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A New Kalman Filter Model for Nonlinear Systems Based on Ellipsoidal BoundingFeb 08 2018In this paper, a new filter model called set-membership Kalman filter for nonlinear state estimation problems was designed, where both random and unknown but bounded uncertainties were considered simultaneously in the discrete-time system. The main loop ... More

On $[A,A]/[A,[A,A]]$ and on a $W_n$-action on the consecutive commutators of free associative algebraOct 12 2006Oct 16 2006We consider the lower central filtration of the free associative algebra $A_n$ with $n$ generators as a Lie algebra. We consider the associated graded Lie algebra. It is shown that this Lie algebra has a huge center which belongs to the cyclic words, ... More

The geometry of second-order ordinary differential equationsFeb 02 2016These are lecture notes of the Summer school on the geometry of differential equations held in Nordfjordeid, Norway in 1996. They cover geometric structures related to scalar second order ODEs, the construction of the associated Cartan connection, techniques ... More

Models with varying structureOct 30 2017In this paper the problems of the retrospective analysis of models with time-varying structure are considered. These models include contamination models with randomly switching parameters and multivariate classification models with an arbitrary number ... More

On the models of submaximal symmetric rank 2 distributions in 5DNov 27 2013Jun 11 2014There are two different approaches to exhibit submaximal symmetric rank 2 distributions in 5D via Monge equations. In this note we establish precise relations between these models, find auto-equivalences of one family, and treat two special equations. ... More

Tree-like curves and their inflection pointsAug 12 1997We give a criterion when a planar tree-like curve, i.e. a generic immersed plane curve each double point of which cuts it into two disjoint parts, can be send by a diffeomorphism of the plane onto a curve with no inflection points. We also present some ... More

On Hamiltonian perturbations of hyperbolic systems of conservation laws, II: universality of critical behaviourOct 10 2005Oct 20 2005Hamiltonian perturbations of the simplest hyperbolic equation $u_t + a(u) u_x=0$ are studied. We argue that the behaviour of solutions to the perturbed equation near the point of gradient catastrophe of the unperturbed one should be essentially independent ... More

Systematics of Evaluated Half-Lives of Double-Beta DecayFeb 27 2013Jul 08 2014A new evaluation of 2beta-decay half lives and their systematics is presented. These data extend the previous evaluation and include the analysis of all recent measurements. The nuclear matrix elements for 2beta-decay transitions in 12 nuclei have been ... More

Complete calculation of evaluated Maxwellian-averaged cross sections and their uncertainties for s-process nucleosynthesisAug 27 2010Jan 10 2011Present contribution represents a significant improvement of our previous calculation of Maxwellian-averaged cross sections and astrophysical reaction rates. Addition of newly-evaluated neutron reaction libraries, such as ROSFOND and Low-Fidelity Covariance ... More

Stellar Nucleosynthesis Nuclear Data MiningOct 05 2011Mar 07 2012Stellar nucleosynthesis is an important nuclear physics phenomenon that is responsible for presently observed chemical elements and isotope abundances. It is also one of the corner stone hypotheses that provides basis for our understanding of Nature. ... More

Generalized Wilczynski invariants for non-linear ordinary differential equationsFeb 09 2007Apr 05 2007We show that classical Wilczynski--Se-ashi invariants of linear systems of ordinary differential equations are generalized in a natural way to contact invariants of non-linear ODEs. We explore geometric structures associated with equations that have vanishing ... More

An explicit construction of the Quillen homotopical category of dg Lie algebrasJun 09 2007Let $\g_1$ and $\g_2$ be two dg Lie algebras, then it is well-known that the $L_\infty$ morphisms from $\g_1$ to $\g_2$ are in 1-1 correspondence to the solutions of the Maurer-Cartan equation in some dg Lie algebra $\Bbbk(\g_1,\g_2)$. Then the gauge ... More

On the $A_\infty$-Formality conjectureSep 21 1998It is proved that the associative differential graded algebra of (polynomial) polyvector fields on a vector space (may be infinite- dimensional) is quasi-isomorphic to the corresponding cohomological Hochschild complex of (polynomial) functions on this ... More

Random dense countable sets: characterization by independenceNov 01 2005A random dense countable set is characterized (in distribution) by independence and stationarity. Two examples are `Brownian local minima' and `unordered infinite sample'. They are identically distributed; the former ad hoc proof of this fact is now superseded ... More

Brownian local minima and other random dense countable setsAug 22 2005We compare two examples of random dense countable sets, `Brownian local minima' and `unordered uniform infinite sample'. They appear to be identically distributed. A framework for such notions is proposed. In addition, random elements of other singular ... More

Subproduct systems of Hilbert spaces: dimension twoJun 23 2009A subproduct system of two-dimensional Hilbert spaces can generate an Arveson system of type I1 only. All possible cases are classified up to isomorphism. This work is triggered by a question of Bhat: can a subproduct system of n-dimensional Hilbert spaces ... More

A generalization of Quillen's small object argumentJan 29 2004Mar 29 2005We generalize the small object argument in order to allow for its application to proper classes of maps (as opposed to sets of maps in Quillen's small object argument). The necessity of such a generalization arose with appearance of several important ... More

Localization with respect to a class of maps II - Equivariant cellularization and its applicationDec 09 2003We present an example of a homotopical localization functor which is not a localization with respect to any set of maps. Our example arises from equivariant homotopy theory. The technique of equivariant cellularization is developed and applied to the ... More

Anisotropy and superconductivityFeb 12 2013The mean field method is applied for analysis of valence electrons in metals. It is shown that at low temperatures electrons have two wave-vector distribution patterns. Isotropic distribution refers to the first pattern. Anisotropic distribution refers ... More

The anisotropic distribution of the interacting electronsJan 21 2013The distribution function for a system of interacting electrons in metals is multivalent in a certain region of wave vectors. One solution among many is isotropic. For other solutions the distribution of electrons over the wave vectors is anisotropic. ... More

Quantum master equation for a system of identical particlesJan 21 2013We consider an open quantum many-particle system in which there are dissipative processes. The evolution of this system is described by a kinetic equation for the density matrix. From the equation describing a random Markov process in this system, we ... More

High $Q^2$ Probe of Nuclear Spectral Function and Color TransparencyNov 11 1993Contrary to widespread opinion, color transparency (CT) brings essential ambiguity to, rather than helps in, study of the nuclear spectral function in quasielastic lepton scattering, $A(l,l'p)A'$, at high $Q^2$. Although the nuclear attenuation vanishes, ... More

In Search for (QUANTUM) Color TransparencyMay 19 1993Color transparency (CT) is an effect of suppression of nuclear shadowing of hard reactions, closely related to the color screening. A brief review of theoretical development and experimental search for CT, failed and successful, are presented. A special ... More

Kinetics of Strongly Non-Equilibrium Bose-Einstein CondensationSep 23 2000We consider the ordering kinetics in a strongly non-equilibrium state of a (weakly) interacting Bose gas, characterized, on one hand, by large occupation numbers, and, on the other hand, by the absence of long-range order. Up to higher-order corrections ... More

Symmetry, compatibility and exact solutions of PDEsNov 24 2011Mar 04 2012We discuss various compatibility criteria for overdetermined systems of PDEs generalizing the approach to formal integrability via brackets of differential operators. Then we give sufficient conditions that guarantee that a PDE possessing a Lie algebra ... More

Noncommutative geometry on the universal envelopping algebra of the Borel subgroup U[sb(2)]Apr 09 2013We study the Borel algebra de ne by [x a ; x b ] = 2 a;1 x b as a noncommutative manifold R 3 . We calculate its noncommutative di erential form relations. We deduce its partial derivative relations and the derivative of a plane wave. After calculating ... More

New relations for the old triangleMay 02 2013In this note we show that in addition to two integers forming a Pythagorean triple, there also exist two irrational numbers in terms of which this Pythagorean triple can also be obtained. We also put forward a relation between these two pairs and the ... More

Neutrino Mass: The Present and the FutureOct 18 2000We argue that the evidence for neutrino mass is quite compelling. This mass raises a number of questions, which we enumerate, about neutrinos. Then we focus on one of these questions---the issue of the possible neutrino mass spectra. In particular, we ... More

Neutrino Physics: Where Do We Stand, and Where Are We Going? -- The Theoretical-Phenomenological PerspectiveJun 09 2003The discoveries and open questions in neutrino physics, as reported at Neutrino 2002 and more recently, are reviewed from a theoretical perspective.

Point classification of 2nd order ODEs: Tresse classification revisited and beyondSep 26 2008In 1896 Tresse gave a complete description of relative differential invariants for the pseudogroup action of point transformations on the 2nd order ODEs. The purpose of this paper is to review, in light of modern geometric approach to PDEs, this classification ... More

Filament eruption with apparent reshuffle of endpointsMay 22 2014Filament eruption on 30 April - 1 May 2010, which shows the reconnection of one filament leg with a region far away from its initial position, is analyzed. Observations from three viewpoints are used for as precise as possible measurements of endpoint ... More

Klt singularities of horospherical pairsSep 22 2015Sep 30 2015Let $X$ be a horospherical $G$-variety and let $D$ be an effective $\mathbb{Q}$-divisor of $X$ that is stable under the action of a Borel subgroup $B$ of $G$ and such that $D+K\_X$ is $\mathbb{Q}$-Cartier. We prove, using Bott-Samelson resolutions, that ... More

Cheeger-Mueller Theorem on manifolds with cuspsNov 03 2014Jan 07 2015We prove equality between the renormalized Ray-Singer analytic torsion and the intersection R-torsion on a Witt-manifold with cusps, up to an error term determined explicitly by the Betti numbers of the cross section of the cusp and the intersection R-torsion ... More

Rankin-Selberg methods for closed string amplitudesJan 17 2014Jul 10 2014After integrating over supermoduli and vertex operator positions, scattering amplitudes in superstring theory at genus $h\leq 3$ are reduced to an integral of a Siegel modular function of degree $h$ on a fundamental domain of the Siegel upper half plane. ... More

On the number of coverings of the sphere ramified over given pointsDec 04 2013Mar 27 2014We present the generating function for the numbers of isomorphism classes of coverings of the two-dimensional sphere by the genus $g$ compact oriented surface not ramified outside of a given set of $m+1$ points in the target, fixed ramification type over ... More

A note on the Trace Theorem for domains which are locally subgraph of a Holder continuous functionNov 13 2013The purpose of this note is to prove a version of the Trace Theorem for domains which are locally subgraph of a H\" older continuous function. More precisely, let $\eta\in C^{0,\alpha}(\omega)$, $0<\alpha<1$ and let $\Omega_{\eta}$ be a domain which is ... More

Differential Invariants and Symmetry: Riemannian metrics and beyondFeb 10 2015We discuss Lie-Tresse theorem for the pseudogroup of diffeomorphisms acting on the space of (pseudo-)Riemannian metrics, and relate this to existence of Killing vector fields. Then we discuss the impact of symmetry in the general case.

Weak-Strong uniqueness for compressible Navier-Stokes system with degenerate viscosity coefficient and vacuum in one dimensionNov 27 2014We prove weak-strong uniqueness results for the compressible Navier-Stokes system with degenerate viscosity coefficient and with vacuum in one dimension. In other words, we give conditions on the weak solution constructed in \cite{Jiu} so that it is unique. ... More

Uniform lamda-adjustment and mu-approximation in Banach spacesApr 17 2008We introduce a new concept of perturbation of closed linear subspaces and operators in Banach spaces called uniform lambda-adjustment which is weaker than perturbations by small gap, operator norm, q-norm, and K2-approximation. In arbitrary Banach spaces ... More

Minimal DFAs for Testing DivisibilitySep 29 2003We present and prove a theorem answering the question "how many states does a minimal deterministic finite automaton (DFA) that recognizes the set of base-b numbers divisible by k have?"

Algebra and logic. Some problemsJun 04 2013The paper has a form of a talk on the given topic. It consists of three parts. The first part of the paper contains main notions, the second one is devoted to logical geometry, the third part describes types and isotypeness. The problems are distributed ... More

Algebraic logic and logical geometry in arbitrary varieties of algebrasMay 28 2012Jun 01 2012The paper consists of two parts. The first part is devoted to logic for universal algebraic geometry. The second one deals with problems and some results. It may be regarded as a brief exposition of some ideas from the book in progress: B.Plotkin, E.Aladova, ... More

Problems in algebra inspired by universal algebraic geometryJun 06 2004Dec 14 2004Let $\Theta$ be a variety of algebras. In every $\Theta$ and every algebra $H$ from $\Theta$ one can consider algebraic geometry in $\Theta$ over $H$. We consider also a special categorical invariant $K_\Theta (H)$ of this geometry. The classical algebraic ... More

Cold asymmetrical fermion superfluids in nonperturbative renormalisation groupMay 26 2006May 29 2006The application of the nonperturbative renormalisation group approach to a system with two fermion species is studied. Assuming a simple ansatz for the effective action with effective bosons, describing pairing effects we derive a set of approximate flow ... More

Superfluidity within Exact Renormalisation Group approachDec 21 2005The application of the exact renormalisation group to a many-fermion system with a short-range attractive force is studied. We assume a simple ansatz for the effective action with effective bosons, describing pairing effects and derive a set of approximate ... More

Spectral Statistics of "Cellular" BilliardsOct 01 2010For a bounded planar domain $\Omega^0$ whose boundary contains a number of flat pieces $\Gamma_i$ we consider a family of non-symmetric billiards $\Omega$ constructed by patching several copies of $\Omega^0$ along $\Gamma_i$'s. It is demonstrated that ... More

On automorphisms of type II Arveson systems (probabilistic approach)Nov 03 2004Apr 30 2008A counterexample to the conjecture that the automorphisms of an arbitrary Arveson system act transitively on its normalized units.

Sums of dilatesNov 11 2007Apr 03 2008The lambda-dilate of a set A is lambda*A={lambda a : a \in A}. We give an asymptotically sharp lower bound on the size of sumsets of the form lambda_1*A+...+lambda_k*A for arbitrary integers lambda_1,...,lambda_k and integer sets A. We also establish ... More

Noise sensitivity on continuous products: an answer to an old question of J. FeldmanJul 02 1999A relation between sigma-additivity and linearizability, conjectured by Jacob Feldman in 1971 for continuous products of probability spaces, is established by relating both notions to a recent idea of noise stability/sensitivity.

Divisibility in the Stone-Čech compactificationOct 24 2014After defining continuous extensions of binary relations on the set N of natural numbers to its Stone-Cech compactification \beta N, we establish some results about one of such extensions. This provides us with one possible divisibility relation on \beta ... More

Measurable sets with excluded distancesMar 28 2007Feb 24 2008For a set of distances D={d_1,...,d_k} a set A is called D-avoiding if no pair of points of A is at distance d_i for some i. We show that the density of A is exponentially small in k provided the ratios d_1/d_2, d_2/d_3, ..., d_{k-1}/d_k are all small ... More

Exponential tropical varieties and complex Monge-Ampere operatorDec 21 2012May 26 2013Sometimes it is possible to extend some using Newton polyhedra computations in algebraic geometry from polynomials to exponential sums. For this purpose it is useful to consider analogues of tropical varieties in complex space. These analogues are called ... More

Gegenbauer-Chebyshev Integrals and Radon TransformsOct 15 2014Jan 23 2015We suggest new modifications of Helgason's support theorems and descriptions of the kernels for several projectively equivalent transforms of integral geometry. The paper deals with the hyperplane Radon transform and its dual, the totally geodesic transforms ... More

Generalized cosine transforms and classes of star bodiesFeb 24 2006The spherical Radon transform on the unit sphere can be regarded as a member of the analytic family of suitably normalized generalized cosine transforms. We derive new formulas for these transforms and apply them to study classes of intersections bodies ... More

The Radon Transform on the Heisenberg Group and the Transversal Radon TransformOct 13 2009The notion of the Radon transform on the Heisenberg group was introduced by R. Strichartz and inspired by D. Geller and E.M. Stein's related work. The more general transversal Radon transform integrates functions on the m-dimensional real Euclidean space ... More

Intersection Bodies and Generalized Cosine TransformsMar 31 2007May 03 2007Intersection bodies represent a remarkable class of geometric objects associated with sections of star bodies and invoking Radon transforms, generalized cosine transforms, and the relevant Fourier analysis. The main focus of this article is interrelation ... More

Non-trivial solutions to a linear equation in integersMar 26 2007Nov 10 2007For k>=3 let A \subset [1,N] be a set not containing a solution to a_1 x_1+...+a_k x_k=a_1 x_{k+1}+...+a_k x_{2k} in distinct integers. We prove that there is an epsilon>0 depending on the coefficients of the equation such that every such A has O(N^{1/2-epsilon}) ... More

Set families with a forbidden subposetMar 26 2008Nov 21 2009We asymptotically determine the size of the largest family F of subsets of {1,...,n} not containing a given poset P if the Hasse diagram of P is a tree. This is a qualitative generalization of several known results including Sperner's theorem.

Multidimensional Kruskal-Katona theoremSep 13 2010Nov 06 2011We present a generalization of a version of the Kruskal-Katona theorem due to Lovasz. A shadow of a d-tuple (S_1,...,S_d) in binom{X}{r}^d consists of d-tuples (S_1',...,S_d') in binom{X}{r-1}^d obtained by removing one element from each of S_i. We show ... More

Spherical Means in Odd Dimensions and EPD equationsNov 13 2007The paper contains a simple proof of the Finch-Patch-Rakesh inversion formula for the spherical mean Radon transform in odd dimensions. This transform arises in thermoacoustic tomography. Applications are given to the Cauchy problem for the Euler-Poisson-Darboux ... More

The spectrum of a Harmonic Oscillator Operator Perturbed by Point InteractionsJul 15 2014We consider the operator $ L = - (d/dx)^2 + x^2 y + w(x) y , y \in L^2(\mathbb{R}) $, where $ w(x) = s [ \delta(x - b) - \delta(x + b)], b \neq 0,$ real, $s \in \mathbb{C}$. This operator has a discrete spectrum: eventually the eigenvalues are simple ... More

Non-existence of orthogonal complex structures on 6-sphere with a metric close to the round oneAug 24 2017I review several proofs for non-existence of orthogonal complex structures on the six-sphere, most notably by G. Bor and L. Hernandez-Lamoneda, but also by K. Sekigawa and L. Vanhecke that we generalize for metrics close to the round one. Invited talk ... More

On random quadratic forms: supports of potential local maximaAug 10 2017Jan 05 2018In the late eighties John Kingman studied the problem of maxima of a quadratic form, with independent, uniformly distributed, coefficients, on a simplex of growing dimension $n$. In particular, he proved that the largest support size (cardinality) $L_n$ ... More

Linear response and moderate deviations: hierarchical approach. IVOct 12 2018The Moderate Deviations Principle (MDP) is well-understood for sums of independent random variables, worse understood for stationary random sequences, and scantily understood for random fields. Here it is established for splittable random fields integrated ... More

Algebraic spectral curves over $\mathbb Q$ and their tau-functionsJul 30 2018Let $W(z)$ be a $n\times n$ matrix polynomial with rational coefficients. Denote $C$ the spectral curve $\det \left( w\cdot{\bf 1}-W(z)\right) =0$. Under some natural assumptions about the structure of $W(z)$ we prove that certain combinations of logarithmic ... More

Recent results from D0 and recent Tevatron combinationsMay 19 2017We discuss recent results obtained by the D0 experiment at the Fermilab Tevatron $p\bar p$ collider and recent combinations of CDF and D0 measurements. Regarding the top quark mass, we present recent measurements obtained at D0, the final Run~I+Run~II ... More

Die Klassifikation der Gruppen bis zur Ordnung p^5Jun 19 2018This paper presents a classification of all p-groups of order p^5 up to isomorphism. It contains a full list of their polycyclic presentations, a short introduction to the basic ideas of the methodes used to classify the groups, and a detailed proof of ... More

Solar coronal loop dynamics near the null point above active region NOAA 2666May 22 2018We analyse observations of a saddle-like structure in the corona above the western limb of the Sun on 2017 July 18. The structure was clearly outlined by coronal loops with typical coronal temperature no more than 1 MK. The dynamics of loops showed convergence ... More

Delone sets and dynamical systemsFeb 07 2018In these expository notes we focus on selected topics around the themes: Delone sets as models for quasicrystals, inflation symmetries and expansion constants, substitution Delone sets and tilings, and associated dynamical systems.

Systematics of oscillatory behavior in hadronic masses and widthsMar 15 2016Jul 05 2016A systematic study of hadron masses and widths shows regular oscillations that can be fitted by a simple cosine function. This property can be observed when the difference between adjacent masses of each family is plotted versus the mean mass.

Universal Function Approximation by Deep Neural Nets with Bounded Width and ReLU ActivationsAug 09 2017Dec 20 2017This article concerns the expressive power of depth in neural nets with ReLU activations and bounded width. We are particularly interested in the following questions: what is the minimal width $w_{\text{min}}(d)$ so that ReLU nets of width $w_{\text{min}}(d)$ ... More

Throughput analysis in networks of WLANsNov 21 2016This paper proposes a simple but accurate approximation to analytically model both the inter-WLANs (Wireless Local Area Networks) interactions and the negative effect of collisions in networks of IEEE 802.11 WLANs. Inter-WLANs interactions are characterized ... More

Addressing the Majorana vs. Dirac Question Using Neutrino DecaysMay 19 2018We explain why it is so hard to determine whether neutrinos are Majorana or Dirac particles as long as the only neutrinos we study are ultra-relativistic. We then show how non-relativistic neutrinos could help, and focus on the angular distributions in ... More

On the twisted tensor product of small dg categoriesMar 03 2018Jul 11 2018Given two small dg categories $C,D$, defined over a field, we introduce their (non-symmetric) twisted tensor product $C\overset{\sim}{\otimes} D$. We show that $-\overset{\sim}{\otimes} D$ is left adjoint to the functor $Coh(D,-)$, where $Coh(D,E)$ is ... More

On the Determination of Star Bodies from Their Half-SectionsSep 07 2016We obtain explicit inversion formulas for the Radon-like transform that assigns to a function on the unit sphere the integrals of that function over hemispheres lying in lower dimensional central cross-sections. The results are applied to determination ... More

Shifts of a Measurable Function and Criterion of p-integrabilityAug 28 2016Nov 15 2016It is shown that two conditions $f(a + \cdot) - f(\cdot) \in L^p(R)$, and $(\sin b \cdot) f(\cdot) \in L^p(R)$ guarantee $f \in L^p(R)$, $1 \leq p < \infty$, if and only if $ab$ is not in $(\pi Z)$.

Nuclear Data for Astrophysical ModelingAug 01 2016Nuclear physics has been playing an important role in modern astrophysics and cosmology. Since the early 1950's it has been successfully applied for the interpretation and prediction of astrophysical phenomena. Nuclear physics models helped to explain ... More

The semantics of the canonical commutation relationApr 26 2016We treat the canonical commutation relations and the conventional calculus based on it as an algebraic syntax of quantum mechanics and establish a geometric semantics of this syntax. This leads us to a geometric model, the space of states with the action ... More

On random stable partitionsMay 23 2017The stable roommates problem does not necessarily have a solution, i.e. a stable matching. We had found that, for the uniformly random instance, the expected number of solutions converges to $e^{1/2}$ as $n$, the number of members, grows, and with Rob ... More

Counting strongly-connected, sparsely edged directed graphsMay 03 2010May 05 2010A sharp asymptotic formula for the number of strongly connected digraphs on $n$ labelled vertices with $m$ arcs, under a condition $m-n\to\infty$, $m=O(n)$, is obtained; this solves a problem posed by Wright back in $1977$. Our formula is a counterpart ... More

Another proof of Harer-Zagier formulaMar 18 2015For a regular $2n$-gon there are $(2n-1)!!$ ways to match and glue the $2n$ sides. The Harer-Zagier bivariate generating function enumerates the gluings by $n$ and the genus $g$ of the attendant surface and leads to a recurrence equation for the counts ... More

Deformation quantization with traces and vanishing of the wheelsApr 12 2000May 01 2000The paper has been withdrawn because the result of math.QA/0002057 "Deformation quantization with traces" holds only for a constant volume form.

Painleve' transcendents and two-dimensional topological field theoryMar 23 1998Apr 14 1998Lecture 1. Algebraic properties of correlators in 2D topological field theory. Moduli of a 2D TFT and WDVV equations of associativity. Lecture 2. Equations of associativity and Frobenius manifolds. Deformed flat connection and its monodromy at the origin. ... More

Geometry of 2d topological field theoriesJul 04 1994These lecture notes are devoted to the theory of equations of associativity describing geometry of moduli spaces of 2D topological field theories. Introduction. Lecture 1. WDVV equations and Frobenius manifolds. {Appendix A.} Polynomial solutions of WDVV. ... More

Geometry and analytic theory of Frobenius manifoldsJul 08 1998Jul 09 1998Main mathematical applications of Frobenius manifolds are in the theory of Gromov - Witten invariants, in singularity theory, in differential geometry of the orbit spaces of reflection groups and of their extensions, in the hamiltonian theory of integrable ... More

Property lattices for independent quantum systemsApr 17 2002Apr 23 2003We consider the description of two independent quantum systems by a complete atomistic ortho-lattice (cao-lattice) L. It is known that since the two systems are independent, no Hilbert space description is possible, i.e. $L\ne P(H)$, the lattice of closed ... More

Pseudo-self-affine tilings in R^dOct 02 2005It is proved that every pseudo-self-affine tiling in R^d is mutually locally derivable with a self-affine tiling. A characterization of pseudo-self-similar tilings in terms of derived Voronoi tessellations is a corollary. Previously, these results were ... More

Abstract cellularization as a cellularization with respect to a set of objectsJul 05 2006Given a simplicial idempotent augmented endofunctor $F$ on a simplicial combinatorial model category $M$, under the assumption of Vopenka's principle, we exhibit a set $A$ of cofibrant objects in $M$ such that $F$ is equivalent to $\CW_A$, the cellularization ... More

An explicit formula for the deformation quantization of Lie bialgebrasFeb 03 2004A model of 3-dimensional topological quantum field theory is rigorously constructed. The results are applied to an explicit formula for deformation quantization of any finite-dimensional Lie bialgebra over the field of complex numbers. This gives an explicit ... More

Vanishing of the Kontsevich integrals of the wheelsJul 13 2000We prove that the Kontsevich integrals (in the sense of the formality theorem) of all even wheels are equal to zero. We deduce this theorem from the result of \cite{FSh} on the deformation quantization with traces.

Monoidal cofibrant resolutions of dg algebrasDec 11 2011Mar 09 2012Let $k$ be a field of any characteristic. In this paper, we construct a functorial cofibrant resolution $\mathfrak{R}(A)$ for the $\mathbb{Z}_{\le 0}$-graded dg algebras $A$ over $k$, such that the functor $A\rightsquigarrow \mathfrak{R}(A)$ is colax-monoidal ... More

Koszul duality in deformation quantization, IJun 15 2007Let $\alpha$ be a polynomial Poisson bivector on a finite-dimensional vector space $V$ over $\mathbb{C}$. Then Kontsevich [K97] gives a formula for a quantization $f\star g$ of the algebra $S(V)^*$. We give a construction of an algebra with the PBW property ... More

The CROCs, non-commutative deformations, and (co)associative bialgebrasJun 09 2003We compactify the spaces $K(m,n)$ introduced by Maxim Kontsevich. The initial idea was to construct an $L_\infty$ algebra governing the deformations of a (co)associative bialgebra. However, this compactification leads not to a resolution of the PROP of ... More

On the cyclic Formality conjectureMar 30 1999Apr 23 1999We conjecture an explicit formula for a cyclic analog of the Formality $L_{\infty}$-morphism [K]. We prove that its first Taylor component, the cyclic Hochschild-Kostant-Rosenberg map, is in fact a morphism (and a quasiisomorphism) of the complexes. To ... More

Bending deformations of complex hyperbolic surfacesAug 30 1996We study deformations of complex hyperbolic surfaces which furnish the simplest examples of: (i) negatively curved K\"ahler manifolds and (ii) negatively curved Riemannian manifolds not having {\it constant} curvature. Although such complex surfaces may ... More

An example of a non-cofibrantly generated model categoryDec 18 2001We show that the model category of diagrams of spaces generated by a proper class of orbits is not cofibrantly generated. In particular the category of maps between spaces may be given a non-cofibrantly generated model structure.

Noise as a Boolean algebra of $σ$-fieldsNov 30 2011Jan 15 2014A noise is a kind of homomorphism from a Boolean algebra of domains to the lattice of $\sigma$-fields. Leaving aside the homomorphism we examine its image, a Boolean algebra of $\sigma$-fields. The largest extension of such Boolean algebra of $\sigma$-fields, ... More

Noise as a Boolean algebra of sigma-fields. III. An old question of Jacob FeldmanOct 16 2011The noise-type completion C of a noise-type Boolean algebra B is generally not the same as the closure of B. As shown in Part I (Introduction, Theorem 2), C consists of all complemented elements of the closure. It appears that C is the whole closure if ... More

Noise as a Boolean algebra of sigma-fields. I. CompletionJul 15 2011Jul 28 2011Nonclassical noises over the plane (such as the black noise of percolation) consist of sigma-fields corresponding to some planar domains. One can treat less regular domains as limits of more regular domains, thus extending the noise and its set of sigma-fields. ... More

Noise as a Boolean algebra of sigma-fields. II. Classicality, blackness, spectrumSep 08 2011Similarly to noises, Boolean algebras of sigma-fields can be black. A noise may be treated as a homomorphism from a Boolean algebra of regular open sets to a Boolean algebra of sigma-fields. Spectral sets are useful also in this framework.