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Extrapolation is a process used to accelerate the convergence of a sequence of approximations to the true value. Different stepsizes are used to obtain approximate solutions, which are combined to increase the order of the approximation by eliminating leading error terms. The smoothing technique is also applied to suppress order reduction and to dampen the oscillatory component in the numerical solution when solving stiff problems. The extrapolation and smoothing technique can be applied in either active, passive or the combination of both active and passive modes. In this paper, the authors investigate the best strategy of implementing extrapolation and smoothing technique and use this strategy to solve stiff ordinary differential equations. Based on the experiment, the authors suggest using passive smoothing in order to reduce the computation time.

The two-step smoothing is a composition of four steps of the symmetric method with different weights. It is used as the final two steps when combined with many steps of the symmetric method. The aim is to preserve symmetry and provide damping for stiff problem and to be more robust than the one-step smoothing. The two-step smoothing is L-stable. The new method is then applied with extrapolation process in passive and active modes to investigate the most efficient and accurate method of implementation.

In this paper, the authors constructed the two-step smoothing to be more robust than the one-step smoothing. The two-step smoothing is constructed to achieve as high order as possible and able to restore the classical order of particular method compared to the one-step active smoothing that is only able to achieve order-1 condition. The two-step smoothing for ITR is also superior in solving stiff case since it has the super-convergent order-4 behavior. In our experiments with extrapolation, it is proven that the two-step smoothing is more accurate and more efficient than the one-step smoothing, namely 1ASAX. It is also observed that the method with smoothing is comparable if not superior to the existing base method in certain cases. Based on the experiment, the authors would suggest using passive smoothing if the aim is to reduce computation time. It is of interest to conduct more experiment to validate the accuracy and efficiency of the smoothing formula with and without extrapolation.

The implementation of extrapolation on two-step symmetric Runge–Kutta method has not been tested on variety of other test problems yet. The two-step symmetrization is an extension of the one-step symmetrization and has not been constructed by other researchers yet. The method is constructed such that it preserves the asymptotic error expansion in even powers of stepsize, and when used with extrapolation the order might increase by 2 at a time. The method is also L-stable and eliminates the order reduction phenomenon when solving stiff ODEs. It is also of interest to observe other ways of implementing extrapolation using other sequences or with interpolation.

The purpose of this paper is to optimize the maintenance strategies for wind turbine (WT) gearboxes to minimize costs associated with PM actions, cooling, production loss and gearbox replacement. Two approaches, periodic imperfect maintenance and a novel design incorporating alternating gearboxes are compared to identify the most cost-effective solution.

This study employs mathematical modeling to analyze the design, operation and maintenance of WT gearboxes. Two maintenance strategies are investigated, involving periodic imperfect maintenance actions and the incorporation of two similar gearboxes operating alternately. The models determine optimal preventive maintenance (PM) and switching periods to minimize total expected costs over the operating time span.

The research findings reveal, for the considered case of a moroccan wind farm, that the use of two similar gearboxes operating alternately is more cost-effective than relying on a single gearbox. The mathematical models developed enable the determination and comparison of optimal strategies for various WT gearbox scenarios and associated maintenance costs.

Limitations may arise from simplifications in the mathematical models and assumptions about degradation, temperature monitoring and maintenance effectiveness. Future research could refine the models and incorporate additional factors for a more comprehensive analysis.

Practically, the study provides insights into optimizing WT gearbox maintenance strategies, considering the trade-offs between PM actions, cooling, production loss and gearbox replacement costs. The findings can inform decisions on maintenance planning and design modifications to enhance cost efficiency.

While the primary focus is on cost optimization, the study indirectly contributes to the broader societal goal of sustainable energy production. Efficient maintenance strategies for WTs help ensure reliable and cost-effective renewable energy, potentially benefiting communities relying on wind power.

This paper introduces two distinct strategies for WT gearbox maintenance, extending beyond traditional periodic maintenance. The incorporation of alternating gearboxes presents a novel design approach. The developed mathematical models offer a valuable tool for determining and comparing optimal strategies tailored to specific WT scenarios and associated maintenance costs.

While there has been discussion of the computer manipulability of classification notations from a theoretical viewpoint, there has been little, if any on practical filing. A practical filing rubric, with explanation of machine filing concepts, is presented here. Some observations on the suitability of Library of Congress and Dewey Decimal notations for computer search follow.

Presents a robust and unconditionally stable return‐mapping algorithm based on the discrete counterpart of the principle of maximum plastic dissipation. Develops the explicit expression for the consistent elasto‐plastic tangent modulus. All expressions are derived via tensor formulation showing the advantage over the classical matrix notation. The integration algorithm is implemented in the formulation of the four‐node isoparametric assumed‐strain finite‐rotation shell element employing the Mindlin‐Reissner‐type shell model. By applying the layered model, plastic zones can be displayed through the shell thickness. Material non‐linearity described by the von Mises yield criterion and isotropic hardening is combined with a geometrically non‐linear response assuming finite rotations. Numerical examples illustrate the efficiency of the present formulation in conjunction with the standard Newton iteration approach, in which no line search procedures are required. Demonstrates the excellent performance of the algorithm for large time respective load steps.

This paper aims to provide an overview of principles and procedures involved in creating a faceted classification scheme for use in resource discovery in an online environment.

Facet analysis provides an established rigorous methodology for the conceptual organization of a subject field, and the structuring of an associated classification or controlled vocabulary. This paper explains how that methodology was applied to the humanities in the FATKS project, where the objective was to explore the potential of facet analytical theory for creating a controlled vocabulary for the humanities, and to establish the requirements of a faceted classification appropriate to an online environment. A detailed faceted vocabulary was developed for two areas of the humanities within a broader facet framework for the whole of knowledge. Research issues included how to create a data model which made the faceted structure explicit and machine‐readable and provided for its further development and use.

In order to support easy facet combination in indexing, and facet searching and browsing on the interface, faceted classification requires a formalized data structure and an appropriate tool for its management. The conceptual framework of a faceted system proper can be applied satisfactorily to humanities, and fully integrated within a vocabulary management system.

The procedures described in this paper are concerned only with the structuring of the classification, and do not extend to indexing, retrieval and application issues.

Many stakeholders in the domain of resource discovery consider developing their own classification system and supporting tools. The methods described in this paper may clarify the process of building a faceted classification and may provide some useful ideas with respect to the vocabulary maintenance tool.

As far as the authors are aware there is no comparable research in this area.

The Integrative Levels Classification (ILC) is a comprehensive “freely faceted” knowledge organization system not previously expressed as SKOS (Simple Knowledge Organization System). This paper reports and reflects on work converting the ILC to SKOS representation.

The design of the ILC representation and the various steps in the conversion to SKOS are described and located within the context of previous work considering the representation of complex classification schemes in SKOS. Various issues and trade-offs emerging from the conversion are discussed. The conversion implementation employed the STELETO transformation tool.

The ILC conversion captures some of the ILC facet structure by a limited extension beyond the SKOS standard. SPARQL examples illustrate how this extension could be used to create faceted, compound descriptors when indexing or cataloguing. Basic query patterns are provided that might underpin search systems. Possible routes for reducing complexity are discussed.

Complex classification schemes, such as the ILC, have features which are not straight forward to represent in SKOS and which extend beyond the functionality of the SKOS standard. The ILC's facet indicators are modelled as rdf:Property sub-hierarchies that accompany the SKOS RDF statements. The ILC's top-level fundamental facet relationships are modelled by extensions of the associative relationship – specialised sub-properties of skos:related. An approach for representing faceted compound descriptions in ILC and other faceted classification schemes is proposed.

Uncertainty is ubiquitous in practical engineering and scientific research. The uncertainties in parameters can be treated as interval numbers. The prediction of upper and lower bounds of the response of a system including uncertain parameters is of immense significance in uncertainty analysis. This paper aims to evaluate the upper and lower bounds of electric potentials in an electrostatic system efficiently with interval parameters.

The Taylor series expansion is proposed for evaluating the upper and lower bounds of electric potentials in an electrostatic system with interval parameters. The uncertain parameters of the electrostatic system are represented by interval notations. By performing Taylor series expansion on the electric potentials obtained using the equilibrium governing equation and by using the properties of interval mathematics, the upper and lower bounds of the electric potentials of an electrostatic system can be calculated.

To evaluate the accuracy and efficiency of the proposed method, the upper and lower bounds of the electric potentials and the computation time of the proposed method are compared with those obtained using the Monte Carlo simulation, which is referred to as a reference solution. Numerical examples illustrate that the bounds of electric potentials of this method are consistent with those obtained using the Monte Carlo simulation. Moreover, the proposed method is significantly more time-saving.

This paper provides a rapid computational method to estimate the upper and lower bounds of electric potentials in electrostatics analysis with interval parameters. The precision of the proposed method is acceptable for engineering applications, and the computation time of the proposed method is significantly less than that of the Monte Carlo simulation, which is the most widely used method related to uncertainties. The Monte Carlo simulation requires a large number of samplings, and this leads to significant runtime consumption.

This paper seeks to outline the central role of concepts in the knowledge universe, and the intertwining roles of works, instantiations, and documents. In particular the authors are interested in ontological and epistemological aspects of concepts and in the question to which extent there is a need for natural languages to link concepts to create meaningful patterns.

The authors describe the quest for the smallest elements of knowledge from a historical perspective. They focus on the metaphor of the universe of knowledge and its impact on classification and retrieval of concepts. They outline the major components of an elementary theory of knowledge interaction.

The paper outlines the major components of an elementary theory of knowledge interaction that is based on the structure of knowledge rather than on the content of documents, in which semantics becomes not a matter of synonymous concepts, but rather of coordinating knowledge structures. The evidence is derived from existing empirical research.

The paper shifts the bases for knowledge organization from a search for a universal order to an understanding of a universal structure within which many context‐dependent orders are possible.

The purpose of this paper is to illustrate the many aspects of Poincare recurrence time theorem for an archetype of a complex system, the logistic map.

At the beginning of the twentieth century, Poincare's recurrence theorem had revolutionized modern mechanics and statistical physics. However, this theorem did not attract considerable attention, at least from a numerical and computational point of view. In a series of relatively recent papers, Balakrishnan, Nicolis and Nicolis have addressed the recurrence time problem in a firm basis, introducing notation, theory, and numerical studies. Motivated by this call, the paper proposes to illustrate the many aspects of Poincare recurrence time theorem for an archetype of a complex system, the logistic map. The authors propose here in different tests and computations, each one illuminating the many aspects of the problem of recurrence. The paper ends up with a short discussion and conclusions.

In this paper, the authors obtain new results on computations, each one illuminating the many aspects of the problem of recurrence. One striking aspect of this detailed work, is that when the sizes of the cells in the phase space became considerable, then the recurrence times assume ordinary values.

The paper extends previous results on chaotic maps to the logistic map, enhancing comprehension, making possible connections with number theory, combinatorics and cryptography.