Chaotic differential operators

We give sufficient conditions for chaos of (differential) operators on Hilbert spaces of entire functions. To this aim we establish conditions on the coefficients of a polynomial P(z) such that P(B) is chaotic on the space lp, where B is the backward shift operator. © 2011 Springer-Verlag.This work was partially supported by the MEC and FEDER Projects MTM2007-64222, MTM2010-14909, and by GVA Project GV/2010/091, and by UPV Project PAID-06-09-2932. The authors would like to thank A. Peris for helpful comments and ideas that produced a great improvement of the paper's presentation. We also thank the referees for their helpful comments and for reporting to us a gap in Theorem 1.Conejero Casares, JA.; Martínez Jiménez, F. (2011). Chaotic differential operators. Revista- Real Academia de Ciencias Exactas Fisicas Y Naturales Serie a Matematicas. 105(2):423-431. https://doi.org/10.1007/s13398-011-0026-6S4234311052Bayart, F., Matheron, É.: Dynamics of Linear Operators, Cambridge Tracts in Mathematics, vol. 179. Cambridge University Press, Cambridge (2009)Bermúdez T., Miller V.G.: On operators T such that f(T) is hypercyclic. Integr. Equ. Oper. Theory 37(3), 332–340 (2000)Bonet J., Martínez-Giménez F., Peris A.: Linear chaos on Fréchet spaces. Int. J. Bifur. Chaos Appl. Sci. Eng. 13(7), 1649–1655 (2003)Chan K.C., Shapiro J.H.: The cyclic behavior of translation operators on Hilbert spaces of entire functions. Indiana Univ. Math. J. 40(4), 1421–1449 (1991)Conejero J.A., Müller V.: On the universality of multipliers on $${\mathcal{H}({\mathbb {C}})}$$ . J. Approx. Theory. 162(5), 1025–1032 (2010)deLaubenfels R., Emamirad H.: Chaos for functions of discrete and continuous weighted shift operators. Ergodic Theory Dyn. Syst. 21(5), 1411–1427 (2001)Devaney, R.L.: An introduction to chaotic dynamical systems, 2nd edn. In: Addison-Wesley Studies in Nonlinearity. Addison-Wesley Publishing Company Advanced Book Program, Redwood City (1989)Godefroy G., Shapiro J.H.: Operators with dense, invariant, cyclic vector manifolds. J. Funct. Anal. 98(2), 229–269 (1991)Grosse-Erdmann K.-G.: Hypercyclic and chaotic weighted shifts. Stud. Math. 139(1), 47–68 (2000)Grosse-Erdmann, K.-G., Peris, A.,: Linear chaos. Universitext, Springer, New York (to appear, 2011)Herzog G., Schmoeger C.: On operators T such that f(T) is hypercyclic. Stud. Math. 108(3), 209–216 (1994)Kahane, J.-P.: Some random series of functions, 2nd edn. In: Cambridge Studies in Advanced Mathematics, vol. 5. Cambridge University Press, Cambridge (1985)Martínez-Giménez F., Peris A.: Chaos for backward shift operators. Int. J. Bifur. Chaos Appl. Sci. Eng. 12(8), 1703–1715 (2002)Martínez-Giménez F.: Chaos for power series of backward shift operators. Proc. Am. Math. Soc. 135, 1741–1752 (2007)Müller V.: On the Salas theorem and hypercyclicity of f(T). Integr. Equ. Oper. Theory 67(3), 439–448 (2010)Protopopescu V., Azmy Y.Y.: Topological chaos for a class of linear models. Math. Models Methods Appl. Sci. 2(1), 79–90 (1992)Rolewicz S.: On orbits of elements. Stud. Math. 32, 17–22 (1969)Salas H.N.: Hypercyclic weighted shifts. Trans. Am. Math. Soc. 347(3), 93–1004 (1995)Shapiro, J.H.: Simple connectivity and linear chaos. Rend. Circ. Mat. Palermo. (2) Suppl. 56, 27–48 (1998

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

CyanoFactory, a European consortium to develop technologies needed to advance cyanobacteria as chassis for production of chemicals and fuels

CyanoFactory, Design, construction and demonstration of solar biofuel production using novel (photo)synthetic cell factories, was an R&D project developed in response to the European Commission FP7-ENERGY-2012-1 call “Future Emerging Technologies” and the need for significant advances in both new science and technologies to convert solar energy into a fuel. CyanoFactory was an example of “purpose driven” research and development with identified scientific goals and creation of new technologies. The present overview highlights significant outcomes of the project, three years after its successful completion. The scientific progress of CyanoFactory involved: (i) development of a ToolBox for cyanobacterial synthetic biology; (ii) construction of DataWarehouse/Bioinformatics web-based capacities and functions; (iii) improvement of chassis growth, functionality and robustness; (iv) introduction of custom designed genetic constructs into cyanobacteria, (v) improvement of photosynthetic efficiency towards hydrogen production; (vi) biosafety mechanisms; (vii) analyses of the designed cyanobacterial cells to identify bottlenecks with suggestions on further improvements; (viii) metabolic modelling of engineered cells; (ix) development of an efficient laboratory scale photobioreactor unit; and (x) the assembly and experimental performance assessment of a larger (1350 L) outdoor flat panel photobioreactor system during two seasons. CyanoFactory - Custom design and purpose construction of microbial cells for the production of desired products using synthetic biology – aimed to go beyond conventional paths to pursue innovative and high impact goals. CyanoFactory brought together ten leading European partners (universities, research organizations and enterprises) with a common goal – to develop the future technologies in Synthetic biology and Advanced photobioreactors

Un marco conceptual para la formalización de crosscutting en desarrollos orientados a aspectos

El concepto de crosscutting suele ser descrito en términos de scattering y tangling. Sin embargo, la distinction entre estos términos no suele ser concisa, llevando a situaciones ambiguas. En muchas ocasiones se hace necesario tener definiciones más precisas, por ejemplo para determinadas áreas de investigación como la identificación formal de asuntos transversales o crosscutting concerns. Proponemos un marco de trabajo conceptual para la formalización de estos conceptos basado en lo que denominamos un patrón de crosscutting que representa la relación entre elementos de dos niveles diferentes, por ejemplo concerns y una representación de dichos concerns. Estos conceptos son definidos formalmente en términos del álgebra lineal y representados mediante matrices y operaciones con dichas matrices. De este modo, el concepto de crosscutting puede ser claramente diferenciado de los términos de scattering y tangling. La utilidad de las matrices de dependencias presentadas se ilustra mediante el análisis de crosscutting a lo largo de una serie de niveles de refinamiento, que puede ser formalizado en lo que hemos denominado la concatenación de patrones de crosscutting