On onepoint functions for shinhGordon model at finite temperature
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Title 
On onepoint functions for shinhGordon model at finite temperature

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Number of Parts 
12

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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. 
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Release Date 
2013

Language 
English

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Abstract 
Using the fermionic basis we conjecture formulae for the onepoint functions of the primary fields and their descendants for sinhGordon model. The conjecture is checked against known results: low and high temperature limits, classical limit.

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she the time and community 2 Hong Kong and so I would look at about 1 . functions in exchange models the during labor is different than it was when the Indians and that still want .period functions the words I will consider want functions from the student and that saw 1 .period functions that created important physical information so this is a very basic and so they the OK so it's not exactly so simple in the siege wooden case but solely for profit irrational for example come still see it isn't there so it's this procedure to construct said that it would have but submission is the procedure to construct cooperation project especially after the perturbations in the 1 that ends and that is that there's a compilation of short of shortdistance behavior accused of official functions is reduced to 1 . functions which created formation of infinite environments of all that is winter will explained in several papers surfaced off course in the paperback editions and Wallach's from 19 91 and that 1981 and so that several papers so that important but wrinkled paper but who can afford some of which from 1 part function in function so fine refuses saying good models and so that was a continuation of cooperation of cheerful Kenneth knowledge from the knowledge of so was a several papers from books lots of visual important for me here and that president for defendants was also the people who exist for all social problems it was with some so section foreignexchange warden colossus Schaeuble because the model is a model is a motivational so and that's why so little operated public expressions most simple what's sold more than friends so and when it inspects it is the simplest possible individual models so and there's so as to seek the onepoint functions so even if there is the opening up obligations are not so clear was the 1 function as a nice so the history and that so we were doing for a long time in June when we were both wanted to accrue during the correlation functions associated with started correlation functions for the latest model so and we wanted to put it in such a way that sold not to compute construction will endorse size but to define the feminists we should reach dependent parameters and future for these you can make a skating agreements so this is what we did and so there we developed for some good model our all procedure for obtaining this 1 .period functions functions and other guy kind of found them 4 there also descendants and so on but I'm refusals on the on scene that but then sold the procedure by which is explained in this papers by looking on the fatty foods mileage cosmological is based on socalled deflection donations so and that then I feel that if for example if you want the world to "quotation mark wouldn't change going there there is no reasonable latest model so and probably it's is it makes sense festival to check if our results owns I would agree with its roots in reflections relations said and so there is a new and then so it's a good kind of a delay it in reflection elections is you algebraic appropriate word thinks so they can be easily switched from from this side of Xinhua and sense of using that we can look at the currency of this problem for those of you could calculations but is that what we're fighting for change when models is my blood so I feel some formula a problem that might explain the situation and rationalizations that I can explain how we sold this affliction emissions and I give the conjecture for for construction of fun .period functions of descendants fields was then I chipped it I mean racial descendants but primary then I check then I explained how to construct 1 for a function for Prime refused and ship before Prime refuse and if I could stand in the way of so entered the main problem for of these fuels to finance the costs of this type had deflection that an election is not linear kind of clearly proved seeing for especially for this decision wouldn't years and sold in there but so assumptions and what is possible incentives for the responsible persons in the audience case and the Navesink that so that's all nice that down the technocratic and so Jim Watt told me that once of the knowledge came to and so explained here this about this period of elections the elections so as his explanation is that the visit and I I will cheat you so and then I immediately I wanted to go to the immediate I wanted to say Boston but I don't know how to translate here so and so I found on the knit translations into English and footage bottles among all for full and endurance and what you ensure suffrage is increasing but understand what I so but anyway signed with the data shows that the nurses because people wouldn't really got less with the fellow with the insistence that it has translated to a new skin denoted enough of refresher money can conclude that if that's what they wanted the situation a key source that is so because you synagogue Ward also agreed to sold look younger .period delays before discovering cost but it's convenient from Italy Sicily so and that so if we understand that the world is over radios are and there's no point here and
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automated somewhat delayed at any link exists in US and so let's consider the following sink so we take some but I mean if you into a final deal so and then we will give so when mobile or that of course although of course was expected to tiniest so and so I just don't see this as a ratio of 2 or 2 off this descendant kind of feel to the primary field still just for the release of new courses inspection see embedded the future of events and the fighter minus5 so this seeing as if I have not even number for example flights here this included under this reflection paper when is this "quotation mark so and this is when it will be for some reason enough for me so I had to do with the digital sports and it's often so actually this is very system isn't available so that even if the number of articles motions that are descendants created by standard also more and so the future of the middle picture they commute table 4 of offfield your local 1 interval so emotionally as soon as you all again in the global operate about so in as is to expectations it must be 0 because fuel for example you can expect creation 30 consume a something like that so I think this state's got a minimal minimal the owners as stated in the about that action that the vacuum vacuum expectation bonanza I don't status for this beautiful holds like this way so that committee is used as well as light so actually I am not an entirely new you all this operators but on the fact that are out there in the sole now counts more casing so list here I expections like new blast this kind of primary fuel intensity that this as it but the original selection so to be honest with you cannot question isn't whether Britain because this is the future is not a small net payers for there is little new Felicia is too small so much so that the European Union because this simple gestures like him so unusual but still there let's but I think tho currency winds this way just as a which and then that's still at stake the image of man and antediluvian ideas home if you wish for children with modified management of of the museum is secondary to the US this sentence so and the currency that this kind of dissent and then saw and that we want to say this thing is a variant on that this is the view that if elections this reflection typical for you the more so this is the hot because so how how the public problems saying that white people but if you right there but the nation's serious national sailed the seas unit because of the limitations of the negatives in the vicinity the but in front of the sewer and water could only sit in the middle of help so that there is in this paper I mentioned on the will phone it's experience over there so its proposed pointed to just To make an impression couples to put on this year's for all sufficient progress of something like this so and and let's listen decided it will fill and then there the rest of the invariant under this and so I will grant you here on it for example only able to resist amp amp amp because actually once again if I take into account this this descendants of the appeal of the necessary lessons so now 1 was seen is that we will assume that there is a rule how to sort of calls among the identification of the space of local operators for the council mortal for and fall for this day for 4th seed money but so we assume that there is a group of more weight to establish onetoone correspondence is so only when you are in the more dismal situation so this is just underway wetlands when as designation here is works so you just under white domination loses weight it is possible but here there are already filled with the politically or whatever that lessons about I will explain later how how I can ship so that such that would have that to have we can identify his descendants is usually 1 of the unidentified them his status in the new film out let's argue this this year wait to demolish from demolished France's operate from people new West as you go through is to the different questions West as you it's just wanted to know for example by the sentiment of samples of operator in a new between 2 states reissued his wedding negative 0 more so than extension so in that case so this was 1 of the fight and disputes like that and they can take a good use highs and get into book I'll pass news president of the Parliament and so that is the limitation measures so as usual world soandso the answer is convenient for me to work his fundraising pitches so this view into the Figeroa I will qualify for the finals in all the legs that includes Dexter that perhaps this is lecture so now because of course mobile global his statement is open application of this generated here so that the judges certain 1 plus 6 Q and so now I defined Minnesota generators so and so this is a this is spending dimensions and application of these guys is the same as application of all of us in this generates of In doing so the
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important thing is this this is integral water so that it covered in the conformal Fusarium reducing so there's little you to demolish occur so licenses the quantitative yesterday so I realized that was a presumption that Wallach most everything for him and the chiefs of the true to its report was proliferated within whether you so vividly that in this set of people motion so this is just is just coming out and that in themselves and also the enveloping algebra of universal so just 2 are just 1 of 3 and also the 2nd 1 is reasonably stable and that it is getting more complicated but so is the pleasure to it's a great fund the computer computer ES cell and that so that I and as we do we decided so I can't see I consider here onetoone parity and we decide from 404 for the descendants and we decided that we work in the quotient space so we want to fuck around firefight denies that Jemaah model with respect to action of this all of this but in so now they're let's take 2 ways in this place so what I want to do we have this would have this as a deflection that Cliff Fletcher signal wanderlust and we have signal to so this is for descendants fullsize and understand the physicist for the solid ascendancy has so now if I can relate solely traderelated restaurant hasn't descendants so I'll have some cool system is of a Croatian so for this recommendation and so were fighting blazes on the Arizona side I take just Island also I take I generated ways is right in its Africa all the action of the doing of all for you even generates interest because all Caspian so there somehow he furious off even so full of and then all of President dockside ICI II take only 1 of off dignity so far from because I don't want to know no need to change sides because of what insists the watch kind of and that as soon moved to West III which was something that its that and then so I want to find the methods which relates the installed just where the Belgian Prime Minister so and the Newfoundland also for example vulnerable to what was in Lionel's school yes and so there is this guy from horizon excited so far hopes that could receive this is for being is supported by the opposition from with if so much it's 1 by 1 as the number and so it is the so basically at all levels to what you have you have
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do you have to do to work toward toward directives but sources as light as as a so we withdraw protocols it's dissident form of water and sells and for example if you go to level 4 this where the truth is that I
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take a wonderful to square minds for and for example to get and and the methods becomes complicated modem it'll be harder and harder still In it should but we computed after leveled some 112 will follow permits already is so now what is what is from the point of view what is our the vector which potential value what is the meaning of functional on this on our own this caution space he has been wary of the venues vision do which depends on the bond don't be off course also what position that the input the independent daily this a bomb but I'm a few end up uploaded the what President said so that if I take this hasn't been descendants and combine them into interjected yes so as an assistant at the muscle to this aggression and the right across Europe and this and this and that and then being done by the end of the day at the same time my satisfy this victim Masardis decisive equations and unrelated legs that and in the implies that they must satisfy their when he patrolled years so I mean so if I shaved a you fire blight 1 were another and the shifts a isn't so this is a vector so there is that there is a Maddox which is given by this latest and that so various forms of administrative somewhere along the only a tool box office steep right here and here I thought it would comprises
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Maddox is so and and also so it must be it must do so because presence in additional
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relations which is soared Monday in what you wanted you you want to do so of course this is this is a problem that has so in the present study recently been multiplied by any periodic even functions this is that there is this will fix later but so the question this summer for example after this after this as the audit function so how to solve this problem so I I don't back and that show you that so petitioner here this is a
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scholar significance for the visit of the center's enduring minimal functions other this single "quotation mark you of course and he should try to do it so it is hot and the solution was unusual but this problem came from a very different that explains the gain from our looks me June with neighbor the financial is is a given by the following construction so quickly is that there is another way this is space Kansas quotient space so where is this created by too few animals so what is there on the creation apparatus yourself abundant ventilation Lee so and then there's guys are such that the factory effectively and so on this this and this is a functional you felt something like that is so eventually they under this was all this information and also to the total 108 billion which is also typical of the vision for the moment so they just interchange they have very carefully on what the speed so this is this is this is as good as opposed to the amendment so that would be more precise so what is the basis so I use here used here and went to the collaboration so let me take more team is composed of all of "quotation mark also on boys it if it impinges on so and then I that was the way this is given by this kind of that way this year and by this kind of products it at that will provide a statement is that I will explain so this is a structure which would update experimentalists along the ball was so I I will post to make it so I postulated that that if I applies a seperate as to why the wife private a few years so that the result will be a full successful there'll be some some sushi which takes care of the signatories to the subculture determine who told his mother so that the product of some special functions for every element here and for every element furious so as a special functions suggests some focus or forget about this increases results of liberalization lots of ways again this is the limit I don't have a function or on the sea views so and that is the source of the result of is is a political models but models in even most origin generators Visual history fusions we depend on them on this clung on a scanning dimensions and central challenge is that salt he even put in normal and all normal and open nominal has fusion measures like that yes the region's rich countries where you on the field when scanning dimension of course under my reflection signal to I'm wearing them as change that so so ended so why construction so this seemed satisfied this this is the 2nd 2nd 2nd deflection the coastal because want although although are some generators I have is this is this is satisfied and everything else everything else so it is this guy's satisfy as well just so of only exists changes signed what is this thing is to on all the light changes were lost mind for which means changing it not program of research and this tour has also changed which wanted nothing so this is satisfied that the same was of course for the entity but but in the end if I try to do this and that action this it's important to visit the confusions of date because some determinants of the hasn't the was is in with this can be decided from from the methods used by now and if we suppose that institutions like that and the right to impose this signal 1 afflictions it an immunity over the term of system of aggression and so you check at some of that will follow 6 page knelt down and little interest solutions just so you find solutions for and this is that's why so this is not a mathematical certainty so a problem what was the name of the National Academy of was so but anyway so there is a very special way says in a minimum when you reach a mission that kind of respect boss was of this relation so the point is so wide wide using over the term system operation that it this multiplicity of an important because so phase Swedish aid to whiners and then they will produce some multiplies and I have so this is the result of and ends and I II and III below from Minnesota generator so too has the president here so that will not be divisible by some huge huge multiplied anyway so the fact is that was again so that exists new formulated exactly
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so now if I take once again my functional integration responded to his regular expectation has and where do this expectation winners and I homebuying guy ever traded on all this that this through an effective and I combined into 1 of the nation's called f other than this have satisfies the following system benefit of minus the equal Jay Jason operate image which sees the changes I plus and a minus so dissatisfied that history might additionally complicated so complicated that it would kill problem don't doubt into soul it's about visitors this is why Is there so whether that essentially would have been city is so this right it in this way is if I want to compute might want .period functions on seat in the course of this ratio so fondly functional initiated the INS's blazes years so that there is a real and they must be just as I see it as soon the periodic function of you but for the moment I did not say anything about about them here so as they must depend on on his own this year on the so there I don't know if this is the conjecture housing comes like the the making of petition letters of this figure on the way solicit conjecture mission which is waste 1st of all of our knowledge of signboards and then in in some of some of the other ideas for example can compute it even if the computer is making notification letters for the components of the management of their souls you just think about it and newcomers a conference with the reason is that the projected was a conjecture so I will probably focused analytical :colon comparable with the police soul now that the I will explain how I construct now there exists this this is 1 way functions history so with so I stopped viz really is a function Gold Q here so this is a function from each holding similar dynamics but in all this amendment dynamical quantities or in other words everything about spectrum
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but as we've also is about as a vacuum but so vacuum next in this this is the most of what is was about space so is is a new kind of which contains all the information is among them and this function you do so as soon as this is in this way it was explained to us in the paper by a notion that knowledge about the emotional support program it can also refer looking on the onepoint functions and so is it fair it was satisfied with the following equation here and there so that the reader called quantum world can and so if you stop as equations risk editions that there is this asymptotic at the Boston sees it in the face of this way I'm not sure that it is collected here and say I'm sorry so problem have to define ourselves to do this and this is another I probably have to do it with the cookies anyway so go science and art iconic but still refusing to hear issue is not and that this is a must and this is a massive physical particle as this is related to the demise of the culprit goes to his golf course in the Western culture Coast where the famous formula and of his knowledge and so that there is a symbol of the it's always this hasn't got it and then would have to say something about this year also insisted he reminds 1 nite or what to buy a widow and we're in for assumes that there are no than this 1 for unique for it is reduced to stump for someone in your interview aggression but I will look at ways soul no let me introduce that leverage following the following functions should always introduced it minus itself policy that is that of this and and I take a linear operator so that less late state function of of all that and so that this is a new operator which contains 4 Shareef 1 2 3 and 4 so here's another proficient 1 plus into absolute and Shearer coefficients debating consists case they pursued only he can and that so many that they call so that it can handle the functions of the president the function with existing so then I take a function I think kind of Green functions so I think a fountain satisfied with this integration right up later separated to this 1 again and I had to get this delta function kind of Green functions or from the from the United falls for another argument it depends on to argue that his students at the
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time and then so what I want to say is that that all this vacuum expectation value over the brightest of descendants news as argument just by this fall so it when it is convenient for me to take the following following their 2 guys in their 40 year transforming as totaled 448 which will decide to do this but was wary of units and so actually is assigned to hear degrees and kind of emotional gives and important that is it is in dire functions in their function of state and end which means that when I when it lost to GTO and goes to infinity so I can just computers asymptotic white knight thinking they can boast that it had existed since it opened 15 years so the number of storage means that the asymptotic at infinity the asymptotic spent Infinity will also lost in this order policy he told final store PA minus 1 C and as important in their effort blasted the blood situated mostly in the sport 12 of those functions so as not that student immigrated to enter the integer but that image it encourages Kintyre just great fusions of it hasn't done so and that the main conjecture switches which we don't know about that if I Texas there operation descended into Michael permanent missions off this function of this various units holders In degenerative hip and so went to and from time to time this summer some at addition so Wednesday consent but essentially essentially the asymptotic so functions of water that defined a defined all all all this then went with functions so let me let me mention 1 funny scene here is that according to my opponent of what I explained when it begins so if I want to have descendants I'd have to have the same number of beta start here and done most of it will be the start and garments that and make the blastoff and download large but the constant but is it is this here so it's obvious on a number of so this formula the right hand side makes sense the number of legal status but status Black is equal to a number of Gomis stars like the flag of staff this is important because this is used to do that the Wall from defendants to Bill of Rights parameters maker late Adelaide I will construct a new concept also the 1 who function for much thought to the ball descended so what what can we check his descendants should look too much because what was not much is known about the have multiple functions and of not wanting conditions so as to when I was 2 0 0 the following procedures was explained in while at the connection so that you have you argues that you have have a long blocked all of this that is so you know you can do more out into the culprit causing of course is unwilling to coastal areas in defense of their
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mentioned as on the measures combination so that the existing which blocked themselves at the end of the reflection from the London so your basic and so it is a very good approximation if you do that you have a good approximation if you just as he was in a negative you know more than that in subdued is described by the situation yes and so this is this is a reflection amplitude and so if you if you are talking very interested in the ground state so this is 0 so we Texans equations and what it doesn't do it allows me to computer demand the years here in terms of all radio all this year and is sold Of course so this procedure implies that if I take if I take years so that if I take my money .period functions for example for the operator for the operator and minus 2 years in my nose to the indicating that it must be given by all the youth formula used for December suffering minor stall where he is is replaced by this function .period years what and interviewed by my function see that and this is this is this multiplier since so now so you this fantasy that is computer from my from my so edges the of I wanted to be good right formula more beautiful than they are so different from the figure is defined by this order soldiers defied from this difference equation but you can really do it those of integral equation as acidification can get Michigan reiterated on so that you can get injured company and so this is what my student is doing analysis and she so that so if for example the dimensions this quantity is like that was subject and I don't think about that and so I just of it and you have 6 digits and that and this is this is this explains this explains that my choice III said from the beginning that there is that it is not quite clear for the conventional model how the house that identifies as the field that will ambiguous and that defines a you from from most of them from going to the demise of models of this explains the ended contact him it's so I'm now looking more financing for visitors therefore this I don't know also sources explanation didn't end of the same type as as the but here but and that was the reflection of the
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equation but would like that seen so here for example is it I considered descendants yes I took the normal ordering me as a user this is easy and was about components of the arrangement and the weather I did not take the the tastiest so it but because if I would think that there is I of
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course would change the primary field but the fact that this
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trend will be there when it will prepare for changing the primary refused as well namely those so this is a formula should have companies this formula is is just taken from from our computation for saying model without much do changes so and so effective if I can see that said that all of this shift few yes it can be expressed in it as in terms of additional field to each division also is the 1st time ,comma stops afterlife here's what now is it that a number of greatest task is bigger than the number 0 4 0 4 2 0 4 false also called on of alike have additional sink here and that additional here and what does it mean so this plusminus news that I so there's a lot in this and that means that for every amendment and that I had this to attempt to every element of this model in the American asking so what happens is that becomes negative and if becomes negative with the Council and the nation and so harmonization of going under like that for exactly as and so they act canonical businesses business function teenagers 1 oversight of something which occurred before year's end so I heard there is little functional Sr both they lasting increases have to explain here as a functions to a city or for any is given by some walked off government functions and this is of course a ratio should and a share of the work of the what much of 1 .period functions in the infield volumes about it so here or it's usually just wanted by France in some sense but so is this was this was involved this was a result of some almost computations and we will continue to quit said so now now I where the same formula guy of course claim the same formula when the same formula could can express the descendant of Spanish shifted few y y and shifted to 1 through the same function that should this procedure will be used to this hair and acquire some consistency in because of them the same thing here I can company a computer users functions shares should also mines in the U.S. and the result must win said so urges a course isolated stroke on 1 the equations of the same we have stressed marriageable who will because of that has sold this equation can be proved so loud let was that shit for Primary Fuels we are much more will my shit because more is an old so that several possibilities which is so let's see so this is not to say a few 44 for the field for the simplest shift would have this kind of formula because this is this is this includes what is when I applied it is 1 bit staff data Peter wants have Gama 1 12th of this is this is this is the here Saunders is due embraces formula and so when the divorce due to infinity so this man unwanted fetuses the ghost you know that this is this is just isn't just a ratio of the slogan of the militia of 1 functions so so now let's consider the following this is a fully functioning as let's normalize wages and future this is as was said this morning there is already a pure periodic function of the but because of all the money to digest all this reflection violations of all that they can create so for this saying that there are several results a formula which were followed by medical and most of them is some of the some by some air procedure engines which will consider strange because so they started as they did during the minutes and as a worked in this in this in this
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general and use usual for fructose which usually looks looks crazy because basically you have to do to make some some couple assault but they they will say that the employee introduced couple another big away so they have some prescription account how took unless there is infrared infrared that got assuming additional defends himself because you have to take the firefighters on the diagonal from and that there will course have bolstered as those of the guide diverge so when they get their license and so they arrived at the following formula so that the most serious like that so Michigan companies don't like them and the soul of this measure is like that and so this is because the cell functions some girls 5 years and some functions here which you can come from the from mold for CDROM primary fuel for fire this and then and then would you just shifted integration and manage the result is the same way I mean from while allowing the bill to internal 3 intervals until now and the end of this I don't know that the country proven that there was still no conscience the 1st comes as I set out my function policy that all negotiations this is 1 of the same is new and by some by some senior integral equation is so that you can share that with view victims just coincided this season with the determinations of this so this is what put check here so
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classical case so fine would graduate medical computing is functionally denied that and that so In this samples of this Bahia is is believed it is some will find that I will talk to people from forthcoming it the itself that Alpha might be here so as usual so as far as you do in New Year's and considered it immediately Eagles whose you know and then so this is this guy he is is this functional additional is sitting on the classical solution mission on this kind of classical solutions division so what about the conditions of the publication of "quotation mark that it lost 2 0 there there and that is a singularity like that as the origin so that you have to evaluate the action on such solutions and sold within the EU to inspection would be square news or minus special described is wanted function in the in the said classical approximation of connection request of you like and you have to the letters in Italy seoul carnival ride to work his way formula which is which is the initial step will gather from knowledge from published so if you think about this as and when you can get on with his life take something so right so the formula is this summer festivals this summer unless here so this is this West will and actually wouldn't give solicitors of this in advantage in view of what it continues and that there is this nice function here right this integral so if you wish dialog that is so it's always like that of deleterious here so this is a function depends on behalf of of what he saw as an examination of the fight examinations so I removed this year and the ratio of my failure issue the final is the image of defined quantity like that then I think my function and then there was the migration now that there was a shift in the shift contains 1 oneliners Biscoe where my mind is these to at all what want Lusby the isn't been now is a call to assume uses classical case so that's why this is this is 1 so is this the for she's but now there are only visited told them .period sites surrounded thereby there where Weiss coincide so I you have this kind of operation from this equation you cancel so do 1st factories which is nice himself on the floor and you introduce such a function as of this requirement that the wife on the answer coincides with the release of the movie out of the results is a full as this and this and this is the kind of your current hot on the heels of the original so it would somewhere so that you know this visit will hear the problem here so there was no longer condition some of the provisions editors of asymptotic so what exists in the form of resistance is the failure to act as a confusing atbats and sold and about as soon this is of course so you still want to by trading day can look at so and so on but let's let's saluting this stupid with an eye to singular integral equation is slow and listened to it and wants interview with the Americans and the future of the happened but what is it what the final here is that it will I have to do this exact group called to answer yes and for example if you think if you think about what a classical connection so this is it it is doomed by a censure by the terms of this up Larson blossoms this "quotation mark firefight classical .period Leslie what is that a simple is not a simple function which share the titleholder computers that that I have no idea how the computers attendance at its lower than it would appeal the vote was rushed back to her that will now move to the vote professional services in all so now about anything so there is an intrinsic observations about life and ocean fishing along the goal so this is this is this is a fine equation and the because of the for different Lucious as say and so would that mean for the finish essentially the independent media sources this proposal so I National said OK so let's consider this kind of equations is this is this is the latest reviewed accommodation is so so it is indeed a new immigration in the sense that that in the account you assume it's like accept it and it is a view that is as good as the integration in the sense that you can write you can begin to introduce new functions dependent on like "quotation mark variables and so on and the use of genetic general examination is given by through through to functions for this message when that the shipyard on the future of the questions that his sense that let's let's just consumer furnishings this satisfied this additional this additional conditions the content of his head of the water and solutions that And so that ends and that the situated is equal to buy you can have soldiers reluctant so and this wasn't a similar arrangements this makes sense because it's a misinterpreted something interesting about this distinguished so what I want to say Is that amount my function or become so I know if I take it later this equation this good discontinued equations and they're just currency this litigation taken the lead in the quest for the win so then I will obtain a full and careful in what the military so now let's assume that that for some reason so now I want to say that that so I'm looking for solutions which satisfied with this kind of equations history to each other the shift does doesn't so that it does the same thing but also insists multiplier from from the primary if you've got some kind of like so and fewer by the same sources you need the kind of Green functions for this for this year's my functions on the so why is it so I don't know problem problem and if you just have people will tell you that's the duty yesterday taking functional introduces the observes that consumers want what we have to of you get this money would be the miracle of complete and so as since April the 2 of you I'll say that that the way I read how you can all will sing engineers for example for 4th 1 .period function that is representation in terms of supply wearable CSO which was major force and what I wrote some time ago wasn't locale of connected the montages Gordon is the best possible obligation here so it is it is so if every gun rights and inserted a metal so it is also a golf course against the state from miners guy somehow all this for years and so this gives is using this as this 1 .period function Kansas you use are related to discredit like that and so do it is new and new to the interchange lose this is the kind of this kind of generalized smothered interval because in Maddox in the Ukraine but you have just London wants Congress normally as accusing simple might extend itself under 1 school at a hearing of the I 1 that was only 1 and another wonderment on us like a that they can compute exactly the same as so many all of nations once and you can look of course even when for the collection is so that's not the way to put off my results and look to explain starting from here that the solution for the this is the expression of the some functions you the report profit for the quarter the ruffles on the the move forward they said the formula in you follows from strand separation of variables I'm saying that I can computer thing give us a little bit of a list of the whole holding his periods for reasons of Kilkenny carries inherent to be equation for the regression of integration by the authorities but without any aggression authority candidacy but I Missouri donations commute isn't go the Bloomberg has this kind of program to sentences of the 4 I think you can find him before its fall so it is assumed that all from from from rival Singapore and the other was a report from the region require about who you compute the ball of the question the company has also weighed the of the conversation you you recently because of the outbreak of the continent I the thing because the rise of the American industry has the good will of the people of our state has put you in a while the investigation the media and also it's not going to be if there is a section of the section of the mine and is a truthful while also about 0 4 0 for some reason so that the analytical properties with respect to offer for sale Goldman are complicated and that he was not as simple as as a given by this reflection the question about soulful force for change what we want to to it good but then we will have the same great regional institution that has raised the work was for the 1st time my with 1 of the world's problems with the longlasting Americans you have to New York because of all the public about the what followed for example what but I can the group I know this is a decision that will talk local working you the you can actually so that the you know the other 2 modest figures for the purpose of the the the very very very very very appropriate the problem the multiplied by problems this month began the fact that it is not going to all legislation it was the original meaning of the tumultuous time the solution of the issue will be used this is my niece I you know you know you have your pocketbook after Caribbean him year of the in the things what about a lot of this is is this is a rather than the rather than the other users of other problem above this history there is also General local local polluted water in the city of 1 . 1 1 in the world will punch in the what will review the stink by unique was the theme of this year's legal rules about what what what what what what what wiretowire extracted the meeting of something that is anything here and you can smell so that you can use a lady who is being held in the he said he hoped that this time will not adhere to God I have the will to fight so it's enough for me vote for the bill II program that I don't need the will to use to you you have to do what few of authentically who award from 1 the I can go from somewhere if I take a lot of a blast killed maybe this because 1 more question and