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Article
Publication date: 1 January 1985

Richard Startup

Mathematics is a hybrid subject with the idea of number tending to unfold while some major geometrical innovations cannot be understood in these terms. The deployment of…

Abstract

Mathematics is a hybrid subject with the idea of number tending to unfold while some major geometrical innovations cannot be understood in these terms. The deployment of evolutionary, critical and non‐evolutionary structuralist conceptions in the analysis of mathematical development draws the conclusion that, in order to fully understand this development, it is necessary to consider mathematics' relations with other (artistic and scientific) concerns, the tendencies implicit in its subsystems, and the connections between its various fields, as well as the ability of mathematicians to appraise critically any given formulation and thereby transcend it.

Details

International Journal of Sociology and Social Policy, vol. 5 no. 1
Type: Research Article
ISSN: 0144-333X

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Article
Publication date: 8 March 2011

Daniel Baldomir, Manuel Pereiro and Juan Arias

The purpose of this paper is to show how the geometrical information of Maxwell's equations is coded into the constitutive equations.

Abstract

Purpose

The purpose of this paper is to show how the geometrical information of Maxwell's equations is coded into the constitutive equations.

Design/methodology/approach

The Maxwell's equations have been written with the tensorial algebra into a three‐dimensional Euclidean space and compared with the usual four‐dimensional relativistic approach.

Findings

This simple geometry allows the finding of the relativistic information coded on the electric and magnetic fields, showing that they are not independent as relativity affirm obtaining their transformation for a moving inertial observer.

Originality/value

The main value of the paper is to present a simple mathematical tool which enables the engineers or applied physicists to obtain the relativistic transformations of the fields without using four‐dimensional geometries and the more sophisticated mathematical techniques.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 30 no. 2
Type: Research Article
ISSN: 0332-1649

Keywords

Content available
Article
Publication date: 10 September 2021

Rafik Medjati, Hanifi Zoubir and Brahim Medjahdi

In the Lorentz Heisenberg space H3 endowed with flat metric g3, a translation surface is parametrized by r(x, y) = γ1(x)*γ2(y), where γ1 and γ2 are two planar curves lying…

Abstract

Purpose

In the Lorentz Heisenberg space H3 endowed with flat metric g3, a translation surface is parametrized by r(x, y) = γ1(x)*γ2(y), where γ1 and γ2 are two planar curves lying in planes, which are not orthogonal. In this article, we classify translation surfaces in H3, which satisfy some algebraic equations in terms of the coordinate functions and the Laplacian operator with respect to the first fundamental form of the surface.

Design/methodology/approach

In this paper, we classify some type of space-like translation surfaces of H3 endowed with flat metric g3 under the conditionΔri = λiri. We will develop the system which describes surfaces of type finite in H3. For solve the system thus obtained, we will use the calculation variational. Finally, we will try to give performances geometric surfaces that meet the condition imposed.

Findings

Classification of six types of translation surfaces of finite type in the three-dimensional Lorentz Heisenberg group H3.

Originality/value

The subject of this paper lies at the border of geometry differential and spectral analysis on manifolds. Historically, the first research on the study of sub-finite type varieties began around the 1970 by B.Y.Chen. The idea was to find a better estimate of the mean total curvature of a compact subvariety of a Euclidean space. In fact, the notion of finite type subvariety is a natural extension of the notion of a minimal subvariety or surface, a notion directly linked to the calculation of variations. The goal of this work is the classification of surfaces in H3, in other words the surfaces which satisfy the condition/Delta (ri) = /Lambda (ri), such that the Laplacian is associated with the first, fundamental form.

Details

Arab Journal of Mathematical Sciences, vol. ahead-of-print no. ahead-of-print
Type: Research Article
ISSN: 1319-5166

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Article
Publication date: 15 March 2011

Wu Xuemou

The purpose of this paper is to state new formulation of the programme‐styled framework of pansystems research and related expansions.

Abstract

Purpose

The purpose of this paper is to state new formulation of the programme‐styled framework of pansystems research and related expansions.

Design/methodology/approach

Pansystems‐generalized extremum principle (0**: (dy/dx=0)**) is presented with recognitions to various logoi of philosophy, mathematics, technology, systems, cybernetics, informatics, relativity, biology, society, resource, communications and related topics: logic, history, humanities, aesthetics, journalism, IT, AI, TGBZ* <truth*goodness*beauty*Zen*>, etc. including recent rediscoveries of 50 or so pansystems logoi.

Findings

A keynote of the paper is to develop the deep logoi of the analytic mathematics, analytic mechanics, variational principles, Hilbert's sixth/23rd problems, pan‐axiomatization to encyclopedic principles and various applications. The 0**‐universal connections embody the transfield internet‐styled academic tendency of pansystems exploration.

Originality/value

The paper includes topics: history megawave, pansystems sublation‐modes, pan‐metaphysics, pansystems dialogs with logoi of 100 thinkers or so, and pansystems‐sublation for a series of logoi concerning the substructure of encyclopedic dialogs such as systems, derivative, extremum, quantification, variational principle, equation, symmetry, OR, optimization, approximation, yinyang, combination, normality‐abnormality, framework, modeling, simulation, relativity, recognition, practice, methodology, mathematics, operations and transformations, quotientization, product, clustering, Banach completeness theorem, Weierstrass approximation theorem, Jackson approximation theorem, Taylor theorem, approximation transformation theorems due to Walsh‐Sewell mathematical school, Hilbert problems, Cauchy theorem, theorems of equation stability, function theory, logic, paradox, axiomatization, cybernetics, dialectics, multistep decision, computer, synergy, vitality and the basic logoi for history, ethics, economics, society OR, aesthetics, journalism, institution, resource and traffics, AI, IT, etc.

Details

Kybernetes, vol. 40 no. 1/2
Type: Research Article
ISSN: 0368-492X

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Book part
Publication date: 26 October 2015

Maria Teresa Tatto, Michael Rodriguez and Yang Lu

Are education systems converging toward a global model of teacher education or do local models tend to predominate in spite of attempts to reform them? How much do global…

Abstract

Are education systems converging toward a global model of teacher education or do local models tend to predominate in spite of attempts to reform them? How much do global, national, and local cultures shape and condition future teachers’ opportunities to learn to teach? How do these opportunities influence teachers’ pedagogical content knowledge? In this chapter we use data from the IEA’s first study of the effectiveness of pre-service teacher education in order to investigate teacher education policy, program structure, and outcomes. Using multilevel modeling we found that across countries individual characteristics have a similar and powerful influence on what future teachers come to know at the end of their pre-service programs. The effects of teacher education curriculum on future teachers’ mathematics pedagogical content knowledge reaffirm the prevalence of local cultures on the implementation of an increasingly globalized ideal. We conclude that while the provision of teacher education shares many common features in goals and structure across countries, it is strongly influenced by local conditions and norms, and by cultural notions of the knowledge that is considered essential – framing how quality is to be defined and operationalized – when learning to teach.

Details

Promoting and Sustaining a Quality Teacher Workforce
Type: Book
ISBN: 978-1-78441-016-2

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Article
Publication date: 1 April 1998

A. Manikas and N.H. Dowlut

This paper reports some investigative results obtained through the application of differential geometry to the array manifold of a direction finding (DF) sensor array. It…

Abstract

This paper reports some investigative results obtained through the application of differential geometry to the array manifold of a direction finding (DF) sensor array. It emphasises the crucial but so far disregarded role of the array manifold in the performance of subspace‐based direction finding (DF) algorithms and then proceeds to a compact mathematical analysis of the array manifold using the tools of differential geometry. The results thus obtained are used to quantify the effects of the array manifold properties on the performance of a DF system and to design superresolution sensor arrays.

Details

Kybernetes, vol. 27 no. 3
Type: Research Article
ISSN: 0368-492X

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Article
Publication date: 24 May 2013

Jyri Leskinen, Hong Wang and Jacques Périaux

The purpose of this paper is to compare the efficiency of four different algorithmic parallelization methods for inverse shape design flow problems.

Abstract

Purpose

The purpose of this paper is to compare the efficiency of four different algorithmic parallelization methods for inverse shape design flow problems.

Design/methodology/approach

The included algorithms are: a parallelized differential evolution algorithm; island‐model differential evolution with multiple subpopulations; Nash differential evolution with geometry decomposition using competitive Nash games; and the new Global Nash Game Coalition Algorithm (GNGCA) which combines domain and geometry decomposition into a “distributed one‐shot” method. The methods are compared using selected academic reconstruction problems using a different number of simultaneous processes.

Findings

The results demonstrate that the geometry decomposition approach can be used to improve algorithmic convergence. Additional improvements were achieved using the novel distributed one‐shot method.

Originality/value

This paper is a part of series of articles involving the GNGCA method. Further tests implemented for more complex problems are needed to study the efficiency of the approaches in more realistic cases.

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Article
Publication date: 6 September 2019

Vahide Bulut

The purpose of this study is to obtain the differential geometric analysis of autonomous wheel-legged robots and their trajectories on the terrain.

Abstract

Purpose

The purpose of this study is to obtain the differential geometric analysis of autonomous wheel-legged robots and their trajectories on the terrain.

Design/methodology/approach

The author uses a wheel using the osculating sphere of the curve on rough terrain. Additionally, the author expresses a triple osculating sphere wheel by taking advantage of differential geometry. Moreover, the author examined the consecutive wheel center-curves to obtain the optimum posture of a micro-hydraulic toolkit (MHT) robot.

Findings

The author examined the terrain path, which is crucial for trajectory planning in terms of the geometric perspective. The author designed the triple MHT wheel using the osculating sphere of the MHT robot trajectory by taking advantage of local differential geometric properties of this curve on the terrain. The consecutive wheel center-curves were expressed and studied based on differential geometry.

Originality/value

The author provides a novel approach for the optimum posture of an MHT robot using consecutive wheel-center curves and provides an original perspective to MHT robot and its trajectory by using differential geometry.

Details

Engineering Computations, vol. 37 no. 2
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 13 June 2019

Debayan Das, Leo Lukose and Tanmay Basak

The purpose of the paper is to study natural convection within porous square and triangular geometries (design 1: regular isosceles triangle, design 2: inverted isosceles…

Abstract

Purpose

The purpose of the paper is to study natural convection within porous square and triangular geometries (design 1: regular isosceles triangle, design 2: inverted isosceles triangle) subjected to discrete heating with various locations of double heaters along the vertical (square) or inclined (triangular) arms.

Design/methodology/approach

Galerkin finite element method is used to solve the governing equations for a wide range of modified Darcy number, Dam = 10−5–10−2 with various fluid saturated porous media, Prm = 0.015 and 7.2 at a modified Rayleigh number, Ram = 106 involving the strategic placement of double heaters along the vertical or inclined arms (types 1-3). Adaptive mesh refinement is implemented based on the lengths of discrete heaters. Finite element based heat flow visualization via heatlines has been adopted to study heat distribution at various portions.

Findings

The strategic positioning of the double heaters (types 1-3) and the convective heatline vortices depict significant overall temperature elevation at both Dam = 10−4 and 10−2 compared to type 0 (single heater at each vertical or inclined arm). Types 2 and 3 are found to promote higher temperature uniformity and greater overall temperature elevation at Dam = 10−2. Overall, the triangular design 2 geometry is also found to be optimal in achieving greater temperature elevation for the porous media saturated with various fluids (Prm).

Practical implications

Multiple heaters (at each side [left or right] wall) result in enhanced temperature elevation compared to the single heater (at each side [left or right] wall). The results of the current work may be useful for the material processing, thermal storage and solar heating applications.

Originality/value

The heatline approach is used to visualize the heat flow involving double heaters along the side (left or right) arms (square and triangular geometries) during natural convection involving porous media. The heatlines depict the trajectories of heat flow that are essential for thermal management involving larger thermal elevation. The mixing cup or bulk average temperature values are obtained for all types of heating (types 0-3) involving all geometries, and overall temperature elevation is examined based on higher mixing cup temperature values.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 9
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 15 June 2010

James M. Gibert, Eric M. Austin and Georges Fadel

The purpose of this paper is to focus on the changing dynamics of the ultrasonic consolidation (UC) process due to changes in substrate geometry. Past research points to a…

Abstract

Purpose

The purpose of this paper is to focus on the changing dynamics of the ultrasonic consolidation (UC) process due to changes in substrate geometry. Past research points to a limiting height to width ranging from 0.7 to 1.2 on build features.

Design/methodology/approach

Resonances of a build feature due to a change in geometry are examined and then a simple non‐linear dynamic model of the UC process is constructed that examines how the geometry change may influence the overall dynamics of the process. This simple model is used to provide estimates of how substrate geometry affects the differential motion at the bonding interface and the amount of energy emitted by friction change due to build height. The trends of changes in natural frequency, differential motion, and frictional energy are compared to experimental limits on build height.

Findings

The paper shows that, at the nominal build, dimensions of the feature the excitation caused by the UC approach two resonances in the feature. In addition trends in regions of changes of differential motion, force of friction, and frictional energy follow the experimental limit on build height.

Originality/value

This paper explores several aspects of the UC process not currently found in the current literature: examining the modal properties of build features, and a lumped parameter dynamic model to account for the changes in of the substrate geometry.

Details

Rapid Prototyping Journal, vol. 16 no. 4
Type: Research Article
ISSN: 1355-2546

Keywords

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