Positive solutions of singular Caputo fractional differential equations with integral boundary conditions

In this paper, we investigate the existence of positive solutions of singular super-linear (or sub-linear) integral boundary value problems for fractional differential equation involving Caputo fractional derivative. Necessary and sufficient conditions for the existence of C³[0, 1] positive solutions are given by means of the fixed point theorems on cones. Our nonlinearity f(t, x) may be singular at t = 0 and/or t = 1.     

Mechanical effects of acupuncture

Acupuncture, a physiotherapy, has been widely accepted all around the world. This study focuses on the influence of membrane structures and explains the acupuncture sensations from the aspect of mechanical properties. By mathematical modeling and numerical simulation, the scientific meaning of the acupuncture depth is investigated and phenomena and theory of acupuncture are discussed. The simulation results show that (a) the fascial structure is the main contributor to the force on the needle, the axial force will gradually increase before piercing the fascial, and suddenly decrease after piercing the fascial; (b) there is an inverse relationship between the needle radius and the maximum radial stress, which indicates that the needle should not be too sharp to cause local stress concentration and piece the fascia layer; and (c) the simulation results of comprehensively considering the static friction and sliding friction is identical with the experiment results. This study proposes a preliminary study of mechanical effects of acupuncture manipulation, clarifies key factors affecting the stress on the needle, and explains the objective requirement of acupuncture depth to effective treatment.     

WEAK CONVERGENCE OF SOME DIRICHLET SERIES

1 Besicovitch Inner ProductIll this paper, we consider Dirichlet serie8where an, tL = 1, 2,' ', are complex nunlbers. They are Besicovitch almost periodic functionsWe see the 8ystenl {e.(t); e.(t) = e--it Iog 1l, 71 = l, 2,' .} fOrnis a1l orthollor11la1 systelll witl1respect to tI1e BesicovitcI1 iIl1ler productThell we call fOrm the gelleralized trigouolnetrical polynolIlialsAccording to tl1e idea developed il1 [l],[2], auy Dirichlet seriesis weakly convergent over K witll respect to …     

A criterion on weighted boundedness for rough multilinear oscillatory singular integrals

In this paper the authors give a criterion on the weighted boundedness of the multilinear oscillatory singular integral operators with rough kernels.

     

构造任意阶的最优带仲裁认证码

本文首次给出了一类具有任意给定阶的最优带仲裁认证码的构造方法.     

冠状动脉狭窄情况下的非牛顿血液流动和大分子传质

针对冠状动脉狭窄的情况,采用数值模拟方法求解了牛顿流体与非牛顿流体(幂次律流体和Casson流体)的定常与脉动的流场。在此基础上,求解了LDL(低密度脂肪蛋白)和Albumin(血清白蛋白)的浓度场。根据计算结果,详细讨论了壁面剪应力、非牛顿流效应、分子大小等因素对大分子传质的影响;并对牛顿流体与非牛顿流体、定常流动与脉动流动的大分子浓度场进行了比较,这些结果对于了解动脉硬化成因与流动特性和大分子传质的联系提供了较为丰富的信息。     

Spatiotemporal dynamics in a predator-prey model with a functional response increasing in both predator and prey densities

In this paper, we studied a diffusive predator-prey model with a functional response increasing in both predator and prey densities. The Turing instability and local stability are studied by analyzing the eigenvalue spectrum. Delay induced Hopf bifurcation is investigated by using time delay as bifurcation parameter. Some conditions for determining the property of Hopf bifurcation are obtained by utilizing the normal form method and center manifold reduction for partial functional differential equation.     

考虑声誉效应的网络众包参与者行为博弈模型及仿真分析

为了控制网络众包交易的风险,以网络众包平台中的发包方和接包方为研究对象,基于微分博弈方法建立了网络众包交易中参与者行为的博弈模型,研究了发包方和接包方在合作和非合作两种情形下的策略选择。本文研究发现在声誉效应满足特定阈值的条件时,合作博弈情形下众包系统的总收益更大;而且,发包方和接包方违约控制的收益及努力程度更大。在网络众包平台的违约罚金超过特定阈值时,随时间推移发包方和接包方违约控制的努力程度逐渐提高,实现帕累托改进。本文结合猪八戒网、InnoCentive等网络众包平台的众包交易机制,采用数值分析对博弈模型的求解结果进行模拟。对于网络众包平台来说,可以通过建立有效的信用评价机制,将信用评价或声誉纳入众包交易定价,引导参与者约束自身行为。     

Periodicity and attractivity of a ratio-dependent Leslie system with impulses

A ratio-dependent Leslie system with impulses is studied. By using a comparison theorem, continuation theorem base on coincidence degree and constructing a suitable Lyapunov function, we establish sufficient and necessary conditions for the existence and global attractivity of periodic solution. Examples show that the obtained criteria are easily verifiable.     

How to recognize nonexpansive mappings and isometric mappings

In two real Banach spaces, we shall present two conditions, under one of which each nonexpansive mapping must be an isometry.