Results for "Rostyslav Lesyuk"

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Insights into the formation mechanism of two-dimensional lead halide nanostructuresApr 09 2018We present a colloidal synthesis strategy for lead halide nanosheets with a thickness of far below 100 nm. Due to the layered structure and the synthesis parameters the crystals of PbI2 are initially composed of many polytypes. We propose a mechanism ... More
Attachment of colloidal nanoparticles to boron nitride nanotubesJan 25 2017There is a strong interest to attach nanoparticles non-covalently to one-dimensional systems like boron nitride nanotubes to form composites. The combination of those materials might be used for catalysis, in solar cells, or for water splitting. Additionally, ... More
Copper sulfide nanosheets with shape-tunable plasmonic properties in the NIRDec 14 20182D copper sulfide nanocrystals are promising building blocks for plasmonic materials in the near-infrared (NIR) spectral region. We demonstrate precise shape and size control (hexagonal/triangle) of colloidal plasmonic copper sulfide (covellite) nano-prisms ... More
In-plane anisotropic faceting of ultralarge and thin single-crystalline colloidal SnS nanosheetsMar 14 2019The colloidal synthesis of large thin two-dimensional (2D) nanosheets is fascinating but challenging, since the growth along the lateral and vertical dimensions need to be controlled independently. In-plane anisotropy in 2D nanosheets is attracting more ... More
Szego asymptotics for matrix-valued measures with countably many bound statesOct 11 2009Nov 09 2009Let $\mu$ be a matrix-valued measure with the essential spectrum a single interval and countably many point masses outside of it. Under the assumption that the absolutely continuous part of $\mu$ satisfies Szego's condition and the point masses satisfy ... More
Asymptotics of the Eigenvalues of Two-Diagonal Jacobi MatricesOct 04 2012We compute the asymptotics of eigenvalues of Jacobi matrices with the zero coefficients on the main diagonal and the off-diagonal coefficients which converge to zero.
Averaged deviations of Orlicz processes and majorizing measuresNov 18 2016This paper is devoted to investigation of supremum of averaged deviations $|X(t)-f(t)-\int_{\mathbb {T}}(X(u)-f(u))\,\mathrm {d}\mu(u)/\mu(\mathbb {T})|$ of a stochastic process from Orlicz space of random variables using the method of majorizing measures. ... More
Spectral and resonance problem for perturbations of periodic Jacobi operatorsNov 18 2012Sep 19 2014Necessary and sufficient conditions are presented for a measure to be the spectral measure of a finite range or exponentially decaying perturbation of a periodic Jacobi operator. As a corollary we can fully solve the inverse resonance problem: given resonances ... More
L1-spectrum of Banach space valued Ornstein-Uhlenbeck operatorsOct 04 2012We characterize the $L^1(E;\mu_\infty)$-spectrum of the Ornstein-Uhlenbeck operator, where $\mu_\infty$ is the invariant measure for the Ornstein-Uhlenbeck semigroup. The main result covers the general case of an infinite-dimensional Banach space E under ... More
Rank one non-Hermitian perturbations of Hermitian $β$-ensemblesOct 15 2015For any $\beta>0$, we provide a tridiagonal matrix model and compute the joint eigenvalue density of a random rank one non-Hermitian perturbation of Gaussian and Laguerre $\beta$-ensembles of random matrices.
Finite range perturbations of finite gap Jacobi and CMV operatorsOct 27 2014Jun 21 2016Necessary and sufficient conditions are presented for a measure to be the spectral measure of a finite range perturbation of a Jacobi or CMV operator from a finite gap isospectral torus. The special case of eventually periodic operators solves an open ... More
Meromorphic continuations of finite gap Herglotz functions and periodic Jacobi matricesOct 17 2012Sep 13 2013We find a necessary and sufficient condition for a Herglotz function $m$ to be the Borel transform of the spectral measure of an exponentially decaying perturbation of a periodic Jacobi matrix. The condition is in terms of meromorphic continuation of ... More
Jost asymptotics for matrix orthogonal polynomials on the real lineApr 04 2011May 18 2011We obtain matrix-valued Jost asymptotics for block Jacobi matrices under an L1-type condition on Jacobi parameters, and give a necessary and sufficient condition for an analytic matrix-valued function to be the Jost function of a block Jacobi matrix with ... More
Equivalence classes of block Jacobi matricesNov 09 2009Dec 08 2009The paper contains two results on the equivalence classes of block Jacobi matrices: first, that the Jacobi matrix of type 2 in the Nevai class has A_n coefficients converging to 1, and second, that under an L1-type condition on the Jacobi coefficients, ... More
Hyperspaces with the Attouch-Wets topology homeomorphic to $l_2$Mar 14 2008It is shown that the hyperspace of all nonempty closed subsets $\Cld_{AW}(X)$ of a separable metric space $X$ endowed with the Attouch-Wets topology is homeomorphic to a separable Hilbert space if and only if the completion of $X$ is proper, locally connected ... More
Colloidal Lead Iodide NanoringsDec 14 2018Colloidal chemistry of nanomaterials experienced a tremendous development in the last decades. In the course of the journey 0D nanoparticles, 1D nanowires, and 2D nanosheets have been synthesized. They have in common to possess a simple topology. We present ... More
Colloidal Tin Sulfide Nanosheets: Formation Mechanism, Ligand-mediated Shape Tuning and Photo-detectionAug 13 2018Colloidal materials of tin(II) sulfide (SnS), as a layered semiconductor with a narrow band gap, are emerging as a potential alternative to the more toxic metal chalcogenides (PbS, PbSe, CdS, CdSe) for various applications such as electronic and optoelectronic ... More
Halogens in the synthesis of colloidal semiconductor nanocrystalsApr 09 2018In this review, we highlight the role of halogenated compounds in the colloidal synthesis of nanostructured semiconductors. Halogen-containing metallic salts used as precursors and halogenated hydrocarbons used as ligands allow stabilizing different shapes ... More
Graph-directed systems and self-similar measures on limit spaces of self-similar groupsJan 13 2010Oct 05 2010Let $G$ be a group and $\phi:H\to G$ be a contracting homomorphism from a subgroup $H<G$ of finite index. V.Nekrashevych [25] associated with the pair $(G,\phi)$ the limit dynamical system $(\lims,\si)$ and the limit $G$-space $\limGs$ together with the ... More
On the lattice of subgroups of the lamplighter groupMar 26 2012The paper is devoted to the study of the lattice of subgroups of the Lamplighter type groups and to the relative gradient rank.
On Lebesgue measure of integral self-affine setsMar 31 2010Jan 17 2011Let $A$ be an expanding integer $n\times n$ matrix and $D$ be a finite subset of $Z^n$. The self-affine set $T=T(A,D)$ is the unique compact set satisfying the equality $A(T)=\cup_{d\in D} (T+d)$. We present an effective algorithm to compute the Lebesgue ... More
Relative Szegő asymptotics for Toeplitz determinantsNov 03 2016In this paper we study the asymptotic behavior, as $n\to\infty$, of ratios $D_n(e^h d\mu)/D_n(d\mu)$ of Toeplitz determinants defined by a measure $\mu$ and a sufficiently smooth function $h$. The approach we follow is based on the Verblunsky coefficients ... More
Analyticity and uniform stability of the inverse singular Sturm--Liouville spectral problemJan 28 2011We prove that the potential of a Sturm--Liouville operator depends analytically and Lipschitz continuously on the spectral data (two spectra or one spectrum and the corresponding norming constants). We treat the class of operators with real-valued distributional ... More
Matrix models and eigenvalue statistics for truncations of classical ensembles of random unitary matricesJan 21 2015Jun 21 2016We consider random non-normal matrices constructed by removing one row and column from samples from Dyson's circular ensembles or samples from the classical compact groups. We develop sparse matrix models whose spectral measures match these ensembles. ... More
On the problem of semiinfinite beam oscillation with internal dampingFeb 12 1997We study the Cauchy problem for the equation of the form $$ \ddot{u}(t) + (\aa A + B)\dot{u}(t) + (A+G)u(t) = 0,\tag* $$ where $A$, $B$, and $G$ are \o s in a Hilbert space $\Cal H$ with $A$ selfadjoint, $\sigma(A)=[0,\infty)$, $B\ge0$ bounded, and $G$ ... More
Relative Szegő asymptotics for Toeplitz determinantsNov 03 2016Sep 06 2017We study the asymptotic behavior, as $n\to\infty$, of ratios of Toeplitz determinants $D_n(e^h d\mu)/D_n(d\mu)$ defined by a measure $\mu$ on the unit circle and a sufficiently smooth function $h$. The approach we follow is based on the theory of orthogonal ... More
Finite-state self-similar actions of nilpotent groupsMay 25 2011Aug 30 2014Let $G$ be a finitely generated torsion-free nilpotent group and $\phi:H\rightarrow G$ be a surjective homomorphism from a subgroup $H<G$ of finite index with trivial $\phi$-core. For every choice of coset representatives of $H$ in $G$ there is a faithful ... More
Inverse spectral problems for energy-dependent Sturm-Liouville equationsMar 21 2012We study the inverse spectral problem of reconstructing energy-dependent Sturm-Liouville equations from their Dirichlet spectra and sequences of the norming constants. For the class of problems under consideration, we give a complete description of the ... More
Analyticity and uniform stability in the inverse spectral problem for Dirac operatorsFeb 15 2011We prove that the inverse spectral mapping reconstructing the square integrable potentials on [0,1] of Dirac operators in the AKNS form from their spectral data (two spectra or one spectrum and the corresponding norming constants) is analytic and uniformly ... More
Schrödinger Operators with Periodic Singular PotentialsSep 19 2001We show that formal Schr\"odinger operators with singular potentials from the space W^{-1}_{2,unif}(R) can be naturally defined to give selfadjoint and bounded below operators, which depend continuously in the uniform resolvent sense on the potential ... More
Half-inverse spectral problems for Sturm--Liouville operators with singular potentialsDec 09 2003Half-inverse spectral problem for a Sturm--Liouville operator consists in reconstruction of this operator by its spectrum and half of the potential. We give the necessary and sufficient conditions for solvability of the half-inverse spectral problem for ... More
Eigenvalue asymptotics for Sturm--Liouville operators with singular potentialsJul 14 2004Oct 03 2006We derive eigenvalue asymptotics for Sturm--Liouville operators with singular complex-valued potentials from the space $W^{\al-1}_{2}(0,1)$, $\al\in[0,1]$, and Dirichlet or Neumann--Dirichlet boundary conditions. We also give application of the obtained ... More
Schrödinger operators with singular Gordon potentialsSep 19 2001Singular Gordon potentials are defined to be distributions from the space W^{-1}_{2,unif}(R) that are sufficiently fast approximated by periodic ones. We prove that Schr\"odinger operators with singular Gordon potentials have no point spectrum and show ... More
On similarity of perturbed multiplication operatorsSep 21 2000Let S be the multiplication operator by an independent variable x in L_2(0,1) and V be an integral operator of Volterra type. We find conditions for T:=S+V to be similar to S and discuss some generalisations of the results obtained to an abstract setting. ... More
Self-adjointness of Schroedinger operators with singular potentialsNov 03 2011Mar 21 2012We study one-dimensional Schroedinger operators S with real-valued distributional potentials q in W^{-1}_{2,loc}(R) and prove an extension of the Povzner-Wienholtz theorem on self-adjointness of bounded below S thus providing additional information on ... More
Invariant random subgroups of the lamplighter groupJun 28 2012Sep 02 2013Let $G$ be one of the lamplighter groups $({\mathbb{Z}/p\bz})^n\wr\mathbb{Z}$ and $\Sub(G)$ the space of all subgroups of $G$. We determine the perfect kernel and Cantor-Bendixson rank of $\Sub(G)$. The space of all conjugation-invariant Borel probability ... More
Characteristic random subgroups of geometric groups and free abelian groups of infinite rankFeb 15 2014May 30 2015We show that if $G$ is a non-elementary word hyperbolic group, mapping class group of a hyperbolic surface or the outer automorphism group of a nonabelian free group then $G$ has $2^{\aleph_0}$ many continuous ergodic invariant random subgroups. If $G$ ... More
Constructions of torsion-free countable, amenable, weakly mixing groupsMay 29 2014Jul 01 2016In this note, we construct torsion-free countable, amenable, weakly mixing groups, which answer a question of V. Bergelson. Some results related to verbal subgroups and crystallographic groups are also presented.
Asymptotics of zeros for some entire functionsOct 19 2004We study the asymptotics of zeros for entire functions of the form \sin z + \int_{-1}^1 f(t)e^{izt}dt with f belonging to a space X \hookrightarrow L_1(-1,1) possessing some minimal regularity properties.
On the smallest number of generators and the probability of generating an algebraJan 17 2010Jan 19 2010In this paper we study algebraic and asymptotic properties of generating sets of algebras over orders in number fields. Let $A$ be an associative algebra over an order $R$ in an algebraic number field. We assume that $A$ is a free $R$-module of finite ... More
JCloudScale: Closing the Gap Between IaaS and PaaSNov 10 2014The Infrastructure-as-a-Service (IaaS) model of cloud computing is a promising approach towards building elastically scaling systems. Unfortunately, building such applications today is a complex, repetitive and error-prone endeavor, as IaaS does not provide ... More
Sobolev mapping properties of the scattering transform for the Schrödinger equationFeb 02 2010We consider the scattering transform for the Schr\"odinger equation with a singular potential and no bound states. Using the Riccati representation for real-valued potentials on the line, we obtain invertibility and Lipschitz continuity of the scattering ... More
Generators of maximal ordersJun 25 2014Let R be the ring of algebraic integers in a number field K and let L be a maximal order in a semisimple K-algebra B. Building on our previous work, we compute the smallest number of algebra generators of L considered as an R-algebra. This reproves and ... More
A unified approach to determining forms for the 2D Navier-Stokes equations - the general interpolants caseSep 01 2013Nov 07 2013In this paper we show that the long time dynamics (the global attractor) of the 2D Navier-Stokes equation is embedded in the long time dynamics of an ordinary differential equation, named {\it determining form}, in a space of trajectories which is isomorphic ... More
Navier-Stokes equations, determining forms, determining modes, inertial manifolds, dissipative dynamical systemsAug 25 2012The determining modes for the two-dimensional incompressible Navier-Stokes equations (NSE) are shown to satisfy an ordinary differential equation of the form $dv/dt=F(v)$, in the Banach space, $X$, of all bounded continuous functions of the variable $s\in\mathbb{R}$ ... More
Structure-preserving tangential interpolation for model reduction of port-Hamiltonian SystemsJan 18 2011Sep 18 2011Port-Hamiltonian systems result from port-based network modeling of physical systems and are an important example of passive state-space systems. In this paper, we develop the framework for model reduction of large-scale multi-input/multi-output port-Hamiltonian ... More
Penalty Robin-Robin domain decomposition schemes for contact problems of nonlinear elastic bodiesSep 05 2012In this paper we propose on continuous level several domain decomposition methods to solve unilateral and ideal multibody contact problems of nonlinear elasticity. We also present theorems about convergence of these methods.
Acoustooptic operation of optical vortex beamsAug 28 2017Using acoustooptic (AO) cells based on TeO2 crystal and silica glass, we have experimentally shown for the first time that the intensity profile and the phase structure of the vortex beam are preserved under AO Bragg diffraction. As a result, the vortex ... More
Domain decomposition methods for problems of unilateral contact between elastic bodies with nonlinear Winkler coversNov 30 2012In this paper we propose on continuous level a class of domain decomposition methods of Robin-Robin type to solve the problems of unilateral contact between elastic bodies with nonlinear Winkler covers. These methods are based on abstract nonstationary ... More
Classification of groups generated by 3-state automata over a 2-letter alphabetMar 25 2008This article contains most of the known results on the classification of groups generated by 3-state automata over a 2-letter alphabet, extending the previous papers 0704.3876 and math/0612178.
Groups generated by 3-state automata over a 2-letter alphabet, IDec 07 2006An approach to a classification of groups generated by 3-state automata over a 2-letter alphabet and the current progress in this direction are presented. Several results related to the whole class are formulated. In particular, all finite, abelian, and ... More
Groups generated by 3-state automata over a 2-letter alphabet, IIApr 30 2007Classification of groups generated by 3-state automata over a 2-letter alphabet started in the first paper (see is continued.
Backward lasing of singly ionized nitrogen ions pumped by femtosecond laser pulsesMar 11 2018We report on the observation of backward lasing at 391.4 nm of nitrogen ions pumped by linearly polarized intense femtosecond pulses at 800 nm. The strongly enhanced spectral intensity at 391.4 nm, as well as the amplification of an externally injected ... More
Lasing without population inversion in airJun 15 2018A cavity-free laser in the sky could lead to revolutionary improvements in optical remote sensing for atmospheric science. Abundant in air, nitrogen molecules are prime candidates as an active medium for such a laser. Nitrogen molecules, either neutral ... More
PubMed Labs: An experimental platform for improving biomedical literature searchJun 11 2018PubMed is a freely accessible system for searching the biomedical literature, with approximately 2.5 million users worldwide on an average workday. We have recently developed PubMed Labs (, an experimental platform for users to test ... More