关于非双倍测度的极大函数的一点注记

用Besicovitch覆盖定理证明了∫Rn（N1f（x））pφ（x）dμ（x）≤∫CRn︱f（x）︱pN2φ（x）dμ（x）,1〈p≤∞,其中μ是Rn上不需要双倍条件的Borel测度,φ（x）是非负可测的函数,N1,N2代表某些极大函数.进一步,还给出了关于这些极大函数的向量值不等式.     

On Modifications of Continuous and Discrete Maximum Principles for Reaction-Diffusion Problems

In this work, we present and discuss some modifications, in the form of two-sided estimation (and also for arbitrary source functions instead of usual sign-conditions), of continuous and discrete maximum principles for the reaction-diffusion problems solved by the finite element and finite difference methods.     

伪单调的广义向量拟均衡问题系统

在Hausdorff拓扑线性空间中,引入一类向量伪单调映射,讨论伪单调映射广义向量拟均衡问题系统的有效解与强解;在较弱的锥连续条件下,利用推广的极大元定理,建立两类解之间的联系,证明两类解的存在定理,而且得到解集的紧性。     

反向混合单调算子的藕合不动点定理

在实Banach空间中,利用锥理论和单调迭代技巧,研究一类反向混合单调算子的藕合不动点存在唯一性和迭代收敛性问题,得到了一些新结果。所得的主要结果推广了最近一些文献中的相应的结论。如文[9]中讨论的减映象的不动点定论。     

多噪声背景下光码分多址多用户干扰的抑制

针对光码分多址(OCDMA)的多用户干扰问题, 研究采用APD光电检测器的系统中存在多种噪声情况下, 基于最大值判决的光码分多址并行干扰抑制方法的多用户干扰抑制效果。阐述了其工作原理, 即在发送端对比特“0”和比特“1”分别使用一个地址码和它的移位变形进行映射, 以避免发送比特“0”时无光脉冲通过, 实现并行干扰抑制; 接收端判决电路采用最大值判决, 以避免门限判决所引起的误判, 进一步减小多用户干扰。系统采用光正交码作为地址码, 分析推导了系统的误码率表达式。根据所得的误码率表达式, 进行了数值仿真并与其他多用户干扰抑制方法进行比较。仿真结果表明, 本方法对多用户干扰的抑制作用与系统用户数和码重有关; 与引入双硬限幅器方法、多比特传输方法的多用户干扰抑制作用相比, 抑制效果要优于多比特传输的方法; 当接收功率较低时, 该方法优于引入双硬限幅器的方法, 因此可以有效的抑制多用户干扰。     

A Dynamical Uncertainty Principle in von Neumann Algebras by Operator Monotone Functions

Suppose that A ₁,…,A _N are observables (selfadjoint matrices) and ρ is a state (density matrix). In this case the standard uncertainty principle, proved by Robertson, gives a bound for the quantum generalized variance, namely for det {Cov  _ρ (A _j ,A _k )}, using the commutators [A _j ,A _k ]; this bound is trivial when N is odd. Recently a different inequality of Robertson-type has been proved by the authors with the help of the theory of operator monotone functions. In this case the bound makes use of the commutators [ρ,A _j ] and is non-trivial for any N. In the present paper we generalize this new result to the von Neumann algebra case. Nevertheless the proof appears to simplify all the existing ones.     

Persoz’s gephyroidal model described by a maximal monotone differential inclusion

Persoz’s gephyroidal model, which consists of elementary rheological models (dry friction element and linear spring), can be covered by the existence and uniqueness theory for maximal monotone operators. Moreover, classical results of numerical analysis allow one to use a numerical implicit Euler scheme, with convergence order of the scheme equal to one. Some numerical simulations are presented.     

Acta Mathematica Scientia

1IntroductionLetfibeaboundeddomainOfR"withsmoothboundaryoff,KCL'(fl)xL'(fl)beasubsetdefinedasfollows:K={(yi,yi)EL'(fl)xL'(fl);yi(x) p(yl(x))30,a.e.infi},(1)withwhichisamaximalmonotonegraphonRxR.Whereaisapositiveconstant.Ourmainproblemisasfollows:(O)MinimizeL(y,u)={'[g(y(t)) h(u(t))]at,overallpairssubjecttotheconditionsOurbasichypothesesaboutgandharethefollowing:(H)Bothgandh:L'(fl)~(--co, co]arelowersendcontinuous,convexsproperfunctionals,withg(y)相似文献   

Nonlinear boundary value problems

In this paper we consider two quasilinear boundary value problems. The first is vector valued and has periodic boundary conditions. The second is scalar valued with nonlinear boundary conditions determined by multivalued maximal monotone maps. Using the theory of maximal monotone operators for reflexive Banach spaces and the Leray-Schauder principle we establish the existence of solutions for both problems.