Instituto de Investigación en Matemáticas (IMUVA)Instituto de Investigación en Matemáticas (IMUVA)https://uvadoc.uva.es/handle/10324/321972024-04-18T02:30:11Z2024-04-18T02:30:11ZTwo characterizations of the dense rankGarcía Lapresta, José LuisMartínez Panero, Miguelhttps://uvadoc.uva.es/handle/10324/663982024-02-27T20:09:19Z2024-01-01T00:00:00ZIn this paper, we have considered the dense rank for assigning positions to alternatives in weak orders. If we arrange the alternatives in tiers (i.e., indifference classes), the dense rank assigns position 1 to all the alternatives in the top tier, 2 to all the alternatives in the second tier, and so on. We have proposed a formal framework to analyze the dense rank when compared to other well-known position operators, such as the standard, modified and fractional ranks. As the main results, we have provided two different axiomatic characterizations which determine the dense rank by considering position invariance conditions along horizontal extensions (duplication), as well as through vertical reductions and movements (truncation, and upward or downward independency).
2024-01-01T00:00:00ZEntanglement-assisted quantum error-correcting codes from subfield subcodes of projective Reed–Solomon codesRuano Benito, DiegoGiménez, Philippe ThierrySan José Rubio, Rodrigohttps://uvadoc.uva.es/handle/10324/654532024-02-01T08:54:39Z2023-01-01T00:00:00ZWe study the subfield subcodes of projective Reed-Solomon codes and their duals: we provide bases for these codes and estimate their parameters. With this knowledge, we can construct symmetric and asymmetric entanglement-assisted quantum error-correcting codes, which in many cases have new or better parameters than the ones available in the literature.
2023-01-01T00:00:00ZSubfield subcodes of projective Reed-Muller codesGiménez, Philippe ThierryRuano Benito, DiegoSan José Rubio, Rodrigohttps://uvadoc.uva.es/handle/10324/646362024-01-17T20:02:18Z2024-01-01T00:00:00ZExplicit bases for the subfield subcodes of projective Reed-Muller codes over the projective plane and their duals are obtained. In particular, we provide a formula for the dimension of these codes. For the general case over the projective space, we generalize the necessary tools to deal with this case as well: we obtain a universal Gröbner basis for the vanishing ideal of the set of standard representatives of the projective space and we show how to reduce any monomial with respect to this Gröbner basis. With respect to the parameters of these codes, by considering subfield subcodes of projective Reed-Muller codes we obtain long linear codes with good parameters over a small finite field.
2024-01-01T00:00:00ZAttractors in almost periodic Nicholson systems and some numerical simulationsVillarragut, Víctor M.Sanz Gil, Ana Maríahttps://uvadoc.uva.es/handle/10324/636102023-12-13T20:00:59Z2023-01-01T00:00:00ZThe existence of a global attractor is proved for the skew-product semiflow
induced by almost periodic Nicholson systems and new conditions are given for the
existence of a unique almost periodic positive solution which exponentially attracts
every other positive solution. Besides, some numerical simulations are included to
illustrate our results in some concrete Nicholson systems.
2023-01-01T00:00:00ZOn the structure of repeated-root polycyclic codes over local ringsBajalan, MaryamMartínez Moro, EdgarSobhani, RezaSzabo, SteveYılmazgüç, Gülsüm Gözdehttps://uvadoc.uva.es/handle/10324/635582023-12-12T20:01:59Z2024-01-01T00:00:00ZThis paper provides the Generalized Mattson Solomon polynomial for repeated-root polycyclic codes over local rings that gives an explicit decomposition of them in terms of idempotents. It also states some structural properties of repeated-root polycyclic codes over finite fields in terms of matrix product codes. Both approaches provide a description of the -dual code for a given polycyclic code.
2024-01-01T00:00:00ZOn real analogues of the Poincaré seriesCampillo López, AntonioDelgado de la Mata, FélixGusein-Zade, Sabir M.https://uvadoc.uva.es/handle/10324/628182023-11-10T20:00:53Z2023-01-01T00:00:00ZThere exist several equivalent equations for the Poincaréseries of a collection of valuations on the ring of germs offunctions on a complex analytic variety. We give defini-tions of the Poincaré series of a collection of valuationsin the real setting (i.e., on the ring of germs of functionson a real analytic variety), compute them for the case ofone curve valuation on the plane and discuss some oftheir properties.
2023-01-01T00:00:00ZCastelnuovo–Mumford regularity of projective monomial curves via sumsetsGiménez, Philippe ThierryGonzález Sánchez, Mariohttps://uvadoc.uva.es/handle/10324/616042023-09-18T19:00:51Z2023-01-01T00:00:00ZLet A={a0,…,an−1} be a finite set of n≥4 non-negative relatively prime integers, such that 0=a0<a1<⋯<an−1=d. The s-fold sumset of A is the set sA of integers that contains all the sums of s elements in A. On the other hand, given an infinite field k, one can associate with A the projective monomial curve CA
parametrized by A,
CA={(vd:ua1vd−a1:⋯:uan−2vd−an−2:ud)∣(u:v)∈P1k}⊂Pn−1k.
The exponents in the previous parametrization of CA
define a homogeneous semigroup S⊂N2. We provide several results relating the Castelnuovo–Mumford regularity of CA to the behavior of the sumsets of A and to the combinatorics of the semigroup S that reveal a new interplay between commutative algebra and additive number theory.
2023-01-01T00:00:00ZDoubly and triply extended MSRD codesMartínez Peñas, Umbertohttps://uvadoc.uva.es/handle/10324/612452023-08-30T19:05:22Z2023-01-01T00:00:00ZIn this work, doubly extended linearized Reed–Solomon codes and triply extended Reed–Solomon codes are generalized. We obtain a general result in which we characterize when a multiply extended code for a general metric attains the Singleton bound. We then use this result to obtain several families of doubly extended and triply extended maximum sum-rank distance (MSRD) codes that include doubly extended linearized Reed–Solomon codes and triply extended Reed–Solomon codes as particular cases. To conclude, we discuss when these codes are one-weight codes.
2023-01-01T00:00:00ZThe exponential ordering for nonautonomous delay systems with applications to compartmental Nicholson systemsObaya, RafaelNovo, SylviaSanz Gil, Ana MaríaVillarragut, Víctor M.https://uvadoc.uva.es/handle/10324/590342023-07-04T09:11:12Z2023-01-01T00:00:00ZThe exponential ordering is exploited in the context of nonautonomous delay
systems, inducing monotone skew-product semiflows under less restrictive conditions
than usual. Some dynamical concepts linked to the order, such as semiequilibria, are
considered for the exponential ordering, with implications for the determination of
the presence of uniform persistence or the existence of global attractors. Also, some
important conclusions on the long-term dynamics and attraction are obtained for
monotone and sublinear delay systems for this ordering. The results are then applied
to almost periodic Nicholson systems and new conditions are given for the existence
of a unique almost periodic positive solution which asymptotically attracts every
other positive solution.
2023-01-01T00:00:00ZOptimal flat functions in Carleman–Roumieu ultraholomorphic classes in sectorsJiménez Garrido, JavierMiguel Cantero, IgnacioSanz Gil, JavierSchindl, Gerhardhttps://uvadoc.uva.es/handle/10324/590002023-03-22T20:03:25Z2023-01-01T00:00:00ZWe construct optimal flat functions in Carleman–Roumieu ultraholomorphic classes associated to general strongly nonquasianalytic weight sequences, and defined on sectors of suitably restricted opening. A general procedure is presented in order to obtain linear continuous extension operators, right inverses of the Borel map, for the case of regular weight sequences in the sense of Dyn’kin. Finally, we discuss some examples (including the well-known q-Gevrey case) where such optimal flat functions can be obtained in a more explicit way.
2023-01-01T00:00:00ZThe asymptotic Samuel function and invariants of singularitiesBenito, AngélicaBravo, AnaEncinas Carrión, Santiagohttps://uvadoc.uva.es/handle/10324/588902023-03-08T14:37:09Z2023-01-01T00:00:00ZThe asymptotic Samuel function generalizes to arbitrary rings the usual order function of a regular local ring. In this paper, we use this function to introduce the notion of the Samuel slope of a Noetherian local ring, and we study some of its properties. In particular, we focus on the case of a local ring at singular point of a variety, and, among other results, we prove that the Samuel slope of these rings is related to some invariants used in algorithmic resolution of singularities.
2023-01-01T00:00:00ZEstimating and pricing commodity futures with time‐delay stochastic processesGómez del Valle, María LourdesMartínez Rodríguez, Juliahttps://uvadoc.uva.es/handle/10324/588652023-03-07T20:00:41Z2023-01-01T00:00:00ZIn commodity futures pricing models, the commodity present price is gener-ally considered to reflect all information in the markets and past information isnot regarded important. However, there is some empirical evidence that showsthat this fact is unrealistic. In this paper, we consider some stochastic mod-els with delay for pricing commodity futures. The functions of the commodityprice stochastic process under the risk-neutral measure are necessary for pricingderivatives. However, the observations in the market have risk. Then, we use atechnique that allows us to estimate the functions of the risk-neutral commodityspot price stochastic process, directly from futures prices traded in the market,and show how to price the commodity futures. Finally, we make an empiricalapplication of this methodology with gold futures traded in the COMEX. Fur-thermore, we make clear the supremacy of the delay models in pricing goldfutures.
2023-01-01T00:00:00ZInfluence of telomerase activity and initial distribution on human follicular aging: Moving from a discrete to a continuum modelPortillo de la Fuente, Ana MaríaVarela, E.García Velasco, J.A.https://uvadoc.uva.es/handle/10324/588192023-03-06T08:05:00Z2023-01-01T00:00:00ZA discrete model is proposed for the temporal evolution of a population of cells sorted according to their telomeric length. This model assumes that, during cell division, the distribution of the genetic material to daughter cells is asymmetric, i.e. chromosomes of one daughter cell have the same telomere length as the mother, while in the other daughter cell telomeres are shorter. Telomerase activity and cell death are also taken into account. The continuous model is derived from the discrete model by introducing the generational age as a continuous variable in , being the Hayflick limit, i.e. the number of times that a cell can divide before reaching the senescent state. A partial differential equation with boundary conditions is obtained. The solution to this equation depends on the initial telomere length distribution. The initial and boundary value problem is solved exactly when the initial distribution is of exponential type. For other types of initial distributions, a numerical solution is proposed. The model is applied to the human follicular growth from preantral to preovulatory follicle as a case study and the aging rate is studied as a function of telomerase activity, the initial distribution and the Hayflick limit. Young, middle and old cell-aged initial normal distributions are considered. In all cases, when telomerase activity decreases, the population ages and the smaller the value, the higher the aging rate becomes. However, the influence of these two parameters is different depending on the initial distribution. In conclusion, the worst-case scenario corresponds to an aged initial telomere distribution.
2023-01-01T00:00:00ZNon-autonomous scalar linear-dissipative and purely dissipative parabolic PDEs over a compact base flowObaya, RafaelSanz Gil, Ana Maríahttps://uvadoc.uva.es/handle/10324/586122023-06-05T20:00:33Z2021-01-01T00:00:00ZIn this paper a family of non-autonomous scalar parabolic PDEs over a general compact and connected flow is considered. The existence or not of a neighbourhood of zero where the problems are linear has an influence on the methods used and on the dynamics of the induced skew-product semiflow. That is why two cases are distinguished: linear-dissipative and purely dissipative problems. In both cases, the structure of the global and pullback attractors is studied using principal spectral theory. Besides, in the purely dissipative setting, a simple condition is given, involving both the underlying linear dynamics and some properties of the nonlinear term, to determine the nontrivial sections of the attractor
2021-01-01T00:00:00ZTopologies of continuity for Carathéodory parabolic PDEs from a dynamical perspectiveObaya, RafaelLongo, Iacopo PaoloSanz Gil, Ana Maríahttps://uvadoc.uva.es/handle/10324/585802023-03-08T12:55:36Z2023-01-01T00:00:00ZSystems of non-autonomous parabolic partial differential equations over a bounded domain with nonlinear term of Carathéodory type are considered. Appropriate topologies on sets of Lipschitz Carathéodory maps are defined in order to have a continuous dependence of the mild solutions with respect to the variation of both the nonlinear term and the initial conditions, under different assumptions on the bound-maps of the nonlinearities.
2023-01-01T00:00:00ZA variational modification of the harmonic balance method to obtain approximate floquet exponentsGadella Urquiza, ManuelLara, Luis Pedrohttps://uvadoc.uva.es/handle/10324/584912023-03-22T15:26:39Z2023-01-01T00:00:00ZWe propose a modification of a method based on Fourier analysis to obtainthe Floquet characteristic exponents for periodic homogeneous linear systems,which shows a high precision. This modification uses a variational principle tofind the correct Floquet exponents among the solutions of an algebraic equation.Once we have these Floquet exponents, we determine explicit approximatedsolutions. We test our results on systems for which exact solutions are knownto verify the accuracy of our method including one-dimensional periodicpotentials of interest in quantum physics. Using the equivalent linear system,we also study approximate solutions for homogeneous linear equations withperiodic coefficients.
2023-01-01T00:00:00Z