Equivariant cohomology distinguishes the geometric structures of toric hyperkähler manifolds

Toric hyperkähler manifolds are the hyperkähler analogue of symplectic toric manifolds. The theory of Bielawski and Dancer tells us that, while a symplectic toric manifold is determined by a Delzant polytope, a toric hyperkähler manifold is determined by a smooth hyperplane arrangement. The purpose of this paper is to show that a toric hyperkähler manifold up to weak hyperhamiltonian T -isometry is determined not only by a smooth hyperplane arrangement up to weak linear equivalence but also by its equivariant cohomology H* _T (M; ?) with a point â in H ²(M;?) \ {0} up to weak H*(BT; ?)-algebra isomorphism preserving â.     

Trigonometric Widths and Best N-Term Approximations of the Generalized Periodic Besov Classes BΩp,θ

In this paper,we determine the estimates exact in order for the trigonometric widths and the best n-term trigonometric approximations of the generalized classes of periodic functions BΩp,θ in the space Lq for some values of parameters p,q.     

A transformation of certain infinite series based on the non-local derangement identity

The aim of the paper is a new transformation of certain infinite series based on an identity from Sylvester also known as the non-local derangement identity. Surprisingly, the result found can be applied to evaluate certain types of the generalized hypergeometric function _p F _q (z) or infinite series involving the combination of hyperbolic functions, irrational functions and polynomials like

Special functions associated with a certain fourth-order differential equation

We develop a theory of “special functions” associated with a certain fourth-order differential operator D_m,n\mathcal{D}_{\mu,\nu} on ℝ depending on two parameters μ,ν. For integers μ,ν≥−1 with μ+ν∈2ℕ₀, this operator extends to a self-adjoint operator on L ²(ℝ₊,x ^μ+ν+1 dx) with discrete spectrum. We find a closed formula for the generating functions of the eigenfunctions, from which we derive basic properties of the eigenfunctions such as orthogonality, completeness, L ²-norms, integral representations, and various recurrence relations.     

Synthesis and NHE1 inhibitory activity of ligustrazine derivatives

A series of novel derivatives of ligustrazine linked with substituted benzoyl guanidine were synthesized. These compounds have not been reported in literature, and their chemical structures were confirmed by IR, 1H NMR and MS. The results of NHE1 inhibitory activity test showed that compounds I2, I3, I4, I6, and I7 possess more potent NHE1 inhibitory activity than cariporide.     

Mechanism of crystallization of enzyme protein thermolysin

The mechanism of crystallization of enzyme protein thermolysin was investigated. The size distribution of thermolysin precipitates was measured by dynamic light scattering during precipitation, and the surface and cross section of the finally obtained precipitate were observed by scanning electron microscopy. The thermolysin precipitates obtained at the initial supersaturation ratio of 8.9 to 164 and pH 7.0 were hexagonal rods having an average size of 9.2×1.5 μm, and were composed of a number of small particles of 15 to 200 nm in diameter. The average size of the small particles was 60 nm in diameter, and the formation of the particles was found to be completed in the early stage of precipitation. Observation of the finally recovered thermolysin precipitate by polarizing microscopy revealed that the precipitate is a crystalline solid. From these data, a possible mechanism of thermolysin crystallization was proposed. The crystallization proceeds through two steps: the first step is the formation of primary particles, and the second step is crystal growth by highly ordered aggregation of the primary particles.     

22Na(p,γ)23Mg反应的实验研究

讨论了目前有关²²Na(p,γ)²³Mg反应的实验研究工作,结合兰州放射性束流线上的放射性束流²³Al的β⁺延发质子衰变实验的测量结果,给出了²³Al延发衰变的质子能谱,并比较了近期实验给出的相关能级的自旋、宇称值,正是由于这种自旋、宇称和能级部分宽度的不确定性,导致了反应率计算的不确定性.计算了同位旋相似态的共振强度.对于测量到的新的延发衰变能级E_d=8.916MeV,由于没有相应的能级宽度值,实验仅给出其相对共振强度值.     

The limiting absorption principle for the two-dimensional inhomogeneous anisotropic elasticity system

In this work we establish the limiting absorption principle for the two-dimensional steady-state elasticity system in an inhomogeneous aniso- tropic medium. We then use the limiting absorption principle to prove the existence of a radiation solution to the exterior Dirichlet or Neumann boundary value problems for such a system. In order to define the radiation solution, we need to impose certain appropriate radiation conditions at infinity. It should be remarked that even though in this paper we assume that the medium is homogeneous outside of a large domain, it still preserves anisotropy. Thus the classical Kupradze's radiation conditions for the isotropic system are not suitable in our problem and new radiation conditions are required. The uniqueness of the radiation solution plays a key role in establishing the limiting absorption principle. To prove the uniqueness of the radiation solution, we make use of the unique continuation property, which was recently obtained by the authors. The study of this work is motivated by related inverse problems in the anisotropic elasticity system. The existence and uniqueness of the radiation solution are fundamental questions in the investigation of inverse problems.

     

A light scattering and fluorescence emission coupled ratiometry using the interaction of functional CdS quantum dots with aminoglycoside antibiotics as a model system

Any signals, if their intensities have simple functional relationship with analyte concentration, can be applied to analytical purposes. Rayleigh light scattering signals and fluorescence signals are twins in flurospectroscopy, so the light scattering signals are the major interference when the Stokes shift is small. Herein, we propose a light scattering and fluorescence emission (LS-FL) coupled ratiometry using CdS quantum dots (QDs) as a fluorescence probe to detect aminoglycoside antibiotics (AGs). As model analytes, AGs, when attached to the surface of CdS-QDs via electrostatic interaction in aqueous medium, result in strong enhanced light scattering (LS) emission characterized at 376 nm and fluorescence quenching of CdS-QDs at 500 nm. Thus, a ratiometry using the coexistent light scattering and fluorescent emission signals has been proposed. Based on the linear relationship between logarithm of light scattering and fluorescence emission ratio (R) and logarithm of AGs concentration, a novel assay of AGs is established with the limits of detection (3σ) being 58-190 nmol l⁻¹, and applied successfully to detect AGs injection and serum samples.