Unbounded B-Fredholm operators on Hilbert spaces

This paper is concerned with the study of a class of closed linear operators densely defined on a Hilbert space H and called B-Fredholm operators. We characterize a B-Fredholm operator as the direct sum of a Fredholm closed operator and a bounded nilpotent operator. The notion of an index of a B-Fredholm operator is introduced and a characterization of B-Fredholm operators with index 0 is given in terms of the sum of a Drazin closed operator and a finite-rank operator. We analyse the properties of the powers Tm of a closed B-Fredholm operator and we establish a spectral mapping theorem

B-Weyl spectrum and poles of the resolvent

AbstractLet T be a bounded linear operator acting on a Banach space and let σBW(T)={λ∈Csuch thatT−λIis not a B-Fredholm operator of index0} be the B-Weyl spectrum of T. Define also E(T) to be the set of all isolated eigenvalues in the spectrum σ(T) of T, and Π(T) to be the set of the poles of the resolvent of T. In this paper two new generalized versions of the classical Weyl's theorem are considered. More precisely, we seek for conditions under which an operator T satisfies the generalized Weyl's theorem: σBW(T)=σ(T)⧹E(T), or the version II of the generalized Weyl's theorem: σBW(T)=σ(T)⧹Π(T)

Corrosive-Abrasive Wear Induced by Soot in Boundary Lubrication Regime

Soot is known to induce high wear in engine components. The mechanism by which soot induces wear is not well understood. Although several mechanisms have been suggested, there is still no consensus. This study aims to investigate the most likely mechanism responsible for soot-induced wear in the boundary lubrication regime. Results from this study have shown that previously suggested mechanisms such as abrasion and additive adsorption do not fully explain the high wear observed when soot is present. Based on the results obtained from tests conducted at varying temperature and soot levels, it has been proven that the corrosive–abrasive mechanism was responsible for high wear that occurred in boundary lubrication conditions

Clinical standards for diagnosis, treatment and prevention of post-COVID-19 lung disease

BACKGROUND: The aim of these clinical standards is to provide guidance on ‘best practice’ care for the diagnosis, treatment and prevention of post-COVID-19 lung disease. METHODS: A panel of international experts representing scientific societies, associations and groups active in post-COVID-19 lung disease was identified; 45 completed a Delphi process. A 5-point Likert scale indicated level of agreement with the draft standards. The final version was approved by consensus (with 100% agreement).RESULTS: Four clinical standards were agreed for patients with a previous history of COVID-19: Standard 1, Patients with sequelae not explained by an alternative diagnosis should be evaluated for possible post-COVID-19 lung disease; Standard 2, Patients with lung function impairment, reduced exercise tolerance, reduced quality of life (QoL) or other relevant signs or ongoing symptoms ≥4 weeks after the onset of first symptoms should be evaluated for treatment and pulmonary rehabilitation (PR); Standard 3, The PR programme should be based on feasibility, effectiveness and cost-effectiveness criteria, organised according to local health services and tailored to an individual patient’s needs; and Standard 4, Each patient undergoing and completing PR should be evaluated to determine its effectiveness and have access to a counselling/health education session. CONCLUSION: This is the first consensus-based set of clinical standards for the diagnosis, treatment and prevention of post-COVID-19 lung disease. Our aim is to improve patient care and QoL by guiding clinicians, programme managers and public health officers in planning and implementing a PR programme to manage post-COVID-19 lung disease

Development of an encapsulated ice air cooler for mining use

SIGLEAvailable from British Library Document Supply Centre- DSC:D170865 / BLDSC - British Library Document Supply CentreGBUnited Kingdo