완효성 비료와 4종복비의 혼용 시용이 팔레놉시스의 생육에 미치는 효과

IT needs courage to produce a text-book on the geometry of N dimensions. The subject is not unduly difficult to those who take an interest in it, but most people have deeply seated prejudices which prevent them from taking it seriously into consideration. One of the pioneers, Schlafli, in spite of his reputation in other branches of mathematics, failed to secure publication for his valuable memoir on hyperspace, and in fact it did not appear in full until after the author's death and fifty years after it was written. An Introduction to the Geometry of N Dimensions. By Prof. D. M. Y. Sommerville. Pp. xvii + 196. (London: Methuen and Co., Ltd., 1929.) 10s. net.

An Introduction to the Geometry of N Dimensions

The emergence of additive manufacturing and 3D printing technologies is introducing industrial skills deficits and opportunities for new teaching practices in a range of subjects and educational settings. In response, research investigating these practices is emerging across a wide range of education disciplines, but often without reference to studies in other disciplines. Responding to this problem, this article synthesizes these dispersed bodies of research to provide a state-of-the-art literature review of where and how 3D printing is being used in the education system. Through investigating the application of 3D printing in schools, universities, libraries and special education settings, six use categories are identified and described: (1) to teach students about 3D printing; (2) to teach educators about 3D printing; (3) as a support technology during teaching; (4) to produce artefacts that aid learning; (5) to create assistive technologies; and (6) to support outreach activities. Although evidence can be found of 3D printing-based teaching practices in each of these six categories, implementation remains immature, and recommendations are made for future research and education policy.

Invited review article: Where and how 3D printing is used in teaching and education

We present MCMAS, a model checker for the verification of multi-agent systems. MCMAS supports efficient symbolic techniques for the verification of multi-agent systems against specifications representing temporal, epistemic and strategic properties. We present the underlying semantics of the specification language supported and the algorithms implemented in MCMAS, including its fairness and counterexample generation features. We provide a detailed description of the implementation. We illustrate its use by discussing a number of examples and evaluate its performance by comparing it against other model checkers for multi-agent systems on a common case study.

/pdf/mcmas-an-open-source-model-checker-for-the-verification-of-4vixm3awd0.pdf

MCMAS: an open-source model checker for the verification of multi-agent systems

The concept of a continuous module is a generalization of that of an injective module, and conditions (), (C) and () are given for this concept in [4]. In this paper, we study modules with properties that are dual to continuity. These will be called discrete and we discuss discrete abelian groups. Throughout R is a ring with identity, M is a module over R, G is an abelian group of finite rank, E is the ring of endomorphisms of G and S is the center of E. Dual to the notion of essential submodules, we define small submodules of a module M over R.(omitted)

On discrete groups

3D printing is quickly becoming a very affordable option for producing physical objects. The term “3D printing” covers a number of closely related technologies, all of which produce a 3-dimensional physical object from a computer model by building it up in successive layers. These technologies were developed primarily for use in rapid prototyping for industrial design; they allow a designer to convert a computer model of a prototype into a physical object quickly in comparison to most previously available technologies. In addition, there are a number of other advantages that make 3D printing attractive for making mathematical models.

3D Printing for Mathematical Visualisation

Agol recently introduced the concept of a veering taut triangulation of a 3–manifold, which is a taut ideal triangulation with some extra combinatorial structure. We define the weaker notion of a “veering triangulation” and use it to show that all veering triangulations admit strict angle structures. We also answer a question of Agol, giving an example of a veering taut triangulation that is not layered.

/pdf/veering-triangulations-admit-strict-angle-structures-16ikfs1jpc.pdf

Veering triangulations admit strict angle structures

Agol recently introduced the concept of a veering taut triangulation, which is a taut triangulation with some extra combinatorial structure. We define the weaker notion of a "veering triangulation" and use it to show that all veering triangulations admit strict angle structures. We also answer a question of Agol, giving an example of a veering taut triangulation that is not layered.

/pdf/veering-triangulations-admit-strict-angle-structures-4ivpqlog51.pdf

In this paper we will promote the 3D index of an ideal triangulation T of an oriented cusped 3-manifold M (a collection of q-series with integer coefficients, introduced by Dimofte-Gaiotto-Gukov) to a topological invariant of oriented cusped hyperbolic 3-manifolds. To achieve our goal we show that (a) T admits an index structure if and only if T is 1-efficient and (b) if M is hyperbolic, it has a canonical set of 1-efficient ideal triangulations related by 2-3 and 0-2 moves which preserve the 3D index. We illustrate our results with several examples.

1-efficient triangulations and the index of a cusped hyperbolic 3-manifold

We describe our initial explorations in simulating non-euclidean geometries in virtual reality. Our simulations of three-dimensional hyperbolic space are available at h3.hypernom.com. Figure 1: A view from H. The properties of euclidean space seem natural and obvious to us, to the point that it took mathematicians over two thousand years to see an alternative to Euclid’s parallel postulate. The eventual discovery of hyperbolic geometry in the 19th century shook our assumptions, revealing just how strongly our native experience of the world blinded us from consistent alternatives, even in a field that many see as purely theoretical. Non-euclidean spaces are still seen as unintuitive and exotic, but we believe that with direct immersive experience we can get a better “feel” for them. The latest wave of virtual reality hardware, in particular the HTC Vive, tracks both the orientation and the position of the headset within a room-sized volume, allowing for such an experience. Most visualisations of hyperbolic space are seen from the outside, as in Escher’s Circle Limit series of prints, which use the Poincaré disk model of two-dimensional hyperbolic space, H2. Three-dimensional The code is available at github.com/hawksley/hypVR. (a) The three torus, giving the {4, 3, 4} honeycomb. (b) The {5, 3, 4} honeycomb. Figure 2: Screenshots from Curved spaces by Jeff Weeks. hyperbolic space, H3, can also be visualised in a similar way, via the Poincaré ball model. In virtual reality, we could simulate this ball model floating in the middle of the room. We would then generate graphics on screen using the standard euclidean graphics pipeline, and motions in real life would translate directly to motions of the virtual camera in the ambient three-dimensional euclidean space, E3, of the Poincaré ball model. Even though you would be able to put your head inside of this virtual Poincaré ball model, it would give an extrinsic experience of H3 – you would experience the metric of the Poincaré model induced from E3, and not directly experience the metric of H3. Such extrinsic visualisations provide a brief, compact snapshot of infinite hyperbolic space, yet the viewer is left to their own imagination to remodel the space to see what life might be like for an inhabitant living inside. Our goal is to make three-dimensional non-euclidean spaces feel more natural by giving people experiences inside those spaces, including the ability to move through those spaces with their bodies. Luckily, computers don’t know or care that people live in a mostly euclidean world, a world where cubes fit together four around an edge because they have 90◦ angles. As long as we program in the correct mathematics, a computer is perfectly happy simulating a hyperbolic space where cubes pack neatly, six around an edge. We took inspiration from Jeff Weeks’ Curved Spaces [5] software, a “flight simulator for multiconnected universes”, which allows the user to “fly” a spaceship through various three-dimensional manifolds, with spherical, euclidean, and hyperbolic geometries (see Figure 2). The user controls the heading of the spaceship using the mouse, and its speed using keyboard controls. With virtual reality technology however, the user controls the direction in which they are looking by turning their head, and their position by moving their body. Thus, we remove barriers between us and the space – it is easier and more natural to access the experience, particularly for users who are not familiar with moving through space using “computer game” controls, and this extra ease allows a user to discover some not-so-obvious properties of these spaces much more readily. We are currently developing a virtual reality simulation of H3, using many of the same ideas as are used in Weeks’ work. Weeks explains the implementation in detail in [6]; we give an overview in this paper. Positional tracking in modern virtual reality headsets lets us experience features of hyperbolic space, such as the effects of parallel transport, geodesic deviation and holonomy, in a very direct way. There are four ingredients that go into our virtual reality simulation of H3 as outlined in this paper: 1. A way to describe the points of H3 numerically, i.e. a model of H3 2. A way to convert points in the model into points in E3 that we can then draw on screen, 3. A way to move around H3 using the motion inputs from the virtual reality headset, and 4. A set of landmarks in H3 to draw, to help the viewer navigate the space – we use a tiling of H3.

/pdf/non-euclidean-virtual-reality-ii-explorations-of-h-e-1y729muduy.pdf

Non-euclidean Virtual Reality II: Explorations of H² ✕ E

Handle everyday research tasks with reliable, citation-backed results

Your personal Research Agent to handle research tasks with citation-backed results

Popular Tasks used by Researchers

How can I help with your research?

Meet SciSpace

Get more enhanced response by uploading the PDFs you want me to reference.

No relevant PDFs in your library

SciSpace is the AI research assistant for academics. Run systematic literature reviews on 280M+ papers, and write papers with cited sources. Trusted by 1M+ students, PhDs & researchers.

SciSpace | AI for Research

Analyze PDFs

Code & Manuscripts

Funding & Grants

Literature & Patents

Medical & Clinical Data

Systematic Review

Visualize & Present

Web & Data

Build a Google Scholar-like website for your research.

Build a website

Create charts and images for your research

Create a Chart

Write a paper for submission to a journal

Draft a manuscript

Patent Search

Design eye-catching scientific posters in minutes.

Scientific Poster Generation

Systematic Literature Review

One task is running at the moment. Your messages will be shown right after.

Drag and drop or click here to browse

Loved by <highlight>1 million+</highlight> researchers

Extract a list of specific topics and their sources from unstructured text

Topics

Compare and analyze relevant papers that matches with your search

Papers

Get insights from PDFs and bookmarked papers from your library

My library

Recent searches

Try searching for:

Catch AI-generated content in scholarly and non-scholarly content

{ai} Detector

Ai Writer

Get PDF Summaries, highlighted text explanations 

Chat with PDF

Effortlessly create in-text citations and bibliographies in APA and 2,500 other formats

Citation generator

Get explanations, summaries, and answers on academic papers

Ease up your research workflow with {scispace}'s cohort of exciting AI tools

Elevate your academic writing skills and convey your ideas the way you want

Paraphraser

Explore our range of reading and writing tools

Your file is being prepared and should be ready in a few minutes. If it's a large file, it might take a bit longer. You can close this window, and we'll email you the file when it's done.

You have reached a maximum limit of <strong>{limit}</strong> columns in the table. Remove at least <strong>1</strong> column to add or create another one.

Henry Segerman

Author Tools

Chat about Author

Papers

3D Printing for Mathematical Visualisation

Veering triangulations admit strict angle structures

Veering triangulations admit strict angle structures

1-efficient triangulations and the index of a cusped hyperbolic 3-manifold

Non-euclidean Virtual Reality II: Explorations of H² ✕ E