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Detection of melting by in-situ observation of spherical-drop formation in laser-heated diamond-anvil cellsApr 07 2011A simple method for detection of melting event in laser-heated diamond anvil cells (DACs) is introduced. The melting is registered optically by the formation of spherical drops of the investigated material as heated in an inert pressure transmitting medium. ... More

Improving Resolution of Solid State NMR in Dense Molecular HydrogenAug 03 2019Recent advancements in radio-frequency resonator designs have led to the implementation of nuclear magnetic resonance in diamond anvil cells (DACs) at pressures well above 100 GPa. However, a relatively low resolution and the absence of decoupling sequences ... More

Novel non-magnetic hard boride Co5B16 synthesized under high pressureApr 09 2014A first cobalt boride with the Co:B ratio below 1:1, Co5B16, was synthesized under high-pressure high-temperature conditions. It has a unique orthorhombic structure (space group Pmma, a = 19.1736(12), b = 2.9329(1), and c = 5.4886(2) {\AA}, R1 (all data) ... More

First non-icosahedral boron allotrope synthesized at high pressure and high temperatureFeb 13 2017Theoretical predictions of pressure-induced phase transformations often become long-standing enigmas because of limitations of contemporary available experimental possibilities. Hitherto the existence of a non-icosahedral boron allotrope has been one ... More

Structural stability and mechanism of compression of stoichiometric B13C2 up to 68 GPaMar 02 2017Boron carbide is a ceramic material with unique properties widely used in numerous, including armor, applications. Its mechanical properties, mechanism of compression, and limits of stability are of both scientific and practical value. Here, we report ... More

Lattice dynamics of coesiteApr 10 2013Apr 11 2013The lattice dynamics of coesite has been studied by a combination of diffuse x-ray scattering, inelastic x-ray scattering and an ab initio lattice dynamics calculation. The combined technique gives access to the full lattice dynamics in harmonic description ... More

Pressure induced crossing of the core-levels in 5d metalsSep 24 2015Pressure induced interaction between core electrons, the core level crossing (CLC) transition has been observed in hcp Os at P~400 GPa [L. Dubrovinksy, et al., Nature 525, 226-229 (2015)]. In this work, we carry out a systematic study of the influence ... More

B1-B2 phase transition in MgO at ultra-high static pressureMar 31 2019Studies of the behaviour of solids at ultra-high pressures, those beyond 200 GPa, contribute to our fundamental understanding of materials properties and allow an insight into the processes happening at such extreme conditions relevant for terrestrial ... More

Comparison of the Discriminatory Processor Sharing PoliciesMar 14 2008Apr 25 2008Discriminatory Processor Sharing policy introduced by Kleinrock is of a great interest in many application areas, including telecommunications, web applications and TCP flow modelling. Under the DPS policy the job priority is controlled by the vector ... More

Low mass X-ray binaries with pre-main sequence companionsNov 07 2006In this Letter we examine the idea that a subset of short-period black-hole low-mass X-ray binaries could be powered by the mass transfer from pre-main sequence donors. As the star contracts towards the main sequence, the strong magnetic fields operate ... More

Modulation of Superconducting Properties by Ferroelectric Polarization in Confined FE-S-FE FilmsNov 17 2003Sep 30 2004We show that the electric polarization at the interface with ultrathin superconducting (S) films sandwiched between ferroelectric (FE) layers allows achievement of substantially stronger modulation of inner carrier density and superconducting transition ... More

Geometric interpretation of the large N=4 indexSep 16 2004We study WZW models with the large N=4 superconformal symetry. Our main result is a geometric interpretation of the large N=4 index. In particular, we find that states contributing to the index belong to spectral flow orbits of special RR ground states. ... More

Condensers with infinitely many touching Borel plates and minimum energy problemsMar 21 2019Defining a condenser in a locally compact space as a locally finite, countable collection of Borel sets $A_i$, $i\in I$, with the sign $s_i=\pm1$ prescribed such that $A_i\cap A_j=\varnothing$ whenever $s_is_j=-1$, we consider a minimum energy problem ... More

Error analysis of an L2-type method on graded meshes for a fractional-order parabolic problemMay 13 2019An initial-boundary value problem with a Caputo time derivative of fractional order $\alpha\in(0,1)$ is considered, solutions of which typically exhibit a singular behaviour at an initial time. An L2-type discrete fractional-derivative operator of order ... More

Constrained Gauss variational problem for condensers with touching platesMay 11 2015We study a constrained minimum energy problem with an external field relative to the Riesz kernel of an arbitrary order for a generalized condenser with touching oppositely-charged plates. Conditions sufficient for the solvability of the problem are obtained. ... More

Extremes in Random Graphs Models of Complex NetworksApr 05 2017Regarding the analysis of Web communication, social and complex networks the fast finding of most influential nodes in a network graph constitutes an important research problem. We use two indices of the influence of those nodes, namely, PageRank and ... More

Probability density cloud as a geometrical tool to describe statistics of scattered lightNov 25 2016Feb 03 2017First-order statistics of scattered light is described using the representation of probability density cloud which visualizes a two-dimensional distribution for complex amplitude. The geometric parameters of the cloud are studied in detail and are connected ... More

Spectral networks and higher web-like structuresSep 09 2014We derive traffic rule for spectral networks for A_2 theory for Riemann surface with punctures and use it to study in details the moduli space M of flat GL(3,C) connections on P^1 with 3 full punctures. We apply the simplified traffic rule to find the ... More

Extremes Control of Complex Systems With Applications to Social NetworkFeb 17 2015The control and risk assessment in complex information systems require to take into account extremes arising from nodes with large node degrees. Various sampling techniques like a Page Rank random walk, a Metropolis-Hastings Markov chain and others serve ... More

Consistency of the posterior distribution in generalised linear inverse problemsNov 14 2012Apr 19 2013For ill-posed inverse problems, a regularised solution can be interpreted as a mode of the posterior distribution in a Bayesian framework. This framework enriches the set the solutions, as other posterior estimates can be used as a solution to the inverse ... More

Properties of the dual planar triangulationsDec 01 2012Dec 26 2012This article is devoted to the properties of the planar triangulations. The conjugated planar triangulation will be introduced and on the base of the properties, which were achieved by the other authors there will be proved some theorems, which will show ... More

Evolution of Binaries in Dense Stellar SystemsJan 14 2011In contrast to the field, the binaries in dense stellar systems are frequently not primordial, and could be either dynamically formed or significantly altered from their primordial states. Destruction and formation of binaries occur in parallel all the ... More

Probability density function and detection threshold in high contrast imaging with partially polarized lightJun 05 2009We obtain an expression for the probability density function (PDF) of partially developed speckles formed by light with an arbitrary degree of polarization. From the probability density we calculate the detection threshold corresponding to the 5sigma ... More

Computing the tree number of a cut-outerplanar graphJun 02 2009While the notion of arboricity of a graph is well-known in graph theory, very few results are dedicated to the minimal number of trees covering the edges of a graph, called the tree number of a graph. In this paper we propose a method for computing in ... More

Lower a posteriori error estimates on anisotropic meshesJun 13 2019Lower a posteriori error bounds obtained using the standard bubble function approach are reviewed in the context of anisotropic meshes. A numerical example is given that clearly demonstrates that the short-edge jump residual terms in such bounds are not ... More

Recovery of the matrix quadratic differential pencil from the spectral dataSep 21 2015We consider a pencil of matrix Sturm-Liouville operators on a finite interval. We study properties of its spectral characteristics and inverse problems that consist in recovering of the pencil by the spectral data: eigenvalues and so--called weight matrices. ... More

An inverse spectral problem for the matrix Sturm-Liouville operator on the half-lineDec 18 2014The matrix Sturm-Liouville operator with an integrable potential on the half-line is considered. We study the inverse spectral problem, which consists in recovering of this operator by the Weyl matrix. The main result of the paper is the necessary and ... More

On badly approximable subspacesOct 17 2018May 08 2019Given an $a$-dimensional linear subspace $\mathfrak{A}$ in $\mathbb{R}^d$ which contains a badly approximable $b$-dimensional subspace $\mathfrak{B} \subset \mathfrak{A}$. We study the badly approximability almost all $c$-dimensional linear subspaces ... More

Classification of Maximal Subgroups of Odd Index in Finite Simple Classical groups: AddendumOct 04 2017Jan 06 2018A classification of maximal subgroups of odd index in finite simple groups was given by Liebeck and Saxl and, independently, Kantor in 1980s. In the cases of alternating groups or classical groups of Lie type over fields of odd characteristics, the classification ... More

High frequency asymptotics of global vibrations in a problem with concentrated massApr 16 2008We consider an elastic system containing a small region where the density is very much higher then elsewhere. Such system possesses two types of eigenvibrations, which are local and global vibrations. Complete asymptotic expansions of global eigenvibrations ... More

Spectral synthesis for the differentiation operator in the Schwartz spaceJan 07 2016We consider the spectral synthesis problem for the differentiation operator D=d/dt in the Schwartz space E(a;b) and the dual problem of local description for closed submodules in a special module of entire functions.

On Koszulity in homology of moduli spaces of stable n-pointed curves of genus zeroApr 23 2013We prove Koszulity of the homology of the of moduli spaces of stable n-pointed curves of genus zero $\bar{M}_{0,n}$ for $n=5$, using its presentation due to Keel and the Priddy criterion of koszulity. For $n=6 $ we show that it is not Koszul by calculating ... More

Batch Processor Sharing with Hyper-Exponential Service TimeMay 03 2007Jun 22 2007We study Batch Processor-Sharing (BPS) queuing model with hyper-exponential service time distribution and Poisson batch arrival process. One of the main goals to study BPS is the possibility of its application in size-based scheduling, which is used in ... More

On the simplest split-merge operator on the infinite-dimensional simplexJun 01 2001We consider the simplest split-merge Markov operator $T$ on the infinite-dimensional simplex $\Sigma_1$ of monotone non-negative sequences with unit sum. For a sequence $x\in\Sigma_1$, it picks a size-biased sample (with replacement) of two elements of ... More

Interior capacities of condensers with infinitely many plates in a locally compact spaceJun 24 2009The study deals with the theory of interior capacities of condensers in a locally compact space, a condenser being treated here as a countable, locally finite collection of arbitrary sets with the sign +1 or -1 prescribed such that the closures of opposite-signed ... More

Hitting times of threshold exceedances and their distributionsJan 07 2015We investigate exceedances of the process over a sufficiently high threshold. The exceedances determine the risk of hazardous events like climate catastrophes, huge insurance claims, the loss and delay in telecommunication networks. Due to dependence ... More

Coisotropic Branes in Toric Calabi-Yau 3-foldsOct 09 2014We study disk-instantons ending on coisotropic branes preserved by real torus action in toric Calabi-Yau 3-folds. In particular, we find fermion zero modes on disk multi-covers ending on a coisotropic brane in local P^1 geometry with normal bundle (-a,a-2). ... More

Evolution of binaries with compact objects in globular clustersJun 23 2017Dynamical interactions that take place between objects in dense stellar systems lead to frequent formation of exotic stellar objects, unusual binaries, and systems of higher multiplicity. They are most important for the formation of binaries with neutron ... More

On the use of hydrogen recombination energy during common envelope eventsApr 27 2018In this Letter we discuss what happens to hydrogen recombination energy that is released during regular common envelope (CE) events, as opposed to self-regulated CE events. We show that the amount of recombination energy that can be transferred away by ... More

Error analysis of an L2-type method on graded meshes for a fractional-order parabolic problemMay 13 2019May 21 2019An initial-boundary value problem with a Caputo time derivative of fractional order $\alpha\in(0,1)$ is considered, solutions of which typically exhibit a singular behaviour at an initial time. An L2-type discrete fractional-derivative operator of order ... More

K-theory of locally finite graph $C^*$-algebrasJul 22 2010Apr 24 2013We calculate the K-theory of the Cuntz-Krieger algebra ${\cal O}_E$ associated with an infinite, locally finite graph, via the Bass-Hashimoto operator. The formulae we get express the Grothendieck group and the Whitehead group in purely graph theoretic ... More

Almost nilpotency of an associative algebra with an almost nilpotent fixed-point subalgebraNov 26 2017Let A be an associative algebra of arbitrary dimension over a field F and G a finite soluble group of automorphisms of A oforder n, prime to the characteristic of F. We prove that if the fixed-point subalgebra of A under the action of G contains a two-sided ... More

CO-activator model for reconstructing Pt(100) surfaces: local microstructures and chemical turbulenceAug 21 2007Jan 18 2008We present the results of the modelling of CO adsorption and catalytic CO oxidation on inhomogeneous Pt(100) surfaces which contain structurally different areas. These areas are formed during the CO-induced transition from a reconstructed phase with hexagonal ... More

Double stage Lyot coronagraph with the apodized reticulated stop for extremely large telescopeNov 11 2005One of the science drivers for the extremely large telescope (ELT) is imaging and spectroscopy of exo-solar planets located as close as 20mas to their parent star. The application requires a well thought-out design of the high contrast imaging instrumentation. ... More

Population of dynamically formed triples in dense stellar systemsSep 18 2005In dense stellar systems, frequent dynamical interactions between binaries lead to the formation of multiple systems. In this contribution we discuss the dynamical formation of hierarchically stable triples: the formation rate, main characteristics of ... More

Topological constraints on stabilized flux vacuaMar 16 2005May 11 2005We study the influence of four-form fluxes on the stabilization of the Kahler moduli in M-theory compactified on a Calabi-Yau four-fold. We find that, under certain non-degeneracy condition on the flux, M5-instantons of a new topological type generate ... More

On badly approximable subspacesOct 17 2018Given an $a$-dimensional linear subspace $\mathfrak{A}$ in $\mathbb{R}^d$ which contains a badly approximable $b$-dimensional subspace $\mathfrak{B} \subset \mathfrak{A}$. We study the badly approximability almost all $c$-dimensional linear subspaces ... More

How accurate are finite elements on anisotropic triangulations in the maximum norm?Nov 13 2018In [Kopteva, Math. Comp., 2014] a counterexample of an anisotropic triangulation was given on which the exact solution has a second-order error of linear interpolation, while the computed solution obtained using linear finite elements is only first-order ... More

Constrained energy problems with external fields for infinite dimensional vector measuresOct 11 2010We consider a constrained minimal energy problem with an external field over noncompact classes of infinite dimensional vector measures on a locally compact space. The components are positive measures (charges) that are constrained from above, satisfy ... More

Constrained energy problems with external fieldsJan 25 2010Given a positive definite kernel in a locally compact space, we study a minimal energy problem in the presence of an external field over the class of all nonnegative Radon measures that are supported by a given closed noncompact set, satisfy certain normalizing ... More

Necessary and sufficient conditions for the solvability of the Gauss variational problem for infinite dimensional vector measuresJul 03 2012We continue our investigation of the Gauss variational problem for infinite dimensional vector measures associated with a condenser $(A_i)_{i\in I}$. It has been shown in Potential Anal., DOI:10.1007/s11118-012-9279-8 that, if some of the plates (say ... More

Equilibrium problems for infinite dimensional vector potentials with external fieldsNov 04 2009The study deals with a minimal energy problem in the presence of an external field over noncompact classes of vector measures of infinite dimension in a locally compact space. The components are positive measures (charges) satisfying certain normalizing ... More

Asymptotically Safe $f(R)$-Gravity Coupled to Matter II: Global SolutionsSep 17 2018Ultraviolet fixed point functions of the functional renormalisation group equation for $f(R)$-gravity coupled to matter fields are discussed. The metric is split via the exponential parameterisation into a background and a fluctuating metric, the former ... More

A characterization of BMO in terms of endpoint bounds for commutators of singular integralsFeb 15 2018We provide a characterization of $\mathrm{BMO}$ in terms of endpoint boundedness of commutators of singular integrals. In particular, in one dimension, we show that $\|b\|_{\mathrm{BMO}}\eqsim B$, where $B$ is the best constant in the endpoint $L\log ... More

Improved energy-norm a posteriori error estimates for singularly perturbed reaction-diffusion problems on anisotropic meshesOct 22 2018May 21 2019In the recent article [Kopteva, N., Numer. Math., 137, 607--642 (2017)] the author obtained residual-type a posteriori error estimates in the energy norm for singularly perturbed semilinear reaction-diffusion equations on anisotropic triangulations. The ... More

Evolution of inverse cascades and formation of precondensate in Gross-Pitaevskii turbulence in two dimensionsSep 16 2017Nov 08 2017Here we study how coherence appears in a system driven by noise at small scales. In the wave turbulence modeled by the Gross-Pitaevskii / nonlinear Schr\"odinger equation, we observe states with correlation scales less than the system size but much larger ... More

Common envelope: progress and transientsJun 23 2017We review the fundamentals and the recent developments in understanding of common envelope physics. We report specifically on the progress that was made by the consideration of the recombination energy. This energy is found to be responsible for the complete ... More

Besov regularity of functions with sparse random wavelet coefficientsOct 14 2013Oct 23 2013This paper addresses the problem of regularity properties of functions represented as an expansion in a wavelet basis with random coefficients in terms of finiteness of their Besov norm with probability 1. Such representations are used to specify a prior ... More

Common envelope: on the mass and the fate of the remnantJan 14 2011One of the most important and uncertain stages in the binary evolution is the common envelope (CE) event. Significant attention has been devoted in the literature so far to the energy balance during the CE event, expected to determine the outcome. However ... More

Analyzing closed frequent itemsets with convex polytopesMar 20 2012Jun 16 2014Computing frequent itemsets in transactional databases is a vital but computationally expensive task. Measuring the difference of two datasets is often done by computing their respective frequent itemsets despite high computational cost. This paper proposes ... More

On estimation of analytic density in L_pOct 10 2011The problem of estimation of analytic density function using L_p minimax risk is considered. A kernel-type estimator of an unknown density function is proposed and the upper bound on its limiting local minimax risk is established. Our result is consistent ... More

Properties of Codes in the Johnson SchemeApr 27 2010Codes which attain the sphere packing bound are called perfect codes. The most important metrics in coding theory on which perfect codes are defined are the Hamming metric and the Johnson metric. While for the Hamming metric all perfect codes over finite ... More

A partial inverse problem for the Sturm-Liouville operator on a star-shaped graphJan 01 2017The Sturm-Liouville operator on a star-shaped graph is considered. We assume that the potential is known a priori on all the edges except one, and study the partial inverse problem, which consists in recovering the potential on the remaining edge from ... More

The chromatic class and the chromatic number of the planar conjugated triangulationJul 30 2013This material is dedicated to the estimation of the chromatic number and chromatic class of the conjugated triangulation (first conversion) and also of the second conversion of the planar triangulation. Also this paper introduces some new hypotheses, ... More

About integrability of almost complex structures on strictly Nearly Kähler 6-manifoldsMay 06 2013We show that any almost complex structure, positively tamed with $\omega$ on nearly K\"{a}hler 6-manifold $(M,g,J,\omega)$ is not integrable

Special Partial GraphsMay 31 2013The attempts to prove the Four Color Problem last for long years. A little hope arises that the properties of the minimal partial triangulations will be very useful for the solution of the Four Color Problem. That is why the material of this paper is ... More

Geometric and algebraic interpretation of primitive Pythagorean triples parametersJul 12 2019The paper found a geometric and algebraic interpretation of the parameters m and n from the formulas for obtaining primitive Pythagorean triples, which are solutions of the equation ${x^2+y^2=z^2}$, namely: ${x=m^2-n^2}$, ${y=2mn}$, ${z=m^2+n^2}$. The ... More

Lightlike foliations on Lorentzian manifolds with weakly irreducible holonomy algebraJun 06 2005We study the lightlike foliations that appear on Lorentzian manifolds with weakly irreducible not irreducible holonomy algebra. We give global structure equations for the foliation that generalize the Gauss and Weingarten equations for one lightlike hypersurface. ... More

An inverse problem for the non-self-adjoint matrix Sturm-Liouville operatorJul 14 2014The inverse problem of spectral analysis for the non-self-adjoint matrix Sturm-Liouville operator on a finite interval is investigated. We study properties of the spectral characteristics for the considered operator, and provide necessary and sufficient ... More

Loops on polyhedral products and diagonal arrangementsJan 19 2009In this paper we establish a connection between the loop space homology of the generalization of wedge defined by a simplicial complex K (so called polyhedral product) and the homology of certain diagonal arrangements associated with K. We illustrate ... More

Concern Regarding "A Non-Inflationary Solution to the Entropy Problem of Standard Cosmology."Mar 03 2008Jan 07 2009We discuss the entropy and the size/homogeneity/horizon problems in power-law expanding universes with one scale initial conditions. We set the minimal scale $\Lambda = 10^{25}$ GeV at which a non-inflationary solution is possible and show that the radiation ... More

Effect of metallicity on low mass X-ray binaries in globular clustersSep 18 2005We propose that the observed difference in the formation rates of bright low-mass X-ray binaries in metal-rich and metal-poor globular clusters can be explained by taking into account the difference in the stellar structure of main sequence donors with ... More

Low Mass X-ray Binaries and Metallicity Dependence: Story of FailuresSep 18 2005Observations of galactic and extra-galactic globular clusters have shown that on average metal-rich clusters are ~3 times as likely to contain a bright X-ray source than their metal-poor counterparts. We propose that this can be explained by taking into ... More

Mechanism of orbital reconstruction at the interfaces of transition metal oxidesJan 28 2009Jul 18 2009Orbital reconstruction at interfaces between YBa2Cu3O6 and SrO-terminated SrTiO3 is studied using local spin density approximation (LSDA) with intra-atomic Coulomb repulsion (LSDA+U). The change of population of interfacial Cu 3d orbitals results in stabilization ... More

Condensers with infinitely many touching Borel plates and minimum energy problemsMar 21 2019Apr 30 2019Defining a condenser in a locally compact space as a locally finite, countable collection of Borel sets $A_i$, $i\in I$, with the sign $s_i=\pm1$ prescribed such that $A_i\cap A_j=\varnothing$ whenever $s_is_j=-1$, we consider a minimum energy problem ... More

Renormalisation Group for Gravity and Dimensional ReductionSep 23 2018The functional renormalisation group for the Einstein-Hilbert action is investigated for the case of four infinite (or large) and one compact dimension. The motivation for this study is given by the suggestion that gravity in more than four dimensions ... More

Logarithm cannot be removed in maximum norm error estimates for linear finite elements in 3DOct 09 2017Jun 05 2018For linear finite element discretizations of the Laplace equation in three dimensions, we give an example of a tetrahedral mesh in the cubic domain for which the logarithmic factor cannot be removed from the standard upper bounds on the error in the maximum ... More

Error analysis of the L1 method on graded and uniform meshes for a fractional-derivative problem in two and three dimensionsSep 26 2017Oct 23 2018An initial-boundary value problem with a Caputo time derivative of fractional order $\alpha\in(0,1)$ is considered, solutions of which typically exhibit a singular behaviour at an initial time. For this problem, we give a simple framework for the analysis ... More

Deformations of Lie algebras of type ${D}_{l}$Dec 05 2017The description of global deformations of Lie algebras is important since it is related to unsolved problem of the classification of simple Lie algebras over a field of small characteristic. In this paper we study global deformations of Lie algebras of ... More

Normal forms for three-parametric families of area-preserving maps near an elliptic fixed pointNov 08 2017We study dynamics of area-preserving maps in a neighbourhood of an elliptic fixed point. We describe simplified normal forms for a fixed point of co-dimension 3. We also construct normal forms for a generic three-parameter family which contains such degeneracy ... More

On Koszulity in homology of moduli spaces of stable n-pointed curves of genus zeroApr 23 2013Nov 20 2017We prove Koszulity of the homology of the of moduli spaces of stable n-pointed curves of genus zero $\overline{M}_{0,n}$ for $n=5$, using its presentation due to Keel and the Priddy criterion of Koszulity. For $n=6 $ we establish that $\overline{M}_{0,6}^!$ ... More

The space of leftinvariant orthogonal almost complex structures on 6-dimensional Lie groupsJan 14 2012Nov 02 2012The space $\mathcal{Z}$ of leftinvariant orthogonal almost complex structures, keeping the orientation, on 6-dimensional Lie groups is researched. To get explicit view of this space elements the isomorphism of $\mathcal{Z}$ and $\mathbb{C}P^3$ is used. ... More

A note on Wilson-'t Hooft operatorsOct 14 2011We find the basic ingredients required to compute the Operator Product Expansion of Wilson-'t Hooft operators in N=4 super-Yang-Mills theory with gauge group G=PSU(3). These include the geometry of certain moduli spaces of BPS configurations in the presence ... More

Inverse scattering on the line for the matrix Sturm-Liouville equationDec 19 2015The inverse scattering problem is studied for the matrix Sturm-Liouville equation on the line. Necessary and sufficient conditions for the scattering data are obtained.

A note on the moduli-induced gravitino problemMar 30 2007Jan 08 2009The cosmological moduli problem has been recently reconsidered. Papers [1,2] show that even heavy moduli (m_\phi > 10^5 GeV) can be a problem for cosmology if a branching ratio of the modulus into gravitini is large. In this paper, we discuss the tachyonic ... More

Coding Theory and Projective SpacesMay 22 2008Sep 08 2011The projective space of order $n$ over a finite field $\F_q$ is a set of all subspaces of the vector space $\F_q^{n}$. In this work, we consider error-correcting codes in the projective space, focusing mainly on constant dimension codes. We start with ... More

Search for B+ -> K+ l+ l- and B0 -> K*0 l+ l-Oct 27 2000Using a sample of 3.7 x 10^6$ Upsilon(4S) -> B Bbar events collected with the BaBar detector at the PEP-II storage ring, we search for the electroweak penguin decays B+ -> K+ e+ e-, B+ -> K+ mu+ mu-, B0 -> K*0 e+ e-, and B0 -> K*0 mu+ mu-. We observe ... More

Minimizing measures on condensers of infinitely many platesJan 25 2010The study deals with a minimal energy problem over noncompact classes of infinite dimensional vector measures in a locally compact space. The components are positive measures (charges) satisfying certain normalizing assumptions and supported by given ... More

Interior capacities of condensers in locally compact spacesFeb 03 2009The study is motivated by the known fact that, in the noncompact case, the main minimum-problem of the theory of interior capacities of condensers in a locally compact space is in general unsolvable, and this occurs even under very natural assumptions ... More

Fully computable a posteriori error estimator using anisotropic flux equilibration on anisotropic meshesApr 14 2017Jul 19 2017Fully computable a posteriori error estimates in the energy norm are given for singularly perturbed semilinear reaction-diffusion equations posed in polygonal domains. Linear finite elements are considered on anisotropic triangulations. To deal with the ... More

Clustering and Hitting Times of Threshold Exceedances and ApplicationsSep 30 2017We investigate exceedances of the process over a sufficiently high threshold. The exceedances determine the risk of hazardous events like climate catastrophes, huge insurance claims, the loss and delay in telecommunication networks. Due to dependence ... More

The Pulsar in the Crab NebulaNov 16 2015The Crab pulsar belongs to one of the most studied stellar objects in the sky. Since its accidental detection in 1968, its pulsed emission has been observed throughout most of the electromagnetic spectrum. Although currently one of more than 2000 known ... More

Binary Evolution: Roche Lobe Overflow and Blue StragglersJun 13 2014One of the principal mechanisms that is responsible for the origin of blue stragglers is mass transfer that takes place while one of the binary companions overfills its Roche lobe. In this Chapter, we overview the theoretical understanding of mass transfer ... More

Fractional Repetition and Erasure Batch CodesMay 04 2014Oct 20 2014Batch codes are a family of codes that represent a distributed storage system (DSS) of $n$ nodes so that any batch of $t$ data symbols can be retrieved by reading at most one symbol from each node. Fractional repetition codes are a family of codes for ... More

Low-Mass X-ray Binaries in Globular Clusters: Puzzles and SolutionsJan 10 2013In dense stellar systems, dynamical interactions between objects lead to frequent formation of exotic stellar objects, unusual binaries, and systems of higher multiplicity. They are especially important for the formation of low mass X-ray binaries (LMXBs), ... More

Common envelope: the progress and the pitfallsAug 04 2011The common envelope event is one of the most important and uncertain evolutionary stages that lead to formation of compact binaries. While the problem is almost 30 years old, its theoretical foundation did not progress much from the first proposed consideration. ... More

How accurate are finite elements on anisotropic triangulations in the maximum norm?Nov 13 2018May 21 2019In [Kopteva, Math. Comp., 2014] a counterexample of an anisotropic triangulation was given on which the exact solution has a second-order error of linear interpolation, while the computed solution obtained using linear finite elements is only first-order ... More

Quantum Gravity from Fundamental Questions to Phenomenological ApplicationsOct 07 2018Investigating quantum gravity requires a comprehension of both, general relativity and quantum field theory. Therefore this thesis starts, after a general introduction to the treated topics, with a brief review of the field theoretical aspects of gravity ... More

A new proof of the dimension gap for the Gauss mapJun 03 2018Kifer, Peres and Weiss showed that the Bernoulli measures for the Gauss map $T(x)= \frac{1}{x} \mod 1$ satisfy a `dimension gap' meaning that for some $c>0$, $\sup_{\mathbf{p}} \dim \mu_{\mathbf{p}} <1-c$, where $\mu_{\mathbf{p}}$ denotes the (pushforward) ... More

On the rationality of the singularities of the $A_2$-lociDec 10 2017Dec 25 2017The rationality of the singularities of the $A_n$-loci is the natural question that arises in the papers devoted to the study of the Thom polynomials and $K$-theoretic invariants of the said loci. In this paper we prove that, in general, the $A_2$-loci ... More