Vertex-disjoint rainbow triangles in edge-colored graphs

Let $G$ be an edge-colored graph of order $n$. The minimum color degree of $G$, denoted by ${\delta }^c\left(G\right)$, is the largest integer $k$ such that for every vertex $v$, there are at least $k$ distinct colors on edges incident to $v$. We say that an edge-colored graph is rainbow if all its edges have different colors. In this paper, we consider vertex-disjoint rainbow triangles in edge-colored graphs. Li (2013) showed that if ${\delta }^c\left(G\right)\ge (n+1)∕2$, then $G$ contains a rainbow triangle and the lower bound is tight. Motivated by this result, we prove that if $n\ge 20$ and ${\delta }^c\left(G\right)\ge (n+2)∕2$, then $G$ contains two vertex-disjoint rainbow triangles. In particular, we conjecture that if ${\delta }^c\left(G\right)\ge (n+k)∕2$, then $G$ contains $k$ vertex-disjoint rainbow triangles. For any integer $k\ge 2$, we show that if $n\ge 16k-12$ and ${\delta }^c\left(G\right)\ge n∕2+k-1$, then $G$ contains $k$ vertex-disjoint rainbow triangles. Moreover, we provide sufficient conditions for the existence of $k$ edge-disjoint rainbow triangles.     

Using multi-exposure of color fringes to measure the beating motion of a moth

A multi-exposure of color fringes method has been developed to improve the capture speed of a conventional color CCD camera. In the method, four groups of projected fringe patterns encoded with different colors and different directions are stored in one CCD frame. Therefore the capture frequency of the conventional CCD can be improved to 200 Hz. It is available to measure the insect wings with low beating frequency, such as dragonfly, moth, or butterfly, whose beating frequency is about 30–40 Hz. We have used the method to measure the beating motion of a moth successfully.     

The Iyengar Type Inequalities with Exact Estimations and the Chebyshev Central Algorithms of Integrals

In this paper, both low order and high order extensions of the Iyengar type inequality are obtained. Such extensions are the best possible in the same sense as that of the Iyengar inequality. hzrthermore, the Chebyshev central algorithms of integrals for some function classes and some related problems are also considered and investigated.     

基于遗传算法和指标满意度求解的第三方物流企业物流中心选址方法

本利用AHP和模糊综合评价法评价物流中心选址的定性指标、用量化选址模型结合遗传算法计算定量指标，再藉助指标满意度求解把定性和定量的指标进行综合，从而为决策对物流中心选址做出科学的决策提供支持。     

γ-辐照对纯Y_2SiO_5和Eu~(3+)∶Y_2SiO_5晶体光谱性能的影响

研究了γ-辐照前后纯Y2SiO5和Eu3+掺杂的Y2SiO5晶体吸收光谱的变化,辐照后,未退火和氢气退火的纯Y2SiO5晶体在260~270 nm和320 nm波段产生了附加吸收峰,分别是由F心和O-心的吸收引起的;经过空气退火的纯YSO晶体中,由于消除了氧空位,因此辐照后没有出现色心吸收峰。在Eu3+∶Y2SiO5晶体中,不但有相同的F心和O-心吸收峰,而且还有Eu2+离子在300 nm和390 nm的吸收峰。随着辐照剂量的增加,色心附加吸收峰增强。空气退火能减少Eu3+∶Y2SiO5晶体中的色心,而氢气退火能增加色心。     

F／Cl比与Eu~（2＋）：BaFCl中F色心的浓度和光激励截面的关系

研究了Ｅｕ（２＋）：ＢａＦｘＣｌ２在紫外线辐照下的光激励发光。通过改变激励方式及激励光的扫描方向，给出了Ｅｕ（２＋）：ＢａＦｘＣｌ２－ｘ光激励发光过程中，两种Ｆ色心的浓度比值与光激励截面比值的测定方法。利用这种测定方法，进一步研究了两种Ｆ色心的浓度比值和光激励截面比值与Ｆ／ＣＩ比值的关系。     

炉液倾动重心近似计算的数学分析

为给转炉设计提供依据,需要计算炉液倾动的重心.利用数学方法将实际问题进行简化,通过分析炉液倾动过程中变量间的相互关系,来确定每个倾动角度对应情况下的液面位置.利用数学中三重积分的有关应用,进一步得出转炉在每个倾动角度为α∈(0,π2)时的重心计算方法及相关结论,在理论上为工程计算重心的方法提供参考.     

CCD光谱谱线标定方法研究

CCD作为光谱分析和测色仪器的光谱接收器件 ,光谱谱线定位受单色仪狭缝和CCD光敏元尺寸影响。提出采用最小二乘法做曲线拟合和质心法来确定光谱线在CCD上的精确定位 ,使光谱谱线的定位精度得到提高 ,并且不受CCD光敏元尺寸限制。实验结果表明 ,两种方法对光谱线的定位 ,具有重复性高 ,稳定性好等特点。在定位精度上 ,两者具有一致性。     

The fixed point property for multivalued nonexpansive mappings

We show some properties concerning geometrical constants of Banach spaces which imply the existence of fixed points for multivalued nonexpansive mappings and we study the relationship between these properties.