Nonnegative Radix Representations for the Orthant

Let be a nonnegative real matrix which is expanding, i.e. with all eigenvalues , and suppose that is an integer. Let consist of exactly nonnegative vectors in . We classify all pairs such that every in the orthant has at least one radix expansion in base using digits in . The matrix must be a diagonal matrix times a permutation matrix. In addition must be similar to an integer matrix, but need not be an integer matrix. In all cases the digit set can be diagonally scaled to lie in . The proofs generalize a method of Odlyzko, previously used to classify the one--dimensional case.

     

由文本至口形的媒体变换技术的研究

本文根据汉语的发音特点,提出了由基本音素口形参数和预先建立的口形模型来生成各种音节相应的正面口形图象的方法,从而完成由文本至口形的媒体变换,首先我们建立变形物体运动模型,然后由此构造一个口唇的动态发音模型,最后采用纹理映射技术,由基本音素口形参数和动态发音模型合成正面发音口形的图象。     

Strain Energies in Homoatomic Nitrogen Clusters N(4), N(6), and N(8)

Strain energies and resonance energies can be obtained as the energy changes for appropriate homodesmotic reactions using ab initio calculated total energies as the energies of the reactants and products involved. Homodesmotic reactions conserve bond types and preserve valence environments at all atoms, requirements that favor the cancellation of basis set and electron correlation errors in the ab initio energies. In this paper we calculate strain energies and resonance energies for N(4), N(6), and N(8) clusters in a number of chemically significant but, for nitrogen, hypothetical structural forms. The nitrogen cluster strain energies are generally of the same order of magnitude as those of isostructural hydrocarbon clusters, and individual differences can be explained by using the ring strain additivity rule and recognizing the effect of the presence of lone pairs of electrons on nitrogen clusters but not on the hydrocarbons. Resonance energies of the nitrogen clusters are much smaller than those of the comparable aromatic hydrocarbons. The differences can be rationalized by considering the relative strengths of CC and NN single and double bonds. Strain and resonance energies of nitrogen clusters are compared with those previously reported for homoatomic clusters of phosphorus and arsenic. Trends through the series are remarkably similar, but strain energies for clusters from lower periods are progressively smaller. Strain and resonance have been important organizing concepts in organic chemistry for many years. Estimates of corresponding parameters for inorganic analogs are only now becoming available.     

Total Synthesis of d,l-Isospongiadiol: An Intramolecular Radical Cascade Approach to Furanoditerpenes

A stereoselective oxidative free-radical cyclization of beta-keto ester polyenes 7 and 19 has been accomplished as a one-step entry to the tricarbocyclic synthons 8and 21 which contain five and six stereogenic centers, respectively. These key synthons possessing an axial carboethoxy group at C-4 were ultimately converted to the spongian skeleton (8--> 14 and 21 --> 25 -->14). The synthesis of d,l-isospongiadiol (3) from the common intermediate 14 was realized after introduction of the 2alpha-hydroxy group in the spongian A-ring via epoxidation of silyl enol ether 28 and subsequent desilylation.