### ?

## Новые подходы к иерархиям топологического типа

Успехи математических наук. 2017. Т. 72. № 5(437). С. 63-112.

Buryak A., Rossi P., Letters in Mathematical Physics 2016 Vol. 106 No. 3 P. 289-317

In this paper we define a quantization of the Double Ramification Hierarchies using intersection numbers of the double ramification cycle, the full Chern class of the Hodge bundle and psi-classes with a given cohomological field theory. We provide effective recursion formulae which determine the full quantum hierarchy starting from just one Hamiltonian, the one associated with ...

Added: September 28, 2020

Buryak A., Communications in Mathematical Physics 2015 Vol. 336 No. 3 P. 1085-1107

It this paper we present a new construction of a hamiltonian hierarchy associated to a cohomological field theory. We conjecture that in the semisimple case our hierarchy is related to the Dubrovin-Zhang hierarchy by a Miura transformation and check it in several examples. ...

Added: September 29, 2020

Dunin-Barkowski P., Norbury P., Orantin N. et al., Journal of the Institute of Mathematics of Jussieu 2019 Vol. 18 No. 3 P. 449-497

We apply the spectral curve topological recursion to Dubrovin's universal Landau-Ginzburg superpotential associated to a semi-simple point of any conformal Frobenius manifold. We show that under some conditions the expansion of the correlation differentials reproduces the cohomological field theory associated with the same point of the initial Frobenius manifold. ...

Added: December 22, 2016

Buryak A., Shadrin S., Zvonkine D., Journal of the European Mathematical Society 2016 Vol. 18 No. 12 P. 2925-2951

We describe the structure of the top tautological group in the cohomology of the moduli space of smooth genus g curves with n marked points. ...

Added: September 27, 2020

Buryak A., Posthuma H., Shadrin S., Journal of Differential Geometry 2012 Vol. 92 No. 1 P. 153-185

We define a hierarchy of Hamiltonian PDEs associated to an arbitrary tau-function in the semi-simple orbit of the Givental group action on genus expansions of Frobenius manifolds. We prove that the equations, the Hamiltonians, and the bracket are weighted-homogeneous polynomials in the derivatives of the dependent variables with respect to the space variable. In the particular ...

Added: September 30, 2020

Buryak A., Moscow Mathematical Journal 2017 Vol. 17 No. 1 P. 1-13

In this paper, using the formula for the integrals of the psi-classes over the double ramification cycles found by S. Shadrin, L. Spitz, D. Zvonkine and the author, we derive a new explicit formula for the n-point function of the intersection numbers on the moduli space of curves. ...

Added: September 27, 2020

Buryak A., Shadrin S., Spitz L. et al., American Journal of Mathematics 2015 Vol. 137 No. 3 P. 699-737

DR-cycles are certain cycles on the moduli space of curves. Intuitively, they parametrize curves that allow a map to the complex projective line with some specified ramification profile over two points. They are known to be tautological classes, but in general there is no known expression in terms of standard tautological classes. In this paper, ...

Added: September 30, 2020

Buryak A., Rossi P., Communications in Mathematical Physics 2016 Vol. 342 No. 2 P. 533-568

In this paper we study various properties of the double ramification hierarchy, an integrable hierarchy of hamiltonian PDEs introduced by the first author using intersection theory of the double ramification cycle in the moduli space of stable curves. In particular, we prove a recursion formula that recovers the full hierarchy starting from just one of the ...

Added: September 28, 2020

Buryak A., Mathematical Research Letters 2016 Vol. 23 No. 3 P. 675-683

In a previous paper we proved that after a simple transformation the generating series of the linear Hodge integrals on the moduli space of stable curves satisfies the hierarchy of the Intermediate Long Wave equation. In this paper we present a much shorter proof of this fact. Our new proof is based on an explicit ...

Added: September 28, 2020

Buryak A., Shadrin S., Advances in Mathematics 2011 Vol. 228 P. 22-42

We give a new proof of Faber's intersection number conjecture concerning the top intersections in the tautological ring of the moduli space of curves $\M_g$. The proof is based on a very straightforward geometric and combinatorial computation with double ramification cycles. ...

Added: October 1, 2020

Buryak A., Posthuma H., Shadrin S., Journal of Geometry and Physics 2012 Vol. 62 No. 7 P. 1639-1651

In our recent paper we proved the polynomiality of a Poisson bracket for a class of infinite-dimensional Hamiltonian systems of PDE's associated to semi-simple Frobenius structures. In the conformal (homogeneous) case, these systems are exactly the hierarchies of Dubrovin-Zhang, and the bracket is the first Poisson structure of their hierarchy. Our approach was based on a very ...

Added: September 30, 2020

Buryak A., Communications in Number Theory and Physics 2015 Vol. 9 No. 2 P. 239-271

In this paper we prove that the generating series of the Hodge integrals over the moduli space of stable curves is a solution of a certain deformation of the KdV hierarchy. This hierarchy is constructed in the framework of the Dubrovin-Zhang theory of the hierarchies of the topological type. It occurs that our deformation of ...

Added: September 29, 2020

Buryak A., Dubrovin B., Guere J. et al., Communications in Mathematical Physics 2018 Vol. 363 No. 1 P. 191-260

In this paper we continue the study of the double ramification hierarchy introduced by the first author. After showing that the DR hierarchy satisfies tau-symmetry we define its partition function as the (logarithm of the) tau-function of the string solution and show that it satisfies various properties (string, dilaton and divisor equations plus some important degree ...

Added: September 27, 2020

Buryak A., Janda F., Pandharipande R., Pure and Applied Mathematics Quarterly 2015 Vol. 11 No. 4 P. 591-631

The relations in the tautological ring of the moduli space $M_g$ of nonsingular curves conjectured by Faber-Zagier in 2000 and extended to the moduli space $\overline{M}_{g,n}$ of stable curves by Pixton in 2012 are based upon two hypergeometric series $A$ and $B$. The question of the geometric origins of these series has been solved in at least two ways (via the Frobenius ...

Added: September 28, 2020

Kazaryan M., Zvonkine D., Lando S., International Mathematics Research Notices 2018 No. 22 P. 6817-6843

We consider families of curve-to-curve maps that have no singularities except those of genus 0 stable maps and that satisfy a versality condition at each singularity. We provide a universal expression for the cohomology class Poincaré dual to the locus of any given singularity. Our expressions hold for any family of curve-to-curve maps satisfying the ...

Added: July 10, 2017

191574970, Functional Analysis and Its Applications 2006 Vol. 40 No. 2 P. 81-90

It is well known that every module M over the algebra ℒ(X) of operators on a finite-dimensional space X can be represented as the tensor product of X by some vector space E, M ≅ = E ⊗ X. We generalize this assertion to the case of topological modules by proving that if X is a stereotype space with the stereotype approximation property, then for each stereotype module M over the ...

Added: September 23, 2016

Losev A. S., Slizovskiy S., JETP Letters 2010 Vol. 91 P. 620-624

Added: February 27, 2013

Ilyashenko Y., Яковенко С. Ю., М. : МЦНМО, 2013

Предлагаемая книга—первый том двухтомной монографии, посвящённой аналитической теории дифференциальных уравнений.
В первой части этого тома излагается формальная и аналитическая теория нормальных форм и теорема о разрешении особенностей для векторных полей на плоскости.
Вторая часть посвящена алгебраически разрешимым локальным задачам теории аналитических дифференциальных уравнений , квадратичным векторным полям и проблеме локальной классификации ростков векторных полей в комплексной области ...

Added: February 5, 2014

Kalyagin V.A., Koldanov A.P., Koldanov P.A. et al., Physica A: Statistical Mechanics and its Applications 2014 Vol. 413 No. 1 P. 59-70

A general approach to measure statistical uncertainty of different filtration techniques for market network analysis is proposed. Two measures of statistical uncertainty are introduced and discussed. One is based on conditional risk for multiple decision statistical procedures and another one is based on average fraction of errors. It is shown that for some important cases ...

Added: July 19, 2014

Maslov V., Теоретическая и математическая физика 2019 Т. 201 № 1 С. 65-83

We study the process of a nucleon separating from an atomic nucleus from the mathematical standpoint
using experimental values of the binding energy for the nucleus of the given substance. A nucleon becomes
a boson at the instant of separating from a fermionic nucleus. We study the further transformations of
boson and fermion states of separation in a ...

Added: November 1, 2019

Pahomov F., Известия РАН. Серия математическая 2016 Т. 80 № 6 С. 173-216

Полимодальная логика доказуемости
GLP была введена Г. К. Джапаридзе в 1986 г. Она является логикой доказуемости для ряда цепочек предикатов доказуемости возрастающей силы. Всякой полимодальной логике соответствует многообразие полимодальных алгебр. Л. Д. Беклемишевым и А. Виссером был поставлен вопрос о разрешимости элементарной теории свободной GLP-алгебры, порожденной константами 0, 1 [1]. В этой статье для любого натурального n решается аналогичный вопрос для логик GLPn, являющихся ...

Added: December 4, 2017

Sinelshchikov D., Кудряшов Н. А., Theoretical and Mathematical Physics 2018 Vol. 196 No. 2 P. 1230-1240

We study a family of nonautonomous generalized Liénard-type equations. We consider the equivalence problem via the generalized Sundman transformations between this family of equations and type-I Painlevé–Gambier equations. As a result, we find four criteria of equivalence, which give four integrable families of Liénard-type equations. We demonstrate that these criteria can be used to construct ...

Added: February 9, 2019

Min Namkung, Younghun K., Scientific Reports 2018 Vol. 8 No. 1 P. 16915-1-16915-18

Sequential state discrimination is a strategy for quantum state discrimination of a sender’s quantum
states when N receivers are separately located. In this report, we propose optical designs that can
perform sequential state discrimination of two coherent states. For this purpose, we consider not
only binary phase-shifting-key (BPSK) signals but also general coherent states, with arbitrary prior
probabilities. Since ...

Added: November 16, 2020

Kotelnikova M. V., Aistov A., Вестник Нижегородского университета им. Н.И. Лобачевского. Серия: Социальные науки 2019 Т. 55 № 3 С. 183-189

The article describes a method that allows to improve the content of disciplines of the mathematical cycle by dividing them into invariant (general) and variable parts. The invariants were identified for such disciplines as «Linear algebra», «Mathematical analysis», «Probability theory and mathematical statistics» delivered to Bachelors program students of economics at several universities. Based on ...

Added: January 28, 2020