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.     

Arbitrage‐free call option surface construction using regression splines

In this work, we suggest a novel quadratic programming‐based algorithm to generate an arbitrage‐free call option surface. The empirical performance of the proposed method is evaluated using S&P 500 Index call options. Our results indicate that the proposed method provides a more precise fit to observed option prices than other alternative methodologies. Copyright © 2014 John Wiley & Sons, Ltd.     

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).     

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。     

半参数线性混合效应模型的联合变量选择

多数基于线性混合效应模型的变量选择方法分阶段对固定效应和随机效应进行选择,方法繁琐、易产生模型偏差,且大部分非参数和半参数的线性混合效应模型只涉及非参数部分的光滑度或者固定效应的选择,并未涉及非参变量或随机效应的选择。本文用B样条函数逼近非参数函数部分,从而把半参数线性混合效应模型转化为带逼近误差的线性混合效应模型。对随机效应的协方差矩阵采用改进的乔里斯基分解并重新参数化线性混合效应模型,接着对该模型的极大似然函数施加集群ALASSO惩罚和ALASSO惩罚两类惩罚,该法能实现非参数变量、固定效应和随机效应的联合变量选择,基于该法得出的估计量也满足相合性、稀疏性和Oracle性质。文章最后做了个数值模拟,模拟结果表明,本文提出的估计方法在变量选择的准确性、参数估计的精度两个方面均表现较好。     

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.     

Regularized Principal Component Analysis for Spatial Data

In many atmospheric and earth sciences, it is of interest to identify dominant spatial patterns of variation based on data observed at p locations and n time points with the possibility that p > n. While principal component analysis (PCA) is commonly applied to find the dominant patterns, the eigenimages produced from PCA may exhibit patterns that are too noisy to be physically meaningful when p is large relative to n. To obtain more precise estimates of eigenimages, we propose a regularization approach incorporating smoothness and sparseness of eigenimages, while accounting for their orthogonality. Our method allows data taken at irregularly spaced or sparse locations. In addition, the resulting optimization problem can be solved using the alternating direction method of multipliers, which is easy to implement, and applicable to a large spatial dataset. Furthermore, the estimated eigenfunctions provide a natural basis for representing the underlying spatial process in a spatial random-effects model, from which spatial covariance function estimation and spatial prediction can be efficiently performed using a regularized fixed-rank kriging method. Finally, the effectiveness of the proposed method is demonstrated by several numerical examples.     

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.