Vector potential theory on nonsmooth domains in R<Superscript>3</Superscript> and applications to electromagnetic scattering

We study boundary value problems for the time-harmonic form of the Maxwell equations, as well as for other related systems of equations, on arbitrary Lipschitz domains in the three-dimensional Euclidean space. The main goal is to develop the corresponding theory for L^p-integrable bounday data for optimal values of p's. We also discuss a number of relevant applications in electromagnetic scattering.     

v-Triazolines. XXXIX . 1,2,4-Triaryl-3-aminopyrroles. Unusual Reaction Products in the Pyrolysis of 5-Amino-v-triazolines and the Crystal Structure of 2-(3-Morpholin-4-yl-2,4-pyrrol-1-yl)benzonitrile

Pyrolysis of 4-aryl-5-amino-v-triazolines affords, generally, amidines and/or benzanilides. Pyrolysis of 4-aryl-5-morpholino-v-triazolines 6 , together with the expected amidines 7 and/or aryanilides 8 , produced the morpholinopyrroles 9 . The reaction mechanism of this unusual transformation is discussed. Influence of solvent dipole moment in pyrrole formation is suggested. Pyrrole 9a [i.e. 2-(3-morpholin-4-yl-2,4-pyrrol-1-yl)-benzonitrile] has been fully characterized and its molecular structure has been determined by X-ray diffraction analysis.     

Oscillatory kinetics and mechanism of the chromate catalyzed decomposition of hydrogen peroxide

Oscillatory change of pH occurs during the chromate-catalyzed decomposition of hydrogen peroxide in a weakly acidic medium at elevated temperature and at high initial concentration of hydrogen peroxide. In a closed system, there are only two or three periods, but sustained oscillation occurs in a CSTR. In a CSTR bistability is also found. In closed systems the temperature exhibits a great maximum (up to 15°C increase), in a CSTR sustained oscillation occurs at a constant stationary temperature.     

On the Besov regularity of conformal maps and layer potentials on nonsmooth domains

We study the Besov regularity of conformal mappings for domains with rough boundary based on the well-posedness for the Dirichlet problem with Besov data. Also, sharp invertibility results for the classical layer potential operators on Sobolev-Besov spaces on the boundary of curvilinear polygons are obtained.     

A general converse theorem for mean‐value theorems in linear elasticity

We prove a rather general mean‐value formula in the theory of elasticity, which expresses the value of the displacement at the centre of a sphere in terms of certain combinations of integral averages over the sphere itself of the traction and the displacement. We also establish the corresponding converse to this mean‐value formula under minimal smoothness assumptions on the displacement. Copyright © 2006 John Wiley & Sons, Ltd.     

Shape recognition of alkylammonium ions by 1,3-bridged calix[5]arene crown-6 ethers: endo- vs exo-cavity complexation

A series of tri-O-substituted 1,3-bridged calix[5]arene crown-6 ethers bearing alkyl, arylalkyl, alkoxyalkyl, and alkoxycarbonylmethyl residues at the lower rim and either (t)()Bu or H substituents at the upper rim have been synthesized. (1)H NMR studies have shown that p-tert-butylcalix[5]crowns, irrespective of the size and nature of their lower rim pendant groups, adopt preorganized conelike conformations, whereas p-H-calix[5]crowns with bulky substituents preferentially exist in solution as partial cone conformers (C(1) symmetry). Calix[5]crown derivatives behave as mono- or ditopic receptors for isomeric butylammonium ions, forming endo-cavity (inside the calixarene cup) and/or exo-cavity (at the crown ether moiety) 1:1 complexes according to the shape of the guest. These two binding modes can be clearly distinguished and monitored by (1)H NMR titration experiments.     

Conductance in homomorphous solvents: Tetrabutylammonium salts and alkali picrates in butyrolactone-sulfolane mixtures

Conductance measurements are reported for LiPi, NaPi, KPi, RbPi, CsPi, Bu₄NPi, Bu₄NBr, Bu₄NClO₄, Bu₄NNO₃, and Bu₄NBBu₄ at 25°C in -butyrolactone-sulfolane mixtures. In these mixtures of solvents that are practically homomorphous, isodielectic and with comparable dipole moments, the ion pair association and ionic mobilities of large ions conform to the expectations of the primitive model. Electrolytes containing lithium or sodium ions show anomalies indicating that other factors besides shape, dipole moment, and polarizability of the solvent molecules are involved in the association and transport processes of these ions.     

Effect of the addition of a nonionic surfactant on the complex poly(asparagine)--cationic surfactant

Poly(asparagine) (pAsn) at 0.1wt % in the presence of dodecyltrimethylammonium bromide (DTAB) and pentaoxyethylene octyl ether (C(8)E(5)) at 1:1 molar ratio leads to the formation of mixed DTAB/C(8)E(5) micelle-like aggregates onto the polypeptide as a total surfactant critical association concentration (cac) is reached, as revealed by surface tension measurements and NMR chemical shifts. Two-dimensional nuclear Overhauser enhancement spectroscopy (NOESY) capable of revealing spatial relationships among proximal protons has been performed on the pAsn-DTAB-C(8)E(5)-water system to study structural details of the surfactant-polypeptide aggregates. NOESY cross-peaks at sample temperature of 298.15 K indicate that the polypeptide interacts with the DTAB/C(8)E(5) micelle-like aggregates. The NOE intermolecular effects also show direct interactions between surfactant and polypeptide in the pAsn-DTAB-water system, whereas no interaction has been revealed in the pAsn-C(8)E(5)-water system. Furthermore, the experimental evidence suggest that the DTAB-polypeptide complex is mainly driven by the polar attraction between the two molecules.     

X-ray structure and circular dichroism of pure rotamers of bis[guanosine-5'-monophosphate(-1)](N,N,N',N'-tetramethylcyclohexyl-1,2-diamine)platinum(II) complexes that have R,R and S,S configurations at the asymmetric diamine

The use of a sterically hindered diamine ligand (Me(4)DACH) has allowed for the first time, the isolation and characterization, both in the solid state (X-ray crystallography) and in solution (circular dichroism), of pure DeltaHT rotamers of [Pt(Me(4)dach)(5'-GMP)(2)] (compounds 1 and 2 for R,R and S,S configurations of the Me(4)DACH ligand, respectively). Comparison of the CD spectra obtained for each rotamer, which differ only in the chirality of the Me(4)DACH ligand (R,R or S,S) or in the chirality of the HT conformation (Delta or Lambda), allowed us to conclude that, in the 200-350 nm range, the contributions to the overall CD spectrum that stem from diamine chirality and diamine-induced chirality of platinum d--d transitions or from sugar chirality are negligible relative to the exciton chiral coupling that occurs for pi-pi* transitions of the cis guanines. Accurate molecular structures of 1.10 D(2)O and 2.14 D(2)O (conventional crystallographic agreement indexes R(1) convergent to 2.07 % and 2.18 %, respectively) revealed that the crystallized rotamers have a DeltaHT conformation that is in agreement with all previously reported X-ray structures of [Pt(diamine)(nucleos(t)ide)(2)] complexes. This conformation allows the 5'-phosphate to be located in proximity to the Me(4)DACH ligand so that (P)O...HC(N) hydrogen-bond interactions exists in both complexes. For both structures, the canting of the guanine planes on the coordination plane is right-handed (R; canting angle (Phi) of 80.9 degrees and 73.2 degrees, respectively); this indicates that the canting direction is driven by the HT conformation chirality (Delta for both compounds) and not by the chirality of the carrier ligand (different for the two compounds). Density functional theory analysis of the conformational space as a function of Phi indicated a good agreement between the computed and experimental structures. The increase in energy for Phi values below 65 degrees and 55 degrees (for 1 and 2, respectively) is mainly due to the short intramolecular contacts between C(8)H and the cis N-Me groups on the same side of the platinum coordination plane.     

Strukturelle Untersuchungen einiger neutraler Komplexe des zweiwertigen Molybdäns

Unit cell parameters have been calculated from x-ray powder diffraction data of Mo₂Br₄ Py ₄ (A), Mo₂I₄ Py ₄ (B), Mo₂I₄ Pic ₄ (C), Mo₂(SCN)₄ Py ₄ (D) and Mo₂(SCN)₄ Pic ₄ (E), A, B and C crystallize tetragonal. A witha=9,4₂,c=15,O₂ Å; B witha=9,4₆,c=14,9₈ Å and C witha=9,6₆ andc=15,7₂ Å D and E crystallize orthorhombic. D witha=10,0₉,b=9,1₄,c=15,0₈ Å; E witha=10,2₂,b=9,4₁ andc=15,1₅ Å.Py=pyridine,Pic=4-methylpyridine.