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The bi-Hamiltonian cohomology of a scalar Poisson pencilMay 14 2015Jan 27 2016We compute the bi-Hamiltonian cohomology of an arbitrary dispersionless Poisson pencil in a single dependent variable using a spectral sequence method. As in the KdV case, we obtain that $BH^p_d(\hat{F}, d_1,d_2)$ is isomorphic to $\mathbb{R}$ for $(p,d)=(0,0)$, ... More

Hypercommutative operad as a homotopy quotient of BVJun 17 2012Dec 04 2012We give an explicit formula for a quasi-isomorphism between the operads Hycomm (the homology of the moduli space of stable genus 0 curves) and BV/$\Delta$ (the homotopy quotient of Batalin-Vilkovisky operad by the BV-operator). In other words we derive ... More

Special cases of the orbifold version of Zvonkine's $r$-ELSV formulaMay 30 2017We prove the orbifold version of Zvonkine's $r$-ELSV formula in two special cases: the case of $r=2$ (complete $3$-cycles) for any genus $g\geq 0$ and the case of any $r\geq 1$ for genus $g=0$.

Towards an orbifold generalization of Zvonkine's $r$-ELSV formulaMar 20 2017We perform a key step towards the proof of Zvonkine's conjectural $r$-ELSV formula that relates Hurwitz numbers with completed $(r+1)$-cycles to the geometry of the moduli spaces of the $r$-spin structures on curves: we prove the quasi-polynomiality property ... More

Changes of variables in ELSV-type formulasFeb 21 2006Jun 25 2007In [5] I.P. Goulden, D.M. Jackson, and R. Vakil formulated a conjecture relating certain Hurwitz numbers (enumerating ramified coverings of the sphere) to the intersection theory on a conjectural Picard variety. We are going to use their formula to study ... More

A group action on Losev-Manin cohomological field theoriesSep 04 2009We discuss an analog of the Givental group action for the space of solutions of the commutativity equation. There are equivalent formulations in terms of cohomology classes on the Losev-Manin compactifications of genus 0 moduli spaces; in terms of linear ... More

Blobbed topological recursion: properties and applicationsFeb 03 2015Feb 18 2015We study the set of solutions $(\omega_{g,n})_{g \geq 0,n \geq 1}$ of abstract loop equations. We prove that $\omega_{g,n}$ is determined by its purely holomorphic part: this results in a decomposition that we call "blobbed topological recursion". This ... More

Givental Action and Trivialisation of Circle ActionApr 11 2013Jun 09 2014In this paper, we show that the Givental group action on genus zero cohomological field theories, also known as formal Frobenius manifolds or hypercommutative algebras, naturally arises in the deformation theory of Batalin--Vilkovisky algebras. We prove ... More

Toric varieties of Loday's associahedra and noncommutative cohomological field theoriesOct 12 2015Oct 24 2018We introduce and study several new topological operads that should be regarded as nonsymmetric analogues of the operads of little 2-disks, framed little 2-disks, and Deligne-Mumford compactifications of moduli spaces of genus zero curves with marked points. ... More

The spectral curve and the Schroedinger equation of double Hurwitz numbers and higher spin structuresJan 23 2013Jun 04 2013We derive the spectral curves for $q$-part double Hurwitz numbers, $r$-spin simple Hurwitz numbers, and arbitrary combinations of these cases, from the analysis of the unstable (0,1)-geometry. We quantize this family of spectral curves and obtain the ... More

Noncommutative $\overline{M}_{0,n+1}$Oct 12 2015We introduce and study noncommutative analogues of the Deligne-Mumford compactifications of moduli spaces of genus zero curves with marked points which exhibit all the remarkable algebraic and geometric features that the Deligne-Mumford compactifications ... More

Quasi-polynomiality of monotone orbifold Hurwitz numbers and Grothendieck's dessins d'enfantsOct 26 2016We prove quasi-polynomiality for monotone and strictly monotone orbifold Hurwitz numbers. The second enumerative problem is also known as enumeration of a special kind of Grothendieck's dessins d'enfants or $r$-hypermaps. These statements answer positively ... More

Poisson cohomology of scalar multidimensional Dubrovin-Novikov bracketsDec 17 2015We compute the Poisson cohomology of a scalar Poisson bracket of Dubrovin-Novikov type with $D$ independent variables. We find that the second and third cohomology groups are generically non-vanishing in $D>1$. Hence, in contrast with the $D=1$ case, ... More

Bihamiltonian cohomology of KdV bracketsJun 21 2014Mar 13 2015Using spectral sequences techniques we compute the bihamiltonian cohomology groups of the pencil of Poisson brackets of dispersionless KdV hierarchy. In particular this proves a conjecture of Liu and Zhang about the vanishing of such cohomology groups. ... More

Givental group action on Topological Field Theories and homotopy Batalin--Vilkovisky algebrasDec 06 2011Jan 14 2013In this paper, we initiate the study of the Givental group action on Cohomological Field Theories in terms of homotopical algebra. More precisely, we show that the stabilisers of Topological Field Theories in genus 0 (respectively in genera 0 and 1) are ... More

Buryak-Okounkov formula for the n-point function and a new proof of the Witten conjectureFeb 08 2019We identify the formulas of Buryak and Okounkov for the n-point functions of the intersection numbers of psi-classes on the moduli spaces of curves. This allows us to combine the earlier known results and this one into a principally new proof of the famous ... More

Pre-Lie deformation theoryFeb 11 2015Mar 27 2016In this paper, we develop the deformation theory controlled by pre-Lie algebras; the main tool is a new integration theory for pre-Lie algebras. The main field of application lies in homotopy algebra structures over a Koszul operad; in this case, we provide ... More

The twisting procedureOct 06 2018This paper provides a conceptual study of the twisting procedure, which amounts to create functorially new differential graded Lie algebras, associative algebras or operads (as well as their homotopy versions) from a Maurer--Cartan element. On the way, ... More

Tautological relations and the r-spin Witten conjectureDec 18 2006Jan 21 2009In a series of two preprints, Y.-P. Lee studied relations satisfied by all formal Gromov-Witten potentials, as defined by A. Givental. He called them "universal relations" and studied their connection with tautological relations in the cohomology ring ... More

De Rham cohomology and homotopy Frobenius manifoldsMar 22 2012May 25 2012We endow the de Rham cohomology of any Poisson or Jacobi manifold with a natural homotopy Frobenius manifold structure. This result relies on a minimal model theorem for multicomplexes and a new kind of a Hodge degeneration condition.

Central invariants revisitedNov 28 2016We give a new proof of the statement of Dubrovin-Liu-Zhang that the Miura-equivalence classes of the deformations of semi-simple bi-Hamiltonian structures of hydrodynamic type are parametrized by the so-called central invariants.

Quasi-polynomiality of monotone orbifold Hurwitz numbers and Grothendieck's dessins d'enfantsOct 26 2016Nov 17 2016We prove quasi-polynomiality for monotone and strictly monotone orbifold Hurwitz numbers. The second enumerative problem is also known as enumeration of a special kind of Grothendieck's dessins d'enfants or $r$-hypermaps. These statements answer positively ... More

Deformations of semisimple Poisson pencils of hydrodynamic type are unobstructedJan 18 2015Sep 21 2016We prove that the bihamiltonian cohomology of a semisimple pencil of Poisson brackets of hydrodynamic type vanishes for almost all degrees. This implies the existence of a full dispersive deformation of a semisimple bihamiltonian structure of hydrodynamic ... More

Half-spin tautological relations and Faber's proportionalities of kappa classesFeb 07 2019We employ the $1/2$-spin tautological relations to provide a particular combinatorial identity. We show that this identity is a statement equivalent to Faber's formula for proportionalities of kappa-classes on $\mathcal{M}_g$, $g\geq 2$. We then prove ... More

Polynomiality of orbifold Hurwitz numbers, spectral curve, and a new proof of the Johnson-Pandharipande-Tseng formulaApr 28 2015In this paper we present an example of a derivation of an ELSV-type formula using the methods of topological recursion. Namely, for orbifold Hurwitz numbers we give a new proof of the spectral curve topological recursion, in the sense of Chekhov, Eynard, ... More

Givental symmetries of Frobenius manifolds and multi-component KP tau-functionsMay 06 2009We establish a link between two different constructions of the action of the twisted loop group on the space of Frobenius structures. The first construction (due to Givental) describes the action of the twisted loop group on the partition functions of ... More

The tautological ring of $\mathcal{M}_{g,n}$ via Pandharipande-Pixton-Zvonkine $r$-spin relationsMar 02 2017We use relations in the tautological ring of the moduli spaces $\overline{\mathcal{M}}_{g,n}$ derived by Pandharipande, Pixton, and Zvonkine from the Givental formula for the $r$-spin Witten class in order to obtain some restrictions on the dimensions ... More

Half-spin tautological relations and Faber's proportionalities of kappa classesFeb 07 2019Feb 11 2019We employ the $1/2$-spin tautological relations to provide a particular combinatorial identity. We show that this identity is a statement equivalent to Faber's formula for proportionalities of kappa-classes on $\mathcal{M}_g$, $g\geq 2$. We then prove ... More

Chiodo formulas for the r-th roots and topological recursionApr 28 2015We analyze Chiodo's formulas for the Chern classes related to the r-th roots of the suitably twisted integer powers of the canonical class on the moduli space of curves. The intersection numbers of these classes with psi-classes are reproduced via the ... More

Chiodo formulas for the r-th roots and topological recursionApr 28 2015Nov 11 2016We analyze Chiodo's formulas for the Chern classes related to the r-th roots of the suitably twisted integer powers of the canonical class on the moduli space of curves. The intersection numbers of these classes with psi-classes are reproduced via the ... More

Towards Lax formulation of integrable hierarchies of topological typeJan 18 2012To each partition function of cohomological field theory one can associate an Hamiltonian integrable hierarchy of topological type. The Givental group acts on such partition functions and consequently on the associated integrable hierarchies. We consider ... More

Jet multiplicities as the QGP thermometerSep 29 2005Feb 10 2006It is proposed to use the energy behavior of mean multiplicities of jets propagating in a nuclear medium as the thermometer of this medium during the collision phases. The qualitative effects are demonstrated in the framework of the fixed coupling QCD ... More

On deformations of quasi-Miura transformations and the Dubrovin-Zhang bracketApr 14 2011In 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 ... More

Dubrovin's superpotential as a global spectral curveSep 23 2015We 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 ... More

Primary invariants of Hurwitz Frobenius manifoldsMay 24 2016It is a classical result that flat coordinates for a Hurwitz Frobenius manifold can be obtained as periods of a differential along cycles on the domain curve. We generalise this construction to primary invariants of the Hurwitz Frobenius manifolds. We ... More

Quantum spectral curve for the Gromov-Witten theory of the complex projective lineDec 18 2013Feb 11 2014We construct the quantum curve for the Gromov-Witten theory of the complex projective line.

Polynomiality of Hurwitz numbers, Bouchard-Mariño conjecture, and a new proof of the ELSV formulaJul 17 2013Dec 31 2013In this paper we give a new proof of the ELSV formula. First, we refine an argument of Okounkov and Pandharipande in order to prove (quasi-)polynomiality of Hurwitz numbers without using the ELSV formula (the only way to do that before used the ELSV formula). ... More

BCOV theory via Givental group action on cohomological field theoriesOct 03 2008In a previous paper (arXiv:0704.1001), Losev, me, and Shneiberg constructed a full descendant potential associated to an arbitrary cyclic Hodge dGBV algebra. This contruction extended the construction of Barannikov and Kontsevich of solution of the WDVV ... More

A definition of descendants at one point in graph calculusJul 05 2005Feb 25 2006We study the genus expansion of Barannikov-Kontsevich solutions of the WDVV equation. In terms of the related graph calculus we give a definition of descendants at one point and prove that this definition satisfies the topological recursion relations ... More

Geometry of meromorphic functions and intersections on moduli spaces of curvesSep 21 2002Mar 18 2006In this paper we study relations between intersection numbers on moduli spaces of curves and Hurwitz numbers. First, we prove two formulas expressing Hurwitz numbers of (generalized) polynomials via intersections on moduli spaces of curves. Then we show, ... More

On the structure of Goulden-Jackson-Vakil formulaOct 03 2008We study the structure of the Goulden-Jackson-Vakil formula that relates Hurwitz numbers to some conjectural "intersection numbers" on a conjectural family of varieties $X_{g,n}$ of dimension $4g-3+n$. We give explicit formulas for the properly arranged ... More

Landau--Kolmogorov inequality revisitedOct 29 2012The Landau-Kolmogorov problem consists of finding the upper bound $M_k$ for the norm of intermediate derivative $|f^{(k)}|$, when the bounds $|f| \le M_0$ and $|f^{(n)}| \le M_n$, for the norms of the function and of its higher derivative, are given. ... More

Physical conditions in nearby active galaxies correlated with ultra-high-energy cosmic rays detected by the Pierre Auger ObservatoryAug 04 2008Mar 29 2010We analyze the active-galaxy correlation reported in 2007 by the Pierre Auger Collaboration. The signal diminishes if the correlation-function approach (counting all "source-event" pairs and not only "nearest neighbours") is used, suggesting that the ... More

Zeroes of the spectral density of the periodic Schroedinger operator with Wigner-von Neumann potentialFeb 25 2011We consider the Schroedinger operator L_{\alpha} on the half-line with a periodic background potential and the Wigner-von Neumann potential of Coulomb type: csin(2\omega x+d)/(x+1). It is known that the continuous spectrum of the operator L_{\alpha} has ... More

Generalized Zero Range Potentials and Multi-Channel Electron-Molecule ScatteringSep 09 2002A multi-channel scattering problem is studied from a point of view of integral equations system. The system appears while natural one-particle wave function equation of the electron under action of a potential with non-intersecting ranges is considered. ... More

Approximate Differentiability of Mappings of Carnot-Carathéodory SpacesJun 22 2012Feb 05 2013We study the approximate differentiability of measurable mappings of Carnot--Carath\'eodory spaces. We show that the approximate differentiability almost everywhere is equivalent to the approximate differentiability along the basic horizontal vector fields ... More

Study of internal wave breaking dependence on stratificationJun 26 2012Mixing effect in a stratified fluid is considered and examined. Euler equations for incompressible fluid stratified by a gravity field are applied to state a mathematical problem and describe the effect. It is found out that a system of Euler equations ... More

Partial hyperbolicity and central shadowingDec 19 2011Feb 11 2012We study shadowing property for a partially hyperbolic diffeomorphism $f$. It is proved that if $f$ is dynamically coherent then any pseudotrajectory can be shadowed by a pseudotrajectory with "jumps" along the central foliation. The proof is based on ... More

On uniquely k-determined permutationsOct 10 2006There are several approaches to study occurrences of consecutive patterns in permutations such as the inclusion-exclusion method, the tree representations of permutations, the spectral approach and others. We propose yet another approach to study occurrences ... More

On Banach spaces of sequences and free linear logic exponential modalitySep 13 2015We introduce a category of vector spaces modelling full propositional linear logic, similar to probabilistic coherence spaces and to Koethe sequences spaces. Its objects are {\it rigged sequences spaces}, Banach spaces of sequences, with norms defined ... More

Waiting time to (and duration of) parapatric speciationJun 05 2000Using a weak migration and weak mutation approximation, I study the average waiting time to and the average duration of parapatric speciation. The description of reproductive isolation used is based on the classical Dobzhansky model and its recently proposed ... More

Who creates the Time: Nature or Human?Jul 16 2014Feb 03 2015The paper defends the thesis that analysis of time meaning in a context of philosophy of physical and mathematical natural sciences and philosophical anthropology allows to clear basis of human being and to construct special model of general understanding ... More

Smale Horseshoe and Grazing Bifurcation in Impact SystemsJun 21 2011Bifurcations of dynamical systems, described by a second order differential equations and by an impact condition are studied. It is shown that the variation of parameters when the number of impacts of a periodic solution increases, leads to the occurrence ... More

On identities of indicator burnside semigroupsSep 13 2010A semigroup variety is said to be a Rees-Sushkevich variety if it is contained in a periodic variety generated by 0-simple semigroups. S. I. Kublanovsky has proven that a variety V is a Rees-Sushkevich variety if and only it does not contain any of special ... More

Apéry constants of homogeneous varietiesApr 15 2016For Fano manifolds we define Ap\'ery constants and Ap\'ery class as particular limits of ratios of coefficients of solutions of the quantum differential equation. We do numerical computations in case of homogeneous varieties. These numbers are identified ... More

On classification of groups of points on abelian varieties over finite fieldsJan 08 2014Dec 22 2015In this paper we improve our previous results on classification of groups of points on abelian varieties over finite fields. The classification is given in terms of the Weil polynomial of abelian varieties in a given $k$-isogeny class.

Geometric theta-lifting for the dual pair SO_{2m}, Sp_{2n}Jan 05 2007Jun 29 2010Let X be a smooth projective curve over an algebraically closed field of characteristic >2. Consider the dual pair H=SO_{2m}, G=Sp_{2n} over X with H split. Write Bun_G and Bun_H for the stacks of G-torsors and H-torsors on X. The theta-kernel on Bun_G\times ... More

Local geometrised Rankin-Selberg method for GL(n)May 05 1999Aug 30 2001Following Laumon [10], to a nonramified $\ell$-adic local system $E$ of rank $n$ on a curve $X$ one associates a complex of $\ell$-adic sheaves $_n{\cal K}_E$ on the moduli stack of rank $n$ vector bundles on $X$ with a section, which is cuspidal and ... More

Geometric Whittaker models and Eisenstein series for Mp_2Nov 07 2012Nov 21 2012Let X be a smooth projective curve over an algebraically closed field of characteristic >2. Let Bun_{Mp_2} be the stack of metaplectic bundles on X of rank 2. In this paper we study the derived category of genuine l-adic sheaves on Bun_{Mp_2} in the framework ... More

Tendencies, Dead-ends, and Promising Ways. From Interface Ideas to New ProgramsJan 08 2014The mechanism of communication between users and devices is called interface. From time to time changes in interface significantly improve our work with computers even without any serious changes in programs themselves. Main ideas in PCs interface were ... More

Deformations of G2-structures with torsionAug 11 2011Aug 12 2011We consider non-infinitesimal deformations of G2-structures on 7-dimensional manifolds and derive an exact expression for the torsion of the deformed G2-structure. We then specialize to a case when the deformation is defined by a vector v and we explicitly ... More

Moduli spaces of G2 manifoldsNov 11 2009Jun 16 2010This paper is a review of current developments in the study of moduli spaces of G2 manifolds. G2 manifolds are 7-dimensional manifolds with the exceptional holonomy group G2. Although they are odd-dimensional, in many ways they can be considered as an ... More

The classification of certain linked $3$-manifolds in $6$-spaceAug 18 2014Sep 22 2015We work entirely in the smooth category. An embedding $f:(S^2\times S^1)\sqcup S^3\rightarrow {\mathbb R}^6$ is {\it Brunnian}, if the restriction of $f$ to each component is isotopic to the standard embedding. For each triple of integers $k,m,n$ such ... More

Smooth shifts along flowsJun 24 2001Jul 07 2004Let $\Phi$ be a flow on a smooth, compact, finite-dimensional manifold $M$. Consider the subsets $E(\Phi)$ and $D(\Phi)$ of $C^{\infty}(M,M)$ consisting of smoothh mappings and diffeomorphisms (respectively) of $M$ preserving the foliation of the flow ... More

On three dimensional stellar manifoldsNov 23 2005Dec 15 2005It is well known that a three dimensional (closed, connected and compact) manifold is obtained by identifying boundary faces from a stellar ball a*S. The study of S/~, two dimensional stellar sphere S with 2-simplexes identified in pairs leads us to the ... More

On a stellar structure for a stellar manifoldNov 14 2002Dec 20 2002It is well known that a compact two dimensional surface is homeomorphic to a polygon with the edges identified in pairs. This paper not only presents a new proof of this statement but also generalizes it for any connected n-dimensional stellar manifold ... More

A new construction of the semi-infinite BGG resolutionMay 29 1996Jun 03 1996We introduce the techniques of semiregular bimodules over a Lie algebra with respect to a Lie subalgebra. Using this techniques in the case of affine Lie algebras we introduce twisting functors on the categories of modules. These functors are enumerated ... More

Superconformal Calogero models as a gauged matrix mechanicsFeb 15 2010We present basics of the gauged superfield approach to constructing N-superconformal multi-particle Calogero-type systems developed in arXiv:0812.4276, arXiv:0905.4951 and arXiv:0912.3508. This approach is illustrated by the multi-particle systems possessing ... More

On parabolic Whittaker functionsNov 18 2010We derive a Mellin-Barnes integral representation for solution to generalized (parabolic) quantum Toda lattice introduced in \cite{GLO}, which presumably describes the $(S^1\times U_N)$-equivariant Gromov-Witten invariants of Grassmann variety.

Exclusive meson production at HERMESJul 08 2016The data were accumulated with the HERMES forward spectrometer using the 27.6 GeV longitudinally polarized electron or positron beam of HERA. Exclusive electroproduction of $\omega$ mesons on unpolarized hydrogen and deuterium targets is studied in the ... More

On a necessary and sufficient cyclicity condition for a quadrilateralOct 08 2004A convex quadrilateral with sides a,b,c,d, and diagonals p,q is cyclic iff abp-bcq+cdp-daq=0. This condition, in spite of its simplicity, appears to be unnoted and unexpectedly proof-resilient. We employ advanced methods of computer algebra and nonlinear ... More

Quasi-Periodic X-ray Oscillations in the Source Sco X-1Oct 24 2002The RXTE observations of Scorpius X-1 in 1996-1999 are presented. The properties of its quasi-periodic X-ray oscillations are studied in detail. The results obtained are used for analysis in terms of the transition-layer model (TLM) and the relativistic-precession ... More

On financial applications of the two-parameter Poisson-Dirichlet distributionJan 08 2015Jul 08 2015Capital distribution curve is defined as log-log plot of normalized stock capitalizations ranked in descending order. The curve displays remarkable stability over periods of time. Theory of exchangeable distributions on set partitions, developed for purposes ... More

Quasi-exact solvability and intertwining relationsOct 06 2004Oct 11 2004We emphasize intertwining relations as a universal tool in constructing one-dimensional quasi-exactly solvable operators and offer their possible generalization to the multidimensional case. Considered examples include all quasi-exactly solvable operators ... More

Matrix equations and trilinear commutation relationsOct 23 2007Dec 24 2007In this paper we discuss a general algebraic approach to treating static equations of matrix models with a mass-like term. In this approach the equations of motions are considered as consequence of parafermi-like trilinear commutation relations. In this ... More

Holder Shadowing on Finite IntervalsJun 20 2011Dec 16 2013For any $\theta, \omega > 1/2$ we prove that, if any $d$-pseudotrajectory of length $\sim 1/d^{\omega}$ of a diffeomorphism $f\in C^2$ can be $d^{\theta}$-shadowed by an exact trajectory, then $f$ is structurally stable. Previously it was conjectured ... More

Gravitational oscillations in multidimensional anisotropic model with cosmological constant and their contributions into the energy of vacuumDec 26 2011Were studied classical oscillations of background metric in the multidimensional anisotropic model of Kazner in the de-Sitter stage. Obtained dependence of fluctuations on dimension of space-time with infinite expansion. Stability of the model could be ... More

About evaluation of radius of compactification and vacuum energy in the Randall-Sundrum modelSep 17 2011Using the base of the RS-model by introducing effective terms in common five-dimensional action an equation for radius of fifth dimension through cosmological constant and Planck mass was defined. Such a model have not a RS limit cause of the dependence ... More

Orthogonal Cherenkov sound in spin-orbit coupled systemsJun 17 2015Conventionally the Cherenkov sound is governed by {\it orbital} degrees of freedom and is excited by {\it supersonic} particles. Additionally, it usually has a {\it forward} nature with a conic geometry known as the Cherenkov cone whose axis is oriented ... More

Linear logic with idempotent exponential modalities: a noteJul 22 2014In this note we discuss a variant of linear logic with idempotent exponential modalities. We propose a sequent calculus system and discuss its semantics. We also give a concrete relational model for this calculus.

Generalization of Arnold-Viro inequalities for real singular algebraic curvesJun 03 1997The Arnold inequalities characterizing the topology of non-singular plane real algebraic curves and the generalization of these inequalities for nodal curves by Viro are extended in this paper for the curves whose singularities have non-degenerated Milnor ... More

Extraction of parton distributions and $α_s$ from DIS data within the Bayesian treatment of systematic errorsNov 02 1996We have performed the NLO QCD global fit of BCDMS, NMC, H1 and ZEUS data with full account of point-to-point correlations using the Bayesian approach to the treatment of systematic errors. Parton distributions in the proton associated with experimental ... More

Motivic Donaldson-Thomas invariants and Kac conjectureMar 10 2011Mar 22 2011We derive some combinatorial consequences from the positivity of Donaldson-Thomas invariants for symmetric quivers conjectured by Kontsevich and Soibelman and proved recently by Efimov. These results are used to prove the Kac conjecture for quivers having ... More

On the multiplicities of the irreducible highest weight modules over Kac-Moody algebrasSep 13 2006Oct 02 2006We prove that the weight multiplicities of the integrable irreducible highest weight module over the Kac-Moody algebra associated to a quiver are equal to the root multiplicities of the Kac-Moody algebra associated to some enlarged quiver. To do this, ... More

Stringy motives of symmetric productsAug 13 2006Given a complex smooth algebraic variety X, we compute the generating function of the stringy motives of its symmetric powers as a function of motive of X. In dimension two we recover the Goettsche formulas for Hilbert schemes. We use the formalism of ... More

Classification of semistable sheaves on a rational curve with one nodeOct 06 2004Oct 02 2006We classify (semi)stable sheaves on a rational curve with one node. The results are based on the classification of indecomposable torsion-free sheaves due to Drozd and Greuel "Tame and wild projective curves and classification of vector bundles", where ... More

Density and metallicity of the Milky-Way circumgalactic gasJul 19 2016The halo of the Milky-Way circumgalactic gas extends up to the virial radius of the Galaxy, ~250 kpc. The halo properties may be deduced from X-ray spectroscopic observations and from studies of the ram-pressure stripping of satellite dwarf galaxies. ... More

Trace formulas for a class of Jacobi operatorsOct 16 2013In this paper we study a class of Jacobi operators, such that each operator is generated by the unit Borel measure with a support consisting of a finite number of intervals on the real line R and a finite number of points in C, located outside the convex ... More

Zeroes of the spectral density of discrete Schroedinger operator with Wigner-von Neumann potentialMar 08 2012We consider a discrete Schroedinger operator whose potential is the sum of a Wigner-von Neumann term and a summable term. The essential spectrum of this operator equals to the interval [-2,2]. Inside this interval, there are two critical points where ... More

From scale invariance to Lorentz symmetryMar 19 2014May 28 2014It is shown that a unitary translationally invariant field theory in (1+1) dimensions satisfying isotropic scale invariance, standard assumptions about the spectrum of states and operators and the requirement that signals propagate with finite velocity ... More

Liouville-type theorems for twisted and warped products manifoldsAug 11 2016In the present paper we prove Liouville-type theorems: non-existence theorems for complete twisted and warped products of Riemannian manifolds which generalize and complement similar results for compact manifolds.

Consecutive shifts along orbits of vector fieldsOct 28 2005Let $M$ be a smooth ($C^{\infty}$) manifold, $F_1,...,F_n$ be vector fields on $M$ generating the corresponding flows $\Phi_1,...,\Phi_n$, and $\alpha_1,...,\alpha_{n}:M\to \mathbb{R}$ smooth functions. Define the following map $f:M\to M$ by $$f(x)= \Phi_n ... More

Hyperbolicity and solvability for linear systems on time scalesSep 10 2017Nov 15 2017We believe that the difference between time scale systems and ordinary differential equations is not as big as people use to think. We consider linear operators that correspond to linear dynamic systems on time scales. We study solvability of these operators ... More

Quasi-exactly solvable models as constrained systemsDec 15 2009We discuss a universal algebraic approach to quasi-exactly solvable models which allows us to interpret them as constrained Hamiltonian systems with a finite number of physical states. Using this approach we reproduce well-known two-dimensional Lie-algebraic ... More

On the representation of bent functions by bent rectanglesFeb 04 2005We propose a representation of boolean bent functions by bent rectangles, that is, by special matrices with restrictions on rows and columns. Using this representation, we exhibit new classes of bent functions, give an algorithm to construct bent functions, ... More

Bent RectanglesApr 01 2008Apr 18 2008We study generalized regular bent functions using a representation by bent rectangles, that is, special matrices with restrictions on rows and columns. We describe affine transformations of bent rectangles, propose new biaffine and bilinear constructions, ... More

Path-components of Morse mappings spaces of surfacesOct 18 1999Dec 24 2015Let $M$ be a compact surface and $P$ be a one dimensional manifold without boundary, that is the line $\mathbb{R}^1$ or a circle $S^1$. The classification of path-components of the space of Morse maps from $M$ into $P$ was recently obtained by S. V. Matveev ... More

Space-time as strongly bent plateOct 10 2000Futher development is made of a consept of space-time as multidimensional elastic plate, proposed earlier in [20,21]. General equilibrium equations, including 4-dimensional tangent stress tensor - energy-momentum tensor of matter - are derived. Comparative ... More

Sections of Lie group actions and a theorem by M. NewmanAug 15 2006Dec 24 2015Let $M$ be a smooth finite-dimensional manifold, $G$ be a Lie group, and $\Phi:G \times M \to M$ be a smooth action. Consider the following mapping $\phi: C^{\infty}(M,G) \to C^{\infty}(M,M)$, defined by $\phi(\alpha)(x) = \alpha(x)\cdot x$, for $\alpha\in ... More

Higher topological complexity of Artin type groupsNov 06 2014We calculate the higher topological complexity TC$_s$ for the complements of reflection arrangements, in other words for the pure Artin type groups of all finite complex reflection groups. In order to do that we introduce a simple combinatorial criterion ... More