A qualitative description of graphs of discontinuous polynomial functions

We prove that, if f:R^n\to R satisfies Fr\'echet's functional equation and f(x_1,...,x_n) is not an ordinary algebraic polynomial in the variables x_1,...,x_n, then f is unbounded on all non-empty open set U of R^n. Furthermore, the closure of its graph contains an unbounded open set.Comment: 9 pages, submitted to a journa

Phosphorus in the landscape: diffuse sources to surface waters. Land and Water Resources Research and Development Corporation. Occasional Paper 16/98

The National Eutrophication Management Program (NEMP) and Environment Australia convened a workshop to develop a coherent overview of the sources and transport of diffuse phosphorus in Australian catchments based on the latest knowledge. The Land and Water Resources Research and Development Corporation (LWRRDC) and the Murray–Darling Basin Commission (MDBC) jointly fund NEMP. A select group of scientists attended the workshop and developed a coherent statement about phosphorus sources and transport in Australian catchments. The group did not extend this statement to include recommended management practices. This paper reports the findings from the workshop. State governments have developed algal and nutrient management strategies in response to concerns about the frequency and severity of algal blooms, including cyanobacterial blooms, in Australian rivers and estuaries. There is an emphasis on phosphorus management, particularly in rural environments, now that nutrients are recognised as fundamental drivers of algal growth. Best management practices (BMPs) were developed for these strategies on the basis of the limited scientific evidence that was available at the time. The absence of a significant body of Australian information meant that there was a reliance on overseas research findings to develop such BMPs. A number of research projects have been completed in recent years on the sources and transport of nutrients in Australian catchments that challenge the Northern Hemisphere model of nutrient behaviour and will have implications for future development of BMPs. Principal conclusions 1. The studies presented in the workshop demonstrate that control of phosphorus entering surface waters must start with land management that minimises accelerated erosion and overland flow of water potentially rich in phosphorus. Heavily grazed lands, irrigation areas and intensive animal and horticultural industries are at risk, especially at the onset of rainy seasons and during periods of high rain intensity. 2. The transport of phosphorus from diffuse sources in landscapes can occur in both dissolved and particulate form. This can be due to different mobilisation and delivery mechanisms operating in different environments. Phosphorus mobilisation and delivery 1. Diffuse sources of phosphorus are the dominant component in most Australian catchments. Episodic rainfall is responsible for the bulk of phosphorus loss from the landscape. The mechanisms vary with each catchment. 2. Particulate phosphorus is carried by overland flow, resulting from run-off and erosion. In high to medium rainfall environments most is carried as filterable reactive phosphorus of less than 0.45 microns. Although most of the coarser materials from high parts of the landscape are deposited before they reach a watercourse, the particles ultimately carried into drainage lines are phosphorus-enriched by processes of sorting and filtration. 3. In river systems studied in the Murray–Darling Basin river sediments that originate from gully erosion and stream-bank collapse of readily dispersible soils carry most of the diffuse-source phosphorus. It is very likely that most of the phosphorus on these sediments is ‘native’ phosphorus coming from subsoils. 2 Phosphorus in the landscape: diffuse sources to surface waters Although the major episodes of gully formation occurred several decades ago, inputs of sediments and phosphorus from these sources continue at a high rate. Reduced input rates can best be achieved by targeting the gullies themselves and stabilising them by conservation works—particularly in small headwater catchments. 4. In larger dry-land catchments, fertiliser phosphorus is generally not an important component of phosphorus loss/export, although it may be locally significant. 5. Local soil, vegetation, terrain and climate conditions dictate whether surface erosion is the dominant source of phosphorus into a watercourse. To describe phosphorus exports from a specific landscape by surface erosion requires local studies. However, guidelines can be developed for management purposes to identify and minimise sources of phosphorus carried by overland flow. 6. Potential sources of diffuse phosphorus run-off occur wherever fertilisers are applied to soils that are already wet at the surface, or that may become wet by seasonally emerging groundwater. The magnitude of the loss will be greater if the application occurs on bare soils, or if it is next to a waterbody. 7. Dissolved phosphorus (from fertilisers and other sources) is readily mobilised and transported directly where the soil has both little ability to bind the phosphorus and a high leaching rate, as occurs in sandy regions of high rainfall around the continent. Phosphorus-laden water then travels via overland or shallow sub-surface flow to surface waterbodies quite quickly, unless other processes impede the movement. If the dissolved phosphorus moves via deep groundwater the time scales for its reappearance in surface water are generally large. 8. Dissolved phosphorus may also enter tributary waterbodies in headwater catchments via shortcircuit pathways, such as macropores, but this is only likely to be important over distances of hundreds of metres. However, these sub-surface pathways may reduce the effectiveness of local management practices that do not take them into account. 9. Large amounts of dissolved phosphorus are also being produced from irrigated dairy pastures (and possibly from other irrigation enterprises also). There is little or no sub-surface movement because soils are generally high in clay and flat. Phosphorus-laden water is pumped or drained across the land surface to channels. The time scale of dissolved phosphorus movement is comparable with the time with which the water itself moves. Once within drainage channels and streambeds the dissolved phosphorus fraction may be partially re-adsorbed onto particulates. 10. Large quantities of dissolved phosphorus are found in surface waters next to areas where animal excreta or over-fertilised market gardens give rise to phosphorus in surface wastewater that flows directly into waterways. These situations are most likely to arise in catchments that contain mixtures of horticultural, dairying, hobby-farming and similar land uses. Where farm dams are abundant a significant fraction of this phosphorus will not enter streams but will be retarded or retained in the landscape

Trends in axillary lymph node dissection for early-stage breast cancer in Europe: Impact of evidence on practice

Background: Data from recently published trials have provided practice-changing recommendations for the surgical approach to the axilla in breast cancer. Patients with T1-2 lesions, treated with breast conservation, who have not received neoadjuvant chemotherapy and have 1\u20132 positive sentinel nodes (Z0011-criteria) may avoid axillary lymph node dissection (ALND). We aim to describe the dissemination of this practice in Europe over an extended period of time. Methods: Our source of data was the eusomaDB, a central data warehouse of prospectively collected information of the European Society of Breast Cancer Specialists (EUSOMA). We identified cases fulfilling Z0011-criteria from 2005 to 2016 from 34 European breast centers and report trends in ALND. Data derived from Germany, Italy, Belgium, Switzerland, Austria, and Netherlands. Results: 6671 patients fulfilled Z0011-criteria. Rates of ALND showed a statistically significant decrease from 2010 (89%) to 2011 (73%), reaching 46% in 2016 (p < 0.001). After multivariable analysis, factors associated with higher probability of ALND were earlier year of surgery, younger age, increasing tumor size and grade, and being operated in Italy (p < 0.001). The minimum and maximal rates of ALND in the most recent two-year period (2015\u20132016) were 0% and 83% in two centers located in different countries (p < 0.001). Conclusion: Our study demonstrates, a decrease in rates of ALND that started after year 2010 through the end of the study period. Wide differences were observed among centers and countries indicating the need to spread unified clinical guidelines in Europe to allow for homogeneous evidence-based practice patterns

2008 Inter-laboratory Comparison Study of a Reference Material for Nutrients in Seawater

Autoclaved natural seawater collected in the North Pacific Ocean was used as a reference material for nutrients in seawater (RMNS) during an inter-laboratory comparison (I/C) study conducted in 2008. This study was a follow-up to previous studies conducted in 2003 and 2006. A set of six samples was distributed to each of 58 laboratories in 15 countries around the globe, and results were returned by 54 of those laboratories (15 countries). The homogeneities of samples used in the 2008 I/C study, based on analyses for three determinants, were improved compared to those of samples used in the 2003 and 2006 I/C studies. Results of these I/C studies indicate that most of the participating laboratories have an analytical technique for nutrients that is sufficient to provide data of high comparability. The differences between reported concentrations from the same laboratories in the 2006 and 2008 I/C studies for the same batch of RMNS indicate that most of the laboratories have been maintaining internal comparability for two years. Thus, with the current high level of performance in the participating laboratories, the use of a common reference material and the adaptation of an internationally accepted nutrient scale system would increase comparability among laboratories worldwide, and the use of a certified reference material would establish traceability. In the 2008 I/C study we observed a problem of non-linearity of the instruments of the participating laboratories similar to that observed among the laboratories in the 2006 I/C study. This problem of non-linearity should be investigated and discussed to improve comparability for the full range of nutrient concentrations. For silicate comparability in particular, we see relatively larger consensus standard deviations than those for nitrate and phosphate

A922 Sequential measurement of 1 hour creatinine clearance (1-CRCL) in critically ill patients at risk of acute kidney injury (AKI)

Meeting abstrac

Significance of gaseous nitrogen loss from a tropical dairy pasture fertilised with urea

This paper reports a study in the wet tropics of Queensland on the fate of urea applied to a dairy pasture in the absence of grazing animals. A nitrogen balance was conducted in cylindrical plots with N-15-labelled urea, and ammonia volatilisation was determined using a mass balance micrometeorological method. The pasture plants took up 42% of the applied nitrogen in the 98 days between fertiliser application and harvest. At harvest 18% of the applied nitrogen was found in the soil, and 40% was lost from the plant-soil system. The micrometeorological study showed that 20% of the unrecovered nitrogen was lost by ammonia volatilisation. As there was no evidence for leaching or runoff losses it was concluded that the remaining 20% of the applied nitrogen was lost by denitrification. It is evident from these results that fertiliser nitrogen is not being used efficiently on dairy pastures, and that practices need to be changed to conserve fertiliser nitrogen and reduce contamination of the environment