On Maximal Unbordered Factors

Given a string $S$ of length $n$, its maximal unbordered factor is the longest factor which does not have a border. In this work we investigate the relationship between $n$ and the length of the maximal unbordered factor of $S$. We prove that for the alphabet of size $\sigma \ge 5$ the expected length of the maximal unbordered factor of a string of length~$n$ is at least $0.99 n$ (for sufficiently large values of $n$). As an application of this result, we propose a new algorithm for computing the maximal unbordered factor of a string.Comment: Accepted to the 26th Annual Symposium on Combinatorial Pattern Matching (CPM 2015

Very fast relaxation in polycarbonate glass

Low-frequency Raman and inelastic neutron scattering of amorphous bis-phenol A polycarbonate is measured at low temperature, and compared. The vibrational density of states and light-vibration coupling coefficient are determined. The frequency dependences of these parameters are explained by propagating vibration modes up to an energy of about 1 meV, and fracton-like modes in more cohesive domains at higher energies. The vibrational dynamics is in agreement with a disorder in the glass, which is principally of bonding or of elasticity instead of density.Comment: 15 pages, 6 figures, to be pub. in EPJ

Equivariant quantization of orbifolds

Equivariant quantization is a new theory that highlights the role of symmetries in the relationship between classical and quantum dynamical systems. These symmetries are also one of the reasons for the recent interest in quantization of singular spaces, orbifolds, stratified spaces... In this work, we prove existence of an equivariant quantization for orbifolds. Our construction combines an appropriate desingularization of any Riemannian orbifold by a foliated smooth manifold, with the foliated equivariant quantization that we built in \cite{PoRaWo}. Further, we suggest definitions of the common geometric objects on orbifolds, which capture the nature of these spaces and guarantee, together with the properties of the mentioned foliated resolution, the needed correspondences between singular objects of the orbifold and the respective foliated objects of its desingularization.Comment: 13 page

Twist Deformation of Rotationally Invariant Quantum Mechanics

Non-commutative Quantum Mechanics in 3D is investigated in the framework of the abelian Drinfeld twist which deforms a given Hopf algebra while preserving its Hopf algebra structure. Composite operators (of coordinates and momenta) entering the Hamiltonian have to be reinterpreted as primitive elements of a dynamical Lie algebra which could be either finite (for the harmonic oscillator) or infinite (in the general case). The deformed brackets of the deformed angular momenta close the so(3) algebra. On the other hand, undeformed rotationally invariant operators can become, under deformation, anomalous (the anomaly vanishes when the deformation parameter goes to zero). The deformed operators, Taylor-expanded in the deformation parameter, can be selected to minimize the anomaly. We present the deformations (and their anomalies) of undeformed rotationally-invariant operators corresponding to the harmonic oscillator (quadratic potential), the anharmonic oscillator (quartic potential) and the Coulomb potential.Comment: 20 page

Projectively equivariant quantizations over the superspace Rp∣q\R^{p|q}

We investigate the concept of projectively equivariant quantization in the framework of super projective geometry. When the projective superalgebra pgl(p+1|q) is simple, our result is similar to the classical one in the purely even case: we prove the existence and uniqueness of the quantization except in some critical situations. When the projective superalgebra is not simple (i.e. in the case of pgl(n|n)\not\cong sl(n|n)), we show the existence of a one-parameter family of equivariant quantizations. We also provide explicit formulas in terms of a generalized divergence operator acting on supersymmetric tensor fields.Comment: 19 page

Fintech and the socialization of the financial industry

Fintech have known an incredible exposure over the last years, attracting investments of large billions of dollars. Fintech are the match between finance and technology and they are imposing a new way of thinking in all the branches of the financial industry. After the financial crisis of 2008, people have changed their way of seeing “Finance” and, more particularly, the role of banks, looking for products and services that correspond to their needs. Moreover, the financial crisis has highlighted a relevant number of dysfunctions on the banking sector and on the financial regulation. Regulators have strengthened their requirements for banks, particularly in their relations with clients. These have opened a breach for Fintech companies and they are using it. Fintech companies rely on a different value proposition to clients that is based on a timesaving, fast and clear experience. Indeed, they propose major innovations in products and processes. Fintech companies put the client back at the center of all their attention and clients are now the top priority.info:eu-repo/semantics/publishedVersio

Decomposition of symmetric tensor fields in the presence of a flat contact projective structure

Let $M$ be an odd-dimensional Euclidean space endowed with a contact 1-form $\alpha$. We investigate the space of symmetric contravariant tensor fields on $M$ as a module over the Lie algebra of contact vector fields, i.e. over the Lie subalgebra made up by those vector fields that preserve the contact structure. If we consider symmetric tensor fields with coefficients in tensor densities, the vertical cotangent lift of contact form $\alpha$ is a contact invariant operator. We also extend the classical contact Hamiltonian to the space of symmetric density valued tensor fields. This generalized Hamiltonian operator on the symbol space is invariant with respect to the action of the projective contact algebra $sp(2n+2)$. The preceding invariant operators lead to a decomposition of the symbol space (expect for some critical density weights), which generalizes a splitting proposed by V. Ovsienko

Low-energy vibrational density of states of plasticized poly(methyl methacrylate)

The low-energy vibrational density of states (VDOS)of hydrogenated or deuterated poly(methyl methacrylate)(PMMA)plasticized by dibutyl phtalate (DBP) is determined by inelastic neutron scattering.From experiment, it is equal to the sum of the ones of the PMMA and DBP components.However, a partition of the total low-energy VDOS among PMMA and DBP was observed.Contrary to Raman scattering, neutron scattering does not show enhancement of the boson peak due to plasticization.Comment: 9 pages, 2 figures (Workshop on Disordered Systems, Andalo

Harmonic oscillator in a background magnetic field in noncommutative quantum phase-space

We solve explicitly the two-dimensional harmonic oscillator and the harmonic oscillator in a background magnetic field in noncommutative phase-space without making use of any type of representation. A key observation that we make is that for a specific choice of the noncommutative parameters, the time reversal symmetry of the systems get restored since the energy spectrum becomes degenerate. This is in contrast to the noncommutative configuration space where the time reversal symmetry of the harmonic oscillator is always broken.Comment: 7 pages Late

Magnetic-Dipole Spin Effects in Noncommutative Quantum Mechanics

A general three-dimensional noncommutative quantum mechanical system mixing spatial and spin degrees of freedom is proposed. The analogous of the harmonic oscillator in this description contains a magnetic dipole interaction and the ground state is explicitly computed and we show that it is infinitely degenerated and implying a spontaneous symmetry breaking. The model can be straightforwardly extended to many particles and the main above properties are retained. Possible applications to the Bose-Einstein condensation with dipole-dipole interactions are briefly discussed.Comment: New references added, implications with Bose-Einstein condensationare discussed and some portions of the manuscript rewritte