The dependency diagram of a mixed integer linear programme

The Dependency Diagram of a Linear Programme (LP) shows how the successive inequalities of an LP depend on former inequalities, when variables are projected out by Fourier- Motzkin Elimination. This is explained in a paper referenced below. The paper, given here, extends the results to the Mixed Integer case (MILP). It is shown how projection of a MILP leads to a finite disjunction of polytopes. This is expressed as a set of inequalities (mirroring those in the LP case) augmented by correction terms with finite domains which are subject to linear congruences

The dependency diagram of a linear programme

The Dependency Diagram of a Linear Programme (LP) shows how the successive inequalities of an LP depend on former inequalities, when variables are projected out by Fourier–Motzkin Elimination. It is also explained how redundant inequalities can be removed, using the method attributed to Chernikov and to Kohler. Some new results are given. The procedure also leads to a transparent explanation of Farkas’ Lemma, LP Duality, the dual form of Caratheodory’s Theorem as well as generating all vertices and extreme rays of the Dual Polytope

The dependency diagram of a mixed integer linear programme

The Dependency Diagram of a Linear Programme (LP) shows how the successive inequalities of an LP depend on former inequalities, when variables are projected out by Fourier- Motzkin Elimination. This is explained in a paper referenced below. The paper, given here, extends the results to the Mixed Integer case (MILP). It is shown how projection of a MILP leads to a finite disjunction of polytopes. This is expressed as a set of inequalities (mirroring those in the LP case) augmented by correction terms with finite domains which are subject to linear congruences

Calculation of a lower bound ratchet limit part 2 : Application to a pipe intersection and dissimilar material join

In an accompanying paper in this issue a lower bound method based on Melan's theorem was derived and implemented into the Linear Matching Method ratchet analysis procedure. This paper presents a ratchet analysis of a pipe intersection subject to cyclic thermo-mechanical loading using the proposed numerical technique. This work is intended to demonstrate the applicability of the lower bound method to a structure commonly seen in industry and also to better understand the behaviour of this component when subjected to cyclic loading. The pipe intersection considered here has multiple materials with temperature dependent properties. Verification of the results is given via full elastic-plastic analysis in Abaqus

Nonlinear optical thresholding in a 4-Channel OCDMA system via two-photon absorption

We demonstrate the use of a Two-Photon Absorption based detector in an OCDMA system. This detector provides a significant performance improvement over standard linear detection

Exploring the concept of interaction computing through the discrete algebraic analysis of the Belousov–Zhabotinsky reaction

Interaction computing (IC) aims to map the properties of integrable low-dimensional non-linear dynamical systems to the discrete domain of finite-state automata in an attempt to reproduce in software the self-organizing and dynamically stable properties of sub-cellular biochemical systems. As the work reported in this paper is still at the early stages of theory development it focuses on the analysis of a particularly simple chemical oscillator, the Belousov-Zhabotinsky (BZ) reaction. After retracing the rationale for IC developed over the past several years from the physical, biological, mathematical, and computer science points of view, the paper presents an elementary discussion of the Krohn-Rhodes decomposition of finite-state automata, including the holonomy decomposition of a simple automaton, and of its interpretation as an abstract positional number system. The method is then applied to the analysis of the algebraic properties of discrete finite-state automata derived from a simplified Petri net model of the BZ reaction. In the simplest possible and symmetrical case the corresponding automaton is, not surprisingly, found to contain exclusively cyclic groups. In a second, asymmetrical case, the decomposition is much more complex and includes five different simple non-abelian groups whose potential relevance arises from their ability to encode functionally complete algebras. The possible computational relevance of these findings is discussed and possible conclusions are drawn

Electrochemistry of uranium in molten LiF–CaF2

This article is focused on the electrochemical behaviour of U ions in molten LiF–CaF2 (79–21 wt.%) eutectic. On aWelectrode, U(III) is reduced in one step to U metal and U(III) can be also oxidised to U(IV). Both systems were studied by cyclic and square wave voltammetry. Reversibility of both systems for both techniques was verified and number of exchanged electrons was determined, as well as diffusion coefficients for U(III) and U(IV). The results are in a good agreement with previous studies. On a Ni electrode,the depolarisation effect due to intermetallic compounds formation was observed. Electrorefining of U metal in a melt containing U and Gd ions was carried out using a reactive Ni electrode with promising results

A programme management approach for ensuring coherence in IS (higher) education

This paper examines IS higher education, concentrating on issues of ‘coherence’ in IS curricula. While curriculum coherence can be jeopardized by poor curriculum design, misalignment between module content and/or misalignment between module or course aims can cause serious coherence issues over time. Misalignment of this type is exacerbated by the traditional processes of curriculum (re)design, which rely heavily on the (singular) interpretation of highly abstract documents, such as module syllabi and course specifications – often produced by curriculum designers in isolation. To improve curriculum coherence, this paper examines the use of a programme management framework as a means of (a) ‘humanizing’ the abstract aims and goals of curricula schemes and (b) managing the delivery and evolution of curricula in relation to the stakeholders in the process of delivery. The practical use of the framework is examined in the context of a Masters-level course in ‘Information Systems Management’. An action research approach is used to demonstrate the practical utility of the framework in terms of (a) improving communication of curricula, (b) improving the coherence between modules and between modules and course and (c) removing content redundancy. Guidelines are presented that generalize the findings in order that key practices may be adopted by others