A comparative study of the static third-order polarizabilities of bowl/non-cage to cage structures: a structure-property correlation study

The average static third-order polarizabilities (γ) have been computed for the bowls and cages having the same number of carbon atoms. The bowls have higher (γ) than their corresponding cages. The dependence of (γ) on the average pyrimidalized angle (Θ_p) and maximal length L can be deduced. Near cages, having one open window (C₇₂ isomers), are capped with C₆ to generate five isolated pentagon rule (IPR) isomers of C₇₈ fullerenes following a circumscribing algorithm. The (γ) values for the C₇₈'s and C₇₂′s are correlated with (Θ_p) and L. The change in (γ) from C₇₂′s to C₇₈′s are correlated with a local parameter like the capped angle (α).     

Normally Ordered Operator Realization of U(1/1) Supergroup and Super-Jaynes-Cummings Model

By making use of the technique ofintegration within an ordered product (IWOP) of operators and the bosonic and fermionic coherent states we derive the normally ordered operator realization of U(1/1) supergroup. Its application in calculating the superpartition function of the supersymmetric Jaynes-Cummings model is demonstrated. The antinormally ordered realization of U(1/1) is also obtained.     

THE MICROSCOPIC CALCULATION OF THE STATISTICAL THEORY OF NUCLEAR FISSION

Based on the statistical fission theory, we have calculated the mass and kinetic energy distributions as well as other physical quantities of ²³⁵U fission induced by thermal neutron using microscopical method. That is, the quantum state densities of the fragments at scission point are calculated by means of BCS hamiltonian. The contribution of the collective deformation of fragments to the quantum state density has been taken into consideration. The potential energy of fragment is calculated by means of Strutinski procedure, and the shelling effect, pairing correlation as well as collective deformation have been taken into consideration in calculating the excitation energy at scission point. The scission point distance is treated as an adjustable parameter.Comparing with other statistical fission theories, our results give better agreement with existing experiments.     

常山碱的比色测定法

根据常山碱和异常山碱分子中的喹唑酮能碱水解而形成邻氨基苯甲酸的特点,制订常山植株中碱类含量的比色方法。邻氨基苯甲酸可与经重氮化的N-1-萘基-乙二胺偶合后,于530毫微米处读光密度。此法的灵敏度以光密度值/微克异常山碱/毫升比色液表示为0.111。用此法检查通常用的氯仿萃取法,得知其所回收的常山碱类尚不及实际含量之半。     

PROLONGATION METHOD OF FINDING BACKLUND TRANSFORMATION AND LAX-PAIR OF ERNST EQUATION AND ERNST-MAXWELL EQUATIONS

In this papsr all the known Backlund trans- formations of the Ernst equation are de}tved by ua}ing prolongation: method. As tile nonlinear realizationsp and infinite-dimensional linear realization for the prolongation structure are used, the inverse scattering equation (Lax-pair) is also derived. And the connection between BT and Lax-pair becomes evident. A systematic procedure for deriving the non-Linear realizations of the algebras is sugested based on the prolongation structure. The two knowniBackl and transformations as well as the Lax-pair of the Ernst-Maxwell equations are obtained bu the same method.     

ON THE MAGNETIC MOMENT OF W± BOSONS IN WEINBERG-SALAM MODEL

We discuss the magnetic moment of W^± bosons in W-S model. First we assume that there is no spontaneous symmetry broking. starting from the formalism of path integrals and using the gauge invariance requirement, we obtain the Ward-Takahashi identities for the 3-line VIB proper vertex functions and prove that its tensor structure is the same form as that of bare vertex couplings, which indicated the W^± bosons have neither anomalous magnetic moment nor electric quadrupole moment. For the realistic case of spontaneous symmetry breaking, we introduce in the Lagrangian an explicit symmetry breaking term. After discussing the problem of analytic continuation for mass of W^± bosons, we prove that prove that the above mentioned conclusion is still valid here.     

Analytical Results for the Critical Exponents of Fully Directed Levy Flights

In this paper we generalize the definition of Levy flight (LF). With the help of a useful definition for the critical exponents of LF by introducing the concept of cutoff steplength, we calculate analytically the exponents of FDLFs in arbitrary d dimensions, utilizing the generating function method.     

AN EXTENDED BOUNDARY INTEGRAL EQUATION METHOD FOR THE REMOVAL OF IRREGULAR FREQUENCY EFFECTS

Numerical techniques for the analysis of wave–body interactions are developed by the combined use of two boundary integral equation formulations. The velocity potential, which is expressed in a perturbation expansion, is obtained directly from the application of Green's theorem (the ‘potential formulation’), while the fluid velocity is obtained from the gradient of the alternative form where the potential is represented by a source distribution (the ‘source formulation’). In both formulations, the integral equations are modified to remove the effect of the irregular frequencies. It is well known from earlier works that if the normal velocity is prescribed on the interior free surface, inside the body, an extended boundary integral equation can be derived which is free of the irregular frequency effects. It is shown here that the value of the normal velocity on the interior free surface must be continuous with that outside the body, to avoid a logarithmic singularity in the source strength at the waterline. Thus the analysis must be carried out sequentially in order to evaluate the fluid velocity correctly: first for the velocity potential and then for the source strength. Computations are made to demonstrate the effectiveness of the extended boundary integral euations in the potential and source formulations. Results are shown which include the added-mass and damping coefficients and the first-order wave-exciting forces for simple three-dimensional bodies and the second-order forces on a tension-leg-platform. The latter example illustrates the importance of removing irregular frequency effects in the context of second-order wave loads.     

SEQUENCES OF POWERS OF TOEPLITZ OPERATORS ON THE BERGMAN SPACE

We consider Toeplitz operators Tu with symbol u on the Bergman space of the unit ball,and then study the convergences and summability for the sequences of power...