Fuzzy Entropy： Axiomatic Definition and Neural Networks Model

The measure of uncertainty is adopted as a measure of information. The measures of fuzziness are known as fuzzy information measures. The measure of a quantity of fuzzy information gained from a fuzzy set or fuzzy system is known as fuzzy entropy. Fuzzy entropy has been focused and studied by many researchers in various fields. In this paper, firstly, the axiomatic definition of fuzzy entropy is discussed. Then, neural networks model of fuzzy entropy is proposed, based on the computing capability of neural networks. In the end, two examples are discussed to show the efficiency of the model.     

测定汞原子塞曼谱线相对强度

在原塞曼效应实验基础上，测定了塞曼分裂各谱线的相对强度，以作为原实验的补充．     

不锈钢丝网上薄膜TiO2光催化剂的Raman光谱研究

用Raman光谱方法来研究用Sol Gel法负载于金属丝网的薄膜TiO2 光催化剂的物相结构、厚度以及粒径大小。研究结果显示 ,薄膜达到一定厚度能够阻止基底Fe元素向薄膜表层的扩散 ;在 4 0 0℃下灼烧制得的薄膜TiO2 光催化剂具有锐钛矿晶型 ,而高于 4 0 0℃时 ,将出现金红石相TiO2 ;锐钛矿晶型TiO2 的Raman特征峰产生偏移 ,表明薄膜粒径的变化 ,通过计算表明 ,薄膜TiO2 的粒径为 10nm左右 ,TEM的分析结果也与之一致。     

Conversion of ketoximes to ketones with trimethylphosphine and 2,2′-dipyridyl diselenide

Use of trimethylphosphine (Me₃P) and 2,2′-dipyridyl diselenide (PySeSePy) is an excellent method for the conversion of ketoximes to the corresponding ketones, since yields higher than 90% are obtained at rt within a few minutes (or hours for the more reluctant substrates, which do not react with Bu₃P/PhSSPh). In the simplest cases, the reaction can be completed with 30 mol % of PySeSePy, provided that an excess of phosphine is present in the reaction medium.     

Eigenvalues of the antiplane-shear crack problem for a power-law material

This paper discusses the problem of finding the eigenvalue spectrum in determining the stress and strain fields at the tip of an antiplane-shear crack in a power-law material. It is shown that the perturbation method provides an analytical dependence of the eigenvalue on the material nonlinearity parameter and the eigenvalue of the linear problem. Thus, it is possible to find the entire spectrum of eigenvalues and not only the eigenvalue of the Hutchinson-Rice-Rosengren problem. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 1, pp. 173–180, January–February, 2008.     

The supersymmetric WKB approximation of ring-shaped oscillator potential in r and θ dimensions with spherical polar coordinates

According to calculation of the energy spectrum of ring-shape oscillator potential by using the supersymmetric WKB approximation, it is shown that the energy spectrum of some noncentral separable potentials can be exactly obtained in r and θ dimensions by above method.     

关于阶乘的Erds-Stewart猜想

摘要:设n是正整数;P_0=1,P_i(i=1,2,…)是第i个素数.本文证明了:方程 n!+1=P_k~aP_(k+1)~b,P_(k-1)0,b>0,仅有解(n,P_k,P_(k+1),a,b)=(1,1,2,1,0),(2,3,5,1,0),(3,5,7,0,1),(4,5,7,2,0),(5,7,11,0,2).上述结果证实了Erds和Stewart提出的一个猜想.     

An Approach to Fuzzy Noncooperative Nash Games

Systems that involve more than one decision maker are often optimized using the theory of games. In the traditional game theory, it is assumed that each player has a well-defined quantitative utility function over a set of the player decision space. Each player attempts to maximize/minimize his/her own expected utility and each is assumed to know the extensive game in full. At present, it cannot be claimed that the first assumption has been shown to be true in a wide variety of situations involving complex problems in economics, engineering, social and political sciences due to the difficulty inherent in defining an adequate utility function for each player in these types of problems. On the other hand, in many of such complex problems, each player has a heuristic knowledge of the desires of the other players and a heuristic knowledge of the control choices that they will make in order to meet their ends.In this paper, we utilize fuzzy set theory in order to incorporate the players' heuristic knowledge of decision making into the framework of conventional game theory or ordinal game theory. We define a new approach to N-person static fuzzy noncooperative games and develop a solution concept such as Nash for these types of games. We show that this general formulation of fuzzy noncooperative games can be applied to solve multidecision-making problems where no objective function is specified. The computational procedure is illustrated via application to a multiagent optimization problem dealing with the design and operation of future military operations.     

HUA’S THEOREM WITH FIVE ALMOSTE QUAL PRIME VARIABLES

§1. IntroductionIn the additive theory of prime numbers, one studies the representation of positive in-tegers by powers of primes. For the quadratic case, Hua [1] proved that each large integercongruent to 5 modulo 24 can be written as the sum of ?ve squ…     

静压下半导体微腔内激子与光子行为的研究

由于腔模与激子对压力的依赖关系不同,所以可以选择不同的压力使激子和光场处于不同的耦合状态,从而实现对耦合的调谐。利用这种办法,我们观测到了代表激子与光场强耦合作用的Rabi分裂。由于在我们现有样品结构中压力对激子本征行为的影响很小,与以前报道的温度、电场等调谐方式相比,这种调谐方法不仅可以有效地调谐半导体微腔内激子与腔模的耦合程度,而且能够保持激子的本征性质在整个调谐过程中基本不变。这有助于研究在强耦合过程中激子极化激元的本征性质。将实验结果与压力下激子与腔模耦合理论进行拟合,得出了正确的Rabi分裂值。