Limiting search cost distribution for the move-to-front rule with random request probabilities

Consider a list of n files whose popularities are random. The list is updated according to the move-to-front rule. When the induced Markov chain is at equilibrium, we explicitly compute the limiting distribution of the search-cost per item as n tends to infinity. The uniform distribution results in the largest search cost.     

Linearization of a class of non-linear systems modelled by multibond graphs

Based on non-linear systems described by multibond graphs, a procedure designed to present symbolic linearization of these multibond graphs, is presented in this paper. Firstly, a junction structure of a multibond graph with multiport gyrators that represent Eulerian junction structures is proposed. In addition, non-linear multiport resistors are considered. By knowing the non-linear causal paths and loops of the non-linear multibond graph, the linearization is obtained by two steps: (1) The original multibond graph on the nominal operating point is evaluated; (2) New and additional paths based on the non-linear causal paths and loops are included. The state space representation of the linearized multibond graph using the corresponding junction structure is presented. An advantage of this methodology is its ability to allow the user to define a nominal operating point in which the linearization will be carried out.

In order to apply the proposed methodology, two physical systems are modelled and linearized by multibond graphs: a synchronous generator and a two degrees of freedom PUMA. Simulation results of these non-linear and linearized systems are shown.     

Cocyclic two-circulant core Hadamard matrices

Journal of Algebraic Combinatorics - The two-circulant core (TCC) construction for Hadamard matrices uses two sequences with almost perfect autocorrelation to construct a Hadamard matrix. A...     

Pappus’ theorem and a construction of complex Kleinian groups with rich dynamics

Pappus’ theorem is used to produce and study discrete subgroups of PSL(3, ?) with very rich dynamics. We get an example of a subgroup of PSL(3, ?) which is not conjugate to any subgroup of PU(2, 1) nor to any subgroup of Aff(?²), its Kulkarni region of discontinuity is non-empty and its complement, the Kulkarni limit set, contains infinitely many complex projective lines in general position. This construction is based on a representation of the group SL(2, ?) in the projective group PSL(3, ?).     

On near-best discrete quasi-interpolation on a four-directional mesh

Spline quasi-interpolants are practical and effective approximation operators. In this paper, we construct QIs with optimal approximation orders and small infinity norms called near-best discrete quasi-interpolants which are based on Ω-splines, i.e. B-splines with octagonal supports on the uniform four-directional mesh of the plane. These quasi-interpolants are exact on some space of polynomials and they minimize an upper bound of their infinity norms depending on a finite number of free parameters. We show that this problem has always a solution, in general nonunique. Concrete examples of such quasi-interpolants are given in the last section.     

Glucose biosensor based on the layer-by-layer self-assembling of glucose oxidase and chitosan derivatives on a thiolated gold surface

This work examines in deep the analytical performance of an example of “first-generation” microdevices: capillary electrophoresis microchip (CE) with end-channel electrochemical detection (ED). A hydroquinone and arbutin separation strategically chosen as route involving pharmaceutical-clinical testing, public safety and food control scenes was carried out. The reproducibility of the unpinched electrokinetic protocol was carefully studied and the technical possibility of working indiscriminately and/or sequentially with both simple cross-injectors was also demonstrated using a real sample (R.S.D.'s less than 7%). The robustness of the injection protocol allowed checking the state of the microchip/detector coupling and following the extraction efficiency of the analyte from real sample. Separation variables such as pH, ionic strength and, separation voltage were also carefully assayed and optimized. Analyte screening was performed using borate buffer (pH 9, 60 mM) in less than 180 s in the samples studied improving dramatically the analysis times used for the same analytes on a conventional scale (15 min), with good precision (R.S.D.'s ranging 5-10%), accuracy (recoveries ranging 90-110%) and acceptable resolution (Rs ≥ 1.0).In addition, the excellent analytical performance of the overall analytical method indicated the quality of the whole analytical microsystem and allowed to introduce the definition of robustness for methodologies developed into the “lab-on-a-chip” scene.     

Surface modification of quarry stone by hexamethyldisiloxane plasma treatment

The surface of quarry stone was modified by continuous plasma polymerization of hexamethyldisiloxane. The hydrophilic surface of the quarry stone was made hydrophobic and impermeable to water. Three different reaction times were analyzed. All of them resulted in the formation of a homogenous layer on the quarry stone surface. Contact angle and FT‐IR analyses show that the hydrophobic character of the surface is due to methyl groups on the surface. The change in the contact angle with temperature and the wetting temperature (T_w) are also discussed. Copyright © 2007 John Wiley & Sons, Ltd.     

Surface correlation effects on gloss

A general expression for gloss within the scalar Kirchhoff's theory is derived in terms of the detector collecting angle, and two statistical parameters that characterize the surface roughness. Analytical expressions for gloss are derived for an exponential and a Gaussian correlation function, and numerical results for these and other quasi-exponential correlation functions are presented. It is shown that the incoherent contribution to gloss is significant in common polymeric surfaces. The latter implies that surface height correlations cannot be neglected in the evaluation of gloss. It is also shown that for a correlation function with a single characteristic length, gloss scales with the correlation length L_c in the same way as with the detector collecting angle. This fact can be used to determine L_c with a glossmeter, and an experimental method to achieve this is proposed. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1321–1334, 1998     

Determination of reactivity ratios for ethylene/α-olefin copolymerization catalysed by the C2H4[Ind]2ZrCl2/methylaluminoxane system

The present study reports values of reactivity ratios for ethylene/1-hexene, ethylene/1-octene and ethylene/1-decene copolymerizations promoted by C₂H₄[Ind]₂ZrCl₂/MAO. The comonomer reactivities are markedly influenced by the number of carbon atoms of the α-olefin. The ethylene/1-decene copolymerization depends on the concentration of α-olefin in the feed.