Dpto. Álgebra, Análisis Matemático, Geometría y Topología96https://uvadoc.uva.es/handle/10324/11292023-03-31T13:31:38Z2023-03-31T13:31:38ZStratification of three-dimensional real flows I: Fitting domainsAlonso González, C.Sanz Sánchez, Fernandohttps://uvadoc.uva.es/handle/10324/589202023-03-13T20:00:16Z2023-01-01T00:00:00ZLet ξ be an analytic vector field in R3 with an isolated singularity at the origin and having only hyperbolic
singular points after a reduction of singularities π : M → R3. The union of the images by π of the local
invariant manifolds at those hyperbolic points, denoted by Λ, is composed of trajectories of ξ accumulating to 0 ∈ R3. Assuming that there are no cycles nor polycycles on the divisor of π , together with a Morse-Smale type property and a non-resonance condition on the eigenvalues at these points, in this paper we prove the existence of a fundamental system {Vn} of neighborhoods well adapted for the description of the local dynamics of ξ : the frontier F r(Vn) is everywhere tangent to ξ except around F r(Vn) ∩ Λ, where transversality is mandatory.
2023-01-01T00:00:00ZTruncated local uniformization of formal integrable differential formsCano Torres, FelipeFernández Duque, Miguelhttps://uvadoc.uva.es/handle/10324/522102022-04-05T07:43:44Z2021-01-01T00:00:00ZWe prove the existence of Local Uniformization for rational codimension one foliations along rational rank one valuations, in any ambient dimension. This result is consequence of the Truncated Local Uniformization of integrable formal differential 1-forms, that we also state and prove in the paper. Thanks to the truncated approach, we perform a classical inductive procedure, based both in the control of the Newton Polygon and in the possibility of avoiding accumulations of values, given by the existence of suitable Tschirnhausen transformations.
2021-01-01T00:00:00ZAccelerated Processing for Maximum Distance Separable Codes using Composite Extension FieldsRuano Benito, DiegoLucani, Daniel E.Geil, Olavhttps://uvadoc.uva.es/handle/10324/401522021-06-23T09:46:34Z2019-01-01T00:00:00ZThis paper describes a new design of Reed-Solomon (RS) codes when using composite extension fields. Our ultimate goal is to provide codes that remain Maximum Distance Separable (MDS), but that can be processed at higher speeds in the encoder and decoder. This is possible by using coefficients in the generator matrix that belong to smaller (and faster) finite fields of the composite extension and limiting the use of the larger (and slower) finite fields to a minimum. We provide formulae and an algorithm to generate such constructions starting from a Vandermonde RS generator matrix and show that even the simplest constructions, e.g., using only processing in two finite fields, can speed up processing by as much as two-fold compared to a Vandermonde RS and Cauchy RS while using the same decoding algorithm, and more than two-fold compared to other RS Cauchy and FFT-based RS.
2019-01-01T00:00:00ZSquares of matrix-product codesCascudo, IgnacioGundersen, Jaron SkovstedRuano Benito, Diegohttps://uvadoc.uva.es/handle/10324/401432021-06-23T09:46:30Z2020-01-01T00:00:00ZThe component-wise or Schur product $C*C'$ of two linear error-correcting codes $C$ and $C'$ over certain finite field is the linear code spanned by all component-wise products of a codeword in $C$ with a codeword in $C'$. When $C=C'$, we call the product the square of $C$ and denote it $C^{*2}$. Motivated by several applications of squares of linear codes in the area of cryptography, in this paper we study squares of so-called matrix-product codes, a general construction that allows to obtain new longer codes from several ``constituent'' codes. We show that in many cases we can relate the square of a matrix-product code to the squares and products of their constituent codes, which allow us to give bounds or even determine its minimum distance. We consider the well-known $(u,u+v)$-construction, or Plotkin sum (which is a special case of a matrix-product code) and determine which parameters we can obtain when the constituent codes are certain cyclic codes. In addition, we use the same techniques to study the squares of other matrix-product codes, for example when the defining matrix is Vandermonde (where the minimum distance is in a certain sense maximal with respect to matrix-product codes).
2020-01-01T00:00:00ZImproved Bounds on the Threshold Gap in Ramp Secret SharingCascudo, IgnacioGundersen, Jaron SkovstedRuano Benito, Diegohttps://uvadoc.uva.es/handle/10324/401362021-06-24T07:41:13Z2019-01-01T00:00:00ZIn this paper, we consider linear secret sharing schemes over a finite field F q , where the secret is a vector in Fℓ q and each of the n shares is a single element of F q . We obtain lower bounds on the so-called threshold gap g of such schemes, defined as the quantity r-t where r is the smallest number such that any subset of r shares uniquely determines the secret and t is the largest number such that any subset of t shares provides no information about the secret. Our main result establishes a family of bounds which are tighter than previously known bounds for ℓ ≳ 2 . Furthermore, we also provide bounds, in terms of n and q , on the partial reconstruction and privacy thresholds, a more fine-grained notion that considers the amount of information about the secret that can be contained in a set of shares of a given size. Finally, we compare our lower bounds with known upper bounds in the asymptotic setting.
2019-01-01T00:00:00ZEntanglement-assisted quantum error-correcting codes over arbitrary finite fieldsGalindo, CarlosHernando, FernandoMatsumoto, RyutarohRuano Benito, Diegohttps://uvadoc.uva.es/handle/10324/401342021-06-24T07:41:10Z2019-01-01T00:00:00ZWe prove that the known formulae for computing the optimal number of maximally entangled pairs required for entanglement-assisted quantum error-correcting codes (EAQECCs) over the binary field hold for codes over arbitrary finite fields as well. We also give a Gilbert-Varshamov bound for EAQECCs and constructions of EAQECCs coming from punctured self-orthogonal linear codes which are valid for any finite field.
2019-01-01T00:00:00ZAn Analytic Study of the Reversal of Hartmann Flows by Rotating Magnetic FieldsNúñez Jiménez, Manuelhttps://uvadoc.uva.es/handle/10324/399482021-06-23T09:46:26Z2012-01-01T00:00:00ZThe effects of a background uniform rotating magnetic field acting in a conducting fluid with a parallel flow are studied analytically. The stationary version with a transversal magnetic field is well known as generating Hartmann boundary layers. The Lorentz force includes now one term depending on the rotation speed and the distance to the boundary wall. As one intuitively expects, the rotation of magnetic field lines pushes backwards or forwards the flow. One consequence is that near the wall the flow will eventually reverse its direction, provided the rate of rotation and/or the magnetic field are large enough. The configuration could also describe a fixed magnetic field and a rotating flow.
2012-01-01T00:00:00ZResonances and oscillatory behavior near multi-species plasma equilibriaNúñez Jiménez, Manuelhttps://uvadoc.uva.es/handle/10324/399452021-06-23T09:46:25Z2014-01-01T00:00:00ZWe consider dynamic multi-species plasma equilibria whose variables depend on a single spatial
coordinate and linear perturbations of these. The linearized system may be reduced to a second-order
one satisfied by the respective fluid streamfunctions. For the two-species case, the electron mass is a
parameter small enough for a WKB asymptotic analysis to be justified. It turns out that the points
where either the ion or electron equilibrium velocity equals the ratio between the temporal
and transversal frequencies of the perturbation are turning or singular points of the system,
connecting exponentially increasing or decreasing solutions to oscillatory ones. The crucial role of
singular points in the balance between the different contributions to the electron kinetic energy is
explored.
2014-01-01T00:00:00ZOn the asymptotic balance between electric and magnetic energies for hydromagnetic relativistic flowsNúñez Jiménez, Manuelhttps://uvadoc.uva.es/handle/10324/399432021-06-23T09:46:24Z2013-01-01T00:00:00ZIn the equations of classical magnetohydrodynamics, the displacement current is considered
vanishingly small due to low plasma velocities. For velocities comparable to the speed of light, the
full relativistic electromagnetic equations must be used. In the absence of gravitational forcings
and with an isotropic Ohm’s law, it is proved that for poloidal magnetic field and velocity and
toroidal electric field, the electric and magnetic energies tend to be equivalent in average for large
times. This represents a partial extension of Cowling’s theorem for axisymmetric fields.
2013-01-01T00:00:00ZBlowup of certain analytic solutions of the Hall magnetohydrodynamic equationsNúñez Jiménez, ManuelÁlvarez López, JorgeRojo García, Jesúshttps://uvadoc.uva.es/handle/10324/399422021-06-23T09:46:23Z2008-01-01T00:00:00ZA recent analytic solution of the Hall magnetohydrodynamics equations is analyzed. It is shown that
its evolution in time depends upon a certain set of inequalities upon the initial values of the velocity
and the magnetic field. For most of the cases, both magnitudes will blow up in a finite time. This
shows that for keeping the original structure of the solution, energy must be introduced into the
system until eventually it cannot hold any longer.
2008-01-01T00:00:00ZDynamo effect of spacetime curvature in force-free magnetospheresNúñez Jiménez, Manuelhttps://uvadoc.uva.es/handle/10324/399412021-06-23T09:46:22Z2012-01-01T00:00:00ZWe study the possibility of growth of the electric and magnetic fields in a force-free plasma due strictly
to the gravitational curvature of the spacetime domain where those fields lie. To this end, we identify a
total energy by analogy with the results of classical magnetohydrodynamics. After obtaining the general
evolution equation for the total energy, we apply to it to the fiducial observers in a number of classical
metrics: Schwarzschild, Boyer-Lindquist, Kerr-Schild, Robertson-Walker, and post-Newtonian approximation.
As a rule the shift velocity plays the role of minus the fluid velocity in Newtonian MHD, but the
details are often highly intricate.
2012-01-01T00:00:00ZUniform estimates on the velocity in Rayleigh–Bénard convectionNúñez Jiménez, Manuelhttps://uvadoc.uva.es/handle/10324/395962021-06-23T09:46:21Z2005-01-01T00:00:00ZThe kinetic energy of a fluid located between two plates at different temperatures is easily bounded by classical inequalities. However, experiments and numerical simulations indicate that when the convection is turbulent, the volume of the domains in which the speed is large, is rather small. This could imply that the maximum of the speed, in contrast with its quadratic mean, does not admit an a priori upper bound. It is proved that, provided the pressure remains bounded, a uniform estimate for the speed maximum does indeed exist, and that it depends on the maxima of certain ratios between temperature, pressure, and velocity.
2005-01-01T00:00:00ZInvariant subspaces of the periodic Navier–Stokes and magnetohydrodynamics equations: Symmetries and inverse cascadesNúñez Jiménez, Manuelhttps://uvadoc.uva.es/handle/10324/395942021-06-23T09:46:20Z2000-01-01T00:00:00ZIt is shown that when the initial condition and the forcing term of the periodic Navier–Stokes or magnetohydrodynamics equations have Fourier coefficients which vanish outside a certain semigroup of frequencies, the same happens to the solutions for all time. Subgroups of frequencies correspond to solutions possessing certain symmetries. By taking as a semigroup the frequencies whose Fourier components are non-negative integers, we get a class of solutions for which the higher modes do not influence the evolution of the lower ones; therefore, the phenomenon of inverse cascading cannot occur for them.
2000-01-01T00:00:00ZExistence theorems for two-fluid magnetohydrodynamicsNúñez Jiménez, Manuelhttps://uvadoc.uva.es/handle/10324/395932021-06-23T09:46:19Z2005-01-01T00:00:00ZThe description of a plasma as composed by two types of fluids, formed by ions
and electrons, is more complete than the classical one-fluid magnetohydrodynamics
MHD model and it has proved necessary to explain the phenomena of fast magnetic
reconnection. We prove a finite-time theorem of existence and uniqueness of
solutions for this system for either Dirichlet or periodic boundary conditions in
dimension three. It turns out that the regularity estimates for the magnetic field are
finer than the MHD ones.
2005-01-01T00:00:00ZPlasma velocity in hydromagnetic dynamosNúñez Jiménez, Manuelhttps://uvadoc.uva.es/handle/10324/395892021-06-23T09:46:18Z2002-01-01T00:00:00ZHydromagnetic dynamos are plasma configurations generating for some time an
exponentially increasing magnetic field. By using a number of functional inequalities,
we estimate the rate of increase of magnetic energy in terms of the plasma
resistivity and diferent norms on the plasma velocity. Our bounds are proved to be
optimal as far as the powers of the relevant magnitudes are concerned.
2002-01-01T00:00:00ZOn the gravitational potential of modified Newtonian dynamicsNúñez Jiménez, Manuelhttps://uvadoc.uva.es/handle/10324/387362021-06-23T09:46:18Z2013-01-01T00:00:00ZThe mathematical structure of the Poisson equation of Modified Newtonian Dynamics
(MOND) is studied. The appropriate setting turns out to be an Orlicz-Sobolev
space whose Orlicz function is related to Milgrom’s μ-function, where there exists
existence and uniqueness of weak solutions. Since these do not have in principle
much regularity, a further study is performed where the gravitational field is not
too large, where MOND is most relevant. In that case the field turns out to be
H¨older continuous. Quasilinear MOND is also analyzed.
2013-01-01T00:00:00Z