Toader型平均的算术与调和平均界

给出了Toader型平均T[A(a,b),G(a,b)]关于调和平均H(a,b)与算术平均A(a,b)组合的精确界.作为应用,发现了几个关于第二类完全椭圆积分的精确不等式.     

高维约束矩阵回归问题

高维约束矩阵回归是指高维情况下带非凸约束的多响应多预测统计回归问题,其数学模型是一个NP-难的矩阵优化,它在机器学习与人工智能、医学影像疾病诊疗、基因表达分析、脑神经网络、风险管理等领域有广泛应用.从高维约束矩阵回归的优化理论和算法两方面总结和评述这些新成果,同时,列出了相应的重要文献.     

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.     

New algebraic structures from Hermitian one-matrix model

Virasoro constraint is the operator algebra version of one-loop equation for a Hermitian one-matrix model, and it plays an important role in solving the model. We construct the realization of the Virasoro constraint from the Conformal Field Theory (CFT) method. From multi-loop equations of the one-matrix model, we get a more general constraint. It can be expressed in terms of the operator algebras, which is the Virasoro subalgebra with extra parameters. In this sense, we named as generalized Virasoro constraint. We enlarge this algebra with central extension, this is a new kind of algebra, and the usual Virasoro algebra is its subalgebra. And we give a bosonic realization of its subalgebra.     

The meta and para OH Substitution Effect on C-Phenyl-Nitrilimine Bond-Shift Isomers

The geometric and electronic structure of 1,3-dipolar species, in particular of nitrile imines, can be surprisingly intricate. A particular example is the C-phenyl-nitrilimine, which exists as two energy minima that constitute bond-shift isomers. To examine the effect of substituents in the phenyl ring, here we investigate the meta and para OH substituted derivatives. These two nitrile imines were generated in an argon matrix by UV-irradiation of 2H-tetrazole precursors and found to photoisomerize to carbodiimides via 1H-diazirines. The different effects of the OH substitution in meta and para positions on the bond-shift isomerism are rationalized with the support of Natural Resonance Theory and Hirshfeld atomic charges. The understanding of how substitution affects the structural characteristics of C-phenyl-nitrilimines, opens a door to modulate the chemistry of those compounds (e. g. in cycloaddition reactions) by appropriate tuning of their substitution (substituent type and position).     

Analysis of Non-innocence of Phosphaquinodimethane Ligands when Charge and Aromaticity Come into Play

Several phosphaquinodimethanes and their M(CO)₅ complexes (M=Cr, Mo, W) and model derivatives have been theoretically investigated regarding the quest of non-innocence. Computed structural and electronic properties of the P-Me/NH₂ substituted phosphaquinodimethanes and tungsten complexes revealed an interesting non-innocent ligand behaviour for the radical anion complexes with distonic ion character and a strong rearomatization of the middle phenyl ring. The latter was further probed taking also geometric aromaticity (HOMA) and quinoid distortion parameters (HOMQc) into account, as well as NICS(1). Furthermore, the effect of the P-substitution was investigated for real (or plausible) complexes and their free ligands focusing on the resulting aromaticity at the middle phenyl ring and vertical one-electron redox processes. The best picture of ligand engagement in redox changes was provided by representing NICS(1) values versus HOMA and the new geometric distortion parameter HOMQc8.     

Theoretical insight of nitric oxide adsorption on neutral and charged Pdn (n = 1–5) clusters

Density functional theory (DFT) calculations within the framework of generalized gradient approximation have been used to systematically investigate the adsorption of nitric oxide (NO) molecule on neutral, cationic, and anionic Pd_n (n = 1–5) clusters. NO coordinate to one Pd atom of the cluster by the end‐on mode, where the tilted end‐on structure is more favorable due to the additional electron in the π* orbital. On the contrary, in the neutral and cationic Pd₂ system, NO coordinates to the bridge site of cluster preferably by the side‐on mode. Charge transfer between Pd clusters and NO molecule and the corresponding weakening of N? O bond is an essential factor for the adsorption. The N? O stretching frequency follow the order of cationic > neutral > anionic. Binding energy of NO on anionic clusters is found to be greater than those of neutral and cationic clusters. © 2015 Wiley Periodicals, Inc.     

关于一类电-力振动模型的建模与分析

从电学、力学的基本原理出发,通过数学方法建立和分析了一种电-力振动模型。这是一种较复杂的电力混合作用的线性振动系统,由模型的特殊结构(类扬声器结构)作者确立了两种磁场,即感生磁场和外磁场两者正交独立,并规定了电学、力学两种不同物理量的坐标取向关系。该模型需要求得三阶正系数常微分方程的收敛解,再求得包含暂态、稳态项的完整解。另外,文章从能量和做功的角度,通过对电压电流间的相位差分析,对所建模型的正确性作了论证,同时也为这类建模引荐了一种论证手段。