Magnification relations in gravitational lensing via multidimensional residue integrals

We investigate the so-called magnification relations of gravitational lensing models. We show that multidimensional residue integrals provide a simple explanation for the existence of these relations, and an effective method of computation. We illustrate the method with several examples, thereby deriving new magnification relations for galaxy lens models and microlensing (point mass lensing).Comment: 16 pages, uses revtex4, submitted to Journal of Mathematical Physic

Automated data acquisition and reduction system for torsional braid analyzer

Automated Data Acquisition and Reduction System (ADAR) evaluates damping coefficient and relative rigidity by storing four successive peaks of waveform and time period between two successive peaks. Damping coefficient and relative rigidity are then calculated and plotted against temperature or time in real time

Long term trends in fertility of soils under continuous cultivation and cereal cropping in southern Queensland. I. Overall changes in soil properties and trends in winter cereal yields

Changes in fertility of some southern Queensland soils resulting from extended periods of cultivation are presented, together with trends in yields of winter cereals on these soils. Six major soils of the cereal-belt, cropped for maximum periods of 20-70 years were examined. These were: Black earths, Waco soil; grey, brown and red clays (brigalow), Langlands-Logie soil; grey, brown and red clays (poplar box), Cecilvale soil; grey, brown and red clays (belah), Billa Billa soil; grey, brown and red clays (coolibah), Thallon soil; red earths, Riverview soil. Organic matter and its constituents, especially total organic C, organic C in the light fraction, total N and mineralizable N, were affected most by cultivation, showing decreases of 19-67% overall. Other soil properties probably associated with organic matter, including bulk density and DTPA (diethylenetriaminepentaacetic acid) extractable manganese, were also significantly affected by cultivation in all soils. Soil properties affected least by cultivation were concentrations of inorganic phosphorus, total and exchangeable potassium, calcium carbonate, and dithionite extractable iron and aluminium. Most other soil properties studied (organic P, total sulfur, pH, exchangeable magnesium and sodium, exchangeable sodium percentage, and oxalate-extractable iron and aluminium) were affected by cultivation in at least four soils. Four factors accounted for 70% of the total variation among the 45 soil properties considered. They appeared to represent organic matter, clay colloids, iron and aluminium oxides, and soluble salts. Dry matter yield and/or N uptake of winter cereal crops (wheat and barley) measured in 1983 showed significant decreasing trends with period of cultivation in all soils

Long-term trends in fertility of soils under continuous cultivation and cereal cropping in southern Queensland. VII* Dynamics of nitrogen mineralization potentials and microbial biomass

The dynamics of nitrogen mineralization potential (N0) and mineralization rate constant (k) were studied in six major soils which had been used for cereal cropping for up to 20-70 years. In the top 0.1 m layer of virgin soils, N0 varied from 110 ± 22 mg kg-1 soil (Riverview) to 217 ± 55 mg kg-1 soil (Langlands-Logie), representing about 13% and 11%, respectively, of total N in these soils. Upon cultivation and cropping, N0 declined by 1 7 ± 0.5 mg kg-1 yr-1 (Riverview) to 4.8 ± 2.0 mg kg -1 yr -1 (Billa Billa). This represented 40% clay and k as 0.066 week-1 at 40°C (0.027 week-1 and 0.054 week-1 at 25°C and 35°C, respectively). Organic C and N contained in the 'stabilized' microbial biomass (determined after 30 weeks' pre-incubation) accounted for 1.7-38% of total organic C and 2.0-5.1% of total N in the six soils studied. The microbial biomass C and N declined with cultivation in most soils, biomass N representing 10-23% of the total annual loss of N0. The microbial biomass, urease activity and total N, in addition to a number of other soil properties [e.g. light-fraction (<2 Mg m-3) C, sand-size C, CEC and ESP], were significantly correlated with N0 and k, thus indicating the existence of a myriad of environments for the activity, association and stability of microbial biomass and potentially mineralizable N in soil