A New Magnitude-Frequency Relation for Earthquakes and a Classification of Relation Types

Summary. In this paper some aspects of the deviations of frequency distributions of earthquakes from a linear trend are considered. For recurrence curves with inflexions, the formula
is proposed as a magnitude-frequency relation, with critical magnitude M _cr. Comparison with actual data shows better agreement than other formulae. The slope of the frequency graph is considered in the most general case to be a function of M and some parameters p ₁, p ₂, …. A classification of the types of magnitude-frequency relation is given and all known types of relations N : M and N: K ( K = log E , E = seismic energy) are summarized.     

A comparison of solar EUV intensities and K-coronameter measurements

Characteristics of the emission observed above the solar limb in four EUV lines, Sixii 499, Mgx 625, Neviii 770, and Ovi 1032 are discussed. The mean temperature of the corona derived from the ratios of the intensities of Sixii 499 and Mgx 625 is 1.8 million K. There do not appear to be significant temperature differences in regions with low EUV intensities and those with high EUV intensities, suggesting that the EUV emission from the lithium-like ions depends primarily on the integral of n _e ² along the line of sight.The EUV data are compared with K-coronameter measurements in order to yield new estimates of the abundances of Si, Mg, Ne and O relative to hydrogen. Within the uncertainties of the analysis, these coronal abundances are in agreement with the corresponding photospheric values.     

Principles of quantitative absorbance measurements in anisotropic crystals

The accurate measurement of absorbance (A=-log T; T=I/I ₀) in anisotropic materials like crystals is highly important for the determination of the concentration and orientation of the oscillator (absorber) under investigation. The absorbance in isotropic material is linearly dependent on the concentration of the absorber and on the thickness of the sample (A=?·c·t). Measurement of absorbance in anisotropic media is more complicated, but it can be obtained from polarized spectra (i) on three random, but orthogonal sections of a crystal, or (ii) preferably on two orthogonal sections oriented parallel to each of two axes of the indicatrix ellipsoid. To compare among different crystal classes (including cubic symmetry) it is useful to convert measured absorbance values to one common basis (the total absorbance A _tot), wherein all absorbers are corrected as if they were aligned parallel to the E-vector of the incident light. The total absorption coefficient (a _tot=A _tot/t) is calculated by $$\left( {\text{i}} \right)a_{{\text{tot}}} = \sum\limits_{i = 1}^3 {(a_{\max ,i} + a_{\min ,i} )} /2, {\text{or}} {\text{by}} {\text{(ii) }}a_{{\text{tot}}} = a_x + a_y + a_z .$$ Only in special circumstances will unpolarized measurements of absorbance provide data useful for quantitative studies of anisotropic material. The orientation of the absorber with respect to the axes of the indicatrix ellipsoid is calculated according to A _x/A _tot=cos² (x < absorber), and analogously for A _yand A _z. In this way, correct angles are obtained for all cases of symmetry. The extinction ratio of the polarizer (Pe=I _crossed/I _parallel) has considerable influence on the measured amplitude of absorption bands, especially in cases of strong anisotropic absorbance. However, if Pe is known, the true absorbance values can be calculated even with polarizers of low extinction ratio, according to A _max=?log[(T _max,obs?0.5·Pe·T _min,obs)/(1?0.5·Pe)], and similar for A _min. The theoretical approach is confirmed by measurements on calcite and topaz.     

Compatible potentials and orbits in synodic systems

For a given family of orbits f(x,y) = c ^* which can be traced by a material point of unit in an inertial frame it is known that all potentials V(x,y) giving rise to this family satisfy a homogeneous, linear in V(x,y), second order partial differential equation (Bozis,1984). The present paper offers an analogous equation in a synodic system Oxy, rotating with angular velocity . The new equation, which relates the synodic potential function (x,y), = –V(x, y) + % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSqaaSqaai% aaigdaaeaacaaIYaaaaaaa!3780!\[\tfrac{1}{2}\]²(x ² + y ²) to the given family f(x,y) = c ^*, is again of the second order in (x,y) but nonlinear.As an application, some simple compatible pairs of functions (x,y) and f(x, y) are found, for appropriate values of , by adequately determining coefficients both in and f.     

The Hard X-ray Imaging Spectrometer (HXIS)

The HXIS, a joint instrument of the Space Research Laboratory at Utrecht, The Netherlands, and the Department of Space Research of the University of Birmingham, U.K., images the Sun in hard X-rays: Six energy bands in energy range 3.5–30 keV, spatial resolution 8 over Ø 240 and 32 over Ø 624 field of view, and time resolution of 0.5–7 s depending on the mode of operation. By means of a flare flag it alerts all the other SMM instruments when a flare sets in and informs them about the location of the X-ray emission. The experiment should yield information about the position, extension and spectrum of the hard X-ray bursts in flares, their relation to the magnetic field structure and to the quasi-thermal soft X-rays, and about the characteristics and development of type IV electron clouds above flare regions.     

Space Telescope Astrometry from CCD images

The astrometric application of the Wide Field Camera and the Planetary Camera is reviewed. It is shown that the digital image centering algorithms can yield a positional accuracy of 0.1 milli-arcsecond. Deconvolution of CCD's sensitivity, non-flatness of the filters, and crinkling of the CCD surface may limit the positional accuracy to 1 milli-arcsecond.Presented at the Symposium Star Catalogues, Positional Astronomy and Celestial Mechanics, held in honor of Paul Herget at the U.S. Naval Observatory, Washington, November 30, 1978.     

Variations of the Effective Temperature Index (ET) in Kenya

Using the Effective Temperature Index (ET) as a measure of climatic comfort conditions in Kenya, this study analyses its spatial, seasonal and diurnal variations. This index is computed using data collected from 57 weather stations spread throughout the country. Isarithmic mapping technique and the conditioning square method are used in this analysis. The results indicate that there exists in Kenya marked spatial, seasonal and diurnal variations of climatic comfort conditions. A classification of the country using this index and the Terjung (1968) system of climatic classification yields six climatic comfort zones. This type of physio-climatic studies has significant implications for Kenya in aspects such as building, clothing, recreation and sporting. This revised version was published online in July 2006 with corrections to the Cover Date.     

Temporal and spatial variations of trace metal concentrations in oysters from the Patuxent River, Maryland

Concentrations of copper (Cu), silver (Ag), and cadmium (Cd) in eastern oysters (Crassostrea virginica) from the upper Patuxent River estuary analyzed since 1986 (Cd since 1991) were high relative to concentrations in other sites in the United States analyzed by the National Oceanic and Atmospheric Administration National Status and Trends program. Patuxent River oysters had above average concentrations of Ag and Cu, and unusually high concentrations of Cd. Metal concentrations were highest in summer, a period in which oyster meat condition index was relatively low. Copper values were highest in 1986–1987, likely elevated by erosion from Cu-Ni alloy condensers at a local power plant. Silver and Cd values exhibited more year-to-year variation. A number of factors were examined as candidates to explain the interannual differences, including river flow, salinity, and oyster condition, but none was able to explain the high and low years. Samples collected in spring and late summer of 1996 at a number of oyster bars located along the length of the Patuxent River showed that concentrations of all three metals increased with distance up-river. For Cd, the upstream increase was linear with distance, while for Ag and Cu, there was a secondary maximum near river km 16. A close correlation was observed between Ag and Cu for individuals at each site, with a poorer correlation between Cd and either Ag or Cu.