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en>Bibcode Bot: Adding 0 arxiv eprint(s), 3 bibcode(s) and 0 doi(s). Did it miss something? Report bugs, errors, and suggestions at User talk:Bibcode Bot

2014-08-17T19:58:04Z

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en>Niceguyedc: WPCleaner v1.27 - Repaired 1 link to disambiguation page - (You can help) - Jordan frame

2013-06-05T08:19:18Z

WPCleaner v1.27 - Repaired 1 link to disambiguation page - (You can help) - Jordan frame

← Older revision		Revision as of 10:19, 5 June 2013
Line 1:		Line 1:
	~~<br><br>When searching for~~ a ~~high powered sander~~, ~~you really want~~ to ~~make positive that you do your analysis properly. For~~ the ~~reason that it is such~~ a ~~heavy-duty machine~~, a ~~drum sander~~ is ~~really high~~-~~priced but you can rent one from tool rental corporations or your regional household improvement retailer~~ if ~~you are refinishing your floors. Belt floor sanders can be used to remove~~ all ~~flooring finishes and take away scratches and gouges~~, ~~but they are normally not as highly effective as a drum sander. If you have any concerns relating to where and also tips on how to work with [http~~:/~~/www~~.~~bestoscillatingtoolreviews~~.~~com/best~~-~~rotary~~-~~tool-reviews/ craftsman nextec rotary tool testimonials], you'll be able to contact us on the page~~. ~~As a result~~ of ~~this style, the sandpaper belt remains~~ in the ~~identical position as you function to ensure a smooth~~, ~~even finish~~.<br><br>~~Makita~~'~~s 3 x 21-Inch Belt Sander~~, ~~model 9903, combines power and speed with ease~~-of~~-use capabilities and significantly less noise for quickly and efficient stock removal~~. ~~The 9903~~ is excellent for woodworkers, carpenters, furnishings makers, floor installers, deck builders and basic contractors who need a ideal-in-class belt sander. Wear 1 with your business enterprise suit and it looks just like a standard dress belt.<br><br>~~A detail sander has to be capable to get the job carried out quickly~~, and ~~the Bosch detail sander orbits up to 19000 OPM to give you the smoothest finish feasible~~. ~~Weighing a mere two.four pounds~~, ~~this detail sander can be applied for hours without becoming uncomfortable, and~~ is ~~built~~ to ~~function as long as you will need it~~ to~~. Belts for~~ the Triton Sander should really continue to be stocked locally by Busy Bee for some time.<br><br>The sander would stall with quite firm pressure, but these have been pieces with a substantial speak to location on the ~~sander. The sanding job for~~ the ~~larger piece ran about 30 minutes with no troubles that a belt cleaner couldn't take care~~ of. ~~We typically uncoverthe Porter Cable 121 transportable spindle sander~~ is ~~handy in our countertop work - and have designed~~ a ~~jig to hold it upside down~~ so ~~it can work as stationary tool on the job website.<br~~>~~<br>The classic flap-front bag~~, ~~irrespective of whether as~~ a ~~clutch (like at Prada~~ & ~~Versus), a messenger~~ (~~like at Stella McCartney~~), ~~or a tote (like at Thakoon), came alive on the Spring 2011 runways in clean, sleek neutrals and brights balanced very carefully with black. Most designers~~ for ~~Spring 2011 kept them very simple (like the tribal style observed Most effective Budget Rotary Tool at Rick Owens~~ & ~~the modern cuffs at Derek Lam)~~, ~~but flashy adornments aren~~'~~t out (like at Chanel and Rag~~ & ~~Bone)~~.<br><br>~~The Makita 9903~~ is ~~a belt sander that offers you with wonderful and highly effective sanding overall performance which considered~~ by ~~lots of individuals as~~ a ~~single~~ of ~~the ideal belt sanders out~~ there ~~on the market in the final handful~~ of ~~years. With its variable speed dial, you have~~ the ~~ability to opt for~~ and ~~match the speed~~ of the ~~belt sander~~ to ~~the application depending~~ on ~~your desires~~ and ~~preference. Yet another reason why this sander is so common is~~ for the ~~reason that of its quiet and smooth operation.~~<br><br>~~Cabinet saws, which are extra high~~-~~priced~~, ~~provide far more accuracy and power~~, ~~whilst~~ the ~~benchtop saw is the smallest and least expensive variety. An orbital air sander is a versatile and uncomplicated to use air tool~~, ~~which is regarded as critical for expert auto body repair jobs, and is also the kind of equipment that each and every hobbyist will want to have in their toolkit in order to guarantee~~ that ~~they can do a great job.~~<br><br>~~The range of sanders to pick out from~~ is ~~pretty lengthy and contains belt sanders~~, ~~random orbit sanders, half sheet sanders, palm sanders~~, and ~~delta sanders~~. ~~Various varieties~~ of ~~coarse grit belts are obtainable for~~ the ~~removal~~ of ~~wood~~, ~~paint or other coatings when fine grade sanding belts are out there where a smooth surface is essential to finish the job~~. ~~Health and Security is generally vital whenever a sander is becoming employed~~. ~~Put the tool on the tool rest away from the belt~~.		In [[functional analysis]], a branch of mathematics, the '''distortion problem''' is to determine by how much one can [[distortion (mathematics)\|distort]] the unit sphere in a given [[Banach space]] using an equivalent norm. Specifically, a Banach space ''X'' is called λ-distortable if there exists an equivalent norm \|''x''\| on ''X'' such that, for all infinite-dimensional subspaces ''Y'' in ''X'',
			:<math>\sup_{y_1,y_2\in Y, \\|y_i\\|=1} \frac{\|y_1\|}{\|y_2\|} \ge \lambda</math>
			(see [[distortion (mathematics)]]). Note that every Banach space is trivially 1-distortable. A Banach space is called distortable if it is λ-distortable for some λ > 1 and it is called arbitrarily distortable if it is λ-distortable for any λ. Distortability first emerged as an important property of Banach spaces in the 1960s, where it was studied by {{harvtxt\|James\|1964}} and {{harvtxt\|Milman\|1971}}.

			James proved that ''c''<sub>0</sub> and ℓ<sup>1</sup> are not distortable. Milman showed that if ''X'' is a Banach space that does not contain an isomorphic copy of ''c''<sub>0</sub> or ℓ<sup>''p''</sup> for some {{nowrap\|1 ≤ ''p'' < ∞}} (see [[sequence space]]), then some infinite-dimensional subspace of ''X'' is distortable. So the distortion problem is now primarily of interest on the spaces ℓ<sup>''p''</sup>, all of which are [[separable metric space\|separable]] and uniform convex.

			In separable and uniform convex spaces, distortability is easily seen to be equivalent to the ostensibly more general question of whether or not every real-valued [[Lipschitz function]] ''&fnof;'' defined on the sphere in ''X'' stabilizes on the sphere of an infinite dimensional subspace, i.e., whether there is a real number a ∈ '''R''' so that for every δ > 0 there is an infinite dimensional subspace ''Y'' of ''X'', so that \|a − ''&fnof;''(''y'')\| < δ, for all ''y'' ∈ ''Y'', with \|\|''y''\|\| = 1. But it follows from the result of {{harvtxt\|Odell\|Schlumprecht\|1994}} that on ℓ<sup>1</sup> there are Lipschitz functions which do not stabilize, although this space is not distortable by {{harvtxt\|James \|1964}}. In a separable [[Hilbert space]], the distortion problem is equivalent to the question of whether there exist subsets of the unit sphere separated by a positive distance and yet intersect every infinite-dimensional closed subspace. Unlike many properties of Banach spaces, the distortion problem seems to be as difficult on Hilbert spaces as on other Banach spaces. On a separable Hilbert space, and for the other ℓ<sup>p</sup>-spaces, 1 < p < ∞, the distortion problem was solved affirmatively by {{harvtxt\|Odell\|Schlumprecht\|1994}}, who showed that ℓ<sup>2</sup> is arbitrarily distortable, using the first known arbitrarily distortable space constructed by
			{{harvtxt\|Schlumprecht\|1991}}.

			==See also==
			* [[Tsirelson space]]
			*[[Banach space]]

			==References==
			*{{citation \|title=Uniformly nonsquare Banach spaces \|first=R.C. \|last=James \|journal=Annals of Mathematics \|year=1964 \|volume=80 \|issue=2 \|pages=542–550}}.
			*{{citation \|last=Milman \|title=Geometry of Banach spaces II, geometry of the unit sphere \|journal=[[Russian Mathematical Surveys]] \|year=1971 \|volume=26 \|pages=79–163}}.
			*{{citation \|chapter=Distortion and asymptotic structure \|first1=E \|last1=Odell \|first2=Th. \|last2=Schlumprecht \|title=Hanbook of the geometry of Banach spaces, Volume 2 \|editors=Johnson, Lindenstrauss \|publisher=Elsevier \|year=2003 \|isbn=978-0-444-51305-2}}.
			*{{Citation \| last1=Odell \| first1=E. \| last2=Schlumprecht \| first2=Th. \| title=The distortion problem of Hilbert space \| mr=1209302 \| year=1993 \| journal= Geom.Funct.Anal \| issn=1016-443X \| volume=3 \| pages=201–207 \| doi=10.1007/BF01896023}}.
			*{{Citation \| last1=Odell \| first1=E. \| last2=Schlumprecht \| first2=Th. \| title=The distortion problem \| mr=1301394 \| year=1994 \| journal= Acta Mathematica \| issn=0001-5962 \| volume=173 \| pages=259–281 \| doi=10.1007/BF02398436}}.
			*{{Citation \| title= An arbitrary distortable Banach space \| first= Th. \|last= Schlumprecht\| mr=1177333 \| year=1991 \| journal= Israel Journal of Mathematics \| issn=0021-2172 \| volume=76 \| pages=81–95}}.
			[[Category:Functional analysis]]

en>Tassedethe: Disambiguated: Jeffrey Harvey → Jeffrey A. Harvey

2012-03-11T18:14:55Z

Disambiguated: Jeffrey Harvey → Jeffrey A. Harvey

New page

When searching for a high powered sander, you really want to make positive that you do your analysis properly. For the reason that it is such a heavy-duty machine, a drum sander is really high-priced but you can rent one from tool rental corporations or your regional household improvement retailer if you are refinishing your floors. Belt floor sanders can be used to remove all flooring finishes and take away scratches and gouges, but they are normally not as highly effective as a drum sander. If you have any concerns relating to where and also tips on how to work with [http://www.bestoscillatingtoolreviews.com/best-rotary-tool-reviews/ craftsman nextec rotary tool testimonials], you'll be able to contact us on the page. As a result of this style, the sandpaper belt remains in the identical position as you function to ensure a smooth, even finish. Makita's 3 x 21-Inch Belt Sander, model 9903, combines power and speed with ease-of-use capabilities and significantly less noise for quickly and efficient stock removal. The 9903 is excellent for woodworkers, carpenters, furnishings makers, floor installers, deck builders and basic contractors who need a ideal-in-class belt sander. Wear 1 with your business enterprise suit and it looks just like a standard dress belt. A detail sander has to be capable to get the job carried out quickly, and the Bosch detail sander orbits up to 19000 OPM to give you the smoothest finish feasible. Weighing a mere two.four pounds, this detail sander can be applied for hours without becoming uncomfortable, and is built to function as long as you will need it to. Belts for the Triton Sander should really continue to be stocked locally by Busy Bee for some time. The sander would stall with quite firm pressure, but these have been pieces with a substantial speak to location on the sander. The sanding job for the larger piece ran about 30 minutes with no troubles that a belt cleaner couldn't take care of. We typically uncoverthe Porter Cable 121 transportable spindle sander is handy in our countertop work - and have designed a jig to hold it upside down so it can work as stationary tool on the job website. The classic flap-front bag, irrespective of whether as a clutch (like at Prada & Versus), a messenger (like at Stella McCartney), or a tote (like at Thakoon), came alive on the Spring 2011 runways in clean, sleek neutrals and brights balanced very carefully with black. Most designers for Spring 2011 kept them very simple (like the tribal style observed Most effective Budget Rotary Tool at Rick Owens & the modern cuffs at Derek Lam), but flashy adornments aren't out (like at Chanel and Rag & Bone). The Makita 9903 is a belt sander that offers you with wonderful and highly effective sanding overall performance which considered by lots of individuals as a single of the ideal belt sanders out there on the market in the final handful of years. With its variable speed dial, you have the ability to opt for and match the speed of the belt sander to the application depending on your desires and preference. Yet another reason why this sander is so common is for the reason that of its quiet and smooth operation. Cabinet saws, which are extra high-priced, provide far more accuracy and power, whilst the benchtop saw is the smallest and least expensive variety. An orbital air sander is a versatile and uncomplicated to use air tool, which is regarded as critical for expert auto body repair jobs, and is also the kind of equipment that each and every hobbyist will want to have in their toolkit in order to guarantee that they can do a great job. The range of sanders to pick out from is pretty lengthy and contains belt sanders, random orbit sanders, half sheet sanders, palm sanders, and delta sanders. Various varieties of coarse grit belts are obtainable for the removal of wood, paint or other coatings when fine grade sanding belts are out there where a smooth surface is essential to finish the job. Health and Security is generally vital whenever a sander is becoming employed. Put the tool on the tool rest away from the belt.

← Older revision		Revision as of 10:19, 5 June 2013
Line 1:		Line 1:
	~~<br><br>When searching for~~ a ~~high powered sander~~, ~~you really want~~ to ~~make positive that you do your analysis properly. For~~ the ~~reason that it is such~~ a ~~heavy-duty machine~~, a ~~drum sander~~ is ~~really high~~-~~priced but you can rent one from tool rental corporations or your regional household improvement retailer~~ if ~~you are refinishing your floors. Belt floor sanders can be used to remove~~ all ~~flooring finishes and take away scratches and gouges~~, ~~but they are normally not as highly effective as a drum sander. If you have any concerns relating to where and also tips on how to work with [http~~:/~~/www~~.~~bestoscillatingtoolreviews~~.~~com/best~~-~~rotary~~-~~tool-reviews/ craftsman nextec rotary tool testimonials], you'll be able to contact us on the page~~. ~~As a result~~ of ~~this style, the sandpaper belt remains~~ in the ~~identical position as you function to ensure a smooth~~, ~~even finish~~.<br><br>~~Makita~~'~~s 3 x 21-Inch Belt Sander~~, ~~model 9903, combines power and speed with ease~~-of~~-use capabilities and significantly less noise for quickly and efficient stock removal~~. ~~The 9903~~ is excellent for woodworkers, carpenters, furnishings makers, floor installers, deck builders and basic contractors who need a ideal-in-class belt sander. Wear 1 with your business enterprise suit and it looks just like a standard dress belt.<br><br>~~A detail sander has to be capable to get the job carried out quickly~~, and ~~the Bosch detail sander orbits up to 19000 OPM to give you the smoothest finish feasible~~. ~~Weighing a mere two.four pounds~~, ~~this detail sander can be applied for hours without becoming uncomfortable, and~~ is ~~built~~ to ~~function as long as you will need it~~ to~~. Belts for~~ the Triton Sander should really continue to be stocked locally by Busy Bee for some time.<br><br>The sander would stall with quite firm pressure, but these have been pieces with a substantial speak to location on the ~~sander. The sanding job for~~ the ~~larger piece ran about 30 minutes with no troubles that a belt cleaner couldn't take care~~ of. ~~We typically uncoverthe Porter Cable 121 transportable spindle sander~~ is ~~handy in our countertop work - and have designed~~ a ~~jig to hold it upside down~~ so ~~it can work as stationary tool on the job website.<br~~>~~<br>The classic flap-front bag~~, ~~irrespective of whether as~~ a ~~clutch (like at Prada~~ & ~~Versus), a messenger~~ (~~like at Stella McCartney~~), ~~or a tote (like at Thakoon), came alive on the Spring 2011 runways in clean, sleek neutrals and brights balanced very carefully with black. Most designers~~ for ~~Spring 2011 kept them very simple (like the tribal style observed Most effective Budget Rotary Tool at Rick Owens~~ & ~~the modern cuffs at Derek Lam)~~, ~~but flashy adornments aren~~'~~t out (like at Chanel and Rag~~ & ~~Bone)~~.<br><br>~~The Makita 9903~~ is ~~a belt sander that offers you with wonderful and highly effective sanding overall performance which considered~~ by ~~lots of individuals as~~ a ~~single~~ of ~~the ideal belt sanders out~~ there ~~on the market in the final handful~~ of ~~years. With its variable speed dial, you have~~ the ~~ability to opt for~~ and ~~match the speed~~ of the ~~belt sander~~ to ~~the application depending~~ on ~~your desires~~ and ~~preference. Yet another reason why this sander is so common is~~ for the ~~reason that of its quiet and smooth operation.~~<br><br>~~Cabinet saws, which are extra high~~-~~priced~~, ~~provide far more accuracy and power~~, ~~whilst~~ the ~~benchtop saw is the smallest and least expensive variety. An orbital air sander is a versatile and uncomplicated to use air tool~~, ~~which is regarded as critical for expert auto body repair jobs, and is also the kind of equipment that each and every hobbyist will want to have in their toolkit in order to guarantee~~ that ~~they can do a great job.~~<br><br>~~The range of sanders to pick out from~~ is ~~pretty lengthy and contains belt sanders~~, ~~random orbit sanders, half sheet sanders, palm sanders~~, and ~~delta sanders~~. ~~Various varieties~~ of ~~coarse grit belts are obtainable for~~ the ~~removal~~ of ~~wood~~, ~~paint or other coatings when fine grade sanding belts are out there where a smooth surface is essential to finish the job~~. ~~Health and Security is generally vital whenever a sander is becoming employed~~. ~~Put the tool on the tool rest away from the belt~~.		In [[functional analysis]], a branch of mathematics, the '''distortion problem''' is to determine by how much one can [[distortion (mathematics)\|distort]] the unit sphere in a given [[Banach space]] using an equivalent norm. Specifically, a Banach space ''X'' is called λ-distortable if there exists an equivalent norm \|''x''\| on ''X'' such that, for all infinite-dimensional subspaces ''Y'' in ''X'',
			:<math>\sup_{y_1,y_2\in Y, \\|y_i\\|=1} \frac{\|y_1\|}{\|y_2\|} \ge \lambda</math>
			(see [[distortion (mathematics)]]). Note that every Banach space is trivially 1-distortable. A Banach space is called distortable if it is λ-distortable for some λ > 1 and it is called arbitrarily distortable if it is λ-distortable for any λ. Distortability first emerged as an important property of Banach spaces in the 1960s, where it was studied by {{harvtxt\|James\|1964}} and {{harvtxt\|Milman\|1971}}.

			James proved that ''c''<sub>0</sub> and ℓ<sup>1</sup> are not distortable. Milman showed that if ''X'' is a Banach space that does not contain an isomorphic copy of ''c''<sub>0</sub> or ℓ<sup>''p''</sup> for some {{nowrap\|1 ≤ ''p'' < ∞}} (see [[sequence space]]), then some infinite-dimensional subspace of ''X'' is distortable. So the distortion problem is now primarily of interest on the spaces ℓ<sup>''p''</sup>, all of which are [[separable metric space\|separable]] and uniform convex.

			In separable and uniform convex spaces, distortability is easily seen to be equivalent to the ostensibly more general question of whether or not every real-valued [[Lipschitz function]] ''&fnof;'' defined on the sphere in ''X'' stabilizes on the sphere of an infinite dimensional subspace, i.e., whether there is a real number a ∈ '''R''' so that for every δ > 0 there is an infinite dimensional subspace ''Y'' of ''X'', so that \|a − ''&fnof;''(''y'')\| < δ, for all ''y'' ∈ ''Y'', with \|\|''y''\|\| = 1. But it follows from the result of {{harvtxt\|Odell\|Schlumprecht\|1994}} that on ℓ<sup>1</sup> there are Lipschitz functions which do not stabilize, although this space is not distortable by {{harvtxt\|James \|1964}}. In a separable [[Hilbert space]], the distortion problem is equivalent to the question of whether there exist subsets of the unit sphere separated by a positive distance and yet intersect every infinite-dimensional closed subspace. Unlike many properties of Banach spaces, the distortion problem seems to be as difficult on Hilbert spaces as on other Banach spaces. On a separable Hilbert space, and for the other ℓ<sup>p</sup>-spaces, 1 < p < ∞, the distortion problem was solved affirmatively by {{harvtxt\|Odell\|Schlumprecht\|1994}}, who showed that ℓ<sup>2</sup> is arbitrarily distortable, using the first known arbitrarily distortable space constructed by
			{{harvtxt\|Schlumprecht\|1991}}.

			==See also==
			* [[Tsirelson space]]
			*[[Banach space]]

			==References==
			*{{citation \|title=Uniformly nonsquare Banach spaces \|first=R.C. \|last=James \|journal=Annals of Mathematics \|year=1964 \|volume=80 \|issue=2 \|pages=542–550}}.
			*{{citation \|last=Milman \|title=Geometry of Banach spaces II, geometry of the unit sphere \|journal=[[Russian Mathematical Surveys]] \|year=1971 \|volume=26 \|pages=79–163}}.
			*{{citation \|chapter=Distortion and asymptotic structure \|first1=E \|last1=Odell \|first2=Th. \|last2=Schlumprecht \|title=Hanbook of the geometry of Banach spaces, Volume 2 \|editors=Johnson, Lindenstrauss \|publisher=Elsevier \|year=2003 \|isbn=978-0-444-51305-2}}.
			*{{Citation \| last1=Odell \| first1=E. \| last2=Schlumprecht \| first2=Th. \| title=The distortion problem of Hilbert space \| mr=1209302 \| year=1993 \| journal= Geom.Funct.Anal \| issn=1016-443X \| volume=3 \| pages=201–207 \| doi=10.1007/BF01896023}}.
			*{{Citation \| last1=Odell \| first1=E. \| last2=Schlumprecht \| first2=Th. \| title=The distortion problem \| mr=1301394 \| year=1994 \| journal= Acta Mathematica \| issn=0001-5962 \| volume=173 \| pages=259–281 \| doi=10.1007/BF02398436}}.
			*{{Citation \| title= An arbitrary distortable Banach space \| first= Th. \|last= Schlumprecht\| mr=1177333 \| year=1991 \| journal= Israel Journal of Mathematics \| issn=0021-2172 \| volume=76 \| pages=81–95}}.
			[[Category:Functional analysis]]