Comments on “Molecular Chirality in Classical Spacetime: Solving the Controversy about the Spinning Cone Model of Rotating Molecules”

A recent mathematical analysis by Michel Petijean aimed at solving the Barron/Mislow controversy concerning the chirality or otherwise of a non-translating spinning cone concluded that both are right: the controversy is a matter of an arbitrary choice of a conversion factor. This reassessment highlights the different physicochemical properties of a stationary spinning cone and a chiral molecule and concludes that Petitjean's analysis is misleading.     

A sufficient optimality theoriem for protoconvex programs

We establish two first order sufficient optimality theorems; one for unconstrained nonlinear minimization problem, and the other for constrained nonlinear minimization problems, both with non-differentiable protoconvex or quasiconvex data functions that are not necessarily locally Lipschitz     

On positive solutions of fractional differential equations with change of sign

We study the existence and uniqueness of positive solutions of fractional differential equations with change of sign where 1 < α ≤ 2, is continuous and does not vanish identically on any subinterval of [0,1].     

High‐throughput method for estimating the time to sustained ignition of polystyrene–clay nanocomposites based on thermogravimetric analysis

Polymer‐modified clay nanocomposites were prepared by melt blending and the time to ignition was measured by cone calorimetry at various heat fluxes. Based on these experimental results, a critical mass flux and critical percentage mass loss (pml_crit) for piloted ignition were identified and validated for both virgin polystyrene and its composites, across a wide range of heating fluxes. Based on the assumption that the polymer degradation kinetics in the heating segment of the cone calorimetry (up to the moment of ignition) and thermogravimetry experiments are similar, and using the pml_crit, we hypothesized that the onset degradation temperature of the TGA samples (defined here as the temperature at pml_crit) could be used to estimate the time to sustained ignition in cone calorimetry experiments. The onset degradation temperature and the time to sustained ignition showed a good correlation, regardless of the heating flux used in cone calorimetry experiments. Copyright © 2009 John Wiley & Sons, Ltd.     

角锥棱镜数字化检测中自准直回像的重影研究

介绍了角锥棱镜的检测方法和存在的主要问题。采用高精度图像传感器将角锥棱镜检测中自准直像数字化,通过分析回像特点,提出了基于实体的自准直图像的重叠与分裂处理技术,以解决角锥棱镜检测中存在的问题,为角锥棱镜规模化生产提供了一种实际可行的检测方法。     

一种紧凑型高功率宽带微波源

 设计了一种高功率宽带微波辐射装置,谐振器采用传输线型谐振器,其中,天线采用单锥喇叭。整个宽带微波产生装置具有结构紧凑、谐振频率较低的特点。用时域有限差分对该装置进行了数值模拟,模拟结果为：辐射场中心频率272 MHz,带宽13.5%。装置与高压脉冲源联试,开关内充电电压为71 kV时,辐射场中心频率为197 MHz,辐射场带宽达到24%,峰值辐射因子为28.3 kV。     

Transition prediction for supersonic and hypersonic boundary layers on a cone with angle of attack

Transition prediction for boundary layers has always been one of the urgent problems waiting for a solution for the development of aero-space technology, yet there is no reliable and effective method due to the complexity of the problem. The e ^N method has been regarded as an effective method for the transition prediction of boundary layers. However, it heavily relies on experiment or experience. And in cases with three-dimensional base flow, for instance, the boundary layer on a cone with angle of attack, the result of its application is not satisfactory. The authors have found its cause and proposed the method for its improvement, which did yield the fairly satisfactory result for a given test case, and also did not rely so much on experiment or experience. However, before people can really apply this method to practical problems, more test cases have to be studied. In this paper, more test cases for the application of the improved e ^N method to problems of transition prediction of supersonic and hypersonic boundary layers on cones with angle of attack will be studied. The results are compared with those obtained by experiments and/or direct numerical simulations, confirming that the improved e ^N method is effective and reliable. We also find that there may be more than one ZARF for each meridian plane, and which one should be chosen for the e ^N method has been clarified. Supported by the National Natural Science Foundation of China (Grant Nos. 10632050 and 90716007), the Special Foundation for the Authors of National Excellent Doctoral Dissertations (Grant No. 200328), and the Foundation of Liu-Hui Center of Applied Mathematics of Nankai University and Tianjin University Contributed by ZHOU Heng     

奇异超线性(k,n-k)多点边值问题的正解

应用锥理论和不动点指数方法,在与相应的线性算子第一特征值有关的条件下,获得奇异超线性(k,n-k)多点边值问题正解的存在性结果,推广和改进了已有的主要结论.