最小偏向角法测三棱镜折射率的相图探究

三棱镜折射率的测量是大学物理实验的重要组成部分,对培养学生的基本实验技能、加深对经典光学理论的理解具有重要作用。本文依据几何光学原理探究了最小偏向角法中在有出射光时最小偏向角与三棱镜顶角、折射率所对应的函数关系,建立了有出射光时入射角、折射率、顶角间以及最小偏向角时折射率、顶角、最小偏向角间的相图,阐明了两相图的物理意义。该研究拓展了三棱镜折射率实验的研究思路。     

基于有机半导体激光材料的高灵敏度溶液检测传感器件

采用光抽运有机激光增益材料产生的放大自发辐射(amplified spontaneous emission ASE), 实现了不同浓度液体的实时检测. 以两种聚合物poly(9, 9-dioctylfluorene-co-benzothiadiazole)和poly(3-hexylthiophene)共混的激光增益介质薄膜作为平面光波导, 观察在滴加少量溶液前后以及不同溶液浓度下, 由于光波导的相对折射率变化导致的放大自发辐射阈值及峰位的变化, 实现对溶液检测. 实验结果显示, 在常温常压下对25 wt.% NaCl溶液检测可得与纯水相比, 放大自发辐射光谱红移了4.5 nm, ASE阈值从0.579 μJ/pulse上升到1.447 μJ/pulse, 约2.5倍, 溶液检测灵敏度达到97.8 nm/RIU(refractive index unit), 精度达到141.9 nm/RIU, 充分说明上述方法能实现高灵敏度溶液检测.     

复合材料冲击损伤监测的概率成像方法*

复合材料在制造、使用和维修过程中不可避免的受外来意外物体的低速冲击,造成结构的损伤。材料本身存在各向异性、纤维铺层方向误差等复杂结构特性,导致延迟-累加损伤成像方法难以实现冲击损伤的准确检测。针对这一问题,本文采用了一种与信号传播速度无关的损伤概率成像方法,该方法利用能量损伤因子,将各路径周围的像素点以椭圆分布的形式对损伤进行概率化表述,然后对各路径损伤因子进行合成成像,实现了复合材料冲击损伤的准确监测。实验结果表明,利用能量损伤因子可以监测复合材料冲击损伤,利用损伤概率成像方法可以实现冲击损伤位置的判别。     

Unicycle Graphs with Maximum Generalized Topological Indices

Let G be an unicycle graph and d _v the degree of the vertex v. In this paper, we investigate the following topological indices for an unicycle graph , , where m ≥ 2 is an integer. All unicycle graphs with the largest values of the three topological indices are characterized. This research is supported by the National Natural Science Foundation of China(10471037)and the Education Committee of Hunan Province(02C210)(04B047).     

Extremal (<Emphasis Type="Italic">n</Emphasis>,<Emphasis Type="Italic">n</Emphasis> + 1)-graphs with respected to zeroth- order general Randić index

A (n, n + 1)-graph G is a connected simple graph with n vertices and n + 1 edges. If d _v denotes the degree of the vertex v, then the zeroth-order general Randić index of the graph G is defined as , where α is a real number. We characterize, for any α, the (n,n + 1)-graphs with the smallest and greatest zeroth-order general Randić index.     

Correlation between CMC and chromatographic index: simple and effective evaluation of the hydrophobic/hydrophilic balance of bile acids

The discovery that bile acids are involved in the modulation of nuclear steroid receptors has prompted renewed interest in this field of research. Due to the nature of research in this field, a technique that enables simple and effective assessment of the hydrophobic/hydrophilic balance, thus improving and speeding up evaluations of the biological profiles of these compounds, is greatly needed. In this context, both CMC value determination and RP-HPLC mobility evaluation were explored as possible approaches. While the CMC was calculated using the noninvasive conductimetric method, the RP-HPLC mobility was assessed by measuring the retention factor at several mobile phase compositions and extrapolating back to the pure aqueous mobile phase. The correlation of the CMC with the derived chromatographic hydrophobic index ϕ ₀ was satisfactory. Figure Experimental versus predicted pCMC values     

Spectrum and analytical indices of the C-algebra of Wiener-Hopf operators

We study multivariate generalisations of the classical Wiener-Hopf algebra, which is the C^∗-algebra generated by the Wiener-Hopf operators, given by convolutions restricted to convex cones. By the work of Muhly and Renault, this C^∗-algebra is known to be isomorphic to the reduced C^∗-algebra of a certain restricted action groupoid, given by the action of Euclidean space on a certain compactification. Using groupoid methods, we construct composition series for the Wiener-Hopf C^∗-algebra by a detailed study of this compactification. We compute the spectrum, and express homomorphisms in K-theory induced by the symbol maps which arise by the subquotients of the composition series in analytical terms. Namely, these symbols maps turn out to be given by an analytical family index of a continuous family of Fredholm operators. In a subsequent paper, we also obtain a topological expression of these indices.     

A speciality theorem for curves in P<Superscript>5</Superscript>

Let be an integral projective curve. One defines the speciality index e(C) of C as the maximal integer t such that , where ω _C denotes the dualizing sheaf of . Extending a classical result of Halphen concerning the speciality of a space curve, in the present paper we prove that if is an integral degree d curve not contained in any surface of degree  < s, in any threefold of degree  < t, and in any fourfold of degree  < u, and if , then Moreover equality holds if and only if C is a complete intersection of hypersurfaces of degrees u, , and . We give also some partial results in the general case , .      

A quadratic programming approach to the Randić index

Let G(k, n) be the set of connected graphs without multiple edges or loops which have n vertices and the minimum degree of vertices is k. The Randi? index χ = χ(G) of a graph G   is defined by χ(G)=_∑(uv)(_δuδv)^-1/2$\chi (G)={\sum }_{(\mathit{uv})}({\delta }_u{\delta }_v{)}^{-1/2}$, where δ_u is the degree of vertex u and the summation extends over all edges (uv) of G. Caporossi et al. [G. Caporossi, I. Gutman, P. Hansen, Variable neighborhood search for extremal graphs IV: Chemical trees with extremal connectivity index, Computers and Chemistry 23 (1999) 469–477] proposed the use of linear programming as one of the tools for finding the extremal graphs. In this paper we introduce a new approach based on quadratic programming for finding the extremal graphs in G(k, n) for this index. We found the extremal graphs or gave good bounds for this index when the number n_k of vertices of degree k is between n − k and n. We also tried to find the graphs for which the Randi? index attained its minimum value with given k (k ? n/2) and n. We have solved this problem partially, that is, we have showed that the extremal graphs must have the number n_k of vertices of degree k less or equal n − k and the number of vertices of degree n − 1 less or equal k.