基于Ph,e下Riemann-Liouville分数阶微分方程解的存在唯一性

利用基于集合P_h,e上的一类混合单调算子不动点定理,研究了一类Riemann Liouville分数阶微分方程两点边值问题,获得了这类方程在集合P_h,e中解的存在性与唯一性,并用一组单调迭代序列逼近了该方程的唯一非平凡解.最后,利用一个实例验证了主要结论.     

Universal critical properties of the Eulerian bond-cubic model

We investigate the Eulerian bond-cubic model on the square lattice by means of Monte Carlo simulations,using an efficient cluster algorithm and a finite-size scaling analysis.The critical points and four critical exponents of the model are determined for several values of n.Two of the exponents are fractal dimensions,which are obtained numerically for the first time.Our results are consistent with the Coulomb gas predictions for the critical O(n) branch for n < 2 and the results obtained by previous transfer matrix calculations.For n=2,we find that the thermal exponent,the magnetic exponent and the fractal dimension of the largest critical Eulerian bond component are different from those of the critical O(2) loop model.These results confirm that the cubic anisotropy is marginal at n=2 but irrelevant for n < 2.     

Formation energies and electronic structures of native point defects in potassium dihydrogen phosphate

The formation energies and the equilibrium concentration of vacancies,interstitial H,K,P,O and antisite structural defects with P and K in KH 2 PO 4 (KDP) crystals are investigated by ab initio total-energy calculations.The formation energy of interstitial H is calculated to be about 2.06 eV and we suggest that it may be the dominant defect in KDP crystal.The formation energy of an O vacancy (5.25 eV) is much higher than that of interstitial O (0.60 eV).Optical absorption centres can be induced by defects of O vacancies,interstitial O and interstitial H.We suggest that these defects may be responsible for the lowering of the damage threshold of the KDP.A K vacancy defect may increase the ionic conductivity and therefore the laser-induced damage threshold decreases.     

Collapsing and the convex hull property in a soap film capillarity model

Soap films hanging from a wire frame are studied in the framework of capillarity theory. Minimizers in the corresponding variational problem are known to consist of positive volume regions with boundaries of constant mean curvature/pressure, possibly connected by “collapsed” minimal surfaces. We prove here that collapsing only occurs if the mean curvature/pressure of the bulky regions is negative, and that, when this last property holds, the whole soap film lies in the convex hull of its boundary wire frame.     

相变与临界乳光现象

分别采用白炽聚光灯和氦氖激光器照射,观察六氟化硫在临界点附近的临界乳光现象.     

WnNim(n+m=8)团簇结构与电子性质的理论研究

采用密度泛函理论(DFT)中的B3LYP方法,在Lanl2dz基组水平上对W_nNi_m(n+m=8)团簇的各种可能构型进行了几何参数全优化,得到了它们的基态构型;并对基态构型的平均结合能、Wiberg键级(WBI)、磁学性质、NBO进行了分析,结果表明:团簇随着W原子数的增多,稳定性增强,n≥5时,结构中都含有纯钨团簇的结构基元;W-W键级高于W-Ni键和Ni-Ni键;W₅Ni₃,W₆Ni₂团簇发生了"磁矩猝灭"的现象;在W,Ni原子内部,轨道电荷发生了转移,产生了"轨道杂化"现象,W,Ni原子之间也发生了电荷转移形成了较强的化学键. 关键词： nNi_m(n+m=8)团簇')" href="#">W_nNi_m(n+m=8)团簇 几何结构 电子性质 密度泛函理论     

基于SD-VF理论的城市限行政策效应研究

随着我国城市化进程不断加快,城市交通供需矛盾日益突出,交通拥堵问题愈发严重,我国各地纷纷实行各种政策措施来缓解交通拥堵。本文以北京市为例,针对城市交通拥堵的现象,从系统的角度出发,运用系统动力学与灰色Verhulst预测相结合的方法(SD-VF),建立城市交通治堵模型,并采用Vensim软件对模型进行动态仿真分析,从经济、社会、环境等方面探究政策措施对城市环境生态承载力、道路生态承载力等的影响。研究结果表明,限行限号政策虽然在一定程度上提高道路生态承载力,但也可能引发“悖论”效应;修路政策并没有根本上解决城市交通拥堵问题,仅仅是把拥堵状况向后推迟;而相对于单一政策,将发展公共交通与限行政策相结合可以有效缓解交通拥堵,改善空气质量,提升环境承载力,是更加科学合理的政策措施。     

三维各向异性耦合谐振子哈密顿量的对角化

根据物理量的可测实在性,应用二次型理论,一般地解决了3个质量与3个频率均不相同、坐标和动量各自具有全耦合谐振子系统的哈密顿量的可对角化问题,并具体给出了哈密顿量对角化的标准形.     

Influence of ligand-bridged substitution on the exchange coupling constant of chromium-wheels host complexes: a density functional theory study

Designing and introducing novel wheel-shaped supramolecular as host complexes with new magnetic properties is the theme of the day. So in this study, new eight binuclear chromium (III) complexes, as models of real chromium-wheel host complexes, were designed based on changing of bridged-ligands and exchange coupling constants (J) of them were calculated using the broken symmetry density functional theory approach. Substitution of fluorine ligand in fluoro-bridged model [Cr₂F(tBuCO₂)₂(H₂O)₂(OH)₄]^?1 by halogen anions (Cl^?, Br^? and I^? ) decreased the antiferromagnetic exchange coupling between Cr(III) centres such that by going from F^? to I^? the J values became more positive. In the case of hydroxo-bridged model [Cr₂OH(tBuCO₂)₂(H₂O)₂(OH)₄]^?1, replacement of hydroxyl by methoxy anion (OMe^?) strengthened the antiferromagnetic property of the complex but substitution by sulfanide (SH^?) and amide (NH₂^?) anions weakened it and changed the nature of complexes to ferromagnetic. Because of their different magnetic properties, these new investigated complexes can be suggested as interesting synthetic targets. Also, the J value changes due to ligand substitution were evaluated and it was found that the Cr–X bond strength and partial charges of involved atoms were the most effective factors on it.     

Substituent effects on gas‐phase homolytic Fe–N bond energies of m‐G‐C6H4NHFe(CO)2(η5‐C5H5) and m‐G‐C6H4N(COMe)Fe(CO)2(η5‐C5H5) studied using density functional theory methods

One of the most fundamental properties in chemistry is the bond dissociation energy, the energy required to break a specific bond of a molecule. In this paper, the Fe–N homolytic bond dissociation energies [ΔH_homo(Fe–N)'s] of 2 series of (meta‐substituted anilinyl)dicarbonyl(η⁵‐cyclopentadienyl) iron [m‐G‐C₆H₄NHFp ( 1 )] and (meta‐substituted α‐acetylanilinyl)dicarbonyl(η⁵‐cyclopentadienyl) iron [m‐G‐C₆H₄N(COMe)Fp ( 2 )] were studied using density functional theory methods with large basis sets. In this study, Fp is (η⁵‐C₅H₅)Fe(CO)₂, and G is NO₂, CN, COMe, CO₂Me, CF₃, Br, Cl, F, H, Me, MeO, and NMe₂. The results show that Tao‐Perdew‐Staroverov‐Scuseria, Minnesota 2006, and Becke's power‐series ansatz from 1997 with dispersion corrections functionals can provide the best price/performance ratio and accurate predictions of ΔH_homo(Fe–N)'s. The ΔΔH_homo(Fe–N)'s ( 1 and 2 ) conform to the captodative principle. The polar effects of the meta‐substituents show the dominant role to the magnitudes of ΔΔH_homo(Fe–N)'s. σ_α· and σ_c· values for meta‐substituents are all related to polar effects. Spin‐delocalization effects of the meta‐substituents in ΔΔH_homo(Fe–N)'s are small but not necessarily zero. RE plays an important role in determining the net substituent effects on ΔH_homo(Fe–N)'s. Insight from this work may help the design of more effective catalytic processes.