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.     

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.     

Catecholamine release from cultured bovine adrenal medullary chromaffin cells in the presence of 60-Hz magnetic fields

Effects of powerline frequency (50/60 Hz) electric and magnetic fields on the central nervous system may involve altered neurotransmitter release. This possibility was addressed by determining whether 60-Hz linearly polarized sinusoidal magnetic fields (MFs) alter the release of catecholamines from cultured bovine adrenal chromaffin cells, a well-characterized model of neural-type cells. Dishes of cells were placed in the center of each of two four-coil Merritt exposure systems that were enclosed within mu-metal chambers in matched incubators for simultaneous sham and MF exposure. Following 15-min MF exposure of the cells to flux densities of 0.01, 0.1, 1.0 or 2 mT, norepinephrine and epinephrine release were quantified by high-performance liquid chromatography (HPLC) coupled with electrochemical detection. No significant differences in the release of either norepinephrine or epinephrine were detected between sham-exposed cells and cells exposed to MFs in either the absence or presence of Bay K-8644 (2 microM) or dimethylphenylpiperazinium (DMPP, 10 microM). Consistent with these null findings is the lack of effect of MF exposure on calcium influx. We conclude that catecholamine release from chromaffin cells is not sensitive to 60-Hz MFs at magnetic flux densities in the 0.01-2 mT range.     

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.     

2-（1,3-Diphenylpropen-1,3-diolato）-1,3,2-（5-formylbenzo）dioxaborol： A ＇Whole-molecule Disorder＇ Crystal Structure

The boron atom in C22H15BO5 is O,O’-chelated by the anions in a tetrahedral geometry, with the planar five-and six-membered chelate rings being orthogonal to each other. The molecule lies on a two-fold rotation axis. The molecule is disordered with respect to another molecule in a 93:7 ratio; the treatment of the ‘whole-molecule disorder’ by employing a large number of restraints is described. Crystal data: C22H15BO5, monoclinic C2/c, a = 17.1804(5), b = 12.9409(4), c = 9.8842(3) , β = 124.832(2)o, V = 1803.82(9) 3 at –173 K.     

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.     

Indexing Non-merohedrally Twinned Crystals by Bruker'sAPEX2 and Agilent's CrysAlis~(PRO), an Example of a Crystal Structure That Can Be Refined through Either the PLATONRoute or the ‘HKLF 5' Route,and, Simultaneous Data Collection of Two Crystals in a Tw

The first part of this report describes the data reduction of non-merohedrally twinned crystals measured on Bruker and Agilent area-detector diffractometers. The image frames of methyl-2-aminopyrazine-3-carboxylate were processed with APEX2 to furnish a set of overlapping diffraction indices that were used for solution and refinement. CrysAlisPRO was used for processing the frames of bis(diethyldicarbamato)nickel, which exists in monoclinic and tetragonal polymorphs, and in untwinned and twinned forms. In the second part, the crystal structure of [(3-formyl-4- hydroxyphenyl)methyl]triphenylphosphanium chloride was refined through the ‘HKLF 5'(based on a combined set of diffraction indices) and PLATON(based on one set of diffraction indices) routes to give identical outcomes because the amount of overlap of the twin domains is small. For the third part, in a proof-of-concept investigation, the diffraction pattern of untwinned and twinned 4-{(E)-(4-aminophenyl)diazenyl]phenylamine was recorded simultaneously in one run; the three domains could be indexed and the crystal structure satisfactorily refined. The refinement was identical to those derived from independent measurements; the crystal structure features two independent centrosymmetric molecules, one of which is ordered and the other whole-molecule-disordered. This two-in-one run opens up the possibility that two or more crystals having different atomic compositions can be measured simultaneously if their reciprocal lattices do not overlap significantly.