What portion of the sample makes a partial sum asymptotically stable or normal?

Summary Let a sequence of independent and identically distributed random variables with the common distribution function in the domain of attraction of a stable law of index 0<2 be given. We show that if at each stage n a number k _n depending on n of the lower and upper order statistics are removed from the n-th partial sum of the given random variables then under appropriate conditions on k _n the remaining sum can be normalized to converge in distribution to a standard normal random variable. A further analysis is given to show which ranges of the order statistics contribute to asymptotic stable law behaviour and which to normal behaviour. Our main tool is a new Brownian bridge approximation to the uniform empirical process in weighted supremum norms.Work done while visiting the Bolyai Institute, Szeged University, partially supported by a University of Delaware Research Foundation Grant     

Review of recent results about theκ-centrum of a tree

This paper is concerned with the-centrum of a graph. This concept, related to a particular location problem, generalizes that of the center and that of the median of a graph: the-centrum is the set of points for which the sum of the (weighted) distances from the farthest vertices is minimized. The paper will review some recent results about this problem. In particular, some properties of cardinality, connectivity and, more generally, of the structure of the-centrum of a weighted tree will be presented.     

Auditory profile analysis of irregular sound spectra

The discrimination of changes in the shapes of sound spectra is reported. The change was always an intensity increment to the 948-Hz component of a multitone complex. First, the ability of naive listeners to learn to discriminate a change in a "regular" background or reference spectrum (equal-level tones equally spaced in logarithmic frequency) was measured as a function of the number of trials. On the average, threshold improved about 10 dB over 3000 trials, with about 50% of the decrease in threshold occurring during the first 750 trials. In a subsequent series of experiments, the overall pattern of spectral shape of the background was varied randomly. Two kinds of perturbations in spectral shape were employed: Randomly choosing the frequencies of the reference spectra and randomly choosing the amplitudes of the components of the reference spectra. The experimental manipulations involved fixing the random spectra across a block of trials, varying the reference spectra from interval to interval of each trial, and providing extensive practice in discriminating specific randomly perturbed reference spectra. The results of the spectrum-learning and random perturbation experiments provide insight into the roles of critical band filtering, sensory variability, and short-term and long-term memory representations in auditory profile analysis. Further, the appropriateness of the generalization of a simple energy detection model is discussed.     

Particle behaviour in shear and electric fields

Summary Observations of the pair interactions of rigid, conducting spheres suspended in a Newtonian dielectric fluid are described for experiments in which the fluid was subjected to combined simple shear of rateG and uniform electric fields of strengthE ₀ where behaviour is predicted to depend on a parameterf proportional toEsk₀/² G. Agreement with theory was excellent for touching spheres which oriented themselves with calculable rates inE ₀ alone and rotated with calculable periods of rotation in subcritical fields (f<1); in supercritical fields(f1) the doublets assumed their stable predicted orientations.The trajectories of separated spheres were found to be in good agreement with theory, with capture observed as predicted provided an experimentally determined minimum value,f _min, was exceeded whose value appeared to depend on the surface roughness of the spheres and on their behaviour during dielectric breakdown of the medium when the spheres were close together. After capture spheres appeared to make physical contact.The capture cross-sections were measured and agreed with the theoretical values except belowf _min.The significance of the phenomena and the possibilities of employing them for measuring physical properties of dielectric liquids are discussed.

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Zusammenfassung Die beobachteten Wechselwirkungen zwischen zwei kleinen, festen, leitenden und in einer dielektrischen (isolierenden) Newtonschen Flüssigkeit schwebenden Kugeln werden für einige Versuche beschrieben, in denen die Flüssigkeit gleichzeitig einer einfachen Scherströmung (mit SchergeschwindigkeitG) und einem gleichmäßigen elektrischen Feld (mit Feldstärke E₀) ausgesetzt wird. Es läßt sich für eine solche Versuchsanordnung erwarten, daß die Wechselwirkungen mit einem definierbaren Parameterf (proportionalE ₀ ² G) in einem direkten Verhältnis stehen sollen. Die Obereinstimmung mit der Theorie war ausgezeichnet für zwei sich berührende Kugeln, die mit errechneter Orientierungsgeschwindigkeit inE ₀ E ₀ (f = ) ausgerichtet wurden und in unterkritischen Feldern (f<1) mit errechneten Rotationszeiten gedreht wurden; die Kugelpaare stellten sich in überkritischen Feldern (f1) auf die erwarteten stabilen Achsenrichtungen genau ein. Die Bewegungsbahnen getrennter Kugeln stimmten gut mit der Theorie überein, sofern ein experimentell bestimmbares,f _minüberschritten wurde, dessen Wert von der Kugeloberflächenrauheit und vom dielektrischen Kurzschlußverhalten bei engstem Kugelabstand abhing. Elektrische Anlagerung wurde mit nachweisbarem physikalischem Kontakt abgeschlossen. Gemessene Anlagerungsquerschnitte entsprachen den von der Theorie abgeleiteten Formen und Größen ausgenommen fürff _min Die Bedeutung dieser Beobachtungen und deren Anwendungsmöglichkeiten zur Messung physikalischer Eigenschaften von dielektrischen Flüssigkeiten wird erläutert.

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Nomenclature d gap distance between Couette cylinders or flat electrodes - E ₀ ^f uniform electric field for forming doublets - f _min minimum (or critical) value off for capture - F _t(j) hydrodynamic forces alongx _i acting on spherej = 1,2 - G _c critical (minimum) shear rate to cause doublet separation - V electric potential difference acrossd Greek symbols error symbol - b size of surface asperities of spheres - _DB ;_min critical gap distance between spheres on dielectric breakdown; minimum gap distance of spheres travelling along trajectories given byB andC = 0 in ([1, 2])¹) whenf = 0 - ₂ ⁱ , ₂ ^f initial and final ₂ before and after applyingE ₀ whenG = 0 - density of suspending liquid With 6 figures and 9 tables     

An Aqueous Thermodynamic Model for the Complexation of Sodium and Strontium with Organic Chelators Valid to High Ionic Strength. II. N-(2-Hydroxyethyl)ethylenedinitrilotriacetic Acid (HEDTA)

This is the second paper in a two part series on the development of aqueous thermodynamic models for the complexation of Na⁺ and Sr²⁺ with organic chelators. In this paper, the development of an aqueous thermodynamic model describing the effects of ionic strength, carbonate concentration, and temperature on the complexation of Sr²⁺ by HEDTA under basic conditions is presented. The thermodynamic model describing the Na⁺ interactions with the HEDTA^3–chelate relies solely on the use of Pitzer ion-interaction parameters. The exclusive use of Pitzer ion-interaction parameters differs significantly from our previous model for EDTA, which required the introduction of a NaEDTA^3– ion pair. Estimation of the Pitzer ion-interaction parameters for HEDTA^3– and SrHEDTA^– with Na⁺ allows the extrapolation of a standard-state equilibrium constant for the SrHEDTA^– species, which is one order of magnitude greater than the 0.1 M reference state value available in the literature. The overall model is developed from data available in the literature on apparent equilibrium constants for HEDTA protonation, the solubility of salts in concentrated HEDTA solutions, and from new data on the solubility of SrCO₃(c) obtained as part of this study. The predictions of the final thermodynamic model for the Na-Sr-OH-CO₃-NO₃-HEDTA-H₂O system are tested by application to chemical systems containing competing metal ions (i.e., Ca²⁺).     

High-performance liquid chromatographic method for the determination of tris(hydroxymethyl)aminomethane (tromethamine) in human plasma.

Determination of tris(hydroxymethyl)aminomethane (tromethamine) in human plasma involved derivatization of the amino and hydroxyl groups with a ultraviolet-absorbing chromophore followed by extraction into an organic phase. Reversed-phase high-performance liquid chromatography with gradient elution was used for the separation of the analyte from the internal standard (2,3-butanediol). The assay was linear in the range 1.0-1000.0 micrograms/ml of plasma and the coefficient of variation varied between 9.6 and 16.3% whereas the accuracy varied between 90 and 108%. The limit of detection for the assay was 0.282 micrograms/ml. Stability of tris(hydroxymethyl)aminomethane in human plasma frozen at -20 degrees C was studied over a period of three month and the data indicated no significant change.     

The study of human nails as an intake monitor for arsenic using neutron activation analysis

Arsenic is toxic to humans with the lethal dose being approximately 1 mg/kg/day. At much lower long-term exposures, arsenic is hypothesized to increase the risk of certain cancers. We have developed an irradiation position for the neutron activation analysis (NAA) of nail specimens for arsenic, in support of a case-control study involving New Hampshire residents consuming well water above the EPA Safe Drinking Water Standard of 0.050 ppm. Arsenic is bound to nail keratin through sulfhydryl groups proportional to intake providing a convenient means of integrating arsenic intake in population-based studies. Our objective was to develop the necessary facilities and procedures by which relatively small samples (i.e. 20 to 100 mg) could be accurately analyzed for arsenic, so that affordable nutritional epidemiology investigations, requiring large numbers of samples (>1000 in this case), could be undertaken. A high-flux reflector position, with minimal axial variation throughout the fuel cycle, suitable for pneumatic-tube irradiations, was characterized by measurement of the neutron flux distribution (thermal and epithermal) within the irradiation capsule over time. Results from application of the method to a case-control study of basal and squamous cell skin cancer will be presented.     

Thermolysis of fluorinated cycloalkylidene fulgides yields a new class of photochromic compounds

A series of fluorinated cycloalkylidene indolylfulgides has been designed, synthesized and characterized; most of the thermolysis products of these fulgides maintain photochromicity and display outstanding thermal and photochemical stability.