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Memorial for our Editorial Board Member Marc Yor
http://ddd.uab.cat/record/119048
Revista Publicacions matemàtiquesThu, 10 Jul 2014 11:55:06 GMThttp://ddd.uab.cat/record/119048The Riesz transform, rectifiability, and removability for Lipschitz harmonic functions
http://ddd.uab.cat/record/119046
We show that, given a set E Rn+1 with finite n-Hausdorff measure Hn, if the n-dimensional Riesz transform is bounded in L2(HnbE), then E is n-rectifiable. From this result we deduce that a compact set E Rn+1 with Hn(E) < 1 is removable for Lipschitz harmonic functions if and only if it is purely n-unrectifiable, thus proving the analog of Vitushkin's conjecture in higher dimensions. Nazarov, FedorThu, 10 Jul 2014 11:51:28 GMThttp://ddd.uab.cat/record/119046Embeddings of local fields in simple algebras and simplicial structures
http://ddd.uab.cat/record/119044
We give a geometric interpretation of Broussous{Grabitz embedding types. We fix a central division algebra D of finite index over a non-Archimedean local field F and a positive integer m. Further we fix a hereditary order a of Mm(D) and an unramified field extension EjF in Mm(D) which is embeddable in D and which normalizes a. Such a pair (E, a) is called an embedding. The embedding types classify the GLm(D)-conjugation classes of these embeddings. Such a type is a class of matrices with non-negative integer entries. We give a formula which allows us to recover the embedding type of (E, a) from the simplicial type of the image of the barycenter of a under the canonical isomorphism, from the set of Ex-fixed points of the reduced building of GLm(D) to the reduced building of the centralizer of Ex in GLm(D). Conversely the formula allows to calculate the simplicial type up to cyclic permutation of the Coxeter diagram. Skodlerack, DanielThu, 10 Jul 2014 11:32:28 GMThttp://ddd.uab.cat/record/119044Comparison principle and constrained radial symmetry for the subdiffusive p-laplacian
http://ddd.uab.cat/record/119042
A comparison principle for the subdiffusive p-Laplacian in a possibly non-smooth and unbounded open set is proved. The result requires that the involved suband supersolution are positive, and the ratio of the former to the latter is bounded. As an application, constrained radial symmetry for overdetermined problems is obtained. More precisely, both Dirichlet and Neumann conditions are prescribed on the boundary of a bounded open set, and the Neumann condition depends on the distance from the origin. The domain of the problem, unknown at the beginning, turns out to be a ball centered at the origin if a positive solution exists. Counterexamples are also discussed. Greco, AntonioThu, 10 Jul 2014 11:16:17 GMThttp://ddd.uab.cat/record/119042Third-power associative absolute valued algebras with a nonzero idempotent commuting with all idempotents
http://ddd.uab.cat/record/119040
This paper deals with the determination of the absolute valued algebras with a nonzero idempotent commuting with the remaining idempotents and satisfying x2x = xx2 for every x. We prove that, in addition to the absolute valued algebras R, C, H, or O of the reals, complexes, division real quaternions or division real octonions, one such absolute valued algebra A can also be isometrically isomorphic to some of the absolute valued algebras C. H or O, obtained from C, H, and O by imposing a new product defined by multiplying the conjugates of the elements. In particular, every absolute valued algebra having the above properties is finite-dimensional. This generalizes some well known theorems of Albert, Urbanik and Wright, and El-Mallah. Cuenca Mira, José AntonioThu, 10 Jul 2014 11:05:23 GMThttp://ddd.uab.cat/record/119040Explicit minimal scherk saddle towers of arbitrary even genera in R3
http://ddd.uab.cat/record/119039
Starting from works by Scherk (1835) and by Enneper-Weierstrass (1863), new minimal surfaces with Scherk ends were found only in 1988 by Karcher (see [9, 10]). In the singly periodic case, Karcher's examples of positive genera had been unique until Traizet obtained new ones in 1996 (see [23]). However, Traizet's construction is implicit and excludes towers, namely the desingularisation of more than two concurrent planes. Then, new explicit towers were found only in 2006 by Martín and Ramos Batista (see [13]), all of them with genus one. For genus two, the first such towers were constructed in 2010 (see [22]). Back to 2009, implicit towers of arbitrary genera were found in [5]. In our present work we obtain explicit minimal Scherk saddle towers, for any given genus 2k, k 3. Yucra Hancco, A. J.Thu, 10 Jul 2014 09:58:13 GMThttp://ddd.uab.cat/record/119039On restricted weak-type constants of Fourier multipliers
http://ddd.uab.cat/record/119038
We exhibit a large class of symbols m: Rd ! C for which the corresponding Fourier multipliers Tm satisfy the following restricted weak-type estimates: if A Rd has finite Lebesgue measure, then. . . In particular, this leads to novel sharp estimates for the real and imaginary part of the Beurling-Ahlfors operator on C. The proof rests on probabilistic methods: we exploit a stochastic representation of the multipliers in terms of Lévy processes and appropriate sharp inequalities for differentially subordinated martingales. Osekowski, AdamThu, 10 Jul 2014 09:46:01 GMThttp://ddd.uab.cat/record/119038On separated Carleson sequences in the unit disc
http://ddd.uab.cat/record/119034
The interpolating sequences S for H∞(D), the bounded holomorphic functions in the unit disc D of the complex plane C, were characterized by L. Carleson using metric conditions on S. Alternatively, to characterize interpolating sequences we can use the existence in H∞(D) of an inﬁnity of functions {ρa}a∈S, uniformly bounded in D, the function ρa being 1 at the point a ∈ S and 0 at any b ∈ S \ {a}. A. Hartmann recently proved that just one function in H∞(D) was enough to characterize interpolating sequences for H∞(D). In this work we use the “hard” part of Carleson’s proof of the corona theorem to extend Hartmann’s result and to answer a question he asked in his paper. Amar, EricWed, 09 Jul 2014 11:45:02 GMThttp://ddd.uab.cat/record/119034Smoothing properties of the discrete fractional maximal operator on Besov and Triebel-Lizorkin spaces
http://ddd.uab.cat/record/119033
Motivated by the results of Korry, and Kinnunen and Saksman, we study the behaviour of the discrete fractional maximal operator on fractional Hajlasz spaces, Hajlasz-Besov, and Hajlasz-Triebel-Lizorkin spaces on metric measure spaces. We show that the discrete fractional maximal operator maps these spaces to the spaces of the same type with higher smoothness. Our results extend and unify aforementioned results. We present our results in a general setting, but they are new already in the Euclidean case. Heikkinen, ToniWed, 09 Jul 2014 11:33:42 GMThttp://ddd.uab.cat/record/119033Atomic decomposition of real-variable type for Bergman spaces in the unit ball of Cn
http://ddd.uab.cat/record/119032
In this paper we show that, for any 0 < p _ 1 and _ > 1, every (weighted) Bergman space Ap _(Bn) admits an atomic decomposition of real-variable type. More precisely, for each f 2 Ap _(Bn) there exist a sequence of (p;1)_-atoms ak with compact support and a scalar sequence f_kg such that f = P k _kak in the sense of distribution and Pk j_kjp . kfkp p and moreover, f = Pk _kP_(ak) in Ap_(Bn); where P_ is the orthogonal projection from L2_(Bn) onto A2_(Bn): The proof is constructive and our construction is based on analysis inside the unit ball Bn associated with a quasimetric. Chen, ZeqianWed, 09 Jul 2014 11:22:57 GMThttp://ddd.uab.cat/record/119032Stable sampling and fourier multipliers
http://ddd.uab.cat/record/119031
We study the relationship between stable sampling sequences for band-limited functions in Lp(Rn) and the Fourier multipliers in Lp. In the case that the sequence is a lattice and the spectrum is a fundamental domain for the lattice the connection is complete. In the case of irregular sequences there is still a partial relationship. Matei, BasarabWed, 09 Jul 2014 11:12:59 GMThttp://ddd.uab.cat/record/119031Groups with normality conditions for subgroups of infinite rank
http://ddd.uab.cat/record/119030
A well-known theorem of B. H. Neumann states that a group has finite conjugacy classes of subgroups if and only if it is central-by-finite. It is proved here that if G is a generalized radical group of infinite rank in which the conjugacy classes of subgroups of infinite rank are finite, then every subgroup of G has finitely many conjugates, and so G=Z(G) is finite. Corresponding results are proved for groups in which every subgroup of infinite rank has fiznite index in its normal closure, and for those in which every subgroup of infinite rank is finite over its core. De Falco, MariaWed, 09 Jul 2014 10:58:09 GMThttp://ddd.uab.cat/record/119030Resultant and conductor of geometrically semi-stable self maps of the projective line over a number field or function field
http://ddd.uab.cat/record/119029
We study the minimal resultant divisor of self-maps of the projective line over a number field or a function field and its relation to the conductor. The guiding focus is the exploration of a dynamical analog to Theorem 1. 1, which bounds the degree of the minimal discriminant of an elliptic surface in terms of the conductor. The main theorems of this paper (5. 5 and 5. 6) establish that, for a degree 2 map, semi-stability in the Geometric Invariant Theory sense on the space of self maps, implies minimality of the resultant. We prove the singular reduction of a semi-stable presentation coincides with the simple bad reduction (Theorem 4. 1). Given an elliptic curve over a function field with semi-stable bad reduction, we show the associated Lattès map has unstable bad reduction Proposition 4. 6). Degree 2 maps in normal form with semi-stable bad reduction are used to construct a counterexample (Example 3. 1) to a simple dynamical analog to Theorem 1. 1. Szpiro, LucienWed, 09 Jul 2014 10:17:17 GMThttp://ddd.uab.cat/record/119029A PDE approach of inflammatory phase dynamics in diabetic wounds
http://ddd.uab.cat/record/119028
The objective of the present paper is the modeling and analysis of the dynamics of macrophages and certain growth factors in the inﬂammatory phase, the ﬁrst one of the wound healing process. It is the phase where there exists a major difference between diabetic and non-diabetic wound healing, an effect that we will consider in this paper. Cónsul, N.Wed, 09 Jul 2014 09:35:13 GMThttp://ddd.uab.cat/record/119028Bautin ideals and Taylor domination
http://ddd.uab.cat/record/118324
Yomdin, Y.Mon, 19 May 2014 17:50:50 GMThttp://ddd.uab.cat/record/118324Uniform methods to stablish Poincaré type linearization theorems
http://ddd.uab.cat/record/118322
We find a uniform method to establish Poincaré type linearization theorems for regular systems including classical autonomous, random and almost periodic ones via modified majorant norm methods. Wu, HaoMon, 19 May 2014 16:35:01 GMThttp://ddd.uab.cat/record/118322Topological and polynomial invariants, moduli spaces, in classification problems of polynomial vector fields
http://ddd.uab.cat/record/118321
We describe the origin and evolution of ideas on topological and polynomial invariants and their interaction, in problems of classification of polynomial vector fields. The concept of moduli space is discussed in the last section and we indicate its value in understanding the dynamics of families of such systems. Our interest here is in the concepts and the way they interact in the process of topologically classifying polynomial vector fields. We survey the literature giving an ample list of references and we illustrate the ideas on the testing ground of families of quadratic vector fields. In particular, the role of polynomial invariants is illustrated in the proof of our theorem in the section next to last. These concepts have proven their worth in a number of classification results, among them the most recent work on the geometric classification of the whole class of quadratic vector fields, according to their configurations of infinite singularities. An analog work including both finite and infinite singularities of the whole quadratic class, joint work with J. C. Artés, J. Llibre, and N. Vulpe, is in progress. Schlomiuk, DanaMon, 19 May 2014 16:31:48 GMThttp://ddd.uab.cat/record/118321Finding Hamiltonian isochronous centers by non-canonical transformations
http://ddd.uab.cat/record/118320
Starting from a class of isochronous Hamiltonian centers, we produce a new class of Hamiltonian isochronous centers by using non-canonical transformations. Sabatini, M.Mon, 19 May 2014 16:28:04 GMThttp://ddd.uab.cat/record/118320A survey on stably dissipative Lotka-Volterra systems with an application to infinite dimensional Volterra equations
http://ddd.uab.cat/record/118318
For stably dissipative Lotka{Volterra equations the dynamics on the attractor are Hamiltonian and we argue that complex dynamics can occur. We also. ; present examples and properties of some infinite dimensional Volterra systems with applications related with stably dissipative Lotka-Volterra equations. We finish by mentioning recent contributions on the subject. Oliva, Waldyr M.Mon, 19 May 2014 16:21:26 GMThttp://ddd.uab.cat/record/118318On nonsmooth perturbations of nondegenerate planar centers
http://ddd.uab.cat/record/118316
We provide sufficient conditions for the existence of limit cycles of non-smooth perturbed planar centers when the discontinuity set is a union of regular curves. We introduce a mechanism which allows us to deal with such systems. The main tool used in this paper is the averaging method. Some applications are explained with careful details. Novaes, Douglas D.Mon, 19 May 2014 16:16:30 GMThttp://ddd.uab.cat/record/118316Invariant tori in the lunar problem
http://ddd.uab.cat/record/118315
Theorems on the existence of invariant KAM tori are established for perturbations of Hamiltonian systems which are circle bundle ows. By averaging the perturbation over the bundle ow one obtains a Hamiltonian system on the orbit (quotient) space by a classical theorem of Reeb. A non-degenerate critical point of the system on the orbit space gives rise to a family of periodic solutions of the perturbed system. Conditions on the critical points are given which insure KAM tori for the perturbed ow. These general theorems are used to show that the near circular periodic solutions of the planar lunar problem are orbitally stable and are surrounded by KAM 2-tori. For the spatial case it is shown that there are periodic solutions of two types, either near circular equatorial, that is, the infinitesimal particle moves close to the plane of the primaries following near circular trajectories and the other family where the ifinitesimal particle moves along the axis perpendicular to the plane of the primaries following near rectilinear trajectories. We prove that the two solutions are elliptic and are surrounded by invariant 3-tori applying a recent theorem of Han, Li, and Yi. In the spatial case a second averaging is performed, and the corresponding or- bit space (called the twice-reduced space) is constructed. The ow of the averaged Hamiltonian on it is given and several families of invariant 3-tori are determined using Han, Li, and Yi Theorem. Meyer, Kenneth R.Mon, 19 May 2014 16:05:15 GMThttp://ddd.uab.cat/record/118315Integrable systems on S3
http://ddd.uab.cat/record/118314
We classify the links of basic periodic orbits of integrable vector fields on S3 generalizing results on two degree of freedom Hamiltonian systems. We also study the case of completely integrable systems and define invariants for the two classes of vector fields. Martínez-Alfaro, JoséMon, 19 May 2014 15:56:53 GMThttp://ddd.uab.cat/record/118314Delayed logistic population models revisited
http://ddd.uab.cat/record/118313
We discuss the global dynamics of some logistic models governed by delay-differential equations. We focus on models of exploited populations, and study the changes in the dynamics as the harvesting effort is increased. We get new results and highlight the link among different logistic equations usually employed in population models. Liz, EduardoMon, 19 May 2014 15:53:33 GMThttp://ddd.uab.cat/record/118313Cubic homogeneous polynomial centers
http://ddd.uab.cat/record/118311
First, doing a combination of analytical and algebraic computations, we determine by first time an explicit normal form depending only on three parameters for all cubic homogeneous polynomial differential systems having a center. After using the averaging method of first order we show that we can obtain at most one limit cycle bifurcating from the periodic orbits of the mentioned centers when they are perturbed inside the class of all cubic polynomial differential systems. Moreover, there are examples with one limit cycles. Li, ChengzhiMon, 19 May 2014 14:35:26 GMThttp://ddd.uab.cat/record/118311Complex length and persistence of limit cycles in a neighborhood of a hyperbolic polycycle
http://ddd.uab.cat/record/118310
Complex limit cycle located in a neighborhood of a hyperbolic polycycle can not vanish under a small deformation that preserves the characteristic values of the vertexes of the polycycle. The cycles either change holomorphically under the change of the parameter, or come to the boundary of the fixed neighborhood of the polycycle. The present paper makes these statements rigorous and proves them. Ilyashenko, YuMon, 19 May 2014 14:31:37 GMThttp://ddd.uab.cat/record/118310