6 resultados para Spectral isometries, Jordan isomorphisms, commutative Banach algebras

em Brock University, Canada


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The mass spectra of compounds of t he series (C6F5 )3-n MP~ (n = 1,2,3, M = P and As ), (C6F5>3Sb, Ph) Sb and (C6F5 )2SbPh have been studied in detail and the important modes of fragmentation were e1ucidated, a ided by metastable ions. Various trends attributed to the central atom and or the . substituent groups have been noted and, where applicable, compared to recent studies on related phenyl and pentafluorophenyl compounds of groups IV and V. The mass spectra of fluorine containing organometallic compounds exhibit characteristic migrations of fluorine to t he central atom, giving an increasing abundance of MF+, MF2+' and RMF+ (R = Ph or C6F5) ions on descending the group_ The mass spectra of pentafluorophenyl , antimony, and arsenic compounds show a greater fragmentation of the aromatic ring than those of phosphorus. The mixed phenyl pentafluorophenyl derivatives show a characteristic pattern depending on the number of phenyl grm.lps present but show t he general characteristics of both the tris(phenyl) and tris(pentafluorophenyl) compounds. The diphenyl pentafluorophenyl der ivatives show the loss of biphenyl ion as the most import ant step, the los s of phenyl t o give the i on PhMC6F5 + being of secondary importance. The ,bis(pentafluorophenyl) phenyl derivatives fragment primarily by loss of PhC6F5 to give C6F5M+ ions, the abundance of t hese increasing r apidly from phosphorus to arsenic. This species then, exhibits a characteristic fragmentation observed in the tris(penta- fluorophenyl ) compounds. However, the abundance of (C6F5)2M+ species in these compounds i s small. I ons of the type C6H4MC6F4 + and tetrafluorobiphenylene ions C6H4C6F4 + also are observed on substitution of a phenyl group for a penta- fluorophenyl group. The fully fluorinated species (C6F4)2M+ is not observed, although octafluorobiphenylene ions , (C6F4)2+' are evident in several spectra . The appearance potentials of the major ions were obtatned from the ionisation efficiency curves. Attempts were made to correlate these to the effect of the central atom in substituent groups, but the large errors involved prevented the reaching of quantitative conclusions, although it would appear that the electron is removed from the ligand in the ionisation of t he parent molecule .

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2-Carboxy-2?-methyldiphenyl sulfide was prepared by the Ullmann reaction and cyclodehydrated by sulfuric acid to afford 4-methylthioxanthone. 1-Methylthioxanthone was separated from the reaction mixture obtained upon cyclodehydration of 2-carboxy-3f-methyldiphenyl sulfide. In addition, 1-, 2-, 3- and 4-methylthioxanthone 10,10-dioxides were synthesized by oxidation of the corresponding thioxanthones. o-, m- and p-N-Tolylanthranilic acids were prepared by the Ullmann reaction and used as precursors for the preparation of 1-, 2- and 4- methyl-9-chloroacridine and finally 1-, 2-, 3- and 4-methylacridone. High resolution, 60 MHz PMR spectra were obtained on the four monomethyl isomers of xanthone, thioxanthone, thioxanthone 10,10-dioxide and acridone, and on 1-, 2- and 4-methyl-9-chloroacridine. For some compounds, coupling of all three different aromatic protons to the methyl was observed, two of the couplings typically being smaller than the third. With the large (ortho) coupling being on the order of 0.5 to 1.0 Hz, it was necessary to decouple the aromatic part of the spectrum. The magnitude of the ortho benzylic constant may be related to an incomplete Tr-bond delocalization in the molecules.

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Relation algebras and categories of relations in particular have proven to be extremely useful as a fundamental tool in mathematics and computer science. Since relation algebras are Boolean algebras with some well-behaved operations, every such algebra provides an atom structure, i.e., a relational structure on its set of atoms. In the case of complete and atomic structure (e.g. finite algebras), the original algebra can be recovered from its atom structure by using the complex algebra construction. This gives a representation of relation algebras as the complex algebra of a certain relational structure. This property is of particular interest because storing the atom structure requires less space than the entire algebra. In this thesis I want to introduce and implement three structures representing atom structures of integral heterogeneous relation algebras, i.e., categorical versions of relation algebras. The first structure will simply embed a homogeneous atom structure of a relation algebra into the heterogeneous context. The second structure is obtained by splitting all symmetric idempotent relations. This new algebra is in almost all cases an heterogeneous structure having more objects than the original one. Finally, I will define two different union operations to combine two algebras into a single one.

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High chromium content in kimberlite indicator minerals such as pyrope garnet and diopside is often correlated with the presence of diamonds. In this study, kimberlite indicator minerals were examined using visible light reflectance spectroscopy to determine if chromium content can be correlated with spectral absorption features. The depth of absorption features in the visible spectral region were correlated with the molecular percentage of chromium and other first series transition metal elements obtained by electron microprobe data. In the visible part of the spectrum, chromium is evident by 3 absorption features in the pyrope reflectance spectrum; one isolated and narrow feature at the wavelength 689 nm was used to correlate with the chromium mol %. The isolation of this feature in the pyrope spectra is advantageous since it is not directly affected by other proximal absorption bands that could be caused by other transition metals. Analysis of the feature indicates that as grain volume increases the depth of the absorption feature will also increase. Clustering grain volumes into fractions yields better correlation between absorption depth and mol % chromium. Other types of garnet (almandine, grossular, spessartine) and kimberlite indicator minerals (olivine, diopside, chromite, ilmenite) were analyzed to determine if other absorption features could be used to predict the proportion of specific transition metal elements. Diopside in particular illustrates the same isolated chromium absorption feature as pyrope and may indicate mol percent but needs further study with larger sample sets.

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Basic relationships between certain regions of space are formulated in natural language in everyday situations. For example, a customer specifies the outline of his future home to the architect by indicating which rooms should be close to each other. Qualitative spatial reasoning as an area of artificial intelligence tries to develop a theory of space based on similar notions. In formal ontology and in ontological computer science, mereotopology is a first-order theory, embodying mereological and topological concepts, of the relations among wholes, parts, parts of parts, and the boundaries between parts. We shall introduce abstract relation algebras and present their structural properties as well as their connection to algebras of binary relations. This will be followed by details of the expressiveness of algebras of relations for region based models. Mereotopology has been the main basis for most region based theories of space. Since its earliest inception many theories have been proposed for mereotopology in artificial intelligence among which Region Connection Calculus is most prominent. The expressiveness of the region connection calculus in relational logic is far greater than its original eight base relations might suggest. In the thesis we formulate ways to automatically generate representable relation algebras using spatial data based on region connection calculus. The generation of new algebras is a two pronged approach involving splitting of existing relations to form new algebras and refinement of such newly generated algebras. We present an implementation of a system for automating aforementioned steps and provide an effective and convenient interface to define new spatial relations and generate representable relational algebras.