Momentum transport and torque scaling in Taylor-Couette flow from an analogy with turbulent convection

We generalize an analogy between rotating and stratified shear flows. This analogy is summarized in Table 1. We use this analogy in the unstable case (centrifugally unstable flow vs. convection) to compute the torque in Taylor-Couette configuration, as a function of the Reynolds number. At low Reynolds numbers, when most of the dissipation comes from the mean flow, we predict that the non-dimensional torque G = T/ν² L, where L is the cylinder length, scales with Reynolds number R and gap width η, G = 1.46η^3/2(1 - η)^-7/4 R ^3/2. At larger Reynolds number, velocity fluctuations become non-negligible in the dissipation. In these regimes, there is no exact power law dependence the torque versus Reynolds. Instead, we obtain logarithmic corrections to the classical ultra-hard (exponent 2) regimes: G = 0.50 . These predictions are found to be in excellent agreement with avail-able experimental data. Predictions for scaling of velocity fluctuations are also provided. Received 7 June 2001 and Received in final form 7 December 2001     

Bounds on the maximum numbers of clear two-factor interactions for 2^{(n_1 + n_2 ) - (k_1 + k_2 )} fractional factorial split-plot designs

Fractional factorial split-plot (FFSP) designs have an important value of investigation for their special structures. There are two types of factors in an FFSP design: the whole-plot (WP) factors and sub-plot (SP) factors, which can form three types of two-factor interactions: WP2fi, WS2fi and SP2fi. This paper considers FFSP designs with resolution III or IV under the clear effects criterion. It derives the upper and lower bounds on the maximum numbers of clear WP2fis and WS2fis for FFSP designs, and gives some methods for constructing the desired FFSP designs. It further examines the performance of the construction methods.     

Three Electrons in a Two-Dimensional Parabolic Trap: The Relative Motion Solution

In agreement with the Kohn theorem the relative motion (rel) of three electrons in a two-dimensional parabolic trap separates from the centre-of-mass (CM) motion. By introducing new coordinates the Hamiltonian for relative motion in the approximation of non-interacting electrons can be taken to the normal form. The eigenstates of the normalized Hamiltonian are products of the Fock-Darwin states for normal modes. The energy levels for relative motion are obtained by diagonalizing the exact Hamiltonian in the eigenbasis for the non-interacting case. In this basis the interaction matrix elements can be obtained in the analytical form. Since the rank of the Hamiltonian matrix is significantly reduced, the calculations are faster and more accurate than those for the full (CM + rel) motion. This advantage is especially important for the calculations of excited states and the analysis of energy spectra.     

Two inequalities involving Hadamard products of positive semi-definite Hermitian matrices

We extend two inequalities involving Hadamard products of positive definite Hermitian matrices to positive semi-definite Hermitian matrices. Simultaneously, we also show the sufficient conditions for equalities to hold. Moreover, some other matrix inequalities are also obtained. Our results and methods are different from those which are obtained by S. Liu in [J. Math. Anal. Appl. 243:458–463(2000)] and B.-Y. Wang et al. in [Lin. Alg. Appl. 302–303: 163–172(1999)].     

Large set of P3‐decompositions

Let G=(V(G),E(G)) be a graph. A (n,G, λ)‐GD is a partition of the edges of λK_n into subgraphs (G‐blocks), each of which is isomorphic to G. The (n,G,λ)‐GD is named as graph design for G or G‐decomposition. The large set of (n,G,λ)‐GD is denoted by (n,G,λ)‐LGD. In this work, we obtain the existence spectrum of (n,P₃,λ)‐LGD. © 2002 Wiley Periodicals, Inc. J Combin Designs 10: 151–159, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10008     

Canonical Modules of Semigroup Rings and a Conjecture of Reiner

We prove that the homotopy types of two naturally defined simplicial complexes are related in the following way: one is homotopy equivalent to a multiple suspension of the canonical Alexander dual of the other. These simplicial complexes arise in free resolutions of semigroup rings and modules. The relation between their homotopy types was conjectured by Reiner, and was suggested by a homological consequence of a result due independently to Danilov and Stanley on canonical modules of normal semigroup rings. Our proof is purely topological, and gives an alternative proof of their result. We also prove a generalization of a result of Hochster saying that these rings are Cohen—Macaulay, and indicate a new proof of Ehrhart's reciprocity law for rational polytopes. Received October 3, 2000, and in revised form April 2, 2001, and May 10, 2001. Online publication November 7, 2001.     

一种新型彩色三维光学成像系统

提出一种新型三维彩色光学数字成像系统。此系统利用投影结构光对现实世界中的物体进行数字化，同时得到对应的彩色纹理。详细介绍了系统的硬件设计和软件体系结构设计，得到物体彩色纹理的两种不同方法；直接获取和从编码条纹中提取，给出了用该系统得到的实验结果并简单评价了系统的性能。此系统在反求工程、影视制作、三维游戏制作、医学应用等方面有远大的应用前景。     

The Implications of Cognitive-style Findings for Operational Research

Cognitive style refers to differences that can be perceived in individuals due to differing cognitive structures. There has been a large amount of research on how cognitive style affects managerial decision-making, particularly in the context of management information systems, but little or no attempt to relate these findings to operational research. This paper reviews the findings of cognitive-style research from the perspective of operational research, and draws a number of useful inferences concerning the matching of OR aids to managers, the presentation of information and recommendations, the use and acceptance of OR, and the structure of OR groups. Further, it is argued that cognitive-style findings help to give a justification to the move towards ‘soft’ approaches to analysis.     

Evaluating the Efficiency of US Air Force Real-Property Maintenance Activities

The objective of this research is to evaluate a new methodology, data envelopment analysis (DEA), as a tool for measuring and evaluating the operational efficiency of US Air Force organizations. This study involves the application of DEA to locate possible inefficiencies in the performance of US Air Force real-property maintenance activities. Dynamic behaviour, as exhibited via window analyses, is reviewed along with static counterparts. The testing was done in close coordination with Air Force officials, who reviewed the results for accuracy, validity and relevance. We conclude that this type of efficiency analysis does have value for the Air Force, where it can serve as a guide to auditors, budget programmers, managers and others in measuring, evaluating and enhancing operational efficiency.