非线性极限点和极限圆问题

1910年H．weyl首次提出极限点和极限圆问题，导致了上世纪非线性微分方程渐近分析研究的一些新进展。本书是关于这个研究的专著，对问题的产生、发展、扩充及主要结果和研究趋势等方面进行了论述。     

The dead-end elimination theorem and its use in protein side-chain positioning

The prediction of a protein's tertiary structure is still a considerable problem because the huge amount of possible conformational space1 makes it computationally difficult. With regard to side-chain modelling, a solution has been attempted by the grouping of side-chain conformations into representative sets of rotamers2??. Nonetheless, an exhaustive combinatorial search is still limited to carefully indentified packing units?? containing a limited number of residues. For larger systems other strategies had to be developed, such as the Monte Carlo Procedure?? and the genetic algorithm and clustering approach?. Here we present a theorem, referred to as the 'dead-end elimination' theorem, which imposes a suitable condition to identify rotamers that cannot be members of the global minimum energy conformation. Application of this theorem effectively controls the computational explosion of the rotamer combinatorial problem, thereby allowing the determination of the global minimum energy conformation of a large collection of side chains.     

Evolution of the atmosphere and oceans

The residence times of most constituents of the atmosphere and oceans are small fractions of the age of the Earth and, in general, their rate of output has been nearly equal to their rate of input. We are disturbing a number of these dynamic equilibria quite severely. The mineralogy of marine evaporites rules out drastic changes in the composition of sea water during the last 900 Myr. The chemistry of soils formed more than 1,000 Myr ago suggests that the atmosphere then contained significantly more CO2 and less O2 than at present. Hydrogen peroxide may well have been the principal oxidant and formaldehyde the main reductant in rain water between 3,000 and 1,000 Myr ago. Major changes in atmospheric chemistry since that time are almost certainly related to the evolution of the biosphere.     

用爆炸波起爆癸烷云雾的两种模式

用垂直激波管研究了400μm癸烷液滴与空气混合物的爆炸波起爆。每种混合物有两个极限起爆能值,即高值Ecu,和低值Ecl。当起爆能的值高于Ecu时,观察到100%发生爆轰;而当其低于Ecl时,就不会发生爆轰。有趣的是,当起爆能水平在Ecu和Ecl之间时观察到对应于不同的起爆能水平有不同的起爆行为。如实验结果所表明的,爆轰的激发不仅是由于直接起爆,而且也由于“爆燃”到爆轰的转变。