In 1958 E. Lehmer found an explicit description of those primes p for which a given prime q is a cubic residue. Her result states that if one writes 4p = L + 27M, then q is a cubic residue if and only if M/L ≡ (t − 1)/(t − 9t) mod q for some integer t. Recently, Z. Sun has stated a similar result for cubic nonresidues which follows from several corollaries appearing in an earlier paper of his. ...

The phase diagram for a system of model anisotropic particles with six attractive patches in an octahedral arrangement has been computed. This model for a relatively narrow value of the patch width where the lowest-energy configuration of the system is a simple cubic crystal. At this value of the patch width, there is no stable vapor-liquid phase separation, and there are three other crystallin...

To investigate the degree d d connectedness locus, Thurston [On geometry and dynamics of iterated rational maps, Complex Dyn...

In this study, Flake-like magnesium hydroxide (Mg(OH)2) and cubic-like aluminum hydroxide (Al(OH)3) nanostructures were synthesized via a simple co-precipitation method at relatively low temperature. Chemical properties and surface morphology of the magnesium hydroxide and aluminum hydroxide were characterized by X-ray diffraction analysis (XRD), scanning electron microscopy image (SEM), transm...