Differential geometry of intersection curves in R(4) of three implicit surfaces

We present algorithms for computing the differential geometry properties of intersection Curves of three implicit surfaces in R(4), using the implicit function theorem and generalizing the method of X. Ye and T. Maekawa for 4-dimension. We derive t, n, b(1), b(2) vectors and curvatures (k(1), k(2), k(3)) for transversal intersections of the intersection problem. (C) 2008 Elsevier B.V. All rights reserved.

In situ measured cross section geometry of old timber structures and its influence on structural safety

Old timber structures may show significant variation in the cross section geometry along the same element, as a result of both construction methods and deterioration. As consequence, the definition of the geometric parameters in situ may be both time consuming and costly. This work presents the results of inspections carried out in different timber structures. Based on the obtained results, different simplified geometric models are proposed in order to efficiently model the geometry variations found. Probabilistic modelling techniques are also used to define safety parameters of existing timber structures, when subjected to dead and live loads, namely self-weight and wind actions. The parameters of the models have been defined as probabilistic variables, and safety of a selected case study was assessed using the Monte Carlo simulation technique. Assuming a target reliability index, a model was defined for both the residual cross section and the time dependent deterioration evolution. As a consequence, it was possible to compute probabilities of failure and reliability indices, as well as, time evolution deterioration curves for this structure. The results obtained provide a proposal for definition of the cross section geometric parameters of existing timber structures with different levels of decay, using a simplified probabilistic geometry model and considering a remaining capacity factor for the decayed areas. This model can be used for assessing the safety of the structure at present and for predicting future performance.

Adelic convex geometry of numbers

Magdeburg, Univ., Fak. für Mathematik, Diss., 2014

Latitudinal gradient effect on the wing geometry of Auca coctei (Guérin)(Lepidoptera, Nymphalidae)

Latitudinal gradient effect on the wing geometry of Auca coctei (Guérin) (Lepidoptera, Nymphalidae). When the environmental conditions change locally, the organisms and populations may also change in response to the selection pressure, so that the development of individuals may become affected in different degrees. There have been only a few studies in which the patterns of wing morphology variation have been looked into along a latitudinal gradient by means of geometric morphometrics. The aim of this work was to assess the morphologic differentiation of wing among butterfly populations of the species Auca coctei. For this purpose, 9 sampling locations were used which are representative of the distribution range of the butterfly and cover a wide latitudinal range in Chile. The wing morphology was studied in a total of 202 specimens of A. coctei (150 males and 52 females), based on digitization of 17 morphologic landmarks. The results show variation of wing shape in both sexes; however, for the centroid size there was significant variation only in females. Females show smaller centroid size at higher latitudes, therefore in this study the Bergmann reverse rule is confirmed for females of A. coctei. Our study extends morphologic projections with latitude, suggesting that wing variation is an environmental response from diverse origins and may influence different characteristics of the life history of a butterfly.

The electronic spectra and the determination of the excited state geometry of 3A" propynal /|nby Chhiu-Tsu Lin. -- 260 St. Catharines, Ont. : [s. n.],

Impurity free eluission spectra of HCCCHO and DCCCHO have been rephotographed using the electronic-energy-exchange method with benzene as a carrier gas. The near ultraviolet spectra of ReeCHO and DCCCHO were photographed in a sorption under conditions of high resolution with absorption path lengths up to 100 meters. The emission and absorption spectra of Propynal resulting from 3 n 1 t 1\ - A excitation has been reanalyzed in som.e detail. Botrl of the eH out-of-plane wagging modes were found to have negative anharmonicity. A barrier height of 56.8/0.0 cm- 1 and a nonplanar oft , , equilibrium angle of 17 3 /30 are calculated for the V 10/ lJ 11 modes. The in-plane and out-of-plane v1. brational modes in the 3A." and 1a~. ' elec ronic states of Propynal were subjected to a normal coordinate treatment in the approximat :on of tIle Urey-Bradley force field. From the relative oscillator strengths of the trans1·t1·0ns connect i ng t he v ibrat1•0n1ess lA' , state and t,he V1· bron1·C 3· if levels of the A state, the differences in equilibrium configuration were evaluated from an approximate Franck-Condon analysis based on the ground state normal coordinates. As this treatment gave 512 possible geometrical structures for the upper state, it 4 was necessary to resort to a comparison of the observed and calculated moments of inertia along with chemical intuition to isolate the structure. A test of the correctness of the calculated structure change and the vibrational assignment was raade by evaluating the intensities of the inplane and out-oi-plane fundarnental, sequence, and cross sequellce transitions y the exact Franck-Condon method.

An elementary treatise on analytic geometry, embracing plane geometry and an introduction to geometry of threee dimensions with numerous examples.

UANL

Studies in the geometry of the discrete plane

This thesis is an attempt to initiate the development of a discrete geometry of the discrete plane H = {(qmxo,qnyo); m,n e Z - the set of integers}, where q s (0,1) is fixed and (xO,yO) is a fixed point in the first quadrant of the complex plane, xo,y0 ¢ 0. The discrete plane was first considered by Harman in 1972, to evolve a discrete analytic function theory for geometric difference functions. We shall mention briefly, through various sections, the principle of discretization, an outline of discrete a alytic function theory, the concept of geometry of space and also summary of work done in this thesis

Surface geometry of Cu{531}

We present a combined quantitative low-energy electron diffraction (LEED) and density-functional theory (DFT) study of the chiral Cu{531} surface. The surface shows large inward relaxations with respect to the bulk interlayer distance of the first two layers and a large expansion of the distance between the fourth and fifth layers. (The latter is the first layer having the same coordination as the Cu atoms in the bulk.) Additional calculations have been performed to study the likelihood of faceting by comparing surface energies of possible facet terminations. No overall significant reduction in energy with respect to planar {531} could be found for any of the tested combinations of facets, which is in agreement with the experimental findings.

The adsorption geometry of sulphur on Ir{100}: a quantitative LEED study

A quantitative low energy electron diffraction (LEED) analysis has been performed for the p(2 x 2)-S and c(2 x 2)-S surface structures formed by exposing the (1 x 1) phase of Ir{100} to H2S at 750 K. S is found to adsorb on the fourfold hollow sites in both structures leading to Pendry R-factor values of 0.17 for the p(2 x 2)-S and 0.16 for the c(2 x 2)-S structures. The distances between S and the nearest and next-nearest Ir atoms were found to be similar in both structures: 2.36 +/- 0.01 angstrom and 3.33 +/- 0.01 angstrom, respectively. The buckling in the second substrate layer is consistent with other structural studies for S adsorption on fcc{100} transition metal surfaces: 0.09 angstrom for p(2 x 2)-S and 0.02 angstrom for c(2 x 2)-S structures. The (1 x 5) reconstruction, which is the most stable phase for clean Ir{100}, is completely lifted and a c(2 x 2)-S overlayer is formed after exposure to H,S at 300 K followed by annealing to 520 K. CO temperature-programmed desorption (TPD) experiments indicate that the major factor in the poisoning of Ir by S is site blocking. (c) 2005 Elsevier B.V. All rights reserved.

The geometry of optimal control solutions on some six dimensional lie groups

This paper examines optimal solutions of control systems with drift defined on the orthonormal frame bundle of particular Riemannian manifolds of constant curvature. The manifolds considered here are the space forms Euclidean space E-3, the spheres S-3 and the hyperboloids H-3 with the corresponding frame bundles equal to the Euclidean group of motions SE(3), the rotation group SO(4) and the Lorentz group SO(1,3). The optimal controls of these systems are solved explicitly in terms of elliptic functions. In this paper, a geometric interpretation of the extremal solutions is given with particular emphasis to a singularity in the explicit solutions. Using a reduced form of the Casimir functions the geometry of these solutions are illustrated.

The surface geometry of carbonmonoxide and hydrogen co-adsorbed on Ni 111

A combination of photoelectron spectroscopy, temperature programmed desorption and low energy electron diffraction structure determinations have been applied to study the p(2 x 2) structures of pure hydrogen and co-adsorbed hydrogen and CO on Ni {111}. In agreement with earlier work atomic hydrogen is found to adsorb on fcc and hcp sites in the pure layer with H-Ni bond lengths of 1.74Angstrom. The substrate interlayer distances, d(12) = 2.05Angstrom and d(23) = 2.06Angstrom, are expanded with respect to clean Ni {111} with buckling of 0.04Angstrom in the first layer. In the co-adsorbed phase Co occupies hcp sites and only the hydrogen atoms on fcc sites remain on the surface. d(12) is even further expanded to 2.08Angstrom with buckling in the first and second layer of 0.06 and 0.02Angstrom, respectively. The C-O, C-Ni, and H-Ni bond lengths are within the range of values also found for the pure adsorbates.

The surface geometry of carbon monoxide and oxygen co-adsorbed on Ni{111}

Low energy electron diffraction (LEED) structure determinations have been performed for the p(2 x 2) structures of pure oxygen and oxygen co-adsorbed with CO on Ni{111}. Optimisation of the non-geometric parameters led to very good agreement between experimental and theoretical IV-curves and hence to a high accuracy in the structural parameters. In agreement with earlier work atomic oxygen is found to adsorb on fee sites in both structures. In the co-adsorbed phase CO occupies atop sites. The positions of the substrate atoms are almost identical, within 0.02 Angstrom, in both structures, implying that the interaction with oxygen dominates the arrangement of Ni atoms at the surface.

Fractal geometry of aggregate snowflakes revealed by triple wavelength radar measurements

Radar reflectivity measurements from three different wavelengths are used to retrieve information about the shape of aggregate snowflakes in deep stratiform ice clouds. Dual-wavelength ratios are calculated for different shape models and compared to observations at 3, 35 and 94 GHz. It is demonstrated that many scattering models, including spherical and spheroidal models, do not adequately describe the aggregate snowflakes that are observed. The observations are consistent with fractal aggregate geometries generated by a physically-based aggregation model. It is demonstrated that the fractal dimension of large aggregates can be inferred directly from the radar data. Fractal dimensions close to 2 are retrieved, consistent with previous theoretical models and in-situ observations.