Spectral density estimates with partial symmetries and an application to Bahri–Lions-type results

We are concerned with the existence of infinitely many solutions for the problem \(-\Delta u=|u|^{p-2}u+f\) in \(\Omega \), \(u=u_0\) on \(\partial \Omega \), where \(\Omega \) is a bounded domain in \(\mathbb {R}^N\), \(N\ge 3\). This can be seen as a perturbation of the problem with \(f=0\) and \(u_0=0\), which is odd in u. If \(\Omega \) is invariant with respect to a closed strict subgroup of O(N), then we prove infinite existence for all functions f and \(u_0\) in certain spaces of invariant functions for a larger range of exponents p than known before. In order to achieve this, we prove Lieb–Cwikel–Rosenbljum-type bounds for invariant potentials on \(\Omega \), employing improved Sobolev embeddings for spaces of invariant functions.     

Enzymes immobilized in mesoporous silica: A physical–chemical perspective

Mesoporous materials as support for immobilized enzymes have been explored extensively during the last two decades, primarily not only for biocatalysis applications, but also for biosensing, biofuels and enzyme-controlled drug delivery. The activity of the immobilized enzymes inside the pores is often different compared to that of the free enzymes, and an important challenge is to understand how the immobilization affects the enzymes in order to design immobilization conditions that lead to optimal enzyme activity. This review summarizes methods that can be used to understand how material properties can be linked to changes in enzyme activity. Real-time monitoring of the immobilization process and techniques that demonstrate that the enzymes are located inside the pores is discussed by contrasting them to the common practice of indirectly measuring the depletion of the protein concentration or enzyme activity in the surrounding bulk phase. We propose that pore filling (pore volume fraction occupied by proteins) is the best standard for comparing the amount of immobilized enzymes at the molecular level, and present equations to calculate pore filling from the more commonly reported immobilized mass. Methods to detect changes in enzyme structure upon immobilization and to study the microenvironment inside the pores are discussed in detail. Combining the knowledge generated from these methodologies should aid in rationally designing biocatalyst based on enzymes immobilized in mesoporous materials.     

Synthesis, characterization and antimicrobial studies of mixed ligand silver(I) complexes of triphenylphosphine and heterocyclic thiones: Crystal structure of bis[{(μ-diazinane-2-thione)(diazinane-2-thione)(triphenylphosphine)silver(I) nitrate}]

Mixed ligand silver(I) complexes of triphenylphosphine and heterocyclic thiones (imidazolidine-2-thione (Imt), diazinane-2-thione (Diaz) and 2-mercaptopyridine (Mpy)) having the general formulae [(Ph₃P)Ag(thione)₂]NO₃ and [(Ph₃P)₂Ag(thione)]NO₃ were prepared and characterized by elemental analysis, IR and NMR (¹H, ¹³C and ³¹P) spectroscopic methods. The crystal structure of one of the complexes, [Ag(Ph₃P)(Diaz)₂]₂(NO₃)₂ (1) was determined by X-ray crystallography. The title complex (1) is dinuclear, having each silver atom coordinated to three thione sulfur atoms of Diaz and to one phosphorus atom of PPh₃ in a nearly tetrahedral environment, with an average P-Ag-S bond angle of 108.5°. The spectral data of the complexes are consistent with sulfur coordination of the thiones to silver(I). Antimicrobial activities of the complexes were evaluated by minimum inhibitory concentrations and the results showed that the complexes exhibit a wide range of activity against two gram-negative bacteria (E. coli, P. aeruginosa) and molds (A. niger, P. citrinum), while the activities were poor against yeasts (C. albicans, S. cerevisiae).     

The Structure of the “Third‐Generation” Tris(pyrazolyl)borate Caesium Salt p‐BrC6H4TpCs

Slow crystallisation at lowered temperature yielded crystals of the “third‐generation” tris(pyrazolyl)borate transfer agent p‐BrC₆H₄TpCs (Tp′Cs) 1 (triclinic; P$\bar{1}$ ; a = 8.540(4), b = 15.045(6), c = 15.879(7) Å; α = 65.853(8), β = 88.457(8), γ = 75.056(8)°; V = 1791.4(13) Å³; Z = 4). The central caesium ion in 1 interacts with three individual p‐BrC₆H₄Tp ligands in two different chelating fashions.In particular, κ¹‐N‐coordination and η⁵‐π‐coordination of pyrazole moieties as well as η⁶‐π‐coordination of the p‐BrC₆H₄ substituent are observed. Further, comparable coordination of neighbouring caesium ions leads to the formation of polymeric structures connected by two bridging modes.     

Electronic coupling through intramolecular π-π interactions in biscobaltocenes: a structural, spectroscopic, and magnetic study

The paramagnetic dinuclear complexes 1,8-bis(cobaltocenyl)naphthalene (2) and 1,8-bis[(pentamethyl-η(5)-cyclopentadienyl)(η(5)-cyclopentadiendiyl)cobalt(II)]naphthalene (4) were synthesized. The molecular structures were characterized by X-ray structure analysis and consisted of two cobaltocenes linked through a distorted naphthalene clamp. Electronic interactions between the two cobalt atoms were observed by cyclic voltammetric studies. Superconducting quantum interference device (SQUID) measurements of the pure compounds and diluted in their diamagnetic iron derivatives, as well as variable-temperature NMR spectroscopy experiments in solution are presented. Magnetic measurements revealed an antiferromagnetic coupling of the electrons in complexes 2 and 4. From NMR spectroscopy experiments, Curie behavior in the temperature range from -60 to +60 °C can be deduced. The electronic structure and magnetic behavior is supported by results of broken-symmetry DFT and multireference calculations along with UV/Vis spectroscopic data, which revealed an intramolecular through space π-π interaction between the cobaltocene units.     

Computational study of the effect of confinement within microporous structures on the activity and selectivity of metallocene catalysts for ethylene oligomerization

The effect of confinement within some zeolitic structures on the activity and selectivity of metallocene catalysts for the ethylene oligomerization has been investigated using grand canonical Monte Carlo simulations (GCMC). The following zeolite (host) frameworks displaying different pore sizes, have been studied as solid hosts: mazzite (MAZ), AIPO-8 (AET), UTD-1F (DON), faujasite (FAU), and VPI-5 (VFI). Intermediates and transition states involved in the ethylene trimerization reaction catalyzed by a Ti-based catalyst [(η(5)-C(5)H(4)CMe(2)C(6)H(5))TiCl(3)/MAO] have been used as sorbates (guests). We have demonstrated linear correlations with slope a(H,j) between the adsorption enthalpy and the molecular volume V(m) of the sorbates, each holding for a given microporous host below a host-specific threshold V(mmax,j). Beyond this maximal molecular volume, the adsorption vanishes due to steric exclusion. a(H,j) increases, and V(mmax,j) decreases with decreasing host pore size, in line with the confinement concept. We moreover showed that, in the limit of vanishing loading (Henry regime), the enthalpies and entropies of adsorption in a given host are linearly correlated. We have defined a host-specific confinement compensation temperature a(j), which refers to a temperature where the stabilizing adsorption enthalpic interactions are canceled out against the loss in entropy. However, calculated a(j) are much larger than the operating temperatures. With a setup microkinetic model, we predict that the activity and selectivity of the confined Ti-catalyst in ethylene oligomerization can be significantly altered with respect to homogeneous phase conditions, since the adsorption free energies of transition states and intermediates also become functions of a(H,j) and V(m). We have applied this theory to predict the optimum host pore size to get maximum α-octene production, instead of α-hexene, which is primarily produced in the homogeneous phase. We also predict a significantly increased activity for confined catalysts.     

Production of highly conductive textile viscose yarns by chemical vapor deposition technique: a route to continuous process

An oxidative chemical vapor deposition (OCVD) process was used to coat flexible textile fiber (viscose) with highly conductive polymer, poly (3,4‐ethylenedioxythiophene) (PEDOT) in presence of ferric (III) chloride (FeCl₃) oxidant. OCVD is a solvent free process used to get uniform, thin, and highly conductive polymer layer on different substrates. In this paper, PEDOT coated viscose fibers, prepared under specific conditions, exhibited high conductivity 14.2 S/cm. The effects of polymerization conditions, such as polymerization time, oxidant concentration, dipping time of viscose fiber in oxidant solution, and drying time of oxidant treated viscose fiber, were carefully investigated. Scanning electron microscopy (SEM) and FT‐IR analysis revealed that polymerization of PEDOT on surface of viscose fiber has been taken place and structural analysis showed strong interactions between PEDOT and viscose fiber. Thermogravimetric analysis (TGA) was employed to investigate the amount of PEDOT in PEDOT coated viscose fiber and interaction of PEDOT with viscose fiber. The effect of PEDOT coating on the mechanical properties of the viscose fiber was evaluated by tensile strength testing of the coated fibers. The obtained PEDOT coated viscose fiber having high conductivity, could be used in smart clothing for medical and military applications, heat generation, and solar cell demonstrators. Copyright © 2010 John Wiley & Sons, Ltd.     

The radical mechanism of cobalt(II) porphyrin-catalyzed olefin aziridination and the importance of cooperative H-bonding

The mechanism of cobalt(II) porphyrin-mediated aziridination of styrene with PhSO(2)N(3) was studied by means of DFT calculations. The computations clearly indicate the involvement of a cobalt 'nitrene radical' intermediate in the Co(II)(por)-catalyzed alkene aziridination. The addition of styrene to this species proceeds in a stepwise fashion via radical addition of the 'nitrene radical'C to the C=C double bond of styrene to form a γ-alkyl radical intermediate D. The thus formed tri-radical species D easily collapses in an almost barrierless ring closure reaction (TS3) to form the aziridine, thereby regenerating the cobalt(II) porphyrin catalyst. The radical addition of the 'nitrene radical'C to the olefin (TS2) proceeds with a comparable barrier as its formation (TS1), thus providing a good explanation for the first order kinetics in both substrates and the catalyst observed experimentally. Formation of C is clearly accelerated by stabilization of C and TS1 via hydrogen bonding between the S=O and N-H units. The computed radical-type mechanism agrees well with all available mechanistic and kinetic information. The computed free energy profile readily explains the superior performance of the Co(II)(porAmide) system with H-bond donor functionalities over the non-functionalized Co(TPP).     

Development of an online SPE�CLC�CMS-based assay using endogenous substrate for investigation of soluble epoxide hydrolase (sEH) inhibitors

Soluble epoxide hydrolase (sEH) is a promising therapeutic target for the treatment of hypertension, pain, and inflammation-related diseases. In order to enable the development of sEH inhibitors (sEHIs), assays are needed for determination of their potency. Therefore, we developed a new method utilizing an epoxide of arachidonic acid (14(15)-EpETrE) as substrate. Incubation samples were directly injected without purification into an online solid phase extraction (SPE) liquid chromatography electrospray ionization tandem mass spectrometry (LC-ESI-MS-MS) setup allowing a total run time of only 108 s for a full gradient separation. Analytes were extracted from the matrix within 30 s by turbulent flow chromatography. Subsequently, a full gradient separation was carried out on a 50X2.1 mm RP-18 column filled with 1.7 μm core-shell particles. The analytes were detected with high sensitivity by ESI-MS-MS in SRM mode. The substrate 14(15)-EpETrE eluted at a stable retention time of 96 ± 1 s and its sEH hydrolysis product 14,15-DiHETrE at 63 ± 1 s with narrow peak width (full width at half maximum height: 1.5 ± 0.1 s). The analytical performance of the method was excellent, with a limit of detection of 2 fmol on column, a linear range of over three orders of magnitude, and a negligible carry-over of 0.1% for 14,15-DiHETrE. The enzyme assay was carried out in a 96-well plate format, and near perfect sigmoidal dose-response curves were obtained for 12 concentrations of each inhibitor in only 22 min, enabling precise determination of IC(50) values. In contrast with other approaches, this method enables quantitative evaluation of potent sEHIs with picomolar potencies because only 33 pmol L(-1) sEH were used in the reaction vessel. This was demonstrated by ranking ten compounds by their activity; in the fluorescence method all yielded IC(50) ≤ 1 nmol L(-1). Comparison of 13 inhibitors with IC(50) values >1 nmol L(-1) showed a good correlation with the fluorescence method (linear correlation coefficient 0.9, slope 0.95, Spearman's rho 0.9). For individual compounds, however, up to eightfold differences in potencies between this and the fluorescence method were obtained. Therefore, enzyme assays using natural substrate, as described here, are indispensable for reliable determination of structure-activity relationships for sEH inhibition.