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.     

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.     

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.     

Dimethyltin Dichloride-Dibenzyl Sulfoxide, a Compound Crystallizing with Seven Molecules in the Asymmetric Unit

Dimethyltin dichloride-dibenzyl sulfoxide,((CH3)2SnCl2·O=S(CH2C6H5)2),crystallizes in the orthorhombic space group P212121 with a superstructure of dimensions a = 11.9290(1),b = 19.50490(1),c = 55.7390(6) ; Z = 28. The geometry of the five-coordinated tin atom in each of the seven independent adduct molecules is a square pyramid that is displaced towards a cis-trigonal bipyramid; the extent of displacement along the Berry pseudorotation pathway ranges from 20 to 45%.     

The use of X-ray fluorescence (XRF) analysis in predicting the alkaline hydrothermal conversion of fly ash precipitates into zeolites

The use and application of synthetic zeolites for ion exchange, adsorption and catalysis has shown enormous potential in industry. In this study, X-ray fluorescence (XRF) analysis was used to determine Si and Al in fly ash (FA) precipitates. The Si and Al contents of the fly ash precipitates were used as indices for the alkaline hydrothermal conversion of the fly ash compounds into zeolites. Precipitates were collected by using a co-disposal reaction wherein fly ash is reacted with acid mine drainage (AMD). These co-disposal precipitates were then analysed by XRF spectrometry for quantitative determination of SiO₂ and Al₂O₃. The [SiO₂]/[Al₂O₃] ratio obtained in the precipitates range from 1.4 to 2.5. The [SiO₂]/[Al₂O₃] ratio was used to predict whether the fly ash precipitates could successfully be converted to faujasite zeolitic material by the synthetic method of [J. Haz. Mat. B 77 (2000) 123]. If the [SiO₂]/[Al₂O₃] ratio is higher than 1.5 in the fly ash precipitates, it favours the formation of faujasite. The zeolite synthesis included an alkaline hydrothermal conversion of the co-disposal precipitates, followed by aging for 8 h and crystallization at 100 °C. Different factors were investigated during the synthesis of zeolite to ascertain their influence on the end product. The factors included the amount of water in the starting material, composition of fly ash related starting material and the FA:NaOH ratio used for fusing the starting material. The mineralogical and physical analysis of the zeolitic material produced was performed by X-ray diffraction (XRD) and nitrogen Brunauer-Emmett-Teller (N₂ BET) surface analysis. Scanning electron microscopy (SEM) was used to determine the morphology of the zeolites, while inductively coupled mass spectrometry (ICP-MS), Fourier transformed infrared spectrometry (FT-IR) and Cation exchange capacity (CEC) [Report to Water Research Commission, RSA (2003) 15] techniques were used for chemical characterisation. The heavy and trace metal concentrations of the zeolite products were compared to that of the post-synthesis filtrate and of the precipitate materials used as Si and Al feed stock for zeolite formation, in order to determine the trends (increase or decrease) and ultimate fate of any toxic metals incorporated in the co-disposed precipitated residues.     

Electron-stimulated production of molecular oxygen in amorphous solid water on Pt111: precursor transport through the hydrogen bonding network

The low-energy, electron-stimulated production of molecular oxygen from thin amorphous solid water (ASW) films adsorbed on Pt(111) is investigated. For ASW coverages less than approximately 60 ML, the O(2) electron-stimulated desorption (ESD) yield depends on coverage in a manner that is very similar to the H(2) ESD yield. In particular, both the O(2) and H(2) ESD yields have a pronounced maximum at approximately 20 ML due to reactions at the Pt/water interface. The O(2) yield is dose dependent and several precursors (OH, H(2)O(2), and HO(2)) are involved in the O(2) production. Layered films of H(2) (16)O and H(2) (18)O are used to profile the spatial distribution of the electron-stimulated reactions leading to oxygen within the water films. Independent of the ASW film thickness, the final reactions leading to O(2) occur at or near the ASW/vacuum interface. However, for ASW coverages less than approximately 40 ML, the results indicate that dissociation of water molecules at the ASW/Pt interface contributes to the O(2) production at the ASW/vacuum interface presumably via the generation of OH radicals near the Pt substrate. The OH (or possibly OH(-)) segregates to the vacuum interface where it contributes to the reactions at that interface. The electron-stimulated migration of precursors to the vacuum interface occurs via transport through the hydrogen bond network of the ASW without motion of the oxygen atoms. A simple kinetic model of the nonthermal reactions leading to O(2), which was previously used to account for reactions in thick ASW films, is modified to account for the electron-stimulated migration of precursors.     

Electron-stimulated sputtering of thin amorphous solid water films on Pt(111)

The electron-stimulated sputtering of thin amorphous solid water films deposited on Pt(111) is investigated. The sputtering appears to be dominated by two processes: (1) electron-stimulated desorption of water molecules and (2) electron-stimulated reactions leading to the production of molecular hydrogen and molecular oxygen. The electron-stimulated desorption of water increases monotonically with increasing film thickness. In contrast, the total sputtering--which includes all electron-stimulated reaction channels--is maximized for films of intermediate thickness. The sputtering yield versus thickness indicates that erosion of the film occurs due to reactions at both the water/vacuum interface and the Pt/water interface. Experiments with layered films of D2O and H2O demonstrate significant loss of hydrogen due to reactions at the Pt/water interface. The electron-stimulated sputtering is independent of temperature below approximately 80 K and increases rapidly at higher temperatures.     

Effect of magnetic pore surface coating on the NMR relaxation and diffusion signal in quartz sand

Magnetic impurities are ubiquitous in natural porous media such as sand and soil. They generate internal magnetic field gradients because of increased magnetic susceptibility differences between solid and liquid phase in the pore space and because of the presence of magnetic centers. These internal gradients accelerate NMR relaxation rates and thus might limit the possibility of pore space characterization using NMR. In this study, we investigate the effects of coating the surface of natural sands by the antiferromagnetic iron oxyhydroxide goethite on NMR relaxation and diffusion properties. We found a non‐quadratic dependence of the relaxation time distributions on the echo time indicating that the relaxation experiments were not performed in the fast diffusion limit, while the weak dependence on the external magnetic field strength is explained by the preponderance of the surface relaxation over the effect of diffusion in internal gradients. The surface to volume ratio of the pore space, determined by NMR diffusimetry ((S/V)_NMR) remains approximately constant, whereas the same quantity, determined from gas adsorption ((S/V)_BET) increases proportional to the coating density. This is because gas adsorption measures surface roughness on sub‐nanometer scale, whereas NMR diffusimetry averages over structures smaller than few microns. This has consequences for the calculation of the surface relaxivities. The usage of the (S/V)_NMR leads to constant values, whereas the usage of (S/V)_BET leads to apparently decreasing relaxivities with increasing coating, which is unrealistic. Copyright © 2016 John Wiley & Sons, Ltd.