Frames, semi-frames, and Hilbert scales

Given a total sequence in a Hilbert space, we speak of an upper (resp. lower) semi-frame if only the upper (resp. lower) frame bound is valid. Equivalently, for an upper semi-frame, the frame operator is bounded, but has an unbounded inverse, whereas a lower semi-frame has an unbounded frame operator, with bounded inverse. For upper semi-frames, in the discrete and the continuous case, we build two natural Hilbert scales which may yield a novel characterization of certain function spaces of interest in signal processing. We present some examples and, in addition, some results concerning the duality between lower and upper semi-frames, as well as some generalizations, including fusion semi-frames and Banach semi-frames.Comment: 27 pages; Numerical Functional Analysis and Optimization, 33 (2012) in press. arXiv admin note: substantial text overlap with arXiv:1101.285

The 2014 American State Litter Scorecard FINAL: USA's Dirtiest & Cleanest States Includes Statistics and Charts

A NEW State Litter "Scorecard" is released for the 2014 American Society for Public Administration (ASPA) Conference. Every three years, the Scorecard approximates each state's overall public spaces environmental quality through tried-and-true, hard-to-publicly obtain objective and subjective measures, resulting in a total overall jurisdictional score. Readers gain a realistic "picture" of "what's going on" within one or all of the 50 states. Illegal littering and dumping, found frequently on or near transportation paths, creates danger to public safety and health, with 800+ Americans dying each year by vehicle collisions with unmoved roadway debris. Because policy makers, public administrators and citizens are ever more involved in effectuating "green" outcomes, satisfactory public spaces waste removals are vital. Since 2008, major publications (the Boston Globe; TRAVEL+LEISURE; National Cooperative Highway Research Program's "Reducing Litter on Roadsides" Journal) have referred to the Scorecard, an ever valuable, trusted standard for improving debris/litter abatement in states and localities

Fully representable and *-semisimple topological partial *-algebras

We continue our study of topological partial *-algebras, focusing our attention to *-semisimple partial *-algebras, that is, those that possess a {multiplication core} and sufficiently many *-representations. We discuss the respective roles of invariant positive sesquilinear (ips) forms and representable continuous linear functionals and focus on the case where the two notions are completely interchangeable (fully representable partial *-algebras) with the scope of characterizing a *-semisimple partial *-algebra. Finally we describe various notions of bounded elements in such a partial *-algebra, in particular, those defined in terms of a positive cone (order bounded elements). The outcome is that, for an appropriate order relation, one recovers the \M-bounded elements introduced in previous works.Comment: 26 pages, Studia Mathematica (2012) to appea

Partial inner product spaces: Some categorical aspects

We make explicit in terms of categories a number of statements from the theory of partial inner product spaces (PIP spaces) and operators on them. In particular, we construct sheaves and cosheaves of operators on certain PIP spaces of practical interest.Comment: 21 page

Construction of a Complete Set of States in Relativistic Scattering Theory

The space of physical states in relativistic scattering theory is constructed, using a rigorous version of the Dirac formalism, where the Hilbert space structure is extended to a Gel'fand triple. This extension enables the construction of ``a complete set of states'', the basic concept of the original Dirac formalism, also in the cases of unbounded operators and continuous spectra. We construct explicitly the Gel'fand triple and a complete set of ``plane waves'' -- momentum eigenstates -- using the group of space-time symmetries. This construction is used (in a separate article) to prove a generalization of the Coleman-Mandula theorem to higher dimension.Comment: 30 pages, Late

Synthesis and analysis of jet fuels from shale oil and coal syncrudes

The technical problems involved in converting a significant portion of a barrel of either a shale oil or coal syncrude into a suitable aviation turbine fuel were studied. TOSCO shale oil, H-Coal and COED coal syncrudes were the starting materials. They were processed by distillation and hydrocracking to produce two levels of yield (20 and 40 weight percent) of material having a distillation range of approximately 422 to 561 K (300 F to 550 F). The full distillation range 311 to 616 K (100 F to 650 F) materials were hydrotreated to meet two sets of specifications (20 and 40 volume percent aromatics, 13.5 and 12.75 weight percent H, 0.2 and 0.5 weight percent S, and 0.1 and 0.2 weight percent N). The hydrotreated materials were distilled to meet given end point and volatility requirements. The syntheses were carried out in laboratory and pilot plant equipment scaled to produce thirty-two 0.0757 cu m (2-gal)samples of jet fuel of varying defined specifications. Detailed analyses for physical and chemical properties were made on the crude starting materials and on the products

Symmetry Representations in the Rigged Hilbert Space Formulation of Quantum Mechanics

We discuss some basic properties of Lie group representations in rigged Hilbert spaces. In particular, we show that a differentiable representation in a rigged Hilbert space may be obtained as the projective limit of a family of continuous representations in a nested scale of Hilbert spaces. We also construct a couple of examples illustrative of the key features of group representations in rigged Hilbert spaces. Finally, we establish a simple criterion for the integrability of an operator Lie algebra in a rigged Hilbert space

Front localization in a ballistic annihilation model

We study the possibility of localization of the front present in a one-dimensional ballistically-controlled annihilation model in which the two annihilating species are initially spatially separated. We construct two different classes of initial conditions, for which the front remains localized.Comment: Using elsart (Elsevier Latex macro) and epsf. 12 Pages, 2 epsf figures. Submitted to Physica