On the role of the colloidal stability of mesoporous silica nanoparticles as gene delivery vectors

Mesoporous silica nanoparticles have been synthesized and functionalized with four different types of molecules containing amino groups, i.e., with primary amines only, with quaternary amines, with quaternized cyclic amines, or with polyethylenimine (PEI), which is formed by primary, secondary, and tertiary amines. These nanoparticles were then incubated with reporter plasmids and the ability of the resulting complexes to transfect human cells was studied. Only nanoparticles functionalized with PEI were efficient for transfection. The agglomeration behavior and the electrokinetic potential of the nanoparticle–plasmid complexes have been studied, as well as their cell internalization behavior using a fluorescent-labeled plasmid that allows its monitorization by confocal microscopy. The results indicate that the efficiency of PEI-functionalized nanoparticles for transfection resides to some extent in the different characteristics imparted to the nanoparticles regarding agglomeration and surface charge behavior.     

Bounded universal functions in one and several complex variables

We show how to obtain functions that are universal for the ball of , where . The existence of our functions will follow from universality criteria, but we also show how to construct them. Then we study the connection between certain interpolating sequences, runaway automorphisms, and the existence of universal functions on domains in .      

On weak positive supercyclicity

A bounded linear operator T on a separable complex Banach space X is called weakly supercyclic if there exists a vector x ∈ X such that the projective orbit {λT ⁿ x: n ∈ ℕ λ ∈ ℂ} is weakly dense in X. Among other results, it is proved that an operator T such that σ _p (T ^*) = 0, is weakly supercyclic if and only if T is positive weakly supercyclic, that is, for every supercyclic vector x ∈ X, only considering the positive projective orbit: {rT ⁿ x: n ∈ ℂ, r ∈ ℝ₊} we obtain a weakly dense subset in X. As a consequence it is established the existence of non-weakly supercyclic vectors (non-trivial) for positive operators defined on an infinite dimensional separable complex Banach space. The paper is closed with concluding remarks and further directions. Partially supported by MEC MTM2006-09060 and MTM2006-15546, Junta de Andalucía FQM-257 and P06-FQM-02225. Partially supported by Junta de Andalucía FQM-257, and P06-FQM-02225     

Orlicz-Pettis Type Theorems via Strong p-Cesàro Convergence

We obtain a new version of the Orlicz-Pettis theorem within the frame of the strong p-Cesàro convergence.     

Spectral theory and hypercyclic subspaces

A vector in a Hilbert space is called hypercyclic for a bounded operator if the orbit is dense in . Our main result states that if satisfies the Hypercyclicity Criterion and the essential spectrum intersects the closed unit disk, then there is an infinite-dimensional closed subspace consisting, except for zero, entirely of hypercyclic vectors for . The converse is true even if is a hypercyclic operator which does not satisfy the Hypercyclicity Criterion. As a consequence, other characterizations are obtained for an operator to have an infinite-dimensional closed subspace of hypercyclic vectors. These results apply to most of the hypercyclic operators that have appeared in the literature. In particular, they apply to bilateral and backward weighted shifts, perturbations of the identity by backward weighted shifts, multiplication operators and composition operators. The main result also applies to the differentiation operator and the translation operator defined on certain Hilbert spaces consisting of entire functions. We also obtain a spectral characterization of the norm-closure of the class of hypercyclic operators which have an infinite-dimensional closed subspace of hypercyclic vectors.