Enriched model categories and an application to additive endomorphism spectra

We define the notion of an additive model category, and we prove that any additive, stable, combinatorial model category has a natural enrichment over symmetric spectra based on simplicial abelian groups. As a consequence, every object in such a model category has a naturally associated endomorphism ring inside this spectra category. We establish the basic properties of this enrichment. We also develop some enriched model category theory. In particular, we have a notion of an adjoint pair of functors being a 'module' over another such pair. Such things are called "adjoint modules". We develop the general theory of these, and use them to prove a result about transporting enrichments over one symmetric monoidal model category to a Quillen equivalent one.Comment: Sections completely re-organized from previous version. Mathematical content all the sam

Explicit constructions of infinite families of MSTD sets

We explicitly construct infinite families of MSTD (more sums than differences) sets. There are enough of these sets to prove that there exists a constant C such that at least C / r^4 of the 2^r subsets of {1,...,r} are MSTD sets; thus our family is significantly denser than previous constructions (whose densities are at most f(r)/2^{r/2} for some polynomial f(r)). We conclude by generalizing our method to compare linear forms epsilon_1 A + ... + epsilon_n A with epsilon_i in {-1,1}.Comment: Version 2: 14 pages, 1 figure. Includes extensions to ternary forms and a conjecture for general combinations of the form Sum_i epsilon_i A with epsilon_i in {-1,1} (would be a theorem if we could find a set to start the induction in general

Ion Exchange-Precipitation for Nutrient Recovery from Dilute Wastewater

Regulated phosphorus (P) and nitrogen (N) discharges and the cost of fertilizer provide economic drivers for nutrient removal and recovery from wastewater. This study used ion exchange (IX) in dilute (domestic) wastewater to concentrate nutrients with subsequent recovery by struvite precipitation. This is the first tertiary wastewater treatment study directly comparing P removal using a range of Fe, Cu, and Al-based media followed by clinoptilolite IX columns for N removal and precipitation using the combined regenerants. Phosphate removal prior to breakthrough was 0.5–2.0 g P Lmedia−1, providing effluent concentrations −1 PO4-P and −1 NH4-N for ≥80 bed volumes. Dow-FeCu resin provided effective P removal, efficient neutral pH regeneration and 560 mg P L−1 in the regeneration eluate (≥100× concentration factor). Exchange capacity of clinoptilolite in column mode was 3.9–6.1 g N Lmedia−1 prior to breakthrough. Precipitation using the combined cation and anion regenerants resulted in a maximum of 74% P removal using Dow-FeCu. Precipitates contained impurities, including Al3+, Ca2+, and Fe. Overall, the IX-precipitation recovery process removed ≥98% P and 95% N and precipitates contained 13% P and 1.6% N. This sequential process can satisfy increasingly stringent wastewater standards and offers an effective alternative to traditional treatment technologies that simply remove nutrients. Approximately 84% of total P and 97% of total Kjeldahl N entering a treatment plant can be captured (accounting for primary clarifier removal), whereas most existing technologies target side streams that typically contain only 20–30% of influent P and 15–20% of influent N

Nitrogen Contamination of Groundwater in Proximity to a Closed Landfill and Active Agricultural Fields

Carcinogenic compounds in drinking water are becoming a significant health problem. Increased use of artificial fertilizers, disposal of wastes, and land use are the main factors responsible for increased nitrate levels in groundwater over the last 30 years. This study examined the correlation between nitrate levels and proximity to a closed, inactive garbage dump located in Middlesex, Virginia. This study also examined the correlation between nitrate levels and proximity to agricultural fields. Twenty-five sampling sites were identified on the GIS tax maps of Middlesex County, Virginia. Fifteen sites were identified within a two kilometer radius of the VPPSA landfill, also the site of an abandoned town dump, and the remaining ten sample sites were identified around the county outside of the two kilometer radius. The mean nitrate levels at sample sites within a 2 km radius of the landfill were higher. Over the 125 data points sampled, it becomes evident that nitrate levels were higher in well water at sample sites within a 2 km radius of the landfill. Along with increased nitrate levels, nitrite levels exceeding 1 ppm, the highest contamination level for human consumption, were also measured at several locations. Groundwater contamination can cause major health issues, and it is often undetected in well drinking water due to lack of regular testing. Global health and welfare due to unregulated groundwater contamination is a crisis that demands more direct attention

Postnikov extensions of ring spectra

We give a functorial construction of k-invariants for ring spectra and use these to classify extensions in the Postnikov tower of a ring spectrum.Comment: This is the version published by Algebraic & Geometric Topology on 1 November 200

The Impact of Capsid Proteins on Virus Removal and Inactivation During Water Treatment Processes

This study examined the effect of the amino acid composition of protein capsids on virus inactivation using ultraviolet (UV) irradiation and titanium dioxide photocatalysis, and physical removal via enhanced coagulation using ferric chloride. Although genomic damage is likely more extensive than protein damage for viruses treated using UV, proteins are still substantially degraded. All amino acids demonstrated significant correlations with UV susceptibility. The hydroxyl radicals produced during photocatalysis are considered nonspecific, but they likely cause greater overall damage to virus capsid proteins relative to the genome. Oxidizing chemicals, including hydroxyl radicals, preferentially degrade amino acids over nucleotides, and the amino acid tyrosine appears to strongly influence virus inactivation. Capsid composition did not correlate strongly to virus removal during physicochemical treatment, nor did virus size. Isoelectric point may play a role in virus removal, but additional factors are likely to contribute

Recovery of Agricultural Nutrients from Biorefineries

This review lays the foundation for why nutrient recovery must be a key consideration in design and operation of biorefineries and comprehensively reviews technologies that can be used to recover an array of nitrogen, phosphorus, and/or potassium-rich products of relevance to agricultural applications. Recovery of these products using combinations of physical, chemical, and biological operations will promote sustainability at biorefineries by converting low-value biomass (particularly waste material) into a portfolio of higher-value products. These products can include a natural partnering of traditional biorefinery outputs such as biofuels and chemicals together with nutrient-rich fertilizers. Nutrient recovery not only adds an additional marketable biorefinery product, but also avoids the negative consequences of eutrophication, and helps to close anthropogenic nutrient cycles, thereby providing an alternative to current unsustainable approaches to fertilizer production, which are energy-intensive and reliant on nonrenewable natural resource extraction

A curious example of two model categories and some associated differential graded algebras

The paper gives a new proof that the model categories of stable modules for the rings Z/(p^2) and (Z/p)[\epsilon]/(\epsilon^2) are not Quillen equivalent. The proof uses homotopy endomorphism ring spectra. Our considerations lead to an example of two differential graded algebras which are derived equivalent but whose associated model categories of modules are not Quillen equivalent. As a bonus, we also obtain derived equivalent dgas with non-isomorphic K-theories

Rape and Posttraumatic Stress Disorder (PTSD): Examining the Mediating Role of Explicit Sex-Power Beliefs for Men Versus Women

Many rape survivors exhibit symptoms of post-traumatic stress disorder (PTSD), and recent literature suggests survivors\u27 beliefs about sex and control may affect PTSD symptoms. The present study examined beliefs about sex and power as potential mediators of the relationship between rape and PTSD symptoms for men versus women. Participants (N = 782) reported lifetime history of rape, current PTSD symptoms, and beliefs about sex and power. Women reported higher levels of lifetime history of rape than men (19.7% for women; 9.7% for men). While rape history predicted PTSD symptoms for both genders, beliefs about sex and power were shown to be a significant partial mediator of this relationship for men, but not for women. Results extend the literature on rape and PTSD by suggesting that survivors\u27 beliefs about sex and power are connected and can affect their PTSD symptoms. Additionally, results illustrate how sexual violence against men may reaffirm male gender roles that entail power and aggression, and ultimately affect trauma recovery