Qrcode generating for .net
using barcode generator for visual .net control to generate, create qr barcode image in visual .net applications.
F~nC(r) = Fx~r) +
Visual Studio .NET denso qr bar code reader on .net
Using Barcode scanner for .NET Control to read, scan read, scan image in .NET applications.
dX'dy'{ -i~>lIx(r') [Of~~Y) of~:;Y')]
Barcode recognizer for .net
Using Barcode decoder for .net vs 2010 Control to read, scan read, scan image in .net vs 2010 applications.
i~~ 91Iy(r') (Of~~ y) Of~~; y') +
.net Vs 2010 barcode printer for .net
generate, create barcode none with .net projects
ax' [- Of~ y) (x - x') z')
Control qr-codes data on visual c#
qr code data on visual c#.net
I)} +f dx'dy' {G1(R)Fx(r')
(z - z,)]
Control qr codes size for visual basic
to include qr code iso/iec18004 and qr code data, size, image with visual basic.net barcode sdk
. [Of (x, y) (y _ y') oy
Encode barcode with .net
using visual studio .net toaccess bar code with asp.net web,windows application
+ of(x' , y') (x _ x') -
Encode universal product code version a in .net
using .net framework togenerate upc-a on asp.net web,windows application
+ G1(R)Fy(r')
Barcode barcode library with .net
using barcode printing for .net framework crystal control to generate, create barcode image in .net framework crystal applications.
+ of~~; y') (x y')] }
39 Barcode integration in .net
generate, create code 39 extended none in .net projects
UPC - 8 barcode library in .net
using barcode creator for .net crystal control to generate, create ean8 image in .net crystal applications.
Control gs1-128 size on c#
gs1-128 size on c#.net
+ G1 (R)Fn (r') [Of~~ y) (z -
Pdf417 2d Barcode barcode library for none
Using Barcode Control SDK for None Control to generate, create, read, scan barcode image in None applications.
+ (y -
Barcode development with visual c#.net
using barcode implementation for vs .net control to generate, create barcode image in vs .net applications.
Finc(T) = Fy(r) + dx' dY'{_i k1 91Ix(r') y 2 TJ1 + ~ok1 91 I y (_,)Of(X',y')Of(X,y)} r !=l , !=l TJ1 uy uX
Control ucc - 12 image for .net
generate, create gs1-128 none in .net projects
[-1 _of (x', y') of(x, y)] ax' ax
Barcode generation on .net
generate, create bar code none for .net projects
+f dx'dY'{G1 (R)Fx(r') [a f(x', y') (y _ y') _ a f(x, y) (y _ y')] ax' ax
Add code 128 code set b with .net
use ms reporting service code 128a printer togenerate code-128 on .net
+ G1(R)F
Assign 1d for .net
generate, create linear barcode none for .net projects
GS1 128 drawer with .net c#
using .net winforms crystal toinsert ean128 with asp.net web,windows application
[-(Z - z') + of (x', y') (y o~
+ of (x, y) (x fu
+ G 1 (R)Fn (r') [- of~: y) (z - z') - (x - x')]}
Fn(T) 0 - - -2
dx 'd'{ -~ok 1T/1 - 92 I x (-') [Of (x, y) - -----',------'E2 of(x' , y')] y r E1 aX ax'
ok1 TJ1 - 1y(-') 92 [Of(X,y) E2 r !=l E1 uy
Of(x',y')]} !=l' uy
dx'dy' { G2(R)Fx (r') [- Of~: y) oy [Of (x', y') (x _ x') - (z ax' z')
Of~:; y') (y -
+ of(x, y)
Z')] _ (y _ y')]
+ G2(R)Fy(r') [of~: y) (z _
+ Of~~; y') Of~~ y) (x x')]
Of~~; y') Of~: y) (y _
y') oy
+ (x _
+ G2(R)Fn (r')
. [Of (x, y) (x _ x') ax
+ of (x, y) (y -
y') - (z - z')] }
3.1 Integral Equation and SMCG Method
In terms of a matrix notation, the SMCG procedure is as follows. First, the above 6 scalar surface integral equations are discretized into a matrix equation by the moment method. Then, we choose the neighborhood distance r d as the distance which defines the boundary between the weak and strong element of the impedance matrix Z (for example, rd = 2>.). Let
= J(x - x')2 + (y -
represent the horizontal separation between two points on the rough surface (x, y, f(x, y)) and (x', y', f(x', y')). The strong matrix is a sparse matrix. For the weak matrix elements, we expand the Green's function in a Taylor's series about the flat surface, f(x, y) = o. 1 R ) exp(ik 1,2 R ) = ~ (1,2) ( ) G 1,2 (R) = (1 - ik ,2 47fR3 L....t am PR
exp(ik1,2R) 47fR
b(1,2) (
where Zd = f(x, y) - f(x', y'). The above coefficients a~,2) (PR) and b~,2) (PR) are translationally invariant in the horizontal directions. In the numerical results of this section, we keep the expansion terms at 6 (M = 5) in (6.3.23) and (6.3.24). In the following the first 4 coefficients are listed for reference (6.3.25) (6.3.26)
(6.3.28) (6.3.29) (6.3.30)
b(1 '2) (PR)
. exp(~k12PR)
3ik12 - - 2PR - - - ' ''321f 321f
k3 2 -i 1,2 PR { 19 21f
3} +-321fPR
b~1,2) (PR) = exp (ik 12 PR)
k2 1,2PR 321f
13ik12 ' 1921f
The impedance matrix is decomposed into the sum of a strong and a weak matrix.
Z = Z(8)
+ Z(w)
where Z represents near field strong interaction and Z represents nonnear field weak interaction. Next, the weak matrix elements are expanded in a Taylor's series about the horizontal distance between the two points
= L-. Zm
~ =(w)
The zeroth term in (6.3.34) is called the fiat surface contribution
= Zo
The iterative matrix-solving procedure is, for the first-order and higher order solutions
(Z (Z
(6.3.36) (6.3.37) (6.3.38)
(+1) n
-(n+1) ,,=(w) (n)
=b- L-.Zm X
Equations (6.3.36) and (6.3.37) are solved using the conjugate gradient method (CGM). The fiat surface matrix Z which represents the lowest order Taylor expansion term is on the left-hand side of the matrix equation. Without the fiat-surface matrix on the left-hand side, we have observed that the iteration does not converge for rough surfaces with moderate rms heights. Thus, the terms strong and weak refer to the magnitude of the matrix elements, instead of their total contributions to the iterative matrix equation. The product of Z with x can be computed using a 2-D FFT algorithm. Updating the right-hand side is also calculated using the FFT. An
=(FS) =(FS)
3.1 Integral Equation and SMCG Method
additional advantage of the SMCG is that only the Taylor expanded coefficients need to be stored. With the number of Taylor series coefficient fixed at M = 5, for a given rough surface the computational complexity will depend on the number of CGM iterations (6.3.37), SMCG iterations (6.3.38) and the neighborhood distance rd. The total number of operations (multiplications) is approximately NCGM [256rinN