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Droplet phase in a nonlocal isoperimetric problem under confinementSep 12 2016Oct 23 2018We address small volume-fraction asymptotic properties of a nonlocal isoperimetric functional with a confinement term, derived as the sharp interface limit of a variational model for self-assembly of diblock copolymers under confinement by nanoparticle ... More

Symmetric vortices for two-component Ginzburg-Landau systemsNov 24 2012May 01 2013We study Ginzburg--Landau equations for a complex vector order parameter Psi=(psi_+,psi_-). We consider symmetric (equivariant) vortex solutions in the plane R^2 with given degrees n_\pm, and prove existence, uniqueness, and asymptotic behavior of solutions ... More

Stability of symmetric vortices for two-component Ginzburg-Landau systemsAug 05 2013We study Ginzburg-Landau equations for a complex vector order parameter. We consider the Dirichlet problem in the disk in the plane with a symmetric, degree-one boundary condition, and study its stability, in the sense of the spectrum of the second variation ... More

Vortex structure in p-wave superconductorsNov 13 2014Nov 17 2014We study vortices in p-wave superconductors in a Ginzburg-Landau setting. The state of the superconductor is described by a pair of complex wave functions, and the p-wave symmetric energy functional couples these in both the kinetic (gradient) and potential ... More

Weak Anchoring for a Two-Dimensional Liquid CrystalMay 13 2014Aug 15 2014We study the weak anchoring condition for nematic liquid crystals in the context of the Landau-De Gennes model. We restrict our attention to two dimensional samples and to nematic director fields lying in the plane, for which the Landau-De Gennes energy ... More

Minimizers of the Lawrence-Doniach Functional with Oblique Magnetic FieldsSep 08 2010We study minimizers of the Lawrence--Doniach energy, which describes equilibrium states of superconductors with layered structure, assuming Floquet-periodic boundary conditions. Specifically, we consider the effect of a constant magnetic field applied ... More

Thin film limits for Ginzburg--Landau with strong applied magnetic fieldsJun 30 2009Nov 06 2009In this work, we study thin-film limits of the full three-dimensional Ginzburg-Landau model for a superconductor in an applied magnetic field oriented obliquely to the film surface. We obtain Gamma-convergence results in several regimes, determined by ... More

Minimizers of the Landau-de Gennes energy around a spherical colloid particleApr 02 2015May 04 2015We consider energy minimizing configurations of a nematic liquid crystal around a spherical colloid particle, in the context of the Landau-de Gennes model. The nematic is assumed to occupy the exterior of a ball of radius r_0, satisfy homeotropic weak ... More

A machine-assisted view of paraconsistencyDec 16 2013For a newcomer, paraconsistent logics can be difficult to grasp. Even experts in logic can find the concept of paraconsistency to be suspicious or misguided, if not actually wrong. The problem is that although they usually have much in common with more ... More

On compound vortices in a two-component Ginzburg-Landau functionalNov 24 2012We study the structure of vortex solutions in a Ginzburg-Landau system for two complex valued order parameters. We consider the Dirichlet problem in the disk in R^2 with symmetric, degree-one boundary condition, as well as the associated degree-one entire ... More

Sharp interface limit of an energy modelling nanoparticle-polymer blendsAug 05 2015Jan 22 2016We identify the $\Gamma$-limit of a nanoparticle-polymer model as the number of particles goes to infinity and as the size of the particles and the phase transition thickness of the polymer phases approach zero. The limiting energy consists of two terms: ... More

Singular Limits for Thin Film Superconductors in Strong Magnetic Fields - Maan Field Model for Thin FilmsSep 17 2012We consider singular limits of the three-dimensional Ginzburg-Landau functional for a superconductor with thin-film geometry, in a constant external magnetic field. The superconducting domain has characteristic thickness on the scale $\eps>0$, and we ... More

Gamma-convergence of 2D Ginzburg-Landau functionals with vortex concentration along curvesJun 26 2009We study the variational convergence of a family of two-dimensional Ginzburg-Landau functionals arising in the study of superfluidity or thin-film superconductivity, as the Ginzburg-Landau parameter epsilon tends to 0. In this regime and for large enough ... More

Spherical particle in a nematic liquid crystal under an external field: the Saturn ring regimeOct 13 2017We consider a nematic liquid crystal occupying the exterior region in R^3 outside of a spherical particle, with radial strong anchoring. Within the context of the Landau-de Gennes theory, we study minimizers subject to a strong external field, modelled ... More

Thin Film Liquid Crystals with Oblique Anchoring and BoojumsJul 10 2019We study a two-dimensional variational problem which arises as a thin-film limit of the Landau-de Gennes energy of nematic liquid crystals. We impose an oblique angle condition for the nematic director on the boundary, via boundary penalization (weak ... More

Ground-states for the liquid drop and TFDW models with long-range attractionJul 20 2017Sep 21 2017We prove that both the liquid drop model in $\mathbb{R}^3$ with an attractive background nucleus and the Thomas-Fermi-Dirac-von Weizs\"{a}cker (TFDW) model attain their ground-states \emph{for all} masses as long as the external potential $V(x)$ in these ... More

A Degenerate Isoperimetric Problem and Traveling Waves to a Bi-stable Hamiltonian SystemApr 02 2015Sep 12 2015We analyze a non-standard isoperimetric problem in the plane associated with a metric having degenerate conformal factor at two points. Under certain assumptions on the conformal factor, we establish the existence of curves of least length under a constraint ... More

Droplet phase in a nonlocal isoperimetric problem under confinementSep 12 2016Sep 23 2016We address small volume-fraction asymptotic properties of a nonlocal isoperimetric functional with a confinement term, derived as the sharp interface limit of a variational model for self-assembly of diblock copolymers under confinement by nanoparticle ... More

Domain walls in the coupled Gross-Pitaevskii equationsSep 05 2013A thorough study of domain wall solutions in coupled Gross-Pitaevskii equations on the real line is carried out including existence of these solutions; their spectral and nonlinear stability; their persistence and stability under a small localized potential. ... More

Droplet breakup in the liquid drop model with background potentialAug 14 2017Feb 19 2018We consider a variant of Gamow's liquid drop model, with a general repulsive Riesz kernel and a long-range attractive background potential with weight $Z$. The addition of the background potential acts as a regularization for the liquid drop model in ... More

New developments in parsing MizarApr 30 2012The Mizar language aims to capture mathematical vernacular by providing a rich language for mathematics. From the perspective of a user, the richness of the language is welcome because it makes writing texts more "natural". But for the developer, the ... More

Bound state equations in Riemannian geometryApr 30 2018We study formulations of bound state (Bethe-Salpeter) equations on arbitrary Riemannian manifolds. We obtain a hierarchy of equations for multipartice wave functions. These equations, at each number of particles, depend on certain choices of combinatorial ... More

Discrete Scalar Quantum Field TheoryOct 19 2016We begin with a description of spacetime by a 4-dimensional cubic lattice $\sscript$. It follows from this framework that the the speed of light is the only nonzero instantaneous speed for a particle. The dual space $\sscripthat$ corresponds to a cubic ... More

The Universe as a Quantum ComputerMay 04 2014This article presents a sequential growth model for the universe that acts like a quantum computer. The basic constituents of the model are a special type of causal set (causet) called a $c$-causet. A $c$-causet is defined to be a causet that is independent ... More

A covariant causal set approach to discrete quantum gravityNov 15 2013Nov 25 2013A covariant causal set (c-causet) is a causal set that is invariant under labeling. Such causets are well-behaved and have a rigid geometry that is determined by a sequence of positive integers called the shell sequence. We first consider the microscopic ... More

The Orchestral Analog of Molecular BiologyMay 26 2004Signal processing (SP) techniques convert DNA and protein sequences into information that lead to successful drug discovery. One must, however, be aware about the difference between information and entropy1. Eight other physical properties of DNA and ... More

Toy Models for Quantum Field TheoryNov 26 2018In order to better understand quantum field theory we present some toy models on finite dimensional Hilbert spaces. We discuss how these models converge to a discrete spacetime version of quantum field theory. We first define toy fermion, boson and mixed ... More

Causal set approach to discrete quantum gravityApr 25 2012We begin by describing a sequential growth model in which the universe grows one element at a time in discrete time steps. At each step, the process has the form of a causal set and the "completed" universe is given by a path consisting of a discretely ... More

Hilbert Space Representations of Decoherence Functionals and Quantum MeasuresNov 08 2010We show that any decoherence functional $D$ can be represented by a spanning vector-valued measure on a complex Hilbert space. Moreover, this representation is unique up to an isomorphism when the system is finite. We consider the natural map $U$ from ... More

Communication on the letter: "Evolutionary Conservation of Motif Constituents in the Yeast Protein Interaction Network."Oct 16 2003Former work on an application of order-disorder theory is recalled as a vehicle to add further development and significance to the recent paper on motifs in protein interactions.

Discrete Spacetime Quantum Field TheoryApr 05 2017This paper begins with a theoretical explanation of why spacetime is discrete. The derivation shows that there exists an elementary length which is essentially Planck's length. We then show how the existence of this length affects time dilation in special ... More

A Characterization For Entangled VectorsFeb 23 2019This article presents a simple characterization for entangled vectors in a finite dimensional Hilbert space $H$. The characterization is in terms of the coefficients of an expansion of the vector relative to an orthonormal basis for $H$. This simple necessary ... More

Labeled Causets in Discrete Quantum GravityMar 31 2014We point out that labeled causets have a much simpler structure than unlabeled causets. For example, labeled causets can be uniquely specified by a sequence of integers. Moreover, each labeled causet processes a unique predecessor and hence has a unique ... More

Existence of continuous euclidean embeddings for a weak class of ordersAug 03 2015Aug 09 2016We prove that if $X$ is a topological space that admits Debreu's classical utility theorem (eg.\ $X$ is separable and connected, second countable, etc.), then order relations on $X$ satisfying milder completeness conditions can be continuously embedded ... More

Measuring Prestige in Online Social NetworksJul 25 2014We study the locally-defined social capital metric of Palasek (2013) for determining individuals' prestige within an online social network. From it we derive an equivalent global measure by considering random walks over the network itself. This result ... More

Properties of solutions of the "naive" functional Schroedinger equation for QCDJun 02 2018In this paper we consider the simplest functional Schroedinger equation of a quantum field theory (in particular QCD) and study its solutions. We observe that the solutions to this equation must possess a number of properties. Its Taylor coefficients ... More

k-Nearest Neighbour Classification of Datasets with a Family of DistancesNov 29 2015The $k$-nearest neighbour ($k$-NN) classifier is one of the oldest and most important supervised learning algorithms for classifying datasets. Traditionally the Euclidean norm is used as the distance for the $k$-NN classifier. In this thesis we investigate ... More

A note on Veraverbeke's theoremOct 30 2014We give an elementary probabilistic proof of Veraverbeke's Theorem for the asymptotic distribution of the maximum of a random walk with negative drift and heavy-tailed increments. The proof gives insight into the principle that the maximum is in general ... More

Non-Cooperativity in Bayesian Social LearningJul 02 2014We describe a Bayesian model for social learning of a random variable in which agents might observe each other over a directed network. The outcomes produced are compared to those from a model in which observations occur randomly over a complete graph. ... More

A Unified Approach to Discrete Quantum GravityMar 21 2014May 06 2014This paper is based on a covariant causal set (c-causet) approach to discrete quantum gravity. A c-causet is a partially ordered set $(x,<)$ that is invariant under labeling. We first consider the microscopic picture which describes the detailed structure ... More

On the Strategic Allocation of Social GratificationSep 09 2013Jun 16 2016Members of social networks are given opportunities to bestow positive recognition upon one another by means of constructs such as "likes" and "retweets." Although recipients no doubt experience utility from these actions, one might question why these ... More

A Dynamics for Discrete Quantum GravityMar 02 2013This paper is based on the causal set approach to discrete quantum gravity. We first describe a classical sequential growth process (CSGP) in which the universe grows one element at a time in discrete steps. At each step the process has the form of a ... More

Discrete Quantum Gravity Is Not IsometricSep 05 2011Dec 04 2011We show that if a discrete quantum gravity is not classical, then it cannot be generated by an isometric dynamics. In particular, we show that if the quantum measure {\mu} (or equivalently the decoherence functional) is generated by an isometric dynamics, ... More

The Elementary Particle CubeMar 14 2017Jul 28 2017Postulating that spacetime is discrete, we assume that physical space is described by a 3-dimensional cubic lattice.The corresponding symmetry group of rotations has order 24 and motivates the introduction of a cubic shaped graph with 27 vertices and ... More

Least worst regret analysis for decision making under uncertainty, with applications to future energy scenariosAug 02 2016Least worst regret (and sometimes minimax) analysis are often used for decision making whenever it is difficult, or inappropriate, to attach probabilities to possible future scenarios. We show that, for each of these two approaches and subject only to ... More

Discrete Quantum Gravity and Quantum Field TheoryMar 08 2016We introduce a discrete 4-dimensional module over the integers that appears to have maximal symmetry. By adjoining the usual Minkowski distance, we obtain a discrete 4-dimensional Minkowski space. Forming universe histories in this space and employing ... More

Wave Equations for Discrete Quantum GravityAug 29 2015This article is based on the covariant causal set ($c$-causet) approach to discrete quantum gravity. A $c$-causet $x$ is a finite partially ordered set that has a unique labeling of its vertices. A rate of change on $x$ is described by a covariant difference ... More

An Isometric Dynamics for a Causal Set Approach to Discrete Quantum GravitySep 12 2014We consider a covariant causal set approach to discrete quantum gravity. We first review the microscopic picture of this approach. In this picture a universe grows one element at a time and its geometry is determined by a sequence of integers called the ... More

Primordial RNA Replication and Applications in PCR TechnologyMay 23 2013The emergence of self-replication and information transmission in life's origin remains unexplained despite extensive research on the topic. A hypothesis explaining the transition from a simple organic world to a complex RNA world is offered here based ... More

Convex and Sequential Effect AlgebrasFeb 05 2018We present a mathematical framework for quantum mechanics in which the basic entities and operations have physical significance. In this framework the primitive concepts are states and effects and the resulting mathematical structure is a convex effect ... More

Quantum measures and the coevent interpretationMay 13 2010Jul 24 2010This paper first reviews quantum measure and integration theory. A new representation of the quantum integral is presented. This representation is illustrated by computing some quantum (Lebesgue)${}^2$ integrals. The rest of the paper only considers finite ... More

Radiation Hydrodynamics of Line-Driven WindsAug 11 2009Aug 11 2009Dimtri Mihalas' textbooks in the 70's and 80's on "Stellar Atmospheres" and "Foundations of Radiation Hydrodynamics" helped lay the early groundwork for understanding the moving atmospheres and winds of massive, luminous stars. Indeed, the central role ... More

A note on insensitivity in stochastic networksNov 17 2006We give a simple and direct treatment of insensitivity in stochastic networks which is quite general and which provides probabilistic insight into the phenomenon. In the case of multi-class networks, the results generalise those of Bonald and Proutiere ... More

Searches for MSSM Higgs bosons at ATLAS and CMSMar 17 2013The Minimal Supersymmetric extension of the Standard Model (MSSM) predicts the existence of three neutral and two charged Higgs bosons. Searches for these MSSM Higgs bosons are presented, based on proton-proton collisions recorded in 2011 and 2012 by ... More

A Reputation-Based Model for Decision-Making in Online Social NetworksSep 13 2014The online exchange of social recognition including, for instance, the Facebook "like" appears to produce a scarce allocation without a clear utility function defined for anyone involved. Given the importance attached to such digital commodities by both ... More

Dependencies in Formal Mathematics: Applications and Extraction for Coq and MizarSep 16 2011Mar 16 2012Two methods for extracting detailed formal dependencies from the Coq and Mizar system are presented and compared. The methods are used for dependency extraction from two large mathematical repositories: the Coq Repository at Nijmegen and the Mizar Mathematical ... More

Toward a structure theory for Lorenzen dialogue gamesNov 08 2013Dec 16 2013Lorenzen dialogues provide a two-player game formalism that can characterize a variety of logics: each set $S$ of rules for such a game determines a set $\mathcal{D}(S)$ of formulas for which one of the players (the so-called Proponent) has a winning ... More

Escape to Mizar for ATPsApr 30 2012May 01 2012We announce a tool for mapping derivations of the E theorem prover to Mizar proofs. Our mapping complements earlier work that generates problems for automated theorem provers from Mizar inference checking problems. We describe the tool, explain the mapping, ... More

Eliciting implicit assumptions of proofs in the MIZAR Mathematical Library by property omissionSep 03 2011When formalizing proofs with interactive theorem provers, it often happens that extra background knowledge (declarative or procedural) about mathematical concepts is employed without the formalizer explicitly invoking it, to help the formalizer focus ... More

Sentence complexity of theorems in MizarNov 08 2013As one of the longest-running computer-assisted formal mathematics projects, large tracts of mathematical knowledge have been formalized with the help of the Mizar system. Because Mizar is based on first-order classical logic and set theory, and because ... More

Optimal scheduling of energy storage resourcesAug 17 2018Jan 15 2019It is likely that electricity storage will play a significant role in the balancing of future energy systems. A major challenge is then that of how to assess the contribution of storage to capacity adequacy, i.e. to the ability of such systems to meet ... More

A Stochastic Heisenberg InequalityJun 17 2003An analogue of the Fourier transform will be introduced for all square integrable continuous martingale processes whose quadratic variation is deterministic. Using this transform we will formulate and prove a stochastic Heisenberg inequality.

The Quadrahelix: A Nearly Perfect Loop of TetrahedraOct 02 2016In 1958, S. \'Swierczkowski proved that there cannot be a closed loop of congruent interior-disjoint regular tetrahedra that meet face-to-face. Such closed loops do exist for the other four regular polyhedra. It has been conjectured that, for any positive ... More

The Most Luminous SupernovaeFeb 15 2016Mar 13 2016Recent observations have revealed an amazing diversity of extremely luminous supernovae, seemingly increasing in radiant energy without bound. We consider here the physical limits of what existing models can provide for the peak luminosity and total radiated ... More

When a Tweet is Actually Sexist. A more Comprehensive Classification of Different Online Harassment Categories and The Challenges in NLPFeb 27 2019Sexism is very common in social media and makes the boundaries of freedom tighter for feminist and female users. There is still no comprehensive classification of sexism attracting natural language processing techniques. Categorizing sexism in social ... More

Roget's Thesaurus: a Lexical Resource to TreasureApr 01 2012This paper presents the steps involved in creating an electronic lexical knowledge base from the 1987 Penguin edition of Roget's Thesaurus. Semantic relations are labelled with the help of WordNet. The two resources are compared in a qualitative and quantitative ... More

Inferring hot-star-wind acceleration from Line Profile VariabilityNov 11 2004The migration of profile sub-peaks identified in time-monitored optical emission lines of Wolf-Rayet star spectra provides a direct diagnostic of the dynamics of their stellar winds via a measured line-of-sight velocity change per unit time. Inferring ... More

Boolean Inner product Spaces and Boolean MatricesFeb 08 2009This article discusses the concept of Boolean spaces endowed with a Boolean valued inner product and their matrices. A natural inner product structure for the space of Boolean n-tuples is introduced. Stochastic boolean vectors and stochastic and unitary ... More

Vortices with antiferromagnetic cores in the SO(5) theory of high temperature superconductivityDec 16 1998Apr 16 1999We consider the problem of superconducting Ginzburg-Landau (G-L) vortices with antiferromagnetic cores which arise in Zhang's SO(5) model of antiferromagnetism (AF) and high temperature superconductivity (SC). This problem was previously considered by ... More

Tipi: A TPTP-based theory development environment emphasizing proof analysisApr 04 2012Apr 13 2012In some theory development tasks, a problem is satisfactorily solved once it is shown that a theorem (conjecture) is derivable from the background theory (premises). Depending on one's motivations, the details of the derivation of the conjecture from ... More

Premise Selection for Mathematics by Corpus Analysis and Kernel MethodsAug 17 2011Apr 12 2012Smart premise selection is essential when using automated reasoning as a tool for large-theory formal proof development. A good method for premise selection in complex mathematical libraries is the application of machine learning to large corpora of proofs. ... More

The optimal control of storage for arbitrage and buffering, with energy applicationsSep 18 2015We study the optimal control of storage which is used for both arbitrage and buffering against unexpected events, with particular applications to the control of energy systems in a stochastic and typically time-heterogeneous environment. Our philosophy ... More

Visual Word Selection without Re-Coding and Re-PoolingJul 23 2014The Bag-of-Words (BoW) representation is widely used in computer vision. The size of the codebook impacts the time and space complexity of the applications that use BoW. Thus, given a training set for a particular computer vision task, a key problem is ... More

Very Low Energy Supernovae from Neutrino Mass LossMar 20 2013The continuing difficulty of achieving a reliable explosion in simulations of core-collapse supernovae, especially for more massive stars, has led to speculation concerning the observable transients that might be produced if such a supernova fails. Even ... More

Loss networksMar 03 2009We review the theory of loss networks, including recent results on their dynamical behaviour. We give also some new results.

The maximum on a random time interval of a random walk with long-tailed increments and negative driftMar 18 2013We study the asymptotics for the maximum on a random time interval of a random walk with a long-tailed distribution of its increments and negative drift. We extend to a general stopping time a result by Asmussen (1998), simplify its proof, and give some ... More

The Quadrahelix: A Nearly Perfect Loop of TetrahedraOct 02 2016Nov 07 2016In 1958, S. \'Swierczkowski proved that there cannot be a closed loop of congruent interior-disjoint regular tetrahedra that meet face-to-face. Such closed loops do exist for the other four regular polyhedra. It has been conjectured that, for any positive ... More

Some problems with two axiomatizations of discussive logicMar 30 2014Problems in two axiomatizations of Ja\'skowski's discussive (or discursive) logic D2 are considered. A recent axiomatization of D2 and completeness proof relative to D2's intended semantics seems to be mistaken because some formulas valid according to ... More

Dialogues for proof searchMay 08 2014Dialogue games are a two-player semantics for a variety of logics, including intuitionistic and classical logic. Dialogues can be viewed as a kind of analytic calculus not unlike tableaux. Can dialogue games be an effective foundation for proof search ... More

mizar-items: Exploring fine-grained dependencies in the Mizar Mathematical LibraryJul 24 2011Sep 19 2011The Mizar Mathematical Library (MML) is a rich database of formalized mathematical proofs (see http://mizar.org). Owing to its large size (it contains more than 1100 "articles" summing to nearly 2.5 million lines of text, expressing more than 50000 theorems ... More

Complete independence of an axiom system for central translationsNov 08 2013A recently proposed axiom system for Andr\'e's central translation structures is improved upon. First, one of its axioms turns out to be dependent (derivable from the other axioms). Without this axiom, the axiom system is indeed independent. Second, whereas ... More

Exploring Steinitz-Rademacher polyhedra: A challenge for automated reasoning toolsJan 05 2014Jan 08 2014This note reports on some experiments, using a handful of standard automated reasoning tools, for exploring Steinitz-Rademacher polyhedra, which are models of a certain first-order theory of incidence structures. This theory and its models, even simple ... More

A Wiki for Mizar: Motivation, Considerations, and Initial PrototypeMay 25 2010Formal mathematics has so far not taken full advantage of ideas from collaborative tools such as wikis and distributed version control systems (DVCS). We argue that the field could profit from such tools, serving both newcomers and experts alike. We describe ... More

MatlabMPIMay 06 2003The true costs of high performance computing are currently dominated by software. Addressing these costs requires shifting to high productivity languages such as Matlab. MatlabMPI is a Matlab implementation of the Message Passing Interface (MPI) standard ... More

Asymptotics for the maximum of a modulated random walk with heavy-tailed incrementsMar 18 2013We consider asymptotics for the maximum of a modulated random walk whose increments $\xi_n^{X_n}$ are heavy-tailed. Of particular interest is the case where the modulating process $X$ is regenerative. Here we study also the maximum of the recursion given ... More

The Progenitor Stars of Gamma-Ray BurstsAug 08 2005Those massive stars that, during their deaths, give rise to gamma-ray bursts (GRBs) must be endowed with an unusually large amount of angular momentum in their inner regions, one to two orders of magnitude greater than the ones that make common pulsars. ... More

Asymptotic behaviour of solutions to fractional diffusion-convection equationsMar 08 2017Feb 13 2018We consider a convection-diffusion model with linear fractional diffusion in the sub-critical range. We prove that the large time asymptotic behavior of the solution is given by the unique entropy solution of the convective part of the equation. The proof ... More

Stochastic sequences with a regenerative structure that may depend both on the future and on the pastDec 06 2012Mar 18 2013Many regenerative arguments in stochastic processes use random times which are akin to stopping times, but which are determined by the future as well as the past behaviour of the process of interest. Such arguments based on "conditioning on the future" ... More

Proof identity for mere mortalsMar 04 2014The proof identity problem asks: When are two proofs the same? The question naturally occurs when one reflects on mathematical practice. The problem understandably can be seen as a challenge for mathematical logic, and indeed various perspectives on the ... More

Sharpening independence results for Huntington's affine geometryDec 16 2013We improve upon Huntington's affine geometry by showing that his independence proofs can be, in some cases, simplified. We carry out a systematic investigation of the strict notion of betweenness that Huntington employs (the three arguments are supposed ... More

Large Formal Wikis: Issues and SolutionsJul 16 2011We present several steps towards large formal mathematical wikis. The Coq proof assistant together with the CoRN repository are added to the pool of systems handled by the general wiki system described in \cite{DBLP:conf/aisc/UrbanARG10}. A smart re-verification ... More

Two-Site Quantum Random WalkMay 03 2011We study the measure theory of a two-site quantum random walk. The truncated decoherence functional defines a quantum measure $\mu_n$ on the space of $n$-paths, and the $\mu_n$ in turn induce a quantum measure $\mu$ on the cylinder sets within the space ... More

The Effect of Magnetic Field Tilt and Divergence on the Mass Flux and Flow Speed in a Line-Driven Stellar WindOct 07 2003We carry out an extended analytic study of how the tilt and faster-than-radial expansion from a magnetic field affect the mass flux and flow speed of a line-driven stellar wind. A key motivation is to reconcile results of numerical MHD simulations with ... More

Asymptotic behaviour of the doubly nonlinear equation $u_t=Δ_p u^m$ on bounded domainsJun 07 2012We study the homogeneous Dirichlet problem for the doubly nonlinear equation $u_t = \Delta_p u^m$, where $p>1,\ m>0$ posed in a bounded domain in $\mathbb{R}^N$ with homogeneous boundary conditions and with non-negative and integrable data. In this paper ... More

The Fisher-KPP equation with nonlinear fractional diffusionMar 27 2013We study the propagation properties of nonnegative and bounded solutions of the class of reaction-diffusion equations with nonlinear fractional diffusion: $u_{t} + (-\Delta)^s (u^m)=f(u)$. For all $0<s<1$ and $m> m_c=(N-2s)_+/N $, we consider the solution ... More

Dispersive Properties for Discrete Schrodinger EquationsJul 25 2010In this paper we prove dispersive estimates for the system formed by two coupled discrete Schr\"odinger equations. We obtain estimates for the resolvent of the discrete operator and prove that it satisfies the limiting absorption principle. The decay ... More

Evidence for Primordial Black Hole Final Evaporation: Swift, BATSE and KONUS and Comparisons of VSGRBs and Observations of VSB That Have PBH Time SignaturesAug 10 2009More than a decade ago we identified a class of VSGRB (T90 < 100 ms) as having unusual properties: (1) galactic position asymmetry, (2) very hard gamma spectrum, (3) possible evidence for galactic origin of these events. We now study the recent Swift ... More

Multiple species atom source for laser-cooling experimentsMar 24 2005Jun 02 2005We describe the design of a single beam, multiple species atom source in which the flux of any component can be separately adjusted. Using this design we have developed a 23Na-6Li atom source for ultracold atom experiments. The fluxes of lithium and sodium ... More

Magnetic Spin-Up of Line-Driven WindsOct 07 2003We summarize recent 2D MHD simulations of line-driven stellar winds from rotating hot-stars with a dipole magnetic field aligned to the star's rotation axis. For moderate to strong fields, much wind outflow is initially along closed magnetic loops that ... More

A note on a local limit theorem for Wiener space valued random variablesMar 23 2015We prove a local limit theorem, i.e. a central limit theorem for densities, for a sequence of independent and identically distributed random variables taking values on an abstract Wiener space; the common law of those random variables is assumed to be ... More