On the dynamics of floating structures
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Formal Metadata
Title 
On the dynamics of floating structures

Title of Series  
Part Number 
21

Number of Parts 
23

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. 
DOI  
Publisher 
Institut des Hautes Études Scientifiques (IHÉS)

Release Date 
2016

Language 
English

Content Metadata
Subject Area  
Abstract 
The goal of this talk is to derive some equations describing the interaction of a floating solid structure and the surface of a perfect fluid. This is a double free boundary problem since in addition to the water waves problem (determining the free boundary of the fluid region), one has to find the evolution of the contact line between the solid and the surface of the water. The socalled floating body problem has been studied so far as a threedimensional problem. Our first goal is to reduce it to a twodimensional problem that takes the form of a coupled compressibleincompressible system. We will also show that the hydrodynamic forces acting on the solid can be partly put under the form of an added mass inertia matrix, which turns out to be affected by the dispersive terms of the equations.

00:00
Addition
Group action
Multiplication sign
Projective plane
Algebraic structure
Algebraic structure
Wave
Wave
Lecture/Conference
Universe (mathematics)
Aerodynamics
Game theory
Units of measurement
Physical system
01:10
Group action
Dynamical system
Time zone
Water vapor
Variable (mathematics)
Explosion
Summation
Fluid statics
Group representation
Velocity
Object (grammar)
Negative number
Continuous function
Bounded variation
Physical system
Constraint (mathematics)
Interior (topology)
Mass
Food energy
Flow separation
Position operator
Radical (chemistry)
Numeral (linguistics)
Randbedingung <Mathematik>
Spectrum (functional analysis)
Slide rule
Threedimensional space
John, Fritz
Constraint (mathematics)
Connectivity (graph theory)
Division (mathematics)
Mass
Infinity
Number
Wave
Frequency
Mixture model
Numerical analysis
Term (mathematics)
Energy level
Equation
Units of measurement
Focus (optics)
Surface
Prisoner's dilemma
Content (media)
Algebraic structure
Mathematical model
Line (geometry)
Set (mathematics)
Cartesian coordinate system
Greatest element
Rigid body
Vector potential
Field extension
Game theory
Family
Freezing
Greatest element
Interior (topology)
INTEGRAL
Multiplication sign
Direction (geometry)
Mathematical model
Icosahedron
Mereology
Derivation (linguistics)
Plane (geometry)
Positional notation
Position operator
Area
Linear regression
Functional (mathematics)
Bilinear form
Time domain
Entire function
Fluid
Hausdorff dimension
Equation
Condition number
Relief
Harmonic analysis
Geometry
Surface
Pressure
Divisor
Time domain
Analytic continuation
Subtraction
Linear map
Condition number
Axiom of choice
Validity (statistics)
Conservation of energy
Forcing (mathematics)
Projective plane
Estimator
Positional notation
Computer animation
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Gravitation
Object (grammar)
Conservation law
Boundary value problem
Pressure
Local ring
14:45
Euclidean vector
Group action
Greatest element
INTEGRAL
Multiplication sign
Time zone
Mathematical model
Propositional formula
Mereology
Variable (mathematics)
Summation
Fluid statics
Strategy game
Object (grammar)
Physical system
Area
Process (computing)
Spacetime
Interior (topology)
Mass
Variable (mathematics)
Functional (mathematics)
Position operator
Hausdorff dimension
Differential equation
Surface
Pressure
Threedimensional space
Free group
John, Fritz
Line (geometry)
Connectivity (graph theory)
Division (mathematics)
Barrelled space
Mass
Number
Time domain
Wave
Measurement
Numerical analysis
Network topology
Divergence
Equation
Free group
Analytic continuation
Field (mathematics)
Linear map
Condition number
Modal logic
Rule of inference
Forcing (mathematics)
Surface
Water vapor
Mathematical model
Set (mathematics)
Inclusion map
Summation
Computer animation
Vertical direction
Momentum
Boundary value problem
Conservation law
Pressure
Freezing
20:14
Greatest element
Spacetime
Constraint (mathematics)
Surface
Direction (geometry)
Moment (mathematics)
1 (number)
Propositional formula
Division (mathematics)
Inverse element
Insertion loss
Functional (mathematics)
Food energy
Scheduling (computing)
Wave
Category of being
Computer animation
Average
Right angle
Equation
Pressure
Subtraction
23:33
Pressure
Surface
Line (geometry)
Constraint (mathematics)
Connectivity (graph theory)
Multiplication sign
Algebraic structure
Division (mathematics)
Water vapor
Average
Food energy
Variable (mathematics)
Time domain
Thermodynamisches System
Equation
Free group
Subtraction
Area
Numerical digit
Constraint (mathematics)
Surface
Lemma (mathematics)
Interior (topology)
Propositional formula
Independence (probability theory)
Algebraic structure
Mortality rate
Twodimensional space
Permutation
Computer animation
Condition number
Object (grammar)
Pressure
Marginal distribution
26:38
Pressure
Greatest element
Group action
Connectivity (graph theory)
Multiplication sign
Algebraic structure
Mass
Ordinary differential equation
Distance
Hand fan
Open set
Rotation
Manysorted logic
Meeting/Interview
Velocity
Term (mathematics)
Operator (mathematics)
Negative number
Physical law
Aerodynamics
Equation
Analytic continuation
Position operator
Physical system
Covering space
Standard deviation
Process (computing)
Validity (statistics)
Interior (topology)
Mass
Functional (mathematics)
Bilinear form
Fluid
Velocity
Computer animation
Continuous function
Torque
Helmholtz decomposition
Equation
Pressure
Arithmetic progression
Matrix (mathematics)
Curve fitting
Freezing
Force
30:27
Pressure
Elementary arithmetic
Connectivity (graph theory)
Forcing (mathematics)
Mass
Vector potential
Wave
Inclusion map
Fluid
Summation
Mathematics
Computer animation
Helmholtz decomposition
Differential equation
Right angle
Condition number
32:08
Point (geometry)
Musical ensemble
Greatest element
Vacuum
INTEGRAL
Line (geometry)
Multiplication sign
Mass
Regular graph
Food energy
Event horizon
Number
Cumulant
Wave
Goodness of fit
Term (mathematics)
Average
Oval
Square number
Hausdorff dimension
Energy level
Physical law
Equation
Condition number
Area
Standard deviation
Focus (optics)
Generating set of a group
Moment (mathematics)
Mass
Mereology
Mortality rate
Twodimensional space
Price index
Evolute
Bilinear form
Functional (mathematics)
Fluid
Moment of inertia
Computer animation
Continuous function
Time evolution
Condition number
Boundary value problem
Matrix (mathematics)
Vacuum
36:19
Logical constant
Standard deviation
Group action
Mass flow rate
INTEGRAL
Multiplication sign
Kontraktion <Mathematik>
Mathematical model
Group representation
Duality (mathematics)
Tensor
Strategy game
Oval
Lattice (order)
Square number
Aerodynamics
Differential equation
Physical system
Constraint (mathematics)
Mass flow rate
Interior (topology)
Solid geometry
Term (mathematics)
Bilinear form
Flow separation
Numeral (linguistics)
Fluid statics
Approximation
Pressure
Vacuum
Constraint (mathematics)
Mathematical analysis
Heat transfer
Approximation
Reynolds number
Wave
Field extension
Term (mathematics)
Average
Turbulenztheorie
Equation
Mathematical analysis
Water vapor
Volume (thermodynamics)
Division (mathematics)
Approximation
Lagrange multiplier
Voting
Computer animation
Commutator
Strategy game
Object (grammar)
Pressure
40:47
Point (geometry)
Group action
Decision theory
Multiplication sign
Function (mathematics)
Mereology
Population density
Numerical analysis
Manysorted logic
Wellformed formula
Object (grammar)
Feasibility study
Energy level
Units of measurement
Physical system
Addition
Moment (mathematics)
Cartesian coordinate system
Bilinear form
Radical (chemistry)
Computer animation
Numerical analysis
Object (grammar)
Game theory
Pressure
Damping
Family
00:04
what time I'm I'm I'm I'm From the start of the moment and and important thank you and thank you for this addition here that I want to talk on the enemies of floating structures Pfizer granted me was among the show's title but the emission were stops and the other day that essentially what I will do is just to formulate the pollen for the pollen is deposited Richard by the project with them that can the center of a black man and that kind of cool which is the company working on wave energy so that the problem is that they want to make electricity by using the motion of some protein structure and which is created by the incoming waves especially are working on the mooring systems in this game assuming that the warning this structure and they want to know what will happen when we're there would have been ways and they can handle the and hold the structures for them Of course the key word here is that we would have some nonlinear effects and this is
01:11
what they wanted to understand so the prime and I couldn't could also do it for us for both in the kind of floating structure is that they want to find the motion on the way the solicitor classical with with foreign if I didn't have the structure 44 here the only new thing is that I have 1 here so what it means to me is that I have a rigid body and a part of which which she I recalled the which is region since you I have the value here is in contact with the water and these are part of the bottom of the bowl that I will say that the subprime interest functions attended so the produce for which is which an otherwise this instrumentation the same as in at the last close would just put it here to remember them on on the slide so here I have a deductible you or otherwise this is the same the surface of the water is always from advisory functions it out of here next X is a horizontal dimension and the total ban on the defeated the age this have the rest of the according 0 the bottom will be at minus injured and could conduct without any problem once a month and models they would do it for simplicity where from pistol we want to understand these numbers Friedman the report and said there were few memory because we have 1 for here which has come up with the weather problems and the 2nd 1 is that you have to know the genesis of this moderate forever which is what is the geometry of the witch regional politics seoul 400 stalker will use this notation for interior and exterior region all came from the date in mind my fight so sewer here if I think the projections on the way to reduce on the horizontal plane I find some twodimensional demand which I would go out of the like I'd like India and the compliments of this region on the X by the bursting of the I will be calling the custody which is in external demand so the restoration of any function defined horizontal line the restriction on the external demand will be denoted by the and the restoration of the industrial demand will be denoted by a factor of the and of equations for the question of course basic a question that we have seen that level of some of the words equations and you have 1st in the freedom and so this will be equations alterations 1 of the of the but to get here you press you gradually that is equal to the pressure forces the mine is 1 of a host was a constant custody of the free run and of being and a half year of the full due to gravity the Fed will be assumed to be compressible and also the and then I need some and so far as moderate conditions at the bottom of recognition is the 1 that the prison bananas for the velocity stunned and on the 1 time and that the so fast I have a storm of genetic commission and fast which relates the pen directly over the top to normal component of the validity of that idea is the same displays oversight on the day of July colleagues about and so this genetic conditions state that free but tickets of the surface of the food stays at the surface of the feared this is valid every when the other condition is is that making the most of all I have the pressure and a farce the pressure is L it would be a mistake pressure which will be assumed to be constant I don't have surfaced such offense 2 different estimate of so that the pressure become stands in the extent of media and here and here I would have exactly as in the last stroke I would have but none nonconsumptive some region of the demand and for me this region will be in the India region can to this but India rejected I don't know what is pressure this is a different wisdom must argue that the pressure here for me it's not a given function this is none of the public so my monetary conditions remain Will attention for the pressure is just the tip of indeed extend region the stuff especially if the original discussed and don't have any condition in the entire region for the press Of course you have to complement this With the questions In the region and coping commission at the Monterrey between the 2 regions so the entire region Of course what you have is that you have a constraints the constraint is that the is a sham the surface of the frame coincides with the bottom of the book so was my notation means that the interference that part of also the restriction of that that Linda region coincided with the privatization of the bottom of the focus of this is constraints and intermarriage a mail if you want to give you the coping conditions on the border of at sea which is part of the border between the interior and the exterior region but you need to introduce some some vitamins it's not side mirrors the style of survivors in the water where the company condition will be given on the discharge the discharge it is Q which is the radical and you have "quotation mark and horizontal the the so all the physical condition is that when you the shelves for the continuous functions and when you cross there you know this guy matters of wanting to come from the history of the entire region you assume that's the discharges concert which means that the a Q the extent of the exterior of the value of the shares equal to the integrity of the discharge from the and then you will also have condition .period innovation and the pressure so here for this talk I would assume that the bulk of the borders of my rigid body of radical Of course if I have articles I have I can generalize this commission and would just read the game which is not practical because because of radical award of course have a discontinuity In the surface
07:59
innovation in my case I don't have this constitutes an instrument to discontinue stake in this picture here have that's the extent of any of that I to the dynamiting of behind this continued to hear of the surface innovation and so the pressure of the India pressure here is the corner to the atmosphere on the set pressure which is atmospheric pressure but it has so have 3 continuity conditions it was taken can you the masthead that with the and this was just a really is the kind of content the question of all this and I'm not I'm going to show they said no why would have very few adjust to and the effects of acting on on the both of them so this is a brand which is not new 1 which was formulated by France during the 2 papers in 49 and 50 and see didn't never really has to be filed away so for him she had this rigid body here and the whole world would leads she simplified and the questions he said the I Have a Book and Jeff also this is also true here because I have encompassed indigenous people definitely and he assumed that he had some some of the other crewmembers neglected all the money narratives of the kinetic condition became this 1 and other Bentley question insofar as we can in this way so you have a security area with the question of a local regression for passenger services unit which and then he neglected the evaluation of the Witchazel she said OK the which is is constant respect it's just so as she removed 1 of the monetary problem after the library which is dominating the Bulgarian the Larry and his and then what to did in which the computer corrected that to use some of continued to come recognition of the company here and here which I'm not completely correct because he worked with these applicants and I never which are not very and and to the point and as we saw in good condition could be conditioned on the discharge which is normal quantity with few interpreted in terms of innercity problems and so he as shown and that she had sometime harmonic motion so he could replace the duties established some on that Ireland out of the town which transformed the parliament was because public and so you have been hundreds of papers and this has become a part and then how do you recover the motion of the of the Of the body I well it's just that you use Virginia family questioning the friend was due to the pressure in terms of the veracity of potential and those of us envision the the hydrostatic pressure 2 months left the menu will apply role in the form of all the regions but the soul and dances a conservative of the position of the center of my past is given by it's wait here and the pressure forces exerted by the fruit so it's all on on this monitoring of the Internet pressure the pressure here that this Benjamin and still have integration for the world on the other hand of institutional if you wanted just to do this for the recent oral master it's not enough OK so this is a very simplified by Parliament actually this is the only thing that that leaves that there is and which is used in my engineers now in software for instance when it isn't used old this obvious the armaments and of course you cannot use this software tool understands lonelier effect and that's kind of the money African mentioned you of all the mooring systems so what people also do is a mixture of the competition with a 3 0 winners of the many stocks question through at refunding whole area of sorting them without it's very complicated very heavily and cannot use this to stimulate frightens arrays of ways in way the convective and have several of them so this is the fridge incomes of numerical codes on the other hand you have a recent works on the motion of totally immersed in the city OK so there in the domain which is fixed so the men can be of the press while all me out in the Candace and in this case this edition is much simpler because you'll have your body which is hearing of as before the Denzel in the body so the pressure forces and that you have the denigration of the Fund for surface of course and this is compiled from this condition of the country Jovanovic component of the velocity of the ball around the city there which is that and the number of residents in the freezing cold numerous industry here OK to have some barebreasted the local poses for this and more recently when you are going which you want to get some more some find the information on the motion you have to use another mass effect which is something that will back to I think have been on their handling of the case and 1 of them this was immersed in enough of the press wants we have there is essentially it is that you can prove that at least part of the pressure false here you can put it on this form which is a negative number of times a 2nd derivative of the position of the center of my most all the and so you see that this time yeah can therefore puts lefthand side and instead of having a name and you don't know what you have embarassed in a gym so this is like the hightech 2nd at the mosque in so this is very important for silver bottoms of 1 American but then of course when you are working in the mine was the of this settlement effects depend strongly on the position of the objects this is quite a complicated and of course if you want to handle this but in the 1st of us case you expect to have some relief in Britain because of domain is moving and is free of revelry and the and mob violence in all its computers and that eventuality obliged to to soar at each time a threedimensional image integration in the in the domain for this is if if you are having mind and you rededication this is a new retrieve very expensive and also In this case you don't have a difficulty which is of course to entire exterior coping with it at the dynamics of this thing phenomenon public and I also just to say that this mass effect is very important in many different directions polymers and also especially fond of the representatives of the OK
14:47
so but actually what window
14:49
here and the outline of this talk is that I want to propose another approach because this is a process they said is if we could generalize it's surface scathing will have some very heavy and things will battle to conclude that it must affect the solve of every time threedimensional Connecticut which so I want to use a new set of variables and the 1st step would be to formulate the whatsoever question in a new set of variables which is the top and the bottom of the barrel witches but In the horizontal intelligence I rented a city which is just a pure divided by age so Q is a gage of the soul so that the industry that the mother a conditional on the child is very adept at this formulation because becomes stated that a continuity on the bike don't have any local then I would include the sorting and show how the cooking currency endit which is already here and this is where incidentally regained 1 dimension in the computation of this or of this coping with Syrian and the and the fear is that I will be sure that's the Indian pressure which is essentially the main and another of the party which governs the motion of the body I will push for reform of the plan as a compressible incompatible model and I'm sure that's the pressure and temperature can be seen as an that you can compute with twodimensional instead of a threedimensional then I will analyze this shoulder and it must effect which is the appearance of abuses the because the added Mass Effect is essentially says that when the freedom will mostly moves in the free in the of course has to accelerate its sense has accelerated the fridge which is around him In the case of a floating 1st show its said you don't know in which part of the freeze has accelerated to middle complicated and then I was sure that this strategy a tool to to see the temperature rises as lack about and the plate on the use more than making money show what the integration that the dimension and you can also use it comes with a small and can find some very an official chimerical OK so then he formulating question in this set of eyes Rosita ended up for the 1st time the questions at that substantive of affirmation of the kingdom etiquette questions so this is the reason the dating compatibility conditions of the the horizontal component of the resident W is erratic and once this is the violencefree you integrate from the bottom to the top and you find this aggression which is ,comma of mass aggression this is adopted by regions of the discharge people to this is exactly the doesn't use it will definitely assumptions is very robust OK so what we need to know the question on the eve of virtually renewed aggression on which is injured so if you want to do this the 1st thing that you are going to do that you 1st ,comma the pressure From the Vatican component of the area language so the Vatican component of the migration this integration and this is 1st show that he'd never used to be resurrected the bustle of the orders have been able to and you integrate this between the sum paid zinc and the stuff you know all that other stuff under the pressure the 0 Ireland's atmospheric pressure and so you find keen mind as the show fast thoughtlessly pressure minus yet exist is a good this in the office of this you expression for the for the pressure the 1st stamp here is the focal hydrostatic pressure that is a pressure due to the remedy forces and this Money pressure is called the normal hydrostatic pressure and just reading this simply and then you take the horrors of the government offered a question to the best you can do it before the longing that is equal to the role you bend this be here and you integrate from the bottom to the top he said this integration of the question the G 8 feedback and is what you Jiji about some she is vertical integration of the victims of the breast this which is due to the hypothetical public pressure and in the heart of the grant of Government House Sadiq component this was a refiner they shall I would call it age bias the number of titles at stake acceleration just but is all I have a set of aggression it said the of aggression system executive aggression have automation the question is is integral set of aggression which means that can express all this time he has function of zinc as attached to me and and so you have to prove that if I everybody waiver to reconstruct essentially the diversity hidden in the field so this is the case so you defined 1st in this space to be there set of additional investigations of you for this diversity future in that 2 of the main which divergence free and comfy and that hasn't homogeneous not anomaly components and at the book so proposition
20:16
is deferring once you take that that which is really 1 you cannot assume more on on the surface ,comma physician should you have a longer here at the contact so that a united but the work really is very low is it's going to have more than this so the 1st thing is that you take a as if you'd think he'd never artificial of its horizontal components and so they can prove that it works as as it tries because you see that you if you is that say this and this is such a new image while freshman it's 1 half of the bond and the average yield age because orchestrates has was as a traced and then of course you need the concession that things of you start with a victory which would be never reject want reconstructed the most efficient way to new ways of doing it that you take the right up for the city but on show which find wrestling this is precisely how many can afford demand an Israeli officer fashion the of the addiction among appeared that's the moment mentioned the patent is so just the 2nd among the better we know that it is essentially a rejection from and homogeneous "quotation mark risk of arrest bridges for the onehalf inch this space of H minus onehalf which showed that the alleged of function it from Arkansas the schedule of the United that you need the space so this is well defined in In this homogeneous sorry for for the ones and of course this mapping is delighted just to give regiment or cancel
21:53
this pulled this is of aggression is is closed and can work because it as an aggression on the the and and as OK so now the question is how what happens if I put fruiting bodies so the only difference with energy have made is that I have this return which is exactly as must stock and have the the pressure applied so fast he said that those push other surfaces given by the atmospheric pressure in the eastern region but on the intent agendas in the non fiction that so he said the rise of the yen loss of a lonely left and just left and is you have 2 different ranch correct because the governor can chemical is in directions no it's not that from which country can envision you come out of the French the company which in way but through but you can actually reduce the rights of property but you if you want so so so that it's on its front it's also have the it is not this I OK and soft calls on the way you are going to the combined this internal oppression by using the constraints and the constraints that on the day of gentle .period so that consideration should be want to the politician and the bottom of the book so therefore if you look at this the 1st aggression not that the remnants of a Dubai is minus the chief of the so you see that this pressure that I of buy associated to this Arkansas so you buy
23:35
digressions and this is intelligence is an incompatible ,comma for what should be India should insist is
23:44
that so we don't see any weather was foreign news of his area which is encompassing but then when you write to the question age about environment the search of the question is compressible misses have typical compressible earlier aggression he or cancel the independence of mind and the pollen is is compressible and then in the entire region the
24:12
plan becomes encompasses again that encompassing we'll go from constraint on the profit which is which is this is not the margins for its villages Newman this and that and the question is this for adjusted twodimensional aggression and so you can compute explicitly accident have find simple aggression for the internal pressure to justifying AFS which the acceleration of the specifies that would you look 10 which means its digits digits Quarles atop the guests without benefiting object you see that if you didn't have any floating object that could compute it is Quarles at that rate the king and the energy of this which which should be reported that evidence of this and is a so this is appointed by residents of all this you don't have any forthcoming this in this country and so the reason why you haven't pressure is because in the case of a floating structure the 2nd then derivative and doing the work the book plantation in different from this quantity so this creates intense pressure that you can still by a very simple twodimensional aggression entitlement and share ideas about the recognition under pressure pressure should be continuously put it so this gives me the question for the pressure and what you can prove that you can this literally he moved across because or having the concerns the question is not something have to check component of repentance is independent but it can remove interviewed justified pressure like this so if you have some solution Association Limited opinions that balances the bad news also to know this can't hear and if you have a solution of the aggression satisfying the of aggression with the stuff especially given the demand atmospheric pressure and they have joined by this simple energy policy and then for all time of course if it is satisfied initially for all time the dove I don't know that the politicians the surface of the water would correspond to the surface of the boat in the into because we don't need to have a structure it is automatically so it can forget about it in the and once again this is partial to find it getting it doesn't 102 by this to just have a twodimensional it to keep Parliament this instead of a threedimensional if you have been analyzed the apologize by feature
26:40
I get and what to do and what happens to them actually this is all about this said adequate Acapulco I am not able to show that this fall for question is will posed because of course is needed to Woodacre open forums in terms of speculative funds and you have some sort of hostages ditches the company of a permanent and in some cases a member to pull away was this time which means that for this equation what was that means that you have the small school cover here and there and I got functions that verification the India any exterior was of course and the public this is the kind of business from the that OK so now you have to couple this with the chemical and of the Son sold if you want to look at this you could appeal the progression the pressures might as evidence is developed you this and I want to assure that this summer and the mass effects within less effect is that the battle the false here is of some kind of a negative number applied to them secondary receiver of the position of the center of mass so From the continuity of the nominee validity in here he said that the kids attended the region is the normal validity of the of the city and anomalous Jeffersonian so the veracity of the city at the border is given by the veracity of the center of Mosul yeah axles and of massive this year accessibility and you need and this is the vector of algae and all the guys the younger novelists the subsystem that's what inconsistent is nothing to do and Vatican II can decompose the pressure into Freetown so this is a pressure aggression so 1 component of it will be the contribution for this then the conclusion for December the conclusion that you would have the city the went up when he was just fix so in this case the particulars of the Canadian Forces everything isn't the 1 who gets just formidable then he said that with only the 2nd time that heritage and if I want to see that it must affect what they need is a friend medieval an onagain so 1 might think they you of this so that it can hit this 1 and this 1 so this would be too so this will be the candidate to creates the engine Mass Effect and that time that it can also read out and end here so great mystical terms such as this is the 2nd for them in the form of the at the bottom of the of the and then I have to to cope this with Newton's new jobs low disintegration folder the velocity of sendoff question for its unrealistic so for summer there must have the weight and on the the false visited by the freeze on this offense which isn't out of the Benjamin victory and for the arrival city which have the talk which is a prize which is given the discretion a system that his insurance through the notion that 3 fisheries standard panels that opens insist on this but I want to insisted on the creation of the I it must affect so we just assume that only able was you would to simplify and thing that you have a 15 cents
29:58
and the I'm so let us see how their mass effect as they said they could be decomposed and a 2nd components was given by some the city question minus dividends AG had been too I was given by the my distance and the gardening false and they cannot be to banks and so how can you put this as something like the Getty operator applied to those 2 10 tendencies of them the veracity of the central so this is a very simple competition so you have to
30:29
define in the tape attention to this is inspired by the rejection of the Commission the way to do it so and have 3 components 3 different 3 the city put options on potential the region just by serving the jail inventory potential is so good that this Connecticut which applied to eject component of the monarch was durable this is them under the
30:56
conditions justice through various although the forces people by 2 N but you know all that and definition of the of the inventory prevention is the sum for orders for jet from 1 to 3 off minus dividends of any kind fee of 4 or 5 G Pender Victory in Jesus is the definition of the inventory problems and then disappear closer financial put it on the on the peak the most governors of etiquette debate before due fears of over 2 0 5 1 5 2 4 3 with unyielding questioned by to which stated that this is not about to end just base and that but to just rewrite it to produce the boat you on the right hand side you would think this and then you say that any new book of the same again at Sears and using the definition of the elementary put on shows his mind as evidence of any conflict with the best and then you don't like about once and find out if his minus and sojourn through mathematics stated that you what then is this quantity is gearing up for the women 3 Appleton shall ensure that this is a government faces positive
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and so Indiana you can rewrite aggression and on these forms of emperors of bulletin 3 standards you is equal to the rest of the false OK and June the height of the of the what a number of arrested you have seen by Macy's 6 months rates which is and all that if you want to listen how it happens you can look at the mission onedimensional 1 can make explicit competition from the original 1 intelligence adjustment of Alex minus expressed and didn't assets which come just concluded and it is a square alternating bouts of the function defined in the new intelligence or holding the final sedating functions if you need to remove its average and graduated find it and that's way in some sense determined the quantity of freedom have to accelerate its German data from Atlanta for Express of F over age divided by the date of 1 of its kind from France to its explicit and can really do things varies judges had no question it you need to understand the evolution of the search through the gates of the mission wonders July and so will for the case of of Of the status of everything in the the question What if I want to make it my city that we should to do sold got a kick out it for the twodimensional John cases that were adjusted for this 1 for simplicity so everything is included actually in this continent agree salt as you remember I said that I have surfaced and rational what events same should continues at this point and which meant that each day exterior of CIA pay to express my lessons is a good page indictment of the bike to explore my new band fronted this summer that contains the G H Press eggs adults or the same indeed intend about and then you say that's in the area cumulative Soviet aggression so vintage you were pressured by miners lyrics of aging bottles looking mostly questions can you don't influence energy of age Ontario is a function which is given in terms of the veracity of the center of mass at some level of geographic focus and this is not functions and so from this week over the question for acts not so as
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not to give up by this because we have contact languishing and it's important to commented because it's a it's safe enough the kinds of quitting for instance you could compare it to wield culminating with a vacuum on the recognition of violence came on the condition you have been somewhere folder in the Current integration especially by buying and their young in the Times Square where you want to send information about UFOs peak earlier question which is very soon enough to put this on so accurately In fact should the vacuum I know the Commission is a particular case which could correspond to say that the DirectorGeneral of Asian countries it'll from be the best vanishes into damage and then what happens in this case in this case and for a look at the bottom of the vacuum monetary conditions of things that is given by this so if I have a few mother Commissioner H. Izabel today also is when the shares this vanishes OK we have this and of all this while you experiment readiness to its ancient zigzagging but if you want to use advantages so you just have the index age OK and the exchange data on simplifies and you find that the equal to the wall and the contact so this means that you have the committee conditions for the dynamic of the bomb and this means that if you want to leave them to 2 2 2 visible Parliament then it will essentially have the from his and that will have the regularity of diversity novel this gunbattle integration lose when they met so it's much more singalong of employment is there too look get so this is a generation of this 1 of which is not a genomic Indiana became magic moments what and so it
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was said that you mentioned is workable vacuum in the in the transfer because aggression so a particular question all show what I question the same so let's not try to see if we can pay strategy for simplifying eventual your interest in ending this for obligations so how can you simply find among analysts said this summer fully creations and the Shinawatra aggression license several assumption that can prove the case was also without footing object can prevent rigorously the first one is that this mission had cancer and because it's in some sense in in the heart of all of the those issues think about it already the action as well as another ranch accused that would repay statistical average in in in Germany and then you say that this is just the 1st then which is the the square of the average market basic to do during the summer DB emission which is very robust the 2nd 1 to position integration which Grove and 2nd approximation that you mention that to neglect this not title it all he said there are going to 0 so if you want to and included specific representation is the question of the nite that you cannot understand how the Democrats come to have more competition more than that in the 7 migration them subject to summary super system and at the end and so the division at this you have the pressure of them here and of course if you use the pressure and they gave before the question for the impression that they did before it will no longer be allowed wanted to pick it Japan for this says system of aggression of course not 1 that the question for the depression may be the same approximation so in this damn Christopher acceleration you just make approach because we have now we're good and I wanted to Parliament ,comma exactly the same kind of analysis which include terms for this and for those who know what is there is a remote here is that you could be right this system as contestants from 1 which means that you could write it has a some migration was a appreciative them here and there With such writing come here which says that lots I'm sorry it's not eyes should be on the menu so under the boat so when age this is a failure to work with the body we are dictator region who have no constraints so this is a that is equal to but then when you saturates the contract when H is equal to the to of that's another vote then the pressure in the 0 and didn't like it so the right many mothers say this essentially was difficult equal to the Oval pitch unless I question if you want so you have this aggression rising traffic flow on the floor and husband survives and the day that you are saturated some constants of the call conducive to competition this form to be different because of you and you could do this also for the following questions what Our and then you could extend this to distrust among those may adding terms aggression more complicated times and I will do it but you can do this and then you can also call the percentage of the descriptive and saw notices but just saying that if you'd find himself migration that 1 competition than conservative formed to commuters in the final volume formulations on behalf of the consideration for the 1st year unconscious and its cultivation which is involved and that it shows you from whatever so you have 1st to the 2nd floor for them the Commission for the 1st of what you want but then computes the discretization of this was still in a consistent way as adjusted for to buy up to the United States should come this
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and if you do this as I did for the continuous case you can remove the constraints that age is equal to a about you on the on the on the on the boat it would propagate that much intensity so you have just to some of the questions on the confession of the men without handling the coping on and so this is attempt of numerical efficiencies the same as for summit from 1 and we dealt with a lot of chicken all of this thing goes very and very fast and just to show you that they're not denying it just
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made some competition joined in this case I have Vatican just radical time and indeed is that they put up I loaded my may object to move on the Vatican's Justin that you can completely this level of competition you he want so here and you see that you just and just brought the fore selfisolation and you see that I'm sitting in on this and I put this push up there and you see that this is the 1st facilitation and because of the special permission that it takes exactly the form of my objective here is is as surely as it down many American for 1 of the land saying artificially that this should be equal to the bottom and look at it as a constant it's just automatic people have chosen the discretization and indicates that ultimately we have you got that we wanted to this is to get a feasibility and so this is the same and when knowing eroded what is that support happens to Larry can't you see and then the the seizure and part of the thrill goes and create awareness right into what happens it's not the kind of which would between reference about it is reflected their about having goes on there and you see that in Iran's registered discharged so full of things muddying the destruction because of the disease that presidents of Q is equal to 0 so it is there's going to be a surprise 0 putting virus type managers continues this is wonderful but linkage then if it now this is a false motion tabled the new objectives falls with the conversion and and so in this case we came away an issue that in this case not the discharge under the kind on the boat is and is not considered Monet's you know you have to is to continue encourage them to instruct Commission and of course the way the most interesting cases due to have these putting engaged this case by data communities and I think it's going density in the air and from entering the city of Chavarria able to compute dozens debates where should have particularly of sorts of the indicative images drop mandatory bitterly I'm sorry Tracy goes down and would goal and to stabilize and it's inconvenient but because canceled for this 1 ahead in their share of the region's 1st and this is the end the disarray and in the end it is endemic competition and it is retained competition and if you compare to but this this this this show was full demolition what of Iqaluit from what he meant was full of familial money aggression and not in the days leading up to you could try 1 was but vortex and and found an Indian elections will me and the arrest 1 is the 1 that we will reconcile them out from the application and was mentioning for the resistance of the warning system is that the new center away and it would be because of the fall because of the the way and so on what so now we have receiving with electric initially counted several of them and see what happens and it's very easy in America the efficient and can use it for a application and of course what meant to do isn't always the mother and her 2 beautiful for a moment Book of the year in which at the end of the year .period do the work the knowledge and understanding of national output and what is I'm pretty more complicated units not out of the there is some concern over the of From this vegetarian voltage decency and I know I don't think any of it's true because you you have security you have about the effects on I don't think that you can critical to know you don't you don't really want to city however you would create to city if you have no way addition then anticipated because this is a decision which you have some consumption of foreign foreign foreign engineers and so I think it's OK for the removal of the domestic and use to most of the people vigorously you also have you may at the end of next sold are so for the moment so all conquered the basic and he also I can watch it in this Act which indicated that didn't mention question which is radicals before this have discontinues attacked coaches pressure then in this case it's III intuitive and enumerates in this case at this point will fly 106 here have done that for Moneyball principles in the schools OK but I printed this 1 because for this 1 I can numerical analysis 13 improvement for this 1 American it works Umaru carried an American managers working but I can see this summer and then yes and then I had become composed Washington and the and and also the next episode to create things here that it's raft then I wanted to To and for this wonderfully start moving at this location so I have to regions you madam the I understand that this is a the contact lens after his for this financial year Hollywood you go handinhand compare the pollen in the window of the game for the formula yes I have the probably guest the church which room