Effect of absorbed pump power on the quality of output beam from monolithic microchip lasers

The dependence of the beam propagation factor (M ² parameter) with the absorbed pump power in the case of monolithic microchip laser under face-cooled configuration is extensively studied. Our investigations show that the M ₂ parameter is related to the absorbed pump power through two parameters (α and β) whose values depend on the laser material properties and laser configuration. We have shown that one parameter arises due to the oscillation of higher order modes in the microchip cavity and the other parameter accounts for the spherical aberration associated with the thermal lens induced by the pump beam. Such dependency of M ² parameter with the absorbed pump power is experimentally verified for a face-cooled monolithic microchip laser based on Nd³⁺ -doped GdVO₄ crystal and the values of α and β parameters were estimated from the experimentally measured data points.     

若干图类的邻强边染色

研究了若干图类的邻强边染色 .利用在图中添加辅助点和边的方法 ,构造性的证明了对于完全图 Kn和路 Lm 的笛卡尔积图 Kn× Lm,有χ′as(Kn× Lm) =△ (Kn× Lm) +1 ,其中△ (Kn× Lm)和χ′as(Kn× Lm)分别表示图 Kn× Lm的最大度和邻强边色数 .同理验证了 n阶完全图 Kn的广义图 K(n,m)满足邻强边染色猜想 .     

4一致反超图的最小边数问题

混合超图是在超图的基础上添加一个反超边得到的图．超边和反超边的区别主要体现在着色要求上．在着色中,要求每一超边至少要有两个点着不同的颜色,而每一反超边至少有两个点着相同的颜色．最大最小颜色数分别称为混合超图的上色数和下色数。本文主要研究反超图,即只含反超边的超图。讨论了上色数为3的4一致超图的最小边数问题．给出了上色数为3的4一致反超图的最小边数的一个上界和一个下界．     

研究K4-同胚图K4(α,1,1,δ,ε,η)色性的一个引理

主要介绍了一个引理，这个引理奠定了K4－同胚图K4（α，1，1，δ，ε，η）色性研究的基础。     

推广的奇轮的圆色数

图G的圆色数(又称"星色数")xc(G)是Vince在1988年提出的,它是图的色数 的自然推广.本文由奇轮出发构造了一族平面图,并证明了此类图的圆色数恰恰介于2和 3之间,填补了该领域的空白.     

Circular perfect graphs

For 1 ≤ d ≤ k, let K_k/d be the graph with vertices 0, 1, …, k ? 1, in which i ～j if d ≤ |i ? j| ≤ k ? d. The circular chromatic number χ_c(G) of a graph G is the minimum of those k/d for which G admits a homomorphism to K_k/d. The circular clique number ω_c(G) of G is the maximum of those k/d for which K_k/d admits a homomorphism to G. A graph G is circular perfect if for every induced subgraph H of G, we have χ_c(H) = ω_c(H). In this paper, we prove that if G is circular perfect then for every vertex x of G, N_G[x] is a perfect graph. Conversely, we prove that if for every vertex x of G, N_G[x] is a perfect graph and G ? N[x] is a bipartite graph with no induced P₅ (the path with five vertices), then G is a circular perfect graph. In a companion paper, we apply the main result of this paper to prove an analog of Haj?os theorem for circular chromatic number for k/d ≥ 3. Namely, we shall design a few graph operations and prove that for any k/d ≥ 3, starting from the graph K_k/d, one can construct all graphs of circular chromatic number at least k/d by repeatedly applying these graph operations. © 2005 Wiley Periodicals, Inc. J Graph Theory 48: 186–209, 2005     

Color Zone Map in Peripheral Vision at Various Illuminance Levels

We measured the entire region of mesopic and photopic vision to determine the color zone covering the visual field with unique red, yellow, green, and blue hue components. Eight kinds of test stimuli in the natural color system (NCS) color notation system were used. These stimuli were presented at horizontal and vertical meridians, and at meridians inclined at 45° angles. The illuminance level was set at six levels: 0.01 lx-1000 lx. The evaluation method measured chromatic, white, and black components as well as the hue component of the stimuli. Results show that the color zone of the retina extended further into the periphery with increasing illuminance; the response of opponent colors y-b was shown to be greater than that of the opponent colors r-g.     

汉折射波片用于发散光束的偏振像差分析

本文利用光线追迹法,对双折射波片用于发散光束的偏振像差进行了分析,并以标准1/4波片为例,给出了小角入射时的近似处理方法.     

On the chromatic polynomial of a graph

Let P(G,λ) be the chromatic polynomial of a graph G with n vertices, independence number α and clique number ω. We show that for every λ≥n, ()^α≤≤ () ^{n −ω}. We characterize the graphs that yield the lower bound or the upper bound.?These results give new bounds on the mean colour number μ(G) of G: n− (n−ω)() ^{n −ω}≤μ(G)≤n−α() ^α. Received: December 12, 2000 / Accepted: October 18, 2001?Published online February 14, 2002