منابع مشابه
Strings, Chains, and Ropes
Following Antman [Amer. Math. Mon., 87 (1980), pp. 359–370], we advocate a more physically realistic and systematic derivation of the wave equation suitable for a typical undergraduate course in partial differential equations. To demonstrate the utility of this derivation, three applications that follow naturally are described: strings, hanging chains, and jump ropes.
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What is the longest rope on the unit sphere? Intuition tells us that the answer to this packing problem depends on the rope’s thickness. For a countably infinite number of prescribed thickness values we construct and classify all solution curves. The simplest ones are similar to the seamlines of a tennis ball, others exhibit a striking resemblance to Turing patterns in chemistry, or to ordered ...
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Let us begin with definitions. Fix two points A and B in R. We shall always assume that A = (0, 0, 0) and B = (1, 0, 0) so, in particular, the line AB is the x-axis and the length of the interval [AB] is equal to 1. (We shall write [AB] for the closed interval between A and B, (AB) for the corresponding open interval, and AB for the line passing through A and B.) A rope is a non-singular C-smoo...
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In a recent paper, Gallego, González and Purnaprajna showed that rational 3-ropes can be smoothed. We generalise their proof, and obtain smoothability of rational m-ropes for m ≥ 3.
متن کاملRopes: An Alternative to Strings
Programming languages generally provide a ‘string’ or ‘text’ type to allow manipulation of sequences of characters. This type is usually of crucial importance, since it is normally mentioned in most interfaces between system components. We claim that the traditional implementations of strings, and often the supported functionality, are not well suited to such general-purpose use. They should be...
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ژورنال
عنوان ژورنال: The American Journal of Medicine
سال: 2018
ISSN: 0002-9343
DOI: 10.1016/j.amjmed.2018.06.018