Optimal control and admissible relaxation for subdifferential evolution inclusions

In this paper we study the relaxation of optimal control problems monitored by subdifferential evolution inclusions. First under appropriate convexity conditions, we establish an existence result. Then we introduce the relaxed problem and show that it always has a solution under fairly general hypotheses on the data. Subsequently we examine when the relaxation is admissible. So we show that every relaxed trajectory can be approximated by extremal original ones (i.e. original trajectories generated by bang-bang controls) and that the values of the original and relaxed problems are equal. Some examples are also presented.     

Embeddings of 2-spheres in 4-manifolds

We prove that the action of the orthogonal group of an integral, unimodular lattice whose rank and signature satisfy a certain indefiniteness condition acts transitively on pairs of mutually orthogonal elements with the same isometric invariants.     

The swelling interface number as a criterion for prediction of diffusional solute release mechanisms in swellable polymers

When a glassy polymer containing a uniformly dispersed solute is brought in contact with a penetrant, solute diffusion will be associated with the transport mechanism and penetration velocity of the penetrant in the polymer. Analysis and prediction of mechanisms of diffusional solute release may be obtained through a new dimensionless number, the swelling interface number, Sw, which compares the relative mobilities of the penetrant and the solute in the presence of macromolecular relaxations in the polymer. It is shown that a sufficient and necessary criterion for time-independent diffusional solute release rates from these swellable systems is that the Sw be smaller than 10^?2. The swelling interface number Sw may be related to easily determined structural and thermodynamic parameters of the solute/polymer/penetrant system. Preliminary experimental results of dynamic water swelling of poly(2-hydroxyethyl methacrylate-co-methyl methacrylate) and diffusional release of theophylline from initially glassy copolymers show that decreasing values of Sw are related to increased pseudo-case-II transport kinetics of the solute.     

Modelling of drug diffusion through swellable polymeric systems

A drug diffusion model for the case of diffusion of an initially uniformly distributed drug through a polymeric matrix is presented and solved. Drug diffusion from a single surface is analyzed for the case of countercurrent diffusion of a solvent which is thermodynamically compatible with the polymer. Due to swelling, considerable volume expansion is observed leading to a moving-boundary diffusion problem. Drug concentration profiles within the polymer and drug release rates can be determined. The results are in agreement with experimental data obtained for the system of KCl distributed in hydrophilic hydroxypropyl methyl cellulose matrices, in the form of tablets.     

Anisotropic diffraction and elliptic discrete solitons in two-dimensional waveguide arrays

We demonstrate that both the linear (diffraction) and the nonlinear dynamics of two-dimensional waveguide arrays are considerably more complex and versatile than their one-dimensional counterparts. The discrete diffraction properties of these arrays can be effectively altered, depending on the propagation Bloch k-vector within the first Brillouin zone of the lattice. In general, this diffraction behavior is anisotropic and therefore permits the existence of a new class of discrete elliptic solitons in the nonlinear regime.     

Structural Characterization of Graphene Nanosheets for Miniaturization of Potentiometric Urea Lipid Film Based Biosensors

The present article describes a miniaturized potentiometric urea lipid film based biosensor on graphene nanosheets. Structural characterization of graphene nanosheets for miniaturization of potentiometric urea lipid film based biosensors have been studied through atomic force microscopy (AFM) and transmission electron microscopy (TEM) measurements. UV‐Vis and Fourrier transform IR (FTIR) spectroscopy have been utilized to study the pre‐ and postconjugated surfaces of graphene nanosheets. The presented potentiometric urea biosensor exhibits good reproducibility, reusability, selectivity, rapid response times (～4 s), long shelf life and high sensitivity of ca. 70 mV/decade over the urea logarithmic concentration range from 1×10^?6 M to 1×10^?3 M.     

2,4‐Diamino‐5‐(1‐naphthyl)‐3,5‐diaza‐1‐azoniaspiro[5.5]undeca‐1,3‐diene chloride

The title salt, C₁₈H₂₂N₅⁺·Cl^?, is a member of a new series of lipophilic 4,6‐di­amino spiro‐s‐triazines which are potent in­hib­itors of di­hydro­folate reductase. The protonated triazine ring deviates from planarity, whereas the cyclo­hexane ring adopts a chair conformation. A rather unusual hydrogen‐bonding scheme exists in the crystal. There is a centrosymmetric arrangement involving two amino groups and two triazine ring N atoms, with graph‐set R(8) and an N?N distance of 3.098 (3) Å, flanked by two additional R(8) systems, involving two amino groups, a triazine ring N atom and a Cl^? anion, with N?Cl distances in the range 3.179 (2)–3.278 (2) Å. Furthermore, the Cl^? anion, the protonated triazine ring N atom and an amino group form a hydrogen‐bonding system with graph‐set R(6).     

Synthesis of novel tantalum oxide sub-micrometer hollow spheres with tailored shell thickness

Sub-micrometer-sized hollow tantalum oxide (Ta2O5) spheres with tunable shell thickness and void size have been fabricated exploiting beta-diketone-functionalized polystyrene (PS) beads as sacrificial templates in a sol-gel process. First, a controlled precipitation of Ta2O5 nanoparticles was carried out on the template surface by hydrolyzing tantalum ethoxide (Ta(OEt)5) at room temperature, and subsequently, the polymer core was removed either via chemical treatment with toluene or calcination at 650 degrees C. The thickness of the tantala shell precipitated on the PS core during the coating process was tuned between 100 and 142 nm by varying the concentration of tantala precursor in the reaction media. The obtained Ta2O5-coated PS particles and hollow microspheres were characterized by scanning electron microscopy, transmission electron microscopy, infrared spectroscopy, X-ray diffraction, and thermogravimetric analysis. Due to the unique optical and dielectric properties, these nanostructured materials are envisaged to be used in applications such as novel building blocks for the fabrication of advanced materials, surface coatings, catalysts, and drug delivery systems.