Correspondence of the eigenvalues of a non-self-adjoint operator to those of a self-adjoint operator

We prove that the eigenvalues of a certain highly non-self-adjoint operator that arises in fluid mechanics correspond, up to scaling by a positive constant, to those of a self-adjoint operator with compact resolvent; hence there are infinitely many real eigenvalues which accumulate only at $\pm \infty$. We use this result to determine the asymptotic distribution of the eigenvalues and to compute some of the eigenvalues numerically. We compare these to earlier calculations by other authors.Comment: 29 pages, corrections to section 3, added section

Faith, knowledge and cosmopolitanism: an inaugural lecture given in the University of Rhodesia

An inaugural lecture on the theme Faith, Knowlede and Cosmopolitanism given by Prof. T. A. Burkill.The familiar opposition between faith and knowledge is quite unsatisfactory when the terms are taken to represent mutually exclusive means of cognition. Knowledge involves faith and faith involves knowledge. A person cannot have faith in something of which he is not aware, and he would scarcely claim to identify a certain object unless he had faith in the reliability of his powers of apprehension. Some such truth would seem to apply to the systematic refinements of knowledge, as well as to rudimentary forms of awareness, for both science and scholarship have their unproved presuppositions which constitute indispensable conditions in any research enterprise. Recognition of this circumstance can serve to check the tendency to slip into excessive dogmatism and help to preserve mental flexibility. Cock-sureness is usually born of narrowness — habitual concentration on our successes in the way of demonstration to the neglect of what we fail to demonstrate. We have been conditioned to prize tidiness in our thinking and perhaps find it disturbing to attend to the existentialist possibility that no set of generalisations can explain any individual entity in its concrete uniqueness. Our prompt reaction might well be to dismiss such a disquieting notion as expressive of mere romantic obscurantism. We might harden our minds in resistance, settling down more securely in an assurance of the sufficiency of our generalisations

Asymptotic stability of stochastic differential equations driven by Lévy noise

Using key tools such as Ito's formula for general semimartingales, Kunita's moment estimates for Levy-type stochastic integrals, and the exponential martingale inequality, we find conditions under which the solutions to the stochastic differential equations (SDEs) driven by Levy noise are stable in probability, almost surely and moment exponentially stable

Asymptotic stability of stochastic differential equations driven by Lévy noise

Using key tools such as Ito's formula for general semimartingales, Kunita's moment estimates for Levy-type stochastic integrals, and the exponential martingale inequality, we find conditions under which the solutions to the stochastic differential equations (SDEs) driven by Levy noise are stable in probability, almost surely and moment exponentially stable

Sexual Problems and Distress among Men and Women with Same-Sex and Opposite-Sex Sexual Partners: An Analysis of a Nationally Representative Sample of Adults in Great Britain

Objective: This study aimed to examine differences in reporting sexual problems and distress among men and women with same-sex and opposite-sex sexual partners. Methods: Multinomial regression was undertaken on risk of reporting sexual problems and/or distress using data from the third National Survey of Sexual Attitudes and Lifestyles. Results: Differences were detected between men of different sexual behavior groups when considering the problems “lack of enjoyment in sex,” “felt anxious during sex,” “felt no excitement or arousal during sex,” “lack of interest in sex,” “did not reach/took a long time to reach climax,” and “getting or keeping an erection.” Fewer differences were detected among women. Conclusions: Women reporting same sex sexual partners, and to a greater extent men reporting same sex sexual partners , have different sexual health needs and report sexual health problems and distress to a different extent than is the case for individuals who only have opposite-sex sexual partner

Edible leafy vegetables from West Africa (Guinea-Bissau): consumption, trade and food potential

Wild Edible Plants are common in the diet of rural communities of sub-Saharan Africa. In Guinea-Bissau, West Africa, wild plant resources are widely used in human diet, but very few studies have addressed them. The aim of this study is to reveal: (1) the wild and semi-cultivated leafy vegetables consumed in Guinea-Bissau; and (2) the nutritional composition of those plants traded at the largest country market in Bissau. Our results revealed that 24 native or naturalized species with edible leaves are currently consumed by Guinea-Bissau population. Five of them were found at the market: dried leaves of Adansonia digitata, Bombax costatum and Sesamum radiatum, and fresh leaves and shoots of Amaranthus hybridus and Hibiscus sabdari a. The analysis of the nutritional properties revealed that leaves contain a significant amount of protein (10.1–21.0 g/100 g, dry basis), high values of macronutrients and micronutrients, as well as of phenolic compounds (13.1–40.3 mg GAE/g) and a considerable antioxidant capacity (DPPH 111.5–681.9 mg Eq Trolox). Although price and availability vary among the leafy vegetables analyzed, these traditional foods appear to be a good dietary component that can contribute to food security in Guinea-Bissau and in other West African countries, as these species are widely distributed in this regioninfo:eu-repo/semantics/publishedVersio

Plant capitalism and company science: the Indian career of Nathaniel Wallich

The career of the Danish-born botanist Nathaniel Wallich, superintendent of the Calcutta Botanic Garden from 1815 to 1846, illustrates the complex nature of botanical science under the East India Company and shows how the plant life of South Asia was used as a capital resource both in the service of the Company's economic interests and for Wallich's own professional advancement and international reputation. Rather than seeing him as a pioneer of modern forest conservation or an innovative botanist, Wallich's attachment to the ideology of ‘improvement’ and the Company's material needs better explain his longevity as superintendent of the Calcutta garden. Although aspects of Wallich's career and botanical works show the importance of circulation between Europe and India, more significant was the hierarchy of knowledge in which indigenous plant lore and illustrative skill were subordinated to Western science and in which colonial science frequently lagged behind that of the metropolis

The association between family structure and children’s BMI over time - the mediating role of income

Purpose: Whilst both family structure and income have previously been indicated as being associated with body mass index (BMI), the extent to which the effect of family structure on BMI is mediated through income is incompletely understood. Taking the case of the United Kingdom, this study aims to investigate the association between family structure, defined in this study as whether children live in a one or two adult household, and childhood BMI, and whether this varies by child sex and with increased age. Secondly, the study aims to examine whether family equivalised income as a proxy for socio-economic status, mediates the association between family structure and child’s BMI.Methods: This study uses data from the Millennium Cohort Study (MCS). Data from 7,478 children born between 2000 and 2001 in the UK at the ages of 3, 5, 7, 11, and 14 was used. Mediation analysis was used to consider, at each age, the extent to which the association between living in a one or two adult household and BMI was mediated through income overall, and stratified by sex. To assess the robustness of the mediation analysis estimates, we used both E-values, and multiple confounder adjustment.Results: At ages 3 and 5, there was no direct or indirect effect of family structure mediated by income on BMI. From the age of 7 to 11, the overall proportion of the association mediated vastly increased, from 19.70% at age 7 up to 42.70% at the age of 11. The E-values show that substantial unmeasured confounder associations would be needed to fully explain away the conclusions from the mediation analysis. Results remained significant when models were additionally adjusted for geographic region, main respondent’s (usually mother’s) highest educational attainment, and ethnicity.Conclusions: An increasing proportion of the association between family structure and BMI is mediated by income as children grow older. The study focuses on the mediating role of income between family structure and BMI using the available data as an empirical application of the potential impact of income as mediator in the causal pathway