The Arrow paradox with fuzzy preferences

This note considers a new factorization of a fuzzy weak binary preference relation into its asymmetric and symmetric parts. Arrow’s General Possibility Theorem is then examined within the resulting framework of vague individual and social preferences. The outcome of this exercise is compared with some earlier results available in the literature on the Arrow paradox with fuzzy preferences.     

Hilbert W*-模上的广义框架

本文给出了Hilbert W*-模上的标准广义框架的不相交,强不相交,弱不相交的定义,还给出了Hilbert W*-模上的广义框架的不相交,强不相交,弱不相交成立的条件,并且用算子理论的方法研究了它们的性质.     

模糊值二人零和对策的Nash均衡策略

我们将在Ramik定义的模糊最大序关系基础上研究模糊环境中的二人零和对策。在非对称模糊数基础上,引入模糊环境中的几种Nash均衡策略,讨论各种均衡策略存在的充要条件。并引入含参变量确定性矩阵对策及其均衡策略的概念,讨论含参变量确定性矩阵对策的Nash均衡策略和模糊值矩阵对策的均衡策略的关系。     

A large class of solutions for the instationary Navier–Stokes system

We investigate very weak solutions to the instationary Navier–Stokes system being contained in where is a bounded domain and . The chosen space of data is small enough to guarantee uniqueness of solutions and existence in case of small data or short time intervals. On the other hand, the data space is large enough that every vector field in is a very weak solution for appropriate data. The solutions and the data depend continuously on each other.      

Interpolation on weak martingale Hardy space

By the weak atomic decompositions of weak martingale Hardy spaces, we investigate the interpolation spaces between weak martingale Hardy spaces and martingale Hardy spaces.     

The p-adic quantum plane algebras and quantum Weyl algebra

Let q be a principal unit of the ring of valuation of a complete valued field K, extension of the field of p-adic numbers. Generalizing Mahler basis, K. Conrad has constructed orthonormal basis, depending on q, of the space of continuous functions on the ring of p-adic integers with values in K. Attached to q there are two models of the quantum plane and a model of the quantum Weyl algebra, as algebras of bounded linear operators on the space of p-adic continuous functions. For q not a root of unit, interesting orthonormal (orthogonal) families of these algebras are exhibited and providing p-adic completion of quantum plane and quantum Weyl algebras. The text was submitted by the authors in English.     

直觉判断矩阵的弱传递性与加型一致性研究

定义了直觉判断矩阵的有向图和有向路概念,证明在一定的条件下直觉判断矩阵的有向图有唯一有向路.利用该结论给出一个简洁的排序方法,并指出这种方法的不足之处.通过反例说明了直觉判断矩阵已有的加型一致性概念与弱传递性概念之间没有必然强弱关系.根据直觉模糊数的得分值和精确度值,利用效用的思想给出直觉判断矩阵加型一致性的新定义,并证明了新定义的加型一致性具有弱传递性.针对一般的直觉判断矩阵, 运用新定义的加型一致性概念以及偏差函数的方法给出了求解直觉判断矩阵的直觉模糊数型权重的模型,并通过算例验证了决策方法的实用性.     

Existence and Uniqueness of Weak Solutions to the $p$-Biharmonic Parabolic Equation

We consider an initial-boundary value problem for a $p$-biharmonic parabolic equation. Under some assumptions on the initial value, we construct approximate solutions by the discrete-time method. By means of uniform estimates on solutions of the time-difference equations, we establish the existence of weak solutions, and also discuss the uniqueness.     

弹光调制光电转换放大电路设计

弹光调制干涉具调制的干涉光被探测器接收后输出高速变化的微弱电信号,能否将该电信号提取并放大输出对弹光调制-傅里叶变换光谱仪的研制至关重要。通过对调制干涉光进行理论分析,设计一种具有高信噪比和较高带宽的光电转换放大电路,主要由电源电路、光电转换电路、放大电路、理论通频带为100 kHz~3.5 MHz的带通滤波电路组成。实验结果表明:设计的电路能够将探测器输出的最大频率为1.6 MHz的信号放大至670 mV左右,实现了将探测器输出的微弱速变电信号从背景噪声中有效提取与放大,为后续傅里叶变换提供可靠数据。     

Frictional contact problem for elastic-viscoplastic materials with thermal effect

A dynamic contact problem for elastic-viscoplastic materials with thermal effects is investigated. The contact is bilateral, and the friction is modeled with Tresca’s friction law with heat exchange. A variational formulation of the model is derived, and the existence of a unique weak solution is proved. The proofs are based on the classical result of nonlinear first order evolution inequalities, the equations with monotone operators, and the fixed point arguments. Finally, the continuous dependence of the solution on the friction yield limit is studied.