menelaus’ sphaerica can be considered as the most important classical text in the tradition of spherics books, written with the aim of the solution of problems arising in spherical astonomy. euclid’s elements is the the most important book on plane geometry. this article aims at a comparative study of menelaus’s sphaerica and euclid’s elements, to show that book i of sphaerica is an attempt to ...

By subjecting DNA aqueous solution to evaporate in a curve-on-flat geometry that was composed of either a spherical lens or a cylindrical lens situated on a flat substrate, a set of highly aligned DNA nanowires in the forms of spokes and parallel stripes over a macroscopic area (i.e., millimeter scale) were successfully created. The DNA molecules were stretched and aligned on polymer-coated sub...

PURPOSE To compare the shape and volume of the lenticules of corneal tissue ablated for the correction of spherical, cylindrical, and spherocylindrical refractive errors using Boolean operations of theoretical 3-dimensional (3-D) surfaces. SETTING Department of Ophthalmology, Rothschild Foundation, Paris, France. METHODS Digital modeling software was used to perform graphic representations ...

| A simple and systematic derivation of anisotropic perfectly matched layers (PML) in cylindrical and spherical coordinates is presented. The derivation is based on the analytic continuation of Maxwell's Equations to complex space. Through eld transformations, results for Cartesian anisotropic PML media are recovered and, more importantly, a generalization of the anisotropic PML to cylindrical ...

A simple and systematic derivation of anisotropic perfectly matched layers (PML’s) in cylindrical and spherical coordinates is presented. The derivation is based on the analytic continuation of Maxwell’s Equations to complex space. Through field transformations, results for Cartesian anisotropic PML media are recovered and, more importantly, a generalization of the anisotropic PML to cylindrica...

Using molecular-dynamics simulation, we have calculated the interfacial free energy γ between a hard-sphere fluid and hard spherical and cylindrical colloidal particles, as functions of the particle radius R and the fluid packing fraction η=ρσ(3)/6, where ρ and σ are the number density and hard-sphere diameter, respectively. These results verify that Hadwiger's theorem from integral geometry, w...

In this work, we have studied the miniband and minigaps of GaN/AlN constant total effective radius multi-shells quantum dots (CTER-MSQDs) and Rings (CTERMSQRs).We have investigated effects of the Hydrogenic donor impurities, quantum dots and rings radii, and the number of wells on miniband formation by sub-band energy calculations. We show that in these systems, minigaps can be created and then...