多线性分数次积分迭代型交换子的加权不等式

研究了多线性分数次积分算子的迭代型交换子,给出了双权强型不等式的充分条件,即Fefferman -Phong型条件.对此迭代型交换子,还给出了Fefferman-Stein型加权不等式和Coifman型加权不等式.     

一类狄氏型变换及其联系的马氏过程

本文研究一类狄氏型变换.我们给出狄氏型变换后的二次型是拟正则狄氏型的充分条件,分别讨论关于二阶微分算子和伪微分算子所对应的狄氏型的狄氏型变换,得到变换前后拟正则狄氏型对应的马氏过程间的关系.     

基于两种模型的整车物流运输计划问题研究

运用2014年全国研究生数学建模竞赛E题的数据,针对乘用车整车物流运输计划问题的第三问展开研究.首先建立整数规划模型,得到要运输156辆Ⅰ型、102辆Ⅱ型和39辆Ⅲ型乘用车的1-1型和1-2型轿运车的最优数量分别为25和5.其次建立逐步转化模型,假设297辆乘用车全为Ⅱ型乘用车,使Ⅲ型乘用车数量满足要求,然后仅考虑Ⅰ型和Ⅱ型乘用车,使Ⅰ型和Ⅱ型乘用车数量满足要求,得到的结果与整数规划模型结果相一致.最后给出逐步转化模型的通用算法和程序.     

由李型群得出的一类可解完全群

令Φ是复数域上单李代数 L 的根系.我们知道,单根系Φ总共有以下九种类型:A_l 型,B_l 型,C_l 型,D_l 型,E_(?)、E_7、E_8型,F_4型和 G_2型.令π是Φ的基础根系.π的元素称为根系Φ的基础根,设     

基于BEKK方差模型的干散货航运市场间波动溢出效应分析

针对灵便型、巴拿马型和海岬型干散货航运市场间的互动关系问题,选取波罗的海干散货运价指数,应用多元广义自回归条件异方差中的BEKK方差分析模型,研究了干散货航运市场间的波动溢出效应.发现海岬型干散货航运市场对灵便型和巴拿马型干散货航运市场存在波动溢出效应,而灵便型和巴拿马型干散货航运市场对海岬型干散货航运市场不存在波动溢出效应,灵便型干散货航运市场和巴拿马型干散货航运市场之间存在双向波动溢出效应,Wald检验验证了上述结论的正确性.从而可为航运经营者规避干散货航运市场波动风险提供决策参考.     

单位球上Dirichlet型空间到Z_μ型空间的积分型算子

该文利用泛函分析以及多复变的方法,研究了单位球B上Dirichlet型空间D_p到Zygmund型空间Z_μ积分型算子的有界性和紧性问题.获得了单位球上Dirichlet型空间到Zygmund型空间的积分型算子为有界算子和紧算子的充要条件.     

$I$-有界型线性空间的构造

本文引进了$I$-有界型线性空间的概念, 并给出两个具体的$I$-有界型线性空间. 进而, 研究了两种构造$I$-有界型线性空间方法:一种是利用普通的有界型线性空间诱导出一个新的$I$-有界型线性空间; 另一种是借助$I$-有界型线性映射生成一个新的$I$-有界型线性空间.     

双线性型图与交错型图不是完美图

本文证明了双线性型图与交错型图都不是完美图,从而解决了双线性型图与交错型图的完美图判别问题.     

正交曲线坐标系下极性连续统的动力学方程组

应用非完整系物理标架给出正交曲线坐标系下Bousinesq型、Kirchhof型、Signorini型和Novozhilov型有限变形极性弹性介质动力学方程组的具体形式.     

截断分布族中估计的渐近有效性（II）

本文在一般截断型分布族中给出了参数函数的估计的Ｂａｈａｄｕｒ型渐近有效性的一种定义，验证了常用估计德这种渐近有效性，比较了Ｂａｈａｄｕｒ型与竹内启型渐近有效性之间的关系，系统地给出了具有Ｂａｈａｄｕｒ型但不具竹内启型渐近有效性估计的例子。     

Blow-Up Solutions of Modified Schrödinger Maps

We study blow-up solutions of modified Schrödinger maps. We observe the pseudo-conformal invariance by which explicit blow-up solutions can be constructed.     

A competition between Fujita and Strauss type exponents for blow-up of semi-linear wave equations with scale-invariant damping and mass

We obtain a blow-up result for solutions to a semi-linear wave equation with scale-invariant dissipation and mass and power non-linearity, in the case in which the model has a “wave like” behavior. We perform a change of variables that transforms our starting equation in a strictly hyperbolic semi-linear wave equation with time-dependent speed of propagation. Applying Kato's lemma we prove a blow-up result for solutions to the transformed equation under some assumptions on the initial data. The limit case, that is, when the exponent p is exactly equal to the upper bound of the range of admissible values of p yielding blow-up needs special considerations. In this critical case an explicit integral representation formula for solutions of the corresponding linear Cauchy problem in 1d is derived. Finally, carrying out the inverse change of variables we get a non-existence result for global (in time) solutions to the original model.     

On the deformations of the incompressible Euler equations

We consider systems of deformed system of equations, which are obtained by some transformations from the system of incompressible Euler equations. These have similar properties to the original Euler equations including the scaling invariance. For one form of deformed system we prove that finite time blow-up actually occurs for ‘generic’ initial data, while for the other form of the deformed system we prove the global in time regularity for smooth initial data. Moreover, using the explicit functional relations between the solutions of those deformed systems and that of the original Euler system, we derive the condition of finite time blow-up of the Euler system in terms of solutions of one of its deformed systems. As another application of those relations we deduce a lower estimate of the possible blow-up time of the 3D Euler equations. This research was supported partially by the KOSEF Grant no. R01-2005-000-10077-0     

A lower bound for blow-up time in a fully parabolic Keller–Segel system

In this paper, an explicit lower bound for the blow-up time is obtained to a parabolic–parabolic Keller–Segel system, the blow-up conditions of which were established with an upper bound of blow-up time by Cie?lak and Stinner [T. Cie?lak, C. Stinner, Finite-time blowup and global-in-time unbounded solutions to a parabolic–parabolic quasilinear Keller–Segel system in higher dimensions, J. Differential Equations 252 (2012) 5832–5851].     

Blow-up and pattern formation in hyperbolic models for chemotaxis in 1-D

In this paper we study finite time blow-up of solutions of a hyperbolic model for chemotaxis. Using appropriate scaling this hyperbolic model leads to a parabolic model as studied by Othmer and Stevens (1997) and Levine and Sleeman (1997). In the latter paper, explicit solutions which blow-up in finite time were constructed. Here, we adapt their method to construct a corresponding blow-up solution of the hyperbolic model. This construction enables us to compare the blow-up times of the corresponding models. We find that the hyperbolic blow-up is always later than the parabolic blow-up. Moreover, we show that solutions of the hyperbolic problem become negative near blow-up. We calculate the zero-turning-rate time explicitly and we show that this time can be either larger or smaller than the parabolic blow-up time. The blow-up models as discussed here and elsewhere are limiting cases of more realistic models for chemotaxis. At the end of the paper we discuss the relevance to biology and exhibit numerical solutions of more realistic models.     

Blow-up and pattern formation in hyperbolic models for chemotaxis in 1-D

In this paper we study finite time blow-up of solutions of a hyperbolic model for chemotaxis. Using appropriate scaling this hyperbolic model leads to a parabolic model as studied by Othmer and Stevens (1997) and Levine and Sleeman (1997). In the latter paper, explicit solutions which blow-up in finite time were constructed. Here, we adapt their method to construct a corresponding blow-up solution of the hyperbolic model. This construction enables us to compare the blow-up times of the corresponding models. We find that the hyperbolic blow-up is always later than the parabolic blow-up. Moreover, we show that solutions of the hyperbolic problem become negative near blow-up. We calculate the zero-turning-rate time explicitly and we show that this time can be either larger or smaller than the parabolic blow-up time. The blow-up models as discussed here and elsewhere are limiting cases of more realistic models for chemotaxis. At the end of the paper we discuss the relevance to biology and exhibit numerical solutions of more realistic models.     

Periodic Wave Solutions and Their Limits for the Modified Kd V–KP Equations

In this paper, we use the bifurcation method of dynamical systems to study the periodic wave solutions and their limits for the modified Kd V–KP equations. Some explicit periodic wave solutions are obtained. These solutions contain smooth periodic wave solutions and periodic blow-up solutions. Their limits contain solitary wave solutions, periodic wave solutions, kink wave solutions and unbounded solutions.     

Non-simultaneous blow-up in localized reaction–diffusion equations

This article deals with blow-up solutions in reaction–diffusion equations coupled via localized exponential sources, subject to null Dirichlet conditions. The optimal and complete classification is obtained for simultaneous and non-simultaneous blow-up solutions. Moreover, blow-up rates and blow-up sets are also discussed. It is interesting that, in some exponent regions, blow-up phenomena depend sensitively on the choosing of initial data, and the localized nonlinearities play important roles in the blow-up properties of solutions.     

New exact solutions for the classical Drinfel’d–Sokolov–Wilson equation

In this paper, we investigate the classical Drinfel’d–Sokolov–Wilson equation (DSWE)

where p, q, r, s are some nonzero parameters. Some explicit expressions of solutions for the equation are obtained by using the bifurcation method and qualitative theory of dynamical systems. These solutions contain solitary wave solutions, blow-up solutions, periodic solutions, periodic blow-up solutions and kink-shaped solutions. Some previous results are extended.     

Properties of non-simultaneous blow-up solutions in nonlocal parabolic equations

This paper deals with blow-up solutions in parabolic equations coupled via nonlocal nonlinearities, subject to homogeneous Dirichlet conditions. Firstly, some criteria on non-simultaneous and simultaneous blow-up are given, including four kinds of phenomena: (i) the existence of non-simultaneous blow-up; (ii) the coexistence of non-simultaneous and simultaneous blow-up; (iii) any blow-up must be simultaneous; (iv) any blow-up must be non-simultaneous. Next, total versus single point blow-up are classified completely. Moreover, blow-up rates are obtained for both non-simultaneous and simultaneous blow-up solutions.