Common complements of two subspaces of a Hilbert space

In this paper we find a necessary and sufficient condition for two closed subspaces, and , of a Hilbert space to have a common complement, i.e. a subspace having trivial intersection with and and such that .Unlike the finite-dimensional case the condition is significantly more subtle than simple equalities of dimensions and codimensions, and non-trivial examples of subspaces without a common complement are possible.     

An enhanced common path interference optic measurement system for refractive indices and thickness

This study proposes a common path interference optical system for the measurement of refractive indices and thickness of uniaxial crystal material. The measurement system comprises an accurate Mach–Zehnder laser interferometer, a single-axis rotary stepping motor, and a computer. The laser interferometer is composed of a single-frequency He–Ne laser, two-beam splitters and two reflectors. The Mach–Zehnder laser interferometer measures the optical length difference by using its linear measurement accuracy. The proposed solution procedure enables both the refractive indices and the thickness of the optical waveplate to be obtained. The proposed design differs from conventional designs in that it does not use a heterodyne modulator with a lock-in technique. It is shown that the refractive indices and thickness of the tested optical elements can be measured rapidly and accurately.     

<Emphasis Type="Italic">ϕ</Emphasis>-pairs and common fixed points in cone metric spaces

In this paper we introduce a contractive condition, called ϕ-pair, for two mappings in the framework of cone metric spaces and we prove a theorem which assures existence and uniqueness of common fixed points for ϕ-pairs. Also we obtain a result on points of coincidence. These results extend and generalize well-known comparable results in the literature. The authors are supported by Università degli Studi di Palermo, R. S. ex 60%.     

Fixed point properties for semigroup of nonexpansive mappings on Fréchet spaces

In this paper, we shall establish a fixed point property on Fréchet spaces for left reversible semitopological semigroups generalizing some classical results.     

Convergence analysis of implicit iterative algorithms for asymptotically nonexpansive mappings

In this paper, we consider the weak and strong convergence of an implicit iterative process with errors for two finite families of asymptotically nonexpansive mappings in the framework of Banach spaces. Our results presented in this paper improve and extend the recent ones announced by many others.     

Viscoelastic properties of durum wheat and common wheat dough of different strengths

Linear viscoelastic properties (LVP) were determined for five durum wheat doughs and five common wheat doughs (representing four different classes of Canadian common wheat) of different strength using creep testing. A creep time of 10,000 s was sufficient to reach a state of steady state flow for all of the doughs. Creep compliances were analyzed in terms of a Burgers model. For the durum doughs, the entire elastic compliance curve was shifted to higher values as the strength of the dough (as measured by extensigraph) decreased, while the steady state viscosity increased with strength. For common wheat doughs, the elastic compliance curves were steeper and the steady state viscosities were lower than for durum doughs of comparable extensigraph strength. The retardation strengths associated with a maximum in the retardation spectra were lower for the stronger durum doughs than for common wheat doughs of comparable strength. Differences in the LVP between durum and common wheat doughs of similar extensigraph strength were interpreted in the context of physical gels with crosslinks and entanglements, whose contributions to material properties are difficult to distinguish in short-time creep or dynamic measurements. The increased extensibility of common wheat doughs relative to durum doughs of comparable extensigraph strength was attributed to a higher molecular weight fraction in the polypeptide chains, similar in some respects to end-linked bimodal polymer networks. The idea of considering these doughs as physical gels was supported by their stress relaxation behavior. Received: 6 February 2000 Accepted: 22 August 2000     

Common fixed point results for noncommuting mappings without continuity in cone metric spaces

The existence of coincidence points and common fixed points for mappings satisfying certain contractive conditions, without appealing to continuity, in a cone metric space is established. These results generalize several well-known comparable results in the literature.     

Ranking decision-making units using common weights in DEA

Data envelopment analysis (DEA) is a linear programming technique that is used to measure the relative efficiency of decision-making units (DMUs). Liu et al. (2008) [13] used common weights analysis (CWA) methodology to generate a CSW using linear programming. They classified the DMUs as CWA-efficient and CWA-inefficient DMUs and ranked the DMUs using CWA-ranking rules. The aim of this study is to show that the criteria used by Liu et al. are not theoretically strong enough to discriminate among the CWA-efficient DMUs with equal efficiency. Moreover, there is no guarantee that their proposed model can select one optimal solution from the alternative components. The optimal solution is considered to be the only unique optimal solution. This study shows that the proposal by Liu et al. is not generally correct. The claims made by the authors against the theorem proposed by Liu et al. are fully supported using two counter examples.     

Mizoguchi–Takahashi’s type common fixed point theorem

Recently Kamran extended the result of Mizoguchi and Takahashi for closed multi-valued mappings and proved a fixed point theorem. In this paper we further extend the result concluded by Kamran and prove a common fixed point theorem by using the concept of lower semi-continuity.     

Common fixed points of almost generalized contractive mappings in ordered metric spaces

The existence theorems of common fixed points for two weakly increasing mappings satisfying an almost generalized contractive condition in ordered metric spaces are proved. Some comparative example are constructed which illustrate the values of the obtained results in comparison to some of the existing ones in literature.