Lucas aggregate supply function - Revision history

151.70.12.102: /* Background */

2014-07-28T16:36:27Z

Background

← Older revision		Revision as of 18:36, 28 July 2014
Line 1:		Line 1:
	In [~~[mathematics~~]~~] (and particularly~~ in ~~[[combinatorics]])~~, the ~~'''major index''' of~~ a ~~[[permutation]] is defined as~~ the ~~sum of~~ the ~~positions~~ of ~~the [[Permutation#Ascents, descents and runs\|descents]] of the permutation~~. ~~In symbols, the major index of the permutation~~ '~~'w'' is~~		<br><br>If you happen to be searching for a [http://Ziatina4Ever.Altervista.org/userinfo.php?uid=28714 single tool] that will meet a number of requirements whilst taking up much less space in your tool box or backpack than person tools, you might want to contemplate a multi tool. These Gerber multi tool testimonials will help you decide which one will be most effective for you.<br><br>And, not surprisingly, the tool looks really good. Jay from CopTool has a great critique up at his web site that puts the tool head to head with the Fein. So this a single was just a matter of time. We're actually [http://mynewfriendz.com/biding/item.php?id=39659&mode=1 shocked] it took so long for Milwaukee to get with the [http://69.89.27.245/~kickbox6/socialecorner/groups/where-to-buy-a-machete/ oscillating tool] plan and on top of that, we're basically disappointed that they opted for a cordless version. We privately had high hopes for a corded version that would give King Fein some competitors. No such luck. It looks like this oscillating tool has all of the trappings of yet an additional strong Milwaukee offering a metal gear case, a nice gripping location, and simple controls. The kit comes with two batteries and an accessory adapter which makes it compatible with most available accessories.<br><br>I used to cart my leatherman around all the time and [http://wiki.myriadtalk.com/index.php?title=Best_Bolo_Machete ultimately stopped] when I realized most of the time I necessary to reduce something and I frequently made use of a modest pocket knife for that. I have owned each Leatherman tools and Gerber tools. The Gerber ones are DEFINATELY inferior to the Leatherman ones. Gerber doesn't make pretty fantastic knives in basic. They use soft, inferior grade steels. I picked up a Leatherman Core yesterday and am happy with it. I bought it particularly for the reason that it did NOT have a pair of scissors which I see as a waste of space and weight. I also like that the tools and blades lock open. a two.9-inch 420HC knife (HC stands for “high carbon,” which implies the knife will hold an edge superior) Keychain carry of the tiny and burly Leatherman PS4.<br><br>Its not also loud, not to heavy, utilizing it with no the supplied strap now. I believe the engine may have to have a tweak to get the most effective out of it. Tools do transform but can be fiddly to get inserted suitable just about every time. The stainless steel handles on the SOG B66N-CP supply comfort when doing the toughest duties. Even though this multi-tool features gear covers and hex bolts it is lightweight and portable with dimensions of just 5.five x 1.6 x 2. If you have any kind of questions pertaining to where and exactly how to utilize [http://Www.thebestpocketknifereviews.com/best-survival-machete-on-the-market-today/ best survival machete], you can call us at our site. 9 inches. As with other SOG items, the SOG B66N-CP multi-tool is backed by a lifetime warranty that protects it against defects in manufacturing and supplies. Item Description When equipped with a narrow blade, a multi-tool can make plunge cuts in boards, flooring or drywall.

	: ~~<math>~~
	~~\operatorname{maj}(w)~~ = ~~\sum_{w(i)>w(i+~~1~~)} i~~.
	</~~math>~~

	~~For example, if ''w'' is given in [[Permutation#Notation\|one~~-~~line notation~~]~~] by ''w'' = 351624 (~~that is, '~~'w'' is~~ the ~~permutation~~ of {1, 2, ~~3, 4, 5, 6} such that ''w''(1) = 3, ''w''(2) = 5, etc~~.~~) then ''w'' has descents at positions 2 (from 5 to 1)~~ and ~~4 (from 6~~ to 2) and ~~so maj(''w'') = 2 + 4~~ = 6.

	~~This [[permutation statistic\|statistic]] is named after [[Percy Alexander MacMahon\|Major Percy Alexander MacMahon]~~] ~~who showed in [[#CITEREFMacMahon1913\|1913]] that the distribution~~ of the ~~major index on all permutations~~ of a ~~fixed length is~~ the ~~same as the distribution of [[Permutation#Inversions\|inversions]]~~. ~~That is~~, the ~~number~~ of ~~permutations~~ of ~~length ''n'' with ''k'' inversions is~~ the ~~same as the number of permutations of length ''n'' with major index equal to ''k''~~. (~~These numbers are known as ''Mahonian numbers''~~, ~~also in honor~~ of ~~MacMahon~~.<~~ref~~>~~M. Bóna~~, ~~Combinatorics of Permutations~~, ~~2004, p~~. ~~43ff, ISBN 1-58488-434-7.</ref>) In fact,~~ a ~~stronger result is true:~~ the ~~number~~ of ~~permutations of length ''n'' with major index ''k'' and ''i'' inversions is~~ the ~~same as~~ the ~~number of permutations of length ''n'' with major index ''i''~~ and ~~''k'' inversions, that~~ is~~, the two statistics are equidistributed. For example, the number of permutations of length 4~~ with ~~given major index and number~~ of ~~inversions is given in the table below~~.
	~~:<math>\begin{array}{c\|ccccccc}~~
	~~& 0&~~1~~&2&3&4&5&~~6 \\
	~~\hline~~
	~~0&1&0&0&0&0&0&0 \\~~
	~~1&0&1&1&1&0&0&0 \\~~
	2~~&0&1&2&1&1&0&0 \\~~
	~~3&0&1&1&2&1&1&0 \\~~
	~~4&0&0&1&1&2&1&0 \\~~
	~~5&0&0&0&1&1&1&0 \\~~
	~~6&0&0&0&0&0&0&1~~
	~~\end{array}~~
	</~~math>~~
	~~== References ==~~
	~~<references~~ />
	*{{Cite journal
	~~\| last1=MacMahon \| first1=P~~. A. ~~\| author1~~-~~link=Percy Alexander MacMahon~~
	~~\| title=The indices of permutations and~~ the ~~derivation therefrom of functions of a single variable associated~~ with the ~~permutations of any assemblage of objects~~
	~~\| year=1913~~
	~~\| journal=Amer~~. ~~J. Math.~~
	~~\| volume=35~~
	~~\| number=3~~
	~~\| pages=281–322~~
	~~\| jstor=2370312}}~~.

	~~{{DEFAULTSORT:Major Index}}~~
	~~[[Category:Permutations]]~~

	~~{{combin-stub}}~~

en>EdJohnston: /* See also */ Lucas islands model -- target has moved per WP:RM

2013-12-05T17:30:45Z

See also: Lucas islands model -- target has moved per WP:RM

← Older revision		Revision as of 19:30, 5 December 2013
Line 1:		Line 1:
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The Christy Sliding Blade Pocket Knives are still made on~~ the ~~original fifty three-operation production line and equipment, which is now operated and produced by machinist Hal R~~. ~~Christy~~, ~~son~~ of ~~Earl Christy. There are very few fourth-generation, household owned firms on this planet, and this one continues to offer “the best pocket knife ever designed” obtainable within~~ the ~~Companion~~ (~~nickel plated~~)~~, Govt~~ (~~polished black nickel plated~~)~~, and the Traveler~~ (~~matte end Teflon nickel plated~~). ~~Options & perform~~<br><br>Notice that this knife is put together utilizing pins , and cannot be taken apart by you the consumer. This may be a deal breaker for some people. It virtually was for me, however then I obtained to considering that Spyderco is thought for good customer service, and every model of the Native has a superb fame. It appeared like a reasonably protected selection. Sure, ~~I would prefer screw construction, however not~~ if ~~I have to surrender the FRN. Otherwise I would just buy the G10 model. So, the pinned construction~~ is an appropriate trade-off provided that this knife shows as 2.6 ounces on my scale.<br><br>Victorinox is extensively known for making swiss military knives. It has all the time delivered the best of knives. This time Victorinox got here with Swiss army basic pocket knife which is principally a compact device set for all campers and hikers. The traditional SD pocket knife is cased in ~~a solid-coloured housing with~~ [~~http://sas.optimaltoolkit.com/index.php/Spyderco_Tenacious_Legal_In_California Victorinox] brand on~~ one ~~aspect. This pocket knife incorporates [http://www.thebestpocketknifereviews.com/spyderco~~-~~tenacious-review/ Spyderco Tenacious Pocket Knife~~] all of the necessary Swiss army instruments similar to pair of mini scissors, sharp blade for slicing, a nail file with a screwdriver tip, key ring, tweezer and a toothpick. The Bear Grylls Compact Scout knife is ~~a great common objective blade for accountable Scouts~~, ~~hikers, bikers, campers and weekend warriors.<br><br>Within the kitchen, additionally it~~ is ~~essential to have~~ the ~~precision~~, ~~sturdiness and sharpness that a kitchen instrument should have. It does not make kitchen work faster and simpler~~, ~~it also makes it safer with sharp-edged knives Smoky Mountain Knife works provide you with only the most effective names in kitchen ware and goals to do so each time. 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Certain, this is not going to hold up in opposition to your Spyderco’s or Benchmade’s for those who need something tactical but for most campers~~ and ~~general outdoorsmen it is a very inexpensive pocket knife that gained’t disappoint. >> Click on here for [http://Sss.Chaoslab.ru/tracker/mim_plugs/newticket?reporter~~=~~anonymous&summary=AttributeError%3A~~+~~%27Environment%27+object+has+no+attribute+%27get_db_cnx%27&description~~=~~Among+the+best+sellers+on+Amazon%2C+the+Spyderco+Tenacious+plain+edge+blade+pocket+knife+~~is~~+3+3%2F8%E2%80%B3+~~in~~+size+and+1%2Feight%E2%80%B3+thick.+A+plain+edge+blade+is+extra+suited+to+~~the~~+carving+and+chopping+actions+that+this+knife+is+likely+to+be+used+for+than+a+serrated+edge.+The+burden+~~of+the~~+knife+is+just+four.6+ounces+which+implies+it+can+be+carried+around+simply+~~on~~+tenting+expeditions+or+even+just+across+the+dwelling+for+DIY+purposes.+You%27ll+never+feeling+the+burden+bringing+in+down.%0D%0A%0D%0A%0D%0A%0D%0AThe+Spyderco+Tenacious+G-10+has+~~a~~+8Cr13Mov+stainless-steel+blade.+It+~~is~~+skinny+on+~~the~~+very+tip+for+intricate%2C+detailed+slicing.+The+three.39%E2%80%B3+blade+thickens+in+~~the~~+direction+~~of~~+the+middle+and+into+the+spine~~.~~++If+you+have+any+inquiries+about+exactly+where+and+how+to+use+%5Bhttp%3A%2F%2Fwww.thebestpocketknifereviews.com%2Fspyderco-tenacious-review%2F+~~the~~+best+pocket+knife+reviews%5D%2C+you+can+make+contact+~~with~~+us+at+our+internet+site.+Stainless+steel+~~is~~+a+superb+material+for+knives+which+might+be+used+every+single+day.+It+is+resistant+to+rust+and+stays+sharp+for+a+long+time.+This+blade+is+excessive-quality+and+in+keeping+with+most+customers%2C+~~the~~+knife+has+no+wiggle+or+blade+play+when+opened+This+is+important+for+chopping+and+slicing+since+you+do+not+want+to+have+any+blade+wiggle.%0D%0A%0D%0AGeneral+this+can+be+a+superb+quality+knife+for+~~the~~+price+even+though+it%27s+made+in+China.+The+handle+is+very+snug+to+carry+and+won%27t+cause+fatigue%2C+even+when+used+for+lengthy+durations.+The+blade+is+sharp+as+soon+as+it%27s+out+~~of~~+the+box+and+can+retain+this+sharpness+for+fairly+a+while.+The+knife+is+very+light-weight+and+can+be+used+for+quite+a+lot+~~of~~+functions+and+will+stand+up+~~to~~+all+of+those+makes+use+of+nicely~~.~~+It+is+the+superb+knife+for+use+~~as~~+an+on+a+regular+basis+knife~~.~~%0D%0A%0D%0AI+came+from+a+SOG+Flash+II~~.~~+It+was+the+partially+serrated+version%2C+and+I+did+not+ever+use+the+serrations%2C+and+I+personally+suppose+they+are+a+pain+to+sharpen~~.~~+I+like+that+this+has+a+full+non~~-~~serrated+blade+and+the+option+to+mount+the+pocket+clip+in+4+completely+different+locations+or+simply+take+it+off%2C+but+this+knife+is+a+bit+huge+to+trip+unclipped+in+your+pocket~~.+In~~+case+you+are+interested+in+%5Bhttp%3A%2F%2FWww.Google.Co.uk%2Fsearch%3Fhl%3Den%26gl%3Dus%26tbm%3Dnws%26q%3Dshopping%26gs_l%3Dnews+shopping%5D+for+~~a~~+top+rated+pocket+knife+out+there+as+we+speak%2C+this+article+~~is~~+for+you.+Below+is+a+compilation+of+top+rated+pocket+knives+in+~~the+market+today.+The+listing+has+been+compiled+after+rigorously+contemplating+the+features%2C+worth+and+buyer+critiques+among+many+other+components+it%27s+best+to+consider+whenever+you+want+to+purchase+one+of~~+the+best%2Fonly+pocket+knife.+variations+~~of~~+edge+~~and~~+colours+now.%0D%0A%0D%0AThe+circulate-through+pillar+building+helps+maintain+~~the~~+inside+~~of~~+the+knife+debris+free%2C+~~and~~+lets+you+clearly+see+~~the~~%C2%A0milled+steel+liners~~.~~+Those+metal+liners+and+solid+liner+lock+make+~~the~~+Tenacious+a+powerful+knife+made+for+day+by+day+use.+Definitely+for+these+searching+for+a+mid+sized+EDC+knife+on+a+little+bit+~~of~~+a+budget%2C+or+one+thing+that+can+afford+to+take+slightly+punishment+the+Tenacious+will+get+my+hearty+suggestion.+The+Tenacious+is+a+beautiful+knife+~~and+is+clad+on+this+G-10+polymer+stuff.+It%27s+imagined+to+be+indestructible.+That+said%2C+I%27ve+solely+had+it+two+weeks.+Designed+with+an+outsized+Spyderco+Spherical+Hole+and+textured+backbone+jimping%2C+this+lets+you+position+your+thumb+on+the+spine+and+open+the~~+blade+in+slip-proof+confidence~~.~~+Return+to+Jack%27s+Finest+Knives~~&~~create=Create current pricing] and critiques on the Buck a hundred and ten. Spyderco Tenacious reviewers online gave this knife four.~~5 ~~out of~~ 5 stars. Their evaluations said that the knife was “sturdy, strong and really sharp,” “blade is beyond razor sharp,” and “virtually excellent.” KnifeUp recommends this knife for infrequent utility use. #6 ~~Kershaw Blur~~<br><br>~~When individuals consider overseas made knives, there are Swiss blades from Klotzli, which have~~ a ~~reputation similar to that~~ of ~~Swiss watches~~. ~~There are German knives that individuals recognize and Italian made knives that individuals are starting to really like~~. ~~Spyderco followers rejoice when Taichung Taiwan makes a blade, but to this point China has not received any love~~. ~~CASE XX Clean Antique Bone Russlock 1/500 Pocket Knife Knives~~.~~Today~~ [~~http~~:~~//abcnews.go.com/blogs/politics/2013/03/tsa-to-allow-pocket~~-knives-on-planes/ personalized pocket knives] I have a very valuable present given to friends and people who are fascinated them. In fact, it is good and straight with you. The model is exclusive, straightforward to make use of with out special learning specialties or skills.		In [[mathematics]] (and particularly in [[combinatorics]]), the '''major index''' of a [[permutation]] is defined as the sum of the positions of the [[Permutation#Ascents, descents and runs\|descents]] of the permutation. In symbols, the major index of the permutation ''w'' is

			: <math>
			\operatorname{maj}(w) = \sum_{w(i)>w(i+1)} i.
			</math>

			For example, if ''w'' is given in [[Permutation#Notation\|one-line notation]] by ''w'' = 351624 (that is, ''w'' is the permutation of {1, 2, 3, 4, 5, 6} such that ''w''(1) = 3, ''w''(2) = 5, etc.) then ''w'' has descents at positions 2 (from 5 to 1) and 4 (from 6 to 2) and so maj(''w'') = 2 + 4 = 6.

			This [[permutation statistic\|statistic]] is named after [[Percy Alexander MacMahon\|Major Percy Alexander MacMahon]] who showed in [[#CITEREFMacMahon1913\|1913]] that the distribution of the major index on all permutations of a fixed length is the same as the distribution of [[Permutation#Inversions\|inversions]]. That is, the number of permutations of length ''n'' with ''k'' inversions is the same as the number of permutations of length ''n'' with major index equal to ''k''. (These numbers are known as ''Mahonian numbers'', also in honor of MacMahon.<ref>M. Bóna, Combinatorics of Permutations, 2004, p. 43ff, ISBN 1-58488-434-7.</ref>) In fact, a stronger result is true: the number of permutations of length ''n'' with major index ''k'' and ''i'' inversions is the same as the number of permutations of length ''n'' with major index ''i'' and ''k'' inversions, that is, the two statistics are equidistributed. For example, the number of permutations of length 4 with given major index and number of inversions is given in the table below.
			:<math>\begin{array}{c\|ccccccc}
			& 0&1&2&3&4&5&6 \\
			\hline
			0&1&0&0&0&0&0&0 \\
			1&0&1&1&1&0&0&0 \\
			2&0&1&2&1&1&0&0 \\
			3&0&1&1&2&1&1&0 \\
			4&0&0&1&1&2&1&0 \\
			5&0&0&0&1&1&1&0 \\
			6&0&0&0&0&0&0&1
			\end{array}
			</math>
			== References ==
			<references />
			*{{Cite journal
			\| last1=MacMahon \| first1=P. A. \| author1-link=Percy Alexander MacMahon
			\| title=The indices of permutations and the derivation therefrom of functions of a single variable associated with the permutations of any assemblage of objects
			\| year=1913
			\| journal=Amer. J. Math.
			\| volume=35
			\| number=3
			\| pages=281–322
			\| jstor=2370312}}.

			{{DEFAULTSORT:Major Index}}
			[[Category:Permutations]]

			{{combin-stub}}

en>Helpful Pixie Bot: ISBNs (Build KE)

2012-05-09T21:48:16Z

ISBNs (Build KE)

New page

The Christy knife has a very lengthy storied previous from being in the hands of both girls and gentleman, and our servicemen during WWII. The knife even has been featured as a 007 knife in a James Bond movie — it’s that versatile. For me the burden, sharp looks, ease of use, incredible edge, and extraordinarily cheap price make this an distinctive knife that can be [http://www.thebestpocketknifereviews.com/spyderco-tenacious-review/ Spyderco Tenacious G-10] used for slicing anything by anybody who just want a useful little knife. Specs This knife is inexpensive and may maintain up properly since it's made from high quality supplies. It will be very useful for a wide range of needs whereas fishing. Right this moment the company nonetheless lives on even stronger than it was five or ten years ago in the identical town where it was based with a new location and an updated web site. The Christy Sliding Blade Pocket Knives are still made on the original fifty three-operation production line and equipment, which is now operated and produced by machinist Hal R. Christy, son of Earl Christy. There are very few fourth-generation, household owned firms on this planet, and this one continues to offer “the best pocket knife ever designed” obtainable within the Companion (nickel plated), Govt (polished black nickel plated), and the Traveler (matte end Teflon nickel plated). Options & perform Notice that this knife is put together utilizing pins , and cannot be taken apart by you the consumer. This may be a deal breaker for some people. It virtually was for me, however then I obtained to considering that Spyderco is thought for good customer service, and every model of the Native has a superb fame. It appeared like a reasonably protected selection. Sure, I would prefer screw construction, however not if I have to surrender the FRN. Otherwise I would just buy the G10 model. So, the pinned construction is an appropriate trade-off provided that this knife shows as 2.6 ounces on my scale. Victorinox is extensively known for making swiss military knives. It has all the time delivered the best of knives. This time Victorinox got here with Swiss army basic pocket knife which is principally a compact device set for all campers and hikers. The traditional SD pocket knife is cased in a solid-coloured housing with [http://sas.optimaltoolkit.com/index.php/Spyderco_Tenacious_Legal_In_California Victorinox] brand on one aspect. This pocket knife incorporates [http://www.thebestpocketknifereviews.com/spyderco-tenacious-review/ Spyderco Tenacious Pocket Knife] all of the necessary Swiss army instruments similar to pair of mini scissors, sharp blade for slicing, a nail file with a screwdriver tip, key ring, tweezer and a toothpick. The Bear Grylls Compact Scout knife is a great common objective blade for accountable Scouts, hikers, bikers, campers and weekend warriors. Within the kitchen, additionally it is essential to have the precision, sturdiness and sharpness that a kitchen instrument should have. It does not make kitchen work faster and simpler, it also makes it safer with sharp-edged knives Smoky Mountain Knife works provide you with only the most effective names in kitchen ware and goals to do so each time. Obviously, you will have to pay extra money for a hard and fast blade searching knife , but when deliberate doing a lot of hunting, it can in all probability be value it. They're much better for-skinning larger animals, and if you happen to do plan do a number of looking, again, the funding is definitely worth it. I couldn't believe how easy this knife was when I began opening it. Being a liner lock I anticipated some friction resistance from the tip of the liner lock riding on the end of the blade, however there was none. Upon additional scrutiny I found why. There's [http://www.thefreedictionary.com/pocket+knife how to sharpen a pocket knife] a small ball bearing mounted in the long run the liner lock surface which mates up to the blade. The liner lock guarantees zero up/down play and aspect to side play, if it were to develop, will be remedied by tightening the blade pivot. Over 250 reviews at Amazon with an average score of 4.9 (yes, 4.9 out of 5.0!) can’t be improper. 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