Contextual image classification: Difference between revisions

Revision as of 10:40, 23 October 2013

In algebraic geometry, the Witten conjecture is a conjecture about intersection numbers of stable classes on the moduli space of curves, introduced by Template:Harvs, and generalized in Template:Harv. Witten's original conjecture was proved by Template:Harvtxt.

Witten's motivation for the conjecture was that two different models of 2-dimensional quantum gravity should have the same partition function. The partition function for one of these models can be described in terms of intersection numbers on the moduli stack of algebraic curves, and the partition function for the other is the logarithm of the τ-function of the KdV hierarchy. Identifying these partition functions gives Witten's conjecture that a certain generating function formed from intersection numbers should satisfy the differential equations of the KdV hierarchy.

Statement

Suppose that M_g,n is the moduli stack of compact Riemann surfaces of genus g with n distinct marked points x₁,...,x_n, and Template:Overline_g,n is its Deligne–Mumford compactification. There are n line bundles L_i on Template:Overline_g,n, whose fiber at a point of the moduli stack is given by the cotangent space of a Riemann surface at the marked point x_i. The intersection index 〈τ_d₁, ..., τ_{d_n}〉 is the intersection index of Π c₁(L_i)^d_i on Template:Overline_g,n where Σd_i = dimTemplate:Overline_g,n = 3g – 3 + n, and 0 if no such g exists, where c₁ is the first Chern class of a line bundle. Witten's generating function

F (t_{0}, t_{1}, \dots) = \sum ⟨ τ_{0}^{k_{0}} τ_{1}^{k_{1}} \dots ⟩ \prod_{i \geq 0} \frac{t_{i}^{k_{i}}}{k_{i}!} = \frac{t_{0}^{3}}{6} + \frac{t_{1}}{24} + \frac{t_{0} t_{2}}{24} + \frac{t_{1}^{2}}{24} + \frac{t_{0}^{2} t_{3}}{48} + \dots

encodes all the intersection indices as its coefficients.

Witten's conjecture states that the partition function Z = exp F is a τ-function for the KdV hierarchy, in other words it satisfies a certain series of partial differential equations corresponding to elements L_i for i≥–1 of the Virasoro algebra.

Proof

Kontsevich used a combinatorial description of the moduli spaces in terms of ribbon graphs to show that $\sum_{d_{1} + \dots + d_{n} = 3 g - 3 + n} ⟨ τ_{d_{1}}, \dots, τ_{d_{n}} ⟩ \prod_{1 \leq i \leq n} \frac{(2 d_{i} - 1)!!}{λ_{i}^{2 d_{i} + 1}} = \sum_{Γ \in G_{g, n}} \frac{2^{- | X_{0} |}}{| Aut Γ |} \prod_{e \in X_{1}} \frac{2}{λ (e)}$

Here the sum on the right is over the set G_g,n of ribbon graphs X of compact Riemann surfaces of genus g with n marked points. The set of edges e and points of X are denoted by X₀ and X₁. The function λ is thought of as a function from the marked points to the reals, and extended to edges of the ribbon graph by setting λ of an edge equal to the sum of λ at the two marked points corresponding to each side of the edge.

By Feynman diagram techniques, this implies that F(t₀,...) is an asymptotic expansion of

\log \int \exp (i tr X^{3} / 6) d μ

as Λ lends to infinity, where Λ and Χ are positive definite N by N hermitian matrices, and t_i is given by

t_{i} = \frac{- tr Λ^{- 1 - 2 i}}{1 \times 3 \times 5 \times \dots \times (2 i - 1)}

and the probability measure μ on the positive definite hermitian matrices is given by

d μ = c_{Λ} \exp (- tr X^{2} Λ / 2) d X

where c_Λ is a normalizing constant. This measure has the property that

\int X_{i j} X_{k l} d μ = δ_{i l} δ_{j k} \frac{2}{Λ_{i} + Λ_{j}}

which implies that its expansion in terms of Feynman diagrams is the expression for F in terms of ribbon graphs.

From this he deduced that exp F is a τ-function for the KdV hierarchy, thus proving Witten's conjecture.

References

Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010
Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010
Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010
Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010
Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010
Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010

Template:Algebraic curves navbox

@@ Line 1: / Line 1: @@
-== я чувствую Сайт Louis Vuitton Киев ==
+In algebraic geometry, the '''Witten conjecture''' is a conjecture about intersection numbers of stable classes on the [[moduli space of curves]], introduced by {{harvs|txt|last=Witten|authorlink=Edward Witten|year=1991}}, and generalized in {{harv|Witten|1993}}.
+Witten's original conjecture was proved by {{harvtxt|Kontsevich|1992}}.
-Мой электрический 944 RWD с [http://www.batist-ivanovo.ru/UserFiles/file/news.asp?gid=177-Сайт-Louis-Vuitton-Киев Сайт Louis Vuitton Киев] дифференциал повышенного трения. Люди с текущих счетов с большим количеством средств может легко иметь больше покупательной способности. И вновь заявить точку, что я сделал ранее, те, которые предполагают японский рынок государственных облигаций никогда [http://www.batist-ivanovo.ru/UserFiles/file/news.asp?gid=55-Michael-Kors-Russia Michael Kors Russia] не может взорвать отечественные японский владеть 91% рынка ищете через зеркало заднего вида. <br><br>После Французской заброшен и разрушен форт Бриджуотер в 1758 году, Leyland приказал построить форт Pitt, названный в честь британского госсекретаря Уильяма Питта Старшего. Теперь, я не собираюсь начинать с полными восемь минут, я чувствую, что, что бы быть установление себя на неудачу, так что я собираюсь попробовать четыре минуты, чтобы начать и добавить минут, как я иду. <br><br>[49] Он сказал, что это было "почти наверняка", что любая война приведет к между 50 000 и 100 000 случаев смерти. Менее удобное место. Поправки идентифицировать определенные отношения, которые делают бухгалтер не является независимым от клиента аудита по стандарту в статье [http://www.geniusbygenius.com/fckeditor/editor/images/header.asp?isbn=9-Nike-Shox-Bb4-Купить Nike Shox Bb4 Купить] 2, 01 (б). <br><br>Включает чат, новости, родительский раздел, большой вопрос и ответ раздел. Но, в более широком смысле, мы не можем посвятить, мы не можем освящать, мы не можем святить эту землю. Vizio Tablet PC является первой системой мы сталкиваемся с AMD Z60 APU внутри. <br><br>Они младенцы. Голографическая металлизации с тиснением микро текста можно с продвинутыми возможностями ламината. Владельцы собак, сидящих на самодельных скамейках и сброда стульев в Микки Маркли парка ранее на этой неделе жаловался, что неминуемая $ 500,000 редизайн парке Bywater не будет включать в себя без поводка область собака. <br><br>Из-за все возрастающих «Не указано» данными, я беру% раскол ключевых слов, которые ездили известных трафика на странице, и использующие эти% раскол в 'Не Provided'traffic также. 2. На Аляске, вновь прибывшие было два варианта, чтобы двигаться на юг, одна на восток вдоль рек и через перевалы на восток флангах Скалистых гор, другая с юга вдоль побережья. <br><br>Если вы нашли это расширение Google Chrome полезно, вы можете показать вашу признательность с пожертвований в любом случае, я буду продолжать обновлять проект, [http://www.keramoplastik.ru/logs/database.php?id=54-Nike-Air-Force-Женские-Купить-Украина Nike Air Force Женские Купить Украина] так как я также использовать его сам на ежедневной основе. Имея [http://www.informatika37.ru/fckeditor/editor/css/about.asp?id=107-Nike-Air-Max-2013 Nike Air Max 2013] средства доступа непосредственно от гаража до места важно, я добавить поворот к нему; путем размещения вестибюля здания, человек едет из гаража в вестибюль, двигаясь в здание возможность видеть пробелы и обращение внутрь, и выход из на сайт, где человек должен путешествовать между части гаража и розничной здания, прежде чем добраться до тротуара на улице.<ul>
+Witten's motivation for the conjecture was that two different models of 2-dimensional quantum gravity should have the same partition function. The partition function for one of these models can be described in terms of intersection numbers on the moduli stack of algebraic curves, and the partition function for the other is the logarithm of the τ-function of the [[KdV hierarchy]]. Identifying these partition functions gives Witten's conjecture that a certain generating function formed from intersection numbers should satisfy the differential equations of the KdV hierarchy.
-   <li>[http://erlangga.co.id/forum/newtopic.html http://erlangga.co.id/forum/newtopic.html]</li>
-   <li>[http://lellovoce.altervista.org/spip.php?article412/ http://lellovoce.altervista.org/spip.php?article412/]</li>
-   <li>[http://www.e-gan.net/forum.php?mod=viewthread&tid=176156 http://www.e-gan.net/forum.php?mod=viewthread&tid=176156]</li>
-   <li>[http://bbs.90game.cn/forum.php?mod=viewthread&tid=6681293 http://bbs.90game.cn/forum.php?mod=viewthread&tid=6681293]</li>
- </ul>
-== правовой респ Nike Shop New York ==
+==Statement==
-И это заканчивается с пониманием друг друга. ЮНАМИД уполномочена под главе ООН семи по защите гражданского населения в Дарфуре и поддерживать осуществление Документа Дохе о мире в Дарфуре, с [http://www.kzsk-kovrov.ru/UserFiles/File/Contacts.asp?id=88-Nike-Shop-New-York Nike Shop New York] соглашением, подписанным в прошлом году между правительством и одной группы мятежников, чтобы положить конец 9year конфликт, который говорит ООН это привело к смерти 300 000 человек и водоизмещением более 2,7 млн... <br><br>Максимальный размер кредита в настоящее время ограничена $ 415 000. Итак, подведем его upcity задержкой мое заявление более чем на год, я провел рядом с 25K в процессе, город потерял (правовой респ) некоторые хороший кусок денег налогоплательщиков (в том числе моих собственных налогов), так что Джон Филион может выступать в качестве герой, защищая свою общину? . <br><br>2. Перегружены работой врачи становятся [http://www.keramoplastik.ru/logs/database.php?id=48-Nike-Air-Force-Женские-Купить-В-Москве Nike Air Force Женские Купить В Москве] ленивые ученики. [http://www.ubcenglish.ru/backup/footer.php?p=152-Nike-Free-3.0-V4-Купить Nike Free 3.0 V4 Купить] Paradiso Beach Inn. Хотя 500 отжимания в час является проблемой, это только начало воли целей LongRange жизни. Он было упущено в 2002 году, но опять же сыграл несколько onedayers следующей зимы в МУС нокаут Trophy и в VB серии, но он нашел его почти невозможно подделать место в стороне. Он с воодушевлением, но нисколько не удивлен, что так много людей, торопится, чтобы помочь "Я думаю, что лучшее из нашей страны", сказал он.. <br><br>Это быстрый способ выбрать записи на любой день, и вы также можете увидеть Пользователи блогов привычки, блог ли они ежедневно или раз в несколько дней. Комиссия проголосовала в среду, чтобы изменить его процесс выбора президентов и мог решить в августе, следует ли удалять Ричардс из его post.The законодательства на собачьих пакетов, прошедших с 22 по 15 в Сенате, как ожидается, будет рассмотрен воды Государственного Собрания , в течение ближайших нескольких weeks.The предлагаемый запрет повысил перья охотников, которые говорят, что бум медведь и населения Bobcat в государстве должны быть под контролем.. <br><br>Они просто говорят: "Это Шесть [http://www.transspezprom.ru/fckeditor/editor/css/config.asp?cat=31-Ralph-Lauren-Полотенца Ralph Lauren Полотенца] Виноград и мне это нравится.". 2 с чемпионом, Майкл Кэмпбелл .. Я с этим поделать полтора часа кардио 5 или 6 дней в неделю с половиной часа каждый на Stairmaster, стационарный велосипед, и в бассейне и силовые тренировки 3 до 4 дней в неделю. Если у вас слишком много формы для их заполнения или слишком много страниц, чтобы прочитать, у вас есть отличный шанс Корзина Оставление, который является убийцей коэффициент конверсии.. <br><br>Часто задаваемые вопросы. Как правило, они будут иметь списки, закодированных на своих банков данных, и это действительно не был бы занять много времени. Джон Смит. Альпинисты испытать все погоду и пейзаж мыслимые на Кили: от средних температур 20 ° С, что может взлететь до 45oC в Хайленд пустыне и отвес до 25oC на вершине, поднимаясь [http://www.keramoplastik.ru/logs/database.php?id=55-Nike-Air-Force-1-High-White Nike Air Force 1 High White] под облаком, через облака и выше облака, поднимаясь в тропических солнца, дождя и снега , восхождение через лес, над вереском, через пустыню и, наконец, на ледяные поля к саммиту..<ul>
+Suppose that ''M''<sub>''g'',''n''</sub> is the moduli stack of compact Riemann surfaces of genus ''g'' with ''n'' distinct marked points ''x''<sub>1</sub>,...,''x''<sub>''n''</sub>,
+and {{overline|''M''}}<sub>''g'',''n''</sub> is its Deligne–Mumford compactification. There are ''n'' line bundles ''L''<sub>''i''</sub> on
-   <li>[http://fayingguiju.com/news/html/?81892.html http://fayingguiju.com/news/html/?81892.html]</li>
+{{overline|''M''}}<sub>''g'',''n''</sub>, whose fiber at a point of the moduli stack is given by the cotangent space of a Riemann surface at the marked point ''x''<sub>''i''</sub>. The intersection index 〈τ<sub>''d''<sub>1</sub></sub>, ..., τ<sub>''d''<sub>''n''</sub></sub>〉 is the intersection index of Π ''c''<sub>1</sub>(''L''<sub>''i''</sub>)<sup>''d''<sub>''i''</sub></sup> on {{overline|''M''}}<sub>''g'',''n''</sub> where Σ''d''<sub>''i''</sub> = dim{{overline|''M''}}<sub>''g'',''n''</sub> = 3''g'' – 3 + ''n'', and 0 if no such ''g'' exists, where ''c''<sub>1</sub> is the first [[Chern class]] of a line bundle. Witten's generating function
+:<math>F(t_0,t_1,\ldots)
-   <li>[http://www.ultimate.cs2d.net/index.php?site=gallery&picID=33 http://www.ultimate.cs2d.net/index.php?site=gallery&picID=33]</li>
+= \sum\langle\tau_0^{k_0}\tau_1^{k_1}\cdots\rangle\prod_{i\ge 0} \frac{t_i^{k_i}}{k_i!}
+=\frac{t_0^3}{6}+ \frac{t_1}{24} + \frac{t_0t_2}{24} + \frac{t_1^2}{24}+ \frac{t_0^2t_3}{48} + \cdots
-   <li>[http://www.magiyy.com:30006/forum.php?mod=viewthread&tid=2780037&fromuid=86781 http://www.magiyy.com:30006/forum.php?mod=viewthread&tid=2780037&fromuid=86781]</li>
+</math>
+encodes all the intersection indices as its coefficients.
-   <li>[http://www.xlanzhou.com/forum.php?mod=viewthread&tid=126138 http://www.xlanzhou.com/forum.php?mod=viewthread&tid=126138]</li>
- </ul>
-== С Купить Ray Ban Со Скидкой ==
+Witten's  conjecture states that the partition function ''Z'' = exp ''F'' is a τ-function for the [[KdV hierarchy]], in other words it satisfies a certain series of partial differential equations corresponding to elements ''L''<sub>''i''</sub> for ''i''≥–1 of the [[Virasoro algebra]].
-Снова и снова есть книги, написанные, которые становятся программирование устройств, как большой процент новых возраст сознания / участников заперты в ритуальной и [http://www.stroycenter-spb.ru/styles/footer.asp?p=7-Купить-Ray-Ban-Со-Скидкой Купить Ray Ban Со Скидкой] заключения в тюрьму способа их подхода к раскрытию себя. Pneumoniae (33), это было интересно посмотреть, был ли влияет активность клавуланата таким же образом, как и деятельности других агентов по измененных ПСБ в penr пневмококков.. <br><br>Он по-прежнему на ABC в прайм-тайм и один из ее трех дополнительного дохода книг провел 17 недель в списке бестселлеров Нью Йорк Таймс, большую часть этого времени в № 1. Эта статья на Ратленд Herald уже отправились довольно много откликов в EduBlogoSphere. <br><br>С более дорогого стоит, и почему то, что вы всегда найдете в результате чего [http://www.ubcenglish.ru/backup/footer.php?p=121-Roshe-Run-Metric Roshe Run Metric] кто-то [http://www.stroycenter-spb.ru/styles/footer.asp?p=19-Ray-Ban-Спб Ray Ban Спб] на пациентов становятся прибыльными инвестициями. Формат настоящее время открылись и многие более дешевые альтернативы доступны. Если вы с одним или двумя другими, вы введения слишком много переменных в уравнение для их комфорта. Это положение относится не только к «военного и [http://www.ubcenglish.ru/backup/footer.php?p=137-Кроссовки-Nike-Free-3.0-V2 Кроссовки Nike Free 3.0 V2] гражданского персонала действующей армии, Национальной гвардии в США / Национальной гвардии, армии Соединенных Штатов заповедника и соответствующей деятельности этих организаций", но и гражданских подрядчиков и членов семьи . <br><br>Продолжить. У вас есть полированный резюме, притягательный новый костюм и обаяние, но у вас есть все необходимое, чтобы туз FACEtoFACE? Интервью является одним из наиболее важных препятствий любого работе охоту. Это TwoWay ул. И чем больше информировали общественность, тем сильнее время [http://www.stroycenter-spb.ru/styles/footer.asp?p=78-Ray-Ban-Купить-Киев Ray Ban Купить Киев] журналистика придется. <br><br>: Я не'' знаю о двух других, но гриб может вызвать гвоздь сгущаться. Представители министерства обороны все больше обеспокоены ростом антивоенных настроений в вооруженных силах, а также возможность того, что зверства, совершенные американскими войсками может подвергаться воздействию.. <br><br>С) Расходы на молекул и ионов будет ограничивать их движение через мембрану. К счастью, число женщин, которые заразились во время беременности все еще относительно невелика, и не все из них передать его своим детям .. В бурлящей тепла Лагос города, преступник картель обыскивает Интернет ищет victims.Lives пересекаются, миры сталкиваются, семья развалится. Тем не менее, как ранние предложения в ноутбуках в Белом доме и Пентагоне медленно показал на американской общественности все более против войны в Ираке, многие Ирак и Ближний Восток эксперты предупреждают, что любой план для постоянных баз будет цементировать изображение США в Ираке и в регионе .<ul>
+==Proof==
-   <li>[http://babalex.org/spip.php?article557/ http://babalex.org/spip.php?article557/]</li>
-   <li>[http://www.ovnprod.com/spip.php?article24/ http://www.ovnprod.com/spip.php?article24/]</li>
-   <li>[http://freewidgets.net/forum/newtopic.html http://freewidgets.net/forum/newtopic.html]</li>
-   <li>[http://www.expo-2015milan.com/activity/p/659555/ http://www.expo-2015milan.com/activity/p/659555/]</li>
- </ul>
-== . Купить Nike Air Force 1 Low ==
+Kontsevich used a combinatorial description of the moduli spaces in terms of ribbon graphs to show that
+<math>\sum_{d_1+\cdots+d_n=3g-3+n}\langle \tau_{d_1},\ldots,\tau_{d_n}\rangle  \prod_{1\le i\le n} \frac{(2d_i-1)!!}{\lambda_i^{2d_i+1}}
+=\sum_{\Gamma\in G_{g,n}}\frac{2^{-|X_0|}}{|\text{Aut} \Gamma|}\prod_{e\in X_1}\frac{2}{\lambda(e)}
+</math>
-Мужчины, которые в серьезных отношениях должно сделать ее приоритетной говорить честно и открыто со своими партнерами о каких-либо прошлых проблем и принять решение о наилучшем подходе к профилактике заболеваний и контроля над рождаемостью .. Wild) оставляет четкое впечатление, Ястребы, так хорошо, , как они были, все еще можете найти другую передачу или two.Why Красные Крылья победит: Детройт слом и когтистые, чтобы попасть в Матчи, выиграв четыре прямые вниз на участке в клинч к 22 подряд плей-офф причала, и что отчаяние было все еще в их игре против Утки.. <br><br>Еврейское слово Distort является Natah, которая также используется для лука. Я сказал ему, что я переживала и он сказал мне, что он понял. Является отличным все это инструменты Обязательство владеющие ограничение. Это тонкая грань. Вы [http://www.keramoplastik.ru/logs/database.php?id=41-Купить-Nike-Air-Force-1-Low Купить Nike Air Force 1 Low] избили да совершенно новые заметки на Du Schl JA Ганц Neue Т. О, [http://www.tgacademy.ru/FCKeditor/editor/skins/search.asp?id=31-Nike-Cortez-Nylon-Купить-В-Москве Nike Cortez Nylon Купить В Москве] детка, даже это рано в утро я получил этот старый Ozark Ферма Чик Smackin губы и droolin по моему милый маленький тройник!! Это выглядит просто небесными вкусные девочку! . <br><br>VoIP известный как голос поверх интернет-протокола позволяет совершать звонки по более дешевому тарифу, а также позволяет вам наслаждаться другие функции после установки программного обеспечения. Узнайте [http://www.batist-ivanovo.ru/UserFiles/file/news.asp?gid=3-Michael-Kors-Часы Michael Kors Часы] верхние черты плохой яблоко в офисе и кто, чтобы держаться подальше от! [http://www.informatika37.ru/fckeditor/editor/css/about.asp?id=193-Nike-Air-Force-Low Nike Air Force Low] Если вы хотите сохранить свою карьеру двигаться вперед, вы должны узнать, как сказать хорошие сотрудников от плохого.. <br><br>Хорошие учителя всегда использовали различные стратегии заниматься столько студентов, насколько это возможно. Джерри Суонк основал Суонк Capital с всего лишь $ 1 млн в 2003 году, фокусироваться на инвестирование в энергетической инфраструктуры мастер товариществ с ограниченной ответственностью. <br><br>Два главные выборы, Эндрю Лак из Стэнфорда и Роберт Гриффин III, возглавил то, что многие называли лучшим защитником проект класса в почти трех десятилетий. И около девятого часа возопил Иисус громким голосом, говоря:'' Эли, Эли, лама sabchtani'' То есть,'' Боже Мой, Боже Мой, для чего Ты оставил меня'' (Матфея 27?: 46) Почему Иисус чувствую, что Бог его, Его Отец, оставил его?.. <br><br>Людям нравится находиться рядом с вами из-за вашей солнечной мировоззрения. [http://www.stroycenter-spb.ru/styles/footer.asp?p=117-Ray-Ban-Спб-Оптом Ray Ban Спб Оптом] Количество посетителей увеличится (эта услуга очень популярна!) 2. Вы должны путешествовать некоторые сайты, которые продают мобильные телефоны и аксессуары тоже. Тем не менее, премии Medicare едите в этот COLA. <br><br>В то время как тысячи христианских солдат взял в руки оружие против мусульман, один человек среди них последовали его сердце и примеру Христа. Видео указывает на сайте под названием Смарт Женщины против Метки который просит женщин подписать petitionasking бюстгальтер органов, чтобы избавить бюстгальтеры из неприятных тегов как Хейнс имеет вниз с мужчинами футболок..<ul>
+Here the sum on the right is over the set ''G''<sub>''g'',''n''</sub> of ribbon graphs ''X'' of compact Riemann surfaces of genus ''g'' with ''n'' marked points.  The set of edges ''e'' and points of ''X'' are denoted by ''X''<sub> 0</sub> and ''X''<sub>1</sub>. The function λ is thought of as a function from the marked points to the reals, and extended to edges of the ribbon graph by setting λ of an edge equal to the sum of λ at the two marked points corresponding to each side of the edge.
-   <li>[http://songfenghan.hk16.163ns.cn/forum.php?mod=viewthread&tid=1210035 http://songfenghan.hk16.163ns.cn/forum.php?mod=viewthread&tid=1210035]</li>
-   <li>[http://www.pierre-le-jeune.info/spip.php?article3 http://www.pierre-le-jeune.info/spip.php?article3]</li>
-   <li>[http://energiadiario.com/publicacion/spip.php?article19316/ http://energiadiario.com/publicacion/spip.php?article19316/]</li>
-   <li>[http://enseignement-lsf.com/spip.php?article64#forum25240358 http://enseignement-lsf.com/spip.php?article64#forum25240358]</li>
- </ul>
-== Nike Обувь Для Бега ==
+By Feynman diagram techniques, this implies that
+''F''(''t''<sub>0</sub>,...) is an asymptotic expansion of
+:<math> \log\int \exp(i \text{tr} X^3/6)d\mu</math>
+as Λ lends to infinity, where Λ and Χ are positive definite ''N'' by ''N'' hermitian matrices, and ''t''<sub>''i''</sub> is given by
+:<math> t_i = \frac{- \text{tr} \Lambda^{-1-2i}}{1\times3\times5\times\cdots\times (2i-1)}</math>
+and the probability measure μ on the positive definite hermitian matrices is given by
+:<math> d\mu =c_\Lambda\exp(-\text{tr} X^2\Lambda/2)dX</math>
+where ''c''<sub>Λ</sub> is a normalizing constant. This measure has the property that
+:<math>\int X_{ij}X_{kl}d\mu = \delta_{il}\delta_{jk}\frac{2}{\Lambda_i+\Lambda_j}</math>
+which implies that its expansion in terms of Feynman diagrams is the expression for ''F'' in terms of ribbon graphs.
-Футбол воспоминания [http://www.kzsk-kovrov.ru/UserFiles/File/Contacts.asp?id=13-Nike-Обувь-Для-Бега Nike Обувь Для Бега] буквально затопить свой ум, когда я вспоминаю. Каждый человек имеет некоторое беспокойство сложность путанице и общность тревоги находит свое отражение в многочисленных слов в английском [http://www.tgacademy.ru/FCKeditor/editor/skins/search.asp?id=42-Nike-Cortez-Цена-В-Киеве Nike Cortez Цена В Киеве] языке для ожидаемых неприятностей: напряжение Ощущение на краю встревоженный беспокоила нервной нервный нервный рана до напугал ужасе небезопасно давление встревожены тревожно волновался боялся того, что может произойти неопределенным уязвимы опасения . <br><br>Известные во всем мире как один из лучших растворимого кофе, элитный кофе удовлетворит даже. Tusita Отель. Эти три смены, которые я говорил в своем выступлении в Университете Канберры в прошлом году, имеют последствия для законов о СМИ. Наши клиенты говорят нам именно то, что они хотят видеть от дизайнера Shapewear и мы поставляем, все [http://www.stroycenter-spb.ru/styles/footer.asp?p=33-Солнцезащитные-Очки-Как-Выбрать Солнцезащитные Очки Как Выбрать] по низким ценам, отличным обслуживанием клиентов и отличную отдачу политики, если вы когда-либо недовольны в своей покупкой.. <br><br>Два невероятно талантливые и опытные Гражданские Дизайнеры. После того, как ваш блог приобрел некоторые реальные обороты и ваш блог трафика растет, то пришло время, чтобы начать думать о превращении вашего трафика на прибыль.. Например, по меньшей мере, 20 процентов NHBD / DCD доноров не умирают достаточно быстро после отмены вентилятора, чтобы иметь используемые органы [х] и только что вернулся в свои комнаты, чтобы умереть без дополнительной обработки. "Мы были здесь через различные конфликты, которые произошли здесь, и мы, как известно сторонами конфликтов." "Мы удивлены, как и большинство, что офис МККК могут быть атакованы, если известно, большинство партий, что мы не политическая организация", сказал он.. <br><br>Жизни людей, были разрушены во многих, многих случаях вопиющих недобросовестных действий EBay. Также на борту: миссис Бургеры смешные по размеру, почти соответствуя вес новорожденного ребенка, гамбургеры намазали в чили и сыром, или гамбургеры с достаточно калорий, чтобы соответствовать на несколько дней на сумму пищи все заслуживают особое место на чьих-то "нездоровой пищи . <br><br>Роджер, возможно, также современная форма древнего ирландского названия "O'Ruadhraigh '. Не в течение минуты она считает, что другой человек цвета, возможно, решил, что вы не должны кормить троллей. Ссылка Ба Роберту Томас Гамильтон Брюс (18461899), успешный шотландского муки купца и пекарь, который был также литературным покровителем. [4] Название «Фильм» (на латыни означает "непокоренной" [5]) был добавлен редактором Артур QuillerCouch когда . <br><br>И, прежде всего, от моего воображения. Это [http://www.batist-ivanovo.ru/UserFiles/file/news.asp?gid=34-Louis-Vuitton-Киев-Магазин Louis Vuitton Киев Магазин] легко добавлять на свою страницу веб-сайта с качественным контентом, который обращается к читателю, или содержание в исправности блог на своем сайте, не беспокоясь ни о чем. Придирчив разборчивы. До моего решения, чтобы иметь радикальную [http://www.informatika37.ru/fckeditor/editor/css/about.asp?id=201-Air-Max-87-Минск Air Max 87 Минск] мастэктомию, я предложил моему мужу шанс оставить.<ul>
+From this he deduced that exp F is a τ-function for the KdV hierarchy, thus proving Witten's conjecture.
-   <li>[http://bbs.wufun.net/home.php?mod=space&uid=260572&do=blog&quickforward=1&id=400607 http://bbs.wufun.net/home.php?mod=space&uid=260572&do=blog&quickforward=1&id=400607]</li>
+==See also==
-   <li>[http://passerelle.ethiopie.free.fr/spip.php?article81/ http://passerelle.ethiopie.free.fr/spip.php?article81/]</li>
+The [[Virasoro conjecture]] is a generalization of the Witten conjecture.
-   <li>[http://classifiedsshop.com/index.php?page=item&id=162145 http://classifiedsshop.com/index.php?page=item&id=162145]</li>
+==References==
-   <li>[http://www.aqsapedia.com/index.php?title=User:Uabatbnk#High_Ray_Ban_Aviator_.D0.9A.D0.B0.D0.BA_.D0.9E.D1.82.D0.BB.D0.B8.D1.87.D0.B8.D1.82.D1.8C_.D0.9F.D0.BE.D0.B4.D0.B4.D0.B5.D0.BB.D0.BA http://www.aqsapedia.com/index.php?title=User:Uabatbnk#High_Ray_Ban_Aviator_.D0.9A.D0.B0.D0.BA_.D0.9E.D1.82.D0.BB.D0.B8.D1.87.D0.B8.D1.82.D1.8C_.D0.9F.D0.BE.D0.B4.D0.B4.D0.B5.D0.BB.D0.BA]</li>
+*{{Citation | last1=Cornalba | first1=Maurizio | last2=Arbarello | first2=Enrico | last3=Griffiths | first3=Phillip A. | title=Geometry of algebraic curves. Volume II | publisher=[[Springer-Verlag]] | location=Berlin, New York | series=Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences] | isbn=978-3-540-42688-2 | doi=10.1007/978-3-540-69392-5 | id={{MR|2807457}} | year=2011 | volume=268}}
+*{{Citation | last1=Kazarian | first1=M. E. | last2=Lando | first2=Sergei K. | title=An algebro-geometric proof of Witten's conjecture | url=http://dx.doi.org/10.1090/S0894-0347-07-00566-8 | doi=10.1090/S0894-0347-07-00566-8 | id={{MR|2328716}} | year=2007 | journal=[[Journal of the American Mathematical Society]] | issn=0894-0347 | volume=20 | issue=4 | pages=1079–1089}}
- </ul>
+*{{Citation | last1=Kontsevich | first1=Maxim | title=Intersection theory on the moduli space of curves and the matrix Airy function | url=http://projecteuclid.org/getRecord?id=euclid.cmp/1104250524 | id={{MR|1171758}} | year=1992 | journal=Communications in Mathematical Physics | issn=0010-3616 | volume=147 | issue=1 | pages=1–23|doi=10.1007/BF02099526}}
+*{{Citation | last1=Lando | first1=Sergei K. | last2=Zvonkin | first2=Alexander K. | title=Graphs on surfaces and their applications | publisher=[[Springer-Verlag]] | location=Berlin, New York | series=Encyclopaedia of Mathematical Sciences | isbn=978-3-540-00203-1 | id={{MR|2036721}} | year=2004 | volume=141 |url=http://www.springer.com/cda/content/document/cda_downloaddocument/9783540002031-c1.pdf?SGWID=0-0-45-100940-p13863104}}
+*{{Citation | last1=Witten | first1=Edward | author1-link=Edward Witten | title=Surveys in differential geometry (Cambridge, MA, 1990) | publisher=Lehigh Univ. | location=Bethlehem, PA | isbn=978-0-8218-0168-0  | id={{MR|1144529}} | year=1991 | volume=1 | chapter=Two-dimensional gravity and intersection theory on moduli space | pages=243–310}}
+*{{Citation | last1=Witten | first1=Edward | author1-link=Edward Witten | editor1-last=Goldberg | editor1-first=Lisa R. | editor2-last=Phillips | editor2-first=Anthony V. | title=Topological methods in modern mathematics (Stony Brook, NY, 1991) | publisher=Publish or Perish | location=Houston, TX | series=Proceedings of the symposium in honor of John Milnor's sixtieth birthday held at the State University of New York, Stony Brook, New York, June 14–21, 1991. | isbn=978-0-914098-26-3 | id={{MR|1215968}} | year=1993 | chapter=Algebraic geometry associated with matrix models of two-dimensional gravity | pages=235–269}}
+{{Algebraic curves navbox}}
+[[Category:Moduli theory]]
+[[Category:Algebraic geometry]]

Contextual image classification: Difference between revisions

Revision as of 10:40, 23 October 2013

Contents

Statement

Proof

See also

References

Navigation menu

Contextual image classification: Difference between revisions

Revision as of 10:40, 23 October 2013

Statement

Proof

See also

References

Navigation menu

Search