Version Of Construction Research Articles

Limits of quotients of bivariate real analytic functions

Necessary and sufficient conditions for the existence of limits of the form lim(x,y)→(a,b)f(x,y)/g(x,y) are given, under the hypothesis that f and g are real analytic functions near the point (a,b), and g has an isolated zero at (a,b). The given criterion uses a constructive version of Henselʼs Lemma which could be implemented in a computer algebra system in the case where f and g are polynomials with rational coefficients, or more generally, with coefficients in a real finite extension of the rationals. A high level description of an algorithm for determining the existence of the limit as well as its computation is provided.

Constructive version of Boolean algebra

The notion of overlap algebra introduced by G. Sambin provides a constructive version of complete Boolean algebra. Here we first show some properties concerning overlap algebras: we prove that the notion of overlap morphism corresponds classically to that of map preserving arbitrary joins; we provide a description of atomic set-based overlap algebras in the language of formal topology, thus giving a predicative characterization of discrete locales; we show that the power-collection of a set is the free overlap algebra join-generated from the set. Then, we generalize the concept of overlap algebra and overlap morphism in various ways to provide constructive versions of the category of Boolean algebras with maps preserving arbitrary existing joins.

Construct validity and case validity in assessment.

Clinical assessment relies on both construct validity, which focuses on the accuracy of conclusions about a psychological phenomenon drawn from responses to a measure, and case validity, which focuses on the synthesis of the full range of psychological phenomena pertaining to the concern or question at hand. Whereas construct validity is grounded in understanding causal influences of a distinct phenomenon on responses to various measures and life contexts, case validity encompasses the joint influences of multiple phenomena on individuals' responses. Two sets of distinctions essential to understanding psychological phenomena, hence to understanding construct validity, are (a) implicit and explicit versions of personality constructs and (b) ability and personality as versions of constructs measured by performance tests presenting maximal and typical conditions, respectively. Since both implicit and explicit versions of constructs interface with maximal or typical performance conditions, case validity requires systematic inclusion of these distinctions in assessment protocols.

A constructive version of Ky Fan's coincidence theorem

In this paper we examine Ky Fan's coincidence theorem from the point of view of Bishop style constructive mathematics using constructive versions of Kakutani's fixed point theorem, Berge's maximum theorem and the separating hyperplane theorem.

Modal logic and the approximation induction principle

We prove a compactness theorem in the context of Hennessy–Milner logic and use it to derive a sufficient condition on modal characterisations for the approximation induction principle to be sound modulo the corresponding process equivalence. We show that this condition is necessary when the equivalence in question is compositional with respect to the projection operators. Furthermore, we derive different upper bounds for the constructive version of the approximation induction principle with respect to simulation and decorated trace semantics.

Constructivist and structuralist foundations: Bishop’s and Lawvere’s theories of sets

Bishop’s informal set theory is briefly discussed and compared to Lawvere’s Elementary Theory of the Category of Sets (ETCS). We then present a constructive and predicative version of ETCS, whose standard model is based on the constructive type theory of Martin-Löf. The theory, CETCS, provides a structuralist foundation for constructive mathematics in the style of Bishop.

Elementary proof of constructive versions of the tangent direction theorem and the implicit function theorem

Elementary proof of constructive versions of the tangent direction theorem and the implicit function theorem

The intermediate value theorem in constructive mathematics without choice

In Bishop’s constructive mathematics without choice axioms, it seems that in order to construct an object you require it to satisfy some (strong) uniqueness property. As a consequence, it seems unlikely that the standard constructive version of the intermediate value theorem—requiring only the additional hypothesis that the function is locally nonzero—carries over to the setting of Bishop’s constructive mathematics without choice. We give a weaker version of the intermediate value theorem which does hold without choice; the uniqueness of the root constructed follows from it being minimal.

Analogical Matrices in Young Children and Students with Intellectual Disability: Reasoning by Analogy or Reasoning by Association?

Analogical reasoning (AR) is renowned for being a complex activity. Young children tend to reason by association, rather by analogy, and people with intellectual disability present problems of memorization. Both these populations usually show low performances in AR. The present author investigated whether familiar material and external memories could enable them to obtain better performances. Our computerized AR test uses a touch screen. The 2 × 2 matrices are composed of familiar pictures and relations, and declined in two versions. The classic version requires memorizing all the relations involved in order to discover the solution, whereas the construction version requires constructing the answer part by part by using external memories, which potentially unload the memory. Our results showed that people with intellectual disability reached lower performances than typically developing children in the classic version, but similar performances in the construction version. In addition, both these populations reasoned mostly by analogy and not by association.

Conjugacy in normal subgroups of hyperbolic groups

Let N be a finitely generated normal subgroup of a Gromov hyperbolic group G. We establish criteria for N to have solvable conjugacy problem and be conjugacy separable in terms of the corresponding properties of G/N. We show that the hyperbolic group from F. Haglund's and D. Wise's version of Rips's construction is hereditarily conjugacy separable. We then use this construction to produce first examples of finitely generated and finitely presented conjugacy separable groups that contain non-(conjugacy separable) subgroups of finite index.

Systems of dyadic cubes in a doubling metric space

A number of recent results in Euclidean Harmonic Analysis have exploited several adjacent systems of dyadic cubes, instead of just one fixed system. In this paper, we extend such constructions to general spaces of homogeneous type, making these tools available for Analysis on metric spaces. The results include a new (non-random) construction of boundedly many adjacent dyadic systems with useful covering properties, and a streamlined version of the random construction recently devised by H. Martikainen and the first author. We illustrate the usefulness of these constructions with applications to weighted inequalities and the BMO space; further applications will appear in forthcoming work.

The Effects of Constructive Learning Method on Students' Academic Achievement, Retention of Knowledge, Gender and Attitudes Towards Science Course in “Matter of Structure and Characteristics” Unit

Abstract The purpose of this research is to examine on students academic achievement, retention of knowledge and attitudes towards science course in matter of structural and characteristic subject with constructivist education version. This study was conducted with students 7/A (N=34) and 7/B (N=34) located in Ankara, during the spring period of 2008-2009 academic year. The study used a quasi-experimental research design with pre-test and post-test control group was used in this study. According to this research model achievement test and the scale of attitudes towards science were administered before and after instructional intervention. Achievement test were given both groups three months after intervention as retention test. Students in the control group were taught by traditional teaching method (narrative, question and answer, discussion, etc). The experimental group was taught constructive education besides traditional teaching method. The implementation was carried out in a four week period. After implementation, post-test (achievement test) was administered to both groups. The independent samples t-test was used to compare pretests and posttests of control and experimental groups.The findings of the study show that there is a significant difference in favour of the experimental group who taught by constructive education version over the control group regarding to averages of academic achievement scores. Achievement test scores of experimental group were found higher than the control group after instructional intervention. Results of the study showed no meaningful difference between the experiment and control group according to attitudes towards science course. It can be stated that the teaching method used in experimental group was more successful, thus students in experimental group was scored high in the achievement test for retention.

Revisiting the Viability Algorithm for Hybrid Systems Using Optimal Control

In this paper, we revisit the problem of approximating viability sets for hybrid systems with nonlinear continuous dynamics and competing inputs. As usual in the literature, an iterative algorithm, based on the alternating application of a continuous and a discrete operator, is employed. Three different cases, based on whether the continuous evolution and the number of discrete transitions are finite or infinite, are considered. A complete characterization of the reach-avoid computation (involved in the continuous time calculation) is provided based entirely on optimal control. Moreover, we show convergence of the iterative process by using a constructive version of Tarski's fixed point theorem, to determine the maximal fixed point of a monotone operator on a complete lattice of closed sets. To illustrate its performance, the viability algorithm is applied to investigate voltage stability for a single machine-load system in case of a line fault.

Computation of the Smith Form for Multivariate Polynomial Matrices Using Maple

In this paper we show how the transformations associated with the reduction to the Smith form of some classes of mul-tivariate polynomial matrices are computed. Using a Maple implementation of a constructive version of the Quillen-Suslin Theorem, we present two algorithms for the reduction to a particular Smith form often associated with the simplification of linear systems of multidimensional equations.

A constructive version of the Boyle–Handelman theorem on the spectra of nonnegative matrices

A constructive version of the celebrated Boyle–Handelman theorem on the non-zero spectra of nonnegative matrices is presented.

Constructing and Testing Alternative Versions of the Fama-French and Carhart Models in the UK

The aim of this paper is to construct and test alternative versions of the Fama-French and Carhart models for the UK market. We conduct a comprehensive analysis of such models, forming risk factors using approaches advanced in the recent literature including value weighted factor components and various decompositions of the risk factors. We also test whether such factor models can at least explain the returns of large firms. Despite these various approaches, we join Michou, Mouselli and Stark (2007) and Fletcher (2010) in demonstrating that such factor models fail to reliably describe the cross-section of returns in the UK.

Statistical properties of dynamical systems – Simulation and abstract computation

We survey an area of recent development, relating dynamics to theoretical computer science. We discuss some aspects of the theoretical simulation and computation of the long term behavior of dynamical systems. We will focus on the statistical limiting behavior and invariant measures. We present a general method allowing the algorithmic approximation at any given accuracy of invariant measures. The method can be applied in many interesting cases, as we shall explain. On the other hand, we exhibit some examples where the algorithmic approximation of invariant measures is not possible. We also explain how it is possible to compute the speed of convergence of ergodic averages (when the system is known exactly) and how this entails the computation of arbitrarily good approximations of points of the space having typical statistical behaviour (a sort of constructive version of the pointwise ergodic theorem).

A constructive version of Birkhoffʼs ergodic theorem for Martin-Löf random points

We prove the effective version of Birkhoffʼs ergodic theorem for Martin-Löf random points and effectively open sets, improving the results previously obtained in this direction (in particular those of Vyugin, Nandakumar and Hoyrup, Rojas). The proof consists of two steps. First, we prove a generalization of Kučeraʼs theorem, which is a particular case of effective ergodic theorem: a trajectory of a computable ergodic mapping that starts from a random point cannot remain inside an effectively open set of measure less than 1. Second, we show that the full statement of the effective ergodic theorem can be reduced to this special case. Both steps use the statement of classical ergodic theorem but not its usual classical proof. Therefore, we get a new simple proof of the effective ergodic theorem (with weaker assumptions than before). This result was recently obtained independently by Franklin, Greenberg, Miller and Ng.

Deconstructing national leadership: Politicians’ accounts of electoral success and failure in the Irish Lisbon Treaty referenda

The Self Categorization approach to national leadership proposes that leaders rhetorically construct national identity as essentialized and inevitable in order to consensualize and mobilize the population. In contrast, discursive studies have demonstrated how national politicians flexibly construct the nation to manage their own accountability in local interactions, though this in turn has neglected broader leadership processes. The present paper brings both approaches together to examine how and when national politicians construct versions of national identity in order to account for their failure as well as success in mobilizing the electorate. Eight semi-structured conversational style interviews were conducted with a strategic sample of eight leading Irish politicians on the subject of the 2008/2009 Irish Lisbon Treaty referenda. Using a Critical Discourse Psychology approach, the hegemonic repertoire of the 'settled will' of the informed and consensualized Irish nation was identified across all interviews. Politicians either endorsed the 'settled will' repertoire as evidence of their successful leadership, or rejected the repertoire by denying the rationality or unity of the populace to account for their failure. Our results suggest national identity is only constructed as essentialized and inevitable to the extent that it serves a strategic political purpose.

Sequent calculi and decidability for intuitionistic hybrid logic

In this paper we study the proof theory of the first constructive version of hybrid logic called Intuitionistic Hybrid Logic ( IHL) in order to prove its decidability. In this perspective we propose a sequent-style natural deduction system and then the first sequent calculus for this logic. We prove its main properties like soundness, completeness and also the cut-elimination property. Finally we provide, from our calculus, the first decision procedure for IHL and then prove its decidability.