Thesis Work on Algebraic Geometry The homogeneous cubic polynomials in four variables x, y, z and w form a 20 dimensional vector space over C. Let S ⊂ P be a surface defined by the equation f(x, y, z, w) = a0x 3 + a1x y + · · ·+ a19w = 0, which naturally determines a point [a0, . . . , a19] ∈ P. X admits a natural G = SL(4;C) action. Let X denote the smooth cubic surfaces, X the semistable ones...

This paper describes an implementation of the Cubic Rational Polynomial Camera model developed as part of the FOCUS project. FOCUS ([1]) is on ongoing “shared vision” IR&D project jointly sponsored by Lockheed Martin Missiles and Space (LMMSS/Sunnyvale) and General Electric CR&D. A cubic camera has the advantage that all cameras, such as projective, affine and the linear pushbroom, which map th...

Approximating complex curves with simple parametric curves is widely used in CAGD, CG, and CNC. This paper presents an algorithm to compute a certified approximation to a given parametric space curve with cubic B-spline curves. By certified, we mean that the approximation can approximate the given curve to any given precision and preserve the geometric features of the given curve such as the to...

We study polynomials with coefficients in a field L as dynamical systems where L is any algebraically closed and complete ultrametric field with dense valuation group and characteristic zero residual field. We give a complete description of the dynamical and parameter space of cubic polynomials. In particular we characterize cubic polynomials with compact Julia sets. Also, we prove that any inf...

Low-energy electron diffraction patterns, produced from quasicrystal surfaces by ion sputtering and annealing to temperatures below ∼700 K, can be assigned to various terminations of the cubic CsCl structure. The assignments are based upon ratios of spot spacings, estimates of surface lattice constants, bulk phase diagrams vs surface compositions, and comparisons with previous work. The CsCl ov...

The growth of GaN films on silicon or sapphire substrates has not been straightforward due to their large mismatch ('13%). SiC is structurally the closest material to GaN (especially cubic form) and has a small lattice mismatch (3.5%) between SiC and GaN, and therefore can be useful as the substrate for GaN. Single-crystal wafers of cubic SiC and GaN, however, are hard to obtain and have not be...

Efforts to improve the oral bioavailability of cyclosporine A (CyA) remains a challenge in the field of drug delivery. In this study, glyceryl monooleate (GMO)/poloxamer 407 cubic nanoparticles were evaluated as potential vehicles to improve the oral bioavailability of CyA. Cubic nanoparticles were prepared via the fragmentation of a bulk GMO/poloxamer 407 cubic phase gel by sonication and homo...

In the past two decades, the geometric pathways involved in the transformations between inverse bicontinuous cubic phases in amphiphilic systems have been extensively theoretically modeled. However, little experimental data exists on the cubic-cubic transformation in pure lipid systems. We have used pressure-jump time-resolved X-ray diffraction to investigate the transition between the gyroid Q...

Possibly the best-characterized cubic membrane transition has been observed in the mitochondrial inner membranes of free-living giant amoeba (Chaos carolinense). In this ancient organism, the cells are able to survive in extreme environments such as lack of food, thermal and osmolarity fluctuations and high levels of reactive oxygen species. Their mitochondrial inner membranes undergo rapid cha...

Ab initio molecular dynamics simulations were performed to investigate the elasticity of cubic CaSiO3 perovskite at high pressure and temperature. All three independent elastic constants for cubic CaSiO3 perovskite, C11, C12, and C44, were calculated from the computation of stress generated by small strains. The elastic constants were used to estimate the moduli and seismic wave velocities at t...