Exact solutions of an asymmetric double well potential

Journal of Mathematical Chemistry - The analytical solutions of an asymmetric double well potential $$V(x)=a\, x^2-b\, x^3+c\, x^4$$ are found to be a triconfluent Heun function $$H_{T}(\alpha ,...     

单斜层状LiMnO2的球磨-离子交换法合成及其电化学性能研究

通过球磨促进固相反应法合成出了具有单斜层状结构的前驱物NaMnO₂，随后通过离子交换得到了单斜层状LiMnO₂。XRD测试结果显示产物为单相。扫描电镜(SEM)和透射电镜(TEM)观测结果显示LiMnO₂的粒子尺寸为300～500 nm，HRTEM分析显示干扰条纹的间距为0.485 nm，基本对应于m-LiMnO₂的(001)晶面间距。红外吸收光谱(IR)和X射线光电子能谱(XPS)被用来测量m-LiMnO₂中Mn-O键的伸缩和弯曲振动吸收和Mn元素的价态。合成的m-LiMnO₂在电化学充放电循环初期表现了较好的电化学性能，但其循环寿命仍需要进一步改善。     

Complex dynamics in a periodically perturbed electro-chemical system

Dynamical response of a passivation model subjected to parametric periodic and stochastic perturbations is studied numerically. In response to weak periodic modulation, the system exhibits a rich variety of resonance behavior and induced dynamics, including periodically induced oscillation, birhythmicity, switching between two bistable states, selection of one of the bistable states, mixed-mode and chaotic oscillations. These phenomena are discussed in terms of the stability of saddle focus and an incomplete homoclinic connection. Our numerical results are relevant for a wide class of electro-chemical oscillatory systems, where the re-injection of unstable trajectory on the neighborhood of a saddle focus is a typical feature in the phase space.     

Synthesis and Crystal Structure of 3-（Trichloroacetyl） Indole

1 INTRODUCTION Indole and its derivatives have attracted much at-tention due to their chemical properties as well asbiological activities[1, . They have been widely used 2]as the materials for producing pigment, perfume,plant growth regulators, etc. Recently, it has alsobeen found that some indole derivatives present anti-tumor and antiviral activities[3～5]. During our sear-ches for bioactive compounds, a series of indole deri-vatives were synthesized, among …     

网胰藻Hydroclathrus clathratus的化学成分研究

报道从中国南海网胰藻Hydroclathrus clathratus中分离得到3个单体化合物,经过MS,IR,1HNMR,13CNMR(DEPT),HMQC和HMBC等波谱技术鉴定为:(6R,7aS)-6-羟基-4,4,7a-三甲基-2,4,5,6,7,7a-六氢苯并呋喃-2-酮(1),1-(2-脱氧-β-D-呋喃核糖)-5-甲基-1,2,3,4-四氢嘧啶-2,4-二酮(2),尿嘧啶(3),并通过X射线单晶衍射实验确定化合物1的立体结构,其中化合物1是首次从自然界中分离得到.     

QSAR Studies on the COX-2 Inhibition by 3,4-Diarylcycloxazolones Based on MEDV Descriptor

Selective inhibition of cyclooxygenase-2 (COX-2) might avoid the side effects of current available nonsteroidal antiinflammatory drugs while retaining their therapeutic efficacy. A novel variable selection and modeling method based on prediction is developed to construct the quantitative structure-activity relationships (QSAR) between the molecular electronegativity distance vector (MEDV) based on 13 atomic types and the biological activities of a set of selective cyclooxygenase-2 inhibitory molecules, 3,4-diarylcycloxazolones (DAA) plus indomethacin,naproxen, and celecoxib. Using multiple linear regression, a 5-variable linear model is developed with the calibrated correlation coefficient of 0.9271 and root mean square error of 0.17 in modeling stage and the validated correlation coefficient of 0.9030 and root mean square error of 0.20 in leave-one-out validation step, respectively. To further test the predictive ability of the model, 20 DAA compounds are picked up to construct a training set which is used to build a QSAR model and then the model is employed to predict the biological activities of the balance compounds. The predicted correlation coefficient and root mean square error are 0.9332 and 0.19, respectively.     

Interbasis expansions for isotropic harmonic oscillator

The exact solutions of the isotropic harmonic oscillator are reviewed in Cartesian, cylindrical polar and spherical coordinates. The problem of interbasis expansions of the eigenfunctions is solved completely. The explicit expansion coefficients of the basis for given coordinates in terms of other two coordinates are presented for lower excited states. Such a property is occurred only for those degenerated states for given principal quantum number n.     

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 of the Schrödinger Equation with Inverse-Power Potential

The Schrödinger equation for stationary states is studied in a central potential V(r) proportional to r ^– in an arbitrary number of spatial dimensions. The presence of a single term in the potential makes it impossible to use previous algorithms, which only work for quasi-exactly-solvable problems. Nevertheless, the analysis of the stationary Schrödinger equation in the neighbourhood of the origin and of the point at infinity is found to provide relevant information about the desired solutions for all values of the radial coordinate. The original eigenvalue equation is mapped into a differential equation with milder singularities, and the role played by the particular case = 4 is elucidated. In general, whenever the parameter is even and larger than 4, a recursive algorithm for the evaluation of eigenfunctions is obtained. Eventually, in the particular case of two spatial dimensions, the exact form of the ground-state wave function is obtained for a potential containing a finite number of inverse powers of r, with the associated energy eigenvalue.     

Quantum Spectrum of Some Anharmonic Central Potentials: Wave Functions Ansatz

Based on the ansatz to the wave functions, the quasi-exact solutions of the 2D Schrödinger equation with some anharmonic potentials are reviewed and analyzed if admitting restrictions on the parameters of the potential and the angular momentum m. These potentials are taken as the screened Coulomb potential V(r)=a/r+b/(r+), the singular one-fraction power one V(r)=ar ^–1/2+br ^–3/2 and the singular two-fraction one V(r)=ar ^2/3+br ^–2/3+cr ^–4/3. The latter one is found that the hidden symmetry exists if substituting r–ir. It will reverse the signs of E and c of quantum system, leaving the remaining parameters invariant.