The structural and spectroscopic properties for uranium oxides

The equilibrium structures, the charge population, and the spectroscopic properties of UO, UO 2 , UO 3 , and U 2 O 3 molecules are systematically investigated using the density functional theory (DFT) with the method of generalized gradient approximation (GGA). The bond lengths and the vibrational frequencies of the ground states of UO, UO 2 , and UO 3 molecules are all in agreement with available experimental data. For U 2 O 3 molecules, our calculations indicate that the ground state of the U 2 O 3 molecule is an X 7 A ′ 1 state with D 3h (trigonal bipyramid) symmetry (R 1 (U–O)=0.2113 nm, R 2 (U 1 –U 2 )=0.2921 nm, ∠U 1 OU 2 = 87.5 , dihedral angle Θ(U,O 1 ,O 2 ,O 3 )=62.40 ). The harmonic frequency, the IR intensity and the spin density of the U 2 O 3 molecule are all obtained for the first time in theory. For the ground state of U 2 O 3 molecules, the vibrational frequencies are 178.46 (A ′ 1 ), 276.79 (E ′′ 1 ), 310.77 (E ′ 1 ), 396.63 (A ′′ 2 ), 579.15 (E ′ 1 ), and 614.98 (A ′ 1 ) cm 1 . The vibrational modes corresponding to the IR maximum peaks are worked out for UO 3 and U 2 O 3 molecules. Besides, the results of Gophinatan–Jug bond order indicate that UO, UO 2 , and UO 3 molecules possess U=O double bonds and that the U 2 O 3 molecule possesses U–O single bonds and a U–U single bond.     

具有反馈控制的单种群对数模型稳定性

研究具有反馈控制的单种群对数模型．通过构造适当的Lyapunov函数．我们让得系统的正平衡点是无条件全局稳定的．所得结果补充和完善了已有的结果．     

The comparison between Homotopy Analysis Method and Optimal Homotopy Asymptotic Method for nonlinear age-structured population models

This paper presents comparison between Homotopy Analysis Method (HAM) and Optimal Homotopy Asymptotic Method (OHAM) for the solution of nonlinear age-structured population models. Three examples have been presented to illustrate and compare these methods. In OHAM the convergence region can be easily adjusted and controlled. Comparison between our solution and the exact solution shows that the both methods are effective and accurate in solving nonlinear age-structured population models with HAM being the more accurate for the same number of terms. It was also found that OHAM require more CPU time.     

青冈常绿阔叶林中青冈种群结构与分布格局

通过群落与种群的调查，对浙江北部几个地区的青冈常绿阔叶林中青冈种群的数量特征，从分株和分株 萌生枝两个层次上进行了研究．结果表明：青冈种群的大小结构在分株层次上，有两种类型：纺锤形结构和不典型的金字塔形结构(倒“J”型)，在分株 萌生枝层次上，都为金字塔形结构；青冈种群主要是集群分布格局；动态分布格局是从集群分布到随机分布．     

一类非线性人口问题的渐近解

本研究了一类非线奇摄动人口问题.在适当的条件下,首先求出了原问题的外部解,然后利用伸长变量和幂级数展开理论构造出解的形式渐近展开式.最后利用微分不等式理论,讨论了问题解的-致有效性.     

Commentaries on quantum similarity (1): Density gradient quantum similarity

Computation of density gradient quantum similarity integrals is analyzed, while comparing such integrals with overlap density quantum similarity measures. Gradient quantum similarity corresponds to another kind of numerical similarity assessment between a pair of molecular frames, which contrarily to the usual up to date quantum similarity definitions are not measures, that is: strictly positive definite integrals. As the density gradient quantum similarity integrals are defined as scalar products of three real functions, they appear to possess a richer structure than the corresponding positive definite density overlap quantum similarity measures, while preserving the overall similarity trends, when the molecular frames are relatively moved in three‐dimensional space. Similarity indices are also studied when simple cases are analyzed in order to perform more comparisons with density overlap quantum similarity. Multiple gradient quantum similarity integrals are also defined. General GTO formulae are given. Numerical results within the atomic shell approximation (ASA) framework are presented as simple examples showing the new performances of the gradient density quantum similarity. Fortran 90 programs illustrating the proposed theoretical development can be downloaded from appropriate websites. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Control of delocalization and structural changes by means of an electric field

The strength and, mainly, the direction of a static electric field can be used to control delocalization effects occurring in a non-polar pi-system. The delocalization energy, the weights, and the probabilities of some local electronic structures, the behavior of electron pairs, and the electronic fluctuations are considered and examined in cis-butadiene, used as model system. The effects of the electric field are detected and evaluated in the basis of natural orbital spaces appropriate to investigate the behavior of one- and poly-electron distributions. The consequences of modifying the delocalization effects on structural changes are also investigated. Full geometry optimizations in both Hartree-Fock and MP2 levels show that the changes in bond lengths, guided by the changes of the behavior of the electronic assembly, can be controlled by means of the electric field.     

Stabilization in a 3D eco-epidemiological model: From the complete extinction of a predator population to their self-healing

In this paper, using the localization method of compact invariant sets, we examine the ultimate dynamics of the 3D prey–predator model containing two subpopulations of susceptible and infected predators. Our attention is focused to finding ultimate sizes of interacting populations, and, in addition, we show the existence of a global attracting set. Then, we derive various global conditions of ultimate extinction of at least one of the predators subpopulations and describe conditions under which all types of internal bounded dynamics are ruled out. In particular, we describe convergence conditions to omega-limit sets located (1) in the intersection of the prey-free plane with the infected predators-free plane and (2) in the infected predators-free plane. Based on the dynamical analysis of the 2D infection-free subsystem, we obtain conditions of global attraction to (i) the prey-only disease-free equilibrium point, (ii) the disease-free prey-predator equilibrium point (self-healing of the predator population), and (iii) the omega-limit set containing an equilibrium point or a periodic orbit. Main theoretical results are illustrated by numerical simulation. Tools and techniques developed in this work can be appropriated in the studies within predictive population ecology of more complex eco-epidemiological models.