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Dark trions and biexcitons in WS2 and WSe2 made bright by e-e scatteringJan 05 2017The direct band gap character and large spin-orbit splitting of the valence band edges (at the K and K' valleys) in monolayer transition metal dichalcogenides have put these two-dimensional materials under the spot-light of intense experimental and theoretical ... More

Fast relaxation of photo-excited carriers in 2D transition metal dichalcogenidesOct 21 2015We predict a fast relaxation of photo-excited carriers in monolayer transition metal dichalcogenides (TMDCs), which is mediated by the emission of longitudinal optical (LO) phonons. By evaluating Born effective charges for ${\rm MoS_2, MoSe_2,WS_2}$, ... More

Four phases of angular-momentum buildup in high-z galaxies: from cosmic-web streams through an extended ring to disc and bulgeJul 26 2014Jan 04 2015We study the angular-momentum (AM) buildup in high-$z$ massive galaxies using high-resolution cosmological simulations. The AM originates in co-planar streams of cold gas and merging galaxies tracing cosmic-web filaments, and it undergoes four phases ... More

Co-planar streams, pancakes, and angular-momentum exchange in high-z disc galaxiesOct 27 2011Jan 12 2012We study the feeding of massive galaxies at high redshift through streams from the cosmic web using the Mare Nostrum hydro-cosmological simulation. Our statistical sample consists of 350 dark-matter haloes of ~10^12 Msun at z = 2.5. We find that ~70% ... More

Resonantly hybridised excitons in moiré superlattices in van der Waals heterostructuresApr 12 2019Atomically-thin layers of two-dimensional materials can be assembled in vertical stacks held together by relatively weak van der Waals forces, allowing for coupling between monolayer crystals with incommensurate lattices and arbitrary mutual rotation. ... More

Auger recombination of dark excitons in ${\rm WS_2}$ and ${\rm WSe_2}$ monolayersJul 04 2016We propose a novel phonon assisted Auger process unique to the electronic band structure of monolayer transition metal dichalcogenides (TMDCs), which dominates the radiative recombination of ground state excitons in Tungsten based TMDCs. Using experimental ... More

Hybrid k$\cdot$p tight-binding model for subbands and infrared intersubband optics in few-layer films of transition-metal dichalcogenides: MoS$_2$, MoSe$_2$, WS$_2$ and WSe${}_2$Aug 04 2018We present a density functional theory parametrized hybrid k$\cdot$p tight binding model for electronic properties of atomically thin films of transition-metal dichalcogenides, 2H-$MX_2$ ($M$=Mo, W; $X$=S, Se). We use this model to analyze intersubband ... More

Localized interlayer complexes in heterobilayer transition metal dichalcogenidesFeb 16 2018Jun 01 2018We present theoretical results for the radiative rates and doping-dependent photoluminescence spectrum of interlayer excitonic complexes localized by donor impurities in MoSe$_2$/WSe$_2$ twisted heterobilayers, supported by quantum Monte Carlo calculations ... More

Dissociation of two-dimensional excitons in monolayer WSe2Apr 19 2018Two-dimensional (2D) semiconducting materials are promising building blocks for optoelectronic applications, many of which require efficient dissociation of excitons into free electrons and holes. However, the strongly bound excitons arising from the ... More

Nano-imaging of intersubband transitions in van der Waals quantum wellsJun 25 2018The science and applications of electronics and optoelectronics have been driven for decades by progress in growth of semiconducting heterostructures. Many applications in the infrared and terahertz frequency range exploit transitions between quantized ... More

Thermal stability of cold clouds in galaxy halosJul 02 1999Oct 14 1999We consider the thermal properties of cold, dense clouds of molecular hydrogen and atomic helium. For cloud masses below 10^-1.7 Msun, the internal pressure is sufficient to permit the existence of particles of solid or liquid hydrogen at temperatures ... More

Extreme scattering events and Galactic dark matterFeb 10 1998Mar 20 1998Extreme Scattering Events (ESEs) are attributed to radio-wave refraction by a cloud of free-electrons crossing the line-of-sight. We present a new model in which these electrons form the photo-ionized 'skin' of an underlying cool, self-gravitating cloud ... More

High velocity gas from the Galactic dark haloNov 13 1998We present the germ of a new model for High Velocity Clouds, derived from the idea that the dark matter halo of our Galaxy is in the form of cold, planetary-mass gas clouds. In this picture HVCs arise as a result of disruptive collisions between dark ... More

Order-Revealing Encryption and the Hardness of Private LearningMay 03 2015An order-revealing encryption scheme gives a public procedure by which two ciphertexts can be compared to reveal the ordering of their underlying plaintexts. We show how to use order-revealing encryption to separate computationally efficient PAC learning ... More

Continuity in Discrete SetsJan 30 2010Continuous models used in physics and other areas of mathematics applications become discrete when they are computerized, e.g., utilized for computations. Besides, computers are controlling processes in discrete spaces, such as films and television programs. ... More

Some Results on the Functional Decomposition of PolynomialsApr 30 2010If g and h are functions over some field, we can consider their composition f = g(h). The inverse problem is decomposition: given f, determine the ex- istence of such functions g and h. In this thesis we consider functional decom- positions of univariate ... More

Full Square Rhomboids and Their Algebraic ExpressionsMay 12 2013The paper investigates relationship between algebraic expressions and graphs. We consider a digraph called a full square rhomboid that is an example of non-series-parallel graphs. Our intention is to simplify the expressions of full square rhomboids and ... More

Automatic Identification of Support Verbs: A Step Towards a Definition of Semantic WeightOct 25 1995Oct 26 1995Current definitions of notions of lexical density and semantic weight are based on the division of words into closed and open classes, and on intuition. This paper develops a computationally tractable definition of semantic weight, concentrating on what ... More

Resource Letter TF-1: Turbulence in FluidsJun 14 1999This Resource Letter provides a guide to the literature on fully developed turbulence in fluids. It is restricted to mechanically driven turbulence in an incompressible fluid described by the Navier-Stokes equations of hydrodynamics, and places greatest ... More

Constraining Reionization with Lyman Alpha Emitting GalaxiesNov 04 2015Neutral diffuse intergalactic gas that existed during the Epoch of Reionization (EoR) suppresses Lyman Alpha (Lya) flux emitted by background galaxies. In this chapter I summarise the increasing observational support for the claim that Lya photons emitted ... More

Theory of the Stark Effect for P donors in SiJan 11 2005May 09 2005We develop a multi-valley effective mass theory for substitutional donors in silicon in an inhomogeneous environment. Valley-orbit coupling is treated perturbatively. We apply the theory to the Stark effect in Si:P. The method becomes more accurate at ... More

A Faster Tableau for CTL*Jul 17 2013There have been several recent suggestions for tableau systems for deciding satisfiability in the practically important branching time temporal logic known as CTL*. In this paper we present a streamlined and more traditional tableau approach built upon ... More

Bounds to unitary evolutionMay 13 2007Upper and lower bounds are established for the survival probability $|<\psi(0)|\psi(t)>|^{2}$ of a quantum state, in terms of the energy moments $<\psi(0)|H^{n}|\psi(0)>$. Introducing a cut-off in the energy generally enables considerable improvement ... More

The evolution of oscillator wave functionsSep 20 2015We consider some of the methods that can be used to reveal the general features of how wave functions evolve with time in the harmonic oscillator. We first review the periodicity properties over each multiple of a quarter of the classical period of oscillation. ... More

Infrared Behaviour, sources and the Schwinger action principleMay 28 1994Nov 07 1994The paper describes a dynamical analogy for the renormalization group which leads to insights into its structure.

Collisional excitation of OH(6049 MHz) masers in supernova remnant - molecular cloud interactionsMar 19 2007Apr 16 2007OH (1720 MHz) masers serve as indicators of SNR - molecular cloud interaction sites. These masers are collisionally excited in warm (50-100K) shocked gas with densities of order 1e5 cm^-3 when the OH column density is in the range 1e16-1e17 cm^-2. Here ... More

A Note on the Quantum Collision and Set Equality ProblemsDec 04 2013Dec 11 2013The results showing a quantum query complexity of $\Theta(N^{1/3})$ for the collision problem do not apply to random functions. The issues are two-fold. First, the $\Omega(N^{1/3})$ lower bound only applies when the range is no larger than the domain, ... More

Comments on the observation of high multiplicity events at the LHCMay 11 2011Aug 04 2011We analyze the structure of the high multiplicity events observed by the CMS collaboration at the LHC. We argue that the bulk of the observed correlations is due to the production of a pair of jets with p_t > 15 GeV/c. We also suggest that high multiplicity ... More

High-energy hadron physics at future facilitiesNov 11 2007We outline several directions for future investigations of the three-dimensional structure of nucleon, including multiparton correlations, color transparency, and branching processes at hadron colliders and at hadron factories. We also find evidence that ... More

On distance two in Cayley graphs of Coxeter groupsApr 05 2014Apr 28 2014We consider the Cayley graph ${\rm C}(W,S)$ of a Coxeter system $(W,S)$ and describe all maximal $2$-cliques in this graph, i.e. maximal subsets in the vertex set such that the distance between any two distinct elements is equal to $2$. As an application, ... More

Isometric embeddings of half-cube graphs in half-spin GrassmanniansJun 27 2011Jan 11 2014Let $\Pi$ be a polar space of type $\textsf{D}_{n}$. Denote by ${\mathcal G}_{\delta}(\Pi)$, $\delta\in \{+,-\}$ the associated half-spin Grassmannians and write $\Gamma_{\delta}(\Pi)$ for the corresponding half-spin Grassmann graphs. In the case when ... More

On geometry of symplectic involutionsApr 20 2005Let $V$ be a $2n$-dimensional vector space over a field $F$ and $\Omega$ be a non-degenerate symplectic form on $V$. Denote by ${\mathfrak H}_{k}(\Omega)$ the set of all $2k$-dimensional subspaces $U\subset V$ such that the restriction $\Omega|_{U}$ is ... More

On embeddings of Grassmann graphs in polar Grassmann graphsMar 13 2015We establish that every embedding of a Grassmann graph in a polar Grassmann graph can be reduced to an embedding in a Grassmann graph or to an embedding in the collinearity graph of a polar space. Also, we consider $3$-embeddings, i.e. embeddings preserving ... More

The first galaxies: structure and stellar populationsApr 03 2000The Hubble Deep Fields continue to be a valuable resource for studying the distant universe, particularly at z>2 where their comoving volume becomes large enough to encompass several hundred L* galaxies or their progenitors. Here I present recent results ... More

Searches for High Redshift ClustersDec 18 1996High redshift galaxy clusters have traditionally been a fruitful place to study galaxy evolution. I review various search strategies for finding clusters at z > 1. Most efforts to date have concentrated on the environments of distant AGN. I illustrate ... More

Metrics of positive scalar curvature and generalised Morse functions, part IIOct 12 2009Jul 14 2011The surgery technique of Gromov and Lawson may be used to construct families of positive scalar curvature metrics which are parameterised by Morse functions. This has played an important role in the study of the space of metrics of positive scalar curvature ... More

Holographic Renormalisation and the Electroweak Precision ParametersMar 15 2010Oct 11 2010We study the effects of holographic renormalisation on an AdS/QCD inspired description of dynamical electroweak symmetry breaking. Our model is a 5D slice of AdS_5 geometry containing a bulk scalar and SU(2) times SU(2) gauge fields. The scalar field ... More

Astronomical Seeing from the Summits of the Antarctic PlateauDec 04 2001Jan 30 2002From the South Pole, microthermal turbulence within a narrow surface boundary layer some 200m thick provides the dominant contribution to the astronomical seeing. We present results for the seeing at a wavelength of 2.4um. The narrow turbulence layer ... More

Fluctuations and Bubble Dynamics in First-Order Phase TransitionsJun 28 1996Sep 26 1996We numerically examine the effect of thermal fluctuations on a first-order phase transition in 2+1 dimensions. By focusing on the expansion of a single bubble we are able to calculate changes in the bubble wall's velocity as well as changes in its structure ... More

Critical Exponents without the Epsilon ExpansionMar 22 1994We argue that the sharp-cutoff Wilson renormalization group provides a powerful tool for the analysis of second-order and weakly first-order phase transitions. In particular, in a computation no harder than the calculation of the 1-loop effective potential, ... More

Color superconducting quark matter in compact starsOct 11 2001When nuclear matter reaches a high enough density, we expect that the nucleons will overlap so much as to lose their separate identities, and merge into quark matter. In this talk I will review some theoretical expectations and speculations about quark ... More

Quantum Field Theory: Spin One HalfSep 02 2004This is a draft version of Part II of a three-part textbook on quantum field theory.

Axions: Past, Present, and FutureOct 17 2002I give a pedagogical and historical introduction to axion physics, and briefly review the present status of axions in our understanding of particle physics and cosmology. This is a contribution to Continuous Advances in QCD 2002/Arkadyfest, held in honor ... More

Is Purity Eternal?Jun 12 1992Jul 08 1993Phenomenological and formal restrictions on the evolution of pure into mixed states are discussed. In particular, it is argued that, if energy is conserved, loss of purity is incompatible with the weakest possible form of Lorentz covariance.

Thermal Abundances of Heavy ParticlesJan 11 2000Mar 23 2000Matsumoto and Yoshimura [hep-ph/9910393] have argued that there are loop corrections to the number density of heavy particles (in thermal equilibrium with a gas of light particles) that are not Boltzmann suppressed by a factor of e^(-M/T) at temperatures ... More

Residual properties of 1-relator groupsJan 16 2010This is a survey of two papers joint with A. Borisov and a paper joint with I. Spakulova. It is based on my lectures at the conference "Groups St. Andrews 2009", Bath (August 2009). We prove that almost all 1-related groups with at least 3 generators ... More

The Rapid Decay property and centroids in groupsMay 05 2014Dec 17 2015This is a survey of methods of proving or disproving the Rapid Decay property in groups. We present a centroid property of group actions on metric spaces. That property is a generalized (and corrected) version of the property (**)-relative hyperbolicity" ... More

Aspherical groups and manifolds with extreme propertiesMar 20 2011Apr 26 2011We prove that every finitely generated group with recursive aspherical presentation embeds into a group with finite aspherical presentation. This and several known facts about groups and manifolds imply that there exists a 4-dimensional closed aspherical ... More

Algorithmic and asymptotic properties of groupsFeb 10 2006This is a survey of the recent work in algorithmic and asymptotic properties of groups. I discuss Dehn functions of groups, complexity of the word problem, Higman embeddings, and constructions of finitely presented groups with extreme properties (monsters). ... More

Nonlinear Harmonic Forms and an Indefinite Bochner FormulaNov 01 2014Oct 21 2015We introduce the study of nonlinear harmonic forms. These are forms which minimize the $L_2$ energy in a cohomology class subject to a nonlinear constraint. In this note, we include only motivations and the most basic existence results. We also introduce ... More

Large Rapidity Gap Events in Deep Inelastic ScatteringJan 31 1997Large Rapidity Gap Events in Deep Inelastic Scattering are discussed in terms of lightcone wave functions for quarks and gluons inside the photon. It is shown that this approach is consistent with earlier, conventional Feynman diagram calculations. An ... More

Traceable 2D finite-element simulation of the whispering-gallery modes of axisymmetric electromagnetic resonatorsNov 09 2006Mar 19 2007This paper explains how a popular, commercially-available software package for solving partial-differential-equations (PDEs), as based on the finite-element method (FEM), can be configured to calculate, efficiently, the frequencies and fields of the whispering-gallery ... More

The Deformation Space of Calabi-Yau n-folds with canonical singularities can be obstructedFeb 25 1994This paper gives a simple example of a family of Calabi-Yaus of any dimension with canonical singularities of dimension one, whose Kuranishi space is singular. Thus the Bogomolov-Tian-Todorov unobstructedness theorem is not true for Calabi-Yaus with canonical ... More

Motions of Classical Charged TachyonsMar 13 2002It is shown by numerical simulation that classical charged tachyons have self-orbiting helical solutions in a narrow neighborhood of certain discrete values for the velocity when the electromagnetic interaction is described by Feynman-Wheeler electrodynamics. ... More

The Lorentz-Dirac equation in complex space-timeSep 20 2011Aug 24 2012A hypothetical equation of motion is proposed for Kerr-Newman particles. It is obtained by analytic continuation of the Lorentz-Dirac equation into complex space-time. A new class of "runaway" solutions are found which are similar to Zitterbewegung. Electromagnetic ... More

A Dynamical Theory of Markovian DiffusionOct 08 2001A dynamical treatment of Markovian diffusion is presented and several applications discussed. The stochastic interpretation of quantum mechanics is considered within this framework. A model for Brownian movement which includes second order quantum effects ... More

A Seifert-van Kampen Theorem for Legendrian Submanifolds and Exact Lagrangian CobordismsNov 11 2015We prove a Seifert-van Kampen theorem for Legendrian submanifolds and exact Lagrangian cobordisms, and use it to calculate the change in the DGA caused by critical Legendrian ambient surgery.

Revstack sort, zigzag patterns, descent polynomials of $t$-revstack sortable permutations, and Steingrímsson's sorting conjectureApr 05 2014In this paper we examine the sorting operator $T(LnR)=T(R)T(L)n$. Applying this operator to a permutation is equivalent to passing the permutation reversed through a stack. We prove theorems that characterise $t$-revstack sortability in terms of patterns ... More

X-ray Constraints on Cluster Magnetic FieldsJul 05 1998Lower limits to the intracluster magnetic field are derived from modeling broad band X-ray spectra of 6 galaxy clusters with radio halos (A401, A754, A1367, Coma (A1656), A2256, and A2319). The 0.7 - 10 keV spectra for all clusters were obtained with ... More

Strangeness production in small and large collisions systems at RHICApr 13 2006We present measurements of strange and multi-strange hadrons in p+p collisions at $\sqrt{s}$= 200 GeV measured by STAR. We will compare these preliminary results to leading-order (LO) and next-to-leading order (NLO) perturbative QCD models widely believed ... More

Heavy flavor measurements using high-pt electrons in the ALICE EMCalJun 07 2010Heavy flavor hadrons, i.e. those containing charm and bottom quarks, will be abundantly produced at the LHC and are important probes of the Quark-Gluon Plasma (QGP). Of particular interest is the investigation of parton energy loss in the medium. Using ... More

Non-backtracking random walks and a weighted Ihara's theoremMar 17 2016We study the mixing rate of non-backtracking random walks on graphs by looking at non-backtracking walks as walks on the directed edges of a graph. A result known as Ihara's Theorem relates the adjacency matrix of a graph to a matrix related to non-backtracking ... More

Battling the Digital Forensic Backlog through Data DeduplicationOct 02 2016In everyday life. Technological advancement can be found in many facets of life, including personal computers, mobile devices, wearables, cloud services, video gaming, web-powered messaging, social media, Internet-connected devices, etc. This technological ... More

Toric Degenerations and Batyrev-Borisov DualityJun 09 2004Jul 22 2005This is an extended example of the study of mirror symmetry via log schemes and the discrete Legendre transform on affine manifolds, introduced by myself and Bernd Siebert in "Mirror Symmetry via Logarithmic Degeneration Data I" (math.AG/0309070). In ... More

Topological Mirror SymmetrySep 02 1999Nov 03 1999This paper focuses on a topological version on the Strominger-Yau-Zaslow mirror symmetry conjecture. Roughly put, the SYZ conjecture suggests that mirror pairs of Calabi-Yau manifolds are related by the existence of dual special Lagrangian torus fibrations. ... More

Special Lagrangian Fibrations II: GeometrySep 14 1998Feb 25 1999We continue the study of the Strominger-Yau-Zaslow mirror symmetry conjecture. Roughly put, this states that if two Calabi-Yau manifolds X and Y are mirror partners, then X and Y have special Lagrangian torus fibrations which are dual to each other. Much ... More

Differential Geometry on SU(3) with Applications to Three State SystemsJul 28 1998The left and right invariant vector fields are calculated in an ``Euler angle'' type parameterization for the group manifold of SU(3), referred to here as Euler coordinates. The corresponding left and right invariant one-forms are then calculated. This ... More

Modelling the Role of Nitric Oxide in Cerebral AutoregulationDec 30 2015Malfunction of the system which regulates the bloodflow in the brain is a major cause of stroke and dementia, costing many lives and many billions of pounds each year in the UK alone. This regulatory system, known as cerebral autoregulation, has been ... More

Visualising Large Datasets in TOPCAT v4Oct 24 2014TOPCAT is a widely used desktop application for manipulation of astronomical catalogues and other tables, which has long provided fast interactive visualisation features including 1, 2 and 3-d plots, multiple datasets, linked views, color coding, transparency ... More

The classification of Rank 3 Reflective Hyperbolic Lattices over Z[\sqrt{2}]Dec 03 2015There are 432 strongly squarefree symmetric bilinear forms of signature $(2,1)$ defined over $\Z[\sqrt{2}]$ whose integral isometry groups are generated up to finite index by finitely many reflections. We adapted Allcock's method (based on Nikulin's) ... More

Separation of a Lower Dimensional Free Boundary in a Two Phase ProblemMar 28 2012This paper studies local properties of a two phase free boundary problem for the fractional Laplacian. The main result states that the two free boundaries of the positive and negativity sets cannot touch.

On the Numerical Stability of the Einstein EquationsAug 08 2000We perform a von Neumann stability analysis on a common discretization of the Einstein equations. The analysis is performed on two formulations of the Einstein equations, namely, the standard ADM formulation and the conformal-traceless (CT) formulation. ... More

Topological modular and automorphic formsJan 23 2019Feb 06 2019This article is a brief survey of the theory of topological modular forms (TMF) and the theory of topological automorphic forms (TAF). It will be a chapter in forthcoming "Handbook of Homotopy Theory" edited by Haynes Miller.

The weak Bernoulli property for matrix Gibbs statesJun 13 2018Oct 10 2018We study the ergodic properties of a class of measures on $\Sigma^{\mathbb{Z}}$ for which $\mu_{\mathcal{A},t}[x_{0}\cdots x_{n-1}]\approx e^{-nP}\left \|A_{x_{0}}\cdots A_{x_{n-1}}\right \| ^{t}$, where $\mathcal{A}=(A_{0}, \ldots , A_{M-1})$ is a collection ... More

Connectedness of projective codes in the Grassmann graphJun 07 2018Jun 13 2018Using the concept of projective systems for linear codes and elementary linear algebra, we show that projective $[n,k]_q$ codes form a connected subgraph in the Grassmann graph consisting of $k$-dimensional subspaces of an $n$-dimensional vector space ... More

The Space of Positive Scalar Curvature Metrics on a Manifold with BoundaryNov 10 2014Jul 02 2015We study the space of Riemannian metrics with positive scalar curvature on a compact manifold with boundary. These metrics extend a fixed boundary metric and take a product structure on a collar neighbourhood of the boundary. We show that the weak homotopy ... More

Mirror symmetry for P^2 and tropical geometryMar 08 2009Oct 16 2009This paper explores the relationship between mirror symmetry for P^2, at the level of big quantum cohomology, and tropical geometry. The mirror of P^2 is typically taken to be ((C^*)^2,W), where W is a Landau-Ginzburg potential of the form x+y+1/xy. The ... More

Schroedinger's equation and "bike tracks" - a connectionMay 07 2014This note demonstrates an equivalence between two classes of objects: the stationary Schroedinger equation on the one hand and the "bicycle tracks" on the other.

Boolean-type Retractable State-finite Automata Without OutputsOct 01 2015Oct 05 2015An automaton $\bf A$ is called a retractable automaton if, for every subautomaton $\bf B$ of $\bf A$, there is at least one homomorphism of $\bf A$ onto $\bf B$ which leaves the elements of $B$ fixed (such homomorphism is called a retract homomorphism ... More

Linear Fractionally Damped OscillatorAug 12 2009In this paper the linearly damped oscillator equation is considered with the damping term generalized to a Caputo fractional derivative. The order of the derivative being considered is 0 less than or equal to nu which is less than or equal to 1 . At the ... More

Joint and conditional estimation of tagging and parsing modelsMay 07 2001This paper compares two different ways of estimating statistical language models. Many statistical NLP tagging and parsing models are estimated by maximizing the (joint) likelihood of the fully-observed training data. However, since these applications ... More

Type-driven semantic interpretation and feature dependencies in R-LFGNov 21 1997Once one has enriched LFG's formal machinery with the linear logic mechanisms needed for semantic interpretation as proposed by Dalrymple et. al., it is natural to ask whether these make any existing components of LFG redundant. As Dalrymple and her colleagues ... More

Memoization of Top Down ParsingApr 25 1995This paper discusses the relationship between memoized top-down recognizers and chart parsers. It presents a version of memoization suitable for continuation-passing style programs. When applied to a simple formalization of a top-down recognizer it yields ... More

Fuzzy Limits of FunctionsDec 22 2006The goal of this work is to introduce and study fuzzy limits of functions. Two approaches to fuzzy limits of a function are considered. One is based on the concept of a fuzzy limit of a sequence, while another generalizes the conventional epsilon-delta ... More

Special Lagrangian ConesMay 17 2000We study special Lagrangian cones in $\C^n$ with isolated singularities. Our main result constructs an infinite family of special Lagrangian cones in $\C^3$ each of which has a toroidal link. We obtain a detailed geometric description of these tori. We ... More

A Fractional Free Boundary Problem Related to a Plasma ProblemJul 22 2015We study a fractional analogue of a plasma problem arising from physics. Specifically, for a fixed bounded domain $\Omega$ we study solutions to the eigenfunction equation \[ (- \Delta)^s u = \lambda(u- \gamma)_+ \] with $u \equiv 0$ on $\partial \Omega$. ... More

Languages, Algorithms, Procedures, Calculi, and MetalogicJan 04 2007Logicians study and apply a multiplicity of various logical systems. Consequently, there is necessity to build foundations and common grounds for all these systems. This is done in metalogic. Like metamathematics studies formalized mathematical theories, ... More

Excited against the tide: A random walk with competing driftsJan 28 2009We study a random walk that has a drift $\frac{\beta}{d}$ to the right when located at a previously unvisited vertex and a drift $\frac{\mu}{d}$ to the left otherwise. We prove that in high dimensions, for every $\mu$, the drift to the right is a strictly ... More

Classification of Vector-Valued modular Forms of Dimension less than SixMar 22 2010The first half of this dissertation reviews the basic notion of vector-valued modular forms and its connection to differential equations. The main purpose of the dissertation is to classify spaces of vector-valued modular forms associated to irreducible, ... More

Characterization of isometric embeddings of Grassmann graphsMar 01 2012Let $V$ be an $n$-dimensional left vector space over a division ring $R$. We write ${\mathcal G}_{k}(V)$ for the Grassmannian formed by $k$-dimensional subspaces of $V$ and denote by $\Gamma_{k}(V)$ the associated Grassmann graph. Let also $V'$ be an ... More

Fourier coefficients of three-dimensional vector-valued modular formsJan 25 2012Mar 31 2015A thorough analysis is made of the Fourier coefficients for vector-valued modular forms associated to three-dimensional irreducible representations of the modular group. In particular, the following statement is verified for all but a finite number of ... More

A lower bound for Torelli-K-quasiconformal homogeneitySep 10 2013Mar 25 2014A closed hyperbolic Riemann surface M is said to be K-quasiconformally homogeneous if there exists a transitive family F of K-quasiconformal homeomorphisms. Further, if all [f] in F act trivially on H1(M;Z), we say M is Torelli-K-quasiconformally homogeneous. ... More

Vanishing theorems and character formulas for the Hilbert scheme of points in the planeJan 16 2002Earlier we showed that the Hilbert scheme of $n$ points in the plane can be identified with the Hilbert scheme of regular $S_n$ orbits on $C^{2n}$. Using this result, together with a recent theorem of Bridgeland, King and Reid on the generalized McKay ... More

Free left and right adequate semigroupsApr 06 2009May 08 2009Recent research of the author has given an explicit geometric description of free (two-sided) adequate semigroups and monoids, as sets of labelled directed trees under a natural combinatorial multiplication. In this paper we show that there are natural ... More

Topological Complexity and non-immersions of real projective spaceDec 07 2009Apr 14 2011This article has been withdrawn due to an error in a proof of the main result.

The four genus of a link, Levine-Tristram signatures and satellitesMay 22 2016Sep 12 2016We give a new proof that the Levine-Tristram signatures of a link give lower bounds for the minimal sum of the genera of a collection of oriented, locally flat, disjointly embedded surfaces that the link can bound in the 4-ball. We call this minimal sum ... More

Homotopy theory of comodules over a Hopf algebroidJan 21 2003Given a good homology theory E and a topological space X, the E-homology of X is not just an E_{*}-module but also a comodule over the Hopf algebroid (E_{*}, E_{*}E). We establish a framework for studying the homological algebra of comodules over a well-behaved ... More

Base subsets of symplectic GrassmanniansFeb 27 2006Let $V$ and $V'$ be $2n$-dimensional vector spaces over fields $F$ and $F'$. Let also $\Omega: V\times V\to F$ and $\Omega': V'\times V'\to F'$ be non-degenerate symplectic forms. Denote by $\Pi$ and $\Pi'$ the associated $(2n-1)$-dimensional projective ... More

Order preserving transformations of the Hilbert grassmannian: complex caseApr 23 2007Let $H$ be a separable complex Hilbert space. Denote by ${\mathcal G}_{\infty}(H)$ the Grassmannian consisting of closed linear subspaces with infinite dimension and codimension. This Grassmannian is partially ordered by the inclusion relation. We show ... More

The Common HOL PlatformJul 31 2015The Common HOL project aims to facilitate porting source code and proofs between members of the HOL family of theorem provers. At the heart of the project is the Common HOL Platform, which defines a standard HOL theory and API that aims to be compatible ... More