An elliptical invisible cloak is proposed using a coordinate transformation in the ellipticalcylindrical coordinate system, which crushes the cloaked object to a line segment instead of a point. The elliptical cloak is reduced to a nearly-circular cloak if the elliptical focus becomes very small. The advantage of the proposed invisibility cloak is that none of the parameters is singular and the...

Sérsic (1968) generalized the de Vaucouleurs law which follows the projected (observed) one dimensional radial profile of elliptical galaxies closely and Dehnen (1993) proposed an analytical formula of the 3-dimensional light distributions whose projected line profile resembles the de Vaucouleurs law. This paper is involved to recover the Dehnen model and generalize the model to account for gal...

The classical numerical range of a quadratic operator is an elliptical disk. This result is extended to different kinds of generalized numerical ranges. In particular, it is shown that for a given quadratic operator, the rank-k numerical range, the essential numerical range, and the q-numerical range are elliptical disks; the c-numerical range is a sum of elliptical disks, and the Davis-Wieland...

Visual insights into a wide variety of statistical methods, for both didactic and data analytic purposes, can often be achieved through geometric diagrams and geometrically based statistical graphs. This paper extols and illustrates the virtues of the ellipse and her higher-dimensional cousins for both these purposes in a variety of contexts, including linear models, multivariate linear models ...

The colour-magnitude relation (CMR) of cluster elliptical galaxies has been widely used to constrain their star formation histories (SFHs) and to discriminate between the monolithic collapse and merger paradigms of elliptical galaxy formation. We use a ΛCDM hierarchical merger model of galaxy formation to investigate the existence and redshift evolution of the elliptical galaxy CMR in the merge...

The goal of this paper is to propose efficient and adaptive regularized estimators for the nonparametric component, mean and covariance matrix in both high and fixed dimensional situations. Although, semiparametric estimation of elliptical distribution has also been discussed in [8], we wish to expand the model in two ways. First, study adaptive estimation methods with a novel scheme of estimat...