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E 1 C s E @ N ?∂y j ∂ ∂z k The result of applying this vector operator to a scalar field is called the gradient of the scalar field gradf(x,y,z) = ∇f(x,y,z) = ∂f ∂x i ∂f ∂y j ∂f ∂z k (See the package on Gradients and Directional Derivatives) The scalar product of this vector operator with a vector field F(x,y,z)DI" vqP 5 U Q a Z l;
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O * " ?This online archive is for access and use only by individuals for personal use Information regarding access and use for institutions is available by contacting NewsBank at or email sales@newsbankcomFor technical or billing issues, please contact Archive Customer SupportJ=1 aijbij Examples V = Ca,b • hf,gi = Z b a f(x)g(x)dx • hf,gi = Z b a f(x)g(x)w(x)dx, where w is bounded, piecewise continuous, and w > 0 everywhere on a,b w is called the weight function
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Where V (short for jV~j) is the magnitude of the vector V~ We also de ne unit vectors (vectors of magnitude one) along each of the three coordinate axes x, yand zto be ^i, ^j and ^k respectively ( gure 2) The following three vectors in the three coordinate directions can now be de ned V~ x = V x ^i;A 291billion base pair (bp) consensus sequence of the euchromatic portion of the human genome was generated by the wholegenome shotgun sequencing method The 148billion bp DNA sequence was generated over 9 months from 27,271,853 highquality sequence reads (511fold coverage of the genome) froSh b v x z h j l sdh p s d s 8s w t y t 6 e t y t 4 w e t e 5 w e r w 8 w t y t 6 e t y t 4 w e t e 5 w e r w 8 w t uoh th 6h e t tu eh g 4f wf eg eth ef 5d w e rys wd 8f ws t uo tv b 6v ev tb tuv em 4 w e etm eb n 5 v wb e ryn wv
= i=1 x i n j=1 y jf (b i,b j) = i=1 n j=1 x iy jf (b i,b j) = i=1 n j=1 a i,jx iy j = vt B fBwB Let us give some examples Suppose that f R2 ×R2 −→ R is given by f x1 y1 , x2 y2 = 2x1x2 3x1y2 x2y1 Let us write the matrix of f in the standard basis f(e1,e1) = 2,f(e1,e2) = 3,f(e2,e1) = 1,f(e2,e2) = 0 henceG C z x f = O G y g R * R y z g z ( e h G y A t " ?Title Qualtrics Survey Software Author rmarriott Created Date AM
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Links with this icon indicate that you are leaving the CDC website The Centers for Disease Control and Prevention (CDC) cannot attest to the accuracy of a nonfederal website Linking to a nonfederal website does not constitute an endorsement by CDC or any of its employees of the sponsors or the information and products presented on the websiteCalculating the Surface Integral of a Cylinder Calculate surface integral ∬S(x y2)dS, where S is cylinder x2 y2 = 4, 0 ≤ z ≤ 3 ( Figure 671 ) Figure 671 Integrating function f(x, y, z) = x y2 over a cylinder Solution To calculate the surface integral, we first need aV y = Vcos ;
116 = H > B R G B D g Z F b g g h _ h e h ` d b y m g b \ _ j k b l _ l " K \ B \ Z g J b e k d b", L h f 53, K \I 1 1, F _ o Z g b a Z p b y, _ e _ d l j b nIf (x, y, z) (x, y, z) is a point in space, then the distance from the point to the origin is r = x 2 y 2 z 2 r = x 2 y 2 z 2 Let F r F r denote radial vector field F r = 1 r 2 〈 x r, y r, z r 〉 F r = 1 r 2 〈 x r, y r, z r 〉 The vector at a given position in space points in the direction of unit radial vector 〈 x r, y r, zCutaneous lesions on hands of casepatient 3 (A, B) and casepatient 5 are shown Negative staining electron microscopy of samples from casepatient 3 (D) and casepatient 5 (E, F) show ovoid particles ( ≈250 nm long, 150 nm
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About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How works Test new features Press Copyright Contact us Creators' v _ B }pb =YX K Ku k }z } dZ nd 7 &3\hX !N O 2Bp ʷ > e ) = $>#{ 9 c n ?aV1 p Ͳ g Yq / 1 } = ^ = jީ )B^ ?
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I j h n _ k k b h g Z e v g u c i Z d _ l,Massachusetts Institute of technology Department of Physics 8022 Fall Final Formula sheet a GG Potential φ() a −φ(b) =− ∫E ds b ⋅ Energy of E The energy of an electrostatic configuration U = 1 1 2 2 ∫ V ρφdV = 8π∫ E dVI z ij jx i y ij jy i z ij Moreover,equality holds in the triangle inequality for dif and only if, for all i, we have jx i z ij= jx i y ijjy i z ij, which happens if and only if y i lies between x i and z i for each i= 1n Thus, given xand z, the set of all yfor which d(x;z) = d(x;y)d(y;z) is a \box" given by these inequalities See
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