双湖记

长期以来,俄国都拥有着本文将着力研究的两个湖的主权:西伯利亚的贝加尔湖和南极的罗斯托克湖。它们都有着诱人的秘密:关于气候的变化、物种的进化、生物怎样在极端恶劣的环境下生存,也许还有关于其他星球上的生命。     

矩阵范数的界和方阵的ρ-条件数

本文给出了长方矩阵的p-范数及更广一类矩阵范数的上、下界又给出了方阵的p-条件数等于1的条件。(1≤p≤ ∞)。文[1]则是p=2的情况。前三节讨论p-条件数,第四节讨论长方矩阵范数的界。     

时变系统的稳定性

§1 引言文献[1—3]都对变系数线性系统的稳定性进行了研究,特别在文[3]中利用Ляпунов函数法对缓变系数系统稳定性的研究,得到较好的结果,我们于本文中借助于文[3]的思想,讨论了一般变系数线性系统的稳定性,得到一些结果,改进和推广了这方面的研究。     

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.