Schur proved that for any finite partition of the naturals, some cell contains two numbers and their sum. We use Ramsey’s theorem to prove a noncommutative Schur theorem for permutation quadruples {x, y, xy, yx}. By Schur’s theorem [2], for any r ∈ N, there exists n ∈ N such that for any r-coloring of {1, 2, . . . , n}, one has a monochromatic “Schur triple.” That is, a 3-element set of the for...

This compendium presents new mathematical techniques for modeling Point Absorbers. A combined frequency-time domain framework is developed. It is used to simulate the energy generated by the wave farms. With Matlab and Fortran as a base, this leads to obtain physical variables of primary importance, namely position, velocity and power to energy net balance relationships of absorption. Integrati...

arc, with two end-plates energized by a common negative voltage referred to the central arc. Note that these are actually experimental results for a real central uranium arc, operating at about 50 volts, for more than 100 tests, at total arc currents of 1-100 amperes. The floating cylinder was about 4 feet in diameter, and the negatively energized circular end-plates were separated by about 3 f...

This study investigated the effect on piston assembly friction after treating surfaces with a fine particle bombarding process, using measurement apparatus floating cylinder liner, similar to an eco-mileage vehicle engine. Friction was measured in four conditions: (1) no treatment (standard commercially-available engine), (2) micro dimple (45 μm ceramic particles were air-blasted onto surface),...

an oral sustained-release floating tablet formulation of metformin hcl was designed and developed. effervescence and swelling properties were attributed on the developed tablets by sodium bicarbonate and hpmc-peo polymer combination, respectively. tablet composition was optimized by response surface methodology (rsm). seventeen (17) trial formulations were analyzed according to box-behnken desi...

A unique and potentially useful fluid configuration which is possible in zero gravity is the liquid cylinder. One example is floating-zone crystal growth which, in zero gravity, involves a cylindrical melt bridging two solid cylinders. In low gravity, when the length of a cylindrical liquid bridge exceeds it's circumference, the bridge becomes unstable and breaks. A liquid bridge of length L an...

In the present work, the open source Computational Fluid Dynamics (CFD) packageOpen Field Operation and Manipulation (OpenFoam®) is used to simulate wave-structure interactions and a new wave boundary condition is developed for extreme waves. The new wave boundary condition is implemented for simulation of interaction with a fixed/floating truncated cylinder and a simplified Floating Production...