Positivity, rational Schur functions, Blaschke factors, and other related results in the Grassmann algebra

We begin a study of Schur analysis in the setting of the Grassmann algebra, when the latter is completed with respect to the $1$-norm. We focus on the rational case. We start with a theorem on invertibility in the completed algebra, and define a notion of positivity in this setting. We present a series of applications pertaining to Schur analysis, including a counterpart of the Schur algorithm, extension of matrices and rational functions. Other topics considered include Wiener algebra, reproducing kernels Banach modules, and Blaschke factors.Comment: 35 page

Thrust vector control requirements for launch vehicles using a 260-inch solid rocket first stage

Gimbaled nozzle and liquid injection thrust vector control requirements for solid rocket two stage launch vehicle

Radial and angular rotons in trapped dipolar gases

We study Bose-Einstein condensates with purely dipolar interactions in oblate (pancake) traps. We find that the condensate always becomes unstable to collapse when the number of particles is sufficiently large. We analyze the instability, and find that it is the trapped-gas analogue of the ``roton-maxon'' instability previously reported for a gas that is unconfined in two dimensions. In addition, we find that under certain circumstances, the condensate wave function attains a biconcave shape, with its maximum density away from the center of the gas. These biconcave condensates become unstable due to azimuthl excitation - an angular roton.Comment: 4 pages, 3 figure

Group field theory and simplicial gravity path integrals: A model for Holst-Plebanski gravity

In a recent work, a dual formulation of group field theories as non-commutative quantum field theories has been proposed, providing an exact duality between spin foam models and non-commutative simplicial path integrals for constrained BF theories. In light of this new framework, we define a model for 4d gravity which includes the Immirzi parameter gamma. It reproduces the Barrett-Crane amplitudes when gamma goes to infinity, but differs from existing models otherwise; in particular it does not require any rationality condition for gamma. We formulate the amplitudes both as BF simplicial path integrals with explicit non-commutative B variables, and in spin foam form in terms of Wigner 15j-symbols. Finally, we briefly discuss the correlation between neighboring simplices, often argued to be a problematic feature, for example, in the Barrett-Crane model.Comment: 26 pages, 1 figur

Wave Mechanics of a Two Wire Atomic Beamsplitter

We consider the problem of an atomic beam propagating quantum mechanically through an atom beam splitter. Casting the problem in an adiabatic representation (in the spirit of the Born-Oppenheimer approximation in molecular physics) sheds light on explicit effects due to non-adiabatic passage of the atoms through the splitter region. We are thus able to probe the fully three dimensional structure of the beam splitter, gathering quantitative information about mode-mixing, splitting ratios,and reflection and transmission probabilities

Distribution Spaces and a New Construction of Stochastic Processes Associated with the Grassmann Algebra

We associate with the Grassmann algebra a topological algebra of distributions, which allows the study of processes analogous to the corresponding free stochastic processes with stationary increments, as well as their derivatives

Stereolabile and Configurationally Stable Atropisomers of Hindered Aryl Carbinols.

CAN 143:132926 AN 2005:441860 CAPLUS (COPYRIGHT (C) 2008 ACS ON SCIFINDER (R)) ABSTRACT CARBINOLS OF THE AR-C(OH)R2 TYPE, AR BEING O-ISOPROPYLPHENYL, EXIST AS STEREOLABILE SYN-CLINAL (S.C.) AND ANTI-PERIPLANAR (AP) ATROPISOMERS WHEN R = ME, ET, I-PR. IN THE LATTER COMPD., THE MAJOR ATROPISOMER ALSO COMPRISES TWO ENANTIOMERIC FORMS THAT INTERCHANGE WITH A BARRIER OF 6.4 KCAL MOL-1. X-RAY DIFFRACTION, NOE EXPTS., AND AB INITIO CALCNS. INDICATE THAT THE S.C.-ATROPISOMER IS THE MORE STABLE FORM WHEN R = ME, I-PR, T-BU BUT IS THE LESS STABLE ONE WHEN R = ET. NMR SPECTRA AT VARIABLE TEMP. ALLOWED THE DETN. OF THE BARRIERS FOR THE INTERCONVERSION OF THE S.C.- INTO THE AP-ATROPISOMERS (ΔG.THERMOD. = 7.6, 8.8, AND 13.5 KCAL MOL-1 FOR ME, ET, I-PR, RESP.). WHEN R IS A TERT-BU GROUP, THE TWO ATROPISOMERS ARE CONFIGURATIONALLY STABLE: THE AP-ATROPISOMER IS OBTAINED AS THE KINETIC CONTROLLED COMPD., WHICH CAN BE TRANSFORMED INTO THE THERMODYNAMICALLY MORE STABLE S.C.-..

A General Setting for Functions of Fueter Variables: Differentiability, Rational Functions, Fock Module and Related Topics

We develop some aspects of the theory of hyperholomorphic functions whose values are taken in a Banach algebra over a field—assumed to be the real or the complex numbers—and which contains the field. Notably, we consider Fueter expansions, Gleason’s problem, the theory of hyperholomorphic rational functions, modules of Fueter series, and related problems. Such a framework includes many familiar algebras as particular cases. The quaternions, the split quaternions, the Clifford algebras, the ternary algebra, and the Grassmann algebra are a few examples of them