混合单调算子的两点拉伸型不动点定理

本文首次提出了混合单调算子不动点的两点拉伸型条件.同时,利用锥映象的不动点指数理论建立了一类特殊的两点拉伸型混合单调算子的不动点存在性定理,并将所得结论应用于带有超线性项的积分方程与微分方程上,得到了新的结论.因而在本质上推进了混合单调算子不动点问题的研究.     

A TWO-LEVEL FINITE ELEMENT GALERKIN METHOD FOR THE NONSTATIONARY NAVIER-STOKES EQUATIONS I： SPATIAL DISCRETIZATION

In this article we consider a two-level finite element Galerkin method using mixed finite elements for the two-dimensional nonstationary incompressible Navier-Stokes equations. The method yields a $H^1$-optimal velocity approximation and a $L_2$-optimal pressure approximation. The two-level finite element Galerkin method involves solving one small, nonlinear Navier-Stokes problem on the coarse mesh with mesh size $H$, one linear Stokes problem on the fine mesh with mesh size $h << H$. The algorithm we study produces an approximate solution with the optimal, asymptotic in $h$, accuracy.     

Proton–neutron structure of the N=52 nucleus Zr

Following the successful identification of mixed-symmetric one- and two-phonon states in the N=52 nuclei ⁹⁴Mo and ⁹⁶Ru, we have performed a photon scattering experiment on the N=52 isotone ⁹²Zr. Experimental data and shell model calculations show that both, single particle and collective degrees of freedom are present in the low-lying levels of ⁹²Zr. The second excited quadrupole state shows the signatures of the one-phonon mixed-symmetric 2⁺ state, while calculations and data indicate an almost pure neutron configuration for the 2⁺₁ state, in contradiction with the F-spin symmetric limit. Furthermore, two strong dipole excitations, which are candidates for the two-phonon quadrupole–octupole coupled E1 excitation and for the mixed-symmetric 1⁺ two-phonon state, were observed.     

On General Mixed Quasivariational Inequalities

In this paper, we suggest and analyze several iterative methods for solving general mixed quasivariational inequalities by using the technique of updating the solution and the auxiliary principle. It is shown that the convergence of these methods requires either the pseudomonotonicity or the partially relaxed strong monotonicity of the operator. Proofs of convergence is very simple. Our new methods differ from the existing methods for solving various classes of variational inequalities and related optimization problems. Various special cases are also discussed.     

Mixed integer programming for a special logic constrained optimal control problem

Integrating logical constraints into optimal control problems is not an easy task. In fact, optimal control problems are usually continuous while logical constraints are naturally expressed by integer (binary) variables. In this article we are interested is a particular form of an LQR optimal control problem: the energy (control L² norm) is to be minimized, system dynamic is linear and logical constraints on the control use are to be fulfilled. Even if the starting continuous problem is not a complicated one, difficulties arise when integrating the additional logical constraints. First, we will present two different ways of modeling the problem, both of them leading us to Mixed Integer Problems. Furthermore, algorithms (Generalized Outer Approximation, Benders Decomposition and Branch and Cut) are applied on each model and results analyzed. We also present a Benders Decomposition algorithm variant that is adapted to our problem (taking into account its particular form) and we will conclude by looking at the optimal solutions obtained in an interesting physical example: the harmonic spring.     

A Posteriori Error Estimates of Mixed Methods for Parabolic Optimal Control Problems

In this article, we shall give a brief review on the fully discrete mixed finite element method for general optimal control problems governed by parabolic equations. The state and the co-state are approximated by the lowest order Raviart–Thomas mixed finite element spaces and the control is approximated by piecewise constant elements. Furthermore, we derive a posteriori error estimates for the finite element approximation solutions of optimal control problems. Some numerical examples are given to demonstrate our theoretical results.     

Convergence theorems for mixed equilibrium problems, variational inequality problem and uniformly quasi-?-asymptotically nonexpansive mappings

We introduce a modified block hybrid projection algorithm for finding a common element of the set of common fixed points of an infinite family of closed and uniformly quasi-?-asymptotically nonexpansive mappings, the set of the variational inequality for an α-inverse-strongly monotone operator, the set of solutions of the mixed equilibrium problems. Then, we obtain strong convergence theorems for the sequences generated by this process in a 2-uniformly convex and uniformly smooth Banach space. Our results extend and improve ones from several earlier works.     

An efficient computational method for a stochastic dynamic lot-sizing problem under service-level constraints

We provide an efficient computational approach to solve the mixed integer programming (MIP) model developed by Tarim and Kingsman [8] for solving a stochastic lot-sizing problem with service level constraints under the static-dynamic uncertainty strategy. The effectiveness of the proposed method hinges on three novelties: (i) the proposed relaxation is computationally efficient and provides an optimal solution most of the time, (ii) if the relaxation produces an infeasible solution, then this solution yields a tight lower bound for the optimal cost, and (iii) it can be modified easily to obtain a feasible solution, which yields an upper bound. In case of infeasibility, the relaxation approach is implemented at each node of the search tree in a branch-and-bound procedure to efficiently search for an optimal solution. Extensive numerical tests show that our method dominates the MIP solution approach and can handle real-life size problems in trivial time.     

Modeling of mixed liquor inorganic suspended solids and membrane flux at different ratio of SRT to HRT in a submerged membrane bioreactor

In order to investigate the influence of mixed liquor inorganic suspended solids (MLISS) on membrane flux at different ratio of sludge retention time (SRT) to hydraulic retention time (HRT) in a submerged membrane bioreactor (SMBR), a pilot scale test was conducted for 452 days using traditional Chinese medicine (TCM) wastewater as influent. SRT/HRT was controlled at 150, 480 and 750, respectively. The experimental results showed that the average values of MLISS were 1271.9, 1664.5 and 6898.8 mg/L at different SRT/HRT, respectively; MLISS were accumulated from 265.5 g/h to 4912.93 g/h, which indicated that SMBR could not steadily operate for a long period without sludge withdrawal. Sludge oxygen utilized rate (SOUR) decreased from 5.115 to 1.292 mgO₂/(gVSS h) and volume oxygen utilized rate (VOUR) increased from 10.84 to 18.13 mgO₂/(L h). Model of membrane flux and MLISS were developed under different temperature and operational pressure by regressions, which were then satisfactorily employed to predict the trend of membrane flux during the experiment.     

Structure, oxygen stoichiometry and electrical conductivity in the system Sr-Ce-Co-O

Mixed oxides in the system S-Ce-Co-O were prepared by solid state reaction and by freeze-drying of precursor compounds followed by thermal treatment. Two types of perovskite oxides exist in the system: Solid solutions of the type Sr_{1 − y}Ce_yCoO_{3 − x} and mixed oxides of the type (1 − y)SrCeO₃ − ySrCoO_{3 − x}. Microstructures and phase compositions were determined by electron microscopy and X-ray diffraction. SrCoO_{3 − x} forms a solid solution of ceria on the A-site in the strontium cobaltite lattice up to 0.15 mol Ce. This solid solution corresponds to the high-temperature structure of pure SrCoO_{3 − x} and is characterized by high oxygen exchange and electrical conductivity. The oxygen deficiency x was measured by solid electrolyte coulometry. The oxygen deficiency of solid solutions Sr_{1 − y}Ce_yCoO_{3 − x} increases with temperature and decreases with pO₂ in the ambient atmosphere and with increasing Ce dopant concentration. The pO₂-T-x diagram of the solid solution was determined. The T, pO₂ and dopant concentration dependencies of electrical conductivity were measured by a four-point d.c. technique. By Ce doping strontium cobaltite becomes a stabilized high-conductive material (maximum conductivity: 500 S cm⁻¹ at 400 °C, E_a = 0.025 eV, p-type). Above this temperature the T-coefficient of the conductivity changes from positive (semiconducting) to negative values.