Convergence Properties and Fixed Points of Two General Iterative Schemes with Composed Maps in Banach Spaces with Applications to Guaranteed Global Stability

This paper investigates the boundedness and convergence properties of two general iterative processes which involve sequences of self-mappings on either complete metric or Banach spaces. The sequences of self-mappings considered in the first iterative scheme are constructed by linear combinations of a set of self-mappings, each of them being a weighted version of a certain primary self-mapping on the same space. The sequences of self-mappings of the second iterative scheme are powers of an iteration-dependent scaled version of the primary self-mapping. Some applications are also given to the important problem of global stability of a class of extended nonlinear polytopic-type parameterizations of certain dynamic systems.

A New Type of Coincidence and Common Fixed Point Theorem with Applications

Coincidence and common fixed point theorems for a class of 'Ciric-Suzuki hybrid contractions involving a multivalued and two single-valued maps in a metric space are obtained. Some applications including the existence of a common solution for certain class of functional equations arising in a dynamic programming are also discussed..

Variation in the type and frequency of postoperative invasive Staphylococcus aureus infections according to type of surgical procedure.

OBJECTIVE: To determine the epidemiological characteristics of postoperative invasive Staphylococcus aureus infection following 4 types of major surgical procedures.design. Retrospective cohort study. SETTING: Eleven hospitals (9 community hospitals and 2 tertiary care hospitals) in North Carolina and Virginia. PATIENTS: Adults undergoing orthopedic, neurosurgical, cardiothoracic, and plastic surgical procedures. METHODS: We used previously validated, prospectively collected surgical surveillance data for surgical site infection and microbiological data for bloodstream infection. The study period was 2003 through 2006. We defined invasive S. aureus infection as either nonsuperficial incisional surgical site infection or bloodstream infection. Nonparametric bootstrapping was used to generate 95% confidence intervals (CIs). P values were generated using the Pearson chi2 test, Student t test, or Wilcoxon rank-sum test, as appropriate. RESULTS: In total, 81,267 patients underwent 96,455 procedures during the study period. The overall incidence of invasive S. aureus infection was 0.47 infections per 100 procedures (95% CI, 0.43-0.52); 227 (51%) of 446 infections were due to methicillin-resistant S.aureus. Invasive S. aureus infection was more common after cardiothoracic procedures (incidence, 0.79 infections per 100 procedures [95%CI, 0.62-0.97]) than after orthopedic procedures (0.37 infections per 100 procedures [95% CI, 0.32-0.42]), neurosurgical procedures (0.62 infections per 100 procedures [95% CI, 0.53-0.72]), or plastic surgical procedures (0.32 infections per 100 procedures [95% CI, 0.17-0.47]) (P < .001). Similarly, S. aureus bloodstream infection was most common after cardiothoracic procedures (incidence, 0.57 infections per 100 procedures [95% CI, 0.43-0.72]; P < .001, compared with other procedure types), comprising almost three-quarters of the invasive S. aureus infections after these procedures. The highest rate of surgical site infection was observed after neurosurgical procedures (incidence, 0.50 infections per 100 procedures [95% CI, 0.42-0.59]; P < .001, compared with other procedure types), comprising 80% of invasive S.aureus infections after these procedures. CONCLUSION: The frequency and type of postoperative invasive S. aureus infection varied significantly across procedure types. The highest risk procedures, such as cardiothoracic procedures, should be targeted for ongoing preventative interventions.

Spaces of observation and obscurity: cinematic prisons of light and dark

In The Eye of Power, Foucault delineated the key concerns surrounding hospital architecture in the latter half of the eighteenth century as being the ‘visibility of bodies, individuals and things'. As such, the ‘new form of hospital' that came to be developed ‘was at once the effect and support of a new type of gaze'. This was a gaze that was not simply concerned with ways of minimising overcrowding or cross-contamination. Rather, this was a surveillance intended to produce knowledge about the pathological bodies contained within the hospital walls. This would then allow for their appropriate classification. Foucault went on to describe how these principles came to be applied to the architecture of prisons. This was exemplified for him in the distinct shape of Bentham's panopticon. This circular design, which has subsequently become an often misused synonym for a contemporary culture of surveillance, was premised on a binary of the seen and the not-seen. An individual observer could stand at the central point of the circle and observe the cells (and their occupants) on the perimeter whilst themselves remaining unseen. The panopticon in its purest form was never constructed, yet it conveys the significance of the production of knowledge through observation that became central to institutional design at this time and modern thought more broadly. What is curious though is that whilst the aim of those late eighteenth century buildings was to produce wellventilated spaces suffused with light, this provoked an interest in its opposite. The gothic movement in literature that was developing in parallel conversely took a ‘fantasy world of stone walls, darkness, hideouts and dungeons…' as its landscape (Vidler, 1992: 162). Curiously, despite these modern developments in prison design, the façade took on these characteristics. The gothic imagination came to describe that unseen world that lay behind the outer wall. This is what Evans refers to as an architectural ‘hoax'. The façade was taken to represent the world within the prison walls and it was the façade that came to inform the popular imagination about what occurred behind it. The rational, modern principles ordering the prison became conflated with the meanings projected by and onto the façade. This confusion of meanings have then been repeated and reenforced in the subsequent representations of the prison. This is of paramount importance since it is the cinematic and televisual representation of the prison, as I argue here and elsewhere, that maintain this erroneous set of meanings, this ‘hoax'.

Investigation of DNA polymorphisms in SMAD genes for genetic predisposition to diabetic nephropathy in patients with type 1 diabetes mellitus

Aims/hypothesis: SMAD proteins are involved in multiple signalling pathways and are key modulators of gene expression. We hypothesised that genetic variation in selected SMAD genes contributes to susceptibility to diabetic nephropathy. Methods: We selected 13 haplotype tag (ht) single nucleotide polymorphisms (SNPs) from 67 variants identified by resequencing the SMAD2 and SMAD3 genes. For SMAD1, SMAD4 and SMAD5 genes, genotype data were downloaded for 217 SNPs from Phase II of the International HapMap project. Of these, 85 SNPs met our inclusion criteria, resulting in the selection of 13 tag SNPs for further investigation. A case-control approach was employed, using 267 nephropathic patients and 442 controls with type 1 diabetes from Ireland. Two further populations (totalling 1,407 patients, 2,238 controls) were genotyped to validate initial findings. Genotyping was conducted using iPLEX, TaqMan and gel electrophoresis.
Results: The distribution of genotypes was in Hardy-Weinberg equilibrium. Analysis by the ? 2 test of genotype and allele frequencies in patients versus controls in the Irish population (n?=?709) revealed evidence for the association of one allele at 5% level of significance (rs10515478, p uncorrected?=?0.006; p corrected?=?0.04). This finding represents a relatively small difference in allele frequency of 6.4% in the patient group compared with 10.7% in the control group; this difference was not supported in subsequent investigations using DNA from European individuals with similar phenotypic characteristics.
Conclusions/interpretation: We selected an appropriate subset of variants for the investigation of common genetic risk factors and assessed SMAD1 to SMAD5 genes for association with diabetic nephropathy. We conclude that common polymorphisms in these genes do not strongly influence genetic susceptibility to diabetic nephropathy in white individuals with type 1 diabetes mellitus.

1-amenability of A(X) for Banach spaces with 1-unconditional bases

The main result of the note is a characterization of 1-amenability of Banach algebras of approximable operators for a class of Banach spaces with 1-unconditional bases in terms of a new basis property. It is also shown that amenability and symmetric amenability are equivalent concepts for Banach algebras of approximable operators, and that a type of Banach space that was long suspected to lack property A has in fact the property. Some further ideas on the problem of whether or not amenability (in this setting) implies property A are discussed.

Generation of metallosupramolecular polymer gels from multiply functionalized grid-type complexes

A ditopic ligand (1), containing two tridentate bis(acylhydrazone) subunits and bearing both long alkyl chains and hydrogen-bonding groups, has been synthesised. Metal cation binding in the presence of a base leads to hierarchical self-assembly, forming first a neutral [2 x 2] grid-type complex (2) that hierarchically assembles into metallosupramolecular polymer gels in toluene.

Boundary value problems for analytic functions in the class of Cauchy-type integrals with density in

We study the Riemann boundary value problem , for analytic functions in the class of analytic functions represented by the Cauchy-type integrals with density in the spaces with variable exponent. We consider both the case when the coefficient is piecewise continuous and it may be of a more general nature, admitting its oscillation. The explicit formulas for solutions in the variable exponent setting are given. The related singular integral equations in the same setting are also investigated. As an application there is derived some extension of the Szegö-Helson theorem to the case of variable exponents.

A model for information retrieval driven by conceptual spaces

A retrieval model describes the transformation of a query into a set of documents. The question is: what drives this transformation? For semantic information retrieval type of models this transformation is driven by the content and structure of the semantic models. In this case, Knowledge Organization Systems (KOSs) are the semantic models that encode the meaning employed for monolingual and cross-language retrieval. The focus of this research is the relationship between these meanings’ representations and their role and potential in augmenting existing retrieval models effectiveness. The proposed approach is unique in explicitly interpreting a semantic reference as a pointer to a concept in the semantic model that activates all its linked neighboring concepts. It is in fact the formalization of the information retrieval model and the integration of knowledge resources from the Linguistic Linked Open Data cloud that is distinctive from other approaches. The preprocessing of the semantic model using Formal Concept Analysis enables the extraction of conceptual spaces (formal contexts)that are based on sub-graphs from the original structure of the semantic model. The types of conceptual spaces built in this case are limited by the KOSs structural relations relevant to retrieval: exact match, broader, narrower, and related. They capture the definitional and relational aspects of the concepts in the semantic model. Also, each formal context is assigned an operational role in the flow of processes of the retrieval system enabling a clear path towards the implementations of monolingual and cross-lingual systems. By following this model’s theoretical description in constructing a retrieval system, evaluation results have shown statistically significant results in both monolingual and bilingual settings when no methods for query expansion were used. The test suite was run on the Cross-Language Evaluation Forum Domain Specific 2004-2006 collection with additional extensions to match the specifics of this model.

Variational approach in weighted Sobolev spaces to scattering by unbounded rough surfaces

We consider the problem of scattering of time harmonic acoustic waves by an unbounded sound soft surface which is assumed to lie within a finite distance of some plane. The paper is concerned with the study of an equivalent variational formulation of this problem set in a scale of weighted Sobolev spaces. We prove well-posedness of this variational formulation in an energy space with weights which extends previous results in the unweighted setting [S. Chandler-Wilde and P. Monk, SIAM J. Math. Anal., 37 (2005), pp. 598–618] to more general inhomogeneous terms in the Helmholtz equation. In particular, in the two-dimensional case, our approach covers the problem of plane wave incidence, whereas in the three-dimensional case, incident spherical and cylindrical waves can be treated. As a further application of our results, we analyze a finite section type approximation, whereby the variational problem posed on an infinite layer is approximated by a variational problem on a bounded region.

A note on the Fredholm properties of Toeplitz operators on weighted Bergman spaces with matrix-valued symbols

We characterize the essential spectra of Toeplitz operators Ta on weighted Bergman spaces with matrix-valued symbols; in particular we deal with two classes of symbols, the Douglas algebra C+H∞ and the Zhu class Q := L∞ ∩VMO∂ . In addition, for symbols in C+H∞ , we derive a formula for the index of Ta in terms of its symbol a in the scalar-valued case, while in the matrix-valued case we indicate that the standard reduction to the scalar-valued case fails to work analogously to the Hardy space case. Mathematics subject classification (2010): 47B35,

Toeplitz operators on Bergman spaces with locally integrable symbols

We study the boundedness of Toeplitz operators $T_a$ with locally integrable symbols on Bergman spaces $A^p(\mathbb{D})$, $1 < p < \infty$. Our main result gives a sufficient condition for the boundedness of $T_a$ in terms of some ``averages'' (related to hyperbolic rectangles) of its symbol. If the averages satisfy an ${o}$-type condition on the boundary of $\mathbb{D}$, we show that the corresponding Toeplitz operator is compact on $A^p$. Both conditions coincide with the known necessary conditions in the case of nonnegative symbols and $p=2$. We also show that Toeplitz operators with symbols of vanishing mean oscillation are Fredholm on $A^p$ provided that the averages are bounded away from zero, and derive an index formula for these operators.

The Brownian traveller on manifolds

We study the inuence of the intrinsic curvature on the large time behaviour of the heat equation in a tubular neighbourhood of an unbounded geodesic in a two-dimensional Riemannian manifold. Since we consider killing boundary conditions, there is always an exponential-type decay for the heat semigroup. We show that this exponential-type decay is slower for positively curved manifolds comparing to the at case. As the main result, we establish a sharp extra polynomial-type decay for the heat semigroup on negatively curved manifolds comparing to the at case. The proof employs the existence of Hardy-type inequalities for the Dirichlet Laplacian in the tubular neighbourhoods on negatively curved manifolds and the method of self-similar variables and weighted Sobolev spaces for the heat equation.

Toeplitz operators on Dirichlet-Besov spaces

We study Toeplitz operators on the Besov spaces in the case of the open unit disk. We prove that a symbol satisfying a weak Lipschitz type condition induces a bounded Toeplitz operator. Such symbols do not need to be bounded functions or have continuous extensions to the boundary of the open unit disk. We discuss the problem of the existence of nontrivial compact Toeplitz operators, and also consider Fredholm properties and prove an index formula.