Multistrain edge‐based compartmental model on networks

Multistrain diseases, which are infected through individual contacts, pose severe public health threat nowadays. In this paper, we build competitive and mutative two‐strain edge‐based compartmental models using probability generation function (PGF) and pair approximation (PA). Both of them are ordinary differential equations. Their basic reproduction numbers and final size formulas are explicitly derived. We show that the formula gives a unique positive final epidemic size when the reproduction number is larger than unity. We further consider competitive and mutative multistrain diseases spreading models and compute their basic reproduction numbers. We perform numerical simulations that show some dynamical properties of the competitive and mutative two‐strain models.     

Powers of edge ideals with linear resolutions

We show that if G is a gap-free and diamond-free graph, then I(G)^s has a linear minimal free resolution for every s≥2.     

A novel rigid wheel for agricultural machinery applicable to paddy field with muddy soil

The working performance of agricultural machinery is largely determined by the walking performance of the wheel when driving in complex unstructured soil. However, the driving performance of existing wheels is not satisfactory for paddy field with muddy soil. The purpose of the current study is therefore to propose a novel rigid wheel for agricultural machinery which is applicable to paddy field with muddy soil. Firstly, a novel arc edge shaped wheel was designed based on the principles of mechanics on the ground. Then the driving performance of this arc edge shaped wheel was evaluated using FE modeling of interaction between rigid wheel and soil. Finally, the structure originally designed arc edge shaped wheel was improved according to FE modeling results, and this improved design was further evaluated by both FE simulation and prototype experiments. Both FE modeling and experimental results indicate that the improved arc edge shaped wheel proposed in this study has a good driving performance with regarding to wheel sinkage and soil reaction force. The proposed arc edge shaped wheel could be used as an effective component of rice harvester for paddy field with muddy soil.     

Edge proximity and matching extension in projective planar graphs

A graph $G$ with at least $2m+2$ vertices is said to be distance $d$ $m$-extendable if, for any matching $M$ of $G$ with $m$ edges in which the edges lie at distance at least $d$ pairwise, there exists a perfect matching of $G$ containing $M$. In this paper we prove that every 5-connected triangulation on the projective plane of even order is distance 3 7-extendable and distance 4 $m$-extendable for any $m$.     

Implementation of a separate fluid-neutral energy equation in SOLPS-ITER and its impact on the validity range of advanced fluid-neutral models

In plasma edge transport codes for nuclear fusion devices, fluid-neutral models offer an interesting alternative to the currently used kinetic Monte Carlo simulations, especially for cases of high ion-neutral collisionality. In this paper, we elaborate a separate neutral energy equation in the state-of-the-art SOLPS-ITER code suite, which previously assumed perfect ion-neutral temperature equilibration. Furthermore, we study the coupled plasma-neutral solutions for a range of divertor operating regimes, proving the validity of these fluid-neutral models for high-recycling and detached regimes.     

基于光子晶体带边效应的表面增强拉曼基底

将光子晶体的带边效应与金纳米粒子的拉曼散射增强作用相结合,制备了一种新型光子晶体表面增强拉曼散射基底(PC-AuNPs),利用罗丹明B(RhB)作为报告分子,对所得基底性能进行检测.PC-AuNPs基底的制备包括3个步骤:在SiO2微球表面修饰氨基,再通过垂直沉降自组装得到蛋白石结构光子晶体(PC), 最后, 在光子晶体表面负载金纳米粒子(AuNPs).结果表明,光子晶体的带隙范围及AuNPs的负载量直接影响了PC-AuNPs基底的检测效果;以所得的PC-AuNPs基底测定RhB分子,其拉曼散射特征峰强度与浓度对数值呈现良好的线性关系,线性方程为I=1711lg[RhB(mol/L)]+15244,线性相关系数R2=0.9994,检出限为1×10-8 mol/L,表明此PC-AuNPs基底可用于目标物的定性及定量检测.本方法提高了传统拉曼散射光谱检测灵敏度,操作简单,具有良好的重现性,可为其它新型检测基底的制备提供.     

On the Minimum Number of Spanning Trees in k‐Edge‐Connected Graphs

We show that a k‐edge‐connected graph on n vertices has at least spanning trees. This bound is tight if k is even and the extremal graph is the n‐cycle with edge multiplicities . For k odd, however, there is a lower bound , where . Specifically, and . Not surprisingly, c₃ is smaller than the corresponding number for 4‐edge‐connected graphs. Examples show that . However, we have no examples of 5‐edge‐connected graphs with fewer spanning trees than the n‐cycle with all edge multiplicities (except one) equal to 3, which is almost 6‐regular. We have no examples of 5‐regular 5‐edge‐connected graphs with fewer than spanning trees, which is more than the corresponding number for 6‐regular 6‐edge‐connected graphs. The analogous surprising phenomenon occurs for each higher odd edge connectivity and regularity.