47, 605–614, 2015     

The mixing time of the giant component of a random graph

We show that the total variation mixing time of the simple random walk on the giant component of supercritical and is . This statement was proved, independently, by Fountoulakis and Reed. Our proof follows from a structure result for these graphs which is interesting in its own right. We show that these graphs are “decorated expanders” — an expander glued to graphs whose size has constant expectation and exponential tail, and such that each vertex in the expander is glued to no more than a constant number of decorations. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 45, 383–407, 2014     

A Concentration Theorem of (R,p)-anders on Hadamard Manifolds

In this note, we prove a concentration theorem of (R, p)-anders. As a simple corollary, one can prove that (X, p)-anders do not admit coarse embeddings into Hadamard manifolds with bounded sectional curvatures.     

卡塞格林望远系统与激光束参数匹配

 在激光工程系统中,把卡塞格林望远系统等效为一个扩束器和环形光阑的组合形式,研究了激光束的光腰半径与卡塞格林望远系统的参数匹配问题。推导出光束扩束后通过环形光阑衍射的场分布解析表达式,并由此数值计算了由环形光阑引起的能量损失,以及光束扩束后光腰半径与环形光阑外径的比值K对Strehl比的影响。结果表明,在卡塞格林望远系统参数确定的条件下,存在最佳比值K,使损失能量最小,并可以获得较高的Strehl比,得到最大的峰值光强。     

CO_2跨临界制冷循环中应用两相螺杆膨胀机的理论分析

本文在介绍利用环保、安全的ＣＯ２作为制冷剂的跨临界循环的基础上,分析了系统各部件的■损失情况,并通过与常规工质对比,提出了采用汽液两相螺杆膨胀机取代系统中节流阀的方法。该方法可明显提高系统的ＣＯＰ,具有广阔的实际应用前景。文章结合ＣＯ２超临界流体的实际特点,对研制、开发ＣＯ２两相螺杆膨胀机提出了设计思想和建议。