James Geer

A mathematical analysis of information-preserving transformations between probabilistic and possibilistic formulations of uncertainty

It is now generally recognized that uncertainty can be formalized in different mathematical theories. Two of these theories, on which we focus in this paper, are probability theory and possibility theory. The paper deals with transformations from probabilistic formalizations of uncertainty into their possibilistic counterparts that contain the same amount of uncertainty and, consequently, the same amount of information (expressed as a reduction of uncertainty) as well; it also deals with the inverse uncertainty and information preserving transformations. Since well-justified and unique measures of uncertainty (and information) are now well established in both probability theory and possibility theory, the transformations are well defined. Mathematical properties of the transformations are analyzed in the paper under the assumption that probabilities and possibilities are connected via interval or log-interval scales. The primary results are: (i) the interval scale transformation that preserves information...

Power Series Expansions for the Frequency and Period of the Limit Cycle of the Van Der Pol Equation

A power series expansion in the damping coefficient a is developed for the frequency

Perturbation analysis of the limit cycle of the free van der Pol equation

\nu ( \varepsilon )

Exponentially Accurate Approximations to Piece-Wise Smooth Periodic Functions

of the limit cycle of the van der Pol equation

Rational trigonometric approximations using Fourier series partial sums

\ddot U + U = \varepsilon \dot U( 1 - U^2 )( 0\leqq \varepsilon < \infty )

Stokes flow past a slender body of revolution

. The expansion is computed to

Discord in possibility theory

O( \varepsilon ^{24} )

A hybrid perturbation Galerkin technique with applications to slender body theory

in rational arithmetic using the MACSYMA symbolic manipulation system and to

Vertical slender jets with surface tension

O( \varepsilon ^{164} )

Uniform asymptotic solutions for potential flow about a slender body of revolution

in floating-point arithmetic using FORTRAN.A Pade analysis of the power series expansion indicates that the singularities in the complex-