A note on the quantization for probability measures with respect to the geometric mean error

We study the quantization with respect to the geometric mean error for probability measures μ on for which there exist some constants C, η > 0 such that for all ε > 0 and all . For such measures μ, we prove that the upper quantization dimension of μ is bounded from above by its upper packing dimension and the lower one is bounded from below by its lower Hausdorff dimension. This enables us to calculate the quantization dimension for a large class of probability measures which have nice local behavior, including the self-affine measures on general Sierpiński carpets and self-conformal measures. Moreover, based on our previous work, we prove that the upper and lower quantization coefficient for a self-conformal measure are both positive and finite.     

Consistency of modified MLE in EV model with replicated observations

In case that replicated observations are available in some experimental points, the parameters estimation of one-dimensional linear errors-in-variables (EV) models was studied. Weak and strong consistency was proved under mild conditions.     

ASYMPTOTIC NORMALITY OF PARAMETERSESTIMATION IN EV MODEL WITH REPLICATEDOBSERVATIONS

1 IntroductionFOrnully the EV (Errors-ill-Vaiables) nrodel is just tlie regressiOli medel with both depen-dent aud iudependeut variables arc subject to error (see, fOr exan1ple, [21~[71 alid tlie literaturecited tl1ere). Collsiderillg tliat iu mauy practical aPplications, taking replicated observationspresellts lio esseutial dimculties. heuce can offer a couveuiellt choice in avoidillg artilicia1 as-sunWtions about tlie nlodel. This case was studied ill essay [11, in which estinators of a …     

取代基对α-氨基乙腈热解反应影响的研究

用MINDO/3方法洋细研究了取代基对α-氨基乙腈热消除反应的影响. 研究表明, 对于孤立分子的气相反应, 给电子基使活化势垒降低, 吸电子基使活化势垒上升; 而对OH~-催化下的反应, 给电子基和吸电子基均使活化势垒上升.     

MINDO/3研究胞嘧啶异构体间异构化反应——Ⅰ. N1-氢-4-氨基-2-羰基胞嘧啶与4-亚氨基-2-羰基胞嘧啶异构反应

本文报导用半经验方法研究N_1-氢-4-氨基-2-羰基胞嘧啶与4-亚氨基-2-羰基胞嘧啶异构化反应。用MINDO/3能量梯度法优化了孤立体系的全部自由度, 计算结果表明氨型比亚氨型稳定, △E=33.85 kJ mol~(-1); 限定分子体系在同一平面, 用Powell法优化过渡态几何构型, 计算所得正反应活化势垒为168.87 kJ mol~(-1), 逆反应活化势垒为135.02 kJ mol~(-1)。从IRC途径分析了该异构化反应的物理实质。     

Linear EV model with replicate observations on independent variables

This paper studies the linear EV model when replicate observations are made only on independent variables. We construct the estimates of regression coefficients and prove the consistency and asymptotic normality under some proper conditions. Results obtained reveal the difference between the case where the independent and dependent variables are observed repeatedly and simultaneously and the case studied in this article.     

碳酸及碳酸酯热消除反应的量子化学研究

用AM1方法研究了碳酸和碳酸酯的热消除反应．发现迁移基团R和基团R’共同制约这类吸热反应的活化能。     

Asymptotic uniformity of the quantization error for the Ahlfors-David probability measures

Let μ be an Ahlfors-David probability measure on R~q;therefore,there exist some constants s_0 0 and ε_0,C_1,C_2 0 such that C_1ε~(s_0)≤μ(B(x,ε))≤C_2ε~(s_0) for all ε∈(0,ε_0) and x ∈ supp(μ).For n≥ 1,let α_n be an n-optimal set for μ of order r;furthermore,let {P_a(α_n)}_(a∈α_n) be an arbitrary Voronoi partition with respect to α_n.The n-th quantization error e_(n,r)(μ) for μ of order r can be defined as e_(n,r)~r(μ):=∫ d(x,α_n)~r dμ(x).We define I_a(α_n,μ):=∫_(P_a(α_n)) d(x,α_n)~r dμ(x),a ∈α_n,and prove that,the three quantities ■ are of the same order as that of 1/ne_(n,r)~r(μ).Thus,our result exhibits that,a weak version of Gersho's conjecture holds true for the Ahlfors-David probability measures on R~q.     

自动位移计在树坪滑坡中的应用

用自动位移计对长江干流的树坪滑坡进行了近一年的连续性观测,数据结果显示树坪滑坡体变形的控制因素为降雨和库水波动,滑坡目前变形速率较小,不会失稳。自动位移计通过连续记录数据,对树坪滑坡体的变形特征给予了准确的反映,且数据采集方便,值得在三峡库区边坡监测中推广应用。