Mapping properties for oscillatory integrals in d-dimensions

AbstractFor aj,bj⩾1, j=1,2,…,d, we prove that the operator Kf(x)=∫R+dk(x,y)f(y)dy maps Lp(R+d) into itself for p=1+1r, where r=a1b1=⋯=adbd, and k(x,y)=φ(x,y)eig(x,y), φ(x,y) satisfies (1.2) (e.g. φ(x,y)=|x−y|iτ,τ real) and the phase g(x,y)=xa⋅yb. We study operators with more general phases and for these operators we require that aj,bj>1, j=1,2,…,d, or al=bl⩾1 for some l∈{1,2,…,d}

Humulus lupulus L.

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An Examination of Support Structures to Encourage Persistence through Graduation at Central Maine Community College

Central Maine Community College (CMCC) services Androscoggin, Franklin and Oxford counties. Enrollment for CMCC has grown impressively over the last eleven years, since transitioning from a Technical College. While enrollment has increased, retaining students through graduation (persistence) is still an area of concern, particularly because its service area still has some of the lowest percentages of adults with college credentials in Maine

Precautionary labelling of foods for allergen content: are we ready for a global framework?

© 2014 Allen et al.; licensee BioMed Central Ltd.Food allergy appears to be on the rise with the current mainstay of treatment centred on allergen avoidance. Mandatory allergen labelling has improved the safety of food for allergic consumers. However an additional form of voluntary labelling (termed precautionary allergen labelling) has evolved on a wide range of packaged goods, in a bid by manufacturers to minimise risk to customers, and the negative impact on business that might result from exposure to trace amounts of food allergen present during cross-contamination during production. This has resulted in near ubiquitous utilisation of a multitude of different precautionary allergen labels with subsequent confusion amongst many consumers as to their significance. The global nature of food production and manufacturing makes harmonisation of allergen labelling regulations across the world a matter of increasing importance. Addressing inconsistencies across countries with regards to labelling legislation, as well as improvement or even banning of precautionary allergy labelling are both likely to be significant steps forward in improved food safety for allergic families. This article outlines the current status of allergen labelling legislation around the world and reviews the value of current existing precautionary allergen labelling for the allergic consumer. We strongly urge for an international framework to be considered to help roadmap a solution to the weaknesses of the current systems, and discuss the role of legislation in facilitating this

Who Needs Guidance?

A key issue in guidance provision is how to make services flexible and responsive to client need. A model is presented which distinguishes between individuals with high, medium and low levels of readiness for career decisionmaking. It is suggested that those with high levels can be referred to self-help services; those with moderate readiness to brief staff-assisted services; and those with low readiness to individual case-managed services. The theoretical basis for the model, the use of diagnostic instruments within the model, its implications for career resource rooms and Internet websites, and its staffing implications, are discussed. Elements of the model are currently being applied in a careers service setting in Coventry. The main principles of this work are described, and the more general relevance to the model to current policy issues in the UK is examined. The Centre for Guidance Studies was created in 1998 by the University of Derby and five careers service companies (the Careers Consortium (East Midlands Ltd.). The centre aims to bridge the gap between guidance theory and practice. It supports and connects guidance practitioners, policy-makers and researchers through research activities and learning opportunities; and by providing access to resources related to guidance and lifelong learning