UN-Sector and Compositeness Conditions in the Bronzan-Lee Model

1974 ◽  
Vol 29 (11) ◽  
pp. 1531-1542
Author(s):  
A. L. Choudhury
Keyword(s):  
Fourier Transform ◽  
Composite Particle ◽  
Composite Model ◽  
The Other ◽  
Final States ◽  
Lee Model ◽  
Other Hand ◽  
Initial States ◽  
The Fourier Transform ◽  
Limiting Values

The Lehmann-Symanzik-Zimmermann (LSZ) technique has been used to calculate all τ -functions of the UN-sector of the Bronzan-Lee model. Using the prescription of Liossatos, the ZV → 0 limit has been carried out for the fourier transform of the τ-functions in the sector. These limiting functions τ̂α,LUN are then compared with the τ̂C,αUN functions derived from a composite model, proposed by the foregoing author, where V is considered to be a composite particle. It has been found that when the so called composite V-particle does not appear in the initial and the final states, these τ-functions coincide. On the other hand, the limiting values of some τ-functions differ from those of the composite model, when such particles appear in the final or initial states.

Necessary Conditions for Integrability of the Fourier Transform

2009 ◽  
Vol 16 (3) ◽  
pp. 553-559
Author(s):  
Elijah Liflyand
Keyword(s):  
Fourier Transform ◽  
Fourier Series ◽  
Necessary Conditions ◽  
The Other ◽  
Necessary Condition ◽  
Convergent Fourier Series ◽  
Other Hand ◽  
The Fourier Transform

Abstract We prove the necessary conditions for the integrability of the Fourier transform. The result is a generalization, on one hand, of the well known necessary condition for absolutely convergent Fourier series and, on the other hand, of an earlier multidimensional result of Trigub.

The infrared spectrum of CS

1984 ◽  
Vol 62 (12) ◽  
pp. 1414-1419 ◽  
Author(s):  
R. J. Winkel Jr. ◽  
Sumner P. Davis ◽  
Rubén Pecyner ◽  
James W. Brault
Keyword(s):  
Fourier Transform ◽  
Infrared Emission ◽  
Solar Observatory ◽  
Band Head ◽  
The Other ◽  
Fourier Transform Spectrometer ◽  
National Solar Observatory ◽  
Carbon Monosulfide ◽  
Vibration Rotation ◽  
The Fourier Transform

The infrared emission spectrum of carbon monosulfide was observed as a sequence of vibration–rotation bands in the X1Σ+ state, with strong heads of the Δν = 2 sequence degraded to the red. Eight bands of 12C32S were identified, and bands corresponding to the isotope 12C34S were also observed. The most prominent band head, that of the (2–0) band, is at 2585 cm−1, with the other heads spaced approximately 26 cm−1 to smaller wavenumbers. Our data, taken with the Fourier transform spectrometer at the National Solar Observatory (Kitt Peak) include the first reported laboratory observations of the band heads and as many as 200 lines in each band. These observations allowed the calculation of vibrational and rotational constants to higher order than previously reported.

scholarly journals Effect of Spheroidization Annealing on Pearlite Banding

2019 ◽  
Vol 949 ◽  
pp. 40-47 ◽  
Author(s):  
Sergey Guk ◽  
Eva Augenstein ◽  
Maksim Zapara ◽  
Rudolf Kawalla ◽  
Ulrich Prahl
Keyword(s):  
Empirical Model ◽  
Initial Conditions ◽  
The Other ◽  
Experimental Investigations ◽  
Initial State ◽  
Ferritic Matrix ◽  
Other Hand ◽  
Initial States ◽  
Hot Rolled

The present paper deals with the influence of the duration of isothermal spheroidization annealing on the evolution of pearlite bands in various initial states. In this study, two initial conditions of the steel 16MnCrS5 are considered: a) industrially hot-rolled pearlite structures in their ferritic matrix and b) a specifically adjusted microstructure in the lab condition. Based on the experimental investigations and quantitative microstructural analyses, an empirical model for the prediction of pearlite banding within a broad range of annealing durations could be derived. Both, experiment and model, agree that pronounced pearlite bands in the initial state almost disappear after 25 h of spheroidization annealing. On the other hand, a marginal degree of pearlite banding in the initial state increases slightly during annealing. This fact could be explained by inhomogeneous cementite formation inside and outside the primary segregation regions of manganese.

ORIGINATIONS AND EXTINCTIONS: ANALYSES OF FOSSIL DATA AND SIMULATIONS

2000 ◽  
Vol 11 (02) ◽  
pp. 277-285 ◽  
Author(s):  
TANE RAY ◽  
LEO MOSELEY ◽  
NAEEM JAN
Keyword(s):  
Fourier Transform ◽  
Frequency Dependence ◽  
Frequency Spectrum ◽  
Fossil Record ◽  
Trophic Levels ◽  
The Other ◽  
Simulation Data ◽  
The Past ◽  
Other Hand ◽  
Fossil Data

We analyse the fossil data of Benton1 with and without interpolation schemes. By Fourier transform analysis, we find a frequency dependence of the amplitude of 1/f for the various interpolation schemes used in the past. We illustrate that shuffling the interpolated data changes the spectra only slightly. On the other hand, an identical analysis performed on the raw (uninterpolated) fossil data gives a flat frequency spectrum. We conclude that the 1/f behavior is an artifact of the interpolation schemes. We next introduce a simulation of extinctions driven only by interactions between two trophic levels. Fourier transform analysis of the simulation data shows a frequency dependence of 1/f. When the data are grouped into a form resembling the fossil record the frequency dependence vanishes, giving a flat spectrum. Our simulation produces a frequency spectrum that agrees with the observed fossil record.

Tempered distributions with spectral gaps

1989 ◽  
Vol 106 (1) ◽  
pp. 143-162 ◽  
Author(s):  
Jean-Pierre Gabardo
Keyword(s):  
Fourier Transform ◽  
Fourier Transforms ◽  
The Other ◽  
Convolution Operators ◽  
Spectral Gaps ◽  
Tempered Distributions ◽  
Tempered Distribution ◽  
Other Hand

AbstractA tempered distribution on ℝ whose Fourier transform is supported in an interval [−Ω,Ω], where Ω>0, can be characterized by the behaviour of its successive derivatives. On the other hand, a tempered distribution on ℝ whose Fourier transform vanishes in an interval (−Ω,Ω), where Ω>0, can be characterized by the behaviour of a particular sequence of successive antiderivatives. Similar considerations apply to general convolution operators acting on J′(ℝn) and yield characterizations for tempered distributions having their Fourier transforms supported in sets of the form or , where and Ω>0.

Parameters Estimation and Waveform Reconstruction of Chirp Signal Based on FRFT

2014 ◽  
Vol 989-994 ◽  
pp. 3993-3996 ◽  
Author(s):  
Yan Jun Wu ◽  
Gang Fu ◽  
Fei Liu
Keyword(s):  
Fourier Transform ◽  
Fractional Fourier Transform ◽  
Signal Reconstruction ◽  
Parameters Estimation ◽  
The Other ◽  
Fourier Domain ◽  
Chirp Signal ◽  
The Fourier Transform ◽  
Definition Of ◽  
Noisy Background

The fractional Fourier transform (FRFT) is a generalization of the Fourier transform. The article first introduces the definition of FRFT transformation; then analyzed FRFT Chirp signal based on this humble proposed restoration Chirp signal in a noisy background in two ways: one is based on parameter estimation, and the other is based on the scores Fourier domain filtering to achieve signal reconstruction; Finally, simulation verify the feasibility of the above analysis.

scholarly journals Analysis of Stock Market Indices with Multidimensional Scaling and Wavelets

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
J. Tenreiro Machado ◽  
Fernando B. Duarte ◽  
Gonçalo Monteiro Duarte
Keyword(s):  
Fourier Transform ◽  
Stock Market ◽  
Multidimensional Scaling ◽  
The Other ◽  
Second Phase ◽  
Continuous Wavelets ◽  
Considerable Research ◽  
Shannon Wavelet ◽  
Chaotic Nature ◽  
The Fourier Transform

Stock market indices (SMIs) are important measures of financial and economical performance. Considerable research efforts during the last years demonstrated that these signals have a chaotic nature and require sophisticated mathematical tools for analyzing their characteristics. Classical methods, such as the Fourier transform, reveal considerable limitations in discriminating different periods of time. This paper studies the dynamics of SMI by combining the wavelet transform and the multidimensional scaling (MDS). Six continuous wavelets are tested for analyzing the information content of the stock signals. In a first phase, the real Shannon wavelet is adopted for performing the evaluation of the SMI dynamics, while their comparison is visualized by means of the MDS. In a second phase, the other wavelets are also tested, and the corresponding MDS plots are analyzed.

scholarly journals The spectrum of H 2 . The Bands analogous to the parhelium line spectrum. —Part II

1929 ◽  
Vol 123 (792) ◽  
pp. 466-488 ◽  
Keyword(s):  
The Other ◽  
Line Spectrum ◽  
Final States ◽  
Intensity Measures ◽  
Initial States

Errata in Part I . —On p. 70, line 22, the three values of 2α should read 1∙935, 1∙635 and 1∙465. These give an “average α” = 0∙839 which is identical with the value 0∙85 0 got in the other way. We now learn from a letter from Prof. Birge that this “constant” (the α in B n = B 0 —α n ) has the same value for the initial states of Dieke and Hopfield’s AB bands as for the final states of our systems. In Tables I and IX the intensity measures attributed to Kapuscinski and Eymers are not in many cases the values finally published by them. Their paper should be consulted if accurate values are required. The final values show an even better agreement with our classification than the preliminary ones.

scholarly journals Filling a Box with Translates of Two Bricks

10.37236/1857 ◽  
2004 ◽  
Vol 11 (1) ◽  
Author(s):  
Mihail N. Kolountzakis
Keyword(s):  
Fourier Transform ◽  
The Other ◽  
Interesting Fact ◽  
The Fourier Transform

We give a new proof of the following interesting fact recently proved by Bower and Michael: if a $d$-dimensional rectangular box can be tiled using translates of two types of rectangular bricks, then it can also be tiled in the following way. We can cut the box across one of its sides into two boxes, one of which can be tiled with the first brick only and the other one with the second brick. Our proof relies on the Fourier Transform. We also show that no such result is true for translates of more than two types of bricks.

scholarly journals WAVELET TRANSFORM AND LIP MODEL

2011 ◽  
Vol 21 (2) ◽  
pp. 121 ◽  
Author(s):  
Guy Courbebaisse ◽  
Frederic Trunde ◽  
Michel Jourlin
Keyword(s):  
Image Processing ◽  
Fourier Transform ◽  
Wavelet Transform ◽  
The Other ◽  
Mathematical Framework ◽  
Fast Computation ◽  
Microscope Images ◽  
Computation Algorithm ◽  
Logarithmic Image Processing ◽  
The Fourier Transform

The Fourier transform is well suited to the study of stationary functions. Yet, it is superseded by the Wavelet transform for the powerful characterizations of function features such as singularities. On the other hand, the LIP (Logarithmic Image Processing) model is a mathematical framework developed by Jourlin and Pinoli, dedicated to the representation and processing of gray tones images called hereafter logarithmic images. This mathematically well defined model, comprising a Fourier Transform "of its own", provides an effective tool for the representation of images obtained by transmitted light, such as microscope images. This paper presents a Wavelet transform within the LIP framework, with preservation of the classical Wavelet Transform properties. We show that the fast computation algorithm due to Mallat can be easily used. An application is given for the detection of crests.

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