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Пространство модулей пучков и обобщение формулы Мак-Магона
Функциональный анализ и его приложения. 2013. Т. 47. № 2. С. 18-26.
M. Vuletic has recently found a two-parameter generalization of MacMahon’s formula. In this paper we show that the coefficients in her formula are the Betti numbers of certain subvarieties in the moduli space of sheaves on the projective plane.
Feigin B. L., Mytafyan G. S., Functional Analysis and Its Applications 2013 Vol. 47 No. 1 P. 50-61
The generating function of plane partitions {ai,j} subject to the constraint am,n = 0 is expressed and calculated as the character of an irreducible representation of the quantum toroidal algebra gl1 in the case K = q1 mq2 n. ...
Added: March 28, 2013
Mytafyan G. S., Feigin B. L., Функциональный анализ и его приложения 2013 Т. 47 № 1 С. 62-76
Доказана формула для производящей функции плоских разбиений $\{a_{i,j}\}$ с ограничением $a_{m,n}=0$, являющейся характером неприводимого представления квантовой тороидальной алгебры $\widehat{\widehat{\mathfrak{gl}}}_1$ в случае $K=q_1^mq_2^n$. ...
Added: February 6, 2013
Mytafyan G. S., Feigin B. L., Функциональный анализ и его приложения 2014 Т. 48 № 1 С. 46-60
An expression for the generating function of plane partitions ai,j subject to the con-straints am, n=0 and ai,j≥kj,1≤j≤n, which is the character of an irreducible representation of the quantum toroidal algebra gl1ˆˆ, is obtained. ...
Added: November 7, 2014
Smirnov E., М. : МЦНМО, 2014
Сколько есть способов разбить натуральное число в сумму нескольких слагаемых, если суммы, отличающиеся только порядком слагаемых, считаются одинаковыми? Оказывается, что простого ответа на этот, казалось бы, элементарный вопрос дать не получается. Зато теория, начинающаяся с этого вопроса, оказывается очень интересной, а ее результаты находят свое применение в самых разных разделах математики и математической физики.
Настоящая брошюра ...
Added: December 2, 2013
Pyatov P. N., de Gier J., Zinn-Justin P., Journal of Combinatorial Theory, Series A 2009 Vol. 116 P. 772-794
We consider partial sum rules for the homogeneous limit of the solution of the q-deformed Knizhnik–Zamolodchikov equation with reflecting boundaries in the Dyck path representation of the Temperley–Lieb algebra. We show that these partial sums arise in a solution of the discrete Hirota equation, and prove that they are the generating functions of τ 2-weighted ...
Added: October 16, 2012
Galkin S., Belmans P., Mukhopadhyay S., Experimental Mathematics 2019
We give the first examples of smooth Fano and Calabi–Yau varieties violating the (narrow) canonical strip hypothesis, which concerns the location of the roots of Hilbert polynomials of polarized varieties. They are given by moduli spaces of rank 2 bundles with fixed odd-degree determinant on curves of sufficiently high genus, hence our Fano examples have ...
Added: October 4, 2019
Jardim M., Markushevich D., Tikhomirov A. S., Moscow Mathematical Journal 2018 Vol. 18 No. 1 P. 117-148
Abstract. Let I(n) denote the moduli space of rank 2 instanton bundles of charge n on P3 . It is known that I(n) is an irreducible, nonsingular and affine variety of dimension 8n − 3. Since every rank 2 instanton bundle on P3 is stable, we may regard I(n) as an open subset of the ...
Added: August 20, 2018
Jardim M., Markushevich D., Tikhomirov A. S., Annali di Matematica Pura ed Applicata 2017 Vol. 196 No. 4 P. 1573-1608
We describe new components of the Gieseker–Maruyama moduli scheme (Formula presented.) of semistable rank 2 sheaves E on (Formula presented.) with (Formula presented.), (Formula presented.) and (Formula presented.) whose generic point corresponds to nonlocally free sheaves. We show that such components grow in number as n grows, and discuss how they intersect the instanton component. ...
Added: February 18, 2017
Feigin B. L., Buryak A., Journal of Geometry and Physics 2012 Vol. 62 No. 7 P. 1652-1664
The moduli space M(r,n) of framed torsion free sheaves on the projective plane with rank r and second Chern class equal to n has the natural action of the (r+2)-dimensional torus. In this paper, we look at the fixed point set of different one-dimensional subtori in this torus. We prove that in the homogeneous case ...
Added: September 20, 2012
Tikhomirov A. S., Markushevich D., Trautmann G., Central European Journal of Mathematics 2012 Vol. 19 No. 4 P. 1331-1355
We announce some results on compactifying moduli spaces of rank 2 vector bundles on surfaces by spaces of vector vector bundles on trees of surfaces. This is thought as an algebraic counterpart of the so-called bubbling of vector bundled connections an in differential geometry. The new moduli spaces are algebraic spaces arising as quotients ...
Added: October 21, 2014
Bershtein M., Feigin B. L., Merzon G., Selecta Mathematica, New Series 2018 Vol. 24 No. 1 P. 21-62
We study plane partitions satisfying condition a_{n+1,m+1}=0 (this condition is called “pit”) and asymptotic conditions along three coordinate axes. We find the formulas for generating function of such plane partitions. Such plane partitions label the basis vectors in certain representations of quantum toroidal gl1 algebra, therefore our formulas can be interpreted as the characters of ...
Added: October 24, 2018
Feigin B. L., Jimbo M., Miwa T. et al., Journal of Algebra 2013 Vol. 380 P. 78-108
We define and study representations of quantum toroidal gln with natural bases labeled by plane partitions with various conditions. As an application, we give an explicit description of a family of highest weight representations of quantum affine gln with generic level. ...
Added: February 28, 2013
Smirnov E., Merzon G., European Journal of Mathematics 2016 Vol. 2 No. 1 P. 227-245
We prove new determinantal identities for a family of flagged Schur polynomials. As a corollary of these identities we obtain determinantal expressions of Schubert polynomials for certain vexillary permutations. ...
Added: October 2, 2015
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
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
Kolokolov I., Lebedev V., Sizov G. A., Journal of Experimental and Theoretical Physics 2011 Vol. 140 No. 2 P. 387-400
We analyze magnetic kinematic dynamo in a conducting fluid where the stationary shear flow is accompanied by relatively weak random velocity fluctuations. The diffusionless and diffusion regimes are described. The growth rates of the magnetic field moments are related to the statistical characteristics of the flow describing divergence of the Lagrangian trajectories. The magnetic field ...
Added: February 2, 2017
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
ООО Фирма "Элист", 2014
В книге представлены тезисы докладов I тура XV Всероссийской научно-технической конференции и школы молодых ученых, аспирантов и студентов. ...
Added: October 17, 2014