Latest results of the LHCf experiment at LHC

Size: px
Start display at page:

Download "Latest results of the LHCf experiment at LHC"

Transcription

1 at LHC Uiversity of Cataia ad INFN Sezioe di Cataia, Cataia, Italy I 6 the LHCf experimet has fulfilled its origial goal of measurig the spectra of the eutral particles produced i the very forward directio at LHC at the highest eergy ever available. The mai purpose of these measuremets is ideed to provide the Cosmic Ray ad High Eergy Physics commuities with a missig uique set of iformatio for the improvemet of the hadroic iteractio models used to simulate air showers developmet produced i the iteractio of primary High Eergy Cosmic Rays (HECR) with the Earth atmosphere. The last data sets collected by the LHCf experimet have bee obtaied durig p+p collisios, at a eergy of TeV i the CM frame, ad p+pb collisio, at a eergy of the collidig ucleo pair of 5. TeV ad 8. TeV i the CM frame. A review of the mai results of LHCf ad of the recet ad o-goig activities are preseted. The Europea Physical Society Coferece o High Eergy Physics 5- July, 7 Veice Speaker. O behalf of the LHCf Collaboratio. c Copyright owed by the author(s) uder the terms of the Creative Commos Attributio-NoCommercial-NoDerivatives. Iteratioal Licese (CC BY-NC-ND.).

2 . Itroductio The origi ad properties of Ultra High Eergy Cosmic Rays is a log stadig questio i astroparticle Physics. Dedicated extesive air shower experimets are i place sice may years ad have strogly cotributed to our uderstadig of High ad Ultra High Eergy Cosmic (UHECR) Ray Physics. Recetly, i particular, the Pierre Auger Collaboratio [] ad the Telescope Array Collaboratio [], thaks to the excellet performace of their hybrid detector arrays, are providig us ew excitig observatios of UHECRs. Although these recet results have brought a deeper isight i primary cosmic ray properties, still they are largely affected by the poor kowledge of the uclear iteractios i the earth s atmosphere. I the aalyses of observed data, compariso with Mote Carlo simulatios of air showers is uavoidable, ad the results are sesitive to the choice of hadroic iteractio model used i the simulatio []. A calibratio of the eergy scale i the 5 7 ev eergy rage accessible to LHC provides crucial iput for a better iterpretatio of primary cosmic ray properties, i the regio betwee the kee ad the GZK cut-off. Thaks to the LHC Ru data, some iteractio models have bee updated, ad the dispersio foud i the predictios of air shower observables decreased. However there is still sigificat differece betwee the model predictios especially i the forward regio ad eve some aalyses coclude o-realistic iterpretatios []. The Large Hadro Collider forward (LHCf) experimet was desiged with the aim to provide a calibratio of the hadroic iteractio models i the whole eergy rage spaed by LHC by measurig the eutral forward particle produced i p-p as well as i p-io collisios. More tuigs of the models usig the forward particle productio are ecessary. I fact, the forward particles carry a large fractio of the collisio eergy ad are resposible to determie the shape of air showers [5]. The LHCf experimet has ideed take data i p-p collisios at s =.9,.76, 7 ad TeV ad i p-pb collisios at s = 5. TeV thus collectig a whole set of data of uvaluable importace for the tuig of the models i such a difficult regio.. The LHCf experimet The LHCf experimet is composed by two idepedet positio sesitive electromagetic calorimeters, located o both side of the ATLAS experimet, m away from the LHC-IP iteractio poit, iside the zero-degree eutral absorber (Target Neutral Absorber, TAN). Charged particles from the IP are swept away by the ier beam separatio dipole before reachig the TAN, so that oly photos maily from π decays, eutros ad eutral kaos reach the LHCf calorimeters. Each calorimeter (ARM ad ARM) has a double tower structure, with the smaller tower located at zero degree collisio agle, approximately coverig the regio with pseudo-rapidity η > ad the larger oe, approximately coverig the regio with 8. < η <. Four X-Y layers of positio sesitive detectors (scitillatig fibers i ARM, silico micro-strip detectors i ARM) provide measuremets of the trasverse profile of the showers. The two tower structure allows to recostruct the π decayig i two γs, hittig separately the two towers, hece providig a very precise absolute eergy calibratio of the detectors. I the rage E> GeV, the LHCf

3 detectors have eergy ad positio resolutios for electromagetic showers better tha 5% ad µm, respectively. A detailed descriptio of the LHCf experimetal set-up ad of the expected physics performaces ca be foud i Ref. [6].. Results at s= TeV pp collisios The LHCf experimet has collected data durig the proto-proto collisio periods at s=.9 TeV (9 ad ),.76 TeV (), 7 TeV () ad TeV (5). Photo spectra at pseudorapidity η larger tha 8.8 were published for the proto-proto collisio data take at s=.9 TeV [7] ad 7 TeV [8]. The results were compared with the predictios by several hadroic iteractio models, ad it was foud oe of the models ca perfectly match with the experimetal results. The iclusive eergy spectra of photos produced i p-p collisios at TeV for two pseudorapidity rages together with the predictios of DPMJET.6 [9], EPOS-LHC [], PYTHIA 8. [], QGSJETII- [] ad SIBYLL. [] hadroic iteractio models are show i Fig.. ] - dn/de [GeV /N ie MC/Data Data QGSJET II- EPOS-LHC DPMJET.6 SIBYLL. PYTHIA 8. LHCf s=tev photo η >.9, φ=8 - Ldt=.9b 5 6 ] - dn/de [GeV /N ie LHCf s=tev photo 8.8<η<8.99, φ= - Ldt=.9b 5 6 Figure : Iclusive photo eergy spectra for pseudorapidity regio η >.9 (left) ad 8.8 < η < 8.99 (right). Data are represeted by black poits while MC predictio from several models are represeted by coloured histograms. Gree shaded area represets statistical+systematic errors of data. Spectra are ormalized to the total umber of ielastic collisios. Bottom paels show the ratio of MC predictios to data. MC/Data The results at TeV cofirms what has bee already reported at lower eergies.the LHCf data lie betwee MC predictios but there is ot a uique model with a good agreemet i the whole eergy rage ad i both rapidity regios. I the pseudorapidity rage η >.9, QGSJET ad EPOS presets a good overall agreemet with experimetal data; SIBYLL predicts a lower yield of photos, eve if it features a shape similar to data; PYTHIA spectrum agrees with data util.5 TeV but become harder at higher eergies; DPMJET is geerally harder tha data. I the pseudorapidity rage 8.8 < η < 8.99, EPOS ad PYTHIA spectra agree with data util

4 TeV, while they become harder at higher eergies; SIBYLL has a good agreemet util TeV, the also it becomes harder tha data; QGSJET presets a lower yield of photos, while DPMJET geerally predict a harder spectrum tha experimetal data. A deeper study of the discrepacy has brought to the coclusio that the mai differeces betwee data ad models were attributable to a less-tha-complete uderstadig of the soft hadroic iteractios implemeted i the models as diffractive processes [, 5]. Productio cross sectios of eutros were also published usig the 7 TeV proto-proto collisio data [6]. The result coverig degree productio agle showed a characteristic peak at aroud.5 TeV, ad such high-eergy excess was oly qualitatively explaied by the QGSJET II- model. All the other models studied sigificatly uder-predict the LHCf result. At the off- degree oly the DPMJET model [9] well explaied the LHCf results. The LHCf results showed that the ratio of eergies carried by the eutros to the photos is largest i the experimetal data tha ay model predictios. Results at TeV have ot yet bee published, however the prelimiary spectra obtaied for the forward eutro productio usig the ARM detectors, show i Fig., seems to cofirm the same tred observed at 7 TeV, i particular, the peak at -degree for eergy 5.5 TeV i the data which is reproduced oly qualitatelively by the QGSJET II- model while all the other models studied sigificatly uder-predict the LHCf result. At the off- degree the agreemet betwee data ad models is also poor η > < η < < η < 8.99 LHCf p p s. = TeV QGSJET II EPOS LHC DPMJET.6 PYTHIA 8. SIBYLL. 5 6 Figure : Iclusive eutro eergy spectra of ARM detector for pseudorapidity regio η >.76 (left), 8.99 < η < 9. (ceter) ad 8.8 < η < 8.99 (right). Data are represeted by black poits while MC predictio from several models are represeted by coloured histograms. Grey shaded area represets statistical+systematic errors of data. Spectra are ormalized to the total umber of ielastic collisios. Bottom paels show the ratio of MC predictios to data. This measuremet is particularly importat sice it is expected to provide a importat hit for the problem of cosmic-ray muo excess reported by both Auger [7] ad TA [8]. This excess could be ideed iterpreted i terms of a uderestimatio of the baryo productio i the hadroic iteractio models used to derive the CR spectra [9].

5 . Summary ad Plas The LHCf experimet has successful take data at various collisio coditio at LHC thus providig a uique set of measuremets i the before-uexplored forward regio to costrait the particle productio relevat for the high eergy Cosmic Ray physics. The so far published photo, eutro ad π results are compared with the iteractio models providig uvaluable iput for the models tuig. The discrepacy foud betwee data ad models may related to the diffractive/odiffractive compoets ad may beefit of combied aalysis betwee LHCf ad ATLAS which will be the aim of future work. I additio, the comparisos betwee the data at differet collisio eergies reveal the scalig or scalig break of the partile spectra. The LHCf results idicate the scalig of photos ad π spectra at s=.76, 7 ad TeV, while the ISR, PHENIX ad LHCf idicate a scalig break of eutro spectra betwee GeV ad TeV. A ew experimet, RHICf, has hece bee prepared to test the scalig (or break) at s = 5 GeV at RHIC. The experimet uses oe of the LHCf detector, ARM, ad has take data at the ed of Jue. Results from RHICf will come i the ear future ad will brig further importat iformatio from Cosmic Ray physics. Refereces [] F. Feu [Pierre Auger Collaboratio], Proc. of 5th It. Cosmic Ray Cof., Bexo, Busa, Korea (7), C7-7-, p [] R. U. Abbasi et al. [Telescope Array Collaboratio], Astropart. Phys. 8 (6) [] Pierre Auger Collaboratio, Phys. Rev. D 9, 5 (). [] K.-H. Kampert ad M. Uger, Astropart. Phys. 5 () 66. [5] K. Akiba et al., J. Phys. G: Nucl. Part. Phys. (6). [6] O. Adriai et al., JINST (8) S86. [7] O. Adriai et al., Phys. Lett. B75 () 98. [8] O. Adriai et al., Phys. Lett. B7 () 8. [9] F.W. Bopp et al., Phys. Rev. C77 (8) 9. [] K. Werer et al., Nucl.Phys.Proc.Suppl (8) [] T. Sjöstad, et al., Comput. Phys. Comm. 78 (8) 85. [] S. Ostapcheko, Phys. Rev. D8 () 8. [] E.-J. Ah et al., Phys. Rev. D8 (9) 9. [] The ATLAS ad the LHCf Collaboratios, ATL-PHYS-PUB-5-8. [5] Q.D. Zhou, Y. Itow, H. Mejo ad T. Sako, Eur. Phys. J. C 77 (7). [6] O. Adriai et al., Phys. Lett. B 75 (5) 6. [7] P. Abreu et al. [The Pierre Auger Collaboratio], Proc. of th It. Cosmic Ray Cof., Beijig (), [arxiv:7.8 [astro-ph.he]]. [8] T. Abu-Zayyad, et al. [TA Collaboratio], Astrophys. J. 768 () L [9] T. Pierog ad K. Warer, Phys. Rev. Lett. (8) 7.

Neutral particles energy spectra for 900 GeV and 7 TeV p-p collisions, measured by the LHCf experiment

Neutral particles energy spectra for 900 GeV and 7 TeV p-p collisions, measured by the LHCf experiment Neutral particles energy spectra for 900 GeV and 7 TeV p-p collisions, measured by the LHCf experiment Raffaello D Alessandro 1 Department of Physics Università di Firenze and INFN-Firenze I-50019 Sesto

More information

Zero degree neutron energy spectra measured by LHCf at s = 13 TeV proton-proton collision

Zero degree neutron energy spectra measured by LHCf at s = 13 TeV proton-proton collision Zero degree neutron energy spectra measured by LHCf at s = TeV proton-proton collision Nagoya university, ISEE E-mail: ueno.mana@isee.nagoya-u.ac.jp The Large Hadron Collider forward (LHCf) experiment

More information

arxiv:hep-ph/ v1 13 Oct 2004

arxiv:hep-ph/ v1 13 Oct 2004 arxiv:hep-ph/6v 3 Oct 2 Scearios for multiplicity distributios i pp collisios i the TeV eergy regio Roberto Ugoccioi ad Alberto Giovaii Dipartimeto di Fisica Teorica, Uiversità di Torio ad INFN, Sezioe

More information

LIGHT ION REACTION MECHANISM

LIGHT ION REACTION MECHANISM Proceedigs of the 1983 RCNP Iteratioal Symposium o LIGHT ION REACTION MECHANISM 16-20 MAY, 1983 Edited by H. Ogata, T. Kammuri ad I. Katayama RESEARCH CENTER FOR NUCLEAR PHYSICS OSAKA UNIVERSITY IBARAKI,

More information

CERN Council - Open Session 18 December Lorenzo Bonechi - INFN Firenze, Italy On behalf of the LHCf Collaboration

CERN Council - Open Session 18 December Lorenzo Bonechi - INFN Firenze, Italy On behalf of the LHCf Collaboration CERN Council - Open Session 18 December 2015 Lorenzo Bonechi - INFN Firenze, Italy On behalf of the LHCf Collaboration LHC and cosmic rays Cosmic rays: flux of charged particles hitting the Earth atmosphere

More information

OPTIMAL ALGORITHMS -- SUPPLEMENTAL NOTES

OPTIMAL ALGORITHMS -- SUPPLEMENTAL NOTES OPTIMAL ALGORITHMS -- SUPPLEMENTAL NOTES Peter M. Maurer Why Hashig is θ(). As i biary search, hashig assumes that keys are stored i a array which is idexed by a iteger. However, hashig attempts to bypass

More information

Measurement uncertainty of the sound absorption

Measurement uncertainty of the sound absorption Measuremet ucertaity of the soud absorptio coefficiet Aa Izewska Buildig Research Istitute, Filtrowa Str., 00-6 Warsaw, Polad a.izewska@itb.pl 6887 The stadard ISO/IEC 705:005 o the competece of testig

More information

a b c d e f g h Supplementary Information

a b c d e f g h Supplementary Information Supplemetary Iformatio a b c d e f g h Supplemetary Figure S STM images show that Dark patters are frequetly preset ad ted to accumulate. (a) mv, pa, m ; (b) mv, pa, m ; (c) mv, pa, m ; (d) mv, pa, m ;

More information

arxiv: v2 [hep-ex] 24 Nov 2017

arxiv: v2 [hep-ex] 24 Nov 2017 Measurement of forward photon production cross-section in proton proton collisions at s = 13 TeV with the LHCf detector arxiv:1703.07678v2 [hep-ex] 24 Nov 2017 O. Adriani a,b, E. Berti a,b, L. Bonechi

More information

Sensitivity Analysis of Daubechies 4 Wavelet Coefficients for Reduction of Reconstructed Image Error

Sensitivity Analysis of Daubechies 4 Wavelet Coefficients for Reduction of Reconstructed Image Error Proceedigs of the 6th WSEAS Iteratioal Coferece o SIGNAL PROCESSING, Dallas, Texas, USA, March -4, 7 67 Sesitivity Aalysis of Daubechies 4 Wavelet Coefficiets for Reductio of Recostructed Image Error DEVINDER

More information

The Wave Function and Quantum Reality

The Wave Function and Quantum Reality The Wave Fuctio ad Quatum Reality Sha Gao Uit for History ad Philosophy of Sciece & Cetre for Time, SOPHI Uiversity of Sydey, Sydey, NSW 006, Australia Abstract. We ivestigate the meaig of the wave fuctio

More information

On the Combined Analysis of Muon Shower Size and Depth of Shower Maximum

On the Combined Analysis of Muon Shower Size and Depth of Shower Maximum On the Combined Analysis of Muon Shower Size and Depth of Shower Maximum, Petr Trávníček Institute of Physics of the Academy of Sciences of the Czech Republic, Na Slovance, 18 1 Prague 8 E-mail: vicha@fzu.cz

More information

ABSTRACT 1. INTRODUCTION

ABSTRACT 1. INTRODUCTION Iwamura, Y., T. Itoh, ad M. SakaNo. Nuclear Products ad Their Time Depedece Iduced by Cotiuous Diffusio of Deuterium Through Multi-layer Palladium Cotaiig Low Work Fuctio Material. i 8th Iteratioal Coferece

More information

ISMD October

ISMD October ISMD 05 4-9 October Searchig for hidde sectors i multiparticle productio @ the LHC Miguel-Agel Sachis-Lozao Departameto de Física Teórica - IFIC Uiversidad de Valecia CSIC Edward Sarkisa-Gribaum Uiversit

More information

Double Stage Shrinkage Estimator of Two Parameters. Generalized Exponential Distribution

Double Stage Shrinkage Estimator of Two Parameters. Generalized Exponential Distribution Iteratioal Mathematical Forum, Vol., 3, o. 3, 3-53 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/.9/imf.3.335 Double Stage Shrikage Estimator of Two Parameters Geeralized Expoetial Distributio Alaa M.

More information

Hiroaki MENJO (KMI, Nagoya University, Japan) On behalf of the LHCf collaboration

Hiroaki MENJO (KMI, Nagoya University, Japan) On behalf of the LHCf collaboration Forward photon energy spectrum at 7TeV p-p collisions measured by the LHCf experiment Hiroaki MENJO (KMI, Nagoya University, Japan) On behalf of the LHCf collaboration ISMD 2011, Hiroshima, Japan, 26-30

More information

The Quark Puzzle A 3D printable model and/or paper printable puzzle that allows students to learn the laws of colour charge through inquiry.

The Quark Puzzle A 3D printable model and/or paper printable puzzle that allows students to learn the laws of colour charge through inquiry. The Quark Puzzle A 3D pritable model ad/or paper pritable puzzle that allows studets to lear the laws of colour charge through iquiry. It is available at this lik: https://zeodo.org/record/1252868#.w3ft-gzauk

More information

11TH INTERNATIONAL SYMPOSIUM ON PARTICLE IMAGE VELOCIMETRY - PIV15 Santa Barbara, California, Sept , 2015

11TH INTERNATIONAL SYMPOSIUM ON PARTICLE IMAGE VELOCIMETRY - PIV15 Santa Barbara, California, Sept , 2015 11TH INTERNATIONAL SYMPOSIUM ON PARTICLE IMAGE VELOCIMETRY - PIV15 Sata Barbara, Califoria, Sept. 14-16, 2015 ABSTRACT HELE-SHAW RHEOMETRY BY MEANS OF PARTICLE IMAGE VELOCIMETRY Sita Drost & Jerry Westerweel

More information

Recent Results from T2K

Recent Results from T2K Recet Results from T2K Alessadro Bravar o behalf of the T2K Collaboratio TAU 2016 Beijig Sept. 22, 16 The T2K Experimet 11 coutries ~500 members 2 JPARC - accelerator complex NA61 hadroproductio far detector

More information

Chapter 13, Part A Analysis of Variance and Experimental Design

Chapter 13, Part A Analysis of Variance and Experimental Design Slides Prepared by JOHN S. LOUCKS St. Edward s Uiversity Slide 1 Chapter 13, Part A Aalysis of Variace ad Eperimetal Desig Itroductio to Aalysis of Variace Aalysis of Variace: Testig for the Equality of

More information

Science case for recording protonoxygen collisions at the LHC

Science case for recording protonoxygen collisions at the LHC Science case for recording protonoxygen collisions at the LHC Hans Dembinski MPIK Heidelberg LHC WG Forward Physics and Diffraction 2018-03-20 KASCADE, IceCube, TUNKA Pierre Auger, Telescope Array data

More information

Accuracy assessment methods and challenges

Accuracy assessment methods and challenges Accuracy assessmet methods ad challeges Giles M. Foody School of Geography Uiversity of Nottigham giles.foody@ottigham.ac.uk Backgroud Need for accuracy assessmet established. Cosiderable progress ow see

More information

Comparison Study of Series Approximation. and Convergence between Chebyshev. and Legendre Series

Comparison Study of Series Approximation. and Convergence between Chebyshev. and Legendre Series Applied Mathematical Scieces, Vol. 7, 03, o. 6, 3-337 HIKARI Ltd, www.m-hikari.com http://d.doi.org/0.988/ams.03.3430 Compariso Study of Series Approimatio ad Covergece betwee Chebyshev ad Legedre Series

More information

arxiv: v2 [hep-ph] 4 Sep 2015

arxiv: v2 [hep-ph] 4 Sep 2015 1 Restrictios o pp scatterig amplitude imposed by first diffractio miimum data obtaied by TOTEM at LHC V.N. Kovaleko, A.M. Puchkov, V.V. Vecheri, D.V. Diatcheko Dep. of High Eergy Physics, Sait-Petersburg

More information

Final Examination Solutions 17/6/2010

Final Examination Solutions 17/6/2010 The Islamic Uiversity of Gaza Faculty of Commerce epartmet of Ecoomics ad Political Scieces A Itroductio to Statistics Course (ECOE 30) Sprig Semester 009-00 Fial Eamiatio Solutios 7/6/00 Name: I: Istructor:

More information

6.3 Testing Series With Positive Terms

6.3 Testing Series With Positive Terms 6.3. TESTING SERIES WITH POSITIVE TERMS 307 6.3 Testig Series With Positive Terms 6.3. Review of what is kow up to ow I theory, testig a series a i for covergece amouts to fidig the i= sequece of partial

More information

First indication of LPM effect in LHCf, an LHC experiment

First indication of LPM effect in LHCf, an LHC experiment First indication of LPM effect in LHCf, an LHC experiment M. Del Prete 1,2,a on behalf of LHCf collaboration 1 INFN section of Florence, Italy 2 University of Florence, Italy Abstract. The Large Hadron

More information

MA238 Assignment 4 Solutions (part a)

MA238 Assignment 4 Solutions (part a) (i) Sigle sample tests. Questio. MA38 Assigmet 4 Solutios (part a) (a) (b) (c) H 0 : = 50 sq. ft H A : < 50 sq. ft H 0 : = 3 mpg H A : > 3 mpg H 0 : = 5 mm H A : 5mm Questio. (i) What are the ull ad alterative

More information

Recent Experimental Results in ADITYA Tokamak

Recent Experimental Results in ADITYA Tokamak Recet Experimetal Results i ADITYA Tokamak R. Jha ad the ADITYA Team Istitute for Plasma Research, Bhat, Gadhiagar-382 428, INDIA e-mail:rjha@ipr.res.i Abstract. Recet studies o measuremets of edge turbulece

More information

Modified Decomposition Method by Adomian and. Rach for Solving Nonlinear Volterra Integro- Differential Equations

Modified Decomposition Method by Adomian and. Rach for Solving Nonlinear Volterra Integro- Differential Equations Noliear Aalysis ad Differetial Equatios, Vol. 5, 27, o. 4, 57-7 HIKARI Ltd, www.m-hikari.com https://doi.org/.2988/ade.27.62 Modified Decompositio Method by Adomia ad Rach for Solvig Noliear Volterra Itegro-

More information

Coherent and incoherent DVCS and π 0 production on 4 He

Coherent and incoherent DVCS and π 0 production on 4 He Coheret ad icoheret DVCS ad π 0 productio o 4 He S. Stepaya (JLAB) Nucleo ad Resoace Structure with Hard Exclusive Processes IPN-ORSAY, May 29 31, 2017 Outlie 2 DVCS ad p 0 productio o spi ad isospi zero

More information

Frank Laboratory of Neutron Physics, JINR, Dubna, Russia. Institute of Heavy Ion Physics, Peking University, Beijing, P.R. China. 1.

Frank Laboratory of Neutron Physics, JINR, Dubna, Russia. Institute of Heavy Ion Physics, Peking University, Beijing, P.R. China. 1. SYSTEMATICS OF (,α) CROSS SECTIONS FOR 4-6 MeV NEUTRONS G.Khuukhekhuu 1, Yu.M.Gledeov, Guohui Zhag 3, M.V.Sedysheva, J.Mukhsaikha 1, M.Odsure 1 1) Nuclear Research Ceter, Natioal Uiversity of Mogolia,

More information

Probability, Expectation Value and Uncertainty

Probability, Expectation Value and Uncertainty Chapter 1 Probability, Expectatio Value ad Ucertaity We have see that the physically observable properties of a quatum system are represeted by Hermitea operators (also referred to as observables ) such

More information

Kinetics of Complex Reactions

Kinetics of Complex Reactions Kietics of Complex Reactios by Flick Colema Departmet of Chemistry Wellesley College Wellesley MA 28 wcolema@wellesley.edu Copyright Flick Colema 996. All rights reserved. You are welcome to use this documet

More information

Experimental and theoretical problems:

Experimental and theoretical problems: Workshop o Nuclear Physics, Beijig, September 211 2 t p 6 He 5 H Experimetal ad theoretical problems: We ca ot rely o the theory predictios Reactio mechaism affects the shape of the spectra The overlappig

More information

Positron annihilation on atomic core electrons + positive ions

Positron annihilation on atomic core electrons + positive ions ositro aihilatio o atomic core electros positive ios Dermot Gree ad Gleb Gribaki Departmet of Applied Mathematics ad Theoretical hysics, Quee s Uiversity Belfast, Norther Irelad, UK Motivatio ositro aihilatio

More information

Research Article Health Monitoring for a Structure Using Its Nonstationary Vibration

Research Article Health Monitoring for a Structure Using Its Nonstationary Vibration Hidawi Publishig Corporatio Advaces i Acoustics ad Vibratio Volume 2, Article ID 69652, 5 pages doi:.55/2/69652 Research Article Health Moitorig for a Structure Usig Its Nostatioary Vibratio Yoshimutsu

More information

Review of accelerator data of relevance to air shower simulations

Review of accelerator data of relevance to air shower simulations Y.Itow, Review of Accelerator data UHECR2012@ 14Feb2012 Review of accelerator data of relevance to air shower simulations Yoshitaka Itow STE Lab / Kobayashi-Maskawa Inst. Nagoya University UHECR 2012 Feb

More information

The LHCf experiment at LHC

The LHCf experiment at LHC The LHCf experiment at LHC Measurement of π 0 production cross section in the very forward region at LHC Equivalent laboratory energy 10 17 ev LHCf physics Description of the experiment Some results on

More information

(Intentional blank page) Please remove this page and make both-sided copy from the next page.

(Intentional blank page) Please remove this page and make both-sided copy from the next page. (Itetioal blak page) Please remove this page ad make both-sided copy from the ext page. Statistical Data Aalysis by Excel for Impact Evaluatio (Basic Course) Text Histogram, average & stadard deviatio

More information

Research Article Health Monitoring for a Structure Using Its Nonstationary Vibration

Research Article Health Monitoring for a Structure Using Its Nonstationary Vibration Advaces i Acoustics ad Vibratio Volume 2, Article ID 69652, 5 pages doi:.55/2/69652 Research Article Health Moitorig for a Structure Usig Its Nostatioary Vibratio Yoshimutsu Hirata, Mikio Tohyama, Mitsuo

More information

An Improved Proportionate Normalized Least Mean Square Algorithm with Orthogonal Correction Factors for Echo Cancellation

An Improved Proportionate Normalized Least Mean Square Algorithm with Orthogonal Correction Factors for Echo Cancellation 202 Iteratioal Coferece o Electroics Egieerig ad Iformatics (ICEEI 202) IPCSI vol. 49 (202) (202) IACSI Press, Sigapore DOI: 0.7763/IPCSI.202.V49.33 A Improved Proportioate Normalized Least Mea Square

More information

CKM Matrix and CP Violation in Standard Model

CKM Matrix and CP Violation in Standard Model CKM Matrix ad CP Violatio i Stadard Model Origi of CKM Matrix. B meso produc,o at B factories Lecture 13 Shahram Rahatlou Fisica delle Par,celle Elemetari, Ao Accademico 2015-16 http://www.roma1.if.it/people/rahatlou/particelle/

More information

Example: Find the SD of the set {x j } = {2, 4, 5, 8, 5, 11, 7}.

Example: Find the SD of the set {x j } = {2, 4, 5, 8, 5, 11, 7}. 1 (*) If a lot of the data is far from the mea, the may of the (x j x) 2 terms will be quite large, so the mea of these terms will be large ad the SD of the data will be large. (*) I particular, outliers

More information

Structure and evolution of AGB stars

Structure and evolution of AGB stars Structure ad evolutio of AGB stars M bol T eff The mai s-process s i AGB stars H 12 C(p,γ) 13 N(β + υ) 13 C 13 C(α,) He-flash eutro source 13 C(α,) 16 dy 13 dt dy dt C = Y = x 13 Y C X Y 4 Y He ρ N ρ N

More information

The Random Walk For Dummies

The Random Walk For Dummies The Radom Walk For Dummies Richard A Mote Abstract We look at the priciples goverig the oe-dimesioal discrete radom walk First we review five basic cocepts of probability theory The we cosider the Beroulli

More information

Forward photon energy spectrum at LHC 7TeV p-p collisions measured by LHCf

Forward photon energy spectrum at LHC 7TeV p-p collisions measured by LHCf Forward photon energy spectrum at LHC 7TeV p-p collisions measured by LHCf Hiroaki MENJO (KMI, Nagoya University, Japan) On the held of the LHCf collaboration RICAP 2011, Roma, Italy, 25-27 May 2011 Contents

More information

Stat 139 Homework 7 Solutions, Fall 2015

Stat 139 Homework 7 Solutions, Fall 2015 Stat 139 Homework 7 Solutios, Fall 2015 Problem 1. I class we leared that the classical simple liear regressio model assumes the followig distributio of resposes: Y i = β 0 + β 1 X i + ɛ i, i = 1,...,,

More information

ANALYSIS OF EXPERIMENTAL ERRORS

ANALYSIS OF EXPERIMENTAL ERRORS ANALYSIS OF EXPERIMENTAL ERRORS All physical measuremets ecoutered i the verificatio of physics theories ad cocepts are subject to ucertaities that deped o the measurig istrumets used ad the coditios uder

More information

TRACEABILITY SYSTEM OF ROCKWELL HARDNESS C SCALE IN JAPAN

TRACEABILITY SYSTEM OF ROCKWELL HARDNESS C SCALE IN JAPAN HARDMEKO 004 Hardess Measuremets Theory ad Applicatio i Laboratories ad Idustries - November, 004, Washigto, D.C., USA TRACEABILITY SYSTEM OF ROCKWELL HARDNESS C SCALE IN JAPAN Koichiro HATTORI, Satoshi

More information

1 Review of Probability & Statistics

1 Review of Probability & Statistics 1 Review of Probability & Statistics a. I a group of 000 people, it has bee reported that there are: 61 smokers 670 over 5 960 people who imbibe (drik alcohol) 86 smokers who imbibe 90 imbibers over 5

More information

PHYS-3301 Lecture 7. CHAPTER 4 Structure of the Atom. Rutherford Scattering. Sep. 18, 2018

PHYS-3301 Lecture 7. CHAPTER 4 Structure of the Atom. Rutherford Scattering. Sep. 18, 2018 CHAPTER 4 Structure of the Atom PHYS-3301 Lecture 7 4.1 The Atomic Models of Thomso ad Rutherford 4.2 Rutherford Scatterig 4.3 The Classic Atomic Model 4.4 The Bohr Model of the Hydroge Atom 4.5 Successes

More information

Measurements of the elastic, inelastic and total cross sections in pp collisions with ATLAS subdetectors

Measurements of the elastic, inelastic and total cross sections in pp collisions with ATLAS subdetectors Measurements of the elastic, inelastic and total cross sections in pp collisions with ATLAS subdetectors 1 On behalf of the ATLAS collaboration University of Bologna Viale Berti Pichat 6/2,40127 Bologna,

More information

Review of LHCb results on MPI, soft QCD and diffraction

Review of LHCb results on MPI, soft QCD and diffraction Review of LHCb results on MPI, soft QCD and diffraction Marcin Kucharczyk on behalf of LHCb collaboration HNI Krakow EDS Blois 2015, Borgo (Corse), 30.06.2015 Outline LHCb - general purpose forward experiment

More information

Chapter 11 Output Analysis for a Single Model. Banks, Carson, Nelson & Nicol Discrete-Event System Simulation

Chapter 11 Output Analysis for a Single Model. Banks, Carson, Nelson & Nicol Discrete-Event System Simulation Chapter Output Aalysis for a Sigle Model Baks, Carso, Nelso & Nicol Discrete-Evet System Simulatio Error Estimatio If {,, } are ot statistically idepedet, the S / is a biased estimator of the true variace.

More information

Accuracy of TEXTOR He-beam diagnostics

Accuracy of TEXTOR He-beam diagnostics Accuracy of TEXTOR He-beam diagostics O. Schmitz, I.L.Beigma *, L.A. Vaishtei *, A. Pospieszczyk, B. Schweer, M. Krychoviak, U. Samm ad the TEXTOR team Forschugszetrum Jülich,, Jülich, Germay *Lebedev

More information

OFFSET CORRECTION IN A DIGITAL INTEGRATOR FOR ROTATING COIL MEASUREMENTS

OFFSET CORRECTION IN A DIGITAL INTEGRATOR FOR ROTATING COIL MEASUREMENTS XX IMEKO World Cogress Metrology for Gree Growth September 9 4, 0, Busa, Republic of Korea OFFSET CORRECTION IN A DIGITAL INTEGRATOR FOR ROTATING COIL MEASUREMENTS P. Arpaia,, P. Cimmio,, L. De Vito, ad

More information

ULTRA-HIGH ENERGY COSMIC RAY COMPOSITION and MUON CONTENT vs. HADRONIC MODELS. Esteban Roulet Bariloche, Argentina

ULTRA-HIGH ENERGY COSMIC RAY COMPOSITION and MUON CONTENT vs. HADRONIC MODELS. Esteban Roulet Bariloche, Argentina ULTRA-HIGH ENERGY COSMIC RAY COMPOSITION and MUON CONTENT vs. HADRONIC MODELS Esteban Roulet Bariloche, Argentina Many observables are sensitive to CR composition Shower maximum TA APP 64 (2014) Auger

More information

Cosmic Ray Interaction Models: an Overview

Cosmic Ray Interaction Models: an Overview EPJ Web of Conferences will be set by the publisher DOI: will be set by the publisher c Owned by the authors, published by EDP Sciences, 2016 Cosmic Ray Interaction Models: an Overview Sergey Ostapchenko

More information

SECTION 2 Electrostatics

SECTION 2 Electrostatics SECTION Electrostatics This sectio, based o Chapter of Griffiths, covers effects of electric fields ad forces i static (timeidepedet) situatios. The topics are: Electric field Gauss s Law Electric potetial

More information

Effect of Temperature Variations on Strain Response of Polymer Bragg Grating Optical Fibers

Effect of Temperature Variations on Strain Response of Polymer Bragg Grating Optical Fibers Iraq J. Electrical ad Electroic Egieerig Vol.13 No.1, 17 مجلد 13 العدد 17 1 Effect of Temperature Variatios o Strai Respose of Polymer Bragg Gratig Optical Fibers Hisham K. Hisham Electrical Egieerig Departmet,

More information

The improvement of the volume ratio measurement method in static expansion vacuum system

The improvement of the volume ratio measurement method in static expansion vacuum system Available olie at www.sciecedirect.com Physics Procedia 32 (22 ) 492 497 8 th Iteratioal Vacuum Cogress The improvemet of the volume ratio measuremet method i static expasio vacuum system Yu Hogya*, Wag

More information

Available online at ScienceDirect. Physics Procedia 57 (2014 ) 48 52

Available online at  ScienceDirect. Physics Procedia 57 (2014 ) 48 52 Available olie at www.sciecedirect.com ScieceDirect Physics Procedia 57 (214 ) 48 52 27th Aual CSP Workshops o Recet Developmets i Computer Simulatio Studies i Codesed Matter Physics, CSP 214 Applicatio

More information

MCT242: Electronic Instrumentation Lecture 2: Instrumentation Definitions

MCT242: Electronic Instrumentation Lecture 2: Instrumentation Definitions Faculty of Egieerig MCT242: Electroic Istrumetatio Lecture 2: Istrumetatio Defiitios Overview Measuremet Error Accuracy Precisio ad Mea Resolutio Mea Variace ad Stadard deviatio Fiesse Sesitivity Rage

More information

A statistical method to determine sample size to estimate characteristic value of soil parameters

A statistical method to determine sample size to estimate characteristic value of soil parameters A statistical method to determie sample size to estimate characteristic value of soil parameters Y. Hojo, B. Setiawa 2 ad M. Suzuki 3 Abstract Sample size is a importat factor to be cosidered i determiig

More information

Error & Uncertainty. Error. More on errors. Uncertainty. Page # The error is the difference between a TRUE value, x, and a MEASURED value, x i :

Error & Uncertainty. Error. More on errors. Uncertainty. Page # The error is the difference between a TRUE value, x, and a MEASURED value, x i : Error Error & Ucertaity The error is the differece betwee a TRUE value,, ad a MEASURED value, i : E = i There is o error-free measuremet. The sigificace of a measuremet caot be judged uless the associate

More information

Modified Logistic Maps for Cryptographic Application

Modified Logistic Maps for Cryptographic Application Applied Mathematics, 25, 6, 773-782 Published Olie May 25 i SciRes. http://www.scirp.org/joural/am http://dx.doi.org/.4236/am.25.6573 Modified Logistic Maps for Cryptographic Applicatio Shahram Etemadi

More information

pa at the LHC and Extensive Air Shower Development

pa at the LHC and Extensive Air Shower Development Muons in pa at the LHC and Extensive Air Shower Development Tanguy Pierog Karlsruhe Institute of Technology, Institut für Kernphysik, Karlsruhe, Germany Workshop on pa@lhc, ECT* Trento, Italy May the 9th

More information

Research on real time compensation of thermal errors of CNC lathe based on linear regression theory Qiu Yongliang

Research on real time compensation of thermal errors of CNC lathe based on linear regression theory Qiu Yongliang d Iteratioal Coferece o Machiery, Materials Egieerig, Chemical Egieerig ad Biotechology (MMECEB 015) Research o real time compesatio of thermal errors of CNC lathe based o liear regressio theory Qiu Yogliag

More information

PHYS-3301 Lecture 5. CHAPTER 3 The Experimental Basis of Quantum. 3.8: Compton Effect. 3.8: Compton Effect. Sep. 11, 2018

PHYS-3301 Lecture 5. CHAPTER 3 The Experimental Basis of Quantum. 3.8: Compton Effect. 3.8: Compton Effect. Sep. 11, 2018 CHAPTER 3 The Experimetal Basis of Quatum PHYS-3301 Lecture 5 Sep. 11, 2018 3.1 Discovery of the X Ray ad the Electro 3.2 Determiatio of Electro Charge 3.3 Lie Spectra 3.4 Quatizatio 3.5 Blackbody Radiatio

More information

Run-length & Entropy Coding. Redundancy Removal. Sampling. Quantization. Perform inverse operations at the receiver EEE

Run-length & Entropy Coding. Redundancy Removal. Sampling. Quantization. Perform inverse operations at the receiver EEE Geeral e Image Coder Structure Motio Video (s 1,s 2,t) or (s 1,s 2 ) Natural Image Samplig A form of data compressio; usually lossless, but ca be lossy Redudacy Removal Lossless compressio: predictive

More information

The standard deviation of the mean

The standard deviation of the mean Physics 6C Fall 20 The stadard deviatio of the mea These otes provide some clarificatio o the distictio betwee the stadard deviatio ad the stadard deviatio of the mea.. The sample mea ad variace Cosider

More information

577. Estimation of surface roughness using high frequency vibrations

577. Estimation of surface roughness using high frequency vibrations 577. Estimatio of surface roughess usig high frequecy vibratios V. Augutis, M. Sauoris, Kauas Uiversity of Techology Electroics ad Measuremets Systems Departmet Studetu str. 5-443, LT-5368 Kauas, Lithuaia

More information

1 Inferential Methods for Correlation and Regression Analysis

1 Inferential Methods for Correlation and Regression Analysis 1 Iferetial Methods for Correlatio ad Regressio Aalysis I the chapter o Correlatio ad Regressio Aalysis tools for describig bivariate cotiuous data were itroduced. The sample Pearso Correlatio Coefficiet

More information

REGRESSION (Physics 1210 Notes, Partial Modified Appendix A)

REGRESSION (Physics 1210 Notes, Partial Modified Appendix A) REGRESSION (Physics 0 Notes, Partial Modified Appedix A) HOW TO PERFORM A LINEAR REGRESSION Cosider the followig data poits ad their graph (Table I ad Figure ): X Y 0 3 5 3 7 4 9 5 Table : Example Data

More information

Complex Number Theory without Imaginary Number (i)

Complex Number Theory without Imaginary Number (i) Ope Access Library Joural Complex Number Theory without Imagiary Number (i Deepak Bhalchadra Gode Directorate of Cesus Operatios, Mumbai, Idia Email: deepakm_4@rediffmail.com Received 6 July 04; revised

More information

The LHCf experiment at LHC

The LHCf experiment at LHC The LHCf experiment at LHC CALOR 2006 Chicago, 5-9 June 2006 University and INFN Firenze On behalf of the LHCf Collaboration The LHCf collaboration O. Adriani,, L. Bonechi, M. Bongi, P. Papini,, R. D AlessandroD

More information

Lecture 1 Probability and Statistics

Lecture 1 Probability and Statistics Wikipedia: Lecture 1 Probability ad Statistics Bejami Disraeli, British statesma ad literary figure (1804 1881): There are three kids of lies: lies, damed lies, ad statistics. popularized i US by Mark

More information

Infinite Sequences and Series

Infinite Sequences and Series Chapter 6 Ifiite Sequeces ad Series 6.1 Ifiite Sequeces 6.1.1 Elemetary Cocepts Simply speakig, a sequece is a ordered list of umbers writte: {a 1, a 2, a 3,...a, a +1,...} where the elemets a i represet

More information

A CONFINEMENT MODEL OF HIGH STRENGTH CONCRETE

A CONFINEMENT MODEL OF HIGH STRENGTH CONCRETE 3 th World Coferece o Earthquake Egieerig Vacouver, B.C., Caada August -6, 24 Paper No. 873 A CONFINEMENT MODEL OF HIGH STRENGTH CONCRETE Nobutaka NAKAZAWA, Kazuhiko KAWASHIMA 2, Gakuho WATANABE 3, Ju-ichi

More information

G. R. Pasha Department of Statistics Bahauddin Zakariya University Multan, Pakistan

G. R. Pasha Department of Statistics Bahauddin Zakariya University Multan, Pakistan Deviatio of the Variaces of Classical Estimators ad Negative Iteger Momet Estimator from Miimum Variace Boud with Referece to Maxwell Distributio G. R. Pasha Departmet of Statistics Bahauddi Zakariya Uiversity

More information

a. For each block, draw a free body diagram. Identify the source of each force in each free body diagram.

a. For each block, draw a free body diagram. Identify the source of each force in each free body diagram. Pre-Lab 4 Tesio & Newto s Third Law Refereces This lab cocers the properties of forces eerted by strigs or cables, called tesio forces, ad the use of Newto s third law to aalyze forces. Physics 2: Tipler

More information

x a x a Lecture 2 Series (See Chapter 1 in Boas)

x a x a Lecture 2 Series (See Chapter 1 in Boas) Lecture Series (See Chapter i Boas) A basic ad very powerful (if pedestria, recall we are lazy AD smart) way to solve ay differetial (or itegral) equatio is via a series expasio of the correspodig solutio

More information

Lecture 1 Probability and Statistics

Lecture 1 Probability and Statistics Wikipedia: Lecture 1 Probability ad Statistics Bejami Disraeli, British statesma ad literary figure (1804 1881): There are three kids of lies: lies, damed lies, ad statistics. popularized i US by Mark

More information

Position Time Graphs 12.1

Position Time Graphs 12.1 12.1 Positio Time Graphs Figure 3 Motio with fairly costat speed Chapter 12 Distace (m) A Crae Flyig Figure 1 Distace time graph showig motio with costat speed A Crae Flyig Positio (m [E] of pod) We kow

More information

A Simple Optimum-Time FSSP Algorithm for Multi-Dimensional Cellular Automata

A Simple Optimum-Time FSSP Algorithm for Multi-Dimensional Cellular Automata A Simple Optimum-Time FSSP Algorithm for Multi-Dimesioal Cellular Automata HIROSHI UMEO Uiversity of Osaka Electro-Commuicatio umeo@cyt.osakac.ac.jp KINUO NISHIDE Uiversity of Osaka Electro-Commuicatio

More information

Statistical Fundamentals and Control Charts

Statistical Fundamentals and Control Charts Statistical Fudametals ad Cotrol Charts 1. Statistical Process Cotrol Basics Chace causes of variatio uavoidable causes of variatios Assigable causes of variatio large variatios related to machies, materials,

More information

Assessment of extreme discharges of the Vltava River in Prague

Assessment of extreme discharges of the Vltava River in Prague Flood Recovery, Iovatio ad Respose I 05 Assessmet of extreme discharges of the Vltava River i Prague M. Holický, K. Jug & M. Sýkora Kloker Istitute, Czech Techical Uiversity i Prague, Czech Republic Abstract

More information

Simona Malace University of South Carolina

Simona Malace University of South Carolina Simoa Malace Uiversity of South Carolia i collaboratio with Y. Kah, W. Melitchouk, S.A. Kulagi, C. Keppel MENU010, May 31 Jue 4, 010 Williamsburg, VA Outlie New metho : etract from uclear Applicatio of

More information

Proposal PR : n. He(e,e ) Reaction

Proposal PR : n. He(e,e ) Reaction Proposal PR12-12-011: Asymmetry Measuremets to Extract G E ad G M at Q 2 = 1 2.6 (GeV/c) 2 from the Iclusive He(e,e ) Reactio Vicet Sulkosky Massachusetts Istitute of Techology O Behalf of T. Averett (W&M),

More information

PoS(DIS2017)208. Nuclear PDF studies with proton-lead measurements with the ALICE detector

PoS(DIS2017)208. Nuclear PDF studies with proton-lead measurements with the ALICE detector Nuclear PDF studies with proton-lead measurements with the ALICE detector a,b for the ALICE Collaboration a Institute for Subatomic Physics, Department for Physics and Astronomy and EMMEφ, Faculty of Science,

More information

5. Fast NLMS-OCF Algorithm

5. Fast NLMS-OCF Algorithm 5. Fast LMS-OCF Algorithm The LMS-OCF algorithm preseted i Chapter, which relies o Gram-Schmidt orthogoalizatio, has a compleity O ( M ). The square-law depedece o computatioal requiremets o the umber

More information

R is a scalar defined as follows:

R is a scalar defined as follows: Math 8. Notes o Dot Product, Cross Product, Plaes, Area, ad Volumes This lecture focuses primarily o the dot product ad its may applicatios, especially i the measuremet of agles ad scalar projectio ad

More information

6.867 Machine learning, lecture 7 (Jaakkola) 1

6.867 Machine learning, lecture 7 (Jaakkola) 1 6.867 Machie learig, lecture 7 (Jaakkola) 1 Lecture topics: Kerel form of liear regressio Kerels, examples, costructio, properties Liear regressio ad kerels Cosider a slightly simpler model where we omit

More information

Mechatronics. Time Response & Frequency Response 2 nd -Order Dynamic System 2-Pole, Low-Pass, Active Filter

Mechatronics. Time Response & Frequency Response 2 nd -Order Dynamic System 2-Pole, Low-Pass, Active Filter Time Respose & Frequecy Respose d -Order Dyamic System -Pole, Low-Pass, Active Filter R 4 R 7 C 5 e i R 1 C R 3 - + R 6 - + e out Assigmet: Perform a Complete Dyamic System Ivestigatio of the Two-Pole,

More information

Observation of Landau levels on nitrogen-doped flat graphite. surfaces without external magnetic fields

Observation of Landau levels on nitrogen-doped flat graphite. surfaces without external magnetic fields Supplemetary Iformatio Observatio of Ladau levels o itroge-doped flat graphite surfaces without exteral magetic fields Takahiro Kodo,, oghui Guo, Taishi Shikao, Tetsuya Suzuki, Masataka Sakurai, Susumu

More information

Correction for PMT temperature dependence of the LHCf calorimeters

Correction for PMT temperature dependence of the LHCf calorimeters Journal of Physics: Conference Series OPEN ACCESS Correction for PMT temperature dependence of the LHCf calorimeters To cite this article: Eri Matsubayashi and the LHCf collaboration 2015 J. Phys.: Conf.

More information

Assignment 2 Solutions SOLUTION. ϕ 1 Â = 3 ϕ 1 4i ϕ 2. The other case can be dealt with in a similar way. { ϕ 2 Â} χ = { 4i ϕ 1 3 ϕ 2 } χ.

Assignment 2 Solutions SOLUTION. ϕ 1  = 3 ϕ 1 4i ϕ 2. The other case can be dealt with in a similar way. { ϕ 2 Â} χ = { 4i ϕ 1 3 ϕ 2 } χ. PHYSICS 34 QUANTUM PHYSICS II (25) Assigmet 2 Solutios 1. With respect to a pair of orthoormal vectors ϕ 1 ad ϕ 2 that spa the Hilbert space H of a certai system, the operator  is defied by its actio

More information

Statistics 511 Additional Materials

Statistics 511 Additional Materials Cofidece Itervals o mu Statistics 511 Additioal Materials This topic officially moves us from probability to statistics. We begi to discuss makig ifereces about the populatio. Oe way to differetiate probability

More information

Physics Methods in Art and Archaeology

Physics Methods in Art and Archaeology Physics Methods i Art ad Archaeology Michael Wiescher PHYS 78 Archaeologist i the 90ties Somewhere i South America 80 years later --- i the Valley of the Kigs, gypt Physics Tools & Techology Dager & Adveture

More information