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Article Citations From References:0From Reviews:0MR232071941A17(30C15)Borwein,Peter (3-SFR-MS);Erd´e lyi,Tam´a s (1-TXAM)Lower bounds for the number of zeros of cosine polynomials in the period:a problem of Littlewood.Acta Arith.128(2007),no.4,377–384.{A review for this item is inprocess.}cCopyright American Mathematical Society 2007Article Citations From References:0From Reviews:0MR2312975(Review)11M26(11Y35)Borwein,Peter (3-SFR);Fee,Greg (3-SFR);Ferguson,Ron (3-SFR);van der Waall,Alexa (3-SFR)Zeros of partial sums of the Riemann zeta function.(English summary)Experiment.Math.16(2007),no.1,21–39.The authors of the paper under review are concerned with the study of the zeros of the truncated Riemann zeta function ζN (s )=N n =11n s ,and of the truncated alternating zeta functionηN (s )=N n =1(−1)n +11n s,where N is a positive integer,and s =σ+it ,for some real numbers σand t .The paper under review is organised into five sections.After a well-presented introduction in which a very interesting picture of the first 10,000normalised zeros of ζ5(s )is given,a concise background to the Riemann zeta function is presented in the second section.In the third section,the authors prove their first theorem,which improves a result of R.Spira [p.20(1966),542–550;MR0203910(34#3757)].They show that if s =σ+it is a zero of ζN (s )or ηN (s ),then s satisfies σ≤α,where αis the positive root of ζ(σ)=2,and in particular,σ<1.73.Also,s satisfies σ≥βN ,where βN is the negative root of ζN −1(σ)=N −σ.Moreover,applying their project to write a robust zero finder in MAPLE,they illustrate the first 3000zeros of ζ211(s ),and the first 1000zeros of η109(s ),in Figure 2and 3,respectively.In the fourth section,the authors present 15figures,and provefive theorems.The first three figures,Figures 4,5,and 6,are concerned with the zeros of ζ3(s ),while the first two theorems,Theorem 4.3and 4.4,justify these figures,and are concerned with the density and distribution of the zeros of ζ3(s )over the specified periods.Figure 7is used in the proof of Theorem 4.4.In the third theorem,Theorem 4.5,the authors show that the zeros of ζN,p,q (s ),reduced modulo |2πi/(m 1log p +m 2log q )|,lie on a period of a curve,where (m 1,m 2)=(0,1),or (1,0),or m 1and m 2are coprime integers,and ζN,p,q (s )is an exponential sum composed of terms c n /n s ,where c n is constant and n is divisible only by the primes p and q .The authors give three examples applying Theorem 4.5to ζ3(s ),η4(s )andπ24(s )= n ∈T 1n s ,where T ={1,2,3,4,6,8,9,12,16,18,24},with corresponding Figures 8,9,and 10.In the fourth theorem,Theorem 4.9,the authors show that the zeros of f under the composition R ◦I are dense in the zeros of F in R × k j =1[0,πj ],whereF (x,y 1,...,y k ):R k +1→Cis continuously differentiable and periodic in the variables y 1,...,y k with periods π1,...,πk ,which are rationally independent,I :C →R k +1is the injection x +iy →(x,y,...,y ),R :R k +1→R ×k j =1[0,πj ]is the reduction map taking each y j to its equivalent modulus in the period [0,πj ],f (x +iy )=F (x,y,...,y )=F ◦Idefines a complex analytic function,and{(x,y 1,...,y k ):dF/dx =0}is dense in R k +1.The authors use Theorem 4.9together with Theorem 3.1in order to establish the fifth and last theorem of the fourth section,Theorem 4.10,that for prime Ninf {σ:ζN (s )=0}=βN ,where βN is the negative root of ζN −1(βN )=N −βN ,and obtain Corollary 4.11directly,that the zeros of f reduced into the period 0≤y <πk are dense in P (V ),where V is the set of zeros of F in R × k j =1[0,πj ],and P is the projection (x,y 1,...,y k )→x +iy k .In Figures 11and 12,and 13and 14,the authors illustrate Corollary 4.11,by plotting zeros of ζ5(s )and η5(s )modulo 2πi/log 5with bounding curve,and by plotting zeros of ζ6(s )and η6(s )modulo 2πi/log 6with bounding curve,respectively.The last 4figures are concerned with the zeros of ζ5(s ),ζ6(s )and ζ10(s ),and the corresponding ηN (s )’s,reduced modulo various moduli.Finally,in the fifth section,the authors discuss further planned work.Reviewed by Robert JuricevicReferences1.Wieb Bosma,John Cannon,and Catherine Playoust.”The Magma Algebra System I:The UserLanguage.”J.Symbolic Comput.24:3–4(1997),235–265.MR14844782.J.Brian Conrey.”The Riemann Hypothesis.”Notices Amer.Math.Soc.50:3(2003),341–353.MR1954010(2003j:11094)3.J.B.Conrey.”More Than Two Fifths of the Zeros of the Riemann Zeta Function Are on theCritical Line.”J.Reine Angew.Math.399(1989)1–26.MR1004130(90g:11120)4.H.M.Edwards.Riemann’s Zeta Function.Mineola,NY:Dover Publications Inc.,2001.Reprintof the1974original,New York:Academic Press.MR1854455(2002g:11129)5.R.Jentzsch.”Untersuchungen zur Theorie der Folgen analytischer Functionen.Acta Math.41(1918),219–251.MR1555151nger.”On the Zeros of Exponential Sums and Integrals.”Bull.Amer.Math.Soc.37(1931),213–239.7.J.van de Lune and H.J.J.te Riele.”Numerical Computation of Special Zeros of Partial Sums ofRiemann’s Zeta Function.”In Computational Methods in Number Theory,Part II,pp.371–387, Math.Centre Tracts155.Amsterdam:Math.Centrum,1982.8.H.L.Montgomery.”Zeros of Approximations to the Zeta Function.”In Studies in Pure Math-ematics,pp.497–506.Basel:Birkh¨a user,1983.MR0820245(87a:11081)9.S.J.Patterson.An Introduction to the Theory of the Riemann Zeta Function.Cambridge:Cambridge University Press,1988.MR0933558(89d:11072)10.Robert Spira.”Zeros of Sections of the Zeta Function I.”p.20(1966),542–550.MR0203910(34#3757)11.E.C.Titchmarsh.The Theory of the Riemann Zeta Function,Second edition.New York:OxfordUniversity Press,1986.MR0882550(88c:11049)12.P.Tur´a n.”On Some Approximative Dirichlet-Polynomials in the Theory of the Zeta Functionof Riemann.”Danske Vid.Selsk.Mat.-Fys.Medd.24:17(1948),36.MR0027305(10,286a) 13.P.Tur´a n.”Nachtrag zu meiner Abhandlung‘On Some Approximative Dirichlet Polynomialsin the Theory of the Zeta Function of Riemann.”Acta Math.Acad.Sci.Hungar.10(1959) 277–298(unbound insert).MR0115977(22#6774)14.Charles E.Wilder.”Expansion Problems of Ordinary Linear Differential Equations with Aux-iliary Conditions at More Than Two Points.”Trans.Amer.Math.Soc.18:4(1917),415–442.MR1501077Note:This list reflects references listed in the original paper as accurately as possible with no attempt to correct errors.c Copyright American Mathematical Society2007 ArticleCitations From References:0 From Reviews:0MR2280202(2007h:30005)30C10(26C1026D0530C1542A05)Borwein,Peter(3-SFR-MS);Mossinghoff,Michael J.(1-DVD);Vaaler,Jeffrey D.(1-TX) Generalizations of Gonc¸alves’inequality.(English summary)Proc.Amer.Math.Soc.135(2007),no.1,253–261(electronic).Let F(z)= Nn=0a n z n be a polynomial with complex coefficients and rootsα1,...,αN,and letF p be its L p norm over the unit circle.The authors generalize Gonc¸alves’inequality by provingthatF p≥B p|a N| Nn=1max{1,|αn|p}+Nn=1min{1,|αn|p}1/pfor1≤p≤2,whereB p:=Γ(p+1)2Γ(p/2+1)21/p.Gonc¸alves’inequality is recovered in the special case p=2.Reviewed by Vania D.MascioniReferences1.Gon¸calves,J.V.,L’in’egalit’e de W.Specht,1950,Univ.Lisboa Revista Fac.Ci.A(2),1,167–171.MR0039835(12,605j)2.Hardy,G.H.,Littlewood,J.E.,P’olya,G.,Inequalities,Cambridge Univ.Press,Cambridge,1988.MR0944909(89d:26016)3.Katznelson,Y.,An introduction to harmonic analysis,3rd ed.,Cambridge Univ.Press,Cam-bridge,2004.MR2039503(2005d:43001)4.Mignotte,M.,S¸tef˘a nescu,D.,Polynomials:an algorithmic approach,Springer-Verlag,Singa-pore,1999.MR1690362(2000e:12001)5.Mignotte,M.,An inequality about factors of polynomials,1974,p.,28,1153–1157.MR0354624(50#7102)6.Ostrowski,A.M.,On an inequality of J.Vicente Gon¸calves,1960,Univ.Lisboa Revista Fac.Ci.A(2),8,115–119.MR0145049(26#2585)Note:This list,extracted from the PDF form of the original paper,may contain data conversion errors,almost all limited to the mathematical expressions.c Copyright American Mathematical Society2007 ArticleCitations From References:0 From Reviews:0MR2255202(2007h:11036)11C08(26C05)Borwein,Peter (3-SFR);Choi,Kwok-Kwong Stephen (3-SFR)The average norm of polynomials of fixed height.(English summary)Trans.Amer.Math.Soc.359(2007),no.2,923–936(electronic ).Let n ≥0be any integer and let L n :={ n i =0a i z i :a i =±1},F n :={ n i =0a i z i :a i =0,±1}and F n (H ):={ n i =0a i z i :|a i |≤H,a i ∈Z }for a positive integer H ,and define µn (m ):=12n +1 P ∈L n P m m ,βn (m ):=13n +1 P ∈F n P m m and βn (m,H ):=1(2H +1)n +1 P ∈F n (H ) P m m re-spectively,where P m m is the m th power of the L m norm on the boundary of the unit disc.In thispaper,the authors explore a variety of questions concerning the average norm of certain classes of polynomials on the unit disk.In this respect,they obtain various elegant results,giving the ex-act formulae for µn (m ),βn (m )and βn (m,H )for various values of m ,as well as some related results for reciprocal polynomials and for polynomials of degree ≤n whose coefficients are k th roots of unity (generalized Littlewood polynomials).For instance,they obtain the following exact formulae:µn (2)=n +1,µn (4)=2n 2+3n +1(the formula for µn (4)is due to D.J.Newman and J.S.Byrnes [Amer.Math.Monthly 97(1990),no.1,42–45;MR1034349(91d:30006)],the authors providing here a different proof),µn (6)=6n 3+9n 2+4n +1,µn (8)=24n 4+30n 3+4n 2+5n +4−3(−1)n ,βn (2)=23(n +1),βn (4)=89n 2+149n +23,βn (6)=169n 3+4n 2+269n +23,βn (4,H )=29H 2(H +1)2n 2+145H (H +1)(19H 2+19H −3)n +115H (H +1)(3H 2+3H −1).In addition to these formulae,several results of independent interest have been also obtained.A particularly nice result is a formula for the sum k −1j =0|z +ζj k |2m ,where 1≤m ≤k ,ζk =e 2πi k and z is a fixed,arbitrarily chosen complex number.Reviewed by Nicolae Ciprian BonciocatReferences1.A.T.Bharucha-Reid and M.Sambandham,Random Polynomials ,Academic Press,Orlando,1986.MR0856019(87m:60118)2.P.Borwein Computational Excursions in Analysis and Number Theory ,Springer–Verlag,2002.MR1912495(2003m:11045)3.P.Borwein and S.Choi,Explicit merit factor formulae for Fekete and Turyn Polynomials.Trans.Amer.Math.Soc.354(2002),219–234.MR1859033(2002i:11065)4.P.Borwein and R.Lockhart,The expected Lp norm of random polynomials,Proc.Amer.Math.Soc.129(2001),no.5,1463–1472.MR1814174(2001m:60124)5.M.J.Golay,The merit factor of long low autocorrelation binary sequences.IEEE Transac-tions on Information Theory28(1982),543–549.6.J.-P.Kahane,Sur les polynˆo mes’a coefficients unimodulaires.Bull.London Math.Soc.12(1980),321–342.MR0587702(82a:30003)7.J.E.Littlewood,Some Problems in Real and Complex Analysis,Heath Mathematical Mono-graphs,Lexington,Massachusetts,1968.MR0244463(39#5777)8.T.Mansour,Average norms of polynomials.Adv.in Appl.Math.32(2004),no.4,698–708.MR2053841(2004m:30008)9.D.J.Newman and J.S.Byrnes,The L4norm of a polynomial with coefficients±1,Amer.Math.Monthly97(1990),no.1,42–45.MR1034349(91d:30006)10.B.Saffari,Barker sequences and Littlewood’s“two-sided conjectures”on polynomials with±1coefficients,S’eminaire d’Analyse Harmonique.Anne’e1989/90,139–151,Univ.Paris XI, Orsay,1990.MR1104693(92i:11032)Note:This list,extracted from the PDF form of the original paper,may contain data conversion errors,almost all limited to the mathematical expressions.c Copyright American Mathematical Society2007 ArticleCitations From References:0 From Reviews:0MR2231907(2007e:41014)41A17(46E15)Borwein,Peter(3-SFR-MS);Erd´e lyi,Tam´a s(1-TXAM)Nikolskii-type inequalities for shift invariant function spaces.(English summary)Proc.Amer.Math.Soc.134(2006),no.11,3243–3246(electronic).Let V n⊂C[a,b]be a vector space of complex-valued functions defined on R of dimension n+1 over C such that for every a∈R,f∈V n implies that f(·):=f(·−a)∈V n.Let p∈(0,2].The authors show thatf L∞[a+δ,b−δ]≤22/p2n+1δ1/pf Lp[a,b]for every f∈V n andδ∈(0,12(b−a)).This extends an earlier result of the authors[Math.Ann.316(2000),no.1,39–60;MR1735078(2001a:41015)],obtained in the case where V n= span{eλ0t,eλ1t,...,eλn t},whereλ0,λ1,...,λn are distinct real numbers.They also ask the ques-tion of whether the above result still holds for every p>0.Reviewed by Wiesław Ple´s niakReferences1.P.B.Borwein and T.Erd’elyi,Polynomials and Polynomials Inequalities,Springer-Verlag,NewYork,1995.MR1367960(97e:41001)2.P.B.Borwein and T.Erd’elyi,Pointwise Remez-and Nikolskii-type inequalities for exponentialsums,Math.Ann.316(2000),39–60.MR1735078(2001a:41015)3.D.Dryanov and Q.I.Rahman,On certain mean values of polynomials on the unit interval,J.Approx.Theory101(1999),92–120.MR1724028(2000j:41015)4.T.Erd’elyi,Markov-Nikolskii-type inequalities for exponential sums on afinite interval,Adv.in Math.,to appear.cf.MR2003m:410185.S.M.Nikolskii,Inequalities for entire functions offinite degree and their application in thetheory of differentiable functions of several variables,Trudy Mat.Inst.Steklov38(1951), 244–278.MR0048565(14,32e)6.G.Szeg˝o and A.Zygmund,On certain mean values of polynomials,J.Anal.Math.3(1954),225–244.MR0064910(16,355c)Note:This list,extracted from the PDF form of the original paper,may contain data conversion errors,almost all limited to the mathematical expressions.c Copyright American Mathematical Society2007 ArticleCitations From References:0 From Reviews:0MR2176410(2006f:11007)11B13(68R0594A11)Borwein,Peter(3-SFR);Choi,Stephen[Choi,Kwok-Kwong Stephen](3-SFR);Chu,Frank(3-SFR)An old conjecture of Erd¨o s-Tur´a n on additive bases.(English summary)p.75(2006),no.253,475–484(electronic).This paper concerns a computational aspect of the Erd˝o s-Tur´a n conjecture.For any set B of nonnegative integers and any integer x,let r B(x)be the number of pairs(b,b )∈B×B such that x=b+b .The Erd˝o s-Tur´a n conjecture[P.Erd˝o s and P.Tur´a n,J.London Math.Soc.16(1941), 212–215;MR0006197(3,270e)]asserts that sup n≥0r B(n)=+∞whenever inf n≥0r B(n)>0. Improving a previous result by G.Grekos et al.[J.Number Theory102(2003),no.2,339–352; MR1997795(2004j:11011)],it is shown that,under the assumption that inf n≥0r B(n)>0,one has sup n≥0r B(n)≥8.The method is the following:it is checked by an inductive computational csearch that given any positive integer1≤k≤7,there exists a positive integer n such that for any finite set of nonnegative integers B with r B(m)>0for all m=0,1,...,n,we have r B(x)>k for some x.The method does not seem to be easily transposable in order to obtain the same lower bound of sup m≥0r B(m)under the weaker assumption that r B(n)>0for n large enough.Reviewed by Franc¸ois HennecartReferences1.Martin Dowd,Questions related to the Erd˝o s-Tur’an conjecture,SIAM J.Discrete Math.1(1988),no.1,142–150.MR0936616(89h:11006)2.P.Erd˝o s and R.Frued,On Sidon-sequences and related problems,pok(New Ser.)(1991/2(in Hungarian)),no.1,1–44.3.P.Erd˝o s and P.Tur’an,On a problem of Sidon in additive number theory,and on some relatedproblems,J.London Math.Soc.16(1941),212–215.MR0006197(3,270e)4.P.Erd˝o s and R.L.Graham,Old and new problems and results in combinatorial number theory:van der Waerden’s theorem and related topics,Enseign.Math.(2)25(1979),no.3-4,325–344 (1980).MR0570317(81f:10005)5.G.Grekos,L.Haddad,C.Helou,and J.Pihko,On the Erd˝o s-Tur’an conjecture,J.NumberTheory102(2003),no.2,339–352.MR1997795(2004j:11011)6.Melvyn B.Nathanson,Unique representation bases for the integers,Acta Arith.108(2003),no.1,1–8.MR1971077(2004c:11013)7.Csaba S’andor,Range of bounded additive representation functions,Period.Math.Hungar.42(2001),no.1-2,169–177.MR1832703(2002f:11010)Note:This list,extracted from the PDF form of the original paper,may contain data conversion errors,almost all limited to the mathematical expressions.c Copyright American Mathematical Society2006,2007 ArticleCitations From References:0 From Reviews:0MR2241514(2007b:94203)94A55Borwein,Peter(3-SFR);Ferguson,Ron(3-SFR)Polyphase sequences with low autocorrelation.(English summary)IEEE rm.Theory51(2005),no.4,1564–1567.Summary:“Low autocorrelation for sequences is usually described in terms of low base energy, i.e.,the sum of the sidelobe energies,or the maximum modulus of its autocorrelations,a Barker sequence occurring when this value is≤1.We describefirst an algorithm applying stochastic methods and calculus to the problem offinding polyphase sequences that are good local minima for the base energy.Starting from these,a second algorithm uses calculus to locate sequences that are local minima for the maximum modulus on autocorrelations.In our tabulation of smallest base energies found at various lengths,statistical evidence suggests we have good candidates for global minima or ground states up to length45.We extend the list of known polyphase Barker sequences to length63.”References1.R.H.Barker,”Group synchronization of binary digital systems,”in Communication Theory,W.Jackson,Ed.London,U.K.:Butterworths,1953,pp.273–287.2.L.Boemer and M.Antweiler,”Polyphase Barker sequences,”Electron.Lett.,vol.25,no.23,pp.1577–1579,1989.3.P.Borwein,R.Ferguson,and J.Knauer,”The merit factor of binary sequences,”preprint,2003,to be published.cf.MR2001a:940204.A.R.Brenner,”Polyphase Barker sequences up to length45with small alphabets,”IEE Elec-tron.Lett.,vol.34,no.16,pp.1576–1577,1998.5.B.Dawkins,”Siobhan’s problem:The coupon collector revisited,”Amer.Statistician,vol.45,pp.76–82,1991.6.M.Friese,”Polyphase Barker sequences up to length36,”IEEE Trans.Inf.Theory,vol.42,no.4,pp.S.1248-S.1250,Jul.1996.7.M.Friese and H.Zottmann,”Polyphase Barker sequences up to length31,”Electron.Lett.,vol.30,no.4,1996.8.M.J.E.Golay,”1982The merit factor of long low autocorrelation binary sequences,”IEEETrans.Inf.Theory,vol.IT-28,no.3,pp.543–549,May1982.9.S.W.Golomb and R.A.Scholtz,”Generalized Barker sequences,”IEEE Trans.Inf.Theory,vol.IT-11,no.4,pp.533–537,Oct.1965.MR0189924(32#7342)ngford and ngford,”Solution of the inverse collector’s problem,”Math.Scientist,vol.27,pp.32–35,2002.MR1913927(2003f:65018)11.S.Mertens,”Exhaustive search for low autocorrelation binary sequences,”J.Phys.A:Math.Gen.,vol.29,pp.L473–L481,1996.MR1419192(97i:82050)12.N.Zhang and S.W.Golomb,”Sixty-phase generalized Barker sequences,”IEEE Trans.Inf.Theory,vol.35,no.4,pp.911–912,Jul.1989.Note:This list reflects references listed in the original paper as accurately as possible with no attempt to correct errors.c Copyright American Mathematical Society2007 ArticleCitations From References:1 From Reviews:0MR2132173(2005k:11054)11C08Borwein,Peter(3-SFR);Choi,Kwok-Kwong Stephen(3-SFR);Ferguson,Ron(3-BC) Norms of cyclotomic Littlewood polynomials.(English summary)Math.Proc.Cambridge Philos.Soc.138(2005),no.2,315–326.A Littlewood polynomial has all its coefficients equal to±1.In an earlier paper[Experiment. Math.8(1999),no.4,399–407;MR1737235(2000m:11121)],thefirst two authors conjecturedthat every Littlewood polynomial composed entirely of cyclotomic polynomials has the formP (x )=±Φp 1(ε1x )Φp 2(ε2x p 1)...Φp r (εr x p 1p 2···p r −1),where p 1,...,p r are all primes,not necessarily distinct,each εi =±1,and Φp (x )=1+x +···+x p −1.Let P 4denote the L 4norm of P over the unit circle.In the present paper,the authors compute the value of P 4/√N for polynomials of this form,where N =1+deg P =p 1p 2...p r .They show that for fixed r the minimum value of this quantity occurs when each p i =2and each εi =−1.This minimum value is computed explicitly,and in this case P 4 N 0.589....The problem of minimizing the normalized L 4norm of a Littlewood polynomial is related to questions of Littlewood,Erd˝o s,and Golay.Reviewed by Michael J.MossinghoffReferencesputational Excursions in Analysis and Number Theory (Springer–Verlag,2002).MR1912495(2003m:11045)2.P.Borwein and S.Choi.Explicit merit factor formulae for Fekete and Turyn polynomials.Trans.Amer.Math.Soc.354(2002),219–234.MR1859033(2002i:11065)3.P.Borwein and S.Choi.On cyclotomic polynomials with ±1coefficients.Experimental Math.8(1999),399–407.MR1737235(2000m:11121)4.D.Boyd.On a problem of Byrnes concerning polynomials with restricted coeffip.66(1997),1697–1703.MR1433263(98a:11033)5.S.Choi.On cyclotomic polynomials with ±1coefficients II,in preparation (2003).6.M.J.Golay.The merit factor of long low autocorrelation binary sequences.IEEE Transactions on Information Theory 28(1982),543–549.7.J.-P.Kahane.Sur les polynˆo mes ´acoefficients unimodulaires.Bull.London Math.Soc.12(1980),321–342.MR0587702(82a:30003)8.J.E.Littlewood.Some Problems in Real and Complex Analysis (Heath Mathematical Mono-graphs,1968).MR0244463(39#5777)9.H.Maier.The coefficients of cyclotomic polynomials,in Analytic Number Theory (Allerton Park,1989),349–366.Progr.Math.85(Birk¨u ser,1990).MR1084190(92a:11110)10.H.Maier.Cyclotomic polynomials with large coefficients.Acta Arith.64(1993),no.3,227–235.MR1225426(94g:11074)11.H.Maier.The size of the coefficients of cyclotomic polynomials,in Analytic Number TheoryVol.2(Allerton Park,1995)(ed.B.C.Berndt et al.),Progr.Math.139(Birkh¨a user,1996),633–639.MR1409383(97g:11106)12.D.J.Newman and J.S.Byrnes.The L 4norm of a polynomial with coefficients ±1.Amer.Math.Monthly 97(1990),no.1,42–45.MR1034349(91d:30006)Note:This list reflects references listed in the original paper as accurately as possible with noattempt to correct errors.c Copyright American Mathematical Society 2005,2007Article Citations From References:2From Reviews:0MR2127575(2006d:41017)41A21(41A63)Borwein,P.B.(3-SFR-MS);Cuyt,A.(B-UA-CS);Zhou,P.[Zhou,Ping 2](3-SFX-MSC)Explicit construction of general multivariate Pad´e approximants to an Appell function.(English summary)put.Math.22(2005),no.3,249–273.The Appell functions generalize the Gauss hypergeometric function 2F 1(a,b ;c ;z )to two variables.The authors derive an explicit formula for the multivariate Pad´e approximants [M/N ]E (x,y )=P (x,y )/Q (x,y )to the Appell function F 1(a,1,1;a +1;x,y )= ∞i,j =0a x i y j /(i +j +a ),wherea is a positive integer.Their approach is to first construct the general Pad´e approximants for the q -analogue L q (x,y )= ∞i,j =0(q a −1)x i y j /(q i +j +a −1),where |q |>1and |x |,|y |<|q |.This uses the residue theorem and the functional equation method.From the explicit results they are able toprove normality of a particular Pad´e table of multivariate approximants to F (a,1,1;a +1;x,y ).Reviewed by C.C.Rousseau cCopyright American Mathematical Society 2006,2007Article Citations From References:2From Reviews:0MR210349494A55Borwein,Peter (3-SFR);Choi,Kwok-Kwong Stephen (3-SFR);Jedwab,Jonathan (3-SFR)Binary sequences with merit factor greater than 6.34.(English summary)IEEE rm.Theory 50(2004),no.12,3234–3249.{There will be no review of this item.}References1.S.Mertens and H.Bauke.(2004)Ground States of the Bernasconi Model with Open BoundaryConditions.[Online].Available:http://odysseus.nat.uni-magdeburg.de/∼mertens/bernasconi/open.da2.C.de Groot,D.W¨u rtz,and K.Hoffmann,”Low autocorrelation binary sequences:Exactenumeration and optimization by evolutionary strategies,”Optimization ,vol.23,pp.369–384,1992.MR12384353.M.Golay,”The merit factor of Legendre sequences,”IEEE rm.Theory ,vol.IT-29,pp.934–936,Nov.1983.4.T.Høholdt and H.Jensen,”Determination of the merit factor of Legendre sequences,”IEEErm.Theory,vol.34,pp.161–164,Jan.1988.5.A.Kirilusha and G.Narayanaswamy,”Construction of new asymptotic classes of binary se-quences based on existing asymptotic classes,”put.Sci.,Univ.Richmond,Richmond,V A,Summer Science Program Tech.Rep.,1999.6.R.Turyn,”Sequences with small correlation,”in Error Correcting Codes,H.Mann,Ed.NewYork:Wiley,1968,pp.195–228.MR0242566(39#3897)7.R.Turyn and J.Storer,”On binary sequences,”Proc.Amer.Math.Soc.,vol.12,pp.394–399,1961.MR0125026(23#A2333)8.R.Turyn,”Character sums and difference sets,”Pacific J.Math.,vol.15,pp.319–346,1965.MR0179098(31#3349)9.T.Beth,D.Jungnickel,and H.Lenz,Design Theory,2nd ed.Cambridge,U.K.:CambridgeUniv.Press,1999,vol.I and II.MR0890103(88b:05021)10.M.Golay,”A class offinite binary sequences with alternate autocorrelation values equal tozero,”IEEE rm.Theory,vol.IT-18,pp.449–450,May1972.11.P.Erd¨o s,”An inequality for the maximum of trigonometric polynomials,”Ann.Polon.Math.,vol.12,pp.151–154,1962.MR0141933(25#5330)12.P.Borwein,Computational Excursions in Analysis and Number Theory.New York:Springer-Verlag,2002,CMS Books in Mathematics.MR1912495(2003m:11045)13.B.Schmidt,”Cyclotomic integers andfinite geometry,”J.Amer.Math.Soc.,vol.12,pp.929–952,1999.MR1671453(2000a:05042)14.S.Mertens,”Exhaustive search for low-autocorrelation binary sequences,”J.Phys.A:Math.Gen.,vol.29,pp.L473–L481,1996.MR1419192(97i:82050)15.M.Golay,”Sieves for low autocorrelation binary sequences,”IEEE rm.Theory,vol.IT-23,pp.43–51,Jan.1977.16.M.Golay and D.Harris,”A new search for skewsymmetric binary sequences with optimalmerit factors,”IEEE rm.Theory,vol.36,pp.1163–1166,Sept.1990.17.J.Knauer.(2004)Merit Factor Records.[Online].Available:http://www.cecm.sfu.ca/∼jknauer/labs/re18.M.Golay,”The merit factor of long low autocorrelation binary sequences,”IEEE rm.Theory,vol.IT-28,pp.543–549,May1982.19.J.Bernasconi,”Low autocorrelation binary sequences:Statistical mechanics and configurationstate analysis,”J.Phys.,vol.48,pp.559–567,1987.20.J.Jensen,H.Jensen,and T.Høholdt,”The merit factor of binary sequences related to differencesets,”IEEE rm.Theory,vol.37,pp.617–626,May1991.MR1145821(92j:94009)21.P.Stadler,”Landscapes and their correlation functions,”J.Math.Chem.,vol.20,pp.1–45,1996.MR1426283(99a:92021)22.G.Beenker,T.Claasen,and P.Hermens,”Binary sequences with a maximallyflat amplitudespectrum,”Philips J.Res.,vol.40,pp.289–304,1985.itzer,M.Zamparelli,and D.Beule,”Evolutionary search for low autocorrelated binarysequences,”IEEE put.,vol.2,pp.34–39,Apr,1998.24.V.de Oliveira,J.Fontanari,and P.Stadler,”Metastable states in high order short-range spinglasses,”J.Phys.A:Math.Gen.,vol.32,pp.8793–8802,1999.25.F.Ferreira,J.Fontanari,and P.Stadler,”Landscape statistics of the low autocorrelated bi-nary string problem,”J.Phys.A:Math.Gen.,vol.33,pp.8635–8647,2000.MR1801459 (2001j:82054)26.D.Newman and J.Byrnes,”The L4norm of a polynomial with coefficients±1,”Amer.Math.Monthly,vol.97,pp.42–45,1990.MR1034349(91d:30006)27.P.Borwein and K.-K.Choi,”Explicit merit factor formulae for Fekete and Turyn polynomials,”Trans.Amer.Math.Soc.,vol.354,pp.219–234,2002.MR1859033(2002i:11065)28.C.Mauduit and A.S´a rk¨o zy,”Onfinite pseudorandom binary sequences I:Measure of pseu-dorandomness,the Legendre symbol,”Acta Arith.,vol.82,pp.365–377,1997.MR1483689 (99g:11095)29.A.Weil,Sur les Courbes Alg´e briques et les Vari´e t´e s qui s’en D´e duisent,ser.Act.Sci.Ind.Paris,France:Hermann,1948,vol.1041.30.T.Apostol,Introduction to Analytic Number Theory,ser.UTM.New York:Springer-Verlag,1976.MR0434929(55#7892)31.R.Kristiansen,”On the Aperiodic Autocorrelation of Binary Sequences,”Master’s thesis,Univ.Bergen,Bergen,Norway,2003.32.R.Kristiansen and M.Parker,”Binary sequences with merit factor>6.3,”IEEE rm.Theory,to be published.MR2103513Note:This list reflects references listed in the original paper as accurately as possible with no attempt to correct errors.c Copyright American Mathematical Society2007 ArticleCitations From References:1 From Reviews:1MR2065455(2005h:11001)11-00(01A0501A7511-03)Berggren,Lennart[Berggren,John L.](3-SFR);Borwein,Jonathan(3-DLHS-FC); Borwein,Peter(3-SFR)Pi:a source book.Third edition.Springer-Verlag,New York,2004.xx+797pp.$89.95.ISBN0-387-20571-3This is the third edition of the by now classical Pi:a source book.The carefully selected70 articles onπof thefirst edition[see Pi:a source book,Springer,New York,1997;MR1467531 (98f:01001)]have been supplemented by an appendix with translations of work of Vi`e te and Huygens,and‘A pamphlet on Pi’.The latter contains some notes on the computation of individual (binary)digits ofπ,some considerations on the normality of the decimal expansion ofπ,and two more sections on the history ofπ.This book is still a classic work of reference for anyone with an。

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论文引用的主要类型有哪些？

论文引用的主要类型有哪些？

论文引用的主要类型有哪些？什么是“引用”?很多留学生对这个术语不太熟悉，也不知道具体在学术论文中如何进行引用。

“引用”这个概念对于论文来说是非常重要的，因为我们不可避免地会用到它。

当我们在文章中借鉴了著名作者和研究者的观点和话语时，必要明确标注出来。

这类标注就是我们通常所说的“引用”。

在我们引用一篇essay或者按照一定的思路来改写著作者话语的时候，要注意使用合适恰当的论文引用格式，包括参考文献引用格式或论文脚注。

接下来我们来给大家介绍一下，论文引用有哪些重要性以及主要包含哪几种类型。

什么是引用?“引用” 的英文翻译是“Citation”。

所谓“引用”，是指在论文的文本中采用他人的论述。

为表明文章或报告中特定信息的来源，作者必须及时在所引信息之后进行引文标注。

论文引用是所有研究性文章的一部分，它可以提供所引用原文须知的信息，便于读者在参考目录或者引用页面上找到与该原文相关的细节。

论文引用包含的信息有：作者姓名;文章标题;期刊或出版社的名称和地址;论文发表日期;引用文献的页码。

论文引用的三种主要类型 1. 文内引用 (IN-TEXT CITATION)文内引用，即in-text citation，是在学术论文中的正文内采取的引用。

文内引用是用来提醒读者，你写的东西借鉴了别人的观点和资料。

在写in-text citation的过程中，要在文中标明相关引文。

文内引用需要注意以下几点：在句子中介绍著者或在括号内标注著者;标明出版年份;不同文献用分号分开;若采用MLA引用格式，要求标注可以找到所引信息的页码范围;如果没有著者姓名，使用文献名称;如果使用网络来源，标注著者姓名和网址;若采用Chicago引用格式时，需要使用脚注或尾注;按照引文在论文中出现的次序把脚注编上号码，每个引文都有自己的编号，论文脚注需要提到有关著者和著作信息;用来介绍被引用文献的短语称之为信号短语，通常在介绍引用信息之前就先进行简单论述。

论文引用格式（Citationformat）

论文引用格式（Citationformat）

论文引用格式（Citation format）The national standard "Bibliographic References" (GB7714-87), "presentation of scientific and Technical Periodicals" (GB/T3179-92) and "Chinese academic journals (CD) data retrieval and evaluation standards", and used the sequence encoding tagging system.1. citation documents in the text annotation formatThe documents quoted in the thesis should be marked with square brackets in the upper right corner of the author or the text of the result, or as part of the sentence. Such as:In 1981, Japan gave only the vertical impact velocity formula of flat wheels impacting rails (1),......Xue, Du, et al. [2] pointed out that gossypol excreted slowly from the body.[literature 2] pointed out that gossypol excreted slowly from the body.Proof of theorem see document [3].Refer to many articles or the same authors of articles, only the papers number are all listed in brackets, the serial number "," separate; in case of serial number, available "~" connection, omitting the middle number. Such as:Findings from earlier studies [2, 4, 6-9] indicate that,......2. bibliographic reference format and example(1) a book or treatiseAuthor. Title [M]. Edition (first edition is not marked). Publication: publisher, publication year. Initial or start page number of the citation1 Zhai Wanming. Vehicle track coupling dynamics [M]. Beijing: China Railway Press, 1997.74 - 80.2 nachod Kim M in traction motor design [M] Li Zhongwu, Fan Junjie, Li Tieyuan. Beijing: China Railway Press, 1983.21-25.[3] Eisson, H, N.Immunology:an, introduction, to, molecular, and, principles, of, the, immune,, respones [M],.5th, ed., New, York:Harper, and, Row, cellular, 1974.3-6.(2) periodicals (Serials)The number of authors (articles). Title: [J]. journal, publication year, volume number (issue): the citation starting or page number.Shi Feng, Li Zhizhong. Optimization algorithm of railway vehicle flow path [J]. Journal of China Railway, 1993, 15 (3):70.[2] You, C, H, Lee, K, Y, Chey, R, F, et, al., Electrogastrographic, study, of, patients, with, unexplained, nausea, bloating, and, vomiting[J]., Gastroenterology,1980,79:311-314.(3) the literature published in the proceedings of the conference, the paper and the compilation of the papers[serial number] precipitation literature author. Title (article) name [A]. see (in English use In): original author, thesis collection name [C]. publication place: publisher, publication year. Quotation start or start stop page number1 Zhang Yuxin. Heavy truck high friction composite brake shoes the development and application of [A]. in: Chinese Railway Society compiled. Special international heavy haul braking Association Symposium [C]. Beijing: Chinese Railway Society, 1988.242.[2] Hunninghaks, G, W, Gadek, J, B, Szapiel, S, V, et, al.人的肺泡巨噬细胞[A]。

citation

citation


P8
Integral citation
LOGO
Integral citations tend to give greater prominence to the cited author.
e.g.5: However, most of the companies in Elliot and Patton’s(1998) sample did not know whether the costs were recovered, which may mean that other elements play amore important role in the decision of the company to carry out an audit.
P10
Non-integral citation Non-integral citations tend to give greater prominence to the cited content.
LOGO
e.g.2: n the absence of an audit , companies can be suspected of disclosing only positive information (Niskanen and Nieminen 2001) or information that will have a positive influence on their image (Deegan and Gordon 1996).
LOGO
Citation
Name : Number:
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Citation types
LOGO
Integral （完整引用）
Harvard_citation_hlp

Harvard_citation_hlp

Harvard guide to citingreferencesThe examples here follow the Open University LTS Referencing Guide , which uses a version of the Harvard system of citing references, but some OU courses may use other referencing systems. Please check the details for your course before using this guide.1. In text citationsIn the Harvard system, references in the text (in text citations) are referred to by the author’s name and year of publication , for example:It is stated that…(Bloggs, 2007) or Bloggs 2007 states…In the reference list or bibliography items are listed only once in alphabetical order . In some cases you may refer to more than one publication by an author for a specific year. To help identify these different items for your in text citation and reference list, you should add a letter of the alphabet to the year of publication, for example:(Thomson 2004a), (Thomson 2004b) and (Thomson 2004c) where a, b and c refer to the order in which they are cited in your text .When you come across a publication with 3 or more authors you only list the first author for the in text citation followed by et al. For example:(Jones, G. et al., 2007), but in the reference list or bibliography you would list each author in full.2. Secondary referencingYou may want to use a quotation, or an idea from a source referenced in another work. You haven‟t read the original, but have discovered it through a secondary source. This is known as secondary referencing. Ideally you should try and get hold of the original, but if you can‟t then you need to make it clear in your work that you have not read the original, for example:In text citation: Bloggs, quoted in Smith (2007 p.4) states “I love chocolate”. Or Bloggs, cited in Smith (2007 p.4) loves chocolate.In the reference list you would provide details for the source you read it in e.g.:Smith, J. (2007) Musings from chocolate lovers , Bicester, JFJ Press3. URLs for e-journalsFor electronic journal articles you are advised to put the name of the service the item is from, or the URL . Some databases and electronic journals provide persistent urls . This is a URL that should get you direct to the article - use this if given. Other journal articles may have a DOI digital object identifier. Again this is a unique address to find the article and if you have this put that beside the “Available from” information. If neither of these apply, and your article is from a database we would recommend just listing the name of the database L i b r a r y S e r v i c e syou got it from. This is because if you copy the address from the database, it is unlikely to work for someone else using it to find the article.4. Books: book, book chapter and ebookBookThe book How to succeed as a working parent, by Steve Chalke (published in London by Hodder & Stoughton, in 2003) would be referred to in the text as (Chalke, 2003).Author's (or editor's) surname and initials, year of publication (in brackets), title (in italics, capitalise first word and proper nouns only), edition (if not first) place of publication, publisher; for example:Chalke, S. (2003) How to succeed as a working parent, London, Hodder &Stoughton.Book chapterAuthor of chapter’s surname and initials, year of publication (in brackets), title of chapter (enclosed in single inverted commas, capitalise first word and proper nouns only), in Editor's surname and initials(ed.) title of book (in italics, capitalise first word and proper nouns only), edition (if not first) place of publication, publisher, page reference if known; for example:Mason, R. (1994) …The educational value of ISDN‟, in Mason, R. and Bacsich, P.(eds.), ISDN: applications in education and training, Exeter, Short Run PressIn text citation: (Mason, 1994) or Mason (1994) states…EbooksAuthor's (or editor's) surname and initials, year of publication (in brackets), title (in italics, capitalise first word and proper nouns only), name of ebook supplier, [Online] Available from: information such as the URL and, in round brackets, the date you accessed the site; for example:Willie, Sarah Susannah (2003) Acting black: college, identity and the performanceof race, Taylor & Francis e-book collection, [Online] Available from:/linking/index.php?id=311027 (Accessed 10 April 2006)In text citation: (Willie, 2003) or Willie (2003) states…5. Journals: journal and ejournal articlesJournal articleAn article by Kristin Thompson, Fantasy, Franchises, and Frodo Baggins: The Lord of the Rings and Modern Hollywood, published in Fall 2003 in issue no 52 of the journal The Velvet Light Trap, on pages 45-63, would be referred to in the text as (Thompson, 2003). Author's surname and initials, year of publication (in brackets), title of article (enclosed in single inverted commas, capitalise first word and proper nouns only), the title of the journal (in italics, capitalise first word and proper nouns only), the volume, issue number and, if given, the date, and the pages on which the article appears; for example: Thompson, K. (2003) 'Fantasy, franchises, and Frodo Baggins : the Lord of theRings and modern Hollywood', The velvet light trap, no. 52, Fall, pp. 45-63.Ejournal articlesAuthor's surname and initials, year of publication (in brackets), title of article (enclosed in single inverted commas), the title (in italics) of the journal, if given, the volume and issue number of the journal, Online in square brackets, 'available from' information such as the name of the service and/or URL and, in round brackets, followed by the date you accessed the site; for example:Virkus, S. (2003) 'Information literacy in Europe: a literature review.' Informationresearch, 8(4), [Online] paper no. 159. Available from: /ir/8-4/paper159.html (Accessed 28 October 2003)In text cita tion: (Virkus 2003) or Virkus (2003) states…6. OU course materialsCourse textsThe course text T281 Basic physical science for technology, Unit 9, 'Thermochemistry' (published in Milton Keynes by the Open University, in 1984) would be referred to in thetext as (T281, Unit 9).The Open University as the author, year of publication (in brackets), course code, course title (in italics, capitalise the first word of the course title only), unit, unit title (in single quotes) place of publication, publisher; for example:The Open University (1984) T281 Basic physical science for technology, Unit 9,'Thermochemistry', Milton Keynes, The Open University.Course DVDsThe T320 course DVD1: video case studies would be referred to in the text as (T320,DVD1). Below is how it would appear in a reference listThe Open University as the author, year of publication (in brackets), course code, course title (in italics, capitalise the first word of the course title only), DVD number and title (in single quotes) place of publication, publisher; for example:The Open University (2008) T320 E-business technologies: foundations andpractice, …DVD 1: video case studies‟, Milton Keynes, The Open UniversitySecondary referencing of work cited in course unitsIf you wish to cite an author whose work is discussed in a course unit but you haven’t read the original you need to make this clear in your script, for example:In text citation: Porter (cited in B820, Unit 2, p.19) identifies five competitive forces.In the references list you would provide details only for the source you actually read: The Open University (2006) B820 Strategy, Unit 2, …Analysing the externalenvironment‟, Milton Keynes, The Open University.7. Newspapers: Print and onlineNewspaper: printAuthor's surname and initials, year of publication (in brackets), title of the article (enclosed in single inverted commas, capitalise the first word and proper nouns only), title of the newspaper in italics, date i.e. day and month, page number; for example:Mackay, C. (2002) 'Alert over big cat', The Daily Mirror, 4th July, p.28.In text citation: (Mackay, 2002) or Mackay (2002) states…Newspaper: onlineAuthor's surname and initials, year of publication (in brackets), title of the article (enclosed in single inverted commas, capitalise the first word and proper nouns only), title of the newspaper in italics, date i.e. day and month, [online] Available from URL and, in round brackets, the date you accessed the site; for example:MacLeod, D. (2007) 'Oxbridge trainee teachers twice as likely to get jobs',Education Guardian, 3rd August, [online] Available from/higher/news/story/0,,2140513,00.html?gusrc=rss&fe ed=8 (Accessed 3 August 2007)In text citation: (MacLeod, 2007) or MacLeod (2007) states…8. ReportsAuthor's surname and initials or organisation, year of report (in brackets), title (in italics), issuing organisation, and report number; for example:Halliday, J. (1995) Assessment of the accuracy of the DTI's database of the UKwind speeds, Energy Technology Support Unit, ETSU-W-11/00401/REP.In text citation: (Halliday, 1995) or Halliday (1995) states…9. Conference papersAuthor's surname and initials, year of publication (in brackets), title of paper (enclosed in single inverted commas, capitalise the first word and proper nouns only), title of conference (in italics), location and date of conference, place of publication, publisher, pages on which the paper appears; for example:Jones, J. (1994), 'Polymer blends based on compact disc scrap', in Proceedings of the Annual Technical Conference - Society of Plastics Engineers, San FranciscoMay 1-5 1994, Brookfield, CT, Society of Plastics Engineers, pp. 2865-2867.In text citation: (Jones, 1994) or Jones (1994) states…10. ThesesAuthor’s surname and initials, Year of submission (in brackets), Title: subtitle (if any) (in italics, capitalise first word and proper nouns only), Degree statement (e.g. Unpublished PhD thesis, Unpublished Degree dissertation), place of publication (if not clear from institution name, e.g. Cambridge University), Awarding institution; for example: Morishita, M. (2003) Empty museums : transculturation and the development ofpublic art museums in Japan. Unpublished PhD. thesis, Milton Keynes, OpenUniversity.In text citation: (Morishita, 2003) or Morishita (2003) claims…11. Internet: World Wide Web documents, personal sites, blogs andpodcastsWorld Wide Web documentsAuthor's surname and initials, year of publication if given (in brackets), title of document (in italics, capitalise first word and proper nouns only), [online], place of publication if given, publisher, 'available from information such as the URL, and, in round brackets, the date you accessed the site; for example:Spitzer, K. L., Eisenberg, M.B., & Lowe, C. A. (1998) Information literacy: essential skills for the information age, [online], Syracuse, N.Y.: ERIC Clearinghouse onInformation and Technology, Syracuse University (ED 427 780) Available from:/toc/infoliteracytoc.shtml (Accessed 28 October 2003)In text citation: (Spitzer et al., 1998) or Spitzer et al. (1998) state…Personal or Organisational sitesAuthor's surname and initials or organisation name, year of publication/ last updated if given (in brackets), title of site (in italics, capitalise first word and proper nouns only), Available from: information such as the URL, and, in round brackets, the date you accessed the site; for example:Open University Library (January 2005) Welcome to the Open University Library,Available from: / (Accessed 2 February 2006)In text citation: (Open University Library, 2005) or Open University Library (2005)states…BlogsAuthor of message, Year that site was published/last updated (in brackets), Title of message (enclosed in single inverted commas), Title of Internet site in italics, Day/Month of posted message, Available at: information such as the URL and, in round brackets, the date you accessed the site; for example:Sloniowski, L. (2005) …Because sharing is nice‟, Information literacy in Canada, 30June. Available at: http://blog.uwinnipeg.ca/ilig/archives/learning_objects/(Accessed 2 February 2006)In text citation: (Sl oniowski, 2005) or Sloniowski (2005) states…Note: Some blog authors may choose to remain anonymous by using an alias. Use this instead of surname and initials if that is all that is available.PodcastsTitle of podcast in italics, year of publication (in brackets), podcast type, podcaster, place of podcast. Available from information such as the URL and, in round brackets, the date you accessed the site; for example:The wings of a butterfly (2005), podcast radio programme, ABC Radio National,Sydney. Available from: .au/rn/podcast/default.htm#mind(Accessed 16th September 2005)In text citation: (The wings of a butterfly, 2005) or In The wings of a butterfly (2005) it is said…12. Messages: emails and forumsEmailsAuthor's surname and initials, full date of message (in brackets), subject of message (in single quotes), 'email to' followed by the recipient's name; for example:Knight, C. J., (May 29 1997), …Cumbrian windfarms‟, e-mail to J.Q.Parker-KnollIn text citation: (Knight, 1997) o r Knight (1997) states…Please note: You should always check with the author of the e-mail that they are happy for you to use the content of the e-mail before using the material.Conference messagesAuthor's surname and initials, followed by full date of message (in brackets), subject of message (in single quotes), …conference message to ' followed by the name of the conference; for example:Burrage, R. (10 August 2004) …Virus information‟, conference message to OUService NewsIn text citation: (Burrage, 2004) or Burrage (2004) states…Please note: You should always check with the author of the e-mail that they are happy for you to use the content of the e-mail before using the material.13. Images: online and works of artOnline imagesTitle of image, or a description in italics, year of publication (in brackets), [online] Available from information such as the URL, filename including extension, and in round brackets date accessed; for example:Mary of Modena, fleeing with her son James Francis Edward Stewart (c.1688)[online], (Accessed 2 February 2006)In text citation: When looking at the image “Mary of Modena, fleeing with her sonJames Francis Edward Stewart” (c.1688) it is obvious that…Works of artArtist, title of work (in italics), date, medium, size, location; for example:Horan, David. Kipper in the cats mouth, 2002, watercolour, 20 x 30 cm, NationalGallery, London.In text citation: (Horan, 2002) or Horan (2002) illustrates…14. Audiovisual material: TV programmes, films and DVDsTV programmeTitle of programme(in italics), Year (in brackets), Channel, Date of transmission (day and month) for example:The apprentice, (2008), BBC1, 11 JuneIn text citation: Sir Alan Sugar (The apprentice, 2008) exemplifies…If you are citing something a character from a programme says then the character name is used in the reference e.g. if you were quoting Donna Noble, the assistant from Dr Who: In text citation: but Doctor (Noble, 2008)Reference list: Noble D. (2008) Dr Who, BBC1, 14 JuneIf you are accessing the programme online e.g. via BBC i-player then you would amend the reference as follows:Noble D. (2008) Dr Who, BBC1, 14 June [online] Available from BBC i-player/iplayer/ [Accessed 16 June 2008]Film/movieTitle of film/movie (in italics), Year of distribution (in brackets), Directed by Director, Medium (in square brackets), Place of distribution, Distribution companyLord of the rings: the two towers (2003) Directed by Peter Jackson [Film], New York, Newline Productions IncIn text citation: The animation of the Ents is a good example of … (Lord of the rings: two towers, 2003)YouTube itemTitle of item(in italics), Year of distribution (in brackets), YouTube video, added by details of who uploaded it [Online] Available from information such as URL, Date accessed (in brackets)Google privacy: a look at cookies (2008) YouTube video [Online] added bygoogleprivacy. Available from /watch?v=XfZLztx8cKI[Accessed 12 June 2008]In text citation: Maile Ohye discusses (Google privacy: a look at cookies, 2008)。