Design and fabrication of fluid controlled dynamic optical lens system

A novel small fluid controlled optical lens system that is capable of displaying dynamic variation of its focal length and field-of-view (FOV) is designed and fabricated. In this active lens system, appropriate volume of the optical fluid can be pumped into or out of the lens chamber to provide double-convex (DCX) or double-concave (DCV) lens effect. Simple optical imaging experiments were performed using different sets of glass lenses with fixed focal lengths to determine the optimum lens configuration required for designing a dynamic optical lens system. The experimental results obtained from the glass lenses demonstrate that a combination of a single DCX lens with three DCV lenses provides a wider FOV. The flexible membranes for fluid controlled lenses were fabricated using polydimethylsiloxane polymer material, which has good optical transparency and elasticity. A simple fluid injection system is used to vary the radius of curvature of the lenses, and thereby to change the focal length. A dynamic optical lens system with a combination of one DCX and multiple variable focal length DCV lenses as designed here can image an object with a wide range of focal length and FOV. With this fluid controlled optical system, the FOV and focal length could be continuously varied and a maximum FOV of 118.3° could be achieved. The smallest f-number (f_/#) for this fluid controlled single lens system was found to be 1.3, which corresponds to the numerical aperture value of 0.35.     

On the Spectral Radius of Trees with the Given Diameter d

Let T denote a tree with the diameter d(d≥2) and order n. Let P^*d,r,n-d-1denote the tree obtained by identifying the rth vertex of path Pd l and the center of starKl,K1,n-d-1, where r = r(d) is the integer part about d 2/2. Then p(T)≤ p(P^*d,r,n-d-1), andequality holds if and only if T≌P^*d,r,n-d-1     

Stability of Markovian structure observed in high frequency foreign exchange data

Contrary to the common sense in economics and financial engineering, price fluctuations at very fine level of motion exhibit various evidences against the efficient market hypothesis. We attempt to investigate this issue by studying extensive amount of foreign currency exchange data for over five years at the finest level of resolution. We specifically focus on the proposed stability in binomial conditional probabilities originally found in much smaller examples of financial time series. In order to handle very large data, we have written an efficient program in C that automatically generates those conditional probabilities. It is found that the stability is maintained for extremely large time duration that covers almost the entire period. Based on the length of conditions for which the conditional probabilities are distinguishable each other, we identify the length of memory being less than 3 movements.     

Computing homotopic shortest paths in the plane

We address the problem of computing homotopic shortest paths in the presence of obstacles in the plane. Problems on homotopy of paths received attention very recently [Cabello et al., in: Proc. 18th Annu. ACM Sympos. Comput. Geom., 2002, pp. 160–169; Efrat et al., in: Proc. 10th Annu. European Sympos. Algorithms, 2002, pp. 411–423]. We present two output-sensitive algorithms, for simple paths and non-simple paths. The algorithm for simple paths improves the previous algorithm [Efrat et al., in: Proc. 10th Annu. European Sympos. Algorithms, 2002, pp. 411–423]. The algorithm for non-simple paths achieves O(log²n) time per output vertex which is an improvement by a factor of O(n/log²n) of the previous algorithm [Hershberger, Snoeyink, Comput. Geom. Theory Appl. 4 (1994) 63–98], where n is the number of obstacles. The running time has an overhead O(n²⁺) for any positive constant . In the case k<n²⁺, where k is the total size of the input and output, we improve the running to O((n+k+(nk)^2/3)log^O(1)n).     

Deactivation reactions in the modeled 2,2,6,6‐tetramethyl‐1‐piperidinyloxy‐mediated free‐radical polymerization of styrene: A comparative study with the 2,2,6,6‐tetramethyl‐1‐piperidinyloxy/acrylonitrile system

The competitiveness of the combination and disproportionation reactions between a 1‐phenylpropyl radical, standing for a growing polystyryl macroradical, and a 2,2,6,6‐tetramethyl‐1‐piperidinyloxy (TEMPO) radical in the nitroxide‐mediated free‐radical polymerization of styrene was quantitatively evaluated by the study of the transition geometry and the potential energy profiles for the competing reactions with the use of quantum‐mechanical calculations at the density functional theory (DFT) UB3‐LYP/6‐311+G(3df, 2p)//(unrestricted) Austin Model 1 level of theory. The search for transition geometries resulted in six and two transition structures for the radical combination and disproportionation reactions, respectively. The former transition structures, mainly differing in the out‐of‐plane angle of the N? O bond in the transition structure TEMPO molecule, were correlated with the activation energy, which was determined to be in the range of 8.4–19.4 kcal mol^?1 from a single‐point calculation at the DFT UB3‐LYP/6‐311+G(3df, 2p)//unrestricted Austin Model 1 level. The calculated activation energy for the disproportionation reaction was less favorable by a value of more than 30 kcal mol^?1 in comparison with that for the combination reaction. The approximate barrier difference for the TEMPO addition and disproportionation reaction was slightly smaller for the styrene polymerization system than for the acrylonitrile polymerization system, thus indicating that a β‐proton abstraction through a TEMPO radical from the polymer backbone could diminish control over the radical polymerization of styrene with the nitroxide even more than in the latter system. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 232–241, 2007     

Implementation and experimental study on fast object modeling based on multiple structured stripes

In this paper, a practical structured light-based system for fast object modeling and reconstruction is reported. The system consists of an off-the-shelf digital projector, a video camera and a turntable. The system calibration is implemented accurately and automatically by taking a single image of an illuminated calibration template. The multiple color light stripes emitted by the projector adopt only three colors and the color can be modified easily according to the surface texture of the object. This makes the system widely applicable in many situations, and the assumption about color neutrality, which is a limitation to other similar systems, can be largely relaxed. The registration and merging algorithm is greatly simplified by employing a turntable. The validity and high accuracy of the method are demonstrated by extensive real experiments.     

Motion Control by ZV Shaper Synthesis Extended for Fractional Systems and Its Application to CRONE Control

Shaping command input or preshaping is used for reducing system oscillation in motion control. Desired systems inputs are altered so that the system finishes the requested move without residual oscillation. This technique, developed by N.C. Singer and W.P. Seering, is used for example in the aerospace field, in particular in flexible structure control. This paper presents the study of ZV shaper for explicit fractional derivative systems (generalized derivative systems). A robustness study of ZV shaper is then presented and applied to improve second generation CRONE control response time. Results from simulation and from a DC motor bench are also given.     

Material-Adapted Design of Textile-Reinforced Composite Structures with Optimized Vibro-Acoustic and Damping Properties Including Shear Effects

Advanced analytical models have been developed at the ILK, which offer a possibility of calculating the vibro-acoustic and damping behavior of textile-reinforced composite shells and plates with account of shear effects. The simulation models elaborated have been verified on selected examples, and the analytical results were fully corroborated by accompanying numerical calculations for typical lay-ups.__________Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 41, No. 3, pp. 289–302, May–June, 2005.     

数学建模与素质教育

面对二十一世纪知识经济的挑战 ,我国高等教育模式应由应试教育 ,专业教育向素质教育转变 ,培养学生自主意识 ,效率意识 ,竞争意识 ,创新意识和民主意识 ,即高校教育应重视大学生的创新能力、实践能力和创业精神 ,普遍提高大学生的人文素质和科学素质 .本文拟就提高大学生素质的有效层面 ,对开展数学建模教学与实践进行深入分析 ,以窥探数学建模与素质教育之关系 .在深入把握数学建模教学与实践内涵的同时 ,分析得出这种以不打扰现行正常秩序的教育是提高大学生素质的有效途径之一     

Note on André's reflection principle

This note generalizes André's reflection principle to give a new combinatorial proof of a formula for the number of lattice paths lying within certain trapezoids.