The representability number of a chain

For each pair of linear orderings (L,M), the representability number repr_M(L) of L in M is the least ordinal α such that L can be order-embedded into the lexicographic power . The case is relevant to utility theory. The main results in this paper are as follows. (i) If κ is a regular cardinal that is not order-embeddable in M, then repr_M(κ)=κ; as a consequence, for each κω₁. (ii) If M is an uncountable linear ordering with the property that A×_lex2 is not order-embeddable in M for each uncountable AM, then for any ordinal α; in particular, . (iii) If L is either an Aronszajn line or a Souslin line, then .     

向量场的Nielsen数

对于紧致流形M上的任意一个向量场X，定义了一个由向量场X确定的自映射fX：M→M，使得向量场X的奇异点均为fX的不动点．证明了向量场的Nielsen数是不依赖于向量场选取的量．     

Electromigration of ionic micelles by the use of an isotachophoretic apparatus

Electromigration experiments of ionic surfactants were performed by using a capillary tube isotachophoretic apparatus. The zone of the migrated surfactant was collected after separation, and the surfactant concentration of the migrated zone was determined by HPLC analysis. The surfactant concentration of the migrated zone was increased with an increase in electrolyte concentration, and was in accord with the prediction of the Kohlrausch equation. When the electrolyte concentration further increased, the surfactant molecules began to migrate as a micellar state. Moreover, the mixed systems of ionic-non ionic and ionic-ionic surfactants were also examined and revealed the migration as mixed micelle.     

The system Y2O3−CaO−P2O5

The ternary system Y₂O₃?CaO?P₂O₅ has been examined by DTA, X-ray diffraction, IR and microscopic methods. Its phase diagram has been provided within the composition range YPO₄?Ca₃(PO₄)₂?P₂O₅. The occurrence of four mixed phosphates: Ca₃Y(PO₄)₃, CaYP₃O₁₀, CaY(PO₃)₅, Ca₂Y(PO₃)₇ has been discovered in the system. Basic X-ray data have been determined for these newly discovered compounds and several methods of their synthesis developed.     

Average distribution of prime ideals in families of number fields

We view an algebraic curve over ℚ as providing a one-parameter family of number fields and obtain bounds for the average value of some standard prime ideal counting functions over these families which are better than averaging the standard estimates for these functions.      

On Hyers-Ulam-Rassias stability of functional equations

In this paper, we investigate the stability of functional equation given by the pseudoadditive mappings of the mixed quadratic and Pexider type in the spirit of Hyers, Ulam, Rassias and Gavruta.     

图的双控制的一些新结果

图G=(V,E)的每个顶点控制它的闭邻域的每个顶点.S是一个顶点子集合,如果G的每一个顶点至少被S中的两个顶点控制,则称S是G的一个双控制集.把双控制集的最小基数称为双控制数,记为dd(G).本文探讨了双控制数和其它控制参数的一些新关系,推广了[1]的一些结果.并且给出了双控制数的Nordhaus-Gaddum类型的结果.     

γ-稳定图

本文我们引进γ- 稳定图,γ 稳定图和γ稳定图的概念,图G是γ- 稳定图(γ 稳定图),若任意删去G(增加G)的一条边都不改变G的控制数γ(G).一个γ稳定图指既是γ- 稳定图又是γ 稳定图的图.我们给出一些γ-(γ ,γ) 稳定图的性质和实例.     

ANALYTIC SOLUTIONS OF AN ITERATIVE EQUATION WITH FIRST ORDER DERIVATIVE

This paper is concerned with a nonlinear iterative equation with first order derivative. By construction a convergent power series solution, analytic solutions for the original equation are obtained.     

微小尺度下自然对流换热特性实验研究

采用直接电加热法对平均为101 μm、403μm及801μm的铜丝进行加热,使用高精度电阻仪测量电加热前及电加热后的铜丝的电阻值,根据温度与金属电阻之间的关系能够相当精确的测量整个铜丝电加热后的平均温度值。电加热时的电压及电流也同时被测量。实验结果表明,在自然对流条件下,实验得到的努谢尔特数与经典的准则关联式得到的努谢尔特数随着外径的减小,其偏差越来越大,最大偏差超过50％。