Moment integrals of 1/sint and related zeta-values

In this paper we shall discuss the moment integrals of 1/sint as a generalization of one of the integral representations of the Catalan constant. As an application of our formulas, we shall derive several relations among the Riemann zeta-, the Dirichlet L-, and multiple L-values mod 4.     

Underwater acoustics and cavitating flow of water entry

The fluid mechanics of water entry is studied through investigating the underwater acoustics and the supercavitation. Underwater acoustic signals in water entry are extensively measured at about 30 different positions by using a PVDF needle hydrophone. From the measurements we obtain (1) the primary shock wave caused by the impact of the blunt body on free surface; (2) the vapor pressure inside the cavity; (3) the secondary shock wave caused by pulling away of the cavity from free surface; and so on. The supercavitation induced by the blunt body is observed by using a digital high-speed video camera as well as the single shot photography. The periodic and 3 dimensional motion of the supercavitation is revealed. The experiment is carried out at room temperature. The project supported by the “BaiRen Plan” of Chinese Academy of Sciences     

Flow of a viscous fluid past a flexible membrane at low Reynolds numbers

The numerical calculation of a steady two-dimensional viscous flow past a flexible membrane is treated. Both edges of the membrane are fixed in the flow and its chord is set normal to the flow. The Navier-Stokes equation in terms of the stream function and the vorticity is transformed to the body fitted coordinate system. The numerical calculations, based on a finite difference method and relaxation method, are carried out for several values of the membranes tension for cases when the Reynolds numbers are 5, 10 and 20. It is found that two different shapes of the membranes are possible at a given value of tension and Reynolds number: one with a small deformation, and the other with a large deformation. Two vortices appear in the concave region of the membrane if its deformation increases beyond a certain extent.     

CCAP for Universal Discrete Quantum Groups

We show that the discrete duals of the free orthogonal quantum groups have the Haagerup property and the completely contractive approximation property. Analogous results hold for the free unitary quantum groups and the quantum automorphism groups of finite-dimensional C^*-algebras. The proof relies on the monoidal equivalence between free orthogonal quantum groups and SU _q (2) quantum groups, on the construction of a sufficient supply of bounded central functionals for SU _q (2) quantum groups, and on the free product techniques of Ricard and Xu. Our results generalize previous work in the Kac setting due to Brannan on the Haagerup property, and due to the second author on the CCAP.     

Radiative X(3872) Decays in Charmonium-Molecule Hybrid Model

We study the radiative decays of the X(3872) in the charmonium-molecule model combined with the quark potential model. We obtain \({\Gamma(X(3872) \to J/\psi \, \gamma) = 29.2\,{\rm keV}}\) and \({\Gamma(X(3872) \to \psi' \, \gamma) = 6.3\,{\rm keV}}\) . The ratio of these two is 0.22, which is much smaller than the BABAR observation. We find that the result is very sensitive to the amount of the \({\chi_{c1}(1P)}\) component in the X(3872).     

Possible Existence of {(c\bar{c})} –Nucleus Bound States

Charmonium ( \({c \bar{c}}\) ) bound states in few-nucleon systems, ²H, ⁴He and ⁸Be, are studied via Gaussian Expansion Method (GEM). We adopt a Gaussian potential as an effective \({(c \bar{c})}\) –nucleon (N) interaction. The relation between two-body \({(c \bar{c})}\) –N scattering length \({a_{c\bar{c}-N}}\) and the binding energies B of \({(c \bar{c})}\) –nucleus bound states are given. Recent lattice QCD data of \({a_{c\bar{c}-N}}\) corresponds to \({B \simeq 0.5}\) MeV for \({(c \bar{c})-^{4}}\) He and 2 MeV for \({(c \bar{c})-^{8}}\) Be in our results.     

Four Classes of Surfaces with Constant Mean Curvature in S 3 × R and H 3 × R

Deforming rotation surfaces with constant mean curvature in S ³ and H ³ to S ³ × R and H ³ × R respectvely, we give four classes of surfaces with mean curvature vector of constant length in S ³ × R and H ³ × R. We have complete minimal surfaces in S ³ × R and H ³ × R. Also we obtain minimal 2-tori in S ³ × S ¹, some of which are embedded.     

Homotopically equivalent simple loops on 2-bridge spheres in 2-bridge link complements (III)

This is the last of a series of papers which give a necessary and sufficient condition for two essential simple loops on a 2-bridge sphere in a 2-bridge link complement to be homotopic in the link complement. The first paper of the series treated the case of the 2-bridge torus links, and the second paper treated the case of 2-bridge links of slope \(n/(2n+1)\) and \((n+1)/(3n+2)\) , where \(n \ge 2\) is an arbitrary integer. In this paper, we first treat the case of 2-bridge links of slope \(n/(mn+1)\) and \((n+1)/((m+1)n+m)\) , where \(m \ge 3\) is an arbitrary integer, and then treat the remaining cases by induction.