Stability of inner planetary systems

The model of the planar restricted problem of three bodies is used to evaluate the stability of the inner planets of planetary systems with arbitrary mass ratios. A quantitative measure of stability is introduced by finding the difference between the critical value of the Jacobian constant (at which bifurcation may occur) and the value of the Jacobian constant that corresponds to planetary type orbits. Hill's definition of stability is used according to which inner planetary orbits are stable if they are bounded in a region enclosing only the larger primary. For small values of the massparameter (<10^–3) the maximum value of the dimensionless radius of the orbit for Hill-stability is given by 1–2.4 µ^1/3.

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Zusammenfassung Die Stabilität von inneren Planetensystemen mit beliebigen Massenverhältnissen wird am Modell des ebenen restringierten Dreikörperproblems untersucht. Aufgrund der Differenz zwischen dem kritischen Wert der Jacobi-Konstanten (wo Bifurkation eintreten kann) und dem einer Planetenbahn entsprechenden Wert wird ein quantitatives Stabilitätsmass eingeführt. Dabei wird die Hillsche Stabilitätsdefinition verwendet, d.h. eine innere Planetenbahn heisst stabil, wenn sie ein nur den grösseren Zentralkörper enthaltendes Gebiet nicht verlassen kann. Für klein Werte des Massenparameters (<10^–3) beträgt der maximale (dimensionslose) Radius einer Hill-stabilen Planetenbahn 1–2.4 µ^1/3.

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Dedicated to Professor Eduard Stiefel     

Congruence theorems for compact hypersurfaces of a riemannian manifold

Summary Let M^m, ^m be two m-dimensional compact oriented hypersurfaces of class C³ immersed in a Riemannian manifold R^m+1 of constant sectional curvature. Suppose that R^m+1 admits a one-parameter continuous group G of conformal transformations satisfying a certain condition (which holds automatically when G is a group of isometric transformations). Suppose further that there is a1 − 1 transformation T_τ ∈ G between M^m and ^m such that for each P ∈ M^m and each ^m. If the r-th mean curvature for any r, 1 ⩽ r ⩽ m, of M^m at each point P ∈ M^m is equal to that of ^m at the corresponding point , together with other conditions, then M^m and ^m are congruent mod G. This is a generalization of a joint theorem ofH. Hopf andY. Katsurada [5] in which G is a group of isometric transformations. Entrata in Redazione il 13 Giugno 1975. The first author was partially supported by the National Science Foundation grant GP-33944.     

Exploration of the Crystal Structure and Thermal and Spectroscopic Properties of Monoclinic Praseodymium Sulfate Pr2(SO4)3

Praseodymium sulfate was obtained by the precipitation method and the crystal structure was determined by Rietveld analysis. Pr₂(SO₄)₃ is crystallized in the monoclinic structure, space group C2/c, with cell parameters a = 21.6052 (4), b = 6.7237 (1) and c = 6.9777 (1) Å, β = 107.9148 (7)°, Z = 4, V = 964.48 (3) ų (T = 150 °C). The thermal expansion of Pr₂(SO₄)₃ is strongly anisotropic. As was obtained by XRD measurements, all cell parameters are increased on heating. However, due to a strong increase of the monoclinic angle β, there is a direction of negative thermal expansion. In the argon atmosphere, Pr₂(SO₄)₃ is stable in the temperature range of T = 30–870 °C. The kinetics of the thermal decomposition process of praseodymium sulfate octahydrate Pr₂(SO₄)₃·8H₂O was studied as well. The vibrational properties of Pr₂(SO₄)₃ were examined by Raman and Fourier-transform infrared absorption spectroscopy methods. The band gap structure of Pr₂(SO₄)₃ was evaluated by ab initio calculations, and it was found that the valence band top is dominated by the p electrons of oxygen ions, while the conduction band bottom is formed by the d electrons of Pr³⁺ ions. The exact position of ZPL is determined via PL and PLE spectra at 77 K to be at 481 nm, and that enabled a correct assignment of luminescent bands. The maximum luminescent band in Pr₂(SO₄)₃ belongs to the ³P₀ → ³F₂ transition at 640 nm.     

Physical Treatment Reduces Trypsin Inhibitor Activity and Modifies Chemical Composition of Marama Bean (Tylosema esculentum)

The utility of the marama bean (MB) as an alternative protein source to soybean (SB) can be limited by the high concentration of trypsin inhibitors (TI). The physical treatment of MB has the potential to ameliorate the antinutritional activities of TI and modify other chemical components. Thus, this study investigated the effects of physical treatments on the chemical components and trypsin inhibitor activity (TIA) of raw MB and SB. The bean substrates were subjected to each of the following treatment methods: (1) room temperature (20–22 °C) soaking for 24 h; (2) electric stove cooking at 100 °C for 10, 20, and 30 min; (3) steam autoclaving at a temperature of 110 °C and pressure of 7 pounds per square inch (psi), as well as a temperature of 121 °C and 7 psi for 5, 15, and 30 min; (4) pre-soaked autoclaving at 110 °C (7 psi) and 121 °C (17 psi) for 5, 15, and 30 min. Treated MB and SB had greater (p < 0.05) crude protein content than untreated samples. All the treatments (except 24 h soaking of MB) reduced (p < 0.05) the TIA and ash content. Marama and SB are similar in protein content, but their amino acids profile and TIA are quite different. Soaking for 24 h was less effective in reducing TIA in MB and SB, compared to the thermal methods, and it was detrimental to the ash and amino acids profile of the two beans. Soaking prior to autoclaving yielded beans with the lowest TI concentrations. In conclusion, thermal methods reduced the TI contents and modified the level of proximate components and amino acids profile of the beans.     

Antiinflammation Derived Suzuki-Coupled Fenbufens as COX-2 Inhibitors: Minilibrary Construction and Bioassay

A small fenbufen library comprising 18 compounds was prepared via Suzuki Miyara coupling. The five-step preparations deliver 9–17% biphenyl compounds in total yield. These fenbufen analogs exert insignificant activity against the IL-1 release as well as inhibiting cyclooxygenase 2 considerably. Both the para-amino and para-hydroxy mono substituents display the most substantial COX-2 inhibition, particularly the latter one showing a comparable activity as celecoxib. The most COX-2 selective and bioactive disubstituted compound encompasses one electron-withdrawing methyl and one electron-donating fluoro groups in one arene. COX-2 is selective but not COX-2 to bioactive compounds that contain both two electron-withdrawing groups; disubstituted analogs with both resonance-formable electron-donating dihydroxy groups display high COX-2 activity but inferior COX-2 selectivity. In silico simulation and modeling for three COX-2 active—p-fluoro, p-hydroxy and p-amino—fenbufens show a preferable docking to COX-2 than COX-1. The most stabilization by the p-hydroxy fenbufen with COX-2 predicted by theoretical simulation is consistent with its prominent COX-2 inhibition resulting from experiments.