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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

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

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

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

Combinatorics of Bousquet-Mélou-Schaeffer numbers in the light of topological recursionAug 12 2019In this paper we prove, in a purely combinatorial way, a structural quasi-polynomiality property for the Bousquet-M\'elou-Schaeffer numbers. Conjecturally, this property should follow from the Chekhov-Eynard-Orantin topological recursion for these numbers ... 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

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.

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

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

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.

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

The twisting procedureOct 06 2018Feb 28 2019This 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

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

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

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

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

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

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

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

Normal forms of dispersive scalar Poisson brackets with two independent variablesJul 12 2017We classify the dispersive Poisson brackets with one dependent variable and two independent variables, with leading order of hydrodynamic type, up to Miura transformations. We show that, in contrast to the case of a single independent variable for which ... More

Poisson cohomology of scalar multidimensional Dubrovin-Novikov bracketsDec 17 2015Dec 12 2016We 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

Buryak-Okounkov formula for the n-point function and a new proof of the Witten conjectureFeb 08 2019Mar 14 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

Ground states of Nicolai and $\mathbb{Z}_2$ Nicolai modelsAug 08 2018We derive explicit recursions for the ground state generating functions of the one-dimensional Nicolai model and $\mathbb{Z}_2$ Nicolai model. Both are examples of lattice models with $\mathcal{N}=2$ supersymmetry. The relations that we obtain for the ... 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

Loop equations and a proof of Zvonkine's $qr$-ELSV formulaMay 11 2019We prove the 2006 Zvonkine conjecture that expresses Hurwitznumbers with completed cycles in terms of intersection numbers with the Chiodo classes via the so-called $r$-ELSV formula, as well as its orbifold generalization, the $qr$-ELSV formula, proposed ... 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

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 $g=0$.

Loop equations and a proof of Zvonkine's $qr$-ELSV formulaMay 11 2019Aug 02 2019We prove the 2006 Zvonkine conjecture that expresses Hurwitz numbers with completed cycles in terms of intersection numbers with the Chiodo classes via the so-called $r$-ELSV formula, as well as its orbifold generalization, the $qr$-ELSV formula, proposed ... 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

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

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

Loop equations and a proof of Zvonkine's $qr$-ELSV formulaMay 11 2019May 21 2019We prove the 2006 Zvonkine conjecture that expresses Hurwitz numbers with completed cycles in terms of intersection numbers with the Chiodo classes via the so-called $r$-ELSV formula, as well as its orbifold generalization, the $qr$-ELSV formula, proposed ... 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

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

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

Combinatorial structure of colored HOMFLY-PT polynomials for torus knotsDec 22 2017Mar 05 2018We rewrite the (extended) Ooguri-Vafa partition function for colored HOMFLY-PT polynomials for torus knots in terms of the free-fermion (semi-infinite wedge) formalism, making it very similar to the generating function for double Hurwitz numbers. This ... More

Cut-and-join equation for monotone Hurwitz numbers revisitedJul 11 2018Nov 15 2018We give a new proof of the cut-and-join equation for the monotone Hurwitz numbers, derived first by Goulden, Guay-Paquet, and Novak. Our proof in particular uses a combinatorial technique developed by Han. The main interest in this particular equation ... 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

Dubrovin's superpotential as a global spectral curveSep 23 2015Dec 25 2016We 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

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

Primary invariants of Hurwitz Frobenius manifoldsMay 24 2016Dec 25 2016Hurwitz spaces parameterizing covers of the Riemann sphere can be equipped with a Frobenius structure. In this review, we recall the construction of such Hurwitz Frobenius manifolds as well as the correspondence between semisimple Frobenius manifolds ... 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.

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

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

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

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

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

Inverse shadowing and related measuresJul 15 2019We study various weaker forms of inverse shadowing property for discrete dynamical systems on a smooth compact manifold. First, we introduce the so-called Ergodic Inverse Shadowing property (Birhhoff averages of continuous functions along the exact trajectory ... 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

A compactification and the Euler characteristic of the spaces of real meromorphic functionsFeb 07 2002For any connected component $H_0$ of the space of real meromorphic functions we build a compactification $N(H_0)$ of the space $H_0$. Then we express the Euler characteristics of the spaces $H_0$ and $N(H_0)$ in terms of topological invariants of functions ... More

A remark on deformations of Hurwitz Frobenius manifoldsDec 27 2009In this note we use the formalism of multi-KP hierarchies in order to give some general formulas for infinitesimal deformations of solutions of the Darboux-Egoroff system. As an application, we explain how Shramchenko's deformations of Frobenius manifold ... More

On the Markov inequality in the $L_2$-norm with the Gegenbauer weightJan 26 2017Let $w_{\lambda}(t) := (1-t^2)^{\lambda-1/2}$, where $\lambda > -\frac{1}{2}$, be the Gegenbauer weight function, let $\|\cdot\|_{w_{\lambda}}$ be the associated $L_2$-norm, $$ \|f\|_{w_{\lambda}} = \left\{\int_{-1}^1 |f(x)|^2 w_{\lambda}(x)\,dx\right\}^{1/2}\,, ... More

Combinatorics of binomial decompositions of the simplest Hodge integralsOct 31 2003We reduce the calculation of the simplest Hodge integrals to some sums over decorated trees. Since Hodge integrals are already calculated, this gives a proof of a rather interesting combinatorial theorem and a new representation of Bernoulli numbers.

Intersections in genus 3 and the Boussinesq hierarchyJul 24 2003In this note we prove that the enlarged Witten's conjecture is true in the case of the Boussinesq hierarchy for correlators in genus 3 with descendants only at one point.

A new proof of Faber's intersection number conjectureDec 27 2009We 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 ... More

Markov $L_2$-inequality with the Laguerre weightMay 10 2017Let $w_\alpha(t) := t^{\alpha}\,e^{-t}$, where $\alpha > -1$, be the Laguerre weight function, and let $\|\cdot\|_{w_\alpha}$ be the associated $L_2$-norm, $$ \|f\|_{w_\alpha} = \left\{\int_{0}^{\infty} |f(x)|^2 w_\alpha(x)\,dx\right\}^{1/2}\,. $$ By ... More

Intersection numbers with Witten's top Chern classJan 04 2006Witten's top Chern class is a particular cohomology class on the moduli space of Riemann surfaces endowed with r-spin structures. It plays a key role in Witten's conjecture relating to the intersection theory on these moduli spaces. Our first goal is ... More

Belorousski-Pandharipande relation in dGBV algebrasJul 05 2005Mar 18 2006We prove that the genus expansion of solutions of the WDVV equation constructed from dGBV algebras satisfy the differential equation determined by the Belorousski-Pandharipande relation in cohomology of the moduli space of curves $\bar{\mathcal{M}}_{2,3}$. ... More

From Zwiebach invariants to Getzler relationJun 02 2005Apr 02 2006We introduce the notion of Zwiebach invariants that generalize Gromov-Witten invariants and homotopical algebra structures. We outline the induction procedure that induces the structure of Zwiebach on the subbicomplex, that gives the structure of Gromov-Witten ... More

On the $L_2$ Markov Inequality with Laguerre WeightMay 09 2016Let $w_{\alpha}(t)=t^{\alpha}\,e^{-t}$, $\alpha>-1$, be the Laguerre weight function, and $|\cdot|_{w_\alpha}$ denote the associated $L_2$-norm, i.e., $$ | f|_{w_\alpha}:=\Big(\int_{0}^{\infty}w_{\alpha}(t)| f(t)|^2\,dt\Big)^{1/2}. $$ Denote by ${\cal ... More

Some relations for one-part double Hurwitz numbersOct 05 2003In this very short note we slightly generalize some relations for one-part double Hurwitz numbers from math.AG/0209282.

On Markov-Duffin-Schaeffer inequalities with a majorant. IIOct 29 2012We are continuing out studies of the so-called Markov inequalities with a majorant. Inequalities of this type provide a bound for the $k$-th derivative of an algebraic polynomial when the latter is bounded by a certain curved majorant $\mu$. A conjecture ... More

On almost everywhere convergence of orthogonal spline projections with arbitrary knotsAug 22 2013Nov 26 2013The main result of this paper is a proof that, for any $f \in L_1[a,b]$, a sequence of its orthogonal projections $(P_{\Delta_n}(f))$ onto splines of order $k$ with arbitrary knots $\Delta_n$, converges almost everywhere provided that the mesh diameter ... 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

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

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

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

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

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.

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

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

Completeness theorem for the system of eigenfunctions of the complex Schrödinger operator $L=-d^2/dx^2+cx^{2/3}$Mar 25 2019We prove the completeness of the system of eigenfunctions of the complex Schr\"odinger operator $L=-d^2/dx^2+cx^{2/3}$ on the semiaxis in $L_2(0,+\infty)$ with Dirichlet boundary conditions for all $c$: $|\arg c|<\pi/2+\theta_0$, where $\theta_0\in(\pi/10,\pi/9)$ ... More

RF heating efficiency of the terahertz superconducting hot-electron bolometerApr 21 2014Apr 30 2014We report results of the numerical solution by the Euler method of the system of heat balance equations written in recurrent form for the superconducting hot-electron bolometer (HEB) embedded in an electrical circuit. By taking into account the dependence ... More

Majorana finite frequency nonequilibrium quantum noiseApr 11 2019Quantum finite frequency noise is one of fundamental aspects in quantum measurements performed during quantum information processing where currently Majorana bound states offer an efficient way to implement fault-tolerant quantum computation via topological ... More