On Multiple zeta values and their q-analogues

Video thumbnail (Frame 0) Video thumbnail (Frame 12017) Video thumbnail (Frame 24034) Video thumbnail (Frame 36051) Video thumbnail (Frame 48067) Video thumbnail (Frame 60882) Video thumbnail (Frame 73080)
Video in TIB AV-Portal: On Multiple zeta values and their q-analogues

Formal Metadata

Title
On Multiple zeta values and their q-analogues
Alternative Title
Hopf-Algebraic Renormalization of Multiple Zeta Values and their q-analogues
Title of Series
Author
Contributors
License
CC Attribution 3.0 Unported:
You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
Identifiers
Publisher
Release Date
2021
Language
English

Content Metadata

Subject Area
Abstract
After a brief introductory account, I’ll explain how a quasi-shuffle compatible definition (by no means unique) of multiple zeta values can be given for integer arguments of any sign, through Connes-Kreimer’s Hopf-algebraic renormalization. Finally, I’ll introduce the Ohno-Okuda-Zudilin model of q-analogues for multiple zeta values, describe the algebraic structure which governs it, and explain how it could open a way to the more delicate renormalization of shuffle relations.
INTEGRAL Weight Multiplication sign Mathematical singularity Kontraktion <Mathematik> Parameter (computer programming) Mereology Grothendieck topology Variable (mathematics) Group representation Coefficient of determination Roundness (object) Different (Kate Ryan album) Bernoulli number Extension (kinesiology) Position operator Theory of relativity Sigma-algebra Moment (mathematics) Complex (psychology) Maxima and minima Perturbation theory Price index Term (mathematics) Time domain 19 (number) Hand fan Series (mathematics) Number theory Theorem Relation <Mathematik> Summierbarkeit Spacetime Functional (mathematics) Rule of inference Product (business) Time domain Gezeitenkraft Causality Modulform Homomorphismus Engineering physics Multiplication Matching (graph theory) Quantum state Forcing (mathematics) Weight Gender Skewness Volume (thermodynamics) Numerical analysis Voting Function (mathematics) Factory (trading post) Network topology Object (grammar) Musical ensemble Integer
Commutative property Complex (psychology) Presentation of a group Open set Variable (mathematics) Explosion Group representation Roundness (object) Different (Kate Ryan album) Isomorphieklasse Forest Bernoulli number Renormalization Pole (complex analysis) Proof theory Potenz <Mathematik> Theory of relativity Infinity Meromorphe Funktion Product (business) Hand fan Duality (mathematics) Helmholtz decomposition Relation <Mathematik> Theorem Analytic continuation Point (geometry) Slide rule Twin prime Sine Diagonal Similarity (geometry) Drop (liquid) Infinity Regular graph Axonometric projection Rule of inference Product (business) Wave Morphismus Goodness of fit Term (mathematics) Complex number Helmholtz decomposition Modulform Maß <Mathematik> Newton's law of universal gravitation Complex analysis Matching (graph theory) Quantum state Lemma (mathematics) Operator (mathematics) Exponential function Line (geometry) Mortality rate Group action Convolution Sign (mathematics) General relativity Spring (hydrology) Function (mathematics) Musical ensemble Integer Greatest element Multiplication sign 1 (number) Kontraktion <Mathematik> Iterated function system Parameter (computer programming) Mereology Hopf algebra Duality (mathematics) Cuboid Series (mathematics) Recursion Algebra Position operator Logarithm Renormalization Polylogarithmische Funktion Physicalism Price index Proof theory Isomorphieklasse Pareto distribution Right angle Pole (complex analysis) Resultant Blind spot (vehicle) Differenz <Mathematik> 2 (number) Local Group Mach's principle Prime ideal Gezeitenkraft Well-formed formula Operator (mathematics) Spacetime Antiderivative Analytic continuation Homomorphismus Hydraulic jump Linear map INTEGRAL Military base Projective plane Expression Icosahedron Continuous function Positional notation Algebra Combinatory logic Group representation Extension (kinesiology) Vacuum
Commutative property Convolution Group action Beta function Multiplication sign Correspondence (mathematics) Mathematical singularity Kontraktion <Mathematik> Parameter (computer programming) Mereology Cuboid Renormalization Recursion Pole (complex analysis) Position operator Proof theory Propositional formula Maxima and minima Hopf algebra Statistics Meromorphe Funktion Element (mathematics) Product (business) Hand fan Category of being Proof theory Phase transition Order (biology) Mathematical singularity Theorem Right angle Ideal (ethics) Analytic continuation Electric current Spacetime Slide rule Functional (mathematics) Maxima and minima Differenz <Mathematik> Axonometric projection Subgroup Event horizon Theory 2 (number) Product (business) Local Group Prime ideal Goodness of fit Network topology Profil (magazine) Well-formed formula Modulform Spacetime Analytic continuation Maß <Mathematik> Alpha (investment) Condition number Metre Quantum state Weight Expression Projective plane Line (geometry) Mortality rate Group action Limit (category theory) Numerical analysis Kontraktion <Mathematik> General relativity Algebra Function (mathematics) Musical ensemble Maß <Mathematik>
Commutative property Complex (psychology) Model theory Analogy Divisor (algebraic geometry) Open set Johann Peter Hebel Estimator Negative number Hill differential equation Multiplication Descriptive statistics Regulator gene Infinity Parameter (computer programming) Product (business) Hand fan Series (mathematics) Duality (mathematics) Number theory Relation <Mathematik> Summierbarkeit Spacetime Sine Beat (acoustics) Endomorphismenmonoid Maxima and minima Drop (liquid) Regular graph Shift operator Product (business) Term (mathematics) Associative property Maß <Mathematik> Matching (graph theory) Quantum state Uniqueness quantification Weight Classical physics Model theory Operator (mathematics) Algebraic structure Basis <Mathematik> Line (geometry) Limit (category theory) Inequality (mathematics) Perspective (visual) Sign (mathematics) Mathematics General relativity Finite difference Function (mathematics) Cubic graph Integer Building INTEGRAL Weight Multiplication sign Parameter (computer programming) Food energy Grothendieck topology Thomas Kuhn Square number Cuboid Series (mathematics) Algebra Position operator Covering space Process (computing) Renormalization Algebraic number Moment (mathematics) Complex (psychology) Inverse element Special unitary group String theory Term (mathematics) Variable (mathematics) 19 (number) Element (mathematics) Exterior algebra Right angle Identical particles Associative property Combinatorics Metre Computer programming Flock (web browser) Functional (mathematics) Link (knot theory) Blind spot (vehicle) Real number Tube (container) Limit (category theory) Equivalence relation Power (physics) Well-formed formula IRIS-T Operator (mathematics) Green's function Hydraulic jump Linear map Noise (electronics) Shift operator INTEGRAL Forcing (mathematics) Polygon Projective plane Inclusion map Combinatory logic Maß <Mathematik> Extension (kinesiology)
Axiom of choice Link (knot theory) Direction (geometry) Blind spot (vehicle) Multiplication sign 1 (number) Routing Limit (category theory) Parameter (computer programming) Shift operator Group representation Sign (mathematics) Copenhagen interpretation Negative number Extension (kinesiology) Analytic continuation Symmetric matrix Process (computing) Theory of relativity Generating set of a group Mass flow rate Expression Computability Commutator Analytic set Special unitary group Mortality rate Lattice (order) Product (business) Mathematics Arithmetic mean Charge carrier Relation <Mathematik> Summierbarkeit Musical ensemble Odds ratio Resultant
[Music] 5 very much to touzet organizer are special two g?rard fordisme nice invitation au ici des six de la space au to jump to the beginning sorry for de hockey here we go so i also where they steal votes multiples and to his 5 stones in stock and will go slightly quickr on ging his azioune with multiple zetas are 10 intelligence among the trees that they were you sting your multiples the state will use the enjoys art positivity joss a divine if i want serristes converge yoni from anyone bigger than two hockey you can't go slightly behind you could go to enjoy positive in negative bots you must have in one place and it's all strict angie bigger than just for any jet from one touquet which are to what one aux in tedjar that is 22 some of the unjust is the weight hockey are just let me but this moment their historical watch beef at amina customs ouch start with other in eighteenth century news multiples and as in depth one two three guys lot of relations '' between them not all we know are are at lot they swap now back up to life inc fifteen years ago only once we win win your game ready for your hands and the big gap tonne-t-il nineteen eighties drop 10 gap is not completely a little big boss for example mines indicating that you can't find some example elsewhere in aix in the work of nilsen begging of the last century entre vennes up to my knowledge multiples and years the worst first at the ruling see that fleury callune nineteen and iwan the functions resurgent volume of hockey so what about multiple state works not thus argued even complex balls there are two thresholds we are except do you have jace complex art our indian customs hylton 100 dates here semi-trailers sync function is variable this is the world as we japanese researchers akiyama et gamines tanigawa of a convergys provided service is restarted because we are strict and virginie jay and you can extent mermoz-marty parcels to school site the key oui ce vari?ty of things like this which is described as follows [Music] in depth key of singles in the heart of cairo he says he is fine dallas paulos des cistes jose they thought that is her z one big one to one or ziouane poetry to belong to set your form to buy all accept everything at zero and or their exist forms touitou key only date 10 by only thing here under this word their Shoulders everything so I s all you can see the difference between the one to one ce we however underline that the date single the state works a can be contes inuit analytical evolve with 70 one out for dobles and his ten roses come from the fact date bernoulli numbers de haute bernoulli numbers hall vanish accept the first one ok its island describe the bulge fabrication what causes we will see generalization jo frost who did not dare to product of two single zetas is some of sweet home stuber et ? saintes de diagonale tort witches guen singles to states and profit forces this laughter you you get the domain d'oussouye parts and - bigger than two monines smaller than two testify all and all things thompson diagonal but worse ok with a describe moss general 3 eichhoffen relations are safe it multiplies all multiple states either 9 of eps pee or a hot dog skew eynden you get some after death of death pipe lost you mind of something is something is more is the number of contraction will finish tome en tome factory dext overall to cross eichhoffen the pitch your mother of all the time of oak is a teaser on six sigma from one up to be lost you want to one up to pick losc human us size aps object hussein relations '' once in shooter mind of earth too thin and cool to something of the second round of a fabric to the contractions jones draws from the arguments cindy contracts from multiple and to different people the sums proud indices sums if you think about it he counted there are one but beetroots your hockey notebook are probably the only one with integrals representation of multiple offers the state value August 10 where maxim concewitz enters coded bae dont zag and a ninety nine tifo oil crisis to which are multiples and downstream you here now enjoy his gender positivity he says he is not a fan hysteria full tease is 8 and rhythm to this match at the wait until you going green tic integrated iphone only form stiti opportunity over you want
miles austin lynch has wrong to offer it you have and thorns soul to gather after that you have and soul to gather in den pierre engels all together graff different shapes stiti with nettles except last of the pack is here said yu hwan dynasty of caunes six points on the second round on purpose of product of two multiples and its line to combine shirt with heating collar relation for example to hits multiple assets akbar hesitate at all it is quadruple integral with different wines only forms a small integrate overs product of two simply 6 1/10 product of two simply 6/10 cintu compound 6 strong dimensional simply 6,1 des nuggets x top four times and in taiwan place to time and aof still ok to regularize elections amorfini the simplest one is the world in home builders and house to one is equal to et ? autrui et need you now one ok you will say to me that of one's own exists ok this is just owning determines is still seen in stock samara au yukon decided that of magical zero rate baptized the stone age and ermine is an if your idols and before all in the united states singh starting with you want is also elsewhere jones sono to wilrijk in ten product in two different ways open jaws by formulated using to cross eichhoffen relations and the bottom line is just for money by using chauffeur relations and then i fiul if you equest or even bros the red tails disappear like in clinical reaction a tube get en france this one 10 th coin il a toi nantes you get the wailers collection and of physical everything is off to one to which are briefed explain the bird driver relationship dope the driver fat regularization haunting driver to adapt our soccer relationship for example raf must tell him things like a form of chengdu variable the dj ikk aux to one man city james ellroy presentation ban ahly pull the pampers by des idioties boys from the bulge for example 10,6 de faire ce exemple of duality ans you have we said as we have seen on the balshaw jump end a goal you have valve springs and the relationships that exist between principle to be explosives bat as far as they know it's still duality religion as from beautiful things ok there is hockey are multiple politocards considers justin wang variable her face already explodes her rudder clichy multiple paulilles to the boys at some type twin 0 in one he says to himself fan base are there on x different bases disintegration s25 multiple forms and enough that this date instead of going for zero to one you stop and i want someone is the world he wants multiple levels and downstream you would be divergent and stop at his strictly smaller than one he distils like georges issiot to whom his name and one two weeks press 10 multiple poles he parked his hymn to operators yeah ok 066 de formula you can't think the bottom of the slide on you start with the coast depending on the cultures and you lie and operators big one which is multiplied by malfunctions one over one man city ok wine reply from operators arts a witch's by primitive operators parents would have made physical to the primitive of f vanishing and 0 10 and 0 tobacco stop inheriting to the box in vein and we continue or like this you play non operator x86 bits multiply multiply bailly molex and six officials one oberti eynden operative etc etc over 800 dancers way to two two rewrite concewitz integrale performance 9 multiple polished logs hockey unless our want is called to one you will cover the multiple stages at the wimax checkouts ten representations by words yoyo introduce infinite alphabet alphabets why why star of this of words twitter chinese look at the line up and of the world un pipe k23 eichhoffen produces his bail point of view there are at hodiall to the wall explained bailly mines instead of using concatenation products dijon fco product will use de quazal shuffle product in conquests and nations co productive there ok it's up to crises to cross eichhoffen product so it's like that he was eichhoffen relation where we are poor from sat 3:22 pm rue sipilou xv th ri similar serious contraction of eleven countries that we say ah ok except or later use one gets worse define disc white pearl project kahn stick to jean winshuttle to min ? cannes stick to war equal to zero so high tech smaller are one of the few sodi fine associatif product which is no ordinary only product bastille landis infinite alphabets are taken as an example three eichhoffen hirai a life turns including by this to contraction term ce bati fault 10 cardiac driver product at the crates bone 10 6 3 10 a white star annotation managed account jones j call to this time switch d'hondt start with my
one and for any world for any converging world with andy fiennes and aquoise eichhoffen of the world is equal toulouse et tarbes the corresponding europhile 10 battle afghan risk of attack that annick stand in early between de quazal chauffeur relation with who wants to the fact that they state it is to cross eichhoffen in the character do fort de quazal surfer product is morphism of course we would like to go from counter jones world to a newer de that's what i mean explained hao tour et gueulard eyes the world switch arnott convergent which are six young people example we cross reformulation written in terms of the coast choppers product with 1go duvet whatever we say ok sound haiti from first ryzolt eyes open with sylvie fishermen are scabbard hugo boots extentions all argument except and nice i'm ok said because of quazal surfers pro doc to you can extended to the world slater seen in if hockey his camping form strong argument except positive out negative sign hockey on what will prove ii x2 following their this character form 10 extended algebra with the crash of product in tour de complexes moeurs so that just to the mad fayos life easyquote to the external states fit for any convergent world ok it's when you read strong uni world with the positive negative letter only that the multiple and to can be defined by analytic continues and shenzhen the character that a series of 8.6 analytical y extended value are a particular firefly neeskens equal to and aof mindset his bernoulli line-up a place either new rules or are followers to fail of mind hossein mindset prime jcall toulouse and mainz germany this premium sauser this webmaster the value read ifs enterprise fraud clue that does not give and say expression in this fire bernoulli nos news so we got the wolf of value in depth all in any case except alioune il rises diagonale cyr have all the same value except the very last one and one note for example 10 one ok 10 value its obtained by analytical continuation diagonal rises ce are not only for example there will be walsall paper by the iguana bintang the little bee for us they also have tech of the value it offer is different boots of course 2 drops diagonal squeeze out because analytical continuation ok there you me guy basket of proof are they those who like kreiner regularization a renormalization vehicle ok this we have the right of oil products together with concatenation you get connected filter up jay bryson by the index of names xtend October 10 at 12 p.m. or letter sin of complex numbers sow extended match my style or quest for europe thrills its fans arms yes to cross eichhoffen product replaced by the chauffeur product hockey at the results paris michael hoffman 10 to have fun I brush orphic rhizome the tunes are explicit isomorphism victor mappy their regularization map so we said fanny tons of wood warms up a europe version algebra solidaire considers paul bigard of the world is the c word between 10.6 shifted bezina like this ok and then we will use dissent of man exponential luis witches from europe parisot mon physio eynden from the gold regularization in ayguette regularization bee artiles christine galzin hoffman exponential except twisted regularization respects corner ike pro surfers of anticosti first regularization houde respects driver product sino on three now yes says character fan big five from 10 and the browser for product design by this horgen zh and what to heat zamal kippel the state works it gives me back orfi which is not in complex variables they are by defeating this is it that it ex cintu value of mary murphy which works if one complex variable eynden then we have the birkhoff kreiner decomposition gold au big big fail character can be composing like this are a 6.2 convolution of product a tops if their style characters three axes a relation sarr style verified faille plus au viie solo morphy cadic wall to zero forest new world we want this is what we want it because non ok 10:10 hour of formulation gate 2 to peace is fine to the faults more of my agricultural goods quickly as it works your mirror fiq works algebra explains into parts of paul pierce and mind at Formalin breast sparta series and it cries ok so if socalled minimoys abstraction of skimming physics and then you can define recursive lifan magnussen flaw more 06/08/10 formula register the writer speech of bogoliubov
preparation of maps and even if you ou tu exeo positive project in good for the party is sure that we find you projectim of formalin service parts which was to ana?s character and then de character we will look for you just evan lloyd de grosses parts said what the zero rate of 10 seconds or a style verify horse ok so we are quite shrinks ryzolt eynden few years after that we wanted with crochet brahimi fardin day one thing we wanted to describe olsen ocean of the problem is quite the set characters winch external multiple state functions if linda 100 Gbagbo respecting mines crossed against a background of relation normalizes this mesh sound band he has heavy rain say ok a tone is 7000 and mrsweets28 general ryzolt to sad stories commutative connected filter of europe angie brad i will be any commutative unit which jim brown jr will be the group's characters witz val using products given by the construction of disco ni potence property witch et disco soul to make some recursive hockey argument proposal of kids as follows ue arises date big ny will be there ideal tco where they respect each other or reduce the product reviews product is this delta tilda who stares form relaxation extract and / or extreme turns hockey and then it's you look at 17.6 hey you look at the characters alpha with the vanishing wright that elsewhere visiting this group from profits what quiksilver in the blind proves the sunlights or the world it was said was take two and the hands sales fans cattle ne t'y as you want to prove that alfa-beta manos one i still in this way to prove it is this group titled you say that in there the characters event composition of the antipodes and yes yes place of a type to the hosts bdx recursive expression one of the nude can alphan manas beta of the boys or prime in cairo between new look of the youth of right right cori crider property to say that is vanishes hockey so we call it de renormalization associated groups all that it doesn?t like this district you look at work the different characters your mix it if i'm only and co hayden interview arises date is respected unit between x multiplicative whenever twitter define the sweetest belong to and not to loket ex et ? l'oeil easy call to those flaw underline two groups of seals almost restricted to indicate 12 states ok outdoor intelligence of the six main homogeneous and space yes yes poor straw and yes his left ibrahim sy lighthouse of the oan's ignore if this homogeneous principle and space administration crisis fringe positive in two squat profiles similar to the proof of being told i was group ok skip say ok no yes the dish it says gerald framework to our people zetas sobeys phillies from reading numbers of fate gibrat is this one with des arguments end i'm into you of total i embroider will be just complex our morals the white white world is the line hispanophone singer words that means that the world in which way down like this and switch poe le fil district conditions switch the contrarie of the singularity conditions except the beginning of the top weight and has to be different from one in one person to as to be outside 17 ans disparue le sol forgetfulness phase outside 17 hockey between ten times ok 10 big and so cute read aitzol ford concatenation mister k say yes we say choose six hours additional and pro ported on the stephen barry contraction this exists ok yungas men consecutive their health where we are and mup the slips and nice people by this properties which are sigma will biz complementary n hockey en sauce ig markets group that the corresponding mobile home staging du abb local what is a bit by that define characters and how will be at ok will be multiple state will user baikonur johnson in theory did are out of broom analytics continuation of sound hockey to this offers a solution while initiating the forum it given by the run ar re normalize groupe acti ngon one solution fortune holding as we had proved with sylvie p?cha that one 'solution' exists ok sowind vesti gay title little big disk group just to say that it's very big fuel audi has destroyed or also to this crazy lotto but to which his agent or cumana locks at the box let me in mind what is jackson integrale in the given by the ugly formula bat baby it's easy to grasp
ict on the slide are recreated an example whiskey or equal to one he in order to finish pew shoulders everything will be ok it's quite view that if you go to one the classical limits who dare ordinary man intego hockey drums raouf you will be
considered as the nine determines not to kandy find my mind care dropt to baxter operators domingo this vineyard to exist f finally variability will be fo this type the ffq tools plus fo fuel qwerty etc operator qtes invert ibl because of the six duos any amicable agreement to be written and they call themselves formalin algebra service into variable holmes your starting list y hockey a green kitchen carpet ibowl live earth is given kew beat difference operators force team and safety a confession modified half this role fendick you this is life identity beaten rave diagonals for a weekend up with it we equipment identity ce one ford glisse one ford 10,1 three months two mixed hockey his name with a multiple define ku poli logs the same way you lie place de riemann integrale operators parisot jackson integrity hockey of the six exactly the same I test we rush its strong letters use as he will need operators bar offer multiplication basis does it work over one man of steel but for the movement ? just mimiques de formula 1 political force harrison reply singh from riemann intego le perito parisot jackson interroll operators ok his name ah yes the speaker bad ono au elbow to elbow and multiple links and rated this model on wii kolda from multiple details given by evaluating de paulilles ogg and one here we evacuated live west of kew poli log out your hand in times of east and his biographer formulated so in de nu merited to adductors monks is an idea of nominees serious wrongs powers of few winters hockey ok jump forecomm day jones worlds want you go to one you will cover the ordinary man who pays the state wink yugos to one reason had rented ok ok yes yes ravony alternative description in terms of the operator piqthiu ? ok les sosies tube harris de modified multiples and grabbed ku multiplied by one man of you to the mind of the weight hockey without daring 6 10 internity of sums un petit is given by this way of operators tugging at the two biggest allowing big ben to witch's of operators multiplication by ten in show we are other models for cutie screw and jeff monson few from schlesinger 5000 bottle modem or evaluate qp oligatoires not hate you here and now bradley swiss model ne deserves gold he makes fun of complicated and he is a sculptor power caire a turkish of bartender that a multiple to arrive depending on the model but the xiu xiu one ok dot we like this model by renault au coude ? new delhi nikos et ses different argument shapes except one design if you take enjoy sine die stille make sense of you gonna have this estimate quan qzone complex of modulus strictly smaller than one all the sun what we want a style rises formula ten operators formula 1 for computing if by kew hockey rebuild negative power except pillagers positive power except said g?rard his example this site at kew barre 0 bari it you want you were here also just and awakening keep the power kenzi tabarka of mind is nice jazz is so if you were made man has your mind of open stew square want you skweres et interistes line of the basis barre that to the fans they say lambert series we are of you to them to over one manosque you to de m ok en tire not only we rave meaning for any size but we have complique doubleshot picchu actually takeyama has also doble fict horse pictures batting of bradley models are from picture is more complicated in title are extenso argument except and nissan to which its first of all eyez describe the you show fabrication ok but all live so you look at the alphabet you will go which will and to boots or oppose date deep is equal to feed the world to one ok and we have come out their flocks are null 90th 'world rights unique lille existse to the end and why toupie to the heineken why we the enjoys positive negative non fine bar kyosho fall of world by this you show fun of the corresponding of angels extend leonard hockey a shot with youth of product and his 10 space of words between recursive define libya formation isolation kind I stop abstraction except 10 relation we have you expect to say yes to the permit all ok a tweet hebel to prove that products commutative to associative pickaxe relation just tonight is this barque you should the character force10
on the ground-ground product her name white hilda is the infinite alphab?tes jean bodart hitchens with any n'zi internal product is the same z ait contract? de weeds and james ives you will give you z eickhoff jay white hilda this price of this os x 10 7 hours otherwise white hilda star will be the ordinary cross iphone 22 to oasis of product is the ordinary 3 eichhoffen moved by this operation of here shift 2 forster of the world ok forbidden fine coise eichhoffen zubar function value like this night extend the energy endk was accused of which might like this kind character design for product reviews example their tubes the functions must all doors the product of single who you are at function 6 given by ordinary krasic felton place whitelock thorn o what do they note concerned that if you wish you go to the ordinary wayne modified ku zetas and you have this one man of stew infront peering so you can hills country the fact that one and limits which use to one drop torso disappears nuggets and ordinary queryshuttle the goal bars here you have no regularization of elections you have the east peace bridge et on aura tout vu waldis design of cooking and wind to 2 to alphabets hugo sicard bigard 22 russian iris udder a bunch of changelog coding waits like this your job forum queryshuttle and astou chauffer les zetas with this bed and soul of the six define strong argument except and nissan these are our problems smile at fquih life foundation of early show off coddington soa review un example of competition in using by benq chauffeur she rents cadiz product hockey from m we can write on youtube to one baby something string sur les dc the first of all eyes duvet cover chauffeur their relationship our twitter space x tones ordinary kaiserslautern of so you think you so far so hype en slate into the world is this product hockey ayacucho feu de world peace with the world pee why they know you there will be given by tokyu driver formula 1 laughs fed and we go there's a hiccup insue lines said and a happy few chauffeur bar of this way the combination of words and day translate back to the bars hockey his name this town of physical to this town below zero kwaito lot of noise cancellation un indian hyundai i10 hockey if you wemhoff de bars you have this formula attracts a tweet your good to want you go back to your relation which was obtained by regularization then build regulator risk per cubic meter so to speak hockey interests 9-10 identity can be found in the works by pelli nineteen sortie 6 are this was founded by vadim dit line entre b?lie attributes 10 identity toubel en small rise learned bae said jim hawkins positive who are the distinguishes to conclude but weird to sisters williams gives two doubles driver also duality rich in spectacle at the time to develop this we would like mon combinator gueule description of the few shuffle product a tweed like to find compatible coup product hockey here under the titles tootoosis navigation your trump card must standardize three years driver and the chances yes oxidize in that some way watrous of mines extends un chauffeur relation to the negative said that means that you will have to show fun any negative containing save package do not die of cards 209 beds bat bad twinz exist you parameters dos 2005 since my so we would like to find to change the structure tonight as a note schroders forexpros the moment yes blind style of project to go back to this it is at the quai d'orsay from youtube by cubic meter the regular he is in the west box your normal in eysines want you go to one hand ok it is line of wind and again this early that all x gaud?rique broadhurst has to be what about it would pig exercises a real sprint bail de rigoni anne klein schmitt botte de beale et bio ans de lombers strong service that at good to want your good except unit seals at least for it as to the fans we have complique pictures which yesterday between bizots you got cool good by two to do the same for the author qml tippett a value from goodwood program and dominique merit yaya minister is activated match 33 made galleries bac creation
when I do not neglect weekend of the 6 and to negative by excusing news by results from [Music] suitcases and expanding share like and reindeer ok you say you say you say analytical continuation discovery the iss process is ok on may 2 all kids like from outside the way analytical extensions available with a freedom of back choice caudines eighteen years [Music] we remember all the strengths of our side we are satisfied with all teams yes i do conform one death one of the two drivers producers at least lively to haguenau meaning of nagui negative side three pregnancies [Music] so he is queen ah well there ok bah everything ira falls with mixed swiss arguments signs and then you by arnaud notre fiercely bleeding insistence for the world I will do the whif rationalize the stars full or empty rate to the researchers 7.5 offers is pronounced this stadium in fresnes exposed it q the stars sun satisfaction about of the council s island this is therefore flow of link morning but beeharry on sum sum at this stage there on orly ouch ouch buyer molko and stefan bradl and at [Music] taiwan king bed in commutative symmetric spirit faction bat it is not the same at least present for a long time wen a work stephen shiu shuttle ace generators squat route on unity oates au hockey my own is you say that it was commutative un massage associative yes we did not trivial but also relations do you have is your argument as direct computation the lease we are to rings and easy by only to hics kind of carriers of the ordinary cross eichhoffen you can see this expression hockey au kidnapping or things to the ps all chose chapple from ischios coisy bats who chose schaefer a ok to shuffle the story of kew schaefer luis alldis reelation ago ok ok there why de kew chauffeur high as it was before there actually x rite is proven bye bye bye by auxonne from handover of letters an expression elsewhere well city stands collided with the players of the direct generated copenhagen and the commutative flora it is easy for associative et id studio slipknot difficult to be built from this meeting girl ok hat your told her royal dont he knows of raiffeisen representation of albi and it will be using de representation louis harris faithfull so we had to ride or abstract lise de food in cairo the standard [Music]
Feedback