The astronomical work of Carl Friedrich Gauss (1777–1855)

Gauss's interest in astronomy dates from his student-days in Göttingen, and was stimulated by his reading of Franz Xavier von Zach's Monatliche Correspondenz… where he first read about Giuseppe Piazzi's discovery of the minor planet Ceres on 1 January 1801. He quickly produced a theory of orbital motion which enabled that faint star-like object to be rediscovered by von Zach and others after it emerged from the rays of the Sun. Von Zach continued to supply him with the observations of contemporary European astronomers from which he was able to improve his theory to such an extent that he could detect the effects of planetary perturbations in distorting the orbit from an elliptical form. To cope with the complexities which these introduced into the calculations of Ceres and more especially the other minor planet Pallas, discovered by Wilhelm Olbers in 1802, Gauss developed a new and more rigorous numerical approach by making use of his mathematical theory of interpolation and his method of least-squares analysis, which was embodied in his famous Theoria motus of 1809. His laborious researches on the theory of Pallas's motion, in which he enlisted the help of several former students, provided the framework of a new mathematical formulation of the problem whose solution can now be easily effected thanks to modern computational techniques.Up to the time of his appointment as Director of the Göttingen Observatory in 1807, Gauss had little opportunity for engaging himself in practical astronomical work. His first systematic observations were concerned with re-establishing the latitude of of that observatory, which had been well-determined by Tobias Mayer more than fifty years earlier. However, he found a small but not negligible discrepancy between results obtained independently from stellar and solar observations, as well as irregularities among later measurements of polar altitudes (made at the new observatory completed in 1816), which he was never able to explain, despite repeated attempts to do so using different instruments and observational techniques. Similar anomalies were also detected by a number of other astronomers at around this time. These may have been associated--at any rate, partially--with the phenomenon identified later in the century as a “variation of latitude” due to minor periodic fluctuations in the Earth's axis of rotation produced by meteorological and geological factors.     

Null spaces and ranges for the classical and spherical Radon transforms

Let R be the classical Radon transform that integrates a function over hyperplanes in Rⁿ and let SM be the transform that integrates a function over spheres containing the origin in Rⁿ. We prove continuity results for both transforms and explicitly give the null space of R for a class of square integrable functions on the exterior of a ball in Rⁿ as well as the null space of SM for square integrable functions on a ball. We show SM: L²(Rⁿ) → L²(Rⁿ) is one-one, and we characterize the range of SM on classes of smooth functions and square integrable functions by certain moment conditions. If g(x) is a Schwartz function on Rⁿ that is zero to infinite order at x = 0, we prove moment conditions sufficient for g to be in the range of SM(C^∞(Rⁿ)). We apply our results on SM to existence and uniqueness theorems for solutions to a characteristic initial value problem for the Darboux partial differential equation.     

Thermal analysis of cobalt,nickel and copper complexes of 2-aminothiazole

The thermal decomposition of 2-aminothiazole (2-amt) complexes of general formula M(2-amt)₂X₂ [M = Co(II) and Cu(II)] and Ni(2-amt)₄X₂ [X = Cl and Br] have been studied in air and argon by TG and DTG as well as by DTA in nitrogen; end products from the decompositions in air have been characterised by X-ray powder diffraction. Decomposition stoichiometries have been proposed and factors governing the thermal decomposition have been discussed.     

Effect of orientation,anisotropy, and water on the relaxation behavior of nylon 6 from 4.2 to 300°K

The relaxation behavior of nylon 6 from 4.2 to 300°K was investigated as a function of orientation, anisotropy and moisture content by using an inverted free-oscillating torsion pendulum. Three new relaxations, δ at 53°K, ? below 4.2°K, and ζ at 20°K, were discovered. The characteristics of these new relaxations strongly depend on the orientation anisotropy, and concentration of adsorbed water in the specimens. The results suggest that the mechanism of the γ process is associated with the motions of both the polar and methylene units. The mechanism of the β relaxation is postulated to originate with motions of both non-hydrogen-bonded polar groups and polymer—water complex units. The behavior of the α peak is consistent with the hypothesis that it originates with the rupture of interchain hydrogen bonding due to the motions of long-chain segments in the amorphous regions. Finally, the data strongly support the proposition that two types of water, tightly bound and loosely bound, exist in nylon 6.     

Optimal stopping,exponential utility,and linear programming

This paper uses linear programming to compute an optimal policy for a stopping problem whose utility function is exponential. This is done by transforming the problem into an equivalent one having additive utility and nonnegative (not necessarily substochastic) transition matrices.Research was supported by NSF Grant ENG 76-15599.     

Geometry of the de-Sitter universe

By making use of the fact that the de-Sitter metric corresponds to a hyperquadric in a five-dimensional flat space, it is shown that the three Robertson-Walker metrics for empty spacetime and positive cosmological constant, corresponding to 3-space of positive, negative and zero curvative, are geometrically equivalent. The 3-spaces correspond to intersections of the hyperquadric by hyperplanes, and the time-like geodesics perpendicular to them correspond to intersections by planes, in all three cases.     

Comparison of three sequential extraction procedures to describe metal fractionation in anaerobic granular sludges

In the last few decades, several sequential extraction procedures have been developed to quantify the chemical status of metals in the solid phase. In this study, three extraction techniques (modified [A. Tessier, P.G.C. Campbell, M. Bisson, Anal. Chem. 51 (1979) 844]; [R.C. Stover, L.E. Sommers, D.J. Silvera, J. Water Pollut. Con. F. 48 (1976) 2165]; and the Bureau Communautaire de Reference (BCR) [K.F. Mossop, C.M. Davidson, Anal. Chim. Acta 478 (2003) 111]) were applied to study the distribution of trace (Co, Ni, Zn and Cu) and major (Mn and Fe) elements in two different anaerobic granular sludges from full-scale methanogenic wastewater treatment plants. The Stover scheme displayed a higher number of fractions that induces a poor recovery compared to the other schemes. The sequential extraction scheme recommended by BCR and the modified Tessier scheme gave similar trends and are sufficiently repeatable and reproducible for application in fractionation studies. However, the BCR scheme seems to be of limited utilisation to study anaerobic matrixes because the extraction stage for its reducible fraction may release substantial amounts of trace elements bound to the organic/sulfides fraction, and consequently, the recovery of trace elements in the oxide fraction may be overestimated at the expense of the oxidisable fraction. As a final conclusion, the modified Tessier scheme seems to be the most suitable scheme to study the metal partitioning in anaerobic granular sludges.     

Direct measurement of the counterion distribution within swollen polyelectrolyte films

The depth profile of the counterion concentration within thin polyelectrolyte films was measured in situ using contrast variant specular neutron reflectivity to characterize the initial swelling stage of the film dissolution. We find substantial counterion depletion near the substrate and enrichment near the periphery of the film extending into the solution. These observations challenge our understanding of the charge distribution in polyelectrolyte films and are important for understanding film dissolution in medical and technological applications.