101 results for Report, 1997

  • Recent Developments in Organic Food Production in New Zealand: Part 2: Kiwifruit in the Bay of Plenty

    Campbell, Hugh; Fairweather, John; Steven, David (1997)

    Report
    University of Otago

    This report presents the findings of research into the development of organic kiwifruit production in the Bay of Plenty. These results form the second of four case studies which constitute the Public Good Science Fund programme ‘Optimum Development of Certified Organic Horticulture in New Zealand’. The other case study regions are Canterbury (Campbell 1996), Gisborne (to be completed during 1997) and Nelson (to be completed by 1998). The primary objective of this report is to document developments in the organic export industry in the Bay of Plenty. Comparisons between Canterbury and the Bay of Plenty have occasionally been included in this report in order to provide more clarity about the development of organic production in the Bay of Plenty itself. While there is some discussion of the differences between Canterbury and the Bay of Plenty in the Conclusion, these are only brief. Full comparison of the regional factors influencing the development of organic exporting will be set aside until all four case studies have been completed.

    View record details
  • A Constructive Proof of Gleason's Theorem

    Richman, F; Bridges, D.S (1997-05)

    Report
    The University of Auckland Library

    Gleason's theorem states that any totally additive measure on the closed subspaces, or projections, of a Hilbert space of dimension greater than two is given by a positive operator of trace class. In this paper we give a constructive proof of that theorem. A measure μ on the projections of a real or complex Hilbert space assigns to each projection P a nonnegative real number μ(P) such that if σ = ∑Pi, where the Pi are mutually orthogonal, then μ(σ) =∑μ(Pi). Such a measure is determined by its values on the one-dimensional projections. Let W be the measure of the identity projection, and Px the projection onto the 1-dimensional space spanned by the unit vector x. Then the measure μ is determined by the real-valued function f(x) = μ(Px) on the unit sphere, a function which has the property that [see pdf for formula] for each orthonormal basis E. Gleason calls such a function f a frame function of weight W. If T is a positive operator of trace class, then f(x) = ‹Tx,x› is a frame function. Gleason's theorem is that every frame function arises in this way. The original reference for Gleason's theorem is [4], which can also be found in Hooker [6]. Cooke, Keane and Moran [3] gave a proof that is elementary in the sense that it does not appeal to the theory of representations of the orthogonal group, which the original proof does. However, some of the reasoning in [3] seems hopelessly nonconstructive, so we follow the general outline of [4] until we come to the end of the 3-dimensional real case, at which point we modify some arguments in [3] rather than attempt a constructive development of the necessary representation theory. Any Hermitian form B on a finite-dimensional inner product space gives rise to a frame function f(x) = B(x; x) whose weight is equal to the trace of the matrix of B. The essence of Gleason's theorem is the following converse. -- from Introduction

    View record details
  • A Genius' Story: Two Books on Godel

    Calude, C.S (1997-06)

    Report
    The University of Auckland Library

    Undoubtly, Gödel was the greatest logician of the twentieth century. There is no trace of exaggeration in saying, following Wang, that Gödel's contribution to mathematics has the same status as Freudian psychology, Einstein's theory of relativity, Bohr's principle of complementarity, Heisenberg's uncertainty principle, keynesian economics, and Watson and Crick double helix model of DNA. Yet, with a few notable exceptions, most of the personal details of Gödel's life remained a mystery

    View record details
  • Clusters of Two Player Games and Restricted Determinacy Theorem

    Khoussainov, B; Yakhnis, A; Yakhnis, V (1997-05)

    Report
    The University of Auckland Library

    We introduce a new notion of a cluster of infinite two player games between players 0 and 1. This is an infinite collection of games whose game trees can be composed into a graph which is similar to a tree except that the graph might not have the initial node. For each node of the graph there is an ancesstor node. We call this graph the arena of the cluster. For a game cluster we introduce a notion of a winner for the whole cluster. This notion is weaker than the requirement to win every game of the cluster. Any two player game can be viewed as a game cluster consisting of all its residual games [3, 18]. We extend the restricted memory determinacy (RMD) theorem of Gurevich-Harrington (GH), [3] to game clusters. We think that the notion of a game cluster improves the modeling power of two player games used to give semantics for concurrent processes [10, 11].

    View record details
  • Imprecise Reasoning about Geographic Information

    Guesgen, H.W (1997-09)

    Report
    The University of Auckland Library

    This report summarizes preliminary work on a framework for imprecise reasoning about spatial information, in particular spatial information in geographic information systems. It is based on papers previously published by Jonathan Histed, Ute Lörch, David Poon, and the author. Geographic information systems have gained an increasing interest over the recent years. However, their abilities are restricted in that they usually reason about precise quantitative information only, which means that they fail whenever exact matches cannot be found. They do not allow for any form of reasoning with imprecision. In this report, we describe a way of incorporating imprecise qualitative spatial reasoning with quantitative reasoning in geographic information systems. In particular, we show how tessellation data models can be extended to allow for qualitative spatial reasoning. The idea is to associate qualitative information with fuzzy sets whose membership grades are computed by applying the concept of proximity. In addition, we will show how images like geographic maps or satellite images can be analyzed by computing the distances between given reference colors and the colors that occur in the image, and how the results of this analysis can be used in the fuzzy spatial reasoner.

    View record details
  • DNA Computing Based on Splicing: Universality Results

    Paun, G (1997-12)

    Report
    The University of Auckland Library

    First, we recall some characterizations of recursively enumerable languages by means of finite H systems with certain regulations on the splicing operation. Then, we consider a variant of the splicing operation where the splicing proceeds always in couples of steps: the two strings obtained after a splicing enter immediately a second splicing (the rules used in the two steps are not prescribed). Somewhat surprising if we take into account the loose control on the performed operations, extended H systems with finite sets of axioms and of splicing rules, using this double splicing operation, can again characterize the recursively enumerable languages. Finally, we consider two types of distributed H systems: communicating distributed H systems and time-varying distributed H systems. For the first type of devices, we give a new proof of the recent result of [24] that (in the extended case) such systems with three components characterize the recursively enumerable languages. In what concerns the second mentioned distributed model, we prove that time-varying H systems with seven components can characterize the recursively enumerable languages. The optimality of these two last mentioned results is open.

    View record details
  • Effective Presentability of Boolean Algebras of Cantor-Bendixson Rank 1

    Downey, R.G; Jockusch Jr, C.G (1997-08)

    Report
    The University of Auckland Library

    We show that there is a computable Boolean algebra B and a computably enumerable ideal I of B such that the quotient algebra B=I is of Cantor-Bendixson rank 1 and is not isomorphic to any computable Boolean algebra. This extends a result of L. Feiner and is deduced from Feiner's result even though Feiner's construction yields a Boolean algebra of infinite Cantor-Bendixson rank.

    View record details
  • Cooperating Distributed Splicing Systems

    Martin-Vide, C; Paun, G (1997-12)

    Report
    The University of Auckland Library

    We introduce a new class of cooperating distributed H systems which consist of a given set of splicing systems (sets of splicing rules plus sets of axioms), similar in form to the cooperating distributed grammar systems. By applying iteratively the components of such a system (starting from a given initial string), in a sequence which runs nondeterministically, in such a way that a step is considered correctly finished only if no more splicing is possible, we obtain a language. Somewhat surprisingly if we take into account the loose control on the operations we carry out, a characterization of recursively enumerable languages is obtained, by mechanisms as above with only three components. We also characterize the recursively enumerable languages by cooperating distributed H systems with the components containing at most three splicing rules (in this case the number of components is no longer bounded).

    View record details
  • Deterministic Incomplete Automata: Simulation, Universality and Complementarity

    Calude, E; Lipponen, M (1997-06)

    Report
    The University of Auckland Library

    We study finite deterministic incomplete automata without initial states. This means that at any stage of a computation there is at most one transition to the next state. We will first investigate how two incomplete automata can simulate each other. Further on we construct an incomplete automaton which simulates a given automaton S and has the minimum number of states compared to any other automaton simulating S. Finally, we study Moore's uncertainty principles for incomplete automata. In contrast with the case of complete automata, it is possible to construct incomplete three-state automata displaying both types of complementarity.

    View record details
  • The Effective Riemann Mapping Theorem

    Hertling, P (1997-11)

    Report
    The University of Auckland Library

    The main results of the paper are two effective versions of the Riemann mapping theorem. The first, uniform version is based on the constructive proof of the Riemann mapping theorem by Bishop and Bridges and formulated in the computability framework developed by Kreitz and Weihrauch. It states which topological information precisely one needs about a nonempty, proper, open, connected, and simply connected subset of the complex plane in order to compute a description of a holomorphic bijection from this set onto the unit disk, and vice versa, which topological information about the set can be obtained from a description of a holomorphic bijection. The second version, which is derived from the first by considering the sets and the functions with computable descriptions, characterizes the subsets of the complex plane for which there exists a computable holomorphic bijection onto the unit disk. This solves a problem posed by Pour-El and Richards. We also show that this class of sets is strictly larger than a class of sets considered by Zhou, which solves an open problem posed by him. In preparation, recursively enumerable open subsets and closed subsets of Euclidean spaces are considered and several effective results in complex analysis are proved.

    View record details
  • Adjoints, Absolute Values and Polar Decompostions

    Bridges, D.S; Richman, F; Schuster, P (1997-11)

    Report
    The University of Auckland Library

    Various questions about adjoints, absolute values and polar decompositions of operators are addressed from a constructive point of view. The focus is on bilinear forms. Conditions are given for the existence of an adjoint, and a general notion of a polar decomposition is developed. The Riesz representation theorem is proved without countable choice.

    View record details
  • Small Trivalent Graphs of Large Girth

    Conder, M (1997-06)

    Report
    The University of Auckland Library

    Definitions are given for seven trivalent Cayley graphs, of girths 17; 18; 20; 21; 22; 23 and 24. At the time of writing (June 1997) each of these is the smallest known trivalent graph of the corresponding girth.

    View record details
  • An Explicit Construction of a Universal Extended H System

    Alford, G (1997-08)

    Report
    The University of Auckland Library

    Lately there has been much interest concerning H systems, a generative mechanism based on the splicing operation, itself a language-theoretic equivalent of DNA recombination. Păun et al. have shown that regular extended H systems are theoretically universal but one has not yet been explicitly constructed. In this paper we explicitly construct a universal extended H system containing 182 axioms and 270 groups of rules.

    View record details
  • On Initial Segments of Computable Linear Orders

    Coles, R.J; Downey, R.G; Khoussainov, B (1997-03)

    Report
    The University of Auckland Library

    We show there is a computable linear order with a π02 initial segment that is not isomorphic to any computable linear order.

    View record details
  • Games with Unknown Past

    Khoussainov, B; Yakhnis, A; Yakhnis, V (1997-08)

    Report
    The University of Auckland Library

    We define a new type of two player game occurring on a tree. The tree may have no root and may have arbitrary degrees of nodes. These games extend the class of games considered by Gurevich-Harrington in [5]. We prove that in the game one of the players has a winning strategy which depends on finite bounded information about the past part of a play and on future of each play that is isomorphism types of tree nodes. This result extends further the Gurevich- Harrington (GH) determinacy theorem from [5].

    View record details
  • Minimal Deterministic Incomplete Automata

    Calude, E; Lipponen, M (1997-10)

    Report
    The University of Auckland Library

    We construct a minimal automaton for an output-incomplete Moore automa- ton. The approach is motivated by physical interpretation of seeing deterministic finite automata as models for elementary particles. When compared to some classical methods our minimal automaton is unique up to an isomorphism and preserves also the undefined or unspecified behaviour of the original automaton.

    View record details
  • The Constructive Implicit Function Theorem and Applications in Mechanics

    Bridges, D.S; Calude, C; Pavlov, B; Stefanescu, D (1997-11)

    Report
    The University of Auckland Library

    We examine some ways of proving the Implicit Function Theorem and the Inverse Function Theorem within Bishop's constructive mathematics. Section 2 contains a new, entirely constructive proof of the Implicit Function Theorem. The paper ends with some comments on the application of the Implicit Function Theorem in classical mechanics

    View record details
  • Finite Nondeterministic Automata: Simulation and Minimality

    Calude, C.S; Calude, E; Khoussainov, B (1997 -09)

    Report
    The University of Auckland Library

    Motivated by recent applications of finite automata to theoretical physics, we study the minimization problem for nondeterministic automata (with outputs, but no initial states). We use Ehrenfeucht-Fraïsse-like games to model automata responses and simulations. The minimal automaton is constructed and, in contrast with the classical case, proved to be unique up to an isomorphism. Finally, we investigate the partial ordering induced by automata simulations. For example, we prove that, with respect to this ordering, the class of deterministic automata forms an ideal in the class of all automata.

    View record details
  • Practical Enumeration Methods for Graphs of Bounded Pathwidth and Treewidth

    Dinneen, Michael (1997-09)

    Report
    The University of Auckland Library

    Using an algebraic representation for graphs of bounded pathwidth or treewidth we provide simple methods for generating these families in increasing order of the number of vertices and edges. We also study canonic representions of fixed- and free- boundaried graphs of bounded width.

    View record details
  • Chaitin Omega Numbers and Strong Reducibilities

    Calude, C.S; Nies, A (1997-10)

    Report
    The University of Auckland Library

    We prove that any Chaitin Ω number (i.e., the halting probability of a universal self-delimiting Turing machine) is wtt-complete, but not tt-complete. In this way we obtain a whole class of natural examples of wtt-complete but not tt-complete r.e. sets. The proof is direct and elementary.

    View record details