Hadronic Tau Decays at BaBar
|
|
- Οινώνη Μεσσηνέζης
- 5 χρόνια πριν
- Προβολές:
Transcript
1 Hadronic Tau Decays at BaBar Swagato Banerjee Joint Meeting of Pacific Region Particle Physics Communities (DPF006+JPS006 Honolulu, Hawaii 9 October - 3 November 006 (Page: 1
2 Hadronic τ decays Only lepton that decays into hadrons Hadronic Branching Fraction 65% Initial state represents perfect QCD vacuum τ h ν τ probes hadronic V A current: h d θ γ µ (1 γ 5 u 0, where d θ = cos θ C d + sin θ C s Cabibbo allowed and suppressed decays Ideal for measurements of fundamental quantities like V us, m s, α s Several resonance (sub-structure waiting to be observed Hadronic τ (Page:
3 Strange Spectral Function Inclusive study of strange spectral functions from final states with net strangeness of unity world s best measurement of V us, m s Branching Fractions ( 10 3 [PDG 005] Preliminary B(τ K π 0 ν τ and B(τ K π π + ν τ reported with better precision than the world average (TAU06, Pisa Hadronic τ (Page: 3
4 τ -factory PEP-II B-factory: also a τ-factory At Υ (4S: s = GeV σ(e + e BB = 1.05 nb σ(e + e τ + τ = 0.89 nb Experiment # of τ-pairs LEP CLEO Hadronic τ (Page: 4
5 The Detector Excellent K/π separation dedx Cherenkov angle Hadronic τ (Page: 5
6 Recent Results from Runs 1-4 Data (L 30 fb 1 τ π π } π {{ + π } 0 ω τ π π π + η }{{} f 1 (185 τ K }{{ π } 0 ν τ K (89 ν τ ν τ Most analyses use leptonic tag Runs 1-5 Data (L 340 fb 1 τ π π π + ν τ τ K π π + ν τ τ π K } {{ K + } φ τ K K } {{ K + } φ ν τ ν τ Hadronic τ (Page: 6
7 τ π π π + π 0 ν τ 411K e-tagged events Background: 10% (τ + τ events with extra π 0 (Preliminary: B(τ π π π + π 0 ν τ = (4.39 ± 0.01 ± PDG (Aleph, CLEO: (4.46 ± Entries π π π + π m(4π (GeV/c Fit Breit-Wigner convoluted with 5000 Gaussian (resolution: 6.1 MeV π π + π 0 plus polynomial background 0000 ( 6% from τ + τ with extra π Preliminary: B(τ π ων τ = 5000 (1.97 ± 0.01 ± Aleph: (1.91 ± 0.07 ± m(3π (GeV/c Events / ( GeV/c Hadronic τ (Page: 7
8 τ π π π + ην τ Fit with Novosibirsk function: (160 ± 56 η candidates qq Background: (54 ± 16 (Preliminary: B(τ π π π + ην τ = (1.84 ± 0.09 ± PDG : (.3 ± Mass (GeV/c Events/0.003 GeV/c γ γ Fit Breit-Wigner convoluted with Gaussian (resolution: 7 MeV (951 ± 78 f 1 (185 candidates (Preliminary: B(τ π f 1 ν τ = (3.83 ± 0.3 ± 0.0 ± : (4.6 ± 1. ± using f 1 (185 π π π + π + decays Events/0.005 GeV/c π π + η Mass (GeV/c Hadronic τ (Page: 8
9 Resonant Contributions Ratio of Branching Fractions ( Preliminary: R ( τ π ω π π π + π 0 ν τ τ π π π + π 0 ν τ = ± 0.00 ± R ( τ π f 1 π π π + ην τ τ π π π + ην τ = 0.73 ± 0.01 ± 0.04 τ π π π + ην }{{} τ decays η Suppressed by G-parity ( nd Class Current Expected at the level of isospin breaking m u m d We fit the region around η (958 and find no signal (Preliminary: B(τ π η ν τ < % C.L. CLEO: Upper Limit = % C.L. Hadronic τ (Page: 9
10 τ K π 0 ν τ 78K e/µ-tagged events: τ + τ mostly; qq, µ + µ small Background sources: K/π mis-id, π 0 reconstruction in-efficiency ALEPH (5.±0.04± CLEO (5.1±0.10± ALEPH ( (4.44±0.06± OPAL ( (4.71±0.059± BaBar Preliminary (4.39±0.003± PDG Fit (4.5± BR (% Hadronic τ (Page: 10
11 τ π π π + ν τ 1.6M e/µ-tagged events: τ + τ mostly (extra π 0 ; qq < 0.1% Particle-ID component of efficiency migration matrix: π π π + K π π + K π K + K K K %.8% 4.8% 1.0% Events/(0MeV/c CLEO III (9.13±0.05± M (GeV/c BaBar Preliminary - (9.11±0.01± PDG Fit (9.0± BR (% Hadronic τ (Page: 11
12 τ K π π + ν τ 69K e/µ-tagged events: non-cross-feed background small Particle-ID component of efficiency migration matrix: π π π + K π π + K π K + K K K + 1.4% 74.7% 16.3% 6.5% 8 Events/(0MeV/c OPAL ( (3.60±0.08± ALEPH (.14±0.037± CLEO (3.46±0.03± CLEO (3.84±0.14± OPAL ( (4.15±0.53± BaBar Preliminary (.88±0.0± PDG Fit (3.33± M (GeV/c BR (% Hadronic τ (Page: 1
13 τ K π K + ν τ 18K e/µ-tagged events: non-cross-feed background negligible Particle-ID component of efficiency migration matrix: π π π + K π π + K π K + K K K + 0.5% 60.1% 5.8% Events/(0MeV/c M (GeV/c ALEPH (1.63±0.1± CLEO (1.45±0.13± OPAL ( (0.87±0.56± CLEO III (1.55±0.06± BaBar Preliminary (1.373±0.011± PDG Fit (1.53± BR (% Hadronic τ (Page: 13
14 τ K K K + ν τ (75 ± 17 e/µ-tagged events: non-cross-feed background < 1% Particle-ID component of efficiency migration matrix: π π π + K π π + K π K + K K K + 0.3% 50.7% Events/(5MeV/c CLEO III -5 <3.7 90%CL M (GeV/c 1 BaBar Preliminary -5 (1.59±0.14± BR (% Hadronic τ (Page: 14
15 New decay modes via φ resonance Events/(5MeV/c φ Entries/(5MeV/c φ (GeV/c M K + - K (GeV/c M K + - K FIRST MEASUREMENTS of π φ and inclusive K K K + states: B(τ π φν τ = (3.49 ± 0.55 ± (Significance: 5.5σ B(τ K φν τ = (3.48 ± 0.0 ± (Significance: 10.6σ τ K φν τ consistent with saturating τ K K K + ν τ channel Consistent with Belle: B(τ K φν τ = (4.06 ± 0.5 ± Hadronic τ (Page: 15
16 Conclusions B-Factories are also τ-factories On-going efforts to better understand systematic errors π 0, η reconstruction efficiency uncertainty in production cross-section σ e+ e τ + τ % dataset expected to be doubled by 008 Expect lots of more τ-physics in near future: High precision tests of QCD Measurements of fundamental quantities: V us, m s, α s Resonance sub-structure of hadronic final states Search for second class currents Search for violation of charge-parity symmetry in τ decays Hadronic τ (Page: 16
Dong Liu State Key Laboratory of Particle Detection and Electronics University of Science and Technology of China
Dong Liu State Key Laboratory of Particle Detection and Electronics University of Science and Technology of China ISSP, Erice, 7 Outline Introduction of BESIII experiment Motivation of the study Data sample
Διαβάστε περισσότεραEPS On Behalf of Belle Collaboration. Takayoshi Ohshima Nagoya University, Japan
1 τ-decays at Belle On Behalf of Belle Collaboration Takayoshi Ohshima Nagoya University, Japan KEKB/ Belle PEP-II/ BaBar 1. τ K s π ν τ study Branching ratio Mass spectrum (vector & scalar FF; mass &
Διαβάστε περισσότεραPrecise measurement of hadronic tau-decays
Precise measurement of hadronic tau-decays with eta mesons at Belle 2008.9.23 Tau08 Yoko Usuki Nagoya Univ. K. Inami and Belle collaboration Belle 1 Introduction Belle detector has collected the τ-pair
Διαβάστε περισσότεραΥπολογιστική Φυσική Στοιχειωδών Σωματιδίων
Υπολογιστική Φυσική Στοιχειωδών Σωματιδίων 4ο Εξάμηνο2004-2005 Διακριτική ικανότητα ανιχνευτή-υπόβαθρο- Υπολογισμός του σήματος Διδάσκοντες : Χαρά Πετρίδου Δημήτριος Σαμψωνίδης 18/4/2005 Υπολογ.Φυσική
Διαβάστε περισσότεραLIGHT UNFLAVORED MESONS (S = C = B = 0)
LIGHT UNFLAVORED MESONS (S = C = B = 0) For I = 1 (π, b, ρ, a): ud, (uu dd)/ 2, du; for I = 0 (η, η, h, h, ω, φ, f, f ): c 1 (uu + d d) + c 2 (s s) π ± I G (J P ) = 1 (0 ) Mass m = 139.57018 ± 0.00035
Διαβάστε περισσότεραBaryon Studies. Dongliang Zhang (University of Michigan) Hadron2015, Jefferson Lab September 13-18, on behalf of ATLAS Collaboration
Λ b Baryon Studies Dongliang Zhang (University of Michigan) on behalf of Collaboration Hadron215, Jefferson Lab September 13-18, 215 Introduction Λ b reconstruction Lifetime measurement Helicity study
Διαβάστε περισσότεραStudy of CP Violation at BABAR
Study of CP Violation at BABAR Roland Waldi, Univ. Rostock Introduction Direct CP Violation in B Decay The Easy Part: β Additional Information: β and α Summary and Outlook März 25 CP Violation = asymmetry
Διαβάστε περισσότεραˆ ˆŠ Œ ˆ ˆ Œ ƒ Ÿ Ä664
ˆ ˆŠ Œ ˆ ˆ Œ ƒ Ÿ 2017.. 48.. 5.. 653Ä664 ˆ Œ ˆ ˆ e + e K + K nπ (n =1, 2, 3) Š Œ ŠŒ -3 Š - ˆ Œ Š -2000 ƒ.. μéμ Î 1,2, μé ³ ±μ²² μ Í ŠŒ -3: A.. ß ±μ 1,2,. Œ. ʲÓÎ ±μ 1,2,.. ̳ ÉÏ 1,2,.. μ 1,.. ÏÉμ μ 1,.
Διαβάστε περισσότεραLight Hadrons and New Enhancements in J/ψ Decays at BESII
Light Hadrons and New Enhancements in J/ψ Decays at BESII Guofa XU Representing BES Collaboration Institute of High Energy Physics Chinese Academy of Sciences Beijing, China xugf@ihep.ac.cn Outline Introduction
Διαβάστε περισσότεραLEPTONS. Mass m = ( ± ) 10 6 u Mass m = ± MeV me + m e
LEPTONS e J = 1 2 Mass m = (548.5799110 ± 0.0000012) 10 6 u Mass m = 0.510998902 ± 0.000000021 MeV me + m e /m < 8 10 9, CL = 90% qe + + q / e e < 4 10 8 Magnetic moment µ =1.001159652187 ± 0.000000000004
Διαβάστε περισσότεραmeasured by ALICE in pp, p-pb and Pb-Pb collisions at the LHC
Σ(85) Ξ(5) Production of and measured by ALICE in pp, ppb and PbPb collisions at the LHC for the ALICE Collaboration Pusan National University, OREA Quark Matter 7 in Chicago 7.. QM7 * suppressed, no suppression
Διαβάστε περισσότεραSecond Order RLC Filters
ECEN 60 Circuits/Electronics Spring 007-0-07 P. Mathys Second Order RLC Filters RLC Lowpass Filter A passive RLC lowpass filter (LPF) circuit is shown in the following schematic. R L C v O (t) Using phasor
Διαβάστε περισσότεραe + e - physics in the tau charm energy region Part I Frederick A. Harris University of Hawaii Jan. 5, 2005
e + e - physics in the tau charm energy region Part I Frederick A. Harris University of Hawaii Jan. 5, 2005 OUTLINE Introduction Oldies but goodies τ mass measurement and R scan ψ(2s) scan and radiative
Διαβάστε περισσότεραThree coupled amplitudes for the πη, K K and πη channels without data
Three coupled amplitudes for the πη, K K and πη channels without data Robert Kamiński IFJ PAN, Kraków and Łukasz Bibrzycki Pedagogical University, Kraków HaSpect meeting, Kraków, V/VI 216 Present status
Διαβάστε περισσότεραPredictions on the second-class currents
Predictions on the second-class currents τ η ( ) ν τ decays Sergi Gonzàlez-Solís Institut de Física d Altes Energies Universitat Autònoma de Barcelona in collaboration with Rafel Escribano and Pablo Roig,
Διαβάστε περισσότερα0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Value of csv bjet tag Entries 8 6 4 8 6 4 69.8 events (MC) 8 events () 9.4 fb -...3.4.5.6.7.8.9 7 /MC.5.5...3.4.5.6.7.8.9 R between reco W lepton and closest gen lepton 3 54.8 events (MC) - 9.4 fb 8 -..4.6.8...4
Διαβάστε περισσότεραPaul Bloom*, Phil Clark, Wolfgang Gradl and Alan Robertson. pclark. *Swarthmore College University of Edinburgh I V
Rare B decays B η K & B η ρ Paul Bloom*, Phil Clark, Wolfgang Gradl and Alan Robertson http://www.ph.ed.ac.uk/ pclark *Swarthmore College University of Edinburgh E U N I V E R S I T Y T H O H F E D I N
Διαβάστε περισσότεραΣύντομο Βιογραφικό Σημείωμα
Σύντομο Βιογραφικό Σημείωμα Πίνακας επιλεγμένων βιογραφικών στοιχείων Όνομα Θέση στο Έργο Θέση στο Ίδρυμα Προπτυχιακοί τίτλοι σπουδών Μεταπτυχιακοί τίτλοι σπουδών Ειδικές γνώσεις στο γνωστικό αντικείμενο
Διαβάστε περισσότεραTh, Ra, Rn, Po, Pb, Bi, & Tl K x-rays. Rn Kα1. Rn Kα2. 93( 227 Th)/Rn Kβ3. Ra Kα2. Po Kα2 /Bi K α1 79( 227 Th)/Po Kα1. Ra Kα1 /Bi K β1.
Page -1-10 8 10 7 10 6 10 5 10 4 334 ( Th) Counts/Channel 10 3 10 2 10 1 49 ( Th)/ 50 ( Th)/ 50 ( Fr) 0 100 200 300 400 500 600 700 800 900 1000 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 Channel
Διαβάστε περισσότεραPHOS π 0 analysis, for production, R AA, and Flow analysis, LHC11h
PHOS π, ask PHOS π analysis, for production, R AA, and Flow analysis, Henrik Qvigstad henrik.qvigstad@fys.uio.no University of Oslo --5 PHOS π, ask ask he task we use, AliaskPiFlow was written prior, for
Διαβάστε περισσότεραCharmonium experimental overview
Charmonium experimental overview Stephen Lars Olsen Seoul National University Topical Seminar on Frontier of Particle Physics Hu Yu Village, Beijing CHINA August 27-28, 2010 outline Lecture1: History &
Διαβάστε περισσότεραSection 8.3 Trigonometric Equations
99 Section 8. Trigonometric Equations Objective 1: Solve Equations Involving One Trigonometric Function. In this section and the next, we will exple how to solving equations involving trigonometric functions.
Διαβάστε περισσότεραTest Beam Analysis of Czochralski Silicon Strip Detector. John Kennedy, Alison Bates, Chris Parkes, Paula Collins, Juan Palacios & Doris Eckstein
Test Beam Analysis of Czochralski Silicon Strip Detector John Kennedy, Alison Bates, Chris Parkes, Paula Collins, Juan Palacios & Doris Eckstein Overview LHCb Detector and Motivation Radiation Hard Material?
Διαβάστε περισσότεραCE 530 Molecular Simulation
C 53 olecular Siulation Lecture Histogra Reweighting ethods David. Kofke Departent of Cheical ngineering SUNY uffalo kofke@eng.buffalo.edu Histogra Reweighting ethod to cobine results taken at different
Διαβάστε περισσότεραSection 7.6 Double and Half Angle Formulas
09 Section 7. Double and Half Angle Fmulas To derive the double-angles fmulas, we will use the sum of two angles fmulas that we developed in the last section. We will let α θ and β θ: cos(θ) cos(θ + θ)
Διαβάστε περισσότεραΦυσική Στοιχειωδών Σωματιδίων ΙΙ (8ου εξαμήνου) Μάθημα 5: Σκέδαση αδρονίων και χρυσός κανόνας του Fermi. Λέκτορας Κώστας Κορδάς
Φυσική Στοιχειωδών Σωματιδίων ΙΙ (8ου εξαμήνου) Μάθημα 5: Σκέδαση αδρονίων και χρυσός κανόνας του Fermi Λέκτορας Κώστας Κορδάς Αριστοτέλειο Πανεπιστήμ ιο Θεσσαλονίκης Στοιχειώδη ΙΙ, Αριστοτέλειο Παν. Θ/νίκης,
Διαβάστε περισσότεραExercises 10. Find a fundamental matrix of the given system of equations. Also find the fundamental matrix Φ(t) satisfying Φ(0) = I. 1.
Exercises 0 More exercises are available in Elementary Differential Equations. If you have a problem to solve any of them, feel free to come to office hour. Problem Find a fundamental matrix of the given
Διαβάστε περισσότεραΕΙΣΑΓΩΓΗ ΣΤΗ ΣΤΑΤΙΣΤΙΚΗ ΑΝΑΛΥΣΗ
ΕΙΣΑΓΩΓΗ ΣΤΗ ΣΤΑΤΙΣΤΙΚΗ ΑΝΑΛΥΣΗ ΕΛΕΝΑ ΦΛΟΚΑ Επίκουρος Καθηγήτρια Τµήµα Φυσικής, Τοµέας Φυσικής Περιβάλλοντος- Μετεωρολογίας ΓΕΝΙΚΟΙ ΟΡΙΣΜΟΙ Πληθυσµός Σύνολο ατόµων ή αντικειµένων στα οποία αναφέρονται
Διαβάστε περισσότεραBelle Hawaii activities in Belle New particles in BES & Belle
Belle Hawaii activities in Belle New particles in BES & Belle S. L. Olsen Belle highlights 2002-03 1 st measurement of φ 2 from B!π + π 1 st observation of B!K*l + l Discovery of a new charmonium state
Διαβάστε περισσότεραSolar Neutrinos: Fluxes
Solar Neutrinos: Fluxes pp chain Sun shines by : 4 p 4 He + e + + ν e + γ Solar Standard Model Fluxes CNO cycle e + N 13 =0.707MeV He 4 C 1 C 13 p p p p N 15 N 14 He 4 O 15 O 16 e + =0.997MeV O17
Διαβάστε περισσότεραSolutions to Exercise Sheet 5
Solutions to Eercise Sheet 5 jacques@ucsd.edu. Let X and Y be random variables with joint pdf f(, y) = 3y( + y) where and y. Determine each of the following probabilities. Solutions. a. P (X ). b. P (X
Διαβάστε περισσότεραCONSULTING Engineering Calculation Sheet
E N G I N E E R S Consulting Engineers jxxx 1 Structure Design - EQ Load Definition and EQ Effects v20 EQ Response Spectra in Direction X, Y, Z X-Dir Y-Dir Z-Dir Fundamental period of building, T 1 5.00
Διαβάστε περισσότεραDerivation of Optical-Bloch Equations
Appendix C Derivation of Optical-Bloch Equations In this appendix the optical-bloch equations that give the populations and coherences for an idealized three-level Λ system, Fig. 3. on page 47, will be
Διαβάστε περισσότεραÓ³ Ÿ , º 6(148).. 865Ä873. Ñ Ò É ÉÊÉ Ö ÒÌ ² μ, Ê É É, μ Ö
Ó³ Ÿ. 2008.. 5, º 6(148).. 865Ä873 ˆ ˆŠ Œ ˆ ˆ Œ ƒ Ÿ. Š ˆŒ Œ ˆ ˆ Š - ˆ - LHC.. ³μ,.. μ μö,.. Ö±μ,.. Ê ±μ Î Ñ Ò É ÉÊÉ Ö ÒÌ ² μ, Ê É É, μ Ö ³μÉ μ ³μ μ ÉÓ μ Ê Ö Éμ - É Éμ - μ μ ³ ³ 700, 1000, 1500, 2000 3000
Διαβάστε περισσότεραTMA4115 Matematikk 3
TMA4115 Matematikk 3 Andrew Stacey Norges Teknisk-Naturvitenskapelige Universitet Trondheim Spring 2010 Lecture 12: Mathematics Marvellous Matrices Andrew Stacey Norges Teknisk-Naturvitenskapelige Universitet
Διαβάστε περισσότερα상대론적고에너지중이온충돌에서 제트입자와관련된제동복사 박가영 인하대학교 윤진희교수님, 권민정교수님
상대론적고에너지중이온충돌에서 제트입자와관련된제동복사 박가영 인하대학교 윤진희교수님, 권민정교수님 Motivation Bremsstrahlung is a major rocess losing energies while jet articles get through the medium. BUT it should be quite different from low energy
Διαβάστε περισσότεραFundamental Physical Constants Extensive Listing Relative std. Quantity Symbol Value Unit uncert. u r
UNIVERSAL speed of light in vacuum c, c 0 299 792 458 m s 1 exact magnetic constant µ 0 4π 10 7 N A 2 = 12.566 370 614... 10 7 N A 2 exact electric constant 1/µ 0 c 2 ɛ 0 8.854 187 817... 10 12 F m 1 exact
Διαβάστε περισσότεραInformation*Loss*and* Entanglement*in* Quantum*Theory* Jürg%Fröhlich% ETH%Zurich%&%IHES%
Information*Loss*and* Entanglement*in* Quantum*Theory* Jürg%Fröhlich% ETH%Zurich%&%IHES% Some-basic-claims-to-be-justi>ied,-afterwards)- 1. The%quantum'mechanical-state-the% wave%function )%does% not-have%an%
Διαβάστε περισσότεραKaon physics at KLOE. M.Palutan. Frascati for the KLOE collaboration Moriond-EW 2006
Kaon physics at KLOE M.Palutan Palutan,, INFN/Frascati Frascati for the KLOE collaboration Moriond-EW 2006 1 The DAΦNE e + e collider Collisions at c.m. energy around the φ mass: s ~ 1019.4 MeV Angle between
Διαβάστε περισσότεραL. F avart. CLAS12 Workshop Genova th of Feb CLAS12 workshop Feb L.Favart p.1/28
L. F avart I.I.H.E. Université Libre de Bruxelles H Collaboration HERA at DESY CLAS Workshop Genova - 4-8 th of Feb. 9 CLAS workshop Feb. 9 - L.Favart p./8 e p Integrated luminosity 96- + 3-7 (high energy)
Διαβάστε περισσότεραb. Use the parametrization from (a) to compute the area of S a as S a ds. Be sure to substitute for ds!
MTH U341 urface Integrals, tokes theorem, the divergence theorem To be turned in Wed., Dec. 1. 1. Let be the sphere of radius a, x 2 + y 2 + z 2 a 2. a. Use spherical coordinates (with ρ a) to parametrize.
Διαβάστε περισσότερα3.4 SUM AND DIFFERENCE FORMULAS. NOTE: cos(α+β) cos α + cos β cos(α-β) cos α -cos β
3.4 SUM AND DIFFERENCE FORMULAS Page Theorem cos(αβ cos α cos β -sin α cos(α-β cos α cos β sin α NOTE: cos(αβ cos α cos β cos(α-β cos α -cos β Proof of cos(α-β cos α cos β sin α Let s use a unit circle
Διαβάστε περισσότεραAssalamu `alaikum wr. wb.
LUMP SUM Assalamu `alaikum wr. wb. LUMP SUM Wassalamu alaikum wr. wb. Assalamu `alaikum wr. wb. LUMP SUM Wassalamu alaikum wr. wb. LUMP SUM Lump sum lump sum lump sum. lump sum fixed price lump sum lump
Διαβάστε περισσότεραΕΘΝΙΚΟ ΜΕΤΣΟΒΙΟ ΠΟΛΥΤΕΧΝΕΙΟ
ΕΘΝΙΚΟ ΜΕΤΣΟΒΙΟ ΠΟΛΥΤΕΧΝΕΙΟ ΣΧΟΛΗ ΑΓΡΟΝΟΜΩΝ ΚΑΙ ΤΟΠΟΓΡΑΦΩΝ ΜΗΧΑΝΙΚΩΝ ΤΟΜΕΑΣ ΓΕΩΓΡΑΦΙΑΣ ΚΑΙ ΠΕΡΙΦΕΡΕΙΑΚΟΥ ΣΧΕ ΙΑΣΜΟΥ, ΠΕΡΙΟΧΗ ΟΙΚΙΣΤΙΚΩΝ ΚΑΙ ΠΟΛΕΟ ΟΜΙΚΩΝ ΘΕΜΑΤΩΝ ΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ: ΠΟΛΕΟ ΟΜΙΚΕΣ ΚΑΙ ΚΥΚΛΟΦΟΡΙΑΚΕΣ
Διαβάστε περισσότεραΑΝΙΧΝΕΥΣΗ ΓΕΓΟΝΟΤΩΝ ΒΗΜΑΤΙΣΜΟΥ ΜΕ ΧΡΗΣΗ ΕΠΙΤΑΧΥΝΣΙΟΜΕΤΡΩΝ ΔΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ
ΕΘΝΙΚΟ ΜΕΤΣΟΒΙΟ ΠΟΛΥΤΕΧΝΕΙΟ ΣΧΟΛΗ ΗΛΕΚΤΡΟΛΟΓΩΝ ΜΗΧΑΝΙΚΩΝ ΚΑΙ ΜΗΧΑΝΙΚΩΝ ΥΠΟΛΟΓΙΣΤΩΝ ΤΟΜΕΑΣ ΕΠΙΚΟΙΝΩΝΙΩΝ ΗΛΕΚΤΡΟΝΙΚΗΣ ΚΑΙ ΣΥΣΤΗΜΑΤΩΝ ΠΛΗΡΟΦΟΡΙΚΗΣ ΑΝΙΧΝΕΥΣΗ ΓΕΓΟΝΟΤΩΝ ΒΗΜΑΤΙΣΜΟΥ ΜΕ ΧΡΗΣΗ ΕΠΙΤΑΧΥΝΣΙΟΜΕΤΡΩΝ
Διαβάστε περισσότεραJesse Maassen and Mark Lundstrom Purdue University November 25, 2013
Notes on Average Scattering imes and Hall Factors Jesse Maassen and Mar Lundstrom Purdue University November 5, 13 I. Introduction 1 II. Solution of the BE 1 III. Exercises: Woring out average scattering
Διαβάστε περισσότεραA Finite Precision of Private Information Precision of Private Information Approaching Infinity 0 θ1 * θ Session Cost of Action A First 20 Last 20 Rounds Rounds Information in Stage 2 First 20 Last
Διαβάστε περισσότεραBayesian statistics. DS GA 1002 Probability and Statistics for Data Science.
Bayesian statistics DS GA 1002 Probability and Statistics for Data Science http://www.cims.nyu.edu/~cfgranda/pages/dsga1002_fall17 Carlos Fernandez-Granda Frequentist vs Bayesian statistics In frequentist
Διαβάστε περισσότεραFundamental Physical Constants Extensive Listing Relative std. Quantity Symbol Value Unit uncert. u r
UNIVERSAL speed of light in vacuum c, c 0 299 792 458 m s 1 exact magnetic constant µ 0 4π 10 7 N A 2 = 12.566 370 614... 10 7 N A 2 exact electric constant 1/µ 0 c 2 ɛ 0 8.854 187 817... 10 12 F m 1 exact
Διαβάστε περισσότεραΦυσική Στοιχειωδών Σωματιδίων ΙΙ (8ου εξαμήνου) Μάθημα 3β: Σκέδαση αδρονίων και χρυσός κανόνας του Fermi
Φυσική Στοιχειωδών Σωματιδίων ΙΙ (8ου εξαμήνου) Μάθημα 3β: Σκέδαση αδρονίων και χρυσός κανόνας του Fermi Λέκτορας Κώστας Κορδάς Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης Στοιχειώδη ΙΙ, Αριστοτέλειο Παν. Θ/νίκης,
Διαβάστε περισσότεραPolarizations of B V V in QCD factorization
Polarizations of B V V in QCD factorization Based on collaborations with M.Beneke and J.Rohrer April 2008 1 Motivation B V V decays share the roles of B PP, PV decays in the determination of CKM matrix
Διαβάστε περισσότερα2-2 -1-1 Flux x E ν ( m sec sr GeV ) 1 3 1 2 Honda BGS νµ + νµ νe + νe 1 1 1-2 1-1 1 1 1 Neutrino Energy (GeV) 2.5 Honda ν µ + ν µ ν + e ν e 2.5 BGS ν µ + ν µ ν + e ν e 2. 2. Flux Ratios 1.5 ν e 1.5 ν
Διαβάστε περισσότεραΑναζητώντας παράξενα σωµατίδια στο ALICE
Αναζητώντας παράξενα σωµατίδια στο ALICE K 0 s π+ π - Λ π - p Ξ - π - Λ π - p π - 7.7.018 Δέσποινα Χατζηφωτιάδου 1 παράξενα σωµατίδια µεσόνιο βαριόνιο s K 0 s ds, ds Λ uds αδρόνια που περιέχουν τουλάχιστον
Διαβάστε περισσότεραMath 6 SL Probability Distributions Practice Test Mark Scheme
Math 6 SL Probability Distributions Practice Test Mark Scheme. (a) Note: Award A for vertical line to right of mean, A for shading to right of their vertical line. AA N (b) evidence of recognizing symmetry
Διαβάστε περισσότεραIsospin breaking effects in B ππ, ρρ, ρπ
Isospin breaking effects in B ππ, ρρ, ρπ Jure Zupan Carnegie Mellon University based on M. Gronau, J.Z., hep-ph/0502139 J. Zupan Isospin breaking effects in B ππ,ρρ,ρπ CKM2005 p. 1 Outline Effect of isospin
Διαβάστε περισσότεραCHAPTER 25 SOLVING EQUATIONS BY ITERATIVE METHODS
CHAPTER 5 SOLVING EQUATIONS BY ITERATIVE METHODS EXERCISE 104 Page 8 1. Find the positive root of the equation x + 3x 5 = 0, correct to 3 significant figures, using the method of bisection. Let f(x) =
Διαβάστε περισσότεραthe total number of electrons passing through the lamp.
1. A 12 V 36 W lamp is lit to normal brightness using a 12 V car battery of negligible internal resistance. The lamp is switched on for one hour (3600 s). For the time of 1 hour, calculate (i) the energy
Διαβάστε περισσότεραResurvey of Possible Seismic Fissures in the Old-Edo River in Tokyo
Bull. Earthq. Res. Inst. Univ. Tokyo Vol. 2.,**3 pp.,,3,.* * +, -. +, -. Resurvey of Possible Seismic Fissures in the Old-Edo River in Tokyo Kunihiko Shimazaki *, Tsuyoshi Haraguchi, Takeo Ishibe +, -.
Διαβάστε περισσότεραˆŒˆ ˆŸ ˆ Œ ƒ LEPTO/JETSET Ÿ ˆ ƒ
Ó³ Ÿ. 2014.. 11, º 4(188).. 817Ä827 Š Œ œ ƒˆˆ ˆ ˆŠ ˆŒˆ ˆŸ ˆ Œ ƒ LEPTO/JETSET Ÿ ˆ ƒ Ÿ.. ² ± Ì,. Œ. ŠÊ Íμ,.. μ ± Ö 1, Œ. ƒ. μ ±μ Ñ Ò É ÉÊÉ Ö ÒÌ ² μ, Ê Ò Ê²ÓÉ ÉÒ ³ ÒÌμ μ ÉÖ ²ÒÌ μ μ É μ μ ²Ê μ±μ - Ê Ê μ³ Ö
Διαβάστε περισσότεραD Alembert s Solution to the Wave Equation
D Alembert s Solution to the Wave Equation MATH 467 Partial Differential Equations J. Robert Buchanan Department of Mathematics Fall 2018 Objectives In this lesson we will learn: a change of variable technique
Διαβάστε περισσότεραHOMEWORK 4 = G. In order to plot the stress versus the stretch we define a normalized stretch:
HOMEWORK 4 Problem a For the fast loading case, we want to derive the relationship between P zz and λ z. We know that the nominal stress is expressed as: P zz = ψ λ z where λ z = λ λ z. Therefore, applying
Διαβάστε περισσότεραQuestions on Particle Physics
Questions on Particle Physics 1. The following strong interaction has been observed. K + p n + X The K is a strange meson of quark composition u s. The u quark has a charge of +2/3. The d quark has a charge
Διαβάστε περισσότεραAreas and Lengths in Polar Coordinates
Kiryl Tsishchanka Areas and Lengths in Polar Coordinates In this section we develop the formula for the area of a region whose boundary is given by a polar equation. We need to use the formula for the
Διαβάστε περισσότεραA Search for the Rare Decay B->tau+tau- at the BaBar Experiment
SLAC-R-85 A Search for the Rare Decay B->tau+tau- at the BaBar Experiment Christopher Thomas Potter Stanford Linear Accelerator Center Stanford University Stanford, CA 9439 SLAC-Report-85 Prepared for
Διαβάστε περισσότεραAdS black disk model for small-x DIS
AdS black disk model for small-x DIS Miguel S. Costa Faculdade de Ciências da Universidade do Porto 0911.0043 [hep-th], 1001.1157 [hep-ph] Work with. Cornalba and J. Penedones Rencontres de Moriond, March
Διαβάστε περισσότεραReview Test 3. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Review Test MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the exact value of the expression. 1) sin - 11π 1 1) + - + - - ) sin 11π 1 ) ( -
Διαβάστε περισσότεραDERIVATION OF MILES EQUATION FOR AN APPLIED FORCE Revision C
DERIVATION OF MILES EQUATION FOR AN APPLIED FORCE Revision C By Tom Irvine Email: tomirvine@aol.com August 6, 8 Introduction The obective is to derive a Miles equation which gives the overall response
Διαβάστε περισσότεραCHAPTER 101 FOURIER SERIES FOR PERIODIC FUNCTIONS OF PERIOD
CHAPTER FOURIER SERIES FOR PERIODIC FUNCTIONS OF PERIOD EXERCISE 36 Page 66. Determine the Fourier series for the periodic function: f(x), when x +, when x which is periodic outside this rge of period.
Διαβάστε περισσότεραPrecision Electroweak Measurements on the Z Resonance
SLAC-R-774 September 2005 Precision Electroweak Measurements on the Z Resonance Submitted to Physics Reports Stanford Linear Accelerator Center, Stanford University, Stanford, CA 94309 Work supported by
Διαβάστε περισσότεραCRASH COURSE IN PRECALCULUS
CRASH COURSE IN PRECALCULUS Shiah-Sen Wang The graphs are prepared by Chien-Lun Lai Based on : Precalculus: Mathematics for Calculus by J. Stuwart, L. Redin & S. Watson, 6th edition, 01, Brooks/Cole Chapter
Διαβάστε περισσότεραSCHOOL OF MATHEMATICAL SCIENCES G11LMA Linear Mathematics Examination Solutions
SCHOOL OF MATHEMATICAL SCIENCES GLMA Linear Mathematics 00- Examination Solutions. (a) i. ( + 5i)( i) = (6 + 5) + (5 )i = + i. Real part is, imaginary part is. (b) ii. + 5i i ( + 5i)( + i) = ( i)( + i)
Διαβάστε περισσότεραThe Θ + Photoproduction in a Regge Model
The Θ + Photoproduction in a Regge Model Herry Kwee College of illiam and Mary Cascade 5 Jefferson Lab December 3, 5 1 1. Introduction. Photoproduction γn Θ + K for spin-1/ Θ + γp Θ + K for spin-1/ Θ +
Διαβάστε περισσότεραElements of Information Theory
Elements of Information Theory Model of Digital Communications System A Logarithmic Measure for Information Mutual Information Units of Information Self-Information News... Example Information Measure
Διαβάστε περισσότεραSpherical Coordinates
Spherical Coordinates MATH 311, Calculus III J. Robert Buchanan Department of Mathematics Fall 2011 Spherical Coordinates Another means of locating points in three-dimensional space is known as the spherical
Διαβάστε περισσότεραCHAPTER 48 APPLICATIONS OF MATRICES AND DETERMINANTS
CHAPTER 48 APPLICATIONS OF MATRICES AND DETERMINANTS EXERCISE 01 Page 545 1. Use matrices to solve: 3x + 4y x + 5y + 7 3x + 4y x + 5y 7 Hence, 3 4 x 0 5 y 7 The inverse of 3 4 5 is: 1 5 4 1 5 4 15 8 3
Διαβάστε περισσότεραLocal Approximation with Kernels
Local Approximation with Kernels Thomas Hangelbroek University of Hawaii at Manoa 5th International Conference Approximation Theory, 26 work supported by: NSF DMS-43726 A cubic spline example Consider
Διαβάστε περισσότεραFourier Series. MATH 211, Calculus II. J. Robert Buchanan. Spring Department of Mathematics
Fourier Series MATH 211, Calculus II J. Robert Buchanan Department of Mathematics Spring 2018 Introduction Not all functions can be represented by Taylor series. f (k) (c) A Taylor series f (x) = (x c)
Διαβάστε περισσότεραHERA. Halle NORD (H1) Hall NORTH (H1) Hall nord (H1) Halle OST (HERMES) Hall EAST (HERMES) Hall est (HERMES)
Karshon Uri Institute of Science Weizmann PENTAQUARK5 U.S.A. JLab, Search for the c (31) Pentaquark Pentaquark Searches in Israel on behalf of the Collaboration - October, 5 U T L I N E Introduction +
Διαβάστε περισσότεραΠΕΡΙΕΧΟΜΕΝΑ. Κεφάλαιο 1: Κεφάλαιο 2: Κεφάλαιο 3:
4 Πρόλογος Η παρούσα διπλωµατική εργασία µε τίτλο «ιερεύνηση χωρικής κατανοµής µετεωρολογικών µεταβλητών. Εφαρµογή στον ελληνικό χώρο», ανατέθηκε από το ιεπιστηµονικό ιατµηµατικό Πρόγραµµα Μεταπτυχιακών
Διαβάστε περισσότεραStatistical Inference I Locally most powerful tests
Statistical Inference I Locally most powerful tests Shirsendu Mukherjee Department of Statistics, Asutosh College, Kolkata, India. shirsendu st@yahoo.co.in So far we have treated the testing of one-sided
Διαβάστε περισσότεραΑπόκριση σε Μοναδιαία Ωστική Δύναμη (Unit Impulse) Απόκριση σε Δυνάμεις Αυθαίρετα Μεταβαλλόμενες με το Χρόνο. Απόστολος Σ.
Απόκριση σε Δυνάμεις Αυθαίρετα Μεταβαλλόμενες με το Χρόνο The time integral of a force is referred to as impulse, is determined by and is obtained from: Newton s 2 nd Law of motion states that the action
Διαβάστε περισσότεραPractice Exam 2. Conceptual Questions. 1. State a Basic identity and then verify it. (a) Identity: Solution: One identity is csc(θ) = 1
Conceptual Questions. State a Basic identity and then verify it. a) Identity: Solution: One identity is cscθ) = sinθ) Practice Exam b) Verification: Solution: Given the point of intersection x, y) of the
Διαβάστε περισσότεραApproximation of distance between locations on earth given by latitude and longitude
Approximation of distance between locations on earth given by latitude and longitude Jan Behrens 2012-12-31 In this paper we shall provide a method to approximate distances between two points on earth
Διαβάστε περισσότεραPhys460.nb Solution for the t-dependent Schrodinger s equation How did we find the solution? (not required)
Phys460.nb 81 ψ n (t) is still the (same) eigenstate of H But for tdependent H. The answer is NO. 5.5.5. Solution for the tdependent Schrodinger s equation If we assume that at time t 0, the electron starts
Διαβάστε περισσότεραΨηφιακή Επεξεργασία Φωνής
ΕΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΡΗΤΗΣ Ψηφιακή Επεξεργασία Φωνής Διάλεξη: Προσαρμόσιμο Αρμονικό Μοντέλο Παρουσίαση: Gilles Degottex Στυλιανού Ιωάννης Τμήμα Επιστήμης Υπολογιστών A Full-Band Adaptive Harmonic
Διαβάστε περισσότεραSrednicki Chapter 55
Srednicki Chapter 55 QFT Problems & Solutions A. George August 3, 03 Srednicki 55.. Use equations 55.3-55.0 and A i, A j ] = Π i, Π j ] = 0 (at equal times) to verify equations 55.-55.3. This is our third
Διαβάστε περισσότεραΜάθημα 2c Ενεργός διατομή, μέση ελεύθερη διαδρομή και ρυθμός διασπάσεων
Στοιχειώδη Σωμάτια ΙΙ (8ου εξαμήνου, εαρινό 2011-12) Χ. Πετρίδου Μάθημα 2c Ενεργός διατομή, μέση ελεύθερη διαδρομή και ρυθμός διασπάσεων Στοιχειώδη ΙΙ, Αριστοτέλειο Παν. Θ/νίκης, 6 Μαρτίου 2014 Μαθηµα
Διαβάστε περισσότεραΑΛΛΗΛΕΠΙ ΡΑΣΗ ΜΟΡΦΩΝ ΛΥΓΙΣΜΟΥ ΣΤΙΣ ΜΕΤΑΛΛΙΚΕΣ ΚΑΤΑΣΚΕΥΕΣ
ΕΘΝΙΚΟ ΜΕΤΣΟΒΙΟ ΠΟΛΥΤΕΧΝΕΙΟ ΤΜΗΜΑ ΠΟΛΙΤΙΚΩΝ ΜΗΧΑΝΙΚΩΝ Τοµέας οµοστατικής Εργαστήριο Μεταλλικών Κατασκευών ΑΛΛΗΛΕΠΙ ΡΑΣΗ ΜΟΡΦΩΝ ΛΥΓΙΣΜΟΥ ΣΤΙΣ ΜΕΤΑΛΛΙΚΕΣ ΚΑΤΑΣΚΕΥΕΣ ιπλωµατική Εργασία Ιωάννη Σ. Προµπονά
Διαβάστε περισσότεραAreas and Lengths in Polar Coordinates
Kiryl Tsishchanka Areas and Lengths in Polar Coordinates In this section we develop the formula for the area of a region whose boundary is given by a polar equation. We need to use the formula for the
Διαβάστε περισσότεραLecture 21: Scattering and FGR
ECE-656: Fall 009 Lecture : Scattering and FGR Professor Mark Lundstrom Electrical and Computer Engineering Purdue University, West Lafayette, IN USA Review: characteristic times τ ( p), (, ) == S p p
Διαβάστε περισσότεραReminders: linear functions
Reminders: linear functions Let U and V be vector spaces over the same field F. Definition A function f : U V is linear if for every u 1, u 2 U, f (u 1 + u 2 ) = f (u 1 ) + f (u 2 ), and for every u U
Διαβάστε περισσότεραAbstract Storage Devices
Abstract Storage Devices Robert König Ueli Maurer Stefano Tessaro SOFSEM 2009 January 27, 2009 Outline 1. Motivation: Storage Devices 2. Abstract Storage Devices (ASD s) 3. Reducibility 4. Factoring ASD
Διαβάστε περισσότεραΣΧΕΔΙΑΣΜΟΣ ΔΙΚΤΥΩΝ ΔΙΑΝΟΜΗΣ. Η εργασία υποβάλλεται για τη μερική κάλυψη των απαιτήσεων με στόχο. την απόκτηση του διπλώματος
ΣΧΕΔΙΑΣΜΟΣ ΔΙΚΤΥΩΝ ΔΙΑΝΟΜΗΣ Η εργασία υποβάλλεται για τη μερική κάλυψη των απαιτήσεων με στόχο την απόκτηση του διπλώματος «Οργάνωση και Διοίκηση Βιομηχανικών Συστημάτων με εξειδίκευση στα Συστήματα Εφοδιασμού
Διαβάστε περισσότεραΠΑΝΔΠΗΣΖΜΗΟ ΠΑΣΡΩΝ ΓΗΑΣΜΖΜΑΣΗΚΟ ΠΡΟΓΡΑΜΜΑ ΜΔΣΑΠΣΤΥΗΑΚΩΝ ΠΟΤΓΩΝ «ΤΣΖΜΑΣΑ ΔΠΔΞΔΡΓΑΗΑ ΖΜΑΣΩΝ ΚΑΗ ΔΠΗΚΟΗΝΩΝΗΩΝ» ΣΜΖΜΑ ΜΖΥΑΝΗΚΩΝ Ζ/Τ ΚΑΗ ΠΛΖΡΟΦΟΡΗΚΖ
ΠΑΝΔΠΗΣΖΜΗΟ ΠΑΣΡΩΝ ΓΗΑΣΜΖΜΑΣΗΚΟ ΠΡΟΓΡΑΜΜΑ ΜΔΣΑΠΣΤΥΗΑΚΩΝ ΠΟΤΓΩΝ «ΤΣΖΜΑΣΑ ΔΠΔΞΔΡΓΑΗΑ ΖΜΑΣΩΝ ΚΑΗ ΔΠΗΚΟΗΝΩΝΗΩΝ» ΣΜΖΜΑ ΜΖΥΑΝΗΚΩΝ Ζ/Τ ΚΑΗ ΠΛΖΡΟΦΟΡΗΚΖ ΣΜΖΜΑ ΖΛΔΚΣΡΟΛΟΓΩΝ ΜΖΥΑΝΗΚΩΝ ΚΑΗ ΣΔΥΝΟΛΟΓΗΑ ΤΠΟΛΟΓΗΣΩΝ ΣΜΖΜΑ
Διαβάστε περισσότεραA Bonus-Malus System as a Markov Set-Chain. Małgorzata Niemiec Warsaw School of Economics Institute of Econometrics
A Bonus-Malus System as a Markov Set-Chain Małgorzata Niemiec Warsaw School of Economics Institute of Econometrics Contents 1. Markov set-chain 2. Model of bonus-malus system 3. Example 4. Conclusions
Διαβάστε περισσότεραHigher Derivative Gravity Theories
Higher Derivative Gravity Theories Black Holes in AdS space-times James Mashiyane Supervisor: Prof Kevin Goldstein University of the Witwatersrand Second Mandelstam, 20 January 2018 James Mashiyane WITS)
Διαβάστε περισσότεραCORDIC Background (4A)
CORDIC Background (4A Copyright (c 20-202 Young W. Lim. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version.2 or any later
Διαβάστε περισσότεραˆ ˆŠ Œ ˆ ˆ Œ ƒ Ÿ Ä ³ Éμ. Ñ Ò É ÉÊÉ Ö ÒÌ ² μ, Ê ƒμ Ê É Ò Ê É É Ê, Ê, μ Ö
ˆ ˆŠ Œ ˆ ˆ Œ ƒ Ÿ 2018.. 49.. 4.. 1291Ä1301 Š œ Š ˆŒ CMS LHC ˆ Š ˆ ˆŠˆ ŒŠ Œˆ Œ ˆ.. ³ Éμ Ñ Ò É ÉÊÉ Ö ÒÌ ² μ, Ê ƒμ Ê É Ò Ê É É Ê, Ê, μ Ö μ É Ö ± ɱ μ μ ʲÓÉ Éμ Ô± ³ É CMS μ²óïμ³ μ μ³ ±μ²² μ μ ±Ê Ë ± ³± ³
Διαβάστε περισσότεραˆ ˆŠ Œ ˆ ˆ Œ ƒ Ÿ Ä616 Š ˆŒ CMS LHC
ˆ ˆŠ Œ ˆ ˆ Œ ƒ Ÿ 2017.. 48.. 5.. 604Ä616 œ ˆ Š ˆ ˆ ˆ Š ˆŒ CMS LHC ˆ.. ƒμ²êé 1,.. ³ Éμ 1,2, 1 Ñ Ò É ÉÊÉ Ö ÒÌ ² μ, Ê 2 ƒμ Ê É Ò Ê É É Ê, Ê, μ Ö É ² Ò Ê²ÓÉ ÉÒ Ô± ³ É CMS, μ²êî Ò μ μ ÒÌ - μ μ Í ±² μéò LHC
Διαβάστε περισσότεραEE 570: Location and Navigation
EE 570: Location and Navigation INS Initialization Aly El-Osery Kevin Wedeward Electrical Engineering Department, New Mexico Tech Socorro, New Mexico, USA In Collaboration with Stephen Bruder Electrical
Διαβάστε περισσότερα