Bubbling blow  up in critical parabolic problems
Formal Metadata
Title 
Bubbling blow  up in critical parabolic problems

Title of Series  
Part Number 
5

Number of Parts 
21

Author 

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 
2016

Language 
English

Content Metadata
Subject Area  
Abstract 
We construct solutions that blow up in the form of energy invariant, time dependent space scalings of steady states for some problems where such steady states exist.

00:00
Functional (mathematics)
Mass flow rate
Observational study
State of matter
Multiplication sign
Harmonic function
Characteristic polynomial
Similarity (geometry)
Infinity
Mereology
Power (physics)
Mechanism design
Different (Kate Ryan album)
Square number
Negative number
Modulform
Nichtlineares Gleichungssystem
Associative property
Initial value problem
Linear map
Condition number
Physical system
Area
Standard deviation
Trajectory
Mass flow rate
Weight
Physical law
Convolution
Voting
Diffusionsgleichung
Computer animation
Mathematical singularity
Nichtlineares Gleichungssystem
Local ring
Spacetime
Harmonic analysis
06:19
Building
Mass flow rate
State of matter
Multiplication sign
Parameter (computer programming)
Food energy
Heegaard splitting
Mathematics
Invariant (mathematics)
Manysorted logic
Insertion loss
Local ring
Physical system
Social class
Family
Area
Predictability
Process (computing)
Mass flow rate
Point (geometry)
Gradient
Parameter (computer programming)
Food energy
Time domain
Entire function
Category of being
Arithmetic mean
Number theory
Mathematical singularity
Nichtlineares Gleichungssystem
Bounded variation
Sinc function
Spacetime
Directed graph
Harmonic analysis
Point (geometry)
Classical physics
Computer programming
Functional (mathematics)
Existence
LAN party
Characteristic polynomial
Translation (relic)
Infinity
Entire function
Theory
Kritischer Exponent
Regular graph
Wellformed formula
Finite set
Profil (magazine)
Uniqueness quantification
Spacetime
Glattheit <Mathematik>
Nichtlineares Gleichungssystem
Set theory
Initial value problem
Condition number
Multiplication sign
Addition
Standard deviation
Scaling (geometry)
Chemical equation
Classical physics
Model theory
Physical law
State of matter
Algebraic structure
Continuous function
Transformation (genetics)
Existence
Numerical analysis
Fermat's Last Theorem
Computer animation
Social class
Object (grammar)
Hydraulic jump
Family
Local ring
17:00
State of matter
Multiplication sign
Parameter (computer programming)
Solid geometry
Sphere
Food energy
Area
Dirac equation
Square number
Stability theory
Physical system
Rhombus
Area
Theory of relativity
Correspondence (mathematics)
Point (geometry)
Complex (psychology)
Infinity
Mass
Food energy
Lattice (order)
Sequence
Flow separation
Category of being
Arithmetic mean
Steady state (chemistry)
Order (biology)
Nichtlineares Gleichungssystem
Right angle
Moving average
Conformal map
Resultant
Harmonic analysis
Point (geometry)
Rational number
Functional (mathematics)
Existence
Conformal map
Modulform
Infinity
Distance
Entire function
Axonometric projection
Mortality rate
Sequence
Hexagon
Pi
Differenz <Mathematik>
Degree (graph theory)
Complex number
Modulform
Energy level
Glattheit <Mathematik>
Nichtlineares Gleichungssystem
Maß <Mathematik>
Hydraulic jump
Rational function
Condition number
Multiplication sign
Dependent and independent variables
Multiplication
Scaling (geometry)
Projective plane
Physical law
Mortality rate
Density of states
Affine space
Numerical analysis
Similarity (geometry)
Computer animation
Function (mathematics)
Ranking
Hydraulic jump
Family
25:05
Group action
Metric system
State of matter
Multiplication sign
Mathematical singularity
Range (statistics)
Insertion loss
Parameter (computer programming)
Mereology
Food energy
Dirac equation
Fraction (mathematics)
Estimator
Manysorted logic
Physical law
Series (mathematics)
Descriptive statistics
Social class
Proof theory
Rotation
Point (geometry)
Infinity
Mass
Special unitary group
Food energy
Lattice (order)
Measurement
Sequence
Uniformer Raum
Mathematical singularity
Moving average
Resultant
Sinc function
Stability theory
Harmonic analysis
Point (geometry)
Functional (mathematics)
Modulform
Mathematical analysis
Entire function
Mortality rate
Sequence
Frequency
Crosscorrelation
Formal power series
Modulform
Spacetime
Nichtlineares Gleichungssystem
Set theory
Initial value problem
Condition number
Sine
Weight
Model theory
Projective plane
State of matter
Mathematical analysis
Mortality rate
Numerical analysis
Similarity (geometry)
Computer animation
Function (mathematics)
Social class
Family
33:49
Complex (psychology)
Group action
State of matter
Correspondence (mathematics)
Multiplication sign
1 (number)
Orthogonality
Parameter (computer programming)
Bound state
Special unitary group
Food energy
Perspective (visual)
Grothendieck topology
Cartesian coordinate system
Rotation
Different (Kate Ryan album)
Moving average
Hausdorff dimension
Social class
Stability theory
Rotation
Mass flow rate
Point (geometry)
Food energy
Flow separation
Symmetric matrix
Order (biology)
Natural number
Theorem
Manifold
Summierbarkeit
Right angle
Volume
Resultant
Stability theory
Spacetime
Point (geometry)
Observational study
Connectivity (graph theory)
Modulform
Maxima and minima
Barrelled space
Heat transfer
Rule of inference
Power (physics)
Element (mathematics)
Time domain
Frequency
Profil (magazine)
Finite set
Radius
Operator (mathematics)
Modulform
Energy level
Summierbarkeit
Absolute value
Maß <Mathematik>
Initial value problem
Set theory
Condition number
Supremum
Standard deviation
Scaling (geometry)
Forcing (mathematics)
Weight
Physical law
Mortality rate
Euler angles
Numerical analysis
Computer animation
Function (mathematics)
Network topology
Social class
Collision
Musical ensemble
Boundary value problem
Ranking
Matrix (mathematics)
42:39
Point (geometry)
Statistical hypothesis testing
State of matter
Multiplication sign
Direction (geometry)
Maxima and minima
Insertion loss
Food energy
Grothendieck topology
Frequency
Mathematics
MKS system of units
Crosscorrelation
Network topology
Lecture/Conference
Different (Kate Ryan album)
Profil (magazine)
Moving average
Modulform
Physical law
Nichtlineares Gleichungssystem
Analytic continuation
Category of being
Maß <Mathematik>
Initial value problem
Social class
Area
Rule of inference
Sine
Physical law
Model theory
Food energy
Continuous function
Cue sports
Arithmetic mean
Network topology
Calculation
Theorem
Orientation (vector space)
Manifold
Analytic continuation
48:29
Axiom of choice
Complex (psychology)
Group action
Length
Interior (topology)
Direction (geometry)
Multiplication sign
Uniform convergence
Parameter (computer programming)
Mereology
Food energy
Dimensional analysis
Mathematics
Manysorted logic
Meeting/Interview
Square number
Flag
Series (mathematics)
Position operator
Physical system
Stability theory
Area
Rotation
Constraint (mathematics)
Generating set of a group
Nominal number
Price index
Lattice (order)
Arithmetic mean
Order (biology)
Nichtlineares Gleichungssystem
Spacetime
Point (geometry)
Standard error
Functional (mathematics)
Connectivity (graph theory)
Division (mathematics)
Drop (liquid)
Mass
Frequency
Thermodynamisches System
Nichtlineares Gleichungssystem
Analytic continuation
Initial value problem
Condition number
Focus (optics)
Forcing (mathematics)
Model theory
Neighbourhood (graph theory)
Mathematical analysis
Content (media)
Numerical analysis
Family
Local ring
00:04
sometimes are you and where would like to thank you run for the introduction of invitations from the bank and the other nicest so it's great to be here is my 1st thank you in so they the topic of my talk he said he the film is essentially equations so long not really connected with way phenomenon it however where they will discuss this what so that of course asked what has been the peace study already has In other violence it will singularity formation ballot voters except appear the mechanics of the biggest cities efficient so airmen I will I will mention next act it's the Dolans yeah that haven't violence similar features and of course with a lot of things differences 1 respect each other but with a but with a common framework I would only speak about I would only have time to speed 1 of them so with a to to say that the more about 1 of them specific so but 1 of them was 1 of the examples actually over the battle phenomenon I would like to see where perhaps is easier displaying what happens he said it set sail the broadened suddenly mention actually is I have been study lot used them in a bit of weight standards leadership was saying 1 of them is that this is not the time and the reaction official equation with this especially by what was it which is the key to console export say we can consider for instance the problem of finding positive solutions the with on the conditions on the fight after some time can be that the that Clinton being fees so a 2nd problem which is the 1 I would really talk about is there come on in my throwing stole from being tossed all this is the special case is a special case of course the flow of harmonic maps saying that Lucian problem for commanding lapse it but that in the case of violence in the stole it takes a particularly seen before it which is these estimating equation when the nonlinear editing a cavernous these square and there some specificially sexually professional the floor he is the fact that the absolutely fuel 1 you already have values into school so we consider this problem in the area In abound in the lane although most of what I would mention is vital the space also addresses will embolden the maze of bustling let and after finally thinking I would consider sprawling with a given by the conditions and a corresponding initial conditions that Issel attempt Nolan but of of despite this the killer Siegel equations begin a silly questions in local question you want or assistance so this is simply the heat equation to stand the heat equation modified by adding the beneath it that depends on you on air on the sea and what is this being the sleaziness blossomed fear which by the conditions for me would be simply a convolution of fuel with the ferment of social discipline mentioned in which also right to cancel writers from neighbors form In the latest although when having called it 1 of them was a very important part on the but make the problems it somehow nice is the fact that they all have in common yet the function is actually this is loaded them just for the political power but for any powers wish formally In the same area dysfunctional defining the issues that have a function of being in fact stricken decreasing it unless we have extend states of the Swiss case states aren't as what precisely is just a computation former computation persist that the time of this guy it is levying lines and feel free to squares of snake their association official would have for the handling the flow lawful information actually ease the flow of implementing the inflow for the initial and fought with hearings is you have slammed into a school an and would have the same characteristics for it'll State loses to create singalong solutions some of those solutions on the use of non non stop aren't there was perhaps a little bit more complicated but still singular is 3rd the Canarsie in system because he question the Canarsie in local acquittal which can be read this form of mentioned and it does so that the of functionality is hereby wanted which is a little bit different now the medieval this guy along solutions amongst solutions negative but now the righthand side is given by the
06:20
although the sole area this is what you know this is 1 feature of the fact that they have the stature of this variation structure but in another 1 but that they share that is very special for this performance the following is the best sense of special family Austin status the Vatican being most states but the continuum of those states depending on scaling parameters the people always have special scheme insists under another scintillating on singular say 1 way meaning mean readers consider these which is suspicious the solution of this into space but in fact all solutions of the scandalridden us a translation skimming of this function they had their own given by this formula is None of the possible solutions mean of a man and a characteristic they have stunned the you'll have the same energy the same energy in the world before so he's sexually calls them along this case so we have energy mining and finally managing mining continues the states which of the ballot take splitting the people and the gold going to 0 say this function becomes singular of course away from those in this coastal 0 about exactly at the origin In this is 1 our land and restore powerless to feed the solution despite so that OK so what is the corresponding alleging that they would consider this is not the only 1 unlike the critical exponent equation in savings an object that seems to play a similar role is the following the 2nd warning about this function is 2nd a morning map it had money much of is when the conditions still staple for their control and this function indeed songs this is question him with stops along the way In we call it a day when quotation from another standard 1 Prohibition it again we have a saying by Paul translation Bayern's will still have a initially messages in this case the argument of the the energy is assess the energy meaning that initially of interview this time no alumnus in front of course it wasn't worth mentioning in each 1 but there is a next and that is an excellent balance but this speech saying you rotate the use of ICT solicit in if you rotated by her phone and information call for the menu you still get a solution of the equation and they'll have the same image was an Islamic 0 this of course does not grow up itself it has absolute 1 but what will he the gradient and called off you please actually going to feed it now what is the corresponding object in the Canarsie health systems in the Guinness legal system saying that because he'll equation in the too a :colon the well a national object to refer here use function on this function tests again the characteristics that you skated now this way you still hear solutions on this scale servicing and managing this fund managers general will beginning it added have an additional features that they all have mustered fight Everton OK so what it is that
10:20
all the leaders of the topic of the store or actually this is the issue that I would like to analyze for the 3 Rollins but in reality will refer only to lose a 1 it is the construction of solutions but had lower phenomenon exceed lower phenomenon as the approaches finally time within it on the wettest especially pattern of Milwaukee that these equations succeed or that only promised known but the demo that there is no arising in this way it is precisely might the it is precisely in the form of around to find a number of points maybe 1 or maybe more it will have the profile of lower me on the air near each of the law .period East since it's a scaling a simple together singular it assembles the scaling and some of the early singular skidding off status that of 1 of these in preserving insistence that is not surprising since the images say the energy often object like light here actually gets fabulous now because the skin doesn't change the energy so this is what is so special that I think is Brindisi dispose that said Fisher sometimes called Peter Gallagher from 1 OK so now I would like to refer to the handling of flow from 1 to interest Lynn I conceded they said in this program which from now on I will call In so I consider this to be the but would equation to song given anything be that the domain on entire tool in the tool but before May I saw that the whole space a considerable conditions of an initial conditions so of course most mediation on the Commission have to go into a store if if that's the case that property of having absolutely no 1 is in the ascendant on the floor OK so there is a lot of leadership around especially if they would like to make like a sort of a of mobile source a lot of people of work on these things longer will aid but have 1 month it wasn't alleles development model adjusting the settings the twodimensional setting let us say as they issued only control to name the inflow for the addition then Indiana for months between 2 more generally when a money you it added was introduced to wait to meet in the coming months the so this this the flows was introduced by basins on substance many years or 50 years a 1 concerning for instance the building of existence local existence and banal classical solutions this was the 1st thing makes him something of themselves story and then there for the case of compartment and then for the case of the motherland emboldened by Casey him 85 OK so and repeat what I said before I had a say in the media shouldn't think release in is it's actually strategically increasing along with the projected non the victory is not a stationary politically from the In a and we have decided to do so the Energy East decreasing now is increasing along the floor along the flow as long as the solution remains small but something that it has become good became known is not in Jenin and we don't expect a exists in the lower of his most solutions yes that's the beginning of the case not the Beagley but it may not be the case the saying that the solutions remains most of those times when the Bienvenue become known up much later however it is still there In eager for cities and important result of of the of the theory actually both the following that even ball the solution may be levied develop singularities singularities can more or less be understood yeah on it can be understood only in all In the case of a it's all there so that a solution can actually be continued International What if I become the continued anyway a company lesser the weeks solutions can be continuous image 1 week solution it's where a big energy has discontinued the energy standards is what the 1st jumped in him because is the well what happens when the definition of it was cemented a fact it does summed up only in defining number of points since spanked in spacetime sold only up only for finite number times and 40 should those times and define a number of points we can have real what it the animals points of Goldstein's dance the Indian adults nouns in the energy of the place In a safety this is the solid favor in 2 thousand people in it carefully he keeps to build up there but for the 2nd class of solutions where energy is decreasing even if it jobs a day the solution is unique so that means that the definition of school ease in the way it will definition end OK after that that was recently I don't remember exactly the reference book many recently
17:01
stolen store when it ruled that even the jumps it save the solution may not have the casing jumps say even if you have a quick solution with Johnson the energy that could even while waiting to be done but not too much the Socialist Unity it will administer the endowment's us I will tell you what you have to be delayed the Johnson the energy it out there quantized in fact In examples this is John cannot be less than 4 pies and I think vision of the sole duty sir still a solution that the energy and still when Wenger which is singular OK so as he mentioned the it In say EU itself does not rule out because no 1 has absolute 1 Monday gave him no such when we have a real what it so in fact if I if I call countered that the the 1st time at which regulates lost which is issued to bolster the US we know it we must have the degrading most infinity us the walls from it from below delivered to to the tank evidenced but I will mention although we making statements not completely precise I will make it like a I was stated publicly that this is a summary of results by several people who worked the war condition 80's and 90's starting would still win on several other officers and the ministry here and the salt so the question is how best the solution looks like when he grows up at the seldom quite a bit of it can be said the solution actually Maslow what he feared that if the best you could roll up in Osaka in the form do In the form that I mentioned before namely us skating so we are all behind a number of points all steady states steadystate stays they'd life which are not necessarily the you've got a role before the now so more precisely so the result is that many severely beat Wigan but still quick quick and strong assumptions if we approach covered the only sequence there and then can expect such sequences such knocked it out for the final number of boys Q 1 of those who gave the following calls you all along that sequence it resembles and each 1 function some of these levels they said this is the subtraction of the infinity of the bubble which makes sense the under the safe way this guy saying this is just 1 of the most stations a where the sexually bolsters 0 the speed and St. Paul Weiss Boeing ways of away from a waste from the points she wife he weighed in with approaching each of the and this alumni as 0 effective will leadoff important information that can be obtained about the relations between the scaling parameters on the mission distances of the points which is this fight this number here for a different from Jabal to defeated when does this mean that what happens is that if the points for instance QI I don't was separated 1 from each other state this is ultimately going to satisfy the from other wouldbe sees this goes to the meeting he was disposal 0 right it badly it communiques about points QIA orders or find a number of them coincide with have what this says is that if they coincide if they coincide for instance then disclosed affinity which means that the rates are not compatible 1 of the it's much smaller than the other so he was carrying around a point that means that you see just a single thing use alumni the genuine Jesse 1 so this is the name whether when the property salt there may be licensing mentioned so heavily muscled energy in in diamonds sold in celebrities and and they you ice by solutions of this equation when in women's store I was fine and energy with finding them which is natural and we're starting with a finer than as coffee lesson so the need we should see something with the also stand the fact it is that the EU is a function that will select to school but I could guaranteed after stability projections of functional from acting but from the complex numbers into complex numbers or there or with the composition and away from a splinter into safe I can regardless as of function from complex to competition from store but stalled a soul the system known this is all 5 Amy this must sound safer conformance and in stall and that makes the well they in fact that when he went see the West stole it becomes a function so loudly particularly eventually working Feeney DC feed is 1 of the polls in the school it's welldefined area solid fire that is known is that the single respondents in the complex numbers with a rational functions on a and it and the fact that this also holds so we will compute the chemical from a lack conformity school saving to square out to be a more notable for buying for buying a stake in the office 1 of the semidesert state office offices and this fact calls for and in international so in particular the energy is known to and we must In almost family must have energy for quite some
23:44
distance from the 4 by admission before it is so in particularly say in whether we want to have women to have adopted the ECU along piano rolls weekly to start with the nationwide 1 it on onto the energy saving defect with respect to the mill was the square of precisely a simple before that for the submission for the East um this year may be so simple to use simply integer multiples of 4 4 byes finds the enactment of the corresponding law .period tho this is the way to visualize quickly what the statement said it OK so of course there are many questions around it that this is a very interesting phenomena by the time all too was resourceful menu of and many others that they mention it was not really much known so much knowledge about existence for instance of such patterns for further properties of it in stopping in 2004 it but it is very interesting facts noted that deflates and which in the lineitem admitted the scale of these these lower rates of around each of the bubbles in In this the
25:06
composition is winning so
25:08
what'll be improved ease sales of sequences that means that some other SAA he proved that these lower rates have to leave this form so they they goal to seal faster than the males the Dubai where we have in fact they this to make you find societies in the bid saying with the Loganton winning it but when the says in the language of the statement amended projects for all of us actually of many for the simulator formation phenomena in what this says is that this singularity developed must necessarily be off by 2 vital means a singularity that cannot be captured you are with us obscene uniform this is more or less what what it needs and underlies late for that indeed in the coming months always this 1 so and I actually also see faster than the socialite in origin but it's not just in the storm in fact opened finds examples that show that this estimate is is it is in fact optimal approximately opting not examples for which of money forceful which you can get a blow operates as the main most people would have blast built Fellini with OK there so In many losses and now they have the function yielded an ankle 0 they the stomach coming up this summer :colon last laughter actually when you just anything that this approach from Atlanta to stall but if you take it from bullion Blackpool in the sustained entities so this is just this just comes from state that projection in its sole undisguised exactly energy given by 4 by the anyone who yeah undivided infinity of them of course as you weekly series citizen the assault led me there is no mention of what is in long concerning In concerning him assistance "quotation mark go up but it's a fact that only few examples Nos it and a and in fact the examples not only concern seemed to be lot points where the unified is like these but more than that example schools and very semantic the rotation and 1 actually more precisely placed in medical settings all of which this is being used as the new me more precise in 1 conurbations solution of the conundrum of fellow is a solution that has this form this is of course no spherical according the weight of the present effect saying store in it poignant store it and I assume that the sound must know this and will unviable December always eagerly faded and political were at the time of the requirements I'm there and the functions of a policeman call what is very nice is that it when the sun sets the combined with producers scattered which and this is going by would equation East is actually very simple this meeting was to love blossomed it mollified by this guy not in which is the sort by the way income tightening and with the knowledge of what but it was something that can be observed is that the CIA has has the following state the only model known find them as you would use this stage is given by the case since I always by dysfunction this explicit solutions off station a solution of the question after a William overweight and if we related that movies the same we obtain exactly the using the English before that the standard about OK self concerning it really does in fact it had been set aside Sunday in the paper it can be in actually previously conjecture that in making the case that novel what feasible but there's no roll up in the in there In this industry family muffle attending a 191 a founded in readiness example we mean they want probationers class In fact as when they are able to find is a solution of the sky equation V which looks like this the state bold new skates this way by some smaller number land of the or equivalently for the actual religion of family wrote this solution is associated looks like the U 0 at attics 11 of the the when this land of peoples to the approaches can be done so what they do is they is very very nice arguments the they capture the in matters so they proved that there is no way using some special measures both medicine many sensitive to what demand conditions now so it is necessary to take them on a condition since at the range is more than 2 2 people said the phenomenon they take initial conditions seen Monday the among the values Savion vampirism .period and they also these phenomena well for the 1 consultation as solution this was proven many years later in 2009 it under the watch of a a following in much stronger estimate 4 the setting for this special solutions for this especially if you have money muffle English stolen 1 correlation that made themselves to me it must modernize the most at 1 half at the cell to be loaded of capital the ministry and this would be proved In 2009 actually the issued Monday because of hunting in 2000 the amended anywhere in the world or older was beautiful paper for my papers in which they describe a lot of phenomena around the 1 consultation up it they know what they're 1 condition taste it out when they discovered formally than the normal rate what Henderson mistaken import usually square than simply will not work know many Newfoundland with little more than 1 in the streets by the way when they discovered is the land of the East said recently services unjustly long there'll be minus the amount actually mollified with a look squarely in the denominator so the solemn and in Amendment Montana which of their East there is we give the statement of course it is a vigorous dismissal it don't the results that that is much more recent any traffic to some 15 it is not direct financial In a middle learning important they succeed 2 make a construction of a natural solutions 1 quotation solution that blows exactly with this race the for the construction is medics with not based on various he's actually machinery closer please specify the things special questions for analysis of what best for a on it and they found a very very very nice description of their solution would divide up and they went in will also established it had this many interesting part the it proved that this rate In the language in the formal
33:49
language of these authors say they say but they find they also generate freight so say the generic rate should be used with it team is a soul of financial aid had lost some of that but were not exactly what they this but for the solution they constructive it may take a small populations of initial conditions of the initial condition for that is that a solution then a basis in safe and I mean they say still go out with the same rate of course at this late in different times yeah this is in the end they want probationary antiSemitic class so and the some examples yeah not good for them from 1 the gospel of policy we know it now that I of course and national question now is to investigate what happens in the region in the normal situation on a situation where there among the conditions the case of mention the setting wasn't those spaces a so the question is question well I they have solutions that are in no way at the moment and raise a number of Semitic settings places Is it possible to have 1 elements selecting still was the composition of the bubbling for solutions although several bottles in different places and you have powers of bottles of leveled the sum it said that many questions on a and of course the question of study because it might perfecting indicates that the solution stable within the realism of the class that would you make preparations which you all the various middleclass perhaps stunning destroyed they want In a awareness of Justice Society is the following saying we we that if we take any finite number of points of Romania In fact I should say the following yeah exactly the same Felix K .period saliva then you can call initial conditions among many conditions Monday which is in the independent it is so that it real absolution with exactly those getting human .period exceeds no this is the this is essentially the result of the butterfly he's like for financially scaling or order or something and it is a scaling of the using of With plates that can be computed explicitly and they coincide with the 1 for many diet and vigorously found on the net and Juno and Digicel also kind the a result that supports their post city In a statement In this at least about me at 1 point in exactly 120 states yeah this is hardly connected with some work by fund kept inside it His In this together in heat flow where solutions will find a number of points were filed but added that he believes in the so holding them such as the fate all cases all the really quickly let me let me say call when you have history of of opponents who who have no idea where none of my desk nonetheless none on Monday that the cold no no the fact that you know he for the stable phenomenon immediately told us that when the bodies taken by parameters many thanks in topology so I actually roll the picture from a prominent perspective but many bands in the municipal political ascension to the law but here will you think is the right way way to put it is that he had we we put all the blame in initial conditions site all apology immediate savings in the initial Commission which I wouldn't say whether he would you know 1 of the movement of aviation it is actually the only country sold that we ate aware In fact it provided a grievance all possible 1 of our claims that was the pedals this study the effect that he said it aims to abate the medicines they debated by Vandenberg think and Williams but I learned from Peter from it that In a conjecture that Mladic and that if you destroyed this is that the list see whether than the solution may what it makes other than the 1 leading strife of the 2nd but state OK so long as they mentioned the energies of lawful these designs for it then we considered phenomenon just have a total operations that also at the summit site will consider special ones that corresponds simply cannot take this matter on the way the axis debt which means you writing encompass form simply multiplied the forceful components Britain and complex as a pompous number may all the way back to their solicitor I however what a statement when we aren't able to prove is the following a giveandtake .period singing on the from the standpoint that exceed the initial along that anything in that exceeds the initial on missions such that solution :colon afloat for those data it will stop out exactly those key points and the profile of those people and is given by it say I mean by a convergence of sealing the each 1 and uniform census and this 1 in front In a way out of the bobbling takes the form of simply a suitable rotation around the access it binds the corresponding skating so long it will now he corrected to where the lower parameters such as like this so we have in particular these energy for standards mainly from convergence by the way he said Bill protecting about in the composition at about that level it only mentions something very quickly when the bank Wallstreet features so if you will actually along the palace may signal for the for the flow down from before the issue of you go oil solution but what I want to feel the effect all prom this amount for instance the school just 2 0 uniformly east sometimes called the not make from it so it is not known in these holes Indiana in the final rule think well of course when barrels to hear this case is a money much it that he said they provide to the topic where it is proven that the FBI powers a form and the feeding and then it all the elements of the of the powerful except the 1st 1 must be either ecological and all conduits of column of the at the same time not will mostly effectiveness but still is that 1 would approve having sold anyway a result of financial aid often mention Bloomberg this the meaning the it within the 1 collision class on the hearing mentioned recently got waterway London Williams the sole heir it is up to it and actually mentioned the stymied the the stability to stabilize the moving more precise it's a little bit more precise it say when fought the single book the single what is stable in the sense if you but that initial data then said exactly the same phenomenon where of course these
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numbers fell 5 is capped by status in the community and the points you have slightly will leave this
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year and if you consider that lower .period at exactly the point that phenomenon is not stable which is I think no wonder I mean that the law .period the times may not coincides with but if he sees that the take place in exactly those key points you can change the the initial data in it equally mentioned K remains 1 month around the initial conditions it is OK so it did mention knowledge that they that we filed a request with Frank when he insisting that this also addressed in the in the form of papers by the London and quotient and and the French and in vigorous work by the people in which she's continuation after blowout by you make anything called rest bombing In I win say very quickly when the lease it is a state where happens is that the Commission of stoneware state test someplace official of the energy but there dams means say it change in the home model because I actually it does so that that means a change in the commodity open the Model class of the image of you yeah start of the war now as you'll it not not just a change of the attention model it is sold the question is on the all the type of continuations of the blowup that are kind of nice in the sense that they also need to send some of the topology of the for the and it pulping proposed a way to lease a buildup there is a continuation it with these features and in the end in the 1 in the 1 quotation case he proved that it is attending and solution can be "quotation mark deal with a profile very similar however it with 1 difference is small the 1 corporation Standard Bible what would you see after the time but after the lawabiding did you see the same thing but in diversity patient the conjugated you want him on area and that is the so I think that it the same so this is Eagle 1 like the other but around in 1 single in the opposite direction so a The title procedurally sees what is called she must money it is sold in
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the 1st modern cars in the energy in the future that is different from store fact is nice a way because the energy in fact contains continuously except accepted binding when he goes now will summon up from 11 the casing blank unique but if you leave the existing but do allow the Getty's fixable discontinued in the energy than solution what would prove is that this continuation is possible for the solutions would be in the solutions we be can be continued with exactly the same defiance it except that after that when the wall from a bold amortizing solution is defined tools the blast from the the and out just see these yeah it is solved concerning the construction the some saying that made greeted may be reasonable to think is that this bank of profiles that we'd be we may actually be quite generous said it said it may even be genetic I'm really saying on saying that in the way blowup takes place there why don't we say this is not the snowboarders have all reasonable but it said the question ECC possible took about those older than those induced by Uzi almost on that with its conjugate because that I will have money must dedicate quotations from with Haley so is it possible that amplifies they that and it does filed that indicate conurbation blast which also leads to some senior :colon equation it does sell . 4 tied it In the head calculation class this also 1 with and site in April that this is not possible in fact they proved that this was not possible for acquisition and that badly congestion at the schools for lower it it was a that said in his London revival of the loss of sovereignty these included actually there novelties in fine thanks a lot hours and this is another thing yeah it is about just the 1 correlation classes in the evening kind Tobin found them In the final bubbling to the idea exceeds a at least with some special frightened sites I mean abandonment a and all the lights and also possible this they have been found by the financially aid the worker edition at less than that is but they have nongenetically comes with different but of the so this was too short to be here anyway not just that me in 1 2nd let me let me say how the
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solution we find we find made the fact that have planned to to discuss it unfortunately it the meaning you're talking then was like for complexity no hate the solution this solution is Maine in the following way OK the solution is made us that model and actually this whole thing that I have written in the breeze pages was still a attempting to justify a how scanning parameter is chosen on it the way chosen is connected following the initial conditions is made in the following way like the battle but blossomed remainders of this tremendous 2nd on it I would not say that means that when these masses to correct the error with this and that is to collect the to alumni in is faraway that I mean when you scabies to create than ever before and this just corrected far away but this case little beast yet this is a function of projected in the dungeons space of his fiancee the followup to you and if you start if a solution to the the question and this is a little like the this explicit but before from so and this guy has to have the following probity if it is fair he said that feeling in the collection would be components of the that the ladies some suspect when would the focal point and we need a presence currently went 2 0 and languages disease so to Kanopolis is studded with The Sealed whether that during the meeting these guys engineering you really that the dimension of this type in order to find it reasonable acquittal for lung and other recent publication for land that is there is still a question this is an equation is seasonal locally which isn't lookalike whittling these additional evaluation when this place sexually something that we cannot solve exactly but would also approximately at the very high precision it looks like we can build a new Soviet flag in a undefeated cesspool I mean this is not difficult to see the inner questionnaire seats in local equation but incestuous solution despite where case accepted proportionate to way they visions of so this is swept down on them and on Sunday was the 1st time I talked spokeswoman just look at what increments the "quotation mark question becomes the continuation of the Kosovo the use of the economy really has something some problems we all know just it the index construction the sexually explicit say let me put it this way in in the lead with just about all of which except have uncovered the appeal drop get new functioned very scared some them you have have to remember that information the issue of the work in each of the 2 of you know what you mean by anything I think I think that's a very good question all we have lost our sense that question No I understood the question yes I week Alaska the these the right consolation in knowing him another guests would love to go the truth is that which I think anything in fact a season that he was having we have asked work with them not the question ourselves not that you know the question is the regularized your phone say you put you in a new power plant sits in themselves and those of us Solis consult say secondary has been you analyze what is happening around them around lot and Senator conditions when related civil disease that celebrities solution will go up but the question the better solution it's the fact that at all softer blow up so is the solution we are constructing the he said would question the fact that myopia and my opinion is yes but Michael forced open and is still possible by place is not really what really have appeared as luck would no absolutely absolutely no women women will annulled the system will help the the choice that seems to delaying the imaging work continues on the other hand you know if you will the convergence is not so nice in the way of because to have the the babbling well with 1 rotation Abdul the role of tank but then that operational changes the changes direction so if you will from beginning 1 2 minus 1 sold any sort of discontinuing in and all that apologies I'm not sorry for the people of India and and I'm sorry this AC saying way the commodity the homotopy glasses beside but there but there but if you see what is happening immediately after immediately before saying there is no uniform convergence beneath us between by the blasts if city on the above the length of it's not something that most of you have this year In the late on stand and similar to what be the original and analysts promising to call a useful you you have to change the cost from 1 of you know I think most of the year honors himself so soldiers as to years lot history what missing in the some something should view also with a lot of things about me and you open communication in the area of knowledge nothing lost actually save energy and energy sort of goes on come things nicely smoking areas hit any of this city officials phenomenon so maybe enlightenment maybe maybe slightly different from the uses of the word of this illuminated inflation and constraints stemming from the the University of presidential primaries and all regional always it is possible that lies along the work you do have that opinion you don't have the funds to which 1 act mandated that is the same dimensions when you will when you construct the reverse marbling effect in fact that many of the worst batting greats that you can get confided in anyone is not this 1 if you will give you ball from positive :colon tools 0 you can construct a blowup solution but but you can get all the rights and that the began latest not Woodlock square but would look at the solace among the best use of the office who just won't guests let's also made a major chose mainly independently and 1 that would use mention of which used to be you know that you you he said the use force through the use of the human yes and of course on international the have been more than a year yeah I know so it may actually not of this is very instability in the office made you know approximately 2 books written in the Soviet reasonable ways of fighting generation wanted to know what Americans initially fell below and maybe this is a list of some the player making about stability has very honestly must answer to general whose content in home would you like to see more easily the example is based on the the work of which is theirs is going to come back the singular time no resigned to his qualifications to be prime and you and you still get the legendary nonvoting the fish you can take initial the generous quantities this is the point at the absolutely that what our construction something extremely local say these financial system had passed an isolated serial number generate false there and there are a lot of constraints if you put up slightly from each year of the extended his nomination of models using you use a solution men in a neighbor in the neighborhood of that special yet generalities not may be called "quotation mark knows what will happen if there are good and some the dinner will make his England squad escape .period but you include changing a normal the the trading near the absolutely and in fact this is in fact the bound condition is consistent without where virgins may have been the assumption is saying we we we we went heist the fact it is consistent with the best thing for your answers to some of the profits of the of 1 uses a revolt in years some analysis and 1 part of 1 2 you know how much of the the 2 of you want to know that cost me writing he added id say now I mean we have really standing out there I understand understand about will understand thereby was sort of isolated fact the became the pool is the number generosity of the of the about say if you analyze the leading ice equation for the family around depending Benedict with fresh commented that the where the Kennelly submitted Justice New motions so there's nothing like a taken from you so I assault on ice because and denying them and then all the type of shape and hooping it was clearly not the environment here yeah that is the 5th few and