Global smooth solutions for a class of parabolic integrodifferential equations

The existence and uniqueness of smooth global large data solutions of a class of quasilinear partial integrodifferential equations in one space and one time dimension are proved, if the integral kernel behaves like near with . An existence and regularity theorem for linear equations with variable coefficients that are related to this type is also proved in arbitrary space dimensions and with no restrictions for .

     

Nonlinear oscillations of second order differential equations of Euler type

We consider the nonlinear equation , where satisfies for , but is not assumed to be sublinear or superlinear. We discuss whether all nontrivial solutions of the equation are oscillatory or nonoscillatory. Our results can be applied even to the case , which is most difficult.

     

一类三阶非线性系统的全局稳定性分析

本文运用“类比法”构造了一类三阶非线性系统的李雅普诺夫函数,从而推出了该系统全局稳定的条件．     

Prediction of Oligopeptide Conformations via Deterministic Global Optimization

A deterministic global optimization method is described for identifying the global minimum potential energy conformation of oligopeptides. The ECEPP/3 detailed potential energy model is utilized for describing the energetics of the atomic interactions posed in the space of the peptide dihedral angles. Based on previous work on the microcluster and molecular structure determination [21, 22, 23, 24], a procedure for deriving convex lower bounding functions for the total potential energy function is developed. A procedure that allows the exclusion of domains of the (ø, ) space based on the analysis of experimentally determined native protein structures is presented. The reduced disjoint sub-domains are appropriately combined thus defining the starting regions for the search. The proposed approach provides valuable information on (i) the global minimum potential energy conformation, (ii) upper and lower bounds of the global minimum energy structure and (iii) low energy conformers close to the global minimum one. The proposed approach is illustrated with Ac-Ala4-Pro-NHMe, Met-enkephalin, Leu-enkephalin, and Decaglycine.     

孔结构对铜基甲醇合成催化剂宏观反应速率的影响Ⅰ．未中毒颗粒催化剂

催化剂的宏观反应速率受颗粒内扩散过程的影响，而内扩散过程又取决于催化剂颗粒的孔结构。以铜基甲醇合成催化剂为研究体系，通过改变压片压强和共沉淀条件，制备具有不同孔结构参数（比表面、孔隙率、孔径分布、孔容、颗粒密度、曲折因子）的颗粒催化剂，由反应工程中的扩散－反应方程，按照平行交联孔模型计算有效扩散系数，模拟计算单颗粒催化剂在工业生产条件下的宏观反应速率，从而研究孔结构对未中毒铜基甲醇合成催化剂宏观反应速率的影响。     

A fast annealing evolutionary algorithm for global optimization

By combining the aspect of population in genetic algorithms (GAs) and the simulated annealing algorithm (SAA), a novel algorithm, called fast annealing evolutionary algorithm (FAEA), is proposed. The algorithm is similar to the annealing evolutionary algorithm (AEA), and a very fast annealing technique is adopted for the annealing procedure. By an application of the algorithm to the optimization of test functions and a comparison of the algorithm with other stochastic optimization methods, it is shown that the algorithm is a highly efficient optimization method. It was also applied in optimization of Lennard-Jones clusters and compared with other methods in this study. The results indicate that the algorithm is a good tool for the energy minimization problem.     

Towards protein folding with evolutionary techniques

We present design details and first tests of a new evolutionary algorithm approach to ab initio protein folding. It does not focus on dihedral angles exclusively, but mainly operates on introduction, extension, break-up, and destruction of secondary structure elements, given as correlated dihedral angle values. In first test applications to polyalanines (up to 60 residues) and random primary sequences (up to 40 residues), we demonstrate that this use of prior knowledge is well balanced: On the one hand, it ensures quick introduction of secondary structure elements if they are favorable for a given primary sequence, but still allows for efficient location of pure random coil solutions without enforcing any secondary structure elements, if folds of this type are preferred by the given primary sequence. Furthermore, the algorithm is clearly able to pack several secondary structure elements into favorable tertiary structure arrangements, although no part of the algorithm is explicitly designed to do this. In first test examples on real-life peptides between 21 and 44 residues from the Protein Data Bank, the quality of the results depends on the force field used (as expected); nevertheless, we can show that the algorithm is able to find structures in good agreement with the targets easily and consistently, if the force field allows for that.     

Theoretical Investigations of the Inclusion Processes of (4-tert-butylphenyl) (3-sulfonatophenyl) (phenyl) Phosphine in β-Cyclodextrin

Quantum mechanical calculations on the (4-tert-butylphenyl)(3-sulfonatophenyl) (phenyl) phosphine/-cyclodextrin inclusion complex werecarried out using semi-empirical calculations. Inclusion process pathways are describedand the most probable structures of the 1:1 complex are sought through a global potentialenergy scan. The calculations suggest that the most stable structure is obtained whenthe aromatic ring bearing the tert-butyl group is includedinto the hydrophobic cavity of the -cyclodextrin from theside of the primary hydroxyl groups.     

Ab initio prediction of helical segments in polypeptides

An ab initio method has been developed to predict helix formation for polypeptides. The approach relies on the systematic analysis of overlapping oligopeptides to determine the helical propensity for individual residues. Detailed atomistic level modeling, including entropic contributions, and solvation/ionization energies calculated through the solution of the Poisson-Boltzmann equation, is utilized. The calculation of probabilities for helix formation is based on the generation of ensembles of low energy conformers. The approach, which is easily amenable to parallelization, is shown to perform very well for several benchmark polypeptide systems, including the bovine pancreatic trypsin inhibitor, the immunoglobulin binding domain of protein G, the chymotrypsin inhibitor 2, the R69 N-terminal domain of phage 434 repressor, and the wheat germ agglutinin.     

Using copositivity for global optimality criteria in concave quadratic programming problems

In this note we specify a necessary and sufficient condition for global optimality in concave quadratic minimization problems. Using this condition, it follows that, from the perspective of worst-case complexity of concave quadratic problems, the difference between local and global optimality conditions is not as large as in general. As an essential ingredient, we here use the-subdifferential calculus via an approach of Hiriart-Urruty and Lemarechal (1990).