01194nam--2200397---450-99000054262020331620090213114154.088-464-3000-X0054262USA010054262(ALEPH)000054262USA01005426220010704d2001----km-y0itay0103----baitaIt||||||||001yy<<I>> mercati del petrolio e la loro volatilitàFabio Di BenedettoMilanoFranco Angelicopyr. 2001169 p.23 cmUniversità272001Università27PetrolioCommercio internazionalePetrolioEconomia338.27DI BENEDETTO,Fabio546290ITsalbcISBD990000542620203316338.27 DIB 1 (IEP I 216)9568 E.C.IEP I00075894BKECOCHIARA4020010704USA01133120020403USA011703PATRY9020040406USA011638RSIAV29020090213USA011141Mercati del petrolio e la loro volatilità885965UNISA02049nam 2200421Ia 450 99638738100331620200824132636.0(CKB)4940000000084679(EEBO)2240900571(OCoLC)ocm24299224e(OCoLC)24299224(EXLCZ)99494000000008467919910827d1634 uy |engurbn||||a|bb|The historie of the life and reigne of that famous princesse Elizabeth[electronic resource] containing a briefe memoriall of the chiefest affaires of state that haue passed in these kingdomes of England, Scotland, France or Ireland since the yeare of the fatall Spanish invasion to that of her sad and ever to be deplored dissolution : wherevnto also is annexed an appendix of animadversions vpon severall passages, corrections of sundry errours, and additions of some remarkable matters of this history never before imprintedLondon Printed for William Webbe booke-seller in Oxford1634[34], 384 [i.e. 376], [103] pTranslation of William Camden's "Annales rerum Anglicarum et Hibernicarum"--Cf. STC (2nd ed.) and NUC pre-1956 imprints.Translator's dedication signed: Tho. Browne.Signatures: [fleuron]⁴(-[fleuron]1) a-c⁴ d² A-3O⁴.Includes index.Marginal notes.Errata: p. [6] at beginning.Numerous errors in paging.Reproduction of original in the All Soul's College (University of Oxford). Library.eebo-0004Great BritainHistoryElizabeth, 1558-1603Great BritainKings and rulersBiographyCamden William1551-1623.694594Browne Thomas1604?-1673.1002358EBLEBLWaOLNBOOK996387381003316The historie of the life and reigne of that famous princesse Elizabeth2353135UNISA04902nam 22006495 450 991030053390332120200706042205.03-319-78732-210.1007/978-3-319-78732-9(CKB)4100000003359609(MiAaPQ)EBC5355975(DE-He213)978-3-319-78732-9(PPN)226697584(EXLCZ)99410000000335960920180420d2018 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierApproximate Quantum Markov Chains /by David Sutter1st ed. 2018.Cham :Springer International Publishing :Imprint: Springer,2018.1 online resource (124 pages)SpringerBriefs in Mathematical Physics,2197-1757 ;283-319-78731-4 Introduction -- Classical Markov chains -- Quantum Markov chains -- Outline -- Preliminaries -- Notation -- Schatten norms -- Functions on Hermitian operators -- Quantum channels -- Entropy measures -- Background and further reading -- Tools for non-commuting operators -- Pinching -- Complex interpolation theory -- Background and further reading -- Multivariate trace inequalities -- Motivation -- Multivariate Araki-Lieb-Thirring inequality -- Multivariate Golden-Thompson inequality -- Multivariate logarithmic trace inequality -- Background and further reading -- Approximate quantum Markov chains -- Quantum Markov chains -- Sufficient criterion for approximate recoverability -- Necessary criterion for approximate recoverability -- Strengthened entropy inequalities -- Background and further reading -- A A large conditional mutual information does not imply bad recovery -- B Example showing the optimality of the Lmax-term -- C Solutions to exercises -- References -- Index.This book is an introduction to quantum Markov chains and explains how this concept is connected to the question of how well a lost quantum mechanical system can be recovered from a correlated subsystem. To achieve this goal, we strengthen the data-processing inequality such that it reveals a statement about the reconstruction of lost information. The main difficulty in order to understand the behavior of quantum Markov chains arises from the fact that quantum mechanical operators do not commute in general. As a result we start by explaining two techniques of how to deal with non-commuting matrices: the spectral pinching method and complex interpolation theory. Once the reader is familiar with these techniques a novel inequality is presented that extends the celebrated Golden-Thompson inequality to arbitrarily many matrices. This inequality is the key ingredient in understanding approximate quantum Markov chains and it answers a question from matrix analysis that was open since 1973, i.e., if Lieb's triple matrix inequality can be extended to more than three matrices. Finally, we carefully discuss the properties of approximate quantum Markov chains and their implications. The book is aimed to graduate students who want to learn about approximate quantum Markov chains as well as more experienced scientists who want to enter this field. Mathematical majority is necessary, but no prior knowledge of quantum mechanics is required.SpringerBriefs in Mathematical Physics,2197-1757 ;28Quantum theoryMathematical physicsCondensed matterStatistical physicsQuantum computersSpintronicsQuantum Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/P19080Mathematical Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/M35000Condensed Matter Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/P25005Statistical Physics and Dynamical Systemshttps://scigraph.springernature.com/ontologies/product-market-codes/P19090Quantum Information Technology, Spintronicshttps://scigraph.springernature.com/ontologies/product-market-codes/P31070Quantum theory.Mathematical physics.Condensed matter.Statistical physics.Quantum computers.Spintronics.Quantum Physics.Mathematical Physics.Condensed Matter Physics.Statistical Physics and Dynamical Systems.Quantum Information Technology, Spintronics.519.233Sutter Davidauthttp://id.loc.gov/vocabulary/relators/aut833856BOOK9910300533903321Approximate Quantum Markov Chains1864306UNINA