一个R2上含双曲函数核的Hilbert型不等式

通过引入参数，构造了一个全平面上的、含双曲函数的非齐次核函数。利用正切函数的有理分式展开，建立了最佳常数因子与正切函数高阶导数相关联的Hilbert型积分不等式。 作为应用，通过赋予参数不同的值，建立了一些有意义的特殊结果。     

On a sufficient condition for a Fano manifold to be covered by rational N-folds

In this paper, we prove a conjecture by T. Suzuki, which says if a smooth Fano manifold satisfies some positivity condition on its Chern characters, then it can be covered by rational N-folds. We prove this conjecture by using purely combinatorial properties of Bernoulli numbers.     

不同的灰熔点调控方式对煤灰熔融特性的影响

对两种原始煤灰进行混合,并分别搭配不同的添加剂,得到3种元素组成相同的煤灰,灰熔点测试结果显示,三者的灰熔点存在较大差异。结合X射线衍射技术和SEM-EDX(扫描电子显微镜与能谱联用)分析了3种煤灰(>800 ℃)在高温时的矿物质转化过程。结果表明,不同的灰熔点调控手段对不同煤的影响是不同的。原因是高温时矿物质组成不仅与煤灰化学元素组成相关,更与元素在矿物质中的赋存状态有关。两者共同决定了煤灰的熔融特性。     

Virtual screening of protein kinase C inhibitors from natural product library to modulate general anaesthetic effects

Protein kinase C (PKC) plays a key role in neurotransmission in the central nervous system, and targeting PKC domain is considered as a strategy to modulate the anaesthetic effects. In this study, we described a synthetic pipeline to perform high-throughput virtual screening against a large library of 3D structural natural products released recently in order to discover those potential PKC modulators. A total of 100 natural products with top scores were raised, from which 12 promising candidates were tested to determine their inhibitory potencies against PKC. As might be expected, the promiscuous kinase inhibitor staurosporine showed a high PKC inhibitory activity (IC₅₀ = 64 nM), and other two tested compounds, i.e. fisetin and tetrahydropapaverine, were also highly potent with their activities at nanomolar level (IC₅₀ = 370 and 190, respectively).     

Polymerization of Blending Cholesteryl Acrylate and Methyl Phenyl Benzoyl Acrylate

Liquid crystal is a material which is between solid and liquid phase and commonly called mesophase. Blends of liquid crystal are of great interest because of their unique optical properties. Blending in this study using two monomers of liquid crystal were cholesteryl acrylate and methyl phenyl benzoyl acrylate. The polymerization process using uv curing techniques by irradiation UV ray and without irradiation UV ray. Polymerization of blending liquid crystal acrylate using initiator 2-hydroxy-2-methyl-1-phenylpropane. Based on peak at GPC curve of polymerization by irradiation UV ray, type of that polymer is copolymer. Therefore the polymerization without UV ray, type of that polymer is homopolymer. SEM images of liquid crystal acrylate polymer showed lamella chain models that are characteristic of a polymer chains. Type of polymer liquid crystal acrylate was the type of Side Chain Liquid Crystalline Polymers (SCLCPs). Therefore acrylate polymer liquid crystal in this research has semi-crystalline phase, which contained crystalline phase and amorphous phase on the XRD pattern. The results of FT-IR spectroscopic characterization of the two monomers showed a peak at the wave number of 1600.43 cm ^-1 and 1622.86 cm^-1 which indicates a double bond (C=C) were obtained from acrylation. While the spectroscopy on the product blending the wave number of the peak regions is reduced that shows that carbon double bonds (C=C) in the acrylate group has polymerized. It also strengthened with a very sharp peak for CC functional groups on the wave number of 2855.15 cm^-1. The results of this study indicate that the liquid crystal polymer acrylic polymerization results with radiation UV ray and without UV ray, respectively absorb light in the UV wavelength region 363 nm and 351 nm.     

色谱柱分类数据库用于指导天然药物化学对照品色谱纯度测定时色谱柱理性选择

由于中药化学对照品多数来源于动植物药材,很容易混有结构类似物,故有机杂质测定是可能影响其化学对照品赋值准确性的关键风险因素。中药化学对照品的有机杂质测定通常采用药典收载或文献报道的高效液相色谱法,这些方法通常仅规定“以十八烷基硅烷键合硅胶为填充剂”,无适宜色谱柱的品牌信息,或者实验室无文献所用的色谱柱品牌,而目前市场上已有800多种品牌的C₁₈柱,生产工艺的不同导致不同品牌C₁₈柱的选择性有差异,甚至差异显著。这很容易出现由于色谱柱选择不适宜而导致测定结果不准确的风险。该文采用国外色谱柱分类数据库指导对照品纯度考察时色谱柱的理性选择,尽可能减少色谱柱盲选可能导致的纯度结果不准确的风险。首先,用数据库挑选2根选择性差异显著的色谱柱（选择性因子F≥6）进行平行实验,以尽可能反映采用不同品牌色谱柱可能出现的分离效果差异。如果这2根色谱柱的分离效果及纯度测定结果无显著性差异,则可以交叉验证该对照品纯度测定的准确性。否则需要从数据库中选择另外1根与之前试验中分离效果更好、选择性相似的色谱柱进行纯度结果验证。在N-反式-p-对香豆酰基酪胺和表儿茶素没食子酸酯首批对照品的纯度考察中,使用了上述策略并验证了其有效性和科学性,计划推广应用至更多的中药化学对照品,特别当其可能含碱性或弱酸性化合物时,更应该尝试采用本文推荐的色谱柱选择策略交叉验证其纯度测定结果的准确性。     

Adaptive Fourier decomposition‐based Dirac type time‐frequency distribution

The Dirac‐type time‐frequency distribution (TFD), regarded as ideal TFD, has long been desired. It, until the present time, cannot be implemented, due to the fact that there has been no appropriate representation of signals leading to such TFD. Instead, people have been developing other types of TFD, including the Wigner and the windowed Fourier transform types. This paper promotes a practical passage leading to a Dirac‐type TFD. Based on the proposed function decomposition method, viz., adaptive Fourier decomposition, we establish a rigorous and practical Dirac‐type TFD theory. We do follow the route of analytic signal representation of signals founded and developed by Garbo, Ville, Cohen, Boashash, Picinbono, and others. The difference, however, is that our treatment is theoretically throughout and rigorous. To well illustrate the new theory and the related TFD, we include several examples and experiments of which some are in comparison with the most commonly used TFDs. Copyright © 2016 John Wiley & Sons, Ltd.     

Statistical and Geometrical Way of Model Selection for a Family of Subdivision Schemes

The objective of this article is to introduce a generalized algorithm to produce the m-point n-ary approximating subdivision schemes(for any integer m, n ≥ 2). The proposed algorithm has been derived from uniform B-spline blending functions. In particular, we study statistical and geometrical/traditional methods for the model selection and assessment for selecting a subdivision curve from the proposed family of schemes to model noisy and noisy free data. Moreover, we also discuss the deviation of subdivision curves generated by proposed family of schemes from convex polygonal curve. Furthermore, visual performances of the schemes have been presented to compare numerically the Gibbs oscillations with the existing family of schemes.     

A matrix rational Lanczos method for model reduction in large‐scale first‐ and second‐order dynamical systems

In the present paper, we describe an adaptive modified rational global Lanczos algorithm for model‐order reduction problems using multipoint moment matching‐based methods. The major problem of these methods is the selection of some interpolation points. We first propose a modified rational global Lanczos process and then we derive Lanczos‐like equations for the global case. Next, we propose adaptive techniques for choosing the interpolation points. Second‐order dynamical systems are also considered in this paper, and the adaptive modified rational global Lanczos algorithm is applied to an equivalent state space model. Finally, some numerical examples will be given.     

Rees–Shishikura’s theorem for geometrically finite rational maps

In this paper, we generalize Rees–Shishikura’s theorem to the class of geometrically finite rational maps.