Some additive results on Drazin Inverses

In this paper, some additive results on Drazin inverse of a sum of Drazin invertible elements are derived. Some converse results are also presented.Fundação Luso Americana para o DesenvolvimentoUniversidade do Minho. Centro de Matemática (CMAT)Fundação para a Ciência e a Tecnologia (FCT

The (2,2,0) drazin inverse problem

We consider the additive Drazin problem and we study the existence of the Drazin inverse of a two by two matrix with zero (2,2) entry.This research was financed by FEDER Funds through ``Programa Operacional Factores de Competitividade - COMPETE'' and by Portuguese Funds through FCT - ``Fundação para a Ciência e a Tecnologia'', within the project PEst-C/MAT/UI0013/2011

The influence of electric fields and surface tension on Kelvin-Helmholtz instability in two-dimensional jets

We consider nonlinear aspects of the flow of an inviscid two-dimensional jet into a second immiscible fluid of different density and unbounded extent. Velocity jumps are supported at the interface, and the flow is susceptible to the Kelvin–Helmholtz instability. We investigate theoretically the effects of horizontal electric fields and surface tension on the nonlinear evolution of the jet. This is accomplished by developing a long-wave matched asymptotic analysis that incorporates the influence of the outer regions on the dynamics of the jet. The result is a coupled system of long-wave nonlinear, nonlocal evolution equations governing the interfacial amplitude and corresponding horizontal velocity, for symmetric interfacial deformations. The theory allows for amplitudes that scale with the undisturbed jet thickness and is therefore capable of predicting singular events such as jet pinching. In the absence of surface tension, a sufficiently strong electric field completely stabilizes (linearly) the Kelvin–Helmholtz instability at all wavelengths by the introduction of a dispersive regularization of a nonlocal origin. The dispersion relation has the same functional form as the destabilizing Kelvin–Helmholtz terms, but is of a different sign. If the electric field is weak or absent, then surface tension is included to regularize Kelvin–Helmholtz instability and to provide a well-posed nonlinear problem. We address the nonlinear problems numerically using spectral methods and establish two distinct dynamical behaviors. In cases where the linear theory predicts dispersive regularization (whether surface tension is present or not), then relatively large initial conditions induce a nonlinear flow that is oscillatory in time (in fact quasi-periodic) with a basic oscillation predicted well by linear theory and a second nonlinearly induced lower frequency that is responsible for quasi-periodic modulations of the spatio-temporal dynamics. If the parameters are chosen so that the linear theory predicts a band of long unstable waves (surface tension now ensures that short waves are dispersively regularized), then the flow generically evolves to a finite-time rupture singularity. This has been established numerically for rather general initial conditions

Marketing strategy implementation in higher education. A mixed approach for model development and testing

This study seeks to extend our knowledge of marketing strategy implementation in the context of international student recruitment. Strategy implementation remains an area of limited focus in the marketisation of higher education literature. Employing a mixed-design methodology on universities in the UK, US, Australia, and New Zealand, a conceptual model is presented and tested on 570 mid-level international marketing managers. Four overall constructs are found to be significant strategy implementation factors: implementation related outcome variables, dimensions of commitment, strategy, and role factors. In light of these findings, several implications are advanced for university management. The study also makes important theoretical contributions: it contributes to a growing body of literature on marketing of higher education; it adds a more nuanced theoretical foundation of marketing strategy implementation by focusing on academic institutions rather than business firms; and it enriches the theory of marketing strategy implementation by taking a cross-national analytical approach