Twistor theory on a finite graph

We show how the description of a shear-free ray congruence in Minkowski space as an evolving family of semi-conformal mappings can naturally be formulated on a finite graph. For this, we introduce the notion of holomorphic function on a graph. On a regular coloured graph of degree three, we recover the space-time picture. In the spirit of twistor theory, where a light ray is the more fundamental object from which space-time points should be derived, the line graph, whose points are the edges of the original graph, should be considered as the basic object. The Penrose twistor correspondence is discussed in this context

DynPeak : An algorithm for pulse detection and frequency analysis in hormonal time series

The endocrine control of the reproductive function is often studied from the analysis of luteinizing hormone (LH) pulsatile secretion by the pituitary gland. Whereas measurements in the cavernous sinus cumulate anatomical and technical difficulties, LH levels can be easily assessed from jugular blood. However, plasma levels result from a convolution process due to clearance effects when LH enters the general circulation. Simultaneous measurements comparing LH levels in the cavernous sinus and jugular blood have revealed clear differences in the pulse shape, the amplitude and the baseline. Besides, experimental sampling occurs at a relatively low frequency (typically every 10 min) with respect to LH highest frequency release (one pulse per hour) and the resulting LH measurements are noised by both experimental and assay errors. As a result, the pattern of plasma LH may be not so clearly pulsatile. Yet, reliable information on the InterPulse Intervals (IPI) is a prerequisite to study precisely the steroid feedback exerted on the pituitary level. Hence, there is a real need for robust IPI detection algorithms. In this article, we present an algorithm for the monitoring of LH pulse frequency, basing ourselves both on the available endocrinological knowledge on LH pulse (shape and duration with respect to the frequency regime) and synthetic LH data generated by a simple model. We make use of synthetic data to make clear some basic notions underlying our algorithmic choices. We focus on explaining how the process of sampling affects drastically the original pattern of secretion, and especially the amplitude of the detectable pulses. We then describe the algorithm in details and perform it on different sets of both synthetic and experimental LH time series. We further comment on how to diagnose possible outliers from the series of IPIs which is the main output of the algorithm.Comment: Nombre de pages : 35 ; Nombre de figures : 16 ; Nombre de tableaux :

Trkalian fields: ray transforms and mini-twistors

We study X-ray and Divergent beam transforms of Trkalian fields and their relation with Radon transform. We make use of four basic mathematical methods of tomography due to Grangeat, Smith, Tuy and Gelfand-Goncharov for an integral geometric view on them. We also make use of direct approaches which provide a faster but restricted view of the geometry of these transforms. These reduce to well known geometric integral transforms on a sphere of the Radon or the spherical Curl transform in Moses eigenbasis, which are members of an analytic family of integral operators. We also discuss their inversion. The X-ray (also Divergent beam) transform of a Trkalian field is Trkalian. Also the Trkalian subclass of X-ray transforms yields Trkalian fields in the physical space. The Riesz potential of a Trkalian field is proportional to the field. Hence, the spherical mean of the X-ray (also Divergent beam) transform of a Trkalian field over all lines passing through a point yields the field at this point. The pivotal point is the simplification of an intricate quantity: Hilbert transform of the derivative of Radon transform for a Trkalian field in the Moses basis. We also define the X-ray transform of the Riesz potential (of order 2) and Biot-Savart integrals. Then, we discuss a mini-twistor respresentation, presenting a mini-twistor solution for the Trkalian fields equation. This is based on a time-harmonic reduction of wave equation to Helmholtz equation. A Trkalian field is given in terms of a null vector in C3 with an arbitrary function and an exponential factor resulting from this reduction.Comment: 37 pages, http://dx.doi.org/10.1063/1.482610

Coupling coefficients of SO(n) and integrals over triplets of Jacobi and Gegenbauer polynomials

The expressions of the coupling coefficients (3j-symbols) for the most degenerate (symmetric) representations of the orthogonal groups SO(n) in a canonical basis (with SO(n) restricted to SO(n-1)) and different semicanonical or tree bases [with SO(n) restricted to SO(n'})\times SO(n''), n'+n''=n] are considered, respectively, in context of the integrals involving triplets of the Gegenbauer and the Jacobi polynomials. Since the directly derived triple-hypergeometric series do not reveal the apparent triangle conditions of the 3j-symbols, they are rearranged, using their relation with the semistretched isofactors of the second kind for the complementary chain Sp(4)\supset SU(2)\times SU(2) and analogy with the stretched 9j coefficients of SU(2), into formulae with more rich limits for summation intervals and obvious triangle conditions. The isofactors of class-one representations of the orthogonal groups or class-two representations of the unitary groups (and, of course, the related integrals involving triplets of the Gegenbauer and the Jacobi polynomials) turn into the double sums in the cases of the canonical SO(n)\supset SO(n-1) or U(n)\supset U(n-1) and semicanonical SO(n)\supset SO(n-2)\times SO(2) chains, as well as into the_4F_3(1) series under more specific conditions. Some ambiguities of the phase choice of the complementary group approach are adjusted, as well as the problems with alternating sign parameter of SO(2) representations in the SO(3)\supset SO(2) and SO(n)\supset SO(n-2)\times SO(2) chains.Comment: 26 pages, corrections of (3.6c) and (3.12); elementary proof of (3.2e) is adde

An Absolute Flux Density Measurement of the Supernova Remnant Casseopia A at 32 GHz

We report 32 GHz absolute flux density measurements of the supernova remnant Cas A, with an accuracy of 2.5%. The measurements were made with the 1.5-meter telescope at the Owens Valley Radio Observatory. The antenna gain had been measured by NIST in May 1990 to be $0.505 \pm 0.007 \frac{{\rm mK}}{{\rm Jy}}$. Our observations of Cas A in May 1998 yield $S_{cas,1998} = 194 \pm 5 {\rm Jy}$. We also report absolute flux density measurements of 3C48, 3C147, 3C286, Jupiter, Saturn and Mars.Comment: 30 pages, 4 figures; accepted for publication by AJ. Revised systematic error budget, corrected typos, and added reference

BMQ

BMQ: Boston Medical Quarterly was published from 1950-1966 by the Boston University School of Medicine and the Massachusetts Memorial Hospitals

Enhanced gas-liquid mass transfer of an oscillatory constricted-tubular reactor

The mass transfer performance has been tested for gas-liquid flow in a new tubular reactor system, the oscillating mesotube (OMT), which features the oscillatory movement of fluid across a series of smooth constrictions located periodically along the vertical 4.4 mm internal diameter tube. The effect of the fluid oscillations (frequency,f, and center-to-peak amplitude, x(0), in the range of 0-20 s(-1) and 0-3 mm, respectively) on the overall volumetric mass transfer coefficient (k(L)a) has been tested by measuring the oxygen saturation levels with a fiber-optical microprobe (oxygen micro-optrode), and a mathematical model has been produced to describe the oxygen mass transport in the OMT. The oxygen mass transfer rates were about I order of magnitude higher (k(L)a values up to 0.16 s(-1)) than those values reported for gas-liquid contacting in a 50 mm internal diameter oscillatory flow reactor (OFR), for the same peak fluid oscillatory velocity, i.e., 2 pi fx(0). This represents remarkable oxygen transfer efficiencies, especially when considering the very low mean superficial gas velocity involved in this work (0.37 mm s(-1)). The narrower constrictions helped to increase the gas fraction (holdup) by reducing the rise velocity of the bubbles. However, the extent of radial mixing and the detachment of vortex rings from the surface of the periodic constrictions are actually the main causes of bubbles retention and effective gas-liquid contacting and are, thus, responsible for the enhancement of k(L)a in the OMT.N.R. thanks the Portuguese Foundation for Science and Technology (FCT) for financial support of his work (SFRH/BD/6954/2001)

Pola Penyakit Transmigran Jawa dan Transmigran Lokal di Daerah Hiperendemis Malaria Armopasp2, Kecamatan Bonggo, Kabupaten Jayapura, Papua, Tahun 1996-1999

POLA PENYAKIT TRANSMIGRAN JAWA DAN TRANSMIGRAN LOKAL DI DAERAH HIPERENDEMIS MALARIA ARMOPASP2, KECAMATAN BONGGO, KABUPATEN JAYAPURA, PAPUA , TAHUN 1996-199