The flavor symmetry in the standard model and the triality symmetry

A Dirac fermion is expressed by a 4 component spinor which is a combination of two quaternions and which can be treated as an octonion. The octonion possesses the triality symmetry, which defines symmetry of fermion spinors and bosonic vector fields. The triality symmetry relates three sets of spinors and two sets of vectors, which are transformed among themselves via transformations $G_{23}, G_{12}, G_{13}$, $G_{123}$ and $G_{132}$. If the electromagnetic (EM) interaction is sensitive to the triality symmetry, i.e. EM probe selects one triality sector, EM signals from the 5 transformed world would not be detected, and be treated as the dark matter. According to an astrophysical measurement, the ratio of the dark to ordinary matter in the universe as a whole is almost exactly 5. We expect quarks are insensitive to the triality, and triality will appear as three times larger flavor degrees of freedom in the lattice simulation.Comment: 16 pages 8 figures, To be published in International Journal of Modern Physics

Hamming weights and Betti numbers of Stanley-Reisner rings associated to matroids

To each linear code over a finite field we associate the matroid of its parity check matrix. We show to what extent one can determine the generalized Hamming weights of the code (or defined for a matroid in general) from various sets of Betti numbers of Stanley-Reisner rings of simplicial complexes associated to the matroid

On character generators for simple Lie algebras

We study character generating functions (character generators) of simple Lie algebras. The expression due to Patera and Sharp, derived from the Weyl character formula, is first reviewed. A new general formula is then found. It makes clear the distinct roles of ``outside'' and ``inside'' elements of the integrity basis, and helps determine their quadratic incompatibilities. We review, analyze and extend the results obtained by Gaskell using the Demazure character formulas. We find that the fundamental generalized-poset graphs underlying the character generators can be deduced from such calculations. These graphs, introduced by Baclawski and Towber, can be simplified for the purposes of constructing the character generator. The generating functions can be written easily using the simplified versions, and associated Demazure expressions. The rank-two algebras are treated in detail, but we believe our results are indicative of those for general simple Lie algebras.Comment: 50 pages, 11 figure

Calculated corrections to superallowed Fermi beta decay: New evaluation of the nuclear-structure-dependent terms

The measured $ft$-values for superallowed $0^{+} \to 0^{+}$ nuclear $\beta$-decay can be used to obtain the value of the vector coupling constant and thus to test the unitarity of the Cabibbo-Kobayashi-Maskawa matrix. An essential requirement for this test is accurate calculations for the radiative and isospin symmetry-breaking corrections that must be applied to the experimental data. We present a new and consistent set of calculations for the nuclear-structure-dependent components of these corrections. These new results do not alter the current status of the unitarity test -- it still fails by more than two standard deviations -- but they provide calculated corrections for eleven new superallowed transitions that are likely to become accessible to precise measurements in the future. The reliability of all calculated corrections is explored and an experimental method indicated by which the structure-dependent corrections can be tested and, if necessary, improved.Comment: Revtex4, one figur

Applying knowledge management strategies to economic development in sub-Saharan Africa

Sustainability looks to achieve best outcomes for human and natural environments both now and in the indefinite future. It relates to the continuity of economic, social, institutional and environmental aspects of human society, as well as the non-human environment. This paper examines economic development as one aspect of sustainability, with a focus on knowledge management as an economic development strategy. Using Grey’s categories of knowledge management, the authors address sustainable economic development in the context of sub-Saharan Africa. Production capability is no longer completely dependent on capital and equipment; information and knowledge assets are increasingly important. In this information economy, success comes from harnessing the information and knowledge of a community. Such “indigenous knowledge,” local and often tacit, exists in every community, every region and every country. This knowledge is useful in identifying new entrepreneurial opportunities, as well as for sustaining and advancing local businesses. Sub-Saharan Africa provides an excellent case study. No other region of the world is in more dire need of development. The 700 million people in this area face tremendous challenges, including the world’s highest incidence of HIV/AIDS, deep poverty, unemployment, political instability, and a host of related problems. Key factors for using knowledge management as an economic development strategy in the region will include ICT (Information and Communication Technologies) literacy; uncovering and developing local intellectual assets; capturing tacit knowledge; internal and external knowledge sharing; and managing political, social and technological barriers. Other specific recommendations include promoting ICT literacy through training programs; leveraging internet and email technologies for community building; investing financial resources in R & D; and developing metrics for outcome assessment.Keywords: Knowledge management, economic development, sub-Saharan Africa

Further Comparisons of Finite Difference Schemes for Computational Modelling of Biosensors

Simulations are presented for a reaction-diffusion system within a thin layer containing an enzyme, fed with a substrate from the surrounding electrolyte. The chemical term is of the nonlinear Michaelis-Menten type and requires a technique such as Newton iteration for solution. It is shown that approximating the nonlinear chemical term in these systems by a linearised form reduces both the accuracy and, in the case of second-order methods such as Crank-Nicolson, reduces the global error order from O(δT2) to O(δT). The first-order methods plain backwards implicit with and without linearisation, and Crank-Nicolson with linearisation are all of O(δT) and very similar in performance, requiring, for a given accuracy target, an order of magnitude more CPU time than the efficient methods backward implicit with extrapolation and Crank-Nicolson, both with Newton iteration to handle the nonlinearity. Steady state computations agree with expectations, tending to the known solutions for limiting cases. The Crank-Nicolson method shows some concentration oscillations close to the outer layer boundary but this does not propagate to the inner boundary at the electrode. The backward implicit methods do not result in such oscillations and if concentration profiles are of interest, may be preferred

Intrinsic electrochemical activity of single walled carbon nanotube–Nafion assemblies

The intrinsic electrochemical properties and activity of single walled carbon nanotube (SWNT) network electrodes modified by a drop-cast Nafion film have been determined using the one electron oxidation of ferrocene trimethyl ammonium (FcTMA+) as a model redox probe in the Nafion film. Facilitated by the very low transport coefficient of FcTMA+ in Nafion (apparent diffusion coefficient of 1.8 × 10−10 cm2 s−1), SWNTs in the 2-D network behave as individual elements, at short (practical) times, each with their own characteristic diffusion, independent of neighbouring sites, and the response is diagnostic of the proportion of SWNTs active in the composite. Data are analysed using candidate models for cases where: (i) electron transfer events only occur at discrete sites along the sidewall (with a defect density typical of chemical vapour deposition SWNTs); (ii) all of the SWNTs in a network are active. The first case predicts currents that are much smaller than seen experimentally, indicating that significant portions of SWNTs are active in the SWNT–Nafion composite. However, the predictions for a fully active SWNT result in higher currents than seen experimentally, indicating that a fraction of SWNTs are not connected and/or that not all SWNTs are wetted completely by the Nafion film to provide full access of the redox mediator to the SWNT surface

Molecular detection of carbapenemase-producing genes in referral Enterobacteriaceae in South Africa: A short report

Molecular confirmation of carbapenemase-producing Enterobacteriaceae (CPE) was introduced in South Africa (SA) at the end of 2011. We report on the detection of these resistance genes based on referral isolates. Enterobacteriaceae with non-susceptibility to any of the carbapenems according to defined criteria for antimicrobial susceptibility testing results were sent to a reference laboratory. A proportion of isolates had limited demographic, epidemiological and clinical data available. Organism identification was reconfirmed using reference laboratory methods, and the presence of carbapenemases was confirmed with a real-time polymerase chain reaction. We analysed 1 503 significant isolates received for confirmation from the National Health Laboratory Service and some private laboratories during 2012 - 2015 and confirmed one or more carbapenemase-producing genes in 68% of isolates, the most common organism being Klebsiella pneumoniae (60%). The most common carbapenemase genes were blaNDM, followed by blaOXA-48 and its variants. BlaOXA-48 and its variants demonstrated non-susceptibility to ertapenem in 89% of the isolates when analysed by the phenotypic method, and to ceftazidime in 34%. Overall, the detection rate for carbapenemases in K. pneumoniae blood isolates in the public sector was 1.9% during the 4-year period. This report indicates the presence of CPE in SA, and it is important for all healthcare workers to be aware of this major public health threat so that infection prevention and control measures can be implemented to prevent the spread of CPE in healthcare facilities

Age of diagnosis for congenital hearing loss at Universitas Hospital, Bloemfontein

Background. Congenital hearing loss affects 3 - 6/1 000 children worldwide. The benefits of early identification of hearing loss and early intervention have been clearly established. There are no previous studies reporting on the age of diagnosis of congenital hearing loss in the Free State province.Objectives. To determine the age of diagnosis of congenital hearing loss in the Otorhinolaryngology Clinic at Universitas Hospital. Secondary aims included determining age at first visit, as well as the time delay between first visit and diagnosis, and documenting any interventions which took  place.Methods. A retrospective, descriptive study was undertaken, analysing data from 2001 to 2010.Results. A total of 260 cases of congenital hearing loss were analysed. The median age of diagnosis of hearing loss was 44.5 months. The median age of first visit was 40.9 months, and the median delay between first visit and diagnosis was 49 days.Conclusions. The median age of diagnosis far exceeds national and  international benchmarks. This has a profoundly negative impact on the development and outcomes of children with hearing loss. These results have been used to motivate for the expansion of hearing screening and diagnostic services in the province