K2 of families of curves with non-torsion differences in divisorial support

2021 ◽  
pp. 106915
Author(s):  
Haixu Wang ◽  
Hang Liu ◽  
Guoping Tang
Keyword(s):  
Families Of Curves

MEASUREMENT OF THE COMPLEX DIELECTRIC CONSTANT OF LIQUIDS AT CENTIMETER AND MILLIMETER WAVELENGTHS

1957 ◽  
Vol 35 (9) ◽  
pp. 995-1003 ◽  
Author(s):  
A. G. Mungall ◽  
John Hart
Keyword(s):  
Dielectric Constant ◽  
Methyl Alcohol ◽  
Free Space ◽  
Normal Incidence ◽  
Complex Dielectric Constant ◽  
Families Of Curves ◽  
Millimeter Wavelengths ◽  
Centimeter Wave ◽  
Space Technique ◽  
Wave Region

The measurement of the complex dielectric constant of lossy liquids in the millimeter and centimeter wave region by a free-space technique is described. The method involves the measurement of absorption per wavelength and of reflectance at normal incidence. Families of curves are given for the relations between these two quantities and the real and imaginary parts of the complex dielectric constant. Results for ethyl and methyl alcohol at 9 and 13 mm. wavelength are compared with those obtained by waveguide techniques.

scholarly journals Distribution of points on Abelian covers over finite fields

2018 ◽  
Vol 14 (05) ◽  
pp. 1375-1401 ◽  
Author(s):  
Patrick Meisner
Keyword(s):  
Finite Fields ◽  
Galois Extension ◽  
Random Variables ◽  
Families Of Curves ◽  
Abelian Covers ◽  
Distribution Of Points ◽  
Genus Formula

We determine in this paper the distribution of the number of points on the covers of [Formula: see text] such that [Formula: see text] is a Galois extension and [Formula: see text] is abelian when [Formula: see text] is fixed and the genus, [Formula: see text], tends to infinity. This generalizes the work of Kurlberg and Rudnick and Bucur, David, Feigon and Lalin who considered different families of curves over [Formula: see text]. In all cases, the distribution is given by a sum of [Formula: see text] random variables.

Master curves for the response of layered systems to compressional seismic waves

1967 ◽  
Vol 57 (3) ◽  
pp. 515-543 ◽  
Author(s):  
Luis M. Fernandez
Keyword(s):  
Seismic Waves ◽  
Transfer Functions ◽  
Point Of View ◽  
Time Lags ◽  
Master Curves ◽  
Layer System ◽  
Crust And Upper Mantle ◽  
Response Characteristics ◽  
Families Of Curves ◽  
Short Time

abstract The layers of the earth's crust act as a filter with respect to seimic energy arriving at a given station. Consequently the motion recorded at the surface depends not only on the frequency content of the source and on the response characteristics of the recording instrument, but also on the elastic parameters and thicknesses of the transmitting layers. This latter dependence is the basis for a method of investigating the structure of the crust and upper mantle. To facilitate this investigation a set of master curves for the transfer functions of the vertical and horizontal component of longitudinal waves and their ratios is presented. The calculation of these curves is in terms of a dimensionless parameter. This calculation allows one to group the curves corresponding to different crustal models into families of curves. The characteristics of these curves are discussed from the point of view of their “periodicity” in the frequency domain and of their amplitude in order to investigate the influence of the layer parameters. Considerations, either of constructive interference or of Fourier analysis of a pulse multiply reflected within the layer system, reveal that the amplitudes of the transfer curves depend on the velocity contrasts at the interfaces of the system. The “periodicity” or spacing of the peaks depends on the time lags between the first arrivals and the arrivals of the different reverberations. Closely spaced fluctuations correspond to large-time lags, and widely spaced fluctuations to short-time lags.

Temperature Distribution in a Cylindrical Rod Moving From a Chamber at One Temperature to a Chamber at Another Temperature

1964 ◽  
Vol 86 (2) ◽  
pp. 265-270 ◽  
Author(s):  
G. Horvay ◽  
M. Dacosta
Keyword(s):  
Heat Transfer ◽  
Temperature Distribution ◽  
Arbitrary Constant ◽  
Families Of Curves ◽  
Special Cases ◽  
Method Of Solution ◽  
Lower Chamber ◽  
Higher Temperature ◽  
Hopf Method ◽  
The Heat Transfer Coefficient

When an infinitely long cylindrical rod travels from a chamber at one temperature ϑa to a chamber (insulated from the first) at a higher temperature ϑf, then heat will leak out along the rod from the second chamber to the first, whose amount decreases as the speed of the rod increases. Using the Wiener-Hopf method of solution, we determine the temperature distribution in the rod for the case where in the second chamber the heat-transfer coefficient h+ is infinite, while in the first chamber it has an arbitrary constant value h. Families of curves illustrate the temperature distribution in the two special cases where h = ∞ (isothermal boundary conditions in lower chamber) and where h = 0 (rod is insulated in lower chamber).

INVESTIGATION PARAMETERS ULTRASONIC DEVICE ON PHASED ARRAYS. FOCUSING MODES FOR ULTRASONIC DEVICE TYPE OF OMNISCAN

2021 ◽  
pp. 24-35
Author(s):  
V. Yu. Titov
Keyword(s):  
Phased Arrays ◽  
Near Field ◽  
Signal Amplitude ◽  
Drill Hole ◽  
Flaw Detector ◽  
Amplitude Dependence ◽  
Large Variability ◽  
Ultrasonic Device ◽  
Families Of Curves ◽  
Significant Difference

The article is devoted to possibilities of regular focusing of Omniscan device on phased arrays. Questions are raised about evaluation of testing results when using linear and sector scan-ning with different focus parameters. The question of size near-field for phased arrays and asso-ciated choice of focus mode is discussed. The article is based on experiments conducted on samples with artificial reflectors at the same size, but different in type: a non-directional reflector (a side-drill hole) and a directional reflector (a flat-bottomed reflector), located at the same depth. The study was conducted for transducers with different frequencies. Families of curves of the signal amplitude dependence are obtained: on depth reflector, on focus depth setting, and on type reflector. The results emphasize need for precise focusing with-in the near-field of the transducer for small thicknesses or shallow depth of occurrence of discontinuities, and large variability in choice of focusing for depths in far-field. The study notes a significant difference in values of depth reflector at different focusses at a fixed position of transducer. In this article, in addition to considering possibility of focusing a flaw detector with phased arrays, the focus is on interpretation of results and reliability of testing in the analysis and comparison data. An integral part of the technological testing protocol for phased array is the depth of focus and the type of scanning. The obtained data do not depend on the frequency of transducer, which means that conclusions are applicable to general range of flaw detectors on phased arrays.

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