Porphyrin-like porous nanomaterials as drug delivery systems for ibuprofen drug

In recent years, nanomaterial-based drug delivery carriers have become some of the most attractive to be studied. The purpose of this study is to investigate the interaction of C60 fullerene, carbon nanotube and graphene having porphyrin-like FeN4 clusters with a non-steroidal anti-inflammatory drug (ibuprofen) by means of the density functional theory. Results showed that the graphene with FeN4 clusters could remarkably increase the tendency of graphene for adsorption of ibuprofen drug. Also, our ultraviolet–visible results show that the electronic spectra of the complexes exhibit a blue shift toward lower wavelengths (higher energies). It was found that Ibp/FeN4-graphene had high chemical reactivity, which was important for binding of the drug onto the target site. In order to go further and gain insight into the binding features of considered systems with ibuprofen drug, the Atoms in Molecules analysis was performed. Our results determine the electrostatic features of the Ibp/FeN4-graphene bonding. Consequently, the results demonstrated that the FeN4-graphene could be used as potential carriers for the delivery of ibuprofen drug.     

Photoluminescence of green nanophosphors Sr2MgSi2O7 doped with Tb3+ under 374-nm excitation

A series of Sr₂MgSi₂O₇:Tb³⁺ nanophosphors is prepared using a high-temperature solid-state reaction. The x-ray diffraction patterns show that the crystal structure of the sample is not significantly affected by Tb³⁺ ions. However, the images of the scanning electron microscope illustrate that the average size of nanoparticles becomes larger with the increase of Tb³⁺ concentration. Unlike earlier investigations on down-conversion emission of Tb³⁺ ion excited by deep ultraviolet light, in this work, the photoluminescence characteristics of Sr₂MgSi₂O₇ nanophosphors doped with different Tb³⁺ concentrations are analyzed under 374-nm excitations. The intense green emission at 545 nm is observed at an optimal doping concentration of 1.6 mol%. The main reason for the concentration quenching is due to the electric dipole-electric dipole interaction among Tb³⁺ ions.     

Singular Hamiltonian elliptic systems with critical exponential growth in dimension two

We will focus on the existence of nontrivial solutions to the following Hamiltonian elliptic system where are numbers belonging to the interval [0, 2), V is a continuous potential bounded below on by a positive constant and the functions f and g possess exponential growth range established by Trudinger–Moser inequalities in Lorentz–Sobolev spaces. The proof involves linking theorem and a finite‐dimensional approximation.     

Weighted estimates for the multilinear maximal function on the upper half‐spaces

For a general dyadic grid, we give a Calderón–Zygmund type decomposition, which is the principle fact about the multilinear maximal function on the upper half‐spaces. Using the decomposition, we study the boundedness of . We obtain a natural extension to the multilinear setting of Muckenhoupt's weak‐type characterization. We also partially obtain characterizations of Muckenhoupt's strong‐type inequalities with one weight. Assuming the reverse Hölder's condition, we get a multilinear analogue of Sawyer's two weight theorem. Moreover, we also get Hytönen–Pérez type weighted estimates.     

Isomorphisms of spaces with large distortion

Let K and S be locally compact Hausdorff spaces and let X be a strictly convex Banach space of finite dimension at least 2. In this paper, we prove that if there exists an isomorphism T from onto satisfying then K and S are homeomorphic. Here denotes the Schäffer constant of X. Even for the classical cases , and , this result is the X‐valued Banach–Stone theorem via isomorphism with the largest distortion that is known so far, namely . On the other hand, it is well known that this result is not true for , even though K and S are compact Hausdorff spaces.     

‐Theory for Schrödinger systems

In this article, we study for the ‐realization of the vector‐valued Schrödinger operator . Using a noncommutative version of the Dore–Venni theorem due to Monniaux and Prüss, we prove that the ‐realization of , defined on the intersection of the natural domains of the differential and multiplication operators which form , generates a strongly continuous contraction semigroup on . We also study additional properties of the semigroup such as extension to L¹, positivity, ultracontractivity and prove that the generator has compact resolvent.