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On the formation of singularities of solutions of nonlinear differential systems in antistokes directionsFeb 22 2002Aug 13 2006We determine the position and the type of spontaneous singularities of solutions of generic analytic nonlinear differential systems in the complex plane, arising along antistokes directions towards irregular singular points of the system. Placing the ... More

Exponential asymptotics, transseries, and generalized Borel summation for analytic rank one systems of ODE'sAug 16 2006For analytic nonlinear systems of ordinary differential equations, under some non-degeneracy and integrability conditions we prove that the formal exponential series solutions (trans-series) at an irregular singularity of rank one are Borel summable (in ... More

Topological construction of transseries and introduction to generalized Borel summabilityAug 13 2006Transseries in the sense of \'Ecalle are constructed using a topological approach. A general contractive mapping principle is formulated and proved, showing the closure of transseries under a wide class of operations. In the second part we give an overview ... More

On Borel summation and Stokes phenomena of nonlinear differential systemsAug 16 2006In this paper we study analytic (linear or) nonlinear systems of ordinary differential equations, at an irregular singularity of rank one, under nonresonance conditions. It is shown that the formal asymptotic exponential series solutions (transseries ... More

Singularity barriers and Borel plane analytic properties of 1+ difference equationsAug 12 2006The paper addresses generalized Borel summability of ``$1^+$'' difference equations in ``critical time''. We show that the Borel transform $Y$ of a prototypical such equation is analytic and exponentially bounded for $\Re(p)<1$ but there is no analytic ... More

Correlation between pole location and asymptotic behavior for Painlevé I solutionsSep 21 1997We extend the technique of asymptotic series matching to exponential asymptotics expansions (transseries) and show that the extension provides a method of finding singularities of solutions of nonlinear differential equations, using asymptotic information. ... More

Rigorous WKB for finite order linear recurrence relations with smooth coefficientsAug 16 2006We study the $\epsilon \to 0$ behavior of recurrence relations of the type $\sum_{j=0}^l a_j(k\epsilon,\epsilon)y_{k+j}=0,$ $k\in \zdd$ ($l$ fixed). The $a_j$ are $C^{\infty}$ functions in each variable on $I\times [0,\e_0]$ for a bounded interval $I$ ... More

Failure of analytic hypoellipticity in a class of PDOsDec 12 2002For the hypoelliptic differential operators $P={\partial^2_ x}+(x^k\partial_ y -x^l{\partial_t})^2$ introduced by T. Hoshiro, generalizing a class of M. Christ, in the cases of $k$ and $l$ left open in the analysis, the operators $P$ also fail to be {\em{analytic}} ... More

A new type of factorial series expansions and applicationsAug 02 2016Aug 13 2016We construct a new type of convergent asymptotic representations, dyadic factorial expansions. Their convergence is geometric and the region of convergence can include Stokes rays, and often extends down to 0^+. For special functions such as Bessel, Airy, ... More

Singular normal form for the Painlevé equation P1Oct 27 1997We show that there exists a rational change of coordinates of Painlev\'e's P1 equation $y''=6y^2+x$ and of the elliptic equation $y''=6y^2$ after which these two equations become analytically equivalent in a region in the complex phase space where $y$ ... More

Nonlinear Stokes phenomena in first or second order differential equationsAug 12 2006We study singularity formation in nonlinear differential equations of order $m\leqslant 2$, $y^{(m)}=A(x^{-1},y)$. We assume $A$ is analytic at $(0,0)$ and $\partial_y A(0,0)=\lambda\ne 0$ (say, $\lambda=(-1)^m$). If $m=1$ we assume $A(0,\cdot)$ is meromorphic ... More

Machine Learning at Microsoft with ML .NETMay 14 2019May 15 2019Machine Learning is transitioning from an art and science into a technology available to every developer. In the near future, every application on every platform will incorporate trained models to encode data-based decisions that would be impossible for ... More

Asymptotic properties of a family of solutions of the Painleve equation PVIFeb 22 2002Mar 05 2002In this paper we study the asymptotic behavior for large argument of a family of solutions of the Painlev\'e equation P$_{\rm VI} arising in the context of Random Matrix Theory [1]. We show this family of solutions are uniquely determined by their asymptotic ... More

Boundary blow-up solutions in the unit ball : asymptotics, uniqueness and symmetry (v3)Mar 18 2010We calculate the full asymptotic expansion of boundary blow-up solutions, for any nonlinearity f. Our approach enables us to state sharp qualitative results regarding uniqueness and ra-dial symmetry of solutions, as well as a characterization of nonlinearities ... More

Nonlinear perturbations of Fuchsian systems: corrections and linearization, normal formsJun 15 2007Jul 01 2008Nonlinear perturbation of Fuchsian systems are studied in a region including two singularities. It is proved that such systems are generally not analytically equivalent to their linear part (they are not linearizable) and the obstructions are found constructively, ... More

Farthest points on flat surfacesJul 10 2018Sep 18 2018We consider the distance function from an arbitrary point $p$ on a flat surface, and determine the set $F_{p}$ of all \emph{farthest points} (i.e., points at maximal distance) from $p$.

The connected components of the space of Alexandrov surfacesOct 31 2013Denote by $\mathcal{A}(\kappa)$ the set of all compact Alexandrov surfaces with curvature bounded below by $\kappa$ without boundary, endowed with the topology induced by the Gromov-Hausdorff metric. We determine the connected components of $\mathcal{A}(\kappa)$ ... More

Resurgence of the fractional polylogarithmsJan 25 2007Jul 16 2009The fractional polylogarithms, depending on a complex parameter $\a$, are defined by a series which is analytic inside the unit disk. After an elementary conversion of the series into an integral presentation, we show that the fractional polylogarithms ... More

Oscillatory critical amplitudes in hierarchical models and the tail of the Harris random variableJun 07 2012Oscillatory critical amplitudes have been repeatedly observed in hierarchical models and, in the cases that have been taken into consideration, these oscillations are so small to be hardly detectable. Hierarchical models are tightly related to iteration ... More

On the geometry of Julia setsOct 28 2009We show that the Julia set of quadratic maps with parameters in hyperbolic components of the Mandelbrot set is given by a transseries formula, rapidly convergent at any repelling periodic point. Up to conformal transformations, we obtain $J$ from a smoother ... More

Boundary blow-up solutions in the unit ball : asymptotics, uniqueness and symmetryJan 27 2009Mar 19 2009We calculate the full asymptotic expansion of boundary blow-up so- lutions, for any nonlinearity f . Our approach enables us to state sharp qualitative results regarding uniqueness and ra- dial symmetry of solutions, as well as a characterization of nonlinearities ... More

Nonlinear evolution PDEs in R^+ \times C^d: existence and uniqueness of solutions, asymptotic and Borel summabilityAug 11 2006We consider a system of $n$-th order nonlinear quasilinear partial differential equations of the form $${\bf u}_t + \mathcal{P}(\partial_{\bf x}^{\bf j}){\bf u}+{\bf g} \left( {\bf x}, t, \{\partial_{\bf x}^{{\bf j}} {\bf u}\}) =0; {\bf {u}}({\bf x}, ... More

Analyzability in the context of PDEs and applicationsAug 13 2006We discuss the notions of resurgence, formalizability, and formation of singularities in the context of partial differential equations. The results show that Ecalle's how analyzability theory extends naturally to PDEs.

The first return map for planar vector fields with nilpotent linear part with a center or a focusMay 20 2009The return map for planar vector fields with nilpotent linear part (having a center or a focus and under an assumption generically satisfied) is found as a convergent power series whose terms can be calculated iteratively. The first nontrivial coefficient ... More

Farthest points on most Alexandrov surfacesDec 03 2014Oct 24 2017We study global maxima of distance functions on most Alexandrov surfaces with curvature bounded below, where "most" is used in the sense of Baire categories.

Behavior of lacunary series at the natural boundaryOct 16 2008We develop a local theory of lacunary Dirichlet series of the form $\sum\limits_{k=1}^{\infty}c_k\exp(-zg(k)), \Re(z)>0$ as $z$ approaches the boundary $i\RR$, under the assumption $g'\to\infty$ and further assumptions on $c_k$. These series occur in ... More

Tronquée solutions of the Painlevé equation \P1Oct 20 2013Apr 04 2015We analyze the one parameter family of tronqu\'ee solutions of the Painlev\'e equation \P1 in the pole-free sectors together with the region of the first array of poles. We find a convergent expansion for these solutions, containing one free parameter ... More

Rigorous bounds of Stokes constants for some nonlinear ODEs at rank one irregular singularitiesAug 13 2006A rigorous way to obtain sharp bounds for Stokes constants is introduced and illustrated on a concrete problem arising in applications.

A direct method to find Stokes multipliers in closed form for P1 and more general integrable systemsMay 03 2012Oct 19 2015We introduce a new rigorous method, based on Borel summability and asymptotic constants of motion generalizing \cite{invent} and \cite{ode1}, to analyze singular behavior of nonlinear ODEs in a neighborhood of infinity and provide global information about ... More

Resurgence of the Euler-MacLaurin summation formulaMar 21 2007Aug 27 2007The Euler-MacLaurin summation formula relates a sum of a function to a corresponding integral, with a remainder term. The remainder term has an asymptotic expansion, and for a typical analytic function, it is a divergent (Gevrey-1) series. Under some ... More

Sets of tetrahedra, defined by maxima of distance functionsJul 14 2012We study tetrahedra and the space of tetrahedra from the viewpoint of local and global maxima for intrinsic distance functions.

Analytic linearization of nonlinear perturbations of Fuchsian systemsJun 15 2007Jul 01 2008Nonlinear perturbation of Fuchsian systems are studied in regions including two singularities. Such systems are not necessarily analytically equivalent to their linear part (they are not linearizable). Nevertheless, it is shown that in the case when the ... More

The return map for a planar vector field with nilpotent linear part: a direct and explicit derivationMay 18 2009Using a direct approach the return map near a focus of a planar vector field with nilpotent linear part is found as a convergent power series which is a perturbation of the identity and whose terms can be calculated iteratively. The first nontrivial coefficient ... More

Analytical approximation of Blasius' similarity solution with rigorous error boundsMar 06 2013We use a recently developed method \cite{Costinetal}, \cite{Dubrovin} to find accurate analytic approximations with rigorous error bounds for the classic similarity solution of Blasius of the boundary layer equation in fluid mechanics, the two point boundary ... More

Resonance Theory for Schroedinger OperatorsDec 08 2000Feb 22 2002Resonances which result from perturbation of embedded eigenvalues are studied by time dependent methods. A general theory is developed, with new and weaker conditions, allowing for perturbations of threshold eigenvalues and relaxed Fermi Golden rule. ... More

Matrix valued polynomials generated by the scalar-type Rodrigues' formulasJun 22 2008The properties of matrix valued polynomials generated by the scalar-type Rodrigues' formulas are analyzed. A general representation of these polynomials is found in terms of products of simple differential operators. The recurrence relations, leading ... More

Farthest points on most Alexandrov surfacesDec 03 2014We study global maxima of distance functions on most Alexandrov surfaces with curvature bounded below, where "most" is used in the sense of Baire categories.

Decay estimates for One-dimensional wave equations with inverse power potentialsAug 16 2012Oct 23 2014We study the one-dimensional wave equation with an inverse power potential that equals $const.x^{-m}$ for large $|x|$ where $m$ is any positive integer greater than or equal to 3. We show that the solution decays pointwise like $t^{-m}$ for large $t$, ... More

Gamow vectors and Borel summabilityFeb 04 2009We analyze the detailed time dependence of the wave function $\psi(x,t)$ for one dimensional Hamiltonians $H=-\partial_x^2+V(x)$ where $V$ (for example modeling barriers or wells) and $\psi(x,0)$ are {\em compactly supported}. We show that the dispersive ... More

Quantum Alternation: Prospects and ProblemsNov 05 2015We propose a notion of quantum control in a quantum programming language which permits the superposition of finitely many quantum operations without performing a measurement. This notion takes the form of a conditional construct similar to the IF statement ... More

Borel summability of Navier-Stokes equation in $\mathbb{R}^3$ and small time existenceDec 02 2006Dec 20 2006We consider the Navier-Stokes initial value problem, $$v_t - \nabla v = -\mathcal{P} [ v \cdot \nabla v \right ] + f, v(x, 0) = v_0 (x), x \in \mathbb{R}^3 $$ where $\mathcal{P}$ is the Hodge-Projection to divergence free vector fields in the assumption ... More

Complex Singularity Analysis for a nonlinear PDEAug 12 2006We introduce a method of rigorous analysis of the location and type of complex singularities for nonlinear higher order PDEs as a function of the initial data. The method is applied to determine rigorously the asymptotic structure of singularities of ... More

Orthogonality of Jacobi and Laguerre polynomials for general parameters via the Hadamard finite partJan 19 2009Orthogonality of the Jacobi and of Laguerre polynomials, P_n^(a,b) and L_n^(a), is established for a,b complex (a,b not negative integers and a+b different from -2,-3,...) using the Hadamard finite part of the integral which gives their orthogonality ... More

Truncated Solutions of Painlevé Equation ${\rm P}_{\rm V}$Apr 30 2018Oct 31 2018We obtain convergent representations (as Borel summed transseries) for the five one-parameter families of truncated solutions of the fifth Painlev\'e equation with nonzero parameters, valid in half planes, for large independent variable. We also find ... More

Differential systems with Fuchsian linear part: correction and linearization, normal forms and multiple orthogonal polynomialsAug 26 2008Differential systems with a Fuchsian linear part are studied in regions including all the singularities in the complex plane of these equations. Such systems are not necessarily analytically equivalent to their linear part (they are not linearizable) ... More

Existence and uniqueness for a class of nonlinear higher-order partial differential equations in the complex planeMar 05 2002We prove existence and uniqueness results for nonlinear third order partial differential equations of the form $$ f_t - f_{yyy} = \sum_{j=0}^3 b_j (y, t; f) ~f^{(j)} + r(y, t) $$ where superscript $j$ denotes the $j$-th partial derivative with respect ... More

Simple closed geodesics on most Alexandrov surfacesNov 19 2013We study the existence of simple closed geodesics on most (in the sense of Baire category) Alexandrov surfaces with curvature bounded below, compact and without boundary. We show that it depends on both the curvature bound and the topology of the surfaces. ... More

Global reconstruction of analytic functions from local expansionsDec 05 2006Jun 22 2012A new summation method is introduced to convert a relatively wide family of infinite sums and local expansions into integrals. The integral representations yield global information such as analytic continuability, position of singularities, asymptotics ... More

Resurgence of the Kontsevich-Zagier power seriesSep 21 2006Aug 09 2010The paper is concerned with the Kontsevich-Zagier formal power series $$ f(q)=\sum_{n=0}^\infty (1-q)... (1-q^n) $$ and its analytic properties. To begin with, we give an explicit formula for the Borel transform of the associated formal power series $F(x)=e^{-1/(24x)}f(e^{-1/x})$ ... More

A class of matrix-valued polynomials generalizing Jacobi PolynomialsApr 23 2008A hierarchy of matrix-valued polynomials which generalize the Jacobi polynomials is found. Defined by a Rodrigues formula, they are also products of a sequence of differential operators. Each class of polynomials is complete, satisfies a two-step recurrence ... More

From Taylor series of analytic functions to their global analysisJul 25 2014We analyze the conditions on the Taylor coefficients of an analytic function to admit global analytic continuation, complementing a recent paper of Breuer and Simon on general conditions for natural boundaries to form. A new summation method is introduced ... More

Solution of the time dependent Schrödinger equation leading to Fowler-Nordheim field emissionAug 02 2018Jan 22 2019We solve the time-dependent Schr\"odinger equation describing the emission of electrons from a metal surface by an external electric field $E$, turned on at $t=0$. Starting with a wave function $\psi(x,0)$, representing a generalized eigenfunction when ... More

Time asymptotics of the Schroedinger wave function in time-periodic potentialsAug 13 2006We study the transition to the continuum of an initially bound quantum particle in $\RR^d$, $d=1,2,3$, subjected, for $t\ge 0$, to a time periodic forcing of arbitrary magnitude. The analysis is carried out for compactly supported potentials, satisfying ... More

Evolution of a model quantum system under time periodic forcing: conditions for complete ionizationNov 01 2000We analyze the time evolution of a one-dimensional quantum system with an attractive delta function potential whose strength is subjected to a time periodic (zero mean) parametric variation $\eta(t)$. We show that for generic $\eta(t)$, which includes ... More

On the Construction of Particle Distributions with Specified Single and Pair DensitiesMay 21 2004We discuss necessary conditions for the existence of probability distribution on particle configurations in $d$-dimensions i.e. a point process, compatible with a specified density $\rho$ and radial distribution function $g({\bf r})$. In $d=1$ we give ... More

The Operator Spectrum of the Six-dimensional (1,0) TheoryJan 13 1999We study the large N operator spectrum of the (1,0) superconformal chiral six-dimensional theory with E_8 global symmetry. This spectrum is dual to the Kaluza-Klein spectrum of supergravity on AdS_7 X S^4/Z_2 with a ten-dimensional E_8 theory at its singular ... More

Every graph is a cut locusMar 09 2011Sep 14 2013We prove that every connected graph can be realized as the cut locus of some point on some Riemannian surface $S$ which, in some cases, has constant curvature. We study the stability of such realizations, and their generic behavior.

Cut locus structures on graphsMar 09 2011Motivated by a fundamental geometrical object, the cut locus, we introduce and study a new combinatorial structure on graphs.

Gaussian Fluctuation in Random MatricesDec 06 1994Let $N(L)$ be the number of eigenvalues, in an interval of length $L$, of a matrix chosen at random from the Gaussian Orthogonal, Unitary or Symplectic ensembles of ${\cal N}$ by ${\cal N}$ matrices, in the limit ${\cal N}\rightarrow\infty$. We prove ... More

Convergence from DivergenceMay 26 2017We show how to convert divergent series, which typically occur in many applications in physics, into rapidly convergent inverse factorial series. This can be interpreted physically as a novel resummation of perturbative series. Being convergent, these ... More

Sharp Hardy-Leray inequality for axisymmetric divergence-free fieldsMar 05 2007Apr 04 2007We show that the sharp constant in the classical $n$-dimensional Hardy-Leray inequality can be improved for axisymmetric divergence-free fields, and find its optimal value. The same result is obtained for $n=2$ without the axisymmetry assumption.

Ionization by an Oscillating Field: Resonances and PhotonsOct 15 2017We describe new exact results for a model of ionization of a bound state, induced by an oscillating potential. In particular we have obtained exact expressions, in the form of readily computable rapidly convergent sums, for the energy distribution of ... More

Nonperturbative time dependent solution of a simple ionization modelJun 21 2017Jul 23 2017We present a non-perturbative solution of the Schr\"odinger equation $i\psi_t(t,x)=-\psi_{xx}(t,x)-2(1 +\alpha \sin\omega t) \delta(x)\psi(t,x)$, written in units in which $\hbar=2m=1$, describing the ionization of a model atom by a parametric oscillating ... More

On optimal truncation of divergent series solutions of nonlinear differential systems; Berry smoothingAug 16 2006We prove that for divergent series solutions of nonlinear (or linear) differential systems near a generic irregular singularity, the common prescription of summation to the least term is, if properly interpreted, meaningful and correct, and we extend ... More

Analytic methods for obstruction to integrability in discrete dynamical systemsAug 13 2006A unique analytic continuation result is proved for solutions of a relatively general class of difference equations, using techniques of generalized Borel summability. This continuation allows for Painlev\'e property methods to be extended to difference ... More

Optimal uniform estimates and rigorous asymptotics beyond all orders for a class of ODE'sAug 16 2006For first order differential equations of the form $y'=\sum_{p=0}^P F_p(x)y^p$ and second order homogeneous linear differential equations $y''+a(x)y'+b(x)y=0$ with locally integrable coefficients having asymptotic (possibly divergent) power series when ... More

Movable singularities of solutions of difference equations in relation to solvability and a study of a superstable fixed pointAug 13 2006A unique analytic continuation result is proven for solutions of a relatively general class of difference equations by using techniques of generalized Borel summability. We overview applications exponential asymptotics and analyzable function theory to ... More

Conical Existence of Closed Curves on Convex PolyhedraFeb 04 2011Feb 14 2011Let C be a simple, closed, directed curve on the surface of a convex polyhedron P. We identify several classes of curves C that "live on a cone," in the sense that C and a neighborhood to one side may be isometrically embedded on the surface of a cone ... More

Orientable cut locus structures on graphsMar 16 2011We showed in another paper [arXiv:1103.1759] that every connected graph can be realized as the cut locus of some point on some riemannian surface $S$. Here, criteria for the orientability of $S$ are given, and are applied to classify the distinct, orientable, ... More

On the number of cut locus structures on graphsMar 09 2011We proved in another paper that every connected graph can be realized as the cut locus of some point on some riemannian surface. Here we give upper bounds on the number of such realizations.

Jacobi series for general parameters and applicationsJun 08 2016Dec 19 2018Representation of analytic functions as convergent series in Jacobi polynomials $P_n^{(a,b)}$ is reformulated using a unified approach for almost all complex $a, b$. The coefficients of the series are given as usual integrals in the classical case (when ... More

Resurgent Extrapolation: Rebuilding a Function from Asymptotic Data. Painleve IApr 25 2019Extrapolation is a generic problem in physics and mathematics: how to use asymptotic data in one parametric regime to learn about the behavior of a function in another parametric regime. For example: extending weak coupling expansions to strong coupling, ... More

Nonperturbative analysis of a model quantum system under time periodic forcingAug 16 2006We analyze the time evolution of a one-dimensional quantum system with an attractive delta function potential whose strength is subjected to a time periodic (zero mean) parametric variation. We show that for generic forcing which includes the sum of any ... More

Jacobi series for general parameters and applicationsJun 08 2016Representation of analytic functions as convergent series in Jacobi polynomials P_n^(a,b) is reformulated using a unified approach for all complex a, b (except for negative integers). The coefficients of the series are given as usual integrals in the ... More

Foundational aspects of singular integralsJan 27 2014Aug 19 2014We investigate integration of classes of real-valued continuous functions on (0,1]. Of course difficulties arise if there is a non-$L^1$ element in the class, and the Hadamard finite part integral ({\em p.f.}) does not apply. Such singular integrals arise ... More

Lower bounds for testing complete positivity and quantum separabilityMay 04 2019In this work, we study the separability problem in quantum property testing, where one is given $n$ copies of an unknown mixed quantum state $\varrho$ on $\mathbb{C}^d \otimes \mathbb{C}^d$, and one wants to test whether $\varrho$ is separable or $\epsilon$-far ... More

Uniqueness of large solutionsFeb 10 2012Given a nondecreasing nonlinearity $f$, we prove uniqueness of large solutions in the following two cases: the domain is the ball or the domain has nonnegative mean curvature and the nonlinearity is asymptotically convex.

Mode stability of self-similar wave maps in higher dimensionsApr 01 2016Aug 24 2016We consider co-rotational wave maps from Minkowski space in $d+1$ dimensions to the $d$-sphere. Recently, Bizo\'n and Biernat found explicit self-similar solutions for each dimension $d\geq 4$. We give a rigorous proof for the mode stability of these ... More

Decay versus survival of a localized state subjected to harmonic forcing: exact resultsAug 13 2006We investigate the survival probability of a localized 1-d quantum particle subjected to a time dependent potential of the form $rU(x)\sin{\omega t}$ with $U(x)=2\delta (x-a)$ or $U(x)= 2\delta(x-a)-2\delta (x+a)$. The particle is initially in a bound ... More

Ionization of a Model Atom: Exact Results and Connection with ExperimentMay 18 1999We prove that a model atom having one bound state will be fully ionized by a time periodic potential of arbitrary strength $r$ and frequency $\omega$. The survival probability is for small $r$ given by $e^{-\Gamma t}$ for times of order $\Gamma^{-1} \sim ... More

DSP Based System for Real time Voice Synthesis Applications DevelopmentMar 03 2008This paper describes an experimental system designed for development of real time voice synthesis applications. The system is composed from a DSP coprocessor card, equipped with an TMS320C25 or TMS320C50 chip, voice acquisition module (ADDA2),host computer ... More

Exact Results for the Ionization of a Model Quantum SystemAug 16 2006We prove that a model atom having one bound state will be fully ionized by a time periodic potential of arbitrary strength r and frequency omega. Starting with the system in the bound state, the survival probability is for small r given by exp(-Gamma ... More

Global behavior of solutions of nonlinear ODEs in $\CC$: first order equationsApr 04 2010Aug 10 2011We show that the solutions of first order nonlinear ODEs can be controlled globally in the complex domain, using a finite set of constants of motion defined in regions of $\CC$. These constants of motion enable us to obtain quantitative behaviors of the ... More

Ionization in a 1-Dimensional Dipole ModelSep 25 2006Jun 04 2007We study the evolution of a one dimensional model atom with $\delta$-function binding potential, subjected to a dipole radiation field $E(t) x$ with $E(t)$ a $2\pi/\omega$-periodic real-valued function. Starting with $\psi(x,t=0)$ an initially localized ... More

Polyhedra with simple dense geodesicsApr 17 2017Feb 13 2018We determine (non-necessarily convex) polyhedra having simple dense geodesics.

With respect to whom are you critical?Mar 26 2019For any compact Riemannian surface $S$ and any point $y$ in $S$, $Q_y^{-1}$ denotes the set of all points in $S$, for which $y$ is a critical point. We proved \cite{BIVZ} together with Imre B\'ar\'any that card$Q_y^{-1} \geq 1$, and that equality for ... More

Integral formulation of 3-D Navier-Stokes and longer time existence of smooth solutionsAug 27 2008We consider the 3-D Navier-Stokes initial value problem, $$ v_t - \nu \Delta v = -\mathcal{P} [ v \cdot \nabla v ] + f , v(x, 0) = v_0 (x), x \in \mathbb{T}^3 (*) $$ where $\mathcal{P}$ is the Hodge projection. We assume that the Fourier transform norms ... More

Borel summation of adiabatic invariantsAug 13 2006Borel summation techniques are developed to obtain exact invariants from formal adiabatic invariants (given as divergent series in a small parameter) for a class of differential equations, under assumptions of analyticity of the coefficients; the method ... More

Envelopes of $α$-sectionsSep 07 2015Let $K$ be a planar convex body af area $|K|$, and take $0 \textless{} \alpha \textless{} 1$.An $\alpha$-section of $K$ is a line cutting $K$ into two parts, one of whichhas area $\alpha|K|$. This article presents a systematic study of the envelope of ... More

Moderate smoothness of most Alexandrov surfacesAug 18 2013May 17 2014We show that, in the sense of Baire category, most Alexandrov surfaces with curvature bounded below by $\kappa$ have no conical points. We use this result to prove that at most points of such surfaces, the lower and the upper Gaussian curvatures are equal ... More

Automated Dynamic Firmware Analysis at Scale: A Case Study on Embedded Web InterfacesNov 11 2015Embedded devices are becoming more widespread, interconnected, and web-enabled than ever. However, recent studies showed that these devices are far from being secure. Moreover, many embedded systems rely on web interfaces for user interaction or administration. ... More

On the spectral properties of L_{+-} in three dimensionsJul 01 2011This paper is part of the radial asymptotic stability analysis of the ground state soliton for either the cubic nonlinear Schrodinger or Klein-Gordon equations in three dimensions. We demonstrate by a rigorous method that the linearized scalar operators ... More

A Proof for the Mode Stability of a Self-similar Wave MapNov 11 2014Dec 18 2014We study the fundamental self-similar solution to the SU(2) sigma model, found by Shatah and Turok-Spergel. We give a rigorous proof for its mode stability. Based on earlier results by the second author, the present paper constitutes the last building ... More

On the Theorem of the Three PerpendicularsJul 05 2013We show that the theorem of the three perpendiculars holds in any n-dimensional space form.

D-Brane Actions with Local Kappa SymmetryOct 31 1996Nov 23 1996We formulate world-volume actions that describe the dynamics of Dirichlet p-branes in a flat 10d background. The fields in these theories consist of the 10d superspace coordinates and an abelian world-volume gauge field. The global symmetries are given ... More

Proof of the Dubrovin conjecture and analysis of the tritronquée solutions of $P_I$Sep 05 2012Oct 23 2014We show that the tritronqu\'ee solution of the Painlev\'e equation $\P1$, $ y"=6y^2+z$ which is analytic for large $z$ with $ \arg z \in (-\frac{3\pi}{5}, \pi)$ is pole-free in a region containing the full sector ${z \ne 0, \arg z \in [-\frac{3\pi}{5}, ... More

On the complete ionization of a periodically perturbed quantum systemFeb 02 2000We analyze the time evolution of a one-dimensional quantum system with zero range potential under time periodic parametric perturbation of arbitrary strength and frequency. We show that the projection of the wave function on the bound state vanishes, ... More

Integration on the Surreals: a Conjecture of Conway, Kruskal and NortonMay 11 2015Aug 24 2015In his monograph On Numbers and Games, J. H. Conway introduced a real-closed field No of surreal numbers containing the reals and the ordinals, as well as a vast array of less familiar numbers. A longstanding aim has been to develop analysis on No as ... More

The lifetime of shape oscillations of a bubble in an unbounded, inviscid and compressible fluid with surface tensionOct 01 2012General perturbations of a spherical gas bubble in a compressible and inviscid fluid with surface tension were proved in Shapiro and Weinstein (2011), in the linearized approximation, to decay exponentially, $\sim e^{-\Gamma t}, \Gamma>0$, as time advances. ... More

On the proof of universality for orthogonal and symplectic ensembles in random matrix theoryOct 25 2006We give a streamlined proof of a quantitative version of a result from [DG1] which is crucial for the proof of universality in the bulk [DG1] and also at the edge [DG2] for orthogonal and symplectic ensembles of random matrices. As a byproduct, this result ... More