Abstract:
A unified framework of FETI-DP algorithms is proposed for solving the system of linear equations arising from the mixed finite element approximation of incompressible Stokes equations. A distinctive feature of this framework is that it allows using both continuous and discontinuous pressures in the algorithm, while previous FETI-DP methods only apply to discontinuous pressures. A preconditioned conjugate gradient method is used in the algorithm with either a lumped or a Dirichlet preconditioner, and scalable convergence rates are proved. This framework is also used to describe several previously developed FETI-DP algorithms and greatly simplifies their analysis. Numerical experiments of solving a two-dimensional incompressible Stokes problem demonstrate the performances of the discussed FETI-DP algorithms represented under the same framework.

Abstract:
The FETI-DP algorithms, proposed by the authors in [SIAM J. Numer. Anal., 51 (2013), pp.~1235--1253] and [Internat. J. Numer. Methods Engrg., 94 (2013), pp.~128--149] for solving incompressible Stokes equations, are extended to three-dimensional problems. A new analysis of the condition number bound for using the Dirichlet preconditioner is given. An advantage of this new analysis is that the numerous coarse level velocity components, required in the previous analysis to enforce the divergence free subdomain boundary velocity conditions, are no longer needed. This greatly reduces the size of the coarse level problem in the algorithm, especially for three-dimensional problems. The coarse level velocity space can be chosen as simple as for solving scalar elliptic problems corresponding to each velocity component. Both Dirichlet and lumped preconditioners are analyzed using a same framework in this new analysis. Their condition number bounds are proved to be independent of the number of subdomains for fixed subdomain problem size. Numerical experiments in both two and three dimensions demonstrate the convergence rate of the algorithms.

Abstract:
A non-overlapping domain decomposition algorithm is proposed to solve the linear system arising from mixed finite element approximation of incompressible Stokes equations. A continuous finite element space for the pressure is used. In the proposed algorithm, Lagrange multipliers are used to enforce continuity of the velocity component across the subdomain domain boundary. The continuity of the pressure component is enforced in the primal form, i.e., neighboring subdomains share the same pressure degrees of freedom on the subdomain interface and no Lagrange multipliers are needed. After eliminating all velocity variables and the independent subdomain interior parts of the pressures, a symmetric positive semi-definite linear system for the subdomain boundary pressures and the Lagrange multipliers is formed and solved by a preconditioned conjugate gradient method. A lumped preconditioner is studied and the condition number bound of the preconditioned operator is proved to be independent of the number of subdomains for fixed subdomain problem size. Numerical experiments demonstrate the convergence rate of the proposed algorithm.

Abstract:
In order to deal with the problems in P2P systems such as unreliability of the Service, security risk and attacks caused by malicious peers, a novel trust model MSL-TM based on the Multinomial Subjective Logic is proposed. The model uses multinomial ratings and Dirichlet distribution to compute the expectation of the subjective opinion and accordingly draws the peer’s reputation value and risk value, and finally gets the trust value. The decay of time, rating credibility and the risk value are introduced to reflect the recent behaviors of the peers and make the system more sensitive to malicious acts. Finally, the effectiveness and feasibility of the model is illustrated by the simulation experiment designed with peersim.

This
study was conducted to investigate the feasibility of vermicomposting by
using vermicast as the substrate for the stabilization of municipal activated sludge,
called hereafter as direct vermistabilization, in which the
pre-treatment and bulking materials required in previous practices were all
omitted. For this purpose, two epigeic earthworm species, namely Eisenia foetida and Bimastus parvus, were inoculated into substrate for
composting fresh dewatered activated sludge. Direct vermistabilization resulted in significant reductions
in pH, TOC, C/N ratio and the content of heavy metals, as well as increases in
EC, total N, total P and total K in the final vermicast. Moreover, both Eisenia foetida and Bimastus parvus showed
faster growth rate and higher cocoon production. The results of
this study suggest that the direct vermistabilization has the advantages of
being simple, cost-effective and efficient, and can thus be used as a
feasible vermicomposting approach to
convert fresh dewatered activated sludge into a valuable product for agricultural use. The results also suggest
that Bimastus parvus can be used as a new potential candidate
for vermicomposting of municipal activated sludge.

Abstract:
In this paper, we discuss the topological classification of higher order singular point of plane n-degree differential system, and give a criterion according to the right-hand polynomial coefficients.

Abstract:
To elucidate the effects of the hydrogenation and oxygenation of the boron-doped diamond (BDD) electrode on its electrochemical behaviors, the surface morphologies and phases of the two surface-adsorption BDD films have been investigated and the cyclic voltammograms and AC impedance spectra have been measured at these two BDD electrodes. The results indicate that compared with the hydrogen-adsorption BDD film, oxygen-adsorption BDD film is less conductive, and has a larger surface roughness and a lower sp3/sp2 ratio. The oxygenated BDD film electrode possesses a wider electrochemical window, larger diamond film resistance and capacitance and a larger polarization resistance than hydrogenated BDD electrode. In addition, the effect mechanism of the surface-adsorption of BDD electrode on its electrochemical behaviors has been discussed.

Abstract:
By means of first principles method on the basis of density functional theory (DFT), the equilibrium geometries and density of states (DOS) of the two oxygenated diamond (100) surfaces, bridging model and on-top model are calculated. The results indicate that there are no surface states located in the band gap of the bridging model of oxygenated diamond (100) surface, and the occupied surface states in the valence band are attributed to the non-bonded O 2p orbital, O 2p and C 2p bonding orbitals, and C 2p and H 1s bonding orbitals. By contrast, for the on-top model of oxygenated diamond (100) surface, the unoccupied surface states exist in the band gap, which originate from non-bonded C 2p and O 2p orbitals. In addition, the occupied surface states in the valence band are induced by non-bonded O 2p orbital and the C=O π bond.