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.

Beliefs, cultures, proliferation and use of nuclear weapons

This article demonstrates the centrality of mentality, culture, beliefs and historical lessons for nuclear prolifertion. Using the historical casestudies of Britain, France, and West Germany, it encourages researchers to look at the mentality/culture of potential proliferators rather than apply a culture-less "Realist" IR theory approach that assumes that desicion-makers the world over think like Bismarck.

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.

Pharmacological properties of purinergic receptors and their effects on proliferation and induction of neuronal differentiation of P19 embryonal carcinoma cells

We have used P19 embryonal carcinoma cells as in vitro model for early neurogenesis to study ionotropic P2X and metabotropic P2Y receptor-induced Ca2+ transients and their participation in induction of proliferation and differentiation. In embryonic P19 cells, P2Y(1), P2Y(2) and P2X(4) receptors or P2X-heteromultimers with similar P2X4 pharmacology were responsible for ATP and ATP analogue-induced Ca2+ transients. In neuronal-differentiated cells, P2Y(2), P2Y(6), P2X(2) and possibly P2X(2)/P2X(6) heteromeric receptors were the major mediators of the elevations in intracellular free calcium concentration [Ca2+](i). We have collected evidence for the involvement of metabotropic purinergic receptors in proliferation induction of undifferentiated and neural progenitor cells by using a BrdU-incorporation assay. ATP-, UTP-, ADP-, 2-MeS-ATP- and ADP-beta S-induced proliferation in P19 cells was mediated by P2Y, and P2Y2 receptors as judged from pharmacological profiles of receptor responses. ATP-provoked acceleration of neuronal differentiation, determined by analysis of nestin and neuron-specific enolase gene and protein expression, also resulted from P2Y, and P2Y2 receptor activation. Proliferation- and differentiation-induction involved the activation of inositol-trisphosphate sensitive intracellular Ca2+ stores. (C) 2008 ISDN. Published by Elsevier Ltd. All rights reserved.

Role of acetylcholine receptors in proliferation and differentiation of P19 embryonal carcinoma cells

Coordinated proliferation and differentiation of progenitor cells is the base for production of appropriate numbers of neurons and glia during neuronal development in order to establish normal brain functions. We have used murine embryonal carcinoma P19 cells as an in vitro model for early differentiation to study participation of nicotinic (nAChR) and muscarinic acetylcholine (mAChR) receptors in the proliferation of neural progenitor cells and their differentiation to neurons. We have previously shown that functional nicotinic acetylcholine receptors (nAChRs) already expressed in embryonic cells mediate elevations in cytosolic free calcium concentration ([Ca2+](i)) via calcium influx through nAChR channels whereas intracellular stores contribute to nAChR- and mAChR-mediated calcium fluxes in differentiated cells [Resende et al., Cell Calcium 43 (2008) 107-121]. In the present study, we have demonstrated that nicotine provoked inhibition of proliferation in embryonic cells as determined by BrdU labeling. However, in neural progenitor cells nicotine stimulated proliferation which was reversed in the presence of inhibitors of calcium mobilization from intracellular stores, indicating that liberation of intracellular calcium contributed to this proliferation induction. Muscarine induced proliferation stimulation in progenitor cells by activation of G alpha(q/11)-coupled M-1, M-3 and M-5 receptors and intracellular calcium stores, whereas G alpha(i/o)-protein coupled M-2 receptor activity mediated neuronal differentiation. (C) 2008 Elsevier Inc. All rights reserved.

EGFR is involved in control of gastric cell proliferation through activation of MAPK and Src signalling pathways in early-weaned rats

Objectives: Early weaning (EW) increases proliferation of the gastric epithelium in parallel with higher expression of transforming growth factor alpha and its receptor epidermal growth factor receptor (EGFR). The primary objective of the present study was to examine involvement of EGFR signalling in regulating mucosal cell proliferation during the early weaning period. Materials and methods: Fifteen-day-old rats were split into two groups: suckling (control) and EW, in which pups were separated from the dam. Animals were killed daily until the 18th day, 3 days after onset of treatment. To investigate the role of EGFR in proliferation control, EW pups were injected with AG1478, an EGFR inhibitor; signalling molecules, proliferative indices and cell cycle-related proteins were evaluated. Results: EW increased ERK1/2 and Src phosphorylation at 17 days, but p-Akt levels were unchanged. Moreover, at 17 days, AG1478 administration impaired ERK phosphorylation, whereas p-Src and p-Akt were not altered. AG1478 treatment reduced mitotic and DNA synthesis indices, which were determined on HE-stained and BrdU-labelled sections. Finally, AG1478 injection decreased p21 levels in the gastric mucosa at 17 days, while no changes were detected in p27, cyclin E, CDK2, cyclin D1 and CDK4 concentrations. Conclusions: EGFR is part of the mechanism that regulates cell proliferation in rat gastric mucosa during early weaning. We suggest that such responses might depend on activation of MAPK and/or Src signalling pathways and regulation of p21 levels.

Periodic geodesics and geometry of compact Lorentzian manifolds with a Killing vector field

We study the geometry and the periodic geodesics of a compact Lorentzian manifold that has a Killing vector field which is timelike somewhere. Using a compactness argument for subgroups of the isometry group, we prove the existence of one timelike non self-intersecting periodic geodesic. If the Killing vector field is nowhere vanishing, then there are at least two distinct periodic geodesics; as a special case, compact stationary manifolds have at least two periodic timelike geodesics. We also discuss some properties of the topology of such manifolds. In particular, we show that a compact manifold M admits a Lorentzian metric with a nowhere vanishing Killing vector field which is timelike somewhere if and only if M admits a smooth circle action without fixed points.

Fuzzy Logic and Geostatistical Techniques for Spatialization of Soil Texture in Region with Rough Terrains

From the geotechnical standpoint, it is interesting to analyse the soil texture in regions with rough terrain due to its relation with the infiltration and runoff processes and, consequently, the effect on erosion processes. The purpose of this paper is to present a methodology that provides the soil texture spatialization by using Fuzzy logic and Geostatistic. The results were correlated with maps drawn specifically for the study area. The knowledge of the spatialization of soil properties, such as the texture, can be an important tool for land use planning in order to reduce the potential soil losses during rain seasons. (c) 2011 Published by Elsevier Ltd. Selection and peer-review under responsibility of Spatial Statistics 2011

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.