Dimension sets for infinite IFSs: the Texan Conjecture

We consider the set of Hausdorff dimensions of limit sets of finite subsystems of an infinite conformal iterated function system and refer to it as the restricted dimension set. The corresponding set for all subsystems will be referred to as the complete dimension set. We give sufficient conditions for a point to belong to the complete dimension set and consequently to be an accumulation point of the restricted dimension set. We also give sufficient conditions on the system for both sets to be nowhere dense in some interval. Both general results are illustrated by examples. Applying the first result to the case of continued fraction we are able to prove the Texan Conjecture, that is we show that the set of Hausdorff dimensions of bounded type continued fraction sets is dense in the unit interval.     

On the upper and lower quantization coefficient for probability measures on multiscale Moran sets

Given a finite set of patterns, we consider the Moran sets determined by using each of these patterns with a prescribed frequency. For certain infinite product measures μ on such Moran sets, we determine the exact values of the quantization dimensions D_r(μ). We give various sufficient conditions for the D_r(μ)-dimensional upper quantization coefficient and the lower one to be positive and finite. We also construct an example to illustrate our main result.     

乙酰丙酮热分解反应的理论研究

用MINDO/3方法研究了乙酰丙酮的热分解反应，研究结果表明，醇式构型比酮式构型稳定；具有最低能垒的两个反应通道──反应(1)和(2)的活化位垒分别为210.250和225.501 kJ·mol~(-1)．     

AM1研究甲酰和苯甲酰叠氮的热分解反应

叠氮化合物是良好的炸药和火箭推进剂，广泛用于国防和工农业问．近一个世纪以来，许多化学工作者对叠氮化合物的研究表现出浓厚的兴趣[1－4]．Curtius等人对酸基叠氮的热分解反应进行了大量的实验研究[2,3]．为了从理论上探明这类反应的机理，我们用AM1方法研究甲酸和苯甲酸叠     

MINDO/3研究胞嘧啶异构体间异构化反应——Ⅲ. N3-氢-4-氨基-2-羰基胞嘧啶与异4-氨基-2-羟基胞嘧啶异构化反应

本文采用MINDO/3方法研究N_3-氢-4-氨基-2-羰基胞嘧啶与异4-氨基-2-羟基胞嘧啶异构化反应途径。对所研究的分子体系运用能量梯度法, 给出了计算优化的几何构型。用Powell法优化了过渡态几何构型, 并给出了该异构化反应的IRC。计算表明, 前者比后者在能量上稳定4.9 kcal mol~(-1), 正反应与逆反应的活化势垒分别为43.4和38.5kcal_mol~(-1)。本文对几个胞嘧啶异构化反应的物理实质也作了总结, 试图揭示该类反应的一致性规律。     

SCRCR′CO重排反应的量子化学研究

用MINDO／3方法研究SCRCR′CO的热重排反应的机理，给出了活化能和IRC途径，讨论了活化能与取代基R′和迁移基R的性质之间的内在联系．     

苯并二氢吡喃热分解反应的量子化学研究

用AM1方法（采用非限制的哈特利－福克UHF计算）研究了苯并二氢吡喃的热分解反应。研究表明，目标反应可按两条竞争的自由基路径进行。     

邻乙酰基环酮热分解反应的理论研究

酸基化合物是一类极为重要的有机物,早在三十年代末,Hard等人就对式（1）所示的反应进行了实验研究问．近几十年来,这类化合物气相热分解反应的实验研究常有报导t’－7］,并且指出式（1）是途经六元环过渡态的单分子反应．为了配合实验工作,我们曾对酸氧基甲酸酯同、二乙酸亚胺和硫代乙酸胺的反应机理做过理论研究,并作了报导同．本文用PM3方法［‘’］研究邻乙酸基环戊酮和邻乙酸基环已酿的气相热分解反应,力图得到比此两种目标反应的实验研究［“］结果更详细的信息．h十算细节研究过程中,对平衡几何构型用能量梯度法全优化;对…     

Robust high-dimensional regression for data with anomalous responses

Annals of the Institute of Statistical Mathematics - The accuracy of response variables is crucially important to train regression models. In some situations, including the high-dimensional case,...