Microsoft Word - 九大物理集中講義テキスト'13.doc
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2 . DFT DFT Hohenberg Kohn DFT DFT 999 DFT DFT DFT 964 J.. ercus [,2] DFT ercus Hyper-netted chan HC [2,3] ercus DFT DFT 2
3 DFT. DFT + ercus 2. DFT 2. DFT DFT. 2. DFT 3. ercus
4 ercus DFT DFT 3. DFT 3.. H r,p = 2 p + v r # r j + r, 3. 2m < j m v r r : [ ] = $, dr * exp -. r + z #! * + < exp -.v r - r j * = B T T B z z = #3 exp $µ 3.3 µ 3. p = 2#$! 2 m 2 3.4! = h 2 h 3.2 = # $ log, 3.5 4
5 $ µ # T,V = r = = $ µ T,V $ r * -* r + dr. -* +. + exp $ r, /, r /, z! z! = r $ r * -* -* + dr. + r $ r. + exp $ r, /, /, -*. + /, < -*. + /, < exp $v r $ r j -. / exp $v r $ r j n r 3.6 = r # r f Drac r r f n r -. / n r = r # r [ r ] T,V #$ r # r l l # n r n r 3.7 n r = 3.6 = $ z! dr. * $, r - r * exp -/v r - r j + + # < n 3.8 n r = n 3.7 n r = r # r [ r ] T,V, = #$ r # r + r # r r # r l l = = n # r $ r + n 2 g r $ r $ n 2 * + # n r = n r = n # r $ r + n 2 h r $ r
6 n 2 g r r # 3.9 r # r $ h r r # Ornsten-ZerneOZ 3.32 = g r h r n d r d = d d z $ $ $, - # dr,* r + r # exp +/ d r!. 3. = n exp # d r n d r d = = d = z n,. z! - $ # $ dr, * r + r n d r d T,V, d = #$ d r 3. = n r # r 3.2 DFT DFT n 3.2. DFT 3.6 [ ] r µ [ ] n r F[ n] F[ n] #[ ] $ dr $ µ # [ r $ µ ] T,V r = [ ] # $ dr n r [ r # µ ] 3.3 6
7 3.6 T, V F[ n] F[ n] = #[ ] $ dr n r [ r $ µ ] $ dr $ µ # [ r $ µ ] T,V r = $ dr # n r r µ 3.6 T, V [ ] # $ = dr µ # r 3.4 [ r µ ] 3.5 T,V 3.4 F n T,V = µ # r n r 3.6 DFT F[ n] F [ n] F n = # $ dr n r T,V T,V n r [ r $ µ ] T,V n r n r = # n r T,V + µ $ r 3.7 # T,V = 3.8 n r 3.6 r n r DFT DFT 7
8 F n T,V = µ n r # r 3.9 r r # r $ n r T,V, = #$ r = n r # r n r n r n r = n r 3.2 r r = r + F [ n ] # F n n r T,V n r T,V # µ # µ 3.22 F ex [ n] µ ex F ex [ n] F[ n] # F [ n] 3.23 µ ex = µ µ r = r + F ex [ n] # µ ex n r 3.25 T, V 3.25 n 8
9 r r + #F ex [ n] + $ dr n= n #n r #F ex n #n r #n r µ ex n r n n= n = r + dr #F ex n #n r #n r, 3.26 n r $ n n= n 3.25 r = r = F ex n n= n = µ ex n r $ C r r # F ex [ n] n r n r # n= n r = n r # r n r # n = n n= n r # r $ n r = n [ r ] r # r + n 2 h r # r 3.29 = #$ #[ $ r ] = # r $ r 3.3 #n r = n= n #n r dr # $ r Ornsten-ZerneOZ = $ r r # $ r r # +$ *C *$ r r # + $ * C * n h r r # h r r # n 3.3 F r f # g r = $ dr f r # g r r F r f r g r f ˆ g ˆ F ˆ = f ˆ g ˆ 9
10 r r OZ OZ DFT OZ r = r = # r 3.3 OZ [2] = C r r # + C * n h r r # 3.32 h r r # 3.3 # r n r 3.33 DFT C r OZ 3.32 h r C r h r = C r +C * n C r +C * n C * n C r! C r 3. h r OZ h r C r C r OZ h r C r OZ C r C r OZ h r = C r h r f = exp #v r h r v r
11 C r = h r #$v r C r C r r # 3.26 r = r # $ dr C r r 3.34 n r n r = n exp # r 3.35 n r 3.34 = n exp # r 3.36 n r 3.34 F[ n] C r r # n r n r C r r # Hyper-netted chanhc ercus-yevcy OZ [2,3] C r r # C r r # DFT
12 3.3. ercus 96 ercus 958 ercus-yevcy [2,3] ercus ercus dea [] ercus DFT DFT ercus HC HC DFT ercus ercus ercus DFT ercus ercus 3.9 2
13 + = $ r r n 2 h r r # = = z z! / * +, dr -*. + l $ r # r l l =, 2 $ r r $ r # r l -*. + 2 < j exp v r r j z,, / * dr -* $ r r -* exp v r r #! r r R r r, 2 -*. + 2 < j, exp v r r j, # v r $ r n 2 h r r # + = z z -. dr $ *-, r r *! + + / exp R r r # = z R $ 2 * + 2 # r $ r < j exp v r r j 2 * + 2 R R ercus relaton 3.8 n = = z = z z $ $ $, - # dr,* r + r # exp +/v r + r j.! < j z + $ + $ + $ +, - # dr # exp +/v r + r # exp +/v r + r j. +! < j z + $ + $ + $ +, - # dr # exp +/ R r r # exp +/v r + r j. +! < j = z [ R ] h r r # = n r R n 3.4 h r r # 3.38 R r r # v r $ r r r 3
14 n r E ercus r = v r # C $ n h r = v r # h r + C r 3.42 = exp # r h r 3.43 HC [2,3] DFT +ercus HC DFT ercus DFT 3.4. Weghted-densty approxmaton WDA DFT Weghted-densty approxmaton WDA Local densty approxmaton, LDA F ex [ n] F ex [ n] = dr n r f n r 3.44 f n A ex n r Tarazona WDA = dr w r # r n r F ex [ n] = dr n r f n r 3.46 [4] 3.45 w r weght functon WDA n r w r w r [4] weght functon 3.45 WDA [5] effectve densty approxmaton EDA [6] 4
15 EDA WDA F ex [ n] = dr n r f n eff r n 3.47 n eff r n F ex [ n] n eff r n n eff r n n eff #n r n eff r n = n + dr + 2! = f n eff r n #n r n # 2 n eff r n dr dr 2 #n r #n r 2 [ n r $ n ] n [ n r $ n ] n r 2 [ $ n ] ! 3.47 F ex eff [ n] n + # dr n r f $ n eff r r n n 3.49 n r n r f n f n C r r # = 2$f # n +n $f ## n +n $f # n r n n r # n eff dr dr n n r n n eff r n n r # n r n n eff r n 2 n eff r n n r n # 3.5 f n f n F ex [ n] n eff r n n r 2 n eff r n n n r n r # n 5
16 3.49 n eff r n n r n r n eff r n n r n eff r n n n r n r # n W r 3.48, 3.49, 3.5 : F ex [ n] n r r n + # dr W r $ r n r f n eff r n, 3.5 n eff r n = n + dr W r # r [ n r # n ], 3.52 C r r # = 2$f # n W r r # + n $f ## n dr W r r r # r = n r = = n µ ex : µ ex = f n + n f n # dr W r $ r W r 3.54 atra Ghosh WDA[7] weght functon W r n eff r n n eff r n n r W r n eff r n n r n r # n W r ercus OZ W r EDA HC Y 3.34 HC Ref WDA EDA 3.24 W r 3.5. DFT
17 [ ] = F d [ n] + F ex [ n] + # dr n r [ r $ µ ] 3.55 F d [ n] F d [ n] 3.3, 3., 3. d r = µ d # ln $3 n d r d µ d = ln# 3 n = # ln $3 n d r d 3.57 T,V F d n d n d r d!f d! n d # $ = dr!f d! n d # $!n d r d =! dr n d r d! T,V =!!n d r d ln # 3 n d r d =! dr n d r d ln # 3 n d r d! # $ µ d d r!nd r d $! dr ln! 3 n d r d # $!nd r d! dr!n d r d 3.58 =! dr n d r d! dr!n d r d! Ref.2 88 F d! n d # $ 3.56 F ex [ n] F ex [ n] = F ex [ n ] + µ ex dr [ n r # n ] # 3.59 dr dr 2 C r # r 2 [ n r # n ][ n r 2 # n ] 2$ ![ ] =!! n # dr $ n r + # dr dr 2 C r r 2 $ n r 2! = F ex n! # n + n # dr dr 2 C r r 2 $ n r 2! n n $ n r $! µ ex 3.6 r = v r 3.4 ercus
18 OZ HC [8] µ ex = = v # = # n dr C r + n 3.62 dr h r [ h r # C r ] $ 2$ EDA [ ] 4. DFT 4.. R X R,# X R,# v X,X j X X R,# 3.32 Ornsten ZerneMOZ X OZ 3.42 X HC MOZ/HC [2] [2] RISM [2] RISM DFT Hohenberg Kohn 8
19 DFT DFT X R,# 3.2 : [ ] = z $ $, * # dx # exp -. X! + $ # < exp -.v X,X j 4. X X X X #[ ] = n X 4.2 [ $ µ ] T,V X X X n X n X R R R R n R R n R n R R X R n R n R n R n X n R n Appendx DFT DFT 9
20 [9]: [{ # }] = a $ $ dr $ +, $ z a a / - $ $ exp, a r! * *. s ab r a b $ $, r a<b a * $ $ < a,b a= a= exp,v ab r a b, r j * * 4.3 z a a z a = #3 a exp $µ a a µ a a a r a v ab r a b r j a j b s ab r a b r a b L ab 2 s ab r = r # L ab 4$L ab 4.4 r Drac s ab r s ab r { r } = n [ µ ] r $ T,V # { $ } r { } 4.5 { n r { } } { n r { } } X 2
21 DFT DFT n r { # } r # T,V, $ = n # r { $ } r { } = n * # r r + n 2 h # r r # r r, 4.6 #$ r r h # r $ r 4.4 #$ r = #$ r + #$ s #$ r 4.7 #$ = # # $ n d d r { # } = n a. $ dr 2 a= * + r, r 2 3 = exp,- d b 2 / b r b= s ab r a b $ 2, r 2 a<b 6 2,r 2 =r * $ b= b r 2 exp,- b d * 4.8 n 2,r 2 # =r { r 2 } 2 r 2,r 2 # =r ercus ercus 2
22 a = 3 dr h # r $ r 2 a= R n r # R # r { r } * +, - r $ r # * a 7 dr + a=, - r $ r # 3 2 s ab r a b $ r a<b s ab r a b $ r a<b { } r b $ v b r r b= $ 4 R [{ }] 6 * +,. / * +,. 4 R R [{ / }] n r { / } n 6 $ 5 { } 5 4.9, 4. { } a # dr a= R [{ # }] 4.9 r r R n r # { } { } { r } R # r r r h # r R [{ # }] ercus 4.3. DFT DFT DFT DFT 4.5 [ ] { r } # µ [ ] { n r { } } F[ { n }] a # $ [{ }] dr F { n } a [ a r µ a ] a n a r { } 4. a= 4.5 T, V F[ { n }] = $ dr a F { n # } a [ a r $ µ a ] a n a r { # } 4.2 a= 22
23 [{ }] { } F n # T,V = µ $ $ r n $ r # =,!, 4.3 DFT F[ { n }] { n r { } } DFT 4.8 n n r { # } = n r # r { # } n r # { } { } =,!, 4.4 { r } r ex #F [{ n $ }] =,!, 4.5 r = r + #n r { $ } µ ex F ex [ n] µ ex T, V F ex { n } { } { } # F[ n ] $ F [ n ] 4.6 µ ex = µ # µ 4.7 { } { } 4.5 n r n 23
24 r = r # $ b dr C b b r # r b= b [ n b r { } # n ] 4.8 $# C # r $ r F ex { n } n r { }n # r { } { } = $# r n r # n n $ { }= n { }= n $# r n # r { } n { }= n #n $ r { } # b r b b * dr = # b # b r #n r { } $ # r r b= { }= { n }= n 4.2 Ornsten-ZerneOZ = # r $ r $ # r $ r h # r $ r n + b *C bc * c# r $ r + b b= c= b= c= * C bc * n h c# r $ r 4.2 #$ r #$ r 4.2 OZ #$ r = #$ r 4.2 OZ Reference Interacton Ste Model RISM = b *C bc * c# r $ r h # r $ r + b *C bc * n h c# r $ r 4.22 b= c= b= c= DFT C # r $ r RISM DFT RISM 4.8, 4.9, 4., 4.4, 4.8 h # n d d [ r 2 { } n ] # r = dr 2 $ r r 2 r,
25 n d d r { # } = n a. $ dr 2 d # r { r } ˆ h a= * + r, r 2 = exp,- d b 2 / b r 2 b= b = v b r $ r = ˆ C ˆ ˆ + ˆ ˆ ˆ h # s ab r a b $ 2, r 2 a<b # { r } 6 2,r 2 =r * $ a= a r 2 exp,- a d b [ n b r $ n ] *, 4.24 $ b dr C b b= b= b r $ r { #, 4.25 C n ˆ h h # r f # = 4 $ rsn r f rdr ercus RISM RISM DFT HC DFT 4.24,r# =r { r } { r 2 } 2 d # r { r } 4.24 r 4.24 FFT r d r r # { } r { } 4.25 [] 25
26 + R n r { # } $ n c * + c r r c=, { #$ r } 4.9 = dr b b 2 b r $ r 2 h # r $ r b# r b 2 $ r b= #$ r #$ r r = dr b b 2 h #b r r 2 b$ r b 2 r b= # c r { r } = v c r $ r c= eff c $ v c r $ r, 4.3 c= 4.3 eff v c r # r $ n dr a 2 dr b a 2 C a r # r 2 h ab r a b 2 # r 2 # bc r b 2 # r $, 4.3 a= b= = n dr a 2 dr b a 2 C #a r $ r 2 ab r a b 2 $ r 2 C bc r b 2 $ r a= b= 4.32 ab r RISM 4.32 Donley, Curro, and McCoy DCM DCM [] 4.32 [] RISM eff v #c $ a r $ r 2 h ab r a b 2 $ r 2 $ bc r b 2 $ r $ C #c r $ r, 4.33 r $ r = dr a 2 dr b 2 #a a= b= HC 4.23, 4.24, 4.26, 4.33 Ref DFT
27 4.3 #$ r r #$ #$ r h # r [3] Chandler RISM polaron [4] RISM polaron Schwezer Curro olymer RISM RISM [5] [6] DFT L # # #3 a Q p = p + $ dr s r a a + $ # r exp #,u pp r a b $ # r a= * a= * a +<b * exp #,- s[ sp] 5. s r 4.4 u pp r s [ sp ] 27
28 a = v sp R # r sp R{ r } $ 5.2 a= 5. s sp s sp = #ln $ s [ sp ] 5.2 r { } a v sp R r 5. exp #$ s [ sp ] 5. s [ sp ] DFT s [ sp ] { r } a n s R sp = n s $ [ R # r +] 5.3 a= 3.6 { r } s [ sp ] = F ex s [ n s ] # µ ex s s # n s + n s 2 $ $ c= c dr [ R # r +] c dr dr 2 C ss R # R 2 R 2 # r + W pp r c d # r c= c= d = W pp r c d r { r } = n s 2 W pp r r # 2$ dr dr 2 r R C ss R R 2 R r #, W pp r c d r 28
29 W pp r 5.5 r 5. pp r # r $ = + * p p c d + --, r # r *, r # r c= d = p p -- c= d = #3. p a= Q p 3 a c d 6 / dr 4, r # r, r # r Q # 7 exp #8u pp r a b / # r 2 a +<b exp #89 s sp # s r a a + / # r a= RISM Q p 5. RISM = $ n s h ps r R + # # = $ p c * r r c= p * c= s * R R 3 + p a= = Q p - - a c 3., dr r r Q / 2 / - 4 exp 5u pp r a b., r / a +<b s r a a +., r a= 2 2 exp 56 s[ sp ]n s R sp 5.7 h ps r 5.7 ercus h ps r R = dr # pp r r $ r R
30 ˆ sp = h ˆ ps ˆ # $ pp 5.9 f r ˆ f = 4 # $ rsn r f rdr W pp r ˆ W pp 2 # $ pp = n s 2 ˆ ˆ h ps ˆ C ss ˆ h sp ˆ # $ pp = H pc { r } + W pp r a b $ # r H eff { r } $, 5.2 a= b= deal polymer chan W ˆ pp ˆ pp ˆ pp C ˆ ss 5. h ˆ ps ˆ pp 5.2 ˆ h ps DFT DFT h ps r DFT DFT u pp r 3
31 u pp r u pp r FFT DFT DFT h ss r h ps r ss ps = exp # ss = $ # r 5.3, a * dr - +. / r r,, c s r a a + * r - exp a 3 2 * ps r c= r = v ss r r = v ps r a= # C sp $ n p a= a= 5.4 [ h ps r + C ss $ n s h ss r ] 5.5 [ h ps r + C ps $ n s h ss r ] 5.6 # C pp $ n p ercus h ss r = n s r R p = v ps, R s = v ss n s, 5.7 h ps r = n p r R p = v ps, R s = v ss n p, , 5.6 C # r $ [ r ] C # r $ r n # r # n { = n } $ $ r n # r p, s n { = n } 5.9 3
32 = n p C # $ ˆ pp n s + n ˆ p h pp n ˆ p h ps n s h sp n p n s + n ˆ s h ss # n ˆ p pp n ˆ $ s 2 2 = ˆ C $ ˆ D = ˆ ˆ pp # + n ˆ { s h ss D } n ˆ p ˆ h sp D ˆ pp + n ˆ p h pp + n ˆ s h ss D ˆ { # ˆ } n s # n p n ˆ s h ps h ps pp + n ˆ p h pp ˆ D ˆ C h sp r = v r # t r, 5.23 = ˆ t # ˆ $ C pp C sp C ˆ ps # n p h ˆ ps C ˆ ss n ˆ $ s h ss, = t $ h ˆ ps # ˆ pp h ˆ sp n ˆ p h ps ˆ h ps h ˆ pp h ˆ ps + n ˆ s h ss D + ˆ D ˆ h ˆ ss # ˆ pp + n ˆ p n ˆ s h ss D ˆ + h ˆ ss D 5.25 n p lm t = n p h ˆ ps # $ pp # $ ˆ $ ˆ pp pp n ˆ s ˆ $ ˆ + ˆ pp 2 + n ˆ s h ss h ps n ˆ s h ss h ss ˆ $ pp + n ˆ s h ss * * t r = v s r # $ 5.26 dexp # rˆ t,
33 t ˆ s = C ˆ ss n ˆ s h ss, 5.28 t ˆ p = ˆ pp # ˆ pp ˆ h ˆ h ˆ ps + ps pp ˆ pp C ˆ ss, 5.29 ˆ pp n s 3.32 OZ HC 5.29 HC h ps r 5.7 { r } n s R sp n s R sp DFT h ps r pp r DFT h ps r 5.6 pp r 33
34 n s R sp 5.3 n s R sp n s R sp 5.3 I. 5.3, 5.27, 5.28 HC C ss r II. ˆ dc pp ˆ pp 5.3, 5.3, 5.32 h ps r h ps r = # # s r a a + * r * a $ dr a= r * r c $ exp *+ a -, $ ps r * c= a= a= r = v s r # $ # 5.3 dexp # rˆ t, 5.3 t ˆ p = ˆ pp # ˆ pp ˆ h ˆ h ˆ pp ˆ pp ps + ps ˆ pp n ˆ sc ss III. h ps r pp r ˆ W pp 2 # $ pp = n s 2 ˆ H eff { r } ˆ h ps ˆ C ss ˆ h sp ˆ # $ pp = H pc { r } + W pp r a b $ # r a= b=, 5.33 $
35 IV. pp r II II III h ps r pp r [7] [8] [9] [2] [2] DFT 5.3 $!2 2m Q # 2 + Q r * r = + * r, h QC r h QC r = exp #$ r 2 exp #$ fp r DFT fp r 5.35 QQ r d QQ r 5.33 DFT [22] [23] 6. DFT 35
36 DFT DFT. DFT DFT 3. DFT 4. Fundamental measure theory DFT 5. DFT DFT 36
37 [] G. Stell, The Equlbrum Theory of Classcal Fluds, edted by H. L. Frsch and J. L. Lebowtz Benjamn, ew Yor, 964 Vol. II-33. [2] J.. Hansen and I. R. McDonald, Theory of Smple Lquds, 2 nd ed. Academc, ew Yor 99. [3],, 2. [4] R. Evans, n Fundamentals of Inhomogeneous Fluds, edted by D. Henderson Deer, ew Yor, 992. [5] T. Sum and H. Seno, J. hys. Soc. Jpn. 77, [6] J. Chhara, rog. Theor. hys. 59, [7] C.. atra and S. K. Ghosh, J. Chem. hys. 6, [8] T. Morta, and K. Hroe, rog. of Theo. hys. 25, [9] D. Chandler and L. R. ratt, J. Chem. hys. 65, [] S. Ten-no and S. Iwata, J. Chem. hys., [] J.. Donley, J G. Curro, J. D. McCoy, J. Chem. hys,, [2] T. Sum and H. Seno, J. Chem. hys, 25, [3] D. Chandler and. G. Wolynes, J. Chem. hys. 74, [4] D. Chandler, Y. Sngh, and D. M. Rchardson, J. Chem. hys. 8, [5] K. S. Schwezer and J. G. Curro, Adv. Chem. hys. 98, 997. [6] K. S. Schwezer, K. G. Honnell, and J. G. Curro, J. Chem. hys. 96, [7] T. Sum and H. Seno, J. Chem. hys. 22, [8] T. Sum and H. Seno, J. Chem. hys. 2, [9] T. Sum and H. Seno, Chem. hys. Lett. 47, [2] T. Sum, K. Kobayash, and H. Seno, J. Chem. hys. 27, [2] T. Sum, C. Suzu, and H. Seno, J. Chem. hys. 3, [22] T. Sum and H. Seno, J. Chem. hys. 25, 94526, [23] T. Sum and H. Seno, J. Chem. hys. 28, 4472, [24]. Matubayas and M. aahara, J. Chem. hys. 3, [25]. Matubayas and M. aahara, J. Chem. hys. 7,
38 p.4 Lennard-Jones Coulomb Lennard-Jones : p exp!µ #[ ] = dr dp exp! H r, p 3 $$ h! 3 p.5-6 : p p.6 3. z $ - + # dr! * r r =. d, 6 p.6 : II 9 B 7 p.9 Ornsten-Zerne
39 8 p. f OZ HC : Hansen and McDonald; Theory of Smple Lquds, 3rd ed.; Secton 3.8 and p.2-22 ercus 4.9 p.4 Appendx DFT 39
40 Appendx: DFT [24,25] DFT 3.6 #[ ] = dr [ µ ] T,V $ # r [ r µ ] $ T,V r = dr $ r r A 3.2 r n r 3.6 r # = r $# A A2 A A2 #[ ] = dr [ µ ] T,V $ r $n r = r n $ $ A3 A3 dr# r $ n r # n# = dr [ # ] T,V $ $# d r r r *, + r $ r r $ r l -, l r $# r l l $ # $ #., $ n r n r /, $ n # n # A3 A dr# r $ A4 4
41 r r r n r n A3 A4 DFT A4 n# = # $ # [ # ] T,V, = $ n # = + r $# l # $ #n # = $ # r l + n # = = $ n # = n # = n # = h #,# A5 n = # n $ dr r A6 h,# A5 h,# A6 n = A6 z n d d = -. $ dr # d [ d ] -+ d r, $ exp, d r /! * * * = z. dr+ d r,exp, d r A7 =. dr+ d r,n d r d 4
42 A7 n d # d T,V, = $ d # = z # $ # dr $# d r = # $ #n d # d = A8 3.3 F[ n] #[ ] $ d $ µ # [ $ µ ] A9 T,V 3.6 F n T,V = µ $ # n # A 3.25 = + #F ex [ n] $ µ ex #n A # + d $ F ex n n n A2 n n = n= n $ C,# F ex [ n] n n # n= n = n # n # n = n n= n A3 A = # $ d C, [ # n = ] A4 n A3 OZ 42
43 = C,# + d h,# $ C, n = h,# A5 A = # $ - d /./ # dr r # 3 dr r # n r dr 2 r 2 dr r # # n r # r 2 dr 2 r 2 # n r # r 2 + n 2 h r # r 2 [ # n ] *, + { } *, 2 2, + 2 A6 A A F d [ n] = # d n d d µ d $ d $ # d n d d A7 3.6![ ] =!! # d $ n n! = + # d d 2 C, 2 n! =! + # d d 2 C, 2 $ n! 2! $ n! 2 n! 2 = n! = $ n! 2 n! 2 = A8 43
44 µ ex =![ = v uv ]! = # d $ n = v uv! n = + # d d 2 C, 2 n =! + # d d 2 C, 2 $ n = v uv 2! $ n 2 = v uv n 2 = n = n 2 = $ n = v 2 uv A9 C, 2 n = r v uv r dr# v uv r $ DFT DFT [24,25] X R,# r X 44
「産業上利用することができる発明」の審査の運用指針（案）
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