A fuzzy stochastic model for telecommunications bandwidth brokers under probabilistic QoS measures

In this paper, we model and solve profit maximization problem of a telecommunications Bandwidth Broker (BB) under uncertain market and network infrastructure conditions. The BB may lease network capacity from a set of Backbone Providers (BPs) or from other BBs in order to gain profit by leasing already purchased capacity to end-users. BB’s problem becomes harder to deal with when bandwidth requests of end-users, profit and cost margins are not known in advance. The novelty of the proposed work is the development of a mechanism via combining fuzzy and stochastic programming methodologies for solving complex BP selection and bandwidth demand allocation problem in communication networks, based on the fact that information needed for making these decisions is not available prior to leasing capacity. In addition, suggested model aims to maximize BB’s decision maker’s satisfaction ratio rather than just profit. As a solution strategy, the resulting fuzzy stochastic programming model is transformed into deterministic crisp equivalent form and then solved to optimality. Finally, the numerical experiments show that on the average, proposed approach provides 14.30% more profit and 69.50% more satisfaction ratio compared to deterministic approaches in which randomness and vagueness in the market and infrastructure are ignored.     

确界原理的一个修正证明

分析了华东师大版《数学分析》（第四版）教材中关于确界原理证明的不足之处,给出更为细致的修正证明.     

高等数学课程分层次教学理念的思考和举措

高等数学课程是高校所有专业的基础课程之一,对实现高校的人才培养目标起着十分重要的作用.本文遵循因材施教的原则,科学设计了分层次教学模式,对于开展分层次教学的意义和理论依据作了阐述,提出了分层次教学模式的组织与实施,并就教学内容、教学方法、考核模式的改革给出相应的实施方案.     

从数学修养到数学文化

解析了数学修养与数学文化的主要内涵,并强调其对于高素质人才的重要性.     

Finite element modelling of surface waves in a channel

A variational formulation of the vertically-integrated differential equations for free surface wave motion is presented. A finite element model is derived for solving this nonlinear system of hydrodynamic equations. The time integration scheme employed is discussed and the results obtained demonstrate its good stability and accuracy.Several applications of the model are considered: the first problem is an open channel of uniform depth and the second an open channel of linearly varying depth. The ‘inflow’ boundary condition is prescribed in terms of the velocity which represents a wavemaker and/or a flow source, while the ‘outflow’ boundary condition is specified in terms of the water elevation. The outflow condition is adjusted for two cases, a reflecting boundary (finite channel) and a non-reflecting boundary (open-ended channel). The latter boundary condition is examined in some detail and the results obtained show that the numerical model can produce the non-reflecting boundary that is similar to the analytical radiation condition for waves. Computational results for a third problem, involving wave reflection from a submerged cylinder, are also presented and compared with both experimental data and analytical predictions.The simplicity and the performance of the computational model suggest that free surface waves can be simulated without excessively complicated numerical schemes. The ability of the model to simulate outflow boundary conditions properly is of special importance since these conditions present serious problems for many numerical algorithms.     

Extending the applicability of Secant methods and nondiscrete induction

We use nondiscrete mathematical induction to extend the applicability of the Secant methods for solving equations in a Banach setting. Our approach has the following advantages over earlier works under the same information: weaker sufficient convergence conditions; tighter error bounds on the distances involved and more information on the location of the solution. Numerical examples where our results apply but earlier ones fail to solve nonlinear equation as well as tighter error bounds are also provided in this study.     

Nonlinear mathematical model of pulsed-therapy of heterogeneous tumors

In this paper, we deal with a nonlinear impulsive differential equations modelling the chemotherapy of a heterogeneous tumor. We consider the case of several drugs with instantaneous effects. We take into account the interactions between sensitive cells and drug resistant cells. We are interested in the stability of the disease. We also study the loss of stability and the bifurcation of nontrivial solutions.     

Closed paths of light trapped in a closed Fermat curve

Geometric constructions have previously been shown that can be interpreted as rays of light trapped either in polygons or in conics, by successive reflections. The same question, trapping light in closed Fermat curves, is addressed here. Numerical methods are used to study the behaviour of the reflection points of a triangle when the degree of the curve varies, including a generalization to non integer powers.     

‘New mathematics’ and teaching

Inside the scientific world it is not always understood that the mood of mathematics, which is a product and a part of culture, can change with time. This is partly why many have been surprised by the coming of the so‐called new mathematics.

In the truly creative mathematical mind two opposite tendencies coexist: the logical and the imaginative. Apparently it seems that new mathematics can be reduced to a purely logical machinery. In fact it contains as much imaginative contributions as classical mathematics. But it is difficult to show simultaneously the logical sequence of propositions and the clumsy progression of research itself. Mathematical exposition does not always follow the ‘ most natural slopes’ of the mind. Unfamiliar presentations often give an impression of ‘ abstraction ‘, more familiar ones an impression of concreteness ‘.

So it appears that difficulties with new mathematics are mostly of psychological origin. Misuses of it can easily raise up intolerance reactions and emotional blocks. Perhaps insisting upon the fact that, here as elsewhere, it is important to be able to guess, to realize that intuition and imagination are essential, could help to make new mathematics better understood, more useful and more able to be considered as a unifing element among sciences.     

Formulation of commons dilemma: Dawes model reconsidered

This paper examines Dawes (1975) model on commons dilemma (CD) situation and proposes an alternative model which formulates CD. Firstly, it makes clear that Dawes model does not have the characteristics of CD. Secondly, it specifies “resource unit condition” which models of commons dilemma must satisfy. Thirdly, it presents CD model, which is obtained by setting the condition in Dawes model. And lastly, it examines some nature of the proposed model and find that in CD situation, fine is distributed proportionally to each player's property.