Academic literature on the topic 'Computability index'

At least seven kinds of misconceptions about constructive and computable mathematics prevail in economics. In this paper, the infelicitous claims of computable or constructive frameworks for the excess demand functions of microeconomics, constructive general equilibrium theory and computable general equilibrium modeling, agent-based economics, search theory, game theory, index number theory and Neo Ricardian economics and the fundamental theorems of welfare economics are considered. The claims are shown to be misleading from the point of view of formal computability theory or constructive mathematics (especially but not only when based on Brouwerian Intuitionistic Logic).

AbstractWe address the computational spectral theory of Jacobi operators that are compact perturbations of the free Jacobi operator via the asymptotic properties of a connection coefficient matrix. In particular, for Jacobi operators that are finite-rank perturbations we show that the computation of the spectrum can be reduced to a polynomial root finding problem, from a polynomial that is derived explicitly from the entries of a connection coefficient matrix. A formula for the spectral measure of the operator is also derived explicitly from these entries. The analysis is extended to trace-class perturbations. We address issues of computability in the framework of the Solvability Complexity Index, proving that the spectrum of compact perturbations of the free Jacobi operator is computable in finite time with guaranteed error control in the Hausdorff metric on sets.

The quality performance of a green building will have an overarching effect on its objectives because of the high compliance needed to achieve superior performance expectations. Achieving sustainability objectives is challenging and requires the collaboration of diverse professionals that resume unique responsibilities. In this study, the different managerial practitioners involved in green-building projects were investigated in terms of their awareness levels regarding the quality performance measures, their perceived abilities to influence quality failure consequences, the degree to which the cost-of-quality (CoQ) of components can be evaluated, and the effect the sustainability traits have on the quality performance. Accordingly, a survey approach was adopted, and the results were analyzed using Pearson’s chi-squared (χ2) test, the relative importance index (RII), Mann–Whitney U-Test, and Student’s T-test. According to the results, the priorities of the different managerial types and their overall impressions of cost computability were different, which needs to be considered when CoQ evaluations are done based on practitioners’ views. In addition, the sustainability traits of green buildings impact achieving quality metrics with the consequences of design rework occurring in the construction stage may lead to denouncing sustainability traits. The results of this research study reveal the need to consider the differences between managerial types when evaluating CoQ for projects and the increased sensitivity for such evaluation in a green building context. The paper contributes to underscoring the important connection between quality performance and sustainability traits of a green building project and calls for researchers to formulate methods with more rigor to reach a set structure for quality cost accounting as an industry standard. Intricate evaluation methods will enable strategic decision making on quality performance budgets to be more substantiated.

Purpose Despite the widespread use of univariate empirical mode decomposition (EMD) in financial market forecasting, the application of multivariate empirical mode decomposition (MEMD) has not been fully investigated. The purpose of this study is to forecast the stock price index more accurately, relying on the capability of MEMD in modeling the dependency between relevant variables. Design/methodology/approach Quantitative and comprehensive assessments were carried out to compare the performance of some selected models. Data for the assessments were collected from three major stock exchanges, namely, the standard and poor 500 index from the USA, the Hang Seng index from Hong Kong and the Shanghai Stock Exchange composite index from China. MEMD-based support vector regression (SVR) was used as the modeling framework, where MEMD was first introduced to simultaneously decompose the relevant covariates, including the opening price, the highest price, the lowest price, the closing price and the trading volume of a stock price index. Then, SVR was used to set up forecasting models for each component decomposed and another SVR model was used to generate the final forecast based on the forecasts of each component. This paper named this the MEMD-SVR-SVR model. Findings The results show that the MEMD-based modeling framework outperforms other selected competing models. As per the models using MEMD, the MEMD-SVR-SVR model excels in terms of prediction accuracy across the various data sets. Originality/value This research extends the literature of EMD-based univariate models by considering the scenario of multiple variables for improving forecasting accuracy and simplifying computability, which contributes to the analytics pool for the financial analysis community.

Gegenstand dieser Dissertation ist eine umfassende Analyse der Stabilität von Asteroidenbahnen im Edgeworth-Kuiper-Gürtel am Beispiel der 3:5-, 4:7- und der 1:2-Bahnresonanz mit Neptun. Einen weiteren Schwerpunkt der Arbeit bildet die Untersuchung der numerischen Berechenbarkeit der Lyapunov-Zeit von Asteroidenbahnen. Ausgehend von einer allgemeinen Beschreibung der bei numerischen Berechnungen auftretenden Rundungs- und Diskretisierungsfehler wird deren Wachstum bei numerischen Integrationen ermittelt. Diese, teilweise maschinenabhängigen, Fehler beeinflussen die berechnete Trajektorie des Asteroiden ebenso wie die daraus abgeleitete Lyapunov-Zeit. Durch Beispielrechnungen mit unterschiedlichen Rechnerarchitekturen und Integrationsmethoden wird der Einfluss auf die erhaltenen Lyapunov-Zeiten eingehend untersucht. Als Maß zur Beschreibung dieser Abhängigkeit wird ein Berechenbarkeitsindex $\kappa$ definiert. Weiterhin wird gezeigt, dass die allgemeine Struktur des Phasenraumes robust gegenüber diesen Änderungen ist. Unter Nutzung dieser Erkenntnis werden anschließend ausgewählte Bahnresonanzen im Edgeworth-Kuiper-Gürtel untersucht. Grundlegende Charakteristika, wie die Resonanzbreiten, werden dabei aus einfachen Modellen abgeleitet. Eine möglichst realitätsnahe Beschreibung der Stabilität wird durch numerische Integration einer Vielzahl von Testkörpern zusammen mit den Planeten Jupiter bis Neptun erreicht. Die erhaltenen Ergebnisse werden dabei mit der beobachteten Verteilung der Asteroiden im Edgeworth-Kuiper-Gürtel verglichen. ---- Hinweis: Beim Betrachten der pdf-Version dieses Dokumentes mit dem Acrobat Reader mit einer Version kleiner 8.0 kann es unter Windows zu Problemen in der Darstellung der Abbildungen auf den Seiten 46, 72, 74, 79 und 86 kommen. Um die Datenpunkte zu sehen ist eine Vergrößerung von mehr als 800% notwendig. Alternativ kann in den Grundeinstellungen der Haken für das Glätten von Vektorgraphiken entfernt werden
This dissertation presents a comprehensive description of the stability of asteroid orbits in the Edgeworth-Kuiper belt taking the 3:5, 4:7 and 1:2 mean motion resonance with Neptune as example. Further emphasis is given to the numerical computability of the Lyapunov time of asteroids. Starting with a general description of rounding and approximation errors in numerical computations, the growth of these errors within numerical integrations is estimated. These, partly machine-dependent errors influence the calculated trajectory of the asteroid as well as the derived Lyapunov time. Different hardware architectures and integration methods were used to investigate the influence on the computed Lyapunov time. As a measure of this dependence a computability index $\kappa$ is defined. Furthermore it is shown, that the general structure of phase space is robust against these changes. Subsequently, several selected mean motion resonances in the Edgeworth-Kuiper belt are investigated using these findings. Basic properties, like the resonance width, are deduced from simple models. To get a realistic description of the stability, a huge number of test particles was numerically integrated together with the planets Jupiter to Neptune. The obtained results are compared to the observed distribution of asteroids in the Edgeworth-Kuiper belt. ---- Additional information: If the pdf-file of this document is viewed using Acrobat Reader with a version less 8.0 under Windows the figures on page 46, 72, 74, 79 and 86 are shown incomplete. To see the data points a zoom factor larger than 800% is necessary. Alternatively the smoothing of vector graphics should be disabled in the settings of the reader