An algorithm to detect linearly separable clusters of binary patterns

The clusters of binary patterns can be considered as Boolean functions of the (binary) features. Such a relationship between the linearly separable (LS) Boolean functions and LS clusters of binary patterns is examined. An algorithm is presented to answer the questions of the type: “Is the cluster formed by the subsets of the (binary) data set having certain features AND/NOT having certain other features, LS from the remaining set?” The algorithm uses the sequences of Numbered Binary Form (NBF) notation and some elementary (NPN) transformations of the binary data.

An algorithm to detect linearly separable clusters of binary patterns

The clusters of binary patterns can be considered as Boolean functions of the (binary) features. Such a relationship between the linearly separable (LS) Boolean functions and LS clusters of binary patterns is examined. An algorithm is presented to answer the questions of the type: “Is the cluster formed by the subsets of the (binary) data set having certain features AND/NOT having certain other features, LS from the remaining set?” The algorithm uses the sequences of Numbered Binary Form (NBF) notation and some elementary (NPN) transformations of the binary data.

Designing Creativity Through Clusters - A periodisation of cluster discourse

The thesis focuses on one of the most dominant articulations of the relation between geographical place and development, clusters - internationally competing place-bound economic system of production in related industries. The dominant articulation of cluster discourse represents the subnational region as a system of production, and as a means for competitiveness for Western countries. Its reproduction in theories has become one of the most prolific exports of economic geography to other disciplines and for policymaking. By analysing cluster discourse the thesis traces how the languages and processes of globalization have over time altered the understandings of the relation between geographical place and the economy. It shows how in its latest incarnation of the cluster discourse, the language of mainstream economics is combined with ‘softer’ elements (e.g. community, learning, creativity) in the economic geographic discourse. This is typical for the idea of soft capitalism, wherein it is assumed that economic success emanates from soft characteristics, such as knowledge, learning and creativity, rather than straightforward technological or cost advantages. A reoccurring critique against the dominant understanding of the relationship between competitiveness and regions, as articulated in cluster discourse, has pinpointed the perspective’s inability to reconcile the respective and reciprocal roles of local standard of living with firm competitiveness. The thesis traces how such critique is increasingly appropriated through the fusion of the economic, social and cultural landscape into the language of capitalism. It shows how cluster discourse has appropriated its critique, by focusing on creativity, with its strong associations to arts, individual artists and the cultural sphere in general, while predominantly creating its meaning in relation to competitiveness. The thesis consists of six essays that each outlines the development of the cluster discourse. The essays show how meaning systems and strategies are created, accepted and naturalized in cluster discourse, how this affects individuals, the economic landscape and society at large, as well as showing which understandings are marginalized in the process. The thesis argues that clusters are a) inseparable from ideology and politics and b) they are the result of purposeful social practice. It calls for increased reflexivity within corporate and economic geographic research on clusters, and underlines the importance of placing issues of power at the centre of analysis.

A comparative study of the interaction of nickel clusters with buckminsterfullerene, C60, and graphite

Interaction of nickel deposited on multilayer films of C60 has been investigated in comparison with that on amorphized graphite by employing photoemission spectroscopy. It is shown that unlike with graphite, Ni interacts strongly with C60 causing large changes in C(1s) and C(2p) binding energies. The increase in the Ni(2p) binding energy at small Ni coverages is also far greater on c60 than on graphite.

An investigation of well-characterized small gold clusters by photoelectron spectroscopy, tunneling spectroscopy, and cognate techniques

After microscopic characterization of the size distributions of gold clusters, deposited on carbon substrates by vacuum evaporation or by soft landing, Au(4f') binding energy of the clusters has been measured as a function of the mean cluster size. Similar measurements have been carried out on Au clusters prepared from sols by chemical means and high-nuclearity cluster compounds. In general, small clusters with a mean diameter of $2 nm show significantly larger binding energies than the bulk metal value, due to the onset of nonmetallicity. Nonmetallicity manifests itself in terms of a tunneling conductance gap only in clusters of diameter ;5 1 nm containing 40 atoms or fewer.

A study of chemically prepared small metal clusters in the nonmetallic regime

Small gold clusters [mean diameter (d)[less, similar] 1.4 nm], unlike larger clusters, show a higher Au(4f) binding energy relative to the bulk value and the presence of a conductance gap in tunnelling measurements, just as the molecular cluster compound, Au55(PPh3)12Cl6; small platinum clusters show similar nonmetallic features.

Fascinating chemistry of metal clusters and carbon clusters (fullerenes)

Investigations of a variety of transition metal clusters by means of high-energy spectroscopies including BIS show the occurrence of a metal-insulator transition with decrease in the cluster size. The chemical reactivity of the clusters also varies significantly with the size. Among the many fascinating properties of the fullerenes C60 and C70, a noteworthy one is the interaction between metal clusters and fullerenes. Phase transitions of fullerenes involving orientational disorder and pressure-induced decrease in the band gap of C60 are other novel features of interest.

Dependence of the strength of interaction of carbon monoxide with transition metal clusters on the cluster size

The interaction of CO with Cu, Pd, and Ni at different coverages of the metals on solid substrates has been investigated by He II and core-level spectroscopies, after the nature of variation of the metal core-level binding energies with the coverage or the cluster size is established. The separation between the (1 pi + 5 sigma) and 4 sigma levels of CO increases with a decrease in the size of the metal clusters, accompanied by an increase in the desorption temperature. In the case of Cu, the intramolecular shakeup satellite of CO disappears on small clusters. More importantly, CO dissociates on small Ni clusters, clearly confirming that metal-CO interaction strength increases with a decrease in the cluster size.

Variations in the copper(I)-copper(I) distances in multinuclear clusters with identical coordination geometries. Short metal-metal contacts induced by oligomerization

Factors contributing to the variations in the Cu(I)-Cu(I) distances in two clusters with identical ligand and coordination geometries have been analyzed. While the hexamer, 4, exhibits metal-metal distances in the range 2.81-3.25 Angstrom, shorter contacts are found in the corresponding tetramer, 3 (2.60-2.77 Angstrom). EHT calculations reveal relatively little attractive interactions in the corresponding Cu-4(4+) and Cu-6(6+) cores. Introduction of the ligands lowers the reduced overlap populations between the metals further. MNDO calculations with model electrophiles have been carried out to determine the bite angle requirements of the ligands. These are satisfactorily met in the structures of both 3 and 4. The key geometric feature distinguishing 3 and 4 is the Cu-S-Cu angle involving the bridging S- unit. In 4, the corresponding angles are about 90 degrees, while the values in 3 are smaller (70-73 degrees). Wider angles are computed to be energetically favored and are characterized by an open three-center bond and a long Cu-Cu distance. The bridging angles are suggested to be primarily constrained by the mode of oligomerization. Implications of these results for the stability and reactivity of these clusters and for short metal-metal distances in d(10) systems in general are discussed.

A comparative study of the interaction of CO with Cu and Cu-Zn alloy clusters

Interaction of CO with Cu clusters deposited on a ZnO(0001) crystal and on ZnO/Zn surfaces (prepared in the electron spectrometer) has been examined by UV and X-ray photoelectron spectroscopy. The interaction is stronger with the small Cu clusters deposited on ZnO/Zn surfaces. Interaction of CO is evert stronger with annealed Cu/ZnO/Zn surfaces where Cu-Zn alloy particles are present. Copyright (C) 1996 Published by Elsevier Science Ltd

Metal-insulator transitions in metal clusters: a high-energy spectroscopy study of palladium and silver clusters

Bremsstrahlung isochromat spectroscopy (BIS) along with ultraviolet and X-ray photoelectron spectroscopy (UPS and XPS) has been employed to investigate the electron states of Pd and Ag deposited on amorphous graphite at different coverages. The metal core level binding energies increase with decreasing cluster size while the UPS valence bands show a decrease in the 4d states at E(F) accompanied by a shift in the intensity maximum to higher binding energies. BIS measurements show the emergence of new states closer to E(F) with increase in the cluster size. It is pointed out that the observed spectral shifts cannot be accounted for by final-state effects alone and that initial-state effects have a significant role. It therefore appears that a decrease in cluster size is accompanied by a metal-insulator transition.

Synthesis, Structures, and Magnetic Behavior of a Series of Copper(II) Azide Polymers of Cu-4 Building Clusters and Isolation of a New Hemiaminal Ether as the Metal Complex

Four new neutral copper azido polymers, Cu-4(N-3)(8)(L-1)(2)](n) (1), Cu-4(N-3)(8)(L-2)(2)](n) (2), Cu-4(N-3)(8)(L-3)(2)](n) (3), and Cu-9(N-3)(18)(L-4)(4)](n) (4) L1-4 are formed in situ by reacting pyridine-2-carboxaldehyde with 22-(methylamino)ethyl]pyridine (mapy, L-1), N,N-dimethylethylenediamine (N,N-dmen, L-2), N,N-diethylethylenediamine (N,N-deen, L-3), and N,N,2,2-tetramethylpropanediamine (N,N,2,2-tmpn, L-4)], have been synthesized by using 0.5 mol equiv of the chelating tridentate ligands with Cu-(NO3)(2)center dot 3H(2)O and an excess of NaN3. Single-crystal X-ray structures show that the basic unit of these complexes, especially 1-3, contains very similar Cu-4(II) building blocks. The overall structure of 3 is two-dimensional, while the other three complexes are one-dimensional in nature. Complex 1 represents a unique example containing hemiaminal ether arrested by copper(R). Complexes 1 and 2 have a rare bridging azido pathway: both end-on and end-to-end bridging azides between a pair of Cu-II centers. Cryomagnetic susceptibility measurements over a wide range of temperature exhibit dominant ferromagnetic behavior in all four complexes. Density functional theory calculations (B3LYP functional) have been performed on complexes 1-3 to provide a qualitative theoretical interpretation of their overall ferromagnetic behavior.

Inverse surface melting in confined clusters: Ar-13 in zeolite L

Monte Carlo and molecular dynamics simulations on an Ar-13 cluster in zeolite L have been carried out at a series of temperatures to understand the rigid-nonrigid transition corresponding to the solid-liquid transition exhibited by the free Ar-13 cluster. The icosahedral geometry of the free cluster is no longer preferred when the cluster is confined in the zeolite. The root-mean-squared pair distance fluctuation, delta, exhibits a sharp, well-defined rigid-nonrigid transition at 17 K as compared to 27 K for the free cluster. Multiple peaks in the distribution of short-time averages of the guest-host interaction energy indicate coexistence of two phases.; It is shown that this transition is associated with the inner atoms becoming mobile at 17 K even while the outer layer atoms, which are in close proximity to the zeolitic wall, continue to be comparatively immobile. This may be contrasted with the melting of large free clusters of 40 or more atoms which exhibit surface melting. Guest-host interactions seem to play a predominant role in determining the properties of confined clusters. We demonstrate that the volume of the cluster increases rather sharply at 17 and 27 K respectively for the confined and the free cluster. Power spectra suggest that the motion of the inner atoms is generally parallel to the atoms which form the cage wall.

Monte Carlo and molecular dynamics simulation of argon clusters andn-alkanes in the confined regions of zeolites

Geometry and energy of argon clusters confined in zeolite NaCaA are compared with those of free clusters. Results indicate the possible existence of magic numbers among the confined clusters. Spectra obtained from instantaneous normal mode analysis of free and confined clusters give a larger percentage of imaginary frequencies for the latter indicating that the confined cluster atoms populate the saddle points of the potential energy surface significantly. The variation of the percentage of imaginary frequencies with temperature during melting is akin to the variation of other properties. It is shown that confined clusters might exhibit inverse surface melting, unlike medium-to-large-sized free clusters that exhibit surface melting. Configurational-bias Monte Carte (CBMC) simulations of n-alkanes in zeolites Y and A are reported. CBMC method gives reliable estimates of the properties relating to the conformation of molecules. Changes in the conformational properties of n-butane and other longer n-alkanes such as n-hexane and n-heptane when they are confined in different zeolites are presented. The changes in the conformational properties of n-butane and n-hexane with temperature and concentration is discussed. In general, in zeolite Y as well as A, there is significant enhancement of the gauche population as compared to the pure unconfined fluid.