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.

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.

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.

(S,N)-implications on bounded lattices

Since the birth of the fuzzy sets theory several extensions have been proposed. For these extensions, different sets of membership functions were considered. Since fuzzy connectives, such as conjunctions, negations and implications, play an important role in the theory and applications of fuzzy logics, these connectives have also been extended. An extension of fuzzy logic, which generalizes the ones considered up to the present, was proposed by Joseph Goguen in 1967. In this extension, the membership values are drawn from arbitrary bounded lattices. The simplest and best studied class of fuzzy implications is the class of (S,N)-implications, and in this chapter we provide an extension of (S,N)-implications in the context of bounded lattice valued fuzzy logic, and we show that several properties of this class are preserved in this more general framework.

Experimental and theoretical investigation of compression of a cylinder using a rotating platen

A rig was constructed to carry out compression of an aluminum cylinder with a monotonically rotating platen. The tests carried out showed that the compression load decreased and the side wall bulge severity reduced when the die was rotated. Not all the work supplied by the rotating dies was transferred to the work-piece; circumferential slippage was frequently observed at the die/material interface. This slippage was quantified by comparing measurements made during interrupted testing with the angular velocity of the die. A compound velocity field based on an exponential cusp description of the barreling was employed in an upper bound analysis. An approximate analytical solution was obtained for the degree of barreling and the compression pressure. The model is able to reproduce the decrease in barreling and compression loads with increasing die rotation.

Stress analysis of compression of aluminium with rotating tools

Compression tests carried out on aluminium specimens showed that when the die was rotated the compression load dropped. A slab method is employed to examine this process. The load reduction is explained by the deviation of friction vector due to the relative circumferential movement between the die and the material. This mechanism is incorporated into a theoretical model and an expression is derived for compression pressure. Analytical solutions established compare favourably with experimental results. It is also shown that there is a limitation to the load reduction: the compressive load can never be lower than 70 percent of the yield limit.

Hyperstereopsis in helmet-mounted NVDs : slope perception

Modern helmet-mounted night vision devices, such as the Thales TopOwl helmet, project imagery from intensifiers mounted on the sides of the helmet onto the helmet faceplate. This produces a situation of hyperstereopsis in which binocular disparities are magnified. This has the potential to distort the perception of slope in depth (an important cue to landing), because the slope cue provided by binocular disparity conflicts with veridical cues to slope, such as texture gradients and motion parallax. In the experiments, eight observers viewed sparse and dense textured surfaces tilted in depth under three viewing conditions: normal stereo hyper-stereo (4 times magnification), and hypostereo (1 / 4 magnification). The surfaces were either stationary, or rotated slowly around a central vertical axis. Stimuli were projected at 6 metres to minimise conflict between accommodation and convergence, and stereo viewing was provided by a Z-screen and passive polarised glasses. Observers matched perceived visual slope using a small tilt table set by hand. We found that slope estimates were distorted by hyperstereopsis, but to a much lesser degree than predicted by disparity magnification. The distortion was almost completely eliminated when motion parallax was present.

Influences of steady and cyclic die rotation on the compression of aluminium

A series of experiments are reported for compression of an aluminum cylinder with monotonic and cyclic die rotation. When the die is monotonically rotated, a higher angular velocity or a lower compression speed of the tool leads to a greater load reduction in comparison of that seen with a stationary die. The test results also show that cyclic die rotation causes a cyclic fluctuation in the load-displacement curve. During the die deceleration phase, the compression load increases until it reaches the level obtained in conventional compression with stationary dies. However, the compression load is observed to reduce to levels lower than those obtained in monotonic rotating compression tests during the die acceleration phase. The frequency of rotating direction change seems to affect the position of load peaks only, not the amplitude of the peaks.

Spatial memory in a food storing corvid I. Near tall landmarks are primarily used

This work suggests how food storing corvids use spatial memory to relocate caches, and how they can do this after some landmarks surrounding caches have become hidden due to leaf fall, snow fall or plant growth. Experiments involved training European jays (Garrulus glandarius) to find buried food, the location of which was specified by an array of 12 landmarks. Tests were then performed with the array rotated, or with certain landmarks removed from the array. The.main findings were: (1) birds primarily remembered the position of the goal using the near tall landmarks (15-30 cm from the goal and 20 cm high); (2) birds obtained a sense of direction both from the landmark array and something external to the array; (3) birds did not use smell or marks in the surface of the ground to find the goal. Memory of near tall landmarks is likely to be functional for these birds since (a) nearer landmarks provide a more accurate fix, and (b) taller landmarks are less likely to be completely obscured by snow fall, leaf fall or intervening vegetation. The work also demonstrates the use of G.I.S. software for the analysis and representation of animal search patterns.

Fine structure of shear bands formed during hot deformation of two austenitic steels

Shear bands formed during both cold and hot plastic deformation have been linked with several proposed mechanisms for the formation of ultrafine grains. The aim of the present work was to undertake a detailed investigation of the microstructural and crystallographic characteristics of the shear bands formed during hot deformation of a 22Cr-19Ni-3Mo (mass%) austenitic stainless steel and a Fe-30 mass%Ni based austenitic model alloy. These alloys were subjected to deformation in torsion and plane strain compression (PSC), respectively, at temperatures of 900°C and 950°C and strain rates of 0.7s_-1 and 10s_-1, respectively. Transmission electron microscopy and electron backscatter diffraction in conjunction with scanning electron microscopy were employed in the investigation. It has been observed that shear bands already started to form at moderate strains in a matrix of pre-existing microbands and were composed of fine, slightly elongated subgrains (fragments). These bands propagated along a similar macroscopic path and the subgrains, present within their substructure, were rotated relative to the surrounding matrix about axes approximately parallel to the sample radial and transverse directions for deformation in torsion and PSC, respectively. The subgrain boundaries were largely observed to be non-crystallographic, suggesting that the subgrains generally formed via multiple slip processes. Shear bands appeared to form through a co-operative nucleation of originally isolated subgrains that gradually interconnected with the others to form long, thin bands that subsequently thickened via the formation of new subgrains. The observed small dimensions of the subgrains present within shear bands and their large misorientations clearly indicate that these subgrains can serve as potent nucleation sites for the formation of ultrafine grain structures during both subsequent recrystallisation, as observed during the present PSC experiments, and phase transformation.

EBSD study of the orientation dependence of substructure characteristics in a model Fe-30wt%Ni alloy subjected to hot deformation

The aim of the present investigation was to determine the orientation dependence of substructure characteristics in an austenitic Fe−30wt%Ni model alloy subjected to hot plane strain compression. Deformation was carried out at a temperature of 950 °C using a strain rate of 10 s^₋₁ to equivalent strain levels of approximately 0.2, 0.4, 0.6 and 0.8. The specimens obtained were analysed using a fully automatic electron backscatter diffraction technique. The crystallographic texture was characterized for all the strain levels studied and the subgrain structure was quantified in detail at a strain of 0.4. The substructure characteristics displayed pronounced orientation dependence. The major texture components, namely the copper, S, brass, Goss and rotated Goss, generally contained one or two prominent families of parallel larger-angle extended subboundaries, the traces of which on the longitudinal viewing plane appeared systematically aligned along the {111} slip plane traces, bounding long microbands subdivided into slightly elongated subgrains by short lower-angle transverse subboundaries. Relatively rare cube-orientated grains displayed pronounced subdivision into coarse deformation bands containing large, low-misorientated subgrains. The misorientation vectors across subboundaries largely showed a tendency to cluster around the sample transverse direction. Apart from the rotated Goss texture component, the stored energy levels for the remaining components were principally consistent with the corresponding Taylor factor values.