An Additive Problem with Primes in Arithmetic Progressions

In this paper, we extend a classical result of Hua to arithmetic progressions with large moduli. The result implies the Linnik Theorem on the least prime in an arithmetic progression.     

Some alternating sums of Lucas numbers

We consider alternating sums of squares of odd and even terms of the Lucas sequence and alternating sums of their products. These alternating sums have nice representations as products of appropriate Fibonacci and Lucas numbers.     

Direct numerical simulation of settling of a large solid particle during bioconvection

Settling of a large solid particle in bioconvection flow caused by gyrotactic microorganisms is investigated. The particle is released from the top of the bioconvection chamber; its settling pattern depends on whether it is released in the centre of the bioconvection plume or at its periphery. The Chimera method is utilized; a subgrid is generated around a moving particle. The method suggested by Liu and Wang (Comput. Fluid 2004; 33 :223–255) is further developed to account for the presence of a moving boundary in the streamfunction‐vorticity formulation using the finite‐difference method. A number of cases for different release positions of the particle are computed. It is demonstrated that bioconvection can either accelerate or decelerate settling of the particle depending on the initial position of the particle relative to the plume centre. It is also shown that the particle impacts bioconvection plume by changing its shape and location in the chamber. Copyright © 2005 John Wiley & Sons, Ltd.     

Calculation of Normal Vibrations of Chlorin by the Method of Density Functionals

Using the DFT/B3LYP method with a 6-31G(d) basis set, the structure, normal vibration frequencies, and the absolute band intensities in the IR spectra of the chlorin molecule and its four symmetric isotopomers have been calculated. Scaling of the force field by the Pulay method in independent and natural coordinates has been carried out. A method for obtaining effective force fields without using experimental data on the fundamental vibration frequencies is proposed. By comparing the vibration modes and constructing special matrices, complete assignment of the fundamental frequencies of porphin and chlorin has been carried out. It has been shown that the majority of porphin macroring vibrations upon pyrrolenine ring hydrogenation are frequency-characteristic and only 12 vibrations change considerably. A frequency correlation with regard for the mode transition between chlorin and all its isotopomers under consideration has been established. Comparative analysis of the force fields of porphin and chlorin in dependent natural coordinates has revealed the unique nonlocal character of the change in force constants of the macroring upon hydrogenation of one pyrrolenine ring. Modeling of the IR spectra of chlorin and its isotopomers has been performed. Assignment and interpretation of the normal vibrations of the molecules under consideration have been carried out.     

The method of lines solution of discrete ordinates method for radiative heat transfer in cylindrical enclosures

A radiation code based on method of lines solution of discrete ordinates method for radiative heat transfer in axisymmetric cylindrical enclosures containing absorbing-emitting medium was developed and tested for predictive accuracy by applying it to (i) test problems with black and grey walls (ii) a gas turbine combustor simulator enclosing a non-homogeneous absorbing-emitting medium and benchmarking its steady-state predictions against exact solutions and measurements. Comparisons show that it provides accurate solutions for radiative heat fluxes and can be used with confidence in conjunction with CFD codes based on the same approach.     

New poly(butylene succinate)/layered silicate nanocomposites. II. Effect of organically modified layered silicates on structure,properties, melt rheology,and biodegradability

A series of new poly(butylene succinate) (PBS)/layered silicate nanocomposites were prepared successfully by simple melt extrusion of PBS and organically modified layered silicates (OMLS). Three different types of OMLS were used for the preparation of nanocomposites: two functionalized ammonium salts modified montmorillonite and a phosphonium salt modified saponite. The structure of the nanocomposites in the nanometer scale was characterized with wide-angle X-ray diffraction and transmission electron microscopic observations. With three different types of layered silicates modified with three different types of surfactants, the effect of OMLS in nanocomposites was investigated by focusing on four major aspects: structural analysis, materials properties, melt rheological behavior, and biodegradability. Interestingly, all these nanocomposites exhibited concurrent improvements of material properties when compared with pure PBS. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 3160–3172, 2003     

Living/controlled radical copolymerization of N‐substituted maleimides with styrene in 1‐butyl‐3‐methylimidazolium hexafluorophosphate and anisole

The atom transfer radical copolymerization of N‐substituted maleimides such as N‐phenylmaleimide (PhMI), N‐cyclohexylmaleimide (ChMI), and N‐butylmaleimide (NBMI) with styrene initiated with dendritic polyarylether 2‐bromoisobutyrates in an ionic liquid, 1‐butyl‐3‐methylimidazolium hexafluorophosphate ([bmim][PF₆]), at room temperature and anisole at 110 °C was investigated. The dendritic‐linear block copolymers obtained in ionic liquid possessed well‐defined molecular weight and low polydispersity (1.05 < M_w/M_n < 1.32) and could be used as a macroinitiator for chain‐extension polymerization, suggesting the living nature of the reaction system. The ionic liquids containing catalyst could be recycled in the atom transfer radical polymerization systems without further treatment. Compared with polymerization conducted in anisole, the polymerization in ionic liquid had a stronger tendency for alternation. The tendency for alternation decreased in the order PhMI > NBMI > ChMI in [bmim][PF₆] and PhMI > ChMI > NBMI in anisole. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 2156–2165, 2003     

Yellow‐light‐emitting cyano‐substituted poly[(1,3‐phenylene vinylene)‐alt‐(1,4‐phenylene vinylene)] derivative: Its synthesis and optical properties

A soluble cyano‐substituted poly[(1,3‐phenylene vinylene)‐alt‐(1,4‐phenylene vinylene)] derivative ( 9 ) was synthesized and characterized. Comparison between 9 and its model compound ( 10 ) showed that the chromophore in 9 remained to be well defined as a result of a π‐conjugation interruption at adjacent m‐phenylene units. The attachment of a cyano substituent only at the β position of the vinylene allowed the maximum electronic impact of the cyano group on the optical properties of the poly(p‐phenylene vinylene) material. At a low temperature (?108 or ?198 °C), the vibronic structures of 9 and 10 were partially resolved. The absorption and emission spectra of a film of 9 were less temperature‐dependent than those of a film of 10 , indicating that the former had a lower tendency to aggregate. A light‐emitting diode (LED) based on 9 emitted yellow light (λ_max ≈ 578 nm) with an external quantum efficiency of 0.03%. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 3149–3158, 2003     

数码相机CMOS图像传感器的特性参数与选择

介绍了数码相机的核心器件———CMOS图像传感器的特性参数和在数码相机设计过程中CMOS图像传感器的选择。选择CMOS图像传感器,不仅需要考虑包括传感器的尺寸、像素总数和有效像素数、最小照度、动态范围、灵敏度、分辨力、光电响应不均匀性以及光谱响应等在内的特性参数,而且还要考虑电源管理和功耗、模数转换位数、开发的简便性以及成本等因素。     

大口径光束波前采样器(孔栅)的研制

应用平面波角谱理论，分析了采样器对光波场采样和分光的基本原理以及对空间采样频率的选择规则，描述了实际研制的大口径采样器的结构设计，并通过数值方法和高能激光大气传输实验研究了高能激光经采样器前／后的远场光斑分布关系。结果表明：利用光束波前采样器能高保真地实现对高能激光束的分光。