Three eigenvalue bounds are derived for the instability of ideal compressible stratified magnetohydrodynamic shear flows in which base velocity, density, and magnetic field vary two directions. The first bound can be obtained by combining Howard semi-circle theorem with energy principle Lagrangian displacement. Remarkably, no special conditions needed to use this bound, some cases, we establish...

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The epithelium lining the mouse larynx occupied the transitional zone between the keratinized stratified squamous epithelium lining the oral cavity and the ciliated columnar one continuing to the trachea. The epithelium showed gradations ranging from stratified squamous through stratified cuboidal to ciliated stratified low-columnar type. It is suggested that the epithelium is identical with th...

Let C be an isolated plane curve singularity, and (C, l) be a decorated curve. In this article we compare the equisingular deformations of C and the sandwiched singularity X(C, l). We will prove that for l ≫ 0 the functor of equisingular deformations of C and (C, l) are equivalent. From this we deduce a proof of a formula for the dimension of the equisingular stratum. Furthermore we will show h...

In this study, we propose a two stage randomized response model. Improved unbiased estimators of the mean number of persons possessing a rare sensitive attribute under two different situations are proposed. The proposed estimators are evaluated using a relative efficiency comparison. It is shown that our estimators are efficient as compared to existing estimators when the parameter of rare unre...