The link between regularity and strong-pi-regularity

It is shown that if all powers of a ring element $a$ are regular, then $a$ will be strongly-pi-regular exactly when a suitable word in the powers of $a$ and their inner inverses is a unit.Research with financial support provided by the Research Centre of Mathematics of the University of Minho (CMAT) through the FCT Pluriannual Funding Program

Invariance under outer inverses

We shall use the minus partial order combined with Pierce’s decomposition to derive the class of outer inverses for idempotents, units and group invertible elements. Subsequently we show, for matrices over a field F, that the triplet BA^ C is invariant under all choices of outer inverses of A if and only if B= 0 or C= 0.FCT - Fundação para a Ciência e a Tecnologia (UID-MAT-00013/2013)info:eu-repo/semantics/publishedVersio

INS and OUTS of Inclusion–Exclusion

Inclusion-Exclusion identities and inequalities are obtained for valuations. Applications to cardinality, probability, max/min and least common multiples are presented

The group inverse of the nivellateur

We shall derive necessary and sufficient conditions for the nivellateur to have a group inverse over an algebraically closed field. We then extend these results to arbitrary fields.- Partially supported by FCT-'Fundacao para a Ciencia e a Tecnologia', within the project [UID-MAT-00013/2013]

Classical dimers on the triangular lattice

We study the classical hard-core dimer model on the triangular lattice. Following Kasteleyn's fundamental theorem on planar graphs, this problem is soluble by Pfaffians. This model is particularly interesting for, unlike the dimer problems on the bipartite square and hexagonal lattices, its correlations are short ranged with a correlation length of less than one lattice constant. We compute the dimer-dimer and monomer-monomer correlators, and find that the model is deconfining: the monomer-monomer correlator falls off exponentially to a constant value sin(pi/12)/sqrt(3) = .1494..., only slightly below the nearest-neighbor value of 1/6. We also consider the anisotropic triangular lattice model in which the square lattice is perturbed by diagonal bonds of one orientation and small fugacity. We show that the model becomes non-critical immediately and that this perturbation is equivalent to adding a mass term to each of two Majorana fermions that are present in the long wavelength limit of the square-lattice problem.Comment: 15 pages, 5 figures. v2: includes analytic value of monomer-monomer correlator, changes titl

Sub therapeutic drug levels among HIV/TB co-infected patients receiving Rifampicin in northwestern Tanzania: A cross sectional clinic based study

Background: Tuberculosis/Human Immunodeficiency Virus (TB/HIV) is a very common co-infection which carries a high mortality rate. Though World Health Organization recommends co-treatment of TB/HIV to improve its outcome, Rifampicin potentially induces metabolism and sub-therapeutic antiretroviral plasma levels of non nucleoside reverse transcriptase inhibitors and protease inhibitors which may cause inadequate virological suppression if corrections are not timely done. In Tanzania Therapeutic drug monitoring is not done; so the proportion of sub-therapeutic ARV plasma levels among TB/HIV patients co-treated with anti-tuberculous drugs is not known. The aim of this study was therefore to determine the magnitude and risk factors of sub-therapeutic ARV plasma levels among adult HIV patients co-treated with anti tuberculous Medications.Materials and methods: A cross sectional hospital based study was conducted among adult HIV patients on ARV and TB co-treatment for at least one month. Patients were serially enrolled through routine HIV care and treatment services until the sample size was reached. The information about demographic, clinical and adherence level, Anti-TB duration, viral load, baseline and enrollment CD4 counts, Hepatitis B co-infection and ARV plasma levels was collected and analyzed using STATA 12 software.Results: In total 118 patients were included in this study; of whom 26 (22%) had sub-therapeutic ARV plasma levels. The sub-therapeutic ARV levels were independently associated with adherence <95% (OR =6.8, p= 0.001), female gender (OR = 3.4, p= 0.028) and virological failure (OR= 3.8, p= 0.016). NVP based regimen was associated with sub-therapeutic drug levels on univariate model (OR = 2.1, p= 0.010).Conclusion: The magnitude of sub-therapeutic ARV plasma levels is high among adult HIV/TB coinfected patients on anti-TB co-treatment in Tanzania. These patients stand a high risk of inadequate virological suppression with a potential resistance development and a long term poor clinical outcome. Identifying at risk patients and adherence enhancement could potentially improve the overall outcome of this subgroup of patients in resource restricted setting like ours where TDM is not available.Keywords: HIV; HIV/TB co-infection; HIV/TB co-treatment Rifampicin; Antiretroviral therapy; Plasma ARV drug levels; Therapeutic drug monitorin