基于特征值分析的多尺度结构优化设计方法

基于特征值分析，提出了多尺度结构优化设计方法.该方法被用于分析宏观结构上作用有最不利荷载时，使宏观结构刚度最大的宏观拓扑结构和微观材料分布.引入约束条件为最不利荷载的Euclid范数等于1，根据Rayleigh-Ritz定理，可以将结构的柔顺度转换为一个与局部荷载向量维数相同的对称矩阵，这样就将作用有最不利荷载的柔顺度最小问题转换为求解对称矩阵的最大特征值最小问题，同时最不利荷载可以通过最大特征值矩阵的特征向量求得.最后通过算例验证所提多尺度结构优化设计方法的有效性，并说明宏观拓扑结构和微观材料分布的合理性.所提出的多尺度优化方法具有迭代稳定、收敛迅速等特点.该文拓扑优化中密度函数的更新是基于灵敏度分析和移动渐近线方法（method of moving asymptotes，MMA）.     

Anti-control of Hopf Bifurcation in a Delayed Predator-prey Gompertz Model

A delayed predator-prey Gompertz model is investigated. The stability is ana- lyzed. Anti-control of Hopf bifurcation for the model is presented. Numerical simulations are performed to confirm that the new feedback controller using time delay is efficient in creating Hopf bifurcation. Finally, main conclusions are included.     

Palladium-catalyzed cross-coupling of benzylzinc reagents with 2-bromo-3,3,3-trifluoropropene

α-Trifluoromethyl alkenes can be used as peptide isosteres, moreover, the pre-installed vinyl group make it possible that transformation to diverse fluorine-containing unities. However, the cross-coupling of benzyl group with α-trifluoromethyl alkenes has yet to be developed. In this report, we describe a general method for the cross-coupling of benzylzinc reagents with 2-bromo-3,3,3-trifluoropropene (BTP) to afford diverse α-trifluoromethylalkene derivatives by using Pd(TFA)₂ as catalyst. This method takes advantage of cheap industrial available fluorine building blocks and easily prepared benzylzinc reagents to generate α-trifluoromethylalkene derivatives, which features with mild reaction conditions, wide substrate scope and feasibility of product transformations.     

Application of wavelet transform in-ray spectra analysis

The frequency distribution of different ingredients in-ray spectra,e.g.,photo-peak,fluctuations of counts and Compton region,is separately analyzed.After wavelet transform of-ray spectra,the wavelet coefficients of a photo-peak increase with transforming scales and these coefficients show direct proportion with intensity of peak at determinate scale.A novel algorithm based on wavelet transform is proposed and studied.The results indicate that most of the photo-peaks in multi-spectra can be determined accurately,the-rays energy and intensity of the peak can also be determined.This method has the prospect of being applied in on-line multi-spectra analysis in such fields as radioprotection and nuclear safety monitoring.     

A Structural Entropy Measurement Principle of Propositional Formulas in Conjunctive Normal Form

The satisfiability (SAT) problem is a core problem in computer science. Existing studies have shown that most industrial SAT instances can be effectively solved by modern SAT solvers while random SAT instances cannot. It is believed that the structural characteristics of different SAT formula classes are the reasons behind this difference. In this paper, we study the structural properties of propositional formulas in conjunctive normal form (CNF) by the principle of structural entropy of formulas. First, we used structural entropy to measure the complex structure of a formula and found that the difficulty solving the formula is related to the structural entropy of the formula. The smaller the compressing information of a formula, the more difficult it is to solve the formula. Secondly, we proposed a λ-approximation strategy to approximate the structural entropy of large formulas. The experimental results showed that the proposed strategy can effectively approximate the structural entropy of the original formula and that the approximation ratio is more than 92%. Finally, we analyzed the structural properties of a formula in the solution process and found that a local search solver tends to select variables in different communities to perform the next round of searches during a search and that the structural entropy of a variable affects the probability of the variable being flipped. By using these conclusions, we also proposed an initial candidate solution generation strategy for a local search for SAT, and the experimental results showed that this strategy effectively improves the performance of the solvers CCAsat and Sparrow2011 when incorporated into these two solvers.     

2,2-双(4-氯-2-氟苄基)丙二酸二乙酯的晶体结构和密度泛函理论研究

标题化合物是一个重要的精细化工中间体,可用于制备嘧啶类、吡唑类等产品。本文利用红外光谱(IR)、质谱(MS)、核磁共振氢谱(¹H NMR)、核磁共振碳谱(¹³C NMR)和X-射线单晶衍射对此化合物进行了表征,并在B3LYP/6-311G(d, p)模式下使用密度泛函理论(DFT)计算了此化合物的最稳定晶体结构以及最高占有分子轨道(HOMO)和最低占有分子轨道(LUMO)能量。结果表明,通过DFT优化的分子结构与X-射线单晶衍射确定的晶体结构基本一致,该化合物属于单斜方P2(1)/n空间群,晶胞参数为:a=1.563 9(10) nm, b=0.778 6(4) nm, c=1.838 2(10) nm,Z=4, ρ_c＝1.345 g·cm^-3,R=0.047 7,R_w=0.138 7。     

Sc、Ce掺杂CrSi2的电子结构与光学性质的第一性原理

采用基于密度泛函理论的第一性原理赝势平面波方法对Sc、Ce单掺和共掺后CrSi₂的几何结构、电子结构、复介电函数、吸收系数和光电导率进行了计算。结果表明:Sc、Ce掺杂CrSi₂的晶格常数增大,带隙变小。本征CrSi₂的带隙为0.386 eV,Sc、Ce单掺及共掺CrSi₂的禁带宽度分别减小至0.245 eV、0.232 eV、0.198 eV,费米能级均向低能区移动进入价带。由于Sc的3d态电子和Ce的4f态电子的影响,Sc、Ce掺杂的CrSi₂在导带下方出现了杂质能级。掺杂后的CrSi₂介电函数虚部第一介电峰峰值增加且向低能方向移动,说明Sc、Ce掺杂使得CrSi₂在低能区的光跃迁强度增强,Sc-Ce共掺时更明显。Sc、Ce掺杂的CrSi₂吸收边在低能方向发生红移,在能量大于21.6 eV特别是在位于31.3 eV的较高能量附近,本征CrSi₂几乎不吸收光子,Sc单掺和Sc-Ce共掺CrSi₂吸收光子的能力有所增强,并在E=31.3 eV附近形成了第二吸收峰。说明掺杂Sc、Ce改善了CrSi₂对红外和较高能区光子的吸收。在小于3.91 eV的低能区掺杂后的CrSi₂光电导率增加。在20.01 eV<E<34.21 eV时,本征CrSi₂光电导率为零,但Sc、Ce掺杂后的体系不为零,掺杂拓宽了CrSi₂的光响应范围。研究结果为CrSi₂基光电器件的应用与设计提供了理论依据。     

A Class of Accelerated Subspace Minimization Conjugate Gradient Methods

Journal of Optimization Theory and Applications - The subspace minimization conjugate gradient methods based on Barzilai–Borwein method (SMCG_BB) and regularization model (SMCG_PR), which...     

Multiple bifurcation trees of period-1 motions to chaos in a periodically forced,time-delayed,hardening Duffing oscillator

In this paper, bifurcation trees of periodic motions in a periodically forced, time-delayed, hardening Duffing oscillator are analytically predicted by a semi-analytical method. Such a semi-analytical method is based on the differential equation discretization of the time-delayed, nonlinear dynamical system. Bifurcation trees for the stable and unstable solutions of periodic motions to chaos in such a time-delayed, Duffing oscillator are achieved analytically. From the finite discrete Fourier series, harmonic frequency-amplitude curves for stable and unstable solutions of period-1 to period-4 motions are developed for a better understanding of quantity levels, singularity and catastrophes of harmonic amplitudes in the frequency domain. From the analytical prediction, numerical results of periodic motions in the time-delayed, hardening Duffing oscillator are completed. Through the numerical illustrations, the complexity and asymmetry of period-1 motions to chaos in nonlinear dynamical systems are strongly dependent on the distributions and quantity levels of harmonic amplitudes. With the quantity level increases of specific harmonic amplitudes, effects of the corresponding harmonics on the periodic motions become strong, and the certain complexity and asymmetry of periodic motion and chaos can be identified through harmonic amplitudes with higher quantity levels.     

Research on the target coverage algorithms for 3D curved surface

To solve the target covering problems in three-dimensional space, putting forward a deployment strategies of the target points innovatively, and referencing to the differential evolution (DE) algorithm to optimize the location coordinates of the sensor nodes to realize coverage of all the target points in 3-D surface with minimal sensor nodes. Firstly, building the three-dimensional perception model of sensor nodes, and putting forward to the blind area existing in the process of the sensor nodes sensing the target points in 3-D surface innovatively, then proving the feasibility of solving the target coverage problems in 3-D surface with DE algorithm theoretically, and reflecting the fault tolerance of the algorithm.