en>Yobot: /* References */Remove invisible unicode control characters + other fixes using AWB (10482)

2014-10-23T06:26:45Z

References: Remove invisible unicode control characters + other fixes using AWB (10482)

en>Bubka42: Repairing links to disambiguation pages (Normalization) - You can help!

2013-06-11T11:56:41Z

Repairing links to disambiguation pages (Normalization) - You can help!

← Older revision		Revision as of 13:56, 11 June 2013
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	~~<br><br>Discuss glossy and classy~~, the ~~Buck Nobleman~~ is ~~the epitome~~ of ~~a gentleman’~~[~~http://doc.Froza.ru/index.php/Spyderco_Delica_4_Torture_Test s folder~~]~~. You may get it~~ in ~~chrome steel but we choose the titanium coated variant as pictured~~. The ~~blade~~ is ~~a 440A stainless steel drop point a little longer than~~ two and ~~a half inches~~. ~~The overall knife length is three~~ and ~~1 / 4 inches when closed so it’s a pleasant dimension for~~ the ~~pocket~~. The ~~deal with~~ is ~~rubberized carbon fiber over stainless-steel which has a regal yet menacing look to it. This knife is simply putting and cuts elegantly time after time. >> See newest pricing for~~ the ~~Buck Nobleman.~~<br><br>~~If looking for~~ a ~~looking knife~~ , ~~Winchester Looking Knives offer good selections. They function drop level or intestine hook blades~~, ~~full [http://www~~.~~friendszz.com~~/groups/spyderco-delica-4-trainer/ tang development] and either wood or Ersatz Micarta deal with scales. Take a better have a look at one model, the Massive Winchester Looking Knife to get an concept of the benefits of Winchester knives This knife incorporates a four.83" drop level fixed blade fabricated from surgical stainless steel and of course the Winchester etch. It ~~has full tang construction and a wood handle with stainless steel bolster, in addition to a lined lanyard gap. A nylon sheath~~ can be ~~included.~~<br><br>~~Small spiral notebooks have been around since I used to be in grammar faculty~~ - ~~that was~~ a ~~long time ago~~. ~~Preserve one of those little pads useful for taking notes and telephone numbers or freely giving directions~~ or a ~~shopping record. Imagine it or not, the whole world does not carry~~ a ~~Palm Pilot or Blackberry. However everybody needs to hold away information from~~ a ~~conversation now and then~~. ~~You~~'~~ll be able to write down what they want, tear of the web page and slip it into somebody~~'~~s pocket in beneath a minute. Unlike~~ the ~~volume~~ of ~~crap that ends up in your Blackberry~~, a ~~single piece of paper stands out~~.<br><br>~~There was~~ a ~~time when made in America wasn't something you had to search for. It was only~~ a ~~given. Right now~~, ~~not~~ a ~~lot. Now we have to look to see if one thing is made in America~~, and ~~sometimes it's a lot tougher to search out than one may suppose. It~~ [~~http~~:~~//www.thebestpocketknifereviews.com/spyderco~~-~~delica~~-~~4-review~~/ ~~Www.Thebestpocketknifereviews.Com~~] ~~is laborious to discover~~ a ~~business or manufacturer who places their country and high quality before sales and revenue. It appears~~ a ~~lot easier to ship work overseas for cheaper labor, or to purchase abroad for~~ a ~~cheaper product. As an~~ end end ~~result~~, the ~~quality of~~ the ~~product and our country suffers~~.<br><br>~~The blade that opens from the side is very like other pocket knives You push the button and the blade swings out the facet like any other knife The out~~-~~the~~-~~entrance or the OTF switchblade~~, ~~pops out the front because the identify recommend~~. ~~Now there~~ are ~~two different types of OTF blades a single~~ and ~~double motion~~. ~~The one motion is once you push~~ the ~~button~~ and the ~~blade pops out and then you must manually push the blade back in. The double action is identical this~~ the ~~totally different of that~~ to ~~place~~ the ~~blade again in you simply push~~ the ~~button once more.~~<br><br>If the ~~knife has an extra~~ of ~~sticky or dirty buildup that will not come out with both of those methods~~, ~~attempt putting~~ the ~~knife in~~ a ~~bowl of heat water~~, ~~which ought to assist loosen~~ the ~~grime. A comment beneath from Instructable person Denger mentions that one must be careful or avoid utilizing this methodology on knives using natural supplies resembling wood~~, ~~abalone, or mother~~-~~of-pearl~~, and ~~that even synthetic handles could also be broken if left for too long in water at~~ or ~~near boiling temperatures. Then try~~ the ~~probing method, adopted~~ by ~~the wash method~~. ~~This should care~~ for ~~even~~ the ~~hardest residue~~.		{{Orphan\|date=September 2011}}

			{{see also\|Vector algebra relations}}

			In [[mathematics]], the '''quadruple product''' is a product of four [[vector (geometric)\|vectors]] in three-dimensional [[Euclidean space]]. The name "quadruple product" is used for two different products,<ref>{{harvnb\|Gibbs\|Wilson\|1901\|loc=§42 of section "Direct and skew products of vectors", p.77 \|year=1901}}</ref> the scalar-valued '''scalar quadruple product''' and the vector-valued '''vector quadruple product'''.

			== Scalar quadruple product ==
			The '''scalar quadruple product''' is defined as the [[dot product]] of two [[cross product]]s:
			:<math> (\mathbf{a \times b})\mathbf {\cdot}(\mathbf{c}\times \mathbf{d}) \ ,</math>
			where '''a, b, c, d''' are vectors in three-dimensional Euclidean space.<ref name=autogenerated1>{{harvnb\|Gibbs\|Wilson\|1901\|p=76}}</ref> It can be evaluated using the identity:<ref name=autogenerated1 />
			:<math> (\mathbf{a \times b})\mathbf {\cdot}(\mathbf{c}\times \mathbf{d}) = (\mathbf{a \cdot c})(\mathbf{b \cdot d}) - (\mathbf{a \cdot d})(\mathbf{b \cdot c}) \ . </math>
			or using the [[determinant]]:
			:<math>(\mathbf{a \times b})\mathbf {\cdot}(\mathbf{c}\times \mathbf{d}) =\begin{vmatrix} \mathbf{a\cdot c} & \mathbf{a\cdot d} \\
			\mathbf{b\cdot c} & \mathbf{b\cdot d} \end{vmatrix} \ . </math>

			==Vector quadruple product ==
			The '''vector quadruple product''' is defined as the [[cross product]] of two cross products:
			:<math> (\mathbf{a \times b}) \mathbf{\times} (\mathbf{c}\times \mathbf{d}) \ ,</math>
			where '''a, b, c, d''' are vectors in three-dimensional Euclidean space.<ref name=autogenerated2>{{harvnb\|Gibbs\|Wilson\|1901\|pp=77 ''ff''}}</ref> It can be evaluated using the identity:<ref>{{harvnb\|Gibbs\|Wilson\|1901\|p=77}}</ref>
			:<math> (\mathbf{a \times b} )\mathbf{\times} (\mathbf{c}\times \mathbf{d}) = [\mathbf{a,\ b, \ d}] \mathbf c - [\mathbf{a,\ b, \ c}] \mathbf d \ ,</math>
			This identity can also be written using [[tensor]] notation and the [[Einstein summation]] convention as follows:
			:<math>(\mathbf{a \times b} )\mathbf{\times} (\mathbf{c}\times \mathbf{d})=\varepsilon_{ijk} a^i c^j d^k b^l - \varepsilon_{ijk} b^i c^j d^k a^l=\varepsilon_{ijk} a^i b^j d^k c^l - \varepsilon_{ijk} a^i b^j c^k d^l</math>
			using the notation for the [[triple product]]:
			:<math>[\mathbf{a,\ b, \ d}] = (\mathbf{a \times b}) \mathbf{\cdot d } = \begin{vmatrix} \mathbf{a\cdot }\hat {\mathbf i} & \mathbf{b \cdot} \hat {\mathbf i} & \mathbf{d\cdot} \hat {\mathbf i}\\
			\mathbf{a\cdot }\hat {\mathbf j} & \mathbf{b\cdot} \hat {\mathbf j} & \mathbf{d\cdot}\hat {\mathbf j}\\ \mathbf{a\cdot} \hat {\mathbf k} & \mathbf{b\cdot} \hat {\mathbf k} & \mathbf{d\cdot }\hat {\mathbf k} \end{vmatrix} = \begin{vmatrix} \mathbf{a\cdot }\hat {\mathbf i} & \mathbf{a \cdot} \hat {\mathbf j} & \mathbf{a\cdot} \hat {\mathbf k}\\
			\mathbf{b\cdot }\hat {\mathbf i} & \mathbf{b\cdot} \hat {\mathbf j} & \mathbf{b\cdot}\hat {\mathbf k}\\ \mathbf{d\cdot} \hat {\mathbf i} & \mathbf{d\cdot} \hat {\mathbf j} & \mathbf{d\cdot }\hat {\mathbf k} \end{vmatrix}
			\ ,</math>
			where the last two forms are determinants with <math> \hat {\mathbf i}, \ \hat {\mathbf j}, \ \hat {\mathbf k} </math> denoting unit vectors along three mutually orthogonal directions.

			Equivalent forms can be obtained using the identity:<ref>{{harvnb\|Gibbs\|Wilson\|year=1901\|loc=Equation 27, p. 77}}</ref>
			:<math>[\mathbf{b,\ c, \ d}]\mathbf a - [\mathbf{c,\ d, \ a}]\mathbf b+[\mathbf{d,\ a, \ b}]\mathbf{c} -[\mathbf{a,\ b, \ c}]\mathbf d = 0 \ . </math>

			== Application==
			The quadruple products are useful for deriving various formulas in spherical and plane geometry.<ref name=autogenerated2 /> For example, if four points are chosen on the unit sphere, ''A, B, C, D'', and unit vectors drawn from the center of the sphere to the four points, '''a, b, c, d''' respectively, the identity:
			:<math>(\mathbf{a \times b})\mathbf{\cdot}(\mathbf{c \times d}) = (\mathbf {a\cdot c })(\mathbf {b\cdot d })-(\mathbf{ a\cdot d })(\mathbf {b\cdot c }) \ , </math>
			in conjunction with the relation for the magnitude of the cross product:
			:<math>\\|\mathbf{a \times b}\\| = a b \sin \theta_{ab} \ , </math>
			and the dot product:
			:<math>\\|\mathbf{a \cdot b}\\| = a b \cos \theta_{ab} \ , </math>
			where ''a = b'' = 1 for the unit sphere, results in the identity among the angles attributed to Gauss:
			:<math>\sin \theta_{ab}\sin \theta_{cd}\cos x = \cos\theta_{ac}\cos\theta_{bd} - \cos\theta_{ad} \cos \theta_{bc} \ , </math>
			where ''x'' is the angle between '''a × b''' and '''c × d''', or equivalently, between the planes defined by these vectors.

			[[Josiah Willard Gibbs]]'s pioneering work on vector calculus provides several other examples.<ref name=autogenerated2 />

			==Notes==
			{{reflist\|colwidth=30em}}

			==References==
			*{{cite book \|last1=Gibbs\|last2=Wilson \|first1=Josiah Willard \|first2= Edwin Bidwell \|title=Vector analysis: a text-book for the use of students of mathematics \|url=http://www.archive.org/details/vectoranalysiste00gibbiala \|publisher=Scribner \|year=1901 \|ref=harv}}

			==See also==
			*[[Binet–Cauchy identity]]
			*[[Lagrange's identity]]

			[[Category:Vectors]]
			[[Category:Linear algebra]]

en>Luckas-bot: r2.7.1) (Robot: Adding zh:对比性质

2012-02-22T04:40:13Z

r2.7.1) (Robot: Adding zh:对比性质

New page

Discuss glossy and classy, the Buck Nobleman is the epitome of a gentleman’[http://doc.Froza.ru/index.php/Spyderco_Delica_4_Torture_Test s folder]. You may get it in chrome steel but we choose the titanium coated variant as pictured. The blade is a 440A stainless steel drop point a little longer than two and a half inches. The overall knife length is three and 1 / 4 inches when closed so it’s a pleasant dimension for the pocket. The deal with is rubberized carbon fiber over stainless-steel which has a regal yet menacing look to it. This knife is simply putting and cuts elegantly time after time. >> See newest pricing for the Buck Nobleman. If looking for a looking knife , Winchester Looking Knives offer good selections. They function drop level or intestine hook blades, full [http://www.friendszz.com/groups/spyderco-delica-4-trainer/ tang development] and either wood or Ersatz Micarta deal with scales. Take a better have a look at one model, the Massive Winchester Looking Knife to get an concept of the benefits of Winchester knives This knife incorporates a four.83" drop level fixed blade fabricated from surgical stainless steel and of course the Winchester etch. It has full tang construction and a wood handle with stainless steel bolster, in addition to a lined lanyard gap. A nylon sheath can be included. Small spiral notebooks have been around since I used to be in grammar faculty - that was a long time ago. Preserve one of those little pads useful for taking notes and telephone numbers or freely giving directions or a shopping record. Imagine it or not, the whole world does not carry a Palm Pilot or Blackberry. However everybody needs to hold away information from a conversation now and then. You'll be able to write down what they want, tear of the web page and slip it into somebody's pocket in beneath a minute. Unlike the volume of crap that ends up in your Blackberry, a single piece of paper stands out. There was a time when made in America wasn't something you had to search for. It was only a given. Right now, not a lot. Now we have to look to see if one thing is made in America, and sometimes it's a lot tougher to search out than one may suppose. It [http://www.thebestpocketknifereviews.com/spyderco-delica-4-review/ Www.Thebestpocketknifereviews.Com] is laborious to discover a business or manufacturer who places their country and high quality before sales and revenue. It appears a lot easier to ship work overseas for cheaper labor, or to purchase abroad for a cheaper product. As an end end result, the quality of the product and our country suffers. The blade that opens from the side is very like other pocket knives You push the button and the blade swings out the facet like any other knife The out-the-entrance or the OTF switchblade, pops out the front because the identify recommend. Now there are two different types of OTF blades a single and double motion. The one motion is once you push the button and the blade pops out and then you must manually push the blade back in. The double action is identical this the totally different of that to place the blade again in you simply push the button once more. If the knife has an extra of sticky or dirty buildup that will not come out with both of those methods, attempt putting the knife in a bowl of heat water, which ought to assist loosen the grime. A comment beneath from Instructable person Denger mentions that one must be careful or avoid utilizing this methodology on knives using natural supplies resembling wood, abalone, or mother-of-pearl, and that even synthetic handles could also be broken if left for too long in water at or near boiling temperatures. Then try the probing method, adopted by the wash method. This should care for even the hardest residue.

Reduced properties - Revision history

en>Yobot: /* References */Remove invisible unicode control characters + other fixes using AWB (10482)

en>Bubka42: Repairing links to disambiguation pages (Normalization) - You can help!

en>Luckas-bot: r2.7.1) (Robot: Adding zh:对比性质