具有时滞的非自治的捕食-食饵系统的全局吸引

考虑一个具有离散时滞的非自治的捕食—食饵系统。系统是由3种群组成的，其中一个为捕食者，另两个为食饵种群。本文的目的是给出时滞对系统的持续生存是无害的，从而确定了系统的周期解全局吸引的条件。     

Duality theorems for convex problems with time delay

In this paper, we examine a class of convex problems of Bolza type, involving a time delay in the state. It encompasses a variety of time-delay problems arising in the calculus of variations and optimal control. A duality analysis is carried out which, among other things, leads to a characterization of minimizers in terms of the Euler-Lagrange inclusion. The results obtained improve in significant respects on what is achievable by techniques previously employed, based on elimination of the time delay by introduction of an infinite-dimensional state space or on the method of steps.     

Stability analysis of structurally unstable man–machine system involving time delays

In this paper, a structurally unstable man–machine system is considered and a rigorous mathematical analysis is performed to study the influence of time delays in the control force on stability of the equilibrium solution of this system. Results on stability, instability and conditions for the preservation of stability (instability), besides the existence of bifurcation are presented.     

The k-means range algorithm for personalized data clustering in e-commerce

This paper describes the k-means range algorithm, a combination of the partitional k-means clustering algorithm with a well known spatial data structure, namely the range tree, which allows fast range searches. It offers a real-time solution for the development of distributed interactive decision aids in e-commerce since it allows the consumer to model his preferences along multiple dimensions, search for product information, and then produce the data clusters of the products retrieved to enhance his purchase decisions. This paper also discusses the implications and advantages of this approach in the development of on-line shopping environments and consumer decision aids in traditional and mobile e-commerce applications.     

Representing workloads in GI/G/1 queues through the preemptive-resume LIFO queue discipline

We give in this paper a detailed sample-average analysis of GI/G/1 queues with the preemptive-resume LIFO (last-in-first-out) queue discipline: we study the long-run state behavior of the system by averaging over arrival epochs, departure epochs, as well as time, and obtain relations that express the resulting averages in terms of basic characteristics within busy cycles. These relations, together with the fact that the preemptive-resume LIFO queue discipline is work-conserving, imply new representations for both actual and virtual delays in standard GI/G/1 queues with the FIFO (first-in-first-out) queue discipline. The arguments by which our results are obtained unveil the underlying structural explanations for many classical and somewhat mysterious results relating to queue lengths and/or delays in standard GI/G/1 queues, including the well-known Bene's formula for the delay distribution in M/G/l. We also discuss how to extend our results to settings more general than GI/G/1.     

Exponential stability of discrete-time systems with slowly time-varying delays

Slowly time-varying delays are seldom, but do need to be, considered in the context of discrete-time systems. This paper addresses the exponential stability issue of discrete-time systems with slowly time-varying delays. The basic idea is to transform, by utilizing the switching transformation approach, the original system with slowly time-varying delays into an equivalent switched system with special switching signal. Different types of delays correspond to different types of switching signals, and the stability issue of the original system is converted into that of a switched system. It is the first time that the method of switched homogeneous polynomial Lyapunov function is applied to general delayed systems. Some sufficient exponential stability conditions for the original system are proposed in several situations. It is numerically shown that the conservativeness of the proposed conditions reduces as the degree of the switched homogeneous polynomial Lyapunov function increases.     

Existence and Uniqueness of Solutions to Time-delays Stochastic Fractional Differential Equations with Non-Lipschitz Coefficients

In this paper, we consider the existence and uniqueness of solutions to time-varying delays stochastic fractional differential equations (SFDEs) with non-Lipschitz coefficients. By using fractional calculus and stochastic analysis, we can obtain the existence result of solutions for stochastic fractional differential equations.     

The matching of electrostatic extrema: A useful method in drug design? A study of phosphodiesterase III inhibitors

Summary Ligands which bind to a specific protein binding site are often expected to have a similar electrostatic environment which complements that of the binding site. One method of assessing molecular electrostatic similarity is to examine the possible overlay of the maxima and minima in the electrostatic potential outside the molecules and thereby match the regions where strong electrostatic interactions, including hydrogen bonds, with the residues of the binding site may be possible. This approach is validated with accurate calculations of the electrostatic potential, derived from a distributed multipole analysis of an ab initio charge density of the molecule, so that the effects of lone pair and -electron density are correctly included. We have applied this method to the phosphodiesterase (PDE) III substrate adenosine-3,5-cyclic monophosphate (cAMP) and a range of nonspecific and specific PDE III inhibitors. Despite the structural variation between cAMP and the inhibitors, it is possible to match three or four extrema to produce relative orientations in which the inhibitors are sufficiently sterically and electrostatically similar to the natural substrate to account for their affinity for PDE III. This matching of extrema is more apparent using the accurate electrostatic models than it was when this approach was first applied, using semiempirical point charge models. These results reinforce the hypothesis of electrostatic similarity and give weight to the technique of extrema matching as a useful tool in drug design.     

On the electrostatic and steric similarity of lactam compounds and the natural substrate for bacterial cell-wall biosynthesis

Summary Electrostatic and structural properties of a set of -lactam, -lactam and nonlactam compounds have been analyzed and compared with those of a model of the natural substrate d-alanyl-d-alanine for the carboxy- and transpeptidase enzymes. This first comparison of the electrostatic properties has been based on a distributed multipole analysis of high-quality ab initio wave functions of the substrate and potential antibiotics. The electrostatic similarity of the substrate and active compounds is apparent, and contrasts with the electrostatic properties of the noninhibitors. This has been quantified to give a reasonable correlation with the MIC (Minimum Concentration for Inhibition) and with kinetic data (k₂/K) in accordance with the model for interaction of the lactam compounds with dd-peptidase. These correlations provide a better prediction of antibacterial activity than purely structural criteria.     

On the representation of electrostatic fields around ab initio charge distributions

Summary We compare two methods (Mulliken charges and a distributed multipole analysis, DMA) of representing an ab initio charge distribution for calculating the electrostatic field and potential outside the molecule, using pyrimidine and the RNA base uracil as examples. This is done using a 3-D graphical display of the electrostatic fields, which, when used with real-time rotation, zooming and clipping, has many advantages for qualitatively assessing the electrostatic interactions of a molecule. The errors involved in using Mulliken point charges may be of similar magnitude to the total electrostatic field in regions which are important in recognition processes. The DMA representation automatically includes the anisotropic electrostatic effects of non-spherical features in the charge distribution of each atom, and yet the displayed electrostatic fields around the atoms which have lone-pair density do not show marked anisotropy.