total 3604took 0.08s

Some families of special Lagrangian toriNov 09 2000We give a simple proof of the local version of a result of R. Bryant, stating that any 3-dimensional Riemannian manifold can be isometrically embedded as a special Lagrangian submanifold in a Calabi-Yau manifold. We refine the theorem proving that a certain ... More

Isometric embeddings of families of special Lagrangian submanifoldsMar 23 2005We prove that certain Riemannian manifolds can be isometrically embedded inside Calabi-Yau manifolds. For example we prove that given any real-analytic one parameter family of Riemannian metrics $g_t$ on a 3-dimensional manifold $Y$ with volume form independent ... More

Lagrangian submanifolds from tropical hypersurfacesApr 04 2018We prove that a smooth tropical hypersurface in $\mathbb{R}^3$ can be lifted to a smooth embedded Lagrangian submanifold in $(\mathbb{C}^*)^3$. This completes the proof of the result announced in the article "Lagrangian pairs pants" arXiv:1802.02993. ... More

Lagrangian pairs of pantsFeb 08 2018We construct a Lagrangian submanifold, inside the cotangent bundle of a real torus, which we call a Lagrangian pair of pants. It is given as the graph of the differential of a smooth function defined on the real blow up of a Lagrangian coamoeba. Lagrangian ... More

On homological mirror symmetry of toric Calabi-Yau three-foldsMar 12 2015We use Lagrangian torus fibrations on the mirror $X$ of a toric Calabi-Yau threefold $\check X$ to construct Lagrangian sections and various Lagrangian spheres on $X$. We then propose an explicit correspondence between the sections and line bundles on ... More

On homological mirror symmetry of toric Calabi-Yau three-foldsMar 12 2015Feb 08 2019We use Lagrangian torus fibrations on the mirror $X$ of a toric Calabi-Yau threefold $\check X$ to construct Lagrangian sections and various Lagrangian spheres on $X$. We then propose an explicit correspondence between the sections and line bundles on ... More

Conifold transitions via affine geometry and mirror symmetryJan 14 2013Sep 15 2014Mirror symmetry of Calabi-Yau manifolds can be understood via a Legendre duality between a pair of certain affine manifolds with singularities called tropical manifolds. In this article, we study conifold transitions from the point of view of Gross and ... More

Symmetries of Lagrangian fibrationsAug 07 2009We construct fiber-preserving anti-symplectic involutions for a large class of symplectic manifolds with Lagrangian torus fibrations. In particular, we treat the K3 surface and the quintic threefold. We interpret our results as corroboration of the view ... More

Lagrangian 3-torus fibrationsNov 06 2006We give a method to construct singular Lagrangian 3-torus fibrations over certain a priori given integral affine manifolds with singularities, which we call simple. The main result of this article is the proof that the topological Calabi-Yau compactifications ... More

Semi-global invariants of piecewise smooth Lagrangian fibrationsMar 21 2006We study certain types of piecewise smooth Lagrangian fibrations of smooth symplectic manifolds, which we call stitched Lagrangian fibrations. We extend the classical theory of action-angle coordinates to these fibrations by encoding the information on ... More

Some functional inequalities on polynomial volume growth Lie groupsSep 16 2010Jan 21 2011We study in this article some Sobolev-type inequalities on polynomial volume growth Lie groups. We show in particular that improved Sobolev inequalities can be extended without the use of the Littlewood-Paley decomposition to this general framework.

An extension of the classical derivativeMar 22 2006Mar 24 2006We extend the usual definition of the derivative in a way that Calculus I students can easily comprehend and which allows calculations at branch points.

Some remarks on the Wu-Sprung potential. Preliminary reportOct 17 2005Some observations on the Wu-Sprung potential.

How to build a gravity generatorJun 25 2012Aug 04 2013This article explores a simple way to construct an electric device capable to generate an artificial gravitational field by exploiting a resonance phenomenon.

Three amalgams with remarkable normal subgroup structuresJun 15 2005We construct three groups $\Lambda_1$, $\Lambda_2$, $\Lambda_3$, which can all be decomposed as amalgamated products $F_9 \ast_{F_{81}} F_{9}$ and have very few normal subgroups of finite or infinite index. Concretely, $\Lambda_1$ is a simple group, $\Lambda_2$ ... More

On infinite groups generated by two quaternionsFeb 24 2005Oct 06 2006Let $x$, $y$ be two integral quaternions of norm $p$ and $l$, respectively, where $p$, $l$ are distinct odd prime numbers. We investigate the structure of $<x,y>$, the multiplicative group generated by $x$ and $y$. Under a certain condition which excludes ... More

Counting $(1,β)$-BM relations and classifying $(2,2)$-BM groupsJul 11 2006In the first part, we prove that the number of $(1,\beta)$-BM relations is $3 \cdot 5 \cdot \ldots \cdot (2\beta + 1)$, which was conjectured by Kimberley. In the second part, we construct two isomorphisms between certain $(2,2)$-BM groups. This completes ... More

Holographic dark energy and late cosmic accelerationOct 02 2006It has been persuasively argued that the number of the effective degrees of freedom of a macroscopic system is proportional to its area rather than to its volume. This entails interesting consequences for cosmology. Here we present a model based on this ... More

Nonperturbative Ground State of the Stochastic Stabilization of 2D Quantum GravityOct 14 1993May 23 1994I construct the ground state, up to first nonperturbative order, of the stochastic stabilization of the zero dimensional matrix model which defines 2D Quantum Gravity. It is given by the linear combination of a perturbative wave function and a nonperturbative ... More

Reduction of internal degrees of freedom in the large N limit in matrix modelsJun 02 1997Nov 05 1998In this paper the large $N$ limit of one hermitian matrix models coupled to an external matrix is considered. It is shown that in the large N limit the number of degrees of freedom are reduced to be order N even though it is order $N^{2}$ for finite N. ... More

Hard X-ray Emission from Magnetars : A Case Study for Simbol XJan 16 2008The magnetar model involves an isolated neutron star with a very high magnetic field (B~10^14-10^15 G), and is invoked to explain the emission processes of two classes of sources, the Anomalous X-ray Pulsars (AXPs) and the Soft Gamma-Ray Repeaters (SGRs). ... More

INTEGRAL Results on Gamma-Ray BurstsFeb 20 2013Despite being a general observatory, and not a Gamma-Ray Bursts (GRBs) oriented mission, INTEGRAL has contributed to several important discoveries in the GRB field. This has been obtained thanks to its unprecedented localization capabilities, and sensitivity ... More

Multiwavelength Gamma-Ray Bursts Observations with ECLAIRsSep 17 2007ECLAIRs is the next space borne instrument that will be fully dedicated to multi-wavelength studies of Gamma-Ray Bursts (GRBs). It consists of a coded mask telescope with a wide (~2 sr) field of view, made of 6400 CdTe pixels (~1000 cm^2), which will ... More

Fourvector algebraNov 20 2007The algebra of fourvectors is described. The fourvectors are more appropriate than the Hamilton quaternions for its use in Physics and the sciences in general. The fourvectors embrace the 3D vectors in a natural form. It is shown the excellent ability ... More

Powers of two as sum of two generalized Fibonacci numbersSep 09 2014For $k\geq 2$, the $k$-generalized Fibonacci sequence $(F_n^{(k)})_{n}$ is defined by the initial values $0,0,\ldots,0,1$ ($k$ terms) and such that each term afterwards is the sum of the $k$ preceding terms. In this paper, we search for powers of two ... More

On the use of energy loss mechanisms to constrain Lorentz invariance violationsJan 13 2014Mar 20 2014In light of recent and probably upcoming observations of very high energy astroparticles, such as those reported by the IceCube collaboration, we readdress the energy loss mechanism by Lorentz violating particles. We analytically show that Cohen-Glashow's ... More

Solar Flare Measurements with STIX and MiSolFANov 04 2014Solar flares are the most powerful events in the solar system and the brightest sources of X-rays, often associated with emission of particles reaching the Earth and causing geomagnetic storms, giving problems to communication, airplanes and even black-outs. ... More

Cohomogeneity one Einstein-Sasaki 5-manifoldsJun 14 2006Mar 19 2007We consider hypersurfaces in Einstein-Sasaki 5-manifolds which are tangent to the characteristic vector field. We introduce evolution equations that can be used to reconstruct the 5-dimensional metric from such a hypersurface, analogous to the (nearly) ... More

Bayesian regression of piecewise homogeneous Poisson processesFeb 17 2017In this paper, a Bayesian method for piecewise regression is adapted to handle counting processes data distributed as Poisson. A numerical code in Mathematica is developed and tested analyzing simulated data. The resulting method is valuable for detecting ... More

Towards the Use of Deep Reinforcement Learning with Global Policy For Query-based Extractive SummarisationNov 10 2017Nov 14 2017Supervised approaches for text summarisation suffer from the problem of mismatch between the target labels/scores of individual sentences and the evaluation score of the final summary. Reinforcement learning can solve this problem by providing a learning ... More

Théorèmes de dualité pour les corps de fonctions sur des corps locaux supérieurs et applications arithmétiquesMay 08 2014Jun 01 2014Let $K$ be the function field of a smooth projective curve $X$ over a higher-dimensional local field $k$. We define Tate-Shafarevich groups of a commutative group scheme via cohomology classes locally trivial at each completion of $K$ coming from a closed ... More

Variations on a Theme by James StirlingFeb 28 2006We present the history and previous approaches to the proof of Stirling's series. We use a different procedure, based on the asymptotic analysis of the difference equation $\Gamma(z+1)=z\Gamma(z)$. The method reproduces Stirling's series very easily and ... More

Asymptotic analysis of the derivatives of the inverse error functionJul 09 2006Jun 05 2007The inverse of the error function, $\operatorname{inverf}(x),$ has applications in diffusion problems, chemical potentials, ultrasound imaging, etc. We analyze the derivatives $\frac{d^{n}}{dz^{n}} \operatorname*{inverf}(z) |_{z=0}$, as $n\to \infty$ ... More

Dualité et principe local-global sur des corps locaux de dimension 2May 04 2016Let $k$ be an algebraically closed field, a finite field or a $p$-adic field. Let $K_0=k((x,y))$ be the field of Laurent series in two variables over $k$. We define Tate-Shafarevich groups of a commutative group scheme over $K_0$ via cohomology classes ... More

Vanishing theorems and Brauer-Hasse-Noether exact sequences for the cohomology of higher-dimensional fieldsMar 23 2018Jun 07 2018Let $k$ be a finite field, a $p$-adic field or a number field. Let $K$ be a finite extension of the Laurent series field in $m$ variables $k((x_1,...,x_m))$ or, more generally, a finite extension of the field of rational functions $k((x_1,...,x_m))(y_1,...,y_n)$. ... More

Integral representation of the Ising modelOct 17 2005The partition function of the 2D Ising model coupled to an external magnetic field is studied. We show that the sum over the spin variables can be reduced to an integration over a finite number of variables. This integration must be performed numerically. ... More

A remark on Besov spaces interpolation over the 2-adic groupApr 19 2011Motivated by a recent result which identifies in the special setting of the 2-adic group the Besov space $\dot{B}^{1,\infty}_{1}(\mathbb{Z}_2)$ with $BV(\mathbb{Z}_2)$, the space of function of bounded variation, we study in this article some functional ... More

Remarks on a fractional diffusion transport equation with applications to the dissipative quasi-geostrophic equationJul 22 2010Jan 22 2013In this article I study H\"older regularity for solutions of a transport equation based in the dissipative quasi-geostrophic equation. Following a recent idea of A. Kiselev and F. Nazarov, I will use the molecular characterization of local Hardy spaces ... More

On Taylor series and Kapteyn series of the first and second typeDec 16 2010We study the relation between the coefficients of Taylor series and Kapteyn series representing the same function. We compute explicit formulas for expressing one in terms of the other and give examples to illustrate our method.

The arrangement field of the space-time pointsJan 18 2012Oct 24 2012Arrangement field theory is a theory of everything which describes all particles as different manifestations of an unique field, the gauge field Sp(12,C). All fields (bosons and fermions in three families) fill up the adjoint representation of Lie group ... More

Thermodynamic limit of the first-order phase transition in the Kuramoto modelSep 07 2005Oct 19 2005In the Kuramoto model, a uniform distribution of the natural frequencies leads to a first-order (i.e., discontinuous) phase transition from incoherence to synchronization, at the critical coupling parameter $K_c$. We obtain the asymptotic dependence of ... More

Abelianization conjectures for some arithmetic square complex groupsAug 08 2005We extend a conjecture of Kimberley-Robertson on the abelianizations of certain square complex groups.

Anti-tori in square complex groupsNov 24 2004Jul 21 2005An anti-torus is a subgroup $<a,b>$ in the fundamental group of a compact non-positively curved space $X$, acting in a specific way on the universal covering space $\tilde{X}$ such that $a$ and $b$ do not have any commuting non-trivial powers. We construct ... More

A finitely presented torsion-free simple groupNov 24 2004We construct a finitely presented torsion-free simple group $\Sigma_0$, acting cocompactly on a product of two regular trees. An infinite family of such groups has been introduced by Burger-Mozes ([2,4]). We refine their methods and get $\Sigma_0$ as ... More

Effective upliftings in Large volume compactificationsFeb 04 2015Aug 05 2015After reviewing several mechanisms proposed to get a dS/Minkowski vacuum in moduli stabilization scenarios of type-IIB superstring orientifold compactifications we propose a criterium for characterizing those that may effectively lead to a positive small ... More

On UltraViolet effects in protected inflationary modelsOct 29 2014Inflationary models are usually UV sensitive. Several mechanism have been proposed to protect the necessary features of the potential, and most notably (softly broken) global symmetries as shift-symmetry. We show that, even in presence of these protecting ... More

Objective Bayesian analysis of "on/off" measurementsJul 24 2014Oct 20 2014In high-energy astrophysics, it is common practice to account for the background overlaid with the counts from the source of interest with the help of auxiliary measurements carried on by pointing off-source. In this "on/off" measurement, one knows the ... More

A cluster expansion approach to the Heilmann-Lieb liquid crystal modelJun 07 2015Nov 24 2015A monomer-dimer model with a short-range attractive interaction favoring colinear dimers is considered on the lattice $\mathbb{Z}^2$. Although our choice of the chemical potentials results in more horizontal than vertical dimers, the horizontal dimers ... More

Physical quantities and dimensional analysis: from mechanics to quantum gravityNov 09 2015Jan 30 2016Physical quantities and physical dimensions are among the first concepts encountered by students in their undergraduate career. In this pedagogical review, I will start from these concepts and, using the powerful tool of dimensional analysis, I will embark ... More

Modified gravity and binary pulsars: the Lorentz violating caseJan 18 2016The dynamics of binary pulsars can be used to test different aspects of gravitation. This is particularly important to constrain alternatives to general relativity in regimes which are not probed by other methods. In this short contribution, I will describe ... More

Mutation of representations and nearly Morita equivalenceOct 20 2015Oct 26 2015Buan-Iyama-Reiten-Smith proved, based on Derksen-Weyman-Zelevinsky work, that the Jacobian algebra of two quivers with potential related by a QP-mutation are nearly Morita equivalent. They proved, using Axiom of Choice, that the natural functor $\mu_k$ ... More

On Formal Methods for Collective Adaptive System Engineering. {Scalable Approximated, Spatial} Analysis Techniques. Extended AbstractJul 08 2016In this extended abstract a view on the role of Formal Methods in System Engineering is briefly presented. Then two examples of useful analysis techniques based on solid mathematical theories are discussed as well as the software tools which have been ... More

Alternating register automata on finite words and treesFeb 17 2012Mar 07 2012We study alternating register automata on data words and data trees in relation to logics. A data word (resp. data tree) is a word (resp. tree) whose every position carries a label from a finite alphabet and a data value from an infinite domain. We investigate ... More

Complexity of Path-Following Methods for the Eigenvalue ProblemAug 13 2011May 24 2013A unitarily invariant projective framework is introduced to analyze the complexity of path-following methods for the eigenvalue problem. A condition number, and its relation to the distance to ill-posedness, is given. A Newton map appropriate for this ... More

Godel's theorem is invalidOct 21 2005Goedel's results have had a great impact in diverse fields such as philosophy, computer sciences and fundamentals of mathematics. The fact that the rule of mathematical induction is contradictory with the rest of clauses used by Goedel to prove his undecidability ... More

Named Entity Recognition on Noisy Data using Images and Text (1-page abstract)Sep 03 2018Named Entity Recognition (NER) is an important subtask of information extraction that seeks to locate and recognise named entities. Despite recent achievements, we still face limitations in correctly detecting and classifying entities, prominently in ... More

Study of the all orders multiplicative renormalizability of a local matter confining Gribov-Zwanziger action in the MAGFeb 27 2019We address the issue of the all order multiplicative renormalizability of $SU(2)$ Gribov-Zwanziger theories quantized in the maximal Abelian gauge in presence of confined matter fields. The non-linear character of the maximal Abelian gauge requires the ... More

Asymptotic analysis of solutions related to the game-theoretic p-laplacianFeb 27 2019We consider the (viscosity) solution $u(x,t)$ of the nonlinear evolution equation $u_t-\Delta^G_p u=0$ in a (not necessarily bounded) domain $\Omega$, such that $u=0$ in $\Omega$ at time $t=0$ and $u=1$ on the boundary of $\Omega$ at all times. Here, ... More

A-Foliations of codimension two on compact simply-connected manifoldsMar 17 2019We show that a singular Riemannian foliation of codimension $2$ on a compact simply-connected Riemannian $(n + 2)$-manifold, with regular leaves homeomorphic to the $n$-torus, is given by a smooth effective $n$-torus action.

SU(3)-holonomy metrics from nilpotent Lie groupsAug 11 2011One way of producing explicit Riemannian 6-manifolds with holonomy SU(3) is by integrating a flow of SU(2)-structures on a 5-manifold, called the hypo evolution flow. In this paper we classify invariant hypo SU(2)-structures on nilpotent 5-dimensional ... More

Symbolic computations in differential geometryApr 20 2008We introduce the C++ library Wedge, based on GiNaC, for symbolic computations in differential geometry. We show how Wedge makes it possible to use the language C++ to perform such computations, and illustrate some advantages of this approach with explicit ... More

Intrinsic torsion in quaternionic contact geometryJun 04 2013Jul 10 2014We investigate quaternionic contact (qc) manifolds from the point of view of intrinsic torsion. We argue that the natural structure group for this geometry is a non-compact Lie group K containing Sp(n)H^*, and show that any qc structure gives rise to ... More

Asymptotic analysis of nested derivativesApr 26 2012We analyze the nested derivatives of a function $\mathfrak{D}^{n}[f]\,(x)$ asymptotically, as $n\rightarrow\infty,$ using a discrete version of the ray method. We give some examples showing the accuracy of our formulas.

Mehler-Heine type formulas for Charlier and Meixner polynomialsJun 24 2014We derive Mehler--Heine type asymptotic formulas for Charlier and Meixner polynomials, and also for their associated families. These formulas provide good approximations for the polynomials in the neighborhood of $x=0,$ and determine the asymptotic limit ... More

An application of Kapteyn series to a problem from queueing theoryAug 02 2007We obtain exact solutions of a problem arising from queueing theory using properties of Kapteyn series.

Asymptotic analysis of generalized Hermite polynomialsJun 14 2006We analyze the polynomials $H_{n}^{r}(x)$ considered by Gould and Hopper, which generalize the classical Hermite polynomials. We present the main properties of $H_{n}^{r}(x)$ and derive asymptotic approximations for large values of $n$ from their differential-difference ... More

Burer-Monteiro guarantees for general semidefinite programsApr 15 2019Consider a semidefinite program (SDP) involving an $n\times n$ positive semidefinite matrix $X$. The Burer-Monteiro method consists in solving a nonconvex program in $Y$, where $Y$ is an $n\times p$ matrix such that $X=Y Y^T$. Despite nonconvexity, Boumal ... More

A molecular method applied to a non-local PDE in stratified Lie groupsJul 03 2013In this article we study a transport-diffusion equation in the framework of the stratified Lie groups. For this equation we will study the existence of the solutions, a maximum principle, a positivity principle and H\"older regularity.

Improved Sobolev Inequalities and Muckenhoupt weights on stratified Lie groupsJul 23 2010We study in this article the Improved Sobolev inequalities with Muckenhoupt weights within the framework of stratified Lie groups. This family of inequalities estimate the Lq norm of a function by the geometric mean of two norms corresponding to Sobolev ... More

Non-local diffusion equations with Lévy-type operators and divergence free driftMay 13 2012Dec 13 2012We are interested in some properties related to the solutions of non-local diffusion equations with divergence free drift. Existence, maximum principle and a positivity principle are proved. In order to study Holder regularity, we apply a method that ... More

On direct product subgroups of $\mathrm{SO}_3(\mathbb{R})$Aug 11 2006Let $G_1 \times G_2$ be a subgroup of $\mathrm{SO}_3(\mathbb{R})$ such that the two factors $G_1$ and $G_2$ are non-trivial groups. We show that if $G_1 \times G_2$ is not abelian, then one factor is the (abelian) group of order 2, and the other factor ... More

An incoherent simple groupJul 18 2005We give an example of a finitely presented simple group containing a finitely generated subgroup which is not finitely presented.

AFT Gravitational Model - Unity of All Elementary Particles in Sp(12,C)Feb 09 2010Oct 09 2012A new unifying theory was recently proposed by the author in the publication "Arrangement field theory - beyond strings and loop gravity -". Such theory describes all fields (gravitational, gauge and matter fields) as entries in a matricial superfield ... More

Nonexistence of simple hyperbolic blow-up for the quasi-geostrophic equationNov 01 1998The problem we are concerned with is whether singularities form in finite time in incompressible fluid flows. It is well known that the answer is ``no'' in the case of Euler and Navier-Stokes equations in dimension two. In dimension three it is still ... More

Asymptotic analysis of the Bell polynomials by the ray methodSep 03 2007We analyze the Bell polynomials $B_{n}(x)$ asymptotically as $n\to\infty$. We obtain asymptotic approximations from the differential-difference equation which they satisfy, using a discrete version of the ray method. We give some examples showing the ... More

Autour d'une conjecture de Kato et KuzumakiApr 03 2017In 1986, Kato and Kuzumaki stated several conjectures in order to give a diophantine characterization of cohomological dimension of fields. In this article, we first prove a local-global principle in this context for number fields. This allows us to give ... More

Invariant forms, associated bundles and Calabi-Yau metricsApr 26 2007Oct 25 2007We develop a method, initially due to Salamon, to compute the space of ``invariant'' forms on an associated bundle X=P\times_G V, with a suitable notion of invariance. We determine sufficient conditions for this space to be d-closed. We apply our method ... More

Some remarks on a paper by L. CarlitzApr 22 2005We study a family of orthogonal polynomials which generalizes a sequence of polynomials considered by L. Carlitz. We show that they are a special case of the Sheffer polynomials and point out some interesting connections with certain Sobolev orthogonal ... More

Embedding into manifolds with torsionDec 22 2008Mar 26 2009We introduce a class of special geometries associated to the choice of a differential graded algebra contained in \Lambda R^n. We generalize some known embedding results, that effectively characterize the real analytic Riemannian manifolds that can be ... More

Regularity of the derivatives of $p$-orthotropic functions in the plane for $1<p<2$Feb 12 2018We present a proof of the $C^1$ regularity of $p$-orthotropic functions in the plane for $1<p<2$, based on the monotonicity of the derivatives. Moreover we achieve an explicit logarithmic modulus of continuity.

A novel measurement of $B^0_s$ and $D^-_s$ lifetimes using semileptonic decays at LHCbOct 06 2017Oct 24 2017I report new, world-leading LHCb results on heavy meson lifetimes. We use a novel approach that suppresses the shortcomings typically associated with reconstruction of semileptonic decays, allowing for precise measurements of lifetimes and other properties ... More

On the Parameters of r-dimensional Toric CodesDec 13 2005From a rational convex polytope of dimension $r\ge 2$ J.P. Hansen constructed an error correcting code of length $n=(q-1)^r$ over the finite field $\fq$. A rational convex polytope is the same datum as a normal toric variety and a Cartier divisor. The ... More

Variétés abéliennes sur les corps de fonctions de courbes sur des corps locaux supérieursSep 25 2015Let $k$ be a higher-dimensional local field and $X$ be a smooth projective geometrically integral curve over $k$. Let $K$ be the function field of $X$. We define Tate-Shafarevich groups of an abelian variety via cohomology classes locally trivial at each ... More

A convex relaxation to compute the nearest structured rank deficient matrixApr 21 2019Given an affine space of matrices $L$ and a matrix $\theta \in L$, consider the problem of finding the closest rank deficient matrix to $\theta$ on $L$ with respect to the Frobenius norm. This is a nonconvex problem with several applications in estimation ... More

Error estimates for the Gregory-Leibniz series and the alternating harmonic series using Dalzell integralsAug 30 2018The computation of Dalzell integrals $\int_0^1 \frac{x^m (1-x)^n}{1+x^2} \, dx > 0$ gives new error estimates for the partial sums of the Gregory-Leibniz series $1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} \pm \ldots$ and for the alternating harmonic ... More

Nonlinear Schrödinger equation on graphs: recent results and open problemsApr 03 2013Apr 08 2013In the present paper an introduction to the new subject of nonlinear dispersive hamiltonian equations on graphs is given. The focus is on recently established properties of solutions in the case of nonlinear Schr\"odinger equation. Special consideration ... More

A strong factor for the reduction of inequalityAug 17 2006Dec 08 2006The inequality is computed through the so-called Gini index. The population is assumed to have the variable of interest distributed according to the Gamma probability distribution. The results show that the Gini index is reduced when the population is ... More

On an Improvement of the Planck radiation Energy DistributionMar 15 2006Jul 18 2006The probability distribution function for thermodynamics and econophysics is obtained by solving an equilibrium equation. This approach is different from the common one of optimizing the entropy of the system or obtaining the state of maximum probability, ... More

3 fermionic families naturally arise from hyperionic formalismJun 16 2012Mar 06 2013We'll show as a quantum theory based on hyperions (said also "complex quaternions") gives reason straightforwardly for the existence of three fermionic families, dark matter and superfields which don't require never seen particles.

A next-to-leading Luescher formulaSep 16 2013Oct 16 2013We propose a next-to-leading Luescher-like formula for the finite-size corrections of the excited states energies in integrable theories. We conjecture the expressions of the corrections for both the energy and the particles' rapidities by interpreting ... More

On the $C^{1,α}$ Regularity of $p$-Harmonic Functions in the Heisenberg GroupJun 25 2016Sep 17 2016We present a proof of the local H\"older regularity of the horizontal derivatives of weak solutions to the $p$-Laplace equation in the Heisenberg group $\mathbb{H}^1$ for $p>4 $.

Lectures on S-matrices and IntegrabilityJun 09 2016Aug 31 2016In these notes we review the S-matrix theory in (1+1)-dimensional integrable models, focusing mainly on the relativistic case. Once the main definitions and physical properties are introduced, we discuss the factorization of scattering processes due to ... More

Homotopy groups of generic leaves of logarithmic foliationsNov 17 2017We study the homotopy groups of generic leaves of logarithmic foliations on complex projective manifolds. We exhibit a relation between the homotopy groups of a generic leaf and of the complement of the polar divisor of the logarithmic foliation.

A Geometric Proof to Cantor's Theorem and an Irrationality Measure for Some Cantor's SeriesApr 29 2008Dec 25 2010Generalizing a geometric idea due to J. Sondow, we give a geometric proof for the Cantor's Theorem. Moreover, it is given an irrationality measure for some Cantor series.

Working with 2s and 3sApr 09 2007We establish an equivalent condition to the validity of the Collatz conjecture, using elementary methods. We derive some conclusions and show several examples of our results. We also offer a variety of exercises, problems and conjectures.

On the Specification of Constraints for Dynamic ArchitecturesMar 20 2017In dynamic architectures, component activation and connections between components may vary over time. With the emergence of mobile computing such architectures became increasingly important and several techniques emerged to support in their specification. ... More

Nested Derivatives: A simple method for computing series expansions of inverse functionsJan 04 2005Jan 04 2005We give an algorithm to compute the series expansion for the inverse of a given function. The algorithm is extremely easy to implement and gives the first $N$ terms of the series. We show several examples of its application in calculating the inverses ... More

Macquarie University at BioASQ 6b: Deep learning and deep reinforcement learning for query-based multi-document summarisationSep 14 2018Dec 06 2018This paper describes Macquarie University's contribution to the BioASQ Challenge (BioASQ 6b, Phase B). We focused on the extraction of the ideal answers, and the task was approached as an instance of query-based multi-document summarisation. In particular, ... More

An Arithmetic MetricJun 03 2009What is the distance between 11 (a prime number) and 12 (a highly composite number)? If your answer is 1, then ask yourself "is this reasonable?" In this work, we will introduce a distance between natural numbers based on their arithmetic properties, ... More

The proof of a conjecture concerning the intersection of k-generalized Fibonacci sequencesAug 24 2012Nov 04 2012For $k\geq 2$, the $k$-generalized Fibonacci sequence $(F_n^{(k)})_{n}$ is defined by the initial values $0,0,...,0,1$ ($k$ terms) and such that each term afterwards is the sum of the $k$ preceding terms. In 2005, Noe and Post conjectured that the only ... More