Jahn-Teller effects on π-stacking and stereoselectivity in the phenylethaniminopyridine tris-chelates Cu(NN')3(2+)

Optically pure phenylethaniminopyridine (S(C)-L) tris-chelates of Fe(II) and other first row transition metal systems have previously been shown to give exclusively the fac structures in the solid state. Here it is shown by powder X-ray diffraction that the complex [CuL(3)][ClO(4)](2) crystallises exclusively as the mer isomer, although--for a given absolute configuration of the ligand--of the same helicity (Δ/Λ) as that displayed by the other metal complexes. The similar ligand R(C)-L(F), which contains a peripheral (19)F spin label, gave [CuL(F)(3)][ClO(4)](2) which also adopts exclusively the mer structure in the crystal, but is shown by NMR spectroscopy to have a fac:mer ratio of 1:6 in solution at low temperature. Molecular mechanics calculations for a number of isomers and conformers are consistent with the presence of such a mixture of isomers in solution for both complexes. The origin of the difference in behaviour between Fe(II) and Cu(II) is the presence of a Jahn-Teller distortion (and the generally longer M-N bonds) in the Cu(II) complexes. This disturbs intra-ligand π-stacking, leading to the poor fac/mer stereoselectivity while leaving enantioselectivity Δ/Λ apparently unaffected.     

Synchronization of the minimal models of bursting neurons coupled by delayed chemical or electrical synapses

The minimal two-dimensional model of bursting neuronal dynamics is used to study the influence of time-delay on the properties of synchronization of bursting neurons. Generic properties of bursting and dependence of the stability of synchronization on the time-lag and the strength of coupling are described, and compared with the two common types of synaptical coupling, i.e., time-delayed chemical and electrical synapses.     

On Supervised Classification of Feature Vectors with Independent and Non-Identically Distributed Elements

In this paper, we investigate the problem of classifying feature vectors with mutually independent but non-identically distributed elements that take values from a finite alphabet set. First, we show the importance of this problem. Next, we propose a classifier and derive an analytical upper bound on its error probability. We show that the error probability moves to zero as the length of the feature vectors grows, even when there is only one training feature vector per label available. Thereby, we show that for this important problem at least one asymptotically optimal classifier exists. Finally, we provide numerical examples where we show that the performance of the proposed classifier outperforms conventional classification algorithms when the number of training data is small and the length of the feature vectors is sufficiently high.     

Synthesis, structural characterization, and anion binding ability of sterically congested adamantane-calix[4]pyrroles and adamantane-calixphyrins

Novel adamantane derivatives of calix[4]pyrroles 4-8 and calixphyrin 9 have been synthesized. The structure of 8 has been characterized by X-ray powder diffraction and the structure of 9 by single crystal X-ray analysis. Whereas calixphyrin 9 does not bind anions, analogous calyx[4]pyrrole 8 forms a complex with Cl⁻ in the DMSO solution and in the solid state. The solid state complexation has been accomplished on grinding in a mill, which is the first example of complex formation with an anion in the solid state.     

MIC(0) preconditioning of 3D FEM problems on unstructured grids: Conforming and non-conforming elements

In this study, the topics of grid generation and FEM applications are studied together following their natural synergy. We consider the following three tetrahedral grid generators: NETGEN, TetGen, and Gmsh. After that, the performance of the MIC(0) preconditioned conjugate gradient (PCG) solver is analyzed for both conforming and non-conforming linear FEM problems. If positive off-diagonal entries appear in the corresponding matrix, a diagonal compensation is applied to get an auxiliary M$M$-matrix allowing a stable MIC(0) factorization. The presented numerical experiments for elliptic and parabolic problems well illustrate the similar PCG convergence rate of the MIC(0) preconditioner for both, structured and unstructured grids.     

Numerical algorithm for natural frequencies computation of an axially moving beam model

An algorithm for numerical computation of natural frequencies of the axially moving Euler-Bernoulli beam is presented. It is tested against data found in the literature and against known analytical expressions of its limiting models—axially moving string and stationary beam—where good agreements were found. The numerical algorithm always stays within real algebra. Roots of the polynomial can be computed out of only three real numbers and the expressions for determinant evaluations are deduced in a numerically stable way.     

Anion-Sensing Properties of Cyclopentaphenylalanine

Cyclic pentaphenylalanine was studied as an efficient anion sensor for halides, thiocyanate and oxoanions in acetonitrile and methanol. Stability constants of the corresponding complexes were determined by means of fluorimetric, spectrophotometric, ¹H NMR, and microcalorimetric titrations. A detailed structural overview of receptor–anion complexes was obtained by classical molecular dynamics (MD) simulations. The results of ¹H NMR and MD studies indicated that the bound anions were coordinated by the amide groups of cyclopeptide, as expected. Circular dichroism (CD) titrations were also carried out in acetonitrile. To the best of our knowledge, this is the first example of the detection of anion binding by cyclopeptide using CD spectroscopy. The CD spectra were calculated from the structures obtained by MD simulations and were qualitatively in agreement with the experimental data. The stoichiometry of almost all complexes was 1:1 (receptor:anion), except for dihydrogen phosphate where the binding of dihydrogen phosphate dimer was observed in acetonitrile. The affinity of the cyclopeptide receptor was correlated with the structure of anion coordination sphere, as well as with the solvation properties of the examined solvents.