Spectra Analysis of a Novel Ti-Doped LiAlO2 Single Crystal

LiAlO2 single crvstals doped with Ti at concentration 0.2at.% are grown by the Czochralskl technique with dimensions φ42×55mm. Ti ions in the crystal are quadrivalence proven by comparing the absorption and fluorescence spectra of pure LiAlO2 and Ti： LiAlO2. After air and Li-rich atmosphere annealing, the absorption peaks in the range of 600-800nm disappear. We conclude that 682 and 756nm absorption peaks are attributed to the VLi and Vo absorptions, respectively： The peaks at 716nm and 798nm may stem from the VLi^＋ and absorptions. The colour-centre model can be applied to explain the experimental phenomena. Ti^4＋-doping produces more lithium vacancies in the LiAlO2 crystal. The intensities of [LiO4] and the associated bonds remain unchanged, which improves the anti-hydrolyzation and thermal stability of LiAlO2 crystals.     

NECESSARY CONDITIONS FOR OPTIMAL CONTROLS OF SEMILINEAR ELLIPTIC VARIATIONAL INEQUALITIES INVOLVING STATE CONSTRAINT

This paper deals with maximum principle for some optimal control problem governed by some elliptic variational inequalities. Some state constraints are discussed. The basic techniques used here are based on those in [1] and a new penalty functional defined in this paper.     

周期势场中定向扩散流的蒙特卡罗计算

提出一种稳定和精确的坐标变换和闭合积分方法，用以求解描述周期势场中布朗粒子作定向运动的乘性朗之万方程。     

高维铁磁链系统与p—调和映射

研究了与ｐ－Ｌａｐｌａｃｅ算子对映的铁磁甸系统的Ｌａｎｄａｕ－Ｌｉｆｓｈｉｔｚ方程，证明了该方程的从ｍ（ｍ≥３）维紧流形Ｍ（不带边界）映射到Ｒ＾３中的单位球面Ｓ＾２上的整体弱解的存性；建立了ｐ调和映射理论与该方程的联系。     

时滞种群模型的正周期解对所有正解的吸引性

建立了对数种群模型Ｎ′（ｔ）＝Ｎ（ｔ）｛ｒ（ｔ）－ａ１（ｔ）ｌｎ［Ｎ（ｔ）］－ａ２（ｔ）ｌｎ［Ｎ（ｔ－τ（ｔ））］｝的周期正解的存在性，并得到了正周期解对所有正解的吸引性．     

一类整除性定理

本给出复域上多元多项式环C[x1,x2…，xn]的一类整除性定理，它是[1]中整除定理的直接推广。     

THE EXISTENCE THEOREM OF THE CONE-WEAK SUBDIFFERENTIAL OF SET-VALUED MAPPING

In this paper, the existence theorem of the cone-weak subdiflerential of set-valued mapping in locally convex topological vector space is proved.     

SINGULAR BOUNDARY PROPERTIES OF HARMONIC FUNCTIONS AND FRACTAL ANALYSIS

ＳＩＮＧＵＬＡＲＢＯＵＮＤＡＲＹＰＲＯＰＥＲＴＩＥＳＯＦＨＡＲＭＯＮＩＣＦＵＮＣＴＩＯＮＳＡＮＤＦＲＡＣＴＡＬＡＮＡＬＹＳＩＳＷＥＮＺＨＩＹＩＮＧＺＨＡＮＧＹＩＰＩＮＧＭａｎｕｓｃｒｉｐｔｒｅｃｅｉｖｅｄＪａｎｕａｒｙ１１，１９９５．Ｒｅｖｉ...