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This paper aims to present a comparison of numerical methods for determining the contact pattern of Gleason-type bevel gears. The mathematical model of tooth contact analysis and the finite element method were taken into consideration. Conclusions have been drawn regarding the usefulness of the considered methods and the compatibility of results. The object of the analysis was a bevel gear characterised by an 18:43 gear ratio and arc tooth line, and manufactured according to the spiral generated modified-roll method.

The mathematical model of tooth contact analysis consists of both the mathematical model of tooth generating and the mathematical model of operating gear set. The first model is used to generate tooth flanks of the pinion and the ring gear in the form of grids of points. Then, such tooth surfaces are used for the tooth contact analysis performed with the other model. It corresponds to the no-load gear meshing condition. The finite element method model was built on the basis of the same tooth flanks obtained with the former model. The commercial finite element method software Abaqus was used to perform two instances of the contact analysis: a very light load, corresponding to the former no-load condition, and the operating load condition. The results obtained using the two models, in the form of the contact pattern for no-load condition, were compared. The effect of heavy load on contact pattern position, shape and size was shown and discussed.

The mathematical models correctly reproduce the shape, position and size of the contact pattern; thus, they can be reliably used to assess the quality of the bevel gear at the early stage of its design.

Determination of the correct geometry of the flank surfaces of the gear and pinion teeth through the observation of contact pattern is a fundamental step in designing of a new aircraft bevel gear.

A possibility of the independent use of the mathematical analysis of the contact pattern has been shown, which, thanks to the compatibility of the results, does not have to be verified experimentally.

Current ethnographic research is marked by an expanding variety of approaches that indicates not only the infusion of paradigmatic proliferation into the field but also the expansion of technologies mediating ethnographic exploration as well as the growth in research agendas of educational research. Current researchers therefore have much to draw upon but the diversity of approaches indicates and presents major challenges (Walford, 2002). In particular, the double crisis of representation and legitimation that has become apparent in qualitative research has problematized the very possibility of valid/trustworthy/authentic/useful research. Thus, before an ethnographer even steps one foot, gingerly, in the research site, she would have had to grapple with weighty issues, such as the transparency of language, that have considerable bearing on the formulation of research questions and on the construction of an initial frame for her study. More importantly, the agency of the researcher, as well as the agency of her research subjects – vis-à-vis the structural constraints of epistemic access to the nature of reality – has been cast into doubt, as has the capacity of the researcher and the research subjects to produce a meaningful, dare we say truthful, account of their ways of knowing.

In this paper we will try to reach a twofold goal. First we will give an analysis of mathematical terminology in order to give practical hints for assigning subject headings to a book. Secondly, we will propose a method which could be helpful for the subject analysis of a given document. The main basis for this method is the connection between a special classification scheme, the Subject Classification Scheme of the American Mathematical Society, and the task of indexing books by subject headings. Examples of this method are given, and they are compared with Library of Congress Subject Headings and PRECIS entries. With both the study of the terminology and the proposed method, it should be possible to increase quality and consistency of the library indexing results for mathematical books. A thesaurus for mathematics with entries along the lines of the PRECIS rules and connected with the subject classification scheme of the American Mathematical Society, would be desirable, as would the printing of appropriate classification data, assigned to them by their authors, inside the books.

The purpose of this paper is to explore students' mathematization through a flow of lessons using the Thailand Lesson Study Incorporated Open Approach (TLSOA) to improve the excellence of instruction.

A total of 16 Grade 4 students were selected because they have been taught using the TLSOA model for four years. Six Lesson Study (LS) team members participated, and two instruments were utilized, namely student worksheets, and field notes. An ethnographic research design was employed.

The results revealed that the students' mathematical ideas were developed from the real world to the mathematical world through a flow of lessons based on the four phases of the Open Approach (OA).

Firstly, the students demonstrated their ability to represent the real world independently when the teacher posed an open-ended problem. Secondly, the students demonstrated their ability to use semi-concrete aids to develop their ideas while self-learning. Thirdly, the students showed how they developed their ideas to solve the open-ended problem using relevant objects or related concepts as part of a whole-class discussion and comparison exercise. Finally, the students demonstrated their abilities to represent the mathematical world using numbers and symbols to communicate their ideas when they were required to make a summary by connecting their mathematical ideas.

This study adds new insight to the literature on students' mathematization using the TLSOA model.

Gives the background to human resource planning (HRP) and argues that HRP tools are still an essential management requirement. Looks, therefore, to HRP tools that are not so mathematically complex as to be of little use to the average practitioner. Provides an approach which harnesses modern spreadsheet technology to implement the previously esoteric tools of analysis ‐ “holonic modelling”. Holonic modelling recognizes that computer power and the flexibility of software packages allow problems to be structured in a flexible manner. Goes on to demonstrate the use of holonic modelling in the context of HRP.

To identify, discuss and provide a solution for a common problem in the mathematical analyses in business analyses, namely, paralysis by analysis.

The paper first discusses the scale and frequency of the paralysis by analysis problem, before discussing it in more depth before addressing a fundamental problem, which is an important root of the paralysis by analysis problem, the indiscriminate usage of central tendency measures. Finally, it discusses how variance can be turned from being a liability into an asset. The approach is conversational but examples and a case study are provided to substantiate the arguments.

The paper provides some recommendations for avoiding paralysis by analysis.

Basically, the paper shows by argument and example why practitioners and some researchers need to better understand the limitations and promises of mathematical analyses and to some extent how to incorporate this understanding into their work.

There is nothing really new in this paper, but it discusses a problem that for some reason is often ignored by practitioners and some researchers. The true value of the paper therefore lies in making practitioners, in particular, more aware of the limitations as well as the possibilities in the mathematical analyses performed in business analytics so that they can better understand what they are doing and hence get behind the numbers, as it were.

The purpose of this paper is to survey briefly how harmonic analyis started and developed throughout the centuries to reach its modern status and its surprisingly wide range of applications.

The author traces applications of harmonic analysis back to Mesopotamia, ancient Egypt and the Indus Valley, showing how the Greeks have applied trigonometry and influenced its birth, then the important developments in India in the sixth century laying the first brick to modern trigonometry with the definition of the sinus, then medieval India founding modern mathematical analysis. Trigonometry was developed further by the Arabs until the fourteenth century, then by the Europeans. The eighteenth century in France was particularly important when Bernoulli solved, with an infinite trigonometric series, the vibrating string problem, then Fourier, who studied these series extensively. The author goes on to harmonic analysis on locally compact groups, and ends up with a quick personal view on harmonic analysis nowadays. The last section of the paper presents some of the modern applications. Harmonic analysis is, of course, still used for navigation but also has many other very surprising applications such as signal processing, quantum mechanics, neuroscience, tomography, etc.

The power of harmonic analysis lies in giving the solutions to various problems as infinite series of basic functions, so to be able to produce algorithms for FFT boxes, it must be understood how these series came about and the convergence of these series.

The review should be useful to people interested in studying and/or applying harmonic analysis.

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.

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.

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.

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.

Quality Function Deployment (QFD) proposes to take into account the “voice of the customer,” through a list of customer needs, which are (qualitatively) mapped to technical requirements in House One. But customers do not perceive products in this space, nor do they not make purchase decisions in this space. Marketing specialists use statistical models to map between a simpler space of customer perceptions and the long and detailed list of needs. For automobiles, for example, the main axes in perceptual space might be categories such as luxury, performance, sport, and utility. A product’s position on these few axes determines the detailed customer requirements consistent with the automobiles’ position such as interior volume, gauges and accessories, seating type, fuel economy, door height, horsepower, interior noise level, seating capacity, paint colors, trim, and so forth. Statistical models such as factor analysis and principal components analysis are used to describe the mapping between these spaces, which we call House Zero.

This paper focus on House One. Two important steps of the product development process using House One are: (1) setting technical targets; (2) identifying the inherent tradeoffs in a design including a position of merit. Utility functions are used to determine feature preferences for a product. Conjoint analysis is used to capture the product preference and potential market share. Linear interpolation and the slope point formula are used to determine other points of customer needs. This research draws from the formal mapping concepts developed by Nam Suh and the qualitative maps of quality function deployment, to present unified information and mapping paradigm for concurrent product/process design. This approach is the virtual integrated design method that is tested upon data from a business design problem.