Large Deviations Behavior for the Quadratic Error of Density Estimate

For a projection estimator f_n of an unknown density f we investigate the behavior of large deviations probability P{T_n > r_n} when r_n , where T_n is appropriately centered and normed quadratic error f_n-f)².     

Insights into positron annihilation lifetime spectroscopy by molecular dynamics simulations

The relationship between free-volume properties measured from positron annihilation lifetime spectroscopy (PALS) and calculated from molecular dynamics simulations has been investigated for glassy and liquid glycerol in the temperature range 150–400 K. A virtual probing procedure has been developed to retrieve information on the basic free-volume properties of the simulated microstructures, i.e. mean cavity volume and free-volume cavity fractions. Our data leads us to infer on the occurrence of experimentally non-detectable small cavities with mean equivalent radius of 1.8–1.9 Å between 250 and 275 K. The size of these limiting cavities is found to be temperature dependent, being smaller at low temperatures. At high temperatures, above a characteristic PALS temperature Tb2L , the formation of very large cavities is predicted. This finding suggests that, when the dimension of the holes in the system exceeds a given value, the PALS measurements become unable to catch the complete structural information and phenomena of dynamical origin enter into play in the PALS signal decay. The calculated number of cavities is found to be almost independent on the temperature from the glassy up to the liquid phase, thus furnishing a certain support to theoretical models proposed to evaluate the free-volume cavity fractions.     

Investigation of the negative thermal expansion mechanism of zeolite chabazite using the pair distribution function method

We have used the pair distribution function (PDF) method to gain insight into the mechanism of contraction of zeolite chabazite. Using this method we followed how the interatomic distances of the local structure changed with temperature. By optimization of the structure by free energy minimization and using the Reverse Monte Carlo technique we were able to find structural models at low and at high temperatures that agreed quantitatively with our experimental PDFs. From these models we conclude that the mechanism of contraction with temperature cannot involve rocking of the tetrahedra as rigid unit modes as there are distortions of the tetrahedra with temperature (indicating internal vibrations) and also that the mechanism of contraction probably involves a mode that translates along the Si-O3-Si-O4-Si linkages inside of the D6R of zeolite chabazite.     

Solution of the Truncated Parabolic Moment Problem

Given real numbers with ₀₀ >0 , the truncated parabolic moment problem for entails finding necessary and sufficient conditions for the existence of a positive Borel measure , supported in the parabola p(x, y) = 0, such that We prove that admits a representing measure (as above) if and only if the associated moment matrix is positive semidefinite, recursively generated and has a column relation p(X, Y) = 0, and the algebraic variety () associated to satisfies card In this case, admits a rank -atomic (minimal) representing measure.Submitted: August 25, 2003     

Completeness theorem for propositional probabilistic models whose measures have only finite ranges

A propositional logic is defined which in addition to propositional language contains a list of probabilistic operators of the form P_s (with the intended meaning the probability is at least s). The axioms and rules syntactically determine that ranges of probabilities in the corresponding models are always finite. The completeness theorem is proved. It is shown that completeness cannot be generalized to arbitrary theories.This research was supported by Ministarstvo za nauku, tehnologije i razvoj Republike Srbije, through Matematiki institut, under grant 1379Mathematics Subject Classification (2000): 03C70, 03B48     

Collision of a Solid with an Incompressible Fluid

We give a predictive theory of the collisions of a viscous incompressible fluid with solids. The theory is based on interior percussions which account for the very large stresses and contact forces resulting from the kinematic incompatibilities responsible for the collision. New equation of motion and constitutive laws result from the theory. Examples dealing with a fluid colliding with its container and with a diver impacting the water of a swimming pool are studied.