Phonon anomalies in transition metal nitrides: δ-NbN

The phonon dispersion curves in δ-NbN have been measured at room temperature in the high symmetry directions Δ, Σ, and ? by coherent inelastic neutron scattering. Anomalies in the dispersion of the acoustic branches have been detected which are quite different from those which have already been reported for superconducting transition metal compounds with 9 valence electrons. In the 10 valence electron compound δ-NbN the soft mode region has moved from the middle of the Σ-direction to the zone boundary. The experimental results are well described by a double shell model which has also been used to calculate the density of states. Using the formalism of Varma and Weber the measured dispersion curves have been reproduced. This shows that the change in the anomalies when going from 9 to 10 valence electrons, is due to a shift in Fermi energy in an essentially rigid band scheme.     

On nonnormal matrices

For the eigenvalues λ_i of an n × n matrix A the inequality

$\text{∑}\text{i}\text{|λ}{}_{\mathrm{i}}\text{|}{}^2\text{(6A6}{}^4\text{?}\text{1}\text{2}\text{6D6}{}^2\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$

is proved, where $\text{D ? AA}{}^1\text{? A}{}^1\text{A}$ and 6 ● 6; denotes the euclidean norm. Conditions for equality are stated.     

Die behandlung zweier randwertprobleme für die vektorielle poissongleidiung nach einer integralgleichungsmethode

Ohne Zusammenfassung Vorgelegt von H. Görtler     

Density functional theory investigation of decamethyldizincocene

A density functional investigation into the structure and vibrational properties of the recently synthesized, novel, Zn(I)-containing species decamethyldizincocene has been performed. Our analysis is in agreement with the general structural properties of the experimental results. We have corroborated the experimental geometry as a true minimum on the global molecular energy surface, confirmed the experimental hypothesis that the Zn atoms are in a Zn(I) state, and provided a detailed analysis of the experimentally undefined Zn-dominant IR and Raman spectral bands of this unusual Zn(I) species.     

The use of jacobi's lemma in unimodularity theory

The paper applies Jacobi's fundamental result on minors of the adjoint matrix to obtain properties on determinants of unimodular matrices.     

On the numerical solution of a logarithmic integral equation of the first kind for the Helmholtz equation

Summary We describe a quadrature method for the numerical solution of the logarithmic integral equation of the first kind arising from the single-layer approach to the Dirichlet problem for the two-dimensional Helmholtz equation in smooth domains. We develop an error analysis in a Sobolev space setting and prove fast convergence rates for smooth boundary data.     

Huygens’ principle and iterative methods in inverse obstacle scattering

The inverse problem we consider in this paper is to determine the shape of an obstacle from the knowledge of the far field pattern for scattering of time-harmonic plane waves. In the case of scattering from a sound-soft obstacle, we will interpret Huygens’ principle as a system of two integral equations, named data and field equation, for the unknown boundary of the scatterer and the induced surface flux, i.e., the unknown normal derivative of the total field on the boundary. Reflecting the ill-posedness of the inverse obstacle scattering problem these integral equations are ill-posed. They are linear with respect to the unknown flux and nonlinear with respect to the unknown boundary and offer, in principle, three immediate possibilities for their iterative solution via linearization and regularization. In addition to presenting new results on injectivity and dense range for the linearized operators, the main purpose of this paper is to establish and illuminate relations between these three solution methods based on Huygens’ principle in inverse obstacle scattering. Furthermore, we will exhibit connections and differences to the traditional regularized Newton type iterations as applied to the boundary to far field map, including alternatives for the implementation of these Newton iterations.     

Convergence of Discrete Green's Functions for Finite Difference Schemes

AMS(MOS): 65L10

The convergence of the discrete Green's function g_h is studied for finite difference schemes approximating m-th order linear two-point boundary value problems. Schemes of noncompact form and in part of the paper also nonuniform grids are admitted. Sharp convergence results are obtained for the difference quotients of g_h up to order m-1.     

Incorporation of nanogels within calcite single crystals for the storage,protection and controlled release of active compounds

Nanocarriers have tremendous potential for the encapsulation, storage and delivery of active compounds. However, current formulations often employ open structures that achieve efficient loading of active agents, but that suffer undesired leakage and instability of the payloads over time. Here, a straightforward strategy that overcomes these issues is presented, in which protein nanogels are encapsulated within single crystals of calcite (CaCO₃). Demonstrating our approach with bovine serum albumin (BSA) nanogels loaded with (bio)active compounds, including doxorubicin (a chemotherapeutic drug) and lysozyme (an antibacterial enzyme), we show that these nanogels can be occluded within calcite host crystals at levels of up to 45 vol%. Encapsulated within the dense mineral, the active compounds are stable against harsh conditions such as high temperature and pH, and controlled release can be triggered by a simple reduction of the pH. Comparisons with analogous systems – amorphous calcium carbonate, mesoporous vaterite (CaCO₃) polycrystals, and calcite crystals containing polymer vesicles – demonstrate the superior encapsulation performance of the nanogel/calcite system. This opens the door to encapsulating a broad range of existing nanocarrier systems within single crystal hosts for the efficient storage, transport and controlled release of various active guest species.

Nanocarriers have tremendous potential for the encapsulation, storage and delivery of active compounds.     

Regio‐ and Enantio‐selective Chemo‐enzymatic C−H‐Lactonization of Decanoic Acid to (S)‐δ‐Decalactone

The conversion of saturated fatty acids to high value chiral hydroxy‐acids and lactones poses a number of synthetic challenges: the activation of unreactive C?H bonds and the need for regio‐ and stereoselectivity. Here the first example of a wild‐type cytochrome P450 monooxygenase (CYP116B46 from Tepidiphilus thermophilus) capable of enantio‐ and regioselective C5 hydroxylation of decanoic acid 1 to (S)‐5‐hydroxydecanoic acid 2 is reported. Subsequent lactonization yields (S)‐δ‐decalactone 3 , a high value fragrance compound, with greater than 90 % ee. Docking studies provide a rationale for the high regio‐ and enantioselectivity of the reaction.