Mean Value on the Difference Between a Quadratic Residue and Its Inverse Modulo p

The main purpose of this paper is to use the generalized Bernoulli numbers, Gauss sums and the mean value theorems of Dirichlet L-functions between a quadratic residue and its inverse modulo p value formula. to study the asymptotic property of the difference （a prime）, and to give an interesting hybrid mean     

Measurement of small-signal and large-signal responses of packaged laser modules at high temperature

In this paper, the pulsed injection method is extended to measure the chip temperature of various packaged laser modules, such as the DFB laser modules, the FP laser modules, and the EML laser modules. An optimal injection condition is obtained by investigating the dependence of the lasing wavelength on the width and period of the injection pulse in a relatively wide temperature range. The small-signal frequency responses and large-signal performances of packaged laser modules at different chip temperature are measured. The adiabatic small-signal modulation characteristics of packaged LD are first extracted. In the large-signal measurement, the effects of chip temperature, bias current and driving signal on the performances of the laser modules are discussed. It has been found that the large-signal performances of the EML modules depend on the different red-shift speeds of the DFB and EAM sections as chip temperature varying, and the optimal characteristics may be achieved at higher temperature.     

Hamiltonian formulation of generalized quantum dynamics

The Hamiltonian formulation of the usual complex quantum mechanics in the theory of generalized quantum dynamics is discussed. After the total trace Lagrangian, total trace Hamiltonian and two kinds of Poisson brackets are introduced, both the equations of motion of some total trace functionals which are expressed by total trace Poisson brackets and the equations of motion of some operators which are expressed by the without-total-trace Poisson brackets are obtained. Then a set of basic equations of motion of the usual complex quantum mechanics are obtained, which are also expressed by the Poisson brackets and total trace Hamiltonian in the generalized quantum dynamics. The set of equations of motion are consistent with the corresponding Heisenberg equations. Project supported by Prof. T.D. Lee’s NNSC Grant, the National Natural Science Foundation of China, the Foundation of Ph. D. Directing Programme of Chinese University, and the Chinese Academy of Sciences.     

（±）—Salvinolone的全合成研究

以２－（３，４－环己基类二氧－５－异丙基）苯基乙醇（２）和３－异丙氧基－５，５－二甲基－１，３－环己烯酮（４）为原料，利用羰基α－位的烷基化反应和分子内的Ｆｒｉｅｄｅｌ－Ｃａｒｆｔｓ反应为关键步骤，经９步反应，合成了多氧芳香型三环二萜类天然产物Ｓａｌｖｉｎｏｌｏｎｅ。     

二、三分枝甘露糖簇衍生物的合成

采取一种有效途径合成了二、三分支的甘露糖簇分子．甘露糖经烯丙苷化、乙 酰基保护后，将其烯丙基的双键氧化得到带有羧基连接臂的甘露糖衍生物，然后再 分别与l，6-己二胺和三(2-氨乙基)胺进行缩合反应，最后脱掉保护基，得到二分 枝甘露糖簇化合物6和三分枝甘露糖簇化合物8．     

meso-四(对烷氧苯基)卟啉金属配合物的合成和性能研究(Ⅳ)

合成了系列卟啉乙酸合锰配合物9个,其中6个为未见文献报道的新化合物.用UV,1HNMR,IR,MS,元素分析等表征确证了配合物的结构,总结了锰与卟啉类配体配合的IR,UV,1H NMR判据.采用差示扫描量热法(DSC)和偏光显微镜(PM)研究了该系列配合物的液晶性能,发现8个配合物具有液晶性.考察了烷氧基链长、配位金属离子和分子空间结构对液晶性能的影响.     

A Two-dimensional Lanthanide Coordination Framework with a New Amide-type Tripodal Ligand, 2,2′,2＂-Nitrilotris{[（2′- benzylaminoformyl）phenoxy]ethyl}amine

The La(III) complex with a new amide‐type tripodal ligand,2,2′.2″‐nitrilotris{[(2′‐benzylaminofomyl)‐phenoxylethyl)amine (L), was synthesized and characterized by X‐ray crystallographic analysis. Crystal data: C₄₈H_55.50LaN₇O_18.75, M_r=1169.40, monoclinic. space group, P2₁/n, a= 1.0644(3) nm. b=2.3889(5) nm, c= 2.1917(5) nm, β=90.65°, V=5.573(2) nm³, Z=1, D_c=1.394 g°cm^?3, R₁=0.0487, wR [1>2s?(I)]=0.1266. The results reveal that each La(III) ion binds to 9 oxygen atoms, three of which belong to carbonyl groups from three tripodal ligands and six to three bidentate nitrate groups and a two‐dimensional sheet of 4.8² networks is assembled by metal‐ligand coordination interaction. L, a heptadentate compound, merely acts as a tridentate bridging spacer due to its steric hindrance and links the La(III) ions as three‐connected nodes.     

Studies on synthesis and infrared and fluorescence spectra of new europium and terbium complexes with an amide-based open-chain crown ether

An amide-based open-chain crown ether ligand and its complexes with europium and terbium were synthesized. The complexes were characterized by elemental analysis, infrared spectra and conductivity. The europium and terbium ions were found to coordinate to the C=O oxygen atoms and pyridine nitrogen atoms. The fluorescence properties of these complexes in DMF and CH3OH/CHCl3 were studied. Under the excitation of UV light, these complexes exhibit characteristic fluorescence of europium and terbium ions. The solvent factors influencing the fluorescent intensity are discussed.