J-TEXT托卡马克高速单色成像系统研制

在 J-TEXT 托卡马克上研制了一套高速单色成像系统用于研究等离子体杂质行为与磁流体力学(MHD) 不稳定性之间的关系。用 STRAH 代码模拟估算了碳杂质(CV227.09nm,CIII464.7nm)辐射强度。采用光纤耦合方 法设计了系统光路结构,光路覆盖高场侧区域 0.3a~0.95a(a 为小半径),其空间分辨率为 1.3cm。选用光电倍增管 (PMT)作为系统的探测器,结合跨阻电路与有源滤波器的电路方案,系统实现 5×10⁵VA^-1 电流增益,其电路带宽 为 100kHz,时间分辨率达到 10μs。初步实验结果表明,系统可以监测到 J-TEXT 中等离子体 MHD 不稳定性放电 中 CV 分布的变化。      

Ramsey数的性质研究

本文得出了若干有关Ramsey数性质的结论,这些结论可直接用来推导Ram-sey数的下界公式,也可用来改进已有的Ramsey数的下界结果,本文中定理的证明思路,还能用于研究其它的图论和组合数学问题。     

Colorful monochromatic connectivity

An edge-coloring of a connected graph is monochromatically-connecting if there is a monochromatic path joining any two vertices. How “colorful” can a monochromatically-connecting coloring be? Let mc(G) denote the maximum number of colors used in a monochromatically-connecting coloring of a graph G. We prove some nontrivial upper and lower bounds for mc(G) and relate it to other graph parameters such as the chromatic number, the connectivity, the maximum degree, and the diameter.     

单色化X射线对薄膜表面高分子降解行为的影响

采用聚甲基丙烯酸甲酯(PMMA)和苯乙烯-丙烯腈无规共聚物(SAN)薄膜体系, 在不同的实验温度下, 研究了单色化的X射线对其中一个组分(PMMA)降解行为的影响.     

Large monochromatic components in colorings of complete 3-uniform hypergraphs

Let f(n,r) be the largest integer m with the following property: if the edges of the complete 3-uniform hypergraph are colored with r colors then there is a monochromatic component with at least m vertices. Here we show that and . Both results are sharp under suitable divisibility conditions (namely if n is divisible by 7, or by 6 respectively).     

Gallai–Ramsey numbers for cycles

For given graphs G and H and an integer k, the Gallai–Ramsey number is defined to be the minimum integer n such that, in any k coloring of the edges of K_n, there exists a subgraph isomorphic to either a rainbow coloring of G or a monochromatic coloring of H. In this work, we consider Gallai–Ramsey numbers for the case when G=K₃ and H is a cycle of a fixed length.     

PGP成像光谱仪的全视场自动化光谱定标方法

为了对PGP成像光谱仪所获得的光谱数据进行定量化分析,需对PGP成像光谱仪进行光谱定标,以获得各光谱通道的中心波长、光谱分辨率及成像光谱仪的光谱弯曲等光谱特性信息。采用单色准直光法设计了一套全视场自动化的光谱定标系统,系统中引入球面镜为待测的成像光谱仪光谱定标提供准直光,通过可自动控制的折转镜改变定标入射光线的入射角,以此实现待测成像光谱仪空间维不同视场的自动化光谱定标。运用该定标系统对PGP成像光谱仪进行光谱定标实验,得到该成像光谱仪的光谱性能参数,并结合定标系统的结构特点,对实验的结果进行了精度分析。实验分析结果表明该系统对PGP成像光谱仪的中心波长定标精度达到0.1 nm,光谱分辨率定标精度达到1.3%。该研究设计的全视场自动化光谱定标系统具有结构新颖紧凑、通用性较强、光谱定标精度较高等特点,且由于自动化的控制,避免了由于人为参与定标过程所带来的额外误差。该系统可用于实现PGP成像光谱仪及其他同类型成像光谱仪的光谱定标。     

Equation-regular sets and the Fox–Kleitman conjecture

Given $k\ge 1$, the Fox–Kleitman conjecture from 2006 states that there exists a nonzero integer $b$ such that the $2k$-variable linear Diophantine equation

$\sum _{i=1}^k(x_i?y_i)=b$

is $(2k?1)$-regular. This is best possible, since Fox and Kleitman showed that for all $b\ge 1$, this equation is not $2k$-regular. While the conjecture has recently been settled for all $k\ge 2$, here we focus on the case $k=3$ and determine the degree of regularity of the corresponding equation for all $b\ge 1$. In particular, this independently confirms the conjecture for $k=3$. We also briefly discuss the case $k=4$.