Stability of Quadratic Projection Methods

In this paper we discuss the stability of an alternative pollution-free procedure for computing spectra. The main difference with the Galerkin method lies in the fact that it gives rise to a weak approximate problem which is quadratic in the spectral parameter, instead of linear. Previous accounts on this new procedure can be found in Levitin and Shargorodsky (2002) [math.SP/0212087] and Boulton (2006) [math.SP/0503126].Comment: 19 pages, 4 figures. In this updated version we have made a small number of minor correction

Representation of the Resonance of a Relativistic Quantum Field Theoretical Lee-Friedrichs Model in Lax-Phillips Scattering Theory

The quantum mechanical description of the evolution of an unstable system defined initially as a state in a Hilbert space at a given time does not provide a semigroup (exponential) decay law. The Wigner-Weisskopf survival amplitude, describing reversible quantum transitions, may be dominated by exponential type decay in pole approximation at times not too short or too long, but, in the two channel case, for example, the pole residues are not orthogonal, and the evolution does not correspond to a semigroup (experiments on the decay of the neutral $K$-meson system strongly support the semigroup evolution postulated by Lee, Oehme and Yang, and Yang and Wu). The scattering theory of Lax and Phillips, originally developed for classical wave equations, has been recently extended to the description of the evolution of resonant states in the framework of quantum theory. The resulting evolution law of the unstable system is that of a semigroup, and the resonant state is a well-defined function in the Lax-Phillips Hilbert space. In this paper we apply this theory to a relativistically covariant quantum field theoretical form of the (soluble) Lee model. We construct the translation representations with the help of the wave operators, and show that the resulting Lax-Phillips $S$-matrix is an inner function (the Lax-Phillips theory is essentially a theory of translation invariant subspaces). In the special case that the $S$-matrix is a rational inner function, we obtain the resonant state explicitly and analyze its particle ($V, N, \theta$) content. If there is an exponential bound, the general case differs only by a so-called trivial inner factor, which does not change the complex spectrum, but may affect the wave function of the resonant state.Comment: Plain TeX, 33 page

Foreign growth, the dollar, and regional economies, 1970-97

International markets are an important contributor to U.S. economic activity. U.S. regions have varying exposure to the influences of international markets--foreign demand or exchange rate movements. Still, the overriding determinants of regional economic growth is the state of the domestic economy.Foreign exchange rates ; Manufactures ; Middle West ; Exports

Spectroscopic Identification of Type 2 Quasars at Z < 1 in SDSS-III/BOSS

The physics and demographics of type 2 quasars remain poorly understood, and new samples of such objects selected in a variety of ways can give insight into their physical properties, evolution, and relationship to their host galaxies. We present a sample of 2758 type 2 quasars at z $\leq$ 1 from the SDSS-III/BOSS spectroscopic database, selected on the basis of their emission-line properties. We probe the luminous end of the population by requiring the rest-frame equivalent width of [OIII] to be > 100 {\AA}. We distinguish our objects from star-forming galaxies and type 1 quasars using line widths, standard emission line ratio diagnostic diagrams at z < 0.52 and detection of [Ne V]{\lambda}3426{\AA} at z > 0.52. The majority of our objects have [OIII] luminosities in the range 10^8.5-10^10 L$_{\odot}$ and redshifts between 0.4 and 0.65. Our sample includes over 400 type 2 quasars with incorrectly measured redshifts in the BOSS database; such objects often show kinematic substructure or outflows in the [OIII] line. The majority of the sample has counterparts in the WISE survey, with median infrared luminosity {\nu}L{\nu}[12{\mu}m] = 4.2 x 10^44 erg/sec. Only 34 per cent of the newly identified type 2 quasars would be selected by infrared color cuts designed to identify obscured active nuclei, highlighting the difficulty of identifying complete samples of type 2 quasars. We make public the multi-Gaussian decompositions of all [OIII] profiles for the new sample and for 568 type 2 quasars from SDSS I/II, together with non-parametric measures of line profile shapes and identify over 600 candidate double-peaked [OIII] profiles.Comment: 15 pages, 15 figures, 2 tables. Online tables: http://zakamska.johnshopkins.edu/data.ht

Ultrastable reference pulser for high-resolution spectrometers

Solid-state double-pulse generator for a high resolution semiconductor detector meets specific requirements for resolution /0.05 percent/, amplitude range /0.1-13 MeV/, and repetition rate /0.1-1000 pulses per second/. A tag pulse is generated in coincidence with each reference pulse

Long-term survival for a cohort of adults with cerebral palsy

The aim of this study was to investigate long-term survival and examine causes of death in adult patients with cerebral palsy (CP). A 1940–1950 birth cohort based on paediatric case referral allows for long-term survival follow-up. Survival is analyzed by birth characteristics and severity of disability from age 20 years (and age 2y for a subset of the data). Survival outcome compared with that expected in the general population based on English life tables. The main cohort consisted of 341 individuals, with 193 males and 148 females. Conditional on surviving to age 20 years, almost 85% of the cohort survived to age 50 years (a comparable estimate for the general population is 96%). Very few deaths were attributed to CP for those people dying over 20 years of age. Females survived better than males. However, females faced a greater increase in risk relative to the general population than did males. We conclude that survival outlook is good though lower than in the general population. The relative risk of death compared with the UK population decreases with age, although it shows some indication of rising again after age 50 years. Many more deaths were caused by diseases of the respiratory system among those dying in their 20s and 30s than would be expected in the general population. Many fewer deaths than expected in this age group are caused by injuries and accidents. For those people who die in their 40s and 50s, an increase in deaths due to diseases of the circulatory system and neoplasms is observed. More deaths than expected in this age group are due to diseases of the nervous system