The Anomalous Spectral Density Function for Diffusive Motion of Hydrogen in LaNi5H7

1980 ◽  
Vol 3 ◽  
Author(s):  
H. Chang ◽  
I. J. Lowe ◽  
R. J. Karlicek
Keyword(s):  
Magnetic Field ◽  
Spectral Density ◽  
Density Function ◽  
High Frequency ◽  
Diffusion Constant ◽  
Spectral Density Function ◽  
Rotating Magnetic Field ◽  
Frequency Limit ◽  
Diffusive Motion ◽  
High Frequency Limit

ABSTRACTMeasurements of T1 (Bo = 0.94T), and T1r as a function of temperature have been carried out on a LaNi5H7 sample at 4 different rotating magnetic field values. The T1 and T1r data are consistent with earlier data by Karlicek and Lowe [3,4], in which an asymmetry in the slopes of the log T1r vs. T−1 plot was found. The new data has been analyzed assuming a spectral density function J(ω,τc) of form J(ω, τc) = A(τc)B(Ω)F(ωτc), with τc = τc∞ exp(Ea/kT). This assumption leads to a spectral density function that fits all our data well, with Ea = 39 KJ/gm-Atom H, and J(ω)∼ Wω−1.35 in the high frequency limit. This Ea agrees well with the Ea obtained from diffusion constant measurements.

Calculation of the isothermal susceptibility by the Kubo formula

1976 ◽  
Vol 54 (14) ◽  
pp. 1461-1464 ◽  
Author(s):  
T. Morita ◽  
T. Horiguchi
Keyword(s):  
Ising Model ◽  
Spectral Density ◽  
Density Function ◽  
Spectral Density Function ◽  
Kubo Formula ◽  
Frequency Limit ◽  
Frequency Dependent ◽  
Isothermal Susceptibility ◽  
Zero Frequency

The relation between the zero frequency limit of the frequency-dependent susceptibility and the isothermal susceptibility is made clearer by expressing them in terms of the spectral density function. The general formulas are illustrated for the perpendicular susceptibilities of the Ising model.

Evidence of Saturn's magnetic field anomaly from Saturnian kilometric radiation high-frequency limit

1991 ◽  
Vol 96 (A8) ◽  
pp. 14129-14140 ◽  
Author(s):  
Patrick Galopeau ◽  
Arturo Ortega -Molina ◽  
Philippe Zarka
Keyword(s):  
Magnetic Field ◽  
High Frequency ◽  
Frequency Limit ◽  
High Frequency Limit

scholarly journals Temporal Aggregation and Long Memory for Asset Price Volatility

2020 ◽  
Vol 13 (8) ◽  
pp. 182 ◽  
Author(s):  
Pierre Perron ◽  
Wendong Shi
Keyword(s):  
Spectral Density ◽  
Density Function ◽  
High Frequency ◽  
Asset Price ◽  
Low Frequency ◽  
Price Volatility ◽  
Spectral Density Function ◽  
Temporal Aggregation ◽  
Standard And Poor's ◽  
Theoretical Results

The effects of temporal aggregation and choice of sampling frequency are of great interest in modeling the dynamics of asset price volatility. We show how the squared low-frequency returns can be expressed in terms of the temporal aggregation of a high-frequency series. Based on the theory of temporal aggregation, we provide the link between the spectral density function of the squared low-frequency returns and that of the squared high-frequency returns. Furthermore, we analyze the properties of the spectral density function of realized volatility series, constructed from squared returns with different frequencies under temporal aggregation. Our theoretical results allow us to explain some findings reported recently and uncover new features of volatility in financial market indices. The theoretical findings are illustrated via the analysis of both low-frequency daily Standard and Poor’s 500 (S&P 500) returns from 1928 to 2011 and high-frequency 1-min S&P 500 returns from 1986 to 2007.

ON THE SPECTRAL MEASURES OF SOME WEAKLY STATIONARY SEQUENCES INVOLVING RANDOMLY SPACED OBSERVATIONS

2012 ◽  
Vol 12 (01) ◽  
pp. 1150004
Author(s):  
RICHARD C. BRADLEY
Keyword(s):  
Spectral Density ◽  
Density Function ◽  
Spectral Density Function ◽  
Strong Mixing ◽  
Spectral Measures ◽  
Mixing Conditions ◽  
Stationary Sequences ◽  
Second Moments ◽  
The Central Limit Theorem ◽  
Complex Valued

In an earlier paper by the author, as part of a construction of a counterexample to the central limit theorem under certain strong mixing conditions, a formula is given that shows, for strictly stationary sequences with mean zero and finite second moments and a continuous spectral density function, how that spectral density function changes if the observations in that strictly stationary sequence are "randomly spread out" in a particular way, with independent "nonnegative geometric" numbers of zeros inserted in between. In this paper, that formula will be generalized to the class of weakly stationary, mean zero, complex-valued random sequences, with arbitrary spectral measure.

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