Application of refractive index mixing rules in binary systems of hexadecane and heptadecane with n -alkanols at different temperatures

Density and refractive index have been experimentally determined for binary liquid mixtures of hexadecane and heptadecane with 1-butanol, 1-pentanol, 1-hexanol and 1-heptanol at 298.15, 308.15 and 318.15 K. A comparative study of Lorentz—Lorenz (L-L), Weiner (W) and Heller (H), and Gladstone-Dale (G-D) relations for predicting the refractive index of a liquid has been carried out to test their validity for the eight binaries over the entire mole fraction range of hexadecane and heptadecane at the three temperatures. Comparison of various mixing rules has been expressed in terms of average percentage deviation. The performance of the Lorentz-Lorenz and Heller relations is relatively better than that of the Weiner and Gladstone-Dale relations.     

PROPAGATION CHARACTERISTICS OF GAUSSIAN BEAMS WITH ASTIGAMATISM

Transformation of Gaussian beams propagating through an axially asym-metric optical system is studied in detail by means of the complex curvature tensor andthe tensor ABCD law.Some important propagation characteristics of Gaussian beamswith simple or general astigmatism are demonstrated by typical numerical examples.     

K-theory for rickart C*-algebras

We give an explicit index map for any properly infinite closed ideal of a Rickart C ^*-algebra. This generalizes Olsen's work on von Neumann algebras. We use our results to compute the topological and the algebraic K ₁-groups of any quotient algebra of a Rickart C ^*-algebra.     

Measuring the thickness and refractive index of a thick transparent plate by an unexpanded laser beam

The thickness and refractive index of a thick transparent plate are measured by using an unexpanded HeNe laser beam. The laser beam is incident at different angles onto the plate; and then two reflected beams; from the front and back surfaces; are received on a distant screen: the corresponding separations between them are measured. A theoretical relation between the refractive index; thickness; angle of incidence and separation is derived. This relation is experimentally verified and shows good agreement. The errors in the measured thickness and refractive index are analysed. The method is non-contact; non-destructive and low cost.     

Rheological properties and interfacial slip of a multilayer structure under dynamic shear

Interfacial slip between polymer melt under steady shear has been studied using a simplified multilayer structure. In this investigation, interfacial slip under dynamic shear was studied by calculating the angular displacements of the multilayer structure and its component layers. On the basis of the angular displacements, a slip index was defined to quantify the degree of interfacial slip. A relationship governing the rheological behavior of the multilayer structure under slip and nonslip condition was established. These results were correlated with equations derived from consideration of energy equilibrium in the multilayer structure. Polymer multilayer structures of high‐density polyethylene/polystyrene and liquid crystal polymer(LCP)/poly ethylene naphthalate(PEN) were investigated. Of all the polymers investigated, large interfacial slip was found at LCP/PEN interface under dynamic shear. The high rigidity and alignment along the interface of LCP molecules was believed to prevent chain entanglement in the interfacial layer and therefore promote interfacial slip at the interface. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 2683–2693, 2005     

有限群可解和超可解的注记

本文利用文献[1]所引入的极大子群的复合指数的概念，给出了有限群可解及超可解的充分必要条件．     

Edge-forwarding index of star graphs and other Cayley graphs

We present a technique for building, in some Cayley graphs, a routing for which the load of every edge is almost the same. This technique enables us to find the edge-forwarding index of star graphs and complete-transposition graphs.     

广西地区经济指标评价

杨善朝，李志友．广西地区经济指标评价．数理统计与管理，１９９７，１６，（４），１～４本文试用主成分分析方法，对广西七个地区的经济生产情况作出综合评价，分析各地区在广西的经济地位。并提出了一种构造加权综合量的方法     

New Algorithm for Computing LQ Suboptimal Output Feedback Gains of Decentralized Control Systems

In this paper, the problem of computing the suboptimal output feedback gains of decentralized control systems is investigated. First, the problem is formulated. Then, the gradient matrices based on the index function are derived and a new algorithm is established based on some nice properties. This algorithm shows that a suboptimal gain can be computed by solving several ordinary differential equations (ODEs). In order to find an initial condition for the ODEs, an algorithm for finding a stabilizing output feedback gain is exploited, and the convergence of this algorithm is discussed. Finally, an example is given to illustrate the proposed algorithm.