INVESTIGATION OF THE OSL SIGNAL FROM VERY DEEP TRAPS IN NATURAL QUARTZ
|
|
- Rodney Thornton
- 5 years ago
- Views:
Transcription
1 Meiterrnen Arheology n Arheometry, Vol. 010, No., pp Copyright 010 MAA Printe in Greee. All rights reserve. INVESTIGATION OF THE SIGNAL FROM VERY DEEP TRAPS IN NATURAL QUARTZ G. Kitis 1, N.G. Kiyk, G.S. Polymeris, n V. Pgonis 1 Aristotle University of Thessloniki, Nuler Physis Lortory, Thessloniki, Greee ISIK University, Physis Deprtment, Fulty of Siene n Arts, 980 Sile, Istnul, Turkey Culturl n Eutionl Tehnology Institute R.C. Athen/Arheometry Lortory, Xnthi, Greee MDniel College, Physis Dept, Westminster, MD 11, USA Corresponing uthor: gkitis@uth.gr ABSTRACT It hs een reently reporte y severl stuies tht thermlly trnsferre optilly stimulte luminesene (TT ) signl from qurtz grins n e use to exten the ting rnge for qurtz smples. The TT signls re elieve to onsist of reuperte (Re) omponent n si trnsferre (BT ) omponent. In the present work the TT signls from severl types of unfire qurtz smples were stuie. A speil protool ws use, whih llowe the mesure the from very eep trps (VDT) s funtion of the stimultion temperture. It ws foun tht ll qurtz smples exhiit TT signls, whih re epene on smple n on the stimultion temperture. The tivtion energy of the proess ws evlute n the influenes of the TT on the Re ting protool re isusse. KEYWORDS: qurtz, eep trps, TT
2 9 G. KITIS et l INTRODUCTION Severl reent stuies hve shown tht thermlly trnsferre (TT ) signl from qurtz grins n exten the ting rnge for qurtz smples of vrious origins y lmost n orer of mgnitue (Wng et l., 00; Wng et l., 00; Tsukmoto et l., 008). It hs een suggeste tht the TT signl omprises reuperte (Re) omponent n si trnsferre (BT ) omponent, Aitken (1998). Dting protools se on the TT signl ttempt to seprte the BT signl n the Re signl, y therml tretments. It is suggeste tht the Re signl is the mjor ontriutor to the TT signl. BT signl is smller ut signifint omponent. Aitken (1998) suggeste tht the Re results from oule trnsfer proess while the BT ws ue to eletrons 10 SLE ME Stimultion time (se) trppe originlly in light insensitive trps. An lterntive single trnsfer proess for the proution of Re hs een suggeste y Amie et l. (008) n ws moele y Pgonis et l. (008). In the single trnsfer proess, light sensitive trp ts s the soure of eletrons for the Re. It is prole tht the BT signl, or t lest some prt of it, origintes from Very Deep Trps (VDT). As VDT we onsier those trps whih re responsile for TL glow peks with pek mximum temperture of 00 0 C. The im of the present work is to investigte the ontriutions of the signls from the VDT in unfire nturl qurtz of vrious origins, to set protools involving mesurements t high tempertures like Re ting protool ME Stimultion time (se) Figure 1: High effiieny TT urve shpes for qurtz mesure t vrious stimultion tempertures. Curve () C, Curve () 0 0 C n Curve () t 0 C. Curve () orrespons to the kgroun signl mesure t room temperture. MATERIALS AND APPARATUS The smples were qurtz of vrious origins n from iverse lotions of Turkey. Smples with lortory oes SLE n were very young ostl unes ner Istnul, with Gy n Gy equivlent oses (Kiyk n Cnel, 00).Smple ws lso from young otl unes from Inkumu Brtin, in the mile prt of the Blk Se Region with nturl ose 0.0 Gy. Smple PTR ws eposit from Ptr in the Meiterrnen ost n ontin nturl ose out. Gy. Smples SRZ1 n SRZ were from ifferent lyers of mrine terre in Sroz, on the Egen ostl re. These smples re ol n the nturl SAR p
3 INVESTIGATION OF THE SIGNAL FROM VERY DEEP TRAPS IN NATURAL QUARTZ 9 leoose ose in qurtz grins were estimte s 181 n 19 Gy respetively. ME1 n ME were from fluvil terre seiments from n re lose to the Mrmr Ereglisi, in Europen prt of the Mrmr Region with 1 n 1 Gy pleooses.. The smples s reeive were wet sieve, n qurtz grins with imensions etween 90 n 180 μm were selete n eposite on stinless steel isks of 1 m re. Qurtz purity of the smples ws previously verifie y IRSL mesurements t mient temperture. Blue light emitting ioes (LEDs) (0 nm, 0 mw/m ) were use for stimultion intensities linerly inrese etween 0 n mw/m. All mesurements were performe using the RISØ TL/ reer (moel TL/ DA 1) equippe with out 0.1 Gy/s 90 Sr/Y β ry soure. The reer is fitte with n EMI 9QA PM Tue. Luminesene signls were etete through U 0 filters. The TL reout PTR heting rte use ws 1 K/s for ll mesurements. EXPERIMENTAL RESULTS AND DIS CUSSION The multi liquot protool use to stuy the effiieny of TT from VDT ws the following: Step 1: Nturl smple+00gy et ose. Step : TL reout to 00 0 C. Step : Test ose (TD= 10 Gy) n TL to 00 0 C. Step : Blue CW t vrile stimultion temperture Ti (1C C in steps of C) for 000 s. Step : Resiul TL up to 00 0 C. Step : TD n TL to 00 0 C. Step : Repet steps 1 for new smple n new stimultion temperture Ti SRZ Stimultion time (se) 10 SRZ Stimultion time (se) Figure : Low effiieny TT lue urve shpes for qurtz mesure t vrious mesuring tempertures. Curve () C, Curve () 0 0 C n Curve () t 0 C. Curve () orrespons to the kgroun signl mesure t room temperture Sine the egree of filling of VDT y the geologil ose in not known, n itionl irrition is given in step 1 to ensure the filling of the VDT. In step, ny trpping level responsile for TL glow peks up to 00 0 C is erse. The mesurement in step is use to evlute the sensitivity to low test ose n verify tht the heting up to 00 0 C erses the TL signl
4 9 G. KITIS et l ove 00 0 C own to the kgroun level. Step ims to stuy the mgnitue of the TT signl from VDT s funtion of the stimultion temperture. Step is pplie to fin whether TL signl ppers etween C fter the stimultion t high tempertures, ue, for exmple, to phototrnsfer proess. Finlly step will evlute the sensitivity to the low test ose s in step n llows to evlute how the pplie protool ffets the sensitivity of the qurtz smple. The protool ws pplie to the speifi eight ifferent qurtz smples esrie ove. In six of these smples only three mesuring tempertures were use (190, 0 n 0 C). On the other hn, sine the mesurement t high tempertures is thermlly tivte optil stimultion proess, two smples were selete, one with high n nother with low TT signls. In these two smples the optil stimultion ws stuie in the whole temperture region from 1 to 0 C in steps of 0 C. The purpose of this experiment is to evlute the tivtion energy vlues of the thermlly tivte optilly stimulte proess. The min result of this experiment respons iretly to the first question set in the present work, nmely to show tht ll qurtz smples exhiit TT signls. The intensity of the signls from VDT ws foun to epen on the type of qurtz smple use. The TT urves from VDT re shown in Figs. 1 n. In Fig. 1 the smples hving very high effiieny for TT re presente wheres Fig. shows the smples hving low TT effiieny. In ll ses the kgroun level is inlue. It is useful here to present in Fig. the results of the steps 1,,, n of the protool. The glow urve () of Fig. results fter the irrition with 00 Gy. The glow urve () reeive in step gives (i) the sensitivity to low ose fter the hevy irrition in step 1 n ssures (ii) the TL reout in step erses the TL ove 00 o C to the usul kgroun level n it oes not leves ny intense resiul TL signl t the very high tempertures. The sene of ny signl in urve () of step, shows tht the optil stimultion t the high tempertures of step oes not use ny re trpping to the low temperture glow peks. Finlly, the glow urve (), whih lmost oinies with glow urve () shows tht the smple tretment in steps to oes not influene the sensitivity of the smples. TL(.u.) , Temperture ( 0 C) Figure : ) NTL plus 00 Gy et ose. () TL glowurve from step. () Resiul TL fter lue CW stimultion t the temperture of o C () TL from step. The si hrteristi of TT urve is tht the TT signl inreses from zero to higher level n then tkes the form of more or less stle emission. However, in some smples for very short stimultion times fst omponent ppers. These ses re shown in Fig., where only the first 00 s of the stimultion urves re inlue in the plot. Furthermore, it ppers only for stimultion tempertures lower thn 1 0 C, n not for higher stimultion tempertures. Oviously this omponent n not e relte to the known fst omponent originting from the eletron trp responsile for the 0 C TL glow pek of qurtz, sine this eletron trp ws emptie y the TL reout up to 00 0 C. Fig. shows the ehvior of the totl TT s funtion of the stimultion temperture. The exponentil nture of the ehvior llows the evlution of the tivtion energy of the optil stimultion t high tempertures for two of the smples. The respetive Arrhenius plots re shown in Fig.. In the se of qurtz smple whih exhiits strong TT signl, the tivtion energy ws foun to e E=0.±0.0 ev, wheres for the se of qurtz, whih shows wek TT signl, it ws foun to e E=0.±0.0 ev 0 TL (.u)
5 INVESTIGATION OF THE SIGNAL FROM VERY DEEP TRAPS IN NATURAL QUARTZ Stimultion time (s) Figure : Exmples of TT urves showing fst omponent t very short stimultion times. Curve () qurtz, urve () PTR qurtz, urve () SLE qurtz n urve () the kgroun. Sine the therml quenhing effet is often reporte in qurtz, it is neessry to exmine the results of Fig. uner the influene of therml quenhing. Assuming tht the therml quenhing prmeters C=.8 x10 n W=0. ev, given y Wintle (19) s representtive for qurtz, it is possile to orret the intensities ue to therml quenhing s follows. Initilly, the vlues of the therml quenhing effiieny were evlute for eh one of the stimultion tempertures. Then the intensity t eh temperture is orrete ue to therml quenhing y iviing it with the evlute orresponing therml quenhing effiieny. Then the logrithm of the orrete vlues is plotte ginst 1/kT (Arrhenius plots). The results for oth integrte regions re shown in Fig.. The resulting vlues of the tivtion energies were foun to e E=1.0±0.0 ev, n E=0.9±0.0 ev for n. Using only the present t, it is not possile to eie whih vlues re the orret ones. Therefore, seprte experiments of TL s funtion of heting rte re require in orer to investigte if the therml quenhing effet is present or not in the speifi qurtz smples stuie.. CONCLUSIONS Uner the omine tion of therml tivtion n optil stimultion eletrons trppe t VDT re lierte to the onution n n reomine emitting photons. This is known s TT signl. Eight unfire qurtz smples of vrious origins tht were stuie, exhiite TT signls in wie region of stimultion tempertures. It ws foun tht the TT signl epens strongly on the type of qurtz smple stuie. This TT signl oul e n ppreile omponent of the BT signl involve in the TT ting protools. Aoring to the results of the present work, the importne of the BT prt of the TT ting protool epens lso on the smple stuie, n we reommen tht the BT signls re inlue in TT protools, rther thn eing omitte. (.u.) () 1E E E T ( 0 C) ln() , E=0. ±0.0, E=0. ±0.0 () / k T Figure : Arrhenius plot showing the tivtion energy evlution for the TT signl without tking into ount therml quenhing. qurtz E=0.±0.0 ev n qurtz E=0.±0.0 ev
6 98 G. KITIS et l (.u.) () E8 E8 1E8 0E0 ln() , E = 1.0 +/- 0.,0, E = 0.9 +/- 0.0 () T ( 0 C) / k T Figure : Arrhenius plot showing the tivtion energy evlution for the TT signl tking into ount therml quenhing. qurtz E=1.0±0.0 ev n qurtz E=0.9 ±0.0 ev REFERENCES Amie, G.A., Biley, R.M., Wng, X.L., Wintle, A.G., 008. The mehnism of thermllytrnsferre optilly stimulte luminesene. J. Phys. D: Appl. Phys. 1, 10. Aitken, M.J., An Introution to Optil Dting. Oxfor University Press, Oxfor. Bulur, E., 000. A simple trnsformtion for onverting CW urves to LM urves. Rit. Mes., Kitis, G. An Pgonis, V Computerize urve eonvolution nlysis for LM. Rit. Mesur., 1. Kiyk, N.G., Cnel, T., 00. Equivlent ose in qurtz from young smples using the SAR protool n the effet of prehet temperture. Rit. Mes. 1, Pgonis, V., Wintle, A.G., Chen, R., Wng, X.L., 008. A theoretil moel for new ting protool for qurtz se on thermlly trnsferre (TT ). Rit. Mes., Tsukmoto, S., Duller, G.A.T., Wintle, A.G., 008. Chrteristis of thermlly trnsferre optilly stimulte luminesene (TT ) in qurtz n its potentil for ting seiments. Rit. Mes., Wng, X.L., Lu, Y.C., Wintle, A.G., 00. Reuperte ting of fine grine qurtz in Chinese loess. Qut. Geohronol. 1, Wng, X.L., Wintle, A.G., Lu, Y.C., 00. Thermlly trnsferre luminesene in fine grine qurtz from Chinese loess: si oservtions. Rit. Mes. 1, 9 8. Wng, X.L., Wintle, A.G., Lu, Y.C., 00. Testing single liquot protool for reuperte ting. Rit. Mes.,
Numbers and indices. 1.1 Fractions. GCSE C Example 1. Handy hint. Key point
GCSE C Emple 7 Work out 9 Give your nswer in its simplest form Numers n inies Reiprote mens invert or turn upsie own The reiprol of is 9 9 Mke sure you only invert the frtion you re iviing y 7 You multiply
More informationCounting Paths Between Vertices. Isomorphism of Graphs. Isomorphism of Graphs. Isomorphism of Graphs. Isomorphism of Graphs. Isomorphism of Graphs
Isomorphism of Grphs Definition The simple grphs G 1 = (V 1, E 1 ) n G = (V, E ) re isomorphi if there is ijetion (n oneto-one n onto funtion) f from V 1 to V with the property tht n re jent in G 1 if
More informationMATH 122, Final Exam
MATH, Finl Exm Winter Nme: Setion: You must show ll of your work on the exm pper, legily n in etil, to reeive reit. A formul sheet is tthe.. (7 pts eh) Evlute the following integrls. () 3x + x x Solution.
More informationAppendix A: HVAC Equipment Efficiency Tables
Appenix A: HVAC Equipment Effiieny Tles Figure A.1 Resientil Centrl Air Conitioner FEMP Effiieny Reommention Prout Type Reommene Level Best Aville 11.0 or more EER 14.6 EER Split Systems 13.0 or more SEER
More informationSurds and Indices. Surds and Indices. Curriculum Ready ACMNA: 233,
Surs n Inies Surs n Inies Curriulum Rey ACMNA:, 6 www.mthletis.om Surs SURDS & & Inies INDICES Inies n surs re very losely relte. A numer uner (squre root sign) is lle sur if the squre root n t e simplifie.
More informationTHE INFLUENCE OF MODEL RESOLUTION ON AN EXPRESSION OF THE ATMOSPHERIC BOUNDARY LAYER IN A SINGLE-COLUMN MODEL
THE INFLUENCE OF MODEL RESOLUTION ON AN EXPRESSION OF THE ATMOSPHERIC BOUNDARY LAYER IN A SINGLE-COLUMN MODEL P3.1 Kot Iwmur*, Hiroto Kitgw Jpn Meteorologil Ageny 1. INTRODUCTION Jpn Meteorologil Ageny
More informationCS 491G Combinatorial Optimization Lecture Notes
CS 491G Comintoril Optimiztion Leture Notes Dvi Owen July 30, August 1 1 Mthings Figure 1: two possile mthings in simple grph. Definition 1 Given grph G = V, E, mthing is olletion of eges M suh tht e i,
More informationElectronic Circuits I Revision after midterm
Eletroni Ciruits I Revision fter miterm Dr. Ahme ElShfee, ACU : Fll 2018, Eletroni Ciruits I -1 / 14 - MCQ1 # Question If the frequeny of the input voltge in Figure 2 36 is inrese, the output voltge will
More informationANALYSIS AND MODELLING OF RAINFALL EVENTS
Proeedings of the 14 th Interntionl Conferene on Environmentl Siene nd Tehnology Athens, Greee, 3-5 Septemer 215 ANALYSIS AND MODELLING OF RAINFALL EVENTS IOANNIDIS K., KARAGRIGORIOU A. nd LEKKAS D.F.
More information1 This diagram represents the energy change that occurs when a d electron in a transition metal ion is excited by visible light.
1 This igrm represents the energy hnge tht ours when eletron in trnsition metl ion is exite y visile light. Give the eqution tht reltes the energy hnge ΔE to the Plnk onstnt, h, n the frequeny, v, of the
More information22: Union Find. CS 473u - Algorithms - Spring April 14, We want to maintain a collection of sets, under the operations of:
22: Union Fin CS 473u - Algorithms - Spring 2005 April 14, 2005 1 Union-Fin We wnt to mintin olletion of sets, uner the opertions of: 1. MkeSet(x) - rete set tht ontins the single element x. 2. Fin(x)
More informationLecture 6: Coding theory
Leture 6: Coing theory Biology 429 Crl Bergstrom Ferury 4, 2008 Soures: This leture loosely follows Cover n Thoms Chpter 5 n Yeung Chpter 3. As usul, some of the text n equtions re tken iretly from those
More informationParticle Physics. Michaelmas Term 2011 Prof Mark Thomson. Handout 3 : Interaction by Particle Exchange and QED. Recap
Prtile Physis Mihelms Term 2011 Prof Mrk Thomson g X g X g g Hnout 3 : Intertion y Prtile Exhnge n QED Prof. M.A. Thomson Mihelms 2011 101 Rep Working towrs proper lultion of ey n sttering proesses lnitilly
More informationVISIBLE AND INFRARED ABSORPTION SPECTRA OF COVERING MATERIALS FOR SOLAR COLLECTORS
AGRICULTURAL ENGINEERING VISIBLE AND INFRARED ABSORPTION SPECTRA OF COVERING MATERIALS FOR SOLAR COLLECTORS Ltvi University of Agriulture E-mil: ilze.pelee@llu.lv Astrt Use of solr energy inreses every
More informationCIT 596 Theory of Computation 1. Graphs and Digraphs
CIT 596 Theory of Computtion 1 A grph G = (V (G), E(G)) onsists of two finite sets: V (G), the vertex set of the grph, often enote y just V, whih is nonempty set of elements lle verties, n E(G), the ege
More informationThe Stirling Engine: The Heat Engine
Memoril University of Newfounln Deprtment of Physis n Physil Oenogrphy Physis 2053 Lortory he Stirling Engine: he Het Engine Do not ttempt to operte the engine without supervision. Introution Het engines
More information6.5 Improper integrals
Eerpt from "Clulus" 3 AoPS In. www.rtofprolemsolving.om 6.5. IMPROPER INTEGRALS 6.5 Improper integrls As we ve seen, we use the definite integrl R f to ompute the re of the region under the grph of y =
More informationNow we must transform the original model so we can use the new parameters. = S max. Recruits
MODEL FOR VARIABLE RECRUITMENT (ontinue) Alterntive Prmeteriztions of the pwner-reruit Moels We n write ny moel in numerous ifferent ut equivlent forms. Uner ertin irumstnes it is onvenient to work with
More informationCS 2204 DIGITAL LOGIC & STATE MACHINE DESIGN SPRING 2014
S 224 DIGITAL LOGI & STATE MAHINE DESIGN SPRING 214 DUE : Mrh 27, 214 HOMEWORK III READ : Relte portions of hpters VII n VIII ASSIGNMENT : There re three questions. Solve ll homework n exm prolems s shown
More informationSystem Validation (IN4387) November 2, 2012, 14:00-17:00
System Vlidtion (IN4387) Novemer 2, 2012, 14:00-17:00 Importnt Notes. The exmintion omprises 5 question in 4 pges. Give omplete explntion nd do not onfine yourself to giving the finl nswer. Good luk! Exerise
More informationReview Topic 14: Relationships between two numerical variables
Review Topi 14: Reltionships etween two numeril vriles Multiple hoie 1. Whih of the following stterplots est demonstrtes line of est fit? A B C D E 2. The regression line eqution for the following grph
More informationMCH T 111 Handout Triangle Review Page 1 of 3
Hnout Tringle Review Pge of 3 In the stuy of sttis, it is importnt tht you e le to solve lgeri equtions n tringle prolems using trigonometry. The following is review of trigonometry sis. Right Tringle:
More informationMomentum and Energy Review
Momentum n Energy Review Nme: Dte: 1. A 0.0600-kilogrm ll trveling t 60.0 meters per seon hits onrete wll. Wht spee must 0.0100-kilogrm ullet hve in orer to hit the wll with the sme mgnitue of momentum
More informationF / x everywhere in some domain containing R. Then, + ). (10.4.1)
0.4 Green's theorem in the plne Double integrls over plne region my be trnsforme into line integrls over the bounry of the region n onversely. This is of prtil interest beuse it my simplify the evlution
More information50 AMC Lectures Problem Book 2 (36) Substitution Method
0 AMC Letures Prolem Book Sustitution Metho PROBLEMS Prolem : Solve for rel : 9 + 99 + 9 = Prolem : Solve for rel : 0 9 8 8 Prolem : Show tht if 8 Prolem : Show tht + + if rel numers,, n stisf + + = Prolem
More informationSECTION A STUDENT MATERIAL. Part 1. What and Why.?
SECTION A STUDENT MATERIAL Prt Wht nd Wh.? Student Mteril Prt Prolem n > 0 n > 0 Is the onverse true? Prolem If n is even then n is even. If n is even then n is even. Wht nd Wh? Eploring Pure Mths Are
More information2.4 Theoretical Foundations
2 Progrmming Lnguge Syntx 2.4 Theoretil Fountions As note in the min text, snners n prsers re se on the finite utomt n pushown utomt tht form the ottom two levels of the Chomsky lnguge hierrhy. At eh level
More informationNecessary and sucient conditions for some two. Abstract. Further we show that the necessary conditions for the existence of an OD(44 s 1 s 2 )
Neessry n suient onitions for some two vrile orthogonl esigns in orer 44 C. Koukouvinos, M. Mitrouli y, n Jennifer Seerry z Deite to Professor Anne Penfol Street Astrt We give new lgorithm whih llows us
More informationSolutions for HW9. Bipartite: put the red vertices in V 1 and the black in V 2. Not bipartite!
Solutions for HW9 Exerise 28. () Drw C 6, W 6 K 6, n K 5,3. C 6 : W 6 : K 6 : K 5,3 : () Whih of the following re iprtite? Justify your nswer. Biprtite: put the re verties in V 1 n the lk in V 2. Biprtite:
More informationa) Read over steps (1)- (4) below and sketch the path of the cycle on a P V plot on the graph below. Label all appropriate points.
Prole 3: Crnot Cyle of n Idel Gs In this prole, the strting pressure P nd volue of n idel gs in stte, re given he rtio R = / > of the volues of the sttes nd is given Finlly onstnt γ = 5/3 is given You
More informationAP CALCULUS Test #6: Unit #6 Basic Integration and Applications
AP CALCULUS Test #6: Unit #6 Bsi Integrtion nd Applitions A GRAPHING CALCULATOR IS REQUIRED FOR SOME PROBLEMS OR PARTS OF PROBLEMS IN THIS PART OF THE EXAMINATION. () The ext numeril vlue of the orret
More informationSOME INTEGRAL INEQUALITIES FOR HARMONICALLY CONVEX STOCHASTIC PROCESSES ON THE CO-ORDINATES
Avne Mth Moels & Applitions Vol3 No 8 pp63-75 SOME INTEGRAL INEQUALITIES FOR HARMONICALLY CONVE STOCHASTIC PROCESSES ON THE CO-ORDINATES Nurgül Okur * Imt Işn Yusuf Ust 3 3 Giresun University Deprtment
More informationTIME-VARYING AND NON-LINEAR DYNAMICAL SYSTEM IDENTIFICATION USING THE HILBERT TRANSFORM
Proeeings of ASME VIB 5: th Biennil Conferene on Mehnil Virtion n Noise Septemer 4-8, 5 Long Beh, CA, USA DETC5-84644 TIME-VARYING AND NON-LINEAR DYNAMICAL SYSTEM IDENTIFICATION USING THE HILBERT TRANSFORM
More informationFactorising FACTORISING.
Ftorising FACTORISING www.mthletis.om.u Ftorising FACTORISING Ftorising is the opposite of expning. It is the proess of putting expressions into rkets rther thn expning them out. In this setion you will
More informationSTRUCTURAL AND MAGNETIC PROPERTIES OF Fe/Si x Fe 1! x MULTILAYERS
MOLECULAR PHYSICS REPORTS 0 (00) 8-86 STRUCTURAL AND MAGNETIC PROPERTIES OF Fe/ x Fe! x MULTILAYERS P. WANDZIUK, M. KOPCEWICZ, B. SZYMAŃSKI, AND T. LUCIŃSKI Institute of Moleculr Physics, Polish Acdemy
More informationApplied. Grade 9 Assessment of Mathematics. Multiple-Choice Items. Winter 2005
Applie Gre 9 Assessment of Mthemtis Multiple-Choie Items Winter 2005 Plese note: The formt of these ooklets is slightly ifferent from tht use for the ssessment. The items themselves remin the sme. . Multiple-Choie
More informationfor all x in [a,b], then the area of the region bounded by the graphs of f and g and the vertical lines x = a and x = b is b [ ( ) ( )] A= f x g x dx
Applitions of Integrtion Are of Region Between Two Curves Ojetive: Fin the re of region etween two urves using integrtion. Fin the re of region etween interseting urves using integrtion. Desrie integrtion
More informationA Primer on Continuous-time Economic Dynamics
Eonomis 205A Fll 2008 K Kletzer A Primer on Continuous-time Eonomi Dnmis A Liner Differentil Eqution Sstems (i) Simplest se We egin with the simple liner first-orer ifferentil eqution The generl solution
More information18.06 Problem Set 4 Due Wednesday, Oct. 11, 2006 at 4:00 p.m. in 2-106
8. Problem Set Due Wenesy, Ot., t : p.m. in - Problem Mony / Consier the eight vetors 5, 5, 5,..., () List ll of the one-element, linerly epenent sets forme from these. (b) Wht re the two-element, linerly
More informationMid-Term Examination - Spring 2014 Mathematical Programming with Applications to Economics Total Score: 45; Time: 3 hours
Mi-Term Exmintion - Spring 0 Mthemtil Progrmming with Applitions to Eonomis Totl Sore: 5; Time: hours. Let G = (N, E) e irete grph. Define the inegree of vertex i N s the numer of eges tht re oming into
More informationEigenvectors and Eigenvalues
MTB 050 1 ORIGIN 1 Eigenvets n Eigenvlues This wksheet esries the lger use to lulte "prinipl" "hrteristi" iretions lle Eigenvets n the "prinipl" "hrteristi" vlues lle Eigenvlues ssoite with these iretions.
More informationProject 6: Minigoals Towards Simplifying and Rewriting Expressions
MAT 51 Wldis Projet 6: Minigols Towrds Simplifying nd Rewriting Expressions The distriutive property nd like terms You hve proly lerned in previous lsses out dding like terms ut one prolem with the wy
More informationProbability. b a b. a b 32.
Proility If n event n hppen in '' wys nd fil in '' wys, nd eh of these wys is eqully likely, then proility or the hne, or its hppening is, nd tht of its filing is eg, If in lottery there re prizes nd lnks,
More informationDIFFERENCE BETWEEN TWO RIEMANN-STIELTJES INTEGRAL MEANS
Krgujev Journl of Mthemtis Volume 38() (204), Pges 35 49. DIFFERENCE BETWEEN TWO RIEMANN-STIELTJES INTEGRAL MEANS MOHAMMAD W. ALOMARI Abstrt. In this pper, severl bouns for the ifferene between two Riemn-
More informationFirst compression (0-6.3 GPa) First decompression ( GPa) Second compression ( GPa) Second decompression (35.
0.9 First ompression (0-6.3 GP) First deompression (6.3-2.7 GP) Seond ompression (2.7-35.5 GP) Seond deompression (35.5-0 GP) V/V 0 0.7 0.5 0 5 10 15 20 25 30 35 P (GP) Supplementry Figure 1 Compression
More informationNEW CIRCUITS OF HIGH-VOLTAGE PULSE GENERATORS WITH INDUCTIVE-CAPACITIVE ENERGY STORAGE
NEW CIRCUITS OF HIGH-VOLTAGE PULSE GENERATORS WITH INDUCTIVE-CAPACITIVE ENERGY STORAGE V.S. Gordeev, G.A. Myskov Russin Federl Nuler Center All-Russi Sientifi Reserh Institute of Experimentl Physis (RFNC-VNIIEF)
More informationCSE 332. Sorting. Data Abstractions. CSE 332: Data Abstractions. QuickSort Cutoff 1. Where We Are 2. Bounding The MAXIMUM Problem 4
Am Blnk Leture 13 Winter 2016 CSE 332 CSE 332: Dt Astrtions Sorting Dt Astrtions QuikSort Cutoff 1 Where We Are 2 For smll n, the reursion is wste. The onstnts on quik/merge sort re higher thn the ones
More informationNote 12. Introduction to Digital Control Systems
Note Introduction to Digitl Control Systems Deprtment of Mechnicl Engineering, University Of Ssktchewn, 57 Cmpus Drive, Ssktoon, SK S7N 5A9, Cnd . Introduction A digitl control system is one in which the
More informationStatistics in medicine
Sttistis in meiine Workshop 1: Sreening n ignosti test evlution Septemer 22, 2016 10:00 AM to 11:50 AM Hope 110 Ftm Shel, MD, MS, MPH, PhD Assistnt Professor Chroni Epiemiology Deprtment Yle Shool of Puli
More informationERT 316: REACTION ENGINEERING CHAPTER 3 RATE LAWS & STOICHIOMETRY
ER 316: REIO EGIEERIG HER 3 RE LWS & SOIHIOMERY 1 OULIE R 1: Rte Lws Reltive Rtes of Retion Retion Orer & Rte Lw Retion Rte onstnt, k R 2: Stoihiometry th System Stoihiometri le low System Stoihiometri
More informationIf we have a function f(x) which is well-defined for some a x b, its integral over those two values is defined as
Y. D. Chong (26) MH28: Complex Methos for the Sciences 2. Integrls If we hve function f(x) which is well-efine for some x, its integrl over those two vlues is efine s N ( ) f(x) = lim x f(x n ) where x
More information8 THREE PHASE A.C. CIRCUITS
8 THREE PHSE.. IRUITS The signls in hpter 7 were sinusoidl lternting voltges nd urrents of the so-lled single se type. n emf of suh type n e esily generted y rotting single loop of ondutor (or single winding),
More informationAlgebra 2 Semester 1 Practice Final
Alger 2 Semester Prtie Finl Multiple Choie Ientify the hoie tht est ompletes the sttement or nswers the question. To whih set of numers oes the numer elong?. 2 5 integers rtionl numers irrtionl numers
More informationPart 4. Integration (with Proofs)
Prt 4. Integrtion (with Proofs) 4.1 Definition Definition A prtition P of [, b] is finite set of points {x 0, x 1,..., x n } with = x 0 < x 1
More informationSection 4: Integration ECO4112F 2011
Reding: Ching Chpter Section : Integrtion ECOF Note: These notes do not fully cover the mteril in Ching, ut re ment to supplement your reding in Ching. Thus fr the optimistion you hve covered hs een sttic
More informationU Q W The First Law of Thermodynamics. Efficiency. Closed cycle steam power plant. First page of S. Carnot s paper. Sadi Carnot ( )
0-9-0 he First Lw of hermoynmis Effiieny When severl lterntive proesses involving het n work re ville to hnge system from n initil stte hrterize y given vlues of the mrosopi prmeters (pressure p i, temperture
More informationSpacetime and the Quantum World Questions Fall 2010
Spetime nd the Quntum World Questions Fll 2010 1. Cliker Questions from Clss: (1) In toss of two die, wht is the proility tht the sum of the outomes is 6? () P (x 1 + x 2 = 6) = 1 36 - out 3% () P (x 1
More information1B40 Practical Skills
B40 Prcticl Skills Comining uncertinties from severl quntities error propgtion We usully encounter situtions where the result of n experiment is given in terms of two (or more) quntities. We then need
More informationSection 2.1 Special Right Triangles
Se..1 Speil Rigt Tringles 49 Te --90 Tringle Setion.1 Speil Rigt Tringles Te --90 tringle (or just 0-60-90) is so nme euse of its ngle mesures. Te lengts of te sies, toug, ve very speifi pttern to tem
More informationI 3 2 = I I 4 = 2A
ECE 210 Eletril Ciruit Anlysis University of llinois t Chigo 2.13 We re ske to use KCL to fin urrents 1 4. The key point in pplying KCL in this prolem is to strt with noe where only one of the urrents
More information1 PYTHAGORAS THEOREM 1. Given a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
1 PYTHAGORAS THEOREM 1 1 Pythgors Theorem In this setion we will present geometri proof of the fmous theorem of Pythgors. Given right ngled tringle, the squre of the hypotenuse is equl to the sum of the
More informationReview of Gaussian Quadrature method
Review of Gussin Qudrture method Nsser M. Asi Spring 006 compiled on Sundy Decemer 1, 017 t 09:1 PM 1 The prolem To find numericl vlue for the integrl of rel vlued function of rel vrile over specific rnge
More informationRadiation Measurements
Rdition Mesurements xxx (2012) 1e7 Contents lists ville t SciVerse ScienceDirect Rdition Mesurements journl homepge: www.elsevier.com/locte/rdmes Modeling of the shpe of infrred stimulted luminescence
More informationOverview of Calculus
Overview of Clculus June 6, 2016 1 Limits Clculus begins with the notion of limit. In symbols, lim f(x) = L x c In wors, however close you emn tht the function f evlute t x, f(x), to be to the limit L
More informationWelcome. Balanced search trees. Balanced Search Trees. Inge Li Gørtz
Welome nge Li Gørt. everse tehing n isussion of exerises: 02110 nge Li Gørt 3 tehing ssistnts 8.00-9.15 Group work 9.15-9.45 isussions of your solutions in lss 10.00-11.15 Leture 11.15-11.45 Work on exerises
More informationEstimation of Global Solar Radiation in Onitsha and Calabar Using Empirical Models
Communitions in Applied Sienes ISS 0-77 Volume, umer, 0, 5-7 Estimtion of Glol Solr dition in Onitsh nd Clr Using Empiril Models M.. nuhi, J. E. Ekpe nd G. F Ieh Deprtment of Industril Physis, Eonyi Stte
More informationLogic, Set Theory and Computability [M. Coppenbarger]
14 Orer (Hnout) Definition 7-11: A reltion is qusi-orering (or preorer) if it is reflexive n trnsitive. A quisi-orering tht is symmetri is n equivlene reltion. A qusi-orering tht is nti-symmetri is n orer
More informationEmission of K -, L - and M - Auger Electrons from Cu Atoms. Abstract
Emission of K -, L - nd M - uger Electrons from Cu toms Mohmed ssd bdel-rouf Physics Deprtment, Science College, UEU, l in 17551, United rb Emirtes ssd@ueu.c.e bstrct The emission of uger electrons from
More informationLecture Notes No. 10
2.6 System Identifition, Estimtion, nd Lerning Leture otes o. Mrh 3, 26 6 Model Struture of Liner ime Invrint Systems 6. Model Struture In representing dynmil system, the first step is to find n pproprite
More information= f (c) f (c) the height of the rectangle guaranteed by the MVT for integrals.
Get Rey: Given (t) = 8t n v() = 6, fin the isplcement n istnce of the oject from t= to t= If () = 4, fin the position of the prticle t t= I. Averge Vlue of Function Wht oes represent? Cn we rw rectngle
More information6.3.2 Spectroscopy. N Goalby chemrevise.org 1 NO 2 CH 3. CH 3 C a. NMR spectroscopy. Different types of NMR
6.. Spetrosopy NMR spetrosopy Different types of NMR NMR spetrosopy involves intertion of mterils with the lowenergy rdiowve region of the eletromgneti spetrum NMR spetrosopy is the sme tehnology s tht
More information5. Every rational number have either terminating or repeating (recurring) decimal representation.
CHAPTER NUMBER SYSTEMS Points to Rememer :. Numer used for ounting,,,,... re known s Nturl numers.. All nturl numers together with zero i.e. 0,,,,,... re known s whole numers.. All nturl numers, zero nd
More informationSOME COPLANAR POINTS IN TETRAHEDRON
Journl of Pure n Applie Mthemtis: Avnes n Applitions Volume 16, Numer 2, 2016, Pges 109-114 Aville t http://sientifivnes.o.in DOI: http://x.oi.org/10.18642/jpm_7100121752 SOME COPLANAR POINTS IN TETRAHEDRON
More informationTutorial Worksheet. 1. Find all solutions to the linear system by following the given steps. x + 2y + 3z = 2 2x + 3y + z = 4.
Mth 5 Tutoril Week 1 - Jnury 1 1 Nme Setion Tutoril Worksheet 1. Find ll solutions to the liner system by following the given steps x + y + z = x + y + z = 4. y + z = Step 1. Write down the rgumented mtrix
More informationA Lower Bound for the Length of a Partial Transversal in a Latin Square, Revised Version
A Lower Bound for the Length of Prtil Trnsversl in Ltin Squre, Revised Version Pooy Htmi nd Peter W. Shor Deprtment of Mthemtil Sienes, Shrif University of Tehnology, P.O.Bo 11365-9415, Tehrn, Irn Deprtment
More informationProbability The Language of Chance P(A) Mathletics Instant Workbooks. Copyright
Proility The Lnguge of Chne Stuent Book - Series L-1 P(A) Mthletis Instnt Workooks Copyright Proility The Lnguge of Chne Stuent Book - Series L Contents Topis Topi 1 - Lnguge of proility Topi 2 - Smple
More informationINTEGRATION. 1 Integrals of Complex Valued functions of a REAL variable
INTEGRATION NOTE: These notes re supposed to supplement Chpter 4 of the online textbook. 1 Integrls of Complex Vlued funtions of REAL vrible If I is n intervl in R (for exmple I = [, b] or I = (, b)) nd
More informationConservation Law. Chapter Goal. 6.2 Theory
Chpter 6 Conservtion Lw 6.1 Gol Our long term gol is to unerstn how mthemticl moels re erive. Here, we will stuy how certin quntity chnges with time in given region (sptil omin). We then first erive the
More informationDorf, R.C., Wan, Z. T- Equivalent Networks The Electrical Engineering Handbook Ed. Richard C. Dorf Boca Raton: CRC Press LLC, 2000
orf, R.C., Wn,. T- Equivlent Networks The Eletril Engineering Hndook Ed. Rihrd C. orf Bo Rton: CRC Press LLC, 000 9 T P Equivlent Networks hen Wn University of Cliforni, vis Rihrd C. orf University of
More informationSIMPLE NONLINEAR GRAPHS
S i m p l e N o n l i n e r G r p h s SIMPLE NONLINEAR GRAPHS www.mthletis.om.u Simple SIMPLE Nonliner NONLINEAR Grphs GRAPHS Liner equtions hve the form = m+ where the power of (n ) is lws. The re lle
More informationUniversity of Sioux Falls. MAT204/205 Calculus I/II
University of Sioux Flls MAT204/205 Clulus I/II Conepts ddressed: Clulus Textook: Thoms Clulus, 11 th ed., Weir, Hss, Giordno 1. Use stndrd differentition nd integrtion tehniques. Differentition tehniques
More information, g. Exercise 1. Generator polynomials of a convolutional code, given in binary form, are g. Solution 1.
Exerise Genertor polynomils of onvolutionl ode, given in binry form, re g, g j g. ) Sketh the enoding iruit. b) Sketh the stte digrm. ) Find the trnsfer funtion T. d) Wht is the minimum free distne of
More informationLogarithms LOGARITHMS.
Logrithms LOGARITHMS www.mthletis.om.u Logrithms LOGARITHMS Logrithms re nother method to lulte nd work with eponents. Answer these questions, efore working through this unit. I used to think: In the
More informationChapter 9 Definite Integrals
Chpter 9 Definite Integrls In the previous chpter we found how to tke n ntiderivtive nd investigted the indefinite integrl. In this chpter the connection etween ntiderivtives nd definite integrls is estlished
More informationAP Calculus BC Chapter 8: Integration Techniques, L Hopital s Rule and Improper Integrals
AP Clulus BC Chpter 8: Integrtion Tehniques, L Hopitl s Rule nd Improper Integrls 8. Bsi Integrtion Rules In this setion we will review vrious integrtion strtegies. Strtegies: I. Seprte the integrnd into
More informationCompression of Palindromes and Regularity.
Compression of Plinromes n Regulrity. Kyoko Shikishim-Tsuji Center for Lierl Arts Eution n Reserh Tenri University 1 Introution In [1], property of likstrem t t view of tse is isusse n it is shown tht
More informationExercise 3 Logic Control
Exerise 3 Logi Control OBJECTIVE The ojetive of this exerise is giving n introdution to pplition of Logi Control System (LCS). Tody, LCS is implemented through Progrmmle Logi Controller (PLC) whih is lled
More informationTable of Content. c 1 / 5
Tehnil Informtion - t nd t Temperture for Controlger 03-2018 en Tble of Content Introdution....................................................................... 2 Definitions for t nd t..............................................................
More informationSolids of Revolution
Solis of Revolution Solis of revolution re rete tking n re n revolving it roun n is of rottion. There re two methos to etermine the volume of the soli of revolution: the isk metho n the shell metho. Disk
More informationSEMI-EXCIRCLE OF QUADRILATERAL
JP Journl of Mthemtil Sienes Volume 5, Issue &, 05, Pges - 05 Ishn Pulishing House This pper is ville online t http://wwwiphsiom SEMI-EXCIRCLE OF QUADRILATERAL MASHADI, SRI GEMAWATI, HASRIATI AND HESY
More informationGeneralization of 2-Corner Frequency Source Models Used in SMSIM
Generliztion o 2-Corner Frequeny Soure Models Used in SMSIM Dvid M. Boore 26 Mrh 213, orreted Figure 1 nd 2 legends on 5 April 213, dditionl smll orretions on 29 My 213 Mny o the soure spetr models ville
More informationEquivalent fractions have the same value but they have different denominators. This means they have been divided into a different number of parts.
Frtions equivlent frtions Equivlent frtions hve the sme vlue ut they hve ifferent enomintors. This mens they hve een ivie into ifferent numer of prts. Use the wll to fin the equivlent frtions: Wht frtions
More information6.3.2 Spectroscopy. N Goalby chemrevise.org 1 NO 2 H 3 CH3 C. NMR spectroscopy. Different types of NMR
6.. Spetrosopy NMR spetrosopy Different types of NMR NMR spetrosopy involves intertion of mterils with the lowenergy rdiowve region of the eletromgneti spetrum NMR spetrosopy is the sme tehnology s tht
More informationAluminizing of Nickel-Based Superalloys Grade IN 738 by Powder Liquid Coating
Mterils Trnstions, Vol. 51, No. 5 (2010) pp. 982 to 987 #2010 The Jpn Institute of Metls Aluminizing of Nikel-Bse Superlloys Gre IN 738 y Power Liqui Coting Ptm Visuttipitukul 1; *, Nuntiy Limvnutpong
More informationMath 32B Discussion Session Week 8 Notes February 28 and March 2, f(b) f(a) = f (t)dt (1)
Green s Theorem Mth 3B isussion Session Week 8 Notes Februry 8 nd Mrh, 7 Very shortly fter you lerned how to integrte single-vrible funtions, you lerned the Fundmentl Theorem of lulus the wy most integrtion
More informationParticle Lifetime. Subatomic Physics: Particle Physics Lecture 3. Measuring Decays, Scatterings and Collisions. N(t) = N 0 exp( t/τ) = N 0 exp( Γt/)
Sutomic Physics: Prticle Physics Lecture 3 Mesuring Decys, Sctterings n Collisions Prticle lifetime n with Prticle ecy moes Prticle ecy kinemtics Scttering cross sections Collision centre of mss energy
More informationAnalysis of Temporal Interactions with Link Streams and Stream Graphs
Anlysis of Temporl Intertions with n Strem Grphs, Tiphine Vir, Clémene Mgnien http:// ltpy@ LIP6 CNRS n Soronne Université Pris, Frne 1/23 intertions over time 0 2 4 6 8,,, n for 10 time units time 2/23
More informationAmphenol High Speed Interconnects
MTERIL:. EN ESRIPTION TE PPROVE PROPOSL UG 28/1 J.SI GE: OPPER LLO PLTING OPTION =2: 2.5um MIN.NIKEL PLTING OPTION =:.81um MIN. MTTE TIN OVER 1.27um MIN. NIKEL. OTTOM GE GSKET: ONUTIVE RUER GSKET UL-9V-0
More informationGrade 6. Mathematics. Student Booklet SPRING 2008 RELEASED ASSESSMENT QUESTIONS. Assessment of Reading,Writing and Mathematics, Junior Division
Gre 6 Assessment of Reing,Writing n Mthemtis, Junior Division Stuent Booklet Mthemtis SPRING 2008 RELEASED ASSESSMENT QUESTIONS Plese note: The formt of these ooklets is slightly ifferent from tht use
More informationSection 6.3 The Fundamental Theorem, Part I
Section 6.3 The Funmentl Theorem, Prt I (3//8) Overview: The Funmentl Theorem of Clculus shows tht ifferentition n integrtion re, in sense, inverse opertions. It is presente in two prts. We previewe Prt
More information