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In this paper, we study common fixed point properties for a family of mappings. We present the extensions of Caristi's fixed point theorem and Markov–Kakutani fixed point theorem for a family of set-valued mappings. [ABSTRACT FROM AUTHOR]

Motivated by the beautiful work of M.A. Rieffel (1965) and of M.E. Walter (1974), we obtain characterisations of the Fourier algebra A ( G ) of a locally compact group G in terms of the class of F -algebras (i.e. a Banach algebra A such that its dual A ′ is a W ⁎ -algebra whose identity is multiplicative on A ). For example, we show that the Fourier algebras are precisely those commutative semisimple F -algebras that are Tauberian, contain a nonzero real element, and possess a dual semigroup that acts transitively on their spectrums. Our characterisations fall into three flavours, where the first one will be the basis of the other two. The first flavour also implies a simple characterisation of when the predual of a Hopf–von Neumann algebra is the Fourier algebra of a locally compact group. We also obtain similar characterisations of the Fourier–Stieltjes algebras of G . En route, we prove some new results on the problem of when a subalgebra of A ( G ) is the whole algebra and on representations of discrete groups. [ABSTRACT FROM AUTHOR]

A well-known result of W. Ray asserts that if C is an unbounded convex subset of a Hilbert space, then there is a nonexpansive mapping T : C → C that has no fixed point. In this paper we establish some common fixed point properties for a semitopological semigroup S of nonexpansive mappings acting on a closed convex subset C of a Hilbert space, assuming that there is a point c ∈ C with a bounded orbit and assuming that certain subspace of C b ( S ) has a left invariant mean. Left invariant mean (or amenability) is an important notion in harmonic analysis of semigroups and groups introduced by von Neumann in 1929 [28] and formalized by Day in 1957 [5] . In our investigation we use the notion of common attractive points introduced recently by S. Atsushiba and W. Takahashi. [ABSTRACT FROM AUTHOR]

A major use of residual biomass from forestry and agriculture is densification into biomass pellets. Laboratory-scale fuel pellet research involves data analysis and model building, often using a single pellet mechanical press to make the biomass pellets (mass < 1 g) at a slow production rate. However, this single pelletising approach is considered not practically possible to produce the mass of pellets (∼500 g) required for determining their mechanical durability in accordance with the ISO standard method (ISO 17831-1) adopted by industry. In this study, wood pellets were tested for single pellet durability in a single pellet durability tester. The first test was done to mimic the situation when wood pellets are exposed to humid environmental conditions during storage. It involved six treatments – three types of pellets and two levels of moisture content. The second test mimicked the situation when light rain may expose the pellets to liquid water during the loading and unloading of ships. The main objective was to develop a quantitative relationship between the tumbler durability Dt (industry standard) and Dsp the single pellet durability. Results showed that the variability of Dsp was much larger when single pellet durability had lower values. Dsp was found to be strongly correlated with Dt (R2 = 0.94) when single pellet durability had high values. A linear equation can accurately convert Dsp to Dt when wood pellet moisture content is below 10% w.b. • Single pellet (Dsp) and tumbler (Dt) durability were determined for wood pellets. • Dsp variability was much larger when single pellet durability had lower values. • Dsp strongly correlated with Dt (R2 = 0.94) when single pellet durability was high. • Linear equation accurately converts Dsp to Dt if pellet moisture content <10%. [ABSTRACT FROM AUTHOR]

Abstract: Let G be an admissible compact Hausdorff right topological group, that is, a group with a Hausdorff topology such that for each , the map is continuous, and the set of such that the map is continuous is dense in G. Such groups arise in the study of distal flows. In this paper we study the Fourier–Stieltjes algebra , the linear span of the continuous positive definite functions on G. We show that is isomorphic with the Fourier–Stieltjes algebra of an associated compact topological group. This result is then applied to obtain some geometric properties including the weak and -fixed point properties on . We also study some related properties on the measure algebra . [Copyright &y& Elsevier]

Abstract: This paper is devoted to the study of orthogonality and disjointness preserving linear maps between Fourier and Fourier–Stieltjes algebras of locally compact groups. We show that a linear bijection (resp. ) between two Fourier algebras (resp. Fourier–Stieltjes algebras) of locally compact groups will induce a topological group isomorphism between and , provided that Ψ preserves both disjointness and some kind of orthogonality. This improves earlier results of J.J. Font and M.S. Monfared, where amenability of the groups or continuity of the linear maps are assumed. We also study the structure of bounded and unbounded disjointness preserving linear functionals of Fourier algebras. In the development, general results about disjointness and orthogonality preserving linear maps between -algebras, -algebras and their preduals are obtained. [Copyright &y& Elsevier]

Abstract: In this paper we show that the Fourier–Stieltjes algebra of a non-compact locally compact group G cannot have the fixed point property for nonexpansive mappings. This answers two open problems posed at a conference in Marseille-Luminy in 1989. We also show that a locally compact group is compact exactly if the asymptotic centre of any non-empty closed bounded convex subset C in with respect to a decreasing net of bounded subsets is a non-empty norm compact subset. In particular, when G is compact, has the fixed point property for left reversible semigroups. This generalizes a classical result of T.C. Lim for the circle group. As a consequence of our main results we obtain that a number of properties, some of which were known to hold for compact groups, in fact characterize compact groups. [Copyright &y& Elsevier]

Abstract: In this paper we study fixed point properties for semitopological semigroup of nonexpansive mappings on a bounded closed convex subset of a Banach space. We also study a Schauder fixed point property for a semitopological semigroup of continuous mappings on a compact convex subset of a separated locally convex space. Such semigroups properly include the class of extremely left amenable semitopological semigroups, the free commutative semigroup on one generator and the bicyclic semigroup . [Copyright &y& Elsevier]

Abstract: This paper is an invitation to the study of the Fourier–Stieltjes algebra , the linear span of the continuous positive definite complex-valued functions on a topological group G. We study , when G has a host algebra or a group -algebra, the analogue of the group -algebra of a locally compact group. Our main challenge is that a topological group G cannot have a positive regular Borel measure which is left translation invariant unless G is locally compact. [Copyright &y& Elsevier]

Abstract: In this paper we investigate when various Banach algebras associated to a locally compact group G have the weak or weak∗ fixed point property for left reversible semigroups. We proved, for example, that if G is a separable locally compact group with a compact neighborhood of the identity invariant under inner automorphisms, then the Fourier–Stieltjes algebra of G has the weak∗ fixed point property for left reversible semigroups if and only if G is compact. This generalizes a classical result of T.C. Lim for the case when G is the circle group T. [Copyright &y& Elsevier]

Abstract: In this paper, we explore the properties of projections of norm one on general Banach algebras, in particular the relation with conditional expectations for algebras which arise in harmonic analysis. [Copyright &y& Elsevier]

Abstract: In recent years, there have been considerable interests in the study of when a closed convex subset K of a Banach space has the fixed point property, i.e. whenever T is a non-expansive mapping from K into K, then K contains a fixed point for T. In this paper we shall study fixed point properties of semigroups of non-expansive mappings on weakly compact convex subsets of a Banach space (or, more generally, a locally convex space). By considering the classes of bicyclic semigroups we answer two open questions, one posted earlier by the first author in 1976 (Dalhousie) and the other posted by T. Mitchell in 1984 (Virginia). We also provide a characterization for the existence of a left invariant mean on the space of weakly almost periodic functions on separable semitopological semigroups in terms of fixed point property for non-expansive mappings related to another open problem raised by the first author in 1976. [Copyright &y& Elsevier]

Abstract: The purpose of this addendum is to clarify two shortcomings in the paper of the title. [Copyright &y& Elsevier]

We introduce the notion of a generalised F-algebra as a Banach algebra A whose Banach space dual is a J B W ⁎ -triple with a certain additional condition on a distinguished character of A. This generalises the well-known notion of F -algebras, which in turn, includes as special cases many important classes of Banach algebras on locally compact groups and semigroups. Our main use of this new notion is to give some axiomatic characterisations of the Fourier algebras on locally compact groups, strengthening our previous work [37]. But we also quickly review some well-known results in F -algebras that can be extended to the context of generalised F -algebras. [ABSTRACT FROM AUTHOR]

Durability, a crucial parameter in determining the quality of a wood pellet, is affected by moisture adsorption from the air. The conditions in a confined space in which pellets are stored can be characterised as active or passive. In the active case, the interstitial air within the pile circulates around the pellets, whereas in the passive case, the interstitial air is stagnant. These two cases represent stored pellets in a ventilated silo (active) or in a ship's hold (passive). Commercial wood pellets were exposed to humid air in a humidity chamber with circulating air set at 95% relative humidity (RH) and 30 °C for up to 24 h. The wood pellets were also exposed to a range of RH values (11–90%) for four weeks, created using saturated salt solutions. The durability of pellets, volumetric swelling, and pellet density were measured. For pellets exposed to 95% RH, the durability of pellets, initially at 99%, dropped to below 80% after 10 h. A similar drop in durability was observed for pellets stored above saturated salt solutions but after a longer storage period. The density of pellets initially increased when pellets had a moisture content of 0.05–0.08 decimal dry basis (db). The pellets expanded by 20–80% volumetrically when the moisture content exceeded 0.15 (db), resulting in a marked decrease in pellet density. • CT scans of the cross-section of a wood pellet exhibit axial and radial cracks. • These cracks may be responsible for humid air penetration into a pellet. • Pellet durability drops drastically when the adsorbed moisture exceeds 12%. • Pellet durability drops more severely in ventilated than in unventilated pellets. • The ventilation time with humid air should be short to lessen the durability loss. [ABSTRACT FROM AUTHOR]

The β1-adrenergic receptor (β1AR) has one predicted site of N-linked glycosylation on its extracellular amino-terminus, but the glycosylation and potential functional importance of this site have not yet been examined. We show here that the β1AR is glycosylated in various cell types and that mutation of the single predicted site of N-linked glycosylation (N15A) results in the formation of receptors that are not N-glycosylated. The β1AR N15A mutant exhibited significantly decreased basal surface expression relative to the wild-type receptor but had no detectable deficits in ligand binding or agonist-promoted internalization. Co-immunoprecipitation experiments using Flag-tagged and HA-tagged receptors demonstrated that the β1AR-N15A mutant receptor exhibits a markedly reduced capacity for dimerization relative to wild-type β1AR. These data reveal that the β1AR is glycosylated on Asn15 and that this glycosylation plays a role in regulating β1AR surface expression and dimerization. [Copyright &y& Elsevier]