Nottingham group - Revision history

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2014-05-30T07:31:16Z

References: Added 1 doi to a journal cite using AWB (10216)

← Older revision		Revision as of 09:31, 30 May 2014
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	~~As much more and more growers~~ are ~~choosing LED grow lights~~ for ~~indoor developing~~, ~~there have been lots of new solutions introduced on~~ the ~~market place~~. ~~The study, which~~ is ~~published at HortTechnology , located that every single plant grown utilizing regular HPS lighting made use~~ of ~~1224 kilowatt-hours of energy by means~~ of the ~~season~~, ~~when these beneath LEDs consumed just 294 kilowatt-hours. LED develop lights are exceptionally economical due to the efficiency of transferring power to light power alternatively of heat~~. ~~LED's need approximately 75% significantly less energy compared to MH or HPS lights. The developing final results in studies speak for themselves~~.<br><br><br><br>~~In the course of the vegetative phase (first two months based on strain)~~ the ~~plants should really~~ be ~~given 16~~ to ~~20 hours of light per 24 hours~~. ~~The special LED fixtures were created by GE~~ and ~~emit light at wavelengths optimal~~ for ~~plant development~~. ~~I knew how to grow excellent vegetables biologically~~ and ~~I wanted to integrate that understanding with hardware to make points occur~~,~~” Shimamura says. Herbs grow prolifically indoors under LED lights~~.<br><br>~~Seedlings normally demand~~ a ~~blue light when flowering plants~~ are ~~far more suiteda red light~~. ~~LED lights are typically in~~ the ~~ultraviolet spectrum and invisible to naked eyes. Just use these and watch your plants grow more rapidly. This website includes copyrighted material~~ the use of ~~which has not generally been specifically authorized by~~ the ~~copyright owner~~. These ~~assist in cultivating plants indoor~~ and ~~places where the sun is impossible~~.<br><br>~~Increasing GaN on silicon is fairly a complex process~~,~~” mentioned Humphreys~~. ~~Humphreys believes that the day will arrive when GaN devices will light our residences~~, ~~energy our mobile phones~~, ~~laptops~~, ~~automobiles~~ and ~~aircraft engines~~, ~~and connect us wirelessly~~ to ~~details transmitted~~ from ~~website traffic lights and street lights~~. ~~If you liked this write~~-up, ~~please give~~ it a ~~fast review on reddit~~ or ~~StumbleUpon Thanks! These enhanced LED lights have been received~~ with a ~~lot~~ of ~~constructive response~~.<br><br>~~The unit comes with 82 individual high energy LED lighting chips that are complete replaceable - this is critical as you will discover~~ the ~~odd 1 fails over time~~. ~~This model operates~~ excellent ~~for growing vegetables~~ and ~~seedlings, if you want to develop flowers then~~ a ~~slightly different panel is [http://Maisenhardt~~.~~de/user/?action=user&id=3692 suggested]. Even though the G8 LED~~ is a ~~tiny bit more pricey it features a full 8 band spectrum creating it one particular~~ of ~~the finest possibilities for indoor increasing~~. A ~~single-~~to-one ~~replacement~~ for ~~1000W HPS~~.<br><br>~~LED develop lights have an benefit~~ in ~~that they run at~~ a ~~temperature that~~ is ~~basically warm to the touch, rather~~ than ~~approaching 400 or even 500 degrees~~. ~~When you use~~ the finest ~~LED develop lights, you will have~~ the ~~possibility to grow for years without possessing to replace your lighting program~~. For ~~comparison, many other develop lights tend to last for around 20,000 hours just before needing to be replaced If you~~ have any ~~inquiries relating~~ to ~~where and how you can make use of Cannabis Developing With Led Lights (~~[http://~~bestgrowlightsguide~~.com/~~growing-with-led-lights-its~~-~~possible~~-~~growing~~-~~weed~~-~~with~~-~~led~~-~~lights~~/ ~~click through the following document~~]), ~~you could call~~ us at our ~~web-site.~~ .		Chicago Cutlery Santoku Reviews In case you are taking a appear to shop for Henckels TWIN Master eight" Chef Knife with White Deal with to your. It's in Japan exactly where they make their most current creation, a model developed by Bob Kramer, the American bladesmith who has set the bar higher for kitchen-knife high quality. This chef knife is 1 of the mainstays of my kitchen and I loooove the feel - nicely balanced with a little heft, but absolutely nothing that tires my hand out. If you have compact hands and a compact construct, then a lighter knife could be a excellent fit.<br><br><br><br> When asked for which knives they would suggest to prospects, specialist chefs around the world would be speedy to say the International Skilled knife set. Worth $449.95 on , $450 on , and $479.95 on , this set gives you the finest value for your money. The set incorporates an 8" slicer, an eight" chef's knife, and a specialty paring knife. A fantastic all round knife, You will like this knife.<br><br>The Deal with of a knife are produced applying various types of supplies, which include things like rubber, wood, ceramic and some types are me of steel. The blade is the most essential component of the knife for it is the blade that is made use of to do the cutting. These days they are mostly created of steel and there are distinct varieties of steel employed to make knife blades nowadays. I travel with a tiny knife and it has its own sheath.<br><br>You can get any kitchenware from Rachael Ray and I really should emphasize as soon as once again, ANY KITCHENWARE in ANY Bright C LO R S. Her kitchenware collections include: cookware sets (which includes pots, pans, casserole dish, baking ware set), kitchen utensils (including knife set, spoon, spatula, tongs, ladle, potato peeler, Egg Whisk, pastry brush set, knife sharpener and the list goes on), cutting board even kitchen towel!<br><br>This variety of place will have a structured studying format which will allow all budding chefs to get a excellent grounding in the chef trade. On major of that they will need to know when they must use a unique knife for example from switching from fish to vegetables. Enable a ¼-inch ease all around to make room for the knife.cause is uncomplicated, it is a wonderful classic 6-inch cook's knife.<br><br>The Chicago Cutlery Insignia two set of knives is a good starting point for these who want to obtain a new knife set for the very first time or to add to their existing collection of knives. Chicago Cutlery advise to wash it by hand working with a mild detergent and cover the complete set below a limited lifetime warranty. As a set of expert knives, this set from Chicago Cutlery Insignia two comes genuine close in quality and construct to a set of higher high quality German knives.<br><br>Chef Deagon mentioned 5 things just about every chef need to have in the kitchen. These points are: a fantastic rubber spatula, a superior metal spatula, a excellent set of brief tongs, a fantastic paring knife, and a superior chef's knife. A chef's knife is usually created of stainless steel and can do a quantity of factors, such as slicing, dicing and julienning. A chef's knife usually ranges in size from 8 inches to 10 inches.<br><br>The study also showed that the breakfast-eaters consume about one hundred fewer calories a day, compared with people today who skip their morning meal, CBS News reported. Shun have a globe-wide reputation for creating excellent goods and they don't disappoint with this chef's knife. The blade is also anything you want in a chef's knife and will see off all those chores and carve up the Sunday joint with ease.<br><br>Without having a doubt a good chef's knife will speedily become the most utilized knife in your collection. Superior-top quality knives are exceptionally sharp and will certainly hold their edge longer than a low-priced rolled knife. Generating the ideal chef's knife is a great deal far more labor intensive than reduced good quality knives-and as a result more costly. 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en>BG19bot: WP:CHECKWIKI error fix for #98. Broken sub tag. Do general fixes if a problem exists. -, replaced: _{''p'' → _''p'' using AWB (9957)}

2014-03-01T09:20:57Z

WP:CHECKWIKI error fix for #98. Broken sub tag. Do general fixes if a problem exists. -, replaced: ''p'' → ''p'' using AWB (9957)

← Older revision		Revision as of 11:20, 1 March 2014
Line 1:		Line 1:
	~~In [[mathematics]]~~, ~~a [[metric space]] ''X'' with metric ''d'' is said to be '''doubling''' if~~ there is ~~some constant ''M'' > 0 such~~ that ~~for any ''x'' in ''X'' and ''r'' > 0~~, the ~~ball~~ '~~'B''(''x'', ''r'') = {''y'':\|''d(x, y)'' < ''r''} may be contained~~ in ~~a union of no more than ''M'' many balls with radius ''r''/2~~.<~~ref~~>{{cite book\| last = Heinonen\| first = Juha \| title = Lectures on Analysis on Metric Spaces \| series = Universitext \| publisher = Springer-Verlag \| location = New York \| year = 2001 \| pages = x+140 \| ISBN = 0-387-95104-0}}<~~/ref~~> ~~The base-2 logarithm of ''M'' is often referred to as the '''doubling dimension''' of ''X''. Euclidean spaces '''ℝ'''~~<~~sup~~>~~''d''~~<~~/sup~~> ~~equipped with~~ the ~~usual Euclidean metric are examples~~ of ~~doubling spaces where~~ the ~~doubling constant ''M'' depends~~ on the ~~dimension ''d''~~.		As much more and more growers are choosing LED grow lights for indoor developing, there have been lots of new solutions introduced on the market place. The study, which is published at HortTechnology , located that every single plant grown utilizing regular HPS lighting made use of 1224 kilowatt-hours of energy by means of the season, when these beneath LEDs consumed just 294 kilowatt-hours. LED develop lights are exceptionally economical due to the efficiency of transferring power to light power alternatively of heat. LED's need approximately 75% significantly less energy compared to MH or HPS lights. The developing final results in studies speak for themselves.<br><br><br><br>In the course of the vegetative phase (first two months based on strain) the plants should really be given 16 to 20 hours of light per 24 hours. The special LED fixtures were created by GE and emit light at wavelengths optimal for plant development. I knew how to grow excellent vegetables biologically and I wanted to integrate that understanding with hardware to make points occur,” Shimamura says. Herbs grow prolifically indoors under LED lights.<br><br>Seedlings normally demand a blue light when flowering plants are far more suiteda red light. LED lights are typically in the ultraviolet spectrum and invisible to naked eyes. Just use these and watch your plants grow more rapidly. This website includes copyrighted material the use of which has not generally been specifically authorized by the copyright owner. These assist in cultivating plants indoor and places where the sun is impossible.<br><br>Increasing GaN on silicon is fairly a complex process,” mentioned Humphreys. Humphreys believes that the day will arrive when GaN devices will light our residences, energy our mobile phones, laptops, automobiles and aircraft engines, and connect us wirelessly to details transmitted from website traffic lights and street lights. If you liked this write-up, please give it a fast review on reddit or StumbleUpon Thanks! These enhanced LED lights have been received with a lot of constructive response.<br><br>The unit comes with 82 individual high energy LED lighting chips that are complete replaceable - this is critical as you will discover the odd 1 fails over time. This model operates excellent for growing vegetables and seedlings, if you want to develop flowers then a slightly different panel is [http://Maisenhardt.de/user/?action=user&id=3692 suggested]. Even though the G8 LED is a tiny bit more pricey it features a full 8 band spectrum creating it one particular of the finest possibilities for indoor increasing. A single-to-one replacement for 1000W HPS.<br><br>LED develop lights have an benefit in that they run at a temperature that is basically warm to the touch, rather than approaching 400 or even 500 degrees. When you use the finest LED develop lights, you will have the possibility to grow for years without possessing to replace your lighting program. For comparison, many other develop lights tend to last for around 20,000 hours just before needing to be replaced If you have any inquiries relating to where and how you can make use of Cannabis Developing With Led Lights ([http://bestgrowlightsguide.com/growing-with-led-lights-its-possible-growing-weed-with-led-lights/ click through the following document]), you could call us at our web-site. .

	~~==Assouad's embedding theorem==~~

	~~An important question in metric space geometry is~~ to ~~characterize those metric spaces~~ that ~~can be embedded in some Euclidean space by~~ a ~~[[Lipschitz continuity\|bi-Lipschitz]] function~~. ~~This means that one can essentially think of~~ the ~~metric space as a subset of Euclidean space~~. ~~Not all metric spaces may be embedded in Euclidean space~~. ~~Doubling metric spaces, on~~ the ~~other hand, would seem like they have more~~ of ~~a chance, since~~ the ~~doubling condition says,~~ in ~~a way, that~~ the ~~metric space~~ is not infinite dimensional. However, this is still not the case in general. The [[Heisenberg group]] with its [[Carnot metric]] is an example of a doubling metric space which cannot be embedded in any Euclidean space.<~~ref~~>{{cite journal\| last = Pansu\| first= Pierre \| title = Métriques de Carnot-Carathéodory et quasiisométries des espaces symétriques de rang un\| journal = Ann. of Math. (2)\| volume = 129 \| year = 1989 \| number = 1 \| pages = 1–60}}<~~/ref~~>

	~~'''Assouad's Theorem''' states that, for~~ a ~~''M''-doubling metric space ''X''~~, ~~if we give it~~ the ~~metric ''d''(''x''~~,~~ ''y'')<sup>''ε''</sup> for some 0 < ''ε'' < 1~~, ~~then there is a ''L''-bi-Lipschitz map ''f'':''X'' → '''ℝ'''<sup>''d''</sup>~~, ~~where ''d''~~ and ~~''L'' depend on ''M''~~ and~~ ''ε''~~.

	~~==Doubling Measures==~~

	~~===Definition===~~
	~~A [[Measure (mathematics)\|measure]]~~ on a ~~metric space ''X'' is said to be '''doubling''' if the measure~~ of ~~any ball is approximately the measure of its double, or more precisely, if there is a constant ''C'' > 0 such that~~

	:<~~math~~> ~~\mu(B(x,2r))\leq C\mu(B(x,r)) \,~~ <~~/math~~>

	for ~~all ''x'' in ''X''~~ and ~~''r'' > 0. In this case~~, ~~we say ''μ'' is '''C-doubling'''.~~

	~~A measure space that supports~~ a ~~doubling measure~~ is ~~necessarily a doubling metric space, where the doubling constant depends on the constant ''C''.~~

	~~Conversely, any~~ [~~[complete metric space\|complete]] doubling metric space supports a doubling measure~~.<ref>{{cite journal\| last1 = Luukainen \| last2 = Saksman \| first1 = Jouni \| first2 = Eero \| title = Every complete doubling metric space carries a doubling measure \| journal = Proc. Amer. Math. Soc. \| volume = 126 \| year = 1998 \| number = 2 \| pages = 531–534}}</~~ref>~~

	~~===Examples~~===

	~~A simple example of a doubling measure is [[Lebesgue measure]~~] ~~on a Euclidean space~~. ~~One can, however, have doubling measures on Euclidean space that are [[Singular measures\|singular]] with respect to Lebesgue measure. One example on~~ the ~~real line~~ is ~~the [[weak limit]]~~ of the ~~following sequence of measures:<ref>{{cite book\| last=Zygmund \| first =~~ A. \| title= Trigonometric Series. Vol. I,II \| series = Cambridge Mathematical Library \| edition = Third \| publisher = Cambridge University Press \| year = 2002 \| pages = xii; Vol. I: xiv+383 pp.; Vol. II: viii+364\| ISBN = 0-~~521~~-~~89053-5}}~~<~~/ref~~>

	:<~~math~~> ~~d\mu_n = \prod_{i=1}^n (1+~~a~~\cos (3^i 2\pi x))\~~,~~dx,\;\;\; \|a\|<1~~.~~</math>~~

	~~One can construct another singular doubling measure ''μ'' on~~ the ~~interval [0~~,~~ 1] as follows:~~ for ~~each ''k'' ≥ 0, partition the unit interval [0,1] into 3<sup>''k''</sup> intervals of length 3<sup>−''k''</sup>~~. ~~Let Δ be the collection of all such intervals in [0~~,~~1] obtained~~ for ~~each ''k'' (these are the ''triadic intervals'')~~, and ~~for each such interval ''I'', let ''m''~~(~~''I'') denote~~ its ~~"middle third" interval. Fix 0 < ''δ'' < 1 and let ''μ'' be~~ the ~~measure such that ''μ''([0, 1~~])~~ = 1 and for each triadic interval ''I'', ''μ''(''m''(''I'')) = ''δμ''(''I''). Then this gives a doubling measure on [0~~,~~ 1] singular to Lebesgue measure.<ref>{{cite journal\| last = Kahane \| first = J.~~-~~P. \| title = Trois notes sur les ensembles parfaits linéaires\| journal = Enseignement Math. (2) \| volume = 15 \| year = 1969 \| pages = 185–192}}</ref>~~

	~~==Applications==~~

	~~The definition of a doubling measure may seem arbitrary, or purely of geometric interest~~. ~~However, many results from classical harmonic analysis extend to the setting of metric spaces with doubling measures~~.

	~~==References==~~
	~~<references/>~~

	~~{{DEFAULTSORT:Doubling Measure}}~~
	~~[[Category:Metric geometry]]~~

en>NClement at 19:26, 18 October 2011

2011-10-18T19:26:03Z

New page

In [[mathematics]], a [[metric space]] ''X'' with metric ''d'' is said to be '''doubling''' if there is some constant ''M'' > 0 such that for any ''x'' in ''X'' and ''r'' > 0, the ball ''B''(''x'', ''r'') = {''y'':|''d(x, y)'' < ''r''} may be contained in a union of no more than ''M'' many balls with radius ''r''/2.<ref>{{cite book| last = Heinonen| first = Juha | title = Lectures on Analysis on Metric Spaces | series = Universitext | publisher = Springer-Verlag | location = New York | year = 2001 | pages = x+140 | ISBN = 0-387-95104-0}}</ref> The base-2 logarithm of ''M'' is often referred to as the '''doubling dimension''' of ''X''. Euclidean spaces '''ℝ'''''d'' equipped with the usual Euclidean metric are examples of doubling spaces where the doubling constant ''M'' depends on the dimension ''d''.

==Assouad's embedding theorem==

An important question in metric space geometry is to characterize those metric spaces that can be embedded in some Euclidean space by a [[Lipschitz continuity|bi-Lipschitz]] function. This means that one can essentially think of the metric space as a subset of Euclidean space. Not all metric spaces may be embedded in Euclidean space. Doubling metric spaces, on the other hand, would seem like they have more of a chance, since the doubling condition says, in a way, that the metric space is not infinite dimensional. However, this is still not the case in general. The [[Heisenberg group]] with its [[Carnot metric]] is an example of a doubling metric space which cannot be embedded in any Euclidean space.<ref>{{cite journal| last = Pansu| first= Pierre | title = Métriques de Carnot-Carathéodory et quasiisométries des espaces symétriques de rang un| journal = Ann. of Math. (2)| volume = 129 | year = 1989 | number = 1 | pages = 1–60}}</ref>

'''Assouad's Theorem''' states that, for a ''M''-doubling metric space ''X'', if we give it the metric ''d''(''x'', ''y'')''ε'' for some 0 < ''ε'' < 1, then there is a ''L''-bi-Lipschitz map ''f'':''X'' → '''ℝ'''''d'', where ''d'' and ''L'' depend on ''M'' and ''ε''.

==Doubling Measures==

===Definition===
A [[Measure (mathematics)|measure]] on a metric space ''X'' is said to be '''doubling''' if the measure of any ball is approximately the measure of its double, or more precisely, if there is a constant ''C'' > 0 such that

:<math> \mu(B(x,2r))\leq C\mu(B(x,r)) \, </math>

for all ''x'' in ''X'' and ''r'' > 0. In this case, we say ''μ'' is '''C-doubling'''.

A measure space that supports a doubling measure is necessarily a doubling metric space, where the doubling constant depends on the constant ''C''.

Conversely, any [[complete metric space|complete]] doubling metric space supports a doubling measure.<ref>{{cite journal| last1 = Luukainen | last2 = Saksman | first1 = Jouni | first2 = Eero | title = Every complete doubling metric space carries a doubling measure | journal = Proc. Amer. Math. Soc. | volume = 126 | year = 1998 | number = 2 | pages = 531–534}}</ref>

===Examples===

A simple example of a doubling measure is [[Lebesgue measure]] on a Euclidean space. One can, however, have doubling measures on Euclidean space that are [[Singular measures|singular]] with respect to Lebesgue measure. One example on the real line is the [[weak limit]] of the following sequence of measures:<ref>{{cite book| last=Zygmund | first = A. | title= Trigonometric Series. Vol. I,II | series = Cambridge Mathematical Library | edition = Third | publisher = Cambridge University Press | year = 2002 | pages = xii; Vol. I: xiv+383 pp.; Vol. II: viii+364| ISBN = 0-521-89053-5}}</ref>

:<math> d\mu_n = \prod_{i=1}^n (1+a\cos (3^i 2\pi x))\,dx,\;\;\; |a|<1.</math>

One can construct another singular doubling measure ''μ'' on the interval [0, 1] as follows: for each ''k'' ≥ 0, partition the unit interval [0,1] into 3''k'' intervals of length 3−''k''. Let Δ be the collection of all such intervals in [0,1] obtained for each ''k'' (these are the ''triadic intervals''), and for each such interval ''I'', let ''m''(''I'') denote its "middle third" interval. Fix 0 < ''δ'' < 1 and let ''μ'' be the measure such that ''μ''([0, 1]) = 1 and for each triadic interval ''I'', ''μ''(''m''(''I'')) = ''δμ''(''I''). Then this gives a doubling measure on [0, 1] singular to Lebesgue measure.<ref>{{cite journal| last = Kahane | first = J.-P. | title = Trois notes sur les ensembles parfaits linéaires| journal = Enseignement Math. (2) | volume = 15 | year = 1969 | pages = 185–192}}</ref>

==Applications==

The definition of a doubling measure may seem arbitrary, or purely of geometric interest. However, many results from classical harmonic analysis extend to the setting of metric spaces with doubling measures.

==References==
<references/>

{{DEFAULTSORT:Doubling Measure}}
[[Category:Metric geometry]]

Nottingham group - Revision history

en>Rjwilmsi: /* References */Added 1 doi to a journal cite using AWB (10216)

en>BG19bot: WP:CHECKWIKI error fix for #98. Broken sub tag. Do general fixes if a problem exists. -, replaced: ''p'' → ''p'' using AWB (9957)

en>NClement at 19:26, 18 October 2011

en>BG19bot: WP:CHECKWIKI error fix for #98. Broken sub tag. Do general fixes if a problem exists. -, replaced: _{''p'' → _''p'' using AWB (9957)}