Universal elements for non-linear operators and their applications

We prove that under certain topological conditions on the set of universal elements of a continuous map T acting on a topological space X, that the direct sum T and M_g is universal, where M_g is multiplication by a generating element of a compact topological group. We use this result to characterize R_+-supercyclic operators and to show that whenever T is a supercyclic operator and z_1,...,z_n are pairwise different non-zero complex numbers, then the operator z_1T\oplus ... \oplus z_n T is cyclic. The latter answers affirmatively a question of Bayart and Matheron.

Non-weakly supercyclic operators

Several methods based on an easy geometric argument are provided to prove that a given operator is not weakly supercyclic. The methods apply to different kinds of operators like composition operators or bilateral weighted shifts. In particular, it is shown that the classical Volterra operator is not weakly supercyclic on any of the LP [0, 1] spaces, 1

Sequentially continuous non-linear fundamental systems of solutions of affine equations in locally convex spaces

According to the Mickael's selection theorem any surjective continuous linear operator from one Fr\'echet space onto another has a continuous (not necessarily linear) right inverse. Using this theorem Herzog and Lemmert proved that if $E$ is a Fr\'echet space and $T:E\to E$ is a continuous linear operator such that the Cauchy problem $\dot x=Tx$, $x(0)=x_0$ is solvable in $[0,1]$ for any $x_0\in E$, then for any $f\in C([0,1],E)$, there exists a continuos map $S:[0,1]\times E\to E$, $(t,x)\mapsto S_tx$ such that for any $x_0\in E$, the function $x(t)=S_tx_0$ is a solution of the Cauchy problem $\dot x(t)=Tx(t)+f(t)$, $x(0)=x_0$ (they call $S$ a fundamental system of solutions of the equation $\dot x=Tx+f$). We prove the same theorem, replacing "continuous" by "sequentially continuous" for locally convex spaces from a class which contains strict inductive limits of Fr\'echet spaces and strong duals of Fr\'echet--Schwarz spaces and is closed with respect to finite products and sequentially closed subspaces. The key-point of the proof is an extension of the theorem on existence of a sequentially continuous right inverse of any surjective sequentially continuous linear operator to some class of non-metrizable locally convex spaces.

K-Theory of non-linear projective toric varieties

We define a category of quasi-coherent sheaves of topological spaces on projective toric varieties and prove a splitting result for its algebraic K-theory, generalising earlier results for projective spaces. The splitting is expressed in terms of the number of interior lattice points of dilations of a polytope associated to the variety. The proof uses combinatorial and geometrical results on polytopal complexes. The same methods also give an elementary explicit calculation of the cohomology groups of a projective toric variety over any commutative ring.

Spectral isometries on non-simple C*-algebras

We prove that unital surjective spectral isometries on certain non-simple unital C*-algebras are Jordan isomorphisms. Along the way, we establish several general facts in the setting of semisimple Banach algebras.

Massive MIMO with Non-Ideal Arbitrary Arrays: Hardware Scaling Laws and Circuit-Aware Design

Massive multiple-input multiple-output (MIMO) systems are cellular networks where the base stations (BSs) are equipped with unconventionally many antennas, deployed on colocated or distributed arrays. Huge spatial degrees-of-freedom are achieved by coherent processing over these massive arrays, which provide strong signal gains, resilience to imperfect channel knowledge, and low interference. This comes at the price of more infrastructure; the hardware cost and circuit power consumption scale linearly/affinely with the number of BS antennas N. Hence, the key to cost-efficient deployment of large arrays is low-cost antenna branches with low circuit power, in contrast to today’s conventional expensive and power-hungry BS antenna branches. Such low-cost transceivers are prone to hardware imperfections, but it has been conjectured that the huge degrees-of-freedom would bring robustness to such imperfections. We prove this claim for a generalized uplink system with multiplicative phasedrifts, additive distortion noise, and noise amplification. Specifically, we derive closed-form expressions for the user rates and a scaling law that shows how fast the hardware imperfections can increase with N while maintaining high rates. The connection between this scaling law and the power consumption of different transceiver circuits is rigorously exemplified. This reveals that one can make the circuit power increase as p N, instead of linearly, by careful circuit-aware system design.

A systematic review and meta-analysis of the survival of non-feldspathic porcelain veneers over 5 and 10 years

PURPOSE: This systematic review aimed to report and explore the survival of dental veneers constructed from non-feldspathic porcelain over 5 and 10 years.

MATERIALS AND METHODS: A total of 4,294 articles were identified through a systematic search involving all databases in the Cochrane Library, MEDLINE (OVID), EMBASE, Web of Knowledge, specific journals (hand-search), conference proceedings, clinical trials registers, and collegiate contacts. Articles, abstracts, and gray literature were sought by two independent researchers. There were no language limitations. One hundred sixteen studies were identified for full-text assessment, with 10 included in the analysis (5 qualitative, 5 quantitative). Study characteristics and survival (Kaplan-Meier estimated cumulative survival and 95% confidence interval [CI]) were extracted or recalculated. A failed veneer was one which required an intervention that disrupted the original marginal integrity, had been partially or completely lost, or had lost retention more than twice. A meta-analysis and sensitivity analysis of Empress veneers was completed, with an assessment of statistical heterogeneity and publication bias. Clinical heterogeneity was explored for results of all veneering materials from included studies.

RESULTS: Within the 10 studies, veneers were fabricated with IPS Empress, IPS Empress 2, Cerinate, and Cerec computer-aided design/computer-assisted manufacture (CAD/CAM) materials VITA Mark I, VITA Mark II, Ivoclar ProCad. The meta-analysis showed the pooled estimate for Empress veneers to be 92.4% (95% CI: 89.8% to 95.0%) for 5-year survival and 66% to 94% (95% CI: 55% to 99%) for 10 years. Data regarding other non-feldspathic porcelain materials were lacking, with only a single study each reporting outcomes for Empress 2, Cerinate, and various Cerec porcelains over 5 years. The sensitivity analysis showed data from one study had an influencing and stabilizing effect on the 5-year pooled estimate.

CONCLUSION: The long-term outcome (> 5 years) of non-feldspathic porcelain veneers is sparsely reported in the literature. This systematic review indicates that the 5-year cumulative estimated survival for etchable non-feldspathic porcelain veneers is over 90%. Outcomes may prove clinically acceptable with time, but evidence remains lacking and the use of these materials for veneers remains experimental.

Recruiting faith and non-faith based schools, adolescents and parents to a cluster randomised sexual-health trial: experiences, challenges and lessons from the mixed-methods Jack Feasibility Trial

Background: The move toward evidence-based education has led to increasing numbers of randomised trials in schools. However, the literature on recruitment to non-clinical trials is relatively underdeveloped, when compared to that of clinical trials. Recruitment to school-based randomised trials is, however, challenging; even more so when the focus of the study is a sensitive issue such as sexual health. This article reflects on the challenges of recruiting post-primary schools, adolescent pupils and parents to a cluster randomised feasibility trial of a sexual health intervention, and the strategies employed to address them.
Methods: The Jack Trial was funded by the UK National Institute for Health Research (NIHR). It comprised a feasibility study of an interactive film-based sexual health intervention entitled If I Were Jack, recruiting over 800 adolescents from eight socio-demographically diverse post-primary schools in Northern Ireland. It aimed to determine the facilitators and barriers to recruitment and retention to a school-based sexual health trial and identify optimal multi-level strategies for an effectiveness study. As part of an embedded process evaluation, we conducted semi-structured interviews and focus groups with principals, vice-principals, teachers, pupils and parents recruited to the study as well as classroom observations and a parents’ survey.
Results: With reference to Social Learning Theory, we identified a number of individual, behavioural and environmental level factors which influenced recruitment. Commonly identified facilitators included perceptions of the relevance and potential benefit of the intervention to adolescents, the credibility of the organisation and individuals running the study, support offered by trial staff, and financial incentives. Key barriers were prior commitment to other research, lack of time and resources, and perceptions that the intervention was incompatible with pupil or parent needs or the school ethos.
Conclusions: Reflecting on the methodological challenges of recruiting to a school-based sexual health feasibility trial, this study highlights pertinent general and trial-specific facilitators and barriers to recruitment, which will prove useful for future trials with schools, adolescent pupils and parents.

Non-radial instabilities and progenitor asphericities in core-collapse supernovae

Since core-collapse supernova simulations still struggle to produce robust neutrino-driven explosions in 3D, it has been proposed that asphericities caused by convection in the progenitor might facilitate shock revival by boosting the activity of non-radial hydrodynamic instabilities in the post-shock region. We investigate this scenario in depth using 42 relativistic 2D simulations with multigroup neutrino transport to examine the effects of velocity and density perturbations in the progenitor for different perturbation geometries that obey fundamental physical constraints (like the anelastic condition). As a framework for analysing our results, we introduce semi-empirical scaling laws relating neutrino heating, average turbulent velocities in the gain region, and the shock deformation in the saturation limit of non-radial instabilities. The squared turbulent Mach number, 〈Ma2〉, reflects the violence of aspherical motions in the gain layer, and explosive runaway occurs for 〈Ma2〉 ≳ 0.3, corresponding to a reduction of the critical neutrino luminosity by ∼25∼25 per cent compared to 1D. In the light of this theory, progenitor asphericities aid shock revival mainly by creating anisotropic mass flux on to the shock: differential infall efficiently converts velocity perturbations in the progenitor into density perturbations δρ/ρ at the shock of the order of the initial convective Mach number Maprog. The anisotropic mass flux and ram pressure deform the shock and thereby amplify post-shock turbulence. Large-scale (ℓ = 2, ℓ = 1) modes prove most conducive to shock revival, whereas small-scale perturbations require unrealistically high convective Mach numbers. Initial density perturbations in the progenitor are only of the order of Ma2progMaprog2 and therefore play a subdominant role.