scholarly journals Lattice polygons and families of curves on rational surfaces

2010 ◽  
Vol 34 (2) ◽  
pp. 213-236 ◽  
Author(s):  
Niels Lubbes ◽  
Josef Schicho
Keyword(s):  
Rational Surfaces ◽  
Families Of Curves ◽  
Lattice Polygons

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.

The surfaces whose prime-sections contain a

1934 ◽  
Vol 30 (2) ◽  
pp. 170-177 ◽  
Author(s):  
J. Bronowski
Keyword(s):  
Hyperelliptic Curves ◽  
Ruled Surfaces ◽  
Minimum Order ◽  
Rational Surfaces ◽  
Pencil Of Conics

The surfaces whose prime-sections are hyperelliptic curves of genus p have been classified by G. Castelnuovo. If p > 1, they are the surfaces which contain a (rational) pencil of conics, which traces the on the prime-sections. Thus, if we exclude ruled surfaces, they are rational surfaces. The supernormal surfaces are of order 4p + 4 and lie in space [3p + 5]. The minimum directrix curve to the pencil of conics—that is, the curve of minimum order which meets each conic in one point—may be of any order k, where 0 ≤ k ≤ p + 1. The prime-sections of these surfaces are conveniently represented on the normal rational ruled surfaces, either by quadric sections, or by quadric sections residual to a generator, according as k is even or odd.

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.

A Rational Approach to Lattice Polygons

1987 ◽  
Vol 18 (4) ◽  
pp. 316
Author(s):  
Warren Page
Keyword(s):  
Rational Approach ◽  
Lattice Polygons

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.

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