Renormings and extremal structures

In this paper we use renorming techniques to settle several questions on extremal structures of Banach spaces. We construct a unitary vector in a dual space which is not a weak∧ -unitary. We construct an exposed point in the unit ball of a Banach space X that remains exposed in the unit ball of X(4) but is not extreme in the unit ball of X(6)

The Effects of Stacking on the Configurations and Elasticity of Single Stranded Nucleic Acids

Stacking interactions in single stranded nucleic acids give rise to configurations of an annealed rod-coil multiblock copolymer. Theoretical analysis identifies the resulting signatures for long homopolynucleotides: A non monotonous dependence of size on temperature, corresponding effects on cyclization and a plateau in the extension force law. Explicit numerical results for poly(dA) and poly(rU) are presented.Comment: 4 pages and 2 figures. Accepted in Phys. Rev. E Rapid Com

On peak phenomena for non-commutative H∞H^\infty

A non-commutative extension of Amar and Lederer's peak set result is given. As its simple applications it is shown that any non-commutative $H^\infty$-algebra $H^\infty(M,\tau)$ has unique predual,and moreover some restriction in some of the results of Blecher and Labuschagne are removed, making them hold in full generality.Comment: final version (the presentation of some part is revised and one reference added

Renormings and extremal structures

Abstract. In this paper we use renorming techniques to settle several questions on extremal structures of Banach spaces. We construct a unitary vector in a dual space which is not a weak * -unitary. We construct an exposed point in the unit ball of a Banach space X that remains exposed in the unit ball of X (4) but is not extreme in the unit ball of X (6)

Results from 2 cohort studies in central Africa show that clearance of Wuchereria bancrofti infection after repeated rounds of mass drug administration with albendazole alone is closely linked to individual adherence

BACKGROUND: Two community trials conducted from 2012 to 2018 in the Republic of Congo and the Democratic Republic of the Congo demonstrated the efficacy of semiannual mass drug administration (MDA) with albendazole (ALB) alone on lymphatic filariasis (LF). However, a high interindividual heterogeneity in the clearance of infection was observed. METHODS: We analyzed trial data to assess the effect of individual adherence to ALB MDA on clearance of circulating filarial antigenemia (CFA) and microfilaremia. Community residents were offered a single dose of ALB every 6 months and tested for LF with a rapid test for CFA at baseline and then annually. CFA test results were scored on a semiquantitative scale. At each round, microfilaremia was assessed in CFA-positive individuals. All CFA-positive individuals for whom at least 1 follow-up measure was available were included in the analyses. Parametric survival models were used to assess the influence of treatment adherence on LF infection indicators. RESULTS: Of 2658 individuals enrolled in the trials, 394 and 129 were eligible for analysis of CFA and microfilaremia clearance, respectively. After adjusting for age, sex, and initial CFA score, the predicted mean time for clearing CFA was shorter in persons who had taken 2 doses of ALB per year (3.9 years) than in persons who had taken 1 or 0 dose (4.4 and 5.3 years; P \u3c .001 for both). A similar pattern was observed for microfilaremia clearance. CONCLUSIONS: These results demonstrate a clear dose-response relationship for the effect of ALB on clearance of CFA and microfilaremia

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