Near-Optimal Controls of Discrete-Time Dynamic Systems Driven by Singularly-Perturbed Markov Chains

This work is devoted to near-optimal controls of large-scale discrete-time nonlinear dynamic systems driven by Markov chains; the underlying problem is to minimize an expected cost function. Our main goal is to reduce the complexity of the underlying systems. To achieve this goal, discrete-time control models under singularly-perturbed Markov chains are introduced. Using a relaxed control representation, our effort is devoted to finding near-optimal controls. Lumping the states in each irreducible class into a single state gives rise to a limit system. Applying near-optimal controls of the limit system to the original system, near-optimal controls of the original system are derived.     

Comparative investigation of up-conversion luminescence in Tm/Yb-codoped germanate-niobic and germanium-bismuth glasses: effect of phonon density on up-conversion emission

Tm³⁺/Yb³⁺-codoped germanate-niobic (GN) and germanium-bismuth (GB) glasses have been synthesized by conventional melting and quenching method. Intense blue and weak red emissions centered at 477 and 650 nm, corresponding to the transitions ¹G₄→³H₆ and ¹G₄→³H₄, respectively, were observed at room temperature. The possible up-conversion mechanisms are discussed and estimated. GN glass showed a weaker up-conversion emission than GB glass, which is inconsistent with the prediction from the difference of maximum phonon energy between GN and GB glasses. In this paper, Raman spectroscopy was employed to investigate the origin of the difference in up-conversion luminescence in the two glasses. Compared with phonon side-band spectroscopy, Raman spectroscopy extracts more information including both phonon energy and phonon density. For the first time, our results reveal that, besides the maximum phonon energy, the phonon density of host glasses is also an important factor in determining the up-conversion efficiency.     

Electrochemical behavior of Li intercalation processes into a Li[NixLi(1/3−2x/3)Mn(2/3−x/3)]O2 cathode

Li[Ni_xLi_(1/3−2x/3)Mn_(2/3−x/3)]O₂ (X=0.17, 0.25, 0.33, 0.5) compounds are prepared by a simple combustion method. The Rietvelt analysis shows that these compounds could be classified as having the α-NaFeO₂ structure. The initial charge-discharge and irreversible capacity increases with the decrease of x in Li[Ni_xLi_(1/3−2x/3)Mn_(2/3−x/3)]O₂. Indeed, Li[Ni_0.50Mn_0.50]O₂ compound shows relatively low initial discharge capacity of 200 mAh/g and large capacity loss during cycling, with Li[Ni_0.17Li_0.22Mn_0.61]O₂ and Li[Ni_0.25Li_0.17Mn₀.₅₈]O₂ compounds exhibit high initial discharge capacity over 245 mAh/g and stable cycle performance in the voltage range of 4.8 -2.0 V. On the other hand, XANES analysis shows that the oxidation state of Ni ion reversibly changes between Ni²⁺ and about Ni³⁺, while the oxidation state of Mn ion sustains Mn⁴⁺ during charge-discharge process. This result does not agree with the previously reported ‘electrochemistry model’ of Li[Ni_xLi_(1/3−2x/3)Mn_(2/3−x/3)]O₂, in which Ni ion changes between Ni²⁺ and NI⁴⁺. Based on these results, we modified oxidation-state change of Mn and Ni ion during charge-discharge process.     

三包层WⅠ和WⅡ型单模光纤波导色散特性的研究

研究了三包层WⅠ和WⅡ型单模光纤的波导色散特性。结果发现在相同条件下，三包层WⅠ和WⅡ型单模光纤零色散点的调节范围比传统的双包层W型单模光纤明显增大。详细分析了几何参量P、Q和光学参量R1、R2对单模传输时的波导色散特性和低次模截止频率的影响。所得的研究结果为获得更为理想的色散补偿、色散平坦光纤及设计新型无源光器件提供了重要的依据。计算波导色散的方法可推广到多包层光纤。     

Lower-dimensional linear complementarity problem approaches to the solution of a bi-obstacle problem

A globally convergent Broyden-like method for solving a bi-obstacle problem is proposed based on its equivalent lower-dimensional linear complementarity problem. A suitable line search technique is introduced here. The global and superlinear convergence of the method is verified under appropriate assumptions.     

Oscillation of certain partial difference equations

In this paper we consider a class of nonlinear delay partial difference equations and a class of linear delay partial difference equations with variable coefficients, which may change sign. We obtain oscillation criteria for these equations. There are no results for the oscillation of these equations up to now.     

A new alternating‐direction finite element method for hyperbolic equation

A modified backward difference time discretization is presented for Galerkin approximations for nonlinear hyperbolic equation in two space variables. This procedure uses a local approximation of the coefficients based on patches of finite elements with these procedures, a multidimensional problem can be solved as a series of one‐dimensional problems. Optimal order H₀¹ and L² error estimates are derived. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

A new generalized algebra method and its application in the (2 + 1) dimensional Boiti–Leon–Pempinelli equation

In the present paper, some types of general solutions of a first-order nonlinear ordinary differential equation with six degree are given and a new generalized algebra method is presented to find more exact solutions of nonlinear differential equations. As an application of the method and the solutions of this equation, we choose the (2 + 1) dimensional Boiti Leon Pempinelli equation to illustrate the validity and advantages of the method. As a consequence, more new types and general solutions are found which include rational solutions and irrational solutions and so on. The new method can also be applied to other nonlinear differential equations in mathematical physics.     

Covalent functionalization of multi-walled carbon nanotubes by lipase

Lipase from Candida rugosa was covalently anchored onto acid-treated multi-walled carbon nanotubes (MWNTs) through a self-catalytic mechanism. A variety of characterization techniques including FTIR, Raman spectroscopy, and XPS were employed to demonstrate the formation of the ester linkage between lipase and MWNTs. The MWNTs-lipase biocomposites showed significantly increased solubility in some common-used organic solvents, such as THF, DMF and chloroform. This study may offer a novel and facile route for covalent modification of carbon nanotubes, and expand the potential utilization of both lipases and MWNTs in the fields of biocatalyst and biosensor.