Norm optimization problem for linear operators in classical Banach spaces

The main result of the paper shows that, for 1 < p < ∞ and 1 ≤ q < ∞, a linear operator T: ℓ _p → ℓ _q attains its norm if, and only if, there exists a not weakly null maximizing sequence for T (counterexamples can be easily constructed when p = 1). For 1 < p ≠ q < ∞, as a consequence of the previous result we show that any not weakly null maximizing sequence for a norm attaining operator T: ℓ _p → ℓ _q has a norm-convergent subsequence (and this result is sharp in the sense that it is not valid if p = q). We also investigate lineability of the sets of norm-attaining and non-norm attaining operators.     

Limit Cycles Bifurcating from a k-dimensional Isochronous Center Contained in ?n with k ? n

The goal of this paper is double. First, we illustrate a method for studying the bifurcation of limit cycles from the continuum periodic orbits of a k-dimensional isochronous center contained in ℝ ⁿ with n ⩾ k, when we perturb it in a class of differential systems. The method is based in the averaging theory. Second, we consider a particular polynomial differential system in the plane having a center and a non-rational first integral. Then we study the bifurcation of limit cycles from the periodic orbits of this center when we perturb it in the class of all polynomial differential systems of a given degree. As far as we know this is one of the first examples that this study can be made for a polynomial differential system having a center and a non-rational first integral. The first and third authors are partially supported by a MCYT/FEDER grant MTM2005-06098-C01, and by a CIRIT grant number 2005SGR-00550. The second author is partially supported by a FAPESP–BRAZIL grant 10246-2. The first two authors are also supported by the joint project CAPES–MECD grant HBP2003-0017.     

Distribution of film orientations in free and strained foams

We show that the distribution of film orientations in a free (i.e., unstrained) foam cluster, though in general not uniform, has the same second moments as a uniform distribution. This is, however, in general not true of its other moments, which reflects the internal order of film orientations imposed by Plateau's laws. For a strained cluster, we relate the deviations of the second moments of the orientation distribution from their values for an unstrained cluster, to the stresses acting on the cluster. Our predictions are corroborated by experimental results for free and strained two-dimensional clusters, allowing us to find the force on a cluster bounded by two parallel walls.     

Dynamics of soft and semisoft nematic elastomers

We analyze analytically and numerically the dynamics of how a nematic elastomer-an anisotropic rubber-responds elastically and orientationally to an imposed strain. Because positional and orientational degrees of freedom are coupled, the response is not the simple exponential one might expect for a viscous system. Indeed, as a result of this nonlinear coupling, the different modes decay in two qualitatively different ways: with either two distinct or with the same exponential laws, depending, respectively, on whether there is or there is not complete reorientation of the molecular long axes. In addition, at the special values of the strain that form the boundaries between different equilibrium behaviors, relaxation is much slower, i.e., it follows a power law.     

On the role of leptonic CPV phases in cLFV observables

The European Physical Journal C - We argue that high-quality data on the reaction $$e^+e^-\rightarrow \pi ^+\pi ^-\eta $$ will allow one to determine the doubly-virtual form factor $$\eta...     

Novel Bisphosphonates Derived from 1H‐Indazole, 1H‐Pyrazolo[3,4‐b]Pyridine,and 1H‐Pyrazolo[3,4‐b]Quinoline

Novel tetraethyl ethylene‐1,1‐bisphosphonate esters derived from 1H‐indazole, 1H‐pyrazolo[3,4‐b]pyridine, and 1H‐pyrazolo[3,4‐b]quinoline were synthesized by a Michael addition reaction of tetraethyl ethylidene‐1,1‐bisphosphonate with the corresponding heterocycle, using conventional heating and microwave‐assisted methods. The microwave‐assisted method provides shorter reaction times and better yields. The hydrolysis of bisphosphonates afforded the corresponding bisphosphonic acids or salt, using concentrated hydrochloric acid or TMSBr/collidine, respectively. All new compounds were fully characterized, and their structures were assigned using ¹H, ³¹P, and ¹³C NMR and IR spectroscopies and mass spectrometry. The molecular structure of compound 6 was confirmed by X‐ray diffraction studies.     

A new controlled release system of chlorhexidine and chlorhexidine:βcd inclusion compounds based on porous silica

The purpose of this study was to prepare and characterize a controlled release system based on porous silica loaded with chlorhexidine (Cx) and its inclusion compounds in β-cyclodextrin (βcd), and to evaluate its antimicrobial activity. Acetate chlorhexidine (CxA), gluconate chlorhexidine (CxG), βcd:chlorhexidine acetate 2:1 (βcd:CxA) and βcd:chlorhexidine gluconate 2:1 (βcd:CxG) were incorporated into porous silica. Drug loading was characterized by FTIR, powder X-ray diffraction, thermal analysis and BET, and was shown to be in an amorphous state and porous matrix. The kinetics release parameter of the drug was established, which showed that the Cx systems release profile followed zero order release until 400 h and Higuchi model release until 750 h, after the burst effect at the first 8 h. Chlorhexidine therapeutic range was reached near first hour for all systems. The chlorhexidine porous silica system was biologically active against Enterococcus faecalis and Candida albicans in vitro. The systems showed an efficient Cx controlled release modulated by the presence of the β-cyclodextrin and by the porous silica matrices, providing effective antimicrobial activity.