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Article
Publication date: 1 June 2004

Stanislaw Grygiel, Martin Zwick and Marek Perkowski

Two methods of decomposition of probabilistic relations are presented in this paper. They consist of splitting relations (blocks) into pairs of smaller blocks related to…

Abstract

Two methods of decomposition of probabilistic relations are presented in this paper. They consist of splitting relations (blocks) into pairs of smaller blocks related to each other by new variables generated in such a way so as to minimize a cost function which depends on the size and structure of the result. The decomposition is repeated iteratively until a stopping criterion is met. Topology and contents of the resulting structure develop dynamically in the decomposition process and reflect relationships hidden in the data.

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Kybernetes, vol. 33 no. 5/6
Type: Research Article
ISSN: 0368-492X

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Book part
Publication date: 14 June 2002

Alex R. Hoen

Abstract

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An Input-output Analysis of European Integration
Type: Book
ISBN: 978-0-44451-088-4

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Book part
Publication date: 30 December 2013

Guido Erreygers and Roselinde Kessels

In this chapter we explore different ways to obtain decompositions of rank-dependent indices of socioeconomic inequality of health, such as the Concentration Index. Our…

Abstract

In this chapter we explore different ways to obtain decompositions of rank-dependent indices of socioeconomic inequality of health, such as the Concentration Index. Our focus is on the regression-based type of decomposition. Depending on whether the regression explains the health variable, or the socioeconomic variable, or both, a different decomposition formula is generated. We illustrate the differences using data from the Ethiopia 2011 Demographic and Health Survey (DHS).

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Health and Inequality
Type: Book
ISBN: 978-1-78190-553-1

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Book part
Publication date: 1 December 2006

Massimo Egidi

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Cognitive Economics: New Trends
Type: Book
ISBN: 978-1-84950-862-9

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Article
Publication date: 22 February 2021

Zhimin Cao, Wenjun Zong, Junjie Zhang, Chunlei He, Jiaohu Huang, Wei Liu and Zhiyong Wei

This paper aims to reveal the tribochemical reaction mechanism on the nano-cutting interface between HMX crystal and diamond tool.

Abstract

Purpose

This paper aims to reveal the tribochemical reaction mechanism on the nano-cutting interface between HMX crystal and diamond tool.

Design/methodology/approach

Molecular dynamics simulation of HMX crystal nano-cutting by the reactive force field is carried out in this paper. The affinity of activated atoms and friction damage at the different interface have been well identified by comparing two cutting systems with diamond tool or indenter. The analyses of reaction kinetics, decomposition products and reaction pathways are performed to reveal the underlying atomistic origins of tribocatalytic reaction on the nano-cutting interface.

Findings

The HMX crystals only undergo damage and removal in the indenter cutting, while they appear to accelerate thermal decomposition in the diamond cutting. the C-O affinity is proved to be the intrinsic reason of the tribocatalytic reaction of the HMX-diamond cutting system. The reaction activation energy of the HMX crystals in the diamond cutting system is lower, resulting in a rapid increase in the decomposition degree. The free O atoms can induce the asymmetric ring-opening mode and change the decomposition pathways, which is the underlying atomistic origins of the thermal stability of the HMX-diamond cutting system.

Originality/value

This paper describes a method for analyzing the tribochemical behavior of HMX and diamond, which is beneficial to study the thermal stability in the nano-cutting of HMX.

Details

Industrial Lubrication and Tribology, vol. 73 no. 3
Type: Research Article
ISSN: 0036-8792

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Handbook of Microsimulation Modelling
Type: Book
ISBN: 978-1-78350-570-8

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Article
Publication date: 17 September 2008

Randolph C. Rach

To provide a new proof of convergence of the Adomian decomposition series for solving nonlinear ordinary and partial differential equations based upon a thorough…

Abstract

Purpose

To provide a new proof of convergence of the Adomian decomposition series for solving nonlinear ordinary and partial differential equations based upon a thorough examination of the historical milieu preceding the Adomian decomposition method.

Design/methodology/approach

Develops a theoretical background of the Adomian decomposition method under the auspices of the Cauchy‐Kovalevskaya theorem of existence and uniqueness for solution of differential equations. Beginning from the concepts of a parametrized Taylor expansion series as previously introduced in the Murray‐Miller theorem based on analytic parameters, and the Banach‐space analog of the Taylor expansion series about a function instead of a constant as briefly discussed by Cherruault et al., the Adomian decompositions series and the series of Adomian polynomials are found to be a uniformly convergent series of analytic functions for the solution u and the nonlinear composite function f(u). To derive the unifying formula for the family of classes of Adomian polynomials, the author develops the novel notion of a sequence of parametrized partial sums as defined by truncation operators, acting upon infinite series, which induce these parametrized sums for simple discard rules and appropriate decomposition parameters. Thus, the defining algorithm of the Adomian polynomials is the difference of these consecutive parametrized partial sums.

Findings

The four classes of Adomian polynomials are shown to belong to a common family of decomposition series, which admit solution by recursion, and are derived from one unifying formula. The series of Adomian polynomials and hence the solution as computed as an Adomian decomposition series are shown to be uniformly convergent. Furthermore, the limiting value of the mth Adomian polynomial approaches zero as the index m approaches infinity for the prerequisites of the Cauchy‐Kovalevskaya theorem. The novel truncation operators as governed by discard rules are analogous to an ideal low‐pass filter, where the decomposition parameters represent the cut‐off frequency for rearranging a uniformly convergent series so as to induce the parametrized partial sums.

Originality/value

This paper unifies the notion of the family of Adomian polynomials for solving nonlinear differential equations. Further it presents the new notion of parametrized partial sums as a tool for rearranging a uniformly convergent series. It offers a deeper understanding of the elegant and powerful Adomian decomposition method for solving nonlinear ordinary and partial differential equations, which are of paramount importance in modeling natural phenomena and man‐made device performance parameters.

Details

Kybernetes, vol. 37 no. 7
Type: Research Article
ISSN: 0368-492X

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Article
Publication date: 26 August 2014

Florian Johannsen, Susanne Leist and Reinhold Tausch

The purpose of this paper is to specify the decomposition conditions of Wand and Weber for the Business Process Model and Notation (BPMN). Therefore, an interpretation of…

Abstract

Purpose

The purpose of this paper is to specify the decomposition conditions of Wand and Weber for the Business Process Model and Notation (BPMN). Therefore, an interpretation of the conditions for BPMN is derived and compared to a specification of the conditions for enhanced Event-Driven Process Chains (eEPCs). Based on these results, guidelines for a conformance check of BPMN and eEPC models with the decomposition conditions are shown. Further, guidelines for decomposition are formulated for BPMN models. The usability of the decomposition guidelines is tested with modelling experts.

Design/methodology/approach

An approach building on a representational mapping is used for specifying the decomposition conditions. Therefore, ontological constructs of the Bunge-Wand-Weber ontology are mapped to corresponding modelling constructs and an interpretation of the decomposition conditions for BPMN is derived. Guidelines for a conformance check are then defined. Based on these results, decomposition guidelines are formulated. Their usability is tested in interviews.

Findings

The research shows that the decomposition conditions stemming from the information systems discipline can be transferred to business process modelling. However, the interpretation of the decomposition conditions depends on specific characteristics of a modelling language. Based on a thorough specification of the conditions, it is possible to derive guidelines for a conformance check of process models with the conditions. In addition, guidelines for decomposition are developed and tested. In the study, these are perceived as understandable and helpful by experts.

Research limitations/implications

Research approaches based on representational mappings are subjected to subjectivity. However, by having three researchers performing the approach independently, subjectivity can be mitigated. Further, only ten experts participated in the usability test, which is therefore to be considered as a first step in a more comprising evaluation.

Practical implications

This paper provides the process modeller with guidelines enabling a conformance check of BPMN and eEPC process models with the decomposition conditions. Further, guidelines for decomposing BPMN models are introduced.

Originality/value

This paper is the first to specify Wand and Weber's decomposition conditions for process modelling with BPMN. A comparison to eEPCs shows, that the ontological expressiveness influences the interpretation of the conditions. Further, guidelines for decomposing BPMN models as well as for checking their adherence to the decomposition conditions are presented.

Details

Business Process Management Journal, vol. 20 no. 5
Type: Research Article
ISSN: 1463-7154

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Article
Publication date: 7 March 2016

Monique Eissens-van der Laan, Manda Broekhuis, Marjolein van Offenbeek and Kees Ahaus

Applying “modularity” principles in services is gaining in popularity. The purpose of this paper is to enrich existing service modularity theory and practice by exploring…

Abstract

Purpose

Applying “modularity” principles in services is gaining in popularity. The purpose of this paper is to enrich existing service modularity theory and practice by exploring how services are being decomposed and how the modularization aim and the routineness of the service(s) involved may link to different decomposition logics. The authors argue that these are fundamental questions that have barely been addressed.

Design/methodology/approach

The authors first built a theoretical framework of decomposition steps and the design choices involved that distinguished six decomposition logics. The authors conducted a systematic literature search that generated 18 empirical articles describing 16 service modularity cases. The authors analysed these cases in terms of decomposition logic and two main contingencies: modularization aim and service routineness.

Findings

Only three of the 18 articles explicitly addressed the service decomposition by reflecting on the underlying design choices. By unravelling the decomposition in each case, the authors were able to identify the decomposition logic and found four of the six theoretically derived logics: single-level process oriented; single-level outcome oriented; multilevel outcome oriented; and multilevel combined orientation. Although the authors did not find a direct relationship between the modularization aim and the decomposition logic, the authors did find that single-level decomposition logics seem to be mainly applied in non-routine service offerings whereas the multilevel ones are mainly applied in routine service offerings.

Originality/value

By contributing to a common understanding of modular service decomposition and proposing a framework that explicates the design choices involved, the authors enable an enhanced application of the modularity concept in services.

Details

International Journal of Operations & Production Management, vol. 36 no. 3
Type: Research Article
ISSN: 0144-3577

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Article
Publication date: 1 September 2005

C.K. Chan and S.T. Tan

This paper reports on the work done to decompose a large sized solid model into smaller solid components for rapid prototyping technology. The target geometric domain of…

Abstract

Purpose

This paper reports on the work done to decompose a large sized solid model into smaller solid components for rapid prototyping technology. The target geometric domain of the solid model includes quadrics and free form surfaces.

Design/methodology/approach

The decomposition criteria are based on the manufacturability of the model against a user‐defined manufacturing chamber size and the maintenance of geometrical information of the model. In the proposed algorithm, two types of manufacturing chamber are considered: cylindrical shape and rectangular shape. These two types of chamber shape are commonly implemented in rapid prototyping machines.

Findings

The proposed method uses a combination of the regular decomposition (RD)‐method and irregular decomposition (ID)‐method to split a non‐producible solid model into smaller producible subparts. In the ID‐method, the producible feature group decomposition (PFGD)‐method focuses on the decomposition by recognising producible feature groups. In the decomposition process, less additional geometrical and topological information are created. The RD‐method focuses on the splitting of non‐producible sub‐parts, which cannot be further decomposed by the PFGD‐method. Different types of regular split tool surface are studied.

Originality/value

Combination of the RD‐method and the ID‐method makes up the proposed volume decomposition process. The user can also define the sequence and priority of using these methods manually to achieve different decomposition patterns. The proposed idea is also applicable to other decomposition algorithm. Some implementation details and the corresponding problems of the proposed methods are also discussed.

Details

Rapid Prototyping Journal, vol. 11 no. 4
Type: Research Article
ISSN: 1355-2546

Keywords

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