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Blesson Varghese and Gerard McKee
The purpose of this paper is to address a classic problem – pattern formation identified by researchers in the area of swarm robotic systems – and is also motivated by the need…
Abstract
Purpose
The purpose of this paper is to address a classic problem – pattern formation identified by researchers in the area of swarm robotic systems – and is also motivated by the need for mathematical foundations in swarm systems.
Design/methodology/approach
The work is separated out as inspirations, applications, definitions, challenges and classifications of pattern formation in swarm systems based on recent literature. Further, the work proposes a mathematical model for swarm pattern formation and transformation.
Findings
A swarm pattern formation model based on mathematical foundations and macroscopic primitives is proposed. A formal definition for swarm pattern transformation and four special cases of transformation are introduced. Two general methods for transforming patterns are investigated and a comparison of the two methods is presented. The validity of the proposed models, and the feasibility of the methods investigated are confirmed on the Traer Physics and Processing environment.
Originality/value
This paper helps in understanding the limitations of existing research in pattern formation and the lack of mathematical foundations for swarm systems. The mathematical model and transformation methods introduce two key concepts, namely macroscopic primitives and a mathematical model. The exercise of implementing the proposed models on physics simulator is novel.
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The applications of mathematics to the solving of factual problems should run in a certain prescribed form called a mathematical method. Whereas a mathematical method is an only…
Abstract
The applications of mathematics to the solving of factual problems should run in a certain prescribed form called a mathematical method. Whereas a mathematical method is an only scheme that is a set of mathematical means, rules, hints, procedures, etc. how to solve a factual problem on some body of data, it becomes a Cognitive Problem‐Solver after its implementation on an appropriate computer which is able to solve, if need be, by the help of man, a class of special cognitive problems corresponding to the method arising out of their background and initial knowledge. Computer and man can act here in a symbiotic manner as intelligent agents, realizing each alternately the sequence of conceptual operations prescribed by the given method. The incidental difference between the routine and creative actions of the single agents is discussed, as well as the advantages of natural and artificial intelligence in automatic problem‐solving and automatic cognition.
Nima Gerami Seresht and Aminah Robinson Fayek
Fuzzy numbers are often used to represent non-probabilistic uncertainty in engineering, decision-making and control system applications. In these applications, fuzzy arithmetic…
Abstract
Fuzzy numbers are often used to represent non-probabilistic uncertainty in engineering, decision-making and control system applications. In these applications, fuzzy arithmetic operations are frequently used for solving mathematical equations that contain fuzzy numbers. There are two approaches proposed in the literature for implementing fuzzy arithmetic operations: the α-cut approach and the extension principle approach using different t-norms. Computational methods for the implementation of fuzzy arithmetic operations in different applications are also proposed in the literature; these methods are usually developed for specific types of fuzzy numbers. This chapter discusses existing methods for implementing fuzzy arithmetic on triangular fuzzy numbers using both the α-cut approach and the extension principle approach using the min and drastic product t-norms. This chapter also presents novel computational methods for the implementation of fuzzy arithmetic on triangular fuzzy numbers using algebraic product and bounded difference t-norms. The applicability of the α-cut approach is limited because it tends to overestimate uncertainty, and the extension principle approach using the drastic product t-norm produces fuzzy numbers that are highly sensitive to changes in the input fuzzy numbers. The novel computational methods proposed in this chapter for implementing fuzzy arithmetic using algebraic product and bounded difference t-norms contribute to a more effective use of fuzzy arithmetic in construction applications. This chapter also presents an example of the application of fuzzy arithmetic operations to a construction problem. In addition, it discusses the effects of using different approaches for implementing fuzzy arithmetic operations in solving practical construction problems.
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Considers a Wirkungsgeschichte of Hermann Heinrich Gossen, focusing on the reactions of the three stars of the Marginal Revolution: William Stanley Jevons, Léon Walras and Carl…
Abstract
Considers a Wirkungsgeschichte of Hermann Heinrich Gossen, focusing on the reactions of the three stars of the Marginal Revolution: William Stanley Jevons, Léon Walras and Carl Menger. Although Hermann Heinrich Gossen is today known as one of the forerunners of the Marginal Revolution, it was only in 1879 that Jevons mentioned him in the second edition of the Theory of Political Economy, which contributed greatly toward making Gossen’s name known among English‐speaking readers. Later, in 1885, Walras wrote a famous article in the Journal des Economistes, entitled “Un économiste inconnu: Hermann‐Henri Gossen”. Investigates a Wirkungsgeschichte of Gossen, an ignored German mathematical economist.
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Begins by focusing on the rise of formalism in the post‐war period leading to virtual monopoly as far as the method of economic analysis is concerned, and on the main consequences…
Abstract
Begins by focusing on the rise of formalism in the post‐war period leading to virtual monopoly as far as the method of economic analysis is concerned, and on the main consequences of this process. After mounting criticism of formalism, internal as well as external, it is acknowledged that some signs of renewed interest in a non‐mathematical approach and in its potentialities can be observed, particularly in the 1990s. Moreover, it is postulated that free competition between different methods, as opposed to concentrating on only one, is the best framework for the progress of economics. In particular, it increases the possibilities for dealing with many economic problems in an innovative way. Finally, outlines a possible stage where the two main methods (mathematical and non‐mathematical) have a more balanced and useful role in the course of economic analysis.
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Mohammad Reza Fathi, Mohammad Hasan Maleki, Seyed Mohammad Sobhani and Can Deniz Koksal
The purpose of this study is to formulate exploratory scenarios of Operations Research through the critical uncertainty approach and Soft Systems Methodology.
Abstract
Purpose
The purpose of this study is to formulate exploratory scenarios of Operations Research through the critical uncertainty approach and Soft Systems Methodology.
Design/methodology/approach
In this study, to formulate plausible scenarios, the discipline of operation research internal and external experts’ opinions of this field have been gathered through Delphi approach and uncertainty questionnaires. After use of the most important uncertainties, plausible scenarios of operations research have been mapped with the help of experts through co-thinking workshops.
Findings
Four scenarios are presented in this study. These scenarios include Solar System, Esfandiar's Eye, Rival’s Setraps and Legendary Simurgh. Naturally, the imagination of such a unitary future for all academic communities is an expectation far from reality, and given the conditions of each of these futures or any integration of them is imaginable.
Originality/value
Operations Research models have been faced with variously multiple changes since its emergence until now. Investigation into the future of operations research on the necessity for his planning has not received a reasonable notice in the literature. Sporadic activities that have been carried out are also lacking in the necessary methodology. Also, there has been no research about future study using the soft Operation Research tools (Soft Systems Methodology).
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Ebrahim Babaei and Hamed Mashinchi Mahery
The purpose of this paper is to propose a new method for mathematical modeling of the buck dc‐dc converter in discontinuous conduction mode (DCM). By using the presented modeling…
Abstract
Purpose
The purpose of this paper is to propose a new method for mathematical modeling of the buck dc‐dc converter in discontinuous conduction mode (DCM). By using the presented modeling method, the analysis of the transient and the steady states of the buck dc‐dc converter can be performed.
Design/methodology/approach
The proposed method is based on the two Laplace and Z transforms. In the proposed method, at first, the equations of the inductor current and the capacitor voltage are obtained as the power switch is on and off. Then by using the Laplace and Z transforms, the obtained equations are solved and the relations of the inductor current and the output voltage are obtained. In the proposed method, the Laplace transform is used for determining of the general relations of the inductor current and the output voltage. Also the Z‐transform is used as a tool for determining the initial values of the inductor current and the output voltage.
Findings
The transient and the steady state response of the dc‐dc converter is analyzed by the proposed method. By using the Z‐transform, the transient response of the converter and the effect of the elements of the converter on the time constant of the transient response are investigated. In addition, the effect of the elements of the converter and the load resistance on the electrical parameters of the converter such as the output voltage ripple and the inductor current ripple are investigated.
Originality/value
The proposed method in this paper is a suitable method for mathematical modeling of dc‐dc converters. The acernote of this method is that it can be used in both transient and steady state response, analysis of the dc‐dc converters. By using the final value theorem of the Z‐transform, the steady state response of the converter is investigated. Also by using this transform, the time constants of the transient response of the converter are determined. Finally, the results of the theoretical analysis are compared with the results of simulation in PSCAD/EMTDC and also the experimental results to prove the validity of the presented subjects.
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Ernnie Illyani Basri, Izatul Hamimi Abdul Razak, Hasnida Ab-Samat and Shahrul Kamaruddin
The purpose of this paper is to provide comprehensive information on preventive maintenance (PM) planning and methods used in the industry in order to achieve an effective…
Abstract
Purpose
The purpose of this paper is to provide comprehensive information on preventive maintenance (PM) planning and methods used in the industry in order to achieve an effective maintenance system.
Design/methodology/approach
The literature review is organized in a way that provides the general overview of the researches done in the PM. This paper discusses the literatures that had been reviewed on four main topics, which are the holistic view of maintenance policies, PM planning, PM planning concept and PM planning-based in developing optimal planning in executing PM actions.
Findings
PM policy is one of the original proactive techniques that has been used since the start of researches on maintenance system. Review of the methods presented in this paper shows that most researches analyse effectiveness using artificial intelligence, simulation, mathematical formulation, matrix formation, critical analysis and multi-criteria method. While in practice, PM activities were either planned based on cost, time or failure. Research trends on planning and methods for PM show that the variation of approaches used over the year from early 1990s until today.
Practical implications
Research about PM is known to be extensively conducted and majority of companies applied the policy in their production line. However, most analysis and method suggested in published literatures were done based on mathematical computation rather than focussing on solution to real problems in the industry. This normally would lead to the problems in understanding by the practitioner. Therefore, this paper presented researches on PM planning and suggested on the methods that are practical, simple and effective for application in the real industry.
Originality/value
The originality of this paper comes from its detail analysis of PM planning in term of its research focus and also direction for application. Extensive reviews on the methods adopted in relation to PM planning based on the planning-based such as cost-based, time-based and failure-based were also provided.
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Diagrams are ubiquitous in economics and are uncontestably among the most used, if not the most important workhorses of economists, though they come in many forms. This essay…
Abstract
Diagrams are ubiquitous in economics and are uncontestably among the most used, if not the most important workhorses of economists, though they come in many forms. This essay examines the different uses of graphs and diagrams in the pioneering work of two Victorian economists, Stanley Jevons and Alfred Marshall. We stress the difference between their use as representations and as visual reasoning tools, a difference that became obscured in the twentieth century with the rise of econometrics.
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