on lin-bose problem

This paper study generalized Serre problem proposed by Lin and Bose in multidimensional system theory context [Multidimens. Systems and Signal Process. 10 (1999) 379; Linear Algebra Appl. 338 (2001) 125]. This problem is stated as follows. Let F ∈ Al×m be a full row rank matrix, and d be the greatest common divisor of all the l × l minors of F. Assume that the reduced minors of F generate the unit ideal, where A = K[x 1,...,xn] is the polynomial ring in n variables x 1,...,xn over any coefficient field K. Then there exist matrices G ∈ Al×l and F1 ∈ A l×m such that F = GF1 with det G = d and F 1 is a ZLP matrix. We provide an elementary proof to this problem, and treat non-full rank case.

Kinetic study of hydrolysis of xylan and agricultural wastes with hot liquid water

We investigated the kinetics of hot liquid water (HLW) hydrolysis over a 60-min period using a self-designed setup. The reaction was performed within the range 160-220 °C, under reaction conditions of 4.0 MPa, a 1:20 solid:liquid ratio (g/mL), at 500 rpm stirring speed. Xylan was chosen as a model compound for hemicelluloses, and two kinds of agricultural wastes-rice straw and palm shell-were used as typical feedstocks representative of herbaceous and woody biomasses, respectively. The hydrolysis reactions for the three kinds of materials followed a first-order sequential kinetic model, and the hydrolysis activation energies were 65.58 kJ/mol for xylan, 68.76 kJ/mol for rice straw, and 95.19 kJ/mol for palm shell. The activation energies of sugar degradation were 147.21 kJ/mol for xylan, 47.08 kJ/mol for rice straw and 79.74 kJ/mol for palm shell. These differences may be due to differences in the composition and construction of the three kinds of materials. In order to reduce the decomposition of sugars, the hydrolysis time of biomasses such as rice straw and palm shell should be strictly controlled.

Optimization of biodiesel production from trap grease via acid catalysis

As a kind of waste collected from restaurants, trap grease is a chemically challenging feedstock for biodiesel production for its high free fatty acid (FFA) content. A central composite design was used to evaluate the effect of methanol quantity, acid concentration and reaction time on the synthesis of biodiesel from the trap grease with 50% free fatty acid, while the reaction temperature was selected at 95 degrees C. Using response surface methodology, a quadratic polynomial equation was obtained for ester content by multiple regression analysis. Verification experiments confirmed the validity of the predicted model. To achieve the highest ester content of crude biodiesel (89.67%), the critical values of the three variables were 35.00 (methanol-to-oil molar ratio), 11.27 wt% (catalyst concentration based on trap grease) and 4.59 h (reaction time). The crude biodiesel could be purified by a second distillation to meet the requirement of biodiesel specification of Korea.

Description of a radially polarized Laguerre-Gauss beam beyond the paraxial approximation

Fifth-order corrected expressions for the fields of a radially polarized Laguerre-Gauss (R-TEMn1) laser beams are derived based on perturbative Lax series expansion. When the order of Laguerre polynomial is equal to zero, the corresponding beam reduces to the lowest-order radially polarized beam (R-TEM01). Simulation results show that the accuracy of the fifth-order correction for R-TEMn1 depends not only on the diffraction angle of the beam as R-TEM01 does, but also on the order of the beam. (c) 2007 Optical Society of America.

BAND-STRUCTURE OF MG1-XZNXSYSE1-Y

The empirical pseudopotential method within the virtual crystal approximation is used to calculate the band structure of Mg1-xZnySySe1-y, which has recently been proved to be a potential semiconductor material for optoelectronic device applications in the blue spectral region. It is shown that MgZnSSe can be a direct or an indirect semiconductor depending on the alloy composition. Electron and hole effective masses are calculated for different compositions. Polynomial approximations are obtained for both the energy gap and the effective mass as functions of alloy composition at the GAMMA valley. This information will be useful for the future design of blue wavelength optoelectronic devices as well as for assessment of their properties.

EMPIRICAL PSEUDOPOTENTIAL BAND-STRUCTURE CALCULATION FOR ZN1-XCDXSYSE1-Y QUATERNARY ALLOY

The band structure of the Zn1-xCdxSySe1-y quaternary alloy is calculated using the empirical pseudopotential method and the virtual crystal approximation. The alloy is found to be a direct-gap semiconductor for all x and y composition. Polynomial approximation is obtained for the energy gap as a function of the composition x and y. Electron and hole effective masses are also calculated along various symmetry axes for different compositions and the results agree fairly well with available experimental values.

SEMICLASSICAL AND ENVELOPE-FUNCTION TREATMENT OF MAGNETIC LEVELS IN SUPERLATTICES UNDER AN INPLANE MAGNETIC-FIELD

The theoretical treatment of magnetic levels formed in the minibands of superlattices under an in-plane magnetic field is discussed. It is found that the results of semiclassical and envelope-function treatments based on miniband structures are in good agreement with the results calculated strictly by the quantum-mechanical method, so long as the critical parameter 2hc/eBL2 is larger than 1. The wave functions obtained are in the nature of superlattice envelope functions, which are over and above the usual effective-mass envelope functions for bulk materials.