Nonlinear Filtering in Rieznnnnifln Manifolds

A general formulation of the nonlinear filtering problem inRiemanman manifolds is given by use of the strong solutionsof the stochastic differential equations for the state and observationprocesses in the orthonormal frame bundles of the state andobservation process manifolds, respectively. A general Bayesformula for the conditional expectation of smooth functionsof the state process is given. This is used to give a directderivation of the Zakai equation for the general problem underconsideration. An example is presented.     

Factorization of proper holomorphic maps on irreducible bounded symmetric domains of rank≥2

We obtain rigidity results on arbitrary proper holomorphic maps F from an irreducible bounded symmetric domain Ω of rank ≥2 into any complex space Z. After lifting to the normalization of the subvariety F (Ω) Z, we prove that F must be the canonical projection map to the quotient space of Ω by a finite group of automorphisms. The approach is along the line of the works of Mok and Tsai by considering radial limits of bounded holomorphic functions derived from F and proving that proper holomorphic maps between bounded symmetric domains preserve certain totally geodesic subdomains. In contrast to the previous works, in general we have to deal with multivalent holomorphic maps for which Fatou’s theorem cannot be applied directly. We bypass the difficulty by devising a limiting process for taking radial limits of correspondences arising from proper holomorphic maps and by elementary estimates allowing us to define distinct univalent branches of the underlying multivalent map on certain subsets. As a consequence of our rigidity result, with the exception of Type-IV domains, any proper holomorphic map f : Ω→ D of Ω onto a bounded convex domain D is necessarily a biholomorphism. In the exceptional case where Ω is a Type-IV domain, either f is a biholomorphism or it is a double cover branched over a totally geodesic submanifold which can be explicitly described.     

Robust spatially resolved pressure measurements using MRI with novel buoyant advection-free preparations of stable microbubbles in polysaccharide gels

MRI of fluids containing lipid coated microbubbles has been shown to be an effective tool for measuring the local fluid pressure. However, the intrinsically buoyant nature of these microbubbles precludes lengthy measurements due to their vertical migration under gravity and pressure-induced coalescence. A novel preparation is presented which is shown to minimize both these effects for at least 25 min. By using a 2% polysaccharide gel base with a small concentration of glycerol and 1,2-distearoyl-sn-glycero-3-phosphocholine coated gas microbubbles, MR measurements are made for pressures between 0.95 and 1.44 bar. The signal drifts due to migration and amalgamation are shown to be minimized for such an experiment whilst yielding very high NMR sensitivities up to 38% signal change per bar.     

Scaling law of poly(ethylene oxide) chain permeation through a nanoporous wall

This paper presents a study of the permeation of poly(ethylene oxide) (PEO) chains through the nanoporous wall of hollow polymeric capsules prepared by self-assembly of polyelectrolytes. We employ the method of pulsed field gradient (PFG) NMR diffusion to distinguish chains in different sites, i.e., in the capsule interior and free chains in the dispersion, by their respective diffusion coefficient. From a variation of the observation time, the time scale of the molecular exchange between both sites and thus the permeation rate constant is extracted from a two-site exchange model. Permeation rate constants show two different regimes with a different dependence on chain length. This suggests a transition between two different mechanisms of permeation as the molecular weight is increased. In either regime, the permeation time can be described by a scaling law tau approximately N (b) , with b = (4)/ 3 for short chains and b = (1)/ 3 for long chains. We discuss these exponents, which clearly differ from the theoretical predictions for chain translocation.     

Transfer measurements for the Ti+Ni systems at near barrier energies

Large enhancements have been observed in the sub-barrier fusion cross sections for Ti+Ni systems in our previous studies. Coupled channel calculations incorporating couplings to 2⁺ and 3⁻ states failed to explain these enhancements completely. A possibilty of transfer channels contributing to the residual enhancements had been suggested. In order to investigate the role of relevant transfer channels, measurements of one- and two-nucleon transfer were carried out for ^46,48Ti+⁶¹Ni systems. The present paper gives the results of these studies.     

Electrochemical and Spectroscopic Properties of Fly Ash–Polyaniline Matrix Nanorod Composites

Polyaniline (PANI) nanocomposites were prepared with fly ash (FA) either by aging the starting materials (aniline and FA) before oxidative polymerisation or by including poly(styrene sulphonic acid) (PSSA) eliminating the aging step. The aging procedure formed polymer nanotubes that have cross-sectional diameters of 50–110 nm. The procedure involving PSSA produced nanorods and nanofibres composites that have diameters of 100–500 nm and length of up to 10 μm attributed to the presence of metal oxides and silica in FA. The electrochemical analysis of the PANI–PSSA–FA nanorod composites shows three redox couples with formal potentials, , values of 105 mV, 455 mV and 670 mV, and conductance, C, value of 1.21 × 10⁻² S. The UV-Vis spectroscopy of the polymeric nanorod shows absorption maxima at 340 and 370 nm (due to π–π^* transition of the benzoid rings), and 600–650 nm (due to charge transfer excitons of the quinoid structure), which are characteristic of emeraldine base.     

PFG NMR and internal magnetic field gradients in plant-based materials

In this contribution, it is demonstrated that inner magnetic field gradients can seriously affect the results of stimulated echo PFG NMR experiments on plant-based materials even if there is no notable content of paramagnetic substances. Such effects could be observed both in experiments on water in pharmaceutical grade cellulose powder materials and on eggplant fruit tissue. In both cases, it was observed that the effects of internal magnetic field gradients led to different relative values of the diffusion coefficient compared to values obtained with a gradient-compensating pulse sequence.     

Nonabsolute Integral on Measure Spaces

We define a Henstock-type integral on measure spaces with metrictopologies, and give an example of a function which is integrablebut whose absolute value is not. 1991 Mathematics Subject Classification26A39, 46G12.