140 research outputs found

    Perfect colourings of isonemal fabrics by thin striping

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    Perfect colouring of isonemal fabrics by thin striping of warp and weft and the closely related topic of isonemal prefabrics that fall apart are reconsidered and their relation further explored. The catalogue of isonemal prefabrics that fall apart is extended to order 20 for those of even genus.Comment: 25 pages, 20 figure

    Satin Non-Woven Fabrics for Designing of Self-Regulating Breathable Building Skins

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    In this paper, we introduce the concept of 2-way 2-fold genus-1 non-woven fabrics that can be used to design self-regulating breathable building skins. The advantage of non-woven structures over woven structures for breathable skin design is that they can completely be closed to stop air exchange. We have developed a theoretical framework for such non-woven structures starting from the mathematical theory of biaxial 2-fold Genus-1 woven fabrics. By re-purposing a mathematical notation that is used to describe 2-fold 2-way 2-fold genus-1 woven fabrics, we identify and classify non-woven fabrics. Within this classification, we have identified a special subset that corresponds to satin woven fabrics and allows for maximum air exchange. Any other subset of non-woven structures that correspond to other classical 2-way 2-fold genus-1 fabrics, such as plain or twill, will allow for less air exchange. We also show that there exists another subset of satin non-woven fabrics that can provide the biggest openings.Comment: 10 page

    Perfect Colourings of Isonemal Fabrics by Thick Striping

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    Perfect colouring of isonemal fabrics by thick striping of warp and weft and the closely related topic of isonemal prefabrics that fall apart are reconsidered and their relation further explored. The catalogue of isonemal prefabrics of genus V that fall apart is extended to order 20 with designs that can be used to weave cubes with colour symmetry as well as weaving symmetry.Comment: 50 diagram

    Subject Index Volumes 1–200

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    The Creation of Woven Tiles from the Union of Delaunay Lofts

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    In this work, we build upon the previously established foundations of Delaunay Lofts, which are a new class of shapes inspired by biological phenomena known as scutoids. Delaunay Lofts naturally provides edge collapse and vertex split processes, which make them highly complex in terms of topological structure. Delaunay lofts are obtained by layer-by-layer Voronoi decomposition of points. Therefore, any cross-section of a Delaunay Loft is always a convex polygon. Moreover, the only topology change from one layer to another is the change in the number of sides of cross-section polygons. Through our methodology, we obtain woven tiles as the union of Delaunay Lofts. This extension provides two advantages over the original Delaunay Lofts that can lead to woven tiles: (1) Each cross-section polygon can be non-convex, and (2) we can connect and disconnect polygons. To create woven tiles, we use unions of a linear pattern of points that can produce patterns similar to woven textiles. We have only investigated two widely used woven patterns: plain and twill. Plain woven tiles provide an approach to construct generalized Abeille’s flat vaults, which was introduced by French engineer and architect Joseph Abeille. Twill patterns provide even further generalizations of Abeille’s vaults, thus demonstrating the existence of a general class of woven tiles. By taking the union of several individual Delaunay Lofts, woven tiles appear in the resulting structure. Using this method, we are able to create non-convex polygons, as well as connecting and disconnecting the polygons in any manner we desire. Additionally, we can design the resulting shapes on each layer since we have control of the Voronoi Site locations. In developing this approach, we created a procedural framework that allows for the manipulation of rules and guidelines for the creation of the Delaunay Loft. As a result, we are able to generate a wide variety of Woven Structures based on Delaunay Lofts from tweaking various parameters. Using this method, we 3D printed some Woven Structures in order to help analyze symmetrical, structural, and tiling properties

    Moral reasons : particularism, patterns and practice

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    This is the study of the extent of the patternability of the reason-giving behaviour of morally relevant features in different ethical contexts. Whether or not the way in which a morally relevant feature contributes to the moral evaluation of different cases is generalis able is examined in this research. I argue in favour of a core and constitutive modest-generalistic theme, according to which there are general patterns of word use, to which the reason-giving behaviour of moral vocabulary in different contexts is answerable. To this end, I reject the constitutive particularistic claim which holds that the way in which a morally relevant feature behaves in different cases is fully context-dependent. An account drawn from Wittgenstein with regard to the nature of concepts which emphasises the key role of the concept 'practice' is presented to give an account of how the reason-giving behaviour of a morally relevant feature in different contexts is answerable to general patterns of word use. Ross's ethics is introduced as an example of the modest-generalistic position. To substantiate this modest-generalistic position, an apparent dilemma is presented for particularists, e.g. Dancy. In order to resolve the second horn of the dilemma, which is an example of a general problem with which any generalistic account is confronted, the account drawn from Wittgenstein with regard to the nature of concepts is again used. Finally, a distinction between the first order and the second order account of the concept 'practice' is presented to give a more plausible account of the concept 'practice' which has an indispensable role in the Wittgensteinian account

    LIPIcs, Volume 274, ESA 2023, Complete Volume

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    LIPIcs, Volume 274, ESA 2023, Complete Volum
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