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Almost global solutions for the capillarity wave equation...
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Title  Almost global solutions for the capillarity wave equation... 
Title of Series  Trimestre Ondes Non Linéaires  May conference 
Part Number  8 
Number of Parts  21 
Author 
Delort, Jean Marc

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. 
DOI  10.5446/20765 
Publisher  Institut des Hautes Études Scientifiques (IHÉS) 
Release Date  2016 
Language  English 
Content Metadata
Subject Area  Mathematics 
Abstract  Almost global solutions for the capillarity wave equation with small periodic data We prove that the capillarity waves equation in one dimension and finite depth has solutions over time intervals of length c N\epsion^ for any N, if the Cauchy data are of small size \epsilon and space periodic, and if the gravity, or the surface tension, is taken outside a subset of zero measure. The proof relies on normal forms and on the use of the reversibility of the equation. This is joint work with Massimiliano Berti 
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00:02
around data in on the way to do so and we don't both dropped work with this union ready to Continental was good solutions for Spinnaker ready to get the unique which so we could see the clean safe water which lies between their Fed and Mazie signed in the freezer face which is a Rafael some functional white equals he does what in a week so effectively doubling being guaranteed and that we assume that it is a free compression in the principle of a new edition so that in water the velocity of the freed will be delivered by the gradient of some potential fight and fight resolve aggressive question the president proportion fight you was In his humor about the condition of the which is at the original fight from venues and so even even the value of this potential what difference of faith Romania solving this equation use a vital financial literacy to everywhere so the motion of the fleet is it online life different anytime in Britain restriction site of capital flight the freezer face Italy you right there nearly equations inside visual In movie writer convenient but reconditioned and a freeze of things you get new nutrition equation for the and outside it which eases the socalled Craig students at formulation also has a remedy everybody with the questions that they spread now so different equation in that Nicky .period equals G of the topside with GOV of the .period ease the economic political but change defined the following way so the the functions you saw the the Nunavut problem Weizman revalued signed and so you find the potential capital flight and then you computer notaries actors of potential the WiFi minus needs he did indeed find that the fruits face white equals the cup of tea and any finds Ogilvy topside which he just dressed to the who European amenable the same equation they say that indeed size is given by complicated expression the miners Miners will not such square press Ogilvy directing on Cyprus it's tied meet the Blue Square divided by twice won presidency to the square the stop our age of all where it should be gotten solemn explicit function that's the doing derivative will reject Prime whispering 1 square it upright continued interest needs His only after bombing tourists in that equation in energy which is the gravity and gap which she's the service so we should consider the equations when AEK's the belongs to the 1 that you consider the questions these functions job .period thanks and we wanted to soldier its system for Bloomberg so
04:07
needed the song on results social agreed on the need to draw on side I would just say that question into no coexistence Yuri before the proceeding system recently of that no is most of the major work was due to seize must prove that's when it it's meals to all of 2 instead of 51 when couple potentially 0 and when the free as infinite desk better local solutions exist over something until so that men don't mean quite a lot of other works in treating different of daisies there is only 1 actually mentioned to cities 1 of the ways which obtainable coexistence In the ability fulfilling desk if a positive campaign that is there is a problem we're interested and then Quattro the works devoted to longterm existence when
05:19
you consider small In the danger so in that case you may explode to the specific properties of the question so that a solution souls in resignation we indicate when time goes to infinity in his allusion to prove that even over the death of small inns rooms then you may get a solution the final vote the wrong kind of war and even in some cases the bill also so I shall not to read or is diseases in the name of contributors I would just say that anonymous less also some resorts which have been obtained when you conceded the periodic there move not necessary .period but stated that the list do not indicate at infinity my idea the screamed and ducked out new and also by you and of the year and and then wellington shown different cases that say for instance for the punitive cautioned downtown you over a socalled QB lifespan neckties take caution that all sides at you get solutions the fine over interval time flanks it's known to minus 2 while no coexistence provides a solution if I'm going to refined like sitting on the minds and so would wouldn't want to do is to try and Ogilvy assumptions grew bigger and then I'm getting the sense that you make life span a whether you should ask this question to Daniels and the I'm a free man differences in Eagles a quadratic is corresponds to quartermillion narrative and then when you would have no quarrel and requests your you get 1 already long usually Deuba during a meeting you get well that seems a square but of course has annoying at the sclerotic universalist you get can because Switzerland that's why the originators of the timing of so sudanese CSM friends which shall be working with the lead survey some operational dresses metrics areas which is a matrix 1 0 0 and then say that the a solution he upside offer aware he is reversible even on the eve when the computer volume dissolution of fine minus did to cement acting was solution computer the bank so of course it for a minute free from the quality that he fears this property holds then is the 2nd component so I must finish apparently quality any conversely you start from a cautioned there was a cynical believing she's a prime many a solution will be reversing bulletin was satisfied this quarter and he's just follows from the fact that the new regulation may be written off as a state dug signed he was the sole owner central air upside where s also property that making out geometrics but as the last on carefully topside you get something which is equal to minus F all also his and so reduce immediately from the property Net central dissolution In as of this to the means Europe I will use the property Billiton and the use of a
09:36
couple of conditions but they produced so we should look for the 1st component of the Dow off our solution the man the summary h fold so paramedics entrance tussle with phone interview the shortest you that In a sentence or even In short assumed that it is the average of the top easier so these properties of at least 5 and the initial time then they hold for any positive time as a consequence of the structure of the quick 2 concerning the Simone component but got solid signed from thinking in a space for a space age is when fall all even functions wanted to tolerance and to 1 end of actually in taking a noticeably spaces that based more euro Const so we knew that the could the system is actually 1 defined 1 functions model constants so we may consider suing equation of the system the 1 0 on site projected on functional you constants and natural Caruso the was actually only a went of size you want under the code meaning not sites another year introduced through these notations and definitions I may state the
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ministry so far the furans series you may find it's 0 a subset capital also in the president futures squared fall in the G captain often brevity and surface danger Bacon size is a subset of Sumatra full energy even in Georgia these were 10 the variances Solomon index of gravity 0 Golden Oak said that he had taken S Lauder than 0 when you may find some political instant it's 0 it said that for small until 0 full any function does 0 In suppressed spaces that included the more recent you of rage and even we know only that space more than in long if you solve the new deputy braking systems With cautioned that are at the core 0 even by he does In 0 and then you get a unique solution continues and some enjoyable these values he knows any force space where the banks always of existence involved from below by sea until the so in other words the Suran states that you may get the most noble solutions but the solution is the fight on until Lancs its sales undermines and for any given a priori happen even if they cautioned that the which are small young Mitchell smoothly we chart reversing losses in that sense In decision to send component from 0 at equaled and he should you have taken your barometer was unsigned selected from both 0 To be sure home the this will prove the maker and Malta but Richie that actually you mean reduced was a case when GE cause 1 just using it as you want and it is equation and then there's parameter of the Detikcom outside subsidizing River is just as a parameter and say that this Europe provides there was no real solutions for the caution problems and as the sentence was vindicated we do not know if 1 can obtain a global solution political shipwreck the certain on the old boys because 1 of options and that is that I on use on down on fever examples of global solutions that is a was bank was bearded solutions which is being constructed by betting of and which will be the subject of talk of Kentucky but the review of the decision of the initial up a special because we wanted 1 is with possible solutions so this corresponds to functions which has a Pfizer properties fate would be for the dark side things the acquittal of having made no you merely need to some friends and I shall explain away later it is true or not you think well you know I you know the kind of person when making conjecture when the air so and really not if you do not 1 side of such sites citing units a a reflection of the potential 2 years restriction of the potential to user fees of 0 and news 0 initial losses to service and then let go of it the OK so now we shall a 1st step of .period forget is the explicit expression all physique which introduce ourselves to some party funds reformulation so 1st of all it features patients so if a seems so state function or fixing side such that the CSI be that and you know affordable Bankside Power and miners beat out for Indian and in the down when associates to disease a and the period or by the federal in the following way 1 takes Sollman Gettelfinger mishandling
16:52
supported equal to 1 . 2 0 In 1 defines form a French and a new function a kind it's way what dates the frequency of a little to the during these these 8 out of its 1 multiplied by the cut off kind of feets onto side and dates interest protest and in that way you know defined as a body innovative conversation often different repair as the operator associating to some you a new function even by disease isn't their 1 of the 2 by he did or equals the height it's my side 8 titles for Liverpool side you've wiped the White so have wait 1 gets and operator who made sure his bonded for chest which is miners and poignancy if you assume all just seem a spirited he needs the operator ascended beauty and with centuries of pictures of G 1 2 functions will reach the mainland to Wong and then using so situated bonds are rated bonds valuation formula you may realize you recreation the question restored before the parties to the bridge but the new right initially question but as the following you have capital T authority will be 1 of the idea of a key minus zebra weight associated to the metric symbols capital the same lost the plan on the GOP side because we treated knowing equation and all of that operate or acting on his you know it upside truly equal to the moving operate all that the operators at Wingate Road every that for all and even erosion Member of the connections usually working spaces of French and but did when he so usually when you do that Foreman said was in your ability question you end up with system for which we can't get easy so energy estimates and then eventually recordings it's when the case a water was equally the wellknown that when you do that you get the incomparable because of the military all seemed lost in the new it was a good volumes it was initially thought goes to infinity when excited goes to infinity use the words you laugh instabilities which prevents you from getting an estimated without their electoral sees form such a formulation when you were applies his stories they should method To what was the question so the problem has been solved years ago the 1st of all about she mood design Solomon Islands formulation of the equations that little ones to recall the Detik misses the fact that the amount of time that it was so small that 2 cents on the day of the 2nd half so then there be inclusive approach that has been used relying on socalled wouldn't known of and now buyers are meeting here because of injuries and this is the should adopt and then more recently and Jerry Freeman that will to serve pool choosing Solomon 1 will feature called In we shall use of life said he's wouldn't approach we consistent saying that is the problem that was mentioned comes from the fact that we didn't use known to express a problem and that instead of writing there is the equation on the GOP side as I indeed 1 should introduce instead of which is signed minors where some operate and Damon beat on the dock where the candidacy involves a parade talk is just a function and misadventure and give the site president cited seat and dividing by 1 predicted ticketless it turns out that you systems
22:23
green these unknowns many scenes of amateur so more precisely if we start from the upside the solution weekly should find something don't then introduced a complex and only following call Lambeck about the zipper weighed all the people redundant of D divided by 1 press conference as quick as would fall he's parade demise of fall In the defined from using wooden known on the gap informed the complex function you which is dressed amicable during a press high the amicable deminers 1 before next introduced copied already knew the back door you know any rights your equation and they're operating rights for fund capital so when you do that you obtained the but can be called minus Zubair we see more new metrics of seemed more copies or a view takes CSI I think you equality some of the operate all our you I think know what is important is that information to the other what the structure of the immigrants so a he said Dimitri all seemed also lauded the house so the main contribution In the jumble of older or is given by some foreign carrier In catalysts on where am gavels even explicitly might excite a bit redundant of CSI was also times 1 brisk swear 21 of the diseases similar border which is multiplied by 1 the press the Dow viewed the links in the demining so we invited function and multiplied by Zdenek treats at 1 0 0 9 1 and you also know the contribution of orders we also and captaincy all multiplied by immigrants what the mind 1 .period then the loss of contributions of opposing the from the real world order madam I don't know what sparked or few times so recruits In London 1 of times the advantage these 2 symbols of order 1 large and 1 respectively so the positive but it turns out that net images report is awarded the Maine 1 so often while at least none devoted following and then your contributions also known the war you seems lost 1 the miners 1 out of order mine is 1 of them this year and what is important here is that when you go digital values of the new metrics you get that is usually thought Zaidan values is bounded when CSI goes to infinity which was a property which wasn't true in the initial Foundation it is poverty comes from the fact that using the you make appearance seemed more like the 1 of year which as the imaginary bout of negative order while while you were doing that stoked informed His insurer known to side in the instead of Omega in the car you don't want to see your expression that is usually Balduzzi Seymour would have been a border Steve onehalf it the city's what would be responsible for the fact that it is the as a metric would have had initially balked so at 1 house the Domingo to cheating went single which and this that appointed creates instability in the initial so now that we as this form of the question it may also include that's true properties satisfied democracy most any that we play the central so recalls that they define reversing beauty using a song you know operate analysts and now I recall as a cement minus 0 1 1 0 that's visits was Nacional's the same operate Delbert on generic basis we're using into complex formulation of amid of symbols that you get before the expression of your system so the slices reported just don't want 1st
28:02
Wong save that if you go Pulitzers metrics Seymour a attuned to it's minus CSI and congregated you get minus tests a year viewed United's side so this property just means that when you concede there is the associated operator make it act on the and they going would you obtain these minus S His you operate on Seymour at s I think In this property is that she is a property it just reflects the fact that we're working with a system on the new which she knew well it was a simple equations also system is obtained from the first one may contribute to the city's dressed tho the politically from the fact that we started from equation former system which provides the 2nd properties were destroyed by the metrics and you get a good view of the miners it's my 1st time is equal to you the did it's CSI and means that it is used city to operate all you got to grow preserves in 4 which is to win it seems we should be working with French and finally there is a certain properties is the socalled reverse ability which states that new computer creates a at issue the it's exciting there it is equal to minus a of the U T it's CSI so the meaning of his property it worlds you can see there the right outside offer was system which was all any of you and any new polite to meet S this is equal to minus the operator we see more layoffs this year I think when this In the dress reflects the fact that the system is reversible and the property they used before when I wrote that Ansel some function and of the topside was equal to minus F upside so there's a certain property which will be using to obtain the result of
30:34
look at that and now some ideas about so as a 1st step he's a sequence of the seminude and going texts by some of the major amendment so we not give any details about these reductions we just say that they wouldn't make making the legalization of the single for the and then making sold change able watches sold Barra completion In making good allegations might convenient freedom were grateful you may reduce the systems that I will be formed to assist we just constant question so use the words you may introduce some new and old capital of the the disease Committee expressed explicitly for you but maybe all the same size of chance when Boston himself more you In certain that the new number 1 we solved question To that maybe the so you have difficulty minus and capital deeds Jeffrey deepening Europe that introduced to befall the energies of the AEX people redundant candidates for the oneoff 1 Prescott Pasquin square because was not times some firm trend 1 paralysis did underline all of you in 15 which is only a fraction of so this quest is operator only constantly efficient operator at fixed so the multiplies the military's Daelim entries 1 0 0 1 1 and then you have to look operate capital Rachel viewed the where capital H is a solid data format creates also constant coefficients dutyfree from labels which are overdue 1 and what is important is that the misery brought offer just data the is evil White itself he's a and finally the Borrego H satisfy physical properties of 3 properties that they produce before the new reality Borotra preservation and it is right outside of the question you I love you acting on view where our Indian soldiers and was incorporated that satisfies Eastern free approach so you the words we have reduced ourselves to In recreation weddings are left unsigned of addressed constant coefficients wrinkles and so it's very easy now to get In India estimates when the switch well actually when you you make a energy estimate consequential this is really politics of H India's said Sergeant operate which indeed appears immunity estimates and so what you are left with is just the contributions coming from Zeman's report of rates when she's of 0 so apparatus which abounded 1 the since we have constant questions we may commute as endangering that as we wanted to win we can write as well as a tool so where's the energy system so in other words if you right on the personal Grayson a very basic energy is still you get that sort of normal for a solution of the he's moaning by users of riverknown appends world press stands in from 0 OK often you great all year and age all of you don't cakes acting on Japan dope just show if we knew in addition that is the scene In a report of H. not only supporters 0 but that the she's that normal NHS as and when you lose 2 0 then was approved the future because in this case we could write at the prison inequality saying that was so revival of the at times His body dies of River 1 of you president Taylor from Suu Kyi offer the normal view I'm told nature's power and no of In it seems we work with squishy director of science at at similar it seems to me payment propagating defined that as a solution states of citrus slices over sometimes until Mauritanians isn't there more sees no view to end is of size Epsilon even so that's only elementary Boonstra Parliament we show you that if you consider these quantity only 4 times smaller than seeing the divided by its known to for smaller was then and you will be able ordered to approve an a priori bound saying that the rest side is more than Kate on which carries its own if it's constant and so they the rebound telling investors solution may be extended to such but of course it to do so that we we need to lattices property that is the report of a given me she's like a local views when the rest of the world and this is the truth the variations and she's like a you power once when you with this so we have to the 1st step In order to arrive presentable it the state will be no more funds in so do explain
37:45
these let me call b also Capital some major parliamentary move signals were received Digital and live music for the day the new vermilion on the team even by his explanation all the people view the deeds I think want so in other words I'm still waiting for the equation that was on the preceding slime they indicated miners and gaveled Dietz finds someone president underlined ones using mind 1 Chris H. of utility expecting it costs sums would incorporate at England and with him during his address that idea in decline Z's operate all right disease explaining so since I have a constant coefficients operate also easy so exponential debut viewed candidates commutes we've always operating and so when I'm on making the conjugation of the equation buys it provincial the only new contribution that wouldn't be will call for the conservation of duty respects that he he's will get the military need to be solved of its so that the new known the Tudor satisfies an equation which is a difficult minus interview of utilities minus and get DEC 1 president underlined .period gives you might want Best attributed its indicated that was all of you and what we have to do seems so I recall that what we want to introduce to get to read all the contributions to the report of age the dot Is the nation when it was 2 0 at the Waterloo lower that Solomon used for giving so in his own words introduced to choose a capital B said that his Easter week guns the contributions to the economy from indicate that the advantage but ruled order when used his celebrity to worry about thousand artificial from Ancient are always knock off of course I am also consistency for are a nature of course but you know I you know there's a message is pretty much the same in both cases and so I explained on each so I have construed being so that the can minus ii a report of a of you teach should vanish like new position when you so do go straight to be I'm looking for hours sun also expressions of BP what you you the troubled waters of the Greenpeace the going from 1 of 2 Inman has 1 the last the restatement cancel out each team being sold beginning on lap to restrict because and I go home we could you realize what it was so in the computer meeting the when accompanied Billy the Kid derivative we are successively on which all human on the day and then we replace the corresponding you using unique which ritual was that it did you use so deeper Europe and capital needs I thought it was some metrics Carey which was once you your mind acting on Capitol Hill Best Song knowing on terms which we generate contributions Offiah degree of so you I favor right what they get as a level of contributions and which is of the so I will get BP in reaching placed 1 0 0 units by so the operation said J corresponding to the places only going from 1 piece the ideas medieval times B of a muchneeded they may forget as a playable and I want to truly pp In order to get creative off as a contribution to you a check on what is of degree but they may write us Olmert you every bolt of each piece of you you think and now our essential the question to which might reduce myself to finish so I would again that equation Standard told of the site and it was only they need decompose posts he told children and Capitol Hill as a son North by a summer and all by and breast completely Best Buy minus get where what they do not abide by and it's just as a special project all associated to the end models and apply for and where seems capital you is a convict told the press in the minus the not conviction was the 1st possessing component on that so you everyplace said each of you and you by such a decomposition anybody who cut what happens when they make that Z's operator on for instance by and capital that 1 sees immediately that's as a result of the operation acting on such localized function there need enlightenment implication of the function is a symbol and get computed but so in other words when we're right there is a pressing question replacing you landslide buying 1 pursue by now because you by oneliners you but apparently meant and when you make active illegal on 1 of the 1st terms you just get mitigation by bite and got out of the injury we the breast and of course is the certain multiplication by function move out of the peace Beijing In the same way for his roster when you make up the sudden operator on the last you get multiplication by some and camp of injury in mines so that finally when you compute z said left onside and when place each will argument by respectfully localized long wait to cut you obtained his jester the computer . 0 amendments multiplied by some function India which is due just given by this human capital of from 1 to 112 minus is the same for members 1 so a problem is to deter mined in BP to win orders that he wished be satisfied and so we have just divide by any and so we have to know that 0 so clearly there is a case where Indian maybe 0 whatever you do which is the case when you the same number of terms in Boston and then want to make 2 cancelations between a longterm in the 1st Simon 1 terms if they happen In this case the air economy and so on I have to distinguished to
46:39
consent was the first one being is case when such a scenario does not have so In assume that I am not In the present games that is the case would be easier given L is beautiful to me as a 7 1 in Queens sideways and 1 since interest in this case we have to function you finish in so I must say that you are not in this case then he the permit such as dangerous he stated alongside calling its upset of Sumatra then you may ensure the a small devices the mandate saying that not only the vanish the the hell is going from real life the cost of the times and 1 person represent the Bauer minus sold integer instead the words when we are not the forming in case we should be able to divide my young that that season shall be able to use to to solve the equation we where imprisoned in the at times be out equals high infant bottles chilled it seems nearly as so of course when we make such a decision would lose some growth for all of in 1 president Clinton which means that means something the realities on the question of the week which but he doesn't matter because he said the question of the question :colon low frequencies and accusing me afford to 2 rooms in roles all the managers of these questions if of course we work with swings in effect OK so see sources the equations and we wanted to study in other cases in which exceptions in cases of Cleveland in Austria and in 1 hand and cost and was 1 as we have seen in that case is the vanish identically whatever's value of his apartment and so it can solve the equation means that the last case we use is a street properties that it was mentioned reality preservation and reversible the because combining diseasefree properties when we checked that the right side was the equation In the it shall work image in this case the computer by 1 press you to banking 9 is removing weeds and be satisfied quality thank you she said so that the remaining cases the question can be solved was just as you equals 0 and we knew the substitute which it was even we haven't been able to solve in all Casey's diseases question and that we have seen before only that something he questioned whether we want to eliminate the contributions to EU H L which of the room degree of Watergate and that in doing that we are able to get by Indian quality I wear a time and exists resulted over an interval of time incidents mines and and being there was a level at which we stop this piece of process offered in English so this concludes said was Europe and this concludes might talk which is fortunate because my kind isn't real the move is part the world the other in cancelation this is the 1st of all we have heard that the was general cases "quotation mark those of some of the money on 1 of the terms the 1 which which really are important in the sense that I imagined look closely at the frequency of knowledge and so on this 1 the general so anointed in case you know what what we need to do it was the recipients and that what 1 would like to hear from the year when the is affected the question is an infinite and then use that term so that new cannot eliminate being in its attempt for which is easier other nations correspondent terms depending on the rejection so these terms and this is Eastern's it cannot grow the vessel is lost due grow because independents dressed injections and sources of terms and you need to eliminate In view of normal form using his image and character was and so why didn't we do use approach when he she because offers wooden known the same introduced before when you pass was initially along with wouldn't know when there is a meeting condition Treasury preserve that is the point that suppress forms wooden known to the New England To foster from the old and the new known and is not something that isn't a parties with you know to do that in an turn away if you included you say Here's designed them weight of the doings at step then I'm pretty confident that we could writers would prove Indian confirmed work and Soviettrained all these conditions off a permittee and and reversible of them are in some sort of progress that work in this cities and let them our industries will remember it yet the current military also questioned costs only good news for the wonders of the soul of a Europe of personal low priority areas in the 0 0 1 "quotation mark seasonal flu hit a couple of these investments about withdrawing from the area this always always on original story you need the flexibility to revising the analysis well Mosul this relation to Hollywood Holocaust also notes of so sees usefulness forming essentially from what result said usually name which was a blind to see general Frank transatlantic function satisfying some conditions so the fact that the so the fight between the princes and kept out which was but
54:14
returned yeah so the fact that sees United's offenses that idea in front of a derivative of the order does not matter at all improved offered diseases is going home you read what what what what is important is the fact that we're going to use this function as a function of side to deepen and some cap that is essentially a nontrivial dependence and this is what the rules you have to do to the put dainty service more divided estimated ceased to say that when we evaluate Cecil what true was aquatic as only attempted tourists that then moving into the campaign you may be arranged so that Aziz lower bounce this is a sign of campaigns of all year and does not as a matter of poetry you Yukon no federal kept up and get permit yeah and you can do anything with the intent of this bill will be killed take cognizance of the good oldfashioned offices in some so and it is a amazing is a basic with With amazing stocking boat as saying that the you wanted to they treat offered terms of lower degree in married so to get there gimmick resulted you have to be created all of these aquatic tunnels and narrative I don't know it and in that case and reason that position because he sees the forces yet but the point is that they don't apparently because it's at the level of the party and 1994 which you be essentially no reasons for the move it along with the like of which also revealed this side of the they don't disparity condition the disparity condition actually we needed only to you know to go to the increases the terms and the bad terms ones for which you you you you can make conceal your French trendier and so you need only to get rid of terms offer all degree in United you need to get rid of the pubic them you know unit needed to get rid of the aquatic durable order Kostic ,comma also offers courses the problem you know what the idea except that it's not exactly the same framework will them the bill is the death knell parts of the world that is is what it is yet so you know you would get the picture it doesn't there originally published well I suppose we could but we didn't try to trace down with you really want to know is general think
00:00
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04:05
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09:35
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16:50
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22:23
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Arithmetic mean
Computer animation
Order (biology)
Charge carrier
Equation
Right angle
Energy level
Matrix (mathematics)
Physical system
Imaginary number
30:32
Logical constant
Musical ensemble
Elementary arithmetic
State of matter
Multiplication sign
1 (number)
Water vapor
Divisor (algebraic geometry)
Complete metric space
Solid geometry
Parameter (computer programming)
Food energy
Grothendieck topology
Independence (probability theory)
Explosion
Fraction (mathematics)
Derivation (linguistics)
Order (biology)
Mathematics
Conjugacy class
Square number
Hill differential equation
Relief
Position operator
Physical system
Chisquared distribution
Logical constant
Differential (mechanical device)
Term (mathematics)
Sequence
Functional (mathematics)
Metric tensor
Maxima and minima
Category of being
Lattice (order)
Order (biology)
Equation
Normal (geometry)
Right angle
Bounded variation
Resultant
Free group
Set (mathematics)
Connectivity (graph theory)
Modulform
Inequality (mathematics)
Discrete element method
Power (physics)
Number
Natural number
Helmholtz decomposition
Term (mathematics)
Operator (mathematics)
Reduction of order
Energy level
Normal (geometry)
Units of measurement
Addition
Multiplication
Standard deviation
Conservation of energy
Prisoner's dilemma
Consistency
Expression
Projective plane
Ordinary differential equation
Operator (mathematics)
Mortality rate
Mathematical model
Estimator
Field extension
Database normalization
Summation
Computer animation
Commutator
Function (mathematics)
Diagonal
Matrix (mathematics)
46:38
Group action
Correspondence (mathematics)
Multiplication sign
Decision theory
1 (number)
Mereology
Weight
Independence (probability theory)
Derivation (linguistics)
Order (biology)
Sign (mathematics)
Manysorted logic
Spherical cap
Meeting/Interview
Position operator
Area
Injektivität
Normalform game
Logical constant
Process (computing)
Theory of relativity
Infinity
Functional (mathematics)
Bilinear form
Substitute good
Category of being
Lattice (order)
Order (biology)
Equation
Arithmetic progression
Resultant
Directed graph
Point (geometry)
Rule of inference
Frequency
Term (mathematics)
Energy level
Integer
Gamma function
Units of measurement
Condition number
Forcing (mathematics)
Lemma (mathematics)
Mathematical analysis
Operator (mathematics)
Independence (probability theory)
Incidence algebra
Field extension
Computer animation
Function (mathematics)
Game theory