How Fast can a Subharmonic Function Decay Along a Ray?

Much is known about the connection between the growth and decayof subharmonic functions. The results indicate that there isa general principle: asubharmonic function cannot decay ‘toofast’ relative to its growth.Three theorems are provedwhich, together with work previously published elsewhere, givea fairly complete account of how this principle works out fora subharmonic function having extremal decay along a ray. 1991Mathematics Subject Classification: 30D20, 31A05.     

Chelate von Chinolin-8-ol — Derivaten. XI. Eigenschaften und Struktur von Nickelchelaten alkyl-substituierter Chinolin-8-ole bzw. Chinolin-8-thiole

Reactions of 1,1,3,3-Tetrakis(dimethylamino)-1λ⁵,3λ⁵-diphosphete with N? H and P? H Acidic Compounds 1,1,3,3-Tetrakis(dimethylamino)-1λ⁵,3λ⁵-diphosphete, 1 , reacts with aniline to give by opening of the ring 2,2,4,4-tetrakis(dimethylamino)-1-phenyl-1,2λ⁵,4λ⁵-azadiphosphapenta-1,3-diene, 2 , with p-CN? C₆F₄? NH₂ the product is 1-(4-cyano-2,3,5,6-tetrafluorophenyl)-2,2,4,4-tetrakis(dimethylamino)-1,2λ⁵,4λ⁵-azadiphosphapenta-1,3-diene, 3 . t-Butylamine or diethylamine do not react with 1 . Mesitylphosphane opens the ring system 1 forming by reduction of one phosphorus atom {[bis(dimethylamino)phosphanyl]methylidene}bis(dimethylamino)methylphosphorane, 4 . The same product 4 is obtained by reaction with phenylphosphane. The reaction products 2–4 are characterized by their nmr, mass, and ir spectra. Their way of formation is discussed. In 4 a ⁵J(PH), in 3 a ⁷J(CF) long range coupling constant could be identified.     

Correlations of chemical mass shifts of para-substituted acetophenones and benzophenones with Brown's sigma constants

Relationships between chemical mass shifts and physiochemical properties of ions are sought by examining substituted acetophenones, benzophenones, and pyridines in a modified ion trap mass spectrometer. Systematic changes in chemical mass shift occur with changes in substituent in the acetophenones and the benzophenones. Brown's sigma+ constant, which is a measure of electronic effects of substituents in reactions that involve positive charge development, is shown to correlate linearly with chemical mass shifts in para-substituted acetophenones and benzophenones. Brown's sigma+ constant also correlates with the ease of dissociation of the ions via a correlation with ionization energy. It is suggested that ease of dissociation is the underlying factor in determining chemical mass shifts. The experimental results also suggest that dissociative collisions between ions and buffer gas make a much greater contribution to chemical mass shifts than do elastic collisions.     

Strukturelle und spektroskopische Charakterisierung sechsfach koordinierter Vanadium(V)-Komplexe: Ein Strukturmodell für das aktive Zentrum Vanadium-abhängiger Haloperoxidasen

Structural and Spectroscopic Characterization of Six-Coordinate Vanadium(V) Complexes: A Structural Model for the Active Site of Vanadium-Dependent Haloperoxidases A series of vanadium(V) complexes has been synthesized from ammonium metavanadate and trivalent, pentadentate Schiff base ligands. These aliphatic as well as aromatic hydroxyl groups containing ligands are stabilizing the VO³⁺ unit. The complexes 1–5 are characterized by ¹H-, ¹³C- and ⁵¹V-NMR, virbrational (IR, Raman and resonance Raman) and electronic spectroscopy as well as EHMO calculations. The X-ray crystal structure analysis of 1 (monoclinic space group P2₁/n: a = 1 073.3(2); b = 1 201.1(3); c = 1 165.7(3) pm; β = 101.89(2)°; Z = 4) shows that the vanadium(V) center has a distorded octahedral environment. The LMCT transition of the complexes 1–5 in the electronic spectra has been observed at comparatively high energies (21.8 ? 25.8 × 10³ cm^?1) and are assigned based on resonance Raman spectra and EHMO calculations. The implications of the observed physical properties of the complexes 1–5 to the structural model proposed for the active site of vanadat(V)-dependent haloperoxidases are discussed.     

Qualitative properties of modified equations

Suppose that a consistent one-step numerical method of orderr is applied to a smooth system of ordinary differential equations.Given any integer m 1, the method may be shown to be of orderr + m as an approximation to a certain modified equation. Ifthe method and the system have a particular qualitative propertythen it is important to determine whether the modified equationsinherit this property. In this article, a technique is introducedfor proving that the modified equations inherit qualitativeproperties from the method and the underlying system. The techniqueuses a straightforward contradiction argument applicable toarbitrary one-step methods and does not rely on the detailedstructure of associated power series expansions. Hence the conclusionsapply, but are not restricted, to the case of Runge-Kutte methods.The new approach unifies and extends results of this type thathave been derived by other means: results are presented forintegral preservation, reversibility, inheritance of fixed points.Hamiltonian problems and volume preservation. The techniquealso applies when the system has an integral that the methodpreserves not exactly, but to order greater than r. Finally,a negative result is obtained by considering a gradient systemand gradient numerical method possessing a global property thatis not shared by the associated modified equations.     

Iron Coordination Properties of Gramibactin as Model for the New Class of Diazeniumdiolate Based Siderophores

Gramibactin (GBT) is an archetype for the new class of diazeniumdiolate siderophores, produced by Paraburkholderia graminis, a cereal-associated rhizosphere bacterium, for which a detailed solution thermodynamic study exploring the iron coordination properties is reported. The acid-base behavior of gramibactin as well as its complexing ability toward Fe³⁺ was studied over a wide range of pH values (2≤pH≤11). For the latter the ligand-competition method employing EDTA was used. Only two species are formed: [Fe(GBT)]⁻ (pH 2 to 9) and [Fe(GBT)(OH)₂]³⁻ (pH≥9). The formation of [Fe(GBT)]⁻ and its occurrence in real systems was confirmed by LC-HRESIMS analysis of the bacteria culture broth extract. The sequestering ability of gramibactin was also evaluated in terms of the parameters pFe and pL_0.5. Gramibactin exhibits a higher sequestering ability toward Fe³⁺ than EDTA and of the same order of magnitude as hydroxamate-type microbial siderophores, but smaller than most of the catecholate-type siderophores and much higher than the most known phytosiderophores.     

Synthesis, spectroscopic characterization and biological activity of the metal complexes of the Schiff base derived from phenylaminoacetohydrazide and dibenzoylmethane

A new series of mono and binuclear Mn(II), Fe(III), Co(II), Ni(II), Cu(II), Zn(II), La(III), Ru(III), Hf(IV), ZrO(II) and UO(2)(II) complexes of phenylaminodibenzoylhydrazone have been synthesized and characterized by elementals analyses, IR UV-vis spectra, magnetic moments, conductances, thermal analyses (DTA and TGA) and electron spin resonance (ESR) measurements. The IR spectral data show that, the ligand behaves as a neutral bidentate type (15 and 16), monobasic bidentate type (6), or monobasic tridentate type (5, 7, 8, 10, 11, 13, 14, 17-21) or dibasic tridentate type 2-4, 9 and 12 towards the metal ion. Molar conductances in DMF solution indicate that, the complexes are non-electrolytes. The ESR spectra of solid complexes (9 and 10) show axial and non-axial types indicating a [Formula: see text] ground state with significant covalent bond character. However, complexes (11 and 12), show isotropic type, indicating manganese(II) octahedral geometry. Antibacterial and antifungal tests of the ligand and its metal complexes are also carried out and it has been observed that the complexes are more potent bactericides and fungicides than the ligand.