Phantom maps and chromatic phantom maps

In the first part, we determine conditions on spectra X and Y under which either every map from X to Y is phantom, or no nonzero maps are. We also address the question of whether such all or nothing behaviour is preserved when X is replaced with V smash X for V finite. In the second part, we introduce chromatic phantom maps. A map is n-phantom if it is null when restricted to finite spectra of type at least n. We define divisibility and finite type conditions which are suitable for studying n-phantom maps. We show that the duality functor W_{n-1} defined by Mahowald and Rezk is the analog of Brown-Comenetz duality for chromatic phantom maps, and give conditions under which the natural map Y --> W_{n-1}^2 Y is an isomorphism.Comment: 18 page

Quillen model structures for relative homological algebra

An important example of a model category is the category of unbounded chain complexes of R-modules, which has as its homotopy category the derived category of the ring R. This example shows that traditional homological algebra is encompassed by Quillen's homotopical algebra. The goal of this paper is to show that more general forms of homological algebra also fit into Quillen's framework. Specifically, a projective class on a complete and cocomplete abelian category A is exactly the information needed to do homological algebra in A. The main result is that, under weak hypotheses, the category of chain complexes of objects of A has a model category structure that reflects the homological algebra of the projective class in the sense that it encodes the Ext groups and more general derived functors. Examples include the "pure derived category" of a ring R, and derived categories capturing relative situations, including the projective class for Hochschild homology and cohomology. We characterize the model structures that are cofibrantly generated, and show that this fails for many interesting examples. Finally, we explain how the category of simplicial objects in a possibly non-abelian category can be equipped with a model category structure reflecting a given projective class, and give examples that include equivariant homotopy theory and bounded below derived categories.Comment: 29 pages. v4: Published in Math. Proc. Cambridge Philos. Soc. v5: Minor corrections to published version appear on last pag

Vanishing lines in generalized Adams spectral sequences are generic

We show that in a generalized Adams spectral sequence, the presence of a vanishing line of fixed slope (at some term of the spectral sequence, with some intercept) is a generic property.Comment: 11 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTVol3/paper7.abs.htm

A Spectrophotometric Study on Uranyl Nitrate Complexation to 150 °C

The formation constant of the mononitratouranyl complex was studied spectrophotometrically at temperatures of 25, 40, 55, 70, 100 and 150 °C (298, 313, 328, 343, 373 and 423 K). The uranyl ion concentration was fixed at approximately 0.008 mol⋅kg−1 and the ligand concentration was varied from 0.05 to 3.14 mol⋅kg−1. The uranyl nitrate complex, UO2NO 3 + , is weak at 298 K but its equilibrium constant (at zero ionic strength) increases with temperature from log 10 β 1=−0.19±0.02 (298 K) to 0.78±0.04 (423 K

Operations on integral lifts of K(n)

This very rough sketch is a sequel to arXiv:1808.08587; it presents evidence that operations on lifts of the functors K(n) to cohomology theories with values in modules over valuation rings of local number fields, indexed by Lubin-Tate groups of such fields, are extensions of the groups of automorphisms of the indexing group laws, by the exterior algebras on the normal bundle to the orbits of the group laws in the space of lifts.Comment: \S 2.0 hopefully less cryptic. To appear in the proceedings of the 2015 Nagoya conference honoring T Ohkawa. Comments very welcome

Using a Universal Design for Learning Framework to Provide Multiple Means of Representation in the Early Childhood Classroom

In order to ensure high quality outcomes for all children in the early childhood classroom, teachers are expected to utilize both the Developmentally Appropriate Practices (DAP) provided by the National Association for the Education of Young Children (NAEYC, 2009), as well as the Division of Early Childhood (DEC) Recommended Practices (DEC, 2014). Both NAEYC’s DAP and DEC’s Recommended Practices align with the use of Universal Design for Learning (UDL). UDL is a framework that supports the learning needs of all learners through intentional, proactive, and reflective instruction and interactions. This article provides a brief overview of UDL, with a specific focus on multiple means of representation in the early childhood classroom

Employer and employment agency attitudes towards employing individuals with mental health needs

Background: The positive benefits of paid employment for individuals with mental health needs are well known yet many still remain unemployed (Perkins & Rinaldi, (2002). Unemployment rates among patients with long-term mental health problems: A decade of rising unemployment. Psychiatric Bulletin, 26(8), 295–298.).\ud \ud Aims: Attitudes of employers and employment agencies that may provide short-term contracts to individuals with mental health needs are important to understand if these individuals are to be given access to paid employment.\ud \ud Methods: A mixed methods approach was used to investigate this phenomenon comprising of interviews and a follow-up survey. Interviews were conducted with 10 employment agencies and 10 employers. The results of these interviews then informed a follow-up survey of 200 businesses in Gloucestershire.\ud \ud Results: The findings demonstrated that employment agencies would consider putting forward individuals with previous mental health needs to employers. However, employers had a high level of concern around employing these individuals. Employers reported issues of trust, needing supervision, inability to use initiative and inability to deal with the public for individuals with either existing or previous mental health needs.\ud \ud Conclusions: The findings of this research suggest a need for employers to have more accurate information regarding hiring individuals with mental health needs

Universal Design for Learning (UDL) in Inclusive Preschool Science Classrooms

Science instruction is a critical aspect of early learning. Teachers can support young children’s learning about scientific concepts through the use of the Universal Design for Learning (UDL) framework, which is a proactive approach to instructional planning that helps ensure success for all learners. This teaching techniques article offers preschool teachers practical solutions for implementing in the UDL framework for science instruction in their classrooms