Commutative algebra | Ideals (ring theory)
In mathematics, in the area of commutative algebra, tight closure is an operation defined on ideals in positive characteristic. It was introduced by Melvin Hochster and Craig Huneke . Let be a commutative noetherian ring containing a field of characteristic . Hence is a prime number. Let be an ideal of . The tight closure of , denoted by , is another ideal of containing . The ideal is defined as follows. if and only if there exists a , where is not contained in any minimal prime ideal of , such that for all . If is reduced, then one can instead consider all . Here is used to denote the ideal of generated by the 'th powers of elements of , called the th Frobenius power of . An ideal is called tightly closed if . A ring in which all ideals are tightly closed is called weakly -regular (for Frobenius regular). A previous major open question in tight closure is whether the operation of tight closure commutes with localization, and so there is the additional notion of -regular, which says that all ideals of the ring are still tightly closed in localizations of the ring. found a counterexample to the localization property of tight closure. However, there is still an open question of whether every weakly -regular ring is -regular. That is, if every ideal in a ring is tightly closed, is it true that every ideal in every localization of that ring is also tightly closed? (Wikipedia).
Tight or release orange nut for clamping or repositioning green bar.
From playlist Mechanisms
Loose the screw for moving the stopper to new position and then tighten it. The stopper is kept immobile by wedge mechnism.
From playlist Mechanisms
This knot is very useful for adjusting tie downs quickly and easily. For example, a tarp could be held down by a series of these knots and be made very tight so the wind cannot make it rise, and easily be removed simply by sliding the knots later. A taut line knot is also used to keep larg
From playlist Practical Projects & Skills
Green tube and blue fixed jaw are fixed together. Tight or release grey nut for clamping or repositioning yellow tube. The green tube is cut off for easy understanding.
From playlist Mechanisms
Scientists tie tightest knot ever
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From playlist Materials and technology
Tight or release orange nut for clamping or repositioning violet and yellow tubes simultaneously. The yellow tube is released thanks to the flexibility of the white support. The part below the mechanism is the support, which is cut off half.
From playlist Mechanisms
http://www.mekanizmalar.com This is a flash animation of a hydraulic closed center valve.
From playlist Pneumatic and Hydraulics
Alex Wright - Minicourse - Lecture 5
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From playlist Maryland Analysis and Geometry Atelier
P. Apisa - Marked points in genus two and beyond
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Yoga with Olivia part 5 - Opening up tight shoulders
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From playlist Yoga
Complex geometry of Teichmuller domains (Lecture 2) by Harish Seshadri
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In this Wolfram Technology Conference presentation, Seth Chandler explores the practicalities of using J/Link to establish Mathematica as a communications hub among code developed in Clojure, Scala, and Jython. For more information about Mathematica, please visit: http://www.wolfram.com/m
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Why do shoelaces untie themselves?
Failure to stay knotty is a two-stage process according to a new study of lace mechanics. Learn more: http://scim.ag/2oVypF9
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Kimihiko Motegi: L-space knots in twist families and satellite L-space knots
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From playlist Mathematics
Vyacheslav Egorov: invokedynamic.js | JSConf EU 2014
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From playlist JSConf EU 2014
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From playlist Mathematics
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