Optimal group symmetric localized molecular orbitals

Summary The concept and generating method of optimum group symmetric localized molecular orbitals (OSLMOs) are proposed. The OSLMOs have strong points of orthogonality, equivalence and symmetry, and they are simultaneously as close to the classical VB structure as possible. By using the OSLMOs as one-electron orbitals the multiconfigurational correlation calculations are reduced. The scheme is also a valuable popularization and development to hybridization theory.     

Preferred Conformations of Stabilized Phosphorus Ylides

The stabilized phosphorus ylides, Ph₃P=C(CO.R′)CO.OR; 1, R=Et, R′=CH₂P⁺Ph₃; 2, R=R′=Me; 3, R=Et, R′=Me; 4, R=Prⁱ; R′=Me; 5, R=Bu^t; R′=Me, adopt a near planar conformation in the crystal which allows extensive electronic delocalization. The keto and alkoxylic oxygens are oriented and align favorably with the cationoid phosphorus. These conformations bring methyl hydrogens in the ester residue into proximity with the face of a phenyl group and lead to π-shielding and upfield shifts of the ¹HNMR signals of 3 over a wide temperature range (-50–95°C) in (CD₃)₂CO, CDCl₃ and DMSO_d-6. Geometries of 2 and 3, optimized by using the HF 3-21 (G^*) or 6-31 (G^*) basis sets, are very similar to those in the crystal, but semiempirical treatments generate structures in which either the ester or keto moiety is twisted out of plane.

     

Optimized geometry and electronic structure of graphyne-like silicyne nanoribbons

Silicyne, a silicon allotrope, which is closely related to silicene and has graphyne-like structure, is theoretically investigated in this work. Its optimized geometry and electronic band structure are calculated by means of the first-principles frozen-core projector-augmented wave method implemented in the Vienna ab initio simulation package (VASP). We find that the lattice parameter is 9.5, the silicon chain between hexagons is composed of disilynic linkages (-Si≡Si-) rather than cumulative linkages (=Si=Si=), and the binding energy is 3.41 eV per atom. The band structure is calculated by adopting the generalized gradient approximation and hybrid functionals. The band gap produced by the HSE06 functional is 0.73 eV, which is nearly triple that by the generalized gradient approximation of Perdew-Burke-Ernzerhof functional.     

FRACTAL PROPERTIES OF STATISTICALLY SELF-SIMILAR SETS

1IntroductionIn1981,J.E.Hutchinson[1]establishedthebasictheoryof(strictly)selfsimilarsets.Foragivenset(={S1,'',SN}ofcontractionmapsonacompleteseparableboundedmetricspaceN(X,d),thereexistsauniquecompactsetKsuchthatK=ZSi(K),andKistheclooureofi=1thesetofallfixedpointssi,,..-,iPoffillitecompositionsSi,o''oSi,(wesayKistheselfsimilarNsetwithrespectto().Illaddition,supposep1,-'tPNE(o,1)andZpi=l,thenthereexistsi=1NauuiqueBorelregularmeasurepoftotalmass1suchthatp=Zpipos;'withsuppp=Ki=1(we…     

椭球体易拉罐形状和尺寸的优化设计模型

从材料最省、外观最美、放置稳定的角度设计了"椭球体"易拉罐的形状,然后通过建立非线性规划模型Ⅰ,求出了"椭球体"易拉罐的中腰半径、底面半径和高度.然后从手感舒适的角度建立了优化模型Ⅱ,从而确定了两种型号的"椭球体"易拉罐的最优尺寸.     

TVS-锥度量空间中的统计收敛

本文研究TVS-锥度量空间中的统计收敛以及TVS-锥度量空间的统计完备性.令（X，E，P，d）表示一个TVS-锥度量空间.利用定义在有序Hausdorff拓扑向量空间E上的Minkowski函数ρ，证明了在X上存在一个通常意义下的度量d_ρ，使得X中的序列（x_n）在锥度量d意义下统计收敛到x ∈ X，当且仅当（x_n）在度量d_ρ意义下统计收敛到x.基于此，我们证明了任意一个TVS-锥统计Cauchy序列是几乎处处TVS-锥Cauchy序列，还证明了任意一个TVS-锥统计收敛的序列是几乎处处TVS-锥收敛的.从而，TVS-锥度量空间（X，d）是d-完备的，当且仅当它是d-统计完备的.基于以上结论，通常度量空间中统计收敛的许多性质都可以平行地推广到锥度量空间中统计收敛的情形.     

Comparison of epimeric methyl lithocholate and methyl iso-lithocholate molecules: single crystal X-ray structure of methyl lithocholate, ab initio HF/6-31G* optimized structures and experimental and calculated DFT/B3LYP C NMR chemical shifts

¹³C NMR chemical shifts have been measured and assigned for epimeric methyl 3α/β-hydroxy-5β-cholan-24-oates (methyl lithocholate [3α-OH epimer] and methyl iso-lithocholate [3β-OH epimer]). Their molecular dynamics simulations suggest that for both epimers there exists two predominant gas phase conformations, which have been further forwarded for ab initio/HF optimizations and DFT/GIAO based ¹³C NMR chemical shift calculations. Excellent linear relationships have been observed between experimental and calculated ¹³C NMR chemical shifts for both epimers. For methyl lithocholate (MeLC), the other minimum energy conformation equates very well with the single crystal X-ray structure (orthorhombic, space group P2₁2₁2₁, unit cell ). The crystalline packing of MeLC consists of continuous parallel intermolecular hydrogen bonded [3α-OH?OC24] head-to-tail polymeric chains, which are further cross-linked by many simultaneous weak C(sp³)H?O-type of interactions.     

气相色谱分析过程的计算机仿真模拟与优化

以色谱法的ＬＥＳ模型作为气相色谱分析过程的计算机仿真模拟与优化的理论基础，提出了把两次多阶程度升温实验保留时间作为基本数据进行模拟优化的方法，拓宽了模拟优化方法在复杂组分样品中的应用。软件编程采用了计算数学方法，提高了模拟优化的精度和速度，节省了分析样品的时间。     

水相中荧光CdSe纳米晶的优化合成与表征

Ⅱ-Ⅵ族半导体纳米粒子（也称半导体量子点（semiconductor quantum dots）简称NCs）由于其独特的光学、光化学、电化学以及非线性光学性质已逐渐引起人们的广泛关注。而Ⅱ-Ⅵ族NCs最诱人的 潜在应用是作为荧光探针应用于生物体系,在生命科学研究中起到定性和定量标记分子和细胞的作用。     

公务员招聘的模糊决策模型

运用模糊数学理论与多目标决策模糊优化方法,在不考虑应聘人员的意愿及在考虑应聘人员意愿和用人部门的希望要求的情况下,择优按需录用.分别建立相应的模型.其结果令人满意,具有较强的可靠性和适用性.