Competitive dynamics of e-commerce web sites

The characteristic of “rich gets richer” is much more conspicuous on the Internet, which is the important cause of “power-law” characteristic of the “winner-takes-all” markets. A competitive model of e-commerce web sites is presented in order to explore the effects of competition and the characteristic of “rich gets richer” on Internet economy, and also to investigate how the “winner-takes-all” phenomenon comes forth. Then these ordinary differential equations are qualitatively analyzed and numerically simulated to study the dynamics of competition. The effects of parameters on the dynamic behavior in the model are also discussed.     

Favourite sites of simple random walk

Periodica Mathematica Hungarica - We survey the current status of the list of questions related to the favourite (or: most visited) sites of simple random walk on Z, raised by Pál Erd?s...     

Fibred sites and stack cohomology

The usual notion of the site associated to a stack is expanded to a definition to a site fibred over a presheaf of categories A on a site . If the presheaf of categories is a presheaf of groupoids G, then the associated homotopy theory is Quillen equivalant to the homotopy theory of simplicial presheaves over BG, and so the homotopy theory for the fibred site is an invariant of the homotopy type of G. Similar homotopy invariance results obtain for presheaves of spectra and presheaves of symmetric spectra on . In particular, stack cohomology can be calculated on the fibred site for any representing presheaf of groupoids within a fixed homotopy type.     

Percolation of even sites for random sequential adsorption

Consider random sequential adsorption on a red/blue chequerboard lattice with arrivals at rate 1 on the red squares and rate λ$\lambda$ on the blue squares. We prove that the critical value of λ$\lambda$, above which we get an infinite blue component, is finite and strictly greater than 1.     

The most visited sites of symmetric stable processes

Let X be a symmetric stable process of index α∈ (1,2] and let L ^x _t denote the local time at time t and position x. Let V(t) be such that L _t ^V(t) = sup _{x∈ ℝ} L _t ^x . We call V(t) the most visited site of X up to time t. We prove the transience of V, that is, lim _{t →∞} |V(t)| = ∞ almost surely. An estimate is given concerning the rate of escape of V. The result extends a well-known theorem of Bass and Griffin for Brownian motion. Our approach is based upon an extension of the Ray–Knight theorem for symmetric Markov processes, and relates stable local times to fractional Brownian motion and further to the winding problem for planar Brownian motion. Received: 14 October 1998 / Revised version: 8 June 1999 / Published online: 7 February 2000     

AHP在建设用地项目选址中的应用

本文利用 AHP方法有效地解决了建设用地项目选址中的实际问题 ,为建设项目选址决策提供了科学的依据。     

电子商务网站竞争模型分析及其策略

研究电子商务网站竞争模型,分析其平衡点的稳定性,给出数值模拟图,建立一系列电子商务网站获胜的新策略.     

Fuzzy facility location problem with preference of candidate sites

Models so far considered as facility location problems treat either min–max or max–min criterion, that is, the facility is either desirable or undesirable. We propose the following model considering the satisfaction degree with respect to the distance from the facility for each customer (residents) and preference of the site in an urban area. The objective is to find the site of the facility which maximizes the minimal satisfaction degree among all demand points and maximizes the preference of the site. Since generally speaking, there exists no site that maximizes both criteria, we seek non-dominated sites after defining non-domination.     

On the most visited sites of symmetric Markov processes

A growing body of recent works have been devoted to the study of the favorite points of various concrete Markov processes. We contribute to this subject by showing that for a large class of recurrent strongly symmetric Markov processes, singletons are polar for the most visited site(s).     

Games with allocation of discrete resources to several sites

Games with allocation of discrete scalar resources are considered. Existence of an equilibrium is proved for two-person games with at most three sites. Examples of games without equilibrium are constructed.Translated from Programmno-apparatnye Sredstva i Matematicheskoe Obespechenie Vychislitel'nykh Sistem, pp. 156–162, 1994.     

Extending semilattices to frames using sites and coverages

Each meet semilattice S is well known to be freely extended to a frame by its down-sets DS. In this article we present, first, the complete range of frame extensions generated by S; it turns out to be a sub-coframe of the coframe C of sublocales of DS, indeed, an interval in C, with DS as the top and the extension of S respecting all the exact joins in S as the bottom. Then, the Heyting and Boolean case is discussed; there, the bottom extension is shown to coincide with the Dedekind-MacNeille completion. The technique used is a technique of sites, generalizing that used in [JOHNSTONE, P. T.: Stone Spaces. Cambridge Stud. Adv. Math. 3, Cambridge University Press, Cambridge, 1982].     

Risk assessment for crosswind stability of vehicles on exposed sites

The main purpose of this paper is to provide a reliable evaluation for the crosswind stability of different road vehicles in a realistic physical scenario. Unlike existing approaches, we analyze the wind-vehicle system by probabilistic methods. The aerodynamic coefficients together with the gust parameters are considered as random variables. In addition, on-site measured wind data are used to calibrate the gust model. As the excitation of the vehicle is a stochastic process, risk analyses have to be carried out and failure probabilities are computed. Based on the failure probabilities, guidelines for speed limitations or traffic restrictions can be developed. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Optimal configuration of telephone answering sites in a service industry

The location of facilities, plants, warehouses, distribution centers and the like has always been an important managerial problem. This paper is concerned with the optimal location of telephone answering sites for a non-competitive service organization within the public sector. The answering site network must service the entire United States. The methodological approach taken to addressing the telephone site location problem was integer programming. While the paper to be described herein presents the problem in a conceptual fashion, the approach adopted was in fact the basis of an actual model within a particular national service organization. For reasons of confidentially, the subject organization has requested to remain anonymous.This model and paper presents a conceptual treatment of a portion of a larger study to encompass all aspects of the telephone site location question; that portion directly related to site location and telecommunications. Non-telecommunications aspects such as staffing, space and property considerations, plus other operating cost and non-cost considerations, the latter including organizational and managerial aspects, were also a part of a larger study of which treatment herein will be excluded. The model discussed and developed provided the principal focus and basis for decision making pertaining to this project, primarily due to the large proportion of total costs involved.The study project is national in scope in that callers from all parts of the country have need for various kinds of technical and non-technical information at all times of the year. The location aspect of the telecommunications portion of the telephone model is itself but one aspect of the total problem. Additional aspects include the optimal number of telephone answering sites as well as the appropriate domain (geography served) of each site and the telecommunications (circuitry) configuration at each site.While results of the modelling effort have not been made officially public by the organization under study, it can be stated that the modelling effort resulted in several organization changes including opening and closing of individual offices, domain realignments of new or existing offices, and significant cost savings primarily due to telecommunication cost reductions and increased utilization of telephone answering manpower.     

Pattern analysis for the prediction of fungal pro-peptide cleavage sites

Support vector machines (SVMs) have many applications in investigating biological data from gene expression arrays to understanding EEG signals of sleep stages. In this paper, we have developed an application that will support the prediction of the pro-peptide cleavage site of fungal extracellular proteins which display mostly a monobasic or dibasic processing site. Many of the secretory proteins and peptides are synthesized as inactive precursors and they become active after post-translational processing. A collection of fungal pro-protein sequences are used as a training data set. A specifically designed kernel is expressed as an application of the well-known Gaussian kernel via feature spaces defined for our problem. Rather than fixing the kernel parameters with cross validation or other methods, we introduce a novel approach that simultaneously performs model selection together with the test of accuracy and testing confidence levels. This leads us to higher accuracy at significantly reduced training times. The results of the server ProP1.0 which predicts pro-peptide cleavage sites are compared with the results of this study. A similar mathematical approach may be adapted to pro-peptide cleavage prediction in other eukaryotes.     

林木生长影响模型及其在人工林林地质量评价中的应用

本文基于对立地因子影响林木生长的系统分析，采用途径分析等方法建立了林木生长影响模型，并将其应用于我国长白山林区红松人工林林地质量的评价。