Synthesis and Crystal Structure of 3-(Pyrrole-2''-carboxamido)propanoic Acid·(1/2)H2O

3-(Pyrrole-2'-carboxamido)propanoic acid I has been synthesized from the reaction of β-alanine methyl ester with 2-trichloroacetylpyrrole followed by saponifying and acidating in 85.4% yield, and the crystal structure of 3-(pyrrole-2'-carboxamido)propanoic acid· (1/2)H2O (C8H11N2O3.5, Mr = 191.19) was obtained and determined by X-ray diffraction method. The crystal is of monoclinic, space group C2/c with a = 19.010(4), b = 8.3515(17), c = 13.788(3) (A), β = 125.88(3)°, V = 1773.6(6) (A)3, Z = 8, Dc = 1.432 g/cm3, λ = 0.71073 (A), μ-MoKα) = 0.114 mm-1 and F(000) = 768. The structure was refined to R = 0.0354 and wR = 0.0942 for 1642 observed reflections with I > 2σ(I). It is revealed that the title compound has one pyrrole ring and one propionic acid subchain linked by an amido bond at C(4), and there are 8 molecules of com- pound I and 4 crystal water molecules in each unit cell. The supramolecular layers are stabilized by the hydrogen bonds of N(2) H…O(2), N(1) H…O(4), O(4) H(1W)…O(2) and O(3) H…O(1).     

磁载光催化剂Fe3O4/C/TiO2的制备及对三氯苯酚的降解

以FeCl₃为铁源, 葡萄糖为碳源, 钛酸四丁酯为钛源, 采用水热法制备了磁载光催化剂Fe₃O₄/C/TiO₂, 用TEM、EDX、VSM、XRD和IR对Fe₃O₄/C/TiO₂的粒径、形貌和物相等进行了表征。研究了该催化剂对三氯苯酚的降解性能, 探讨了其重复使用的可能性, 用荧光光谱法推测了可能的反应机理。结果表明该材料结合了光催化与可再生的优点, 1 g·L^-1 Fe₃O₄/C/TiO₂在18 W紫外灯下, 50 min内可将三氯苯酚降解97.9%以上, 6次循环使用后降解率仍保持在95.1%, 降解过程中有羟基自由基生成。     

Exact solutions to the angular Teukolsky equation with s ≠ 0

We first convert the angular Teukolsky equation under the special condition of τ ≠ 0, s ≠ 0, m=0 into a confluent Heun differential equation (CHDE) by taking different function transformation and variable substitution. And then according to the characteristics of both CHDE and its analytical solution expressed by a confluent Heun function (CHF), we find two linearly dependent solutions corresponding to the same eigenstate, from which we obtain a precise energy spectrum equation by constructing a Wronskian determinant. After that, we are able to localize the positions of the eigenvalues on the real axis or on the complex plane when τ is a real number, a pure imaginary number, and a complex number, respectively and we notice that the relation between the quantum number l and the spin weight quantum number s satisfies the relation l=∣s∣+ n, n=0, 1, 2···. The exact eigenvalues and the corresponding normalized eigenfunctions given by the CHF are obtained with the aid of Maple. The features of the angular probability distribution (APD) and the linearly dependent characteristics of two eigenfunctions corresponding to the same eigenstate are discussed. We find that for a real number τ, the eigenvalue is a real number and the eigenfunction is a real function, and the eigenfunction system is an orthogonal complete system, and the APD is asymmetric in the northern and southern hemispheres. For a pure imaginary number τ, the eigenvalue is still a real number and the eigenfunction is a complex function, but the APD is symmetric in the northern and southern hemispheres. When τ is a complex number, the eigenvalue is a complex number, the eigenfunction is still a complex function, and the APD in the northern and southern hemispheres is also asymmetric. Finally, an approximate expression of complex eigenvalues is obtained when n is greater than ∣s∣.     

Energy spectrum of the Manning-Rosen potential including centrifugal term solved by exact and proper quantization rules

The energy spectrum of the Manning-Rosen potential including centrifugal term in higher dimensions is presented by exact quantization rule approach. The result is compared with that by proper quantization rule method. It is found that the latter is better than that of the exact quantization rule. We find that the interdimensional degeneracy exists for the states in different dimensions. For the special case D = 3, the results agree well with those obtained by other methods.     

Quantum information entropies of multiple quantum well systems in fractional Schrödinger equations

In this work, we study the position and momentum information entropies of multiple quantum well systems in fractional Schrödinger equations, which, to the best of our knowledge, have not so far been studied. Through a confining potential, their shape and number of wells (NOW) can be controlled by using a few tuning parameters; we present some interesting quantum effects that only appear in the fractional Schrödinger equation systems. One of the parameters denoted by the L_d can affect the position and momentum probability densities if the system is fractional (1 < α < 2). We find that the position (momentum) probability density tends to be more severely localized (delocalized) in more fractional systems (ie, in smaller values of α). Affecting the L_d on the position and momentum probability densities is a quantum effect that only appears in the fractional Schrödinger equations. Finally, we show that the Beckner Bialynicki-Birula-Mycieslki (BBM) inequality in the fractional Schrödinger equation is still satisfied by changing the confining potential amplitude V_conf, the NOW, the fractional parameter α, and the confining potential parameter L_d .     

K2FeO4-Zn碱性固态电解质电池电化学性能研究

应用溶液铸膜法制备出了交联聚乙烯醇(PVA)/聚丙烯酸(PAA)-KOH-H2O复合碱性固态电解质膜, 其厚度为150 µm左右, SEM测试结果表明其表面呈均相的非晶态结构, 交流阻抗(EIS)测试表明室温离子电导率可达3.5×10－2 S&#8226; cm－1, 循环伏安(CV)测试表明其电化学稳定窗口为3.5 V左右, 将其应用于一次碱性K2FeO4-Zn电池, 通过研究固态电解质膜在不同浓度KOH碱液中预处理和其在不同放电倍率下的放电性能, 结果表明, 9 mol&#8226;L－1为最佳固态电解质膜预处理碱液浓度, 0.4 C为最佳放电倍率, 1.0 V以上容量最高可达222.6 mAh&#8226;g－1, 并表现出良好的放电平台特性.     

Irreducible Bases in Icosahedral Group Space

The irreducible bases in the icosahedral groupspace are calculated explicitly by reducing the regularrepresentation. The symmetry-adapted bases of the systemwith I or I _h symmetry can becalculated easily and generally by applying those irreduciblebases to wavefunctions of the system, if they are notvanishing. As examples, the submatrices of the HuckelHamiltonians for carbon-60 and carbon-240 arerecalculated by the irreducible bases.     

General Theory of Decoy-State Quantum Cryptography with Dark Count Rate Fluctuation

The existing theory of decoy-state quantum cryptography assumes that the dark count rate is a constant, but in practice there exists fluctuation. We develop a new scheme of the decoy state, achieve a more practical key generation rate in the presence of fluctuation of the dark count rate, and compare the result with the result of the decoy-state without fluctuation. It is found that the key generation rate and maximal secure distance will be decreased under the influence of the fluctuation of the dark count rate.     

Decoy state quantum key distribution with finite resources

We apply the finite key analysis to the decoy state quantum key distribution scheme and obtain a practical key rate. By simulating an practical experiment setups and the Vacuum + Weak decoy state method, we show that both the key rate and maximal secure distance are reduced when the finite key analysis is considered.