Doctor Thesis Template

Size: px
Start display at page:

Download "Doctor Thesis Template"

Transcription

1 A Study of Variable Beam-tilted Microstrip Array Antenna

2 LAN(Local Area Network) LAN PC LAN LAN LAN 5.2GHz 20 25Mbps OFDM(Orthogonal Frequency Division Multiplexing)

3 (30,45,60[DEG.]) i

4 kbit/s Bluetooth ITS MMAC(Multimedia-Mobile-Access-Communications) MMAC GHz LAN HiSWANa(High Speed Wireless LAN a) LAN 20 25Mbps 2

5 1-1 LAN PC (LAN : Local Area Network) (LAN ) LAN (1) LAN (2) PC LAN (1) ( ) LAN (2) LAN LAN PC 1-2 PC 3

6 1-2 (NTT DoCoMo vol.8 No.4 pp56 ) ( PC) FTTH(Fiber To The Home) LAN LAN (IEEE) IEEE LAN 5.2GHz a 2.4GHz b 2.4GHz LAN 2.4GHz LAN 11Mbit/s 2.4GHz ISM(Industrial Scientific and Medical) Bluetooth LAN HiSWANa 5.2GHz 5.2GHz 5.2GHz 4

7 LAN 5.2GHz OFD M(Orthogonal Frequency Division Multiplexing ) ( 1-3) [1] OFDM 800ns 4 s 1-3 OFDM MSA MSA [1][2] MSA MSA MSA 5

8 λ/4 εr=4 0 [2] IE3D

9 1.2. LAN / ( ) 1 H 1 0[deg.] 30~60[deg.] 30~60[deg.] 0[deg.] 30~60[deg.] 30~60[deg.] 1-4 7

10 H h 1-5 H: m, h: 1m 8

11 LAN 2 /4 εr=2.6 εr=4.0 IE3D

12 / /

13

14 εr =2.6 εr =4.0 50Ω 12

15 W ε r h 2-5 ε 2 Z0 e = Z ε r 1 ε r + 1 εe = h 2 1 W εe (εr =2.6 h=0.8mm) 50Ω 2.26mm εr =4.0 L 1 5.2GHz L 1 =15mm λg c L1 = = = 15mm 2 2 f ε ( 5.2G) r 2-3 IE3D L 1 W 2 5.2GHz 13

16 2-6 L 1 =11.0mm W 2 =5.0mm 2-7 RL 15dB A L 2 z y x W 2 W 1 L 1 B z y 2-6 L 1 =λ/4=11.0mm, L 2 =λ/2=15.0mm, W 1 =2.0mm, W 2 =5.0mm A ; εr =2.6, B ; εr =4.0, 0.8mm

17 (0mm) 9mm (9mm) E 0.3GHz 10mm 0 9mm -10dB E 0 Return Loss[dB] offset 0mm 1mm 3mm 5mm 7mm 9mm 10mm Frequency[GHz] 2-7 ( ) 15

18 0mm 9mm 2-8 The radiation patch offset 0mm 9mm 2-9 E 16

19 IE3D (2mm) (7mm) mm E mm E

20 L 1 W 1 L 2 50mm 50mm L 1 =11mm L 2 =15mm W 1 = 5mm 2-10 L 1 =11.0mm, L 2 =15.0mm, W 1 =5.0mm, l 1 =50mm 50mm 15mm 50mm 15mm

21 0-5 Return Loss[dB] d=7mm d=2mm mea. cal. mea. cal. d Frequency[GHz] 2-12 Mea. Cal E (d=2mm) 19

22 Mea. Cal E (d=7mm)

23 g θ N 2-4 g ( θ ) N = a e n nu d n= 0 n u = ndsinθ jnu ( ) d j sin ( ) ( ) ( ) (1 2 θ θ = θ θ = ± ) ( θ ) g F D je D π

24 y 0 d x H (d= /4)

25 G( θ ) = F( θ) D( θ) F( θ ) = 1+ sin ( 2πdsinθ) j cos( 2πdsinθ) 2-7 d d T 90 T (a) 90 T 28mm 2-20 (b) 23

26 L1 l2 l1 L2 d z x y B ( 4.0) ε r = z y A 0. 8mm 2-17 MS L 1 =λ/2=15.0mm, L 2 =λ/4=11.0mm l 1 =30.0mm, l 2 =30.0mm, 0.8mm 24

27 0 Return Loss[dB] T-junction offset 0mm 24mm 28mm 4 5 Frequency[GHz] (a)t-junction offset 0mm (b)t-junction offset 28mm

28 (a)t-junction offset 0mm (b)t-junction offset 28mm

29 L 1 d L L 1 =λ/4=11.0mm, A; εr = mm (a)(b) 2-23 (a) 2 (b) 90 E (a) (b) 90 3dB

30 a b a b E d 28

31 d d=0.5λ(20mm) a 2-25(a) 29 a 1mm d=0.3λ(12mm) E 2-25 b 43 d=0.4λ(16mm) 2-25 c 31-15dB - 0 Return Loss[dB] d=20mm d=12mm(the one-side) d=16mm(the both-side) Frequency[GHz]

32 (1) d=0.5λ 29.0 d=0.5λ(20mm) λ (2) 43 d= 0.3λ (12mm) (3) 31 d= 0.4λ (16mm) 2-25 E λ 3mm 41-15dB 30

33 2.5. 3mm 3mm 41[deg.] d= IE3D mm 125mm GHz 4.76GHz 2-30 (a) 2-30(b) 31

34 E 4 44GHz 4 76GHz l3 L1 d z l2 x B ( 4.0) ε r = 0.8mm 2-27 L 1 =λ/2=15.0mm, L 2 =λ/4=11.0mm l 1 =30.0mm, l 2 =30.0mm, l 3 =12.5mm, l 4 =7.0mm, 0.8mm 32

35 12.5cm Square patches 7.0cm Return Loss[dB] Frequency[GHz] cal.(infinite) cal.(finite) mea

36 (a)4.44ghz (b)4.76ghz 2-30 Cal.(IE3D) Mea

37 Cal.(IE3D) Mea λ/ [7] 35

38 λ/4 L λ 0.6λ

39 2-35 L L 1 L L 2-34 ( ) L 1 =λ/2=15.0mm, L 2 =0.4λ g =22.0mm, L 3 =50.0mm H=24.0mm, ; εr =4.0, 0.8mm 37

40 Mea. Cal E T 90 λ λ 38

41 mm d d=0.5λ(20mm) a 2-38 a a 1mm d=0.3λ(12mm) E b 60 d=0.4λ(16mm) c 45-10dB 39

42 l3 L3 L1 L2 d l1 l2 l4 z x y z H B ( 4.0) ε r = y A 2-36 L 1 =λ/2=15.0mm, L 2 =λ/4=11.0mm, L 3 =0.4λ=22.0mm l 1 =30.0mm, l 2 =30.0mm, l 3 =12.5mm, l 4 =7.0mm, H=24.0mm, 0.8mm 40

43 0 Return Loss[dB] Frequency[GHz] No offset oneside patch moved bothside patches moved

44 (1) d=0.5λ -36 d=0.5λ(20mm) λ (2) -60 d= 0.3λ (12mm) (3) -45 d= 0.4λ (16mm) dB 56 42

45 3mm 3mm 56[deg.] d= mm 125mm Stacked patch 24mm

46 E 4.76GHz Return Loss[dB] Frequency[GHz] cal.(infinite) cal.(finite) mea

47 Mea. Cal E 2.4. (30,45,60[deg.]) E 30 d 2-43(1) d=0.15λ 7mm d=0.20λ 20 5mm E 2-45(a) -20dB

48 45 d=0.10λ 2-43(b) d=0.20λ 7mm E 2-45(b) -20dB d=0.05λ 60 3mm (a)(b) -15dB E 2-45(c) 60 5mm 0.15λ (a) 30[deg.] 5mm 7mm 0.2λ 7mm (b)45[deg.] 3mm 0.05λ 3mm (c)60[deg.]

49 0 Return Loss[dB] (a) 30[deg.] (b) 45[deg.] (c) 60[deg.] Frequency[GHz]

50 (a) 30[deg.] (b)45[deg.] (c)60[deg.]

51 λ

52

53 51

54 [1] 5GHz OFDM AP [2] [3] [4] 1987 [5] 1998 [6] p

55 [1] AP May2001 [2] 2 B-1-77 Oct 2001 [3] B March 2001 [4] Kozue HAMAMOTO Hiroyuki ARAI Kenya YONEZAWA and Toshiyuki MAEYAMA " Variable Beam Tilt Microstrip Array for 5GHz Wireless Access System " Asia-Pacific Microwave Conference APMC 2001 TU3E-5 December

3 16 2 27 4497 LAN(Local Area Network) OFDM(Orthogonal Frequency Division Multiplexing) 12 3 3 12 3 12 33. F/B 22.7dB 3 F/B i 1 1 2 3 8 2.1................................. 8 2.2.............................

More information

untitled

untitled ( ) (mm) (GHz)=300( ) 30 300GHz=1 10mm ( 2GHz2Mbps) Gbps= Mbps ( m),? S G=P/Pi30dB=1000 Gm=4πS/λ 2, S= 80λ 2 Gm=30dB η=g/gm, S= 80λ 2,G=27dB η=50% (GHz) 80 70 60 50 40 30 20 10 16 19 22 25 28 31 34 37

More information

PDF.PDF

PDF.PDF 1 2 3 LAN Ethernet( ) TSS(Time Sharing System: ) TSS CPU TSS LAN 3Mbit/s 10Mbit/s 9.6Kbit/s LAN DEC Intel 3 DIX DIX 10Mbit/s 500m 10Base5 LAN IEEE802 IEEE802.3 100Mbit/s 100BaseTX TCP/IP Ethernet LAN 7

More information

LAN Micro AVS LAN i

LAN Micro AVS LAN i 00D8104013K 2004 3 LAN Micro AVS LAN i 1 1 2 LAN 2 2.1 LAN ( Local Area Network ) 2 2.1.1 2 2.1.2 LAN 3 2.1.3 3 2.2 LAN 4 2.3 LAN 5 2.4 LAN 6 3 7 3.1 7 3.1.1 7 3.1.2 7 3.1.3 LAN 7 3.2 9 3.2.1 9 3.2.2 10

More information

64 3 g=9.85 m/s 2 g=9.791 m/s 2 36, km ( ) 1 () 2 () m/s : : a) b) kg/m kg/m k

64 3 g=9.85 m/s 2 g=9.791 m/s 2 36, km ( ) 1 () 2 () m/s : : a) b) kg/m kg/m k 63 3 Section 3.1 g 3.1 3.1: : 64 3 g=9.85 m/s 2 g=9.791 m/s 2 36, km ( ) 1 () 2 () 3 9.8 m/s 2 3.2 3.2: : a) b) 5 15 4 1 1. 1 3 14. 1 3 kg/m 3 2 3.3 1 3 5.8 1 3 kg/m 3 3 2.65 1 3 kg/m 3 4 6 m 3.1. 65 5

More information

MainOfManuscript.dvi

MainOfManuscript.dvi 18 2 28 0244086 IC IC IC (MDA) 20% 60% i 1 1 2 4 2.1................. 4 2.2 UHF............. 9 2.2.1 315MH.......................... 10 2.2.2 433MH.......................... 13 2.2.3.......................

More information

5b_08.dvi

5b_08.dvi , Circularly Polarized Patch Antennas Combining Different Shaped Linealy Polarized Elements Takanori NORO,, Yasuhiro KAZAMA, Masaharu TAKAHASHI, and Koichi ITO 1. GPS LAN 10% [1] Graduate School of Science

More information

IEEE ZigBee 2.4GHz 250kbps O-QPSK DSSS Bluetooth IEEE GHz 3Mbps G-FSK FHSS PC LAN IEEE b 2.4GHz 11Mbps CCK DSSS LAN LAN IEE

IEEE ZigBee 2.4GHz 250kbps O-QPSK DSSS Bluetooth IEEE GHz 3Mbps G-FSK FHSS PC LAN IEEE b 2.4GHz 11Mbps CCK DSSS LAN LAN IEE SMK SMK Corporation Kenji OTSUKA AV AV RF 2.4GHz ISM 2.4GHz ISM 2.4GHz RF IEEE 802.15.4 ZigBee 2.4GHz 250kbps O-QPSK DSSS Bluetooth IEEE 802.15.1 2.4GHz 3Mbps G-FSK FHSS PC LAN IEEE 802.11b 2.4GHz 11Mbps

More information

Gmech08.dvi

Gmech08.dvi 145 13 13.1 13.1.1 0 m mg S 13.1 F 13.1 F /m S F F 13.1 F mg S F F mg 13.1: m d2 r 2 = F + F = 0 (13.1) 146 13 F = F (13.2) S S S S S P r S P r r = r 0 + r (13.3) r 0 S S m d2 r 2 = F (13.4) (13.3) d 2

More information

2005 1

2005 1 2005 1 1 1 2 2 2.1....................................... 2 2.2................................... 5 2.3 VSWR................................. 6 2.4 VSWR 2............................ 7 2.5.......................................

More information

FDTD(Finite Difference Time Domain) Maxwell FDTD FDTD FDTD (FFT) FDTD CP(Contour-Path)-FDTD i

FDTD(Finite Difference Time Domain) Maxwell FDTD FDTD FDTD (FFT) FDTD CP(Contour-Path)-FDTD i FDTD 17 2 7 03GD191 FDTD(Finite Difference Time Domain) Maxwell FDTD FDTD FDTD (FFT) FDTD CP(Contour-Path)-FDTD 45 1 2 i 1 1 1.1 FDTD....................... 1 1.2 FDTD............................ 2 1.3

More information

15228 98441 IMT- 2International Mobile Telecommunication 2 FBFront to Back IMT-2 H E 8 2/15 (2mm)H 5/4 (187mm)E 1 (15mm) FB 24.8dB E 3dB FB (H ) H 45 FB 23.8dB -6.2dB i 1 1 2 6 2.1.....................................

More information

main.dvi

main.dvi FDTD S A Study on FDTD Analysis based on S-Parameter 18 2 7 04GD168 FDTD FDTD S S FDTD S S S S FDTD FDTD i 1 1 1.1 FDTD.................................... 1 1.2 FDTD..................... 3 2 S 5 2.1 FDTD

More information

6 2 2 x y x y t P P = P t P = I P P P ( ) ( ) ,, ( ) ( ) cos θ sin θ cos θ sin θ, sin θ cos θ sin θ cos θ y x θ x θ P

6 2 2 x y x y t P P = P t P = I P P P ( ) ( ) ,, ( ) ( ) cos θ sin θ cos θ sin θ, sin θ cos θ sin θ cos θ y x θ x θ P 6 x x 6.1 t P P = P t P = I P P P 1 0 1 0,, 0 1 0 1 cos θ sin θ cos θ sin θ, sin θ cos θ sin θ cos θ x θ x θ P x P x, P ) = t P x)p ) = t x t P P ) = t x = x, ) 6.1) x = Figure 6.1 Px = x, P=, θ = θ P

More information

12-7 12-7 12-7 12-7 12-8 12-10 12-10 12-10 12-11 12-12 12-12 12-14 12-15 12-17 12-18 10 12-19 12-20 12-20 12-21 12-22 12-22 12-23 12-25 12-26 12-26 12-29 12-30 12-30 12-31 12-33 12-34 12-3 12-35 12-36

More information

A Study of Small Built-in Antenna for Hand held Terminal

A Study of Small Built-in Antenna for Hand held Terminal A Study of Smll Built-in Antenn for Hnd held Terminl 6 9 IMT-2 Interntionl Mobile Telecommunictions-2 2GHz /4 PDA Personl Digitl Assistnt 2 FDTD Finite Difference Time Domin method 6 FDTD 3.6 2.5mm 2.25GHz

More information

WMN Contiguity situation considering route establishment method in WMN assumed real environment performance evaluation 1165057 26 3 20 1 1 2 3 2.1........................................ 3 2.2.............................

More information

, 3, 6 = 3, 3,,,, 3,, 9, 3, 9, 3, 3, 4, 43, 4, 3, 9, 6, 6,, 0 p, p, p 3,..., p n N = p p p 3 p n + N p n N p p p, p 3,..., p n p, p,..., p n N, 3,,,,

, 3, 6 = 3, 3,,,, 3,, 9, 3, 9, 3, 3, 4, 43, 4, 3, 9, 6, 6,, 0 p, p, p 3,..., p n N = p p p 3 p n + N p n N p p p, p 3,..., p n p, p,..., p n N, 3,,,, 6,,3,4,, 3 4 8 6 6................................. 6.................................. , 3, 6 = 3, 3,,,, 3,, 9, 3, 9, 3, 3, 4, 43, 4, 3, 9, 6, 6,, 0 p, p, p 3,..., p n N = p p p 3 p n + N p n N p p p,

More information

( ) e + e ( ) ( ) e + e () ( ) e e Τ ( ) e e ( ) ( ) () () ( ) ( ) ( ) ( )

( ) e + e ( ) ( ) e + e () ( ) e e Τ ( ) e e ( ) ( ) () () ( ) ( ) ( ) ( ) n n (n) (n) (n) (n) n n ( n) n n n n n en1, en ( n) nen1 + nen nen1, nen ( ) e + e ( ) ( ) e + e () ( ) e e Τ ( ) e e ( ) ( ) () () ( ) ( ) ( ) ( ) ( n) Τ n n n ( n) n + n ( n) (n) n + n n n n n n n n

More information

SIP SDP(Session Description Protocol) RTSP(Real-time Streaming Protocol) RTP(Real-time Transport Protocol) IP 1 [1] 1: IP RTP(Real-Time RFC1889 Transf

SIP SDP(Session Description Protocol) RTSP(Real-time Streaming Protocol) RTP(Real-time Transport Protocol) IP 1 [1] 1: IP RTP(Real-Time RFC1889 Transf C4 higa@comm.eng.osaka-u.ac.jp 1 IP 1.1 1. IP IP 2. 1.2 1.2.1 IP IP (Internet Protocol telephone) IP VoIP(Voice over Internet Protocol) IP IP (Network Access Control) IP IP (Call Control) (Terminal Control)

More information

() x + y + y + x dy dx = 0 () dy + xy = x dx y + x y ( 5) ( s55906) 0.7. (). 5 (). ( 6) ( s6590) 0.8 m n. 0.9 n n A. ( 6) ( s6590) f A (λ) = det(a λi)

() x + y + y + x dy dx = 0 () dy + xy = x dx y + x y ( 5) ( s55906) 0.7. (). 5 (). ( 6) ( s6590) 0.8 m n. 0.9 n n A. ( 6) ( s6590) f A (λ) = det(a λi) 0. A A = 4 IC () det A () A () x + y + z = x y z X Y Z = A x y z ( 5) ( s5590) 0. a + b + c b c () a a + b + c c a b a + b + c 0 a b c () a 0 c b b c 0 a c b a 0 0. A A = 7 5 4 5 0 ( 5) ( s5590) () A ()

More information

untitled

untitled 4 1 4.1................................................. 1 4.1.1........................................ 1-1 4 17 11 30 4.1 2001 49% 2,400 47% 6,000 2001 390 8% 2005 3000 1000 IT 1 ADSL(Asymmetric Digital

More information

- 1-150 khz18 GHz CATV MATV IEC 60728-2 A B (ITE) 2 (3) 4.1 (1) 3 (CISPR) 1 (CISPR 16-1-1 2.1 2006) (CISPR 16-1-2 1 2003 12004) (CISPR 16-1-3 2.0 2004) (CISPR 16-1-4 2.0 2007) 30 MHz 1000 MHz (CISPR 16-1-5

More information

C O N T E N T S 1

C O N T E N T S 1 2014 Vol.107 C O N T E N T S 1 Communications 3 Vol.107 2 3 Communications Vol.107 4 5 Communications 7 6 Vol.107 6 7 Communications Vol.107 8 9 Communications Vol.107 10 11 Communications Vol.107 12 13

More information

UWB a) Accuracy of Relative Distance Measurement with Ultra Wideband System Yuichiro SHIMIZU a) and Yukitoshi SANADA (Ultra Wideband; UWB) UWB GHz DLL

UWB a) Accuracy of Relative Distance Measurement with Ultra Wideband System Yuichiro SHIMIZU a) and Yukitoshi SANADA (Ultra Wideband; UWB) UWB GHz DLL UWB a) Accuracy of Relative Distance Measurement with Ultra Wideband System Yuichiro SHIMIZU a) and Yukitoshi SANADA (Ultra Wideband; UWB) UWB GHz DLL UWB (DLL) UWB DLL 1. UWB FCC (Federal Communications

More information

Gmech08.dvi

Gmech08.dvi 63 6 6.1 6.1.1 v = v 0 =v 0x,v 0y, 0) t =0 x 0,y 0, 0) t x x 0 + v 0x t v x v 0x = y = y 0 + v 0y t, v = v y = v 0y 6.1) z 0 0 v z yv z zv y zv x xv z xv y yv x = 0 0 x 0 v 0y y 0 v 0x 6.) 6.) 6.1) 6.)

More information

福岡大学人文論叢47-3

福岡大学人文論叢47-3 679 pp. 1 680 2 681 pp. 3 682 4 683 5 684 pp. 6 685 7 686 8 687 9 688 pp. b 10 689 11 690 12 691 13 692 pp. 14 693 15 694 a b 16 695 a b 17 696 a 18 697 B 19 698 A B B B A B B A A 20 699 pp. 21 700 pp.

More information

Gmech08.dvi

Gmech08.dvi 51 5 5.1 5.1.1 P r P z θ P P P z e r e, z ) r, θ, ) 5.1 z r e θ,, z r, θ, = r sin θ cos = r sin θ sin 5.1) e θ e z = r cos θ r, θ, 5.1: 0 r

More information

q π =0 Ez,t =ε σ {e ikz ωt e ikz ωt } i/ = ε σ sinkz ωt 5.6 x σ σ *105 q π =1 Ez,t = 1 ε σ + ε π {e ikz ωt e ikz ωt } i/ = 1 ε σ + ε π sinkz ωt 5.7 σ

q π =0 Ez,t =ε σ {e ikz ωt e ikz ωt } i/ = ε σ sinkz ωt 5.6 x σ σ *105 q π =1 Ez,t = 1 ε σ + ε π {e ikz ωt e ikz ωt } i/ = 1 ε σ + ε π sinkz ωt 5.7 σ H k r,t= η 5 Stokes X k, k, ε, ε σ π X Stokes 5.1 5.1.1 Maxwell H = A A *10 A = 1 c A t 5.1 A kη r,t=ε η e ik r ωt 5. k ω ε η k η = σ, π ε σ, ε π σ π A k r,t= q η A kη r,t+qηa kηr,t 5.3 η q η E = 1 c A

More information

10 117 5 1 121841 4 15 12 7 27 12 6 31856 8 21 1983-2 - 321899 12 21656 2 45 9 2 131816 4 91812 11 20 1887 461971 11 3 2 161703 11 13 98 3 16201700-3 - 2 35 6 7 8 9 12 13 12 481973 12 2 571982 161703 11

More information

0.45m1.00m 1.00m 1.00m 0.33m 0.33m 0.33m 0.45m 1.00m 2

0.45m1.00m 1.00m 1.00m 0.33m 0.33m 0.33m 0.45m 1.00m 2 24 11 10 24 12 10 30 1 0.45m1.00m 1.00m 1.00m 0.33m 0.33m 0.33m 0.45m 1.00m 2 23% 29% 71% 67% 6% 4% n=1525 n=1137 6% +6% -4% -2% 21% 30% 5% 35% 6% 6% 11% 40% 37% 36 172 166 371 213 226 177 54 382 704 216

More information

21 1 2 1 2

21 1 2 1 2 21 1 2 1 2 1 2 3 ( ) 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 210 0.0 0.0 22 23 25 27 28 29 30 31 32 33 34 35 36 74 pp.4362003.10 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 141224 14 48 10

More information

A Study of Adaptive Array Implimentation for mobile comunication in cellular system GD133

A Study of Adaptive Array Implimentation for mobile comunication in cellular system GD133 A Study of Adaptive Array Implimentation for mobile comunication in cellular system 15 1 31 01GD133 LSI DSP CMA 10km/s i 1 1 2 LS-CMA 5 2.1 CMA... 5 2.1.1... 5 2.1.2... 7 2.1.3... 10 2.2 LS-CMA... 13 2.2.1...

More information

Wireless Mesh Networks

Wireless Mesh Networks WMN MBCR 1155056 25 2 12 1 1 2 3 2.1.............................. 3 2.2 Wireless Mesh Networks............................. 3 2.3............................. 3 2.3.1.............................. 4 2.4.........................

More information

1

1 5-3 Photonic Antennas and its Application to Radio-over-Fiber Wireless Communication Systems LI Keren, MATSUI Toshiaki, and IZUTSU Masayuki In this paper, we presented our recent works on development of

More information

知能科学:ニューラルネットワーク

知能科学:ニューラルネットワーク 2 3 4 (Neural Network) (Deep Learning) (Deep Learning) ( x x = ax + b x x x ? x x x w σ b = σ(wx + b) x w b w b .2.8.6 σ(x) = + e x.4.2 -.2 - -5 5 x w x2 w2 σ x3 w3 b = σ(w x + w 2 x 2 + w 3 x 3 + b) x,

More information

知能科学:ニューラルネットワーク

知能科学:ニューラルネットワーク 2 3 4 (Neural Network) (Deep Learning) (Deep Learning) ( x x = ax + b x x x ? x x x w σ b = σ(wx + b) x w b w b .2.8.6 σ(x) = + e x.4.2 -.2 - -5 5 x w x2 w2 σ x3 w3 b = σ(w x + w 2 x 2 + w 3 x 3 + b) x,

More information

c y /2 ddy = = 2π sin θ /2 dθd /2 [ ] 2π cos θ d = log 2 + a 2 d = log 2 + a 2 = log 2 + a a 2 d d + 2 = l

c y /2 ddy = = 2π sin θ /2 dθd /2 [ ] 2π cos θ d = log 2 + a 2 d = log 2 + a 2 = log 2 + a a 2 d d + 2 = l c 28. 2, y 2, θ = cos θ y = sin θ 2 3, y, 3, θ, ϕ = sin θ cos ϕ 3 y = sin θ sin ϕ 4 = cos θ 5.2 2 e, e y 2 e, e θ e = cos θ e sin θ e θ 6 e y = sin θ e + cos θ e θ 7.3 sgn sgn = = { = + > 2 < 8.4 a b 2

More information

吸収分光.PDF

吸収分光.PDF 3 Rb 1 1 4 1.1 4 1. 4 5.1 5. 5 3 8 3.1 8 4 1 4.1 External Cavity Laser Diode: ECLD 1 4. 1 4.3 Polarization Beam Splitter: PBS 13 4.4 Photo Diode: PD 13 4.5 13 4.6 13 5 Rb 14 6 15 6.1 ECLD 15 6. 15 6.3

More information

1 I 1.1 ± e = = - = C C MKSA [m], [Kg] [s] [A] 1C 1A 1 MKSA 1C 1C +q q +q q 1

1 I 1.1 ± e = = - = C C MKSA [m], [Kg] [s] [A] 1C 1A 1 MKSA 1C 1C +q q +q q 1 1 I 1.1 ± e = = - =1.602 10 19 C C MKA [m], [Kg] [s] [A] 1C 1A 1 MKA 1C 1C +q q +q q 1 1.1 r 1,2 q 1, q 2 r 12 2 q 1, q 2 2 F 12 = k q 1q 2 r 12 2 (1.1) k 2 k 2 ( r 1 r 2 ) ( r 2 r 1 ) q 1 q 2 (q 1 q 2

More information

IEEE802.11n LAN WiMAX(Mobile Worldwide Interoperability for Microwave Access) LTE(Long Term Evolution) IEEE LAN Bluetooth IEEE LAN

IEEE802.11n LAN WiMAX(Mobile Worldwide Interoperability for Microwave Access) LTE(Long Term Evolution) IEEE LAN Bluetooth IEEE LAN 23 IEEE802.11n LAN 43422519 ( ) 24 2 6 IEEE802.11n LAN WiMAX(Mobile Worldwide Interoperability for Microwave Access) LTE(Long Term Evolution) IEEE802.11 LAN Bluetooth 2009 9 IEEE802.11 LAN IEE E802.11n

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

( ) ( ) ( ) ( ) ( )

( ) ( ) ( ) ( ) ( ) NAIST-IS-MT0751044 2.4GHz W-LAN 2008 8 20 ( ) ( ) ( ) ( ) ( ) 2.4GHz W-LAN ISM(Industrial, Sientific and Medical) 2.4GHz IEEE802.11b/gW-LAN 2.4GHz W-LAN 2.4GHz ISM (Industry Scientific and Medical) ISM

More information

CoPt 17

CoPt 17 CoPt 17 1...1 1.1...1 1.2...1 1.2.1...1 1.2.2...1 1.2.3...2 1.3...3 1.4 CoPt...3 1.5...4 2...6 2.1...6 2.1.1...6 2.1.2...6 2.2...7 2.2.1 X...7 2.2.2...7 2.3...8 2.3.1...8 2.3.2...9 3 CoPt...10 3.1...10

More information

limit&derivative

limit&derivative - - 7 )................................................................................ 5.................................. 7.. e ).......................... 9 )..........................................

More information

デジタル通信を支える無線技術

デジタル通信を支える無線技術 Aug. 02, 2008 Copyright 2008 Niigata Internet SOCiety & I.Suzuki All Rights Reserved. 2 1. LAN 2. 3. LAN 4. 802.11 3 4 1. LAN 2. 3. LAN 4. 802.11 5 WMAN 50Km WiMax WLAN 100m 802.11 WPAN 10m ZigBee Bluetooth

More information

2 1 x 1.1: v mg x (t) = v(t) mv (t) = mg 0 x(0) = x 0 v(0) = v 0 x(t) = x 0 + v 0 t 1 2 gt2 v(t) = v 0 gt t x = x 0 + v2 0 2g v2 2g 1.1 (x, v) θ

2 1 x 1.1: v mg x (t) = v(t) mv (t) = mg 0 x(0) = x 0 v(0) = v 0 x(t) = x 0 + v 0 t 1 2 gt2 v(t) = v 0 gt t x = x 0 + v2 0 2g v2 2g 1.1 (x, v) θ 1 1 1.1 (Isaac Newton, 1642 1727) 1. : 2. ( ) F = ma 3. ; F a 2 t x(t) v(t) = x (t) v (t) = x (t) F 3 3 3 3 3 3 6 1 2 6 12 1 3 1 2 m 2 1 x 1.1: v mg x (t) = v(t) mv (t) = mg 0 x(0) = x 0 v(0) = v 0 x(t)

More information

重力方向に基づくコントローラの向き決定方法

重力方向に基づくコントローラの向き決定方法 ( ) 2/Sep 09 1 ( ) ( ) 3 2 X w, Y w, Z w +X w = +Y w = +Z w = 1 X c, Y c, Z c X c, Y c, Z c X w, Y w, Z w Y c Z c X c 1: X c, Y c, Z c Kentaro Yamaguchi@bandainamcogames.co.jp 1 M M v 0, v 1, v 2 v 0 v

More information

II (No.2) 2 4,.. (1) (cm) (2) (cm) , (

II (No.2) 2 4,.. (1) (cm) (2) (cm) , ( II (No.1) 1 x 1, x 2,..., x µ = 1 V = 1 k=1 x k (x k µ) 2 k=1 σ = V. V = σ 2 = 1 x 2 k µ 2 k=1 1 µ, V σ. (1) 4, 7, 3, 1, 9, 6 (2) 14, 17, 13, 11, 19, 16 (3) 12, 21, 9, 3, 27, 18 (4) 27.2, 29.3, 29.1, 26.0,

More information

JGN 2 KDDI NiCT IT 17518 NiCT IT PC ( ) [2], : " ", (%) 100 0 0 T 1 T 2 t1.2 tx t3 t4 t6 (t) 2005 Mobile PC PDA Mobile PC PDA Mobile PC Mobile phone WAN Internet JGN II GIS Japan Gigabit

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

.5 z = a + b + c n.6 = a sin t y = b cos t dy d a e e b e + e c e e e + e 3 s36 3 a + y = a, b > b 3 s363.7 y = + 3 y = + 3 s364.8 cos a 3 s365.9 y =,

.5 z = a + b + c n.6 = a sin t y = b cos t dy d a e e b e + e c e e e + e 3 s36 3 a + y = a, b > b 3 s363.7 y = + 3 y = + 3 s364.8 cos a 3 s365.9 y =, [ ] IC. r, θ r, θ π, y y = 3 3 = r cos θ r sin θ D D = {, y ; y }, y D r, θ ep y yddy D D 9 s96. d y dt + 3dy + y = cos t dt t = y = e π + e π +. t = π y =.9 s6.3 d y d + dy d + y = y =, dy d = 3 a, b

More information

2.2 h h l L h L = l cot h (1) (1) L l L l l = L tan h (2) (2) L l 2 l 3 h 2.3 a h a h (a, h)

2.2 h h l L h L = l cot h (1) (1) L l L l l = L tan h (2) (2) L l 2 l 3 h 2.3 a h a h (a, h) 1 16 10 5 1 2 2.1 a a a 1 1 1 2.2 h h l L h L = l cot h (1) (1) L l L l l = L tan h (2) (2) L l 2 l 3 h 2.3 a h a h (a, h) 4 2 3 4 2 5 2.4 x y (x,y) l a x = l cot h cos a, (3) y = l cot h sin a (4) h a

More information

LD

LD 989935 1 1 3 3 4 4 LD 6 7 10 1 3 13 13 16 0 4 5 30 31 33 33 35 35 37 38 5 40 FFT 40 40 4 4 4 44 47 48 49 51 51 5 53 54 55 56 Abstract [1] HDD (LaserDopplerVibrometer; LDV) [] HDD IC 1 4 LDV LDV He-Ne Acousto-optic

More information

A (1) = 4 A( 1, 4) 1 A 4 () = tan A(0, 0) π A π

A (1) = 4 A( 1, 4) 1 A 4 () = tan A(0, 0) π A π 4 4.1 4.1.1 A = f() = f() = a f (a) = f() (a, f(a)) = f() (a, f(a)) f(a) = f 0 (a)( a) 4.1 (4, ) = f() = f () = 1 = f (4) = 1 4 4 (4, ) = 1 ( 4) 4 = 1 4 + 1 17 18 4 4.1 A (1) = 4 A( 1, 4) 1 A 4 () = tan

More information

07.報文_及川ら-二校目.indd

07.報文_及川ら-二校目.indd 8 01 01 4 4 1 5 16 18 6 006 H 18 4 011 H 6 4 1 5 1 5 007 H 19 5 009 1 5 006 007 009 011 9 10 4 000 H 1 4 5 004 H 16 4 004 009 H 1 5 4 4 5 1 4 006 011 1 1 4m 5m 10m 007 1 7 009 009 1 5 10 1 000kg 10a 006

More information

(1.2) T D = 0 T = D = 30 kn 1.2 (1.4) 2F W = 0 F = W/2 = 300 kn/2 = 150 kn 1.3 (1.9) R = W 1 + W 2 = = 1100 N. (1.9) W 2 b W 1 a = 0

(1.2) T D = 0 T = D = 30 kn 1.2 (1.4) 2F W = 0 F = W/2 = 300 kn/2 = 150 kn 1.3 (1.9) R = W 1 + W 2 = = 1100 N. (1.9) W 2 b W 1 a = 0 1 1 1.1 1.) T D = T = D = kn 1. 1.4) F W = F = W/ = kn/ = 15 kn 1. 1.9) R = W 1 + W = 6 + 5 = 11 N. 1.9) W b W 1 a = a = W /W 1 )b = 5/6) = 5 cm 1.4 AB AC P 1, P x, y x, y y x 1.4.) P sin 6 + P 1 sin 45

More information

2. 2 P M A 2 F = mmg AP AP 2 AP (G > : ) AP/ AP A P P j M j F = n j=1 mm j G AP j AP j 2 AP j 3 P ψ(p) j ψ(p j ) j (P j j ) A F = n j=1 mgψ(p j ) j AP

2. 2 P M A 2 F = mmg AP AP 2 AP (G > : ) AP/ AP A P P j M j F = n j=1 mm j G AP j AP j 2 AP j 3 P ψ(p) j ψ(p j ) j (P j j ) A F = n j=1 mgψ(p j ) j AP 1. 1 213 1 6 1 3 1: ( ) 2: 3: SF 1 2 3 1: 3 2 A m 2. 2 P M A 2 F = mmg AP AP 2 AP (G > : ) AP/ AP A P P j M j F = n j=1 mm j G AP j AP j 2 AP j 3 P ψ(p) j ψ(p j ) j (P j j ) A F = n j=1 mgψ(p j ) j AP

More information

LCR e ix LC AM m k x m x x > 0 x < 0 F x > 0 x < 0 F = k x (k > 0) k x = x(t)

LCR e ix LC AM m k x m x x > 0 x < 0 F x > 0 x < 0 F = k x (k > 0) k x = x(t) 338 7 7.3 LCR 2.4.3 e ix LC AM 7.3.1 7.3.1.1 m k x m x x > 0 x < 0 F x > 0 x < 0 F = k x k > 0 k 5.3.1.1 x = xt 7.3 339 m 2 x t 2 = k x 2 x t 2 = ω 2 0 x ω0 = k m ω 0 1.4.4.3 2 +α 14.9.3.1 5.3.2.1 2 x

More information

B line of mgnetic induction AB MN ds df (7.1) (7.3) (8.1) df = µ 0 ds, df = ds B = B ds 2π A B P P O s s Q PQ R QP AB θ 0 <θ<π

B line of mgnetic induction AB MN ds df (7.1) (7.3) (8.1) df = µ 0 ds, df = ds B = B ds 2π A B P P O s s Q PQ R QP AB θ 0 <θ<π 8 Biot-Svt Ampèe Biot-Svt 8.1 Biot-Svt 8.1.1 Ampèe B B B = µ 0 2π. (8.1) B N df B ds A M 8.1: Ampèe 107 108 8 0 B line of mgnetic induction 8.1 8.1 AB MN ds df (7.1) (7.3) (8.1) df = µ 0 ds, df = ds B

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

B. 41 II: 2 ;; 4 B [ ] S 1 S 2 S 1 S O S 1 S P 2 3 P P : 2.13:

B. 41 II: 2 ;; 4 B [ ] S 1 S 2 S 1 S O S 1 S P 2 3 P P : 2.13: B. 41 II: ;; 4 B [] S 1 S S 1 S.1 O S 1 S 1.13 P 3 P 5 7 P.1:.13: 4 4.14 C d A B x l l d C B 1 l.14: AB A 1 B 0 AB 0 O OP = x P l AP BP AB AP BP 1 (.4)(.5) x l x sin = p l + x x l (.4)(.5) m d A x P O

More information

Microsoft Word - 学士論文(表紙).doc

Microsoft Word - 学士論文(表紙).doc GHz 18 2 1 1 3 1.1....................................... 3 1.2....................................... 3 1.3................................... 3 2 (LDV) 5 2.1................................ 5 2.2.......................

More information

66 σ σ (8.1) σ = 0 0 σd = 0 (8.2) (8.2) (8.1) E ρ d = 0... d = 0 (8.3) d 1 NN K K 8.1 d σd σd M = σd = E 2 d (8.4) ρ 2 d = I M = EI ρ 1 ρ = M EI ρ EI

66 σ σ (8.1) σ = 0 0 σd = 0 (8.2) (8.2) (8.1) E ρ d = 0... d = 0 (8.3) d 1 NN K K 8.1 d σd σd M = σd = E 2 d (8.4) ρ 2 d = I M = EI ρ 1 ρ = M EI ρ EI 65 8. K 8 8 7 8 K 6 7 8 K 6 M Q σ (6.4) M O ρ dθ D N d N 1 P Q B C (1 + ε)d M N N h 2 h 1 ( ) B (+) M 8.1: σ = E ρ (E, 1/ρ ) (8.1) 66 σ σ (8.1) σ = 0 0 σd = 0 (8.2) (8.2) (8.1) E ρ d = 0... d = 0 (8.3)

More information

( ) ,

( ) , II 2007 4 0. 0 1 0 2 ( ) 0 3 1 2 3 4, - 5 6 7 1 1 1 1 1) 2) 3) 4) ( ) () H 2.79 10 10 He 2.72 10 9 C 1.01 10 7 N 3.13 10 6 O 2.38 10 7 Ne 3.44 10 6 Mg 1.076 10 6 Si 1 10 6 S 5.15 10 5 Ar 1.01 10 5 Fe 9.00

More information

c 2009 i

c 2009 i I 2009 c 2009 i 0 1 0.0................................... 1 0.1.............................. 3 0.2.............................. 5 1 7 1.1................................. 7 1.2..............................

More information

all.dvi

all.dvi 38 5 Cauchy.,,,,., σ.,, 3,,. 5.1 Cauchy (a) (b) (a) (b) 5.1: 5.1. Cauchy 39 F Q Newton F F F Q F Q 5.2: n n ds df n ( 5.1). df n n df(n) df n, t n. t n = df n (5.1) ds 40 5 Cauchy t l n mds df n 5.3: t

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

[ ] 0.1 lim x 0 e 3x 1 x IC ( 11) ( s114901) 0.2 (1) y = e 2x (x 2 + 1) (2) y = x/(x 2 + 1) 0.3 dx (1) 1 4x 2 (2) e x sin 2xdx (3) sin 2 xdx ( 11) ( s

[ ] 0.1 lim x 0 e 3x 1 x IC ( 11) ( s114901) 0.2 (1) y = e 2x (x 2 + 1) (2) y = x/(x 2 + 1) 0.3 dx (1) 1 4x 2 (2) e x sin 2xdx (3) sin 2 xdx ( 11) ( s [ ]. lim e 3 IC ) s49). y = e + ) ) y = / + ).3 d 4 ) e sin d 3) sin d ) s49) s493).4 z = y z z y s494).5 + y = 4 =.6 s495) dy = 3e ) d dy d = y s496).7 lim ) lim e s49).8 y = e sin ) y = sin e 3) y =

More information

untitled

untitled 1 17 () BAC9ABC6ACB3 1 tan 6 = 3, cos 6 = AB=1 BC=2, AC= 3 2 A BC D 2 BDBD=BA 1 2 ABD BADBDA ABC6 BAD = (18 6 ) / 2 = 6 θ = 18 BAD = 12 () AD AD=BADCAD9 ABD ACD A 1 1 1 1 dsinαsinα = d 3 sin β 3 sin β

More information

II Karel Švadlenka * [1] 1.1* 5 23 m d2 x dt 2 = cdx kx + mg dt. c, g, k, m 1.2* u = au + bv v = cu + dv v u a, b, c, d R

II Karel Švadlenka * [1] 1.1* 5 23 m d2 x dt 2 = cdx kx + mg dt. c, g, k, m 1.2* u = au + bv v = cu + dv v u a, b, c, d R II Karel Švadlenka 2018 5 26 * [1] 1.1* 5 23 m d2 x dt 2 = cdx kx + mg dt. c, g, k, m 1.2* 5 23 1 u = au + bv v = cu + dv v u a, b, c, d R 1.3 14 14 60% 1.4 5 23 a, b R a 2 4b < 0 λ 2 + aλ + b = 0 λ =

More information

THE INSTITUTE OF ELECTRONICS, INFORMATION AND COMMUNICATION ENGINEERS TECHNICAL REPORT OF IEICE

THE INSTITUTE OF ELECTRONICS, INFORMATION AND COMMUNICATION ENGINEERS TECHNICAL REPORT OF IEICE THE INSTITUTE OF ELECTRONICS, INFORMATION AND COMMUNICATION ENGINEERS TECHNICAL REPORT OF IEICE. 56 8531 1 3 E-mail: morisaka@ec.ee.es.osaka-u.ac.jp, {shiomi,okamura}@ee.es.osaka-u.ac.jp 2.665GHz 29 1.2,

More information

1 s(t) ( ) f c : A cos(2πf c t + ϕ) (AM, Amplitude Modulation) (FM, Frequency Modulation) (PM, Phase Modulation) 2

1 s(t) ( ) f c : A cos(2πf c t + ϕ) (AM, Amplitude Modulation) (FM, Frequency Modulation) (PM, Phase Modulation) 2 (Communication and Network) 1 1 s(t) ( ) f c : A cos(2πf c t + ϕ) (AM, Amplitude Modulation) (FM, Frequency Modulation) (PM, Phase Modulation) 2 1.1 AM s(t) : A(αs(t) + 1) cos 2πf c t A, α : s(t) = cos

More information

総研大恒星進化概要.dvi

総研大恒星進化概要.dvi The Structure and Evolution of Stars I. Basic Equations. M r r =4πr2 ρ () P r = GM rρ. r 2 (2) r: M r : P and ρ: G: M r Lagrange r = M r 4πr 2 rho ( ) P = GM r M r 4πr. 4 (2 ) s(ρ, P ) s(ρ, P ) r L r T

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

,, 2. Matlab Simulink 2018 PC Matlab Scilab 2

,, 2. Matlab Simulink 2018 PC Matlab Scilab 2 (2018 ) ( -1) TA Email : ohki@i.kyoto-u.ac.jp, ske.ta@bode.amp.i.kyoto-u.ac.jp : 411 : 10 308 1 1 2 2 2.1............................................ 2 2.2..................................................

More information

JIS Z803: (substitution method) 3 LCR LCR GPIB

JIS Z803: (substitution method) 3 LCR LCR GPIB LCR NMIJ 003 Agilent 8A 500 ppm JIS Z803:000 50 (substitution method) 3 LCR LCR GPIB Taylor 5 LCR LCR meter (Agilent 8A: Basic accuracy 500 ppm) V D z o I V DUT Z 3 V 3 I A Z V = I V = 0 3 6 V, A LCR meter

More information

[FX11]シリーズカタログ

[FX11]シリーズカタログ May.1.218 Copyright 218 HIROSE ELECTRIC CO., LTD. All Rights Reserved. ICR (db) 6 5 4 3 2 ICR 3mm(Without GND) 1 ICR IEEEspec 1 2 3 4 5 6 7 8 9 1 Frequency (GHz) Z (Ohm) 12 115 11 15 1 95 9 Impedance 3mm(Without

More information

1 12 ( )150 ( ( ) ) x M x 0 1 M 2 5x 2 + 4x + 3 x 2 1 M x M 2 1 M x (x + 1) 2 (1) x 2 + x + 1 M (2) 1 3 M (3) x 4 +

1 12 ( )150 ( ( ) ) x M x 0 1 M 2 5x 2 + 4x + 3 x 2 1 M x M 2 1 M x (x + 1) 2 (1) x 2 + x + 1 M (2) 1 3 M (3) x 4 + ( )5 ( ( ) ) 4 6 7 9 M M 5 + 4 + M + M M + ( + ) () + + M () M () 4 + + M a b y = a + b a > () a b () y V a () V a b V n f() = n k= k k () < f() = log( ) t dt log () n+ (i) dt t (n + ) (ii) < t dt n+ n

More information

さくらの個別指導 ( さくら教育研究所 ) A 2 2 Q ABC 2 1 BC AB, AC AB, BC AC 1 B BC AB = QR PQ = 1 2 AC AB = PR 3 PQ = 2 BC AC = QR PR = 1

さくらの個別指導 ( さくら教育研究所 ) A 2 2 Q ABC 2 1 BC AB, AC AB, BC AC 1 B BC AB = QR PQ = 1 2 AC AB = PR 3 PQ = 2 BC AC = QR PR = 1 ... 0 60 Q,, = QR PQ = = PR PQ = = QR PR = P 0 0 R 5 6 θ r xy r y y r, x r, y x θ x θ θ (sine) (cosine) (tangent) sin θ, cos θ, tan θ. θ sin θ = = 5 cos θ = = 4 5 tan θ = = 4 θ 5 4 sin θ = y r cos θ =

More information

5. F(, 0) = = 4 = 4 O = 4 =. ( = = 4 ) = 4 ( 4 ), 0 = 4 4 O 4 = 4. () = 8 () = 4

5. F(, 0) = = 4 = 4 O = 4 =. ( = = 4 ) = 4 ( 4 ), 0 = 4 4 O 4 = 4. () = 8 () = 4 ... A F F l F l F(p, 0) = p p > 0 l p 0 P(, ) H P(, ) P l PH F PF = PH PF = PH p O p ( p) + = { ( p)} = 4p l = 4p (p 0) F(p, 0) = p O 3 5 5. F(, 0) = = 4 = 4 O = 4 =. ( = = 4 ) = 4 ( 4 ), 0 = 4 4 O 4 =

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

(1) (2) (3) (4) (5) (6) (7) 4 (8) (9) () LAN 1 2 3 ( ) () () () 30 20 5 5 450 450 5 5 30 10 20 15 36 30 6 6 450 450 6 6 36 8 30 14 50 35 20 20 450 450 20 20 50 8 35 14 100 70 20 20 450 450

More information

main.dvi

main.dvi B 15 0150023 16 3 1 1 1 6 2 7 2.1.......................... 7 2.1.1................. 7 2.1.2..................... 7 2.2........................ 8 2.2.1...................... 8 2.2.2 INS................................

More information

#A A A F, F d F P + F P = d P F, F y P F F x A.1 ( α, 0), (α, 0) α > 0) (x, y) (x + α) 2 + y 2, (x α) 2 + y 2 d (x + α)2 + y 2 + (x α) 2 + y 2 =

#A A A F, F d F P + F P = d P F, F y P F F x A.1 ( α, 0), (α, 0) α > 0) (x, y) (x + α) 2 + y 2, (x α) 2 + y 2 d (x + α)2 + y 2 + (x α) 2 + y 2 = #A A A. F, F d F P + F P = d P F, F P F F A. α, 0, α, 0 α > 0, + α +, α + d + α + + α + = d d F, F 0 < α < d + α + = d α + + α + = d d α + + α + d α + = d 4 4d α + = d 4 8d + 6 http://mth.cs.kitmi-it.c.jp/

More information

( ) sin 1 x, cos 1 x, tan 1 x sin x, cos x, tan x, arcsin x, arccos x, arctan x. π 2 sin 1 x π 2, 0 cos 1 x π, π 2 < tan 1 x < π 2 1 (1) (

( ) sin 1 x, cos 1 x, tan 1 x sin x, cos x, tan x, arcsin x, arccos x, arctan x. π 2 sin 1 x π 2, 0 cos 1 x π, π 2 < tan 1 x < π 2 1 (1) ( 6 20 ( ) sin, cos, tan sin, cos, tan, arcsin, arccos, arctan. π 2 sin π 2, 0 cos π, π 2 < tan < π 2 () ( 2 2 lim 2 ( 2 ) ) 2 = 3 sin (2) lim 5 0 = 2 2 0 0 2 2 3 3 4 5 5 2 5 6 3 5 7 4 5 8 4 9 3 4 a 3 b

More information