MOS FET c /(17)

Size: px
Start display at page:

Download "MOS FET c /(17)"

Transcription

1 MOS FT c /(17)

2 (a) VVS: Voltage ontrolled Voltage Source v in µ µ µ 1 µ 1 vin v in (a) VVS( ) (b) S( ) i in i in vin 1 g m v in i in + r m i in - (c) VS( ) (b) VS( ) S: urrent ontrolled urrent Source VS: Voltage ontrolled urrent Source [S] VS: urrent ontrolled urrent Source [Ω] c /(17)

3 VVS V O V I V O = f (V I ) (1 1) 1 2(a) 1 2 V O V I V IL V OL 1 2(b) V I = V D + v sig v sig V O = f (V D + v sig ) = f (V D ) + f (V D ) v sig 1! + f (V D ) v2 sig 2! + f (V D ) + f (V D )v sig (1 2) V O V v sig V = f (V D ) (1 3) v = f (V D )v sig (1 4) (1 4) 1 1 VVS f (V D ) V D V D f (V D ) f (V D ) > 1 v v sig VVS c /(17)

4 v sig V IL 1 2 V O V OL V O V O O V I O t O V I O t (a) (b) 1 2 Spice A 0 V D ( ) A 1 D c /(17)

5 A c /(17)

6 MOS FT FT n p 1 3 pnp npn 2 MOS FT I p n p I V I V V (a) pnp I n p n I V I V V (b) npn 1 3 pnp I = 0 na I O 10 2 V = V 0.6 V 2 mv/ W 1 µm I I I = α 0 I + I O (1 5) α I O I c /(17)

7 I [ma] I [ma] I = 2mA 0 2 I = 10 0 A V [V] V A V [V] (a) I V (b) I V 1 4 npn I = I I (1 6) npn (a) I V V I V 1 4(b) I V 1 4(a) I V V A pnp 1 5(a) r b W Ω I V I = I S (e V/VT 1) I S e V/VT (1 7) V T V T = kt/q q k J/K T [K] T = 300 K 27 V T 26 mv r e = 26 I [ma] [Ω] (1 8) r c 1 5(b) α α 0 r c I = 1 ma 5 50 MΩ c /(17)

8 I i e i b V I D D I r O b i e r e r b r c r b (1- )r c i r b e (a) (b) T (c) T (c) T (1 5) (1 6) I α 0 I = I + I O = β 0 I + (1 + β 0 )I O 1 α 0 1 α 0 (1 9) β 0 = α 0 1 α 0 (1 10) β β 0 β MOS FT V DS V DS V GS V GS I D I D S i 0 2 S G D S i 0 2 S G D p n+ n+ n p n+ n+ n D D G (G 1) S (G 2) G (G 1) S (G 2) (a) (b) 1 6 n MOS FT 1 6 MOS FT Metal-Oxide-Semiconductor Field-ffect Transistor MOS FT G c /(17)

9 V GS V Th n I D V GS V Th D S I D ( I D = 2K V GS V Th V ) DS V DS V DS < V GS V Th (1 11) 2 3 V DS I D V DS I D = K(V GS V Th ) 2 V DS V GS V Th (1 12) 5 (1 12) K K = K 0 W L, K 0 = µ OX 2 (1 13) W L µ OX MOS W L K V Th ( ) V Th = V T0 + γ 2φ f + V S 2φ f (1 14) V T0 γ φ f MOS FT V Th V S = V 1 4 V mv/ K µa/v 2 µa /V 2 MOS FT V Th V GS = 0 MOS FT (1 12) I D = K(V GS V Th ) 2 (1 + λv DS ) (1 15) λ V g m r d g mb I D g m = = 2K(V GS V Th )(1 + λv DS ) (1 16) V GS r d = 1/ I D 1 = (1 17) V DS Kλ(V GS V Th ) 2 g mb = I D V S = γk(v GS V Th )(1 + λv DS ) 2φ f + V S (1 18) c /(17)

10 I D [ A] 150 I D [ A] 150 V GS = 3V V GS = 2.5V V GS = 2V V GS [V] V GS = 1.5V V GS = 0, 0.5V V GS = 1V V DS [V] (a) I D V GS (V DS = 3V) (b) I D V DS 1 7 MOS FT D G v gs g m v gs r d g mb v sb v sb S 1 8 MOS FT p MOS FT 2SK p 2SJ 3 MOS FT S d r e r c ω c r c α α = α jω ω α (1 19) ω α α 1 10 β c /(17)

11 i e r e i e c d r b c c 1 9 T i b r b i b r e c c / (1- ) c d 1 10 T β = α 1 α = β jω ω β ω β = (1 α 0 )ω α ω α β 0 (1 20) (1 21) ω β β β = 1 f T f T 100 M 7 GHz f T r π = r e 1 α, π = d, g m = α o r e (1 22) c /(17)

12 i b r b c c r v b e c g m v b e 1 11 π 2 MOS FT MOS FT 1 12 gd gd D G gs v gs r d ds g m v gs S 1 12 MOS FT c /(17)

13 V I O β 0 S IO = I, S V = I, S β0 = I I O V β 0 IO=0 (1 23) 1 13 I V V R V I V = V R I 1 14 A I = 20 µa Q 2 R I V V I i b 1 13 i b ±15 µa 2 I 10 µa 30 µa Q 1 Q 3 I Q 2 I V V V (sat) I (1 9) I = β 0 I + (1 + β 0 )I O S IO = 1+β 0 S V = 0 S β0 = I β 0 = 200 I = 1 ma c /(17)

14 I A Q Q 2 20 Q1 I = 10 A O 0 V V (sat) I I I 1 14 I O = 1 na na I O = 31 na S IO I O /I 0.62% S /I = 0 S β0 β 0 /I = β 0 /β 0 β 0 β 0 100% I β 0 30% + 40% R = R 1//R 2 + r b V = {R 2 /(R 1 + R 2 )}V V = R I + V + R {(1 + β 0 )I O + β 0 I } I I I = β 0(V V ) + (1 + β 0 )(R + R )I O R + (1 + β 0)R S IO = (1 + β 0)(R + R ) R + (1 + β 0)R β 0 S V = R + (1 + β 0)R S β0 = (V V )(R + R ) {R + (1 + β 0)R } 2 (1 24) (1 25) V = 6 V R 1 = 47 kω R 2 = 20 kω R = 3 kω c /(17)

15 R1 R I V R 2 R 1 15 R I I +(1+ )I O R ' V I ' V ' R V 1 16 R = 1 kω β 0 = 200 V = 0.6 V r b = 500 Ω I O = 1 na I 1.11 ma S IO I O /I 0.040% S /I 8.4% S β0 β 0 /I β 0 /β β 0 I MOS FT MOS FT K V Th 1 17 MOS FT S VTh = I D / V Th S K = I D / K I D = K(V GS V Th ) 2 V GS = V GG I D R S V GG = {R 2 /(R 1 + R 2 )}V DD I D = 1 2R 2 S { 1 ( KRS (V GG V Th ) ) } + 2(V GG V Th )R S K (1 26) V DD = 5 V R 1 = 1 MΩ R 2 = 750 kω R S = 1 kω K = 15 ma/v 2 V Th = 0.8 V I D 1.07 ma S VTh = (1/ 1 + 4KR S (V GG V Th ) 1)/R S 0.89 S K = [{1+2KR S (V GG V Th )}/ 1 + 4KR S (V GG V Th ) 1]/(2K 2 R 2 S ) V Th 2 mv/ 50 V Th = 0.1 V c /(17)

16 R1 R D I D V DD R 2 R S 1 17 S VTh V Th /I D = 8.3% K 100% K = 15 ma/v 2 S K K/I D 11% R S M A MOS FT M A V GS = 0 M A I RF = K A VT 2 I V DD M 0..n K M 0 V GS IRF V GS = K + V Th (1 27) V GS M 1 I O1 = I RF M 2 V DD M A K A I O1 I O2 I On I RF M 0 M 1 M 2 M n V GS I V DD c /(17)

17 I 0 = 0 M 2 V 0 V DD V 0 = I K1 + V Th = V Th + V Th K 2 K 2 (1 28) V DD M 1 K 1 I I 0 M 2 K 2 V MOSFT I 0 = 0 I S I D V GS V GS = I K + V Th (1 29) V 0 V 0 = V 1 V GS = V 1 I/K V Th V Th V DD I 0 V 1 V GS I V c /(17)

( ) : 1997

( ) : 1997 ( ) 2008 2 17 : 1997 CMOS FET AD-DA All Rights Reserved (c) Yoichi OKABE 2000-present. [ HTML ] [ PDF ] [ ] [ Web ] [ ] [ HTML ] [ PDF ] 1 1 4 1.1..................................... 4 1.2..................................

More information

研修コーナー

研修コーナー l l l l l l l l l l l α α β l µ l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l

More information

MOSFET 6-2 CMOS 6-2 TTL Transistor Transistor Logic ECL Emitter Coupled Logic I2L Integrated

MOSFET 6-2 CMOS 6-2 TTL Transistor Transistor Logic ECL Emitter Coupled Logic I2L Integrated 1 -- 7 6 2011 11 1 6-1 MOSFET 6-2 CMOS 6-2 TTL Transistor Transistor Logic ECL Emitter Coupled Logic I2L Integrated Injection Logic 6-3 CMOS CMOS NAND NOR CMOS 6-4 6-5 6-1 6-2 CMOS 6-3 6-4 6-5 c 2011 1/(33)

More information

(4.15a) Hurwitz (4.15a) {a j } (s ) {a j } n n Hurwitz a n 1 a n 3 a n 5 a n a n 2 a n 4 a n 1 a n 3 H = a n a n 2. (4.16)..... a Hurwitz H i H i i H

(4.15a) Hurwitz (4.15a) {a j } (s ) {a j } n n Hurwitz a n 1 a n 3 a n 5 a n a n 2 a n 4 a n 1 a n 3 H = a n a n 2. (4.16)..... a Hurwitz H i H i i H 6 ( ) 218 1 28 4.2.6 4.1 u(t) w(t) K w(t) = Ku(t τ) (4.1) τ Ξ(iω) = exp[ α(ω) iβ(ω)] (4.11) (4.1) exp[ α(ω) iβ(ω)] = K exp( iωτ) (4.12) α(ω) = ln(k), β(ω) = ωτ (4.13) dϕ/dω f T 4.3 ( ) OP-amp Nyquist Hurwitz

More information

nsg04-28/ky208684356100043077

nsg04-28/ky208684356100043077 δ!!! μ μ μ γ UBE3A Ube3a Ube3a δ !!!! α α α α α α α α α α μ μ α β α β β !!!!!!!! μ! Suncus murinus μ Ω! π μ Ω in vivo! μ μ μ!!! ! in situ! in vivo δ δ !!!!!!!!!! ! in vivo Orexin-Arch Orexin-Arch !!

More information

(a) 4 1. A v = / 2. A i = / 3. A p = A v A i = ( )/( ) 4. Z i = / 5. Z o = /( ) = 0 2 1

(a) 4 1. A v = / 2. A i = / 3. A p = A v A i = ( )/( ) 4. Z i = / 5. Z o = /( ) = 0 2 1 http://www.ieicehbkb.org/ 1 7 2 1 7 2 2009 2 21 1 1 3 22 23 24 25 2 26 21 22 23 24 25 26 c 2011 1/(22) http://www.ieicehbkb.org/ 1 7 2 1 7 2 21 2009 2 1 1 3 1 211 2 1(a) 4 1. A v = / 2. A i = / 3. A p

More information

第86回日本感染症学会総会学術集会後抄録(I)

第86回日本感染症学会総会学術集会後抄録(I) κ κ κ κ κ κ μ μ β β β γ α α β β γ α β α α α γ α β β γ μ β β μ μ α ββ β β β β β β β β β β β β β β β β β β γ β μ μ μ μμ μ μ μ μ β β μ μ μ μ μ μ μ μ μ μ μ μ μ μ β

More information

O1-1 O1-2 O1-3 O1-4 O1-5 O1-6

O1-1 O1-2 O1-3 O1-4 O1-5 O1-6 O1-1 O1-2 O1-3 O1-4 O1-5 O1-6 O1-7 O1-8 O1-9 O1-10 O1-11 O1-12 O1-13 O1-14 O1-15 O1-16 O1-17 O1-18 O1-19 O1-20 O1-21 O1-22 O1-23 O1-24 O1-25 O1-26 O1-27 O1-28 O1-29 O1-30 O1-31 O1-32 O1-33 O1-34 O1-35

More information

1 911 9001030 9:00 A B C D E F G H I J K L M 1A0900 1B0900 1C0900 1D0900 1E0900 1F0900 1G0900 1H0900 1I0900 1J0900 1K0900 1L0900 1M0900 9:15 1A0915 1B0915 1C0915 1D0915 1E0915 1F0915 1G0915 1H0915 1I0915

More information

1. 4cm 16 cm 4cm 20cm 18 cm L λ(x)=ax [kg/m] A x 4cm A 4cm 12 cm h h Y 0 a G 0.38h a b x r(x) x y = 1 h 0.38h G b h X x r(x) 1 S(x) = πr(x) 2 a,b, h,π

1. 4cm 16 cm 4cm 20cm 18 cm L λ(x)=ax [kg/m] A x 4cm A 4cm 12 cm h h Y 0 a G 0.38h a b x r(x) x y = 1 h 0.38h G b h X x r(x) 1 S(x) = πr(x) 2 a,b, h,π . 4cm 6 cm 4cm cm 8 cm λ()=a [kg/m] A 4cm A 4cm cm h h Y a G.38h a b () y = h.38h G b h X () S() = π() a,b, h,π V = ρ M = ρv G = M h S() 3 d a,b, h 4 G = 5 h a b a b = 6 ω() s v m θ() m v () θ() ω() dθ()

More information

untitled

untitled MOSFET 17 1 MOSFET.1 MOS.1.1 MOS.1. MOS.1.3 MOS 4.1.4 8.1.5 9. MOSFET..1 1.. 13..3 18..4 18..5 0..6 1.3 MOSFET.3.1.3. Poon & Yau 3.3.3 LDD MOSFET 5 3.1 3.1.1 6 3.1. 6 3. p MOSFET 3..1 8 3.. 31 3..3 36

More information

85 4

85 4 85 4 86 Copright c 005 Kumanekosha 4.1 ( ) ( t ) t, t 4.1.1 t Step! (Step 1) (, 0) (Step ) ±V t (, t) I Check! P P V t π 54 t = 0 + V (, t) π θ : = θ : π ) θ = π ± sin ± cos t = 0 (, 0) = sin π V + t +V

More information

devicemondai

devicemondai c 2019 i 3 (1) q V I T ε 0 k h c n p (2) T 300 K (3) A ii c 2019 i 1 1 2 13 3 30 4 53 5 78 6 89 7 101 8 112 9 116 A 131 B 132 c 2019 1 1 300 K 1.1 1.5 V 1.1 qv = 1.60 10 19 C 1.5 V = 2.4 10 19 J (1.1)

More information

= hυ = h c λ υ λ (ev) = 1240 λ W=NE = Nhc λ W= N 2 10-16 λ / / Φe = dqe dt J/s Φ = km Φe(λ)v(λ)dλ THBV3_0101JA Qe = Φedt (W s) Q = Φdt lm s Ee = dφe ds E = dφ ds Φ Φ THBV3_0102JA Me = dφe ds M = dφ ds

More information

(1) 1 y = 2 = = b (2) 2 y = 2 = 2 = 2 + h B h h h< h 2 h

(1) 1 y = 2 = = b (2) 2 y = 2 = 2 = 2 + h B h h h< h 2 h 6 6.1 6.1.1 O y A y y = f() y = f() b f(b) B y f(b) f() = b f(b) f() f() = = b A f() b AB O b 6.1 2 y = 2 = 1 = 1 + h (1 + h) 2 1 2 (1 + h) 1 2h + h2 = h h(2 + h) = h = 2 + h y (1 + h) 2 1 2 O y = 2 1

More information

5 c P 5 kn n t π (.5 P 7 MP π (.5 n t n cos π. MP 6 4 t sin π 6 cos π 6.7 MP 4 P P N i i i i N i j F j ii N i i ii F j i i N ii li i F j i ij li i i i

5 c P 5 kn n t π (.5 P 7 MP π (.5 n t n cos π. MP 6 4 t sin π 6 cos π 6.7 MP 4 P P N i i i i N i j F j ii N i i ii F j i i N ii li i F j i ij li i i i i j ij i j ii,, i j ij ij ij (, P P P P θ N θ P P cosθ N F N P cosθ F Psinθ P P F P P θ N P cos θ cos θ cosθ F P sinθ cosθ sinθ cosθ sinθ 5 c P 5 kn n t π (.5 P 7 MP π (.5 n t n cos π. MP 6 4 t sin π 6

More information

N cos s s cos ψ e e e e 3 3 e e 3 e 3 e

N cos s s cos ψ e e e e 3 3 e e 3 e 3 e 3 3 5 5 5 3 3 7 5 33 5 33 9 5 8 > e > f U f U u u > u ue u e u ue u ue u e u e u u e u u e u N cos s s cos ψ e e e e 3 3 e e 3 e 3 e 3 > A A > A E A f A A f A [ ] f A A e > > A e[ ] > f A E A < < f ; >

More information

LLG-R8.Nisus.pdf

LLG-R8.Nisus.pdf d M d t = γ M H + α M d M d t M γ [ 1/ ( Oe sec) ] α γ γ = gµ B h g g µ B h / π γ g = γ = 1.76 10 [ 7 1/ ( Oe sec) ] α α = λ γ λ λ λ α γ α α H α = γ H ω ω H α α H K K H K / M 1 1 > 0 α 1 M > 0 γ α γ =

More information

70 : 20 : A B (20 ) (30 ) 50 1

70 : 20 : A B (20 ) (30 ) 50 1 70 : 0 : A B (0 ) (30 ) 50 1 1 4 1.1................................................ 5 1. A............................................... 6 1.3 B............................................... 7 8.1 A...............................................

More information

O x y z O ( O ) O (O ) 3 x y z O O x v t = t = 0 ( 1 ) O t = 0 c t r = ct P (x, y, z) r 2 = x 2 + y 2 + z 2 (t, x, y, z) (ct) 2 x 2 y 2 z 2 = 0

O x y z O ( O ) O (O ) 3 x y z O O x v t = t = 0 ( 1 ) O t = 0 c t r = ct P (x, y, z) r 2 = x 2 + y 2 + z 2 (t, x, y, z) (ct) 2 x 2 y 2 z 2 = 0 9 O y O ( O ) O (O ) 3 y O O v t = t = 0 ( ) O t = 0 t r = t P (, y, ) r = + y + (t,, y, ) (t) y = 0 () ( )O O t (t ) y = 0 () (t) y = (t ) y = 0 (3) O O v O O v O O O y y O O v P(, y,, t) t (, y,, t )

More information

2 0.1 Introduction NMR 70% 1/2

2 0.1 Introduction NMR 70% 1/2 Y. Kondo 2010 1 22 2 0.1 Introduction NMR 70% 1/2 3 0.1 Introduction......................... 2 1 7 1.1.................... 7 1.2............................ 11 1.3................... 12 1.4..........................

More information

7 π L int = gψ(x)ψ(x)φ(x) + (7.4) [ ] p ψ N = n (7.5) π (π +,π 0,π ) ψ (σ, σ, σ )ψ ( A) σ τ ( L int = gψψφ g N τ ) N π * ) (7.6) π π = (π, π, π ) π ±

7 π L int = gψ(x)ψ(x)φ(x) + (7.4) [ ] p ψ N = n (7.5) π (π +,π 0,π ) ψ (σ, σ, σ )ψ ( A) σ τ ( L int = gψψφ g N τ ) N π * ) (7.6) π π = (π, π, π ) π ± 7 7. ( ) SU() SU() 9 ( MeV) p 98.8 π + π 0 n 99.57 9.57 97.4 497.70 δm m 0.4%.% 0.% 0.8% π 9.57 4.96 Σ + Σ 0 Σ 89.6 9.46 K + K 0 49.67 (7.) p p = αp + βn, n n = γp + δn (7.a) [ ] p ψ ψ = Uψ, U = n [ α

More information

arxiv: v1(astro-ph.co)

arxiv: v1(astro-ph.co) arxiv:1311.0281v1(astro-ph.co) R µν 1 2 Rg µν + Λg µν = 8πG c 4 T µν Λ f(r) R f(r) Galileon φ(t) Massive Gravity etc... Action S = d 4 x g (L GG + L m ) L GG = K(φ,X) G 3 (φ,x)φ + G 4 (φ,x)r + G 4X (φ)

More information

1. 2 P 2 (x, y) 2 x y (0, 0) R 2 = {(x, y) x, y R} x, y R P = (x, y) O = (0, 0) OP ( ) OP x x, y y ( ) x v = y ( ) x 2 1 v = P = (x, y) y ( x y ) 2 (x

1. 2 P 2 (x, y) 2 x y (0, 0) R 2 = {(x, y) x, y R} x, y R P = (x, y) O = (0, 0) OP ( ) OP x x, y y ( ) x v = y ( ) x 2 1 v = P = (x, y) y ( x y ) 2 (x . P (, (0, 0 R {(,, R}, R P (, O (0, 0 OP OP, v v P (, ( (, (, { R, R} v (, (, (,, z 3 w z R 3,, z R z n R n.,..., n R n n w, t w ( z z Ke Words:. A P 3 0 B P 0 a. A P b B P 3. A π/90 B a + b c π/ 3. +

More information

A = A x x + A y y + A, B = B x x + B y y + B, C = C x x + C y y + C..6 x y A B C = A x x + A y y + A B x B y B C x C y C { B = A x x + A y y + A y B B

A = A x x + A y y + A, B = B x x + B y y + B, C = C x x + C y y + C..6 x y A B C = A x x + A y y + A B x B y B C x C y C { B = A x x + A y y + A y B B 9 7 A = A x x + A y y + A, B = B x x + B y y + B, C = C x x + C y y + C..6 x y A B C = A x x + A y y + A B x B y B C x C y C { B = A x x + A y y + A y B B x x B } B C y C y + x B y C x C C x C y B = A

More information

TOP URL 1

TOP URL   1 TOP URL http://amonphys.web.fc.com/ 1 19 3 19.1................... 3 19.............................. 4 19.3............................... 6 19.4.............................. 8 19.5.............................

More information

1 9 v.0.1 c (2016/10/07) Minoru Suzuki T µ 1 (7.108) f(e ) = 1 e β(e µ) 1 E 1 f(e ) (Bose-Einstein distribution function) *1 (8.1) (9.1)

1 9 v.0.1 c (2016/10/07) Minoru Suzuki T µ 1 (7.108) f(e ) = 1 e β(e µ) 1 E 1 f(e ) (Bose-Einstein distribution function) *1 (8.1) (9.1) 1 9 v..1 c (216/1/7) Minoru Suzuki 1 1 9.1 9.1.1 T µ 1 (7.18) f(e ) = 1 e β(e µ) 1 E 1 f(e ) (Bose-Einstein distribution function) *1 (8.1) (9.1) E E µ = E f(e ) E µ (9.1) µ (9.2) µ 1 e β(e µ) 1 f(e )

More information

(interferometer) 1 N *3 2 ω λ k = ω/c = 2π/λ ( ) r E = A 1 e iφ1(r) e iωt + A 2 e iφ2(r) e iωt (1) φ 1 (r), φ 2 (r) r λ 2π 2 I = E 2 = A A 2 2 +

(interferometer) 1 N *3 2 ω λ k = ω/c = 2π/λ ( ) r E = A 1 e iφ1(r) e iωt + A 2 e iφ2(r) e iωt (1) φ 1 (r), φ 2 (r) r λ 2π 2 I = E 2 = A A 2 2 + 7 1 (Young) *1 *2 (interference) *1 (1802 1804) *2 2 (2005) (1993) 1 (interferometer) 1 N *3 2 ω λ k = ω/c = 2π/λ ( ) r E = A 1 e iφ1(r) e iωt + A 2 e iφ2(r) e iωt (1) φ 1 (r), φ 2 (r) r λ 2π 2 I = E 2

More information

n (1.6) i j=1 1 n a ij x j = b i (1.7) (1.7) (1.4) (1.5) (1.4) (1.7) u, v, w ε x, ε y, ε x, γ yz, γ zx, γ xy (1.8) ε x = u x ε y = v y ε z = w z γ yz

n (1.6) i j=1 1 n a ij x j = b i (1.7) (1.7) (1.4) (1.5) (1.4) (1.7) u, v, w ε x, ε y, ε x, γ yz, γ zx, γ xy (1.8) ε x = u x ε y = v y ε z = w z γ yz 1 2 (a 1, a 2, a n ) (b 1, b 2, b n ) A (1.1) A = a 1 b 1 + a 2 b 2 + + a n b n (1.1) n A = a i b i (1.2) i=1 n i 1 n i=1 a i b i n i=1 A = a i b i (1.3) (1.3) (1.3) (1.1) (ummation convention) a 11 x

More information

r d 2r d l d (a) (b) (c) 1: I(x,t) I(x+ x,t) I(0,t) I(l,t) V in V(x,t) V(x+ x,t) V(0,t) l V(l,t) 2: 0 x x+ x 3: V in 3 V in x V (x, t) I(x, t

r d 2r d l d (a) (b) (c) 1: I(x,t) I(x+ x,t) I(0,t) I(l,t) V in V(x,t) V(x+ x,t) V(0,t) l V(l,t) 2: 0 x x+ x 3: V in 3 V in x V (x, t) I(x, t 1 1 2 2 2r d 2r d l d (a) (b) (c) 1: I(x,t) I(x+ x,t) I(0,t) I(l,t) V in V(x,t) V(x+ x,t) V(0,t) l V(l,t) 2: 0 x x+ x 3: V in 3 V in x V (x, t) I(x, t) V (x, t) I(x, t) V in x t 3 4 1 L R 2 C G L 0 R 0

More information

08-Note2-web

08-Note2-web r(t) t r(t) O v(t) = dr(t) dt a(t) = dv(t) dt = d2 r(t) dt 2 r(t), v(t), a(t) t dr(t) dt r(t) =(x(t),y(t),z(t)) = d 2 r(t) dt 2 = ( dx(t) dt ( d 2 x(t) dt 2, dy(t), dz(t) dt dt ), d2 y(t) dt 2, d2 z(t)

More information

Gauss Gauss ɛ 0 E ds = Q (1) xy σ (x, y, z) (2) a ρ(x, y, z) = x 2 + y 2 (r, θ, φ) (1) xy A Gauss ɛ 0 E ds = ɛ 0 EA Q = ρa ɛ 0 EA = ρea E = (ρ/ɛ 0 )e

Gauss Gauss ɛ 0 E ds = Q (1) xy σ (x, y, z) (2) a ρ(x, y, z) = x 2 + y 2 (r, θ, φ) (1) xy A Gauss ɛ 0 E ds = ɛ 0 EA Q = ρa ɛ 0 EA = ρea E = (ρ/ɛ 0 )e 7 -a 7 -a February 4, 2007 1. 2. 3. 4. 1. 2. 3. 1 Gauss Gauss ɛ 0 E ds = Q (1) xy σ (x, y, z) (2) a ρ(x, y, z) = x 2 + y 2 (r, θ, φ) (1) xy A Gauss ɛ 0 E ds = ɛ 0 EA Q = ρa ɛ 0 EA = ρea E = (ρ/ɛ 0 )e z

More information

untitled

untitled 5522A 30 2 ( 5522A 5 10 ) tcal ±5 (tcal 5522A ) 7 5 12 Ω ±1 /... 2, 30... 5... IEEE-488(GPIB), RS-232... 0 50 (tcal)... 15 35... -20 70 ; 0 1.09999 A 1.1 A 2.99999 A 50 50 30 90 1 2... tcal +5 1 90 ( 1

More information

K E N Z U 01 7 16 HP M. 1 1 4 1.1 3.......................... 4 1.................................... 4 1..1..................................... 4 1...................................... 5................................

More information

B1 Ver ( ), SPICE.,,,,. * : student : jikken. [ ] ( TarouOsaka). (, ) 1 SPICE ( SPICE. *1 OrCAD

B1 Ver ( ), SPICE.,,,,. * : student : jikken. [ ] ( TarouOsaka). (, ) 1 SPICE ( SPICE. *1 OrCAD B1 er. 3.05 (2019.03.27), SPICE.,,,,. * 1 1. 1. 1 1.. 2. : student : jikken. [ ] ( TarouOsaka). (, ) 1 SPICE ( SPICE. *1 OrCAD https://www.orcad.com/jp/resources/orcad-downloads.. 1 2. SPICE 1. SPICE Windows

More information

X G P G (X) G BG [X, BG] S 2 2 2 S 2 2 S 2 = { (x 1, x 2, x 3 ) R 3 x 2 1 + x 2 2 + x 2 3 = 1 } R 3 S 2 S 2 v x S 2 x x v(x) T x S 2 T x S 2 S 2 x T x S 2 = { ξ R 3 x ξ } R 3 T x S 2 S 2 x x T x S 2

More information

) a + b = i + 6 b c = 6i j ) a = 0 b = c = 0 ) â = i + j 0 ˆb = 4) a b = b c = j + ) cos α = cos β = 6) a ˆb = b ĉ = 0 7) a b = 6i j b c = i + 6j + 8)

) a + b = i + 6 b c = 6i j ) a = 0 b = c = 0 ) â = i + j 0 ˆb = 4) a b = b c = j + ) cos α = cos β = 6) a ˆb = b ĉ = 0 7) a b = 6i j b c = i + 6j + 8) 4 4 ) a + b = i + 6 b c = 6i j ) a = 0 b = c = 0 ) â = i + j 0 ˆb = 4) a b = b c = j + ) cos α = cos β = 6) a ˆb = b ĉ = 0 7) a b = 6i j b c = i + 6j + 8) a b a b = 6i j 4 b c b c 9) a b = 4 a b) c = 7

More information

original: 2011/11/5 revised: 2012/10/30, 2013/12/ : 2 V i V t2 V o V L V H V i V i V t1 V o V H V L V t1 V t2 1 Q 1 1 Q

original: 2011/11/5 revised: 2012/10/30, 2013/12/ : 2 V i V t2 V o V L V H V i V i V t1 V o V H V L V t1 V t2 1 Q 1 1 Q original: 2011/11/5 revised: 2012/10/30, 2013/12/2 1 1 1: 2 V i V t2 V o V L V H V i V i V t1 V o V H V L V t1 V t2 1 Q 1 1 Q 2 2 1 2 1 c 2013 2 2: V i Q 1 I C1 V C1 V B2 I E V E V E Q 1 Q 1 Q 2 Q 2 Q

More information

d ϕ i) t d )t0 d ϕi) ϕ i) t x j t d ) ϕ t0 t α dx j d ) ϕ i) t dx t0 j x j d ϕ i) ) t x j dx t0 j f i x j ξ j dx i + ξ i x j dx j f i ξ i x j dx j d )

d ϕ i) t d )t0 d ϕi) ϕ i) t x j t d ) ϕ t0 t α dx j d ) ϕ i) t dx t0 j x j d ϕ i) ) t x j dx t0 j f i x j ξ j dx i + ξ i x j dx j f i ξ i x j dx j d ) 23 M R M ϕ : R M M ϕt, x) ϕ t x) ϕ s ϕ t ϕ s+t, ϕ 0 id M M ϕ t M ξ ξ ϕ t d ϕ tx) ξϕ t x)) U, x 1,...,x n )) ϕ t x) ϕ 1) t x),...,ϕ n) t x)), ξx) ξ i x) d ϕi) t x) ξ i ϕ t x)) M f ϕ t f)x) f ϕ t )x) fϕ

More information

(τ τ ) τ, σ ( ) w = τ iσ, w = τ + iσ (w ) w, w ( ) τ, σ τ = (w + w), σ = i (w w) w, w w = τ w τ + σ w σ = τ + i σ w = τ w τ + σ w σ = τ i σ g ab w, w

(τ τ ) τ, σ ( ) w = τ iσ, w = τ + iσ (w ) w, w ( ) τ, σ τ = (w + w), σ = i (w w) w, w w = τ w τ + σ w σ = τ + i σ w = τ w τ + σ w σ = τ i σ g ab w, w S = 4π dτ dσ gg ij i X µ j X ν η µν η µν g ij g ij = g ij = ( 0 0 ) τ, σ (+, +) τ τ = iτ ds ds = dτ + dσ ds = dτ + dσ δ ij ( ) a =, a = τ b = σ g ij δ ab g g ( +, +,... ) S = 4π S = 4π ( i) = i 4π dτ dσ

More information

Mott散乱によるParity対称性の破れを検証

Mott散乱によるParity対称性の破れを検証 Mott Parity P2 Mott target Mott Parity Parity Γ = 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 t P P ),,, ( 3 2 1 0 1 γ γ γ γ γ γ ν ν µ µ = = Γ 1 : : : Γ P P P P x x P ν ν µ µ vector axial vector ν ν µ µ γ γ Γ ν γ

More information

http://www.ike-dyn.ritsumei.ac.jp/ hyoo/wave.html 1 1, 5 3 1.1 1..................................... 3 1.2 5.1................................... 4 1.3.......................... 5 1.4 5.2, 5.3....................

More information

i

i 009 I 1 8 5 i 0 1 0.1..................................... 1 0.................................................. 1 0.3................................. 0.4........................................... 3

More information

( ) ( ) 1729 (, 2016:17) = = (1) 1 1

( ) ( ) 1729 (, 2016:17) = = (1) 1 1 1729 1 2016 10 28 1 1729 1111 1111 1729 (1887 1920) (1877 1947) 1729 (, 2016:17) 12 3 1728 9 3 729 1729 = 12 3 + 1 3 = 10 3 + 9 3 (1) 1 1 2 1729 1729 19 13 7 = 1729 = 12 3 + 1 3 = 10 3 + 9 3 13 7 = 91

More information

sm1ck.eps

sm1ck.eps DATA SHEET DS0 0 ASSP, IC,,,,, (VS =. V.%) (VCC = 0. V ) (VR =. V.%) ( ) DIP, SIP, SOP, (DIP-P-M0) (SIP-P-M0) (FPT-P-M0) (FRONT VIEW) (TOP VIEW) C T C T V S V REF V CC V CC V REF V S (DIP-P-M0) (FPT-P-M0)

More information

1. (8) (1) (x + y) + (x + y) = 0 () (x + y ) 5xy = 0 (3) (x y + 3y 3 ) (x 3 + xy ) = 0 (4) x tan y x y + x = 0 (5) x = y + x + y (6) = x + y 1 x y 3 (

1. (8) (1) (x + y) + (x + y) = 0 () (x + y ) 5xy = 0 (3) (x y + 3y 3 ) (x 3 + xy ) = 0 (4) x tan y x y + x = 0 (5) x = y + x + y (6) = x + y 1 x y 3 ( 1 1.1 (1) (1 + x) + (1 + y) = 0 () x + y = 0 (3) xy = x (4) x(y + 3) + y(y + 3) = 0 (5) (a + y ) = x ax a (6) x y 1 + y x 1 = 0 (7) cos x + sin x cos y = 0 (8) = tan y tan x (9) = (y 1) tan x (10) (1 +

More information

振動工学に基礎

振動工学に基礎 Ky Words. ω. ω.3 osω snω.4 ω snω ω osω.5 .6 ω osω snω.7 ω ω ( sn( ω φ.7 ( ω os( ω φ.8 ω ( ω sn( ω φ.9 ω anφ / ω ω φ ω T ω T s π T π. ω Hz ω. T π π rad/s π ω π T. T ω φ 6. 6. 4. 4... -... -. -4. -4. -6.

More information

) ] [ h m x + y + + V x) φ = Eφ 1) z E = i h t 13) x << 1) N n n= = N N + 1) 14) N n n= = N N + 1)N + 1) 6 15) N n 3 n= = 1 4 N N + 1) 16) N n 4

) ] [ h m x + y + + V x) φ = Eφ 1) z E = i h t 13) x << 1) N n n= = N N + 1) 14) N n n= = N N + 1)N + 1) 6 15) N n 3 n= = 1 4 N N + 1) 16) N n 4 1. k λ ν ω T v p v g k = π λ ω = πν = π T v p = λν = ω k v g = dω dk 1) ) 3) 4). p = hk = h λ 5) E = hν = hω 6) h = h π 7) h =6.6618 1 34 J sec) hc=197.3 MeV fm = 197.3 kev pm= 197.3 ev nm = 1.97 1 3 ev

More information

µµ InGaAs/GaAs PIN InGaAs PbS/PbSe InSb InAs/InSb MCT (HgCdTe)

µµ InGaAs/GaAs PIN InGaAs PbS/PbSe InSb InAs/InSb MCT (HgCdTe) 1001 µµ 1.... 2 2.... 7 3.... 9 4. InGaAs/GaAs PIN... 10 5. InGaAs... 17 6. PbS/PbSe... 18 7. InSb... 22 8. InAs/InSb... 23 9. MCT (HgCdTe)... 25 10.... 28 11.... 29 12. (Si)... 30 13.... 33 14.... 37

More information

Microsoft PowerPoint - 2.devi2008.ppt

Microsoft PowerPoint - 2.devi2008.ppt 第 2 章集積回路のデバイス MOSトランジスタダイオード抵抗容量インダクタンス配線 広島大学岩田穆 1 半導体とは? 電気を通す鉄 アルミニウムなどの金属は導体 電気を通さないガラス ゴムなどは絶縁体 電気を通したり, 通さなかったり, 条件によって, 導体と絶縁体の両方の性質を持つことのできる物質を半導体半導体の代表例はシリコン 電気伝導率 広島大学岩田穆 2 半導体技術で扱っている大きさ 間の大きさ一般的な技術現在研究しているところナノメートル

More information

A 2 3. m S m = {x R m+1 x = 1} U + k = {x S m x k > 0}, U k = {x S m x k < 0}, ϕ ± k (x) = (x 0,..., ˆx k,... x m ) 1. {(U ± k, ϕ± k ) 0 k m} S m 1.2.

A 2 3. m S m = {x R m+1 x = 1} U + k = {x S m x k > 0}, U k = {x S m x k < 0}, ϕ ± k (x) = (x 0,..., ˆx k,... x m ) 1. {(U ± k, ϕ± k ) 0 k m} S m 1.2. A A 1 A 5 A 6 1 2 3 4 5 6 7 1 1.1 1.1 (). Hausdorff M R m M M {U α } U α R m E α ϕ α : U α E α U α U β = ϕ α (ϕ β ϕβ (U α U β )) 1 : ϕ β (U α U β ) ϕ α (U α U β ) C M a m dim M a U α ϕ α {x i, 1 i m} {U,

More information

3/4/8:9 { } { } β β β α β α β β

3/4/8:9 { } { } β β β α β α β β α β : α β β α β α, [ ] [ ] V, [ ] α α β [ ] β 3/4/8:9 3/4/8:9 { } { } β β β α β α β β [] β [] β β β β α ( ( ( ( ( ( [ ] [ ] [ β ] [ α β β ] [ α ( β β ] [ α] [ ( β β ] [] α [ β β ] ( / α α [ β β ] [ ] 3

More information

K E N Z U 2012 7 16 HP M. 1 1 4 1.1 3.......................... 4 1.2................................... 4 1.2.1..................................... 4 1.2.2.................................... 5................................

More information

ID POS F

ID POS F 01D8101011L 2005 3 ID POS 2 2 1 F 1... 1 2 ID POS... 2 3... 4 3.1...4 3.2...4 3.3...5 3.4 F...5 3.5...6 3.6 2...6 4... 8 4.1...8 4.2...8 4.3...8 4.4...9 4.5...10 5... 12 5.1...12 5.2...13 5.3...15 5.4...17

More information

1. 1 A : l l : (1) l m (m 3) (2) m (3) n (n 3) (4) A α, β γ α β + γ = 2 m l lm n nα nα = lm. α = lm n. m lm 2β 2β = lm β = lm 2. γ l 2. 3

1. 1 A : l l : (1) l m (m 3) (2) m (3) n (n 3) (4) A α, β γ α β + γ = 2 m l lm n nα nα = lm. α = lm n. m lm 2β 2β = lm β = lm 2. γ l 2. 3 1. 1 A : l l : (1) l m (m 3) (2) m (3) n (n 3) (4) A 2 1 2 1 2 3 α, β γ α β + γ = 2 m l lm n nα nα = lm. α = lm n. m lm 2β 2β = lm β = lm 2. γ l 2. 3 4 P, Q R n = {(x 1, x 2,, x n ) ; x 1, x 2,, x n R}

More information

6 2 T γ T B (6.4) (6.1) [( d nm + 3 ] 2 nt B )a 3 + nt B da 3 = 0 (6.9) na 3 = T B V 3/2 = T B V γ 1 = const. or T B a 2 = const. (6.10) H 2 = 8π kc2

6 2 T γ T B (6.4) (6.1) [( d nm + 3 ] 2 nt B )a 3 + nt B da 3 = 0 (6.9) na 3 = T B V 3/2 = T B V γ 1 = const. or T B a 2 = const. (6.10) H 2 = 8π kc2 1 6 6.1 (??) (P = ρ rad /3) ρ rad T 4 d(ρv ) + PdV = 0 (6.1) dρ rad ρ rad + 4 da a = 0 (6.2) dt T + da a = 0 T 1 a (6.3) ( ) n ρ m = n (m + 12 ) m v2 = n (m + 32 ) T, P = nt (6.4) (6.1) d [(nm + 32 ] )a

More information

TOP URL 1

TOP URL   1 TOP URL http://amonphys.web.fc.com/ 3.............................. 3.............................. 4.3 4................... 5.4........................ 6.5........................ 8.6...........................7

More information

TOP URL 1

TOP URL   1 TOP URL http://amonphys.web.fc2.com/ 1 30 3 30.1.............. 3 30.2........................... 4 30.3...................... 5 30.4........................ 6 30.5.................................. 8 30.6...............................

More information

MOSFET HiSIM HiSIM2 1

MOSFET HiSIM HiSIM2 1 MOSFET 2007 11 19 HiSIM HiSIM2 1 p/n Junction Shockley - - on-quasi-static - - - Y- HiSIM2 2 Wilson E f E c E g E v Bandgap: E g Fermi Level: E f HiSIM2 3 a Si 1s 2s 2p 3s 3p HiSIM2 4 Fermi-Dirac Distribution

More information

日本統計学会誌, 第44巻, 第2号, 251頁-270頁

日本統計学会誌, 第44巻, 第2号, 251頁-270頁 44, 2, 205 3 25 270 Multiple Comparison Procedures for Checking Differences among Sequence of Normal Means with Ordered Restriction Tsunehisa Imada Lee and Spurrier (995) Lee and Spurrier (995) (204) (2006)

More information

1 Ricci V, V i, W f : V W f f(v ) = Imf W ( ) f : V 1 V k W 1

1 Ricci V, V i, W f : V W f f(v ) = Imf W ( ) f : V 1 V k W 1 1 Ricci V, V i, W f : V W f f(v = Imf W ( f : V 1 V k W 1 {f(v 1,, v k v i V i } W < Imf > < > f W V, V i, W f : U V L(U; V f : V 1 V r W L(V 1,, V r ; W L(V 1,, V r ; W (f + g(v 1,, v r = f(v 1,, v r

More information

2009 2 26 1 3 1.1.................................................. 3 1.2..................................................... 3 1.3...................................................... 3 1.4.....................................................

More information

微分積分 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. このサンプルページの内容は, 初版 1 刷発行時のものです.

微分積分 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます.   このサンプルページの内容は, 初版 1 刷発行時のものです. 微分積分 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. ttp://www.morikita.co.jp/books/mid/00571 このサンプルページの内容は, 初版 1 刷発行時のものです. i ii 014 10 iii [note] 1 3 iv 4 5 3 6 4 x 0 sin x x 1 5 6 z = f(x, y) 1 y = f(x)

More information

1 (Berry,1975) 2-6 p (S πr 2 )p πr 2 p 2πRγ p p = 2γ R (2.5).1-1 : : : : ( ).2 α, β α, β () X S = X X α X β (.1) 1 2

1 (Berry,1975) 2-6 p (S πr 2 )p πr 2 p 2πRγ p p = 2γ R (2.5).1-1 : : : : ( ).2 α, β α, β () X S = X X α X β (.1) 1 2 2005 9/8-11 2 2.2 ( 2-5) γ ( ) γ cos θ 2πr πρhr 2 g h = 2γ cos θ ρgr (2.1) γ = ρgrh (2.2) 2 cos θ θ cos θ = 1 (2.2) γ = 1 ρgrh (2.) 2 2. p p ρgh p ( ) p p = p ρgh (2.) h p p = 2γ r 1 1 (Berry,1975) 2-6

More information

S I. dy fx x fx y fx + C 3 C vt dy fx 4 x, y dy yt gt + Ct + C dt v e kt xt v e kt + C k x v k + C C xt v k 3 r r + dr e kt S Sr πr dt d v } dt k e kt

S I. dy fx x fx y fx + C 3 C vt dy fx 4 x, y dy yt gt + Ct + C dt v e kt xt v e kt + C k x v k + C C xt v k 3 r r + dr e kt S Sr πr dt d v } dt k e kt S I. x yx y y, y,. F x, y, y, y,, y n http://ayapin.film.s.dendai.ac.jp/~matuda n /TeX/lecture.html PDF PS yx.................................... 3.3.................... 9.4................5..............

More information

4‐E ) キュリー温度を利用した消磁:熱消磁

4‐E ) キュリー温度を利用した消磁:熱消磁 ( ) () x C x = T T c T T c 4D ) ) Fe Ni Fe Fe Ni (Fe Fe Fe Fe Fe 462 Fe76 Ni36 4E ) ) (Fe) 463 4F ) ) ( ) Fe HeNe 17 Fe Fe Fe HeNe 464 Ni Ni Ni HeNe 465 466 (2) Al PtO 2 (liq) 467 4G ) Al 468 Al ( 468

More information

zsj2017 (Toyama) program.pdf

zsj2017 (Toyama) program.pdf 88 th Annual Meeting of the Zoological Society of Japan Abstracts 88 th Annual Meeting of the Zoological Society of Japan Abstracts 88 th Annual Meeting of the Zoological Society of Japan Abstracts 88

More information

88 th Annual Meeting of the Zoological Society of Japan Abstracts 88 th Annual Meeting of the Zoological Society of Japan Abstracts 88 th Annual Meeting of the Zoological Society of Japan Abstracts 88

More information

_170825_<52D5><7269><5B66><4F1A>_<6821><4E86><5F8C><4FEE><6B63>_<518A><5B50><4F53><FF08><5168><9801><FF09>.pdf

_170825_<52D5><7269><5B66><4F1A>_<6821><4E86><5F8C><4FEE><6B63>_<518A><5B50><4F53><FF08><5168><9801><FF09>.pdf 88 th Annual Meeting of the Zoological Society of Japan Abstracts 88 th Annual Meeting of the Zoological Society of Japan Abstracts 88 th Annual Meeting of the Zoological Society of Japan Abstracts 88

More information

i

i i 3 4 4 7 5 6 3 ( ).. () 3 () (3) (4) /. 3. 4/3 7. /e 8. a > a, a = /, > a >. () a >, a =, > a > () a > b, a = b, a < b. c c n a n + b n + c n 3c n..... () /3 () + (3) / (4) /4 (5) m > n, a b >, m > n,

More information

U.C. Berkeley SPICE Simulation Program with Integrated Circuit Emphasis 1) SPICE SPICE netli

U.C. Berkeley SPICE Simulation Program with Integrated Circuit Emphasis 1) SPICE SPICE netli 1 -- 7 7 2008 12 7-1 7-2 c 2011 1/(12) 1 -- 7 -- 7 7--1 2008 12 1960 1970 1972 U.C. Berkeley SPICE Simulation Program with Integrated Circuit Emphasis 1) SPICE SPICE 7--1--1 7 1 7 1 1 netlist SPICE 2)

More information

4. ϵ(ν, T ) = c 4 u(ν, T ) ϵ(ν, T ) T ν π4 Planck dx = 0 e x 1 15 U(T ) x 3 U(T ) = σt 4 Stefan-Boltzmann σ 2π5 k 4 15c 2 h 3 = W m 2 K 4 5.

4. ϵ(ν, T ) = c 4 u(ν, T ) ϵ(ν, T ) T ν π4 Planck dx = 0 e x 1 15 U(T ) x 3 U(T ) = σt 4 Stefan-Boltzmann σ 2π5 k 4 15c 2 h 3 = W m 2 K 4 5. A 1. Boltzmann Planck u(ν, T )dν = 8πh ν 3 c 3 kt 1 dν h 6.63 10 34 J s Planck k 1.38 10 23 J K 1 Boltzmann u(ν, T ) T ν e hν c = 3 10 8 m s 1 2. Planck λ = c/ν Rayleigh-Jeans u(ν, T )dν = 8πν2 kt dν c

More information

D = [a, b] [c, d] D ij P ij (ξ ij, η ij ) f S(f,, {P ij }) S(f,, {P ij }) = = k m i=1 j=1 m n f(ξ ij, η ij )(x i x i 1 )(y j y j 1 ) = i=1 j

D = [a, b] [c, d] D ij P ij (ξ ij, η ij ) f S(f,, {P ij }) S(f,, {P ij }) = = k m i=1 j=1 m n f(ξ ij, η ij )(x i x i 1 )(y j y j 1 ) = i=1 j 6 6.. [, b] [, d] ij P ij ξ ij, η ij f Sf,, {P ij } Sf,, {P ij } k m i j m fξ ij, η ij i i j j i j i m i j k i i j j m i i j j k i i j j kb d {P ij } lim Sf,, {P ij} kb d f, k [, b] [, d] f, d kb d 6..

More information