The problem of Dirichlet for anisotropic quasilinear degenerate elliptic equations

We consider the Dirichlet problem for a class of anisotropic degenerate elliptic equations. New a priori estimates for solutions and for the gradient of solutions are established. Based on these estimates sufficient conditions guaranteeing the solvability of the problem are formulated. The results are new even in the semilinear case when the principal part is the Laplace operator.     

Creation of entangled states of excitons in coupled quantum dots

We present two methods for the creation of two-particle entangled states of excitons in a coupled quantum dot system. The system contains two identical quantum dots that are coupled by an inter-dot hopping process. The manipulation of the system is succeeded by proper application of an external laser field.     

Learning to align organizational design and data

The relationship between organizational learning and organizational design is explored. In particular, we examine the information processing aspects of organizational learning as they apply to a two-valued decision making task and the relation of such aspects to organizational structure. Our primary contribution is to extend Carley's (1992) model of this process. The original model assumes that all data input into the decision making processes are of equal importance or weight in determining the correct overall organizational decision. The extension described here allows for the more natural situation of non-uniform weights of evidence. Further extensions to the model are also discussed. Such organizational learning performance measures provide an interesting framework for analyzing the recent trend towards flatter organizational structures. This research suggests that flatter structures are not always better, but rather that data environment, ultimate performance goals, and relative need for speed in learning can be used to form a contingency model for choosing organizational structure.     

The effect of charged axial ligands on the EPR parameters in oxovanadium(IV) compounds: an unusual reduction of the Az (51V) values

Two series of octahedral oxovanadium(IV) compounds, containing charged or neutral axial ligands, with the tetradentate amidate molecules Hcapca and H2capcah of the general formulae trans-[V(IV)OX(capca)]0/+ (where X = Cl- (1.CH2Cl2), SCN- (2), N3 (3), CH3COO- (4), PhCOO- (5), imidazole (6. CH3NO2), and eta-nBuNH2 (7)) and cis-[V(VI)OX(Hcapcah)]0/+ (where X = Cl- (8.0.5CH2Cl2), SCN (9), N3 (10.2CH3OH), and imidazole (11)), were synthesized and characterized by X-ray crystallography (1.CH3OH,8.CHCl3, 9.2CH3CN, 10.CH3CN and cis-[VO(imidazole)(Hcapcah)+) and continuous-wave electron paramagnetic resonance (cw EPR) spectroscopy. In addition to the synthesis, crystallographic and EPR studies, the optical, infrared and magnetic properties (room temperature) of these compounds are reported. Ab initio calculations were also carried out on compound 8 CHCl3 and revealed that this isomer is more stable than the trans isomer, in good agreement with the experimental data. The cw EPR studies of compounds 1-5, that is, the V(IV)O2+ species containing monoanionic axial ligands, revealed a novel phenomenon of the reduction of their A, components by about 10% relative to the N4 reference compounds ([V(IV)O-(imidazole)4]2+ and [V(IV)O(2,2-bipyridine)2]2+). In marked contrast, such a reduction is not observed in compounds 6. CH3NO2-11, which contain neutral axial ligands. Based on the spin-Hamiltonian formalism a theoretical explanation is put forward according to which the observed reduction of Az is due to a reduction of the electron - nuclear dipolar coupling (P). The present findings bear strong relevance to cw EPR studies of oxovanadium(IV) in vanadoproteins, V(IV)O2+-substituted proteins, and in V(IV)O2+ model compounds, since the hyperfine coupling constant, Az, has been extensively used as a benchmark for identification of equatorial-donor-atom sets in oxovanadium(IV) complexes.     

Novel rectangular [Fe4(mu4-OHO)(mu-OH)(2)](7+) versus "butterfly" [Fe4(mu3-O2](8+) core topology in the Fe(III)/RCO2(-)/phen reaction systems (R = Me,Ph; phen = 1,10-phenanthroline): preparation and properties of [Fe4(OHO)(OH)(2)(O2CMe)(4)(phen)(4)](ClO4)(3), [Fe4O2(O2CPh)(7)(phen)(2)](ClO4), and [Fe4O2(O2CPh)(8)(phen)(2)

The preparations, X-ray structures, and detailed physical characterizations are presented for three new tetranuclear Fe(III)/RCO(2)(-)/phen complexes, where phen = 1,10-phenanthroline: [Fe(4)(OHO)(OH)(2)(O(2)CMe)(4)(phen)(4)](ClO(4))(3).4.4MeCN.H(2)O (1.4.4MeCN.H(2)O); [Fe(4)O(2)(O(2)CPh)(7)(phen)(2)](ClO(4)).2MeCN (2.2MeCN); [Fe(4)O(2)(O(2)CPh)(8)(phen)(2)].2H(2)O (3.2H(2)O). Complex 1.4.4MeCN.H(2)O crystallizes in space group P2(1)/n, with a = 18.162(9) A, b = 39.016(19) A, c = 13.054(7) A, beta = 104.29(2) degrees, Z = 4, and V = 8963.7 A(3). Complex 2.2MeCN crystallizes in space group P2(1)/n, with a = 18.532(2) A, b = 35.908(3) A, c = 11.591(1) A, beta = 96.42(1) degrees, Z = 4, and V = 7665(1) A(3). Complex 3.2H(2)O crystallizes in space group I2/a, with a = 18.79(1) A, b = 22.80(1) A, c = 20.74(1) A, beta = 113.21(2) degrees, Z = 4, and V = 8166(1) A(3). The cation of 1 contains the novel [Fe(4)(mu(4)-OHO)(mu-OH)(2)](7+) core. The core structure of 2 and 3 consists of a tetranuclear bis(mu(3)-O) cluster disposed in a "butterfly" arrangement. Magnetic susceptibility data were collected on 1-3 in the 2-300 K range. For the rectangular complex 1, fitting the data to the appropriate theoretical chi(M) vs T expression gave J(1) = -75.4 cm(-1), J(2) = -21.4 cm(-1), and g = 2.0(1), where J(1) and J(2) refer to the Fe(III)O(O(2)CMe)(2)Fe(III) and Fe(III)(OH)Fe(III) pairwise exchange interactions, respectively. The S = 0 ground state of 1 was confirmed by 2 K magnetization data. The data for 2 and 3 reveal a diamagnetic ground state with antiferromagnetic exchange interactions among the four high-spin Fe(III) ions. The exchange coupling constant J(bb) ("body-body" interaction) is indeterminate due to prevailing spin frustration, but the "wing-body" antiferromagnetic interaction (J(wb)) was evaluated to be -77.6 and -65.7 cm(-1) for 2 and 3, respectively, using the appropriate spin Hamiltonian approach. M?ssbauer spectra of 1-3 are consistent with high-spin Fe(III) ions. The data indicated asymmetry of the Fe(4) core of 1 at 80 K, which is not detected at room temperature due to thermal motion of the core. The spectra of 2 and 3 analyze as two quadrupole-split doublets which were assigned to the body and wing-tip pairs of metal ions. (1)H NMR spectra are reported for 1-3 with assignment of the main resonances.     

Comparison of small metal clusters: Ni, Pd, Pt, Cu, Ag, Au

Structures of small clusters of Ni, Pd, Pt, Cu, Ag, and Au with n=2–34 and n=55 atoms are calculated as functions of number of atoms and temperature by the simulated annealing Monte Carlo method using an embedded atom potential.     

A new dinuclear vanadium(V)-citrate complex from aqueous solutions. Synthetic,structural, spectroscopic,and pH-dependent studies in relevance to aqueous vanadium(V)-citrate speciation

Vanadium interactions with low molecular mass binders in biological fluids entail the existence of vanadium species with variable chemical and biological properties. In the course of efforts to elucidate the chemistry related to such interactions, we have explored the oxidative chemistry of vanadium(III) with the physiologically relevant tricarboxylic citric acid. Aqueous reactions involving VCl(3) and anhydrous citric acid, at pH approximately 7, resulted in blue solutions. Investigation into the nature of the species arising in those solutions revealed, through UV/visible and EPR spectroscopies, oxidation of vanadium(III) to vanadium(IV). Further addition of H(2)O(2) resulted in the oxidation of vanadium(IV) to vanadium(V), and the isolation of a new vanadium(V)-citrate complex in the form of its potassium salt. Analogous reactions with K(4)[V(2)O(2)(C(6)H(4)O(7))(2)].6H(2)O and H(2)O(2) or V(2)O(5) and citrate at pH approximately 5.5 afforded the same material. Elemental analysis pointed to the molecular formulation K(4)[V(2)O(4)(C(6)H(5)O(7))(2)].5.6H(2)O (1). Complex 1 was further characterized by FT-IR and X-ray crystallography. 1 crystallizes in the triclinic space group P(-)1, with a = 11.093(4) A, b = 9.186(3) A, c = 15.503(5) A, alpha = 78.60(1) degrees, beta = 86.16(1) degrees, gamma = 69.87(1) degrees, V = 1454.0(8) A(3), and Z = 2. The X-ray structure of 1 reveals the presence of a dinuclear vanadium(V)-citrate complex containing a V(V)(2)O(2) core. The citrate ligands are triply deprotonated, and as such they bind to vanadium(V) ions, thus generating a distorted trigonal bipyramidal geometry. Binding occurs through the central alkoxide and carboxylate groups, with the remaining two terminal carboxylates being uncoordinated. One of those carboxylates is protonated and contributes to hydrogen bond formation with the deprotonated terminal carboxylate of an adjacent molecule. Therefore, an extended network of hydrogen-bonded V(V)(2)O(2)-core-containing dimers is created in the lattice of 1. pH-dependent transformations of 1 in aqueous media suggest its involvement in a web of vanadium(V)-citrate dinuclear species, consistent with past solution speciation studies investigating biologically relevant forms of vanadium.     

Synthesis,characterization, and structural investigation of New η5-Cyclopentadienylbis-8-hydroxyquinolinatometal(IV) Complexes

By the interaction of M(η⁵-C₅H₄R)₂Cl₂ (M = Zr, Hf; R = H, Me, SiMe₃) and 8-hydroxyquinoline (oxH) or 5-chloro-8-hydroxyquinoline (ox′H) in dichloromethane solution at 20°C, the compounds M(η⁵-C₅H₄R)Clox₂ and M(η⁵-C₅H₄R)Clox₂′ were prepared respectively. A similar reaction of Ti(η⁵-C₅H₅)Cl₃ with ox′H in acetonitrile solution gave Ti(η⁵-C₅H₅)Clox₂′. All complexes were characterized by elemental microanalysis and by IR and ¹H NMR spectroscopy. X-ray analysis of M(η⁵-C₅H₅R)Clox₂′ (M = Ti, Hf) shows that these molecules may be described in terms of stereochemistry of eight-coordination approximating dodecahedral geometry more closely than octahedral geometry. With respect to octahedral coordination, the nitrogen atoms lie in a cis-configuration and the oxygen atoms in a trans-configuration. Dichloromethane molecules co-crystallize with the hafnium complex and occupy a position on the 2-fold axis. The structural results are compared with those in related compounds.