On a certain two-sided symmetric condition in magnetic field analysis and computations

A special two-sided condition for the incremental magnetic reluctivity is introduced which guarantees the unique existence of both the weak and the approximate solutions of the nonlinear stationary magnetic field distributed on a region composed of different media, as well as a certain estimate of the error between the two solutions. The condition, being discussed from the physical as well as the mathematical point of view, can be easily verified and is fulfilled for various magnetic reluctivity models used in electrotechnical practice.     

Study on a Cross Diffusion Parabolic System

This paper considers a kind of strongly coupled cross diffusion parabolic system,which can be usedas the multi-dimensional Lyumkis energy transport model in semiconductor science.The global existence andlarge time behavior are obtained for smooth solution to the initial boundary value problem.When the initialdata are a small perturbation of an isothermal stationary solution,the smooth solution of the problem under theinsulating boundary condition,converges to that stationary solution exponentially fast as time goes to infinity.     

半正二阶三点边值问题的解和正解

考察了非线性二阶三点边值问题的n个解和正解的存在性,其中允许非线性项有一个负的下界并且n是一个任意的自然数．主要结论表明该问题可以具有n个解或者正解,只要非线性项在某些有界集上的“高度”是适当的．     

中国的百岁老人研究Ⅱ.百岁老人的死亡率、生存率和发展趋势

根据全国人口普查资料,用指数函数拟合法计算了中国百岁老人的死亡率和生存率,得出中国人口的最高自然寿限为120岁,并预测到2010年中国百岁老人绝对数将达4万多人,届时每百万人口中将有30位百岁老人,比2000年增加1倍以上。     

Studies on the Structure and Properties of Cordierite Synthesized by Talc-Magnesite

Homogeneous cordierite has been synthesized at low cost by talc-magnesite and coal gangue as the main raw materials. The mechanism of synthesizing cordierite under such a com- posing system of raw materials, and the effect of temperature on the crystal cell parameters and microstructure and thermal expansion coefficient of cordierite crystal have been studied via testing methods of XRD, SEM, etc. The result shows that the homogeneous cordierite can be synthesized by the systematic composing materials of “talc-magnesite—coal gangue—talc” with heat pre- servation at 1350 ℃ for 1 h; as the keeping time is prolonged, Al3+ and Mg2+ in cordierite crystal are replaced by a few impurity ions such as Fe3+, Fe2+, etc., and the crystal cell parameters of cordierite present an increase trend; as the high-temperature heat preservation is prolonged, the content of glassy phase in the sample is increased, its density is improved, and its thermal expansion coeffi- cient presents an increase trend.     

Synthesis and Crystal Structure of [{Cd(hmbdc)(H2O)3}·2H2O]n

A novel coordination polymer [{Cd(hmbdc)(H2O)3}·2H2O]n (hmbdc=5-hydroxy- isophthalic acid) has been synthesized and characterized by elemental analysis, IR spectra and single-crystal X-ray diffraction. The crystal belongs to monoclinic, space group P21/c, with a=9.599(3), b=18.699(5), c=7.557(2) (A), β= 108.198(4)°, V=1288.6(6) (A)3, Z=4, Mr=382.60, Dc=1.972 g/cm3, F(000)=760, μ=1.740, the final R=0.0555 and wR=0.0995 for 1732 observed reflections with Ⅰ ＞ 2σ(Ⅰ). The structural analysis shows that the intermolecular hydrogen bonds and π-π interactions result in a three-dimensional supramolecular framework.     

Existence of finitely optimal solutions for infinite-horizon optimal control problems

In this paper, we investigate the existence of finitely optimal solutions for the Lagrange problem of optimal control defined on [0, ) under weaker convexity and seminormality hypotheses than those of previous authors. The notion of finite optimality has been introduced into the literature as the weakest of a hierarchy of types of optimality that have been defined to permit the study of Lagrange problems, arising in mathematical economics, whose cost functions either diverge or are not bounded below. Our method of proof requires us to analyze the continuous dependence of finite-interval Lagrange problems with respect to a prescribed terminal condition. Once this is done, we show that a finitely optimal solution can be obtained as the limit of a sequence of solutions to a sequence of corresponding finite-horizon optimal control problems. Our results utilize the convexity and seminormality hypotheses which are now classical in the existence theory of optimal control.This research forms part of the author's doctoral dissertation written at the University of Delaware, Newark, Delaware under the supervision of Professor Thomas S. Angell.     

PREPARATION OF POLY（METHYL METHACRYLATE）/LAYERED DOUBLE HYDROXIDES NANOCOMPOSITES via in situ SOLUTION POLYMERIZATION

An exfoliated layered double hydroxides/poly(methyl methacrylate)(LDHs/PMMA)nanocomposite was prepared by in situ solution polymerization of methyl methacrylate(MMA)in the presence of 4-vinylbenzenesulfonate intercalated LDHs(MgAl-VBS LDHs).MgAl-VBS LDHs was prepared by the ion exchange method,and the structure and composition of the MgA1-VBS LDHs were determined by X-ray diffraction(XRD),infrared spectroscopy and elemental analysis.XRD and transmission electron microscopy(TEM)were employed to examine the structure of LDHs/PMMA nanocomposite.It was indicated that the LDHs layers were well exfoliated and dispersed in the PMMA matrix.The grafting of PMMA onto LDHs was confirmed by the extraction result and the weight fraction of grafted PMMA increased as the weight fraction of LDHs in the nanocomposites increased.     

INTROMISSION OF WATER-REPELLENT AND HYDROSCOPIC PROPERTIES SIMULTANEOUSLY TO PP BY PLASMA DISCHARGE METHOD

Plasma-induced surface graft copolymerization of acrylic acid on polypropylene non-woven fabric (PP-g-AA) and polypropylene membrane were reported. The extents of grafting were controlled by the plasma and polymerization condition. Hexadecyltrimethyl ammonium bromide was then coupled with the carboxyl group of PP-g-AA to obtain a polyion complex (PIC). At last, CF4 plasma was used to give PICs hydrophobic property. The moisture regain and water-repellency of the processed PICs was investigated. The surfaces were characterized using ATR FT-IR and XPS. The result indicates that the products have very high ability to adsorb moisture, even better than cotton fiber. At the same time, the products show excellent hydrophobic property, which can‘t be wetted by those reagents whose surface tensions were higher than 327mN/m.     

On solvability of differential equations with the Riesz fractional derivative

We consider the solvability of fractional differential equations involving the Riesz fractional derivative. Our approach basically relies on the reduction of the problem considered to the equivalent nonlinear mixed Volterra and Cauchy-type singular integral equation and on the theory of fractional calculus. By establishing a compactness property of the Riemann–Liouville fractional integral operator on Lebesgue spaces and using the well-known Krasnoselskii's fixed point theorem, an existence of at least one solution is gleaned. An example is finally included to show the applicability of the theory.