Virtual fixture - Revision history

en>WCS100 at 18:30, 25 September 2014

2014-09-25T18:30:01Z

en>Surenkum: /* Virtual Fixture Control Law */

2014-03-04T15:20:28Z

Virtual Fixture Control Law

← Older revision		Revision as of 17:20, 4 March 2014
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	The ~~'''Hafner–Sarnak–McCurley constant'''~~ is a ~~[[mathematical constant]] representing the [[probability]] that the [[matrix determinant\|determinants]]~~ of ~~two randomly chosen square [[integer matrix\|integer matrices]] will be [[relatively prime]]~~. ~~The probability depends on~~ the ~~matrix size, ''n'',~~ in ~~accordance with the formula~~		The writer is known by the name of Figures Lint. Managing individuals has been his day job for a while. California is where her house is but she requirements to move because of her family. One of the extremely best things in the globe for him is to collect badges but he is struggling to discover time for it.<br><br>Also visit my web page; [http://dore.gia.ncnu.edu.tw/88ipart/node/1326254 dore.gia.ncnu.edu.tw]

	~~:<math>D(n)=\Pi_{k=1}^{\infty}\left\{1-[1-\Pi_{j=1}^n(1-p_k^{-j})]^2\right\},</math>~~

	~~where ''p<sub>k</sub>'' is~~ the ~~''k''th prime number. The constant~~ is ~~the limit of this expression as ''n'' approaches infinity. Its value~~ is ~~roughly 0.3532363719..~~. ~~{{OEIS\|A085849}}; Ilan Vardi has given it the alternate expression~~

	:<~~math~~>~~\Pi_{k=2}^{\infty}{\zeta(k) ^{-a_k}},~~<~~/math~~>

	~~which converges exponentially~~; ~~here ζ(''k'') is the~~ [~~[Riemann zeta function]]. <!-- How are the a_k's determined? -->~~

	~~==References==~~
	*{{Citation \|last=Finch \|first=S. R. \|chapter=§2.5 Hafner-Sarnak-McCurley Constant \|title=Mathematical Constants \|location=Cambridge, England \|publisher=Cambridge University Press \|pages=110–112 \|year=2003 \|isbn=0-521-81805-2 }}.
	*{{Citation \|last=Flajolet \|first=P. \|lastauthoramp=yes \|last2=Vardi \|first=I. \|title=Zeta Function Expansions of Classical Constants \|work=Unpublished manuscript \|year=1996 \|url=http://~~algo~~.~~inria~~.fr/~~flajolet~~/~~Publications~~/~~landau.ps }}.~~
	*{{Citation \|last=Hafner \|first=J. L. \|authorlink2=Peter Sarnak \|last2=Sarnak \|first2=P. \|lastauthoramp=yes \|authorlink3=Kevin McCurley (cryptographer) \|last3=McCurley \|first3=K. \|chapter=Relatively Prime Values of Polynomials \|title=A Tribute to Emil Grosswald: Number Theory and Related Analysis \|editor1-first=M. \|editor1-last=Knopp \|editor2-first=M. \|editor2-last=Seingorn \|location=Providence, RI \|publisher=Amer. ~~Math~~. ~~Soc~~. ~~\|year=1993 \|isbn=0-8218-5155-1 }}~~.
	*{{Citation \|last=Vardi \|first=I. \|title=Computational Recreations in Mathematica \|location=Redwood City, CA \|publisher=Addison-Wesley \|year=1991 \|isbn=0-201-52989-0 }}.

	~~==External links==~~
	* {{MathWorld\|urlname=Hafner-Sarnak-McCurleyConstant\|title=Hafner-Sarnak-McCurley Constant}}

	~~{{DEFAULTSORT:Hafner-Sarnak-McCurley constant}}~~
	~~[[Category:Mathematical constants]~~]

en>Mcewan: /* Virtual Fixture Control Law */Typo, replaced: that effects → that affects using AWB

2013-01-24T17:12:20Z

Virtual Fixture Control Law: Typo, replaced: that effects → that affects using AWB

← Older revision		Revision as of 19:12, 24 January 2013
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	~~I am Oscar and I completely dig~~ that ~~name~~. ~~One of~~ the ~~very best things~~ in the ~~world for me~~ is ~~to do aerobics and now I~~'~~m trying to make money with it~~. ~~Supervising~~ is ~~my profession~~. ~~South Dakota~~ is ~~where me and my husband live~~.<br><br>~~Also visit my web page~~ [http://~~www~~.~~tutorca~~.~~com~~/~~?document_srl~~=~~958819 http~~:~~//www~~.~~tutorca~~.~~com~~]		The '''Hafner–Sarnak–McCurley constant''' is a [[mathematical constant]] representing the [[probability]] that the [[matrix determinant\|determinants]] of two randomly chosen square [[integer matrix\|integer matrices]] will be [[relatively prime]]. The probability depends on the matrix size, ''n'', in accordance with the formula

			:<math>D(n)=\Pi_{k=1}^{\infty}\left\{1-[1-\Pi_{j=1}^n(1-p_k^{-j})]^2\right\},</math>

			where ''p<sub>k</sub>'' is the ''k''th prime number. The constant is the limit of this expression as ''n'' approaches infinity. Its value is roughly 0.3532363719... {{OEIS\|A085849}}; Ilan Vardi has given it the alternate expression

			:<math>\Pi_{k=2}^{\infty}{\zeta(k) ^{-a_k}},</math>

			which converges exponentially; here ζ(''k'') is the [[Riemann zeta function]]. <!-- How are the a_k's determined? -->

			==References==
			*{{Citation \|last=Finch \|first=S. R. \|chapter=§2.5 Hafner-Sarnak-McCurley Constant \|title=Mathematical Constants \|location=Cambridge, England \|publisher=Cambridge University Press \|pages=110–112 \|year=2003 \|isbn=0-521-81805-2 }}.
			*{{Citation \|last=Flajolet \|first=P. \|lastauthoramp=yes \|last2=Vardi \|first=I. \|title=Zeta Function Expansions of Classical Constants \|work=Unpublished manuscript \|year=1996 \|url=http://algo.inria.fr/flajolet/Publications/landau.ps }}.
			*{{Citation \|last=Hafner \|first=J. L. \|authorlink2=Peter Sarnak \|last2=Sarnak \|first2=P. \|lastauthoramp=yes \|authorlink3=Kevin McCurley (cryptographer) \|last3=McCurley \|first3=K. \|chapter=Relatively Prime Values of Polynomials \|title=A Tribute to Emil Grosswald: Number Theory and Related Analysis \|editor1-first=M. \|editor1-last=Knopp \|editor2-first=M. \|editor2-last=Seingorn \|location=Providence, RI \|publisher=Amer. Math. Soc. \|year=1993 \|isbn=0-8218-5155-1 }}.
			*{{Citation \|last=Vardi \|first=I. \|title=Computational Recreations in Mathematica \|location=Redwood City, CA \|publisher=Addison-Wesley \|year=1991 \|isbn=0-201-52989-0 }}.

			==External links==
			* {{MathWorld\|urlname=Hafner-Sarnak-McCurleyConstant\|title=Hafner-Sarnak-McCurley Constant}}

			{{DEFAULTSORT:Hafner-Sarnak-McCurley constant}}
			[[Category:Mathematical constants]]

en>Danim: removed Category:Robot sensing; added Category:Robotic sensing using HotCat

2011-11-02T03:33:56Z

removed Category:Robot sensing; added Category:Robotic sensing using HotCat

New page

I am Oscar and I completely dig that name. One of the very best things in the world for me is to do aerobics and now I'm trying to make money with it. Supervising is my profession. South Dakota is where me and my husband live.<br><br>Also visit my web page [http://www.tutorca.com/?document_srl=958819 http://www.tutorca.com]