Hypercyclic algebras for convolution and composition operators

[EN] We provide an alternative proof to those by Shkarin and by Bayart and Matheron that the operator D of complex differentiation supports a hypercyclic algebra on the space of entire functions. In particular we obtain hypercyclic algebras for many convolution operators not induced by polynomials, such as , , or , where . In contrast, weighted composition operators on function algebras of analytic functions on a plane domain fail to support supercyclic algebras.This work is supported in part by MEC, Project MTM 2016-7963-P. We also thank Angeles Prieto for comments and suggestions.Bès, J.; Conejero, JA.; Papathanasiou, D. (2018). Hypercyclic algebras for convolution and composition operators. Journal of Functional Analysis. 274(10):2884-2905. https://doi.org/10.1016/j.jfa.2018.02.003S288429052741

Collective T=0 pairing in N=Z nuclei? Pairing vibrations around 56Ni revisited

We present a new analysis of the pairing vibrations around 56Ni, with emphasis on odd-odd nuclei. This analysis of the experimental excitation energies is based on the subtraction of average properties that include the full symmetry energy together with volume, surface and Coulomb terms. The results clearly indicate a collective behavior of the isovector pairing vibrations and do not support any appreciable collectivity in the isoscalar channel.Comment: RevTeX, two-column, 5 pages, 4 figure

Subclasses of Presburger Arithmetic and the Weak EXP Hierarchy

It is shown that for any fixed $i>0$, the $\Sigma_{i+1}$-fragment of Presburger arithmetic, i.e., its restriction to $i+1$ quantifier alternations beginning with an existential quantifier, is complete for $\mathsf{\Sigma}^{\mathsf{EXP}}_{i}$, the $i$-th level of the weak EXP hierarchy, an analogue to the polynomial-time hierarchy residing between $\mathsf{NEXP}$ and $\mathsf{EXPSPACE}$. This result completes the computational complexity landscape for Presburger arithmetic, a line of research which dates back to the seminal work by Fischer & Rabin in 1974. Moreover, we apply some of the techniques developed in the proof of the lower bound in order to establish bounds on sets of naturals definable in the $\Sigma_1$-fragment of Presburger arithmetic: given a $\Sigma_1$-formula $\Phi(x)$, it is shown that the set of non-negative solutions is an ultimately periodic set whose period is at most doubly-exponential and that this bound is tight.Comment: 10 pages, 2 figure

The 1999-2000 seismic experiment of Macas swarm (Ecuador) in relation with rift inversion in Subandean foothills

International audienceWe propose to explain the origin of the double trend in seismicity of the Macas swarm in the Subandean Cordillera of Cutucú (Ecuador) and characterize the corresponding active deformation of that region. For that purpose, seismological and geological data have been used, with the deployment of a temporary seismological array, with geological field observations and image processing. We found that some earthquakes are aligned on a well known NNE SSW trend corresponding to the orientation of the nodal planes of the reverse focal mechanism of the Mw=7.0 1995 Macas earthquake as for its aftershocks. Nevertheless, many smaller events are aligned on an unexpected NNW SSE trend inside the Cutucú Cordillera. We interpret these two orientations of the Macas swarm as linked to Subandean basement thrusts inherited from the inversion tectonics of a NNE SSW trending Triassic Jurassic rift, which has been uplifted and partly extruded in the Cutucú Cordillera. The present partitioning of this part of the Subandean deformation is controlled by pre-existing NNE SSW to NNW SSE Triassic Jurassic normal faults that have been subsequently compressed transpressed and reactivated into reverse faults. Major boundary faults of the rift were NNE SSW oriented and correspond now to some main Subandean thrusts as confirms the focal mechanism of the 1995 main shock located on the eastern border (Morona frontal thrust) and the orientation of its aftershocks. In the Cutucú Cordillera, the double orientation of present swarm can be interpreted as the result of accommodation of deformation along NNW SSE pre-existing faults inside the inverted rift system, linked to the motion of the Morona frontal NNE SSW thrust

Bohr Hamiltonian with deformation-dependent mass term

The Bohr Hamiltonian describing the collective motion of atomic nuclei is modified by allowing the mass to depend on the nuclear deformation. Exact analytical expressions are derived for spectra and wave functions in the case of a gamma-unstable Davidson potential, using techniques of supersymmetric quantum mechanics. Numerical results in the Xe-Ba region are discussed.Comment: 13 pages, LaTeX, 3 eps figure

Trees over Infinite Structures and Path Logics with Synchronization

We provide decidability and undecidability results on the model-checking problem for infinite tree structures. These tree structures are built from sequences of elements of infinite relational structures. More precisely, we deal with the tree iteration of a relational structure M in the sense of Shelah-Stupp. In contrast to classical results where model-checking is shown decidable for MSO-logic, we show decidability of the tree model-checking problem for logics that allow only path quantifiers and chain quantifiers (where chains are subsets of paths), as they appear in branching time logics; however, at the same time the tree is enriched by the equal-level relation (which holds between vertices u, v if they are on the same tree level). We separate cleanly the tree logic from the logic used for expressing properties of the underlying structure M. We illustrate the scope of the decidability results by showing that two slight extensions of the framework lead to undecidability. In particular, this applies to the (stronger) tree iteration in the sense of Muchnik-Walukiewicz.Comment: In Proceedings INFINITY 2011, arXiv:1111.267

The sextic oscillator as a γ\gamma-independent potential

The sextic oscillator is proposed as a two-parameter solvable $\gamma$-independent potential in the Bohr Hamiltonian. It is shown that closed analytical expressions can be derived for the energies and wavefunctions of the first few levels and for the strength of electric quadrupole transitions between them. Depending on the parameters this potential has a minimum at $\beta=0$ or at $\beta>0$, and might also have a local maximum before reaching its minimum. A comparison with the spectral properties of the infinite square well and the $\beta^4$ potential is presented, together with a brief analysis of the experimental spectrum and E2 transitions of the $^{134}$Ba nucleus.Comment: 15 pages, 5 figures; to appear in Phys. Rev.

X(3): An Exactly Separable Gamma-Rigid Version of the X(5) Critical Point Symmetry

A gamma-rigid version (with gamma=0) of the X(5) critical point symmetry is constructed. The model, to be called X(3) since it is proved to contain three degrees of freedom, utilizes an infinite well potential, is based on exact separation of variables, and leads to parameter free (up to overall scale factors) predictions for spectra and B(E2) transition rates, which are in good agreement with existing experimental data for 172-Os and 186-Pt. An unexpected similarity of the first beta bands of the X(5) nuclei 150-Nd, 152-Sm, 154-Gd, and 156-Dy to the X(3) predictions is observed.Comment: LaTeX, 12 pagres, including 4 postscript figure