Dubins path - Revision history

en>Saung Tadashi: Removed
which was accidentally added

2014-09-30T18:24:10Z

Removed <br /> which was accidentally added

← Older revision		Revision as of 20:24, 30 September 2014
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	~~Quantity versus quality. That�s an issue that feels relevant in fashion today, with the current focus on fast fashion from high street through to pre-collection. It also feels relevant coming~~ from ~~New York~~, ~~a fashion week~~ with ~~a schedule that at first glance seems rammed, but upon closer inspection, like a mirage, fades away to practically nothing.<br><br>~~		27 yr old Valuer Deandre from Englehart, spends time with hobbies and interests which include exercise, [https://www.youtube.com/watch?v=20KQhsAFzw4&list=PLamGIcKOwjLAkEC1eNEGMRs1281D71Gu7&index=5 the holistic sanctuary] and drawing. Has been a travel maniac and in recent years arrived at Historic Centre (Chorá) with the Monastery of Saint John.

	Nothing of note, in any case. Clocking in at nine days, New York is only rivalled by Paris when it comes to sheer heft, but the city�s fashion direction is really defined by a handful of designers. Despite the name, there wasn�t that much in New York this spring/summer 2015 season that really registered as �new�<br><br>
	~~Instead, what we often saw was a composite of tried-~~and~~-tested crowd pleasers, and maybe a few novel ideas filched from the back catalogues of other designers<br>~~
	That approach - hoodwinking press and buyers with the illusion of novelty, like the man behind the curtain making believe he was the great and all-powerful Oz - is endemic across the industry as a whole. Nevertheless, there�s something about New York that throws it into sharper relief<br><br>
	~~Take Victoria Beckham�s show~~, ~~liberal as it was in its borrowing of stylist tropes culled from past collections by~~ [~~http~~://www.pcs-systems.co.uk/Images/celinebag.aspx Celine handbags] and Jil Sander. Beckham, however, has made no qualms about the fact that she isn�t a trained designer: instead, she acts as an editing eye, more like a magazine stylist - or an especially canny shopper<br><br>
	She and her team (because they deserve a hefty dose of credit as the power behind the throne) are adept at nailing what feels right in a particular moment. Sometimes, of course, what feels right is a moment another designer nailed not that long ago. It looks fine second time around<br><br>
	~~The bags were good. And it�ll sell<br>~~
	~~New York Fashion Week in pictures <br>~~
	Sales are often seen as the key motivating factor in the New York fashion scene. That�s not to say that Milanese, Parisian and London designers don�t shift product. They do, but America was built on a history of mass manufacture, rather than the handmade ethos that still informs the European capitals via the haute couture, alta moda and Savile Row<br><br>
	Maybe that conditions American designers into thinking about their labels as true businesses - young New York designers throw about the word �brand� with wild abandon, in a manner that their French or British counterparts shy away from (young Milanese designers are virtually non-existent, but that�s a discussion for another time, and a different city<br>
	~~Kendall Jenner walks the runway at the Diane Von Furstenberg fashion show during New York Fashion Wee<br>~~
	There�s no designer younger and more branded than Alexander Wang: he founded his label aged 21 in 2005, off the back of a few knitted sweaters. It�s now valued, conservatively, at �20m and Wang is a fashion-week fixture. Wang slots into the Victoria Beckham camp when it comes to design, although he doubtless won�t appreciate the comparison. Nevertheless, his collections aren�t groundbreaki<br><br>

	~~Rather, they�re artful bricolage, fusing existing fashion references, tricky, techy textiles, odd accessories and ever-shifting ideas of co<br>.~~
	~~Bricolage sounds cool, but is actually just French for �tinkering�, which is exactly what Wang does. After a few seasons of duds ([http://pinterest~~.com/~~search/pins/~~?q=~~silly+fur silly fur~~] mittens, tired logo-mania, last season�s ugly utility), this collection got the mix down. Sexed-up, stripped-back sportswear, in neon-flushed fabrics with plenty of Aertex, rubberised treatments and fake function. It wasn�t original in the slightest, but it had enough energy to sweep you al<br><br>

	Quite a few New York designers get by on that, by pumping up the energy around their clothes rather than translating said energy into the garments themselves. It can frequently lead to a zinging, post-show high followed by a crash when you actually see the stuff out of cont<br><br>

	Spring/summer 2015 looks by Jason Wu You sometimes get that with Thom Browne, so complex and convoluted are the catwalk mise en sc�nes within which he places his clothing. This season, models paraded lavishly embroidered tailoring, feather-pricked cardigan suits and sequinned PVC on a freshly-mown lawn, to a spoken-word soundtrack waffling on about a bunch of sisters and ~~what they w<br><br>~~

	~~The story was written by Browne himself, the voice was Diane Kea<br>n~~.
	~~Apparently, the six sisters are~~ a ~~cross between the Beale sisters of Grey Gardens (taste levels)~~ and ~~the [http://Www.Reddit.com/r/howto/search?q=Rockerfellers Rockerfellers] of Park Avenue (cash levels - Browne�s plainest suits come~~ in at ~~around two grand~~). It was an uplifting distraction, and the energy came not from a thumping soundtrack or styling gimmicks, but from the clothes themselves - however untenable they may be for real women�s real li<br><br><br>

	There was a sense of reality to what Lazaro Hernandez and Jack Mccollough offered at Proenza Schouler. �It�s really about American sportswear, and this idea of �normal�,� said Hernandez before a show that was anything but. Their �normal� included leather vests plaited to resemble houndstooth, nylon thread crocheted into openwork dresses, and perforated blouses and skirts in leather so tissue-fine it ended up looking like nylon. �It�s dumb,� they said �It�s the clothes we all wear every day.� Meaning clothes that weren�t clever-clever or trying too hard, and that the work in, say, an argyle dress composed of 144 pattern pieces and executed without fit seams, couldn�t be immediately read in a two-dimensional image but had to be experienced in t<br><br>lesh.

	~~Read more: Marc Jacobs' no makeup models du<br>ng NYFW~~
	~~Victoria Beckha<br>at NYFW~~
	~~Too many New York designers stick to tried and tested recipesThere was a touch of the dumb to Jason Wu�s show, too. The good kind of dumb - the dumb glamour of a bugle-beaded evening gown~~ with the ~~easiness of aT-shirt, or a billowing silk-jersey dress with a Grecian si<br><br>city.~~

	They felt easy, really ready to wear - as opposed to so many of the resoundingly difficult clothes dubbed that way. The final say from New York fashion week comes from Marc Jacobs. This season, he, too, seemed fixated on the notion of ~~real - or perhaps, hy<br><br>real.~~

	His audience listened, via headphones on each seat, to piped-in background noise from a middle-American house, while a distinctly Koonsian reworking of one, 10,000sq ft of shocking pink, sat in the middle of his catwalk. A model presents a creation by Jason Wu Spring/Summer 2015 collection during New York Fash<br>n Week
	Those bore no relation to the clothes, riffs on army surplus in satin punctuated with cartoonish holes and peppered with buckshot spherical embroidery, in plump, doll-like shapes. Barbie meets Action Man - maybe the pink, centre-stage shack was her dream house? <br><br>s me.

	Whatever the rationale, neither clothes nor show looked like anything else this week. Which was precisely the point. Marc Jacobs keeps his eye on what other designers are doing. It�s not to copy them, or even to check if they copy him, but out of a perverse contrariness, a wish to buck the st<br><br> quo.

	If other designers do gingham and sugary-sweet bridesmaid pastels, you can bet Jacobs will show polka dots and sludgy fatigues. Regardless of taste, or even relevance, you have to applaud Jacobs for at least showing us something consistently, contrarily new, in a New York that desperately needs it.

en>Alexander.moriarty: move : from infront of $to now display correctly. prev error was \begin not found$

2014-02-23T10:52:57Z

move : from infront of <math> to now display correctly. prev error was \begin not found

← Older revision		Revision as of 12:52, 23 February 2014
Line 1:		Line 1:
	~~In [[algebra]]~~, the ~~'''Gelfand–Kirillov dimension''' of~~ a ~~[[right module]] ''M'' over~~ a ~~[[K-algebra\|''k''-algebra]] ''A'' is:~~		Quantity versus quality. That�s an issue that feels relevant in fashion today, with the current focus on fast fashion from high street through to pre-collection. It also feels relevant coming from New York, a fashion week with a schedule that at first glance seems rammed, but upon closer inspection, like a mirage, fades away to practically nothing.<br><br>

	:<~~math~~>~~\operatorname{GKdim} = \sup \limsup_{n \~~to ~~\infty} \log_n \dim_k M_0 V^n~~<~~/math~~>		Nothing of note, in any case. Clocking in at nine days, New York is only rivalled by Paris when it comes to sheer heft, but the city�s fashion direction is really defined by a handful of designers. Despite the name, there wasn�t that much in New York this spring/summer 2015 season that really registered as �new�<br><br>
			Instead, what we often saw was a composite of tried-and-tested crowd pleasers, and maybe a few novel ideas filched from the back catalogues of other designers<br>
			That approach - hoodwinking press and buyers with the illusion of novelty, like the man behind the curtain making believe he was the great and all-powerful Oz - is endemic across the industry as a whole. Nevertheless, there�s something about New York that throws it into sharper relief<br><br>
			Take Victoria Beckham�s show, liberal as it was in its borrowing of stylist tropes culled from past collections by [http://www.pcs-systems.co.uk/Images/celinebag.aspx Celine handbags] and Jil Sander. Beckham, however, has made no qualms about the fact that she isn�t a trained designer: instead, she acts as an editing eye, more like a magazine stylist - or an especially canny shopper<br><br>
			She and her team (because they deserve a hefty dose of credit as the power behind the throne) are adept at nailing what feels right in a particular moment. Sometimes, of course, what feels right is a moment another designer nailed not that long ago. It looks fine second time around<br><br>
			The bags were good. And it�ll sell<br>
			New York Fashion Week in pictures <br>
			Sales are often seen as the key motivating factor in the New York fashion scene. That�s not to say that Milanese, Parisian and London designers don�t shift product. They do, but America was built on a history of mass manufacture, rather than the handmade ethos that still informs the European capitals via the haute couture, alta moda and Savile Row<br><br>
			Maybe that conditions American designers into thinking about their labels as true businesses - young New York designers throw about the word �brand� with wild abandon, in a manner that their French or British counterparts shy away from (young Milanese designers are virtually non-existent, but that�s a discussion for another time, and a different city<br>
			Kendall Jenner walks the runway at the Diane Von Furstenberg fashion show during New York Fashion Wee<br>
			There�s no designer younger and more branded than Alexander Wang: he founded his label aged 21 in 2005, off the back of a few knitted sweaters. It�s now valued, conservatively, at �20m and Wang is a fashion-week fixture. Wang slots into the Victoria Beckham camp when it comes to design, although he doubtless won�t appreciate the comparison. Nevertheless, his collections aren�t groundbreaki<br><br>

	~~where the sup is taken over all finite~~-~~dimensional [[Linear subspace\|subspace]]s~~ <~~math~~>~~V \subset A<~~/~~math>~~ and <~~math~~>~~M_0 \subset M~~<~~/math~~>.		Rather, they�re artful bricolage, fusing existing fashion references, tricky, techy textiles, odd accessories and ever-shifting ideas of co<br>.
			Bricolage sounds cool, but is actually just French for �tinkering�, which is exactly what Wang does. After a few seasons of duds ([http://pinterest.com/search/pins/?q=silly+fur silly fur] mittens, tired logo-mania, last season�s ugly utility), this collection got the mix down. Sexed-up, stripped-back sportswear, in neon-flushed fabrics with plenty of Aertex, rubberised treatments and fake function. It wasn�t original in the slightest, but it had enough energy to sweep you al<br><br>

	~~== In~~ the ~~theory~~ of ~~D-Modules ==~~		Quite a few New York designers get by on that, by pumping up the energy around their clothes rather than translating said energy into the garments themselves. It can frequently lead to a zinging, post-show high followed by a crash when you actually see the stuff out of cont<br><br>

	~~Given a right module ''M'' over the [[Weyl algebra]] <math>A_n<~~/~~math>, the Gelfand–Kirillov dimension of ''M'' over the Weyl algebra coincides~~ with ~~the dimension of ''M''~~, ~~which is by definition the degree of the [[Hilbert polynomial]] of ''M''. This enables to prove additivity in [[short exact sequence]]s for the Gelfand–Kirillov dimension~~ and ~~finally to prove [[Weyl_algebra#Properties of~~ the ~~Weyl algebra\|Bernstein's inequality]],~~ which ~~states that the dimension of ''M'' must be at least ''n''~~. This ~~leads to the definition of [[D~~-~~module\|holonomic D~~-~~Module]]s as those with the minimal dimension ''n''~~, and ~~these modules play a great role in the [[geometric Langlands program]].~~		Spring/summer 2015 looks by Jason Wu You sometimes get that with Thom Browne, so complex and convoluted are the catwalk mise en sc�nes within which he places his clothing. This season, models paraded lavishly embroidered tailoring, feather-pricked cardigan suits and sequinned PVC on a freshly-mown lawn, to a spoken-word soundtrack waffling on about a bunch of sisters and what they w<br><br>

	~~== References ==~~		The story was written by Browne himself, the voice was Diane Kea<br>n.
	*{{cite journal\|title=A remark on Gelfand–Kirillov dimension\|url=http://~~www.math~~.~~washington~~.~~edu~~/~~~smith~~/~~Research~~/~~GK-rmk.pdf \|last1~~=~~Smith \|first1=S. Paul \|last2=Zhang \|first2=James J. \|year=1998 \|journal=[[Proceedings of the American Mathematical Society~~]~~] \|volume=126 \|number=2 \|pages=349–352}}~~		Apparently, the six sisters are a cross between the Beale sisters of Grey Gardens (taste levels) and the [http://Www.Reddit.com/r/howto/search?q=Rockerfellers Rockerfellers] of Park Avenue (cash levels - Browne�s plainest suits come in at around two grand). It was an uplifting distraction, and the energy came not from a thumping soundtrack or styling gimmicks, but from the clothes themselves - however untenable they may be for real women�s real li<br><br><br>
	* Coutinho: A primer of ~~algebraic D~~-~~modules~~. ~~Cambridge~~, ~~1995~~

	~~{{DEFAULTSORT:Gelfand~~-~~Kirillov dimension}}~~		There was a sense of reality to what Lazaro Hernandez and Jack Mccollough offered at Proenza Schouler. �It�s really about American sportswear, and this idea of �normal�,� said Hernandez before a show that was anything but. Their �normal� included leather vests plaited to resemble houndstooth, nylon thread crocheted into openwork dresses, and perforated blouses and skirts in leather so tissue-fine it ended up looking like nylon. �It�s dumb,� they said �It�s the clothes we all wear every day.� Meaning clothes that weren�t clever-clever or trying too hard, and that the work in, say, an argyle dress composed of 144 pattern pieces and executed without fit seams, couldn�t be immediately read in a two-dimensional image but had to be experienced in t<br><br>lesh.
	~~[[Category:Algebra]]~~
	~~[[Category:Dimension]]~~

			Read more: Marc Jacobs' no makeup models du<br>ng NYFW
			Victoria Beckha<br>at NYFW
			Too many New York designers stick to tried and tested recipesThere was a touch of the dumb to Jason Wu�s show, too. The good kind of dumb - the dumb glamour of a bugle-beaded evening gown with the easiness of aT-shirt, or a billowing silk-jersey dress with a Grecian si<br><br>city.

	~~{{algebra~~-~~stub}}~~		They felt easy, really ready to wear - as opposed to so many of the resoundingly difficult clothes dubbed that way. The final say from New York fashion week comes from Marc Jacobs. This season, he, too, seemed fixated on the notion of real - or perhaps, hy<br><br>real.

			His audience listened, via headphones on each seat, to piped-in background noise from a middle-American house, while a distinctly Koonsian reworking of one, 10,000sq ft of shocking pink, sat in the middle of his catwalk. A model presents a creation by Jason Wu Spring/Summer 2015 collection during New York Fash<br>n Week
			Those bore no relation to the clothes, riffs on army surplus in satin punctuated with cartoonish holes and peppered with buckshot spherical embroidery, in plump, doll-like shapes. Barbie meets Action Man - maybe the pink, centre-stage shack was her dream house? <br><br>s me.

			Whatever the rationale, neither clothes nor show looked like anything else this week. Which was precisely the point. Marc Jacobs keeps his eye on what other designers are doing. It�s not to copy them, or even to check if they copy him, but out of a perverse contrariness, a wish to buck the st<br><br> quo.

			If other designers do gingham and sugary-sweet bridesmaid pastels, you can bet Jacobs will show polka dots and sludgy fatigues. Regardless of taste, or even relevance, you have to applaud Jacobs for at least showing us something consistently, contrarily new, in a New York that desperately needs it.

en>Michael Hardy at 17:27, 3 June 2012

2012-06-03T17:27:11Z

New page

In [[algebra]], the '''Gelfand–Kirillov dimension''' of a [[right module]] ''M'' over a [[K-algebra|''k''-algebra]] ''A'' is:

:<math>\operatorname{GKdim} = \sup \limsup_{n \to \infty} \log_n \dim_k M_0 V^n</math>

where the sup is taken over all finite-dimensional [[Linear subspace|subspace]]s <math>V \subset A</math> and <math>M_0 \subset M</math>.

== In the theory of D-Modules ==

Given a right module ''M'' over the [[Weyl algebra]] <math>A_n</math>, the Gelfand–Kirillov dimension of ''M'' over the Weyl algebra coincides with the dimension of ''M'', which is by definition the degree of the [[Hilbert polynomial]] of ''M''. This enables to prove additivity in [[short exact sequence]]s for the Gelfand–Kirillov dimension and finally to prove [[Weyl_algebra#Properties of the Weyl algebra|Bernstein's inequality]], which states that the dimension of ''M'' must be at least ''n''. This leads to the definition of [[D-module|holonomic D-Module]]s as those with the minimal dimension ''n'', and these modules play a great role in the [[geometric Langlands program]].

== References ==
*{{cite journal|title=A remark on Gelfand–Kirillov dimension|url=http://www.math.washington.edu/~smith/Research/GK-rmk.pdf |last1=Smith |first1=S. Paul |last2=Zhang |first2=James J. |year=1998 |journal=[[Proceedings of the American Mathematical Society]] |volume=126 |number=2 |pages=349–352}}
* Coutinho: A primer of algebraic D-modules. Cambridge, 1995

{{DEFAULTSORT:Gelfand-Kirillov dimension}}
[[Category:Algebra]]
[[Category:Dimension]]

{{algebra-stub}}

Dubins path - Revision history

en>Saung Tadashi: Removed which was accidentally added

en>Alexander.moriarty: move : from infront of to now display correctly. prev error was \begin not found

en>Michael Hardy at 17:27, 3 June 2012

en>Saung Tadashi: Removed
which was accidentally added

en>Alexander.moriarty: move : from infront of $to now display correctly. prev error was \begin not found$