Minkowski-type and Alexandrov-Type Theorems for Polyhedral Herissons

Classical H. Minkowski theorems on existence and uniqueness of convex polyhedra with prescribed directions and areas of faces as well as the well-known generalization of H. Minkowski uniqueness theorem due to A.D. Alexandrov are extended to a class of nonconvex polyhedra which are called polyhedral herissons and may be described as polyhedra with injective spherical image.     

双曲函数型辅助方程构造具5次强非线性项的波方程的新精确孤波解

在辅助方程法的基础上利用两种函数变换和一种双曲函数型辅助方程，通过符号计算系统Mathematica构造了在力学当中一个重要的模型，有5次强非线性项的波方程的新三角函数型和双曲函数型精确孤波解.这种方法寻找其他具5次强非线性项的非线性发展方程的新精确解方面具有普遍意义. 关键词： 双曲函数型辅助方程 函数变换 具5次强非线性项的波方程 精确孤波解     

Fractional extensions of some boundary value problems in oil strata

In the present paper, we solve three boundary value problems related to the temperature field in oil strata — the fractional extensions of the incomplete lumped formulation and lumped formulation in the linear case and the fractional generalization of the incomplete lumped formulation in the radial case. By using the Caputo differintegral operator and the Laplace transform, the solutions are obtained in integral forms where the integrand is expressed in terms of the convolution of some auxiliary functions of Wright function type. A generalization of the Laplace transform convolution theorem, known as Efros’ theorem is widely used.     

充分发挥计算机辅助教学作用

本文就计算机在物理实验方面的辅助教学进行了较为深刻的研究和探索，并提出可行性的方案。     

Diastereoselective Three Component Reaction of N‐Glyoxyloyl Camphorpyrazolidinone,Amine and Allyltributylstannane: Facile Synthesis of Homoallylic Amines

Diastereoselective allylation of imine derived from N‐glyoxyloyl camphorpyrazolidinone and amines was treated with allyltributylstannane in the presence of triflic acid. The corresponding optically enriched homoallylic amines were obtained in reasonable to high material yields and with practical levels of stereoselectivity in 10 min at ambient temperature.     

新的手性配体促进的二芳基二酸和联萘酚的不对称合成

由手性配体α-D-葡萄糖衍生物5，6，7以及薄荷醇（8）和葑醇（9），经 Ulmann偶联反应得到光学活性的（R）－和（S）－6，6′－二硝基联苯－2，2′－ 二甲酸（4a),(R)-6,6′-二甲基联苯－2，2′-二甲酸（4b),(R)-1,1′－联萘－2 ，2′－二甲酸（13）。以三个手性膦酰胺16，17，18和CuCl组成的手性络合物为 催化剂，通过2－萘酚直接氧化偶联得到（S）－2，2′－联萘酚（15）。产物4， 13，15具有中等ee值的光学活性。     

Optimization of auxiliary basis sets for the LEDO expansion and a projection technique for LEDO-DFT

We present a systematic procedure for the optimization of the expansion basis for the limited expansion of diatomic overlap density functional theory (LEDO-DFT) and report on optimized auxiliary orbitals for the Ahlrichs split valence plus polarization basis set (SVP) for the elements H, Li--F, and Na--Cl. A new method to deal with near-linear dependences in the LEDO expansion basis is introduced, which greatly reduces the computational effort of LEDO-DFT calculations. Numerical results for a test set of small molecules demonstrate the accuracy of electronic energies, structural parameters, dipole moments, and harmonic frequencies. For larger molecular systems the numerical errors introduced by the LEDO approximation can lead to an uncontrollable behavior of the self-consistent field (SCF) process. A projection technique suggested by L?wdin is presented in the framework of LEDO-DFT, which guarantees for SCF convergence. Numerical results on some critical test molecules suggest the general applicability of the auxiliary orbitals presented in combination with this projection technique. Timing results indicate that LEDO-DFT is competitive with conventional density fitting methods.     

Conformationally controlled (entropy effects), stereoselective vibrational quenching of singlet oxygen in the oxidative cleavage of oxazolidinone-functionalized enecarbamates through solvent and temperature variations

On photooxygenation (methylene blue as sensitizer) of E/Z enecarbamates, equipped with the oxazolidinone chiral auxiliary, the oxidative cleavage of the alkenyl functionality releases the enantiomerically enriched methyldesoxybenzoin (MDB) product. The extent (% ee) as well as the sense (R vs S) of the stereoselectivity in the MDB formation depends on the choice of the alkene configuration; the efficacy of stereocontrol may be tuned by appropriate solvent and temperature conditions. Highlighted is the finding that the formation of the preferred MDB enantiomer (R or S) depends for the E isomer on the chosen solvent and temperature, but not for the corresponding Z isomer. The activation parameters for the various solvents disclose that differential entropy effects (ΔΔS^‡) dominate the conformationally more flexible E diastereomers. As mechanistic rationale for this unprecedented conformationally imposed stereochemical behavior, we propose the competitive action of stereoselective vibrational quenching of the attacking singlet oxygen by the enecarbamate versus sterically controlled stereoselective oxidative cleavage of its double bond.     

Highly diastereoselective synthesis of bicyclo[4.2.0]octanone derivatives by the [2+2] photocycloaddition of chiral cyclohexenonecarboxylates to ethylene

The diastereoselective [2+2] photocycloaddition of a cyclohexenonecarboxylate containing (−)-8-(4-nitrophenyl)menthyl as a chiral auxiliary to ethylene gave the photocycloadduct, a bicyclo[4.2.0]octanone derivative, with a high degree of diastereoselectivity. A photoreaction, conducted in CH₂Cl₂ at −78 °C gave the corresponding photocycloadduct in 88% de. In the presence of Ti(OR)₄ or Me₃SnCl, the diastereoselectivity was increased up to 92% de.     

Conversion of N-Acyl-4-phenyl/benzyl-oxazolidine-2-thiones into Thiol Esters in the Presence of EtSH-K2CO3

N-Acyl-β-hydroxy-4-phenyl-oxazolidinethiones could be rapidly converted into their ethyl thiol esters in high yields by treatment with EtSH at 0 ℃ in CH3CN or 9 ： 1 （V ： V） THF-H2O in the presence of a catalytic amount of K2CO3.