Nonlinear Elliptic Differential Equations with Multivalued Nonlinearities

In this paper we study nonlinear elliptic boundary value problems with monotone and nonmonotone multivalued nonlinearities. First we consider the case of monotone nonlinearities. In the first result we assume that the multivalued nonlinearity is de_ned on all . Assuming the existence of an upper and of a lower solution, we prove the existence of a solution between them. Also for a special version of the problem, we prove the existence of extremal solutions in the order interval formed by the upper and lower solutions. Then we drop the requirement that the monotone nonlinearity is defined on all of . This case is important because it covers variational inequalities. Using the theory of operators of monotone type we show that the problem has a solution. Finally, in the last part we consider an eigenvalue problem with a nonmonotone multivalued nonlinearity. Using the critical point theory for nonsmooth locally Lipschitz functionals we prove the existence of at least two nontrivial solutions (multiplicity theorem).     

Thresholds for intersecting D-branes revisited

Gauge threshold corrections for intersecting D6-brane string models on toroidal orbifold backgrounds are reconsidered. Both by dimensionally regularising the appearing open string one-loop diagrams in tree-channel as well as by zeta-function regularisation of the corresponding loop-channel one-loop diagrams, we arrive at a result which takes into account the infrared divergence from the contribution of the massless states in the running of the gauge coupling constant as well as the contribution of states, which become light in certain regions of the moduli space.     

Heterobimetallic complexes containing Ca-Fe or Yb-Fe bonds: synthesis and molecular and electronic structures of [M{CpFe(CO)2}2(THF)3]2 (M = Ca or Yb)

Reaction of calcium or ytterbium amalgam with [CpFe(CO)(2)](2) (Fp(2)) gave the isostructural heavy alkaline earth or divalent rare earth compounds [MFp(2)(THF)(3)](2) (M = Ca or Yb) containing two direct Ca-Fe (3.0185(6) ?) or Yb-Fe (2.9892(4) ?) bonds. Density functional theory supports experiment in finding shorter Yb-Fe than Ca-Fe distances, and Ziegler-Rauk, molecular orbital, and atoms-in-molecules analyses find the M-Fe bonding to be predominantly electrostatic in nature. The Yb-Fe interaction energy and bond critical point electron density are slightly larger than for Ca-Fe, in agreement with the shorter M-Fe bond in the former. The corresponding reaction for magnesium gave MgFp(2)(THF)(4) with two O-bound Fp moieties and no Mg-Fe bond.     

Group 3 and lanthanide boryl compounds: syntheses, structures, and bonding analyses of Sc-B, Y-B, and Lu-B σ-coordinated NHC analogues

Reaction of [Ln(CH(2)SiMe(3))(2)(THF)(n)][BPh(4)] (Ln = Sc, Y, Lu ; n = 3, 4) with Li{B(NArCH)(2)}(THF)(2) (Ar = 2,6-C(6)H(3)(i)Pr(2)) formed the first group 3 and lanthanide boryl compounds, Sc{B(NArCH)(2)}(CH(2)SiMe(3))(2)(THF) and Ln{B(NArCH)(2)}(CH(2)SiMe(3))(2)(THF)(2) (Ln = Y, Lu), which contain two-center, two-electron Ln-B σ bonds. All of these systems were crystallographically characterized. Density functional theory analysis of the Ln-B bonding found it to be predominantly ionic, with covalent character in the σ-bonding Ln-B HOMO.     

Large-scale learning of structure-activity relationships using a linear support vector machine and problem-specific metrics

The goal of this study was to adapt a recently proposed linear large-scale support vector machine to large-scale binary cheminformatics classification problems and to assess its performance on various benchmarks using virtual screening performance measures. We extended the large-scale linear support vector machine library LIBLINEAR with state-of-the-art virtual high-throughput screening metrics to train classifiers on whole large and unbalanced data sets. The formulation of this linear support machine has an excellent performance if applied to high-dimensional sparse feature vectors. An additional advantage is the average linear complexity in the number of non-zero features of a prediction. Nevertheless, the approach assumes that a problem is linearly separable. Therefore, we conducted an extensive benchmarking to evaluate the performance on large-scale problems up to a size of 175000 samples. To examine the virtual screening performance, we determined the chemotype clusters using Feature Trees and integrated this information to compute weighted AUC-based performance measures and a leave-cluster-out cross-validation. We also considered the BEDROC score, a metric that was suggested to tackle the early enrichment problem. The performance on each problem was evaluated by a nested cross-validation and a nested leave-cluster-out cross-validation. We compared LIBLINEAR against a Nai?ve Bayes classifier, a random decision forest classifier, and a maximum similarity ranking approach. These reference approaches were outperformed in a direct comparison by LIBLINEAR. A comparison to literature results showed that the LIBLINEAR performance is competitive but without achieving results as good as the top-ranked nonlinear machines on these benchmarks. However, considering the overall convincing performance and computation time of the large-scale support vector machine, the approach provides an excellent alternative to established large-scale classification approaches.     

Arginine conjugates of metallo-supramolecular cylinders prescribe helicity and enhance DNA junction binding and cellular activity

The conjugation of arginine residues at the ends of a metallo-supramolecular triple-helical cylinder enables absolute control over the helicity of the cylinder core, and boosts the DNA junction recognition by the complexes and their activity against a cancer cell line.     

Catalytic Adsorptive Stripping Chronopotentiometry of Co(II)‐DMG‐Bromate System at an In Situ Plated Lead Film Electrode

A novel catalytic adsorptive stripping chronopotentiometric (CC‐CAdSCP) procedure for the determination of Co(II) traces was developed using a lead film electrode (PbFE). The PbFE was generated in situ on a glassy carbon support from a 0.1 M ammonia buffer containing 1×10^?5 M Pb(II), 6.5×10^?5 M DMG and the target metals. An addition of 0.2 M NaBrO₃ to the solution yielded an 11‐fold catalytic enhancement of chronopotentiometric response of the Co(II)‐DMG complex. The CC‐CAdSCP curves were well‐developed, sharp and reproducible (RSD 5.0 % for 5×10^?9 M Co(II)). The limit of detection for Co(II) for 210 s of accumulation time was 4×10^?10 M (0.024 µg L^?1). In addition, the elaborated method allowed the simultaneous quantification of Co(II) and Ni(II) simultaneously.     

A Calcium Solid State Ion Selective Minisensor Based on Lipid Films on ZnO Nanorods

This article describes the development of a calcium solid minisensor based on lipid films on ZnO nanorods. The lipid film was composed from dipalmitoylphosphatidylcholine (DPPC) and dipalmitoylphosphatidylcic acid (DPPA). The calibration graph was logarithmically related to the concentration of calcium ions in the range from 10^?6 to 10^?3 M. The response times of the electrode were less than 5 s. No memory effects were observed for this electrode. The reproducibility of the electrode was less than 5 %. The electrode has shown good stability for a period of 1 month. The influence of a wide range of metals and anions as potential interferences was checked. The method was applied to the rapid detection of calcium ions in mineral waters.     

Tetravalent metal complexation by Keggin and lacunary phosphomolybdate anions

We report the synthesis, spectroscopic and structural characterization, and computational analysis of a series of phosphomolybdate complexes with tetravalent metal cations. The reaction between Ce (IV) and Th (IV) with phosphomolybdate at the optimum pH for the stabilization of the lacunary heteropolyoxometalate anion, [PMo 11O 39] (7-), results in the formation of compounds containing the anions [Ce(PMo 11O 39) 2] (10-) and [Th(PMo 11O 39) 2] (10-), respectively. Single crystal X-ray diffraction analysis was performed on salts of both species, Cs 10[Ce(PMo 11O 39) 2].20H 2O and (NH 4) 10[Th(PMo 11O 39) 2].22H 2O. In both anionic complexes the f-block metal cation is coordinated to the four unsaturated terminal lacunary site oxygens of each [PMo 11O 39] (7-) anion, yielding 8 coordinate sandwich complexes, analogous to previously prepared related complexes. Spectroscopic characterization points to the stability of these complexes in solution over a reasonably wide pH range. Density functional analysis suggests that the Ce-O bond strength in [Ce(PMo 11O 39) 2] (10-) is greater than the Th-O bond strength in [Th(PMo 11O 39) 2] (10-), with the dominant bonding interaction being ionic in both cases. In contrast, under similar reaction conditions, the dominant solid state Zr (IV) and Hf (IV) complexes formed contain the anions [Zr(PMo 12O 40)(PMo 11O 39)] (6-) and [Hf(PMo 12O 40)(PMo 11O 39)] (6-), respectively. In these complexes the central Group 4 d-block metal cations are coordinated to the four unsaturated terminal lacunary site oxygens of the [PMo 11O 39] (7-) ligand and to four bridging oxygens of a plenary Keggin anion, [PMo 12O 40] (3-). In addition, (NH 4) 5{Hf[PMo 12O 40][(NH 4)PMo 11O 39]}.23.5H 2O can be crystallized as a minor product. The structure of the anion, {Hf[PMo 12O 40][(NH 4)PMo 11O 39]} (5-), reveals coordination of the central Hf (IV) cation via four bridging oxygens on both the coordinated [PMo 11O 39] (7-) and [PMo 12O 40] (3-) anions. Unusually, the highly charged lacunary site remains uncoordinated to the Hf metal center but instead interacts with an ammonium cation. (31)P NMR indicates that complexation of the Keggin anion, [PMo 12O 40] (3-), to Hf (IV) and Zr (IV) will stabilize the Keggin anion to a much higher pH than usually observed.