Condensation of all-cis-tetraphenylcyclotetrasiloxanetetraol in ammonia: new method for preparation of ladder-like polyphenylsilsesquioxanes

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Synthesis and antimycobacterial activity of purine conjugates with (S)-lysine and (S)-ornithine

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FORECASTING MINERAL SUPPLY FROM MINERAL RENT DATA

An optimal control model of exhaustible resources is used to clarify the long run relationship between mineral rent and depletion cost at the industry level. A standard first order condition of the time rate of change of rents is reformulated to reveal that rent data may be used to help forecast the rise in extraction costs resulting from resource depletion. This application of the theory of exhaustible resources is illustrated using historical mineral industry rent and extraction cost data. A forecast of U.S. coal extraction costs, following the method proposed in this paper, suggests that future rates of extraction cost increases will be similar to rates experienced in the past.     

On Series of Ordinals and Combinatorics

This paper deals mainly with generalizations of results in finitary combinatorics to infinite ordinals. It is well-known that for finite ordinals ∑_bT<αβ is the number of 2-element subsets of an α-element set. It is shown here that for any well-ordered set of arbitrary infinite order type α, ∑_bT<αβ is the ordinal of the set M of 2-element subsets, where M is ordered in some natural way. The result is then extended to evaluating the ordinal of the set of all n-element subsets for each natural number n ≥ 2. Moreover, series ∑_β<αf(β) are investigated and evaluated, where α is a limit ordinal and the function f belongs to a certain class of functions containing polynomials with natural number coefficients. The tools developed for this result can be extended to cover all infinite α, but the case of finite α appears to be quite problematic.     

Principe d'Oka-Grauert dansA ∞

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A statistical approach to the solution of ill-posed problems in geophysics

The article surveys the main results of the statistical approach to the solution of ill-posed problems of mathematical physics, in application to specific ill-posed inverse problems in geophysics.Invited paper presented at the International Seminar on Mathematical Foundations of the Interpretation of Geophysical Fields, Moscow, May–June 1972.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 79, pp. 67–81, 1978.     

Existence and Stability for Spherical Crystals Growing in a Supersaturated Solution

We consider the growth of a spherical crystal in a supersaturatedsolution. In the first part, existence and uniqueness resultsfor radially symmetric growth are obtained, provided that thesupersaturation is not too large; conversely, when the far-fieldsupersaturation exceeds a critical value, it is shown that theradially symmetric solution ceases to exist in finite time.In the second part, we examine the linear stability of a radiallysymmetric similarity solution (in which the radius grows ast?) to shape perturbations. The results are compared with previousquasi-static analyses, and, in particular, the critical radiusat which the crystal becomes unstable is found to be largerfor small supersaturations, but smaller for large supersaturations,than those predicted by the quasi-static analysis