Open subgroups of

Let be a locally compact group and let denote the -algebra generated by left translation operators on . Let and be the spaces of almost periodic and weakly almost periodic functionals on the Fourier algebra , respectively. It is shown that if contains an open abelian subgroup, then (1) if and only if is norm dense in ; (2) is a -algebra if is norm dense in , where denotes the set of elements in with compact support. In particular, for any amenable locally compact group which contains an open abelian subgroup, has the dual Bohr approximation property and is a -algebra.

     

Numerical investigation of the effects of sluice spillway roof profiles on the hydraulic characteristics

There is a need for evolving hydraulically efficient roof profile of bellmouth for high head sluice spillways, as sluice roof is susceptible to cavitation damage. In this paper, formulation and development of a numerical model for simulating the spillway flow and its application to a sluice spillway are presented. The main focus of the simulation study is to apply the developed model to investigate the effects of sluice roof profile geometry on the pressure distribution, the discharge coefficient and the nature of flow regime within the sluice bellmouth. From the analysis of results for eight different roof profiles by varying the entry and exit angles of elliptic bellmouth transition, some important observations have been suggested, which are of practical relevance to hydraulic design engineers. The numerical model results are compared for one profile with physical model study. The simulated results are in close agreement with the measured values. Copyright © 2007 John Wiley & Sons, Ltd.     

复合冷凝空调机组的分析

以家用分体式空调作为节能改造对象,将传统单一冷凝改进为复合冷凝,即在压缩机排气管路上串联一个水冷冷凝器,吸收部分冷凝热制备生活热水。并在此基础上建立了分析模型。模拟计算结果表明,复合冷凝空调的目的效率得到了大大的提高,当空调的蒸发温度为0℃、冷凝温度为30℃时,空调目的效率由单一冷凝时的52%上升到70%。     

Common fixed point theorems for expansion mappings in various spaces

We prove expansion mappings theorems in various spaces i.e., metric spaces, generalized metric spaces, probabilistic metric spaces and fuzzy metric spaces, which generalize the results of various authors like Daffer and Kaneko [11], Ahmad, Ashraf and Rhoades [1], Vasuki [38], Rhoades [31] and Wang, Li, Gao and Iseki [40] etc. In the memory of 65^th birthday anniversary of his Father Late Sh. Ram Phool Sharma     

Fixed point theorems of Rothe and Altman types about convex-power condensing operator and application

In this paper, fixed point theorems of Rothe and Altman types about convex-power condensing operator are given and applied to the differential equation of one order with integral boundary conditions in abstract space.     

Strong convergence of an iterative method for non‐expansive mappings

Let E be a real reflexive Banach space having a weakly continuous duality mapping J_φ with a gauge function φ, and let K be a nonempty closed convex subset of E. Suppose that T is a non‐expansive mapping from K into itself such that F (T) ≠ ??. For an arbitrary initial value x₀ ∈ K and fixed anchor u ∈ K, define iteratively a sequence {x_n } as follows: x_{n +1} = α_n u + β_n x_n + γ_n Tx_n , n ≥ 0, where {α_n }, {β_n }, {γ_n } ? (0, 1) satisfies α_n +β_n + γ_n = 1, (C 1) lim_{n →∞} α_n = 0, (C 2) ∑^∞_{n =1} α_n = ∞ and (B) 0 < lim inf_{n →∞} β_n ≤ lim sup_{n →∞} β_n < 1. We prove that {x_n } converges strongly to Pu as n → ∞, where P is the unique sunny non‐expansive retraction of K onto F (T). We also prove that the same conclusions still hold in a uniformly convex Banach space with a uniformly Gâteaux differentiable norm or in a uniformly smooth Banach space. Our results extend and improve the corresponding ones by C. E. Chidume and C. O. Chidume [Iterative approximation of fixed points of non‐expansive mappings, J. Math. Anal. Appl. 318 , 288–295 (2006)], and develop and complement Theorem 1 of T. H. Kim and H. K. Xu [Strong convergence of modified Mann iterations, Nonlinear Anal. 61 , 51–60 (2005)]. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The rate of convergence for the cyclic projections algorithm III: Regularity of convex sets

The cyclic projections algorithm is an important method for determining a point in the intersection of a finite number of closed convex sets in a Hilbert space. That is, for determining a solution to the “convex feasibility” problem. This is the third paper in a series on a study of the rate of convergence for the cyclic projections algorithm. In the first of these papers, we showed that the rate could be described in terms of the “angles” between the convex sets involved. In the second, we showed that these angles often had a more tractable formulation in terms of the “norm” of the product of the (nonlinear) metric projections onto related convex sets.In this paper, we show that the rate of convergence of the cyclic projections algorithm is also intimately related to the “linear regularity property” of Bauschke and Borwein, the “normal property” of Jameson (as well as Bakan, Deutsch, and Li’s generalization of Jameson’s normal property), the “strong conical hull intersection property” of Deutsch, Li, and Ward, and the rate of convergence of iterated parallel projections. Such properties have already been shown to be important in various other contexts as well.     

Hyperbranched polymers generated from oxyanionic vinyl polymerization of commercially available methacrylate inimers

Hyperbranched polymethacrylates were prepared by means of oxyanionic vinyl polymerization of commercially available monomers, including hydroxyethyl methacrylate (HEMA) and poly(ethylene glycol) methacrylate (PEG‐MA). Hyperbranched polymethacrylates with high molecular weight were obtained with the complex of potassium hydride and 18‐crown‐6 as the initiator. The effect of 18‐crown‐6 is very important, and only oligomer can be obtained in the polymerization without 18‐crown‐6. The molecular structure of the hyperbranched polymers was confirmed with ¹H NMR and ¹³C NMR spectra. The ratio of initiator to monomer significantly affects the architecture of the resultant polymers. When the ratio of initiator to monomer equals 1 in the oxyanionic vinyl polymerization of HEMA, the degree of branching of the resulting polymer was calculated to be around 0.49. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 3502–3509, 2005     

Hamilton非二部图的弱泛圈性

图G称为弱泛圈图是指G包含了每个长为t(g(V)≤l≤c(G))的圈,其中g(G),c(v)分别是G的围长与周长.1997年Brandt提出以下猜想:边数大于[n2/4]-n 5的n阶非二部图为弱泛圈图.1999年Bollobas和Thomason证明了边数不小于[n2/4]-n 59的n阶非二部图为弱泛圈图.作者证明了如下结论:设G是n阶Hamilton非二部图,若G的边数不小于[n2/4]-n 12,则G为弱泛圈图.