A note on the variety of projectors

AbstractSomewhat analogous to the case of the variety of Complexes, the variety P of projectors, i.e., idempotents (of rank d on an n-space), is shown to be a principal affine open subset of the product of the Grassmannian Gr(d, n) and its dual Gr(n − d, n). Also P is identified with the affine coset space GL(n)/H for a closed reductive subgroup H of the form GL(d) x GL(n − d); consequently, P is nonsingular and of dimension 2d(n − d). The coordinate ring R of P is described explicitly by generators and relations as the subring of left translation H-invariants of k[GL(n)] as an immediate consequence of the classical Hodge Standard Monomial Basis readily available for R just as for the homogeneous coordinate ring of Gr(d, n) for its Plücker embedding. The GL(n)-module structure of R is shown to be the direct limit of the filtered family of representations of GL(n): mωd ⊗ mωn − d ⊗ (-m) det., mϵZ, where ωd and ωn − d are the fundamental weights of GL(n) corresponding to Gr(d, n) and Gr(n − d, n), respectively, and det. is the determinant character of GL(n)

Ndwae ngone mwaitu: A Postmodern Cultural Phenomenon of Dowry among the Akamba and its influence on Spousal Violence

Dowry, also referred to as bride wealth or bride price, is a consultative, amicable, and quantifiable summation of goods exchanged between the groom’s and bride’s families. Traditionally, dowry (ngasya) payment among the Akamba was an obligation for the parents-in-law (husband’s parents), but that has in the recent past transitioned to the husband paying the dowry himself. An emerging trend is, however, catching up with married women budding together and opting to pay the dowry for themselves, which is not only a cultural shock and an empowering paradigm shift but also a ceremony that could be riddled and clouded with rifts amongst spouses. “Ndwae ngone mwaitu” literally translated to mean “Let us visit my mother,” is a ceremony that is becoming popular among Kenyans from different tribes. The ceremony is organized by one who goes to see his or her biological mother, accompanied by friends of the same age. This paper examines “Ndwae ngone mwaitu” as an emerging postmodern cultural phenomenon in dowry honourship and its relation to spousal violence by analysing couples’ life narratives. The article employs Akachi Adimora-Ezeigbo’s notion of snail-sense feminism to examine the viability of realizing fair and humanistic co-existence for couples after “Ndwae ngone mwaitu” disguised for dowry honourship. Snail-Sense feminism espouses the pattern of the snail to ‘negotiate’ or ‘dialogue’ within its milieu to get around impediments with a ‘well-lubricated tongue.” This theory is adopted as it offers women tactical strategies for achieving emancipation from cultural norms and men’s domination that perpetuate gender-based violence. The paper employed a qualitative design, utilizing interview schedules and focus group discussions to elicit experiential data from men and women attending “Ndwae ngone mwaitu” ceremonies in various parts of Ukambani in Kitui County in Kenya. The article affirms the value of cultural identity, respect, and negotiating power and space that one attains after meeting the societal expectations that come along with the practice, cementing the value of marriage and dowry customs among the Akamba. As such, dowry honourship, even though contested in the contemporary space, is a cultural practice that both men and women ought to navigate tactfully, thus, averting spousal violence

Multifoetal Pregnancies At A Maternity Hospital In Nairobi

Objective: To review some of the aspects of multiple pregnancies.Design: A retrospective review of multiple pregnancy deliveries.Setting: Pumwani Maternity Hospital- Nairobi Kenya, between 1st January and 31st December 2006.Subjects: Three hundred and twenty eight mothers with twins and two sets of triplet deliveries.Results: The total annual deliveries were 15,642. The twinning rate was one in 48 deliveries and the triplet rate was one in 7,821 deliveries. Most of the mothers were of low parity and in the lower age group. Majority had no previous history of twins and were married. The sex differences in both the first and second twins were as of the normal population with males being delivered more than females. Most of the twins were delivered alive through spontaneous vertex delivery (SVD). Majority of first twins had no complications while in second twins the majority had more complications. Most of the deliveries had no obvious congenital malformations. Most of the twins were of low birth weight and were of the same sex (monozygotic). The most common complications in both first and second twins were prematurity and asphyxia. The majority of the twins were diagnosed during the prenatal period and the most common method of diagnosis was by ultrasonography. The majority of the mothers had no complications. The most common maternal complications being pre-eclampia (PET) and anaemia.Conclusion: Most of the mothers with multiple pregnancies were of low parity and in the lower age group. Diagnosis was mainly done by ultrasonography therefore emphasis should be done to improve clinical diagnosis especially in resource constrained facilities. A more detailed study should be undertaken especially the events in the pre-pregnancy and during the antenatal period. The present study assumes that same sex twins are the same as monozygotic twins. A more detailed study on the types of placentation would be useful. As PET, anaemia, prematurity and asphyxia are the most common maternal and neonatal complications medical workers need to be made aware of the appropriate management of the conditions. These babies will need long-term follow-u

Condom Use and Culture of Life: The Roman Catholic Church Dilemma in the Wake of New HIV Infections

The World has devotedly committed to ending HIV and AIDS epidemic by 2030. However, the latest global data demonstrate among other challenges an increase in new HIV infections. In 2015 there was an increase of new HIV infections from 1.8 million to 2.4 million, an average of 2.1 million. In light of this challenge of increasing new HIV infections, a scrutiny on the effectiveness of HIV prevention strategies and measures is important. Abstinence, fidelity and condom use are among the strategies that have been lauded to prevent further transmission of HIV infections. However, the Roman Catholic Church (RCC) stance and repression of condom use by her adherents bars the positive strides of preventing the spread of HIV. This paper addresses the possible grounds for review of the RCC negative stance on condom use. This is premised on the famous Pope John Paul II’s culture of life theology that upholds not only the sanctity of human life but also the intrinsic value and dignity of the human person. A phenomenological approach was employed in guiding this discourse. The following concepts illuminate this worth course. They include the primacy of subjective interiority in sexual choices, valued inter-relational sociability of human persons and pursuance of eschatological hope. In this era of HIV and AIDS, we argue for a relational eschatology rather than a punitive eschaton. This is believed to cushion a time that is permeated with relational challenges that are meant to steer the values of love and trust. Keywords: Condom use, culture of life, HIV and AIDS, new infections, church teaching on sexualit

A Raman- and XRD study of the crystal chemistry of cobalt blue

The aim of this research project was to synthesise both the normal and inverse cobalt aluminate spinels by various methods and characterise them mainly by Raman spectroscopy with the support of X-ray powder diffraction (XRD), Fourier transform infra-red spectroscopy (FT-IR), energy disperse spectroscopy (EDS), and scanning electron microscopy (SEM). Four different synthesis methods (glycine-gel, citrate-gel, polyol and solid-state) were used to synthesise the cobalt aluminate powders with the general formula CoIICoIIIxAl2-xO4 (where x = 0-2). The gel or powder precursors were annealed at various temperatures ranging from 350ºC - 1000ºC. The properties of the intermediate and final products, influenced by the synthesis method, processing temperature, processing time and particle size, were compared. Raman spectra and XRD patterns indicating the presence of both normal and inverse cobalt aluminate spinel were observed. The inverse spinel was identified both as a transitional phase as well as a final phase, depending on the synthesis method and annealing temperature used. The various synthesis methods were also used to gain further insight into the crystal chemistry of cobalt aluminate. The solid-state method is the more traditional synthesis method. Solution techniques (glycine-gel, citrate-gel and polyol) were used in an attempt to synthesise blue cobalt aluminate at relatively low temperatures and processing times in order to obtain homogeneous, nanosized crystals with broad applicability. The polyol method was found to be most favourable for the synthesis of blue cobalt aluminate with regard to processing temperature and processing time. The various characterisation methods used, show that the intensity of the colour of the powders produced are strongly related to the degree of material crystallinity as well as Al/Co ratio. Inverse (Co2AlO4) and Co3O4 spinels are formed at lower temperatures or when the Co/Al ratio is greater than 0.5. The normal spinel (CoAl2O4) is produced at higher temperatures or when the Co/Al ratio is 0.5. The XRD patterns of CoAl2O4, Co2AlO4 and Co3O4, are very similar because they share the same spinel cubic structure (space group Fd3m) differing only slightly in the lattice size. It has been demonstrated that Raman and XRD can be used to distinguish between inverse and normal spinels while FT-IR and EDS are useful for assessing the purity of the powders produced. As predicted by group theory, five Raman and four IR active vibrations were evident in the results.Dissertation (MSc)--University of Pretoria, 2009.Chemistryunrestricte

An Ethical Claim for Administration of Pre-Exposure Prophylaxis (PREP) in HIV and AIDS Burdened Africa

It is morally justifiable for every person of good will to venture into HIV and AIDs prevention among the populace. Pre-exposure Prophylaxis (PrEP) administration promises to help meet the promise of this moral claim, which is founded on two ethical principles of ensuring wellbeing and justice for all. In spite of the efforts, challenges abound, especially in Africa. Some African tenets of sexuality, unavailability of contextualized and harmonized African sexuality theory as well as Africa’s poor economic standing are major threats to the administration of PrEP. This paper highlighted the major challenges and calls for their resolution if PrEP administration is to be of help to the poor and HIV burdened Africans.Key Words: HIV prevention, Preexposure Prophylaxis (PrEP), well-being, justic

Clustering of the Kenyan General Insurance Risk Classes by the Archimedean Copula Theory

Dependence between risks reduces the benefits of diversification. Modern portfolio theory is based on correlation as a measure of dependence while the criterion presented here is based on the copula theory as a measure of the intrinsic relatedness of different risks classes. The dependencies are examined by fitting copulas, estimating the dependence parameters and lastly using distance matrices to cluster the similar risks together. The study derives its data from the general insurance business in Kenya. The motivation of the study was driven by the fact that insurance companies had collapsed in the past, one reason being the type of business classes they engage in. It is therefore important to understand the dependencies between risks for better risk management. Five major clusters stood out each with peculiar characteristics. The first cluster constituted the lines with a high probability of a huge claim amount: Engineering, Liability, Fire industrial and Theft. The second contains lines with moderate claim amounts as compared to the previous cluster but are rather slightly more frequent: Fire domestic, Personal accident, Workman’s compensation, Motor commercial and motor private. In the following cluster we have the less popular lines under the umbrella of the miscellaneous class. Marine and Transit which is completely erratic clusters singly while the Aviation line whose main business is exported to foreign countries forming the last cluster. This will assist the companies seeking diversification of their risk portfolio and also entry into re-insurance treaties as a criterion for the determination of forwarding proportions is proposed here. Keywords: Copula, Measures of dependence, Cluster, Distances, Lines of busines

The Influence of Family Based Determinants on Implementation of Re-Admission Policy of Girls After Teenage Pregnancy in Public Secondary Schools in Kitui County

This study sought to investigate the influence of family based determinants on implementation of re-admission policy of girls after teenage pregnancy in public secondary schools in Kitui County, Kenya. The study objectives sought to determine the influence of; socio-economic status of parents, principals’ opinion on socio-economic status, family size and girls’ awareness of the policy on implementation of re-admission policy. The study was based on the critical theory by the Frankfurt school in German. The target population was 275 principals, 275 guidance and counseling teachers and 275 head girls in the 120 girls’ schools and 155 co-education schools in Kitui County, Kenya. The study also targeted the County Director of Education and all the 16 sub county directors of education in Kitui County. Using stratified and simple random sampling, a sample of 83 principals, 83 guidance and counseling, and 83 head girls were selected for the study. The County Director of Education was purposively selected while four sub-county directors of Education were selected using simple random sampling. Data was collected using questionnaires.  Quantitative data was analyzed using descriptive and inferential statistics. The study established that; there was a statistically significant association between socio-economic status of parents and implementation of re-admission policy of girls after teenage pregnancy. The family size, principals’ opinion on the re-admission policy and girls’ awareness of the policy significantly determined the implementation of the re-admission policy of girls after teenage pregnancy. The study recommends that; Parents should be sensitized on their role to educate girls the same way they would do to the boy child. This would enhance the implementation of the re-admission policy of girls after teenage pregnancy in public secondary schools in Kitui County, Kenya. Keywords: Co-education school, Re-admission Policy, Socio-Economic Status Teenage Pregnancies DOI: 10.7176/JEP/11-11-02 Publication date: April 30th 202

The nullcone in the multi-vector representation of the symplectic group and related combinatorics

We study the nullcone in the multi-vector representation of the symplectic group with respect to a joint action of the general linear group and the symplectic group. By extracting an algebra over a distributive lattice structure from the coordinate ring of the nullcone, we describe a toric degeneration and standard monomial theory of the nullcone in terms of double tableaux and integral points in a convex polyhedral cone.Comment: 21 pages, v2: title changed, typos and errors correcte

Systematic Studies in 'Schoenus' L. (Schoeneae, Cypearaceae)

Infra- and suprageneric classification of 'Schoenus' is uncertain. Like other Cyperaceae, 'Schoenus' L. and allied genera have reduced vegetative and reproductive structures which have resulted in uncertain homologies and hence differences in opinion about its phylogenetic relationships. This study addresses the issues of phylogeny, species limits and usefulness of anatomical data in the genus. Phylogenetic analysis of 195 ingroup samples made up of 123 samples covering 74 species of 'Schoenus' and 72 samples across 56 species from 11 genera in tribe Schoeneae was conducted on a molecular sequence dataset from ITS nrDNA using maximum parsimony and Bayesian inference. Results indicated that 'Schoenus' is non-monophyletic, which corroborates small-scale previous molecular studies. 'Schoenus' subgen. 'Schoenus' had strongly supported lineages whereas S. subgen. 'Pseudomesomelaena', including 'S. grandiflorus', are embedded within other genera in Schoeneae and therefore not in core 'Schoenus'. The ITS data did not fully resolve relationships of 'Schoenus' at species level, but revealed numerous well supported terminal groupings and taxa allowing for further fine-scale study of the complexes to resolve limits and application of names. ... Taxonomic value of culm anatomy has been investigated using phenetic analysis. The results show culm anatomical features have taxonomic value in 'Schoenus' at and below species level and help to clarify patterns of variation at infra and interspecific level and to resolve species complexes. Phylogenetic analysis, however, indicated that the dataset had no power to resolve higher level relationships within 'Schoenus'. A new species has been distinguished from 'S. melanostachys' using morphology and integrating evidence from culm anatomy and scanning electron microscopy