A New Distribution Function for Risk Analysis

This paper presents an alternative to the beta continuous probability distribution for risk analysis. Particular attention has been given to two major applications of distributions, namely project management risk and critical path analysis (PERT). In conjunction with the beta, the triangular and normal distributions are frequently employed in order to give sufficient robustness to risk analysis. The beta distribution, as used in PERT, has a major theoretical implementation flaw. The new distribution was developed to give a possible alternative method of assessing risk. It is shown that the requirement to estimate the most pessimistic variate may be replaced by the probability to exceed the mode. Proposals for other simplifications in risk analysis are discussed. Practical means to validate the most appropriate distributions for risk analysis are outlined, and a cost-data case study is included.     

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.     

Organotellurides as a source of organometallics: application in the synthesis of (+/−)-frontalin

A masked lithium homoenolate, generated by tellurium/lithium exchange, was reacted with epoxides. The lithium compound was also converted into other organometallics such as Grignard, and cuprates and the reactivity of those organometallics with epoxides was evaluated. The same building block was employed in the synthesis of (+/−)-frontalin.     

The acoustic characteristics of clause, sentence and paragraph boundaries in Chinese Putonghua

The acoustic and perceptive characteristics of discourse units, including clauses, simple sentences, compound sentences and paragraphs, were studied. The acoustic characteristics were based on the analysis of a speech corpus consisted of ten monologues. The Perceived Boundary Strength (PBS) of the monologues was labeled on a five-point scale by 25 participants. The main results are as follows: (1) There is a significant difference in the PBS of clauses (corresponding to intonational phrase), sentences (including simple sentences and compound sentences) and paragraphs. But the PBS of simple sentences and compound sentences is the same, and the pitch reset and pause are also not significantly different between these two kinds of boundaries. (2) The pitch-based cue used to distinguish clauses, sentences and paragraphs appears to be the difference between pre- and post-boundary syllables, but not simply the pitch value of either syllable alone. (3) Declination mainly occurs within intonational phrases, whereas there is no consistent global declination in sentences or in paragraphs. (4) Pauses are longer and more varied at the boundary of larger discourse units. Moreover, there is a significant positive correlation between pause duration and degree of pitch reset at clause boundaries, but not at sentence or paragraph boundaries.     

On decomposition of continuity

Summary The main purpose of this paper is to introduce the concepts of η-sets, ηζ-sets,η-continuity and ηζ-continuity and to obtain a decomposition of continuity.     

Isotopic families of contact manifolds for elliptic PDE

A test for a function to be a solution of an elliptic PDE is given in terms of extensions, as solutions, from the boundaries inside the domains belonging to an isotopic family. It generalizes a result of Ehrenpreis for spheres moved along a straight line.