聚电解质渗透汽化膜

介绍了聚电解质渗透汽化膜的研究进展，包括聚电解质以及聚电解质复合物的定义、特点、制备、着重介绍了近年来开发的一些重要的聚电解质渗透汽化膜的制备方法及其分离性能。     

Modelling of CO2 laser welding of magnesium alloys

Laser welding is an important joining process for magnesium alloys. These materials are being increasingly used in different applications such as in aerospace, aircraft, automotive, electronics, etc. To date, carbon dioxide (CO₂) neodymium-doped yttrium aluminum garnet (Nd:YAG) and the high power diode laser have been extensively used to investigate the weldability of magnesium alloys. The present work describes an analytical thermal model for the weldability of magnesium alloys (WE43) using an industrial (CO₂) laser source. The main target of the project is to present to the industrial community a simple and rapid tool for the determination of the penetration depth and the bead width as a function of both the incident laser power and welding speed. The proposed model is based on the Davis thermal approach, largely considered for the characterization of the average radius of the liquid zone, aiming at predicting the joint shape. Moreover, since during the welding process considered in this study, a protecting gas is used to avoid joint oxidation, both thermal convection and radiation phenomena in the welding area have been estimated and introduced in our model for a better characterization of the welding process. The obtained results have been compared to the experimental ones and a satisfactory correlation has been observed, indicating the reliability of the model developed in this study.     

On oscillation of eigenfunctions of a fourth-order problem with spectral parameters in the boundary conditions

In the paper, we study the problem on the number of zeros of eigenfunctions of the fourth-order boundary-value problem with spectral and physical parameters in the boundary conditions. We show that the number of zeros of the eigenfunctions corresponding to eigenvalues of positive type behaves in a usual way (it is equal to the serial number of an eigenvalue increased by 1), but, however, the number of zeros of the eigenfunction corresponding to an eigenvalue of negative type can be arbitrary. In the case of a sufficient smoothness of coefficients of the differential expression, we write the asymptotics in the physical parameter for such a number. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 4, pp. 41–52, 2006.     

Strength considerations of optical waveguide fibers

An important aspect of optical waveguide fiber made of glass is whether it will break under a wide variety of service and manufacturing conditions. This paper covers some of the testing in which stress, length, time, and environment were vaned. The use of Weibull statistics with these data indicates that a statistically predictable behavior exists for populations of glass fibers. Extrapolation from short lengths and short times to very long lengths and very long times must be based on an understanding of the “constants” in the prediction equation. That is, these “constants” can be shown to vary when the three basic parameters cover orders of magnitude in range.     

A Deodhar-type stratification on the double flag variety

We describe a partition of the double flag variety G/B⁺ × G/B^- of a complex semisimple algebraic group G analogous to the Deodhar partition on the flag variety G/B⁺. This partition is a refinement of the stratification into orbits both for B⁺ × B^- and for the diagonal action of G, just as Deodhar's partition refines the orbits of B⁺ and B^-. We give a coordinate system on each stratum, and show that all strata are coisotropic subvarieties. Also, we discuss possible connections to the positive and cluster geometry of G/B⁺ × G/B^-, which would generalize results of Fomin and Zelevinsky on double Bruhat cells and Marsh and Rietsch on double Schubert cells.     

Construction of singular limits for four-dimensional elliptic problems with exponentially dominated nonlinearity

The authors consider the existence of singular limit solution for a family of nonlinear elliptic problems with exponentially dominated nonlinearity and Navier boundary condition.     

Error quantification in strain mapping methods.

In this article a method for determining errors of the strain values when applying strain mapping techniques has been devised. This methodology starts with the generation of a thickness/defocus series of simulated high-resolution transmission electron microscopy images of InAsxP1-x/InP heterostructures and the application of geometric phase. To obtain optimal defocusing conditions, a comparison of different defocus values is carried out by the calculation of the strain profile standard deviations among different specimen thicknesses. Finally, based on the analogy of real state strain to a step response, a characterization of strain mapping error near an interface is proposed.     

Laser pulse control of exciton dynamics in a biological chromophore complex

Femtosecond laser pulse control of exciton dynamics in a biological chromophore complex is studied theoretically. The computations use the optimal control theory specified to open quantum systems and formulated in the framework of the rotating wave approximation. Based on the laser pulse induced formation of an excitonic wave packet the possibility to localize excitation energy at a certain chromophore within a photosynthetic antenna system (FMO complex of green bacteria) is investigated. Details of exciton dynamics driven by a polarization shaped pulse are discussed.     

Oxidative Coupling of Methane over W‐Mn/SiO2 Catalyst

W‐Mn/SiO₂ catalyst has been developed in our laboratory (LICP), which is active, selective and stable for oxidative coupling of methane (OCM) in fixed bed and fluidized bed reactors. The research results have been reproduced at different reaction conditions by two groups of J. H. Lunsford (JH‐LL) from Texas A & M University and R. M. Lambert (RMLL) from University of Cambridge respectively. The basic research aspects on this catalyst systems, reaction performances, structure characterization and reaction mechanism were reviewed. A model on two active sites related to W^6+/5+ and Mn^3+/2+ has been suggested for activation of methane and oxygen respectively.     

Idempotency of linear combinations of three idempotent matrices, two of which are commuting

The considerations of the present paper were inspired by Baksalary [O.M. Baksalary, Idempotency of linear combinations of three idempotent matrices, two of which are disjoint, Linear Algebra Appl. 388 (2004) 67-78] who characterized all situations in which a linear combination P=c₁P₁+c₂P₂+c₃P₃, with c_i, i=1,2,3, being nonzero complex scalars and P_i, i=1,2,3, being nonzero complex idempotent matrices such that two of them, P₁ and P₂ say, are disjoint, i.e., satisfy condition P₁P₂=0=P₂P₁, is an idempotent matrix. In the present paper, by utilizing different formalism than the one used by Baksalary, the results given in the above mentioned paper are generalized by weakening the assumption expressing the disjointness of P₁ and P₂ to the commutativity condition P₁P₂=P₂P₁.