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 local adsorption geometry and electronic structure of alanine on Cu{110}

The adsorption of alanine on Cu {110} was studied by a combination of near edge X-ray absorption fine structure (NEXAFS) spectroscopy, X-ray photoelectron spectroscopy (XPS) and density functional theory (DFT). Large chemical shifts in the C 1s, N 1s, and O 1s XP spectra were found between the alanine multilayer and the chemisorbed and pseudo-(3 x 2) alaninate layers. From C, N, and O K-shell NEXAFS spectra the tilt angles of the carboxylate group (approximate to 26 degrees in plane with respect to [1 (1) over bar0] and approximate to 45 degrees out of plane) and the C-N bond angle with respect to [1 (1) over bar0] could be determined for the pseudo-(3 x 2) overlayer. Using this information three adsorption geometries could be eliminated from five p(3 x 2) structures which lead to almost identical heats of adsorption in the DFT calculations between 1.40 and 1.47 eV/molecule. Due to the small energy difference between the remaining two structures it is not unlikely that these coexist on the surface at room temperature. (c) 2006 Elsevier B.V. All rights reserved.

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.

Facile strategies for the synthesis and crystallization of linear trinuclear nickel(II)-Schiff base, complexes with carboxylate bridges: Tuning of coordination geometry and magnetic properties

Three new linear trinuclear nickel(II) complexes, [Ni-3(salpen)(2)(OAc)(2)(H2O)(2)]center dot 4H(2)O (1) (OAc = acetate, CH3COO-), [Ni-3(salpen)(2)(OBz)(2)] (2) (OBz=benzoate, PhCOO-) and [Ni-3(salpen)(2)(OCn)(2)(CH3CN)(2)] (4) (OCn = cinnamate, PhCH=CHCOO-), H(2)salpen = tetradentate ligand, N,N'-bis(salicylidene)-1,3-pentanediamine have been synthesized and characterized structurally and magnetically. The choice of solvent for growing single crystal was made by inspecting the morphology of the initially obtained solids with the help of SEM study. The magnetic properties of a closely related complex, [Ni-3(salpen)(2)(OPh)(2)(EtOH)] (3) (OPh = phenyl acetate, PhCH2COO-) whose structure and solution properties have been reported recently, has also been studied here. The structural analyses reveal that both phenoxo and carboxylate bridging are present in all the complexes and the three Ni(II) atoms remain in linear disposition. Although the Schiff base ligand and the syn-syn bridging bidentate mode of the carboxylate group remain the same in complexes 1-4, the change of alkyl/aryl group of the carboxylates brings about systematic variations between six- and five-coordination in the geometry of the terminal Ni(II) centres of the trinuclear units. The steric demand as well as hydrophobic nature of the alkyl/aryl group of the carboxylate is found to play a crucial role in the tuning of the geometry. Variable-temperature (2-300 K) magnetic susceptibility measurements show that complexes 1-4 are antiferromagnetically coupled (J = -3.2(1), -4.6(1). -3.2(1) and -2.8(1) cm(-1) in 1-4, respectively). Calculations of the zero-field splitting parameter indicate that the values of D for complexes 1-4 are in the high range (D = +9.1(2), +14.2(2), +9.8(2) and +8.6(1) cm(-1) for 1-4, respectively). The highest D value of +14.2(2) and +9.8(2) cm(-1) for complexes 2 and 3, respectively, are consistent with the pentacoordinated geometry of the two terminal nickel(II) ions in 2 and one terminal nickel(II) ion in 3. (C) 2009 Elsevier Ltd. 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.

Fractal quantization

A Fractal Quantizer is proposed that replaces the expensive division operation for the computation of scalar quantization by more modest and available multiplication, addition and shift operations. Although the proposed method is iterative in nature, simulations prove a virtually undetectable distortion to the naked eve for JPEG compressed images using a single iteration. The method requires a change to the usual tables used in JPEG algorithins but of similar size. For practical purposes, performing quantization is reduced to a multiplication plus addition operation easily programmed in either low-end embedded processors and suitable for efficient and very high speed implementation in ASIC or FPGA hardware. FPGA hardware implementation shows up to x15 area-time savingscompared to standars solutions for devices with dedicated multipliers. The method can be also immediately extended to perform adaptive quantization(1).

Perspex machine VII: The universal perspex machine

The perspex machine arose from the unification of projective geometry with the Turing machine. It uses a total arithmetic, called transreal arithmetic, that contains real arithmetic and allows division by zero. Transreal arithmetic is redefined here. The new arithmetic has both a positive and a negative infinity which lie at the extremes of the number line, and a number nullity that lies off the number line. We prove that nullity, 0/0, is a number. Hence a number may have one of four signs: negative, zero, positive, or nullity. It is, therefore, impossible to encode the sign of a number in one bit, as floating-, point arithmetic attempts to do, resulting in the difficulty of having both positive and negative zeros and NaNs. Transrational arithmetic is consistent with Cantor arithmetic. In an extension to real arithmetic, the product of zero, an infinity, or nullity with its reciprocal is nullity, not unity. This avoids the usual contradictions that follow from allowing division by zero. Transreal arithmetic has a fixed algebraic structure and does not admit options as IEEE, floating-point arithmetic does. Most significantly, nullity has a simple semantics that is related to zero. Zero means "no value" and nullity means "no information." We argue that nullity is as useful to a manufactured computer as zero is to a human computer. The perspex machine is intended to offer one solution to the mind-body problem by showing how the computable aspects of mind and. perhaps, the whole of mind relates to the geometrical aspects of body and, perhaps, the whole of body. We review some of Turing's writings and show that he held the view that his machine has spatial properties. In particular, that it has the property of being a 7D lattice of compact spaces. Thus, we read Turing as believing that his machine relates computation to geometrical bodies. We simplify the perspex machine by substituting an augmented Euclidean geometry for projective geometry. This leads to a general-linear perspex-machine which is very much easier to pro-ram than the original perspex-machine. We then show how to map the whole of perspex space into a unit cube. This allows us to construct a fractal of perspex machines with the cardinality of a real-numbered line or space. This fractal is the universal perspex machine. It can solve, in unit time, the halting problem for itself and for all perspex machines instantiated in real-numbered space, including all Turing machines. We cite an experiment that has been proposed to test the physical reality of the perspex machine's model of time, but we make no claim that the physical universe works this way or that it has the cardinality of the perspex machine. We leave it that the perspex machine provides an upper bound on the computational properties of physical things, including manufactured computers and biological organisms, that have a cardinality no greater than the real-number line.

Characterization and classification of tumor lesions using computerized fractal-based texture analysis and support vector machines in digital mammograms

Objective: This paper presents a detailed study of fractal-based methods for texture characterization of mammographic mass lesions and architectural distortion. The purpose of this study is to explore the use of fractal and lacunarity analysis for the characterization and classification of both tumor lesions and normal breast parenchyma in mammography. Materials and methods: We conducted comparative evaluations of five popular fractal dimension estimation methods for the characterization of the texture of mass lesions and architectural distortion. We applied the concept of lacunarity to the description of the spatial distribution of the pixel intensities in mammographic images. These methods were tested with a set of 57 breast masses and 60 normal breast parenchyma (dataset1), and with another set of 19 architectural distortions and 41 normal breast parenchyma (dataset2). Support vector machines (SVM) were used as a pattern classification method for tumor classification. Results: Experimental results showed that the fractal dimension of region of interest (ROIs) depicting mass lesions and architectural distortion was statistically significantly lower than that of normal breast parenchyma for all five methods. Receiver operating characteristic (ROC) analysis showed that fractional Brownian motion (FBM) method generated the highest area under ROC curve (A z = 0.839 for dataset1, 0.828 for dataset2, respectively) among five methods for both datasets. Lacunarity analysis showed that the ROIs depicting mass lesions and architectural distortion had higher lacunarities than those of ROIs depicting normal breast parenchyma. The combination of FBM fractal dimension and lacunarity yielded the highest A z value (0.903 and 0.875, respectively) than those based on single feature alone for both given datasets. The application of the SVM improved the performance of the fractal-based features in differentiating tumor lesions from normal breast parenchyma by generating higher A z value. Conclusion: FBM texture model is the most appropriate model for characterizing mammographic images due to self-affinity assumption of the method being a better approximation. Lacunarity is an effective counterpart measure of the fractal dimension in texture feature extraction in mammographic images. The classification results obtained in this work suggest that the SVM is an effective method with great potential for classification in mammographic image analysis.

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 interplay between geometry, electronic structure, and reactivity of Cu-Ni bimetallic (111) surfaces

The mutual influence of surface geometry (e.g. lattice parameters, morphology) and electronic structure is discussed for Cu-Ni bimetallic (111) surfaces. It is found that on flat surfaces the electronic d-states of the adlayer experience very little influence from the substrate electronic structure which is due to their large separation in binding energies and the close match of Cu and Ni lattice constants. Using carbon monoxide and benzene as probe molecules, it is found that in most cases the reactivity of Cu or Ni adlayers is very similar to the corresponding (111) single crystal surfaces. Exceptions are the adsorption of CO on submonolayers of Cu on Ni(111) and the dissociation of benzene on Ni/Cu(111) which is very different from Ni(111). These differences are related to geometric factors influencing the adsorption on these surfaces.

Adsorption and dissociation of benzene on bimetallic surfaces - the influence of surface geometry and electronic structure

This topical review discusses the influence of the surface geometry (e.g. lattice parameters and termination) and electronic structure of well-defined bimetallic surfaces on the adsorption and dissociation of benzene. The available data can be divided into two categories with combinations of non-transition metals and transition metals on the one side and combinations of two transition metals on the other. The main effect of non-transition metals in surface alloys is site blocking which can suppress chemisorption and dissociation of the molecules completely. When two transition metals are combined, the effects are less dramatic. They mainly affect the strength of the chemisorption bond and the degree of dissociation due to electronic and template effects.

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.