A remark on the Kochen-Specker theorem and some characterizations of the determinant on sets of Hermitian matrices

In this paper we describe the general forms of all (nonlinear) continuous functionals on the sets of positive definite, positive semi-definite and Hermitian matrices which are multiplicative on the commuting elements. As a consequence, we obtain some new characterizations of the determinant on those classes of matrices.

     

无限维奇Hamilton模李超代数的导子

本文首先确定了无限维奇Hamilton模李超代数的生成元集,然后确定了奇Hamilton模李超代数到广义Witt模李超代数的导子空间,进而确定了无限维奇Hamilton模李超代数的导子代数.     

TUHF代数上的Lie导子

证明了TUHF代数丁上的Lie导子L形如D l．其中D是T上的结合导子，l是从T到它的中心Z上的线性映射且零化T中的括积．     

一阶导数吸光光度法测定碘酸钾碘盐中碘

采用一阶导数吸光光度法测定碘酸钾碘盐中碘 ,线性范围为 0～ 12 μg·ml-1,检出限为1.6μg·ml-1,对盐样进行重复测定 ,相对标准偏差≤ 1.9% ,对样品进行加标回收试验 ,回收率在 97.0 %～ 10 2 .5 % ,结果良好     

Grassmann manifold of aJH-algebra

We study the set of rankp idempotents in a topologically simple Hilbert Jordan algebra (JH-algebra for short). To produce the differential geometric structure on, we establish Jordan algebraic results concerning the structure of some two-generator subalgebras. We identify geodesics, the Riemannian distance and the sectional curvature of by using the Jordan algebraic structure.     

Some remarks on the modulus of continuity of a conformal mapping of the disk onto a Jordan domain

Letd(;z, t) be the smallest diameter of the arcs of a Jordan curve with endsz andt. Consider the rapidity of decreasing ofd(;)=sup{d(;z, t):z, t , ¦z–t¦} (as 0,0) as a measure of nicety of . Letg(x) (x0) be a continuous and nondecreasing function such thatg(x)x,g(0)=0. Put¯g(x)=g(x)+x, h(x)=(¯g(x))². LetH(x) be an arbitrary primitive of 1/h ^–1(x). Note that the functionH ^–1 x is positive and increasing on (–, +),H ^–1 0 asx– andH ^–1+ asx +. The following statement is proved in the paper.Translated fromMatematicheskie Zametki, Vol. 60, No. 2, pp. 176–184, August, 1996.This research was supported by the Russian Foundation for Basic Research under grant No. 93-01-00236 and by the International Science Foundation under grant No. NCF000.     

一阶导数光谱K系数法同时测定硝基酚钠三组分

研究和建立了同时测定硝基酚钠混合三组份的新方法——一阶导数光谱K系数法。确定了最佳实验条件和测定波长,方法简便、快速、准确。通过对动植物细胞赋活增进剂中邻硝基酚钠、对硝基酚钠、5-硝基愈创木酚钠三组份的直接测定,其相对误差小于2%,相对标准偏差小于3%,回收率为99～103%。     

倍数光度滴定法测定微量过氧化苯甲酰

联合应用BPO与KIO3(在KI存在下)的倍增反应和光度滴定数据的二阶导数法处理,使面粉中微量BPO测定的灵敏度较常规碘量法提高了200倍,方法的检出限可达0.1 mg.L-1。在面粉实样分析中,测定结果的RSD值在1.3%~2.8%之间,加标回收率在98.6%~102.2%之间。提出的方法所得测定结果与国标法(GB/T 18415-2001)所得结果一致。     

Jordan operator algebras revisited

Jordan operator algebras are norm‐closed spaces of operators on a Hilbert space with for all . In two recent papers by the authors and Neal, a theory for these spaces was developed. It was shown there that much of the theory of associative operator algebras, in particular, surprisingly much of the associative theory from several recent papers of the first author and coauthors, generalizes to Jordan operator algebras. In the present paper we complete this task, giving several results which generalize the associative case in these papers, relating to unitizations, real positivity, hereditary subalgebras, and a couple of other topics. We also solve one of the three open problems stated at the end of our earlier joint paper on Jordan operator algebras.