The semi‐iterative method applied to the hyper‐power iteration

The semi‐iterative method (SIM) is applied to the hyper‐power (HP) iteration, and necessary and sufficient conditions are given for the convergence of the semi‐iterative–hyper‐power (SIM–HP) iteration. The root convergence rate is computed for both the HP and SIM–HP methods, and the quotient convergence rate is given for the HP iteration. Copyright © 2005 John Wiley & Sons, Ltd.     

Quotient probabilistic normed spaces and completeness results

We introduce the concept of quotient in PN spaces and give some examples. We prove some theorems with regard to the completeness of a quotient.     

Examples of non-Kähler Hamiltonian circle manifolds with the strong Lefschetz property

In this paper we construct six-dimensional compact non-Kähler Hamiltonian circle manifolds which satisfy the strong Lefschetz property themselves but nevertheless have a non-Lefschetz symplectic quotient. This provides the first known counterexamples to the question whether the strong Lefschetz property descends to the symplectic quotient. We also give examples of Hamiltonian strong Lefschetz circle manifolds which have a non-Lefschetz fixed point submanifold. In addition, we establish a sufficient and necessary condition for a finitely presentable group to be the fundamental group of a strong Lefschetz manifold. We then use it to show the existence of Lefschetz four-manifolds with non-Lefschetz finite covering spaces.     

Fuzzy HX环的推广

为改进Fuzzy HX环的结果,使之包含Fuzzy商环,提出了弱Fuzzy HX环的概念,研究了它的性质与结构,并重新讨论了拟Fuzzy商环,证明了在正则条件下拟Fuzzy商环与弱Fuzzy HX环的统一性：同时也得到了一致弱Fuzzy HX环与普通Fuzzy商环的关系。     

Quotient normed cones

Given a normed cone (X, p) and a subconeY, we construct and study the quotient normed cone (X/Y,p) generated byY. In particular we characterize the bicompleteness of (X/Y, ‖·‖ ^p ,p) in terms of the bicompleteness of (X, p), and prove that the dual quotient cone ((X/Y)^*, || · ‖·‖^p,p) can be identified as a distinguished subcone of the dual cone (X ^*, || · ||_{p, u}). Furthermore, some parts of the theory are presented in the general setting of the spaceCL(X, Y) of all continuous linear mappings from a normed cone (X, p) to a normed cone (Y, q), extending several well-known results related to open continuous linear mappings between normed linear spaces.     

单轴晶体内表面入射e光线的双反射

基于光线遵从的Fermat原理,从几何学的角度讨论和分析了在单轴晶体中入射的e光线在界面上的双反射,得到了确定光线反射方向的一般公式,并对几种特殊情况进行了讨论.指出了上述结果与由电磁波的边界条件计算所得结果是一致的.     

On the Statistics of Partial Quotients of Finite Continued Fractions

We refine the remainder estimate in the asymptotic formula, earlier obtained in a joint paper with V. A. Bykovskii, for Arnold's problem about Gauss-Kuzmin statistics.     

A potentiometric investigation of the hydrolysis of chromate (VI) ion in NaCl media to 175°C

The hydrolysis of chromate ion was studied potentiometrically in a concentration cell fitted with hydrogen electrodes by titrating basic NaCl–Na₂CrO₄ solutions with standardized HCl against a NaOH reference solution. The temperature was varied from 25 to 175°C at 25° intervals at the following ionic strengths (I): 0.1140, 0.2346, 0.5337, 0.9988, 2.940, and 5.239 (NaCl). Depending on the ionic strength, the molality of total chromium was varied from 0.001 to 0.100. The resulting titration curves could be resolved best in terms of three equilibria involving the formation of HCrO ₄ ^– (aq), Cr₂O^3– (aq), and CrO₃Cl^– (aq). The equilibrium quotients for all three reactions were fitted as a function of temperature and ionic strength, and the molal thermodynamic parameters that were computed from these relationships are tabulated at specific ionic strengths over the experimental temperature range.     

铁缺乏症对婴幼儿智能发育的影响

为分析铁缺乏症(IDD)对婴幼儿智能发育的影响，随机抽取了6个月至3岁婴幼儿200例，按有否铁缺乏分组，比较了其与智能的关系。结果表明，铁缺乏症检出率为17．5％，铁缺乏组婴幼儿智能发育商(DQ)明显下降，与正常组比较差异有显著性，铁缺乏程度越重，DQ值越低。可见铁缺乏症对婴幼儿大脑发育造成不良影响，对该症无贫血阶段及轻度缺铁性贫血期(IDA)应予重视。     

A constructive proof by elementary transformations of Roth's removal theorems in the theory of matrix equations

W. E. Roth gave necessary and sufficient conditions for the existence of solution(s) of certain types of linear matrix equations. Proofs were based on invariant factors and were long and complicated. Other shorter but non-constructive proofs have since been provided by later authors. We present here very brief constructive proofs based on the simplest of mathematical techniques, namely row- and column-reduction of a matrix.