On the Uniqueness of Solution of Magnetostatic Vector‐potential Problems by Three‐dimensional Finite‐element Methods

In this paper, particular attention is paid to the impact of finite‐element approximation on uniqueness and to approximations implicit in finite element formulations from the uniqueness requirements standpoint. It is also shown that the flux density is unique without qualifications. The theoretical and numerical uniqueness of the magnetic vector potential in three‐dimensional problems is also given. This analysis is restricted to linear, isotropic media with Dirichlet Boundary conditions. As an interesting consequence of this analysis it is shown that, under usual conditions adopted in obtaining three‐dimensional finite‐element solutions, it is not necessary to specify div Ā in order that Ā be uniquely defined

A New Generalization of the Lomax Distribution with Increasing, Decreasing, and Constant Failure Rate

Developing new compound distributions which are more flexible than the existing distributions have become the new trend in distribution theory. In this present study, the Lomax distribution was extended using the Gompertz family of distribution, its resulting densities and statistical properties were carefully derived, and the method of maximum likelihood estimation was proposed in estimating themodel parameters. A simulation study to assess the performance of the parameters of Gompertz Lomax distribution was provided and an application to real life data was provided to assess the potentials of the newly derived distribution. Excerpt from the analysis indicates that the Gompertz Lomax distribution performed better than the Beta Lomax distribution, Weibull Lomax distribution, and Kumaraswamy Lomax distribution

Comparison of Mycobacterium tuberculosis drug susceptibility using solid and liquid culture in Nigeria.

BACKGROUND: This study compares Mycobacterium tuberculosis culture isolation and drug sensitivity testing (DST) using solid (LJ) and liquid (BACTEC-MGIT-960) media in Nigeria. METHODS: This was a cross sectional survey of adults attending reference centres in Abuja, Ibadan and Nnewi with a new diagnosis of pulmonary tuberculosis (TB) or having failed the first-line TB treatment. Patients were requested to provide three sputum specimens for smear-microscopy and culture on LJ and BACTEC-MGIT-960. Positive cultures underwent DST for streptomycin, isoniazid, rifampicin and ethambutol. RESULTS: 527 specimens were cultured. 428 (81%) were positive with BACTEC-MGIT-960, 59 (11%) negative, 36 (7%) contaminated and 4 (1%) had non-tuberculosis mycobacteria (NTM). 411 (78%) LJ cultures were positive, 89 (17%) negative, 22 (4%) contaminated and 5 (1%) had NTM. The mean (SD) detection time was 11 (6) and 30 (11) days for BACTEC-MGIT-960 and LJ. DST patterns were compared in the 389 concordant positive BACTEC-MGIT-960 and LJ cultures. Rifampicin and isoniazid DST patterns were similar. Streptomycin resistance was detected more frequently with LJ than BACTEC-MGIT-960 and ethambutol resistance was detected more frequently with BACTEC-MGIT-960 than LJ, but differences were not statistically significant. MDR-TB was detected in 27 cases by LJ and 25 by BACTEC-MGIT-960 and using both methods detected 29 cases. CONCLUSIONS: There was a substantial degree of agreement between the two methods. However using the two in tandem increased the number of culture-positive patients and those with MDR-TB. The choice of culture method should depend on local availability, cost and test performance characteristics

Abelian-Higgs and Vortices from ABJM: towards a string realization of AdS/CMT

We present ans\"{a}tze that reduce the mass-deformed ABJM model to gauged Abelian scalar theories, using the fuzzy sphere matrices $G^\alpha$. One such reduction gives a Toda system, for which we find a new type of nonabelian vortex. Another gives the standard Abelian-Higgs model, thereby allowing us to embed all the usual (multi-)vortex solutions of the latter into the ABJM model. By turning off the mass deformation at the level of the reduced model, we can also continuously deform to the massive $\phi^4$ theory in the massless ABJM case. In this way we can embed the Landau-Ginzburg model into the AdS/CFT correspondence as a consistent truncation of ABJM. In this context, the mass deformation parameter $\mu$ and a field VEV $$ act as $g$ and $g_c$ respectively, leading to a well-motivated AdS/CMT construction from string theory. To further this particular point, we propose a simple model for the condensed matter field theory that leads to an approximate description for the ABJM abelianization. Finally, we also find some BPS solutions to the mass-deformed ABJM model with a spacetime interpretation as an M2-brane ending on a spherical M5-brane.Comment: 43 pages, latex, explanations added in the introduction, end of section 4, and on page 2