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.     

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 novel method for crack detection in beam-like structures by measurements of natural frequencies

A novel method is proposed for calculating the natural frequencies of a multiple cracked beam and detecting unknown number of multiple cracks from the measured natural frequencies. First, an explicit expression of the natural frequencies through crack parameters is derived as a modification of the Rayleigh quotient for the multiple cracked beams that differ from the earlier ones by including nonlinear terms with respect to crack severity. This expression provides a simple tool for calculating the natural frequencies of the beam with arbitrary number of cracks instead of solving the complicated characteristic equation. The obtained nonlinear expression for natural frequencies in combination with the so-called crack scanning method proposed recently by the authors allowed the development of a novel procedure for consistent identification of unknown amount of cracks in the beam with a limited number of measured natural frequencies. The developed theory has been illustrated and validated by both numerical and experimental results.     

A new framework for implicit restarting of the Krylov–Schur algorithm

This paper introduces a new framework for implicit restarting of the Krylov–Schur algorithm. It is shown that restarting with arbitrary polynomial filter is possible by reassigning some of the eigenvalues of the Rayleigh quotient through a rank‐one correction, implemented using only the elementary transformations (translation and similarity) of the Krylov decomposition. This framework includes the implicitly restarted Arnoldi (IRA) algorithm and the Krylov–Schur algorithm with implicit harmonic restart as special cases. Further, it reveals that the IRA algorithm can be turned into an eigenvalue assignment method. Copyright © 2014 John Wiley & Sons, Ltd.