We study the one-dimensional solution of the shape equation of bilayer membranes within the Helfrich spontaneous curvature model.The general integral of the cylindrical shape equation is obtained which gives a complete classification of the cylindrical surfaces corresponding to the shape equation.For closed vesicles,they are inward noduloids,outward noduloids,alternatively inward and outward noduloids and polygonal shapes.The curvature of the contours of the cross sections of these surfaces can be expressed in terms of elliptic functions of their arc lengths.

General solutions are obtained for a class of quantum dissipative systems. This is achieved by calculating the characteristic function in the Heisenberg picture. The irreversible behavior of these systems is nalyzed. The general formalism is applied to some typical examples and the influence of noise on these systems is gained.

In this paper,vacuum C-metric when m=0 is derived from the metric of a Schwarzschild black hole if its mass and location approach to infinity in an appropriate way.Furthermore,by using coordinate transformation in which there is no acceleration,vacuum C-metric when m=0 is transformed to Rindler metric.The result shows that an infinitesimal neighborhood of the horizon of an infinite Schwarzschild black hole is a Rindler space-time,and the acceleration in the Rindler space-time can arise from the in finite Schwarzschild black hole.

A two-particle cluster theory is presented to study uniaxial nematic liquid crystals formed by biaxial molecules, which interact with each other via dispersion forces. The equation for the molecular orientational distribution functions in two-particle cluster approximation is obtained and is solved by an terativemethod. The temperature dependences of the order parameter and of the internal energy per particle are calculated, and the values of the relevant quantities at the nematic isotropic phase transition are given. The present theory, by taking into account the short range correlations between molecules , yields improved results compared with the mean field theory.

Fast-ion-beam laser spectroscopy which has the characteristics of selective excitation and high accurate measurement was widely used to study isotope shifts, radioactive lifetimes, and hyperfine structures of atoms and ions. In this work, the optical isotope shifts for the transition 4f^{4}5d^{6}K_{13/2}-(25524)^{0}_{13/2} in Nd II were measured by using collinear fast-ion-beam lase r spectroscopy.

The squeezed coherent thermal state is considered. Its various coherent representations, including Q-,P-and Bargmann representations are introduced. The analytic formula for the photon number distribution of such a quantum state is obtained directly from the Bargmann representation. The effects of the squeezing and the thermal noise on the photon distribution are discussed.

PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES

The time-averaged spontaneous radiation power and its spectrum are derived analytically. The collective mode is taken to be electron-cyclotron mode driven by the relativistic electron beam existing in the unstable and late phases of plasma focus. The infrared range radiation calculated is in agreement with experimental observation.

CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES

Self consistent charge and spin polarized local spin-density approximation functional theory calculations based on the discrete variational method have been performed for RCo_{5}(R=Y, La, Ce, Pr, Nd, Sm, Gd, and Tb) compounds. The partial density of states of the Pr atom in the PrCo_{6}Co_{12} cluster is established to be strikingly similar to that of the Ce atom in the CeCo_{6}Co_{12} cluster, supporting the suggestion that the Pr atom is valence fluctuating. The radii ＜r_{4f}＞ and ＜r_{4}f^{2}＞ of the 4f electrons of the R atom from La to Tb, except Ce, show the lanthanide contraction. The crystalline electric field (CEF) parameter A^{0}_{2} at the R site is calculated using a real charge distribution ρ(R) in the cluster, except for Pr and Nd, and is in agreement with that evalu ated based on the single-ion model. This result shows that the CEF parameter A^{0}_{2} is mainly determined by the near electronic structure. There exists a hybridization in a certain degree between the light rare-earth R-4f and Co-3d orbitals in some single-electron-molecular-orbitals, which are n ear the Fermi energy level and occupied by electrons. For light rare-earths the R-4f electrons in R Co_{6}Co_{12}(R=Y, La, Ce, Pr, Nd, and Sm) clu sters are not localized entirely and a small amount of the R-4f electrons have itinerant properties.

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