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Merging Nonlinear Optics and Negative-Index MetamaterialsAug 03 2011The extraordinary properties of nonlinear optical propagation processes in double-domain positive/negative index metamaterials are reviewed. These processes include second harmonic generation, three- and four-wave frequency mixing, and optical parametric ... More

Negative-Index Metamaterials: Second-Harmonic Generation, Manley-Rowe Relations and Parametric AmplificationJan 10 2006Second harmonic generation and optical parametric amplification in negative-index metamaterials (NIMs) are studied. The opposite directions of the wave vector and the Poynting vector in NIMs results in a "backward" phase-matching condition, causing significant ... More

Coherent Nonlinear Optics and Quantum Control in Negative-Index MetamaterialsJun 01 2009The extraordinary properties of laser-induced transparency of a negative-index slab and parametric amplification for a backward-wave signal are investigated. The effects of the idler absorption and phase mismatch on the amplification of the signal are ... More

Hawking radiation and secularly growing loop correctionsAug 29 2015Dec 20 2015We study the expectation value of the energy momentum tensor during thin shell collapse for a massive, real, scalar field theory. At tree-level, we find thermal, Hawking-type, behaviour for the energy flux. Using the Schwinger-Keldysh technique, we calculate ... More

Mirrorless Negative-index Parametric Micro-oscillatorJul 22 2008The feasibility and extraordinary properties of mirrorless parametric oscillations in strongly absorbing negative-index metamaterials are shown. They stem from the backwardness of electromagnetic waves inherent to this type of metamaterials.

Ultraviolet phenomena in AdS self-interacting quantum field theoryFeb 08 2018We study the one-loop corrections to the four-point function in the Anti de Sitter space-time for a $\phi^4$ field theory. Our calculation shows the existence of non-local counterterms which however respect the AdS isometry. Our arguments are quite general ... More

On a conjecture of A. BikchentaevJan 20 2013In \cite{bik1}, A. M. Bikchentaev conjectured that for positive $\tau-$measurable operators $a$ and $b$ affiliated with an arbitrary semifinite von Neumann algebra $\mathcal M$, the operator $b^{1/2}ab^{1/2}$ is submajorized by the operator $ab$ in the ... More

A way to distinguish very compact stellar objects from black holesJan 15 2016Feb 15 2016We propose a way to distinguish compact stellar object, whose size is very close to its Schwarzschild radius, from the collapsing stars. Namely, we show that {\it massive} fields in the vicinity of a very compact stellar object have discrete energy levels. ... More

Atomic collapse in graphene and cyclic RG flowDec 28 2013In this Letter we consider the problem of screening of external charge in graphene from the cyclic RG flow viewpoint. The analogy with conformal Calogero model is used to suggest the interpretation of the tower of resonant states as tower of Efimov states. ... More

Combinatorial Results Implied by Many Zero Divisors in a Group RingJun 10 2016Feb 23 2017It has been recently proved (Croot--Lev--Pach; Ellenberg--Gijswijt) that for a group $G=G_0^n$, where $G_0\ne \{1,-1\}^m$ is a fixed finite Abelian group and $n$ is large, any subset $A$ without 3-terms progressions (triples $x,y,z$ of different elements ... More

The Possibility of Emersion of the Outer Layers in a Massive Star Simultaneously with Iron-Core Collapse: A Hydrodynamic ModelFeb 06 2004We analyze the behavior of the outer envelope in a massive star during and after the collapse of its iron core into a protoneutron star (PNS) in terms of the equations of one-dimensional spherically symmetric ideal hydrodynamics. The profiles obtained ... More

Measurable operators and the asymptotics of heat kernels and zeta functionsJan 17 2012In this note we answer some questions inspired by the introduction, by Alain Connes, of the notion of measurable operators using Dixmier traces. These questions concern the relationship of measurability to the asymptotics of $\zeta-$functions and heat ... More

On Contraction of Algebraic PointsJul 06 2016Mar 08 2017We study contraction of points on $\mathbb{P}^1(\bar{\mathbb{Q}})$ with certain control on local ramification indices, with application to the unramified curve correspondences problem initiated by Bogomolov and Tschinkel.

Evolution of close binaries after the burst of starformation for different IMFsNov 28 1997We use "Scenario Machine" -- the population synthesis simulator -- to calculate the evolution of populations of selected types of X-ray sources after a starformation burst with the total mass in binaries (1--1.5) \cdot 10^6 M_{\odot}$ during the first ... More

Compensation for Booster Leakage Field in the Duke Storage RingMay 21 2016The High Intensity Gamma-ray Source (HIGS) at Duke University is an accelerator-driven Compton gamma-ray source, providing high flux gamma-ray beam from 1 MeV to 100 MeV for photo-nuclear physics research. The HIGS facility operates three accelerators, ... More

Improved Description of One- and Two-Hole States after Electron Capture in 163 Holmium and the Determination of the Neutrino MassJan 18 2015Apr 07 2015The atomic pair 163 Holmium and 163 Dysprosium seems due to the small Q value of about 2.3 to 2.8 keV the best case to determine the neutrino mass by electron capture. The bolometer spectrum measures the full deexcitation energy of Dysprosium by X rays, ... More

Why should we care about the top quark Yukawa coupling?Nov 07 2014Mar 12 2015In the cosmological context, for the Standard Model to be valid up to the scale of inflation, the top quark Yukawa coupling $y_t$ should not exceed the critical value $y_t^{crit}$, coinciding with good precision (about 0.02%) with the requirement of the ... More

An exact renormalization formula for the Maryland modelNov 27 2013We discuss the difference Schr\"odinger equation $\psi_{k+1}+\psi_{k-1}+\lambda \cot(\pi\omega k+\theta)\psi_k=E\psi_k$, $k\in\mathbb{Z}$, where $\lambda$, $\omega$, $\theta$ and $E$ are parameters. We obtain explicit renormalization formulas relating ... More

Algorithmic aspects of immersibility and embeddabilityDec 21 2018We analyze an algorithmic question about immersion theory: for which $m$, $n$, and $CAT=\mathbf{Diff}$ or $\mathbf{PL}$ is the question of whether an $m$-dimensional $CAT$-manifold is immersible in $\mathbb{R}^n$ decidable? As a corollary, we show that ... More

Reflection ranks and ordinal analysisMay 05 2018It is well-known that natural axiomatic theories are well-ordered by consistency strength. However, it is possible to construct descending chains of artificial theories with respect to consistency strength. We provide an explanation of this well-orderness ... More

On the $\text{PGL}_{2}$-invariant quadruples of torsion points of elliptic curvesFeb 23 2019Let $E$ be an elliptic curve and $\pi:E\to\mathbb{P}^{1}$ a standard double cover identifying $\pm P\in E$. It is known that for some torsion points $P_{i}\in E$, $1\leq i\leq4$, the cross ratio of $\{\pi(P_{i})\}_{i=1}^{4}$ is always a constant. In this ... More

On Shirshov bases of graded algebrasJan 27 2012Mar 13 2013We prove that if the neutral component in a finitely-generated associative algebra graded by a finite group has a Shirshov base, then so does the whole algebra.

Traversable wormholes in four dimensionsJul 12 2018Aug 29 2018We present a wormhole solution in four dimensions. It is a solution of an Einstein Maxwell theory plus charged massless fermions. The fermions give rise to a negative Casimir-like energy, which makes the wormhole possible. It is a long wormhole that does ... More

All-optical nanoscale thermometry with silicon-vacancy centers in diamondAug 17 2017We demonstrate an all-optical thermometer based on an ensemble of silicon-vacancy centers (SiVs) in diamond by utilizing a temperature dependent shift of the SiV optical zero-phonon line transition frequency, $\Delta\lambda/\Delta T= 6.8\,\mathrm{GHz/K}$. ... More

Relaxation damping in oscillating contactsOct 13 2014If a contact of two purely elastic bodies with no sliding (infinite coefficient of friction) is subjected to superimposed oscillations in the normal and tangential directions, then a specific damping appears, that is not dependent on friction or dissipation ... More

Geometrically induced spectral effects in tubes with a mixed Dirichlet-Neumann boundaryAug 27 2017Dec 30 2017We investigate spectral properties of the Laplacian in $L^2(Q)$, where $Q$ is a tubular region in $\mathbb{R}^3$ of a fixed cross section, and the boundary conditions combined a Dirichlet and a Neumann part. We analyze two complementary situations, when ... More

Finite subgroups of diffeomorphism groupsOct 24 2013Jan 06 2014We prove:(1) the existence, for every integer n > 3, of a noncompact smooth n-dimensional topological manifold whose diffeomorphism group contains an isomorphic copy of every finitely presented group; (2) a finiteness theorem on finite simple subgroups ... More

Statefinder analysis of the superfluid Chaplygin gas modelMay 22 2011Dec 05 2011The statefinder indices are employed to test the superfluid Chaplygin gas (SCG) model describing the dark sector of the universe. The model involves Bose-Einstein condensate (BEC) as dark energy (DE) and an excited state above it as dark matter (DM). ... More

On the Makar-Limanov, Derksen invariants, and finite automorphism groups of algebraic varietiesJan 08 2010Jul 01 2010A simple method of constructing a big stock of algebraic varieties with trivial Makar-Limanov invariant is described, the Derksen invariant of some varieties is computed, the generalizations of the Makar-Limanov and Derksen invariants are introduced and ... More

Generic algebras: rational parametrization and normal formsNov 24 2014Jan 19 2015For every algebraically closed field $\boldsymbol k$ of characteristic different from $2$, we prove the following: (1) Generic finite dimensional (not necessarily associative) $\boldsymbol k$-algebras of a fixed dimension, considered up to isomorphism, ... More

Two-phonon Raman bands of single-walled carbon nanotubes: a case studyApr 10 2018Jun 21 2018It has been long accepted that the second-order Raman bands in carbon nanotubes are enhanced through the double-resonance mechanism. Although separate aspects of this mechanism have been studied for a few second-order Raman bands, including the most intense ... More

On pairs, triples and quadruples of points on a cubic surfaceOct 13 2018Let $X^{(n)}$ denote $n$-th symmetric power of a cubic surface $X$. We show that $X^{(4)}\times X$ is stably birational to $X^{(3)}\times X$, despite examples when $X^{(4)}$ is not stably birational to $X^{(3)}$.

The vacant set of two-dimensional critical random interlacement is infiniteJun 18 2016Jan 22 2017For the model of two-dimensional random interlacements in the critical regime (i.e., $\alpha=1$), we prove that the vacant set is a.s.\ infinite, thus solving an open problem from arXiv:1502.03470. Also, we prove that the entrance measure of simple random ... More

Hasq Hash ChainsDec 14 2014This paper describes a particular hash-based records linking chain scheme. This scheme is simple conceptually and easy to implement in software. It allows for a simple and secure way to transfer ownership of digital objects between peers.

Integration of Flexible Web Based GUI in I-SOASNov 14 2010It is necessary to improve the concepts of the present web based graphical user interface for the development of more flexible and intelligent interface to provide ease and increase the level of comfort at user end like most of the desktop based applications. ... More

Random walks with unbounded jumps among random conductances I: Uniform quenched CLTOct 03 2012We study a one-dimensional random walk among random conductances, with unbounded jumps. Assuming the ergodicity of the collection of conductances and a few other technical conditions (uniform ellipticity and polynomial bounds on the tails of the jumps) ... More

Cross-sections, quotients, and representation rings of semisimple algebraic groupsAug 06 2009Feb 11 2011Let $G$ be a connected semisimple algebraic group over an algebraically closed field $k$. In 1965 Steinberg proved that if $G$ is simply connected, then in $G$ there exists a closed irreducible cross-section of the set of closures of regular conjugacy ... More

Irregular and singular loci of commuting varietiesJan 20 2008Apr 02 2008We prove that the singular locus of the commuting variety of a noncommutative reductive Lie algebra is contained in the irregular locus and we compute the codimension of the latter. We prove that one of the irreducible components of the irregular locus ... More

Problems for the problem session of Workshop "Affine Algebraic Geometry", Oberwolfach, January 7--14, 2007Feb 18 2007Formulated problems concern the following topics: (1) Birationally nonequivalent linear actions; (2) Cayley degrees of simple algebraic groups; (3) Singularities of two-dimensional quotients.

Problems for problem sessionApr 25 2005Below are the problems that I formulated at Open Problems Session of {\it Workshop on Group Actions on Rational Varieties}, McGill University and University of Montreal, Canada, March 2002. To appear in: "Affine Algebraic Geometry" conference Proceedings ... More

One-dimensional random interlacementsAug 02 2016We base ourselves on the construction of the two-dimensional random interlacements [12] to define the one-dimensional version of the process. For this constructions we consider simple random walks conditioned on never hitting the origin, which makes them ... More

Ordinary reduction of K3 surfacesFeb 09 2009Feb 16 2009Let X be a K3 surface over a number field K. We prove that there exists a finite algebraic field extension L/K such that X has ordinary reduction at every non-archimedean place of L outside a density zero set of places.

Constructing rational curves on K3 surfacesJul 21 2009We develop a mixed-characteristic version of the Mori-Mukai technique for producing rational curves on K3 surfaces. We reduce modulo p, produce rational curves on the resulting K3 surface over a finite field, and lift to characteristic zero. As an application, ... More

Spectral shift function of higher orderDec 16 2009Nov 05 2012This paper resolves affirmatively Koplienko's conjecture of 1984 on existence of higher order spectral shift measures. Moreover, the paper establishes absolute continuity of these measures and, thus, existence of the higher order spectral shift functions ... More

Integrability in dipole-deformed N=4 super Yang-MillsJun 24 2017Jan 31 2019We study the null dipole deformation of N=4 super Yang-Mills theory, which is an example of a potentially solvable "dipole CFT": a theory that is non-local along a null direction, has non-relativistic conformal invariance along the remaining ones, and ... More

On the vector-valued Littlewood-Paley-Rubio de Francia inequalityApr 14 2011The paper studies Banach spaces satisfying the Littlewood-Paley-Rubio de Francia property LPR_p, 2 \leq p < \infty. The paper shows that every Banach lattice whose 2-concavification is a UMD Banach lattice has this property. The paper also shows that ... More

Higher order spectral shift for contractionsOct 31 2012We derive strong estimates for Schatten norms of operator derivatives along paths of contractions and apply them to prove existence of higher order spectral shift functions for pairs of contractions.

One Mirror Descent Algorithm for Convex Constrained Optimization Problems with non-standard growth propertiesMar 04 2018Apr 15 2018The paper is devoted to a special Mirror Descent algorithm for problems of convex minimization with functional constraints. The objective function may not satisfy the Lipschitz condition, but it must necessarily have the Lipshitz-continuous gradient. ... More

Anomalous acoustoelectric effect in La_{0.67}Ca_{0.33}MnO_{3} filmsOct 19 2001We have studied acoustoelectric (AE) effect produced by surface acoustic waves (SAW) in a monolithic layered structure, composed of piezodielectric LiNbO_{3} substrate and La_{0.67}Ca_{0.33}MnO_{3} film. The experiments unexpectedly revealed in the longitudinal ... More

Structure of the two-neutrino double-$β$ decay matrix elements within perturbation theoryJun 02 2015The two-neutrino double-$\beta$ Gamow-Teller and Fermi transitions are studied within an exactly solvable model, which allows a violation of both spin-isospin SU(4) and isospin SU(2) symmetries, and is expressed with generators of the SO(8) group. It ... More

Algebras of log-integrable functions and operatorsSep 10 2015We show that certain spaces of log-integrable functions and operators are complete topological *-algebras with respect to a natural metric space structure. We explore connections with the Nevanlinna class of holomorphic functions.

Holomorphic functional calculus on upper triangular forms in finite von Neumann algebrasOct 09 2013The decompositions of an element of a finite von Neumann algebra into the sum of a normal operator plus an s.o.t.-quasinilpotent operator, obtained using the Haagerup--Schultz hyperinvariant projections, behave well with respect to holomorphic functional ... More

Blow up and regularity for fractal Burgers equationApr 22 2008The paper is a comprehensive study of the existence, uniqueness, blow up and regularity properties of solutions of the Burgers equation with fractional dissipation. We prove existence of the finite time blow up for the power of Laplacian $\alpha < 1/2,$ ... More

Transportation to random zeroes by the gradient flowOct 30 2005Mar 05 2007We consider the zeroes of a random Gaussian Entire Function f and show that their basins under the gradient flow of the random potential U partition the complex plane into domains of equal area. We find three characteristic exponents 1, 8/5, and 4 of ... More

Logarithmic submajorisation and order-preserving linear isometriesAug 31 2018Nov 20 2018Let $\mathcal{E}$ and $\mathcal{F}$ be symmetrically $\Delta$-normed (in particular, quasi-normed) operator spaces affiliated with semifinite von Neumann algebras $\mathcal{M}_1$ and $\mathcal{M}_2$, respectively. We establish a noncommutative version ... More

A $C^*$-algebraic approach to the principal symbol IIJun 19 2018We introduce an abstract theory of the principal symbol mapping for pseudodifferential operators extending the results of a preceding paper and providing a simple algebraic approach to the theory of pseudodifferential operators in settings important in ... More

Dixmier traces generated by exponentiation invariant generalised limitsOct 11 2012We define a new class of singular positive traces on the ideal $\mathcal M_{1,\infty}$ of $B(H)$ generated by exponentiation invariant generalized limits. We prove that this new class is strictly contained in the class of all Dixmier traces. We also prove ... More

On the uniform rectifiability of AD regular measures with bounded Riesz transform operator: the case of codimension 1Dec 20 2012Dec 21 2012We prove that if $\mu$ is a d-dimensional Ahlfors-David regular measure in $\R^{d+1}$, then the boundedness of the $d$-dimensional Riesz transform in $L^2(\mu)$ implies that the non-BAUP David-Semmes cells form a Carleson family. Combined with earlier ... More

The Riesz transform, rectifiability, and removability for Lipschitz harmonic functionsDec 21 2012Dec 05 2013We show that, given a set $E\subset \mathbb R^{n+1}$ with finite $n$-Hausdorff measure $H^n$, if the $n$-dimensional Riesz transform $$R_{H^n|E} f(x) = \int_{E} \frac{x-y}{|x-y|^{n+1}} f(y) dH^n(y)$$ is bounded in $L^2(H^n|E)$, then $E$ is $n$-rectifiable. ... More

Persistence and permanence of mass-action and power-law dynamical systemsOct 15 2010Mar 02 2011Persistence and permanence are properties of dynamical systems that describe the long-term behavior of the solutions, and in particular specify whether positive solutions approach the boundary of the positive orthant. Mass-action systems (or more generally ... More

The fractional Riesz transform and an exponential potentialApr 10 2012Oct 09 2012In this paper we study the $s$-dimensional Riesz transform of a finite measure $\mu$ in $\mathbf{R}^d$, with $s\in (d-1,d)$. We show that the boundedness of the Riesz transform of $\mu$ implies that a nonlinear potential of exponential type is finite ... More

Yang-Mills fields in flux compactifications on homogeneous manifolds with SU(4)-structureMay 17 2010Feb 27 2012The SU(4)-instanton equations are natural BPS equations for instantons on 8-manifolds. We study these equations on nearly Kaehler and Calabi-Yau torsion manifolds of the form M x G/H, with G/H a coset space and M a product of a torus with Euclidean space. ... More

Theoretical polarization dependence of the two-phonon double-resonant Raman spectra of grapheneJun 18 2012Jun 25 2012The experimental Raman spectra of graphene exhibit a few intense two-phonon bands, which are enhanced through double-resonant scattering processes. Though there are many theoretical papers on this topic, none of them predicts the spectra within a single ... More

A pseudo-Daugavet property for narrow projections in Lorentz spacesOct 16 2001Let $X$ be a rearrangement-invariant space. An operator $T: X\to X$ is called narrow if for each measurable set $A$ and each $\epsilon > 0$ there exists $x \in X$ with $x^2= \chi_A, \int x d \mu = 0$ and $\| Tx \| < \epsilon$. In particular all compact ... More

Fast estimation from above of the maximum wave speed in the Riemann problem for the Euler equationsNov 09 2015May 27 2016This paper is concerned with the construction of a fast algorithm for computing the maximum speed of propagation in the Riemann solution for the Euler system of gas dynamics with the co-volume equation of state. The novelty in the algorithm is that it ... More

Invariant domains and first-order continuous finite element approximation for hyperbolic systemsSep 24 2015We propose a numerical method to solve general hyperbolic systems in any space dimension using forward Euler time stepping and continuous finite elements on non-uniform grids. The properties of the method are based on the introduction of an artificial ... More

Viscous regularization of the Euler equations and entropy principlesDec 21 2012This paper investigates a general class of viscous regularizations of the compressible Euler equations. A unique regularization is identified that is compatible with all the generalized entropies a la Harten and satisfies the minimum entropy principle. ... More

Intuitive dyadic calculus: the basicsAug 23 2015This book is a short introduction into dyadic analysis with applications to classical weighted norm inequalities.

Minimum Degree of the Difference of Two Polynomials over $\mathbb Q$. Part II: Davenport-Zannier pairsSep 26 2015Oct 24 2015In this paper we study pairs of polynomials with a given factorization pattern and such that the degree of their difference attains its minimum. We call such pairs of polynomials Davenport--Zannier pairs, or DZ-pairs for short. The paper is devoted to ... More

Long-lived $2s$ state of muonic hydrogen: population and lifetimeSep 04 2008Ab initio study of the density-dependent population and lifetime of the long-lived $(\mu p)_{2s}$ and the yield of $(\mu p)_{1s}$ atoms with kinetic energy 0.9 keV have been performed for the first time. The direct Coulomb $2s\to 1s$ deexcitation is proved ... More

General procedure for solution of contact problems under dynamic normal and tangential loading based on the known solution of normal contact problemAug 18 2015Oct 23 2015In the present paper we show that the normal contact problem between two elastic bodies in the halfspace approximation can always be transformed to an equivalent problem of the indentation of a profile into an elastic Winkler foundation. Once determined, ... More

Fine-grained complexity of integer programming: The case of bounded branch-width and rankJul 18 2016We use the Exponential Time and Strong Exponential Time hypotheses (ETH & SETH) to provide conditional lower bounds on the solvability of the integer programming (IP) problem. We provide evidence that the running times of known pseudo-polynomial time ... More

Johnson-Schechtman inequalities for noncommutative martingalesDec 14 2016In this paper we study Johnson-Schechtman inequalities for noncommutative martingales. More precisely, disjointification inequalities of noncommutative martingale difference sequences are proved in an arbitrary symmetric operator space $E(\mathcal{M})$ ... More

On a Question of A. E. Nussbaum on Measurability of Families of Closed Linear Operators in a Hilbert SpaceFeb 13 2010The purpose of this note is to answer a question A. E. Nussbaum formulated in 1964 about the possible equivalence between weak measurability of a family of densely defined, closed operators T(t), t real, in a separable complex Hilbert space H on one hand, ... More

On the tractability of optimization problems on H-graphsSep 27 2017Apr 25 2018For a graph $H$, a graph $G$ is an $H$-graph if it is an intersection graph of connected subgraphs of some subdivision of $H$. $H$-graphs naturally generalize several important graph classes like interval or circular-arc graph. This class was introduced ... More

On the Index of a Non-Fredholm Model OperatorSep 04 2015Let $\{A(t)\}_{t \in \mathbb{R}}$ be a path of self-adjoint Fredholm operators in a Hilbert space $\mathcal{H}$, joining endpoints $A_\pm$ as $t \to \pm \infty$. Computing the index of the operator $D_A= (d/d t) + A$ acting in $L^2(\mathbb{R}; \mathcal{H})$, ... More

Families of Disjoint Divisors on VarietiesApr 21 2015Jan 20 2016Following the work of Totaro and Pereira, we study sufficient conditions under which collections of pairwise-disjoint divisors on a variety over an algebraically closed field are contained in the fibers of a morphism to a curve. We prove that $\rho_w(X) ... More

YAC: BFT Consensus Algorithm for BlockchainSep 03 2018Consensus in decentralized systems that asynchronously receive events and which are subject to Byzantine faults is a common problem with many real-life applications. Advances in decentralized systems, such as distributed ledger (i.e., blockchain) technology, ... More

Weak type commutator and Lipschitz estimates: resolution of the Nazarov-Peller conjectureJun 02 2015Let $\mathcal{M}$ be a semi-finite von Neumann algebra and let $f: \mathbb{R} \rightarrow \mathbb{C}$ be a Lipschitz function. If $A,B\in\mathcal{M}$ are self-adjoint operators such that $[A,B]\in L_1(\mathcal{M}),$ then $$\|[f(A),B]\|_{1,\infty}\leq ... More

Functions of normal operators under perturbationsAug 10 2010In \cite{Pe1}, \cite{Pe2}, \cite{AP1}, \cite{AP2}, and \cite{AP3} sharp estimates for $f(A)-f(B)$ were obtained for self-adjoint operators $A$ and $B$ and for various classes of functions $f$ on the real line $\R$. In this paper we extend those results ... More

Functions of perturbed normal operatorsMar 27 2010In \cite{Pe1}, \cite{Pe2}, \cite{AP1}, \cite{AP2}, and \cite{AP3} sharp estimates for $f(A)-f(B)$ were obtained for self-adjoint operators $A$ and $B$ and for various classes of functions $f$ on the real line $\R$. In this note we extend those results ... More

Mirror Descent and Constrained Online Optimization ProblemsSep 21 2018We consider the following class of online optimization problems with functional constraints. Assume, that a finite set of convex Lipschitz-continuous non-smooth functionals are given on a closed set of $n$-dimensional vector space. The problem is to minimize ... More

Dividing goods and bads under additive utilitiesOct 12 2016When utilities are additive, we uncovered in our previous paper (Bogomolnaia et al. "Dividing Goods or Bads under Additive Utilities") many similarities but also surprising differences in the behavior of the familiar Competitive rule (with equal incomes), ... More

Generalized derivations of multiplicative $n$-ary Hom-$Ω$ color algebrasSep 23 2016We generalize the results of Leger and Luks, Zhang R. and Zhang Y.; Chen, Ma, Ni, Niu, Zhou and Fan; Kaygorodov and Popov about generalized derivations of color $n$-ary algebras to the case of $n$-ary Hom-$\Omega$ color algebras. Particularly, we prove ... More

Instantons on Special Holonomy ManifoldsMar 12 2012Apr 26 2012We consider cones over manifolds admitting real Killing spinors and instanton equations on connections on vector bundles over these manifolds. Such cones are manifolds with special (reduced) holonomy. We generalize the scalar ansatz for a connection proposed ... More

On the numerical radius of operators in Lebesgue spacesNov 22 2010We show that the absolute numerical index of the space $L_p(\mu)$ is $p^{-1/p} q^{-1/q}$ (where $1/p+1/q=1$). In other words, we prove that $$ \sup\{\int |x|^{p-1}|Tx|\, d\mu \, : \ x\in L_p(\mu),\,\|x\|_p=1\} \,\geq \,p^{-\frac{1}{p}} q^{-\frac{1}{q}}\,\|T\| ... More

On Novel Mechanism of a Pump Electromagnetic Wave Absolute Two-Plasmon Parametric Decay Instability Excitation in Tokamak ECRH ExperimentsMar 07 2016Novel mechanism leading to excitation of absolute two plasmon parametric decay instability (TPDI) of a pump extraordinary (X) wave is discussed. It is shown that the upper hybrid (UH) plasmon can be 3D trapped in the presence of both a nonmonotonous density ... More

Invariant domain preserving discretization-independent schemes and convex limiting for hyperbolic systemsJul 06 2018We introduce an approximation technique for nonlinear hyperbolic systems with sources that is invariant domain preserving. The method is discretization-independent provided elementary symmetry and skew-symmetry properties are satisfied by the scheme. ... More

On the numerical index of real $L_p(μ)$-spacesMar 16 2009Jan 29 2010We give a lower bound for the numerical index of the real space $L_p(\mu)$ showing, in particular, that it is non-zero for $p\neq 2$. In other words, it is shown that for every bounded linear operator $T$ on the real space $L_p(\mu)$, one has $$ \sup{\Bigl|\int ... More

On Enflo and narrow operators acting on $L_p$Jan 19 2012Mar 13 2012The first part of the paper is inspired by a theorem of H. Rosenthal, that if an operator on $L_1[0,1]$ satisfies the assumption that for each measurable set $A \subseteq [0,1]$ the restriction $T \bigl|_{L_1(A)}$ is not an isomorphic embedding, then ... More

The 0nbb-decay nuclear matrix elements with self-consistent short-range correlationsFeb 02 2009A self-consistent calculation of nuclear matrix elements of the neutrinoless double beta decays (0nbb) of 76Ge, 82Se, 96Zr, 100Mo, 116Cd, 128Te, 130Te and 130Xe is presented in the framework of the renormalized quasiparticle random phase approximation ... More

Proton-neutron pairing in the deformed BCS approachAug 15 2003We examine isovector and isoscalar proton-neutron pairing correlations for the ground state of even-even Ge isotopes with mass number A=64-76 within the deformed BCS approach. For N=Z 64Ge the BCS solution with only T=0 proton-neutron pairs is found. ... More

On reduction theory and Brown measure for closed unbounded operatorsSep 10 2015The theory of direct integral decompositions of both bounded and unbounded operators is further developed; in particular, results about spectral projections, functional calculus and affiliation to von Neumann algebras are proved. For operators belonging ... More

Neutrinoless double-beta decay and seesaw mechanismApr 11 2011Oct 11 2011From the standard seesaw mechanism of neutrino mass generation, which is based on the assumption that the lepton number is violated at a large (~10exp(+15) GeV) scale, follows that the neutrinoless double-beta decay is ruled by the Majorana neutrino mass ... More

Rank-width and Tree-width of H-minor-free GraphsOct 01 2009We prove that for any fixed r>=2, the tree-width of graphs not containing K_r as a topological minor (resp. as a subgraph) is bounded by a linear (resp. polynomial) function of their rank-width. We also present refinements of our bounds for other graph ... More

A Jost-Pais-type reduction of Fredholm determinants and some applicationsApr 03 2014Apr 22 2014We study the analog of semi-separable integral kernels in $\cH$ of the type {equation*} K(x,x')={cases} F_1(x)G_1(x'), & a<x'< x< b, \\ F_2(x)G_2(x'), & a<x<x'<b, {cases} {equation*} where $-\infty\leq a<b\leq \infty$, and for a.e.\ $x \in (a,b)$, $F_j ... More

Bidimensionality and KernelsJun 17 2016Feb 05 2019Bidimensionality Theory was introduced by [E.D. Demaine, F.V. Fomin, M.Hajiaghayi, and D.M. Thilikos. Subexponential parameterized algorithms on graphs of bounded genus and H-minor-free graphs, J. ACM, 52 (2005), pp.866--893] as a tool to obtain sub-exponential ... More

On the Parameterized Complexity of Graph Modification to First-Order Logic PropertiesMay 11 2018Feb 26 2019We consider the problems of deciding whether an input graph can be modified by removing/adding at most k vertices/edges such that the result of the modification satisfies some property definable in first-order logic. We establish a number of sufficient ... More

Prismatic Large $N$ Models for Bosonic TensorsAug 13 2018We study the $O(N)^3$ symmetric quantum field theory of a bosonic tensor $\phi^{abc}$ with sextic interactions. Its large $N$ limit is dominated by a positive-definite operator, whose index structure has the topology of a prism. We present a large $N$ ... More

The Spectral shift function and the Witten indexMay 19 2015We survey the notion of the spectral shift function of a pair of self-adjoint operators and recent progress on its connection with the Witten index. We also describe a proof of Krein's Trace Theorem that does not use complex analysis [53] and develop ... More