Applications of Hilbert Module Approach to Multivariable Operator Theory

A commuting $n$-tuple $(T_1, \ldots, T_n)$ of bounded linear operators on a Hilbert space \clh associate a Hilbert module $\mathcal{H}$ over $\mathbb{C}[z_1, \ldots, z_n]$ in the following sense: $$\mathbb{C}[z_1, \ldots, z_n] \times \mathcal{H} \rightarrow \mathcal{H}, \quad \quad (p, h) \mapsto p(T_1, \ldots, T_n)h,$$where $p \in \mathbb{C}[z_1, \ldots, z_n]$ and $h \in \mathcal{H}$. A companion survey provides an introduction to the theory of Hilbert modules and some (Hilbert) module point of view to multivariable operator theory. The purpose of this survey is to emphasize algebraic and geometric aspects of Hilbert module approach to operator theory and to survey several applications of the theory of Hilbert modules in multivariable operator theory. The topics which are studied include: generalized canonical models and Cowen-Douglas class, dilations and factorization of reproducing kernel Hilbert spaces, a class of simple submodules and quotient modules of the Hardy modules over polydisc, commutant lifting theorem, similarity and free Hilbert modules, left invertible multipliers, inner resolutions, essentially normal Hilbert modules, localizations of free resolutions and rigidity phenomenon. This article is a companion paper to "An Introduction to Hilbert Module Approach to Multivariable Operator Theory".Comment: 46 pages. This is a companion paper to arXiv:1308.6103. To appear in Handbook of Operator Theory, Springe

NASTRAN general purpose interface requirements document

This NASTRAN (NASA STRuctural ANalysis) General Purpose Interface Requirements Document (IRD) defines standards for deliverables required of New Capability Contractors (NCCs) and relates these deliverables to the software development cycle. It also defines standards to be followed by NCCs for adding to and modifying the code in the NASTRAN software system and for adding to and modifying the four official NASTRAN manuals: The NASTRAN Theoretical Manual, the NASTRAN User's Manual, The NASTRAN Programmer's Manual, and The NASTRAN Demonstration Problem Manual. It is intended that this General Purpose IRD shall be incorporated by reference in all contracts for a new NASTRAN capability

Noncommutative Gauge Theory on the q-Deformed Euclidean Plane

In this talk we recall some concepts of Noncommutative Gauge Theories. In particular, we discuss the q-deformed two-dimensional Euclidean Plane which is covariant with respect to the q-deformed Euclidean group. A Seiberg-Witten map is constructed to express noncommutative fields in terms of their commutative counterparts.Comment: 5 pages; Talk given by Frank Meyer at the 9th Adriatic Meeting, September 4th-14th, 2003, Dubrovni

Hydrogen contamination in Ge-doped SiO[sub 2] thin films prepared by helicon activated reactive evaporation

Germanium-doped silicon oxidethin films were deposited at low temperature by using an improved helicon plasma assisted reactive evaporation technique. The origins of hydrogen contamination in the film were investigated, and were found to be H incorporation during deposition and postdeposition water absorption. The H incorporation during deposition was avoided by using an effective method to eliminate the residual hydrogen present in the depositionsystem. The microstructure, chemical bonds, chemical etch rate, and optical index of the films were studied as a function of the deposition conditions. Granular microstructures were observed in low-density films, and were found to be the cause of postdeposition water absorption. The granular microstructure was eliminated and the film was densified by increasing the helicon plasma power and substrate bias during deposition. A high-density film was shown to have no postdeposition water absorption and no OH detected by using a Fourier-transform infrared spectrometer

A Photometric Technique to Search for Be Stars in Open Clusters

We describe a technique to identify Be stars in open clusters using Stromgren b, y, and narrow-band Halpha photometry. We first identify the B-type stars of the cluster using a theoretical isochrone fit to the (b-y, y) color-magnitude diagram. The strongest Be stars are easily identified in a (b-y, y-Halpha) color-color diagram, but those with weaker Halpha emission (classified as possible Be star detections) may be confused with evolved or foreground stars. Here we present such photometry plus Halpha spectroscopy of members of the cluster NGC 3766 to demonstrate the accuracy of our technique. Statistical results on the relative numbers of Be and B-type stars in additional clusters will be presented in a future paper.Comment: 15 pages, 6 figures, 1 table. Accepted by Ap

On The Interaction Of D0-Brane Bound States And RR Photons

We consider the problem of the interaction between D0-brane bound state and 1-form RR photons by the world-line theory. Based on the fact that in the world-line theory the RR gauge fields depend on the matrix coordinates of D0-branes, the gauge fields also appear as matrices in the formulation. At the classical level, we derive the Lorentz-like equations of motion for D0-branes, and it is observed that the center-of-mass is colourless with respect to the SU(N) sector of the background. Using the path integral method, the perturbation theory for the interaction between the bound state and the RR background is developed. We discuss what kind of field theory may be corresponded to the amplitudes which are calculated by the perturbation expansion in world-line theory. Qualitative considerations show that the possibility of existence of a map between the world-line theory and the non-Abelian gauge theory is very considerable.Comment: LaTeX, 28 pages, 4 eps figures. v2 and v3: eqs. (3.18) and (B.2) are corrected, very small change

Noninvasive Techniques for Intracranial Pressure Assessment: A Review from Aerospace Medicine Perspective

Microgravity-induced changes in fluid distribution and other physiological factors due to space flight have been implicated as the cause of increased intracranial pressure (ICP) in a number of space crewmembers. The modest levels of ICP elevation and absence of severe symptoms in this group do not warrant invasive diagnostic interventions. However, the long-term trends and residual or consequential changes secondary to the observed ICP elevation in this group are not yet known. Therefore, close attention is needed to evaluate the potential techniques of noninvasively assessing ICP, including those feasible for in-flight use. Of particular interest is continuity between ground and in-flight testing, whereby data from the same or different techniques allow reasonably dependable estimation of ICP trends and responses. Methods: A thorough review of current literature, analysis of NASA data, and interviews with subject matter experts were conducted to construct a presentation that reflects the state of the art for noninvasive ICP measurement and monitoring. Results: Multiple imaging and non-imaging modalities are available to assess ICP in terrestrial clinical and experimental environments. Imaging alternatives include magnetic resonance imaging (MRI) and high-resolution sonography. Non-imaging techniques include transcranial Doppler, certain audiological methods, and venous ophthalmodynamometry, among others. Special functional techniques have been proposed recently that allow the use of advanced MRI methods to calculate ICP in addition to the acquisition of high-resolution images. Our data include many of these applications, with several cases of correlation with lumbar puncture, the invasive "gold standard" measurement of ICP

Growth, Condition, and Trophic Relations of Stocked Trout in Southern Appalachian Mountain Streams

Stream trout fisheries are among the most popular and valuable in the United States, but many are dependent on hatcheries to sustain fishing and harvest. Thus, understanding the ecology of hatchery‐reared trout stocked in natural environments is fundamental to management. We evaluated the growth, condition, and trophic relations of Brook Trout Salvelinus fontinalis, Brown Trout Salmo trutta, and Rainbow Trout Oncorhynchus mykiss that were stocked in southern Appalachian Mountain streams in western North Carolina. Stocked and wild (naturalized) trout were sampled over time (monthly; September 2012–June 2013) to compare condition and diet composition and to evaluate temporal dynamics of trophic position with stable isotope analysis. Relative weights (Wr) of stocked trout were inversely associated with their stream residence time but were consistently higher than those of wild trout. Weight loss of harvested stocked trout was similar among species and sizes, but fish stocked earlier lost more weight. Overall, 40% of 141 stomachs from stocked trout were empty compared to 15% of wild trout stomachs (N = 26). We identified a much higher rate of piscivory in wild trout (18 times that of stocked trout), and wild trout were 4.3 times more likely to consume gastropods relative to stocked trout. Hatchery‐reared trout were isotopically similar to co‐occurring wild fish for both δ13C and δ15N values but were less variable than wild trout. Differences in sulfur isotope ratios (δ34S) between wild and hatchery‐reared trout indicated that the diets of wild fish were enriched in δ34S relative to the diets of hatchery‐reared fish. Although hatcheryreared trout consumed prey items similar to those of wild fish, differences in consumption or behavior (e.g., reduced feeding) may have resulted in lower condition and negative growth. These findings provide critical insight on the trophic dynamics of stocked trout and may assist in developing and enhancing stream trout fisheries

Combinatorics of bicubic maps with hard particles

We present a purely combinatorial solution of the problem of enumerating planar bicubic maps with hard particles. This is done by use of a bijection with a particular class of blossom trees with particles, obtained by an appropriate cutting of the maps. Although these trees have no simple local characterization, we prove that their enumeration may be performed upon introducing a larger class of "admissible" trees with possibly doubly-occupied edges and summing them with appropriate signed weights. The proof relies on an extension of the cutting procedure allowing for the presence on the maps of special non-sectile edges. The admissible trees are characterized by simple local rules, allowing eventually for an exact enumeration of planar bicubic maps with hard particles. We also discuss generalizations for maps with particles subject to more general exclusion rules and show how to re-derive the enumeration of quartic maps with Ising spins in the present framework of admissible trees. We finally comment on a possible interpretation in terms of branching processes.Comment: 41 pages, 19 figures, tex, lanlmac, hyperbasics, epsf. Introduction and discussion/conclusion extended, minor corrections, references adde