Boundary layer analysis of the Navier-Stokes equations with Generalized Navier boundary conditions

We study the weak boundary layer phenomenon of the Navier-Stokes equations in a 3D bounded domain with viscosity, $\epsilon > 0$, under generalized Navier friction boundary conditions, in which we allow the friction coefficient to be a (1, 1) tensor on the boundary. When the tensor is a multiple of the identity we obtain Navier boundary conditions, and when the tensor is the shape operator we obtain conditions in which the vorticity vanishes on the boundary. By constructing an explicit corrector, we prove the convergence of the Navier-Stokes solutions to the Euler solution as the viscosity vanishes. We do this both in the natural energy norm with a rate of order $\epsilon^{3/4}$ as well as uniformly in time and space with a rate of order $\epsilon^{3/8 - \delta}$ near the boundary and $\epsilon^{3/4 - \delta'}$ in the interior, where $\delta, \delta'$ decrease to 0 as the regularity of the initial velocity increases. This work simplifies an earlier work of Iftimie and Sueur, as we use a simple and explicit corrector (which is more easily implemented in numerical applications). It also improves a result of Masmoudi and Rousset, who obtain convergence uniformly in time and space via a method that does not yield a convergence rate.Comment: Additional references and several typos fixe

Back to the Amitsur-Levitzki theorem: a super version for the orthosymplectic Lie superalgebra osp(1, 2n)

We prove an Amitsur-Levitzki type theorem for the Lie superalgebras osp(1,2n) inspired by Kostant's cohomological interpretation of the classical theorem. We show that the Lie superalgebras gl(p,q) cannot satisfy an Amitsur-Levitzki type super identity if p, q are non zero and conjecture that neither can any other classical simple Lie superalgebra with the exception of osp(1,2n).Comment: 11 pages, to be published in Letters in Mathematical Physics; added references, corrected typo

Books

No Abstract

Corporate Governance dan Pengaruhnya terhadap Kinerja Keuangan Perusahaan

Application of corporate governance in the company is a way to handle the agency conflict that impact to company’s financial performance The objective of this research is to analyses the impact of managerial ownership, board size, ownership concentration and debt toward fi nancial performance that measured by ROE. The population of this research is the manufacturer companies which listed at Bursa Efek Indonesia (BEI) over the fi ve years periods on 2009 until 2013. This research used purposive sampling method. The sample of this reseach consist of 90 companies that met the criteria. This study uses multiple regression analysis to see the contribution of each variable in influence financial performance of company. The results showed that: (1) managerial ownership is not signifi cant to eff ect fi nancial performance of company, (2) board size is not signifi cant to eff ect fi nancial performance of company, (3) ownership concentration is signifi cant to eff ect fi nancial performance of company, (4) debt is significant to effect financial performance of compan

Lightning Protection and Earthing System in Universiti Teknologi PETRONAS

The objective of this project will lead to analyze and verify original design and hence in-depth study on the UTP Lightning Protection and Earthing Systems. The project will be carried with obtaining documentations, carry out conceptual studies, site survey, literature review and then recommendation report. The results are shown in pictures and diagrams to enable clearer view of what has been found so far. By the end of this semester, a full report on UTP's Earthing System will be presented together with the simulation of the Earthing System Model

H-statistic with winsorized modified one-step M-estimator as central tendency measure

Two-sample independent t-test and ANOVA are classical procedures which are widely used to test the equality of two groups and more than two groups respectively. However, these parametric procedures are easily affected by non-normality, becoming more obvious when heterogeneity of variances and unbalanced group sizes exist. It is well known that the violation in the assumption of the tests will lead to inflation in Type I error rate and decreasing in the power of test. Nonparametric procedures like Mann-Whitney and Kruskal-Wallis may be the alternative to the parametric procedures, however, loss of information occur due to the ranking data. In mitigating these problems, robust procedures can be used as the other alternative. One of the procedures is H-statistic. When used with modified one-step M-estimator (MOM), the test statistic (MOM-H) produces good control of Type I error rate even under small sample size but inconsistent under certain conditions investigated. Furthermore, power of test is low which might be due to the trimming process. In this study, MOM was winsorized (WMOM) to retain the original sample size. The Hstatistic when combines with WMOM as the central tendency measure (WMOM-H) shows better control of Type I error rate as compared to MOM-H especially under balanced design regardless of the shape of distributions. It also performs well under highly skewed and heavy tailed distribution for unbalanced design. On top of that, WMOM-H also generates better power value, as compared to MOM-H and ANOVA under most of the conditions investigated. WMOM-H also has better control of Type I error rates with no liberal value (>0.075) compared to the parametric (t-test and ANOVA) and nonparametric (Mann-Whitney and Kruskal-Wallis) procedures. In general, this study demonstrates that winsorization process (WMOM) is able to improve the performance of H-statistic in terms of controlling Type I error rate and increasing power of test

Stability of Vortex Solutions to an Extended Navier-Stokes System

We study the long-time behavior an extended Navier-Stokes system in $\R^2$ where the incompressibility constraint is relaxed. This is one of several "reduced models" of Grubb and Solonnikov '89 and was revisited recently (Liu, Liu, Pego '07) in bounded domains in order to explain the fast convergence of certain numerical schemes (Johnston, Liu '04). Our first result shows that if the initial divergence of the fluid velocity is mean zero, then the Oseen vortex is globally asymptotically stable. This is the same as the Gallay Wayne '05 result for the standard Navier-Stokes equations. When the initial divergence is not mean zero, we show that the analogue of the Oseen vortex exists and is stable under small perturbations. For completeness, we also prove global well-posedness of the system we study.Comment: 24 pages, 1 figure, updated to add authors' contact information and to address referee's comment

Changing long-term care realities and futures for older persons in (West) Africa

No Abstract

Can virtual reality have a positive influence on student engagement?

Through the rapid development of virtual reality (VR), South African Higher Educational Institutions (HEIs) have shown interest in the potential VR has in teaching and learning practices. HEIs are further urged by the South African government to use cutting edge educational technology (edtech) tools to promote student engagement and limit the high dropout rates noticeable in HEIs. The researcher explored the perceived impact VR can have on student engagement. A qualitative research methodology was adopted for this study and the research instruments included open-ended questionnaires, semi-structured interviews, and a true experiment. Thirty-six participants took part in the study. The results of the study highlight a 23 per cent higher pass rate and a 180 per cent higher engagement level in students using VR as opposed to students studying via online distance learning. Two themes emerged from the results, namely: (1) the use of VR in teaching and learning, and (2) the influence VR has on student engagement levels. The results of this study further highlight that VR learning yields higher student engagement levels and as a result, students achieve higher marks. The significance of the study lies in the assistance it can offer higher educational institutions in their decision-making process of adopting VR into their teaching and learning processes