scholarly journals On the squashed seven-sphere operator spectrum

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Simon Ekhammar ◽  
Bengt E. W. Nilsson
Keyword(s):  
Mass Spectrum ◽  
Complete Spectrum ◽  
Eigenvalue Spectrum ◽  
Operator Equations ◽  
Operator Spectrum

Abstract We derive major parts of the eigenvalue spectrum of the operators on the squashed seven-sphere that appear in the compactification of eleven-dimensional supergravity. These spectra determine the mass spectrum of the fields in AdS4 and are important for the corresponding $$ \mathcal{N} $$ N = 1 supermultiplet structure. This work is a continuation of the work in [1] where the complete spectrum of irreducible isometry representations of the fields in AdS4 was derived for this compactification. Some comments are also made concerning the G2 holonomy and its implications on the structure of the operator equations on the squashed seven-sphere.

Confocal Raman mapping

1992 ◽  
Vol 50 (2) ◽  
pp. 1514-1515
Author(s):  
J. Barbillat ◽  
M. Delhaye ◽  
P. Dhamelincourt
Keyword(s):  
Chemical Species ◽  
Diffraction Limit ◽  
Microscopic Level ◽  
Raman Mapping ◽  
Complete Spectrum ◽  
Laser Illumination ◽  
Ccd Detector ◽  
Raman Microprobe ◽  
Photodiode Array ◽  
Raman Image

Raman mapping, with a spatial resolution close to the diffraction limit, can help to reveal the distribution of chemical species at the surface of an heterogeneous sample.As early as 1975,three methods of sample laser illumination and detector configuration have been proposed to perform Raman mapping at the microscopic level (Fig. 1),:- Point illumination:The basic design of the instrument is a classical Raman microprobe equipped with a PM tube or either a linear photodiode array or a two-dimensional CCD detector. A laser beam is focused on a very small area ,close to the diffraction limit.In order to explore the whole surface of the sample,the specimen is moved sequentially beneath the microscope by means of a motorized XY stage. For each point analyzed, a complete spectrum is obtained from which spectral information of interest is extracted for Raman image reconstruction.- Line illuminationA narrow laser line is focused onto the sample either by a cylindrical lens or by a scanning device and is optically conjugated with the entrance slit of the stigmatic spectrograph.

On Homogenization of Controlled Objects Described by Operator Equations of Hammerstein Type

2003 ◽  
Vol 35 (11) ◽  
pp. 19-27
Author(s):  
Victor N. Mizernyi ◽  
Peter I. Kogut ◽  
Tatyana N. Rudyanova
Keyword(s):  
Operator Equations

scholarly journals Analysis of Butyl Butyrate Mass Spectrum

2018 ◽  
Vol 10 (1) ◽  
pp. 11
Author(s):  
Abdalla Mustafa Walwil
Keyword(s):  
Mass Spectrum ◽  
Proton Transfer ◽  
Educational Work ◽  
Butyl Butyrate ◽  
Chemistry Students ◽  
Double Proton Transfer

The aim of this educational work is targeting chemistry students and interested instructors. The presented work will analyze the mass spectrum of butyl butyrate (butyl butanoate). The analysis will concentrate on the mechanisms showing how the characteristic fragments are formed. The mechanisms discussed in this paper include α-cleavage, β-cleavage, McLafferty Rearrangements, first and second proton transfer, a double proton transfer. 

scholarly journals An event excess observed in the deeply bound region of the 12C (K−, p) missing-mass spectrum

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Yudai Ichikawa ◽  
Junko Yamagata-Sekihara ◽  
Jung Keun Ahn ◽  
Yuya Akazawa ◽  
Kanae Aoki ◽  
...  
Keyword(s):  
Mass Spectrum ◽  
Binding Energy ◽  
Decay Channel ◽  
Peak Shift ◽  
Bound State ◽  
Elastic Peak ◽  
Missing Mass ◽  
Decay Modes ◽  
Kaon Momentum ◽  
First Time

Abstract We have measured, for the first time, the inclusive missing-mass spectrum of the $^{12}$C$(K^-, p)$ reaction at an incident kaon momentum of 1.8 GeV/$c$ at the J-PARC K1.8 beamline. We observed a prominent quasi-elastic peak ($K^-p \rightarrow K^-p$) in this spectrum. In the quasi-elastic peak region, the effect of secondary interaction is apparently observed as a peak shift, and the peak exhibits a tail in the bound region. We compared the spectrum with a theoretical calculation based on the Green’s function method by assuming different values of the parameters for the $\bar{K}$–nucleus optical potential. We found that the spectrum shape in the binding-energy region $-300 \, \text{MeV} < B_{K} < 40$ MeV is best reproduced with the potential depths $V_0 = -80$ MeV (real part) and $W_0 = -40$ MeV (imaginary part). On the other hand, we observed a significant event excess in the deeply bound region around $B_{K} \sim 100$ MeV, where the major decay channel of $K^- NN \to \pi\Sigma N$ is energetically closed, and the non-mesonic decay modes ($K^- NN \to \Lambda N$ and $\Sigma N$) should mainly contribute. The enhancement is fitted well by a Breit–Wigner function with a kaon-binding energy of 90 MeV and width 100 MeV. A possible interpretation is a deeply bound state of a $Y^{*}$-nucleus system.

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