Minimum span frequency assignment problem on triangular lattices

This paper considers the Minimum Span Frequency Assignment Problem with Interference Graph on Triangular Grid (MSFAP-TG), a special case of the Minimum Span Frequency/Channel Assignment (MSFAP) for cellular systems and optical networks. The MSFAP-TG is interesting in its own right and thus worth studying. In this paper, we propose strong integer programming formulations for the MSFAP-TG and present polyhedral results on these formulations. In solving the MSFAP-TG, we implement these integer programs to obtain exact solutions. We also develop a heuristic for obtaining feasible solutions and upper bounds for the problems. With the use of these upper bounds, and a simple lower bound, the computation time of the exact algorithm can be improved substantially. The heuristic turns out to be quite good in terms of the quality of upper bounds and is extremely efficient in computation time. Last of all, we present new concepts for tackling large scale MSFAP-TGs.

Inverse opal gas sensors : Zn(II)-doped tin dioxide systems for low temperature detection of pollutant gases

Focusing here on the effects of zinc doping in a nanocrystalline matrix of tin dioxide, inverse opal prototype sensors are presented and extensively studied as superior candidates for gas sensing applications. Courtesy of factors including controlled porosity, enhanced surface to volume ratio and homogeneous dispersion of species in the crystalline lattice assured by the sol–gel technique, prototype sensors were prepared with high dopant ratios in a range of new compositions. Exploiting their high sensitivities to low-gas concentrations at low working temperatures, and thanks to the presented templated sol–gel approach, the prepared sensors open up new frontiers in compositional control over the sensing oxide materials, consequently widening the possibilities available in on-demand gas sensor synthesis.

Inverse opal structure of SnO2 and SnO2 : Zn for gas sensing

In the present work, we propose a low cost synthetic sol-gel route that allows to produce high quality oxide nanostructures with inverse opal architecture which, transferred on alumina substrates provided with Pt interdigitated contacts and heater, are tested as gas sensing devices. An opal template of sintered monodisperse polystyrene spheres was filled with alcoholic solutions of metal oxide precursors and transferred on the alumina substrate. The polystyrene template was removed by thermal treatment, leading to the simultaneous sintering of the oxide nanoparticles. Beside SnO₂, a binary oxide well known for gas sensing application, a Zn containing ternary solid solution (SnO₂:Zn, with Zn 10% molar content) was taken into account for sensor preparation. The obtained high quality macro and meso-porous structures, characterized by different techniques, were tested for pollutant (CO, NO₂) and interfering (methanol) gases, showing that very good detection can be reached through the increase of surface area offered by the inverse opal structure and the tailoring of the chemical composition. The electrical characterization performed on the tin dioxide based sensors shows an enhancement of the relative response towards NO₂ at low temperatures in comparison with conventional SnO₂ sensors obtained with sputtering technique. The addition of Zn increases the separation between the operating temperatures for reducing and oxidizing gases and results in a further enhancement of the selectivity to NO₂ detection.

Inverse opal nanoassemblies : novel architectures for gas sensors the SnO2:Zn case

A novel technique is here presented, based on inverse opal metal oxide structures for the production of high quality macro and meso-porous structures for gas sensing. Taking advantage of a sol-gel templated approach. different mixed semiconducting oxides with high surface area, commonly used in chemical sensing application, were synthesized. In this work we report the
comparison between SnO₂ and SnO₂:Zn. As witnessed by Scanning and Transmission Electron Microscopy (SEM and TEM) analyses and by Powder x-ray Diffraction (PX RD), highly ordered meso-porous structures were formed with oxide crystalline size never exceeding 20 nm . The filled templates. in form of thick films, were bound to allumina substrate with Pt interdigitated contacts
and Pt heater, through in situ calcination, in order to perform standard electrical characterization. Pollutant gases like CO and NO₂ and methanol. as interfering gas, were used for the targeted electrical gas tests. All samples showed low detection limits towards both reducing and oxidizing species in low temperature measurements. Moreover, the addition of high molar percentages of Zn( II) affected the beha viour of electrical response improv ing the se lecti vity of the proposed system.

Means on discrete product lattices

We investigate the problem of averaging values on lattices, and in particular on discrete product lattices. This problem arises in image processing when several color values given in RGB, HSL, or another coding scheme, need to be combined. We show how the arithmetic mean and the median can be constructed by minimizing appropriate penalties. We also discuss which of them coincide with the Cartesian product of the standard mean and median.

Synthesis, x-ray structure of ferrocene bearing Bis(Zn-cyclen) complexes and the selective electrochemical sensing of TpT

The new ligand, [Fc(cyclen)₂] (5) (Fc=ferrocene, cyclen=1,4,7,10-tetraazacyclododecane), and corresponding Zn^II complex receptor, [Fc{Zn(cyclen)(CH₃OH)}₂](ClO₄)₄ (1), consisting of a ferrocene moiety bearing one Zn^II-cyclen complex on each cyclopentadienyl ring, have been designed and prepared through a multi-step synthesis. Significant shifts in the ¹H NMR signals of the ferrocenyl group, cf. ferrocene and a previously reported [Fc{Zn(cyclen)}]²⁺ derivative, indicated that the two Zn^II-cyclen units in 1 significantly affect the electronic properties of the cyclopentadienyl rings. The X-ray crystal structure shows that the two positively charged Zn^II-cyclen complexes are arranged in a trans like configuration, with respect to the ferrocene bridging unit, presumably to minimise electrostatic repulsion. Both 5 and 1 can be oxidized in 1:4 CH₂Cl₂/CH₃CN and Tris-HCl aqueous buffer solution under conditions of cyclic voltammetry to give a well defined ferrocene-centred (Fc⁰/+) process. Importantly, 1 is a highly selective electrochemical sensor of thymidilyl(3′-5′)thymidine (TpT) relative to other nucleobases and nucleotides in Tris-HCl buffer solution (pH 7.4). The electrochemical selectivity, detected as a shift in reversible potential of the Fc⁰/+ component, is postulated to result from a change in the configuration of bis(Zn^II-cyclen) units from a trans to a cis state. This is caused by the strong 1:1 binding of the two deprotonated thymine groups in TpT to different Zn^II centres of receptor 1. UV-visible spectrophotometric titrations confirmed the 1:1 stoichiometry for the 1:TpT adduct and allowed the determination of the apparent formation constant of 0.89±0.10×10⁶ M⁻¹ at pH 7.4.

Macrocyclic Zn complexes for DNA detection

Researchers from Monash University have developed an electrocatalytic method based on a charge transport through DNA films, which allows detection of complementary over non-complementary and mismatched DNA sequences in fully hybridized duplexes.

Image reduction using means on discrete product lattices

We investigate the problem of averaging values on lattices, and in particular on discrete product lattices. This problem arises in image processing when several color values given in RGB, HSL, or another coding scheme, need to be combined. We show how the arithmetic mean and the median can be constructed by minimizing appropriate penalties, and we discuss which of them coincide with the Cartesian product of the standard mean and median. We apply these functions in image processing. We present three algorithms for color image reduction based on minimizing penalty functions on discrete product lattices.

Penalty functions over a cartesian product of lattices

In this work we present the concept of penalty function over a Cartesian product of lattices. To build these mappings, we make use of restricted dissimilarity functions and distances between fuzzy sets. We also present an algorithm that extends the weighted voting method for a fuzzy preference relation.

Defining Bonferroni means over lattices

In the face of mass amounts of information and the need for transparent and fair decision processes, aggregation functions are essential for summarizing data and providing overall evaluations. Although families such as weighted means and medians have been well studied, there are still applications for which no existing aggregation functions can capture the decision makers' preferences. Furthermore, extensions of aggregation functions to lattices are often needed to model operations on L-fuzzy sets, interval-valued and intuitionistic fuzzy sets. In such cases, the aggregation properties need to be considered in light of the lattice structure, as otherwise counterintuitive or unreliable behavior may result. The Bonferroni mean has recently received attention in the fuzzy sets and decision making community as it is able to model useful notions such as mandatory requirements. Here, we consider its associated penalty function to extend the generalized Bonferroni mean to lattices. We show that different notions of dissimilarity on lattices can lead to alternative expressions.

Negations generated by bounded lattices t-norms

From the birth of fuzzy sets theory, several extensions have been proposed changing the possible membership values. Since fuzzy connectives such as t-norms and negations have an important role in theoretical as well as applied fuzzy logics, these connectives have been adapted for these generalized frameworks. Perhaps, an extension of fuzzy logic which generalizes the remaining extensions, proposed by Joseph Goguen in 1967, is to consider arbitrary bounded lattices for the values of the membership degrees. In this paper we extend the usual way of constructing fuzzy negations from t-norms for the bounded lattice t-norms and prove some properties of this construction.

Effect of Zn concentration and grain size on prismatic slip in Mg-Zn binary alloys

Mg-Zn binary alloys with concentrations between 0 and 2.8wt% Zn have been prepared and processed via hot rolling and annealing to produce specimens with a strong basal texture and a range of grain sizes. These have been deformed in tension, a condition in which the deformation is dominated by prismatic slip. This data has been used to assess the Hall-Petch parameter as a function of Zn concentration for deformation dominated by prismatic slip. Pure magnesium showed non-linear Hall-Petch behaviour at large grain sizes, and this is compared to the values for prismatic slip measured on single crystals. The differences between critical resolved shear stress measurements made through single crystal, polycrystal and mathematical modelling techniques are also discussed.