A Quantile-Based Probabilistic Mean Value Theorem

For non-negative random variables with finite means we introduce an analogous of the equilibrium residual-lifetime distribution based on the quantile function. This allows us to construct new distributions with support (0, 1), and to obtain a new quantile-based version of the probabilistic generalization of Taylor's theorem. Similarly, for pairs of stochastically ordered random variables we come to a new quantile-based form of the probabilistic mean value theorem. The latter involves a distribution that generalizes the Lorenz curve. We investigate the special case of proportional quantile functions and apply the given results to various models based on classes of distributions and measures of risk theory. Motivated by some stochastic comparisons, we also introduce the “expected reversed proportional shortfall order”, and a new characterization of random lifetimes involving the reversed hazard rate function.

A four moments theorem for Gamma limits on a Poisson chaos

This paper deals with sequences of random variables belonging to a fixed chaos of order q generated by a Poisson random measure on a Polish space. The problem is investigated whether convergence of the third and fourth moment of such a suitably normalized sequence to the third and fourth moment of a centred Gamma law implies convergence in distribution of the involved random variables. A positive answer is obtained for q = 2 and q = 4. The proof of this four moments theorem is based on a number of new estimates for contraction norms. Applications concern homogeneous sums and U-statistics on the Poisson space.

Interactive simulation of the fate of hazardous chemicals during land treatment of oily wastes : RITZ user's guide /

Mode of access: Internet.

Sperner's theorem on maximal-sized antichains and its generation /

Includes bibliographical references.

Theorem proving with abstraction, part II /

Supported in part by the National Science Foundation under grant MCS 77-22830.

Some new results on resolution in automated theorem proving,

Issued also as thesis (M.S.) University of Illinois.

Theorem proving with abstraction, part I /

"UILU-ENG 79-1706."

The electrical admittance of a homogeneous polarized fully electroded circular disc, loss-less and mechanically free : analysis, including Rayleigh correction, data for routine determination of elastic modulus and Piezoelectric coupling, and discussion of limitation of correction, anisotrophy parameters involved, and deductions concerning dimensional standarization /

"ONR Contract No. Nonr-1055(00)."

The Rayleigh disk as a wave direction indicator.

Mode of access: Internet.

Gesammelte werke. Walther Ritz. OEuvres publiécs par la Sociéte suisse de physique

Mode of access: Internet.

Binomial theorem and logarithms. For the use of the midshipmen at the naval school, Philadelphia.

Preface signed: William Chauvenet.

Das Leben des Malers Raphael Ritz von Niederwald.

Text signed: L.L. von Roten.

Analysis of the free vibration of rectangular plates with central cut-outs using the discrete Ritz method

We present an analysis of the free vibration of plates with internal discontinuities due to central cut-outs. A numerical formulation for a basic L-shaped element which is divided into appropriate sub-domains that are dependent upon the location of the cut-out is used as the basic building element. Trial functions formed to satisfy certain boundary conditions are employed to define the transverse deflection of each sub-domain. Mathematical treatments in terms of the continuities in displacement, slope, moment, and higher derivatives between the adjacent sub-domains are enforced at the interconnecting edges. The energy functional results, from the proper assembly of the coupled strain and kinetic energy contributions of each sub-domain, are minimized via the Ritz procedure to extract the vibration frequencies and. mode shapes of the plates. The procedures are demonstrated by considering plates with central cut-outs that are subjected to two types of boundary conditions. (C) 2003 Elsevier Ltd. All rights reserved.

The philosophical significance of Cox's theorem

Cox's theorem states that, under certain assumptions, any measure of belief is isomorphic to a probability measure. This theorem, although intended as a justification of the subjectivist interpretation of probability theory, is sometimes presented as an argument for more controversial theses. Of particular interest is the thesis that the only coherent means of representing uncertainty is via the probability calculus. In this paper I examine the logical assumptions of Cox's theorem and I show how these impinge on the philosophical conclusions thought to be supported by the theorem. I show that the more controversial thesis is not supported by Cox's theorem. (C) 2003 Elsevier Inc. All rights reserved.