In this paper we will determine the multiple point manifolds of certain self-transverse immersions in Euclidean spaces. Following the triple points, these immersions have a double point self-intersection set which is the image of an immersion of a smooth 5-dimensional manifold, cobordant to Dold manifold $V^5$ or a boundary. We will show there is an immersion of $S^7times P^2$ in $mathbb{R}^{1...

A collection of MATLAB classes for computing and using spherical harmonic transforms is presented. Methods of these classes compute differential operators on the sphere and are used to solve simple partial differential equations in a spherical geometry. The spectral synthesis and analysis algorithms using fast Fourier transforms and Legendre transforms with the associated Legendre functions are...

Two novel classes of spherical invisibility cloaks based on nonlinear transformation have been studied. The cloaking characteristics are presented by segmenting the nonlinear transformation based spherical cloak into concentric isotropic homogeneous coatings. Detailed investigations of the optimal discretization (e.g., thickness control of each layer, nonlinear factor, etc.) are presented for b...

The spherical collapse model was first developed by Gunn & Gott 1 for a flat universe with no cosmological constant. It assumes that the process of formation of bound objects in the universe can be at first approximation described by evolution of an uniformly overdense spherical region in otherwise smooth background. Despite its simplicity, the model has been widely used to explain properties o...

DNA based spherical nanostructures are one of the promising nanostructures for several biomedical and biotechnological applications due to their excellent biocompatibility and DNA-directed surface addressability. Herein, we report the synthesis and amphiphilicity-driven self-assembly of two classes of DNA (hydrophilic)-chromophore (hydrophobic) hybrid amphiphiles into spherical nanostructures. ...