The constrained normal form algorithm

This paper describes an algorithm which brings a regularizable polynomial perturbation of a three degree of freedom Kepler problem into a normal form which Poisson commutes with the Kepler Hamiltonian. We illustrate the alogrithm with an example: the quadratic Zeeman effect. For other applications of this algorithm see [1],[4], and [5]. The authors have written a program in MAPLE which implements the constrained normal form.     

Stratigraphic analysis and the asymptotic distribution of the coefficient of cross-association

The asymptotic distribution of the coefficient of cross-association between two sequences of nominal data is investigated under the assumption of independent random sampling from a multinomial distribution slightly modified to suit geological applications. This modification is due to merging consecutive strata of the same rock type into one lithological unit, and can be described by a simple Markov chain. A distinction is made between the case in which the theoretical frequencies are known, and the situation where these have to be estimated from the observed data.     

A Discussion of IGS Solutions and Their Impact on Geodetic and Geophysical Applications

The International Association of Geodesy officially established the International GPS Service (IGS) on Janaury 1, 1994. Its prime objective is to provide support and a rerefence system for a wide variety of scientific and practical applications involving GPS. To fulfill its role the IGS also generates, in addition to its fundamental products (orbital/staion positions and consistent Earth orientation parameters), additional reference-system products providing the necessary infrastructure, standards, and means of calibrations for timing and various atmospheric applications of GPS. The generation and efficient application of IGS products and their impact on a number of positioning and atmospheric applications, including low earth orbit satellites, is reviewed and discussed. @ 1998 John Wiley & Sons, Inc.     

Electrical conductivity of rocks in the heating and cooling cycle

Summary The values of the electrical conductivity, recorded during the heating and cooling cycle, of eclogites and basalts are compared. The observed difference in the values is explained by reversible and irreversible changes which take place in the samples.     

Robotic telescopes for high energy astrophysics in Ondřejov

We report on two small aperture robotic telescopes called BART and D50 operated in Ondřejov. Both telescopes are capable of automatic observation of gamma ray burst (GRB) optical afterglows. Coordinates of GRBs are taken from alerts distributed via Internet. Telescopes observe other interesting high energy sources when there is not any alert. The smaller telescope BART has aperture D = 254 mm. The bigger telescope D50 has a primary mirror of diameter D = 500 mm. Both telescopes are controlled by free software package RTS2 and are accessible through Internet. We describe the two telescopes and related software and show some results such as our first observed optical counterpart of GRB.     

On the origin of rock fragment mulches on Vertisols: A case study from the Ethiopian highlands

Many Vertisols in Tigray, Ethiopia, typically carry a discontinuous rock fragment (RF, size 0.5–> 40 · 10^− 2 m) cover with 10 to 100 RFs m^− 2. Such RF mulches are of agricultural and environmental significance because they influence the water balance in the underlying soils and the crop yield. Natural RF concentrations are mostly considered as eolian or hydraulic lag deposits, or as the result of lateral transport over the soil surface from a rock outcrop, upslope. In cultivated areas RF mulches can develop by tillage.This paper presents the case of a natural RF mulch whose lithology indicates that the RFs are up-squeezed by the local Vertisol. The study site is located in the pass of Enda Maryam, Tigray, Northern Ethiopia (39°8′ E and 13°36′ N). A circular area of 10 m diameter, about 200 m away from the water divide in the valley has been cleared annually between 01/1999 and 05/2003. During this period, 625 RFs, 17 being > 7.5 · 10^− 2 m in size, totalling a mass of nearly 62 kg, have been collected. After correction for measurement procedures, the rate of RF up-warping by the Vertisol at Enda Maryam is assessed at 5 RFs m^− 2 in 3 years. At this rate of appearance, the formation of current RF concentrations on top of active valley Vertisols is only a matter of 10^1–2 years, provided the availability of RFs below the soil surface.Although important underground displacements were measured in the Vertisol between 01/1999 and 05/2002, the supposed link between up-squeezing of RFs and plastic deformations of ‘chimney’, ‘diapir’ or ‘intrusion’-like type in the Vertisol could not be evidenced. Instead, RFs are clearly concentrated on the soil surface as well as in depth, along the existing vertical desiccation cracks, often > 1 m deep which display polygonal configurations at the soil surface. Further, bundles of slickensides containing some RFs, have been mapped at the base of the Vertisol. The slickenside configuration suggests that the RF-bearing substrate is being scraped off.While the underground displacement of RFs along active slickensides seems normal, the process of RFs ascending in ‘upright’ position in the edge of desiccation cracks needs explanation. The closure of a desiccation crack is a peristaltic-like movement, following ascent or descent of the capillary fringe. It is hypothesized that this movement gradually pushes the RF to the surface or to another place or level in the soil profile where the crack closes in last instance.The apparent young age of the valley Vertisol mulches in Ethiopia might indicate the very recent formation of yearly recurrent desiccation cracks of Vertisols in the area. Available information confirms that most valleys in the study area used to be perennially marshy. Under these conditions no movements of RFs in the soil profile are expected to occur. Gullying, leading to pronounced seasonal desiccation of the Vertisols, started in several cases not more than 50 years ago.