Unicity of the Integrated Density of States for Relativistic Schrödinger Operators with Regular Magnetic Fields and Singular Electric Potentials

We show coincidence of the two definitions of the integrated density of states (IDS) for a class of relativistic Schrödinger operators with magnetic fields and scalar potentials introduced in Iftimie et al. (Publ Res Inst Math Sci 43(3):585–623, 2007; Topics in applied mathematics and mathematical physics, Editura Academiei Române, 2008), the first one relying on the eigenvalue counting function of operators induced on open bounded sets with Dirichlet boundary conditions, the other one involving the spectral projections of the operator defined on the entire space. In this way one generalizes the results of Doi et al. (Math Z 237:335–371, 2001) and Iftimie (Publ Res Inst Math Sci 41(2):307–327, 2005) for non-relativistic operators. The proofs needs the magnetic pseudodifferential calculus developed in Iftimie et al. (Publ Res Inst Math Sci 43(3):585–623, 2007), as well as a Feynman-Kac-Itô formula for Lévy processes (Ichinose and Tamura, Commun Math Phys 105(2):239–257, 1986; Iftimie et al. Topics in applied mathematics and mathematical physics, Editura Academiei Române, 2008). In addition, in case when both the magnetic field and the scalar potential are periodic, one also proves the existence of the IDS.     

Producing ORMOSIL scaffolds by femtosecond laser polymerization

Structures with different geometries and sizes were built via direct femtosecond laser writing, starting from new organic/inorganic hybrid monomers based on hybrid methacrylate containing triethoxysilane, in addition to urethane and urea groups. Multifunctional oligomer of urethane dimethacrylate type was chosen as comonomer in polymerization experiments because dimethacrylates give rise to the formation of a polymer network, having a number of favorable properties including biocompatibility and surface nanostructuring. Free standing polymeric structures were designed and created in order to be tested in fibroblast cells culture. Investigations of the cellular adhesion, proliferation, and viability of L929 mouse fibroblasts on free-standing laser processed scaffolds were performed for different scaffold designs.     

Laser processing of ormosils for tissue engineering applications

Hybrid methacrylates based on silane derivates (ormosils) have been considered for applications in electronics, microtechnology, corrosion resistant coatings, dentistry, and biomedical implants. The presence of both inorganic chains, responsible for chemical and thermal stability, hardness, and transparency, and organic groups, which bring new advantages such as the possibility of functionalization and easy, low temperature processing, can result in the appearance of unique properties.     

Unprecedented Relaxivity Gap in pH-Responsive FeIII-Based MRI Probes

Two mononuclear ferric complexes are reported that respond to a pH change with a 27- and 71-fold jump, respectively, in their capacity to accelerate the longitudinal relaxation rate of water-hydrogen nuclei, and this starting from a negligible base value of only 0.06. This unprecedented performance bodes well for tackling the sensitivity issues hampering the development of Molecular MRI. The two chelates also excel in the fully reversible and fatigue-less nature of this phenomenon. The structural reasons for this performance reside in the macrocyclic nature of the hexa-dentate ligand, as well as the presence of a single pendant arm displaying a five-membered lactam or carbamate which show (perturbed) pK_a values of 3.5 in the context of this N6 N5O1 coordination motif.     

Positive radial solutions for Dirichlet problems via a Harnack-type inequality

We deal with the existence and localization of positive radial solutions for Dirichlet problems involving $\varphi$-Laplacian operators in a ball. In particular, $p$-Laplacian and Minkowski-curvature equations are considered. Our approach relies on fixed point index techniques, which work thanks to a Harnack-type inequality in terms of a seminorm. As a consequence of the localization result, it is also derived the existence of several (even infinitely many) positive solutions.