用GGA密度泛函及其长程、色散校正方法计算各类氢键的结合能

应用广义梯度近似(GGA) (PW91和PBE)、含动能密度的广义梯度近似(meta-GGA) (M06-L)、杂化泛函(hyper-GGA)(M06-2X、X3LYP和B3LYP)及其长程校正泛函LC-DFT(CAM-B3LYP、LC-ωPBE和ωB97X)和色散校正密度泛函(DFT-D)(ωB97X-D和B97-D),用多种基函数对15种不同强度的传统氢键和非传统氢键体系的结合能进行了系统的计算与分析.并与高精度的CCSD(T)/aug-cc-pVQZ结果比较发现:在上述各类泛函中,对于氢键结合能的计算M06-2X和ωB97X-D泛函较为精确与可靠,且没有必要使用过大的基函数,6-311++G(2d,2p)或aug-cc-pVDZ水平的基组就已足够,各类泛函所计算结合能的基组重叠误差(BSSE)均较小,除ωB97X和ωB97X-D外,其它9种泛函不经BSSE校正也能得到同样甚至更准确的结果.     

Pt原子在γ-Al2O3(001)表面的吸附及迁移

采用密度泛函理论(DFT)中广义梯度近似(GGA)方法, 对Pt原子与γ-Al₂O₃(001)面的相互作用及迁移性能进行了研究. 分析了各种可能吸附位及吸附构型的松弛和变形现象, 吸附能和迁移能垒的计算结果表明: Pt团簇能够稳定吸附在该表面. Pt原子在表面O位的吸附能明显较高, 这主要是由Pt向基底O原子转移了电子所致. 电荷布居分析表明, Pt原子显电正性, Pt和Al原子之间存在排斥作用, 导致与Al原子产生较弱相互作用. 计算的平均吸附能大小依赖于Pt团簇的大小和形状, 总体趋势是随着Pt原子数增多, 吸附能降低. Pt原子在γ-Al₂O₃(001)表面迁移过程所需克服的迁移能垒最高值为0.51 eV. 随着吸附的Pt原子数增多,更倾向于形成Pt团簇. 因此, Pt原子在γ-Al₂O₃(001)表面的吸附演变不可能形成光滑、均匀平铺的吸附构型, 而在一定条件下容易出现团聚.     

Use of ultra-performance liquid chromatography/time-of-flight mass spectrometry with nozzle-skimmer fragmentation for comprehensive quantitative analysis of secondary metabolites in Arabidopsis thaliana

This study sought to develop techniques for LC/MS-based metabolomics and to verify that an MS/MS spectral tag (MS2T) could be used in practical secondary metabolite profiling. The retention time (RT), precursor ions, and fragment ions generated by nozzle-skimmer fragmentation were determined using ultra-performance liquid chromatography/time-of-flight mass spectrometry (UPLC/TOF-MS) and compared with the MS2T. A standard mix was analyzed with UPLC/TOF-MS under the same conditions as were used to construct the MS2T. The difference in RT for the standards was less than 0.15 min and the average RSD was about 2.8%, suggesting that the analysis was highly repeatable. Both precursor ions and fragment ions were observed when the cone voltage was 75 V. Experimental data and fragmentation pattern in the MS2T annotation list were highly similar. Wild-type and cas-1 mutant Arabidopsis thaliana samples treated with an elicitor were analyzed using UPLC/TOF-MS. Sixty-five peaks were successfully annotated. Fragment ions were observed with nozzle-skimmer fragmentation in 50 of 65 (77%) peaks. The reliability of annotation may have increased as a result of fragment ions. Results of multivariate analysis suggested that cas-1 was related to induction of the biosynthesis of these flavonoids. The devised method facilitated practical secondary metabolite profiling.     

Spectral theory for commutative algebras of differential operators on Lie groups

The joint spectral theory of a system of pairwise commuting self-adjoint left-invariant differential operators L₁,…,Ln on a connected Lie group G is studied, under the hypothesis that the algebra generated by them contains a “weighted subcoercive operator” of ter Elst and Robinson (1998) [52]. The joint spectrum of L₁,…,Ln in every unitary representation of G is characterized as the set of the eigenvalues corresponding to a particular class of (generalized) joint eigenfunctions of positive type of L₁,…,Ln. Connections with the theory of Gelfand pairs are established in the case L₁,…,Ln generate the algebra of K-invariant left-invariant differential operators on G for some compact subgroup K of Aut(G).     

Reconstruction from local discrete averages on the plane

The aim of the paper is to construct a solution for the equation f?μ=g, where f?μ is the convolution of f and μ given by , g is an arbitrary continuous function and μ is a finitely supported measure on the plane.     

Bifurcation diagrams of a p-Laplacian Dirichlet problem with Allee effect and an application to a diffusive logistic equation with predation

We study bifurcation diagrams of positive solutions for the p-Laplacian Dirichlet problem

     

Dynamics of the density dependent predator-prey system with Beddington-DeAngelis functional response

Two models of a density dependent predator-prey system with Beddington-DeAngelis functional response are systematically considered. One includes the time delay in the functional response and the other does not. The explorations involve the permanence, local asymptotic stability and global asymptotic stability of the positive equilibrium for the models by using stability theory of differential equations and Lyapunov functions. For the permanence, the density dependence for predators is shown to give some negative effect for the two models. Further the permanence implies the local asymptotic stability for a positive equilibrium point of the model without delay. Also the global asymptotic stability condition, which can be easily checked for the model is obtained. For the model with time delay, local and global asymptotic stability conditions are obtained.     

Dynamics of a stochastic density dependent predator-prey system with Beddington-DeAngelis functional response

In this paper, we discuss a stochastic density dependent predator-prey system with Beddington-DeAngelis functional response. First, we show that this system has a unique positive solution as this is essential in any population dynamics model. Then, we investigate the asymptotic behavior of this system. When the white noise is small, the stochastic system imitates the corresponding deterministic system. Either there is a stationary distribution, or the predator population will die out. While if the white noise is large, besides the extinction of the predator population, both species in the system may also die out, which does not happen in the deterministic system. Finally, simulations are carried out to conform to our results.     

On the density of integral sets with missing differences from sets related to arithmetic progressions

For a given set M of positive integers, a problem of Motzkin asks for determining the maximal density μ(M) among sets of nonnegative integers in which no two elements differ by an element of M. The problem is completely settled when |M|?2, and some partial results are known for several families of M for |M|?3, including the case where the elements of M are in arithmetic progression. We consider some cases when M either contains an arithmetic progression or is contained in an arithmetic progression.     

Optimal media planning for multi-products in segmented market

Promotion is an essential stage of any product life cycle. All firms either concerned with single or multiple products promote their products. Advertising is the most dominated form of promotion for most of the products. Our research focuses on firms which produces a multiple range of products and advertise them using available media options. The budget constraint forms the major restriction. The existing research in media allocation of multiple products ignores the market segmentation and formulates the media plan assuming all segments alike. In this paper we formulate a media planning problem for allocating the available budget in multiple media that are found suitable for the advertising of multiple products considering marketing segmentation aspect of advertising. The objective is to maximize the total reach in all the segments. Goal programming technique is used to solve the problem. A case study is presented to show the real life application of the model.