Diffraction by an elliptic cone and the solution of the wedge diffraction problem

Contents The paper deals with scalar diffraction by an elliptic cone in the limit case of ellipticity parameterk=0. In this case the elliptic cone degenerates into a wedge with exterior opening angle 2₀. We solve the two-parameter eigenvalue problem for two coupled Lamé differential equations fork=0 and obtain the eigenvalues and the eigenfunctions for the wedge problem by a completely analytical calculation. We utilize a precise transformation of the sphero-conal coordinates into spherical coordinates with the edge of the wedge as polar axis and determine, by substitution of the transformed Lamé products into Green's functions for the elliptic cone, the solution of the scalar diffraction problem for the wedge.The results obtained are in full agreement with those reported in [2]. In the special case of half-plane diffraction (₀=) the solution reduces to that in [1].

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Beugung am elliptischen Kegel und die Lösung des Beugungsproblems für den Keil

Übersicht in dieser Arbeit beschäftigen wir uns mit der skalaren Beugung am Kegel elliptischen Querschnitts im Grenzfall des Elliptizitätsparametersk=0. In diesem Fall entartet der elliptische Kegel in einen Keil mit dem Außenöffnungswinkel 2₀. Wir lösen das zweiparametrige Eigenwertproblem für zwei gekoppelte Lamésche Differentialgleichungen fürk=0 und erhalten über eine vollständig analytische Rechnung die Eigenwerte und die Eigenfunktionen für das Keilproblem. Wir ziehen eine exakte Transformation der elliptischen Kegelkoordinaten in Kugelkoordinaten mit der Keilkante als Polarachse heran und gewinnen, durch Substitution der transformierten Laméschen Produkte in den Greenschen Funktionen für den elliptischen Kegel, die Lösung des skalaren Beugungsproblems für den Keil.Die Ergebnisse stimmen vollständig überein mit denjenigen, die in [2] zitiert werden. Im Spezialfall der Beugung an der Halbebene (₀=) wird die Lösung wieder zurückgeführt auf die in [1] abgeleitete Lösung.

     

Exo-mechanism proximity-accelerated alkylations: investigations of linkers, electrophiles and surface mutations in engineered cyclophilin-cyclosporin systems

Investigations on the scope and utility of exo-mechanism proximity-accelerated reactions in engineered receptor-ligand systems are reported. We synthesized a series of electrophilic cyclosporin (CsA) derivatives by varying electrophiles and linker lengths, prepared a series of nucleophilic cysteine mutations on the surface of cyclophilin A (Cyp), and examined their reactivity and specificity in proximity-accelerated reactions. Acrylamide and epoxide electrophiles afforded useful reactivity and high specificity for alkylation of engineered receptors in Jurkat cell extracts. We found that remote cysteines (>17 A from the ligand) could be alkylated with useful rates under physiological conditions. The results from mutations of the receptor surface suggest that the dominant factors governing the rates of proximity-accelerated reactions are related to the local environment of the reactive group on the protein surface. This study defines several parameters affecting reactivity in exo-mechanism proximity-accelerated reactions and provides guidance for the design of experiments for biological investigations involving proximity-accelerated reactions.     

Single Soybean Seed NMR Calibration for Oil Measurement Using Commercial Cooking Oils

Development of high oil soybeans would reduce the cost of soybean oil production for biodiesel or edible oil applications. An accurate determination of soybean seed oil concentration is essential especially when developing superior cultivars with increased seed oil content. The objective of this study was to develop an oil measurement method for single seeds using NMR spectrometry. An NMR spectrometer was calibrated using commercial cooking oil. Fifteen cultivars of known mean oil content were used to evaluate the calibration curves. The calibration curves developed had a correlation coefficient of 0.99. It was found that soybean and corn oil gave identical results over the calibrated interval.     

Trans isomeric octadecenoic acids are related inversely to arachidonic acid and DHA and positively related to mead acid in umbilical vessel wall lipids

Long-chain PUFA play an important role in early human neurodevelopment. Significant inverse correlations were reported between values of trans isomeric and long-chain PUFA in plasma lipids of preterm infants and children aged 1–15 yr as well as in venous cord blood lipids of full-term infants. Here we report FA compositional data of cord blood vessel wall lipids in 308 healthy, full-term infants (gestational age: 39.7±1.2 wk, birth weight: 3528±429 g, mean±SD). The median (interquartile range) of the sum of 18-carbon trans FA was 0.22 (0.13)% w/w in umbilical artery and 0.16 (0.10)% w/w in umbilical vein lipids. Nonparametric correlation analysis showed significant inverse correlations between the sum of 18-carbon trans FA and both arachidonic acid and DHA in artery (r=−0.38, P<0.01, and r=−0.20, P<0.01) and vein (r=−0.36, P<0.01, and −0.17, P<0.01) wall lipids. In addition, the sum of 18-carbon trans FA was significantly positively correlated to Mead acid, a general indicator of EFA deficiency, in both artery (r=+0.35, P<0.01) and vein (r=+0.31, P<0.01) wall lipids. The present results obtained in a large group of full-term infants suggest that maternal trans FA intake is inversely associated with long-chain PUFA status of the infant at birth.     

Three-dimensional half-plane diffraction: Exact solution and testing of uniform theories

The exact solution of the diffraction problem for a plane electromagnetic wave at oblique incidence on a perfectly conducting half-plane was obtained more than 30 years ago. Recent advances in the high-frequency diffraction theory enable us to present the final solution in much simpler and suggestive forms. This solution is next used to test two uniform theories of edge diffraction. We find that uniform asymptotic theory (UAT) developed by Ahluwalia et al. recovers the exact solution, whereas uniform geometrical theory of diffraction (UTD) developed by Kouyoumjian and Pathak does not. The error of UTD is discussed.     

Characterisation of a TES-Based X-ray Microcalorimeter in the Energy Range from 150 to 1800 eV Using an Adiabatic Demagnetisation Refrigerator

We characterised a TES-based X-ray microcalorimeter in an adiabatic demagnetisation refrigerator (ADR) using synchrotron radiation. The detector response and energy resolution was measured at the beam-line in the PTB radiometry laboratory at the electron storage ring BESSY II in the range from 200 to 1800 eV. We present and discuss the results of the energy resolution measurements as a function of energy, beam intensity and detector working point. The measured energy resolution ranges between 1.5 to 2.1 eV in the investigated energy range and is weakly dependent on the detector set point. A first analysis shows a count-rate capability, without considerable loss of performance, of about 500 counts per second.      

High-frequency diffraction of a line-source field by a half-plane: Solutions by ray techniques

The diffraction of an arbitrary cylindrical wave due to a line source and incident on a half-plane is treated by the uniform asymptotic theory of edge diffraction. For large wavenumberk, an asymptotic solution for the total field up to and including terms of orderk^{-3/2}relative to the incident field is derived. This solution is uniformly valid for all observation points, including points near the edge and the shadow boundaries. In particualr, two special cases are considered: A) the line source is located on the half-plane, and radiates anE-polarized wave and B) the line source is located in the aperture complementary to the half-plane and radiates anH-polarized wave. A companion paper will show that our asymptotic solution for Case A) is in complete agreement with the asymptotic expansion of the exact solution. For the same diffraction problem, asymptotic solutions obtained by the method of slope diffraction coefficients and the method of equivalent currents are also discussed. It is found that the latter solutions agree with the exact one only when i) the observation point is away from the edge and the shadow boundaries, and/or ii) the terms of orderk^{-3/2}in the field solution are ignored.     

Prevalence and severity of the dementia syndrome in homes for the aged and nursing homes. A study in elderly from a rural area near Zwolle

In the Netherlands both nursing homes and homes for the aged serve as a residence for demented elderly. Although these institutions differ considerably regarding financing and care facilities, specific functions of each institute concerning demented elderly have not been clearly defined. In order to know to what extent residential facilities serve demented elderly, the prevalence and severity of dementia among residents aged 65 and over was studied as part of a prevalence study among elderly people in a rural area of the Netherlands. The target population existed of all persons aged 65 and over who were registered in eight general practices. Patients who had to leave the practice on account of ill-health and were admitted to nursing homes were included in the study. In a two stage study the MMSE was applied as a screening instrument. Based on MMSE-score a non-proportional stratified random sample was drawn for the second, diagnostic stage, which existed of the CAMDEX. Prevalence estimates for DSM-III-R-dementia were 21% among residents of homes for the aged, 48% among residents of somatic wards of nursing homes and 100% among those admitted to psychogeriatric wards of nursing homes. Severity of dementia was highest among residents of psychogeriatric wards of nursing homes and lowest among those living in homes for the aged. Prevalence of dementia among residents of homes for the aged can be fully attributed to the age-distribution. The high frequency of dementia among residents of somatic nursing home wards can be explained in several ways: First, admission can be necessary due to a combination of dementia and somatic illness.(ABSTRACT TRUNCATED AT 250 WORDS)     

Singularity in Green's function and its numerical evaluation

The free-space scalar Green's functionghas anR^{-1}singularity, whereRis the distance between the source and observation points. The second derivatives ofghaveR^{-3}singularities, which are not generally integrable over a volume. The derivatives ofgare treated as generalized functions in the manner described by Gel'fand and Shilov, and a new formula is derived that regularizes a divergent convolution integral involving the second derivatives ofg. When the formula is used in the dyadic Green's function formulation for calculating theEfield, all previous results are recovered as special cases. Furthermore, it is demonstrated that the formula is particularly suitable for the numerical evaluation of the field at a source point, because it allows the exclusion of an arbitrary finite region around the singular point from the integration volume. This feature is not shared by any of the previous results on the dyadic Green's function.