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Unusual composition dependence of transformation temperatures in Ti-Ta-X shape memory alloysApr 12 2018Ti-Ta-X (X = Al, Sn, Zr) compounds are emerging candidates as high-temperature shape memory alloys (HTSMAs). The stability of the one-way shape memory effect (1WE), the exploitable pseudoelastic (PE) strain intervals as well as the transformation temperature ... More

Discovery of new stable and high-temperature Ti-Ta-X shape memory alloys from first principles calculationsMay 14 2019In conventional Ti-Ta shape memory alloys (SMAs), high (>100{\deg}C) transformation temperatures cannot be achieved without compromising the stability of the shape memory effect. A solution to this problem is the addition of other elements to form Ti-Ta-X ... More

On the segregation of Re at dislocations in the γ' phase of Ni-based single crystal superalloysSep 24 2018We report evidence of Re and Mo segregation (up to 2.6 at.% and 1 at.%) along with Cr and Co to the dislocations inside of {\gamma}' precipitates in a second generation Ni-based single crystal superalloy, after creep deformation at 750{\deg}C under an ... More

On the maximum rank of Toeplitz block matrices of blocks of a given patternMay 18 2013We show that the maximum rank of block lower triangular Toeplitz block matrices equals their term rank if the blocks fulfill a structural condition, i.e., only the locations but not the values of their nonzeros are fixed.

Curves, dynamical systems and weighted point countingSep 25 2012Suppose X is a (smooth projective irreducible algebraic) curve over a finite field k. Counting the number of points on X over all finite field extensions of k will not determine the curve uniquely. Actually, a famous theorem of Tate implies that two such ... More

Computing abstractions of nonlinear systemsOct 12 2009Feb 15 2011Sufficiently accurate finite state models, also called symbolic models or discrete abstractions, allow one to apply fully automated methods, originally developed for purely discrete systems, to formally reason about continuous and hybrid systems, and ... More

Die Reissner-Nordström-Metrik in der Pseudokomplexen Allgemeinen RelativitätstheorieJun 14 2011This master thesis discusses the Reissner-Nordstr\"om metric and the dirac equation in curved spaces in the pseudo-complex General Relativity (pc-GR) and reviews the original ansatz of pc-GR. It is written in German.

The 2-primary class group of certain hyperelliptic curvesAug 31 1999Sep 01 1999Let G be the separable Galois group of a finite field F of characteristic p, and X/F an imaginary hyperelliptic curve such that G acts transitively on its set W(X) of Weierstrass points. The existence of a G-invariant 2-torsion point on the Jacobian J(X) ... More

Convexity of reachable sets of nonlinear ordinary differential equationsNov 26 2012We present a necessary and sufficient condition for the reachable set, i.e., the set of states reachable from a ball of initial states at some time, of an ordinary differential equation to be convex. In particular, convexity is guaranteed if the ball ... More

A geometric formulation of fiducial probabilityAug 31 2012The geometric formulation of fiducial probability employed in this paper is an improvement over the usual pivotal quantity formulation. For a single parameter and single observation, the new formulation is based on the geometric properties of an ordinary ... More

Mass extinctions and supernova explosionsSep 09 2016A nearby supernova (SN) explosion could have negatively influenced life on Earth, maybe even been responsible for mass extinctions. Mass extinction poses a significant extinction of numerous species on Earth, as recorded in the paleontologic, paleoclimatic, ... More

Random hypersurfaces and embedding curves in surfaces over finite fieldsOct 15 2015Jun 07 2016We use Poonen's closed point sieve to prove two independent results. First, we show that the obvious obstruction to embedding a curve in a smooth surface is the only obstruction over a perfect field, by proving the finite field analogue of a Bertini-type ... More

Infrared transmission spectroscopy of charge carriers in self-assembled InAs quantum dots under surface electric fieldsSep 18 2014We present a study on the intersublevel spacings of electrons and holes in a single layer of InAs self-assembled quantum dots (SAQDs) using Fourier transform infrared (FTIR) transmission spectroscopy without the application of an external magnetic field. ... More

UNIX Resource Managers: Capacity Planning and Resource IssuesJun 08 2000Jun 13 2000The latest implementations of commercial UNIX to offer mainframe style capacity management on enterprise servers include: AIX Workload Manager (WLM), HP-UX Process Resource Manager (PRM), Solaris Resource Manager (SRM), as well as SGI and Compaq. The ... More

Solaris System Resource Manager: All I Ever Wanted Was My Unfair Advantage (And Why You Can't Have It!)Jun 08 2000Traditional UNIX time-share schedulers attempt to be fair to all users by employing a round-robin style algorithm for allocating CPU time. Unfortunately, a loophole exists whereby the scheduler can be biased in favor of a greedy user running many short ... More

Determining both sound speed and internal source in thermo- and photo-acoustic tomographyFeb 04 2015This paper concerns thermoacoustic tomography and photoacoustic tomography, two couple-physics imaging modalities that attempt to combine the high resolution of ultrasound and the high contrast capabilities of electromagnetic waves. We give sufficient ... More

Generalized backscattering and the Lax-Phillips transformDec 27 2007Jan 03 2008Using the free-space translation representation (modified Radon transform) of Lax and Phillips in odd dimensions, it is shown that the generalized backscattering transform (so outgoing angle $\omega =S\theta$ in terms of the incoming angle with $S$ orthogonal ... More

Matrix divisibility sequencesJul 12 2011Sep 04 2011We show that many existing divisibility sequences can be seen as sequences of determinants of matrix divisibility sequences, which arise naturally as Jacobian matrices associated to groups of maps on affine spaces.

Spontaneous waves in muscle fibresJan 28 2009Mechanical oscillations are important for many cellular processes, e.g. the beating of cilia and flagella or the sensation of sound by hair cells. These dynamic states originate from spontaneous oscillations of molecular motors. A particularly clear example ... More

A simple self-organized swimmer driven by molecular motorsJan 21 2009We investigate a self-organized swimmer at low Reynolds numbers. The microscopic swimmer is composed of three spheres that are connected by two identical active linker arms. Each linker arm contains molecular motors and elastic elements and can oscillate ... More

Irrational Numbers of Constant Type --- A New CharacterizationJun 04 1997Jul 28 1997We obtain a new characterization for irrational numbers of constant type -- defined as irrationals with bounded partial quotients in their continued fraction expansion. The result is essential in the formulation of stability criteria for orbits of quantum ... More

Existence, Uniqueness and Regularity of the Projection onto Differentiable ManifoldsNov 26 2018Nov 27 2018We study the maximal open domain $\cE(M)$ on which the projection map onto a subset $M\subseteq \R^d$ can be defined. We show that if $M$ is a $C^2$ submanifold of $\R^d$, then $\cE(M)$ can be described by a continuous function, and the projection and ... More

Recovery of a source term or a speed with one measurement and applicationsMar 06 2011We study the problem of recovery the source $a(t,x)F(x)$ in the wave equation in anisotropic medium with $a$ known so that $a(0,x)\not=0$ with a single measurement. We use Carleman estimates combined with geometric arguments and give sharp conditions ... More

Is a curved flight path in SAR better than a straight one?May 04 2012In the plane, we study the transform $R_\gamma f$ of integrating a unknown function $f$ over circles centered at a given curve $\gamma$. This is a simplified model of SAR, when the radar is not directed but has other applications, like thermoacoustic ... More

Integral points of bounded degree on the projective line and in dynamical orbitsJul 27 2016Let $D$ be a non-empty effective divisor on $\mathbb{P}^1$. We show that when ordered by height, any set of $(D,S)$-integral points on $\mathbb{P}^1$ of bounded degree has relative density zero. We then apply this to arithmetic dynamics: let $\varphi(z)\in ... More

The inverse problem for the local geodesic ray transformOct 07 2012Under a convexity assumption on the boundary we solve a local inverse problem, namely we show that the geodesic X-ray transform can be inverted locally in a stable manner; one even has a reconstruction formula. We also show that under an assumption on ... More

Topology of Diophantine Sets: Remarks on Mazur's ConjecturesJun 20 2000We show that Mazur's conjecture on the real topology of rational points on varieties implies that there is no diophantine model of the rational integers in the rational numbers. We also prove that there is a diophantine model of the polynomial ring over ... More

The perfect power problem for elliptic curves over function fieldsNov 28 2014We generalise the Siegel-Voloch theorem about S-integral points on elliptic curves as follows: let K/F denote a global function field over a finite field F of characteristic p>3, let S denote a finite set of places of K and let E/K denote a non-isotrivial ... More

Quantum Statistical Mechanics, L-series and Anabelian GeometrySep 03 2010Apr 20 2011It is known that two number fields with the same Dedekind zeta function are not necessarily isomorphic. The zeta function of a number field can be interpreted as the partition function of an associated quantum statistical mechanical system, which is a ... More

Reconstruction of coefficients in scalar second-order elliptic equations from knowledge of their solutionsNov 21 2011This paper concerns the reconstruction of possibly complex-valued coefficients in a second-order scalar elliptic equation posed on a bounded domain from knowledge of several solutions of that equation. We show that for a sufficiently large number of solutions ... More

Zur Entartung gezuegelter Gruppenoperationen auf Kurven (Degeneration of restrained group actions on curves)Aug 30 2003An action of a finite group on a smooth projective curve over an algebraically closed field of positive characteristic is called restrained, if all second ramification groups are trivial (e.g., every group action on an ordinary curve is restrained). When ... More

Thermoacoustic tomography arising in brain imagingSep 09 2010We study the mathematical model of thermoacoustic and photoacoustic tomography when the sound speed has a jump across a smooth surface. This models the change of the sound speed in the skull when trying to image the human brain. We derive an explicit ... More

On the microlocal analysis of the geodesic X-ray transform with conjugate pointsFeb 23 2015We study the microlocal properties of the geodesic X-ray transform $\mathcal{X}$ on a manifold with boundary allowing the presence of conjugate points. Assuming that there are no self-intersecting geodesics and all conjugate pairs are nonsingular we show ... More

Nuclear Deep-Inelastic Lepton Scattering and Coherence PhenomenaAug 03 1999This review outlines our present experimental knowledge and theoretical understanding of deep-inelastic scattering on nuclear targets. The emphasis is primarily on nuclear coherence phenomena, such as shadowing, where the key physics issue is the exploration ... More

The attenuated ray transform on simple surfacesApr 14 2010We show that the attenuated geodesic ray transform on two dimensional simple surfaces is injective. Moreover we give a stability estimate and develop a reconstruction procedure.

A GPU accelerated Barnes-Hut Tree Code for FLASH4Sep 24 2015Nov 26 2015We present a GPU accelerated CUDA-C implementation of the Barnes Hut (BH) tree code for calculating the gravitational potential on octree adaptive meshes. The tree code algorithm is implemented within the FLASH4 adaptive mesh refinement (AMR) code framework ... More

A Strong Order 1/2 Method for Multidimensional SDEs with Discontinuous DriftDec 09 2015In this paper we consider multidimensional stochastic differential equations (SDEs) with discontinuous drift and possibly degenerate diffusion coefficient. We prove an existence and uniqueness result for this class of SDEs and we present a numerical method ... More

Propagation of Polarization in Elastodynamics with Residual Stress and Travel TimesJan 17 2002We show that knowing the Dirichlet-to-Neumann map (DN) associated to the equations of elastodynamics with residual stress we can determine the lens relations of presssure and shear waves. We derive several consequences of this for the inverse problem ... More

Stable determination of generic simple metrics from the hyperbolic Dirichlet-to-Neumann mapOct 26 2004We prove H\"older type stability estimates near generic simple Riemannian metrics for the inverse problem of recovering such metrics from the Dirichlet-to-Neumann map associated to the wave equation for the Laplace-Beltrami operator.

Integral geometry of tensor fields on a class of non-simple Riemannian manifoldsJan 09 2006Nov 16 2006We study the geodesic X-ray transform $I_\Gamma$ of tensor fields on a compact Riemannian manifold $M$ with non-necessarily convex boundary and with possible conjugate points. We assume that $I_\Gamma$ is known for geodesics belonging to an open set $\Gamma$ ... More

Boundary rigidity and stability for generic simple metricsAug 05 2004We study the boundary rigidity problem for compact Riemannian manifolds with boundary $(M,g)$: is the Riemannian metric $g$ uniquely determined, up to an action of diffeomorphism fixing the boundary, by the distance function $\rho_g(x,y)$ known for all ... More

Local uniqueness for the Dirichlet-to-Neumann map via the two-plane transformJan 18 2000Nov 09 2000We consider the Dirichlet-to-Neumann map associated to the Schr\"odinger equation with a potential in a bounded Lipschitz domain in three or more dimensions. We show that the integral of the potential over a two-plane is determined by the Cauchy data ... More

Linearizing non-linear inverse problems and an application to inverse backscatteringSep 01 2008We propose an abstract approach to prove local uniqueness and conditional H\"older stability to non-linear inverse problems by linearization. The main condition is that, in addition to the injectivity of the linearization $A$, we need a stability estimate ... More

The point source inverse back-scattering problemMar 07 2014We consider the inverse problem of recovering a potential by measuring the response at a point to a source located at the same point and then varying the point on the surface of a sphere. This is a similar to the inverse back-scattering problem. We show ... More

Uniqueness for the inverse backscattering problem for angularly controlled potentialsJul 02 2013Feb 12 2014We consider the problem of recovering a smooth, compactly supported potential on R^3 from its backscattering data. We show that if two such potentials have the same backscattering data and the difference of the two potentials has controlled angular derivatives ... More

Journey to the Center of the EarthApr 03 2016We survey some results on travel time tomography. The question is whether we can determine the anisotropic index of refraction of a medium by measuring the travel times of waves going through the medium. This can be recast as geometry problems, the boundary ... More

A remark on partial data inverse problems for semilinear elliptic equationsMay 04 2019We show that the knowledge of the Dirichlet-to-Neumann map on an arbitrary open portion of the boundary of a domain in $\mathbb{R}^n$, $n\ge 2$, for a class of semilinear elliptic equations, determines the nonlinearity uniquely.

Absolute continuity of the periodic Schrödinger operator in transversal geometryDec 10 2013Aug 15 2015We show that the spectrum of a Schr\"odinger operator on $\mathbb{R}^n$, $n\ge 3$, with a periodic smooth Riemannian metric, whose conformal multiple has a product structure with one Euclidean direction, and with a periodic electric potential in $L^{n/2}_{\text{loc}}(\mathbb{R}^n)$, ... More

Inverse problems for advection diffusion equations in admissible geometriesApr 19 2017We study inverse boundary problems for the advection diffusion equation on an admissible manifold, i.e. a compact Riemannian manifold with boundary of dimension $\ge 3$, which is conformally embedded in a product of the Euclidean real line and a simple ... More

Which weakly ramified group actions admit a universal formal deformation?Aug 24 2007Apr 02 2008Consider a formal (mixed-characteristic) deformation functor D of a representation of a finite group G as automorphisms of a power series ring k[[t]] over a perfect field k of positive characteristic. Assume that the action of G is weakly ramified, i.e., ... More

Mumford curves with maximal automorphism groupJul 26 2002The maximal number of automorphisms of a Mumford curve over a non-archimedean valued field of positive characteristic is known. In this note, the unique family of curves that attains this bound in genus not equal to 5,6,7 or 8 is explicitly determined, ... More

Interaction effects and transport properties of Pt capped Co nanoparticlesSep 27 2012We studied the magnetic and transport properties of Co nanoparticles (NPs) being capped with varying amounts of Pt. Beside field and temperature dependent magnetization measurements we performed delta-M measurements to study the magnetic interactions ... More

Spontaneous sarcomere dynamicsFeb 03 2012Sarcomeres are the basic force generating units of striated muscles and consist of an interdigitating arrangement of actin and myosin filaments. While muscle contraction is usually triggered by neural signals, which eventually set myosin motors into motion, ... More

$L^p$ bounds on eigenfunctions for operators with double characteristicsApr 05 2015We obtain sharp $L^p$ bounds on the ground states for a class of semiclassical pseudodifferential operators with double characteristics and complex valued symbols, under the assumption that the quadratic approximations along the double characteristics ... More

Fast orthogonal transforms for multi-level quasi-Monte Carlo integrationAug 10 2015We combine a generic method for finding fast orthogonal transforms for a given quasi-Monte Carlo integration problem with the multilevel Monte Carlo method. It is shown by example that this combined method can vastly improve the efficiency of quasi-Monte ... More

Regularized Transformation-Optics Cloaking in Acoustic and Electromagnetic ScatteringSep 02 2014We consider transformation-optics based cloaking in acoustic and electromagnetic scattering. The blueprints for an ideal cloak use singular acoustic and electromagnetic materials, posing server difficulties to both theoretical analysis and practical fabrication. ... More

Convergence of the Euler-Maruyama method for multidimensional SDEs with discontinuous drift and degenerate diffusion coefficientOct 22 2016We prove strong convergence of order 1/5 of the Euler-Maruyama method for multidimensional stochastic differential equations (SDEs) with discontinuous drift and degenerate diffusion coefficient. The proof is based on estimating the difference between ... More

Relational Mathematics ContinuedMar 27 2014This is in some sense an addendum to the book Relational Mathematics by the first-named author. It originated from work on diverse other topics during which a lot of purely relational results with broad applicability have been produced. These include ... More

The geodesic X-ray transform with fold causticsApr 07 2010We give a detailed microlocal study of X-ray transforms over geodesics-like families of curves with conjugate points of fold type. We show that the normal operator is the sum of a pseudodifferential operator and a Fourier integral operator. We compute ... More

Zeta functions that hear the shape of a Riemann surfaceAug 03 2007To a compact hyperbolic Riemann surface, we associate a finitely summable spectral triple whose underlying topological space is the limit set of a corresponding Schottky group, and whose ``Riemannian'' aspect (Hilbert space and Dirac operator) encode ... More

Torsion of Drinfeld modules and equicharacteristic unimodular Galois coversSep 03 2002We prove that the groups PSL(r,q^d) can be realized F_q(T)-regularly as Galois groups over the purely transcendental field F_q(T)(t_1,...,t_{r-1}) if r is even and r/2 is coprime to q^d-1. The method is to use twisted moduli schemes of Drinfeld modules ... More

Tensor tomography in periodic slabsJul 05 2017The X-ray transform on the periodic slab $[0,1]\times\mathbb T^n$, $n\geq0$, has a non-trivial kernel due to the symmetry of the manifold and presence of trapped geodesics. For tensor fields gauge freedom increases the kernel further, and the X-ray transform ... More

On $L^p$ resolvent estimates for elliptic operators on compact manifoldsMar 30 2013We prove uniform $L^p$ estimates for resolvents of higher order elliptic self-adjoint differential operators on compact manifolds without boundary, generalizing a corresponding resul of [3] in the case of Laplace-- Beltrami operators on Riemannian manifolds. ... More

Local lens rigidity with incomplete data for a class of non-simple Riemannian manifoldsJan 21 2007Let $\sigma$ be the scattering relation on a compact Riemannian manifold $M$ with non-necessarily convex boundary, that maps initial points of geodesic rays on the boundary and initial directions to the outgoing point on the boundary and the outgoing ... More

Utility indifference pricing of derivatives written on industrial loss indexesApr 03 2014We consider the problem of pricing derivatives written on some industrial loss index via utility indifference pricing. The industrial loss index is modelled by a compound Poisson process and the insurer can adjust her portfolio by choosing the risk loading, ... More

Photoacoustic and thermoacoustic tomography with an uncertain wave speedJul 05 2013We consider the mathematical model of photoacoustic and thermoacoustic tomography in media with a variable sound speed. When the sound speed is known, the explicit reconstruction formula by P. Stefanov and G. Uhlmann (Inverse Problems, 25(7):075011, 16, ... More

Elliptic divisibility sequences and undecidable problems about rational pointsDec 23 2004Jun 23 2006Julia Robinson has given a first-order definition of the rational integers Z in the rational numbers Q by a formula (\forall \exists \forall \exists)(F=0) where the \forall-quantifiers run over a total of 8 variables, and where F is a polynomial. This ... More

Graph Reconstruction and Quantum Statistical MechanicsSep 25 2012We study in how far it is possible to reconstruct a graph from various Banach algebras associated to its universal covering, and extensions thereof to quantum statistical mechanical systems. It turns out that most the boundary operator algebras reconstruct ... More

Low energy inverse problems in three-body scatteringOct 17 2001We consider low energy inverse problems in three-body scattering and show that if all unknown interactions are small in an appropriate sense then the 2-cluster to 2-cluster S-matrices given at low energies determine the Fourier transform of the effective ... More

Determining a magnetic Schrödinger operator with a continuous magnetic potential from boundary measurementsMay 05 2012We show that the knowledge of the set of the Cauchy data on the boundary of a $C^1$ bounded open set in $\R^n$, $n\ge 3$, for the Schr\"odinger operator with continuous magnetic and bounded electric potentials determines the magnetic field and electric ... More

Rigidity and reconstruction for graphsJan 29 2016We present measure theoretic rigidity for graphs of first Betti number b>1 in terms of measures on the boundary of a 2b-regular tree, that we make explicit in terms of the edge-adjacency and closed-walk structure of the graph. We prove that edge-reconstruction ... More

Mumford curves with maximal automorphism group II: Lame type groups in genus 5-8Jul 26 2002A Mumford curve of genus g=5,6,7 or 8 over a non-archimedean field of characteristic p (such that if p=0, the residue field characteristic exceeds 5) has at most 12(g-1) automorphisms. In this paper, all curves that attain this bound and their automorphism ... More

Convergence of the Euler-Maruyama method for multidimensional SDEs with discontinuous drift and degenerate diffusion coefficientOct 22 2016Jan 22 2019We prove strong convergence of order $1/4-\epsilon$ for arbitrarily small $\epsilon>0$ of the Euler-Maruyama method for multidimensional stochastic differential equations (SDEs) with discontinuous drift and degenerate diffusion coefficient. The proof ... More

Fundamental Limits of Energy-Efficient Resource Sharing, Power Control and Discontinuous TransmissionJul 11 2013The achievable gains via power-optimal scheduling are investigated. Under the QoS constraint of a guaranteed link rate, the overall power consumed by a cellular BS is minimized. Available alternatives for the minimization of transmit power consumption ... More

Edge reconstruction of the Ihara zeta functionJul 13 2015We show that if a graph G has average degree $\bar d \geq 4$, then the Ihara zeta function of G is edge-reconstructible. We prove some general spectral properties of the Bass-Hashimoto edge adjancency operator T: it is symmetric on a Krein space and has ... More

Defining the integers in large rings of number fields using one universal quantifierAug 22 2007Feb 14 2008Julia Robinson has given a first-order definition of the rational integers $\mathbb Z$ in the rational numbers $\mathbb Q$ by a formula $(\forall \exists \forall \exists)(F=0)$ where the $\forall$-quantifiers run over a total of 8 variables, and where ... More

Convergence of families of Dirichlet seriesSep 13 2015We give some conditions under which (uniform) convergence of a family of Dirichlet series to another Dirichlet series implies the convergence of their individual coefficients and/or exponents. We give some applications to some spectral zeta functions ... More

Relative entropy as a measure of inhomogeneity in general relativityAug 31 2010We introduce the notion of relative volume entropy for two spacetimes with preferred compact spacelike foliations. This is accomplished by applying the notion of Kullback-Leibler divergence to the volume elements induced on spacelike slices. The resulting ... More

A Compact Codimension Two Braneworld with Precisely One BraneApr 11 2010Jun 29 2010Building on earlier work on football shaped extra dimensions, we construct a compact codimension two braneworld with precisely one brane. The two extra dimensions topologically represent a 2-torus which is stabilized by a bulk cosmological constant and ... More

Hecke algebra isomorphisms and adelic points on algebraic groupsSep 04 2014Aug 04 2015Let $G$ denote a linear algebraic group over $\mathbf{Q}$ and $K$ and $L$ two number fields. Assume that there is a group isomorphism of points on $G$ over the finite adeles of $K$ and $L$, respectively. We establish conditions on the group $G$, related ... More

Symbolic Optimal ControlSep 21 2017Sep 04 2018We present novel results on the solution of a class of leavable, undiscounted optimal control problems in the minimax sense for nonlinear, continuous-state, discrete-time plants. The problem class includes entry-(exit-)time problems as well as minimum ... More

Uniform and $L^q$-Ensemble Reachability of Parameter-dependent Linear SystemsOct 22 2018We consider families of linear systems that are defined by matrix pairs $\big( A(\theta),B(\theta) \big)$ which depending on a parameter $\theta$ that is varying over a compact set in the plane. The focus of this paper is on the task of steering a family ... More

Classical and strong convexity of sublevel sets and application to attainable sets of nonlinear systemsNov 20 2013Jun 23 2014Necessary and sufficient conditions for convexity and strong convexity, respectively, of sublevel sets that are defined by finitely many real-valued $C^{1,1}$-maps are presented. A novel characterization of strongly convex sets in terms of the so-called ... More

The Calderón problem with partial data for conductivities with $3/2$ derivativesAug 28 2015Sep 04 2015We extend a global uniqueness result for the Calder\'on problem with partial data, due to Kenig-Sj\"ostrand-Uhlmann, to the case of less regular conductivities. Specifically, we show that in dimensions $n\ge 3$, the knowledge of the Diricihlet-to-Neumann ... More

Stability estimates for partial data inverse problems for Schrödinger operators in the high frequency limitDec 17 2017We consider the partial data inverse boundary problem for the Schr\"odinger operator at a frequency $k>0$ on a bounded domain in $\mathbb{R}^n$, $n\ge 3$, with impedance boundary conditions. Assuming that the potential is known in a neighborhood of the ... More

Inverse problems for magnetic Schrödinger operators in transversally anisotropic geometriesFeb 26 2017We study inverse boundary problems for magnetic Schr\"odinger operators on a compact Riemannian manifold with boundary of dimension $\ge 3$. In the first part of the paper we are concerned with the case of admissible geometries, i.e. compact Riemannian ... More

Some consequences of thermodynamic feasibility for the multistability and injectivity in chemical reaction networksMar 02 2014May 21 2014The result of this paper is the elucidation of the consequences for the chemical reaction network theory under the assumption of feasibility with respect to thermodynamic constraints. Thermodynamic feasible reaction networks limit the amount of "allowed" ... More

Equivariant deformation of Mumford curves and of ordinary curves in positive characteristicMar 29 2001Aug 24 2001We compute the dimension of the tangent space to, and the Krull dimension of the pro-representable hull of two deformation functors. The first one is the ``algebraic'' deformation functor of an ordinary curve X over a field of positive charateristic with ... More

A Strong Order 1/2 Method for Multidimensional SDEs with Discontinuous DriftDec 09 2015Dec 11 2018In this paper we consider multidimensional stochastic differential equations (SDEs) with discontinuous drift and possibly degenerate diffusion coefficient. We prove an existence and uniqueness result for this class of SDEs and we present a numerical method ... More

Reconstruction of Lorentzian manifolds from boundary light observation setsMay 03 2017On a time-oriented Lorentzian manifold $(M,g)$ with non-empty boundary satisfying a convexity assumption, we show that the topological, differentiable, and conformal structure of suitable subsets $S\subset M$ of sources is uniquely determined by measurements ... More

Inverse Diffusion Theory of PhotoacousticsOct 14 2009This paper analyzes the reconstruction of diffusion and absorption parameters in an elliptic equation from knowledge of internal data. In the application of photo-acoustics, the internal data are the amount of thermal energy deposited by high frequency ... More

Thermoacoustic tomography with variable sound speedFeb 11 2009May 30 2009We study the mathematical model of thermoacoustic tomography in media with a variable speed for a fixed time interval, greater than the diameter of the domain. In case of measurements on the whole boundary, we give an explicit solution in terms of a Neumann ... More

High-dimensional integration on $\mathbb{R}^d$, weighted Hermite spaces, and orthogonal transformsSep 22 2014It has been found empirically that quasi-Monte Carlo methods are often efficient for very high-dimensional problems, that is, with dimension in the hundreds or even thousands. The common explanation for this surprising fact is that those functions for ... More

Seeing the Forest in the Tree: Applying VRML to Mathematical Problems in Number TheoryDec 31 1999Jun 11 2000We show how VRML (Virtual Reality Modeling Language) can provide potentially powerful insight into the 3x + 1 problem via the introduction of a unique geometrical object, called the 'G-cell', akin to a fractal generator. We present an example of a VRML ... More

Fast Orthogonal transforms for pricing derivatives with quasi-Monte CarloAug 10 2015There are a number of situations where, when computing prices of financial derivatives using quasi-Monte Carlo (QMC), it turns out to be beneficial to apply an orthogonal transform to the standard normal input variables. Sometimes those transforms can ... More

Measure-theoretic rigidity for Mumford curvesJun 21 2011Dec 21 2011One can describe isomorphism of two compact hyperbolic Riemann surfaces of the same genus by a measure-theoretic property: a chosen isomorphism of their fundamental groups corresponds to a homeomorphism on the boundary of the Poincar\'e disc that is absolutely ... More

Fixed energy inverse problem for exponentially decreasing potentialsJul 17 2003In this paper we show that in two-body scattering the scattering matrix at a fixed energy determines real-valued exponentially decreasing potentials. This result has been proved by Novikov previously, see also the work of Novikov and Khenkin using a d-bar-equation. ... More

Existence, Uniqueness and Regularity of the Projection onto Differentiable ManifoldsNov 26 2018Apr 18 2019We investigate the maximal open domain $\mathscr{E}(M)$ on which the orthogonal projection map $p$ onto a subset $M\subseteq \mathbb{R}^d$ can be defined and study essential properties of $p$. We prove that if $M$ is a $C^1$ submanifold of $\mathbb{R}^d$ ... More

Local characterization of strongly convex setsJul 18 2012Apr 04 2013Strongly convex sets in Hilbert spaces are characterized by local properties. One quantity which is used for this purpose is a generalization of the modulus of convexity \delta_\Omega of a set \Omega. We also show that \lim_{\epsilon \to 0} \delta_\Omega(\epsilon)/\epsilon^2 ... More

Local analytic regularity in the linearized Calderón problemDec 14 2013Apr 24 2015We consider the linearization of the Dirichlet-to-Neumann (DN) map as a function of the potential. We show that it is injective at a real analytic potential for measurements made at an open subset of analyticity of the boundary. More generally, we relate ... More