An elementary proof of p(11m+6)≡0 (mod 11)

AbstractLet p(n) denote the number of unrestricted partitions of n. It is known that p(5m+4), p(7m+5), and p(11m+6)≡0 (mod 5, 7, and 11 respectively).Easy proofs of cases 5 and 7 are found in [1]. They depend on writing Π (1−xn)4 and Π(1−xn)6, (n>0), as double series, using well-known formulae of Euler and Jacobi.The most elementary proof of case 11 seems to be found in [2], using different ideas. Another proof, which applies uniformly to cases 5, 7, 11, but is not elementary, is given in [3]. It is natural to ask for one along the same lines as for 5 and 7, i.e., using Π(1−xn)10 expressed as a double series

Renbetet och lokaltopografins inverkan på växt och lav samhällena vid renstaketet längs den finsk-norska riksgränsen

The heath vegetation in the Jauristunturit study area is highly affected by the reindeer fence that was built in the mid-1950s between Finland and Norway, to prevent summer grazing in the Norwegian side. In the study area, the Finnish and Norwegian pastures are used during different seasons, causing differences in reindeer grazing history, and with time differences in vegetation. Additionally, local topography also impacts the vegetation composition and structure creating variation in local vegetation patterns. My research questions are: How vegetation patterns differ between summer- and winter- grazed areas, and which plant functional groups have the most significant difference? How local topography affects vegetation patterns, and does the effect of topography differ between summer and winter pastures? The data was collected from five 400 m long transects that crossed the fence and had vegetation plots with 10-m intervals. The %-cover and height of each vascular plant, bryophyte, and lichen species were estimated from 0.25 m2 plots. Later, species data was grouped into functional groups and general linear models were used to analyze differences in cover, height, species number, biomass, and leaf-area indices between countries. Topography indices were calculated in GIS for each plot and analyzed with random forest models to find out the most important topography indices explaining vegetation patterns. The vegetation data was collected by four teams, and therefore, the comparability in the collected data between teams was analyzed. Significant vegetation differences were found in the ground layer, with higher cover and biomass of bryophytes on the Finnish side (mean biomass 168.2 vs. 65.2 g m-2). Reindeer lichens were more abundant on the Norwegian side (mean biomass 197.0 vs. 2.9 g m-2) which is visible in aerial and satellite images and in the field. Among vascular plants, evergreen dwarf shrubs had higher biomass and leaf area index on the Finnish side and dwarf birch had higher cover and height on the Norwegian side. Topography indices had a higher level of variance explained on the Norwegian side, and higher at the ground layer compared to vascular plants. Elevation had the greatest impact on vegetation, and after that, topography protection index for 50 m and depth to water stream network for 2 and 10 ha. The differences between data collectors were not considered to have a major impact on the results. The results indicate that there are significant differences in vegetation between summer- and winter-grazed areas, mainly in the ground layer, and most differences are caused by differences in reindeer grazing history, but also local topography has an impact.Tundravegetationen i forskningsområdet Jauristunturit påverkas starkt av ren-staketet som byggdes längs gränsen mellan Finland och Norge på 1950 talet för att förhindra sommarrenbetet på den norska sidan. Staterna använder sina betesmarken i forskningsområdet vid olika årstider, vilket orsakat olika stort betes tryck på de olika sidorna, och med tiden har det lett till stora skillnader i växtligheten. Dessutom har topografin också en inverkan, och kan skapa lokala skillnader i vegetations mönstren. Mina forskningsfrågor är följande: Hur skiljer sig vegetationsmönstren mellan sommar- och vinterbetesmarkerna, och vilka funktionella grupper uppvisar största skillnaden? Hur påverkar den lokala topografin på vegetationsmönstren, och finns det skillnader i påverkan mellan sommar- och vinterbetesmarkerna? Datainsamlingen gjordes över fem 400 m långa linjer som korsade ren-staketet, och hade växtrutor med 10 m mellanrum. Den procentuella täckningen och höjden av alla kärlväxter, moss- och lavarter estimerades från de 0.25 m2 stora växtrutorna. Växterna delades in i sina funktionella grupper, och allmänna linjära modeller utfördes för att få skillnaderna i täckning, höjd, biomassa och löv-area indexen mellan länderna. Topografiindex räknades ut med GIS för varje växtruta, och analyserades med random forest modeller för att se vad i topografin som påverkar växtligheten mest. Funktionaliteten av vår datainsamlingsmetod analyserades också eftersom flera olika personer deltog i arbetet. Signifikanta skillnader mellan länderna hittades i markskiktet, med mera mossor på den finska sidan (biomassamedeltal 168.2 mot 65.2 g m-2), och mera renlav på den norska sidan (biomassamedeltal 197.0 mot 2.9 g m-2), vilket man även kan se i flyg och satellitbilder och i fält. Kärlväxterna uppvisade signifikant skillnad med mera vintergröna dvärgbuskarna på den finska sidan, och mera dvärgbjörk på den norska. Den lokala topografin förklarade en större del av vegetationsförändringarna på den norska sidan än den finska, och med en större inverkan på markskiktet än kärlväxterna. Den största inverkan på växtligheten hade höjden över havet, där efter kom index för topografiskt skydd för 50 m och distansen till vattennätverken för 2 och 10 ha. Skillnader mellan växt data insamlarna anses inte ha påverkat resultaten anmärkningsvärt. På basis av resultaten kan jag dra slutsatsen att skillnaden i växtlighet mellan sommar- och vinterbetesmarkerna är stora, i synnerhet i markskiktet, och det är till största delen orsakat av renbetet men också topografin har en påverkan

How Should One be an Outsider?: Virginia Woolf's Common Reader as a Theory of Subjectivity in Interwar England

This project examines Virginia Woolf’s conceptualization of the outsider as a political position with recourse to the figure of the common reader she theorizes early in her writing career. Woolf’s common reader, I argue, is first and foremost a response to the interwar “battle of the brows.” Unique in their belief in the common reader, Woolf’s early essays on form and aesthetics ask readers to consider their position as consumers in relation to the writers who insisted upon the discourse of the great divide between high and middlebrow art. This project suggests the common reader is more than Woolf’s contribution to the “battle of the brows,” however, and it presents the common reader as the precursory figure in a theory of intersectional subjectivity that is the foundation for Woolf’s politics of everyday life, which reached maturity late in her career with the “Society of Outsiders.” Viewing the common reader this way helps connect Woolf’s later works, which are generally viewed as her more political writings, with her early, formally experimental works by way of a theory of subjectivity that makes one’s discursive subject position central to an outsider politics based on performative subversion. Woolf’s focus on subject positions and performative subversion marks hers as a politics of the body, and this work explores the role various social institutions, including the university, the military, the family, and the asylum, play in disciplining subjects and their bodies in Woolf’s fiction and essays. In texts including Jacob’s Room, Mrs Dalloway, A Room of One’s Own, Three Guineas, Between the Acts, as well as a number of Woolf’s shorter essays, I examine Woolf’s depictions of subjects, their bodies, and the institutions that shape and mould them, and through her theorization of the common reader and society of outsiders explore Woolf’s theory of subjectivity designed to confound and subvert these institutions using the very same bodies they sought to discipline and optimize to serve their ideological purposes

Near miss or standard of care? DPYD screening for cancer patients receiving fluorouracil

5-fluorouracil (5-FU) and its pro-drug capecitabine are widely used anticancer agents. Most 5-FU catabolism is dependent on dihydropyrimidine dehydrogenase (DPD) encoded by the DPYD gene, and DPYD variants that reduce DPD function increase 5-FU toxicity. Most DPD deficient patients are heterozygous and can be treated with reduced 5-FU dosing. We describe a patient with a genotype associated with near complete absence of DPD function, and severe and likely fatal toxicity with 5-FU treatment. The patient was treated effectively with alternative systemic therapy. Routine pretreatment DPYD genotyping is recommended by the European Medicines Agency, and guidelines for use of 5-FU in DPD deficient patients are available. However, outside the province of Quebec, routine pretreatment screening for DPD deficiency remains unavailable in Canada. It is likely our patient would have died from 5-FU toxicity under the current standard of care, but instead provides an example of the potential benefit of DPYD screening on patient outcomes

Creating absence to acknowledge presence : relational subjectivity and postmodernism in Carol Shields’s 'The Stone Diaries'

This paper explores the relationship between postmodernist discourses and feminist discourses, asking, firstly, whether or not feminist political action is possible within a postmodernist theoretical climate that scrutinizes the construction of universalizing group identities, and, secondly, how political action might be undertaken in such a theoretical climate. I contend that Carol Shields, reflecting the postmodernist ideology of Jean-François Lyotard and Patricia Waugh, creates Daisy Goodwill Flett’s absence in The Stone Diaries. This absence, in turn, acts to acknowledge the gaps in knowledge that exist within self-legitimating grand narratives. It demonstrates that Daisy’s performance of these grand narratives, particularly heteronormativity, necessarily obstructs her voice and, thereby, marginalizes her ability to act politically within that narrative. The Stone Diaries, then, calls for a plural public space by exposing what remains unknown—women’s lives and narratives—within the current public space

Does hormone replacement therapy benefit cognition in elderly, postmenopausal women : a true or mistaken association?

Hormone replacement therapy (HRT) has been studied as a protective factor for cognitive decline and dementia. However, study findings have been inconsistent. Variation in study findings may be due to differences in study designs, small sample size, exposure ascertainment, diagnostic procedures, and inclusion of relevant risk and confounding factors. Moreover, there may be significant differences between the characteristics of women choosing to use HRT and those opting not to use the therapy. Using a large-scale, population-based, cohort study, we examined the relationship between HRT and cognition while paying particular attention to moderating and confounding factors. The main outcomes of interest were to assess differences in risk for cognitive impairments and dementia between HRT user and never user groups; examine HRT’s impact on age of onset of dementia; and explore the relationship between duration of HRT and cognitive decline. Logistic regression and Cox Proportional Hazards models were used to test HRT as a predictor for cognitive impairments, Alzheimer’s disease and vascular dementia, as well as to assess the effect of duration. Linear regression was used to consider the putative relationship between age at onset of dementia and HRT status. HRT use was found to be a statistically significant predictor for Alzheimer’s disease and vascular dementia. Overall, HRT use did not significantly predict for milder cognitive impairments, although significant interaction effects indicate that HRT may be protective at least for specific sub-groups of women. No durational effect was found for any of the outcomes. Neither did HRT appear to predict for age at onset of dementia. Notably, a large proportion of women in the current study reported using estrogen-only hormone supplements, and therefore generalizations regarding the findings are likely limited to estrogen-only preparations, not combination estrogen-progestin therapies. These findings must be considered within the context of the other known and potential risks and benefits that HRT may afford

Typen erotus ja talteenotto lantaperäisestä nesteestä

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Civil Rights - Legislation - The Civil Rights Act of 1957

It is the purpose of this comment to note the nature of the prior legislation in the civil rights area, the provisions of the new act and the effect of the new act upon civil rights protection