Embedded Surfaces for Symplectic Circle Actions

The purpose of this article is to characterize symplectic and Hamiltonian circle actions on symplectic manifolds in terms of symplectic embeddings of Riemann surfaces.More precisely, it is shown that(1) if(M, ω) admits a Hamiltonian S~1-action, then there exists a two-sphere S in M with positive symplectic area satisfying c1(M, ω), [S] 0,and(2) if the action is non-Hamiltonian, then there exists an S~1-invariant symplectic2-torus T in(M, ω) such that c1(M, ω), [T] = 0. As applications, the authors give a very simple proof of the following well-known theorem which was proved by Atiyah-Bott,Lupton-Oprea, and Ono: Suppose that(M, ω) is a smooth closed symplectic manifold satisfying c1(M, ω) = λ· [ω] for some λ∈ R and G is a compact connected Lie group acting effectively on M preserving ω. Then(1) if λ 0, then G must be trivial,(2) if λ = 0, then the G-action is non-Hamiltonian, and(3) if λ 0, then the G-action is Hamiltonian.     

A simulation study of the effects of adsorbent energy on the diffusion of molecules in slit pores: 1 commensurate slit widths

Equilibrium molecular dynamics simulation has been used to study the self-diffusion coefficients (from correlation of the molecular velocity) and the collective, or centre of mass diffusion coefficients (from correlation of the streaming velocity) of a Lennard-Jones fluid in model slit pores. The slit widths were chosen to be integer multiples of the Lennard-Jones adsorbate diameter, and therefore are close to being commensurate with layered adsorbate structures. Slits of reduced width H* = 3 and 5 were examined at a reduced temperature of T* = 1.0. The adsorbate densities ranged from 0.3 to 0.9 in reduced units. The adsorbent adsorbate interaction was modelled as a simple potential with inverse 4th power attraction plus hard wall repulsion, and systems with reduced parameter u₀* ranging from ?5 to +5 were studied. Molecule-wall scattering was represented by a diffuse reflection algorithm. The density distributions show strong layering in the attractive system, but this is absent in the most repulsive slits, except at very high densities. Self-diffusion is only weakly dependent on u₀* and slit width at high densities, but a strong dependence on u₀* appears at low densities. The collective diffusion coefficient is less easy to calculate with high accuracy; nevertheless, it is clear that there is a strong dependence of this property on u₀* Trajectory plots show zones in which the particles are more or less strongly localized, but undergo irregular oscillatory motion corresponding to regions of high density in the single-particle distributions.     

Separation and Purification of Sesquiterpene Lactones from a Plant,Carpesium Triste var. Manshuricum KITAMURA

Carpesium triste var. manshuricum K. is a plant which is rarely distributed in Korea, and it has long been used as traditional medicinal herb for its antipyretic, analgesic, vermifugic, insectifuge,pain-relief,and antiinflammatory properties. Several sesquiterpene lactones were isolated from the genus Carpesium.     

A controlled search simulated annealing method for the single machine weighted tardiness problem

In this paper, a new controlled search simulated annealing method is developed for addressing the single machine weighted tardiness problem. The proposed method is experimentally shown to solve optimally 99% of fifteen job problems with less than 0.2 CPU seconds, and to solve one hundred job problems as accurately as any existing methods, but with far less computational effort. This superior performance is achieved by using controlled search strategies that employ a good initial solution, a small neighborhood for local search, and acceptance probabilities of inferior solutions that are independent of the change in the objective function value.