Microsoft PowerPoint - Yoshimi_KUR_ ppt
|
|
- めぐの さかいざわ
- 5 years ago
- Views:
Transcription
1 磁力計に関して Rb NMOR - 理研吉見彰洋 011//3 中性子制御デバイスとその応用 京大原子炉
2 EDM measurement = 0 0 E= 0 E // ω + E // ω δd = 1 8 e 4dE ν = h cm = = [ ecm] [ Vcm ] [ s ] 1[ nh] Frequens shift of 1 nh [ evs] δ= 1 pg= 0.1 ft 1 9 = 1 nh s 31 ears ν + +E ω + t µ + de = h ν = E ω t µ de h δφ δν = πt δφ= 1 mrad (0.06 ), T = 1,000 s δν =160 nh Phase measurement: Repeating measurements ν ν average δν i δν i month = 5,90 ksec: 1 3 n δν total δνi δν total = n δνi 160 nh = = = 1 nh n 590
3 Nuclear Spin Maser with Polaried 19 Xe at low field Artificial feedback through the optical spin detection Singnal (V) Maser signal 0 mg Probe laser beam Feedback coil Phase shifter Time (s) Nuclear spin Pumping laser beam Photo diode Lock-in detection Operation at low magnetic field Small field fluctuation High-sensitive magnetometer Long intrinsic T Frequenc precision is ~ nh for ^4 s, but
4 Dual noble gas spin maser / separated cell - Michigan Univ. - Rosenberr and Chupp, PRL (001) 19Xe precession : locked with reference oscillator No drift 0 = 3.0G δν locked Xe 0 nh 000 s - Run Feedback to solenoid current δ 17 pg Pump bulb Measuring 3He maser frequenc EDM signal T [Rb].0 P maser Rb maser = 10 C / cm 3 µh Maser bulb Long term instabilit δν µh ng free He T maser = 40 C [Rb] 5. P Rb maser < / cm 3
5 Frequenc instabilit in Dual noble gas spin maser Sources of frequenc drift Drift of the applied magnetic field 0 Magnetic field generated from polaried atoms Other species: Longitudinal (7mH, 8. mh) Transverse (58 ph, -81 ph) Same species: Longitudinal (3mH,.5 mh) Transverse (-18mH, -5.5mH) From Rb atoms (40 nh, µh) sol et atoms µ Xe Maser Position : (30mH) T Cavit pulling: (0µH) F T atoms Field gradient (0nH, 36nH) T grad Maser posi. Laser properties Temperature Environmental field Shield drift, noise Mechanical instabilit Cavit pul
6 Spin maser at low magnetic field Low magnetic field : 3 G 30 mg 3 mg? 3 kh 30 H 3 H?,000 s maser run = 3.0G Suppression of δ solenoid and gradient Separation between δ solenoid and δ atoms High sensitivit magnetometer can be used 3He is not introduced If possible, comagnetometer = 30mG Xe Cell 1cell cell T [Rb] 6.7 P maser Rb maser = 70 C / cm 3 T 1K up [Rb] % up ν = 0.1mH T maser = 70 C [Rb] 6.7 P Rb maser δν Xe 1[ mh] / cm 3 T maser = 40 C [Rb] 5. P Rb maser δν < 1.5 < Xe µ [ H] / cm 3 δt maser = 1 mk δν Xe < 0.15 [ nh] (cell ) δν Xe 11[ µh] (1cell )
7 中性子と 199Hg のスピンスピン歳差歳差の同時測定 ν n だけの測定値 0.5 mh ν Hg の値を使って補正 0.5μG 199Hg 磁力計 : 0.6μH = 0.8 ng の精度 電場を反転した際の d meas d <.9 n -6 ecm
8 High sensitivit magnetometers θ φ Incident laser beam ε // ε ε ' Atomic alignment Transmitted laser beam 1 µg
9 Magnetometer for Low freq-spin maser EDM eperiment (1) High sensitivit magnetometers () Rb comagnetometer (3) 3He comagnetometer Rb Xe Magnetometer probe Rb Xe Rb Xe He Rb Maser probe Not comagnetometer Rb magnetometer near maser cell Onl Xe and Rb (small, and not pol) δ = 11 G/ H 0 s run ( if constant ): δ = 1 G Comagnetometer of Rb Onl Xe and Rb (small, and not pol) Probrem of Rb Xe interaction? ( Low densit Xe gas? ) Polariabilit problem δ =? G/ H Comagnetometer of 3He ad S/N for He precession for laser probing? but possible
10 NMOR 実験 setup Photo elastic Modulator (PEM) 4-laer magnetic shield eam splitter Linear polarier- Photo diode 3-ais coil Linear Polarier-1 Eternal Cavit Diode Laser Rb cell Rb reference cell Wavemeter PEM driver&controller Lock-in amplifier Oscilloscope Photo diode Reference(50kH) Signal
11
12 NMOR 測定実験 Wide-field scan = 0.44G Fitting function: gfµ / γ ϕ = gfµ / 1+ γ l l 0 + a + b 回転角度 (mrad) Magnetic field (G) Narrow-field scan Magnetic field(mg) Coherence effect g F fitting Transit effect µ / = 1.146± 0.04 γ 1 = = [s ] 1 ( γ π) [ ms] / 1 Rb coherence time : ~ 8 ms 1/400 の狭い共鳴幅を持つ NMOR スペクトラム しかしまだ試作段階 改善していく
13 ノイズと磁場感度 Rotation angle (mrad) 現在の best spectrum dφ 4.8 d [ rad/g] Lock-in 検波 signal (V) ν = ノイズスペクトラム S( ) Noise floor X T ( ν) Sampling 5 H に smoothing δv T [ V/ H] Field (mg) Frequenc (H) δφ = 3.0 = / 5[ mrad/ H] [ mrad/ H] 感度の見積もり δ = = 8.8 [ G / H] 90 ng / H
14 NMOR signal 幅 幅が以前より狭くなっている ( 半分程度 ); 同じ Rb セル Triad 社 φ5 Triad 社 φ5 Horion 社 φ30 = 1.5 mg 原因は? 光学系 : 関係無し 残留磁場 ( 横成分 ) 消磁前 = + 95 µg = µg = µg 消磁 実験時近辺 = + 3 µg = µg = µg Triad 社 φ5 Horion 社 φ30 = 0.75 mg = 0.47 mg ( γ / π) 1 = 16.[ ms] ( γ / π) 1 = 6.6[ ms] 5 日後 = + 98 µg = + 9 µg = µg
15 残留磁場 有効な消磁の仕方の模索中 文献等も調べる必要 磁気シールドメーカーより : スライダックで手動で 60A 0A にもっていく スライダックで手動消磁 波形発生器 +amp で電流制御 今のところ 電流減衰をゆっくり (~1 分くらい ) 周波数は 0-50 H (60A) より ~300 H (7A) = 180 µg = 114 µg = 49 µg = 35 µg = 37 µg = 13 µg = 00 ~ 50 µg = 90 ~ 1 µg = 60 ~ 0 µg = 84 µg = + 4 µg = 45 µg
16 光学回転検出系 今まで : simple な polarier analer 法 0 θ LP PD Analer 透過強度 : sample E P= E E ( cosθ+ sinθ) = ( 1+ sin θ) ( 1 θ) 正しくは ( 準備中 ): balanced polarimeter 法 0 PD#1 sample PD# 準備中 ±45 方向の偏光成分を観測 各成分の強度差 : E0 E P PD1 PPD = = 回転成分のみのみ検出検出できる 0 ( 1+ sin θ) ( 1 sin θ) E sin θ 0
17 セル作製 作製法を伝えて業者に依頼 研究室で自作準備中
18 新たなたなコーティングコーティング剤について Alken-based コーティング (Alpha Olefin Fraction C0-4) Polariation life time ~ 60 s (for Rb atom) Alken C n H n (n>=) オレフィン系 エチレン系炭化水素 Alkane C n H n+ メタン系 パラフィン系炭化水素 これまでの究極磁場感度 1 pg/ H をさらに 桁向上できる
19 90 ng/ H (30 ng/ H) 3 pg/ H まで ^4 セル内壁緩和 : 0 ms 1 s ( 50) 検出系 : (?) シールド改善 ( 横磁場 磁気ノイズ ): ( >) レーザー周波数 電気ノイズ
Electron Ion Collider と ILC-N 宮地義之 山形大学
Electron Ion Collider と ILC-N 宮地義之 山形大学 ILC-N ILC-N Ee Ee == 250, 250, 500 500 GeV GeV Fixed Fixed target: target: p, p, d, d, A A 33-34 cm-2 LL ~~ 10 1033-34 cm-2 ss-1-1 s s == 22, 22, 32 32 GeV GeV
More informationMicrosoft 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 informationELECTRONIC IMAGING IN ASTRONOMY Detectors and Instrumentation 5 Instrumentation and detectors
ELECTRONIC IMAGING IN ASTRONOMY Detectors and Instrumentation 5 Instrumentation and detectors 4 2017/5/10 Contents 5.4 Interferometers 5.4.1 The Fourier Transform Spectrometer (FTS) 5.4.2 The Fabry-Perot
More informationPowerPoint プレゼンテーション
時間反転対称性の破れの探索に向けた ルビジウム磁力計の研究 目次 本研究の目的 冷却フランシウム原子を用いた電子の永久電気双極子能率 (EDM) 探索 EDM 探索に必要とされる磁場精度 ルビジウム (Rb) 磁力計の原理 周波数変調光を用いた非線形磁気光学回転効果 (FM-NMOR) 磁場感度の高い Rb 磁力計の開発 FM-NMOR スペクトルの傾きに対するレーザー周波数, 変調幅, 強度依存性の測定
More information磁気測定によるオーステンパ ダクタイル鋳鉄の残留オーステナイト定量
33 Non-destructive Measurement of Retained Austenite Content in Austempered Ductile Iron Yoshio Kato, Sen-ichi Yamada, Takayuki Kato, Takeshi Uno Austempered Ductile Iron (ADI) 100kg/mm 2 10 ADI 10 X ADI
More informationuntitled
SPring-8 RFgun JASRI/SPring-8 6..7 Contents.. 3.. 5. 6. 7. 8. . 3 cavity γ E A = er 3 πε γ vb r B = v E c r c A B A ( ) F = e E + v B A A A A B dp e( v B+ E) = = m d dt dt ( γ v) dv e ( ) dt v B E v E
More information1 Visible spectroscopy for student Spectrometer and optical spectrum phys/ishikawa/class/index.html
1 Visible spectroscopy for student Spectrometer and optical spectrum http://www.sci.u-hyogo.ac.jp/material/photo phys/ishikawa/class/index.html 1 2 2 2 2.1................................................
More informationPowerPoint プレゼンテーション
東北大学サイクロトロン ラジオアイソトープセンター測定器研究部内山愛子 2 電子の永久電気双極子能率 EDM : Permanent Electric Dipole Moment 電子のスピン方向に沿って生じる電気双極子能率 標準模型 (SM): クォークを介した高次の効果で電子 EDM ( d e ) が発現 d e SM < 10 38 ecm M. Pospelov and A. Ritz,
More informationGmech08.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<4D F736F F D B B83578B6594BB2D834A836F815B82D082C88C60202E646F63>
通信方式第 2 版 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. http://www.morikita.co.jp/books/mid/072662 このサンプルページの内容は, 第 2 版発行当時のものです. i 2 2 2 2012 5 ii,.,,,,,,.,.,,,,,.,,.,,..,,,,.,,.,.,,.,,.. 1990 5 iii 1 1
More informationMicrosoft PowerPoint - machida0206
広帯域制御のためのフォトメカニカルアクチュエータの開発とその応用 東京大学新領域創成科学研究科物質系専攻三尾研究室 M2 町田幸介 重力波研究交流会 (2009 2/6) 1 発表の流れ 実験の背景 広帯域制御のためのアクチュエータ 実験の目的 実験 電磁アクチュエータの作製 電磁アクチュエータの評価 電磁アクチュエータの応用 ( 位相雑音補償と共振器長制御 ) まとめ 2 広帯域制御のためのアクチュエータ
More information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 informationGmech08.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 informationGmech08.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 informationuntitled
- i - - i - Application of All-Optical Switching by Optical Fiber Grating Coupler Yasuhiko Maeda Abstract All-optical switching devices are strongly required for fast signal processing in future optical
More informationOPA277/2277/4277 (2000.1)
R OPA OPA OPA OPA OPA OPA OPA OPA OPA µ µ ± ± µ OPA ±± ±± ± µ Offset Trim Offset Trim In OPA +In -Pin DIP, SO- Output NC OPA Out A In A +In A A D Out D In D +In D Out A In A +In A A B Out B In B +In B
More information1 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 informationUndulator.dvi
X X 1 1 2 Free Electron Laser: FEL 2.1 2 2 3 SACLA 4 SACLA [1]-[6] [7] 1: S N λ [9] XFEL OHO 13 X [8] 2 2.1 2(a) (c) z y y (a) S N 90 λ u 4 [10, 11] Halbach (b) 2: (a) (b) (c) (c) 1 2 [11] B y = n=1 B
More information飽和分光
3 Rb 1 1 4 1.1 4 1. 4 5.1 LS 5. Hyperfine Structure 6 3 8 3.1 8 3. 8 4 11 4.1 11 5 14 5.1 External Cavity Laser Diode: ECLD 14 5. 16 5.3 Polarization Beam Splitter: PBS 17 5.4 Photo Diode: PD 17 5.5 :
More informationnews
ETL NEWS 1999.9 ETL NEWS 1999.11 Establishment of an Evaluation Technique for Laser Pulse Timing Fluctuations Optoelectronics Division Hidemi Tsuchida e-mail:tsuchida@etl.go.jp A new technique has been
More information64 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 information1 7 ω ω ω 7.1 0, ( ) Q, 7.2 ( Q ) 7.1 ω Z = R +jx Z 1/ Z 7.2 ω 7.2 Abs. admittance (x10-3 S) RLC Series Circuit Y R = 20 Ω L = 100
7 7., ) Q, 7. Q ) 7. Z = R +jx Z / Z 7. 7. Abs. admittance x -3 S) 5 4 3 R Series ircuit Y R = Ω = mh = uf Q = 5 5 5 V) Z = R + jx 7. Z 7. ) R = Ω = mh = µf ) 7 V) R Z s = R + j ) 7.3 R =. 7.4) ) f = π.
More information(Compton Scattering) Beaming 1 exp [i (k x ωt)] k λ k = 2π/λ ω = 2πν k = ω/c k x ωt ( ω ) k α c, k k x ωt η αβ k α x β diag( + ++) x β = (ct, x) O O x
Compton Scattering Beaming exp [i k x ωt] k λ k π/λ ω πν k ω/c k x ωt ω k α c, k k x ωt η αβ k α x β diag + ++ x β ct, x O O x O O v k α k α β, γ k γ k βk, k γ k + βk k γ k k, k γ k + βk 3 k k 4 k 3 k
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 =,
[ ] 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 informationOPA134/2134/4134('98.03)
OPA OPA OPA OPA OPA OPA OPA OPA OPA TM µ Ω ± ± ± ± + OPA OPA OPA Offset Trim Offset Trim Out A V+ Out A Out D In +In V+ Output In A +In A A B Out B In B In A +In A A D In D +In D V NC V +In B V+ V +In
More information1. 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 information05Mar2001_tune.dvi
2001 3 5 COD 1 1.1 u d2 u + ku =0 (1) dt2 u = a exp(pt) (2) p = ± k (3) k>0k = ω 2 exp(±iωt) (4) k
More informationMott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橡実験IIINMR.PDF
(NMR) 0 (NMR) 2µH hω ω 1 h 2 1 1-1 NMR NMR h I µ = γµ N 1-2 1 H 19 F Ne µ = Neh 2mc ( 1) N 2 ( ) I =1/2 I =3/2 I z =+1/2 I z = 1/2 γh H>0 2µH H=0 µh I z =+3/2 I z =+1/2 I z = 1/2 I z = 3/2 γh H>0 2µH H=0
More information空気の屈折率変調を光学的に検出する超指向性マイクロホン
23 2 1M36268 2 2 4 5 6 7 8 13 15 2 21 2 23 2 2 3 32 34 38 38 54 57 62 63 1-1 ( 1) ( 2) 1-1 a ( sinθ ) 2J D ( θ ) = 1 (1-1) kaka sinθ ( 3) 1-2 1 Back face hole Amplifier Diaphragm Equiphase wave surface
More informationNMR_wakate_ ppt
NMR 基礎講義 & 2 第 0 回若手 NMR 研究会 2009 年 9 月 4 日 ( 金 )-6 日 ( 日 ) IPC 生産性国際交流センター ( 湘南国際村 ) 大阪大学蛋白質研究所構造プロテオミクス研究系 池上貴久 化学シフトの直積演算子 (product-operator) I " I cos (#t) + I sin (#t) x x y ω : 角速度 (rad/s) z 一周の長さ
More informationMicrosoft PowerPoint - 山形大高野send ppt [互換モード]
, 2012 10 SCOPE, 2012 10 2 CDMA OFDMA OFDM SCOPE, 2012 10 OFDM 0-20 Relative Optical Power [db] -40-60 10 Gbps NRZ BPSK-SSB 36dB -80-20 -10 0 10 20 Relative Frequency [GHz] SSB SSB OFDM SSB SSB OFDM OFDM
More informationLD
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有機4-有機分析03回配布用
NMR( 核磁気共鳴 ) の基本原理核スピンと磁気モーメント有機分析化学特論 + 有機化学 4 原子核は正の電荷を持ち その回転 ( スピン ) により磁石としての性質を持つ 外部磁場によって核スピンのエネルギー準位は変わる :Zeeman 分裂 核スピンのエネルギー準位 第 3 回 (2015/04/24) m : 磁気量子数 [+I,, I ] I: スピン量子数 ( 整数 or 半整数 )]
More information研究室ガイダンス(H28)福山研.pdf
1 2 3 4 5 4 He M. Roger et al., JLTP 112, 45 (1998) A.F. Andreev and I.M. Lifshitz, Sov. Phys. JETP 29, 1107 (1969) Born in 2004 (hcp 4 He) E. Kim and M.H.W. Chan, Nature 427, 225 (2004); Science 305,
More informationBH BH BH BH Typeset by FoilTEX 2
GR BH BH 2015.10.10 BH at 2015.09.07 NICT 2015.05.26 Typeset by FoilTEX 1 BH BH BH BH Typeset by FoilTEX 2 1. BH 1.1 1 Typeset by FoilTEX 3 1.2 2 A B A B t = 0 A: m a [kg] B: m b [kg] t = t f star free
More information08 p Boltzmann I P ( ) principle of equal probability P ( ) g ( )g ( 0 ) (4 89) (4 88) eq II 0 g ( 0 ) 0 eq Taylor eq (4 90) g P ( ) g ( ) g ( 0
08 p. 8 4 k B log g() S() k B : Boltzmann T T S k B g g heat bath, thermal reservoir... 4. I II II System I System II II I I 0 + 0 const. (4 85) g( 0 ) g ( )g ( ) g ( )g ( 0 ) (4 86) g ( )g ( 0 ) 0 (4
More informationSFGÇÃÉXÉyÉNÉgÉãå`.pdf
SFG 1 SFG SFG I SFG (ω) χ SFG (ω). SFG χ χ SFG (ω) = χ NR e iϕ +. ω ω + iγ SFG φ = ±π/, χ φ = ±π 3 χ SFG χ SFG = χ NR + χ (ω ω ) + Γ + χ NR χ (ω ω ) (ω ω ) + Γ cosϕ χ NR χ Γ (ω ω ) + Γ sinϕ. 3 (θ) 180
More information( ) : 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偏極ターゲット開発の現状 @ 山形大学 Current status of development of polarized targets @Yamagata Univ. 山形大学松田洋樹 Yamagata Univ. H. MATSUDA Index 1. 偏極標的と偏極度 (Pol. Target and DoP) 2. 能動核偏極 (Dynamic Nuclear Polarization)
More information02-量子力学の復習
4/17 No. 1 4/17 No. 2 4/17 No. 3 Particle of mass m moving in a potential V(r) V(r) m i ψ t = 2 2m 2 ψ(r,t)+v(r)ψ(r,t) ψ(r,t) Wave function ψ(r,t) = ϕ(r)e iωt steady state 2 2m 2 ϕ(r)+v(r)ϕ(r) = εϕ(r)
More informationPowerPoint Presentation
2010 KEK (Japan) (Japan) (Japan) Cheoun, Myun -ki Soongsil (Korea) Ryu,, Chung-Yoe Soongsil (Korea) 1. S.Reddy, M.Prakash and J.M. Lattimer, P.R.D58 #013009 (1998) Magnetar : ~ 10 15 G ~ 10 17 19 G (?)
More information4/15 No.
4/15 No. 1 4/15 No. 4/15 No. 3 Particle of mass m moving in a potential V(r) V(r) m i ψ t = m ψ(r,t)+v(r)ψ(r,t) ψ(r,t) = ϕ(r)e iωt ψ(r,t) Wave function steady state m ϕ(r)+v(r)ϕ(r) = εϕ(r) Eigenvalue problem
More informationRIBF
MEASUREMENT OF ISOCHRONISM OF RIBF CYCLOTRONS Ryo Koyama 1, A), B), Masaki Fujimaki A), Nobuhisa Fukunishi A), Akira Goto A), Masatake Hemmi A), Masayuki Kase A), Naruhiko Sakamoto A), Tamaki Watanabe
More information第1章 微分方程式と近似解法
April 12, 2018 1 / 52 1.1 ( ) 2 / 52 1.2 1.1 1.1: 3 / 52 1.3 Poisson Poisson Poisson 1 d {2, 3} 4 / 52 1 1.3.1 1 u,b b(t,x) u(t,x) x=0 1.1: 1 a x=l 1.1 1 (0, t T ) (0, l) 1 a b : (0, t T ) (0, l) R, u
More information18 2 F 12 r 2 r 1 (3) Coulomb km Coulomb M = kg F G = ( ) ( ) ( ) 2 = [N]. Coulomb
r 1 r 2 r 1 r 2 2 Coulomb Gauss Coulomb 2.1 Coulomb 1 2 r 1 r 2 1 2 F 12 2 1 F 21 F 12 = F 21 = 1 4πε 0 1 2 r 1 r 2 2 r 1 r 2 r 1 r 2 (2.1) Coulomb ε 0 = 107 4πc 2 =8.854 187 817 10 12 C 2 N 1 m 2 (2.2)
More information磁性物理学 - 遷移金属化合物磁性のスピンゆらぎ理論
email: takahash@sci.u-hyogo.ac.jp May 14, 2009 Outline 1. 2. 3. 4. 5. 6. 2 / 262 Today s Lecture: Mode-mode Coupling Theory 100 / 262 Part I Effects of Non-linear Mode-Mode Coupling Effects of Non-linear
More informationMicrosoft PowerPoint - 島田美帆.ppt
コンパクト ERL におけるバンチ圧縮の可能性に関して 分子科学研究所,UVSOR 島田美帆日本原子力研究開発機構,JAEA 羽島良一 Outline Beam dynamics studies for the 5 GeV ERL 規格化エミッタンス 0.1 mm mrad を維持する周回部の設計 Towards user experiment at the compact ERL Short bunch
More information85 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 information1 filename=mathformula tex 1 ax 2 + bx + c = 0, x = b ± b 2 4ac, (1.1) 2a x 1 + x 2 = b a, x 1x 2 = c a, (1.2) ax 2 + 2b x + c = 0, x = b ± b 2
filename=mathformula58.tex ax + bx + c =, x = b ± b 4ac, (.) a x + x = b a, x x = c a, (.) ax + b x + c =, x = b ± b ac. a (.3). sin(a ± B) = sin A cos B ± cos A sin B, (.) cos(a ± B) = cos A cos B sin
More informationQMII_10.dvi
65 1 1.1 1.1.1 1.1 H H () = E (), (1.1) H ν () = E ν () ν (). (1.) () () = δ, (1.3) μ () ν () = δ(μ ν). (1.4) E E ν () E () H 1.1: H α(t) = c (t) () + dνc ν (t) ν (), (1.5) H () () + dν ν () ν () = 1 (1.6)
More informationuntitled
+ From Tradeoffs of Receive and Transmit Equalization Architectures, ICC006,Bryan Casper, Intel Labs Transmitter Receiver 0 magnitude (db) 0 0 30 40 50 60 0 4 frequency (GHz). Receiver Transmitter FFE
More informationJFE.dvi
,, Department of Civil Engineering, Chuo University Kasuga 1-13-27, Bunkyo-ku, Tokyo 112 8551, JAPAN E-mail : atsu1005@kc.chuo-u.ac.jp E-mail : kawa@civil.chuo-u.ac.jp SATO KOGYO CO., LTD. 12-20, Nihonbashi-Honcho
More information28 Horizontal angle correction using straight line detection in an equirectangular image
28 Horizontal angle correction using straight line detection in an equirectangular image 1170283 2017 3 1 2 i Abstract Horizontal angle correction using straight line detection in an equirectangular image
More informationLMC6082 Precision CMOS Dual Operational Amplifier (jp)
Precision CMOS Dual Operational Amplifier Literature Number: JAJS760 CMOS & CMOS LMC6062 CMOS 19911126 33020 23900 11800 ds011297 Converted to nat2000 DTD Edited for 2001 Databook SGMLFIX:PR1.doc Fixed
More information圧電型加速度センサ Piezoelectric Acceleration sensor 特長 Features 圧電素子に圧電型セラミックを用いた加速度センサは 小型堅牢 高感度で広帯域を特長としております 従って 低い周波数の振動加速度から衝突の様な高い加速度の測定まで 各分野で 幅広く使用されて
圧電型加速度センサ 小型タイプ φ3.5 5.85 2.5(H)mm 加速度 MAX100,000m/s 2 高温タイプ MAX250 小型 3 軸タイプ 8 7 5.5(H)mm Super miniature type φ3.5 5.85 2.5(H)mm 100,000m/s 2 High temperature resistance type MAX250 and Triaxial type
More information¼§À�ÍýÏÀ – Ê×ÎòÅŻҼ§À�¤È¥¹¥Ô¥ó¤æ¤é¤® - No.7, No.8, No.9
No.7, No.8, No.9 email: takahash@sci.u-hyogo.ac.jp Spring semester, 2012 Introduction (Critical Behavior) SCR ( b > 0) Arrott 2 Total Amplitude Conservation (TAC) Global Consistency (GC) TAC 2 / 25 Experimental
More information(e ) (µ ) (τ ) ( (ν e,e ) e- (ν µ,µ ) µ- (ν τ,τ ) τ- ) ( ) ( ) ( ) (SU(2) ) (W +,Z 0,W ) * 1) [ ] [ ] [ ] ν e ν µ ν τ e µ τ, e R,µ R,τ R (2.1a
1 2 2.1 (e ) (µ ) (τ ) ( (ν e,e ) e- (ν µ,µ ) µ- (ν τ,τ ) τ- ) ( ) ( ) ( ) (SU(2) ) (W +,Z 0,W ) * 1) [ ] [ ] [ ] ν e ν µ ν τ e µ τ, e R,µ R,τ R (2.1a) L ( ) ) * 2) W Z 1/2 ( - ) d u + e + ν e 1 1 0 0
More informationThe Physics of Atmospheres CAPTER :
The Physics of Atmospheres CAPTER 4 1 4 2 41 : 2 42 14 43 17 44 25 45 27 46 3 47 31 48 32 49 34 41 35 411 36 maintex 23/11/28 The Physics of Atmospheres CAPTER 4 2 4 41 : 2 1 σ 2 (21) (22) k I = I exp(
More informationCanvas-tr01(title).cv3
Working Group DaiMaJin DaiRittaikaku Multiparticle Jiki-Bunnsekiki Samurai7 Superconducting Analyser for Multi particles from RadioIsotope Beams with 7Tm of bending power (γ,n) softgdr, GDR non resonant
More informationDrift Chamber
Quench Gas Drift Chamber 23 25 1 2 5 2.1 Drift Chamber.............................................. 5 2.2.............................................. 6 2.2.1..............................................
More informationpositron 1930 Dirac 1933 Anderson m 22Na(hl=2.6years), 58Co(hl=71days), 64Cu(hl=12hour) 68Ge(hl=288days) MeV : thermalization m psec 100
positron 1930 Dirac 1933 Anderson m 22Na(hl=2.6years), 58Co(hl=71days), 64Cu(hl=12hour) 68Ge(hl=288days) 0.5 1.5MeV : thermalization 10 100 m psec 100psec nsec E total = 2mc 2 + E e + + E e Ee+ Ee-c mc
More informationi
009 I 1 8 5 i 0 1 0.1..................................... 1 0.................................................. 1 0.3................................. 0.4........................................... 3
More information75 unit: mm Fig. Structure of model three-phase stacked transformer cores (a) Alternate-lap joint (b) Step-lap joint 3 4)
3 * 35 (3), 7 Analysis of Local Magnetic Properties and Acoustic Noise in Three-Phase Stacked Transformer Core Model Masayoshi Ishida Kenichi Sadahiro Seiji Okabe 3.7 T 5 Hz..4 3 Synopsis: Methods of local
More informationkeisoku01.dvi
2.,, Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 4 Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 5 Mon, 2006, 401, SAGA, JAPAN Dept.
More information磁性物理学 - 遷移金属化合物磁性のスピンゆらぎ理論
email: takahash@sci.u-hyogo.ac.jp April 30, 2009 Outline 1. 2. 3. 4. 5. 6. 2 / 260 Today s Lecture: Itinerant Magnetism 60 / 260 Multiplets of Single Atom System HC HSO : L = i l i, S = i s i, J = L +
More informationTable. Stage model parameters. Mass of pole part m.4 kg Mass of table part M 22 kg Thrust viscous constant c x 2. 2 N s/m Twist dumping constant of jo
IIC--7 Precise Positioning Control of High-order Pitching Mode for High-Precision Stage Yushi Seki, Hiroshi Fujimoto (The University of Tokyo), Hideaki Nishino, Kazuaki Saiki (Nikon) Abstract Precision
More information2
Rb Rb Rb :10256010 2 3 1 5 1.1....................................... 5 1.2............................................. 5 1.3........................................ 6 2 7 2.1.........................................
More informationCWContinuous Wave CW 1.1.2 XCT(Computed Tomography) MRI Magnetic Resonance Imaging)PET(Positron Emission Tomography) XCT 2
1.1 1.1.1 RadarRadio Detection and Ranging 1960 1 10 1 CWContinuous Wave CW 1.1.2 XCT(Computed Tomography) MRI Magnetic Resonance Imaging)PET(Positron Emission Tomography) XCT 2 3 XCTMRI XCTMRI XCT /10
More informationII ( ) (7/31) II ( [ (3.4)] Navier Stokes [ (6/29)] Navier Stokes 3 [ (6/19)] Re
II 29 7 29-7-27 ( ) (7/31) II (http://www.damp.tottori-u.ac.jp/~ooshida/edu/fluid/) [ (3.4)] Navier Stokes [ (6/29)] Navier Stokes 3 [ (6/19)] Reynolds [ (4.6), (45.8)] [ p.186] Navier Stokes I Euler Navier
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. 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#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 informationJuly 28, H H 0 H int = H H 0 H int = H int (x)d 3 x Schrödinger Picture Ψ(t) S =e iht Ψ H O S Heisenberg Picture Ψ H O H (t) =e iht O S e i
July 8, 4. H H H int H H H int H int (x)d 3 x Schrödinger Picture Ψ(t) S e iht Ψ H O S Heisenberg Picture Ψ H O H (t) e iht O S e iht Interaction Picture Ψ(t) D e iht Ψ(t) S O D (t) e iht O S e ih t (Dirac
More informationMicrosoft Word - 信号処理3.doc
Junji OHTSUBO 2012 FFT FFT SN sin cos x v ψ(x,t) = f (x vt) (1.1) t=0 (1.1) ψ(x,t) = A 0 cos{k(x vt) + φ} = A 0 cos(kx ωt + φ) (1.2) A 0 v=ω/k φ ω k 1.3 (1.2) (1.2) (1.2) (1.1) 1.1 c c = a + ib, a = Re[c],
More informationkawa (Spin-Orbit Tomography: Kawahara and Fujii 21,Kawahara and Fujii 211,Fujii & Kawahara submitted) 2 van Cittert-Zernike Appendix A V 2
Hanbury-Brown Twiss (ver. 1.) 24 2 1 1 1 2 2 2.1 van Cittert - Zernike..................................... 2 2.2 mutual coherence................................. 3 3 Hanbury-Brown Twiss ( ) 4 3.1............................................
More informationHanbury-Brown Twiss (ver. 2.0) van Cittert - Zernike mutual coherence
Hanbury-Brown Twiss (ver. 2.) 25 4 4 1 2 2 2 2.1 van Cittert - Zernike..................................... 2 2.2 mutual coherence................................. 4 3 Hanbury-Brown Twiss ( ) 5 3.1............................................
More information9 1. (Ti:Al 2 O 3 ) (DCM) (Cr:Al 2 O 3 ) (Cr:BeAl 2 O 4 ) Ĥ0 ψ n (r) ω n Schrödinger Ĥ 0 ψ n (r) = ω n ψ n (r), (1) ω i ψ (r, t) = [Ĥ0 + Ĥint (
9 1. (Ti:Al 2 O 3 ) (DCM) (Cr:Al 2 O 3 ) (Cr:BeAl 2 O 4 ) 2. 2.1 Ĥ ψ n (r) ω n Schrödinger Ĥ ψ n (r) = ω n ψ n (r), (1) ω i ψ (r, t) = [Ĥ + Ĥint (t)] ψ (r, t), (2) Ĥ int (t) = eˆxe cos ωt ˆdE cos ωt, (3)
More information教えてください 1.5Tと3Tでは何がどう違うのか? 腹部領域
第 37 回神奈川 MRI 技術研究会 教えてください 1.5T と 3T では何がどう違うのですか? 腹部領域 東海大学医学部付属病院 梶原 直 3.0T の 1.5T と違う点 1. 化学シフト量の増大 2. 磁化率効果 3. T1 値延長 4. B 0 不均一 5. B 1 不均一 6. SAR 上昇 7. SN 比の向上 Advantage Disadvantage Disadvantage
More information09_organal2
4. (1) (a) I = 1/2 (I = 1/2) I 0 p ( ), n () I = 0 (p + n) I = (1/2, 3/2, 5/2 ) p ( ), n () I = (1, 2, 3 ) (b) (m) (I = 1/2) m = +1/2, 1/2 (I = 1/2) m = +1/2, 1/2 I m = +I, +(I 1), +(I 2) (I 1), I ( )
More information最新耐震構造解析 ( 第 3 版 ) 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, 第 3 版 1 刷発行時のものです.
最新耐震構造解析 ( 第 3 版 ) 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. http://www.morikita.co.jp/books/mid/052093 このサンプルページの内容は, 第 3 版 1 刷発行時のものです. i 3 10 3 2000 2007 26 8 2 SI SI 20 1996 2000 SI 15 3 ii 1 56 6
More informationKamLAND (µ) ν e RSFP + ν e RSFP(Resonant Spin Flavor Precession) ν e RSFP 1. ν e ν µ ν e RSFP.ν e νµ ν e νe µ KamLAND νe KamLAND (ʼ4). kton-day 8.3 < E ν < 14.8 MeV candidates Φ(νe) < 37 cm - s -1 P(νe
More informationuntitled
4/6 S. Hara@ [.ppt] On Road 4/9 4/6 4/ 5/7 4 Scott 5/4 5 Off Road 5/ 5/8 6 7 S. Hara@ [.ppt] ... 4. [] S. Hara@ [.ppt] : 4 ε s ε a ε b Anti-bonding orbital bonding orbital Anion Cation ε c ε a ε a ε b
More informationmain.dvi
6 FIR FIR FIR FIR 6.1 FIR 6.1.1 H(e jω ) H(e jω )= H(e jω ) e jθ(ω) = H(e jω ) (cos θ(ω)+jsin θ(ω)) (6.1) H(e jω ) θ(ω) θ(ω) = KωT, K > 0 (6.2) 6.1.2 6.1 6.1 FIR 123 6.1 H(e jω 1, ω
More informationLCR 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 informationc 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, vol.43, no.2, pp.71 77, Simultaneous Measurement of Film Thickness and Surface Profile of Film-Covered Objects by Using White-Light Interfer
, vol.43, no.2, pp.71 77, 2007. 1 Simultaneous Measurement of Film Thickness and Surface Profile of Film-Covered Objects by Using White-Light Interferometry 1 2 3 1 3 1 ( ) 1-1-45 2 ( ) 1 3 2-12-1 sugi@cs.titech.ac.jp
More informationII 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 informationUSB
2 2018 3 9 icrr granite yuzuru930sakai(at)gmail.com 1 http://granite.phys.s.u-tokyo.ac.jp/sakai/masterthesis.pdf http://granite.phys.s.u-tokyo.ac.jp/sakai/masterthesis0.pdf 2017 Lorentz http://granite.phys.s.u-tokyo.ac.jp/sakai/2017-03
More informationMicrosoft PowerPoint - okamura.ppt[読み取り専用]
TKK の物理的可能性 an extension of the TK neutrino oscillation experiment with a far detector in Korea 岡村直利 ( 京大 基研 ) 関西セミナーハウス (007/03/7( 007/03/7) based on hep-ph/050406 [Phys.Lett.B637,66 (006)] hep-ph/060755
More informationJIS 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 informationnakajima_
SK-Gd (ICRR) 30 2018 12 21 SK-Gd SK!2 !3 ls of SK Solar ν measurement rvation of day-night asymmetry far, B8, 2.5σ indication Hep reported at NEUTRINO2014) nalizing all SK-IV data very of the transition
More information1. z dr er r sinθ dϕ eϕ r dθ eθ dr θ dr dθ r x 0 ϕ r sinθ dϕ r sinθ dϕ y dr dr er r dθ eθ r sinθ dϕ eϕ 2. (r, θ, φ) 2 dr 1 h r dr 1 e r h θ dθ 1 e θ h
IB IIA 1 1 r, θ, φ 1 (r, θ, φ)., r, θ, φ 0 r
More information6 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 informationMEG μ + e + γ ( ) ( MEGA) = (BSM) MEG μ + e + γ ( : a few ) 180 γ μ + e +
MEG ( ) 2011 9 10 MEG μ + e + γ ( ) (1.2 10-11 MEGA) = (BSM) MEG μ + e + γ ( : a few 10-13 ) 180 γ μ + e + μ eγ @MEG DC μ + (590MeV 1.3MW @ ) γ: e + : MEG (900L) (VUV) 846 PMT : PMT : PMT PMT (DRS4) particle
More informationB 1 B.1.......................... 1 B.1.1................. 1 B.1.2................. 2 B.2........................... 5 B.2.1.......................... 5 B.2.2.................. 6 B.2.3..................
More informationcm λ λ = h/p p ( ) λ = cm E pc [ev] 2.2 quark lepton u d c s t b e 1 3e electric charge e color charge red blue green qq
2007 2007 7 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 1 2007 2 4 5 6 6 2 2.1 1: KEK Web page 1 1 1 10 16 cm λ λ = h/p p ( ) λ = 10 16 cm E pc [ev] 2.2 quark lepton 2 2.2.1 u d c s t b + 2 3 e 1 3e electric charge
More information1 1 1 1-1 1 1-9 1-3 1-1 13-17 -3 6-4 6 3 3-1 35 3-37 3-3 38 4 4-1 39 4- Fe C TEM 41 4-3 C TEM 44 4-4 Fe TEM 46 4-5 5 4-6 5 5 51 6 5 1 1-1 1991 1,1 multiwall nanotube 1993 singlewall nanotube ( 1,) sp 7.4eV
More informationN 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