A high-order full-discretization method using Hermite interpolation for periodic time-delayed differential equations

A high-order full-discretization method(FDM)using Hermite interpolation(HFDM) is proposed and implemented for periodic systems with time delay. Both Lagrange interpolation and Hermite interpolation are used to approximate state values and delayed state values in each discretization step. The transition matrix over a single period is determined and used for stability analysis. The proposed method increases the approximation order of the semidiscretization method and the FDM without increasing the computational time. The convergence, precision, and efficiency of the proposed method are investigated using several Mathieu equations and a complex turning model as examples. Comparison shows that the proposed HFDM converges faster and uses less computational time than existing methods.     

Regioselective Ring‐Opening Polymerization of a Polyhydroxycarboxylic Acid for the Synthesis of a Nanoscale Carrier Material with pH‐Dependent Stability and Sustained Drug Release

Synthetic polyesters are usually composed of monohydroxycarboxylic acids to avoid the problem of regioselectivity during ring‐opening polymerization. In contrast, the linear polyester BICpoly contains four secondary OH groups and is nevertheless esterified regioselectively at only one of these positions. Neither the synthesis of the tricyclic monomers nor the ring‐opening polymerization requires protecting groups, making BICpoly an attractive novel and biocompatible polymer. BICpoly nanoparticles can be loaded with low‐molecular weight drugs or coated onto surfaces as thin films. The release of loaded compounds makes BICpoly an attractive depot for drug release, as shown herein by loading BICpoly with dyes or the cytostatic drug doxorubicin. BICpoly is distinguishable from other polymers by its characteristic pH‐dependent degradation.     

Direct Imaging of Octahedral Distortion in a Complex Molybdenum Vanadium Mixed Oxide

Complex Mo,V‐based mixed oxides that crystallize in the orthorhombic M1‐type structure are promising candidates for the selective oxidation of small alkanes. The oxygen sublattice of such a complex oxide has been studied by annular bright field scanning transmission electron microscopy. The recorded micrographs directly display the local distortion in the metal oxygen octahedra. From the degree of distortion we are able to draw conclusions on the distribution of oxidation states in the cation columns at different sites. The results are supported by X‐ray diffraction and electron paramagnetic resonance measurements that provide integral details about the crystal structure and spin coupling, respectively.     

Spin-state dynamics of a photochromic iron(II) complex and its immobilization on oxide surfaces via phenol anchors

This work presents a detailed study of the photo-induced spin-state dynamics of the photochromic iron(II) complex 1, where the metal ion is in the field of a tripodal hexa-imine ligand with protolysable phenol groups. The nature of the complex’s ground state has been identified as a spin singlet by ¹H NMR and steady-state UV/vis spectroscopies, and its distorted octahedral structure was analyzed via crystal structure determination. Sub-picosecond and nanosecond time-resolved laser flash photolysis experiments identify the long-lived quintet state of 1 as the selective product of photoexcitation in the UV/vis spectral region. Thermal barriers of spin-state interconversion as a function of solvent and added base are derived from temperature-dependent rates of transient decay. Ground-state recovery is found to be significantly affected by the solvent and is strongly enhanced, in particular, by base-driven solvolysis of the ligand’s phenol groups. Partial spontaneous deprotonation of the phenolic hydroxyl groups of 1 seems to prevail on metal oxide surfaces, i.e. on alumina. Composite materials, like 1 at Al₂O₃, that retain the characteristic spectral features of the parent iron(II) complex can be readily obtained by wet impregnation of hydrous alumina with solutions of 1.     

An Approach to NMR Assignment of Intrinsically Disordered Proteins

An efficient approach to NMR assignments in intrinsically disordered proteins is presented, making use of the good dispersion of cross peaks observed in [¹⁵N,¹³C′]‐ and [¹³C′,¹H^N]‐correlation spectra. The method involves the simultaneous collection of {3D (H)NCO(CAN)H and 3D (HACA)CON(CA)HA} spectra for backbone assignments via sequential H^N and H^α correlations and {3D (H)NCO(CACS)HS and 3D (HS)CS(CA)CO(N)H} spectra for side‐chain ¹H and ¹³C assignments, employing sequential ¹H data acquisitions with direct detection of both the amide and aliphatic protons. The efficacy of the approach for obtaining resonance assignments with complete backbone and side‐chain chemical shifts is demonstrated experimentally for the 61‐residue [¹³C,¹⁵N]‐labelled peptide of a voltage‐gated potassium channel protein of the Kv1.4 channel subunit. The general applicability of the approach for the characterisation of moderately sized globular proteins is also demonstrated.     

Acceleration of Long‐Range Photoinduced Electron Transfer through DNA by Hydroxyquinolines as Artificial Base Pairs

The C‐nucleoside based on the hydroxyquinoline ligand (Hq) is complementary to itself and forms stable Hq–Hq pairs in double‐stranded DNA. These artificial Hq–Hq pairs may serve as artificial electron carriers for long‐range photoinduced electron transfer in DNA, as elucidated by a combination of gel electrophoretic analysis of irradiated samples and time‐resolved transient absorption spectroscopy. For this study, the Hq–Hq pair was combined with a DNA‐based donor–acceptor system consisting of 6‐N,N‐dimethylaminopyrene conjugated to 2′‐deoxyuridine as photoinducible electron donor, and methyl viologen attached to the 2′‐position of uridine as electron acceptor. The Hq radical anion was identified in the time‐resolved measurements and strand cleavage products support its role as an intermediate charge carrier. Hence, the Hq–Hq pair significantly enhances the electron hopping capability of DNA compared to natural DNA bases over long distances while keeping the self‐assembly properties as the most attractive feature of DNA as a supramolecular architecture.     

Construction of a Lyapunov functional for a class of controlled population balance models

In this paper, we consider a class of controlled population balance equations describing granulation processes in chemical engineering. Such a control system admits an equilibrium which is not asymptotically stable in general. In order to stabilize this equilibrium, we consider the perturbed system and introduce a Lyapunov functional candidate as a weighted L²-norm. It is shown that the weight function for this construction may be defined in terms of solutions to a certain differential inequality. We present a solution of this differential inequality in a particular case and discuss possible extensions of this approach for multidimensional hyperbolic systems. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)