无限秩仿射李代数的紧致实形

给出了无限秩仿射李代数的实形和某种类型的紧效实形的定义，并证明了这种紧致实形在自同构下的唯一性.     

Single machine unbounded parallel-batch scheduling with forbidden intervals

In this paper we consider the single machine parallel-batch scheduling with forbidden intervals. There are some forbidden intervals in which the machine cannot be available. The jobs are processed in batches form in the remaining free time-slots without preemption, where the processing time of a batch is defined to be the maximum processing time of the jobs in this batch. We show that, when the objective is bottleneck form, maximum lateness, or makespan with release dates of jobs, the considered problem can be solved in polynomial time.     

Determination of Hg and Pb in compact fluorescent lamp by slurry sampling inductively coupled plasma optical emission spectrometry

Mercury and lead were determined in an extraction solution applied to compact fluorescent lamps by axial view inductively coupled plasma optical emission spectrometry (ICP OES). The solution contained 50% v/v HNO₃ and 10% v/v H₂O₂. The compact fluorescent lamps were treated by removing the socket and breaking the rest of the lamp inside the solution, followed by placing the mixture in an ultrasonic bath for 1 h. The mixture was filtrated in a coarse paper filter and the resulting extraction slurry was analyzed. The determination of Pb in the slurry required calibration by the analyte addition technique, while for Hg, external calibration was adequate. The quantification limits (10 s, n = 7), for Hg (194.164 nm) and Pb (220.353 nm) were, respectively, 10 and 30 µg per lamp. Analysis of spiked samples demonstrated reasonable accuracy of the method, with recoveries in the range from 99 to 120% for Hg and from 91 to 107% for Pb. Fifteen analyzed samples showed Hg masses per lamp in the range from 1.6 to 27 mg, and six samples were above the limit allowed by the European Community that is 5 mg per compact lamp. The values for Pb were between 0.07 and 0.75 mg per lamp. By filtrating the slurry in a membrane filter, and analyzing the resulting solution, it was found that all Hg was extracted to the liquid phase of the slurry, while a fraction of about 40% m/v of Pb is retained in the solid particles. The lamp cover glass, after extraction of the phosphor layer, was also analyzed for Hg and Pb. The concentration of Hg in the glass is quite low; however, the Pb content is high.     

Gain evaluation of compact designing on Er/Yb codoped germanate glass channel waveguide

Bent waveguide structures (U- and F-bend) based on UV-sensitive Er³⁺/Yb³⁺ codoped germanate glass substrates have been designed to achieve high-gain C-band amplification. Using simulated-bend method, the optimal radius for curved structure is offered to be 1.90 cm with loss coefficient of 0.0015 dB/cm, as the substrate size is minimally schemed. In the wavelength range of 1528–1559 nm, obvious gain enhancement for the bent structure waveguides is anticipated, while, for the F-bend waveguide, the internal gain at 1533.8 nm wavelength is derived to be 22.55 dB, which is much higher than the value of 14.06 dB in the U-bend waveguide, and over three times higher than that of the straight one, after compensating both the bend loss and the transition loss. The simulation results indicate that the bent structure designing is beneficial in attaining high optical gain in Er³⁺/Yb³⁺ codoped germanate glass substrates, which assures that long-period grating can be applied to implement practical C-band gain-flattened amplification.     

OPTIMAL POINT-WISE ERROR ESTIMATE OF A COMPACT FINITE DIFFERENCE SCHEME FOR THE COUPLED NONLINEAR SCHRODINGER EQUATIONS

In this paper, we analyze a compact finite difference scheme for computing a coupled nonlinear SchrSdinger equation. The proposed scheme not only conserves the totM mass and energy in the discrete level but also is decoupled and linearized in practical computa- tion. Due to the difficulty caused by compact difference on the nonlinear term, it is very hard to obtain the optimal error estimate without any restriction on the grid ratio. In order to overcome the difficulty, we transform the compact difference scheme into a special and equivalent vector form, then use the energy method and some important lemmas to obtain the optimal convergent rate, without any restriction on the grid ratio, at the order of O（h4 ＋r2） in the discrete L∞ -norm with time step - and mesh size h. Finally, numerical results are reported to test our theoretical results of the proposed scheme.     

COMPACT DIFFERENCE SCHEMES FOR THE DIFFUSION AND SCHRODINGER EQUATIONS. APPROXIMATION,STABILITY, CONVERGENCE,EFFECTIVENESS, MONOTONY

Various compact difference schemes （both old and new, explicit and implicit, one-level and two-level）, which approximate the diffusion equation and SchrSdinger equation with periodical boundary conditions are constructed by means of the general approach. The results of numerical experiments for various initial data and right hand side are presented. We evaluate the real order of their convergence, as well as their stability, effectiveness, and various kinds of monotony. The optimal Courant number depends on the number of grid knots and on the smoothness of solutions. The competition of various schemes should be organized for the fixed number of arithmetic operations, which are necessary for numerical integration of a given Cauchy problem. This approach to the construction of compact schemes can be developed for numerical solution of various problems of mathematical physics.     

A compact 9 point stencil based on integrated RBFs for the convection–diffusion equation

In this paper, a high-order compact stencil for solving the convection–diffusion equation in two dimensions is proposed. The convection and diffusion terms are both approximated by means of radial basis functions (RBFs) that are constructed over 3×3$3\times 3$ rectangular stencils. Salient features here are that (i) integration is employed to construct local RBF approximations; and (ii) through the constants of integration, values of the convection–diffusion equation at several selected nodes on the stencil are also enforced. Numerical results indicate that (i) the inclusion of the governing equation into the stencil leads to a significant improvement in accuracy; (ii) when the convection dominates, accurate solutions are obtained at a regime of the RBF width which makes the RBFs peaked; and (iii) high levels of accuracy are achieved using relatively coarse grids.     

Compact groups of positive operators on Banach lattices

In this paper, we study groups of positive operators on Banach lattices. If a certain factorization property holds for the elements of such a group, the group has a homomorphic image in the isometric positive operators which has the same invariant ideals as the original group. If the group is compact in the strong operator topology, it equals a group of isometric positive operators conjugated by a single central lattice automorphism, provided an additional technical assumption is satisfied, for which we have only examples. We obtain a characterization of positive representations of a group with compact image in the strong operator topology, and use this for normalized symmetric Banach sequence spaces to prove an ordered version of the decomposition theorem for unitary representations of compact groups. Applications concerning spaces of continuous functions are also considered.