WEAK ISOMETRIES OF HAMMING SPACES

In this thesis we study weak isometries of Hamming spaces. These are permutations of a Hamming space that preserve some but not necessarily all distances. We wish to find conditions under which a weak isometry is in fact an isometry. This type of problem was first posed by Beckman and Quarles for Rn. In chapter 2 we give definitions pertinent to our research. The 3rd chapter focuses on some known results in this area with special emphasis on papers by V. Krasin as well as S. De Winter and M. Korb who solved this problem for the Boolean cube, that is, the binary Hamming space. We attempted to generalize some of their methods to the non-boolean case. The 4th chapter has our new results and is split into two major contributions. Our first contribution shows if n=p or p < n2, then every weak isometry of Hnq that preserves distance p is an isometry. Our second contribution gives a possible method to check if a weak isometry is an isometry using linear algebra and graph theory.

d-cube decompositions of K-n/K-m

Necessary conditions on n, m and d are given for the existence of an edge-disjoint decomposition of K-n\K-m into copies of the graph of a d-dimensional cube. Sufficiency is shown when d = 3 and, in some cases, when d = 2(t). We settle the problem of embedding 3-cube decompositions of K-m into 3-cube decompositions of K-n; where n greater than or equal to m.

La prévisibilité à long terme des rendements des actifs financiers: leur dépendance significative du carré et du cube du ratio dividende-prix.

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eHandbook cube logo source files

The source files and full sized renders of the main eHandbook 'cube' (both Photoshop and .png format). Created by David Davies and Dr Matt Jones.

Proyecto cube : una introducción a la geometría tridimensional.

Se presenta el proyecto CUBE, propuesta de trabajo donde se desarrolla una serie de actividades de introducción a la geometría analítica. El proyecto se divide en 2 partes; una relativa al guión de la película y otra derivada dirigida al desarrollo del currículo de cuarto de ESO en Geometría.

Minimum neighborhood in a generalized cube

Generalized cubes are a subclass of hypercube-like networks, which include some hypercube variants as special cases. Let theta(G)(k) denote the minimum number of nodes adjacent to a set of k vertices of a graph G. In this paper, we prove theta(G)(k) >= -1/2k(2) + (2n - 3/2)k - (n(2) - 2) for each n-dimensional generalized cube and each integer k satisfying n + 2 <= k <= 2n. Our result is an extension of a result presented by Fan and Lin [J. Fan, X. Lin, The t/k-diagnosability of the BC graphs, IEEE Trans. Comput. 54 (2) (2005) 176-184]. (c) 2005 Elsevier B.V. All rights reserved.

A comparison-based diagnosis algorithm tailored for crossed cube multiprocessor systems

Comparison-based diagnosis is an effective approach to system-level fault diagnosis. Under the Maeng-Malek comparison model (NM* model), Sengupta and Dahbura proposed an O(N-5) diagnosis algorithm for general diagnosable systems with N nodes. Thanks to lower diameter and better graph embedding capability as compared with a hypercube of the same size, the crossed cube has been a promising candidate for interconnection networks. In this paper, we propose a fault diagnosis algorithm tailored for crossed cube connected multicomputer systems under the MM* model. By introducing appropriate data structures, this algorithm runs in O(Nlog(2)(2) N) time, which is linear in the size of the input. As a result, this algorithm is significantly superior to the Sengupta-Dahbura's algorithm when applied to crossed cube systems. (C) 2004 Elsevier B.V. All rights reserved.

Diamond mining, rice farming, and a ‘Maggi cube’: a viable survivial strategy in rural Liberia?

Since the conclusion of its 14-year civil war in 2003, Liberia has struggled economically. Jobs are in short supply and operational infrastructural services, such as electricity and running water, are virtually nonexistent. The situation has proved especially challenging for the scores of people who fled the country in the 1990s to escape the violence and who have since returned to re-enter their lives. With few economic prospects on hand, many have elected to enter the artisanal diamond mining sector, which has earned notoriety for perpetuating the country's civil war. This article critically reflects on the fate of these Liberians, many of whom, because of a lack of government support, finances, manpower and technological resources, have forged deals with hired labourers to work artisanal diamond fields. Specifically, in exchange for meals containing locally grown rice and a Maggi (soup) cube, hired hands mine diamondiferous territories, splitting the revenues accrued from the sales of recovered stones amongst themselves and the individual ‘claimholder’ who hired them. Although this cycle—referred to here as ‘diamond mining, rice farming and a Maggi cube’—helps to buffer against poverty, few of the parties involved will ever progress beyond a subsistence level

Hamming and Reed-Solomon codes over certain rings

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Structural refinement and photoluminescence properties of irregular cube-like (Ca-1_Cu-x(x))TiO3 microcrystals synthesized by the microwave-hydrothermal method

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)