61. Manifold -- From Wolfram MathWorld A manifold is a topological space that is locally Euclidean (i.e., around every point, there is a neighborhood that is topologically the same as the open http://mathworld.wolfram.com/Manifold.html

Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Rowland, Todd Manifold A manifold is a topological space that is locally Euclidean (i.e., around every point, there is a neighborhood that is topologically the same as the open unit ball in ). To illustrate this idea, consider the ancient belief that the Earth was flat as contrasted with the modern evidence that it is round. The discrepancy arises essentially from the fact that on the small scales that we see, the Earth does indeed look flat. In general, any object that is nearly "flat" on small scales is a manifold, and so manifolds constitute a generalization of objects we could live on in which we would encounter the round/flat Earth problem, as first codified by Poincaré. More concisely, any object that can be "charted" is a manifold. One of the goals of topology is to find ways of distinguishing manifolds. For instance, a circle is topologically the same as any closed loop, no matter how different these two manifolds may appear. Similarly, the surface of a coffee mug with a handle is topologically the same as the surface of the donut, and this type of surface is called a (one-handled) torus As a topological space , a manifold can be compact or noncompact, and

62. Crocheted Chaos Their crocheted model, called the ‘Lorenz manifold’, is a very helpful tool for If you would like to crochet your own Lorenz manifold in time for http://www.physorg.com/news2395.html

PhysOrg Account: Sign In Sign Up Home Nanotechnology ... General Science Published: 05:04 EST, December 16, 2004 Toolbox Rating: 5 Bookmark Save as PDF Print Email Blog It Digg It del.icio.us Slashdot It! Stumble It! Crocheted chaos The famous Lorenz equations that describe the nature of chaotic systems – such as the weather – have been turned into a beautiful real-life object, by crocheting computer-generated instructions. It is not often that a serious mathematics journal contains a crochet pattern, but the current issue of the Mathematical Intelligencer has instructions on how to crochet your very own model of chaos. It looks like a large Christmas decoration. Dr Hinke Osinga and Professor Bernd Krauskopf, both in Bristol University's Department of Engineering Mathematics, have turned the famous Lorenz equations that describe the nature of chaotic systems – such as the weather or a turbulent river – into a beautiful real-life object, by crocheting computer-generated instructions. Dr Osinga explained: “Imagine a leaf floating in a turbulent river and consider how it passes either to the left or to the right around a rock somewhere downstream. Those special leaves that end up clinging to the rock must have followed a very unique path in the water. Each stitch in the crochet pattern represents a single point (a leaf) that ends up at the rock.” Together all the points (stitches) define a complicated surface, according to the Lorenz equations. Osinga and Krauskopf have developed a method to describe such surfaces using a computer. After months of staring at animations on a screen, they suddenly realised that in fact their computations had naturally generated crochet instructions.

63. Toyota Exhaust Manifold: Modern Replacement Toyota Exhaust Manifolds, Durable An Highperformance Toyota exhaust manifold designed to bring satisfying work for the efficient completion of exhaust system’s role in each Toyota innovation. http://www.innerauto.com/Toyota_Parts/Toyota_Exhaust_Manifold/

Home View Cart Login Retrieve Quote ... Contact Us Order Auto Parts Here Shop For Body Parts, Engine Parts and Accessories - Select Your Vehicle Select Make Select Year Select Model Toyota Exhaust Manifold Can you imagine how a country that fell into the hands of furry stood up from dust and now leads the world when it comes to technological advances? It is unbelievable indeed, but Japan made it there, just where it now lies. A proof of its success is the achievement that Toyota has reached. After sixty years of weaving innovations in automotive machinery, Toyota Motor Co. Ltd has grown as the world’s third largest automotive manufacturer and the Japanese chief in vehicle production. Every six seconds it produces one car or more than 4.5 million yearly. As you stroll or drive along urban places you’ll find Toyotas rolling their wheels in almost every block. Packed with advance technology and improved designs, they gracefully show the world what really is there about a Toyota. The engineers of Toyota see to it that every detail of the products they create is of premium quality. This is evident in the attributes of Toyota exhaust manifolds. As you would know exhaust manifold doesn’t ultimately affect the performance of the machine, but its importance to the whole operation cannot be devalued, thus are as well made to provide quality just as how other Toyota performance do. They are machined through the efficiency of Toyota’s latest technology and run through careful and efficient quality checking.

64. Level Switch Devices - Pressure Switch Instruments - Gems Sensors Gems PreDyne Manifold Assemblies offer features you require, All Gems PreDyne valve families can be integrated into a manifold system. http://www.gemssensors.com/content.aspx?id=340

65. Pall Manifold Assemblies A filter manifold incorporates many of the individual components that protect and operate a complex fluid system. A single manifold module typically http://www.pall.com/Aerospace_2935.asp

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