Results for "Patrick Letendre"

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Truncated convolution of Möbius function and multiplicative energy of an integer $n$Mar 13 2019We establish an interesting upper bound for the moments of truncated Dirichlet convolutions of M\"obius functions, a function noted $M(n,z)$. Our result implies that $M(n,j)$ is usually quite small for $j \in \{1,\dots,n\}$. Also, we establish an estimate ... More
The larger sieve and polynomial congruencesOct 26 2018Dec 24 2018We obtain a small improvement of Gallagher's larger sieve and we extend it to higher dimensions. We also obtain two interesting upper bounds for the number of solutions to polynomial congruences.
Truncated convolution of Möbius function and multiplicative energy of an integer $n$Mar 13 2019Apr 17 2019We establish an interesting upper bound for the moments of truncated Dirichlet convolution of M\"obius function, a function noted $M(n,z)$. Our result implies that $M(n,j)$ is usually quite small for $j \in \{1,\dots,n\}$. Also, we establish an estimate ... More
Subsets of $\mathbb{F}^*_p$ with only small products or ratiosApr 17 2019Let $p$ be a fixed prime. We estimate the number of elements of a set $A \subseteq \mathbb{F}^*_p$ for which $$ s_1s_2 \equiv a \pmod{p} \quad \mbox{for some}\quad a \in [-X,X] \quad \mbox{for all}\quad s_1,s_2 \in A. $$ We also consider variations and ... More
The number of integer points close to a polynomialJan 28 2019Let $f(x)$ be a polynomial of degree $n \ge 1$ with real coefficients and let $X \ge 2$ and $\delta \ge 0$ be real numbers. Let $\|\cdot\|$ be the distance to the nearest integer. We obtain upper bounds for the number of solutions to the inequality $\|f(x)\| ... More
New upper bounds for the number of divisors functionDec 24 2018Let $\tau(n)$ stand for the number of divisors of the positive integer $n$. We obtain upper bounds for $\tau(n)$ in terms of $\log n$ and the number of distinct prime factors of $n$.
Variance of the volume of random real algebraic submanifoldsAug 19 2016Let $\mathcal{X}$ be a complex projective manifold of dimension $n$ defined over the reals and let $M$ denote its real locus. We study the vanishing locus $Z\_{s\_d}$ in $M$ of a random real holomorphic section $s\_d$ of $\mathcal{E} \otimes \mathcal{L}^d$, ... More
Variance of the volume of random real algebraic submanifoldsAug 19 2016Dec 01 2016Let $\mathcal{X}$ be a complex projective manifold of dimension $n$ defined over the reals and let $M$ denote its real locus. We study the vanishing locus $Z\_{s\_d}$ in $M$ of a random real holomorphic section $s\_d$ of $\mathcal{E} \otimes \mathcal{L}^d$, ... More
Neutron capture and the antineutrino yield from nuclear reactorsOct 30 2015We identify a new, flux-dependent correction to the antineutrino spectrum as produced in nuclear reactors. The abundance of certain nuclides, whose decay chains produce antineutrinos above the threshold for inverse beta decay, has a nonlinear dependence ... More
Self-Organizing Machine Translation: Example-Driven Induction of Transfer FunctionsJun 03 1994With the advent of faster computers, the notion of doing machine translation from a huge stored database of translation examples is no longer unreasonable. This paper describes an attempt to merge the Example-Based Machine Translation (EBMT) approach ... More
Electroweak Baryogenesis and the Standard ModelJun 13 1994Jun 14 1994Electroweak baryogenesis is addressed within the context of the standard model of particle physics. Although the minimal standard model has the means of fulfilling the three Sakharov's conditions, it falls short to explaining the making of the baryon ... More
Geometrically constrained magnetic wallApr 26 1999Sep 20 1999The structure and properties of a geometrically constrained magnetic wall in a constriction separating two wider regions are investigated theoretically. They are shown to differconsiderably from those of an unconstrained wall, so that the geometrically ... More
Dynamics of Irreducible Endomorphisms of $F_n$Aug 21 2010Mar 06 2011We consider the class non-surjective irreducible endomorphisms of the free group $F_n$. We show that such an endomorphism $\phi$ is topologically represented by a simplicial immersion $f:G \rightarrow G$ of a marked graph $G$; along the way we classify ... More
Monte Carlo Simulation of Deffuant opinion dynamics with quality differencesJul 05 2004In this work the consequences of different opinion qualities in the Deffuant model were examined. If these qualities are randomly distributed, no different behavior was observed. In contrast to that, systematically assigned qualities had strong effects ... More
Entanglement in Random SubspacesSep 24 2004The selection of random subspaces plays a role in quantum information theory analogous to the role of random strings in classical information theory. Recent applications have included protocols achieving the quantum channel capacity and methods for extending ... More
Submarine neutrino communicationSep 25 2009Aug 20 2010We discuss the possibility to use a high energy neutrino beam from a muon storage ring to provide one way communication with a submerged submarine. Neutrino interactions produce muons which can be detected either, directly when they pass through the submarine ... More
Observation of scattering and absorption centers in lead fluoride crystalsJun 22 2006For the first time, lead fluoride is used as a fast and compact material in electromagnetic calorimetry. Excellent optical and mechanical properties of the pure Cherenkov crystals are necessary for the A4 collaboration to perform a measurement of the ... More
Duality for toric Landau-Ginzburg modelsMar 04 2008We introduce a duality construction for toric Landau-Ginzburg models, applicable to complete intersections in toric varieties via the sigma model / Landau-Ginzburg model correspondence. This construction is shown to reconstruct those of Batyrev-Borisov, ... More
Large-scale bias of dark matter halosSep 06 2010Feb 09 2011We build a simple analytical model for the bias of dark matter halos that applies to objects defined by an arbitrary density threshold, $200\leq\deltas\leq 1600$, and that provides accurate predictions from low-mass to high-mass halos. We point out that ... More
Une propriété de transfert en approximation diophantienneJan 06 2016Given a vector $\omega \in \mathbb{R}^n$,the sequence $T_i$ of periods is defined as the sequence of times of best returns near the origin of the translation $x \longmapsto x+\omega$ on the torus $\mathbb{T}^n$. In the present paper, we study how the ... More
Central conjugate locus of 2-step nilpotent Lie groupsJul 20 2015The goals of this article are twofold : 1) to compute the conjugate locus of a geodesic that lies in the center of a simply connected, 2-step nilpotent Lie group with a left invariant metric 2) compare the isometry types of two such nilpotent Lie groups ... More
Birationality and Landau-Ginzburg modelsAug 29 2016Sep 19 2016We introduce a new technique for approaching birationality questions that arise in the mirror symmetry of complete intersections in toric varieties. As an application we answer affirmatively and conclusively the question of Batyrev-Nill (2008) about the ... More
Multifraction reduction ii: Conjectures for artin-tits groupsJun 29 2016Jul 01 2016Multifraction reduction is a new approach to the Word Problem for Artin-Tits groups and, more generally, for the enveloping group U (M) of a monoid M in which any two elements admit a greatest common divisor. This approach is based on a rewrite system ... More
Quasianalytic Ilyashenko algebrasJun 07 2016Nov 16 2016I construct a quasianalytic field $\mathcal F$ of germs at $+\infty$ of real functions with logarithmic generalized power series as asymp\-totic expansions, such that $\mathcal F$ is closed under differentiation and $\log$-composition; in particular, ... More
Closing the light sbottom mass window from a compilation of e+e- -> hadron dataMar 15 2004Apr 29 2004The e+e- -> hadron cross section data from PEP, PETRA, TRISTAN, SLC and LEP, at centre-of-mass energies between 20 to 209 GeV, are analysed to search for the production of a pair of light sbottoms decaying hadronically via R-parity-violating couplings. ... More
The Light Gluino Mass Window RevisitedFeb 11 2003Apr 03 2003The precise measurements of the ``electroweak observables'' performed at LEP and SLC are well consistent with the standard model predictions. Deviations from the standard model arising from vacuum polarization diagrams (also called ``weak loop corrections'') ... More
The jumping coefficients of non-Q-Gorenstein multiplier idealsOct 19 2014Jan 20 2015Let $\mathfrak a \subset \mathscr O_X$ be a coherent ideal sheaf on a normal complex variety $X$, and let $c \ge 0$ be a real number. De Fernex and Hacon associated a multiplier ideal sheaf to the pair $(X, \mathfrak a^c)$ which coincides with the usual ... More
The generalized Lipman-Zariski problemMay 06 2014Oct 16 2014We propose and study a generalized version of the Lipman-Zariski conjecture: let $(x \in X)$ be an $n$-dimensional singularity such that for some integer $1 \le p \le n - 1$, the sheaf $\Omega_X^{[p]}$ of reflexive differential $p$-forms is free. Does ... More
Convergence in Infinitary Term Graph Rewriting Systems is Simple (Extended Abstract)Feb 26 2013In this extended abstract, we present a simple approach to convergence on term graphs that allows us to unify term graph rewriting and infinitary term rewriting. This approach is based on a partial order and a metric on term graphs. These structures arise ... More
Partial Order Infinitary Term RewritingMar 22 2014Jun 02 2014We study an alternative model of infinitary term rewriting. Instead of a metric on terms, a partial order on partial terms is employed to formalise convergence of reductions. We consider both a weak and a strong notion of convergence and show that the ... More
Erdős' Multiplication Table Problem for Function Fields and Symmetric GroupsApr 23 2018May 06 2018Erd\H{o}s first showed that the number of positive integers up to $x$ which can be written as a product of two number less than $\sqrt{x}$ has zero density. Ford then found the correct order of growth of the set of all these integers. We will use the ... More
Simulating Quantum Circuits by Shuffling PaulisApr 15 2018Verification of NISQ era quantum devices demands fast classical simulation of large noisy quantum circuits. We present an algorithm based on the stabilizer formalism that can efficiently simulate noisy stabilizer circuits. Additionally, the protocol can ... More
Duality for toric Landau-Ginzburg modelsMar 04 2008Dec 16 2016We introduce a duality construction for toric Landau-Ginzburg models, applicable to complete intersections in toric varieties via the sigma model / Landau-Ginzburg model correspondence. This construction is shown to reconstruct those of Batyrev-Borisov, ... More
Braids in trivial braid diagramsNov 19 2003We show that every trivial 3-strand braid diagram contains a disk, defined as a ribbon ending in opposed crossings. Under a convenient algebraic form, the result extends to every Artin--Tits group of dihedral type, but it fails to extend to braids with ... More
Thin groups of fractionsNov 27 2001A number of properties of spherical Artin groups extend to Garside groups, defined as the groups of fractions of monoids where least common multiples exist, there is no nontrivial unit, and some additional finiteness conditions are satisfied \cite{Dgk}. ... More
Differential forms on log canonical spaces in positive characteristicMay 06 2019Given a logarithmic $1$-form on the snc locus of a log canonical surface pair $(X, D)$ over a perfect field of characteristic $p \ge 7$, we show that it extends with at worst logarithmic poles to any resolution of singularities. We also prove the analogous ... More
The QCD crossover at zero and non-zero baryon densities from Lattice QCDJul 15 2018We map out the QCD crossover line $\frac{T_c(\mu_B)}{T_c(0)} = 1 - \kappa_2 \left( \frac{\mu_B}{T_c(0)} \right)^2 - \kappa_4 \left( \frac{\mu_B}{T_c(0)} \right)^4 + \mathcal{O}(\mu_B^6)$ for the first time up to $\mathcal{O}(\mu_B^4)$ for a strangeness ... More
Specializations of elliptic surfaces, and divisibility in the Mordell-Weil groupNov 19 2008Dec 10 2008Let $E$ be an elliptic surface over the curve $C$, defined over a number field $k$, let $P$ be a section of $E$, and let $\ell$ be a rational prime. For any non-singular fibre $E_t$, we bound the number of points $Q$ on $E_t$ of (algebraic) degree at ... More
A note on Flenner's extension theoremMay 06 2019We show that any $p$-form on the smooth locus of a normal complex space extends to a resolution of singularities, possibly with logarithmic poles, as long as $p \le \mathrm{codim}_X (X_{\mathrm{sg}}) - 2$, where $c$ is the codimension of the singular ... More
Infinitely many universally tight torsion free contact structures with vanishing Ozsváth-Szabó contact invariantsDec 27 2009Ozsvath-Szabo contact invariants are a powerful way to prove tightness of contact structures but they are known to vanish in the presence of Giroux torsion. In this paper we construct, on infinitely many manifolds, infinitely many isotopy classes of universally ... More
Quasianalytic Ilyashenko algebrasJun 07 2016May 04 2017I construct a quasianalytic field $\mathcal F$ of germs at $+\infty$ of real functions with logarithmic generalized power series as asymp\-totic expansions, such that $\mathcal F$ is closed under differentiation and $\log$-composition; in particular, ... More
Kinematic consistency relations of large-scale structuresNov 05 2013Nov 30 2014We describe how the kinematic consistency relations satisfied by density correlations of the large-scale structures of the Universe can be derived within the usual Newtonian framework. These relations express a kinematic effect and show how the $(\ell+n)$-density ... More
Source-lens clustering and intrinsic-alignment bias of weak-lensing estimatorsJun 26 2013Jan 16 2014We estimate the amplitude of the source-lens clustering bias and of the intrinsic-alignment bias of weak lensing estimators of the two-point and three-point convergence and cosmic-shear correlation functions. We use a linear galaxy bias model for the ... More
Large-N expansions applied to gravitational clusteringNov 28 2006Jun 19 2007We develop a path-integral formalism to study the formation of large-scale structures in the universe. Starting from the equations of motion of hydrodynamics (single-stream approximation) we derive the action which describes the statistical properties ... More
A Theory of Interactive Debugging of Knowledge Bases in Monotonic LogicsSep 20 2016A broad variety of knowledge-based applications such as recommender, expert, planning or configuration systems usually operate on the basis of knowledge represented by means of some logical language. Such a logical knowledge base (KB) enables intelligent ... More
Double $L$-groups and doubly-slice knotsAug 05 2015Jun 06 2016We develop a theory of chain complex double-cobordism for chain complexes equipped with Poincar\'{e} duality. The resulting double-cobordism groups are a refinement of Ranicki's torsion algebraic $L$-groups for localisations of a commutative ring with ... More
Direct measurement of alpha_QED(mZ) at the FCC-eeDec 17 2015Jan 25 2016When the measurements from the FCC-ee become available, an improved determination of the standard-model "input" parameters will be needed to fully exploit the new precision data towards either constraining or fitting the parameters of beyond-the-standard-model ... More
Kinematics of the Galactic Globular Cluster System: New Radial Velocities for Clusters in the Direction of the Inner GalaxyJun 29 1999HIRES on the Keck I telescope has been used to measure the first radial velocities for stars belonging to eleven, heavily-reddened globular clusters in the direction of the inner Galaxy. The question of kinematic substructuring among the Galactic globular ... More
Quasianalytic Ilyashenko algebrasJun 07 2016Aug 19 2016I construct a quasianalytic field $\mathcal F$ of germs at $+\infty$ of real functions with logarithmic generalized power series as asymp\-totic expansions, such that $\mathcal F$ is closed under differentiation and $\log$-composition; in particular, ... More
Phonetic Ambiguity : Approaches, Touchstones, Pitfalls and New ApproachesAug 29 1996Phonetic ambiguity and confusibility are bugbears for any form of bottom-up or data-driven approach to language processing. The question of when an input is ``close enough'' to a target word pervades the entire problem spaces of speech recognition, synthesis, ... More
Recent Progress in Studies of Pulsar Wind NebulaeNov 07 2007The synchrotron-emitting nebulae formed by energetic winds from young pulsars provide information on a wide range phenomena that contribute to their structure. High resolution X-ray observations reveal jets and toroidal structures in many systems, along ... More
The Devil is in the Details: Compact Structures in Pulsar Wind NebulaeApr 05 2005The large-scale structure of pulsar wind nebulae (PWNe) tells us a considerable amount about their average magnetic fields, the total particle input from the pulsar winds, and the confining pressure at their outer boundaries. However, the details of the ... More
Particle Acceleration in Supernova Remnants and Pulsar Wind NebulaeMay 28 2002While supernova remnants (SNRs) have long been considered prime candidates for the source of cosmic rays, at least to energies up to ~10^14 eV, it is only over the past several years that direct evidence of such energetic particles in SNRs has been uncovered. ... More
Electroweak Constraints on Little Higgs ModelsFeb 03 2004In this talk I will give a brief introduction to Little Higgs models in general, including an overview of all models in existence thus far. I then review some of the generic constraints on these models from electroweak precision measurements.
Laver's results and low-dimensional topologyJan 14 2014In connection with his interest in selfdistributive algebra, Richard Laver established two deep results with potential applications in low-dimensional topology, namely the existence of what is now known as the Laver tables and the well-foundedness of ... More
Monoids of O-type, subword reversing, and ordered groupsApr 14 2012May 08 2012We describe a simple scheme for constructing finitely generated monoids in which left-divisibility is a linear ordering and for practically investigating these monoids. The approach is based on subword reversing, a general method of combinatorial group ... More
Tamari Lattices and the symmetric Thompson monoidSep 24 2011We investigate the connection between Tamari lattices and the Thompson group F, summarized in the fact that F is a group of fractions for a certain monoid F+sym whose Cayley graph includes all Tamari lattices. Under this correspondence, the Tamari lattice ... More
Solutions of the cubic Fermat equation in ring class fields of imaginary quadratic fields (as periodic points of a 3-adic algebraic function)Oct 24 2014Jun 20 2015Explicit solutions of the cubic Fermat equation are constructed in ring class fields $\Omega_f$, with conductor $f$ prime to $3$, of any imaginary quadratic field $K$ whose discriminant satisfies $d_K \equiv 1$ (mod $3$), in terms of the Dedekind $\eta$-function. ... More
Comment on "Quantum Time Crystals": a new paradigm or just another proposal of perpetuum mobile?Oct 15 2012A Comment on Frank Wilczek's paper "Quantum Time Crystals" (Phys. Rev. Lett. 109, 160401 (2012); arXiv:1202.2539).
Quantum geometric phase in Majorana's stellar representation: Mapping onto a many-body Aharonov-Bohm phaseApr 11 2012Jun 13 2012The (Berry-Aharonov-Anandan) geometric phase acquired during a cyclic quantum evolution of finite-dimensional quantum systems is studied. It is shown that a pure quantum state in a (2J+1)-dimensional Hilbert space (or, equivalently, of a spin-J system) ... More
Theory of interlayer exchange interactions in magnetic multilayersJul 27 1999Dec 20 1999This paper presents a review of the phenomenon of interlayer exchange coupling in magnetic multilayers. The emphasis is put on a pedagogical presentation of the mechanism of the phenomenon, which has been successfully explained in terms of a spin-dependent ... More
Zero mode quantization of multi-SkyrmionsApr 21 1998Sep 02 1998A zero mode quantization of the minimal energy SU(2) Skyrmions for nucleon numbers four to nine and seventeen is described. This involves quantizing the rotational and isorotational modes of the configurations. For nucleon numbers four, six and eight ... More
The random greedy algorithm for sum-free subsets of $\mathbb{Z}_{2n}$Feb 05 2015$S \subseteq \mathbb{Z}_{2n}$ is said to be sum-free if $S$ has no solution to the equation $a+b=c$. The sum-free process on $\mathbb{Z}_{2n}$ starts with $S:=\emptyset$, and iteratively inserts elements of $\mathbb{Z}_{2n}$, where each inserted element ... More
The Physics Program at MAMI-CFeb 20 2008Apr 07 2008In February 2007, the fourth stage of the Mainz Microtron, MAMI-C, started operations with a first experiment. The new Harmonic Double-Sided Microtron delivers an electron beam with energies up to 1.5 GeV while preserving the excellent beam quality of ... More
Current Issues in Kaon Photoelectro-Production off the NucleonJan 23 2011The electromagnetic kaon production amplitudes associated to Lambda/Sigma hyperons can be described by phenomenological models, most notably by isobar approaches. Experimental data on kaon production have been collected at ELSA, SPring8, GRAAL, LNS Tohoku, ... More
Rigidity and height bounds for certain post-critically finite endomorphisms of projective spaceOct 15 2013The holomorphic endomorphism f of projective space is called post-critically finite (PCF) if the forward image of the critical locus, under iteration of f, has algebraic support (i.e., is a finite union of hypersurfaces). In the case of dimension 1, a ... More
On the $\mathrm{L}^p$-theory of the Navier--Stokes equations on three-dimensional bounded Lipschitz domainsMar 03 2017Feb 08 2018On a bounded Lipschitz domain $\Omega \subset \mathbb{R}^d$, $d \geq 3$, we continue the study of Shen and of Kunstmann and Weis of the Stokes operator on $\mathrm{L}^p_{\sigma} (\Omega)$. We employ their results in order to determine the domain of the ... More
The asymptotic behaviour of solutions of forced Burgers equation on the circleMar 27 2003We describe the asymptotic behaviour of solutions of unviscid Burgers equation on the circle with time-periodic forcing. These solutions converge to periodic states, but the period of these limit states may be greater than the period of the forcing. We ... More
Moving Charge Distributions in Classical Electromagnetism and the FitzGerald-Lorentz ContractionJun 10 2010In [Eur. J. Phys. {\bf 25} (2004) 123-126], Dragan V. Red{\v z}i\'c is led to the FitzGerald-Lorentz contraction by comparing electromagnetic images of a moving point charge and a moving conducting sphere. We wish to point out that much simpler possibilities ... More
Elicitation of ambiguous beliefs with mixing betsFeb 20 2019I consider the elicitation of ambiguous beliefs about an event. I introduce a mechanism that allows to identify an interval of probabilities (representing ambiguity perception) for several classes of ambiguity averse preferences. The agent reveals her ... More
Renormalization group computation of likelihood functions for cosmological data setsOct 19 2018I show how a renormalization group (RG) method can be used to incrementally integrate the information in cosmological large-scale structure data sets (including CMB, galaxy redshift surveys, etc.). I show numerical tests for Gaussian fields, where the ... More
A cancellativity criterion for presented monoidsFeb 13 2018Sep 14 2018We establish a new, fairly general cancellativity criterion for a presented monoid that properly extends the previously known related criteria. It is based on a new version of the word transformation called factor reversing, and its specificity is to ... More
The Lipman-Zariski conjecture in low genusJan 17 2018We prove the Lipman-Zariski conjecture for complex surface singularities of genus one, and also for those of genus two whose link is not a rational homology sphere. As an application, we characterize complex $2$-tori as the only normal compact complex ... More
SU(3) monopoles and their fieldsApr 22 1997Sep 11 1997Some aspects of the fields of charge two SU(3) monopoles with minimal symmetry breaking are discussed. A certain class of solutions look like SU(2) monopoles embedded in SU(3) with a transition region or ``cloud'' surrounding the monopoles. For large ... More
$\mathcal{N}$-extended Maxwell supergravities as Chern-Simons theories in three spacetime dimensionsMar 07 2019We present a new class of three-dimensional $\mathcal{N}$-extended supergravity theories based on the $\mathcal{N}$-extended Maxwell superalgebra with central charges and $\mathfrak{so}(\mathcal{N})$ internal symmetry generators. The presence of $\mathfrak{so}(\mathcal{N})$ ... More
Modes of Convergence for Term Graph RewritingMay 02 2012May 31 2012Term graph rewriting provides a simple mechanism to finitely represent restricted forms of infinitary term rewriting. The correspondence between infinitary term rewriting and term graph rewriting has been studied to some extent. However, this endeavour ... More
Infinitary Term Graph RewritingJul 04 2011Term graph rewriting provides a formalism for implementing term rewriting in an efficient manner by avoiding duplication. Infinitary term rewriting has been introduced to study infinite term reduction sequences. Such infinite reductions can be used to ... More
Canonical heights and preperiodic points for weighted homogeneous families of polynomialsOct 29 2015Jun 13 2017A family $f_t(z)$ of polynomials over a number field $K$ will be called \emph{weighted homogeneous} if and only if $f_t(z)=F(z^e, t)$ for some binary homogeneous form $F(X, Y)$ and some integer $e\geq 2$. For example, the family $z^d+t$ is weighted homogeneous. ... More
Variation of the canonical height for polynomials in several variablesAug 22 2014Let K be a number field, X/K a curve, and f/X a family of endomorphisms of projective N-space. It follows from a result of Call and Silverman that the canonical height associated to the family f, evaluated along a section, differs from a Weil height on ... More
The dynamics of pseudographs in convex Hamiltonian systemsDec 15 2004Jul 10 2008We study the evolution, under convex Hamiltonian flows on cotangent bundles of compact manifolds, of certain distinguished subsets of the phase space. These subsets are generalizations of Lagrangian graphs, we call them pseudographs. They emerge in a ... More
$\mathcal{N}$-extended Maxwell supergravities as Chern-Simons theories in three spacetime dimensionsMar 07 2019Apr 02 2019We present a new class of three-dimensional $\mathcal{N}$-extended supergravity theories based on the $\mathcal{N}$-extended Maxwell superalgebra with central charges and $\mathfrak{so}(\mathcal{N})$ internal symmetry generators. The presence of $\mathfrak{so}(\mathcal{N})$ ... More
Study of an identityNov 13 2001We solve the word problem of the identity $x(yz) = (xy)(yz)$ by investigating a certain group describing the geometry of that identity. We also construct a concrete realization of the free system of rank~1 relative to the above identity
On the differentiability of hairs for Zorich mapsJan 24 2017Nov 29 2017Devaney and Krych showed that for the exponential family $\lambda e^z$, where $0<\lambda <1/e$, the Julia set consists of uncountably many pairwise disjoint simple curves tending to $\infty$. Viana proved that these curves are smooth. In this article ... More
Regular and exact (virtual) double categoriesMay 04 2015We propose definitions of regular and exact (virtual) double categories, proving a number of results which parallel many basic results in the theory of regular and exact categories. We show that any regular virtual double category admits a factorization ... More
Solutions of diophantine equations as periodic points of $p$-adic algebraic functions, II: The Rogers-Ramanujan continued fractionJun 28 2018Aug 12 2018In this part we show that the diophantine equation $X^5+Y^5=\varepsilon^5(1-X^5Y^5)$, where $\varepsilon=\frac{-1+\sqrt{5}}{2}$, has solutions in specific abelian extensions of quadratic fields $K=\mathbb{Q}(\sqrt{-d})$ in which $-d \equiv \pm 1$ (mod ... More
Projective limits of local shift morphismFeb 03 2019We define the notion of projective limit of local shift morphisms of type $\left( r,s\right) $ and endow the space of such mathematical objects with an adapted differential structure. The notion of shift Poisson tensor $P$ on a Hilbert tower corresponds ... More
Optimal Regularity for a Class of Singular Abstract Parabolic EquationsOct 26 2006A general class of singular abstract Cauchy problems is considered which naturally arises in applications to certain Free Boundary Problems. Existence of an associated evolution operator characterizing its solutions is established and is subsequently ... More
Limites projectives fortes d'algébroïdes de LieDec 03 2010Feb 20 2012We define the notion of strong projective limit of Banach Lie algebroids. We study the associated structures of Fr\'{e}chet bundles and the compatibility with the different morphisms. This kind of structure seems to be a convenient framework for various ... More
Maxwell-Sylvester Multipoles and the Geometric Theory of Irreducible Tensor Operators of Quantum Spin SystemsMar 27 2018A geometric theory of the irreducible tensor operators of quantum spin systems. It is based upon the Maxwell-Sylvester geometric representation of the multipolar electrostatic potential. In the latter, an order-$\ell$ multipolar potential is represented ... More
Epicyclic drifting in anisotropic excitable media with multiple inhomogeneitiesFeb 07 2006Mar 12 2007Spirals have been studied from a dynamical system perspective starting with Barkley's seminal papers linking a wide class of spiral wave dynamics to the Euclidean symmetry of the excitable media in which they are observed. However, in order to explain ... More
Topological methods in 3-dimensional contact geometryMar 05 2013These notes provide an introduction to Giroux's theory of convex surfaces in contact 3-manifolds and its simplest applications. They put a special emphasis on pictures and discussions of explicit examples. The first goal is to explain why all the information ... More
Smooth critical sub-solutions of the Hamilton-Jacobi equationDec 01 2005Jul 10 2008We establish the existence of smooth critical sub-solutions of the Hamilton-Jacobi equation on compact manifolds for smooth convex Hamiltonians, that is in the context of weak KAM theory, under the assumption that the Aubry set is the union of finitely ... More
Towards Quality of Experience Determination for Video in Augmented Binocular Vision ScenariosJun 04 2014Mar 04 2015With the continuous growth in the consumer markets of mobile smartphones and increasingly in augmented reality wearable devices, several avenues of research investigate the relationships between the quality perceived by mobile users and the delivery mechanisms ... More
Multiwavelength Observations of Pulsar Wind NebulaeAug 27 2010The extended nebulae formed as pulsar winds expand into their surroundings provide information about the composition of the winds, the injection history from the host pulsar, and the material into which the nebulae are expanding. Observations from across ... More
High resolution X-ray observations of 3C 58Nov 10 2003As the presumed remnant of SN1181, 3C 58 houses one of the youngest known neutron stars in the Galaxy. The properties of this young pulsar and its associated wind nebula differ considerably from those of the Crab, and may well offer a more typical example ... More
Trajectories of Rubber Balloons used in Balloon Releases: Theory and ApplicationMar 10 2011Balloon releases are one of the main attractions of many fairs. Helium filled rubber balloons are released to carry postcards over preferably long distances. Although such balloons have been considered in atmospheric sciences and air safety analysis, ... More
Coxeter-like groups for groups of set-theoretic solutions of the Yang--Baxter equationMay 16 2013We attach with every finite, involutive, nondegenerate set-theoretic solution of the Yang--Baxter equation a finite group that plays for the associated structure group the role that a finite Coxeter group plays for the associated Artin--Tits group.
Using shifted conjugacy in braid-based cryptographySep 16 2006Conjugacy is not the only possible primitive for designing braid-based protocols. To illustrate this principle, we describe a Fiat--Shamir-style authentication protocol that be can be implemented using any binary operation that satisfies the left self-distributive ... More
Solutions of diophantine equations as periodic points of $p$-adic algebraic functions, IOct 17 2014Aug 30 2015Solutions of the quartic Fermat equation in ring class fields of odd conductor over quadratic fields $K=\mathbb{Q}(\sqrt{-d})$ with $-d \equiv 1$ (mod $8$) are shown to be periodic points of a fixed algebraic function $T(z)$ defined on the punctured disk ... More
Genus theory and the factorization of class equations over $\mathbb{F}_p$Sep 02 2014A new proof using genus theory is given of a Legendre symbol criterion for the class equation corresponding to the Hilbert class field of an imaginary quadratic field $\mathbb{Q}(\sqrt{D})$ to have a linear factor (mod $p$), when $p$ is an odd prime for ... More