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Articles 1 - 8 of 8
Full-Text Articles in Mathematics
The Second Hull Of A Knotted Curve, Jason Cantarella, Greg Kuperberg, Robert B. Kusner, John M. Sullivan
The Second Hull Of A Knotted Curve, Jason Cantarella, Greg Kuperberg, Robert B. Kusner, John M. Sullivan
Robert Kusner
The convex hull of a set K in space consists of points which are, in a certain sense, "surrounded" by K. When K is a closed curve, we define its higher hulls, consisting of points which are "multiply surrounded" by the curve. Our main theorem shows that if a curve is knotted then it has a nonempty second hull. This provides a new proof of the Fary/Milnor theorem that every knotted curve has total curvature at least 4pi.
Sheep Updates 2003 - Wool, Richard Coole, Stephen Gherardi, Chris Oldham, K. Curtis, J. Stanton, Johan Greeff, Chris Oldham, Mike Hyder, Beth Pagamoni, Andrew Thompson, Tom Plaisted, Kazue Tanaka, Mike Ferguson, Darren Gordon, Andrew Peterson, Peter Sommerville
Sheep Updates 2003 - Wool, Richard Coole, Stephen Gherardi, Chris Oldham, K. Curtis, J. Stanton, Johan Greeff, Chris Oldham, Mike Hyder, Beth Pagamoni, Andrew Thompson, Tom Plaisted, Kazue Tanaka, Mike Ferguson, Darren Gordon, Andrew Peterson, Peter Sommerville
Sheep Updates
This session covers six papers from different authors:1.‘Pastures from space’ - an opportunity to increase the profitability of sheep production Richard Coole Farmer Kojonup W.A. Stephen Gherardi Chris Oldham Department of Agriculture Western Australia 2. K. Curtis Department of Agriculture WA J. Stanton Department of Agriculture WA and Curtin University 3. Is selection of ewe hogget replacement on measurement profitable? Johan Greeff Department of Agriculture of Western Australia 4. Optimising the nutrition/grazing management of ewe flocks Chris Oldham Mike Hyder Beth Paganoni Department of Agriculture of Western Australia Andrew Thompson Department of Primary Industries, Hamilton, Victoria Tom Plaisted Kazue Tanaka …
Developing Into Series And Returning From Series: A Note On The Foundations Of Eighteenth-Century Analysis, Giovanni Ferraro, Marco Panza
Developing Into Series And Returning From Series: A Note On The Foundations Of Eighteenth-Century Analysis, Giovanni Ferraro, Marco Panza
MPP Published Research
In this paper we investigate two problems concerning the theory of power series in 18th-century mathematics: the development of a given function into a power series and the inverse problem, the return from a given power series to the function of which this power series is the development. The way of conceiving and solving these problems closely depended on the notion of function and in particular on the conception of a series as the result of a formal transformation of a function. After describing the procedures considered acceptable by 18th-century mathematicians, we examine in detail the different strategies—both direct and …
Stone Coalgebras, Clemens Kupke, Alexander Kurz, Yde Venema
Stone Coalgebras, Clemens Kupke, Alexander Kurz, Yde Venema
Engineering Faculty Articles and Research
In this paper we argue that the category of Stone spaces forms an interesting base category for coalgebras, in particular, if one considers the Vietoris functor as an analogue to the power set functor. We prove that the so-called descriptive general frames, which play a fundamental role in the semantics of modal logics, can be seen as Stone coalgebras in a natural way. This yields a duality between the category of modal algebras and that of coalgebras over the Vietoris functor. Building on this idea, we introduce the notion of a Vietoris polynomial functor over the category of Stone spaces. …
Notes On Interpolation In The Generalized Schur Class. Ii. Nudelman's Problem, Daniel Alpay, T. Constantinescu, A. Dijksma, J. Rovnyak, A. Dijksma
Notes On Interpolation In The Generalized Schur Class. Ii. Nudelman's Problem, Daniel Alpay, T. Constantinescu, A. Dijksma, J. Rovnyak, A. Dijksma
Mathematics, Physics, and Computer Science Faculty Articles and Research
An indefinite generalization of Nudel′man’s problem is used in a systematic approach to interpolation theorems for generalized Schur and Nevanlinna functions with interior and boundary data. Besides results on existence criteria for Pick-Nevanlinna and Carath´eodory-Fej´er interpolation, the method yields new results on generalized interpolation in the sense of Sarason and boundary interpolation, including properties of the finite Hilbert transform relative to weights. The main theorem appeals to the Ball and Helton almost-commutant lifting theorem to provide criteria for the existence of a solution to Nudel′man’s problem.
A Unifying Field In Logics: Neutrosophic Logic Neutrosophy, Neutrosophic Set, Neutrosophic Probability (Chinese Translation), Florentin Smarandache, Feng Liu
A Unifying Field In Logics: Neutrosophic Logic Neutrosophy, Neutrosophic Set, Neutrosophic Probability (Chinese Translation), Florentin Smarandache, Feng Liu
Branch Mathematics and Statistics Faculty and Staff Publications
中智学为何诞生? 中智学(neutrosophy)起源于1995年美国, 它站在东西文化交融的立场上, 从对立统一的角度探索从科学技术到文学 艺术的一切宏观及微观结构, 构造超越一切学科、超越自然科学与社会科学界限的统一场, 以解决当今认知科学、信息 科学、系统科学、经济学、量子力学等科学技术前沿难题——非确定性问题。中智学努力通过新型开放模式改造当今 各自然科学与社会科学, 实现它们的新陈代谢、改革创新和更新换代。中智学在我们中国还属空白, 故借此对学科正式 命名并引入中国。 科学是真理吗? 比如, 当今信息科学的突出问题之一就是知识表达、知识处理及知识交流中的逻辑单一性: 不是真就是假, 从而不 能面对任何矛盾和冲突。由此, 人工智能、计算机网络、数据库、信息工程, 乃至电子商务、电子政务多多少少在走死 胡同。从表面上看, 它是模糊数学或协调逻辑的问题, 而从本质上看, 它属于结构性问题, 涉及到对哲学、逻辑学、集 合论、概率论、认知科学、信息科学基本概念以及众多相关领域的重新认识、重新塑造问题。 众所周知, 我国学习西方, 只图表面, 而不注重科学的内在结构, 不懂科学的概念和原理中也有基础设施 (换句话 说, 就是基础设施的基础设施), 从而建不起高楼大厦, 更谈不上科学上的自主, 从而形成盲目跟从西方的弊病。 科学, 这个被认为是永恒的真理, 其本质上没有半点永恒, 相反, 它时刻处于新老交替、新陈代谢、自我否定、自 我淘汰的动态之中——即使存在什么永恒的真理, 也终究会被后人推翻。科学实际上是一种战争, 而中智学正是关于它 的战略战术的科学。 当今世界上高深的科学莫过于爱因斯坦的相对论, 然而一切的一切, 都是建立在恒定光速的基础上——它正 在被现代的人们推翻!
A Unifying Field In Logics: Neutrosophic Logic Neutrosophy, Neutrosophic Set, Neutrosophic Probability (In Traditional Chinese), Florentin Smarandache, Feng Liu
A Unifying Field In Logics: Neutrosophic Logic Neutrosophy, Neutrosophic Set, Neutrosophic Probability (In Traditional Chinese), Florentin Smarandache, Feng Liu
Branch Mathematics and Statistics Faculty and Staff Publications
No abstract provided.
Strukturationen Der Interaktivität, Rudolf Kaehr