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Ohmic contact engineering in few-layer black Phosphorus field effect transistorsMay 14 2019Achieving good quality Ohmic contacts to van der Waals materials is a challenge, since at the interface between metal and van der Waals material, different conditions can occur, ranging from the presence of a large energy barrier between the two materials ... More

Formal descriptions of Turaev's loop operationsNov 12 2015Aug 21 2016Using intersection and self-intersection of loops, Turaev introduced in the seventies two fundamental operations on the algebra $\mathbb{Q}[\pi]$ of the fundamental group $\pi$ of a surface with boundary. The first operation is binary and measures the ... More

An introduction to the abelian Reidemeister torsion of three-dimensional manifoldsMar 12 2010Oct 12 2010These notes accompany some lectures given at the autumn school "Tresses in Pau" in October 2009. The abelian Reidemeister torsion for 3-manifolds, and its refinements by Turaev, are introduced. Some applications, including relations between the Reidemeister ... More

On local definability of holomorphic functionsDec 19 2017Given a collection A of holomorphic functions, we consider how to describe all the holomorphic functions locally definable from A. The notion of local definability of holomorphic functions was introduced by Wilkie, who gave a complete description of all ... More

The Kontsevich integral for bottom tangles in handlebodiesFeb 02 2017Sep 26 2017The Kontsevich integral is a powerful link invariant, taking values in spaces of Jacobi diagrams. In this paper, we extend the Kontsevich integral to construct a functor on the category of bottom tangles in handlebodies. This functor gives a universal ... More

Generalized Dehn twists on surfaces and homology cylindersFeb 07 2019Let $\Sigma$ be a compact oriented surface. The Dehn twist along every simple closed curve $\gamma \subset \Sigma$ induces an automorphism of the fundamental group $\pi$ of $\Sigma$. There are two possible ways to generalize such automorphisms if the ... More

Quasi-Poisson structures on representation spaces of surfacesMay 22 2012Aug 31 2012Given an oriented surface S with base point * on the boundary, we introduce for all N>0, a canonical quasi-Poisson bracket on the space of N-dimensional linear representations of \pi_1(S,*). Our bracket extends the well-known Poisson bracket on GL_N-invariant ... More

Astrochemical Kinetic Grid Models of Groups of Observed Molecular Abundances: Taurus Molecular Cloud 1 (TMC-1)Oct 24 2018The emission line spectra of cyanoacetylene and methanol reveal chemical and physical heterogeneity on very small (< 0.1 pc) scales toward the peak in cyanopolyyne emission in the Taurus Molecular Cloud, TMC-1 (CP). We generate grids of homogeneous chemical ... More

The ortho-to-para ratio of interstellar NH$_2$: Quasi-classical trajectory calculations and new simulationsSep 08 2016Based on recent $Herschel$ results, the ortho-to-para ratio (OPR) of NH$_2$ has been measured towards the following high-mass star-forming regions: W31C (G10.6-0.4), W49N (G43.2-0.1), W51 (G49.5-0.4), and G34.3+0.1. The OPR at thermal equilibrium ranges ... More

A note on convergence of solutions of total variation regularized linear inverse problemsNov 17 2017Mar 26 2018In a recent paper by A. Chambolle et al. [Geometric properties of solutions to the total variation denoising problem. Inverse Problems 33, 2017] it was proven that if the subgradient of the total variation at the noise free data is not empty, the level-sets ... More

A Uniform Version of the Petrov-Khovanskii TheoremAug 09 2011An Abelian integral is the integral over the level curves of a Hamiltonian $H$ of an algebraic form $\omega$. The infinitesimal Hilbert sixteenth problem calls for the study of the number of zeros of Abelian integrals in terms of the degrees $H$ and $\omega$. ... More

Anisotropic curvature flow of immersed curvesMay 25 2016May 03 2017We prove short-time existence of {\phi}-regular solutions to the anisotropic and crystalline curvature flow of immersed planar curves.

Treatments of the exchange energy in density-functional theoryAug 03 2007Sep 03 2008Following a recent work [Gal, Phys. Rev. A 64, 062503 (2001)], a simple derivation of the density-functional correction of the Hartree-Fock equations, the Hartree-Fock-Kohn-Sham equations, is presented, completing an integrated view of quantum mechanical ... More

The mathematics of functional differentiation under conservation constraintMar 09 2006Dec 12 2006The mathematics of K-conserving functional differentiation, with K being the integral of some invertible function of the functional variable, is clarified. The most general form for constrained functional derivatives is derived from the requirement that ... More

On constrained second derivativesJul 12 2012Aug 13 2012The question of defining unique, generally applicable constrained second, and higher-order, derivatives is investigated. It is shown that second-order constrained derivatives obtained via two successive constrained differentiations provide a proper tool ... More

MESON2016 -- Concluding RemarksSep 15 2016Several topics presented and discussed at MESON2016 are highlighted, including pentaquarks, dibaryons and meson-nuclear bound states.

A Theoretically Grounded Application of Dropout in Recurrent Neural NetworksDec 16 2015May 25 2016Recurrent neural networks (RNNs) stand at the forefront of many recent developments in deep learning. Yet a major difficulty with these models is their tendency to overfit, with dropout shown to fail when applied to recurrent layers. Recent results at ... More

Quantitative estimates in approximation by Bernstein-Durrmeyer-Choquet operators with respect to monotone and submodular set functionsNov 23 2015For the qualitative results of pointwise and uniform approximation obtained in \cite{Gal-Opris}, we present general quantitative estimates in terms of the modulus of continuity and in terms of a $K$-functional, for the generalized multivariate Bernstein-Durrmeyer ... More

Optimizations of Management Algorithms for Multi-Level Memory HierarchyJul 22 2017In the near future the SCM is predicted to modify the form of new programs, the access form to storage, and the way that storage devices themselves are built. Therefore, a combination between the SCM and a designated Memory Allocation Manager (MAM) that ... More

Hopf categories and the categorification of the Heisenberg algebra via graphical calculusDec 20 2016We explore the connection between the notion of Hopf category and the categorification of the infinite dimensional Heisenberg algebra via graphical calculus proposed by M.Khovanov. We show that the existence of a Hopf structure on a semisimple symmetric ... More

Bezout-type Theorems for Differential FieldsJan 13 2015Mar 02 2015We prove analogs of the Bezout and the Bernstein-Kushnirenko-Khovanskii theorems for systems of algebraic differential conditions over differentially closed fields. Namely, given a system of algebraic conditions on the first $l$ derivatives of an $n$-tuple ... More

Multiplicity Estimates: a Morse-theoretic approachJun 07 2014Aug 13 2015The problem of estimating the multiplicity of the zero of a polynomial when restricted to the trajectory of a non-singular polynomial vector field, at one or several points, has been considered by authors in several different fields. The two best (incomparable) ... More

A functorial extension of the Magnus representation to the category of three-dimensional cobordismsApr 23 2016Jul 24 2017Let $R$ be an integral domain and $G$ be a subgroup of its group of units. We consider the category $\mathbf{\mathsf{Cob}}_G$ of 3-dimensional cobordisms between oriented surfaces with connected boundary, equipped with a representation of their fundamental ... More

Multiplicity OperatorsSep 07 2013Jun 23 2014For functions of a single complex variable, points of multiplicity greater than $k$ are characterized by the vanishing of the first $k$ derivatives. There are various quantitative generalizations of this statement, showing that for functions that are ... More

Sharp estimates for the global attractor of scalar reaction-diffusion equations with a Wentzell boundary conditionMar 16 2011Jul 10 2011In this paper, we derive optimal upper and lower bounds on the dimension of the attractor AW for scalar reaction-diffusion equations with a Wentzell (dynamic) boundary condition. We are also interested in obtaining explicit bounds about the constants ... More

A Theoretically Grounded Application of Dropout in Recurrent Neural NetworksDec 16 2015Oct 05 2016Recurrent neural networks (RNNs) stand at the forefront of many recent developments in deep learning. Yet a major difficulty with these models is their tendency to overfit, with dropout shown to fail when applied to recurrent layers. Recent results at ... More

Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep LearningJun 06 2015Oct 04 2016Deep learning tools have gained tremendous attention in applied machine learning. However such tools for regression and classification do not capture model uncertainty. In comparison, Bayesian models offer a mathematically grounded framework to reason ... More

Uniform upper bounds for the cyclicity of the zero solution of the Abel differential equationApr 09 2015Given two polynomials $P,q$ we consider the following question: "how large can the index of the first non-zero moment $\tilde{m}_k=\int_a^b P^k q$ be, assuming the sequence is not identically zero?". The answer $K$ to this question is known as the moment ... More

On the Laws of Large Numbers in Possibility TheoryApr 07 2017In this paper we obtain some possibilistic variants of the probabilistic laws of large numbers, different from those obtained by other authors, but very natural extensions of the corresponding ones in probability theory. Our results are based on the possibility ... More

Real Time Image Saliency for Black Box ClassifiersMay 22 2017In this work we develop a fast saliency detection method that can be applied to any differentiable image classifier. We train a masking model to manipulate the scores of the classifier by masking salient parts of the input image. Our model generalises ... More

Approximation by convolutions with probability densities and applications to PDEsFeb 15 2017Sep 14 2017The purpose of this paper is to introduce several new convolution operators, generated by some known probability densities. By using the inverse Fourier transform and taking inverse steps (in the analogues of the classical procedures used for, e.g., the ... More

Multiplicities of Noetherian deformationsJun 23 2014Aug 12 2015The \emph{Noetherian class} is a wide class of functions defined in terms of polynomial partial differential equations. It includes functions appearing naturally in various branches of mathematics (exponential, elliptic, modular, etc.). A conjecture by ... More

On the Bernstein's constant in convex approximationApr 12 2015Feb 21 2016Denoting by $E_{n}^{(+2)}(f)$ the best uniform approximation of $f$ by convex polynomials of degree $\le n$, there is an open question if there exists the limit $\lim_{n\to \infty}n^{\lambda}E_{n}^{(+2)}(|x|^{\lambda})$ for $\lambda \ge 1$.

Intersection multiplicities of Noetherian functionsAug 08 2011We provide a partial answer to the following problem: \emph{give an effective upper bound on the multiplicity of non-isolated common zero of a tuple of Noetherian functions}. More precisely, consider a foliation defined by two commuting polynomial vector ... More

Conditional Quenching: A detailed look at the SFR-Density Relation at z ~ 0.9 from ORELSEDec 11 2018We present a study of the star-formation rate (SFR)-density relation at z ~ 0.9 using data drawn from the Observations of Redshift Evolution in Large Scale Environments (ORELSE) survey. We find that SFR does depend on environment, but only for intermediate-stellar ... More

Complex Cellular StructuresFeb 21 2018We introduce the notion of a \emph{complex cell}, a complexification of the cells/cylinders used in real tame geometry. Complex cells are equipped with a natural notion of holomorphic extension, and the hyperbolic geometry of a cell within its extension ... More

Complex Cellular StructuresFeb 21 2018Apr 18 2019We introduce the notion of a complex cell, a complexification of the cells/cylinders used in real tame geometry. For $\delta\in(0,1)$ and a complex cell $\mathcal{C}$ we define its holomorphic extension $\mathcal{C}\subset\mathcal{C}^\delta$, which is ... More

Experimental analysis of the Strato-rotational Instability in a cylindrical Couette flowJul 18 2007This study is devoted to the experimental analysis of the Strato-rotational Instability (SRI). This instability affects the classical cylindrical Couette flow when the fluid is stably stratified in the axial direction. In agreement with recent theoretical ... More

Mathematical Model for Detection of Leakage in Domestic Water Supply Systems by Reading Consumption from an Analogue Water MeterJul 25 2017In this article we introduce the principles to detect leakage using a mathematical model based on machine learning and domestic water consumption monitoring in real time. The model uses data which is measured from a water meter, analyzes the water consumption, ... More

Nonlinear elliptic problems with dynamical boundary conditions of reactive and reactive-diffusive typeApr 05 2012Sep 02 2013We investigate classical solutions of nonlinear elliptic equations with two classes of dynamical boundary conditions, of reactive and reactive-diffusive type. In the latter case it is shown that well-posedness is to a large extent independent of the coupling ... More

HYM-flation: Yang-Mills cosmology with Horndeski couplingDec 07 2015We propose new mechanism for inflation using classical SU(2) Yang-Mills (YM) homogeneous and isotropic field non-minimally coupled to gravity via Horndeski prescription. This is the unique generally and gauge covariant ghost-free YM theory with the curvature-dependent ... More

The response of isotropic composites with viscoelastic matricesMay 16 2006Explicit expressions for the behavior of statistically isotropic composites with viscoelastic matrices and linear elastic inclusions are determined by application of the correspondence principle. The behavior of the matrix is linear in dilatation and ... More

On a regularized family of models for the full Ericksen-Leslie systemSep 15 2014Jul 20 2015We consider a general family of regularized systems for the full Ericksen-Leslie model for the hydrodynamics of liquid crystals in $n$-dimensional compact Riemannian manifolds, $n$=2,3. The system we consider consists of a regularized family of Navier-Stokes ... More

On approximation properties of semidirect products of groupsDec 30 2013Let R be a class of groups closed under taking semidirect products with finite kernel and fully residually R-groups. We prove that R contains all R-by-{finitely generated residually finite} groups. It follows that a semidirect product of a finitely generated ... More

Curvature spectra of simple Lie groupsApr 09 2013The Killing form \beta\ of a real (or complex) semisimple Lie group G is a left-invariant pseudo-Riemannian (or, respectively, holomorphic) Einstein metric. Let \Omega\ denote the multiple of its curvature operator, acting on symmetric 2-tensors, with ... More

Long-term behavior of reaction-diffusion equations with nonlocal boundary conditions on rough domainsMar 19 2015We investigate the long term behavior in terms of finite dimensional global and exponential attractors, as time goes to infinity, of solutions to a semilinear reaction-diffusion equation on non-smooth domains subject to nonlocal Robin boundary conditions, ... More

Cohomology rings, Rochlin function, linking pairing and the Goussarov--Habiro theory of three--manifoldsJul 31 2003Nov 18 2003We prove that two closed oriented 3-manifolds have isomorphic quintuplets (homology, space of spin structures, linking pairing, cohomology rings, Rochlin function) if, and only if, they belong to the same class of a certain surgery equivalence relation ... More

Infinitesimal Morita homomorphisms and the tree-level of the LMO invariantSep 26 2008Dec 13 2011Let S be a compact connected oriented surface with one boundary component, and let P be the fundamental group of S. The Johnson filtration is a decreasing sequence of subgroups of the Torelli group of S, whose k-th term consists of the self-homeomorphisms ... More

Classical Solutions for a Class of Burgers EquationMay 20 2019In this paper we consider a class of Burgers equation. We propose a new method of investigation for existence of classical solutions.

On some degenerate non-local parabolic equation associated with the fractional $p$-LaplacianSep 10 2015Oct 14 2016We consider a degenerate parabolic equation associated with the fractional $% p $-Laplace operator $\left( -\Delta \right) _{p}^{s}$\ ($p\geq 2$, $s\in \left( 0,1\right) $) and a monotone perturbation growing like $\left\vert s\right\vert ^{q-2}s,$ $q>p$ ... More

Transmission problems with nonlocal boundary conditions and rough dynamic interfacesSep 10 2015We consider a transmission problem consisting of a semilinear parabolic equation in a general non-smooth setting with emphasis on rough interfaces which bear a fractal-like geometry and nonlinear dynamic (possibly, nonlocal)\ boundary conditions along ... More

Tangent cones and $C^1$ regularity of definable setsMar 15 2017Let $X\subset \mathbb R^n$ be a connected locally closed definable set in an o-minimal structure. We prove that the following three statements are equivalent: (i) $X$ is a $C^1$ manifold, (ii) the tangent cone and the paratangent cone of $X$ coincide ... More

Trajectories in interlaced integral pencils of 3-dimensional analytic vector fields are o-minimalOct 08 2013Let X be an analytic vector field defined in a neighborhood of the origin of R^3, and let I be an analytically non-oscillatory integral pencil of X; that is, I is a maximal family of analytically non-oscillatory trajectories of X at the origin all sharing ... More

10 um wavefront spatial filtering: first results with chalcogenide fibersJan 22 2003Wavefront cleaning by single-mode fibers has proved to be efficient in optical-infrared interferometry to improve calibration quality. For instance, the FLUOR instrument has demonstrated the capability of fluoride glass single-mode fibers in this respect ... More

Elliptical instability of a flow in a rotating shellNov 28 2005A theoretical and experimental study of the spin-over mode induced by the elliptical instability of a flow contained in a slightly deformed rotating spherical shell is presented. This geometrical configuration mimics the liquid rotating cores of planets ... More

Intrinsic ferroelectric properties of strained tetragonal PbZr0.2Ti0.8O3 obtained on layer-by-layer grown, defect-free single crystalline filmsJan 16 2006PbZrxTi1-xO3 (PZT) is one of the technologically most important ferroelectric materials. Bulk single-domain single crystals of PZT have never been synthesized for a significant compositional range across the solid-solution phase diagram. This leaves the ... More

Magnetohydrodynamic simulations of the elliptical instability in triaxial ellipsoidsSep 08 2013The elliptical instability can take place in planetary cores and stars elliptically deformed by gravitational effects, where it generates large-scale three-dimensional flows assumed to be dynamo capable. In this work, we present the first magneto-hydrodynamic ... More

Elliptical instability in terrestrial planets and moonsMar 08 2012The presence of celestial companions means that any planet may be subject to three kinds of harmonic mechanical forcing: tides, precession/nutation, and libration. These forcings can generate flows in internal fluid layers, such as fluid cores and subsurface ... More

Adaptive Distributed Hierarchical Sensing Algorithm for Reduction of Wireless Sensor Network Cluster-Heads Energy ConsumptionJul 24 2017Energy efficiency is a crucial performance metric in sensor networks, directly determining the network lifetime. Consequently, a key factor in WSN is to improve overall energy efficiency to extend the network lifetime. Although many algorithms have been ... More

Hidden symmetries in 5D supergravities and black ringsDec 14 2009We construct generating technique for 5D minimal and $U(1)^3$ supergravities based on hidden symmetries arising in dimensional reduction to three dimensions. In the three-vector case the symmetry is SO(4,4), and the minimal case corresponds to contraction ... More

Improved generating technique for D=5 supergravities and squashed Kaluza-Klein Black HolesDec 12 2008Recently we suggested a solution generating technique for five-dimensional supergravity with three Abelian vector fields based on the hidden SO(4,4) symmetry of the three-dimensionally reduced theory. This technique generalizes the $G_{2(2)}$ generating ... More

On a regularized family of models for homogeneous incompressible two-phase flowsSep 15 2014We consider a general family of regularized models for incompressible two-phase flows based on the Allen-Cahn formulation in n-dimensional compact Riemannian manifolds for n=2,3. The system we consider consists of a regularized family of Navier-Stokes ... More

Goldberg's Conjecture is true for random multigraphsMar 02 2018Feb 06 2019In the 70s, Goldberg, and independently Seymour, conjectured that for any multigraph $G$, the chromatic index $\chi'(G)$ satisfies $\chi'(G)\leq \max \{\Delta(G)+1, \lceil\rho(G)\rceil\}$, where $\rho(G)=\max \{\frac {e(G[S])}{\lfloor |S|/2\rfloor} \mid ... More

Mean curvature flow with obstacles: a viscosity approachSep 26 2014Oct 21 2016We introduce a level-set formulation for the mean curvature flow with obstacles and show existence and uniqueness of a viscosity solution. These results generalize a well known viscosity approach for the mean curvature flow without obstacle by Evans and ... More

Splitting formulas for the LMO invariant of rational homology three-spheresSep 18 2013Apr 16 2014For rational homology 3-spheres, there exist two universal finite-type invariants: the Le-Murakami-Ohtsuki invariant and the Kontsevich-Kuperberg-Thurston invariant. These invariants take values in the same space of "Jacobi diagrams", but it is not known ... More

Magnetic field induced by elliiptical instability in a rotating tidally distorded sphereNov 28 2005It is usually believed that the geo-dynamo of the Earth or more generally of other planets, is created by the convective fluid motions inside their molten cores. An alternative to this thermal or compositional convection can however be found in the inertial ... More

Some finiteness properties for the Reidemeister-Turaev torsion of three-manifoldsJul 11 2005Mar 04 2009We prove for the Reidemeister-Turaev torsion of closed oriented three-manifolds some finiteness properties in the sense of Goussarov and Habiro, that is, with respect to some cut-and-paste operations which preserve the homology type of the manifolds. ... More

On MAXCUT in strictly supercritical random graphs, and coloring of random graphs and random tournamentsMar 13 2016Mar 16 2017We use a theorem by Ding, Lubetzky and Peres describing the structure of the giant component of random graphs in the strictly supercritical regime, in order to determine the typical size of MAXCUT of $G\sim G\left(n,\frac {1+\varepsilon}n\right)$ in terms ... More

Concrete DropoutMay 22 2017Dropout is used as a practical tool to obtain uncertainty estimates in large vision models and reinforcement learning (RL) tasks. But to obtain well-calibrated uncertainty estimates, a grid-search over the dropout probabilities is necessary - a prohibitive ... More

The Grassmann algebra in arbitrary characteristic and generalized signJan 11 2015We define a generalization $\mathfrak{G}$ of the Grassmann algebra $G$ which is well-behaved over arbitrary commutative rings $C$, even when $2$ is not invertible. In particular, this enables us to define a notion of superalgebras that does not become ... More

On Lagrangian Relaxation and Reoptimization ProblemsDec 21 2015We prove a general result demonstrating the power of Lagrangian relaxation in solving constrained maximization problems with arbitrary objective functions. This yields a unified approach for solving a wide class of {\em subset selection} problems with ... More

Pricing of vanilla and first generation exotic options in the local stochastic volatility framework: survey and new resultsDec 19 2013Stochastic volatility (SV) and local stochastic volatility (LSV) processes can be used to model the evolution of various financial variables such as FX rates, stock prices, and so on. Considerable efforts have been devoted to pricing derivatives written ... More

Packing, Counting and Covering Hamilton cycles in random directed graphsJun 01 2015Dec 10 2015A Hamilton cycle in a digraph is a cycle that passes through all the vertices, where all the arcs are oriented in the same direction. The problem of finding Hamilton cycles in directed graphs is well studied and is known to be hard. One of the main reasons ... More

Around the cusp singularity and the breaking of wavesSep 06 2012We record the breaking of water waves focusing at the Huygens Cusp of a parabolic wave maker using a fast video camera at a rate of 2000 images per second. The movie shows the very early time of the water tongue plunging ahead of the wave crest. Soon ... More

Trajectories in interlaced integral pencils of 3-dimensional analytic vector fields are o-minimalOct 08 2013Oct 10 2017Let X be an analytic vector field defined in a neighborhood of the origin of R^3, and let I be an analytically non-oscillatory integral pencil of X; that is, I is a maximal family of analytically non-oscillatory trajectories of X at the origin all sharing ... More

Power-laws and the Conservation of Information in discrete token systems: Part 2 The role of defectSep 07 2012In a matching paper (arXiv:1207.5027), I proved that Conservation of Size and Information in a discrete token based system is overwhelmingly likely to lead to a power-law component size distribution with respect to the size of its unique alphabet. This ... More

Compact Hankel operators on generalized Bergman spaces of the polydiscApr 07 2010We show that for $f$ a continuous function on the closed polydisc $\bar{\mathbb{D}^n}$ with $n\geq 2$, the Hankel operator $H_{f}$ is compact on the Bergman space of $\mathbb{D}^n$ if and only if there is a decomposition $f=h+g$, where $h$ is in the ball ... More

Intrinsic Prices Of RiskMar 03 2014Aug 18 2014We review the nature of some well-known phenomena such as volatility smiles, convexity adjustments and parallel derivative markets. We propose that the market is incomplete and postulate the existence of intrinsic risks in every contingent claim as a ... More

Homology torsion growth and Mahler measureOct 20 2010Nov 14 2012We prove a conjecture of K. Schmidt in algebraic dynamical system theory on the growth of the number of components of fixed point sets. We also generalize a result of Silver and Williams on the growth of homology torsions of finite abelian covering of ... More

Self-adjoint, unitary, and normal weighted composition operators in several variablesJul 25 2012We study weighted composition operators on Hilbert spaces of analytic functions on the unit ball with kernels of the form $(1-<z,w>)^{-\gamma}$ for $\gamma>0$. We find necessary and sufficient conditions for the adjoint of a weighted composition operator ... More

Global Existence and Regularity Results for Large Cross Diffusion Models on Planar DomainsApr 29 2016The global existence of classical solutions to cross diffusion systems of more than 2 equations given on a planar domain is established. The results can apply to generalized Shigesada-Kawasaki-Teramoto (SKT) and food pyramid models whose diffusion and ... More

On the existence and instability of solitary water waves with a finite dipoleDec 08 2018This paper considers the existence and stability properties of two-dimensional solitary waves traversing an infinitely deep body of water. We assume that above the water is vacuum, and that the waves are acted upon by gravity with surface tension effects ... More

A diffusion process associated with Fréchet meansOct 23 2015This paper studies rescaled images, under $\exp^{-1}_{\mu}$, of the sample Fr\'{e}chet means of i.i.d. random variables $\{X_k\vert k\geq 1\}$ with Fr\'{e}chet mean $\mu$ on a Riemannian manifold. We show that, with appropriate scaling, these images converge ... More

Nonlinear stochastic time-fractional diffusion equations on $\mathbb{R}$: moments, Hölder regularity and intermittencyOct 07 2014We study the nonlinear stochastic time-fractional diffusion equations in the spatial domain $\mathbb{R}$, driven by multiplicative space-time white noise. The fractional index $\beta$ varies continuously from $0$ to $2$. The case $\beta=1$ (resp. $\beta=2$) ... More

On the Solvability of a Class of Degenerate or Singular Strongly Coupled Parabolic SystemsJun 16 2017The existence of strong solutions to general class of strongly coupled parabolic systems will be discussed. These systems can be degenerate or singular as boundedness of theirs solutions are unavailable and not assummed. The results greatly improve those ... More

Existence of Strong Solutions to Degenerate or Singular Strongly Coupled Elliptic SystemsMay 16 2017A general class of strongly coupled elliptic systems with quadratic growth in gradients is considered and the existence of their strong solutions is established. The results greatly improve those in a recent paper \cite{dleJFA} as the systems can be either ... More

Weighted Gagliardo-Nirenberg Inequalities Involving BMO Norms and MeasuresDec 28 2016Global and local weighted Gagliardo-Nirenberg inequalities with doubling measures are established. These inequalities are key ingredients for the regularity theory and existence of strong solutions for strongly coupled parabolic and elliptic systems which ... More

Positive definite functions on Coxeter groups with applications to operator spaces and noncommutative probabilityApr 22 2017A new class of positive definite functions related to colour-length function on arbitrary Coxeter group is introduced. Extensions of positive definite functions, called the Riesz-Coxeter product, from the Riesz product on the Rademacher (Abelian Coxeter) ... More

Coleman-Gurtin type equations with dynamic boundary conditionsOct 29 2014We present a new formulation and generalization of the classical theory of heat conduction with or without fading memory which includes the usual heat equation subject to a dynamic boundary condition as a special case. We investigate the well-posedness ... More

Hyperbolic Relaxation of Reaction Diffusion Equations with Dynamic Boundary ConditionsFeb 18 2013Apr 18 2013Under consideration is the hyperbolic relaxation of a semilinear reaction-diffusion equation on a bounded domain, subject to a dynamic boundary condition. We also consider the limit parabolic problem with the same dynamic boundary condition. Each problem ... More

Quasialgebraic FunctionsAug 09 2011Sep 08 2011We introduce and discuss a new class of (multivalued analytic) transcendental functions which still share with algebraic functions the property that the number of their isolated zeros can be explicitly counted. On the other hand, this class is sufficiently ... More

Power-Laws and the Conservation of Information in discrete token systems: Part 1 General TheoryJul 20 2012The Conservation of Energy plays a pivotal part in the development of the physical sciences. With the growth of computation and the study of other discrete token based systems such as the genome, it is useful to ask if there are conservation principles ... More

Boundedness and compactness of composition operators on Segal-Bargmann spacesNov 30 2011For $E$ a Hilbert space, let $\mathcal{H}(E)$ denote the Segal-Bargmann space (also known as the Fock space) over $E$, which is a reproducing kernel Hilbert space with kernel $K(x,y)=\exp(< x,y>)$ for $x,y$ in $E$. If $\phi$ is a mapping on $E$, the composition ... More

Coalescence times for the continuous time Bienaymé-Galton-Watson processMay 08 2014We investigate the distribution of the coalescence time (most recent common ancestor) for two individuals picked at random (uniformly) in the current generation of a continuous time Bienaym\'e-Galton-Watson process founded $t$ units of time ago. We also ... More

On the Dynamics of Glassy SystemsApr 11 2016Glassy systems are disordered systems characterized by extremely slow dynamics. Examples are supercooled liquids, whose dynamics slow down under cooling. The specific pattern of slowing-down depends on the material considered. This dependence is poorly ... More

Relatively Hyperbolic Coxeter Groups with maximal Flats of codimension 1Jun 04 2015We study relatively hyperbolic Coxeter groups of type $HM$ with maximal Euclidean Coxeter subgroups of codimension 1. Our main result in this paper is that the dimension of these groups is bounded above.

A better bound on the largest induced forests in triangle-free planar graphsNov 14 2016Jan 26 2017It is well-known that there exists a triangle-free planar graph of $n$ verticess such that the largest induced forest has size at most $\frac{5n}{8}$. Salavatipour proved that there is a forest of size at least $\frac{5n}{9.41}$ in any triangle-free planar ... More

Elliptic equations with transmission and Wentzell boundary conditions and an application to steady water waves in the presence of windJun 12 2017Jan 23 2018In this paper, we present results about the existence and uniqueness of solutions of elliptic equations with transmission and Wentzell boundary conditions. We provide Schauder estimates and existence results in H\"older spaces. As an application, we develop ... More

Global Existence and Regularity Results for Strongly Coupled Nonregular Parabolic Systems via Iterative MethodsSep 16 2014The global existence of classical solutions to strongly coupled parabolic systems is shown to be equivalent to the availability of an iterative scheme producing a sequence of solutions with uniform continuity in the BMO norms. Amann's results on global ... More

Continuity results for TV-minimizersMay 31 2016This paper deals with continuity preservation when minimizing generalized total variation with a $L^2$ fidelity term or a Dirichlet boundary condition. We extend several recent results in the two cases, mainly by showing comparison principles for the ... More