scholarly journals An Operator Based Approach to Irregular Frames of Translates

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 449
Author(s):  
Peter Balazs ◽  
Sigrid Heineken
Keyword(s):  
Fourier Transform ◽  
Parseval Frame ◽  
Bandlimited Function ◽  
Irregular Case ◽  
Set Of Points ◽  
First Time

We consider translates of functions in L 2 ( R d ) along an irregular set of points, that is, { ϕ ( · − λ k ) } k ∈ Z —where ϕ is a bandlimited function. Introducing a notion of pseudo-Gramian function for the irregular case, we obtain conditions for a family of irregular translates to be a Bessel, frame or Riesz sequence. We show the connection of the frame-related operators of the translates to the operators of exponentials. This is used, in particular, to find for the first time in the irregular case a representation of the canonical dual as well as of the equivalent Parseval frame—in terms of its Fourier transform.

Ground state molecular parameters of phosphine, PH3, from the simultaneous analysis of the high-resolution infrared, microwave and submillimeterwave spectra

1985 ◽  
Vol 50 (11) ◽  
pp. 2480-2492 ◽  
Author(s):  
Soňa Přádná ◽  
Dušan Papoušek ◽  
Jyrki Kauppinen ◽  
Sergei P. Belov ◽  
Andrei F. Krupnov ◽  
...  
Keyword(s):  
Fourier Transform ◽  
High Resolution ◽  
Ground State ◽  
Unitary Transformation ◽  
Point Of View ◽  
Acoustic Detection ◽  
Molecular Parameters ◽  
Microwave Spectrometer ◽  
Fourier Transform Spectra ◽  
First Time

Fourier transform spectra of the ν2 band of PH3 have been remeasured with 0.0045 cm-1 resolution. Ground state combination differences from these data have been fitted simultaneously with the microwave and submillimeterwave data to determine the ground state spectroscopical parameters of PH3 including the parameters of the Δk = ± 3n interactions. The correlation between the latter parameters has been discussed from the point of view of the existence of two equivalent effective rotational operators which are related by a unitary transformation. The ΔJ = 0, +1, ΔK = 0 (A1 ↔ A2, E ↔ E) rotational transitions in the ν2 and ν4 states have been measured for the first time by using a microwave spectrometer and a radiofrequency spectrometer with acoustic detection.

scholarly journals Measurements of hydrogen cyanide (HCN) and acetylene (C<sub>2</sub>H<sub>2</sub>) from the Infrared Atmospheric Sounding Interferometer (IASI)

2013 ◽  
Vol 6 (4) ◽  
pp. 917-925 ◽  
Author(s):  
V. Duflot ◽  
D. Hurtmans ◽  
L. Clarisse ◽  
Y. R'honi ◽  
C. Vigouroux ◽  
...  
Keyword(s):  
Fourier Transform ◽  
Hydrogen Cyanide ◽  
Atmospheric Transport ◽  
Trace Gases ◽  
First Order ◽  
Line Mixing ◽  
Atmospheric Sounding ◽  
First Time ◽  
Order Comparison ◽  
Emission Ratios

Abstract. Hydrogen cyanide (HCN) and acetylene (C2H2) are ubiquitous atmospheric trace gases with medium lifetime, which are frequently used as indicators of combustion sources and as tracers for atmospheric transport and chemistry. Because of their weak infrared absorption, overlapped by the CO2 Q branch near 720 cm−1, nadir sounders have up to now failed to measure these gases routinely. Taking into account CO2 line mixing, we provide for the first time extensive measurements of HCN and C2H2 total columns at Reunion Island (21° S, 55° E) and Jungfraujoch (46° N, 8° E) in 2009–2010 using observations from the Infrared Atmospheric Sounding Interferometer (IASI). A first order comparison with local ground-based Fourier transform infraRed (FTIR) measurements has been carried out allowing tests of seasonal consistency which is reasonably captured, except for HCN at Jungfraujoch. The IASI data shows a greater tendency to high C2H2 values. We also examine a nonspecific biomass burning plume over austral Africa and show that the emission ratios with respect to CO agree with previously reported values.

scholarly journals Apparent Variation of v sin i and Rotational Modulation in Be Stars

2004 ◽  
Vol 215 ◽  
pp. 93-94
Author(s):  
C. Neiner ◽  
S. Jankov ◽  
M. Floquet ◽  
A. M. Hubert
Keyword(s):  
Fourier Transform ◽  
Magnetic Dipole ◽  
Be Stars ◽  
Line Profiles ◽  
Transform Method ◽  
Rotational Modulation ◽  
Be Star ◽  
Apparent Variation ◽  
The Fourier Transform ◽  
First Time

v sin i was determined by applying the Fourier transform method to the line profiles of two classical Be Stars. A variation is observed in the apparent v sin i which corresponds to the main frequencies associated to nrp modes. Rotational modulation is observed in wind sensitive UV lines of the Be star ω Ori and is associated with an oblique magnetic dipole which is discovered for the first time in a classical Be star.

scholarly journals Integrated Band Intensities of Ethylene (C212H4) by Fourier Transform Infrared Spectroscopy

2012 ◽  
Vol 2012 ◽  
pp. 1-5 ◽  
Author(s):  
G. B. Lebron ◽  
T. L. Tan
Keyword(s):  
Fourier Transform ◽  
Infrared Spectroscopy ◽  
Ambient Temperature ◽  
Ftir Spectroscopy ◽  
Fourier Transform Infrared ◽  
Vapor Pressures ◽  
Infrared Band ◽  
Combination Bands ◽  
First Time ◽  
Absorbance Spectra

The integrated band intensities of ethylene (12C2H4) in the 640–3260 cm−1 region were determined by Fourier transform infrared (FTIR) spectroscopy. The infrared absorbance spectra of the ν7 and ν10, ν12, ν7+ν8, ν6+ν10, v11, and ν9 and ν2+ν12 bands of ethylene recorded at a resolution of 0.5 cm−1 were measured at an ambient temperature of 296 K at various vapor pressures ranging from 3×10−5 to 1×10−3 atm to obtain respective Beer-Lambert's law plots. The measured integrated band intensities in cm−1/cm atm were S(ν9andν2+ν12)=112.20±0.24, S(ν11)=55.35±0.14, S(ν12)=41.22±0.30, and S(ν7andν10)=328.66±16.55. In addition, the measured infrared band intensities of the ν7+ν8 and ν6+ν10 combination bands of ethylene are reported for the first time: S(ν7+ν8)=21.701±0.028 cm−1/cm atm and S(ν6+ν10)=2.568±0.025 cm−1/cm atm.

The Centrifugally Induced Pure Rotational Spectrum and the Structure of Sulfur Trioxide. A Microwave Fourier Transform Study of a Nonpolar Molecule

1991 ◽  
Vol 46 (8) ◽  
pp. 710-714 ◽  
Author(s):  
Volker Meyer ◽  
Dieter Hermann Sutter ◽  
Helmut Dreizler
Keyword(s):  
Fourier Transform ◽  
Sulfur Trioxide ◽  
Rotational Spectrum ◽  
Centrifugal Distortion ◽  
Rotational Constants ◽  
Nonpolar Molecule ◽  
Centrifugal Distortion Constants ◽  
First Time

AbstractThe pure rotational spectrum of sulfur trioxide has been observed for the first time. A total of 25 high-J transitions could be assigned. The rotational constants, two quartic centrifugal distortion constants, and three sextic centrifugal distortion constants were determined as: B= 10 449.0667(23) MHz, C = 5216.0330(12) MHz, DJ = 9.2651 (18) kHz, DJK = -16.3922(18) kHz, HJ, = -8.8(34) • 10-3 Hz, HJK= -15.8(73) • 10-3 Hz, and HKJ = 34.2(73) • 10-3 Hz. An r0- and an re -structure are presented: r0= 1.4198(7) Å (calculated from B), r0 = 1.4210(7) Å (calculated from C), and re = 1.4175 Å

Development of Abel's inversion method to extract radially resolved optical emission maps from spectral data cubes collected via push-broom hyperspectral imaging with sub-pixel shifting sampling

2020 ◽  
Vol 35 (1) ◽  
pp. 117-125 ◽  
Author(s):  
Songyue Shi ◽  
Kevin Finch ◽  
Yue She ◽  
Gerardo Gamez
Keyword(s):  
Fourier Transform ◽  
Spectral Data ◽  
Hyperspectral Imaging ◽  
Plasma Diagnostics ◽  
Optical Emission ◽  
Inversion Method ◽  
High Fidelity ◽  
Inversion Algorithm ◽  
Data Cubes ◽  
First Time

The optimization of a Fourier transform-based Abel's inversion algorithm allows the reconstruction of high-fidelity radially resolved OES images from SPS-PbHSI acquisition for plasma diagnostics for the first time.

Lambda doubling in the infrared spectrum of SH

1984 ◽  
Vol 62 (12) ◽  
pp. 1420-1425 ◽  
Author(s):  
R. J. Winkel Jr. ◽  
Sumner P. Davis
Keyword(s):  
Fourier Transform ◽  
Infrared Spectrum ◽  
Ground State ◽  
Solar Observatory ◽  
Fourier Transform Spectrometer ◽  
Multiplet Splitting ◽  
National Solar Observatory ◽  
Vibration Rotation ◽  
The Fourier Transform ◽  
First Time

The (1–0), (2–1), and (3–2) infrared vibration–rotation bands of the X2Π ground state of sulfur monohydride were observed in emission from a furnace. Multiplet splitting produces two subbands, each of which exhibits lambda splitting. The band heads were observed for the first time, 285 lines were measured, and a calculation of lambda-doubling parameters was made. The spectrum was recorded using the Fourier transform spectrometer at the National Solar Observatory (Kitt Peak).

The magnetic dipole a1Δg → X3Σg− transition in the oxygen afterglow

1981 ◽  
Vol 59 (10) ◽  
pp. 1391-1398 ◽  
Author(s):  
C. Amiot ◽  
J. Verges
Keyword(s):  
Fourier Transform ◽  
High Resolution ◽  
Magnetic Dipole ◽  
Molecular Constants ◽  
First Time ◽  
Microwave Data

The magnetic dipole a1Δ →X3Σg− transition has been observed for the first time during the recombination of 16O atoms in an afterglow. The spectrum of the 0–0 band has been recorded with a high resolution Fourier transform interferometer. Accurate molecular constants, obtained by combining ir and microwave data, are given for the a1Δg and X3Σg− (ν = 0) electronic levels.

scholarly journals The infrared multiphoton dissociation of hexafluoroethane

1988 ◽  
Vol 66 (4) ◽  
pp. 609-614 ◽  
Author(s):  
Carl E. Brown ◽  
Donald R. Smith
Keyword(s):  
Gas Chromatography ◽  
Fourier Transform ◽  
High Frequency ◽  
High Sensitivity ◽  
Infrared Multiphoton Dissociation ◽  
Tunable Diode Laser ◽  
Product Analysis ◽  
Multiphoton Dissociation ◽  
First Time

The infrared multiphoton dissociation (IRMPD) of "neat" hexafluoroethane has been investigated for the first time. The stable products of photolysis are CF4, C2F4, C3F8, and C4F10. Product analysis involved tunable diode laser (TDL) and fourier transform infrared spectroscopy, as well as gas chromatography where applicable. The high sensitivity and resolution of the TDL allows for measurement of the stable products CF4 and C2F4 after irradiation by a single infrared laser pulse. The yield of CF3 radicals produced by the IRMPD of C2F6 as a function of fluence was measured via the TDL high frequency modulation technique. The role of added H2, leading to elimination of CF4 and increase of C2F4 as products, is clarified.

Observations of surface-mediated reduction of Pu(VI) to Pu(IV) on hematite nanoparticles by ATR FT-IR

2015 ◽  
Vol 103 (8) ◽  
Author(s):  
Hilary P. Emerson ◽  
Brian A. Powell
Keyword(s):  
Fourier Transform ◽  
Infrared Spectroscopy ◽  
Attenuated Total Reflectance ◽  
Mineral Surfaces ◽  
Hematite Nanoparticles ◽  
Total Reflectance ◽  
Ft Ir ◽  
First Time ◽  
Mediated Reduction

AbstractPrevious studies have shown that mineral surfaces may facilitate the reduction of plutonium though the mechanisms of the reduction are still unknown. The objective of this study is to use batch sorption and attenuated total reflectance Fourier transform infrared spectroscopy experiments to observe the surface-mediated reduction of plutonium on hematite nanoparticles. These techniques allow for in situ measurement of reduction of plutonium with time and may lead to a better understanding of the mechanisms of surface mediated reduction of plutonium. For the first time, ATR FT-IR peaks for Pu(VI) sorbed to hematite are measured at ∼ 916 cm

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