The rst part of this paper classi es all purely cubic function elds over a nite eld of characteristic not equal to 3. In the remainder, we describe a method for computing the fundamental unit and regulator of a purely cubic congruence function eld of unit rank 1 and characteristic at least 5. The technique is based on Voronoi's algorithm for generating a chain of successive minima in a multipli...

We study the existence of a Chow-theoretic decomposition of the diagonal of a smooth cubic hypersurface, or equivalently, the universal triviality of its CH0-group. We prove that for odd dimensional cubic hypersurfaces or for cubic fourfolds, this is equivalent to the existence of a cohomological decomposition of the diagonal, and we translate geometrically this last condition. For cubic threef...

A graph Γ is symmetric if its automorphism group acts transitively on the arcs of Γ, and s-regular if its automorphism group acts regularly on the set of s-arcs of Γ. Tutte (1947, 1959) showed that every cubic finite symmetric cubic graph is s-regular for some s ≤ 5. We show that a symmetric cubic graph of girth at most 9 is either 1-regular or 2-regular (following the notation of Djokovic), or...

There is growing evidence that a metastable phase of ice, cubic ice, plays an important role in the Earth's troposphere and stratosphere. Cubic ice may also be important in diverse fields such as cryobiology and planetary sciences. Using X-ray diffraction, we studied the formation of cubic ice in pure water droplets suspended in an oil matrix as a function of droplet size. The results show that...

Nonlamellar lipid membranes are frequently induced by proteins that fuse, bend, and cut membranes. Understanding the mechanism of action of these proteins requires the elucidation of the membrane morphologies that they induce. While hexagonal phases and lamellar phases are readily identified by their characteristic solid-state NMR line shapes, bicontinuous lipid cubic phases are more difficult ...

The known exact expressions for extended Watson integrals relating to various cubic and modified cubic lattices are summarized. A new closed form expression for Watson's result on the simple cubic lattice is given in terms of gamma functions.

INTRODUCTION The evidence has begun to mount for diminishing the frequency of CD4 count testing. To determine whether these observations were applicable to an urban US population, we used New York City (NYC) surveillance data to explore CD4 testing among stable patients in NYC, 2007-2013. METHODS We constructed a population-based retrospective open cohort analysis of NYC HIV surveillance data...

in this study we produced a new method for solving regular dierential equations with step size h and taylor series. this method analyzes a regular dierential equation with initial values and step size h. this types of equations include quadratic and cubic homogenous equations with constant coecients and cubic and second- level equations.

A new hypersurface of Tzitzeica type is obtained in all three forms: parametric, implicit and explicit. To a two-parameters family of cubic Tzitzeica surfaces we associate a cubic Finsler function for which the regularity is expressed as the non-flatness of the Tzitzeica indicatrix. A natural relationship is obtained between cubic Tzitzeica surfaces and three-dimensional Berwald spaces with cub...

This paper generalizes the classical cubic spline with the construction of the cubic spline coalescence hidden variable fractal interpolation function (CHFIF) through its moments, i.e. its second derivative at the mesh points. The second derivative of a cubic spline CHFIF is a typical fractal function that is self-affine or non-self-affine depending on the parameters of the generalized iterated...