MRS Factorisations and Applications
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00:00
Algebraische StrukturAlgebraisches ModellÄquivalenzklasseModifikation <Mathematik>Funktion <Mathematik>VariableKombinatorikDivergente ReiheNichtlineares GleichungssystemKonstanteGammafunktionPolynomRelation <Mathematik>Harmonische AnalyseSummierbarkeitFluss <Mathematik>TheoremMultifunktionZeitbereichFormale PotenzreiheKommutativgesetzKoeffizientFolge <Mathematik>MathematikOrdnung <Mathematik>PolynomDeskriptive StatistikModulformVariableKategorie <Mathematik>Derivation <Algebra>Ganze ZahlFinitismusGrenzschichtablösungAffiner RaumAnalytische MengeAusgleichsrechnungDifferentialDivergente ReiheEinfacher RingFunktionalImmersion <Topologie>Inverser LimesLeistung <Physik>LogarithmusMereologiePolygonRechenschieberResultanteNichtlineares GleichungssystemTeilbarkeitFormale PotenzreiheNichtlinearer OperatorStetig differenzierbare FunktionFormation <Mathematik>Modifikation <Mathematik>Kartesische KoordinatenKoeffizientGoogolExplosion <Stochastik>MeterJensen-MaßDifferenteObjekt <Kategorie>ZweiAnalysisHarmonische AnalyseHolomorphe FunktionRelativitätstheorieFunktion <Mathematik>MengenlehreProdukt <Mathematik>ZeitbereichIntegralDualitätstheorieIndexberechnungMaßerweiterungMonoidMultiplikationProjektive EbeneZeitrichtungFaktor <Algebra>SummierbarkeitGibbs-VerteilungMultiplikationsoperatorMechanismus-Design-TheorieComputeranimation
09:32
LogarithmusHarmonische AnalyseSummierbarkeitStochastische AbhängigkeitAlgebraisches ModellMorphismusModifikation <Mathematik>Algebraische StrukturZeitzoneGewicht <Ausgleichsrechnung>Hausdorff-DimensionInjektivitätTheoremFaktorisierungKommutativgesetzBasis <Mathematik>DualitätstheorieStammfunktionWurzel <Mathematik>Divergente ReihePolynomAlgebraische StrukturHarmonische AnalysePolynomMengenlehreProdukt <Mathematik>VektorraumMorphismusDivergente ReiheFakultät <Mathematik>FunktionalGrundraumGruppenoperationKoordinatenLogarithmusMultiple RegressionPaarvergleichSigma-AlgebraStellenringStützpunkt <Mathematik>TermWärmeausdehnungWärmeübergangWarteschlangeZentrische StreckungTeilbarkeitRegulärer GraphZeitrichtungBasis <Mathematik>Formation <Mathematik>Modifikation <Mathematik>SummierbarkeitAbstimmung <Frequenz>KoeffizientBimodulArithmetischer AusdruckAuflösung <Mathematik>EinsSingularität <Mathematik>ModelltheorieModulformAsymptoteMereologieMultiplikationTensorWinkelLinearisierungNichtlineares GleichungssystemGewicht <Ausgleichsrechnung>Schnitt <Mathematik>NichtunterscheidbarkeitDifferenteComputeranimation
19:04
PolynomGewicht <Ausgleichsrechnung>Divergente ReiheE-FunktionGruppenkeimIterationMorphismusTransformation <Mathematik>Aussage <Mathematik>Nichtlineares GleichungssystemDualitätstheorieDifferentialgleichungEvolutionsstrategieMathematikNumerische MathematikTransformation <Mathematik>ModelltheorieIterationAsymptotikModulformVariableAusdruck <Logik>MorphismusDifferentialDivergente ReiheEinfach zusammenhängender RaumEinfacher RingFunktionalKette <Mathematik>KoordinatenMereologiePaarvergleichPotenz <Mathematik>Sigma-AlgebraSubstitutionWärmeausdehnungZentrische StreckungNichtlineares GleichungssystemTeilbarkeitBasis <Mathematik>GammafunktionPunktKoeffizientDifferenzkernArithmetischer AusdruckZahlzeichenNichtunterscheidbarkeitKonditionszahlFunktionalgleichungKurveTopologieFunktion <Mathematik>Feasibility-StudieGeradeGruppenoperationStellenringTensorZeitzoneFormation <Mathematik>VollständigkeitSummierbarkeitDifferenteObjekt <Kategorie>Mechanismus-Design-TheorieMaximalfolgeComputeranimation
28:35
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38:07
PolynomRelation <Mathematik>KoeffizientSchranke <Mathematik>OvalModulformAlgebraische ZahlPhysikalisches SystemGroße VereinheitlichungVerschlingungVorzeichen <Mathematik>ÄquivalenzklasseBijektionGarbentheorieUrbild <Mathematik>Gewicht <Ausgleichsrechnung>TermAussage <Mathematik>VektorraumPolynomRelativitätstheorieFunktion <Mathematik>VektorraumAusdruck <Logik>Derivation <Algebra>ÄquivalenzklasseDivisionGarbentheorieGrenzwertberechnungGrundraumGruppenoperationIdeal <Mathematik>MereologiePhysikalisches SystemSigma-AlgebraThetafunktionÜbergangswahrscheinlichkeitNichtlineares GleichungssystemTeilbarkeitFamilie <Mathematik>Gewicht <Ausgleichsrechnung>Formation <Mathematik>SummierbarkeitQuotientNegative ZahlArithmetische FolgeKoeffizientInklusion <Mathematik>RichtungDifferenzkernDifferenteElement <Gruppentheorie>Rechter WinkelAlgebraische StrukturEigenwertproblemMengenlehreFrequenzKette <Mathematik>Lineare DarstellungGammafunktionPunktGibbs-VerteilungMultiplikationsoperatorSchlussregelMinkowski-Metrik
47:39
OvalÄquivalenzklasseBijektionGarbentheorieUrbild <Mathematik>Gewicht <Ausgleichsrechnung>TermPolynomHausdorff-DimensionInjektivitätGraphOrdnung <Mathematik>RelativitätstheorieÄquivalenzklasseAlgebraisches ModellBijektionEindeutigkeitGarbentheorieKontraktion <Mathematik>MomentenproblemPhysikalisches SystemStatistische HypotheseThetafunktionNichtlineares GleichungssystemGewicht <Ausgleichsrechnung>Formation <Mathematik>SummierbarkeitPunktRichtungArithmetischer AusdruckWeg <Topologie>Objekt <Kategorie>Element <Gruppentheorie>MultiplikationsoperatorMengenlehreDelisches ProblemMorphismusLineare DarstellungRechenschieberModifikation <Mathematik>KovarianzfunktionBesprechung/InterviewComputeranimation
Transkript: Englisch(automatisch erzeugt)
00:16
Thank you very much. So I will continue with MRS factorization already presented by Gerard and
00:26
but particularly I will give some application of this MRS factorization. This application concern which I try to explain in the recent report
00:51
published in Kufran's best mathematics. Now I would like to present it in life advice on what I write down. The plan of my talk is follow-up. It's the first part,
01:09
part one and two, I will give some political concern, a political mechanism and some in which I can derive some property about policy and to establish
01:29
a polynomial relation among politics. I mean the technology of so I mean we've got also some important analytical results
01:47
result of that. Before to throw out some consequence of on the sugar output with that I will give some competition of example about
02:08
this formula in particular the pre-equation. The pre-equation give a relation among something like the algorithms on analysis but at this time I try to
02:32
establish the four non-controversial settings of the other. I will finish on the description of the
02:48
image and the canon of the polymorphism. Okay I will explain more why it is a polynomial. First I ask all what is a polytheta? The polytheta is just the spatial values of the
03:08
zeta function on several variables is defined by this but it's a and this is conversion is a domain
03:27
where r here is some positive and where is this conversion? This sum can be considered as a limit
03:43
affinity of harmonic sum and the meter of that go to one of politicalism. Harmonic sum is considered as a payload coefficient of the politicalism over one minus f and the politicalism is defined by
04:07
well defined on the and now sorry the power of the zeta is expanded by the values of politicalism of one.
04:34
Here the multi indices are intercoms with s are quick than one and r is all positive
04:44
and all the values of a harmonic sum are actually here again the multi indices are integral. Okay in this case when the multi indices are integer we can see that
05:05
this can be considered as a sequence of some monoid generated by integers which can be considered as a projection with words over the alphabet y. Again it can be considered as
05:31
a projection with words ending with x1, x1 over the final alphabet x0 and s1.
05:43
Okay now we can we can see that the zeta is some maps over monoid it's not just but it will be mapped on the monoid with value in c and in the case of
06:06
with the can be encoded by words ending with x1 because this can be decoded by iterative and return and the iterative and return in this
06:26
iterative and return you can observe the order of the words and the order of the activity every person. There are iterative integrals of a long after x 0, z 0, z and
06:42
with respect to the different form of the other row and of the other one. So in this we can already see the role of x and y it leads to some consider the window of
07:04
our x and the words over y. x will take the order x 1, x 0 and y 1, x 2, etc.
07:22
Okay and here the calligraphic x in red in the slide is in red will be the x or y. And we will consider of course polynomial and formal power series of x with coefficient
07:41
on some positive thing containing q. And we will consider also the b and gabra concatenation and co-product of the shuffle of the b and gabra over alpha y.
08:05
We keep it as a concatenation and the dual row of stuff okay. She had already gave us a definition of the shuffle and what is shuffle product of the stuff. So I don't need to give one more again.
08:26
Okay in the follows I will consider the ring often consider the ring is some differential ring of holomorphic function as a simply connected domain they keep it the difference
08:43
differentiation partial can be extent of a formal power series of x with coefficient on the holomorphic function by derivation step by step, coefficient by coefficient.
09:07
Now completing the definition of a polylogarism I put polylogarism x arrow of k r is redirected with the path 1 to z associated to the word x arrow of k
09:27
it's just a logarithm power k over factorial k and by this one the maps now become the morphism of angewa from shuffle angewa to angle of polylogarism.
09:49
It is a morphism of angewa and it is injective. So this angewa polylogarism I admit the polylogarism that exists by leading to both i and i are the basis.
10:11
Now if modified we mean modified the polylogarism by taking the polylogarism over one minus z this function is expanded as Taylor expansion and the coefficient of
10:28
is nothing else. And this part again is the morphism of angewa to the
10:40
stuff from angewa to the other part of the polylogarism. Here the morphism is injective so this angewa path admits the bl and exists by a little word for the agaric basis
11:03
for the ada-march model. There is an equivalent between modified polylogarism and their Taylor expansion. So the multiple asymptote from stuff from angewa to the agaric of
11:26
aphorism is injective and now aphorism and exists by little word for the ada-march basis of the agaric of aphorism. I go second is three ones
11:46
the zeta now is really the polymorphism from the stuff from the stuff from the agaric
12:05
of aphorism to the agaric of polyzeta. So the polymorphism zeta for short I would say polyzeta, polymorphism zeta. Kiyakaki have already
12:22
a reason why we adopt the name zeta or polyzeta. Now we have second reason that is polymorphism zeta. Okay this we just need them to have their value after the
12:46
agaric zeta vector. This function is partially defined so we can
13:02
extend it as a character. Now we preside also for the
13:20
the value of polyzeta after the action but here we take the values of oh because the finite part of the singular expansion of logarithm one minus z in this
13:41
comparison scale is zero the same for the asymptotic expansion on this comparison scale give the whole as a constant term those again have
14:04
we have a definition of the z-module generated by polyzeta at weight k we can also introduce the expressed q vector space of polyzeta of longer k or of weight k
14:28
and we can see that zk is q tensor over z of ak and they have a conjecture of that
14:40
the demotion of ak satisfies this equation equation it need to it leads leads to problem the problem to know if this map this row is adjective of that is a cut so let us see now
15:11
to study this to conjecture i now to go to recall the abelite frame by considering the
15:26
juggernaut series on the co-catenation suffer behind this juggernaut series some of the all of the world of the view by the unity resolution of unity is also is a sum of all
15:49
worlds as to the view people view pw view is the Poincare because with linear worlds after overlapping and s nuclear view is your basis
16:02
these two your uh basis are multiplicative so we can fertilize and we are linear worlds so-called or we can recall by and s fertilization it's the same way for the co-catenation stuff the juggernaut series dy
16:27
is some over the view of all works on y star is a sigma n sir some of all works over all works after x y star sigma l pi is
16:51
sigma pw view tensor pi duplicate here again pi one is
17:08
the the pl form basis of the and we obtain here the modify the stuffer modify of mfs factorization
17:30
now use we use the two juggernaut series to form at first the jettison series of polygraphism this is just the image part
17:45
and and i left the identity of the juggernaut series the x and the we've got the local different series of harmonic sum as an image of
18:02
ash bullet concern identity ui and using the factorial field of previous presented factorization we can separate it by at z and hash n is it y and the we can
18:22
take the definition that shuffle either the value of one of l regular here the factorization are conversion because all the coefficient only local coordination coordinator of this series are
18:44
police it up conversion there are no diversions there is in the local coordinator the same for the six shut the stuff one this is fertilizer yeah and again here the local coordinator
19:05
of this supply series are connection and the c3l satisfy the no differentials series this
19:24
okay and satisfied also the asymptotic condition at zero and with the change over reactant x over a point a over two pi
19:43
i and x one minus by b over two pi i is nothing as the equation caset three and the series that shuffle is nothing as the infant associated because now let us consider the third
20:09
and last for me the negative series that gamma where here the coefficient gamma w is
20:21
the one if the view is white work or not it's just the final part of the asymptotic expansion of the as people view on this now is
20:42
in the comparison scale and up to b and up to a and look at it up to b okay and this again is a contact gamma is a character so we just need to have the value you just need to have
21:05
a look at the basis here we take the basis sigma and so so gamma gamma that is there this series is a koopalai series and we can be fertilized by mfs
21:27
mfs and we do up here on the left of this koopalai series the factor exponential of gamma
21:40
y one and you die on the left by zeta stuffer zeta stuffer is this series okay the the coefficient of exponential the coefficient of the x one is zero but in this series the coefficient is gamma
22:09
the left coefficient for the need is the follow i will i predict the model that is a ordinary generate series of pi y1 upper n is the one variable
22:34
series with coefficient on and it's the trailer coefficient of it should be y1
22:47
so i can consider this no competition this ordinary general series is always and using the definition of p1 p y upper y it's nothing as a political x1 over k
23:15
over one minus z with is this expression so we get moon over zeta is this function
23:29
and using the newton general identity of equivalently this star kim star d y k is exponential of this exponential of
23:50
the wrong function is exponential this concern series give taking in this popular the finite part on the left and the right
24:14
number of the symbol we get here b one b y one is nothing as the function one over gamma
24:33
one push y one here you see that the coefficient of y one is gamma again is gamma but
24:44
for behind y1 is a model of a kind the coefficient of y1 is zero we will use this
25:02
local digital series later okay now the local digital series of iterative and all iterative associated to work with the view is nothing as the chain series of the differentials for
25:24
along the path that's the road to set and this series is good life this is also differential uh solution of the no complete differential equation now we take the
25:42
transformation option z map to one minus z this little chance of variable will map on by pullback on the differentials of omega 0 and 1 by g star is equal minus
26:01
open and one and we start opening up one equal minus so the change series associated to along the path g that's the whole is by definition is a local that is of this article
26:23
yeah using the change of variables is nothing is the substitution of the chance series along the path that so by the morphism sigma x o n minus x 1 and sigma x 1 equal minus
26:47
like so and now uh the chance series of this path is relating to the
27:00
look at this ring of a polyorganism by this formula it's the same form along the path g z 0 2 g z okay and use the asymptotic behavior of n at zero we can deduce that
27:22
when z 0 go to zero this chance series is equivalent to sigma and z exponential x 1 look at it at z 0 and we can deduce when z go zero go to zero those uh
27:50
formula linking uh local digit and series apoligaric at one minus z is equal sigma of l z that suffer this morphism is
28:09
evolutive so we can put again and to get uh this coordination now use factorization mfs
28:21
of the local digits in of we get the second identity so we can deduce the work we have here we have here as one of n z is equal x minus x 1 locally one minus z
28:44
and taking the tail of expansion we can also deduce the behavior at affinity finity of ash n is equal to constant n by one another type we get this
29:03
about them okay especially the limit of this political uh multiplied by some this is a comfort there of all
29:25
them in the sand the uh the limitation of and what you actually need of harmonics some ash is a normative jt series of activism multiplied by its
29:45
diagonal now now use in the the last equality we take the finite part and we get the each equation this equation make the relation
30:11
between the and the of okay use the factorization of mfs it is equivalent to this formula okay
30:27
here is that gamma here is that stuff in the second identity
30:43
uh use e prime y y the first i reached the equation use b y 1 in the b y 1 figure gamma but not so after that when we
31:03
uh we don't define the local coordinate of this equation we obtain a relation among what is it
31:31
the coefficient of y1 is l okay oh i i can remark that in this
31:48
asymptotic expansion we can say that uh data shuffled up the review is the coefficient of data shuffled it is a finite part of the secular expansion of an i in this scale the same way
32:09
data shuffled is a coefficient of the data shuffled it is the finite part of ash in this comparison scale and at the present i think this is an only case that we can justify
32:26
how to realize divergent police data simultaneously at x1 and y1 for the stuff and what is the only one case we can justify analytically and automatically
32:48
now let's us back to the differential equation that was just the first of the differential equation the galois differential equation is nothing as half of the group is a group of
33:05
c of where c is some least cities so we can clone solution of da by multiply on the left on the right of n by some exponential of these cities and so we can clone the
33:26
she can add by multiply on the right by the exponential of c and we have again the asymptotic expansion alpha the clone solution at one and then
33:43
they love creation and the other life is again is a sense of okay exactly
34:06
now if we introduce the dma is the group obtained by multiplying on the left of exponent c so c is a sum of these series on the coefficient a and the coefficient of
34:25
x 0 and each one on exponent c is equal to 0 okay in this case here again we obtain the equivalent on the clone of zeta gamma as a clone of zeta
34:44
shuffle by this formula which equation again and it is equivalent to this from we have already solved that the local coordinate of the clone stuffer that stuffer and clone of
35:11
that shuffle we are over notice polynomial on the coefficient with coefficient in a
35:21
when we identify the local coordinate we get correlation among polynomial relation with coefficient in a but these coefficient are these relation are free of constant gamma if gamma is not belong to the ring of our coefficient
35:47
let us see how to use this formula for example for the first equation this single equation okay if we identify the coefficient identify the coefficient
36:03
y1 of the k the produce we get the generalization of the gamma y1 of the k this is a close formula to give polynomial on polytheta coefficient polytheta single zeta values okay and
36:28
gamma the constant gamma is quite here it's not equal to 0 it's the same for the other formula gamma y1 of the formula is more complicated
36:47
but we can implement it and to obtain that expression by exactly coefficient by coefficient here again we can see they are polynomial on and gamma but when we use this same formula
37:14
this equation we make the polynomial but identify the local coordinate we get the polynomial relation among
37:25
polytheta okay these equations are obviously must equate since all the coordinates are operate and we can group up by weight to get this relation okay and i insist again
37:58
that the whole polynomial relation among polytheta are independent of constant gamma
38:07
is the same it's okay for the cloud to clone this equation now since the
38:21
zeta is when we can go put them on the left and after of the equality we get and we do appear here the polynomials of ql ql will generating inside kernel of zeta this polynomial in bright
38:51
homogeneous in weight each polynomial and x is by in the universe and we can take the ideal shape i think by ql
39:02
f y for the stuff one and f x for the structure we went here we can see the inclusion now we place the symbol equal by
39:25
we get here nothing else some refracting system on the local coordinates here we can see that for each and on little words zeta of sigma l
39:43
defined to the polynomial on all the zeta and x is pi okay and on the right of these refracting rule they are the irreducible polytheta because all these step
40:07
if i took it themselves they don't cannot be eligible so they are irreducible and we fought again wait by wait the set of irreducible
40:26
and we put their irritable by the human for all the of that period people as a irritable you can see in this formula that the four point of
40:44
i got a system of the i got part of what is it okay now we take the image um adverse image because now zeta we already see that zeta is subjective so we can take the
41:04
image of the section we get the refracting system over sigma l okay here and irritable is obtained by the ever adverse image of the section of sigma we can get again the chain
41:30
between and irreducible okay we okay the
41:41
sigma l referred to himself is this equivalent to say that the qn is qn right are several or not so let's explain our summary
42:01
summary like that the identification of local coordinate and give us the two family the first family is a irreducible zeta values okay this is obtained by the c chain and
42:27
the the adverse image by the section of zeta so that zeta restricted on q the actuation of q by
42:44
and irreducible to that they somehow this restriction is rejected and it gives also the set of the problem also qn in which for any n the qn is homogeneous in weight the weight
43:11
is nothing as the weight after the rhythm was l so we have to see that there is a equivalent
43:21
say that q is equal zero or that sigma n refers to sigma n of by division sigma n is irreducible in the case of qn is nothing as a whole your ql is a supernomial the little it's little depth is nothing as a sigma l sigma l
43:49
is a an element of it is not belong to l so it is
44:01
such that ql is equal sigma n plus epsilon n epsilon n l is some polynomial on
44:20
q and okay so we can say that i have passed it by sl for l profession can be decomposed by fx plus q and
44:41
this sounds like it's the right sound is a direct sum of wake up space of course so we have already seen that fx is decreasing in the canon of zeta and now if we take any
45:01
polynomial on k zeta not the three of those constant that no without those of that so q can be decomposed on q1 and by direction by fx q1 belong to
45:28
fx so we can see now the image of zeta is nothing as zeta is created by
45:41
and the canon of zeta is exactly the ideal fx by that we can that is a pattern can we put go with that that is kind of pattern because that is a gamma of zeta is obtained as a portion
46:13
of this pattern i get by the pattern in europe okay so that is pattern and now if we take the
46:28
uh any homogeneous polynomial no that will uh belong to caten of zeta homogeneous in weight
46:41
each polynomial c n is of different weight because we have this equation so c could not satisfy the eigenvector solution with coefficient in q
47:01
but for any s in every people s is homogeneous in weight it satisfies the previous scheme so we can say that uh zeta s is constant over q so i i think i
47:29
i finish i must stop my time is up okay thank you very much for your listening thank you mean for more interesting talk questions yes i have a
47:58
question yes if if you go through slide 23 yes
48:19
uh then you say that uh at the middle of point one you say that
48:30
the map going from the algebra generated by linden irreducible to z is uh is active yes can you explain a little more no that's a restriction of zeta because
48:48
zeta is subjective okay yes the the element l r are obtained as ima a verse image of that
49:04
irreducible of the section so the next section of zeta the the map zeta is the the polymorphism of zeta is defined the shapes are given there
49:25
i just between them there are some irreducible zeta i just take them the imager adverse imager by the section and the
49:41
so that on this lr is a reverse image offset irreducible to stop this rejection and the so you constructed a section yeah did you construct it formally or is it
50:02
what the reasonable intuition yeah the contradiction is like that okay from the relation among polytheta okay yes zeta is the morphism so i can
50:25
on the left only polytheta and after that i use that zeta is subjective yes i just affect the relation each relation and exists by this polynomial qn okay i just
50:44
forget everything to take the annexation by qn the section you uh are describing as a unique
51:05
this one is um uh it's not my covariance i take this one but from every suggestion you can always build the section sure fiction yeah i can find the section to just by this way
51:27
but if it is subjective it you you you need this section to be unique at the moment i don't need this hypothesis that it is unique i just take
51:44
after this step i don't suppose that it's unique it is a um it is a good track it is a good proposal to with many many things to check together of course
52:05
and with people who would like to because it is a easy to implement as i see and the if you consider the relations you have by identifying coordinates yes did you recover the relations up to order i i don't know
52:28
up to a certain order yes of course recover the relations that you have with double shuffle um yes of course and formally to prove uh prove that the
52:43
Chris equation the relation obtained by in identification of Chris equation implies the one certain relation and at the weight we have already
53:01
very why is that the old relation obtained by software satisfy the zagia conjecture the emotions of emotion conjecture and we can say that if all are
53:25
correct we obtain the set of i got highly independent okay i am not a specialist of the subject but the zagia paper in the zagia paper i don't remember which one which year but the the direct sum was formal
53:50
direct sum yeah the paper of zagia is this one in uh this paper in uh oh yes yes
54:15
but it was very descriptive in style so as he didn't say that it was formal i think it was
54:24
formal at the time because it is still conjectural yes i i don't know i don't ask yet because in this paper he seemed to say that is give this direction is some something is uh
54:52
abstract and formal direction why is that here is something is closely closely
55:06
constructed over an arithmetic constant i don't know what he mean that this some is direct but this sound is correct no it is direct because it is formal so
55:23
you take the slices ak and you put them in the direct sum in the zagia paper because why define ak maybe dominic i speak under the control of the minute mansion
55:41
who knows the subject much more than me yes so maybe we can uh because in two minutes it has to be stopped by uh natalia okay so maybe we can discuss this later yeah okay thank you thank you