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Proposal to demonstrate the non-locality of Bohmian mechanics with entangled photonsJul 11 2012Bohmian mechanics reproduces all statistical predictions of quantum mechanics, which ensures that entanglement cannot be used for superluminal signaling. However, individual Bohmian particles can experience superluminal influences. We propose to illustrate ... More

A new proof of a Bismut-Zhang formula for some class of representationsApr 19 2013Bismut and Zhang computed the ratio of the Ray-Singer and the combinatorial torsions corresponding to non-unitary representations of the fundamental group. In this note we show that for representations which belong to a connected component containing ... More

Refined analytic torsion as analytic function on the representation variety and applicationsJul 18 2013Mar 24 2016We prove that refined analytic torsion on a manifold with boundary is an analytic section of the determinant line bundle over the representation variety. As a fundamental application we establish a gluing formula for refined analytic torsion on connected ... More

Near-Unitary Spin Squeezing in $^{171}$YbJan 29 2019May 09 2019Spin squeezing can improve atomic precision measurements beyond the standard quantum limit (SQL), and unitary spin squeezing is essential for improving atomic clocks. We report substantial and nearly unitary spin squeezing in $^{171}$Yb, an optical lattice ... More

Impact of Non-Unitary Spin Squeezing on Atomic Clock PerformanceJun 06 2018Oct 13 2018Spin squeezing is a form of entanglement that can improve the stability of quantum sensors operating with multiple particles, by inducing inter-particle correlations that redistribute the quantum projection noise. Previous analyses of potential metrological ... More

Novikov inequalities with symmetryJun 20 1996We establish an equivariant generalization of the Novikov inequalities which allow to estimate the topology of the set of critical points of a closed basic invariant 1-form by means of twisted equivariant cohomology of the manifold. We test and apply ... More

On stability of linear neutral differential equations with variable delaysApr 29 2019We present a review of known stability tests and new explicit exponential stability conditions for the linear scalar neutral equation with two delays $$ \dot{x}(t)-a(t)\dot{x}(g(t))+b(t)x(h(t))=0, $$ where $$ |a(t)|<1,~ b(t)\geq 0, ~h(t)\leq t, ~g(t)\leq ... More

On stability of cooperative and hereditary systems with a distributed delayJun 09 2016We consider a system $\displaystyle \frac{dx}{dt}=r_1(t) G_1(x) \left[ \int_{h_1(t)}^t f_1(y(s))~d_s R_1 (t,s) - x(t) \right], \frac{dy}{dt}=r_2(t) G_2(y) \left[ \int_{h_2(t)}^t f_2(x(s))~d_s R_2 (t,s) - y(t)\right]$ with increasing functions $f_1$ and ... More

On convergence of solutions to difference equations with additive perturbationsJun 06 2016Various types of stabilizing controls lead to a deterministic difference equation with the following property: once the initial value is positive, the solution tends to the unique positive equilibrium. Introducing additive perturbations can change this ... More

Stability conditions for scalar delay differential equations with a nondelay termJun 09 2016The problem considered in the paper is exponential stability of linear equations and global attractivity of nonlinear non-autonomous equations which include a non-delay term and one or more delayed terms. First, we demonstrate that introducing a non-delay ... More

Stochastic control stabilizing unstable or chaotic mapsFeb 21 2019The paper considers a stabilizing stochastic control which can be applied to a variety of unstable and even chaotic maps. Compared to previous methods introducing control by noise, we relax assumptions on the class of maps, as well as consider a wider ... More

Stabilization of structured populations via vector target oriented controlFeb 19 2019In contrast with unstructured models, structured discrete population models have been able to fit and predict chaotic experimental data. However, most of the chaos control techniques in the literature have been designed and analyzed in a one-dimensional ... More

On the interplay of harvesting and various diffusion strategies for spatially heterogeneous populationsApr 29 2019The paper explores the influence of harvesting (or culling) on the outcome of the competition of two species in a spatially heterogeneous environment. The harvesting effort is assumed to be proportional to the space-dependent intrinsic growth rate. The ... More

Contracting Experts With Unknown Cost StructuresApr 29 2014We investigate the problem of a principal looking to contract an expert to provide a probability forecast for a categorical event. We assume all experts have a common public prior on the event's probability, but can form more accurate opinions by engaging ... More

Structured stability radii and exponential stability tests for Volterra difference systemsOct 11 2012Uniform exponential (UE) stability of linear difference equations with infinite delay is studied using the notions of a stability radius and a phase space. The state space $\X$ is supposed to be an abstract Banach space. We work both with non-fading phase ... More

On stability of delay equations with positive and negative coefficients with applicationsApr 29 2019We obtain new explicit exponential stability conditions for linear scalar equations with positive and negative delayed terms $$ \dot{x}(t)+ \sum_{k=1}^m a_k(t)x(h_k(t))- \sum_{k=1}^l b_k(t)x(g_k(t))=0 $$ and its modifications, and apply them to investigate ... More

A finite analog of the AGT relation I: finite W-algebras and quasimaps' spacesAug 21 2010Jan 16 2012Recently Alday, Gaiotto and Tachikawa proposed a conjecture relating 4-dimensional super-symmetric gauge theory for a gauge group G with certain 2-dimensional conformal field theory. This conjecture implies the existence of certain structures on the (equivariant) ... More

Two-Color Magneto-Optical Trap with Small Magnetic Field for YtterbiumFeb 25 2015We report a two-color magneto-optical trap (MOT) for ytterbium atoms operating at a low magnetic field gradient down to 2 G/cm where a conventional MOT using the singlet transition (6s^2 1S0 -> 6s6p 1P1) is unable to trap atoms. By simultaneously applying ... More

Fast Compact Laser Shutter Using a Direct Current Motor and 3D PrintingSep 04 2015Sep 21 2015We present a mechanical laser shutter design that utilizes a DC electric motor to rotate a blade which blocks and unblocks a light beam. The blade and the main body of the shutter are modeled with computer aided design (CAD) and are produced by 3D printing. ... More

On oscillation of difference equations with continuous time and variable delaysApr 29 2019We consider existence of positive solutions for a difference equation with continuous time, variable coefficients and delays $$ x(t+1)-x(t)+ \sum_{k=1}^m a_k(t)x(h_k(t))=0, \quad a_k(t) \geq 0, ~~h_k(t) \leq t, \quad t \geq 0, \quad k=1, \dots, m. $$ ... More

Instanton moduli spaces and $\mathscr W$-algebrasJun 09 2014Sep 17 2016We describe the (equivariant) intersection cohomology of certain moduli spaces ("framed Uhlenbeck spaces") together with some structures on them (such as e.g.\ the Poincar\'e pairing) in terms of representation theory of some vertex operator algebras ... More

On the Taylor Expansion of Value FunctionsApr 13 2018We introduce a framework for approximate dynamic programming that we apply to discrete time chains on $\mathbb{Z}_+^d$ with countable action sets. Our approach is grounded in the approximation of the (controlled) chain's generator by that of another Markov ... More

Vacuum spin squeezingMar 07 2017We investigate the generation of entanglement (spin squeezing) in an optical-transition atomic clock through the coupling to a vacuum electromagnetic field that is enhanced by an optical cavity. We show that if each atom is prepared in a superposition ... More

Exponential Stability of Linear Delay Impulsive Differential EquationsNov 26 1993For ordinary differential equations and functional differential equations the following result is well known. Suppose any solution is bounded on the half-line for each bounded on the half-line right-hand side. Then under certain conditions the equations ... More

On $[A,A]/[A,[A,A]]$ and on a $W_n$-action on the consecutive commutators of free associative algebraOct 12 2006Oct 16 2006We consider the lower central filtration of the free associative algebra $A_n$ with $n$ generators as a Lie algebra. We consider the associated graded Lie algebra. It is shown that this Lie algebra has a huge center which belongs to the cyclic words, ... More

Retrospective change-point detection and estimation in multivariate linear modelsOct 26 2011In this paper the problem of retrospective change-point detection and estimation in multivariate linear models is considered. The lower bounds for the error of change-point estimation are proved in different cases (one change-point: deterministic and ... More

Models with varying structureOct 30 2017In this paper the problems of the retrospective analysis of models with time-varying structure are considered. These models include contamination models with randomly switching parameters and multivariate classification models with an arbitrary number ... More

The geometry of second-order ordinary differential equationsFeb 02 2016These are lecture notes of the Summer school on the geometry of differential equations held in Nordfjordeid, Norway in 1996. They cover geometric structures related to scalar second order ODEs, the construction of the associated Cartan connection, techniques ... More

Carving complex many-atom entangled states by single-photon detectionAug 11 2015Oct 26 2015We propose a versatile and efficient method to generate a broad class of complex entangled states of many atoms via the detection of a single photon. For an atomic ensemble contained in a strongly coupled optical cavity illuminated by weak single- or ... More

Quantum, Nonlocal Aberration CancellationJun 11 2019Phase distortions, or aberrations, can negatively influence the performance of an optical imaging system. Through the use of position-momentum entangled photons, we nonlocally correct for aberrations in one photon's optical path by intentionally introducing ... More

Asymptotically Optimal Detection of Changes in Stochastic Models with Switching RegimesJan 24 2013This paper deals with the problem of asymptotically optimal detection of changes in regime-switching stochastic models. We need to divide the whole obtained sample of data into several sub-samples with observations belonging to different states of a stochastic ... More

Coulomb branches of $3d$ $\mathcal N=4$ quiver gauge theories and slices in the affine Grassmannian (with appendices by Alexander Braverman, Michael Finkelberg, Joel Kamnitzer, Ryosuke Kodera, Hiraku Nakajima, Ben Webster, and Alex Weekes)Apr 13 2016May 30 2018This is a companion paper of arXiv:1601.03586. We study Coulomb branches of unframed and framed quiver gauge theories of type $ADE$. In the unframed case they are isomorphic to the moduli space of based rational maps from ${\mathbb C}P^1$ to the flag ... More

Stabilisation of difference equations with noisy prediction-based controlJun 06 2016We consider the influence of stochastic perturbations on stability of a unique positive equilibrium of a difference equation subject to prediction-based control. These perturbations may be multiplicative $$x_{n+1}=f(x_n)-\left( \alpha + l\xi_{n+1} \right) ... More

Sorted Top-k in RoundsJun 12 2019We consider the sorted top-$k$ problem whose goal is to recover the top-$k$ items with the correct order out of $n$ items using pairwise comparisons. In many applications, multiple rounds of interaction can be costly. We restrict our attention to algorithms ... More

Deformation quantization with traces and vanishing of the wheelsApr 12 2000May 01 2000The paper has been withdrawn because the result of math.QA/0002057 "Deformation quantization with traces" holds only for a constant volume form.

Tempered currents and the cohomology of the remote fiber of a real polynomial mapApr 02 1997Let $p:R^n\to R$ be a polynomial map. Consider the complex $S'\Omega^*(\RR^n)$ of tempered currents on $R^n$ with the twisted differential $d_p=d-dp$ where $d$ is the usual exterior differential and $dp$ stands for the exterior multiplication by $dp$. ... More

Passive intrinsic-linewidth narrowing of ultraviolet extended-cavity diode laser by weak optical feedbackFeb 25 2014We present a simple method for narrowing the intrinsic Lorentzian linewidth of a commercial ultraviolet grating extended-cavity diode laser (TOPTICA DL Pro) using weak optical feedback from a long external cavity. We achieve a suppression in frequency ... More

Tree-like curves and their inflection pointsAug 12 1997We give a criterion when a planar tree-like curve, i.e. a generic immersed plane curve each double point of which cuts it into two disjoint parts, can be send by a diffeomorphism of the plane onto a curve with no inflection points. We also present some ... More

Anisotropy and superconductivityFeb 12 2013The mean field method is applied for analysis of valence electrons in metals. It is shown that at low temperatures electrons have two wave-vector distribution patterns. Isotropic distribution refers to the first pattern. Anisotropic distribution refers ... More

The anisotropic distribution of the interacting electronsJan 21 2013The distribution function for a system of interacting electrons in metals is multivalent in a certain region of wave vectors. One solution among many is isotropic. For other solutions the distribution of electrons over the wave vectors is anisotropic. ... More

Quantum master equation for a system of identical particlesJan 21 2013We consider an open quantum many-particle system in which there are dissipative processes. The evolution of this system is described by a kinetic equation for the density matrix. From the equation describing a random Markov process in this system, we ... More

High $Q^2$ Probe of Nuclear Spectral Function and Color TransparencyNov 11 1993Contrary to widespread opinion, color transparency (CT) brings essential ambiguity to, rather than helps in, study of the nuclear spectral function in quasielastic lepton scattering, $A(l,l'p)A'$, at high $Q^2$. Although the nuclear attenuation vanishes, ... More

In Search for (QUANTUM) Color TransparencyMay 19 1993Color transparency (CT) is an effect of suppression of nuclear shadowing of hard reactions, closely related to the color screening. A brief review of theoretical development and experimental search for CT, failed and successful, are presented. A special ... More

Kinetics of Strongly Non-Equilibrium Bose-Einstein CondensationSep 23 2000We consider the ordering kinetics in a strongly non-equilibrium state of a (weakly) interacting Bose gas, characterized, on one hand, by large occupation numbers, and, on the other hand, by the absence of long-range order. Up to higher-order corrections ... More

Symmetry, compatibility and exact solutions of PDEsNov 24 2011Mar 04 2012We discuss various compatibility criteria for overdetermined systems of PDEs generalizing the approach to formal integrability via brackets of differential operators. Then we give sufficient conditions that guarantee that a PDE possessing a Lie algebra ... More

Noncommutative geometry on the universal envelopping algebra of the Borel subgroup U[sb(2)]Apr 09 2013We study the Borel algebra de ne by [x a ; x b ] = 2 a;1 x b as a noncommutative manifold R 3 . We calculate its noncommutative di erential form relations. We deduce its partial derivative relations and the derivative of a plane wave. After calculating ... More

Neutrino Mass: The Present and the FutureOct 18 2000We argue that the evidence for neutrino mass is quite compelling. This mass raises a number of questions, which we enumerate, about neutrinos. Then we focus on one of these questions---the issue of the possible neutrino mass spectra. In particular, we ... More

Neutrino Physics: Where Do We Stand, and Where Are We Going? -- The Theoretical-Phenomenological PerspectiveJun 09 2003The discoveries and open questions in neutrino physics, as reported at Neutrino 2002 and more recently, are reviewed from a theoretical perspective.

Filament eruption with apparent reshuffle of endpointsMay 22 2014Filament eruption on 30 April - 1 May 2010, which shows the reconnection of one filament leg with a region far away from its initial position, is analyzed. Observations from three viewpoints are used for as precise as possible measurements of endpoint ... More

Klt singularities of horospherical pairsSep 22 2015Sep 30 2015Let $X$ be a horospherical $G$-variety and let $D$ be an effective $\mathbb{Q}$-divisor of $X$ that is stable under the action of a Borel subgroup $B$ of $G$ and such that $D+K\_X$ is $\mathbb{Q}$-Cartier. We prove, using Bott-Samelson resolutions, that ... More

Cheeger-Mueller Theorem on manifolds with cuspsNov 03 2014Jan 07 2015We prove equality between the renormalized Ray-Singer analytic torsion and the intersection R-torsion on a Witt-manifold with cusps, up to an error term determined explicitly by the Betti numbers of the cross section of the cusp and the intersection R-torsion ... More

Rankin-Selberg methods for closed string amplitudesJan 17 2014Jul 10 2014After integrating over supermoduli and vertex operator positions, scattering amplitudes in superstring theory at genus $h\leq 3$ are reduced to an integral of a Siegel modular function of degree $h$ on a fundamental domain of the Siegel upper half plane. ... More

On the number of coverings of the sphere ramified over given pointsDec 04 2013Mar 27 2014We present the generating function for the numbers of isomorphism classes of coverings of the two-dimensional sphere by the genus $g$ compact oriented surface not ramified outside of a given set of $m+1$ points in the target, fixed ramification type over ... More

A note on the Trace Theorem for domains which are locally subgraph of a Holder continuous functionNov 13 2013The purpose of this note is to prove a version of the Trace Theorem for domains which are locally subgraph of a H\" older continuous function. More precisely, let $\eta\in C^{0,\alpha}(\omega)$, $0<\alpha<1$ and let $\Omega_{\eta}$ be a domain which is ... More

Differential Invariants and Symmetry: Riemannian metrics and beyondFeb 10 2015We discuss Lie-Tresse theorem for the pseudogroup of diffeomorphisms acting on the space of (pseudo-)Riemannian metrics, and relate this to existence of Killing vector fields. Then we discuss the impact of symmetry in the general case.

Weak-Strong uniqueness for compressible Navier-Stokes system with degenerate viscosity coefficient and vacuum in one dimensionNov 27 2014We prove weak-strong uniqueness results for the compressible Navier-Stokes system with degenerate viscosity coefficient and with vacuum in one dimension. In other words, we give conditions on the weak solution constructed in \cite{Jiu} so that it is unique. ... More

Algebra and logic. Some problemsJun 04 2013The paper has a form of a talk on the given topic. It consists of three parts. The first part of the paper contains main notions, the second one is devoted to logical geometry, the third part describes types and isotypeness. The problems are distributed ... More

Cold asymmetrical fermion superfluids in nonperturbative renormalisation groupMay 26 2006May 29 2006The application of the nonperturbative renormalisation group approach to a system with two fermion species is studied. Assuming a simple ansatz for the effective action with effective bosons, describing pairing effects we derive a set of approximate flow ... More

Superfluidity within Exact Renormalisation Group approachDec 21 2005The application of the exact renormalisation group to a many-fermion system with a short-range attractive force is studied. We assume a simple ansatz for the effective action with effective bosons, describing pairing effects and derive a set of approximate ... More

Spectral Statistics of "Cellular" BilliardsOct 01 2010For a bounded planar domain $\Omega^0$ whose boundary contains a number of flat pieces $\Gamma_i$ we consider a family of non-symmetric billiards $\Omega$ constructed by patching several copies of $\Omega^0$ along $\Gamma_i$'s. It is demonstrated that ... More

Systematics of oscillatory behavior in hadronic masses and widthsMar 15 2016Jul 05 2016A systematic study of hadron masses and widths shows regular oscillations that can be fitted by a simple cosine function. This property can be observed when the difference between adjacent masses of each family is plotted versus the mean mass.

Non-existence of orthogonal complex structures on 6-sphere with a metric close to the round oneAug 24 2017I review several proofs for non-existence of orthogonal complex structures on the six-sphere, most notably by G. Bor and L. Hernandez-Lamoneda, but also by K. Sekigawa and L. Vanhecke that we generalize for metrics close to the round one. Invited talk ... More

Recent results from D0 and recent Tevatron combinationsMay 19 2017We discuss recent results obtained by the D0 experiment at the Fermilab Tevatron $p\bar p$ collider and recent combinations of CDF and D0 measurements. Regarding the top quark mass, we present recent measurements obtained at D0, the final Run~I+Run~II ... More

Universal Function Approximation by Deep Neural Nets with Bounded Width and ReLU ActivationsAug 09 2017Dec 20 2017This article concerns the expressive power of depth in neural nets with ReLU activations and bounded width. We are particularly interested in the following questions: what is the minimal width $w_{\text{min}}(d)$ so that ReLU nets of width $w_{\text{min}}(d)$ ... More

Throughput analysis in networks of WLANsNov 21 2016This paper proposes a simple but accurate approximation to analytically model both the inter-WLANs (Wireless Local Area Networks) interactions and the negative effect of collisions in networks of IEEE 802.11 WLANs. Inter-WLANs interactions are characterized ... More

Nuclear Data for Astrophysical ModelingAug 01 2016Nuclear physics has been playing an important role in modern astrophysics and cosmology. Since the early 1950's it has been successfully applied for the interpretation and prediction of astrophysical phenomena. Nuclear physics models helped to explain ... More

On the Scattering Aharonov-Bohm effectFeb 27 2019In this paper we review some aspects of the scattering Aharonov-Bohm effect and Berry's phase. Specifically, the problem of scattering of free 2d electrons on the system of an arbitrary number of parallel, infinitely thin and infinitely long coils (non-interacting, ... More

Linear response and moderate deviations: hierarchical approach. IVOct 12 2018The Moderate Deviations Principle (MDP) is well-understood for sums of independent random variables, worse understood for stationary random sequences, and scantily understood for random fields. Here it is established for splittable random fields integrated ... More

Die Klassifikation der Gruppen bis zur Ordnung p^5Jun 19 2018This paper presents a classification of all p-groups of order p^5 up to isomorphism. It contains a full list of their polycyclic presentations, a short introduction to the basic ideas of the methodes used to classify the groups, and a detailed proof of ... More

Addressing the Majorana vs. Dirac Question Using Neutrino DecaysMay 19 2018We explain why it is so hard to determine whether neutrinos are Majorana or Dirac particles as long as the only neutrinos we study are ultra-relativistic. We then show how non-relativistic neutrinos could help, and focus on the angular distributions in ... More

Solar coronal loop dynamics near the null point above active region NOAA 2666May 22 2018We analyse observations of a saddle-like structure in the corona above the western limb of the Sun on 2017 July 18. The structure was clearly outlined by coronal loops with typical coronal temperature no more than 1 MK. The dynamics of loops showed convergence ... More

On the twisted tensor product of small dg categoriesMar 03 2018Jul 11 2018Given two small dg categories $C,D$, defined over a field, we introduce their (non-symmetric) twisted tensor product $C\overset{\sim}{\otimes} D$. We show that $-\overset{\sim}{\otimes} D$ is left adjoint to the functor $Coh(D,-)$, where $Coh(D,E)$ is ... More

Chiral symmetry restoration and correlator mixing at finite densityMar 18 2019Chiral symmetry imposes some constrains on hadron correlation functions in dense medium. These constraints imply a certain general structure of the two- and three-point correlation functions of chiral partners and lead to the effect of mixing arising ... More

Algebraic logic and logical geometry in arbitrary varieties of algebrasMay 28 2012Jun 01 2012The paper consists of two parts. The first part is devoted to logic for universal algebraic geometry. The second one deals with problems and some results. It may be regarded as a brief exposition of some ideas from the book in progress: B.Plotkin, E.Aladova, ... More

Algebraic spectral curves over $\mathbb Q$ and their tau-functionsJul 30 2018Let $W(z)$ be a $n\times n$ matrix polynomial with rational coefficients. Denote $C$ the spectral curve $\det \left( w\cdot{\bf 1}-W(z)\right) =0$. Under some natural assumptions about the structure of $W(z)$ we prove that certain combinations of logarithmic ... More

Non-trivial solutions to a linear equation in integersMar 26 2007Nov 10 2007For k>=3 let A \subset [1,N] be a set not containing a solution to a_1 x_1+...+a_k x_k=a_1 x_{k+1}+...+a_k x_{2k} in distinct integers. We prove that there is an epsilon>0 depending on the coefficients of the equation such that every such A has O(N^{1/2-epsilon}) ... More

Set families with a forbidden subposetMar 26 2008Nov 21 2009We asymptotically determine the size of the largest family F of subsets of {1,...,n} not containing a given poset P if the Hasse diagram of P is a tree. This is a qualitative generalization of several known results including Sperner's theorem.

Problems in algebra inspired by universal algebraic geometryJun 06 2004Dec 14 2004Let $\Theta$ be a variety of algebras. In every $\Theta$ and every algebra $H$ from $\Theta$ one can consider algebraic geometry in $\Theta$ over $H$. We consider also a special categorical invariant $K_\Theta (H)$ of this geometry. The classical algebraic ... More

Point classification of 2nd order ODEs: Tresse classification revisited and beyondSep 26 2008In 1896 Tresse gave a complete description of relative differential invariants for the pseudogroup action of point transformations on the 2nd order ODEs. The purpose of this paper is to review, in light of modern geometric approach to PDEs, this classification ... More

Sums of dilatesNov 11 2007Apr 03 2008The lambda-dilate of a set A is lambda*A={lambda a : a \in A}. We give an asymptotically sharp lower bound on the size of sumsets of the form lambda_1*A+...+lambda_k*A for arbitrary integers lambda_1,...,lambda_k and integer sets A. We also establish ... More

The semantics of the canonical commutation relationApr 26 2016We treat the canonical commutation relations and the conventional calculus based on it as an algebraic syntax of quantum mechanics and establish a geometric semantics of this syntax. This leads us to a geometric model, the space of states with the action ... More

Generalized Wilczynski invariants for non-linear ordinary differential equationsFeb 09 2007Apr 05 2007We show that classical Wilczynski--Se-ashi invariants of linear systems of ordinary differential equations are generalized in a natural way to contact invariants of non-linear ODEs. We explore geometric structures associated with equations that have vanishing ... More

Spherical Means in Odd Dimensions and EPD equationsNov 13 2007The paper contains a simple proof of the Finch-Patch-Rakesh inversion formula for the spherical mean Radon transform in odd dimensions. This transform arises in thermoacoustic tomography. Applications are given to the Cauchy problem for the Euler-Poisson-Darboux ... More

Exponential tropical varieties and complex Monge-Ampere operatorDec 21 2012May 26 2013Sometimes it is possible to extend some using Newton polyhedra computations in algebraic geometry from polynomials to exponential sums. For this purpose it is useful to consider analogues of tropical varieties in complex space. These analogues are called ... More

The spectrum of a Harmonic Oscillator Operator Perturbed by Point InteractionsJul 15 2014We consider the operator $ L = - (d/dx)^2 + x^2 y + w(x) y , y \in L^2(\mathbb{R}) $, where $ w(x) = s [ \delta(x - b) - \delta(x + b)], b \neq 0,$ real, $s \in \mathbb{C}$. This operator has a discrete spectrum: eventually the eigenvalues are simple ... More

New relations for the old triangleMay 02 2013In this note we show that in addition to two integers forming a Pythagorean triple, there also exist two irrational numbers in terms of which this Pythagorean triple can also be obtained. We also put forward a relation between these two pairs and the ... More

Measurable sets with excluded distancesMar 28 2007Feb 24 2008For a set of distances D={d_1,...,d_k} a set A is called D-avoiding if no pair of points of A is at distance d_i for some i. We show that the density of A is exponentially small in k provided the ratios d_1/d_2, d_2/d_3, ..., d_{k-1}/d_k are all small ... More

A generalization of Quillen's small object argumentJan 29 2004Mar 29 2005We generalize the small object argument in order to allow for its application to proper classes of maps (as opposed to sets of maps in Quillen's small object argument). The necessity of such a generalization arose with appearance of several important ... More

Localization with respect to a class of maps II - Equivariant cellularization and its applicationDec 09 2003We present an example of a homotopical localization functor which is not a localization with respect to any set of maps. Our example arises from equivariant homotopy theory. The technique of equivariant cellularization is developed and applied to the ... More

Algorithmische Konstruktionen von GitternNov 07 2004The main objective of this thesis is a classification project for integral lattices. Using Kneser's neighbour method we have developed the computer program tn to classify complete genera of integral lattices. Main results are detailed classifications ... More

Divisibility in the Stone-Čech compactificationOct 24 2014After defining continuous extensions of binary relations on the set N of natural numbers to its Stone-Cech compactification \beta N, we establish some results about one of such extensions. This provides us with one possible divisibility relation on \beta ... More

Another proof of Harer-Zagier formulaMar 18 2015For a regular $2n$-gon there are $(2n-1)!!$ ways to match and glue the $2n$ sides. The Harer-Zagier bivariate generating function enumerates the gluings by $n$ and the genus $g$ of the attendant surface and leads to a recurrence equation for the counts ... More

On random quadratic forms: supports of potential local maximaAug 10 2017Jan 05 2018In the late eighties John Kingman studied the problem of maxima of a quadratic form, with independent, uniformly distributed, coefficients, on a simplex of growing dimension $n$. In particular, he proved that the largest support size (cardinality) $L_n$ ... More

Uniform lamda-adjustment and mu-approximation in Banach spacesApr 17 2008We introduce a new concept of perturbation of closed linear subspaces and operators in Banach spaces called uniform lambda-adjustment which is weaker than perturbations by small gap, operator norm, q-norm, and K2-approximation. In arbitrary Banach spaces ... More

Sketches for Matrix Norms: Faster, Smaller and More GeneralSep 19 2016We design new sketching algorithms for unitarily invariant matrix norms, including the Schatten $p$-norms~$\|{\cdot}\|_{S_p}$, and obtain, as a by-product, streaming algorithms that approximate the norm of a matrix $A$ presented as a turnstile data stream. ... More

Symmetrized Trace and Symmetrized Determinant of Odd Class Pseudo-Differential OperatorsFeb 16 2007Apr 26 2007We introduce a new canonical trace on odd class logarithmic pseudo-differential operators on an odd dimensional manifold, which vanishes on commutators. When restricted to the algebra of odd class classical pseudo-differential operators our trace coincides ... More

On self-adjointness of a Schroedinger operatorJul 28 1996Aug 28 1996Let $M$ be a complete Riemannian manifold and let $\Omega^*(M)$ denote the space of differential forms on $M$. Let $d:\Omega^*(M) \to \Omega^{*+1}(M)$ be the exterior differential operator and let $\Del=dd^*+d^*d$ be the Laplacian. We establish a sufficient ... More

Index theorem for equivariant Dirac operators on non-compact manifoldsNov 27 2000Sep 17 2001Let $D$ be a (generalized) Dirac operator on a non-compact complete Riemannian manifold $M$ acted on by a compact Lie group $G$. Let $v:M --> Lie(G)$ be an equivariant map, such that the corresponding vector field on $M$ does not vanish outside of a compact ... More

Approximations of Schatten Norms via Taylor ExpansionsAug 07 2018In this paper we consider symmetric, positive semidefinite (SPSD) matrix $A$ and present two algorithms for computing the $p$-Schatten norm $\|A\|_p$. The first algorithm works for any SPSD matrix $A$. The second algorithm works for non-singular SPSD ... More

Extremes of Levy processes with light tailsFeb 06 2009We give conditions under which the tail probability of the supremum over unit interval of a Levy process with light tail is equivalent to the tail of the value of the process at the right endpoint.