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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

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

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

Continuity results for TV-minimizersMay 31 2016Apr 13 2017This 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

Canonical extensions of Morita homomorphisms to the Ptolemy groupoidJun 04 2010Jun 27 2011Let S be a compact connected oriented surface with one boundary component. We extend each of Johnson's and Morita's homomorphisms to the Ptolemy groupoid of S. Our extensions are canonical and take values into finitely generated free abelian groups. The ... More

Quadratic functions on torsion groupsJan 06 2003Jul 15 2004We investigate classification results for general quadratic functions on torsion abelian groups. Unlike the previously studied situations, general quadratic functions are allowed to be inhomogeneous or degenerate. We study the discriminant construction ... 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

Brackets in the Pontryagin algebras of manifoldsAug 23 2013Dec 19 2017Given a smooth oriented manifold $M$ with non-empty boundary, we study the Pontryagin algebra $A=H_\ast(\Omega )$ where $ \Omega $ is the space of loops in $M$ based at a distinguished point of $ \partial M$. Using the ideas of string topology of Chas-Sullivan, ... More

Morita's trace maps on the group of homology cobordismsJun 27 2016Sep 18 2018Morita introduced in 2008 a 1-cocycle on the group of homology cobordisms of surfaces with values in an infinite-dimensional vector space. His 1-cocycle contains all the "traces" of Johnson homomorphisms which he introduced fifteen years earlier in his ... More

Chlorine-bearing molecules in molecular absorbers at intermediate redshiftsAug 12 2019We use observations of chlorine-bearing species in molecular absorbers at intermediate redshifts to investigate chemical properties and $^{35}$Cl/$^{37}$Cl isotopic ratios in the absorbing sightlines. Chloronium (H$_2$Cl$^+$) is detected along three independent ... More

The ortho-to-para ratio of H$_2$Cl$^+$: Quasi-classical trajectory calculations and new simulations in light of new observationsAug 29 2017Oct 01 2017Multi-hydrogenated species with proper symmetry properties can present different spin configurations, and thus exist under different spin symmetry forms, labeled as para and ortho for two-hydrogen molecules. We investigated here the ortho-to-para ratio ... More

Influence of dimension on the convergence of level-sets in total variation regularizationNov 29 2018May 15 2019We extend some recent results on the Hausdorff convergence of level-sets for total variation regularized linear inverse problems. Dimensions higher than two and measurements in Banach spaces are considered. We investigate the relation between the dimension ... More

Inductive acceleration of ions in Poynting-flux dominated outflowsAug 18 2019Two-fluid (electron-positron) plasma modelling has shown that inductive acceleration can convert Poynting flux directly into bulk kinetic energy in the relativistic flows driven by rotating magnetized neutron stars and black holes. Here, we generalize ... More

Galactic Cosmic-Rays in a BreezeOct 30 2017We study a scenario in which the Fermi bubbles are formed through a Galactocentric outflow of gas and pre-accelerated cosmic-rays (CR). We take into account CR energy losses due to proton-proton interactions with the gas present in the bubbles, and calculate ... More

Modeling C-Shock Chemistry in Isolated Molecular OutflowsJun 20 2019Shocks are a crucial probe for understanding the ongoing chemistry within ices on interstellar dust grains where many complex organic molecules (COMs) are believed to be formed. However, previous work has been limited to the initial liberation into the ... 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.

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

Maximally additively reducible subsets of the integersAug 14 2019Let $A, B \subseteq \mathbb{N}$ be two finite sets of natural numbers. We say that $B$ is an additive divisor for $A$ if there exists some $C \subseteq \mathbb{N}$ with $A = B+C$. We prove that among those subsets of $\{0, 1, \ldots, k\}$ which have $0$ ... More

Density of algebraic points on Noetherian varietiesApr 03 2017Let $\Omega\subset{\mathbb R}^n$ be a relatively compact domain. A finite collection of real-valued functions on $\Omega$ is called a \emph{Noetherian chain} if the partial derivatives of each function are expressible as polynomials in the functions. ... More

Sulphur chemistry in the L1544 pre-stellar coreJun 04 2018Jun 15 2018The L1544 pre-stellar core has been observed as part of the ASAI IRAM 30m Large Program as well as follow-up programs. These observations have revealed the chemical richness of the earliest phases of low-mass star-forming regions. In this paper we focus ... More

High Spectral Resolution SOFIA/EXES Observations of C2H2 towards Orion-IRc2Sep 12 2017Jan 25 2018We present high-spectral resolution observations from 12.96 - 13.33 microns towards Orion IRc2 using the mid-infrared spectrograph, EXES, on SOFIA. These observations probe the physical and chemical conditions of the Orion hot core, which is sampled by ... 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

Is there a bound Lambda-n-n ?Apr 23 2014Jul 17 2014The HypHI Collaboration at GSI argued recently for a (Lambda-n-n) bound state from the observation of its two-body (t + pi-) weak-decay mode. We derive constraints from several hypernuclear systems, in particular from the A=4 hypernuclei with full consideration ... More

Random-Player Maker-Breaker gamesFeb 02 2015Mar 14 2016In a $(1:b)$ Maker-Breaker game, a primary question is to find the maximal value of $b$ that allows Maker to win the game (that is, the critical bias $b^*$). Erd\H{o}s conjectured that the critical bias for many Maker-Breaker games played on the edge ... More

Real Root Conjecture fails for five and higher dimensional spheresJan 04 2005A construction of convex flag triangulations of five and higher dimensional spheres, whose h-polynomials fail to have only real roots, is given. We show that there is no such example in dimensions lower than five. A condition weaker than realrootedness ... More

Pion-assisted Nucleon-Delta and Delta-Delta dibaryonsJan 14 2014Apr 08 2014N-Delta and Delta-Delta dibaryon candidates are discussed and related quark-based calculations are reviewed. New hadronic calculations of L=0 nonstrange dibaryon candidates are reported. For N-Delta, I(JP)=1(2+) and 2(1+) S-matrix poles slightly below ... More

Distributed Backup Placement in One Round and its Applications to Maximum Matching Approximation and Self-StabilizationAug 15 2019In the distributed backup-placement problem each node of a network has to select one neighbor, such that the maximum number of nodes that make the same selection is minimized. This is a natural relaxation of the perfect matching problem, in which each ... More

On the compositum of all degree d extensions of a number fieldOct 15 2012Aug 16 2013Let k be a number field, and denote by k^[d] the compositum of all degree d extensions of k in a fixed algebraic closure. We first consider the question of whether all algebraic extensions of k of degree less than d lie in k^[d]. We show that this occurs ... More

Approximation by Choquet Integral OperatorsJul 22 2014The main aim of this paper is to show that the nonlinear Choquet integral can be used to construct nonlinear approximation operators, exactly as by the use in probability of the Lebesgue-type integral, linear and positive approximation operators are constructed. ... 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

A Unifying Bayesian View of Continual LearningFeb 18 2019Some machine learning applications require continual learning - where data comes in a sequence of datasets, each is used for training and then permanently discarded. From a Bayesian perspective, continual learning seems straightforward: Given the model ... 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

Wilkie's conjecture for restricted elementary functionsMay 16 2016We consider the structure ${\mathbb R}^{\mathrm{RE}}$ obtained from $({\mathbb R},<,+,\cdot)$ by adjoining the restricted exponential and sine functions. We prove Wilkie's conjecture for sets definable in this structure: the number of rational points ... More

Establishing a New Technique for Discovering Large-Scale Structure Using the ORELSE SurveyMay 22 2019The Observations of Redshift Evolution in Large Scale Environments (ORELSE) survey is an ongoing imaging and spectroscopic campaign initially designed to study the effects of environment on galaxy evolution in high-redshift ($z\sim1$) large-scale structures. ... More

Persistence of the Color-Density Relation and Efficient Environmental Quenching to $z\sim1.4$Dec 11 2018Dec 21 2018Using ~5000 spectroscopically-confirmed galaxies drawn from the Observations of Redshift Evolution in Large Scale Environments (ORELSE) survey we investigate the relationship between color and galaxy density for galaxy populations of various stellar masses ... 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

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

A two-cocycle on the group of symplectic diffeomorphismsOct 04 2010Oct 06 2011We investigate a two-cocycle on the group of symplectic diffeomorphisms of an exact symplectic manifolds defined by Ismagilov, Losik, and Michor and investigate its properties. We provide both vanishing and non-vanishing results and applications to foliated ... 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

Indefinite Einstein metrics on simple Lie groupsSep 26 2012Apr 02 2013The set E of Levi-Civita connections of left-invariant pseudo-Riemannian Einstein metrics on a given semisimple Lie group always includes D, the Levi-Civita connection of the Killing form. For the groups SU(l,j) (or SL(n,R), or SL(n,C) or, if n is even, ... More

Quantitative Classification of Type I Supernovae Using Spectroscopic Features at Maximum BrightnessJul 09 2017We present a set of new quantitative classification criteria for major subclasses of Type I Supernovae (SNe). We analyze peak spectra of 146 SNe Ia from the Berkeley Supernova Ia Program (BSNIP), 12 SNe Ib, 19 SNe Ic (including 5 SNe Ic-BL) and 4 SNe ... 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

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

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

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

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

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

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 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

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

Radial Bayesian Neural Networks: Robust Variational Inference In Big ModelsJul 01 2019We propose Radial Bayesian Neural Networks: a variational distribution for mean field variational inference (MFVI) in Bayesian neural networks that is simple to implement, scalable to large models, and robust to hyperparameter selection. We hypothesize ... 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

Kantorovich's Mass Transport Problem for CapacitiesJul 07 2019Jul 20 2019The aim of the present paper is to extend Kantorovich's mass transport problem to the framework of upper continuous capacities and to prove the cyclic monotonicity of the supports of optimal solutions. As in the probabilistic case, this easily yields ... 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

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

BatchBALD: Efficient and Diverse Batch Acquisition for Deep Bayesian Active LearningJun 19 2019We develop BatchBALD, a tractable approximation to the mutual information between a batch of points and model parameters, which we use as an acquisition function to select multiple informative points jointly for the task of deep Bayesian active learning. ... More

Uniform symplicity of groups with proximal actionFeb 28 2016Feb 28 2017We prove that groups acting boundedly and order-primitively on linear orders or acting extremly proximality on a Cantor set (the class including various Higman-Thomson groups and Neretin groups of almost automorphisms of regular trees, also called groups ... 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

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

Growth of homology torsion in finite coverings and hyperbolic volumeDec 24 2014May 22 2016We give an upper bound for the growth of homology torsions of finite coverings of irreducible 3-manifolds with tori boundary in terms of hyperbolic volume.

On some nonadmissible smooth irreducible representations of $\mathrm{GL}_2$Sep 26 2018Feb 18 2019Let $p>2$ be a prime. We give examples of smooth absolutely irreducible representations of $\mathrm{GL}_2(\mathbb{Q}_{p^3})$ over $\mathbb{F}_{p^3}$ which are not admissible.

An effective Schmidt's subspace theorem for hypersurfaces in subgeneral position in projective varieties over function fieldsSep 24 2015We deduce an effective version of Schmidt's subspace theorem on a smooth projective variety X over function fields of characteristic zero for hypersurfaces located in N-subgeneral position with respect to X.

The Art of Space Filling in Penrose Tilings and FractalsJun 10 2011Mar 23 2012Incorporating designs into the tiles that form tessellations presents an interesting challenge for artists. Creating a viable MC Escher like image that works esthetically as well as functionally requires resolving incongruencies at a tile's edge while ... More

Global Existence and Global Attractors of Cross Diffusion Systems on Planar DomainsMay 17 2016May 18 2016Global existence of strong solutions and the existence of global and atrractors are established for generalized Shigesada-Kawasaki-Teramoto models on planar domains. The cross diffusion and reaction can have polynomial growth of any order.

A refined Luecking's theorem and finite-rank products of Toeplitz operatorsFeb 26 2008For any function $f$ in $L^{\infty}(\mathbb{D})$, let $T_f$ denote the corresponding Toeplitz operator the Bergman space $A^2(\mathbb{D})$. A recent result of D. Luecking shows that if $T_f$ has finite rank then $f$ must be the zero function. Using a ... More

Toeplitz operators on generalized harmonic Bergman spacesApr 06 2010We study Toeplitz operators with uniformly continuous symbols on generalized harmonic Bergman spaces of the unit ball in $\mathbb{R}^n$. We describe their essential spectra and establish a short exact sequence associated with the $C^{*}$-algebra generated ... 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

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

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

Spin Borromean surgeriesApr 05 2001Jan 06 2003In 1986, Matveev defined the notion of Borromean surgery for closed oriented 3-manifolds and showed that the equivalence relation generated by this move is characterized by the pair (first betti number, linking form up to isomorphism). We explain how ... More

Finite-type invariants of three-manifolds and the dimension subgroup problemMay 18 2006Dec 13 2006For a certain class of compact oriented 3-manifolds, M. Goussarov and K. Habiro have conjectured that the information carried by finite-type invariants should be characterized in terms of ``cut-and-paste'' operations defined by the lower central series ... 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

Regularity for Fully Nonlinear P-Laplacian Parabolic Systems: the Degenerate CaseOct 12 2011This paper studies H\"older regularity property of bounded weak solutions to a class of strongly coupled degenerate parabolic systems.

The degenerate Schmidt's subspace theorem for moving hypersurface targetsJun 14 2017Jun 19 2017Our goal is to give Schmidt's subspace theorem for moving hypersurface targets in subgeneral position in projective varieties.

An application of the BHV theorem to a new conjecture on exponential diophantine equationsNov 01 2018Let $A$, $B$ be fixed positive integers such that $\min\{A,B\} > 1$, $\gcd(A,B) = 1$ and $AB \equiv 0 \bmod 2$, and let $n$ be a positive integer with $n>1$. In this paper, using a deep result on the existence of primitive divisors of Lucas numbers due ... More

The commutants of certain Toeplitz operators on weighted Bergman spacesFeb 26 2008For $\alpha>-1$, let $A^2_{\alpha}$ be the corresponding weighted Bergman space of the unit ball in $\mathbb{C}^n$. For a bounded measurable function $f$, let $T_f$ be the Toeplitz operator with symbol $f$ on $A^2_{\alpha}$. This paper describes all the ... More

The zero-product problem for Toeplitz operators with radial symbolsDec 02 2007For any bounded measurable function $f$ on the unit ball $B_n$, let $T_f$ be the Toeplitz operator with symbol $f$ acting on the Bergman space $A^2(B_n)$. The Zero-Product Problem asks: if $f_1,..., f_N$ are bounded measurable functions such that $T_{f_1}... ... More

On a Class of Ideals of the Toeplitz Algebra on the Bergman Space of the Unit BallMay 07 2007Let $\mathfrak{T}$ denote the full Toeplitz algebra on the Bergman space of the unit ball $\mathbb{B}_n.$ For each subset $G$ of $L^{\infty},$ let $\mathfrak{CI}(G)$ denote the closed two-sided ideal of $\mathfrak{T}$ generated by all $T_fT_g-T_gT_f$ ... More

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

Supercharacters and pattern subgroups in the upper triangular groupsAug 13 2010Aug 05 2013Let $U_n(q)$ denote the upper triangular group of degree $n$ over the finite field $\F_q$ with $q$ elements. It is known that irreducible constituents of supercharacters partition the set of all irreducible characters $\Irr(U_n(q)).$ In this paper we ... More

Counting irreducible representations of large degree of the upper triangular groupsDec 02 2009Aug 06 2013Let $U_n(q)$ be the upper triangular group of degree $n$ over the finite field $\F_q$ with $q$ elements. In this paper, we present constructions of large degree ordinary irreducible representations of $U_n(q)$ where $n\geq 7$, and then determine the number ... 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

A proof of the Kazdan-Warner identity via the Minkowski spacetimeFeb 05 2016Any 2-dim Riemannian manifold with spherical topology can be embedded isometrically into a lightcone of the Minkowski spacetime. We apply this fact to give a proof of the Kazdan-Warner identity.

A better bound on the largest induced forests in triangle-free planar graphsNov 14 2016It 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

Almost periodic along subsequencesMay 01 2019Bergelson, Host and Kra show that a multiple correlation can be decomposed into a sum of a uniform limit of nilsequences and a sequence tending to zero in density. Frantzikinakis asks whether one has a similar result along various subsequences. In a previous ... More

Multiplicity one for wildly ramified representationsAug 15 2017Let $F$ be a totally real field in which $p$ is unramified. Let $\overline{r}: G_F \rightarrow \mathrm{GL}_2(\overline{\mathbb{F}}_p)$ be a modular Galois representation which satisfies the Taylor-Wiles hypotheses and is generic at a place $v$ above $p$. ... More

On some nonadmissible smooth irreducible representations of $\mathrm{GL}_2$Sep 26 2018Jun 23 2019Let $p>2$ be a prime. We give examples of smooth absolutely irreducible representations of $\mathrm{GL}_2(\mathbb{Q}_{p^3})$ over $\mathbb{F}_{p^3}$ which are not admissible.

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

Irreducible characters of Sylow p-subgroups of the Steinberg triality groups $^3D_4(p^{3m})$Sep 06 2013In this notes we construct and count all ordinary irreducible characters of Sylow $p$-subgroups of the Steinberg triality groups ${}^3D_4(p^{3m})$.

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

Uniqueness and Regularity of Unbounded Weak Solutions to a Class of Cross Diffusion SystemsJun 08 2019We establish the uniqueness and regularity of weak (and very weak) solutions to a class of cross diffusion systems which is inspired by models in mathematical biology/ecology, in particular the Shigesada-Kawasaki-Teramoto (SKT) model in population biology. ... 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