手性聚酰亚胺的合成、结构与性能

手性聚酰亚胺逐渐成为手性高分子研究的一个重要方面,在分子识别、对映体选择性分离、不对称催化等领域有潜在的应用,日益受到研究者的重视。本文综述了近二十年手性聚酰亚胺的研究进展,将手性聚酰亚胺按照手性结构的引入方式分为侧链手性、主链中心手性和主链轴手性三种类型,并分别加以总结和阐述,介绍了具有代表性的光活性聚酰亚胺的结构、合成和性能,特别关注了手性聚酰亚胺的高次结构的形成以及与其手性光活性相关的性能与应用。最后,本文阐述了手性聚酰亚胺研究面对的挑战与未来发展前景,探索手性聚酰亚胺的合成、性质和应用,建立合理的模型和分析手段,深入探讨手性聚酰亚胺的高次结构仍然是值得深入研究的重点方向。     

A dynamical characterization of contact circles

A simple dynamical condition is given for line fields within a contact structure, which is satisfied exactly by those line fields which are common kernels of contact circles. Some convexity properties are established which are useful in the study of contact circles up to homotopy. A necessary condition for extending a contact form to a contact circle is given. Based on work of Lisca–Matić and Honda, concrete examples are given which show that the condition is not just homotopic but a geometric one. The paper ends with an open question. Dedicated to Fernando Varela, for many reasons.     

On <Emphasis Type="Italic">l</Emphasis><Subscript>2,<Emphasis Type="Italic">p</Emphasis></Subscript>-circle numbers

Circle numbers are defined to reflect the Euclidean area-content and, for p ≠ 2, suitably defined non-Euclidean circumference properties of the l _2,p -circles, p ∈ [1, ∞]. The resulting function is continuous, increasing, and takes all values from [2, 4]. The actually chosen dual l _2,p -geometry for measuring the arc-length is closely connected with a generalization of the method of indivisibles of Cavalieri and Torricelli in the sense that integrating such arc-lengths means measuring area content. Moreover, this approach enables one to look in a new way into the co-area formula of measure theory which says that integrating Euclidean arc-lengths does not yield area content except for p = 2. The new circle numbers play a natural role, e.g., as norming constants in geometric measure representation formulae for p-generalized uniform probability distributions on l _2,p -circles.     

Number-theoretic interpretation and construction of a digital circle

This paper presents a new interpretation of a digital circle in terms of the distribution of square numbers in discrete intervals. The number-theoretic analysis that leads to many important properties of a digital circle succinctly captures the original perspectives of digital calculus and digital geometry for its visualization and characterization. To demonstrate the capability and efficacy of the proposed method, two simple algorithms for the construction of digital circles, based on simple number-theoretic concepts, have been reported. Both the algorithms require only a few primitive operations and are completely devoid of any floating-point computation. To speed up the computation, especially for circular arcs of high radii, a hybridized version of these two algorithms has been given. Experimental results have been furnished to elucidate the analytical power and algorithmic efficiency of the proposed approach. It has been also shown, how and why, for sufficiently high radius, the number-theoretic technique can expedite a circle construction algorithm.     

Novel Features for Binary Time Series Based on Branch Length Similarity Entropy

Branch length similarity (BLS) entropy is defined in a network consisting of a single node and branches. In this study, we mapped the binary time-series signal to the circumference of the time circle so that the BLS entropy can be calculated for the binary time-series. We obtained the BLS entropy values for “1” signals on the time circle. The set of values are the BLS entropy profile. We selected the local maximum (minimum) point, slope, and inflection point of the entropy profile as the characteristic features of the binary time-series and investigated and explored their significance. The local maximum (minimum) point indicates the time at which the rate of change in the signal density becomes zero. The slope and inflection points correspond to the degree of change in the signal density and the time at which the signal density changes occur, respectively. Moreover, we show that the characteristic features can be widely used in binary time-series analysis by characterizing the movement trajectory of Caenorhabditis elegans. We also mention the problems that need to be explored mathematically in relation to the features and propose candidates for additional features based on the BLS entropy profile.     

Defocus and binocular vision based stereo particle pairing method for 3D particle tracking velocimetry

We propose a new method, based on the depth-from-defocus technique and binocular vision, for solving the stereo particle pairing problem in 3D particle tracking velocimetry (PTV). Firstly, the apparent particle depth is measured with a single camera, using the depth-from-defocus technique. Secondly, a strict mathematical model of the particle-to-particle correspondence relationship between the left and right images, taking into account the refractions at the interfaces in the optical path, is presented, with the assumption that the apparent particle depth is measured. Thirdly, based on the apparent particle depth and particle-to-particle correspondence relationship, the epipoplar line is truncated into a short line segment by cutting off, where the apparent particle depth extends beyond its estimated range. For the first time, the range of the blur circle radius is employed as an additional stereo particle pairing constraint. Finally, the optimal pairing particle is selected by applying the epipolar line segment and blur circle radius constraints. The experimental results show that the rate of correct pairing is significantly improved compared with the epipolar line nearest neighbor analysis, especially when the particle density is increasing.     

Weyl-Titchmarsh theory for symplectic difference systems

In this work, we establish Weyl-Titchmarsh theory for symplectic difference systems. This paper extends classical Weyl-Titchmarsh theory and provides a foundation for studying spectral theory of symplectic difference systems.     

Optimal packings of two to four equal circles on any flat torus

We find explicit formulas for the radii and locations of the circles in all the optimally dense packings of two, three or four equal circles on any flat torus, defined to be the quotient of the Euclidean plane by the lattice generated by two independent vectors. We prove the optimality of the arrangements using techniques from rigidity theory and topological graph theory.     

两相流显微PIV/PTV系统的开发

开发了一个能同时测量两相流中两相速度和细颗粒尺寸分布的显微PIV/PTV系统,其硬件系统包括大功率连续激光器、显微镜、高速摄像机;软件系统由改进的球形颗粒图像识别算法、各种图像处理算法和各种先进的PIV/PTV算法组成。其中改进的圆弧识别算法能够进行更准确地进行曲线分割而能对充满噪音并相互重叠的颗粒图像给出较好的识别结果。应用该PIV系统,可以在微秒和微米数量级上捕获细颗粒/气泡图像,并能较准确地同时得到两相速度、颗粒尺寸和浓度分布。对焚香可吸入颗粒物进行了速度和尺寸的同时测量,得到了较满意的结果。