Quantum three-body system in D dimensions

The independent eigenstates of the total orbital angular momentum operators for a three-body system in an arbitrary D-dimensional space are presented by the method of group theory. The Schr\"{o}dinger equation is reduced to the generalized radial equations satisfied by the generalized radial functions with a given total orbital angular momentum denoted by a Young diagram $[\mu,\nu,0,...,0]$ for the SO(D) group. Only three internal variables are involved in the functions and equations. The number of both the functions and the equations for the given angular momentum is finite and equal to $(\mu-\nu+1)$.Comment: 16 pages, no figure, RevTex, Accepted by J. Math. Phy

Shedding light on the formation of the pre-biotic molecule formamide with ASAI

Formamide (NH2CHO) has been proposed as a pre-biotic precursor with a key role in the emergence of life on Earth. While this molecule has been observed in space, most of its detections correspond to high-mass star-forming regions. Motivated by this lack of investigation in the low-mass regime, we searched for formamide, as well as isocyanic acid (HNCO), in 10 low- and intermediate-mass pre-stellar and protostellar objects. The present work is part of the IRAM Large Programme ASAI (Astrochemical Surveys At IRAM), which makes use of unbiased broadband spectral surveys at millimetre wavelengths. We detected HNCO in all the sources and NH2CHO in five of them. We derived their abundances and analysed them together with those reported in the literature for high-mass sources. For those sources with formamide detection, we found a tight and almost linear correlation between HNCO and NH2CHO abundances, with their ratio being roughly constant -between 3 and 10- across 6 orders of magnitude in luminosity. This suggests the two species are chemically related. The sources without formamide detection, which are also the coldest and devoid of hot corinos, fall well off the correlation, displaying a much larger amount of HNCO relative to NH2CHO. Our results suggest that, while HNCO can be formed in the gas phase during the cold stages of star formation, NH2CHO forms most efficiently on the mantles of dust grains at these temperatures, where it remains frozen until the temperature rises enough to sublimate the icy grain mantles. We propose hydrogenation of HNCO as a likely formation route leading to NH2CHO.Comment: 26 pages, 9 figures. Accepted by Monthly Notices of the Royal Astronomical Societ

Properties of tube and fitting scaffold connections under cyclical loads

The standard design procedure for tube and fitting connections assumes that the connections are only subjected to non-cyclical loads. This paper presents the results of experimental tests and theoretical calculations of the moment-rotation capacities of three common connections – sleeve couplers, swivel couplers and right-angled couplers. The results show that under a cyclic side load, such as that occurring by wind loading, looseness affects the capacity of the connections. For all three types of coupler looseness is shown to be relatively high which will reduce the stiffness of the connection under side loads. For sleeve couplers the effects of axial load in the tubes also affects the coupler stiffness and the maximum bending capacity of the joint. This implies that the common European code BS EN 74-1 for the connection should be changed to consider the loss in stiffness and maximum side load capacity under axial loads and looseness which are ignored in the standard. The standard assumption for right-angled and swivel couplers is that the connection can be assumed to be rigid about an axis normal to the plane containing the two tubes being joined. This is shown to be incorrect as the connections are shown to have stiffnesses about this axis which is of a similar order to the stiffnesses about the other axes

Spin-orbit coupling and the conservation of angular momentum

In nonrelativistic quantum mechanics, the total (i.e. orbital plus spin) angular momentum of a charged particle with spin that moves in a Coulomb plus spin-orbit-coupling potential is conserved. In a classical nonrelativistic treatment of this problem, in which the Lagrange equations determine the orbital motion and the Thomas equation yields the rate of change of the spin, the particle's total angular momentum in which the orbital angular momentum is defined in terms of the kinetic momentum is generally not conserved. However, a generalized total angular momentum, in which the orbital part is defined in terms of the canonical momentum, is conserved. This illustrates the fact that the quantum-mechanical operator of momentum corresponds to the canonical momentum of classical mechanics.Comment: 10 pages, as published by Eur. J. Phy

Image hiding in audio file using chaotic method

In this paper, we propose an efficient image hiding method that combines image encryption and chaotic mapping to introduce adaptive data hiding for improving the security and robustness of image data hiding in cover audio. The feasibility of using chaotic maps to hide encrypted image in the high frequency band of the audio is investigated. The proposed method was based on hiding the image data in the noisiest part of the audio, which is the high frequency band that was extracted by the zero crossing filter. Six types of digital images were used, each of size fit the length of used audio, this to facilitate the process of hiding them among the audio samples. The input image was encrypted by a one-time pad method, then its bits were hidden in the audio by the chaotic map. The process of retrieving the image from the audio was in the opposite way, where the image data was extracted from the high frequency band of the audio file, and then the extracted image was decrypted to produce the retrieved image. Four qualitative metrics were used to evaluate the hiding method in two paths: the first depends on comparing the retrieved image with the original image, while the second depends on comparing the audio containing the image data with the original audio once, and another time by comparing the cover audio with the original audio. The results of the quality metrics proved the efficiency of the proposed method, and it showed a slight and unnoticed effect between the research materials, which indicates the success of the hiding process and the validity of the research path

Psychometric comparison of three behavioural scales for the assessment of pain in critically ill patients unable to self-report

International audienc