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A Phase-Field Description for Pressurized and Non-Isothermal Propagating FracturesMar 30 2019In this work, we extend a phase-field approach for pressurized fractures to non-isothermal settings. Specifically, the pressure and the temperature are given quantities and the emphasis is on the correct modeling of the interface laws between a porous ... More

Mesh adaptivity for quasi-static phase-field fractures based on a residual-type a posteriori error estimatorJun 11 2019In this work, we consider adaptive mesh refinement for a monolithic phase-field description for fractures in brittle materials. Our approach is based on an a posteriori error estimator for the phase-field variational inequality realizing the fracture ... More

An Adaptive Global-Local Approach for Phase-Field Modeling of Anisotropic Brittle FractureMay 18 2019This work addresses an efficient Global-Local approach supplemented with predictor-corrector adaptivity applied to anisotropic phase-field brittle fracture. The phase-field formulation is used to resolve the sharp crack surface topology on the anisotropic/non-uniform ... More

An iterative staggered scheme for phase field brittle fracture propagation with stabilizing parametersMar 20 2019This paper concerns the analysis and implementation of a novel iterative staggered scheme for quasi-static brittle fracture propagation models, where the fracture evolution is tracked by a phase field variable. The model we consider is a two-field variational ... More

Parallel solution, adaptivity, computational convergence, and open-source code of 2d and 3d pressurized phase-field fracture problemsJun 26 2018We present a scalable, parallel implementation of a solver for the solution of a phase-field model for quasi-static brittle fracture. The code is available as open source. Numerical solutions in 2d and 3d with adaptive mesh refinement show optimal scaling ... More

On the implementation of a locally modified finite element method for interface problems in deal.IIJun 04 2018In this work, we describe a simple finite element approach that is able to resolve weak discontinuities in interface problems accurately. The approach is based on a fixed patch mesh consisting of quadrilaterals, that will stay unchanged independent of ... More

Dynamical Spin Response Functions for Heisenberg LaddersDec 12 1997We present the results of a numerical study of the 2 by L spin 1/2 Heisenberg ladder. Ground state energies and the singlet-triplet energy gaps for L = (4-14) and equal rung and leg interaction strengths were obtained in a Lanczos calculation and checked ... More

On Non-Linear Quantum Mechanics and the Measurement Problem IV. Experimental TestsAug 06 2019I discuss three proposed experiments that could in principle locate the boundary between the classical and quantum worlds, as well as distinguish the Hamiltonian theory presented in the first paper of this series from the spontaneous-collapse theories. ... More

Matrix-free multigrid solvers for phase-field fracture problemsFeb 21 2019In this work, we present a framework for the matrix-free solution to a monolithic quasi-static phase-field fracture model with geometric multigrid methods. Using a standard matrix based approach within the Finite Element Method requires lots of memory, ... More

A phase-field model for fractures in incompressible solidsJan 16 2019Within this work, we develop a phase-field description for simulating fractures in incompressible materials. Standard formulations are subject to volume-locking when the solid is (nearly) incompressible. We propose an approach that builds on a mixed form ... More

Matrix-free multigrid solvers for phase-field fracture problemsFeb 21 2019Feb 22 2019In this work, we present a framework for the matrix-free solution to a monolithic quasi-static phase-field fracture model with geometric multigrid methods. Using a standard matrix based approach within the Finite Element Method requires lots of memory, ... More

Iterative coupling of flow, geomechanics and adaptive phase-field fracture including level-set crack width approachesOct 23 2016In this work, we present numerical studies of fixed-stress iterative coupling for solving flow and geomechanics with propagating fractures in a porous medium. Specifically, fracture propagations are described by employing a phase-field approach. The extension ... More

Two-side a posteriori error estimates for the DWR methodNov 19 2018In this work, we derive two-sided a posteriori error estimates for the dual-weighted residual (DWR) method. We consider both single and multiple goal functionals. Using a saturation assumption, we derive lower bounds yielding the efficiency of the error ... More

Signature Studies of Cosmic Magnetic MonopolesFeb 01 2001This talk explores the possibility that the Universe may be populated with relic magnetic monopoles. Observations of galactic and extragalactic magnetic fields, lead to the conclusion that monopoles of mass < 10^{14} GeV are accelerated in these fields ... More

Analysis of a Legendre spectral element method (LSEM) for the two-dimensional system of a nonlinear stochastic advection-reaction-diffusion modelsApr 12 2019In this work, we develop a Legendre spectral element method (LSEM) for solving the stochastic nonlinear system of advection-reaction-diffusion models. The used basis functions are based on a class of Legendre functions such that their mass and diffuse ... More

GUT Cosmic Magnetic Fields in a Warm Inflationary UniverseSep 15 1998Nov 03 1998Sources of magnetic fields from grand unified theories are studied in the warm inflation regime. A ferromagnetic Savvidy vacuum scenario is presented that yields observationally interesting large scale magnetic fields. As an intermediate step, a general ... More

Multigoal-oriented optimal control problems with nonlinear PDE constraintsMar 07 2019In this work, we consider an optimal control problem subject to a nonlinear PDE constraint and apply it to the regularized $p$-Laplace equation. To this end, a reduced unconstrained optimization problem in terms of the control variable is formulated. ... More

Generalized moving least squares and moving kriging least squares approximations for solving the transport equation on the sphereApr 11 2019In this work, we apply two meshless methods for the numerical solution of the time-dependent transport equation defined on the sphere in spherical coordinates. The first technique, which was introduced by Mirzaei (BIT Numerical Mathematics, 54 (4) 1041-1063, ... More

Two-Weight Tb Theorems for Well-Localized OperatorsJun 08 2019This paper first defines operators that are "well-localized" with respect to a pair of accretive functions and establishes a global two-weight Tb theorem for such operators. Then it defines operators that are "well-localized" with respect to a pair of ... More

Two Weight Inequalities for Riesz Transforms: Uniformly Full Dimension WeightsDec 20 2013May 18 2016Fix an integer $ n$ and number $d$, $ 0< d\neq n-1 \leq n$, and two weights $ w$ and $ \sigma $ on $ \mathbb R ^{n}$. We two extra conditions (1) no common point masses and (2) the two weights separately are not concentrated on a set of codimension one, ... More

Signatures for a Cosmic Flux of Magnetic MonopolesJan 13 2000Sep 04 2002Any early universe phase transition occurring after inflation has the potential to populate the universe with relic magnetic monopoles. Observations of galactic magnetic fields, as well as observations matched with models for extragalactic magnetic fields, ... More

Measurements of the properties of Lambda_c(2595), Lambda_c(2625), Sigma_c(2455), and Sigma_c(2520) baryonsMay 30 2011Jul 28 2011We report measurements of the resonance properties of Lambda_c(2595)+ and Lambda_c(2625)+ baryons in their decays to Lambda_c+ pi+ pi- as well as Sigma_c(2455)++,0 and Sigma_c(2520)++,0 baryons in their decays to Lambda_c+ pi+/- final states. These measurements ... More

Up to and beyond ninth order in opacity: Radiative energy loss with GLVApr 29 2008A new examination of the GLV all-orders opacity result for radiative energy loss is presented. The opacity expansion is shown to be a Dyson expansion of a Schrodinger-like (or diffusion) equation, a form also found in BDMPS-Z-ASW, AMY and Higher Twist ... More

Elastic, Inelastic, and Path Length Fluctuations in Jet TomographyDec 21 2005Jan 29 2007We propose a possible perturbative QCD solution to the heavy quark tomography problem posed by recent non-photonic single electron data from central Au+Au collisions at $\sqrt{s} = 200$ AGeV. Jet quenching theory is extended to include (1) elastic as ... More

Influence of Bottom Quark Jet Quenching on Single Electron Tomography of Au+AuJul 07 2005High transverse momentum single (non-photonic) electrons are shown to be sensitive to the stopping power of both bottom, b, and charm, c, quarks in AA collisions. We apply the DGLV theory of radiative energy loss to predict c and b quark jet quenching ... More

Frobenius-Perron Theory of Modified ADE Bound Quiver AlgebrasJan 04 2018Sep 27 2018The Frobenius-Perron dimension for an abelian category was recently introduced. We apply this theory to the category of representations of the finite-dimensional radical squared zero algebras associated to certain modified ADE graphs. In particular, we ... More

Results on Charm Baryon Spectroscopy from TevatronMay 03 2011Due to an excellent mass resolution and a large amount of available data, the CDF experiment, located at the Tevatron proton-antiproton accelerator, allows the precise measurement of spectroscopic properties, like mass and decay width, of a variety of ... More

Solar and Supernova Constraints on Cosmologically Interesting NeutrinosDec 13 1997The sun and core-collapse supernovae produce neutrino spectra that are sensitive to the effects of masses and mixing. Current results from solar neutrino experiments provide perhaps our best evidence for such new neutrino physics, beyond the standard ... More

Heavy quark jet quenching with collisional plus radiative energy loss and path length fluctuationsJan 22 2007With the QGP opacity computed perturbatively and with the global entropy constraints imposed by the observed $dN_{ch}/dy\approx1000$, radiative energy loss alone cannot account for the observed suppression of single non-photonic electrons. We show that ... More

Characterizations of product Hardy spaces in Bessel settingJun 10 2016In this paper, we work in the setting of Bessel operators and Bessel Laplace equations studied by Weinstein, Huber, and the harmonic function theory in this setting introduced by Muckenhoupt--Stein, especially the generalised Cauchy--Riemann equations ... More

Hidden Charm Spectroscopy from TevatronMay 03 2011The observation of a narrow structure near the J/psi phi threshold in exclusive B+ to J/psi phi K+ decays produced in p-pbar collisions at sqrt(s) = 1.96 TeV is reported. A signal of 19 +- 6(stat) +- 3(syst) events, with statistical significance of 5.0 ... More

On the quantum mechanical description of the interaction between particle and detectorJan 16 2019Quantum measurements of physical quantities are usually described as ideal measurements. However, only a few measurements fulfil the conditions of ideal measurements. The aim of the present work is to describe real position measurements with detectors ... More

On quantales and spectra of C*-algebrasNov 21 2002We study properties of the quantale spectrum Max A of an arbitrary unital C*-algebra A. In particular we show that the spatialization of Max A with respect to one of the notions of spatiality in the literature yields the locale of closed ideals of A when ... More

A Reconsideration of the b -> s gamma Decay in the Minimal Flavor Violating MSSMOct 16 2008We present a MSSM study of the b -> s gamma decay in a Minimal Flavor Violating (MFV) framework, where the form of the soft SUSY breaking terms is determined by the Standard Model Yukawa couplings. In particular, we address the role of gluino contributions, ... More

A First-Landau-Level Laughlin/Jain Wave Function for the Fractional Quantum Hall EffectOct 23 1995Apr 11 1996We show that the introduction of a more general closed-shell operator allows one to extend Laughlin's wave function to account for the richer hierarchies (1/3, 2/5, 3/7 ...; 1/5, 2/9, 3/13, ..., etc.) found experimentally. The construction identifies ... More

Solar Wakes of Dark Matter FlowsMar 25 2002We analyze the effect of the Sun's gravitational field on a flow of cold dark matter (CDM) through the solar system in the limit where the velocity dispersion of the flow vanishes. The exact density and velocity distributions are derived in the case where ... More

A Note about Stabilization in $A_\R(\D)$Jan 31 2007It is shown that for $A_\R(\D)$ functions $f_1$ and $f_2$ with $$ \inf_{z\in\bar{\D}}(\abs{f_1(z)}+\abs{f_2(z)})\geq\delta>0 $$ and $f_1$ being positive on real zeros of $f_2$ then there exists $A_\R(\D)$ functions $g_2$ and $g_1,g_1^{-1}$ with and $$ ... More

Commutators of multi-parameter flag singular integrals and applicationsFeb 13 2018Sep 18 2018We introduce the iterated commutator for the Riesz transforms in the multi-parameter flag setting, and prove the upper bound of this commutator with respect to the symbol $b$ in the flag BMO space. Our methods require the techniques of semigroups, harmonic ... More

An Algorithm for Computing Stochastically Stable Distributions with Applications to Multiagent Learning in Repeated GamesJul 04 2012One of the proposed solutions to the equilibrium selection problem for agents learning in repeated games is obtained via the notion of stochastic stability. Learning algorithms are perturbed so that the Markov chain underlying the learning dynamics is ... More

Implications of the GALLEX Source Experiment for the Solar Neutrino ProblemMar 16 1995We argue that, prior to the recent GALLEX $^{51}$Cr source experiment, the excited state contributions to the $^{71}$Ga capture cross section for $^{51}$Cr and $^7$Be neutrinos were poorly constrained, despite forward-angle (p,n) measurements. We describe ... More

Stopping the SuperSpreader Epidemic, Part II: MERS Goes PandemicMay 17 2014In a paper of August 2013, I discussed the so-called SuperSpreader (SS) epidemic model and emphasized that it has dynamics differing greatly from the more-familiar uniform (or Poisson) textbook model. In that paper, SARS in 2003 was the representative ... More

Frobenius-Perron theory for projective schemesJul 04 2019The Frobenius-Perron theory of an endofunctor of a $\Bbbk$-linear category (recently introduced in [CG]) provides new invariants for abelian and triangulated categories. Here we study Frobenius-Perron type invariants for derived categories of commutative ... More

Leaf Identification Using a Deep Convolutional Neural NetworkDec 04 2017Convolutional neural networks (CNNs) have become popular especially in computer vision in the last few years because they achieved outstanding performance on different tasks, such as image classifications. We propose a nine-layer CNN for leaf identification ... More

On Non-linear Quantum Mechanics and the Measurement Problem I. Blocking CatsOct 09 2017Working entirely within the Schroedinger paradigm, meaning wavefunction only, I present a modification of his theory that prevents formation of macroscopic dispersion (MD; "cats"). The proposal is to modify the Hamiltonian based on a method introduced ... More

Analytic projections, Corona Problem and geometry of holomorphic vector bundlesFeb 25 2007Dec 02 2007The main result of the paper is the theorem giving a sufficient condition for the existence of a bounded analytic projection onto a holomorphic family of (generally infinite-dimensional) subspaces (a holomorphic sub-bundle of a trivial bundle). This sufficient ... More

A Mathematica script for harmonic oscillator nuclear matrix elements arising in semileptonic electroweak interactionsJun 15 2007Jun 20 2007Semi-leptonic electroweak interactions in nuclei - such as \beta decay, \mu capture, charged- and neutral-current neutrino reactions, and electron scattering - are described by a set of multipole operators carrying definite parity and angular momentum, ... More

Fully Convolutional Neural Networks for Page Segmentation of Historical Document ImagesNov 21 2017Feb 15 2018We propose a high-performance fully convolutional neural network (FCN) for historical document segmentation that is designed to process a single page in one step. The advantage of this model beside its speed is its ability to directly learn from raw pixels ... More

Improving a radiative plus collisional energy loss model for application to RHIC and LHCJan 29 2007Jun 20 2007With the QGP opacity computed perturbatively and with the global entropy constraints imposed by the observed dNch/dy~1000, radiative energy loss alone cannot account for the observed suppression of single non-photonic electrons. Collisional energy loss ... More

On Non-Linear Quantum Mechanics and the Measurement Problem II. The Random Part of the WavefunctionOct 10 2017In the first paper of this series, I introduced a non-linear, Hamiltonian, generalization of Schroedinger's theory that blocks formation of macroscopic dispersion ("cats"). But that theory was entirely deterministic, and so the origin of random outcomes ... More

Stopping the SuperSpreader Epidemic, Part III: PredictionJun 23 2014In two previous papers, I introduced SuperSpreader (SS) epidemic models, offered some theoretical discussion of prevention issues, and fitted some models to data derived from published accounts of the ongoing MERS epidemic (concluding that a pandemic ... More

Stopping the SuperSpreader Epidemic: the lessons from SARS (with, perhaps, applications to MERS)Aug 29 2013I discuss the so-called SuperSpreader epidemic, for which SARS is the canonical examples (and, perhaps, MERS will be another). I use simulation by an agent-based model as well as the mathematics of multi-type branching-processes to illustrate how the ... More

On Non-Linear Quantum Mechanics and the Measurement Problem III. Poincare Probability and ... Chaos?Mar 29 2018Paper I of this series introduced a nonlinear version of quantum mechanics that blocks cats, and paper II postulated a random part of the wavefunction to explain outcomes in experiments such as Stern-Gerlach or EPRB. However, an ad hoc extra parameter ... More

Stabilization in $H^\infty_{\mathbb{R}}(\mathbb{D})$Sep 09 2008Oct 18 2010In this paper we prove the following theorem: Suppose that $f_1,f_2\in H^\infty_\R(\D)$, with $\norm{f_1}_\infty,\norm{f_2}_{\infty}\leq 1$, with $$ \inf_{z\in\D}(\abs{f_1(z)}+\abs{f_2(z)})=\delta>0. $$ Assume for some $\epsilon>0$ and small, $f_1$ is ... More

Characterization of Electro-Optical Devices with Low Jitter Single Photon Detectors -- Towards an Optical Sampling Oscilloscope Beyond 100 GHzOct 12 2018We showcase an optical random sampling scope that exploits single photon counting and apply it to characterize optical transceivers. We study single photon detectors with a jitter down to 40 ps. The method can be extended beyond 100 GHz.

A remark on the multipliers on spaces of weak products of functionsMar 03 2016If $\mathcal{H}$ denotes a Hilbert space of analytic functions on a region $\Omega \subseteq \mathbb{C}^d$, then the weak product is defined by $$\mathcal{H}\odot\mathcal{H}=\left\{h=\sum_{n=1}^\infty f_n g_n : \sum_{n=1}^\infty \|f_n\|_{\mathcal{H}}\|g_n\|_{\mathcal{H}} ... More

Well-Localized Operators on Matrix Weighted $L^2$ SpacesJul 14 2014Jul 29 2015Nazarov-Treil-Volberg recently proved an elegant two-weight T1 theorem for "almost diagonal" operators that played a key role in the proof of the $A_2$ conjecture for dyadic shifts and related operators. In this paper, we obtain a generalization of their ... More

Weighted estimates for the Bergman projection on the Hartogs triangleApr 23 2019We apply modern techniques of dyadic harmonic analysis to obtain sharp estimates for the Bergman projection in weighted Bergman spaces. Our main theorem focuses on the Bergman projection on Hartogs triangle. The estimates of the operator norm are in terms ... More

Weighted estimates for the Bergman projection on the Hartogs triangleApr 23 2019Apr 25 2019We apply modern techniques of dyadic harmonic analysis to obtain sharp estimates for the Bergman projection in weighted Bergman spaces. Our main theorem focuses on the Bergman projection on Hartogs triangle. The estimates of the operator norm are in terms ... More

Thin Sequences and Their Role in Model Spaces and Douglas AlgebrasOct 02 2014May 05 2015We study thin interpolating sequences $\{\lambda_n\}$ and their relationship to interpolation in the Hardy space $H^2$ and the model spaces $K_\Theta = H^2 \ominus \Theta H^2$, where $\Theta$ is an inner function. Our results, phrased in terms of the ... More

Thin SequencesAug 30 2015Oct 04 2015We look at thin interpolating sequences and the role they play in uniform algebras, Hardy spaces, and model spaces.

Two Weight Inequalities for Iterated Commutators with Calderón-Zygmund OperatorsSep 12 2015Given a Calder\'on-Zygmund operator $T$, a classic result of Coifman-Rochberg-Weiss relates the norm of the commutator $[b, T]$ with the BMO norm of $b$. We focus on a weighted version of this result, obtained by Bloom and later generalized by Lacey and ... More

Duality, Tangential Interpolation, and Toeplitz Corona ProblemsDec 11 2009Mar 23 2010In this paper we extend a method of Arveson and McCullough to prove a tangential interpolation theorem for subalgebras of $H^\infty$. This tangential interpolation result implies a Toelitz corona theorem. In particular, it is shown that the set of matrix ... More

Simultaneous Stabilization in $A_\mathbb{R}(\mathbb{D})$Oct 01 2008In this note we study the problem of simultaneous stabilization for the algebra $A_\R(\D)$. Invertible pairs $(f_j,g_j)$, $j=1,..., n$, in a commutative unital algebra are called \textit{simultaneously stabilizable} if there exists a pair $(\alpha,\beta)$ ... More

Alignment and scaling of large-scale fluctuations in the solar windSep 24 2012We investigate the dependence of solar wind fluctuations measured by the Wind spacecraft on scale and on the degree of alignment between oppositely directed Elsasser fields. This alignment controls the strength of the non-linear interactions and, therefore, ... More

Ideal membership in $H^\infty$: Toeplitz corona approachSep 22 2017Sep 19 2018We study the ideal membership problem in $H^\infty$ on the unit disc. Thus, given functions $f,f_1,\ldots,f_n$ in $H^\infty$, we seek sufficient conditions on the size of $f$ in order for $f$ to belong to the ideal of $H^\infty$ generated by $f_1,\ldots,f_n$. ... More

A Study of the Matrix Carleson Embedding Theorem with Applications to Sparse OperatorsMar 22 2015In this paper, we study the dyadic Carleson Embedding Theorem in the matrix weighted setting. We provide two new proofs of this theorem, which highlight connections between the matrix Carleson Embedding Theorem and both maximal functions and $H^1$-BMO ... More

Weak factorization of Hardy spaces in the Bessel settingApr 08 2016Apr 18 2016We provide the weak factorization of the Hardy spaces $H^{p}(\mathbb{R}_+, dm_{\lambda})$ in the Bessel setting, for $p\in \left(\frac{2\lambda + 1}{2\lambda + 2}, 1\right]$. As a corollary we obtain a characterization of the boundedness of the commutator ... More

A Weighted Estimate for the Square Function on the Unit Ball in $\C^n$Jan 29 2007We show that the Lusin area integral or the square function on the unit ball of $\C^n$, regarded as an operator in weighted space $L^2(w)$ has a linear bound in terms of the invariant $A_2$ characteristic of the weight. We show a dimension-free estimate ... More

The Bass and Topological Stable Ranks of $H^\infty_\R(\D)$ and $A_\R(\D)$Jun 18 2008In this note we prove that the Bass stable rank of $H^\infty_\R(\D)$ is two. This establishes the validity of a conjecture by S. Treil. We accomplish this in two different ways, one by giving a direct proof, and the other, by first showing that the topological ... More

Glazman-Krein-Naimark Theory, Left-Definite Theory and the Square of the Legendre Polynomials Differential OperatorOct 26 2015As an application of a general left-definite spectral theory, Everitt, Littlejohn and Wellman, in 2002, developed the left-definite theory associated with the classical Legendre self-adjoint second-order differential operator $A$ in $L^{2}(-1,1)$ which ... More

Weighted estimates for the Bergman projection on the Hartogs triangleApr 23 2019May 01 2019We apply modern techniques of dyadic harmonic analysis to obtain sharp estimates for the Bergman projection in weighted Bergman spaces. Our main theorem focuses on the Bergman projection on the Hartogs triangle. The estimates of the operator norm are ... More

Filling in the details: Perceiving from low fidelity imagesApr 14 2016Humans perceive their surroundings in great detail even though most of our visual field is reduced to low-fidelity color-deprived (e.g. dichromatic) input by the retina. In contrast, most deep learning architectures are computationally wasteful in that ... More

Dirac Magnetic Monopole Production from Photon Fusion in Proton CollisionsJun 07 2007Feb 13 2008We calculate the lowest order cross--section for Dirac magnetic monopole production from photon fusion in p p-bar collisions at sqrt{s}=1.96 TeV, p p collisions at sqrt{s}=14 TeV, and we compare photon fusion with Drell--Yan (DY) production. We find the ... More

A reproducing kernel thesis for operators on Bergman-type function spacesDec 03 2012Nov 05 2013In this paper we consider the reproducing kernel thesis for boundedness and compactness for various operators on Bergman-type spaces. In particular, the results in this paper apply to the weighted Bergman space on the unit ball, the unit polydisc and ... More

Bergman-type Singular Operators and the Characterization of Carleson Measures for Besov--Sobolev Spaces on the Complex BallOct 07 2009Apr 23 2010The purposes of this paper are two fold. First, we extend the method of non-homogeneous harmonic analysis of Nazarov, Treil and Volberg to handle "Bergman--type" singular integral operators. The canonical example of such an operator is the Beurling transform ... More

Compactness of operators on the Bergman space of the Thullen domainOct 13 2018We study compact operators on the Bergman space of the Thullen domain defined by $\{(z_1,z_2)\in \mathbb C^2: |z_1|^{2p}+|z_2|^2<1\}$ with $p>0$ and $p\neq 1$. The domain need not be smooth nor have a transitive automorphism group. We give a sufficient ... More

Bergman-type Singular Integral Operators on Metric SpacesDec 30 2009In this paper we study ``Bergman-type'' singular integral operators on Ahlfors regular metric spaces. The main result of the paper demonstrates that if a singular integral operator on a Ahlfors regular metric space satisfies an additional estimate, then ... More

The Matrix-Valued $H^{p}$ Corona Problem in the Disk and PolydiskSep 25 2004In this paper we consider the matrix-valued $H^{p}$ corona problem in the disk and polydisk. The result for the disk is rather well known, and is usually obtained from the classical Carleson Corona Theorem by linear algebra. Our proof provides a streamlined ... More

On the uniqueness sets in the Fock spaceJun 03 2013It was known to von Neumann in the 1950's that the integer lattice $\mathbb{Z}^2$ forms a uniqueness set for the Bargmann-Fock space. It was later demonstrated by Seip and Wallst\'en that a sequence of points $\Gamma$ that is uniformly close to the integer ... More

Spectral Characteristics and Stable Ranks for the Sarason Algebra $H^\infty+C$Jun 10 2009We prove a Corona type theorem with bounds for the Sarason algebra $H^\infty+C$ and determine its spectral characteristics. We also determine the Bass, the dense, and the topological stable ranks of $H^\infty+C$.

Weak Factorizations of the Hardy space $H^1(\mathbb{R}^n)$ in terms of Multilinear Riesz TransformsMar 08 2016Mar 19 2016This paper provides a constructive proof of the weak factorizations of the classical Hardy space $H^1(\mathbb{R}^n)$ in terms of multilinear Riesz transforms. As a direct application, we obtain a new proof of the characterization of ${\rm BMO}(\mathbb{R}^n)$ ... More

Magnetic Helicity of Solar Wind Fluctuations at Ion-kinetic ScalesMay 13 2019We use magnetic helicity to characterise solar wind fluctuations at ion-kinetic scales. For the first time, we separate the contributions to helicity from fluctuations propagating at angles quasi-parallel and oblique to the local mean magnetic field, ... More

Characterizations of $H^1_{Δ_N}(\mathbb{R}^n)$ and $\rm BMO_{Δ_N}(\mathbb{R}^n)$ via Weak Factorizations and CommutatorsMay 17 2015This paper provides a deeper study of the Hardy $H^1$ and $\rm BMO$ spaces associated to the Neumann Laplacian. For the Hardy space $H^1_{\Delta_N}(\mathbb{R}^n)$ we demonstrate that the space has equivalent norms in terms of Riesz transforms, maximal ... More

The Essential Norm of Operators on $A^p(\mathbb{D}^n)$Aug 29 2012Aug 17 2013In this paper we characterize the compact operators on the Bergman space $A^p(\mathbb{D}^n)$. The main result shows that an operator on $A^p(\mathbb{D}^n)$ is compact if and only if it belongs to the Toeplitz algebra $\mathcal{T}_{p}$ and its Berezin ... More

Corona Solutions Depending Smoothly on Corona DataAug 16 2012In this note we show that if the Corona data depends continuously (smoothly) on a parameter, the solutions of the corresponding Bezout equations can be chosen to have the same smoothness in the parameter.

Weak factorization of Hardy spaces in the Bessel settingApr 08 2016Oct 17 2017We provide the weak factorization of the Hardy spaces $H^{p}(\mathbb{R}_+, dm_{\lambda})$ in the Bessel setting, for $p\in \left(\frac{2\lambda + 1}{2\lambda + 2}, 1\right]$. As a corollary we obtain a characterization of the boundedness of the commutator ... More

Some remarks about interpolating sequences in reproducing kernel Hilbert spacesSep 08 2011Apr 22 2013In this paper we study two separate problems on interpolation. We first give some new equivalences of Stout's Theorem on necessary and sufficient conditions for a sequence of points to be an interpolating sequence on a finite open Riemann surface. We ... More

An optimization principle for the computation of MHD equilibria in the solar coronaDec 21 2006AIMS: We develop an optimization principle for computing stationary MHD equilibria. METHODS: Our code for the self-consistent computation of the coronal magnetic fields and the coronal plasma uses non-force-free MHD equilibria. Previous versions of the ... More

Elagage d'un perceptron multicouches : utilisation de l'analyse de la variance de la sensibilité des paramètresDec 04 2008The stucture determination of a neural network for the modelisation of a system remain the core of the problem. Within this framework, we propose a pruning algorithm of the network based on the use of the analysis of the sensitivity of the variance of ... More

Two-Variable Logic with Two Order RelationsOct 07 2011Mar 03 2012It is shown that the finite satisfiability problem for two-variable logic over structures with one total preorder relation, its induced successor relation, one linear order relation and some further unary relations is EXPSPACE-complete. Actually, EXPSPACE-completeness ... More

Causes and Explanations in the Structural-Model Approach: Tractable CasesDec 12 2012In this paper, we continue our research on the algorithmic aspects of Halpern and Pearl's causes and explanations in the structural-model approach. To this end, we present new characterizations of weak causes for certain classes of causal models, which ... More

On the boundedness of an iteration involving points on the hypersphereJan 11 2010Oct 05 2010For a finite set of points $X$ on the unit hypersphere in $\mathbb{R}^d$ we consider the iteration $u_{i+1}=u_i+\chi_i$, where $\chi_i$ is the point of $X$ farthest from $u_i$. Restricting to the case where the origin is contained in the convex hull of ... More

Dynamic Conjunctive QueriesApr 05 2017The article investigates classes of queries maintainable by conjunctive queries (CQs) and their extensions and restrictions in the dynamic complexity framework of Patnaik and Immerman. Starting from the basic language of quantifier-free conjunctions of ... More

On the quantifier-free dynamic complexity of ReachabilityJun 13 2013Jan 28 2015The dynamic complexity of the reachability query is studied in the dynamic complexity framework of Patnaik and Immerman, restricted to quantifier-free update formulas. It is shown that, with this restriction, the reachability query cannot be dynamically ... More

Sélection de la structure d'un perceptron multicouches pour la réduction dun modèle de simulation d'une scierieDec 05 2008Simulation is often used to evaluate the relevance of a Directing Program of Production (PDP) or to evaluate its impact on detailed sc\'enarii of scheduling. Within this framework, we propose to reduce the complexity of a model of simulation by exploiting ... More

Spectral Correlations in the Crossover Transition from a Superposition of Harmonic Oscillators to the Gaussian Unitary EnsembleJul 20 1998We compute the spectral correlation functions for the transition from a harmonic oscillator towards the Gaussian Unitary Ensemble (GUE). We use a variant of the supersymmetry method to obtain analytical results in a fast and elegant way. In contrast to ... More

How deals with discrete data for the reduction of simulation models using neural networkJun 10 2009Simulation is useful for the evaluation of a Master Production/distribution Schedule (MPS). Also, the goal of this paper is the study of the design of a simulation model by reducing its complexity. According to theory of constraints, we want to build ... More

Heavy quark meson spectroscopy at CDF (X(3872) mass and evidence for Y(4140))Nov 02 2010With growing datasets collected by the CDF II experiment, studies of the spectroscopy of mesons containing heavy quarks become more exciting. The CDF experiment has good capabilities in both charm and bottom sector. This capability allowed also to contribute ... More

Neutrino PhysicsMay 06 1999The basic concepts of neutrino physics are presented at a level appropriate for integration into elementary courses on quantum mechanics and/or modern physics.

The Corona Problem for Kernel Multiplier AlgebrasOct 31 2014Oct 10 2016We prove an alternate Toeplitz corona theorem for the algebras of pointwise kernel multipliers of Besov-Sobolev spaces on the unit ball in $\mathbb{C}^{n}$, and for the algebra of bounded analytic functions on certain strictly pseudoconvex domains and ... More