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Efroymson's approximation theorem for globally subanalytic functionsMay 14 2019Efroymson's approximation theorem asserts that if $f$ is a $\mathcal{C}^0$ semialgebraic mapping on a $\mathcal{C}^\infty$ semialgebraic submanifold $M$ of $\mathbb{R}^n$ and if $\varepsilon:M\to \mathbb{R}$ is a positive continuous semialgebraic function ... More

Geometry of polynomial mappings at infinity via intersection homologyJul 14 2010For given polynomial map $F:\C^2\to\C^2$ with nonvanishing jacobian we associate a variety whose homology or intersection homology describes the geometry of singularities at infinity of this map.

A generalized Sard theorem on real closed fieldsMar 14 2015We work with semi-algebraic functions on arbitrary real closed fields. We generalize the notion of critical values and prove a Sard type theorem in our framework.

On a singular variety associated to a polynomial mappingDec 28 2012In the paper "Geometry of polynomial mapping at infinity via intersection homology" the second and third authors associated to a given polynomial mapping $F : \C^2 \to \C^2$ with nonvanishing jacobian a variety whose homology or intersection homology ... More

On the local geometry of definably stratified setsJan 18 2017We prove that a theorem of Pawlucki, showing that Whitney regularity for a subanalytic set with a smooth singular locus of codimension one implies the set is a finite union of differentiable manifolds with boundary, applies to definable sets in polynomially ... More

Property (T), finite-dimensional representations, and generic representationsNov 13 2017Let $G$ be a discrete group with property (T). It is a standard fact that, in a unitary representation of $G$ on a Hilbert space $\mathcal{H}$, almost invariant vectors are close to invariant vectors, in a quantitative way. We begin by showing that, if ... More

A New Large N Expansion for General Matrix-Tensor ModelsSep 21 2017Apr 21 2019We define a new large $N$ limit for general $\text{O}(N)^{R}$ or $\text{U}(N)^{R}$ invariant tensor models, based on an enhanced large $N$ scaling of the coupling constants. The resulting large $N$ expansion is organized in terms of a half-integer associated ... More

Proper actions of wreath products and generalizationsMay 25 2009Feb 27 2012We study stability properties of the Haagerup property and of coarse embeddability in a Hilbert space, under certain semidirect products. In particular, we prove that they are stable under taking standard wreath products. Our construction also allows ... More

Unbounded symmetric operators in $K$-homology and the Baum-Connes ConjectureDec 18 2004Using the unbounded picture of analytical K-homology, we associate a well-defined K-homology class to an unbounded symmetric operator satisfying certain mild technical conditions. We also establish an ``addition formula'' for the Dirac operator on the ... More

$L^\infty$ cohomology is intersection cohomologyDec 03 2009Jul 06 2012Let $X$ be any subanalytic compact pseudomanifold. We show a De Rham theorem for $L^\infty$ forms. We prove that the cohomology of $L^\infty$ forms is isomorphic to intersection cohomology in the maximal perversity.

A Lefschetz duality intersection homologyDec 13 2010Apr 20 2011We prove a Lefschetz duality result for intersection homology. Usually, this result applies to pseudomanifolds with boundary which are assumed to have a "collared neighborhood of their boundary". Our duality does not need this assumption and is a generalization ... More

Le problème de Kadison-Singer (The Kadison-Singer problem)Sep 20 2014In 1959, R.V. Kadison and I.M. Singer asked whether each pure state of the algebra of bounded diagonal operators on $\ell^2$, admits a unique state extension to $B(\ell^2)$. The positive answer was given in June 2013 by A. Marcus, D. Spielman and N. Srivastava, ... More

Vanishing homologyJan 14 2008In this paper we introduce a new homology theory devoted to the study of families such as semi-algebraic or subanalytic families and in general to any family definable in an o-minimal structure (such as Denjoy-Carleman definable or $ln-exp$ definable ... More

$L^1$ cohomology of bounded subanalytic manifoldsNov 09 2010We prove some de Rham theorems on bounded subanalytic submanifolds of $\R^n$ (not necessarily compact). We show that the $L^1$ cohomology of such a submanifold is isomorphic to its singular homology. In the case where the closure of the underlying manifold ... More

Wreath products with the integers, proper actions and Hilbert space compressionMar 20 2006Mar 29 2006We prove that the properties of acting metrically properly on some space with walls or some CAT(0) cube complex are closed by taking the wreath product with \Z. We also give a lower bound for the (equivariant) Hilbert space compression of H\wr\Z in terms ... More

Whitney stratifications and the continuity of local Lipschitz Killing curvaturesJul 05 2015We prove that local Lipschitz Killing curvatures of definable sets in a polynomially bounded o-minimal structure are continuous along strata of Whitney stratifications and locally Lipschitz if the stratifications are (w)- regular.

Flat currents on definable pseudomanifoldsOct 05 2016We show that the cohomology of flat currents on definable pseudomanifolds in polynomially bounded o-minimal structures is isomorphic to its intersection cohomology in the top perversity.

Spectral element modeling of three dimensional wave propagation in a self-gravitating Earth with an arbitrarily stratified outer coreAug 27 2003This paper deals with the spectral element modeling of seismic wave propagation at the global scale. Two aspects relevant to low-frequency studies are particularly emphasized. First, the method is generalized beyond the Cowling approximation in order ... More

On equivariant embeddings of generalized Baumslag-Solitar groupsDec 30 2012Let G be a group acting cocompactly without inversion on a tree X, with all vertex and edge stabilizers isomorphic to the same free abelian group Z^n. We prove that G has the Haagerup Property if and only if G is weakly amenable, and we give a necessary ... More

K-theory for the $C^*$-algebras of the solvable Baumslag-Solitar groupsApr 19 2016We provide a new computation of the K-theory of the group $C^*$-algebra of the solvable Baumslag-Solitar group $BS(1,n)\;(n\neq 1)$; our computation is based on the Pimsner-Voiculescu 6-terms exact sequence, by viewing $BS(1,n)$ as a semi-direct product ... More

The Mayer-Vietoris Sequence for Graphs of Groups, Property (T), and the First $\ell^2$-Betti NumberDec 11 2014Sep 12 2016We explore the Mayer-Vietoris sequence developed by Chiswell for the fundamental group of a graph of groups when vertex groups satisfy some vanishing assumption on the first cohomology (e.g. property (T), or vanishing of the first $\ell^2$-Betti number). ... More

Solving functional reliability issue for an optical electrostatic switchFeb 21 2008In this paper, we report the advantage of using AC actuating signal for driving MEMS actuators instead of DC voltages. The study is based upon micro mirror devices used in digital mode for optical switching operation. When the pull-in effect is used, ... More

De Rham Theorem for L^\infty forms and homology on singular spacesFeb 22 2010We introduce smooth L^\infty differential forms on a singular (semialgebraic) set X in R^n. Roughly speaking, a smooth L^\infty differential form is a certain class of equivalence of 'stratified forms', that is, a collection of smooth forms on disjoint ... More

Reduced 1-cohomology and relative property (T)Dec 06 2009Shalom characterized property (T) in terms of the vanishing of all reduced first cohomology. We characterize group pairs having the property that the restriction map on all first reduced cohomology vanishes. We show that, in a strong sense, this is inequivalent ... More

On 1-cocycles induced by a positive definite function on a locally compact abelian groupMar 18 2013For $\varphi$ a normalized positive definite function on a locally compact abelian group $G$, we consider on the one hand the unitary representation $\pi_\varphi$ associated to $\varphi$ by the GNS construction, on the other hand the probability measure ... More

Locally compact groups with every isometric action bounded or properMay 02 2017A locally compact group $G$ has property PL if every isometric $G$-action either has bounded orbits or is (metrically) proper. For $p>1$, say that $G$ has property $BP_{L^p}$ if the same alternative holds for the smaller class of affine isometric actions ... More

Expanders and box spacesSep 04 2015We consider box spaces of finitely generated, residually finite groups $G$, and try to distinguish them up to coarse equivalence. We show that, for $n\geq 2$, the group $SL_n(\mathbb{Z})$ has a continuum of box spaces which are pairwise non-coarsely equivalent ... More

Correlated radiative electron capture in ion-atom collisionsAug 30 2010Radiative double electron capture (RDEC) is a one-step process where two free (or quasi-free) target electrons are captured into a bound state of the projectile, e.g. into an empty K-shell, and the energy excess is released as a single photon. This process ... More

On the numbers of 1-factors and 1-factorizations of hypergraphsMar 28 2015Dec 14 2015A hypergraph $G=(X,W)$ is called $d$-uniform if each hyperedge $w$ is a set of $d$ vertices. A 1-factor of a hypergraph $G$ is a set of hyperedges such that every vertex of the hypergraph is incident to exactly one hyperedge from the set. A 1-factorization ... More

Towards an exact adaptive algorithm for the determinant of a rational matrixMay 31 2007In this paper we propose several strategies for the exact computation of the determinant of a rational matrix. First, we use the Chinese Remaindering Theorem and the rational reconstruction to recover the rational determinant from its modular images. ... More

Iterated identities and iterational depth of groupsSep 21 2014Given word on $n$ letters, we study groups which satisfiy "iterated identity" $w$, meaning that for all $x_1, \dots, x_n$ there exists $m$ such that $m$-the iteration of $w$ of Engel type, applied to $x_1, \dots, x_n$, is equal to the identity. We define ... More

Modeling IR SED of AGN with Spitzer and Herschel dataJan 21 2013One of the remaining open issues in the context of the analysis of Active Galactic Nuclei (AGN) is the evidence that nuclear gravitational accretion is often accompanied by a concurrent starburst (SB) activity. What is, in this picture, the role played ... More

On Orbital variety closures in sl_n. III Geometric propertiesJul 25 2005This is the third paper in the series. Here we define a few combinatorial orders on Young tableaux. The first order is obtained from induced Duflo order by the extension with the help of Vogan T_{\alpha, \beta} procedure. We call it Duflo-Vogan order. ... More

The Finite Temperature Effective Potential for Local Composite OperatorsApr 04 1997The method of the effective action for the composite operators $\Phi^2(x)$ and $\Phi^4(x)$ is applied to the termodynamics of the scalar quantum field with $\lambda\Phi^4$ interaction. An expansion of the finite temperature effective potential in powers ... More

Goldstone Bosons in the Gaussian ApproximationAug 18 1995Aug 31 1995The O(N) symmetric scalar quantum field theory with \lambda\Phi^4 interaction is discussed in the Gaussian approximation. It is shown that the Goldstone theorem is fulfilled for arbitrary N.

Gaussian approximation to the condensation of the interacting Bose gasSep 29 2003The effective action formalism of quantum field theory is used to study the properties of the non-relativistic interacting Bose gas. The Gaussian approximation is formulated by calculating the effective action to the first order of the optimized expansion. ... More

Multi-particle States from the Effective Action for Local Composite Operators: Anharmonic OscillatorDec 15 1995Dec 19 1995The effective action for the local composite operator $\Phi^2(x)$ in the scalar quantum field theory with $\lambda\Phi^4$ interaction is obtained in the expansion in two-particle-point-irreducible (2PPI) diagrams up to five-loops. The effective potential ... More

Exploring the Universe with Metal-Poor StarsAug 23 2011The early chemical evolution of the Galaxy and the Universe is vital to our understanding of a host of astrophysical phenomena. Since the most metal-poor Galactic stars (with metallicities down to [Fe/H]\sim-5.5) are relics from the high-redshift Universe, ... More

An embedding resultDec 29 2013In unbounded subset $\Omega$ in $R^n$ we study the operator $u\rightarrow gu$ as an operator defined in the Sobolev space $W^{r,p}(\Omega)$ and which takes values in $L^p(\Omega)$. The functions $g$ belong to wider spaces of $L^p$ connected with the Morrey ... More

Exact Solutions to SupergravityJun 11 1996We find a general p-1-brane solution to supergravity coupled to a p+1-form field strength using the ``standard ansatz'' for the fields. In addition to the well-known elementary and solitonic p-1-brane solutions, which are the only ones preserving half ... More

String Solutions to SupergravityOct 23 1996We find the comlete solution to ten-dimensional supergravity coupled to a three-form field strength, given the ``standard ansatz" for the fields, and show that in addition to the well-known elementary and solitonic (heterotic) string solutions, one of ... More

B0943+10: low-frequency study of subpulse periodicity in the Bright mode with LOFAROct 16 2017We utilise broadband sensitive LOFAR observations in 25-80 MHz frequency range to study the single-pulse emission properties of the mode-switching pulsar PSR B0943+10. We review the derivation of magnetospheric geometry, originally based on low-frequency ... More

Rényi relative entropies and noncommutative $L_p$-spacesSep 27 2016Jun 30 2017We propose an extension of the sandwiched R\'enyi relative $\alpha$-entropy to normal positive functionals on arbitrary von Neumann algebras, for the values $\alpha>1$. For this, we use Kosaki's definition of noncommutative $L_p$-spaces with respect to ... More

Positiveness of the permanent of 4-dimensional polystochastic matrices of order 4Jan 31 2018A nonnegative multidimensional matrix is called polystochastic if the sum of its entries over each line is equal to one. We prove that the permanent of every $4$-dimensional polystochastic matrix of order $4$ is positive.

Torsion and Linking number for a surface diffeomorphismJan 23 2018For a $\mathcal{C}^1$ diffeomorphism $f:\mathbb{R}^2\rightarrow\mathbb{R}^2$ isotopic to the identity, we prove that for any value $l\in\mathbb{R}$ of the linking number at finite time of the orbits of two points there exists at least a point whose torsion ... More

Weakly Interacting, Dilute Bose Gases in 2DJun 01 2005Jun 27 2006This article surveys a number of theoretical problems and open questions in the field of two-dimensional dilute Bose gases with weak repulsive interactions. In contrast to three dimensions, in two dimensions the formation of long-range order is prohibited ... More

Classification of isoparametric hypersurfaces in spheres with $(g,m)=(6,1)$Mar 15 2015Aug 05 2015We classify isoparametric hypersurfaces in spheres with $(g,m)=(6,1)$ and thereby reprove a result of Dorfmeister and Neher.

Harmonic Self-maps of $\mbox{SU}(3)$Dec 22 2015By constructing solutions of a singular boundary value problem we prove the existence of a countably infinite family of harmonic self-maps of $\mbox{SU}(3)$ with non-trivial, i.e. $\neq 0,\pm 1$, Brouwer degree.

Improving LHC searches for strong EW symmetry breaking resonancesMay 18 2015Sep 05 2016Composite Higgs models generically predict the existence of heavy spin-1 resonances with the same quantum numbers as electroweak gauge bosons. The effective lagrangian description of these resonances is presented, pointing out the origin of their interactions ... More

Symmetric waves are traveling waves for a shallow water equation for surface waves of moderate amplitudeFeb 01 2016Following a general principle introduced by Ehrnstr\"{o}m et.al. we prove that for an equation modeling the free surface evolution of moderate amplitude waves in shallow water, all symmetric waves are traveling waves.

Cyclic anamorphic cosmologyOct 10 2016Cyclic models of the universe have the advantage of avoiding initial conditions problems related to postulating any sort of beginning in time. To date, the only known viable examples of cyclic models have been ekpyrotic. In this paper, we show that the ... More

Generalised global supersolutions with mass control for systems with taxisJun 15 2018Mar 27 2019The existence of generalised global supersolutions with a control upon the total muss is established for a wide family of parabolic-parabolic chemotaxis systems and general integrable initial data in any space dimension. It is verified that as long as ... More

Generalised global supersolutions with mass control for systems with taxisJun 15 2018The existence of generalised global supersolutions with a control upon the total muss is established for a wide family of parabolic-parabolic chemotaxis systems and general integrable initial data in any space dimension. It is verified that as long as ... More

Compactifying the Space of Length Functions of a Right-angled Artin GroupOct 20 2015Culler and Morgan proved that the length function of a minimal action of a group on a tree completely determines the action. As a consequence the space of minimal actions of a free group on trees, up to scaling (also known as Outer Space), embeds in infinite ... More

Geometric construction of spinors in orthogonal modular categoriesOct 16 2002Oct 09 2003A geometric construction of Z_2-graded orthogonal modular categories is given. Their 0-graded parts coincide with categories previously obtained by Blanchet and the author from the category of tangles modulo the Kauffman skein relations. Quantum dimensions ... More

RG Smoothing Algorithm Which Makes Data CompressionJun 05 2018I describe a new method for smoothing a one-dimensional curve in Euclidian space with an arbitrary number of dimensions. The basic idea is borrowed from renormalization group theory which previously was applied to biological macromolecules. There are ... More

Contribution of Cosmic Rays from Sources with a Monoenergetic Proton Spectrum to the Extragalactic Diffuse Gamma-Ray EmissionDec 30 2018The extragalactic sources of ultra-high-energy (E > 4x10^19 eV) cosmic rays that make a small contribution to the flux of particles recorded by ground-based arrays are discussed. We show that cosmic rays from such sources can produce a noticeable diffuse ... More

On quantum quasi-relative entropySep 30 2018Jan 27 2019We consider a quantum quasi-relative entropy $S_f^K$ for an operator $K$ and an operator convex function $f$. We show how to obtain the error bounds for the monotonicity and joint convexity inequalities from the recent results for the $f$-divergences ... More

Ranks and Symmetric Ranks of Cubic SurfacesJan 16 2018We study cubic surfaces as symmetric tensors of format $4 \times 4 \times 4$. We consider the non-symmetric tensor rank and the symmetric Waring rank of cubic surfaces, and show that the two notions coincide over the complex numbers. The corresponding ... More

On the determinant of hexagonal grids $H_{k,n}$Aug 31 2013Feb 15 2014We analyse the problem of singularity of graphs for hexagonal grid graphs. We introduce methods for transforming weighted graph, which do not change the determinant of adjacency matrix. We use these methods to calculate the determinant of all hexagonal ... More

Lyapunov theorem for q-concave Banach spacesOct 17 2013Generalization of Lyapunov convexity theorem is proved for vector measure with values in Banach spaces with unconditional bases, which are q-concave for some $q<\infty.$

Bounded Cohomology and GeometryJan 17 2005This work deals with relations between a bounded cohomological invariant and the geometry of Hermitian symmetric spaces of noncompact type. The invariant, obtained from the K\"ahler class, is used to define and characterize a special class of totally ... More

Representations and geometric structuresFeb 10 2016This note summarizes in an informal way some geometric properties of Anosov representations into the symplectic group, which were presented in a talk at the conference What is Next. The mathematical legacy of Bill Thurston, held in June 2014 in Cornell. ... More

Kronecker limit formulas and scattering constants for Fermat curvesNov 04 2011Eisenstein series are real analytic functions which play a central role in spectral theory of the hyperbolic Laplacian. Kronecker limit formulas determine their connection to modular forms. The main result of this work is Theorem 7.2 in which a Kronecker ... More

On $S_n$-invariant conformal blocks vector bundles of rank one on $\overline M_{0,n}$Apr 23 2014For any simple Lie algebra, a positive integer, and tuple of compatible weights, the conformal blocks bundle is a globally generated vector bundle on the moduli space of pointed rational curves. We classify all $S_n$-invariant vector bundles of conformal ... More

A construction of a nonparametric quantum information manifoldNov 21 2005We present a construction of a Banach manifold on the set of faithful normal states of a von Neumann algebra, where the underlying Banach space is a quantum analogue of an Orlicz space. On the manifold, we introduce the exponential and mixture connections ... More

Generalised global supersolutions with mass control for systems with taxisJun 15 2018Apr 10 2019The existence of generalised global supersolutions with a control upon the total muss is established for a wide family of parabolic-parabolic chemotaxis systems and general integrable initial data in any space dimension. It is verified that as long as ... More

Note about Stiefel-Whitney classes on real Bott manifoldsAug 24 2018Real Bott manifolds is a class of flat manifolds with holonomy group $\mathbb Z_2^k$ of diagonal type. In this paper we want to show how we can compute even Stiefel - Whitney classes on real Bott manifolds. This paper is an answer to the question of professor ... More

A minimal scale invariant axion solution to the strong CP-problemMay 30 2017Dec 07 2017We present a scale invariant extension of the Standard model allowing for the Kim-Shifman-Vainstein-Zakharov (KSVZ) axion solution of the strong CP problem in QCD. We add the minimal number of new particles and show that the Peccei-Quinn scalar might ... More

Teichmuller geodesics that do not have a limit in PMFOct 31 2005Nov 17 2010We construct a Teichmuller geodesic which does not have a limit on the Thurston boundary of the Teichmuller space.

Woronowicz construction of compact quantum groups for functions on permutations. Classification result for N=3Jan 28 2014We provide a classification of compact quantum groups, which can be obtained by the Woronowicz construction, when the arrays used in the twisted determinant condition are extensions of functions on permutations. General properties of such quantum groups ... More

Maximally informative ensembles for SIC-POVMs in dimension 3Apr 30 2014Nov 16 2014In order to find out for which initial states of the system the uncertainty of the measurement outcomes will be minimal, one can look for the minimizers of the Shannon entropy of the measurement. In case of group covariant measurements this question becomes ... More

Strong electroweak symmetry breaking (or, if no SM Higgs, then what?)Jun 08 2012While the LHC takes on the challenge of experimentally exploring the electroweak symmetry breaking sector, it is not only interesting but also crucial to explore alternatives to the Standard Model scenario with an elementary scalar Higgs boson. The idea ... More

Detection techniques for the H.E.S.S. II telescope, data modeling of gravitational lensing and emission of blazars in HE-VHE astronomyJul 15 2013This thesis presents the study of four aspects of high energy astronomy. The first part of the thesis is dedicated to an aspect of instrument development for imaging atmospheric Cherenkov telescopes, namely the Level 2 trigger system of the High Energy ... More

Two-weight norm inequalities for potential type and maximal operators in a metric spaceMay 13 2011Dec 31 2012We characterize two-weight norm inequalities for potential type integral operators in terms of Sawyer-type testing conditions. Our result is stated in a space of homogeneous type with no additional geometric assumptions, such as group structure or non-empty ... More

B-orbits of nilpotent order 2 and link patternsMar 13 2007Sep 03 2008In this paper we describe geometry of orbits of upper triangular matrices of nilpotent order 2 under conjugation by the group of upper triangular invertible matrices in terms of link patterns. Further we apply this description to the computations of the ... More

Description of B-orbit closures of order 2 in upper-triangular matricesDec 15 2003Nov 10 2005Let n_n(C) be the algebra of strictly upper-triangular n x n matrices over the field of complex numbers and X_2 the subset of matrices of nilpotent order 2. Let B_n(C) be the group of invertible upper-triangular matrices acting on n_n(C) by conjugation. ... More

Generalized channels: channels for convex subsets of the state spaceMay 10 2011Mar 12 2012Let $K$ be a convex subset of the state space of a finite dimensional $C^*$-algebra. We study the properties of channels on $K$, which are defined as affine maps from $K$ into the state space of another algebra, extending to completely positive maps on ... More

Geodesic distances on density matricesDec 17 2003We find an upper bound for geodesic distances associated to monotone Riemannian metrics on positive definite matrices and density matrices.

Extremality conditions for generalized channelsApr 12 2012A generalized channel is a completely positive map that preserves trace on a given subspace. We find conditions under which a generalized channel with respect to a positively generated subspace J is an extreme point in the set of all such generalized ... More

Resolutions of p-stratifolds with isolated singularitiesNov 18 2003Recently M. Kreck introduced a class of stratified spaces called p-stratifolds [M. Kreck, Stratifolds, Preprint]. He defined and investigated resolutions of p-stratifolds analogously to resolutions of algebraic varieties. In this note we study a very ... More

Current-carrying molecules: a real space pictureJun 30 2005An approach is presented to calculate characteristic current vs voltage curves for isolated molecules without explicit description of leads. The Hamiltonian for current-carrying molecules is defined by making resort to Lagrange multipliers, while the ... More

The Fokker-Planck equation for bistable potential in the optimized expansionNov 21 2001The optimized expansion is used to formulate a systematic approximation scheme to the probability distribution of a stochastic system. The first order approximation for the one-dimensional system driven by noise in an anharmonic potential is shown to ... More

A new structural approach to isoparametric hypersurfaces in spheresOct 22 2014The classification of isoparametric hypersurfaces in spheres with four or six different principal curvatures is still not complete. In this paper we develop a structural approach that may be helpful for a classification. Instead of working with the isoparametric ... More

Stellar Archaeology: New Science with Old StarsDec 06 2010The abundance patterns of metal-poor stars provide us a wealth of chemical information about various stages of cosmic chemical evolution. In particular, these stars allow us to study the formation and evolution of the elements, and the involved nucleosynthesis ... More

On Non-Gaussian Limiting Laws for the Certain Statistics of the Wigner MatricesJan 14 2012We continue investigations of our previous papers, in which there were proved central limit theorems (CLT) for linear eigenvalue statistics Tr f(M_n) and there were found the limiting probability laws for the normalised matrix elements of differential ... More

MCRG study of 12 fundamental flavors with mixed fundamental-adjoint gauge actionDec 28 2011I discuss the infrared behavior of the SU(3) gauge model with 12 fundamental fermions. Using a Monte Carlo renormalization group technique I investigate the fixed point structure in the chiral limit and show that this system has an infrared fixed point ... More

Infrared fixed point of the 12-fermion SU(3) gauge model based on 2-lattice MCRG matchingJun 27 2011I investigate an SU(3) gauge model with 12 fundamental fermions. The physically interesting region of this strongly coupled system can be influenced by an ultraviolet fixed point due to lattice artifacts. I suggest to use a gauge action with an additional ... More

Scaling properties of many-fermion systems from MCRG studiesNov 03 2009Monte Carlo renormalization group methods were designed to study the phase structure and critical behavior of statistical systems. They are well suited to determine the running coupling and to investigate the properties of fixed points of gauge-fermion ... More

Transversals in completely reducible multiary quasigroups and in multiary quasigroups of order 4Dec 06 2016An $n$-ary quasigroup $f$ of order $q$ is an $n$-ary operation over a set of cardinality $q$ such that the Cayley table of the operation is an $n$-dimensional latin hypercube of order $q$. A transversal in a quasigroup $f$ (or in the corresponding latin ... More

Rényi relative entropies and noncommutative $L_p$-spaces IIJun 30 2017We show the relation between two versions of sandwiched R\'enyi relative entropies for von Neumann algebras, introduced recently in [M. Berta et al, arXiv:1608.05317] and [A. Jen\v{c}ov\'a, arXiv:1609.08462]. It is also proved that equality in data processing ... More

Spin-structures on real Bott manifolds with Kähler structuresMar 24 2017Let M be a real Bott manifold with K\"{a}hler structure. Using Ishida characterization we give necessary and sufficient condition for the existence of the Spin-structure on M. In proof we use the technic developed in Popko, Szczepa\'{n}ski "Cohomological ... More

On the convex structure of process POVMsAug 03 2015Measurements on quantum channels are described by so-called process operator valued measures, or process POVMs. We study implementing schemes of extremal process POVMs. As it turns out, the corresponding measurement must satisfy certain extremality property, ... More

Pure spinor indications of ultraviolet finiteness in D=4 maximal supergravityJun 24 2015Aug 17 2015The ultraviolet divergences of amplitude diagrams in maximal supergravity are characterised by a first possible divergence at seven loops for the 4-point amplitude (logarithmic) and, in its absence, at eight loops. We revisit the pure spinor superfield ... More

Self-similarity of Jankins-Neumann zigguratMar 10 2015Primarily having emerged from a topological question, Jankins-Neumann ziggurat also appears in the theory of dynamical systems on the circle. It describes an answer to the following question: given the rotation numbers of two orientation-preserving circle ... More

Ultraviolet divergences in maximal supergravity from a pure spinor point of viewDec 18 2014Aug 17 2015The ultraviolet divergences of amplitude diagrams in maximal supergravity are investigated using the pure spinor superfield formalism in maximal supergravity, with maximally supersymmetric Yang-Mills theory for reference. We comment on the effects of ... More

Rigorous enclosures of rotation numbers by interval methodsSep 24 2015We apply set-valued numerical methods to compute an accurate enclosure of the rotation number. The described algorithm is supplemented with a method of proving the existence of periodic points, which is used to check the rationality of the rotation number. ... More

Almost invariance of distributions for random walks on groupsMar 04 2016Apr 28 2016We study the neighborhoods of a typical point $Z_n$ visited at $n$-th step of a random walk, determined by the condition that the transition probabilities stay close to $\mu^{*n}(Z_n)$. If such neighborhood contains a ball of radius $C \sqrt{n}$, we say ... More

A counterpart of the Verlinde algebra for the small quantum groupJul 19 2001May 07 2002Let $\bar{Pr}$ denote the ideal spanned by the characters of projective modules in the Grothendieck ring of the category of finite dimensional modules over the small quantum group $u_l$. We show that $\bar{Pr}$ admits a description completely parallel ... More

Sturmian numeration systems and decompositions to palindromesOct 31 2017Nov 02 2017We extend the classical Ostrowski numeration systems, closely related to Sturmian words, by allowing a wider range of coefficients, so that possible representations of a number $n$ better reflect the structure of the associated Sturmian word. In particular, ... More