Some remarks on the symplectic pairing on the moduli space of representations of the fundamental group of surfaces

This work grew out of an attempt to understand a conjectural remark made by Professor Kyoji Saito to the author about a possible link between the Fox-calculus description of the symplectic structure on the moduli space of representations of the fundamental group of surfaces into a Lie group and pairs of mutually dual sets of generators of the fundamental group. In fact in his paper [3] , Prof. Kyoji Saito gives an explicit description of the system of dual generators of the fundamental group.

Facile C-O bond scission in alcohols on Zn surfaces

Interaction of methanol, ethanol, and 2-propanol with polycrystalline as well as (0001) surfaces of Zn has been investigated by photoelectron spectroscopy and vibrational energy loss spectroscopy. All the alcohols show evidence for the condensed species along with the chemisorbed species at 80 K. With increase in temperature to similar to 120 K, the condensed species desorbs, leaving the chemisorbed species which decomposes to give the alkoxy species. The alkoxy species is produced increasingly at lower temperatures as we go from methanol to 2-propanol, the 2-propoxy species occurring even at 80 K. The alkoxy species undergo C-O bond scission giving rise to a hydrocarbon species and oxygen. The C-O bond cleavage occurs at a relatively low temperature of similar to 150 K. The effect of preadsorbed oxygen is to stabilize the methoxy species and prevent C-O bond scission. On the other hand, coadsorption of oxygen with methanol favors the formation of the methoxy species and gives rise to hydrocarbon species arising from the C-O bond scission even at 80 K.

An algebraic theory of functional and multivalued dependencies in relational databases

Computation of the dependency basis is the fundamental step in solving the membership problem for functional dependencies (FDs) and multivalued dependencies (MVDs) in relational database theory. We examine this problem from an algebraic perspective. We introduce the notion of the inference basis of a set M of MVDs and show that it contains the maximum information about the logical consequences of M. We propose the notion of a dependency-lattice and develop an algebraic characterization of inference basis using simple notions from lattice theory. We also establish several interesting properties of dependency-lattices related to the implication problem. Founded on our characterization, we synthesize efficient algorithms for (a): computing the inference basis of a given set M of MVDs; (b): computing the dependency basis of a given attribute set w.r.t. M; and (c): solving the membership problem for MVDs. We also show that our results naturally extend to incorporate FDs also in a way that enables the solution of the membership problem for both FDs and MVDs put together. We finally show that our algorithms are more efficient than existing ones, when used to solve what we term the ‘generalized membership problem’.

Effect of chlorine on the adsorption of oxygen on Cu and Ag surfaces

Based on XPS and UVPS studies, it is shown that oxygen is preferentially adsorbed molecularly in the singlet state on Cu and Ag surfaces containing presorbed chlorine. Adsorption of chlorine on Cu and Ag surfaces containing presorbed atomic oxygen causes a disappearance of the oxygen. Extended Hückel calculations predict the observed behaviour.

Algebraic and geometric intersection numbers for free groups

We show that the algebraic intersection number of Scott and Swarup for splittings of free groups Coincides With the geometric intersection number for the sphere complex of the connected sum of copies of S-2 x S-1. (C) 2009 Elsevier B.V. All rights reserved.

Nanopatterning by solid-state dewetting on reconstructed ceramic surfaces

We demonstrate ordered array formation of Au nanoparticles by controlled solid-state dewetting of a metal film on stepped alumina substrates. In situ transmission electron microscopy studies reveal that the dewetting process starts with nucleation of ordered dry regions on the substrate. The chemical potential difference between concave and convex surface regions induces anisotropic metal diffusion leading to the formation of nanowires in the valleys. The nanowires fragment due to Rayleigh instability forming arrays of metal nanoparticles on the substrate. The length scale of reconstruction relative to the starting film thickness is an important parameter in controlling the spatial order of the nanoparticles.

Algebraic characterization of decentralized fixed modes

An input-output, frequency-domain characterization of decentralized fixed modes is given in this paper, using only standard block-diagram algebra, well-known determinantal expansions and the Binet-Cauchy formula.

Scanning electron microscopy study of worn Al-Si alloy surfaces

A pin-on-disc machine was used to wear Al-Si alloy pins under dry conditions. Unmodified and modified binary alloys and commercial multi-component alloys were tested. The surfaces of the worn alloys were examined by scanning electron microscopy to identify distinct topographical features to aid elucidation of the mechanisms of wear.

Interaction of carbon monoxide with transition metal surfaces

XPS studies of the interaction of carbon monoxide with surfaces of Fe, Co and Ni indicate that at 300 K, the disproportionation reaction is prominent up to exposures of 103 L giving rise to high surface concentrations of carbon. At higher exposures and higher temperatures, dissociation of carbon monoxide accompanied by the formation of surface oxide layers becomes more prominent. In the case of copper, disproportionation is prominent up to 104 L even at 500 K followed by dissociation at higher exposures. These results are also supported by Auger spectroscopic studies.

Algebraic design techniques for reliable stabilization

In this paper we study two problems in feedback stabilization. The first is the simultaneous stabilization problem, which can be stated as follows. Given plantsG_{0}, G_{1},..., G_{l}, does there exist a single compensatorCthat stabilizes all of them? The second is that of stabilization by a stable compensator, or more generally, a "least unstable" compensator. Given a plantG, we would like to know whether or not there exists a stable compensatorCthat stabilizesG; if not, what is the smallest number of right half-place poles (counted according to their McMillan degree) that any stabilizing compensator must have? We show that the two problems are equivalent in the following sense. The problem of simultaneously stabilizingl + 1plants can be reduced to the problem of simultaneously stabilizinglplants using a stable compensator, which in turn can be stated as the following purely algebraic problem. Given2lmatricesA_{1}, ..., A_{l}, B_{1}, ..., B_{l}, whereA_{i}, B_{i}are right-coprime for alli, does there exist a matrixMsuch thatA_{i} + MB_{i}, is unimodular for alli?Conversely, the problem of simultaneously stabilizinglplants using a stable compensator can be formulated as one of simultaneously stabilizingl + 1plants. The problem of determining whether or not there exists anMsuch thatA + BMis unimodular, given a right-coprime pair (A, B), turns out to be a special case of a question concerning a matrix division algorithm in a proper Euclidean domain. We give an answer to this question, and we believe this result might be of some independent interest. We show that, given twon times mplantsG_{0} and G_{1}we can generically stabilize them simultaneously provided eithernormis greater than one. In contrast, simultaneous stabilizability, of two single-input-single-output plants, g0and g1, is not generic.

O2- and O1- types of oxygen species on Ni and barium-dosed Ni and Cu surfaces

He II UPS and XPS study of oxygen adsorption on Ni and barium-dosed Ni and Cu surfaces at 300 K show two types of oxygen species which are assigned to O2- and O1- (ad).

Time dependence of effective slip on textured hydrophobic surfaces

In this paper, we present results on water flow past randomly textured hydrophobic surfaces with relatively large surface features of the order of 50 µm. Direct shear stress measurements are made on these surfaces in a channel configuration. The measurements indicate that the flow rates required to maintain a shear stress value vary substantially with water immersion time. At small times after filling the channel with water, the flow rates are up to 30% higher compared with the reference hydrophilic surface. With time, the flow rate gradually decreases and in a few hours reaches a value that is nearly the same as the hydrophilic case. Calculations of the effective slip lengths indicate that it varies from about 50 µm at small times to nearly zero or “no slip” after a few hours. Large effective slip lengths on such hydrophobic surfaces are known to be caused by trapped air pockets in the crevices of the surface. In order to understand the time dependent effective slip length, direct visualization of trapped air pockets is made in stationary water using the principle of total internal reflection of light at the water-air interface of the air pockets. These visualizations indicate that the number of bright spots corresponding to the air pockets decreases with time. This type of gradual disappearance of the trapped air pockets is possibly the reason for the decrease in effective slip length with time in the flow experiments. From the practical point of usage of such surfaces to reduce pressure drop, say, in microchannels, this time scale of the order of 1 h for the reduction in slip length would be very crucial. It would ultimately decide the time over which the surface can usefully provide pressure drop reductions. ©2009 American Institute of Physics

An eels study of water, methanol, formaldehyde and formic acid adsorbed on clean and oxygen-covered zinc(0001) surfaces

Water adsorbs molecularly on a clean Zn(0001) surface; on a surface covered with atomic oxygen, however, hydroxyl species is produced due to proton abstraction by the surface oxygen atoms. Methanol, molecularly adsorbed on a clean surface at 80 K, transforms to methoxy species above 110 K. On an atomic oxygen-covered surface, adsorbed methanol gives rise to methoxy species and water, the latter arising from proton abstraction. HCHO adsorbs molecularly at 80 K on both clean as well as oxygen-covered surfaces and polymerizes at higher temperatures. Formic acid does not adsorb on a clean Zn surface, but on an oxygen-covered surface gives rise to formate and hydroxyl species.

A combined XPS-UPS-EELS study of nitrogen adsorbed on clean and barium-promoted iron surfaces: The nature of the precursor to dissociation

For N2 on a clean Fe surface, the adsorbed precursor in a parallel orientation becomes predominant around 110 K, while at lower temperatures it coexists with a weakly adsorbed species. On a Ba-promoted Fe surface, however, N2 is present exclusively in the precursor state in the temperature range 80–150 K following moderate exposure. Besides exhibiting a low N-N stretching frequency of 1530 cm−1, the precursor shows a clear separation between the 5σ and 1π levels in the UPS; the precursor dissociates to give a nitridic species around 160 K.

Adsorption Of Methanol On The Surfaces Of Copper-Alloys - Ups And Eels Studies

Methanol adsorbs molecularly on the surfaces of Cu–Pd alloys at low temperatures and transforms to CH3O or CO on warming, depending upon the alloy composition. On oxygen presorbed Cu–Pd alloy surfaces, adsorption of methanol gives rise to H2O and H2CO. CH3OH adsorbed molecularly on the surfaces of Cu–Au alloys and CH3O is formed only at relatively high temperatures.