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Spacing gain and absorption in a simple $\mathcal{PT}$-symmetric model: spectral singularities and ladders of eigenvalues and resonancesAug 18 2019We consider a parity-time ($\mathcal{PT}$-) symmetric waveguide consisting of a localized gain and loss elements separated by a variable distance. The situation is modelled by a Schr\"odiner operator with localized complex $\mathcal{PT}$-symmetric potential. ... More

Asymptotics of the eigenvalues of elliptic systems with fast oscillating coefficientsMay 29 2007We consider singularly perturbed second order elliptic system in the whole space with fast oscillating coefficients. We construct the complete asymptotic expansions for the eigenvalues converging to the isolated ones of the homogenized system, as well ... More

Eigenvalues collision for PT-symmetric waveguideJan 24 2014We consider a model of planar PT-symmetric waveguide and study the phenomenon of the eigenvalues collision under the perturbation of boundary conditions. This phenomenon was discovered numerically in previous works. The main result of this work is an ... More

Asymptotic behaviour of the spectrum of a waveguide with distant perturbationsJun 02 2006May 23 2007We consider the waveguide modelled by a $n$-dimensional infinite tube. The operator we study is the Dirichlet Laplacian perturbed by two distant perturbations. The perturbations are described by arbitrary abstract operators ''localized'' in a certain ... More

Initial length scale estimate for waveguides with some random singular potentialsJul 08 2015In this work we consider three examples of random singular perturbations in multi-dimensional models of waveguides. These perturbations are described by a large potential supported on a set of a small measure, by a compactly supported fast oscillating ... More

On mirrors of elliptically fibered K3 surfacesFeb 13 2017Feb 27 2017We study a two-parameter family of K3 surfaces of (generic) Picard rank $18$ which is mirror to the $18$-dimensional family of elliptically fibered K3 surfaces with a section. Members of this family are given as compactifications of hypersurfaces in three ... More

Homogenization of the planar waveguide with frequently alternating boundary conditionsMay 04 2009We consider Laplacian in a planar strip with Dirichlet boundary condition on the upper boundary and with frequent alternation boundary condition on the lower boundary. The alternation is introduced by the periodic partition of the boundary into small ... More

Asymptotic analysis of exit time for dynamical systems with a single well potentialJun 11 2019We study the exit time from a bounded multi-dimensional domain $\Omega$ of the stochastic process $\mathbf{Y}_\varepsilon=\mathbf{Y}_\varepsilon(t,a)$, $t\geqslant 0$, $a\in \mathcal{A}$, governed by the overdamped Langevin dynamics \begin{equation*} ... More

Distant perturbation asymptotics in window-coupled waveguides. I. The non-threshold caseJun 07 2006We consider a pair of adjacent quantum waveguides, in general of different widths, coupled laterally by a pair of windows in the common boundary, not necessarily of the same length, at a fixed distance. The Hamiltonian is the respective Dirichlet Laplacian. ... More

Creation of spectral bands for a periodic domain with small windowsJul 05 2015We consider a Schroediner operator in a periodic system of strip-like domains coupled by small windows. As the windows close, the domain decouples into an infinite series of identical domains. The operator similar to the original one but on one copy of ... More

Exponential splitting of bound states in a waveguide with a pair of distant windowsDec 04 2003We consider Laplacian in a straight planar strip with Dirichlet boundary which has two Neumann ``windows'' of the same length the centers of which are $2l$ apart, and study the asymptotic behaviour of the discrete spectrum as $l\to\infty$. It is shown ... More

Planar waveguide with "twisted" boundary conditions: small widthDec 08 2011Jan 09 2012We consider a planar waveguide with "twisted" boundary conditions. By twisting we mean a special combination of Dirichlet and Neumann boundary conditions. Assuming that the width of the waveguide goes to zero, we identify the effective (limiting) operator ... More

Gap opening and split band edges in waveguides coupled by a periodic system of small windowsMar 01 2012At the example of two coupled waveguides we construct a periodic second order differential operator acting in a Euclidean domain and having spectral gaps whose edges are attained strictly inside the Brillouin zone. The waveguides are modeled by the Laplacian ... More

Complete asymptotic expansions for eigenvalues of Dirichlet Laplacian in thin three-dimensional rodsOct 20 2009Feb 21 2010We consider Dirichlet Laplacian in a thin curved three-dimensional rod. The rod is finite. Its cross-section is constant and small, and rotates along the reference curve in an arbitrary way. We find a two-parametric set of the eigenvalues of such operator ... More

Generalized operads and their inner cohomomorphismsSep 27 2006Jan 07 2011In this paper we introduce a notion of {\it generalized operad} containing as special cases various kinds of operad--like objects: ordinary, cyclic, modular, properads etc. We then construct inner cohomomorphism objects in their categories (and categories ... More

Asymptotics and Estimates of Degrees of Convergence in Three-Dimensional Boundary Value Problem with Frequent Interchange of Boundary ConditionsSep 12 2002We consider a singular perturbed eigenvalue problem for Laplace operator in a cylinder with frequent interchange of type of boundary condition on a lateral surface. These boundary conditions are prescribed by partition of lateral surface in a great number ... More

On spectrum of a periodic operator with a small localized perturbationSep 07 2006Sep 08 2006We study the spectrum of a periodic self-adjoint operator on the axis perturbed by a small localized nonself-adjoint operator. It is shown that the continuous spectrum is independent of the perturbation, the residual spectrum is empty, and the point spectrum ... More

Gap opening in two-dimensional periodic systemsOct 20 2018We present a new method of gap control in two-dimensional periodic systems with the perturbation consisting of a second-order differential operator and a family of narrow potential `walls' separating the period cells in on direction. We show that under ... More

The Pfaffian-Grassmannian derived equivalenceAug 15 2006Sep 25 2006We argue that there exists a derived equivalence between Calabi-Yau threefolds obtained by taking dual hyperplane sections (of the appropriate codimension) of the Grassmannian G(2, 7) and the Pfaffian Pf(7). The existence of such an equivalence has been ... More

On a model boundary value problem for Laplacian with frequently alternating type of boundary conditionAug 06 2002Mar 22 2003Model two-dimensional singular perturbed eigenvalue problem for Laplacian with frequently alternating type of boundary condition is considered. Complete two-parametrical asymptotics for the eigenelements are constructed.

Exponential parameterization of the neutrino mixing matrix - comparative analysis with different data sets and CP violationOct 27 2016The exponential parameterization of Pontecorvo-Maki-Nakagawa-Sakata mixing matrix for neutrino is used for comparative analysis of different neutrino mixing data. The UPMNS matrix is considered as the element of the SU(3) group and the second order matrix ... More

Asymptotics and Estimates for Eigenelements of Laplacian with Frequent Nonperiodic Interchange of Boundary ConditionsSep 02 2002Dec 07 2002We consider singular perturbed eigenvalue problem for Laplace operator in a two-dimensional domain. In the boundary we select a set depending on a character small parameter and consisting of a great number of small disjoint parts. On this set the Dirichlet ... More

On strong exceptional collections of line bundles of maximal length on Fano toric Deligne-Mumford stacksJul 02 2019Jul 16 2019We study strong exceptional collections of line bundles on Fano toric Deligne-Mumford stacks $\mathbb{P}_{\mathbf{\Sigma}}$ with rank of Picard group at most two. We prove that any strong exceptional collection of line bundles generates the derived category ... More

Ladders of eigenvalues and resonances in bipartite complex potentialsAug 18 2019We consider a Schroedinger operator on the axis with a bipartite potential consisting of two compactly supported complex-valued functions, whose supports are separated by a large distance. We show that this operator possesses a sequence of approximately ... More

Sequences of closely spaced resonances and eigenvalues for bipartite complex potentialsAug 18 2019Sep 08 2019We consider a Schroedinger operator on the axis with a bipartite potential consisting of two compactly supported complex-valued functions, whose supports are separated by a large distance. We show that this operator possesses a sequence of approximately ... More

Tunneling resonances in systems without a classical trappingOct 01 2012In this paper we analyze a free quantum particle in a straight Dirichlet waveguide which has at its axis two Dirichlet barriers of lengths $\ell_\pm$ separated by a window of length 2a. It is known that if the barriers are semiinfinite, i.e. we have two ... More

Geometric coupling thresholds in a two-dimensional stripJun 18 2002We consider the Laplacian in a strip $\mathbb{R}\times (0,d)$ with the boundary condition which is Dirichlet except at the segment of a length $2a$ of one of the boundaries where it is switched to Neumann. This operator is known to have a non-empty and ... More

Bound states in weakly deformed strips and layersNov 30 2000We consider Dirichlet Laplacians on straight strips in R^2 or layers in R^3 with a weak local deformation. First we generalize a result of Bulla et al. to the three-dimensional situation showing that weakly coupled bound states exist if the volume change ... More

Electromagnetic Pulse Propagation in Passive Media by the Lanczos MethodOct 28 2004Maxwell's equations are cast in the form of the Schr\"{o}dinger equation. The Lanczos propagation method is used in combination with the fast Fourier pseudospectral method to solve the initial value problem. As a result, a time-domain, unconditionally ... More

Shifted symplectic structures on derived Quot-stacksAug 08 2019Aug 15 2019It is shown that derived Quot-stacks can be mapped into moduli functors of perfect complexes in a formally etale way. In the case of moduli of sheaves on Calabi-Yau manifolds this implies existence of shifted symplectic structures on derived Quot-stacks. ... More

Electron angular correlation in neutrinoless double beta decay and new physicsJan 16 2008The angular correlation of the electrons in the neutrinoless double beta decay ($0\nu2\beta$) is calculated taking into account the nucleon recoil, the $S$ and $P$-waves for the electrons and the electron mass using a general Lorentz invariant effective ... More

Neutrinoless double beta decay: Electron angular correlation as a probe of new physicsJun 07 2006Sep 12 2006The angular distribution of the final electrons in the so-called long range mechanism of the neutrinoless double beta decay ($0\nu2\beta$) is derived for the general Lorentz invariant effective Lagrangian. Possible theories beyond the SM are classified ... More

Effects of heavy Majorana neutrinos at lepton-proton collidersDec 01 2005We discuss the prospects of detecting the processes $e^+p\to\bar\nu_e\ell^+\ell'^+X$ and $\nu_ep\to e\ell^+\ell'^+X$ ($\ell,\ell'=e,\mu,\tau$) under the conditions of the present $ep$ collider HERA and of future colliders. These high-energy processes ... More

Magnetoelectric properties of 500 nm Cr2O3 filmsFeb 22 2016May 12 2016The linear magnetoelectric effect was measured in 500 nm Cr2O3 films grown by rf sputtering on Al2O3 substrates between top and bottom thin film Pt electrodes. Magnetoelectric susceptibility was measured directly by applying an AC electric field and measuring ... More

Neutrinoless double beta decay: searching for new physics with comparison of different nucleiDec 17 2011The neutrinoless double beta decay is analyzed using a general Lorentz invariant effective Lagrangian for various decaying nuclei of current experimental interest: $^{76}$Ge, $^{82}$Se, $^{100}$Mo, $^{130}$Te, and $^{136}$Xe. We work out the half-lives ... More

Probing new physics in the Neutrinoless double beta decay using electron angular correlationJun 28 2007Jan 16 2008The angular correlation of the electrons emitted in the neutrinoless double beta decay ($0\nu2\beta$) is presented using a general Lorentz invariant effective Lagrangian for the leptonic and hadronic charged weak currents. We show that the coefficient ... More

Convolution structures and arithmetic cohomologyJul 27 1998Jan 03 2001In this paper we construct arithmetic analogs of the Riemann-Roch theorem and Serre's duality for line bundles. This improves on the works of Tate and van der Geer - Schoof. We define $H^0(L)$ and $H^1(L)$ as some convolution of measures structures. The ... More

On a Question of Craven and a Theorem of BelyiMay 25 2002Dec 01 2002In this elementary note we prove that a polynomial with rational coefficients divides the derivative of some polynomial which splits in $\Q$ if and only if all of its irrational roots are real and simple. This provides an answer to a question posed by ... More

Derived manifolds and Kuranishi modelsDec 05 2012Jan 12 2014A model structure is defined on the category of derived differentiable schemes, and it is used to analyse the truncation 2-functor from derived manifolds to d-manifolds. It is proved that the induced 1-functor between the homotopy categories is full and ... More

On band spectrum of Schroedinger operator in periodic system of domains coupled by small windowsDec 29 2013We consider a periodic system of domains coupled by small windows. In such domain we study the band spectrum of a Schroedinger operator subject to Neumann condition. We show that near each isolated eigenvalue of the similar operator but in the periodicity ... More

Topological characterization of various types of rings of smooth functionsAug 30 2011Oct 02 2011Topologies on algebraic and equational theories are used to define germ determined, near-point determined, and point determined rings of smooth functions, without requiring them to be finitely generated. It is proved, that any commutative algebra morphism ... More

Boundedness theorem for Fano log-threefoldsFeb 06 1994Feb 07 1994The main purpose of this article is to prove that the family of all Fano threefolds with log-terminal singularities with bounded index is bounded.

Discrete spectrum of thin PT-symmetric waveguideMar 18 2014In a thin multidimensional layer we consider a second order differential PT-symmetric operator. The operator is of rather general form and its coefficients are arbitrary functions depending both on slow and fast variables. The PT-symmetry of the operator ... More

Quotient singularities, integer ratios of factorials and the Riemann HypothesisMay 10 2005The goal of this paper is to reveal a close connection between the following three subjects that have not been studied together in the past: terminal and canonical cyclic quotient singularities, integer ratios of factorials, Nyman's approach to the Riemann ... More

The club of simplicial setsJan 13 2010Dec 15 2010A club structure is defined on the category of simplicial sets. This club generalizes the operad of associative rings by adding "amalgamated" products.

Class of the affine line is a zero divisor in the Grothendieck ringDec 19 2014Mar 12 2015We show that the class of the affine line is a zero divisor in the Grothendieck ring of algebraic varieties over complex numbers. The argument is based on the Pfaffian-Grassmannian double mirror correspondence.

Convex lattice polytopes and cones with few lattice points inside, from a birational geometry viewpointJan 19 2000It is pretty well-known that toric Fano varieties of dimension k with terminal singularities correspond to convex lattice polytopes P in R^k of positive finite volume, such that intersection of P and Z^k consists of the point 0 and vertices of P. Likewise, ... More

Multiscale unique continuation properties of eigenfunctionsOct 04 2014Jul 02 2015Quantitative unique continuation principles for multiscale structures are an important ingredient in a number applications, e.g. random Schr\"odinger operators and control theory. We review recent results and announce new ones regarding quantitative unique ... More

The sum of squared logarithms inequality in arbitrary dimensionsAug 17 2015Nov 02 2015We prove the \emph{sum of squared logarithms inequality} (SSLI) which states that for nonnegative vectors $x, y \in \mathbb{R}^n$ whose elementary symmetric polynomials satisfy $e_k(x)\le e_k(y)$ (for $1\le k < n$) and $e_n(x)=e_n(y)$, the inequality ... More

Asymptotics for the solutions of elliptic systems with fast oscillating coefficientsDec 04 2006May 07 2007We consider a singularly perturbed second order elliptic system in the whole space. The coefficients of the systems fast oscillate and depend both of slow and fast variables. We obtain the homogenized operator and in the uniform norm sense we construct ... More

What is the higher dimensional infinitesimal groupoid of a manifold?Oct 29 2009The construction (by Kapranov) of the space of infinitesimal paths on a manifold is extended to include higher dimensional infinitesimal objects, encoding contractions of infinitesimal loops. This full infinitesimal groupoid is shown to have the algebra ... More

Higher dimensional operadsSep 14 2009Dec 15 2010The theory of operads (May, cyclic, modular, PROPs, etc) is extended to include higher dimensional phenomena, i.e. operations between operations, mimicking the algebraic structure on varieties of arbitrary dimensions, having marked subvarieties of arbitrary ... More

Frameworks for two-dimensional Keller mapsJan 13 2019A Keller map is a counterexample to the Jacobian Conjecture. In dimension two every such map, if exists, leads to a complicated set of conditions on the map between the Picard groups of suitable compactifications of the affine plane. This is essentially ... More

Geometrically Nilpotent SubvarietiesMay 13 2015We construct some examples of polynomial maps over finite fields that admit subvarieties with a peculiar property: every geometric point is mapped to a fixed point by some iteration of the map, while the whole subvariety is not. Several related open questions ... More

Minimal discrepancies of toric singularitiesMar 15 1994Jul 15 1994This is the major revision. The main purpose of this paper is to prove that minimal discrepancies of $n$-dimensional toric singularities can accumulate only from above and only to minimal discrepancies of toric singularities of dimension less than $n$. ... More

Some Interesting Integer Polynomial MapsJan 03 2013We introduce three simple polynomial maps with integer coefficients that have interesting dynamical properties modulo primes.

On classification of toric singularitiesApr 29 1998In 1988 S. Mori, D. Morrison, and I. Morrison gave a computer-based conjectural classification of four-dimensional cyclic quotient singularities of prime index. It was partially proven in 1990 by G. Sankaran. In 1991 Jim Lawrence basically proved this ... More

A geometric approach to the two-dimensional Jacobian ConjectureDec 24 2009Any counterexample to the two-dimensional Jacobian Conjecture gives a rational map from one projective plane to another. We use some ideas of the Minimal Model Program to study the combinatorial structure of a rational surface, that is obtained by resolving ... More

On Resolution of Compactifications of Unramified Planar Self-mapsOct 24 2011Apr 10 2012We use the techniques of birational algebraic geometry and some combinatorial arguments related to weighted trees to study the structure of resolutions of compactifications of hypothetical counterexamples to the two-dimensional Jacobian Conjecture. We ... More

On the spectrum of two quantum layers coupled by a windowFeb 08 2007We consider the Dirichlet Laplacian in a domain two three-dimensional parallel layers having common boundary and coupled by a window. The window produces the bound states below the essential spectrum; we obtain two-sided estimates for them. It is also ... More

Positive positive-definite functions and measures on locally compact abelian groupsJun 18 1999The author was recently able to provide a cohomological interpretation of Tate's Riemann-Roch formula for number fields using some new harmonic analysis objects, ghost-spaces. When trying to investigate these objects in general, we realized the importance ... More

Frameworks for two-dimensional Keller mapsJan 13 2019Aug 04 2019A Keller map is a counterexample to the Jacobian Conjecture. In dimension two every such map, if exists, leads to a complicated set of conditions on the map between the Picard groups of suitable compactifications of the affine plane. This is essentially ... More

Boundedness of Fano threefolds with log-terminal singularities of given indexOct 07 1999Feb 24 2005We prove the boundedness theorem for Fano threefolds with log-terminal singularities of any fixed index. This is an improvement of our earlier result, where we required additionally that the variety is Q-factorial, with Picard number 1. The new ideas ... More

Exchange coupling of a perpendicular ferromagnet to a half-metallic compensated ferrimagnet via a thin hafnium interlayerMay 08 2017A thin Hafnium film is shown to act both as an effective diffusion barrier for manganese at a thickness of 0.7 nm, and as an effective exchange coupling layer in a sandwich structure with perpendicular magnetic anisotropy. The magnetic layers are Co$_{20}$Fe$_{60}$B$_{20}$ ... More

Effect of density on microwave-induced resistance oscillations in back-gated GaAs quantum wellsApr 05 2019We report on microwave-induced resistance oscillations (MIROs) in a tunable-density 30-nm-wide GaAs/AlGaAs quantum well. We find that the MIRO amplitude increases dramatically with carrier density. Our analysis shows that the anticipated increase in the ... More

Variability in Spectropolarimetric properties of Sy 1.5 galaxy Mrk 6Oct 04 2013Jan 31 2014Here we present an analysis of spectro-polarimetric observations of type 1.5 AGN Mrk 6, performed with 6m telescope SAO RAN in 12 epochs (2010 -- 2013). Additionally, the inter-stellar mater (ISM) polarization has been observed and its contribution to ... More

Study of the Effect of Annealing on the Properties of Mn2RuxGa Thin FilmsApr 03 2019The effect of vacuum annealing thin films of the compensated ferrimagnetic half-metal Mn2RuxGa at temperatures from 250 to 400 degree Celsius is investigated. The 39.3 nm films deposited on (100) MgO substrates exhibit perpendicular magnetic anisotropy ... More

Preparation, characterization, and electrical properties of epitaxial NbO2 thin film lateral devicesJun 22 2015Jul 28 2015Epitaxial NbO2 (110) films, 20 nm thick, were grown by pulsed laser deposition on Al2O3 (0001) substrates. The Ar/O2 total pressure during growth was varied to demonstrate the gradual transformation between NbO2 and Nb2O5 phases, which was verified using ... More

Unusual void galaxy DDO68: implications of the HST resolved photometryDec 01 2016Dec 07 2016DDO68 (UGC5340) is an unusual dwarf galaxy with extremely low gas metallicity (12+log(O/H) = 7.14) residing in the nearby Lynx-Cancer void. Despite its apparent isolation, it shows both optical and HI morphological evidence for strong tidal disturbance. ... More

Unusual void galaxy DDO68: implications of the HST resolved photometryDec 01 2016Dec 29 2016DDO68 (UGC5340) is an unusual dwarf galaxy with extremely low gas metallicity (12+log(O/H) = 7.14) residing in the nearby Lynx-Cancer void. Despite its apparent isolation, it shows both optical and HI morphological evidence for strong tidal disturbance. ... More

Dynamic screening of a localized hole during photoemission from a metal clusterMar 22 2012Jun 14 2012Recent advances in attosecond spectroscopy techniques have fueled the interest in the theoretical description of electronic processes taking place in the subfemtosecond time scale. Here we study the coupled dynamic screening of a localized hole and a ... More

Unusual void galaxy DDO\,68: implications of the \textit{HST} resolved photometryDec 01 2016DDO68 (UGC5340) is an unusual dwarf galaxy with extremely low gas metallicity (12+log(O/H) = 7.14) residing in the nearby Lynx-Cancer void. Despite its apparent isolation, it shows both optical and HI morphological evidence for strong tidal disturbance. ... More

Investigation of the new cataclysmic variable 1RXS J180834.7+101041Feb 17 2012We present the results of our photometric and spectroscopic studies of the new eclipsing cataclysmic variable star 1RXS J180834.7+101041. Its spectrum exhibits double-peaked hydrogen and helium emission lines. The Doppler maps constructed from hydrogen ... More

Asymptotics for the expected lifetime of Brownian motion on thin domains in R^nSep 30 2009Apr 26 2011We derive a three-term asymptotic expansion for the expected lifetime of Brownian motion and for the torsional rigidity on thin domains in R^n, and a two-term expansion for the maximum (and corresponding maximizer) of the expected lifetime. The approach ... More

On a one-dimensional quadratic operator pencil with a small periodic perturbationJul 26 2016We consider a quadratic operator pencil with a small periodic perturbation multiplied by the spectral parameter. It is motivated, in particular, by a one-dimensional Klein-Gordon equation with a time-parity-symmetric perturbation. We study in details ... More

Distant perturbations of the Laplacian in a multi-dimensional spaceAug 02 2006Dec 06 2006We consider the Laplacian in $\mathbb{R}^n$ perturbed by a finite number of distant perturbations those are abstract localized operators. We study the asymptotic behaviour of the discrete spectrum as the distances between perturbations tend to infinity. ... More

On dynamics of geometrically thin accretion disksApr 28 2013Sep 05 2013Axisymmetric accretion disks in vicinity of a central compact body are studied. For the simple models such as vertically isothermal disks as well as adiabatic ones the exact solutions to the steady-state MHD (magneto-hydrodynamic) system were found under ... More

Polynomial maps over $p$-adics and residual properties of mapping tori of group endomorphismsOct 02 2008We continue our study of residual properties of mapping tori of free group endomorphisms. In this paper, we prove that each of these groups are virtually residually (finite $p$)-groups for all but finitely many primes$p$. The method involves further studies ... More

Quasi-coherent sheaves in differential geometryJul 04 2017Jul 28 2017It is proved that the category of simplicial complete bornological spaces over $\mathbb R$ carries a combinatorial monoidal model structure satisfying the monoid axiom. For any commutative monoid in this category the category of modules is also a monoidal ... More

On Wronskians of weight one Eisenstein seriesMar 01 2005We describe the span of Hecke eigenforms of weight four with nonzero central value of $L$-function in terms of Wronskians of certain weight one Eisenstein series.

On the conjecture of King for smooth toric Deligne-Mumford stacksJan 18 2008Dec 24 2008We construct full strong exceptional collections of line bundles on smooth toric Fano Deligne-Mumford stacks of Picard number at most two and of any Picard number in dimension two. It is hoped that the approach of this paper will eventually lead to the ... More

Higher elliptic generaFeb 17 2006Oct 17 2008We show that elliptic classes introduced in our earlier paper for spaces with infinite fundamental groups yield Novikov's type higher elliptic genera which are invariants of K-equivalence. This include, as a special case, the birational invariance of ... More

Chiral rings of vertex algebras of mirror symmetrySep 23 2002Nov 10 2003We calculate chiral rings of the N=2 vertex algebras constructed from the combinatorial data of toric mirror symmetry and show that they coincide with the description of stringy cohomology conjectured previously in a joint work with A. Mavlyutov.

Simplicial approach to derived differential manifoldsNov 30 2011Derived differential manifolds are constructed using the usual homotopy theory of simplicial rings of smooth functions. They are proved to be equivalent to derived differential manifolds of finite type, constructed using homotopy sheaves of homotopy rings ... More

Low lying eigenvalues of randomly curved quantum waveguidesNov 06 2012Aug 14 2013We consider the negative Dirichlet Laplacian on an infinite waveguide embedded in $\RR^2$, and finite segments thereof. The waveguide is a perturbation of a periodic strip in terms of a sequence of independent identically distributed random variables ... More

Spectral gaps for self-adjoint second order operatorsOct 02 2010Sep 04 2012We consider a second order self-adjoint operator in a domain which can be bounded or unbounded. The boundary is partitioned into two parts with Dirichlet boundary condition on one of them, and Neumann condition on the other. We assume that the potential ... More

On Calabi-Yau threefolds with large nonabelian fundamental groupsSep 26 2006In this short note we construct Calabi-Yau threefolds with nonabelian fundamental groups of order 64 as quotients of the small resolutions of certain complete intersections of quadrics in $\PP^7$ that were first considered by M. Gross and S. Popescu.

On a problem with nonperiodic frequent alternation of boundary condition imposed on fast oscillating setsJun 21 2003Nov 27 2005We consider singular perturbed eigenvalue problem for Laplace operator in a cylinder with frequent and nonperiodic alternation of boundary conditions imposed on narrow strips lying in the lateral surface. The width of strips depends on a small parameter ... More

McKay correspondence for elliptic generaJun 24 2002We establish a correspondence between orbifold and singular elliptic genera of a global quotient. While the former is defined in terms of the fixed point set of the action, the latter is defined in terms of the resolution of singularities. As a byproduct, ... More

Eigenvalue asymptotics, inverse problems and a trace formula for the linear damped wave equationMay 20 2009We determine the general form of the asymptotics for Dirichlet eigenvalues of the one-dimensional linear damped wave operator. As a consequence, we obtain that given a spectrum corresponding to a constant damping term this determines the damping term ... More

Asymptotics of Dirichlet eigenvalues and eigenfunctions of the Laplacian on thin domains in R^dAug 17 2009We consider the Laplace operator with Dirichlet boundary conditions on a domain in R^d and study the effect that performing a scaling in one direction has on the eigenvalues and corresponding eigenfunctions as a function of the scaling parameter around ... More

On the boundedness of the sectional curvature of almost Hermitian manifoldsAug 11 2010We prove the following results: An almost Hermitian manifold of indefinite metric is of pointwise constant holomorphic sectional curvature if the holomorphic sectional curvature is bounded from above and from below. If the antiholomorphic sectional curvature ... More

Polynomial maps over finite fields and residual finiteness of mapping tori of group endomorphismsSep 06 2003We prove that every mapping torus of any free group endomorphism is residually finite. We show how to use a not yet published result of E. Hrushovski to extend our result to arbitrary linear groups. The proof uses algebraic self-maps of affine spaces ... More

Stringy $E$-functions of Pfaffian-Grassmannian double mirrorsFeb 12 2015Feb 24 2015We establish the equality of stringy $E$-functions for double mirror Calabi-Yau complete intersections in the varieties of skew forms of rank at most $2k$ and at most $n-1-2k$ on a vector space of odd dimension $n$.

On stringy Euler characteristics of Clifford non-commutative varietiesMay 17 2018It was shown by Kuznetsov that complete intersections of $n$ generic quadrics in ${\mathbb P}^{2n-1}$ are related by Homological Projective Duality to certain non-commutative (Clifford) varieties which are in some sense birational to double covers of ... More

Securing Tor Tunnels under the Selective-DoS AttackJul 19 2011Dec 18 2012Anonymous communication systems are subject to selective denial-of-service (DoS) attacks. Selective DoS attacks lower anonymity as they force paths to be rebuilt multiple times to ensure delivery which increases the opportunity for more attack. In this ... More

Detection of spiral structure of the quiescent accretion disk of IP PegasiOct 04 2001We present the results of the spectral investigations of IP Peg in quiescence. Optical spectra obtained on 6-m telescope at the Special Astrophysical Observatory (Russia), and on the 3.5-m telescope at the German-Spanish Astronomical Center (Calar Alto, ... More

Spectropolarimetric Observations of Active Galactic Nuclei with the 6-m BTA TelescopeApr 19 2011We present the results of our spectropolarimetric observations for a number of active galactic nuclei (AGNs) carried out at the 6-m telescope with the SCORPIO focal reducer. The derived wavelength dependences of the polarization have been analyzed by ... More

Photometric observations and preliminary modeling of type IIb supernova 2011dhJul 10 2012CCD UBVRI photometry is presented for type IIb SN 2011dh for about 300 days. The main photometric parameters are derived and the comparison with SNe of similar types is reported. The light curves are similar to those for SN IIb 2008ax, but the initial ... More

IP Pegasi: Investigation of the accretion disk structure. Searching evidences for spiral shocks in the quiescent accretion diskJul 19 2002We present the results of spectral investigations of the cataclysmic variable IP Peg in quiescence. Optical spectra obtained on the 6-m telescope at the Special Astrophysical Observatory (Russia), and on the 3.5-m telescope at the German-Spanish Astronomical ... More