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Modeling emission of acoustic energy during bubble expansion in PICO bubble chambersJun 11 2019The PICO experiment uses bubble chambers filled with superheated C$_3$F$_8$ for spin-dependent WIMP dark matter searches. One of the main sources of background in these detectors is alpha particles from decays of environmental $^{222}\mathrm{Rn}$, which ... More

Sensitivity of the PICO-500 Bubble Chamber to Supernova Neutrinos Through Coherent Nuclear Elastic ScatteringJun 04 2018Nov 05 2018Ton-scale direct dark matter search experiments should be sensitive to neutrino-induced recoil events from either $^8$B solar neutrinos or the brief but intense flux from a core collapse supernova in the Milky Way. These low-threshold detectors are sensitive ... More

Order estimates of best orthogonal trigonometric approximations of classes of infinitely differentiable functionsDec 16 2018In this paper we establish exact order estimates for the best uniform orthogonal trigonometric approximations of the classes of $2\pi$-periodic functions, whose $(\psi,\beta)$-derivatives belong to unit balls of spaces $L_{p}$, $1\leq p<\infty$, in the ... More

Some remarks about system of balls that generate shadow at pointDec 04 2017Problems, related to the determination of the minimal number of balls that generate a shadow at a fixed point in the multi-dimensional Euclidean space $ \mathbb{R}^n $, are considered in present work. Here, the statement "a system of balls generate shadow ... More

On semiconvexity and weak semiconvexityNov 13 2017Properties of two classes of generally convex sets in the n-dimentional real Euclidean space, called m-semiconvex and weakly m-semiconvex, 1<=m<n, are investigated in the present work. In particular, it is established that an open set with smooth boundary ... More

On the shadow problem for domains in the Euclidean spacesFeb 03 2016In the present work, the problem about shadow, generalized on domains of space $\mathbb{R}^n$, $n\le 3$, is investigated. Here the shadow problem means to find the minimal number of balls satisfying some conditions an such that every line passing through ... More

Institutional repository `eKMAIR': establishing and populating a research repository for the National University "Kyiv Mohyla Academy"Mar 12 2012Aug 21 2012University libraries have an increasingly important role to play in supporting open access publishing and dissemination of research outputs.1 In particular, many libraries are playing a leading role in establishing and managing institutional repositories. ... More

Estimates for logarithmic and Riesz energies for spherical $t$-designsJan 02 2019In this paper we find asymptotic equalities for the discrete logarithmic energy of sequences of well separated spherical $t$-designs on the unit sphere ${\mathbb{S}^{d}\subset\mathbb{R}^{d+1}}$, $d\geq2$. Also we establish exact order estimates for discrete ... More

Topological conjugacy classes of affine mapsDec 29 2008Feb 11 2009A map $f: \ff^n \to \ff^n$ over a field $\ff$ is called affine if it is of the form $f(x)=Ax+b$, where the matrix $A \in \ff^{n\times n}$ is called the linear part of affine map and $b \in \ff^n$. The affine maps over $\ff=\rr$ or $\cc$ are investigated. ... More

Topological classification of affine operators on unitary and Euclidean spacesOct 16 2010We classify affine operators on a unitary or Euclidean space U up to topological conjugacy. An affine operator is a map f: U-->U of the form f(x)=Ax+b, in which A: U-->U is a linear operator and b in U. Two affine operators f and g are said to be topologically ... More

Elliptic operators on refined Sobolev scales on vector bundlesAug 15 2017We introduce a refined Sobolev scale on a vector bundle over a closed infinitely smooth manifold. This scale consists of inner product H\"ormander spaces parametrized with a real number and a function varying slowly at infinity in the sense of Karamata. ... More

Hyperuniform point sets on flat tori: deterministic and probabilistic aspectsFeb 08 2019In this paper we study hyperuniformity on flat tori. Hyperuniform point sets on the unit sphere have been studied by J.~Brauchart, P.~Grabner, W.~Kusner and J.~Ziefle. It is shown that point sets which are hyperuniform for large balls, small balls or ... More

Regularizing algorithm for mixed matrix pencilsAug 17 2018P. Van Dooren (1979) constructed an algorithm for computing all singular summands of Kronecker's canonical form of a matrix pencil. His algorithm uses only unitary transformations, which improves its numerical stability. We extend Van Dooren's algorithm ... More

Daugavet centers and direct sums of Banach spacesMar 25 2010A linear continuous nonzero operator G:X->Y is a Daugavet center if every rank-1 operator T:X->Y satisfies ||G+T||=||G||+||T||. We study the case when either X or Y is a sum $X_1 \oplus_F X_2$ of two Banach spaces $X_1$ and $X_2$ by some two-dimensional ... More

Comparison of probabilistic and deterministic point setsMar 23 2018In this paper we make a comparison between certain probabilistic and deterministic point sets and show that some deterministic constructions (spherical $t$-designs) are better or as good as probabilistic ones. We find asymptotic equalities for the discrete ... More

Moments of Riesz measures on Poincaré disk and homogeneous tree - a comparative studyApr 15 2014One of the purposes of this paper is to clarify the strong analogy between potential theory on the open unit disk and the homogeneous tree, to which we dedicate an introductory section. We then exemplify this analogy by a study of Riesz measures. Starting ... More

Asymptotically best possible Lebesque-type inequalities for the Fourier sums on sets of generalized Poisson integralsAug 26 2019In this paper we establish Lebesgue-type inequalities for $2\pi$-periodic functions $f$, which are defined by generalized Poisson integrals of the functions $\varphi$ from $L_{p}$, $1\leq p< \infty$. In these inequalities uniform norms of deviations of ... More

Classification of affine operators up to biregular conjugacyOct 16 2010Let f(x)=Ax+b and g(x)=Cx+d be two affine operators given by n-by-n matrices A and C and vectors b and d over a field F. They are said to be biregularly conjugate if hf=gh for some bijection h: F^n-->F^n being biregular, this means that the coordinate ... More

On nonsymmetric rank one singular perturbations of selfadjoint operatorsAug 24 2016We consider nonsymmetric rank one singular perturbations of a selfadjoint operator, i.e., an expression of the form $\tilde A = A + \alpha\left\langle\cdot, \omega_1\right\rangle\omega_2$, $\omega_1\not = \omega_2$, $\alpha\in{\mathbb C}$, in a general ... More

Upper and lower estimates for numerical integration errors on spheres of arbitrary dimensionJan 16 2018In this paper we study the worst-case error of numerical integration on the unit sphere $\mathbb{S}^{d}\subset\mathbb{R}^{d+1}$, $d\geq2$, for certain spaces of continuous functions on $\mathbb{S}^{d}$. For the classical Sobolev spaces $\mathbb{H}^s(\mathbb{S}^d)$ ... More

Elliptic problems with boundary operators of higher orders in Hörmander-Roitberg spacesFeb 01 2018We investigate elliptic boundary-value problems for which the maximum of the orders of the boundary operators is equal to or greater than the order of the elliptic differential equation. We prove that the operator corresponding to an arbitrary problem ... More

On the growth of Lebesgue constants for convex polyhedraJan 02 2018In the paper, new estimates of the Lebesgue constant $$ \mathcal{L}(W)=\frac1{(2\pi)^d}\int_{\mathbb{T}^d}\bigg|\sum_{{k}\in W\cap \mathbb{Z}^d} e^{i({k},\,{x})}\bigg| {\rm d}{ x} $$ for convex polyhedra $W\subset\mathbb{R}^d$ are obtained. The main result ... More

Inequalities in approximation theory involving fractional smoothness in $L_p$, $0<p<1$Nov 08 2018In the paper, we study inequalities for the best trigonometric approximations and fractional moduli of smoothness involving the Weyl and Liouville-Gr\"unwald derivatives in $L_p$, $0<p<1$. We extend known inequalities to the whole range of parameters ... More

Inference for partial correlation when data are missing not at randomOct 12 2017We introduce uncertainty regions to perform inference on partial correlations when data are missing not at random. These uncertainty regions are shown to have a desired asymptotic coverage. Their finite sample performance is illustrated via simulations ... More

Elliptic boundary-value problems in Hörmander spacesDec 13 2016Dec 29 2016We investigate general elliptic boundary-value problems in H\"ormander inner product spaces that form the extended Sobolev scale. The latter consists of all Hilbert spaces that are interpolation spaces with respect to the Sobolev Hilbert scale. We prove ... More

Elliptic problems in the sense of Lawruk with boundary operators of higher orders in refined Sobolev scaleApr 02 2018In a refined Sobolev scale, we investigate an elliptic boundary-value problem with additional unknown functions in boundary conditions for which the maximum of orders of boundary operators is grater than or equal to the order of the elliptic equation. ... More

Elliptic problems with boundary conditions of high orders in Hörmander spacesAug 10 2017In a class of inner product H\"ormander spaces, we investigate a general elliptic problem for which the maximum of orders of boundary conditions is grater than or equal to the order of elliptic equation. The order of regularity for these spaces is an ... More

Mean value property for nonharmonic functionsSep 19 2013In this article we extend the mean value property for harmonic functions to the nonharmonic case. In order to get the value of the function at the center of a sphere one should integrate a certain Laplace operator power series over the sphere. We write ... More

Topological classification of chains of linear mappingsAug 20 2013We prove that two chains of linear mappings are topologically isomorphic if and only if they are linearly isomorphic.

Topological classification of Mobius transformationsAug 20 2013Linear fractional transformations on the extended complex plane are classified up to topological conjugacy. Recall that two transformations f and g are called topologically conjugate if there exists a homeomorphism h such that hg=fh.

Topological classification of oriented cycles of linear mappingsJan 11 2014We consider the problem of classifying oriented cycles of linear mappings $F^p\to F^q\to\dots\to F^r\to F^p$ over a field $F$ of complex or real numbers up to homeomorphisms in the spaces $F^p,F^q,\dots,F^r$. We reduce it to the problem of classifying ... More

Parameter-elliptic operators on the extended Sobolev scaleDec 04 2012Parameter--elliptic pseudodifferential operators given on a closed smooth manifold are investigated on the extended Sobolev scale. This scale consists of all Hilbert spaces that are interpolation spaces with respect to the Hilbert Sobolev scale. We prove ... More

Global Autoregressive Models for Data-Efficient Sequence LearningSep 16 2019Standard autoregressive seq2seq models are easily trained by max-likelihood, but tend to show poor results under small-data conditions. We introduce a class of seq2seq models, GAMs (Global Autoregressive Models), which combine an autoregressive component ... More

Conditioned point processes with application to Lévy bridgesJan 23 2018Our first result concerns a characterisation by means of a functional equation of Poisson point processes conditioned by the value of their first moment. It leads to a generalised version of Mecke's formula. En passant, it also allows to gain quantitative ... More

Regularizing decompositions for matrix pencils and a topological classification of pairs of linear mappingsMar 11 2014May 03 2014We give a method for constructing a regularizing decomposition of a matrix pencil, which is formulated in terms of the linear mappings. We prove that two pencils are topologically equivalent if and only if their regularizing decompositions coincide up ... More

Perturbation analysis of a matrix differential equation $\dot x=ABx$Aug 17 2018Two complex matrix pairs $(A,B)$ and $(A',B')$ are contragrediently equivalent if there are nonsingular $S$ and $R$ such that $(A',B')=(S^{-1}AR,R^{-1}BS)$. M.I. Garc\'{\i}a-Planas and V.V. Sergeichuk (1999) constructed a miniversal deformation of a canonical ... More

Nonregular elliptic boundary-value problems and Hörmander spacesMar 11 2018We investigate nonregular elliptic problems with boundary conditions of higher orders. We prove that these problems are Fredholm on appropriate pairs of inner product H\"ormander spaces that form a two-sided refined Sobolev scale. We also prove a theorem ... More

Poissonian pair correlation on manifolds via the heat kernelApr 17 2019Aug 07 2019We define a notion of Poissonian pair correlation (PPC) for Riemannian manifolds without boundary and prove that PPC implies uniform distribution in this setting. This extends earlier work by Grepstad and Larcher, Aistleitner, Lachmann, and Pausinger, ... More

A Study of B+->p pbar K+ and a Search for a Theta*++ Pentaquark Candidate in B DecayNov 02 2004A study of the decay B+->ppbarK+ is performed using 81fb-1 of data collected at the Upsilon(4S) with the BaBar detector at PEP-II. The branching fraction of B+->ppbarK+ is measured to be (6.7+/-0.9+/-0.6)x10^-6. An upper limit on the branching fraction ... More

Poissonian pair correlation on manifolds via the heat kernelApr 17 2019We define a notion of Poissonian pair correlation (PPC) for Riemannian manifolds without boundary and prove that PPC implies uniform distribution in this setting. This extends earlier work by Grepstad and Larcher, Aistleitner, Lachmann, and Pausinger, ... More

Sobolev-like Hilbert spaces induced by elliptic operatorsMay 22 2018We investigate properties of function spaces induced by the inner product Sobolev spaces $H^{s}(\Omega)$ over a bounded Euclidean domain $\Omega$ and by an elliptic differential operator $A$ on $\overline{\Omega}$. The domain and the coefficients of $A$ ... More

Simultaneous Approximation of a Multivariate Function and its Derivatives by Multilinear SplinesAug 24 2013In this paper we consider the approximation of a function by its interpolating multilinear spline and the approximation of its derivatives by the derivatives of the corresponding spline. We derive formulas for the uniform approximation error on classes ... More

On approximation of functions by algebraic polynomials in Hölder spacesFeb 16 2016We study approximation of functions by algebraic polynomials in the H\"older spaces corresponding to the generalized Jacobi translation and the Ditzian-Totik moduli of smoothness. By using modifications of the classical moduli of smoothness, we give improvements ... More

On $L_p$-error of bivariate polynomial interpolation on the squareDec 17 2017We obtain estimates of the $L_p$-error of the bivariate polynomial interpolation on the Lissajous-Chebyshev node points for wide classes of functions including non-smooth functions of bounded variation in the sense of Hardy-Krause. The results show that ... More

Roth's solvability criteria for the matrix equations ${AX-\widehat XB=C}$ and ${X-A\widehat{X}B=C}$ over the skew field of quaternions with an involutive automorphism $q\mapsto \hat q$Nov 11 2016The matrix equation $AX-XB=C$ has a solution if and only if the matrices [A&C\\0&B] and [A &0\\0 & B] are similar. This criterion was proved over a field by W.E. Roth (1952) and over the skew field of quaternions by Huang Liping (1996). H.K. Wimmer (1988) ... More

Transportation distances and noise sensitivity of multiplicative Lévy SDE with applicationsNov 24 2015This article assesses the distance between the laws of stochastic differential equations with multiplicative L\'evy noise on path space in terms of their characteristics. The notion of transportation distance on the set of L\'evy kernels introduced by ... More

Wildness of the problems of classifying two-dimensional spaces of commuting linear operators and certain Lie algebrasSep 29 2017For each two-dimensional vector space $V$ of commuting $n\times n$ matrices over a field $\mathbb F$ with at least 3 elements, we denote by $\widetilde V$ the vector space of all $(n+1)\times(n+1)$ matrices of the form $\left[\begin{smallmatrix}A&*\\0&0\end{smallmatrix}\right]$ ... More

DeblurGAN-v2: Deblurring (Orders-of-Magnitude) Faster and BetterAug 10 2019We present a new end-to-end generative adversarial network (GAN) for single image motion deblurring, named DeblurGAN-v2, which considerably boosts state-of-the-art deblurring efficiency, quality, and flexibility. DeblurGAN-v2 is based on a relativistic ... More

Topological classification of sesquilinear forms: reduction to the nonsingular caseApr 19 2016Two sesquilinear forms $\Phi:\mathbb C^m\times\mathbb C^m\to \mathbb C$ and $\Psi:\mathbb C^n\times\mathbb C^n\to \mathbb C$ are called topologically equivalent if there exists a homeomorphism $\varphi :\mathbb C^m\to \mathbb C^n$ (i.e., a continuous ... More

Tame systems of linear and semilinear mappingsDec 10 2014We study systems of linear and semilinear mappings considering them as representations of a directed graph $G$ with full and dashed arrows: a representation of $G$ is given by assigning to each vertex a complex vector space, to each full arrow a linear ... More

Light-induced pitch transitions in photosensitive cholesteric liquid crystals: Effects of anchoring energyOct 15 2013Jan 11 2014We experimentally study how the cholesteric pitch, $P$, depends on the equilibrium one, $P_0$, in planar liquid crystal (LC) cells with both strong and semistrong anchoring conditions. The cholesteric phase was induced by dissolution in the nematic LC ... More

Generalization of Roth's solvability criteria to systems of matrix equationsApr 15 2017W.E. Roth (1952) proved that the matrix equation $AX-XB=C$ has a solution if and only if the matrices $\left[\begin{matrix}A&C\\0&B\end{matrix}\right]$ and $\left[\begin{matrix}A&0\\0&B\end{matrix}\right]$ are similar. A. Dmytryshyn and B. K{\aa}gstr\"om ... More

Black holes in a cubic Galileon universeMay 24 2016Jun 13 2016We find and study the properties of black hole solutions for a subclass of Horndeski theory including the cubic Galileon term. The theory under study has shift symmetry but not reflection symmetry for the scalar field. The Galileon is assumed to have ... More

Lebesgue constants for polyhedral sets and polynomial interpolation on Lissajous-Chebyshev nodesAug 11 2016To analyze the absolute condition number of multivariate polynomial interpolation on Lissajous-Chebyshev node points, we derive upper and lower bounds for the respective Lebesgue constant. The proof is based on a relation between the Lebesgue constant ... More

A constructive proof of Pokrzywa's theorem about perturbations of matrix pencilsJul 07 2019Our purpose is to give new proofs of several known results about perturbations of matrix pencils. Andrzej Pokrzywa (1986) described the closure of orbit of a Kronecker canonical pencil $A-\lambda B$ in terms of inequalities with pencil invariants. In ... More

Lebesgue constants for polyhedral sets and polynomial interpolation on Lissajous-Chebyshev nodesAug 11 2016Nov 10 2017To analyze the absolute condition number of multivariate polynomial interpolation on Lissajous-Chebyshev node points, we derive upper and lower bounds for the respective Lebesgue constant. The proof is based on a relation between the Lebesgue constant ... More

Mn(II)-doped 2D perovskite for light emitting devicesJun 12 2019Low dimensional perovskites are considered good candidates for light emitting applications given the high exciton binding energy which should in principle improve the radiative recombination efficiency. Yet, single-layered two-dimensional (2D) perovskite ... More

The Cartesian product of graphs with loopsNov 25 2014We extend the definition of the Cartesian product to graphs with loops and show that the Sabidussi-Vizing unique factorization theorem for connected finite simple graphs still holds in this context for all connected finite graphs with at least one unlooped ... More

Rotationally-resolved spectroscopy of Jupiter Trojans (624) Hektor and (911) AgamemnonDec 22 2017We present the first-ever rotationally resolved spectroscopic investigation of (624) Hektor and (911) Agamemnon, the two largest Jupiter Trojans. The visible and near-infrared spectra that we have obtained at the TNG telescope (La Palma, Spain) do not ... More

Dimethylsilanone generation from pyrolysis of polysiloxanes filled with nanosized silica and ceria/silicaDec 01 2016Polydimethylsiloxane (PDMS) is a widely used organosilicon polymer often employed in formulations with fine oxide particles for various high temperature applications. Although PDMS is considered to be thermally stable and chemically inert, it is not always ... More

Topological classification of systems of bilinear and sesquilinear formsNov 26 2016Let $\cal A$ and $\cal B$ be two systems consisting of the same vector spaces $\mathbb C^{n_1},\dots,\mathbb C^{n_t}$ and bilinear or sesquilinear forms $A_i,B_i:\mathbb C^{n_{k(i)}}\times\mathbb C^{n_{l(i)}}\to\mathbb C$, for $i=1,\dots,s$. We prove ... More

Electrically controlled terahertz magneto-optical phenomena in continuous and patterned grapheneMar 07 2017The magnetic circular dichroism and the Faraday rotation are the fundamental phenomena of great practical importance arising from the breaking of the time reversal symmetry by a magnetic field. In most materials the strength and the sign of these effects ... More

Direct observation of the M2 phase with its Mott transition in a VO$_2$ filmNov 29 2016In VO$_2$, the explicit origin of the insulator-to-metal transition is still disputable between Peierls and Mott insulators. Along with the controversy, its second monoclinic (M2) phase has received considerable attention due to the presence of electron ... More

Magnetoplasmonic Enhancement of Faraday Rotation in Patterned Graphene MetasurfacesNov 16 2017Faraday rotation is a fundamental property present in all non-reciprocal optical elements. In the THz range, graphene displays strong Faraday rotation; unfortunately, it is limited to frequencies below the cyclotron resonance. Here we show experimentally ... More

Charge photogeneration in few-layer MoS2Dec 17 2014The two-dimensional semiconductor MoS2 in its mono- and few-layer form is expected to have a significant exciton binding energy of several 100 meV, leading to the consensus that excitons are the primary photoexcited species. Nevertheless, even single ... More

Artifact Free Transient Near-Field NanoscopyJun 26 2017Jul 12 2017We report on the first implementation of ultrafast near field nanoscopy carried out with the transient pseudoheterodyne detection method (Tr-pHD). This method is well suited for efficient and artifact free pump-probe scattering-type near-field optical ... More

Strong plasmon reflection at nanometer-size gaps in monolayer graphene on SiCNov 25 2013We employ tip-enhanced infrared near-field microscopy to study the plasmonic properties of epitaxial quasi-free-standing monolayer graphene on silicon carbide. The near-field images reveal propagating graphene plasmons, as well as a strong plasmon reflection ... More

Phase transition in bulk single crystals and thin films of VO2 by nano-infrared spectroscopy and imagingJun 15 2015We have systematically studied a variety of vanadium dioxide (VO2) crystalline forms, including bulk single crystals and oriented thin films, using infrared (IR) near-field spectroscopic imaging techniques. By measuring the IR spectroscopic responses ... More

Data-Driven Modeling of Electron Recoil Nucleation in PICO C$_3$F$_8$ Bubble ChambersMay 29 2019The primary advantage of moderately superheated bubble chamber detectors is their simultaneous sensitivity to nuclear recoils from WIMP dark matter and insensitivity to electron recoil backgrounds. A comprehensive analysis of PICO gamma calibration data ... More

Data-Driven Modeling of Electron Recoil Nucleation in PICO C$_3$F$_8$ Bubble ChambersMay 29 2019Jul 01 2019The primary advantage of moderately superheated bubble chamber detectors is their simultaneous sensitivity to nuclear recoils from WIMP dark matter and insensitivity to electron recoil backgrounds. A comprehensive analysis of PICO gamma calibration data ... More