Fundamental theorem on the density of the spectrum of the real component of a Volterra operator with nuclear imaginary component

1952 ◽  
Vol 5 (4) ◽  
pp. 592
Author(s):  
HA Prime

The power transmission and reflection coefficients of a limited volume of ionized gas (a mercury-vapour discharge) located within a waveguide have been measured at a frequency of approximately 10,000 Mc/s. by a microwave method. From these coefficients the real and imaginary components of the complex conductivity of the discharge are evaluated. The results show that the real component of the conductivity бr is a linearly increasing function of the discharge current, whereas the rate of increase of the imaginary component бi, which is negative, decreases with increasing discharge current. The ratio бi/бr, decreases with increase in current, but is of the order of unit;- due to the fact that the gas pressure is sufficiently high (?1 atm.) to make бr comparable with бi. The theoretical basis of the work is presented in an appendix in which the particular case of high pressure conditions is discussed.


Sensors ◽  
2020 ◽  
Vol 20 (22) ◽  
pp. 6677
Author(s):  
Andrea Vergnano ◽  
Alberto Godio ◽  
Carla Maria Raffa ◽  
Fulvia Chiampo ◽  
Jorge A. Tobon Vasquez ◽  
...  

In the bioremediation field, geophysical techniques are commonly applied, at lab scale and field scale, to perform the characterization and the monitoring of contaminated soils. We propose a method for detecting the dielectric properties of contaminated soil during a process of bioremediation. An open-ended coaxial probe measured the complex dielectric permittivity (between 0.2 and 20 GHz) on a series of six soil microcosms contaminated by diesel oil (13.5% Voil/Vtot). The microcosms had different moisture content (13%, 19%, and 24% Vw/Vtot) and different salinity due to the addition of nutrients (22 and 15 g/L). The real and the imaginary component of the complex dielectric permittivity were evaluated at the initial stage of contamination and after 130 days. In almost all microcosms, the real component showed a significant decrease (up to 2 units) at all frequencies. The results revealed that the changes in the real part of the dielectric permittivity are related to the amount of degradation and loss in moisture content. The imaginary component, mainly linked to the electrical conductivity of the soil, shows a significant drop to almost 0 at low frequencies. This could be explained by a salt depletion during bioremediation. Despite a moderate accuracy reduction compared to measurements performed on liquid media, this technology can be successfully applied to granular materials such as soil. The open-ended coaxial probe is a promising instrument to check the dielectric properties of soil to characterize or monitor a bioremediation process.


2018 ◽  
Vol 32 (2) ◽  
pp. 501-529 ◽  
Author(s):  
Kazuaki Yasunaga ◽  
Satoru Yokoi ◽  
Kuniaki Inoue ◽  
Brian E. Mapes

Abstract The budget of column-integrated moist static energy (MSE) is examined in wavenumber–frequency transforms of longitude–time sections over the tropical belt. Cross-spectra with satellite-derived precipitation (TRMM-3B42) are used to emphasize precipitation-coherent signals in reanalysis [ERA-Interim (ERAI)] estimates of each term in the budget equation. Results reveal different budget balances in convectively coupled equatorial waves (CCEWs) as well as in the Madden–Julian oscillation (MJO) and tropical depression (TD)-type disturbances. The real component (expressing amplification or damping of amplitude) for horizontal advection is modest for most wave types but substantially damps the MJO. Its imaginary component is hugely positive (it acts to advance phase) in TD-type disturbances and is positive for MJO and equatorial Rossby (ERn1) wave disturbances (almost negligible for the other CCEWs). The real component of vertical advection is negatively correlated (damping effect) with precipitation with a magnitude of approximately 10% of total latent heat release for all disturbances except for TD-type disturbance. This effect is overestimated by a factor of 2 or more if advection is computed using the time–zonal mean MSE, suggesting that nonlinear correlations between ascent and humidity would be positive (amplification effect). ERAI-estimated radiative heating has a positive real part, reinforcing precipitation-correlated MSE excursions. The magnitude is up to 14% of latent heating for the MJO and much less for other waves. ERAI-estimated surface flux has a small effect but acts to amplify MJO and ERn1 waves. The imaginary component of budget residuals is large and systematically positive, suggesting that the reanalysis model’s physical MSE sources would not act to propagate the precipitation-associated MSE anomalies properly.


Geophysics ◽  
1979 ◽  
Vol 44 (6) ◽  
pp. 1041-1063 ◽  
Author(s):  
M. T. Taner ◽  
F. Koehler ◽  
R. E. Sheriff

The conventional seismic trace can be viewed as the real component of a complex trace which can be uniquely calculated under usual conditions. The complex trace permits the unique separation of envelope amplitude and phase information and the calculation of instantaneous frequency. These and other quantities can be displayed in a color‐encoded manner which helps an interpreter see their interrelationship and spatial changes. The significance of color patterns and their geological interpretation is illustrated by examples of seismic data from three areas.


2021 ◽  
Vol 14 (6) ◽  
pp. 4755-4771
Author(s):  
William G. K. McLean ◽  
Guangliang Fu ◽  
Sharon P. Burton ◽  
Otto P. Hasekamp

Abstract. This study presents an investigation of aerosol microphysical retrievals from high spectral resolution lidar (HSRL) measurements. Firstly, retrievals are presented for synthetically generated lidar measurements, followed by an application of the retrieval algorithm to real lidar measurements. Here, we perform the investigation for an aerosol state vector that is typically used in multi-angle polarimeter (MAP) retrievals, so that the results can be interpreted in relation to a potential combination of lidar and MAP measurements. These state vectors correspond to a bimodal size distribution, where column number, effective radius, and effective variance of both modes are treated as fit parameters, alongside the complex refractive index and particle shape. The focus is primarily on a lidar configuration based on that of the High Spectral Resolution Lidar-2 (HSRL-2), which participated in the ACEPOL (Aerosol Characterization from Polarimeter and Lidar) campaign, a combined project between NASA and SRON (Netherlands Institute for Space Research). The measurement campaign took place between October and November 2017, over the western region of the USA. Six different instruments were mounted on the aeroplane: four MAPs and two lidar instruments, HSRL-2 and the Cloud Physics Lidar (CPL). Most of the flights were carried out over land, passing over scenes with a low aerosol load. One of the flights passed over a prescribed forest fire in Arizona on 9 November, with a relatively higher aerosol optical depth (AOD), and it is the data from this flight that are focussed on in this study. A retrieval of the aerosol microphysical properties of the smoke plume mixture was attempted with the data from HSRL-2 and compared with a retrieval from the MAPs carried out in previous work pertaining to the ACEPOL data. The synthetic HSRL-2 retrievals resulted for the fine mode in a mean absolute error (MAE) of 0.038 (0.025) µm for the effective radius (with a mean truth value of 0.195 µm), 0.052 (0.037) for the real refractive index, 0.010 (7.20×10-3) for the imaginary part of the refractive index, 0.109 (0.071) for the spherical fraction, and 0.054 (0.039) for the AOD at 532 nm, where the retrievals inside brackets indicate the MAE for noise-free retrievals. For the coarse mode, we find the MAE is 0.459 (0.254) µm for the effective radius (with a mean truth value of 1.970 µm), 0.085 (0.075) for the real refractive index, 2.06×10-4 (1.90×10-4) for the imaginary component, 0.120 (0.090) for the spherical fraction, and 0.051 (0.039) for the AOD. A study of the sensitivity of retrievals to the choice of prior and first guess showed that, on average, the retrieval errors increase when the prior deviates too much from the truth value. These experiments revealed that the measurements primarily contain information on the size and shape of the aerosol, along with the column number. Some information on the real component of the refractive index is also present, with the measurements providing little on absorption or on the effective variance of the aerosol distribution, as both of these were shown to depend heavily on the choice of prior. Retrievals using the HSRL-2 smoke-plume data yielded, for the fine mode, an effective radius of 0.107 µm, a real refractive index of 1.561, an imaginary component of refractive index of 0.010, a spherical fraction of 0.719, and an AOD at 532 nm of 0.505. Additionally, the single-scattering albedo (SSA) from the HSRL-2 retrievals was 0.940. Overall, these results are in good agreement with those from the Spectropolarimeter for Planetary Exploration (SPEX) and Research Scanning Polarimeter (RSP) retrievals.


2018 ◽  
Vol 21 (04) ◽  
pp. 1892001 ◽  
Author(s):  
GABRIEL FRAHM

In order to prove the third fundamental theorem of asset pricing for financial markets with infinite lifetime [G. Frahm (2016) Pricing and valuation under the real-world measure, International Journal of Theoretical and Applied Finance 19, 1650006], we shall assume that the discounted price process is locally bounded. Otherwise, some principal results developed by [F. Delbaen & W. Schachermayer (1997) The Banach space of workable contingent claims in arbitrage theory, Annales de l’Institut Henri Poincaré 1, 114–144] cannot be applied.


1984 ◽  
Vol 7 (2) ◽  
pp. 371-396 ◽  
Author(s):  
R. P. Manandhar ◽  
L. Debnath

A study is made of the Post-Widder inversion operator to a class of generalized functions in the sense of distributional convergence. Necessary and sufficient conditions are proved for a given function to have the representation as therth operate of the Post-Widder inversion operator of generalized functions. Some representation theorems are also proved. Certain results concerning the testing function space and its dual are established. A fundamental theorem regarding the existence of the real inversion operator (1.6) withr=0is proved in section4. A classical inversion theory for the Post-Widder inversion operator with a few other theorems which are fundamental to the representation theory is also developed in this paper.


2015 ◽  
Vol 58 (1) ◽  
pp. 48-55
Author(s):  
Dan Malaescu ◽  
Ioan Grozescu ◽  
Paula Sfirloaga ◽  
Paulina Vlazan ◽  
Catalin N. Marin

Abstract Two samples of NaTaO3 perovskite materials were prepared by the standard hydrothermal method at the same reaction temperature (600 °C) but with different sintering times: 6 hours for sample S1 and 12 hours for sample S2.Using X-ray diffraction (XRD), it shows that samples S1 and S2 are mixtures of Na-Ta oxides (Ta2O5 and the prevailing phase NaTaO3). The scanning electron microscopy analysis (SEM), shows that the grains are connected each other in agglomerated clusters of size about few hundred nanometers.The frequency (f) dependencies of complex impedance, Z(f) = Z’(f) - i Z’’(f) of the samples, over the frequency range 20 Hz - 2 MHz, at room temperature are presented. The real component Z’ of the complex impedance decreases with increasing frequency and the imaginary component Z’’ has two maximum corresponding to two relaxation processes.The results obtained from the complex impedance spectroscopy, Z’’(Z’) showed the appearance of two semicircles, corresponding to grain and grain boundary mechanism. Experimental results have been fitted with two parallel RC equivalent circuits connected in series and the parameters R and C have been evaluated.


1987 ◽  
Vol 20 (4) ◽  
pp. 295-299 ◽  
Author(s):  
C. Nave

The contribution of a particular atom in a molecule to the total X-ray scattering can be altered by varying the wavelength in the region of the absorption edge of the atom. It is shown that only the changes in the real part of the anomalous scattering of the atom provide significant changes in a pattern from a fibre containing molecules with helical symmetry. Changes due to the imaginary component are small and Friedel differences cannot be observed, owing to the fibre disorder. The information which can be obtained is equivalent to that given by a truly isomorphous heavy-atom derivative. For the general case this is not sufficient to provide unambiguous phase information. If a twofold axis is present at right angles to the fibre axis then the amplitudes are real and the phase problem can, in favourable cases, be solved.


2021 ◽  
Vol 10 (36) ◽  
pp. 101-103
Author(s):  
Adriana Ramos de Miranda ◽  
Claudia Takano ◽  
Alvaro Vannucci

Introduction: The Impedance spectroscopy [1] is a technique mainly used to characterize the electrical behavior of solids or liquids samples. This particular technique involves placing the sample of material under investigation between two electrodes (capacitor plates), applying an AC voltage and observing the resulting response across the spectrum of impedance by plotting the real part (Z’) as a function of the imaginary part (Z”) of the impedance. Alternatively, graphs of either the real or the imaginary parts of the impedance can be constructed as a function of the applied voltage frequency. Comparative measurements previously carried out by Miranda et al [2]. have demonstrated clear differences between the impedance values of high dilutions of lithium chloride (LiCl) and the corresponding reference water samples (water which has undergone the same dinamization procedures but without the salt). In this paper the results obtained by applying the spectroscopy of impedance technique in high dilutions of Lycopodium clavatum - Lyc (from 15cH to 30 cH), in comparison to the reference waters, will be presented and discussed. Aims: The objective of this work is to measure the impedance components of both high dilutions of Lycopodium clavatum and reference water samples in the frequency range of 100Hz to 13Mhz, using a successful protocol of sample preparation which has already been used before2. Details of the experimental set-up can be found elsewhere[3]. Methodology: Thirty samples of Lyc solutions and thirty reference water samples were produced using the same preparation and measuring protocol. Both groups of liquid samples were measured for dynamizations ranging from 1cH to 30cH, in accordance to the Hahnemanian dynamization method and following the practice suggested by the Brazilian Homeopathic Pharmacopeia. The Lyc solutions were specifically compared to the reference water samples in the potencies of 15cH, 18cH, 23cH and 30cH. It is important to highlight here that all the Lyc solutions and the corresponding reference water samples measured were prepared from the same lot of initial distilled water and submitted to the same steps of dilution and succussion protocol3. Typically three impedance measurements were carried out for each investigated solution, starting with the highest potency. The sample holder (capacitor cell) used during the experiment was careful and systematically cleaned after each measurement. Results: The results obtained show that by choosing either the real part (Z’) or the imaginary component (Z”) of the impedance, it is possible to clearly differentiate the Lyc solutions from the corresponding reference water samples, for the potencies 15cH, 18cH and 30cH. For the potency 23cH, however, this difference is not very significant, as it can be observed in Figure 1. Conclusion: Impedance spectroscopy has demonstrated itself to be a powerful and sensitive technique for the physical characterization of Lycopodium clavatum in high dilutions. The differences obtained for the LiCl dynamizations and the corresponding pure water samples are noteworthy. Also, the results exhibit a non-monotonic behavior over the process of dynamization, indicating that the possibility of contamination during the samples manipulation can be ruled out.


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