On the Higher Order Edge-Connectivity of Complete Multipartite Graphs

Let G be a connected graph with p ≥ 2 vertices. For k = 1, 2, ..., P-1, the Kth order edge-connectivity of G, denoted by A(K} (e), is defined to be the smallest number of edges whose removal from e leaves a graph with k + 1 connected components. In this note we determine A(K} (e) for any complete multi partite graph G as a consequence, we give a necessary and sufficient condition for the graph Gn to be factored into spanning trees

Deep ocean disposal of sewage sludge off Orange County, California: a research plan

Even though the discharge of sludge into the ocean via an outfall is not now permitted, this research plan has been prepared to show what could be learned with a full scale experimental sludge discharge of 150 dry tons/day by the County Sanitation Districts of Orange County into deep water (over 1000 feet). To provide a wide range of inputs and evaluation, a broad-based Research Planning Committee was established to advise the Environmental Quality Laboratory on the overall content and details of the research plan. Two meetings were held at EQL on: March 4-5, 1982: The entire Committee July 19-20, 1982: A working subgroup of the Committee The entire Committee is listed in Appendix B, with footnotes to indicate meeting attendance. Those unable to come to a meeting were asked to comment on the drafts by mail or telephone. We gratefully acknowledge the members of the Research Planning Committee for their generous help in formulating the research tasks and reviewing report drafts

Electronic states and optical properties of PbSe nanorods and nanowires

A theory of the electronic structure and excitonic absorption spectra of PbS and PbSe nanowires and nanorods in the framework of a four-band effective mass model is presented. Calculations conducted for PbSe show that dielectric contrast dramatically strengthens the exciton binding in narrow nanowires and nanorods. However, the self-interaction energies of the electron and hole nearly cancel the Coulomb binding, and as a result the optical absorption spectra are practically unaffected by the strong dielectric contrast between PbSe and the surrounding medium. Measurements of the size-dependent absorption spectra of colloidal PbSe nanorods are also presented. Using room-temperature energy-band parameters extracted from the optical spectra of spherical PbSe nanocrystals, the theory provides good quantitative agreement with the measured spectra.Comment: 35 pages, 12 figure

Review: Consumption-stage food waste reduction interventions - What works and how to design better interventions

Food waste prevention has become an issue of international concern, with Sustainable Development Goal 12.3 aiming to halve per capita global food waste at the retail and consumer levels by 2030. However there is no review that has considered the effectiveness of interventions aimed at preventing food waste in the consumption stages of the food system. This significant gap, if filled, could help support those working to reduce food waste in the developed world, providing knowledge of what interventions are specifically effective at preventing food waste. This paper fills this gap, identifying and summarizing food-waste prevention interventions at the consumption/consumer stage of the supply chain via a rapid review of global academic literature from 2006 to 2017. We identify 17 applied interventions that claim to have achieved food waste reductions. Of these, 13 quantified food waste reductions. Interventions that changed the size or type of plates were shown to be effective (up to 57% food waste reduction) in hospitality environments. Changing nutritional guidelines in schools were reported to reduce vegetable waste by up to 28%, indicating that healthy diets can be part of food waste reduction strategies. Information campaigns were also shown to be effective with up to 28% food waste reduction in a small sample size intervention. Cooking classes, fridge cameras, food sharing apps, advertising and information sharing were all reported as being effective but with little or no robust evidence provided. This is worrying as all these methods are now being proposed as approaches to reduce food waste and, except for a few studies, there is no reproducible quantified evidence to assure credibility or success. To strengthen current results, a greater number of longitudinal and larger sample size intervention studies are required. To inform future intervention studies, this paper proposes a standardised guideline, which consists of: (1) intervention design; (2) monitoring and measurement; (3) moderation and mediation; (4) reporting; (5) systemic effects. Given the importance of food-waste reduction, the findings of this review highlight a significant evidence gap, meaning that it is difficult to make evidence-based decisions to prevent or reduce consumption-stage food waste in a cost-effective manner

Electronic Structure of Electron-doped Sm1.86Ce0.14CuO4: Strong `Pseudo-Gap' Effects, Nodeless Gap and Signatures of Short Range Order

Angle resolved photoemission (ARPES) data from the electron doped cuprate superconductor Sm$_{1.86}$Ce$_{0.14}$CuO$_4$ shows a much stronger pseudo-gap or "hot-spot" effect than that observed in other optimally doped $n$-type cuprates. Importantly, these effects are strong enough to drive the zone-diagonal states below the chemical potential, implying that d-wave superconductivity in this compound would be of a novel "nodeless" gap variety. The gross features of the Fermi surface topology and low energy electronic structure are found to be well described by reconstruction of bands by a $\sqrt{2}\times\sqrt{2}$ order. Comparison of the ARPES and optical data from the $same$ sample shows that the pseudo-gap energy observed in optical data is consistent with the inter-band transition energy of the model, allowing us to have a unified picture of pseudo-gap effects. However, the high energy electronic structure is found to be inconsistent with such a scenario. We show that a number of these model inconsistencies can be resolved by considering a short range ordering or inhomogeneous state.Comment: 5 pages, 4 figure

Influence of operating parameters on the biodegradation of steroid estrogens and nonylphenolic compounds during biological wastewater treatment processes

This document is the unedited author's version of a Submitted Work that was subsequently accepted for publication in Environmental Science & Technology, copyright © American Chemical Society after peer review. To access the final edited and published work see http://pubs.acs.org/doi/abs/10.1021/es901612v.This study investigated operational factors influencing the removal of steroid estrogens and nonylphenolic compounds in two sewage treatment works, one a nitrifying/denitrifying activated sludge plant and the other a nitrifying/denitrifying activated sludge plant with phosphorus removal. Removal efficiencies of >90% for steroid estrogens and for longer chain nonylphenol ethoxylates (NP4−12EO) were observed at both works, which had equal sludge ages of 13 days. However, the biological activity in terms of milligrams of estrogen removed per day per tonne of biomass was found to be 50−60% more efficient in the nitrifying/denitrifying activated sludge works compared to the works which additionally incorporated phosphorus removal. A temperature reduction of 6 °C had no impact on the removal of free estrogens, but removal of the conjugated estrone-3-sulfate was reduced by 20%. The apparent biomass sorption (LogKp) values were greater in the nitrifying/denitrifying works than those in the nitrifying/denitrifying works with phosphorus removal for both steroid estrogens and nonylphenolic compounds possibly indicating a different cell surface structure and therefore microbial population. The difference in biological activity (mg tonne−1 d−1) identified in this study, of up to seven times, suggests that there is the potential for enhancing the removal of estrogens and nonylphenols if more detailed knowledge of the factors responsible for these differences can be identified and maximized, thus potentially improving the quality of receiving waters.Public Utilities Board (Singapore), Anglian Water Ltd, Severn Trent Water Ltd, Thames Water Utilities Ltd, United Utilities 393 Plc and Yorkshire Water Services