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Regular version of the site
Of all publications in the section: 78
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Article
Gorsky E. Moscow Mathematical Journal. 2009. Vol. 9. No. 2. P. 305-323.

We study the relations between Adams operation on a lambda-ring and the power structure on it, introduced by S. Gusein-Zade, I. Luengo and A. Melle-Hernandez. We give the explicit equations expressing them by each other. An interpretation of the formula of E. Getzler for the equivariant Euler characteristics of configuration spaces is also given.

Article
Bogachev V., Kosov E., Popova S. Moscow Mathematical Journal. 2019. Vol. 19. No. 4. P. 619-654.

A new approach to  Nikolskii-Besov classes is presented.

Article
Amerik E. Moscow Mathematical Journal. 2012. Vol. 12. No. 4. P. 701-704.

This note is a proof of the fact that a lagrangian torus on an irreducible hyperkähler fourfold is always a fiber of an almost holomorphic lagrangian fibration.

Article
A. Klimenko, O. Romaskevich. Moscow Mathematical Journal. 2014. Vol. 14. No. 2. P. 367-384.

A three-parametrical family of ODEs on a torus arises from a model of Josephson effect in a resistive case when a Josephson junction is biased by a sinusoidal microwave current. We  study asymptotics of Arnold tongues of this family on the parametric plane (the third parameter is fixed) and prove that the boundaries of the tongues are asymptotically close to Bessel functions.

Article
Ilyashenko Y., Gusein-Zade S., Kaledin D. B. Moscow Mathematical Journal. 2009. No. 9:1.
Article
Loktev S., Rybnikov L. G., Etingof P. Moscow Mathematical Journal. 2015. Vol. 15. No. 2. P. 185-186.

This issue is dedicated to the 60-th birthday of Borya Feigin.

Article
Zykin A. I. Moscow Mathematical Journal. 2005. Vol. 5. No. 4. P. 961-968.

The classical Brauer-Siegel theorem states that if $k$ runs through the sequence of normal extensions of $\mathbb{Q}$ such that $n_k/\log|D_k|\to 0,$ then $\log h_k R_k/\log \sqrt{|D_k|}\to 1.$ First, in this paper we obtain the generalization of the Brauer-Siegel and Tsfasman-Vl\u{a}du\c{t} theorems to the case of almost normal number fields. Second, using the approach of Hajir and Maire, we construct several new examples concerning the Brauer-Siegel ratio in asymptotically good towers of number fields. These examples give smaller values of the Brauer-Siegel ratio than those given by Tsfasman and Vladut.

Article
Costa A., Natanzon S. M. Moscow Mathematical Journal. 2007. No. 7(3). P. 419-424.
Article
V.A. Vassiliev. Moscow Mathematical Journal. 2001. Vol. 1. No. 1. P. 91-123.
We develop homological techniques for finding explicit combinatorial expressions of finite-type cohomology classes of spaces of knots in Rn,n≥3, generalizing Polyak--Viro formulas for invariants (i.e. 0-dimensional cohomology classes) of knots in R3. As the first applications we give such formulas for the (reduced mod 2) {\em generalized Teiblum--Turchin cocycle} of order 3 (which is the simplest cohomology class of {\em long knots} R1↪Rn not reducible to knot invariants or their natural stabilizations), and for all integral cohomology classes of orders 1 and 2 of spaces of {\em compact knots} S1↪Rn. As a corollary, we prove the nontriviality of all these cohomology classes in spaces of knots in R3.
Article
Zvonkine D., Lando S. Moscow Mathematical Journal. 2007. Vol. 7. No. 1. P. 85-107.
Article
Lando S., Жуков В. И. Moscow Mathematical Journal. 2017. Vol. 17. No. 4. P. 741-755.

Vassiliev (finite type) invariants of knots can be described in terms of weight systems. These are functions on chord diagrams satisfying so-called 4-term relations. The goal of the present paper is to show that one can define both the first and the second Vassiliev moves for binary delta-matroids and introduce a 4-term relation for them in such a way that the mapping taking a chord diagram to its delta-matroid respects the corresponding 4-term relations.

Understanding how the 4-term relation can be written out for arbitrary binary delta-matroids motivates introduction of the graded Hopf algebra of binary delta-matroids modulo the 4-term relations so that the mapping taking a chord diagram to its delta-matroid extends to a morphism of Hopf algebras. One can hope that studying this Hopf algebra will allow one to clarify the structure of the Hopf algebra of weight systems, in particular, to find reasonable new estimates for the dimensions of the spaces of weight systems of given degree.

Article
Kaledin D. B. Moscow Mathematical Journal. 2011. Vol. 11. No. 4. P. 723-803.

For a finite group $G$, the so-called $G$-Mackey functors form an abelian category $M(G)$ that has many applications in the study of $G$-equivariant stable homotopy. One would expect that the derived category $D(M(G))$ would be similarly important as the "homological" counterpart of the $G$-equivariant stable homotopy category. It turns out that this is not so -- $D(M(G))$ is pathological in many respects. We propose and study a replacement for $D(M(G))$, a certain triangulated category $DM(G)$ of "derived Mackey functors" that contains $M(G)$ but is different from $D(M(G))$. We show that standard features of the $G$-equivariant stable homotopy category such as the fixed points functors of two types have exact analogs for the category $DM(G)$.

Article
Феликсон А. А., Natanzon S. M. Moscow Mathematical Journal. 2011. Vol. 11. No. 2. P. 231-258.

We consider the union of two pants decompositions of the same orientable 2-dimensional surface of any genus g. Each pants decomposition corresponds to a handlebody bounded by this surface, so two pants decompositions correspond to a Heegaard splitting of a 3-manifold. We introduce a groupoid acting on double pants decompositions. This groupoid is generated by two simple transformations (called flips and handle twists), each transformation changing only one curve of the double pants decomposition. We prove that the groupoid acts transitively on all double pants decompositions corresponding to Heegaard splittings of a 3-dimensional sphere. As a corollary, we prove that the mapping class group of the surface is contained in the groupoid.

Article
Felikson A., Natanzon S. M. Moscow Mathematical Journal. 2017. Vol. 17. No. 1. P. 51-58.

Double pants decompositions were introduced in [FN] together with a flip-twist groupoid acting on these decompositions. It was shown that flip-twist groupoid acts transitively on a certain topological class of the decompositions, however, recently Randich discovered a serious mistake in the proof. In this note we present a new proof of the result, accessible without reading the initial paper.

Article
A. Omelchenko, Meshkov V., Petrov M. et al. Moscow Mathematical Journal. 2010. Vol. 10. No. 3. P. 611-628.

Exponential generating functions for the Dyck and Motzkin triangles are constructed for various assignments of multiplicities to the arrows of these triangles. The possibility to build such a function provided that the generating function for paths that end on the axis is a priori unknown is analyzed. Asymptotic estimates for the number of paths are obtained for large values of the path length.

Article
Bezrukavnikov R., Finkelberg M. V. Moscow Mathematical Journal. 2008. Vol. 8. No. 1. P. 39-72.
Article
Esterov A. I. Moscow Mathematical Journal. 2008. No. 3. P. 433-442.