Nominal Dispersion Research Articles

Optically Aligned, Space Resolving, Extreme Ultra-Violet and Soft X-ray Spectrograph

We describe in this paper an extreme ultra-violet/soft X-ray (XUV) spectrograph with high sensitivity, high spectral resolution and spatial resolution, which we developed to record XUV emission from a 10 J laser-irradiated gas jet. This spectrograph uses a flat field grazing incidence grating and a grazing incidence collection and imaging mirror. We designed a system where initial positions of elements can be set with a low accuracy of half a millimeter and where the final alignment is done with a visible light low intensity laser beam. High spectral resolution, good spatial resolution and nominal dispersion function have been achieved. A few illustrative results are presented.

The theory of cylindrical photonic wires

The energy modes for a photonic nanowire have been studied and calculated. We model our photonic crystals after Noda et al. (1999) [18] where logs of semiconductor material are stacked to produce photonic band gaps in both the near and far infrared regions. A nominal dispersion relation was adopted in order to achieve qualitatively useful results. Photonic wires were modeled in two schemes, each with two specific geometries. In the first scheme, a pillar of one photonic crystal is embedded in a larger photonic crystal to produce a wire. This pillar was modeled as having either a square or a circular cross-section. The photonic crystals considered consisted of varying proportions of Ga x Al 1− x As, so that the wire could be adjusted. The second scheme investigated was a dielectric material for the central pillar, rather than a photonic crystal. Again, circular and square cross sections were considered. It was found that many more modes fit into the near infrared band gap than the far infrared band gap, and that a circular cross-section permits fewer modes. Finally, a dielectric pillar allows for a wire which is physically much smaller than a wire with a photonic crystal in the middle. As many photonic devices include such wires, these qualitative results could be useful in their design.

Testing for departures from nominal dispersion in generalized nonlinear models with varying dispersion and/or additive random effects

This paper discusses the tests for departures from nominal dispersion in the framework of generalized nonlinear models with varying dispersion and/or additive random effects. We consider two classes of exponential family distributions. The first is discrete exponential family distributions, such as Poisson, binomial, and negative binomial distributions. The second is continuous exponential family distributions, such as normal, gamma, and inverse Gaussian distributions. Correspondingly, we develop a unifying approach and propose several tests for testing for departures from nominal dispersion in two classes of generalized nonlinear models. The score test statistics are constructed and expressed in simple, easy to use, matrix formulas, so that the tests can easily be implemented using existing statistical software. The properties of test statistics are investigated through Monte Carlo simulations.

Wetting Control of Polymer Solution on Roughened Solid Surfaces by Wet-blast Technique

Spreading of organic solution can be improved drastically on a solid surface after the wet-blast treatment. The wet-blast treatment has an ability of morphology control of various kinds of surfaces. Various organic liquid can spread spontaneously on a substrate due to spreading energy S. By analyzing surface energies of the treated surfaces, the wet-blast treatment has a similar effect of the increase of dispersion component γd, that is, hydrophobic surface. Spontaneous spreading of the polymer solutions can be explained to be negative value of the spreading coefficient. High wetting surface can be realized by an oxygen plasma treatment. However, the substrate surfaces become considerable hydrophilic property due to increase of the polar component γp, that is, hydrophilic surface. It can be considered that water vapor adsorbed the hydrophilic substrate and induce corrosion of metal components such as an electrode and micro wire lines. The roughened surface can act to prevent liquid condensation after spreading on the substrate, so-called pinning effect. The spontaneous spreading on the substrate after wet-blast treatment can be explained on the multiplier effect of nominal dispersion increase and pinning.

Testing for Heteroscedasticity in Nonlinear Regression Models

Homogeneity of variance is one of standard assumptions in regression analysis. However, this assumption is not necessarily appropriate. Cook and Weisberg (Cook, R. D., Weisberg, S. (1983). Diagnostics for heteroscedasticity in regression. Biometrika 70:1–10) provided a score test for heteroscedasticity in linear regression. Smith and Heitjan (Smith, P. J., Heitjan, D. F. (1993). Testing and adjusting for departures from nominal dispersion in generalized linear models. Applied Statistics 42:31–41) proposed a method based on the randomization of regression coefficients for detecting departures from nominal dispersion in generalized linear models. This paper is devoted to the tests for non-constant variance in the framework of nonlinear regression models (NLMs). We characterize three types of possible heterogeneity of variance in NLMs. One type is to introduce a variance function for the model, which is the extension of Cook and Weisberg (1983). The other two are based on the randomization of regression coefficients and variance parameters respectively, which are extensions of Smith and Heitjan (1993). For three types of heteroscedasticity, several score tests are developed and illustrated with European rabbit data (Ratkowsky, D. A. (1983). Nonlinear Regression Modelling. New York: Marcel Dekker, 108). The properties of test statistics are investigated through Monte Carlo simulations.

16 x 10 Gb/s WDM transmission over 840-km SMF using eleven broad-band chirped fiber gratings

We demonstrate wavelength-division-multiplexed transmission of 16 10-Gb/s nonreturn-to-zero channels with 50-GHz spacing over 840 km of conventional single-mode fiber (SMF), or 14 times the 10-Gb/s dispersion limit, using a total of eleven chirped fiber gratings for dispersion compensation. Each grating has a nominal dispersion of -1330 ps/nm km for compensating 80 km of SMF and a bandwidth of 6.5 nm, and one grating has additional dispersion slope compensation of -35 ps/nm/sup 2/ equivalent to 480 km of SMF. The large number of closely spaced wavelengths and long transmission distance significantly stress the wavelength uniformity, bandwidth, and cascadability of the fiber gratings.

Straight line 10 Gbit/s soliton transmission over1000 kmof standard fibre with in-line chirped fibre gratingfor partial dispersion compensation

The authors demonstrate a highly practical and robust soliton transmission system with partial dispersion compensation. Error free transmission was obtained for 10 Gbit/s data over 1000 km of standard fibre with nominal dispersion of 17 ps/nm.km. Despite variations in the dispersion compensation ratio and the relatively high UV-induced birefringence of the fibre gratings, the system exhibits BERs < 10–10 for any state of input polarisation provided that the average intra-span dispersion is negative.

Dispersion tests and adjustments for survival and case‐control studies

Cox and Snell have pointed out that when the empirical variance of a measured response y is quite different from its nominal variance under an assumed probability model, standard errors that are not adjusted for the discrepancy may yield misleading inferences. This article describes a test for assessing departures from nominal dispersion in survival analysis and case-control studies. Also, a robust procedure for adjusting standard errors for these models is given.

Testing and Adjusting for Departures from Nominal Dispersion in Generalized Linear Models

SUMMARY In this paper we describe a score test of the hypothesis of no departure from nominal dispersion in a generalized linear model. We also give a method for adjusting the nominal variance-covariance matrix of the estimated regression coefficients when overdispersion is suspected. This procedure is an alternative to the traditional method of adjusting each element of the variance-covariance matrix by the same factor. We illustrate our method for the one-parameter exponential family of distributions in a logistic analysis of a factorial experiment and a Poisson regression analysis of bioassay data.

On the distance to the candidate star coincident with A0620-00

The transient X-ray source (A0620-00) reported by Elvis et al . (1975) was tentatively identified with a star at α ═ 6 h 20 min 11 s, δ ═ – 0° 19' 10" (equinox 1950.0) (Boley & Wolfson 1975), based on plates taken of a field including the X-ray position: α ═ 6 h 20 min 06.4 s, δ ═ 0° 19' 04" (equinox 1950.0) (Matilsky 1975). Dr Boley kindly provided us with a finding chart. Spectra were obtained at a nominal dispersion of 5.1 A/mm (5890 Å) by using the cassegrain echelle spectrograph at the Mayall 4 m telescope at Kitt Peak on the nights of 17, 23, 25 and 26 August 1975. These spectra are described by Gull et al . (1976). Here we briefly summarize the distance estimates derived from the spectra.

OBSERVATIONS OF QUASI-STELLAR AND HARO-LUYTEN BLUE OBJECTS.

be installed at Yerkes Observatory. The spectrograph has a threeinch optical bundle, a perforated grating, and an f/2 folded Schmidt camera. This camera was designed and constructed so that the focus is 0.5 inch beyond any obstruction. This is sufficient to permit the image tube to be placed in a uniform magnetic field of a solenoid with a special pole face. The Schmidt is provided with a field flattener, but the flattener is not in optical contact with the image tube face. Four dispersions are available in factors of two from 50 to 400 Â/mm. Because of a loss of resolution in the image tube and photographic transfer system, these dispersions correspond approximately in resolution to classical spectrograms with approximately one-half the dispersion. In February 1966 the spectrograph was used on the 82-inch telescope of the McDonald Observatory to secure spectrograms of quasi-stellar objects and Haro-Luyten blue objects. The wavelength region covered depended somewhat on the colors of the sources but was generally between 3800 and 7000 Â. A nominal dispersion of 200 Â/mm was used throughout the program. Three of the spectrograms are shown in Plate I. The image tube itself is capable of giving significantly higher resolution, but with the introduction of the transfer lenses and photographic emulsions not only is the resolution reduced but the spectrograms lose the crispness usually associated with classic spectroscopy. The nineteen Haro-Luyten objects were selected according to observing convenience, without reference to their colors, from a set of finding charts kindly supplied by Dr. E. J. Wampler. Only two of them, both shown in Plate I, showed emission lines. An additional 16, which are listed in Table