923 resultados para Geometry of numbers


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New tin(IV) complexes of empirical formula, Sn(NNS)I-3 (NNS = anionic forms of the 2-quinolinecarboxaldehyde Schiff bases of S-methyl- and S-benzyldithiocarbazate) have been prepared and characterized by a variety of physico-chemical techniques. In the solid state, the Schiff bases exist as the thione tautomer but in solution and in the presence of tin(IV) iodide they convert to the thiol tautomer and coordinate to the tin atom in their deprotonated thiolate forms. The structures of the free ligand, Hqaldsbz and its triiodotin(IV) complex, [Sn(qaldsbz)I-3] have been determined by X-ray diffraction. The complex, [Sn(qaldsbz)I-3] has a distorted octahedral structure with the Schiff base coordinated to the tin atom as a uninegatively charged tridentate chelating agent via the quinoline nitrogen atom, the azomethine nitrogen atom and the thiolate sulfur atom. The three iodo ligands are coordinated meridionally to the tin atom. The distortion from an ideal octahedral geometry of [Sn(qaldsbz)I-3] is attributed to the restricted bite size of the tridentate Schiff base ligand. (C) 2004 Elsevier Ltd. All rights reserved.

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Enforcement of chirality upon a macrocyclic tetramine ligand structure by the introduction of an asymmetric pendent arm which does not significantly modify the macrocycle conformation has no significant effect upon the geometry of the coordination sphere of a bound metal. Where substitution engendering chirality does cause a change in the ligand conformation, in particular for a ligand of restricted stereochemistry, these effects can be much greater. Thus, conversion of 3,7-diazacycloheptane to a macrocycle via attachment of chiral sidearms and ring closure through a template reaction leads to cyclam derivatives with unusual coordination properties. (C) 2004 Elsevier Ltd. All rights reserved.

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Earthquakes have been recognized as resulting from stick-slip frictional instabilities along the faults between deformable rocks. A three-dimensional finite-element code for modeling the nonlinear frictional contact behaviors between deformable bodies with the node-to-point contact element strategy has been developed and applied here to investigate the fault geometry influence on the nucleation and development process of the stick-slip instability along an intra-plate fault through a typical fault bend model, which has a pre-cut fault that is artificially bent by an angle of 5.6degrees at the fault center. The numerical results demonstrate that the geometry of the fault significantly affects nucleation, termination and restart of the stick-slip instability along the intra-plate fault, and all these instability phenomena can be well simulated using the current finite-element algorithm.

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Simulations of a complete reflected shock tunnel facility have been performed with the aim of providing a better understanding of the flow through these facilities. In particular, the analysis is focused on the premature contamination of the test flow with the driver gas. The axisymmetric simulations model the full geometry of the shock tunnel and incorporate an iris-based model of the primary diaphragm rupture mechanics, an ideal secondary diaphragm and account for turbulence in the shock tube boundary layer with the Baldwin-Lomax eddy viscosity model. Two operating conditions were examined: one resulting in an over-tailored mode of operation and the other resulting in approximately tailored operation. The accuracy of the simulations is assessed through comparison with experimental measurements of static pressure, pitot pressure and stagnation temperature. It is shown that the widely-accepted driver gas contamination mechanism in which driver gas 'jets' along the walls through action of the bifurcated foot of the reflected shock, does not directly transport the driver gas to the nozzle at these conditions. Instead, driver gas laden vortices are generated by the bifurcated reflected shock. These vortices prevent jetting of the driver gas along the walls and convect driver gas away from the shock tube wall and downstream into the nozzle. Additional vorticity generated by the interaction of the reflected shock and the contact surface enhances the process in the over-tailored case. However, the basic mechanism appears to operate in a similar way for both the over-tailored and the approximately tailored conditions.

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The late Miocene Farallon Negro volcanics, comprising basaltic to rhyodacitic volcano-sedimentary rocks, host the Bajo de la Alumbrera porphyry copper-gold deposit in northwest Argentina. Early studies of the geology of the district have underpinned the general model for porphyry ore deposits where hydrothermal alteration and mineralization develop in and around porphyritic intrusions emplaced at shallow depths (2.5-3.5 km) into stratovolcanic assemblages. The Farallon Negro succession is dominated by thick sequences of volcano-sedimentary breccias, with lavas forming a minor component volumetrically. These volcaniclastic rocks conformably overlie crystalline basement-derived sedimentary rocks deposited in a developing foreland basin southeast of the Puna-Altiplano plateau. Within the Farallon Negro volcanics, volcanogenic accumulations evolved from early mafic to intermediate and silicic compositions. The younger and more silicic rocks are demonstrably coeval and comagmatic with the earliest group of mineralized porphyritic intrusions at Bajo de la Alumbrera. Our analysis of the volcanic stratigraphy and facies architecture of the Farallon Negro volcanics indicates that volcanic eruptions evolved from effusive to mixed effusive and explosive styles, as magma compositions changed to more intermediate and silicic compositions. Air early phase of mafic to intermediate voleanism was characterized by small synsedimentary intrusions with peperitic contacts, and lesser lava units scattered widely throughout the district, and interbedded with thick and extensive successions of coarse-grained sedimentary breccias. These sedimentary breccias formed from numerous debris- and hyperconcentrated flow events. A later phase of silicic volcanism included both effusive eruptions, forming several areally restricted lavas, and explosive eruptions, producing more widely dispersed (up to 5 kin) tuff units, some tip to 30-m thickness in proximal sections. Four key features of the volcanic stratigraphy suggest that the Farallon Negro volcanics need not simply record the construction of a large steep-sided polygenetic stratovolcano: (1) sheetlike, laterally continuous debris-flow and other coarse-grained sedimentary deposits are dominant, particularly in the lower sections; (2) mafic-intermediate composition lavas are volumetrically minor; (3) peperites are present throughout the sequence; and (4) fine-grained lacustrine sandstone-siltstone sequences occur in areas previously thought to be proximal to the summit region of the stratovolcano. Instead, the nature, distribution, and geometry of volcanic and volcaniclastic facies suggest that volcanism occurred as a relatively low relief, multiple-vent volcanic complex at the eastern edge of a broad, > 200-km-wide late Miocene volcanic belt and oil ail active foreland sedimentary basin to the Puna-Altiplano. Volcanism that occurred synchronously with the earliest stages of porphyry-related mineralization at Bajo de la Alumbrera apparently developed in an alluvial to ring plain setting that was distal to larger volcanic edifices.

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Neural networks can be regarded as statistical models, and can be analysed in a Bayesian framework. Generalisation is measured by the performance on independent test data drawn from the same distribution as the training data. Such performance can be quantified by the posterior average of the information divergence between the true and the model distributions. Averaging over the Bayesian posterior guarantees internal coherence; Using information divergence guarantees invariance with respect to representation. The theory generalises the least mean squares theory for linear Gaussian models to general problems of statistical estimation. The main results are: (1)~the ideal optimal estimate is always given by average over the posterior; (2)~the optimal estimate within a computational model is given by the projection of the ideal estimate to the model. This incidentally shows some currently popular methods dealing with hyperpriors are in general unnecessary and misleading. The extension of information divergence to positive normalisable measures reveals a remarkable relation between the dlt dual affine geometry of statistical manifolds and the geometry of the dual pair of Banach spaces Ld and Ldd. It therefore offers conceptual simplification to information geometry. The general conclusion on the issue of evaluating neural network learning rules and other statistical inference methods is that such evaluations are only meaningful under three assumptions: The prior P(p), describing the environment of all the problems; the divergence Dd, specifying the requirement of the task; and the model Q, specifying available computing resources.

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The whole set of the nickel(II) complexes with no derivatized edta-type hexadentate ligands has been investigated from their structural and electronic properties. Two more complexes have been prepared in order to complete the whole set: trans(O5)-[Ni(ED3AP)]2- and trans(O5O6)-[Ni(EDA3P)]2- complexes. trans(O5) geometry has been verified crystallographically and trans(O5O6) geometry of the second complex has been predicted by the DFT theory and spectral analysis. Mutual dependance has been established between: the number of the five-membered carboxylate rings, octahedral/tetrahedral deviation of metal-ligand/nitrogen-neighbour-atom angles and charge-transfer energies (CTE) calculated by the Morokuma’s energetic decomposition analysis; energy of the absorption bands and HOMO–LUMO gap.

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In the bulge test, a sheet metal specimen is clamped over a circular hole in a die and formed into a bulge by the hydraulic pressure on one side of the specirnen. As the unsupported part of the specimen is deformed in this way, its area is increased, in other words, the material is generally stretched and its thickness generally decreased. The stresses causing this stretching action are the membrane stresses in the shell generated by the hydraulic pressure, in the same way as the rubber in a toy balloon is stretched by the membrane stresses caused by the air inside it. The bulge test is a widely used sheet metal test, to determine the "formability" of sheet materials. Research on this forming process (2)-(15)* has hitherto been almost exclusively confined to predicting the behaviour of the bulged specimen through the constitutive equations (stresses and strains in relation to displacements and shapes) and empirical work hardening characteristics of the material as determined in the tension test. In the present study the approach is reversed; the stresses and strains in the specimen are measured and determined from the geometry of the deformed shell. Thus, the bulge test can be used for determining the stress-strain relationship in the material under actual conditions in sheet metal forming processes. When sheet materials are formed by fluid pressure, the work-piece assumes an approximately spherical shape, The exact nature and magnitude of the deviation from the perfect sphere can be defined and measured by an index called prolateness. The distribution of prolateness throughout the workpiece at any particular stage of the forming process is of fundamental significance, because it determines the variation of the stress ratio on which the mode of deformation depends. It is found. that, before the process becomes unstable in sheet metal, the workpiece is exactly spherical only at the pole and at an annular ring. Between the pole and this annular ring the workpiece is more pointed than a sphere, and outside this ring, it is flatter than a sphere. In the forming of sheet materials, the stresses and hence the incremental strains, are closely related to the curvatures of the workpiece. This relationship between geometry and state of stress can be formulated quantitatively through prolateness. The determination of the magnitudes of prolateness, however, requires special techniques. The success of the experimental work is due to the technique of measuring the profile inclination of the meridional section very accurately. A travelling microscope, workshop protractor and surface plate are used for measurements of circumferential and meridional tangential strains. The curvatures can be calculated from geometry. If, however, the shape of the workpiece is expressed in terms of the current radial (r) and axial ( L) coordinates, it is very difficult to calculate the curvatures within an adequate degree of accuracy, owing to the double differentiation involved. In this project, a first differentiation is, in effect, by-passed by measuring the profile inclination directly and the second differentiation is performed in a round-about way, as explained in later chapters. The variations of the stresses in the workpiece thus observed have not, to the knowledge of the author, been reported experimentally. The static strength of shells to withstand fluid pressure and their buckling strength under concentrated loads, both depend on the distribution of the thickness. Thickness distribution can be controlled to a limited extent by changing the work hardening characteristics of the work material and by imposing constraints. A technique is provided in this thesis for determining accurately the stress distribution, on which the strains associated with thinning depend. Whether a problem of controlled thickness distribution is tackled by theory, or by experiments, or by both combined, the analysis in this thesis supplies the theoretical framework and some useful experimental techniques for the research applied to particular problems. The improvement of formability by allowing draw-in can also be analysed with the same theoretical and experimental techniques. Results on stress-strain relationships are usually represented by single stress-strain curves plotted either between one stress and one strain (as in the tension or compression tests) or between the effective stress and effective strain, as in tests on tubular specimens under combined tension, torsion and internal pressure. In this study, the triaxial stresses and strains are plotted simultaneously in triangular coordinates. Thus, both stress and strain are represented by vectors and the relationship between them by the relationship between two vector functions. From the results so obtained, conclusions are drawn on both the behaviour and the properties of the material in the bulge test. The stress ratios are generally equal to the strain-rate ratios (stress vectors collinear with incremental strain vectors) and the work-hardening characteristics, which apply only to the particular strain paths are deduced. Plastic instability of the material is generally considered to have been reached when the oil pressure has attained its maximum value so that further deformation occurs under a constant or lower pressure. It is found that the instability regime of deformation has already occurred long before the maximum pressure is attained. Thus, a new concept of instability is proposed, and for this criterion, instability can occur for any type of pressure growth curves.

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The investigations described in this thesis concern the molecular interactions between polar solute molecules and various aromatic compounds in solution. Three different physical methods were employed. Nuclear magnetic resonance (n.m.r.) spectroscopy was used to determine the nature and strength of the interactions and the geometry of the transient complexes formed. Cryoscopic studies were used to provide information on the stoichiometry of the complexes. Dielectric constant studies were conducted in an attempt to confirm and supplement the spectroscopic investigations. The systems studied were those between nitromethane, chloroform, acetonitrile (solutes) and various methyl substituted benzenes. In the n.m.r. work the dependence of the solute chemical shift upon the compositions of the solutions was determined. From this the equilibrium quotients (K) for the formation of each complex and the shift induced in the solute proton by the aromatic in the complex were evaluated. The thermodynamic parameters for the interactions were obtained from the determination of K at several temperatures. The stoichiometries of the complexes obtained from cryoscopic studies were found to agree with those deduced from spectroscopic investigations. For most systems it is suggested that only one type of complex, of 1:1 stiochiometry, predominates except that for the acetonitrile-benzene system a 1:2 complex is formed. Two sets of dielectric studies were conducted, the first to show that the nature of the interaction is dipole-induced dipole and the second to calculate K. The equilibrium quotients obtained from spectroscopic and dielectric studies are compared. Time-averaged geometries of the complexes are proposed. The orientation of solute, with respect to the aromatic for the 1:1 complexes, appears to be the one in which the solute lies symmetrically about the aromatic six-fold axis whereas for the 1:2 complex, a sandwich structure is proposed. It is suggested that the complexes are formed through a dipole-induced dipole interaction and steric factors play some part in the complex formation.

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Changes in modern structural design have created a demand for products which are light but possess high strength. The objective is a reduction in fuel consumption and weight of materials to satisfy both economic and environmental criteria. Cold roll forming has the potential to fulfil this requirement. The bending process is controlled by the shape of the profile machined on the periphery of the rolls. A CNC lathe can machine complicated profiles to a high standard of precision, but the expertise of a numerical control programmer is required. A computer program was developed during this project, using the expert system concept, to calculate tool paths and consequently to expedite the procurement of the machine control tapes whilst removing the need for a skilled programmer. Codifying the expertise of a human and the encapsulation of knowledge within a computer memory, destroys the dependency on highly trained people whose services can be costly, inconsistent and unreliable. A successful cold roll forming operation, where the product is geometrically correct and free from visual defects, is not easy to attain. The geometry of the sheet after travelling through the rolling mill depends on the residual strains generated by the elastic-plastic deformation. Accurate evaluation of the residual strains can provide the basis for predicting the geometry of the section. A study of geometric and material non-linearity, yield criteria, material hardening and stress-strain relationships was undertaken in this research project. The finite element method was chosen to provide a mathematical model of the bending process and, to ensure an efficient manipulation of the large stiffness matrices, the frontal solution was applied. A series of experimental investigations provided data to compare with corresponding values obtained from the theoretical modelling. A computer simulation, capable of predicting that a design will be satisfactory prior to the manufacture of the rolls, would allow effort to be concentrated into devising an optimum design where costs are minimised.

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The most perfectly structured metal surface observed in practice is that of a field evaporated field-ion microscope specimen. This surface has been characterised by adopting various optical analogue techniques. Hence a relationship has been determined between the structure of a single plane on the surface of a field-ion emitter and the geometry of a binary zone plate. By relating the known focussing properties of such a zone plate to those obtained from the projected images of such planes in a field-ion micrograph, it is possible to extract new information regarding the local magnification of the image. Further to this, it has been shown that the entire system of planes comprising the field-ion imaging surface may be regarded as a moire pattern formed between over-lapping zone plates. The properties of such moire zone plates are first established in an analysis of the moire pattern formed between zone plates on a flat surface. When these ideas are applied to the field-ion image it becomes possible to deduce further information regarding the precise topography of the emitter. It has also become possible to simulate differently proJected field-ion images by overlapping suitably aberrated zone plates. Low-energy ion bombardment is an essential preliminary to much surface research as a means of producing chemically clean surfaces. Hence it is important to know the nature and distribution of the resultant lattice damage, and the extent to which it may be removed by annealing. The field-ion microscope has been used to investigate such damage because its characterisation lies on the atomic scale. The present study is concerned with the in situ sputtering of tungsten emitters using helium, neon, argon and xenon ions with energies in the range 100eV to 1keV, together with observations of the effect of annealing. The relevance of these results to surface cleaning schedules is discussed.

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The decomposition of drugs in the solid state has been studied using aspirin and salsalate as models. The feasibility of using suspension systems for predicting the stability of these drugs in the solid state has been investigated.. It has been found that such systems are inappropriate in defining the effect of excipients on 'the decomposition of the active drug due to chqnges in the degradation pathway. Using a high performance liquid chromatographic method, magnesium stearate was shown to induce the formation of potentlally immunogenic products in aspirin powders. These products which included salicylsalicylic acid .and acetylsalicyclsalicylic acid were not detected in aspirin suspensions which had undergone the same extent of decomposition. By studying the effect of pH and of added excipients on the rate of decomposition of aspirin in suspension systems, it has been shown that excipients such as magnesium stearate containing magnesium oxide, most probably enhance the decomposition of both aspirin and salsalate by alkalinising the aqueous phase. In the solid state, pH effects produced by excipients appear to be relatively unimportant. Evidence is presented to suggest that the critical parameter is a depression in melting point induced by: the added excipient. Microscopical examination in fact showed the formation of clear liquid layers in aspirin samples containing added magnesium stearate but not in control samples. Kinetic equations which take into account both the diffusive barrier presented by the liquid films and the. geometry of the aspirin crystals were developed. Fitting of the .experimental data to these equations showed good agreement. with the postulated theory. Monitorjng of weight issues during the decomposition of aspirin revealed that in the solid systems studied where the bulk of the decomposition product sublimes, it is possible to estimate the extent of degradation from the residual weight, provided the initial weight is known. The corollary is that in such open systems, monitoring of decomposition products is inadequate for assessing the extent of decomposition. In addition to the magnesium stearate-aspirin system, mapyramine maleate-aspirin mixtures were used to model interactive systems. Work carried out in an attempt to stabilise such systems included microencapsulation and film coating. The protection obtained was dependent on the interactive species used. Gelatin for example appeared to stabilise aspirin against the adverse effects of magnesium stearate but increased its decomposition in the presence of mapyramine maleate.

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The mechanism of "Helical Interference" in milled slots is examined and a coherent theory for the geometry of such surfaces is presented. An examination of the relevant literature shows a fragmented approach to the problem owing to its normally destructive nature, so a complete analysis is developed for slots of constant lead, thus giving a united and exact theory for many different setting parameters and a range of cutter shapes. For the first time, a theory is developed to explain the "Interference Surface" generated in variable lead slots for cylindrical work and attention is drawn to other practical surfaces, such as cones, where variable leads are encountered. Although generally outside the scope of this work, an introductory analysis of these cases is considered in order to develop the cylindrical theory. Special emphasis is laid upon practical areas where the interference mechanism can be used constructively and its application as the rake face of a cutting tool is discussed. A theory of rake angle for such cutting tools is given for commonly used planes, and relative variations in calculated rake angle between planes is examined. Practical tests are conducted to validate both constant lead and variable lead theories and some design improvements to the conventional dividing head are suggested in order to manufacture variable lead workpieces, by use of a "superposed" rotation. A prototype machine is manufactured and its kinematic principle given for both linear and non-linearly varying superposed rotations. Practical workpieces of the former type are manufactured and compared with analytical predictions,while theoretical curves are generated for non-linear workpieces and then compared with those of linear geometry. Finally suggestions are made for the application of these principles to the manufacture of spiral bevel gears, using the "Interference Surface" along a cone as the tooth form.

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The research concerns the development and application of an analytical computer program, SAFE-ROC, that models material behaviour and structural behaviour of a slender reinforced concrete column that is part of an overall structure and is subjected to elevated temperatures as a result of exposure to fire. The analysis approach used in SAFE-RCC is non-linear. Computer calculations are used that take account of restraint and continuity, and the interaction of the column with the surrounding structure during the fire. Within a given time step an iterative approach is used to find a deformed shape for the column which results in equilibrium between the forces associated with the external loads and internal stresses and degradation. Non-linear geometric effects are taken into account by updating the geometry of the structure during deformation. The structural response program SAFE-ROC includes a total strain model which takes account of the compatibility of strain due to temperature and loading. The total strain model represents a constitutive law that governs the material behaviour for concrete and steel. The material behaviour models employed for concrete and steel take account of the dimensional changes caused by the temperature differentials and changes in the material mechanical properties with changes in temperature. Non-linear stress-strain laws are used that take account of loading to a strain greater than that corresponding to the peak stress of the concrete stress-strain relation, and model the inelastic deformation associated with unloading of the steel stress-strain relation. The cross section temperatures caused by the fire environment are obtained by a preceding non-linear thermal analysis, a computer program FIRES-T.

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The work described in this thesis is an attempt to elucidate the relationships between the pore system and a number of engineering properties of hardened cement paste, particularly tensile strength and resistances to carbonation and ionic penetration. By examining aspects such as the rate of carbonisation, the pore size distribution, the concentration of ions in the pore solution and the phase composition of cement pastes, relationships between the pore system (pores and pore solution) and the resistance to carbonation were investigated. The study was carried out in two parts. First, cement pastes with different pore systems were compared, whilst secondly comparisons were made between the pore systems of cement pastes with different degrees of carbonation. Relationships between the pore structure and ionic penetration were studied by comparing kinetic data relating to the diffusion of various ions in cement pastes with different pore systems. Diffusion coefficients and activation energies for the diffusion process of Cl- and Na+ ions in carbonated and non-carbonated cement pastes were determined by a quasi-steady state technique. The effect of the geometry of pores on ionic diffusion was studied by comparing the mechanisms of ionic diffusion for ions with different radii. In order to investigate the possible relationship between tensile strength and macroporosity, cement paste specimens with cross sectional areas less than 1mm2 were produced so that the chance of a macropore existing within them was low. The tensile strengths of such specimens were then compared with those of larger specimens.