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.     

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.     

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.     

Monomeric oxovanadium(IV) compounds of the general formula cis-[V(IV)(=O)(X)(L(NN))(2)](+/0) [X = OH(-), Cl(-), SO(4)(2)(-) and L(NN) = 2,2'-bipyridine (bipy) or 4,4'-disubstituted bipy

Reaction of [V(IV)OCl(2)(THF)(2)] in aqueous solution with 2 equiv of AgBF(4) or AgSbF(6) and then with 2 equiv of 2,2'-bipyridine (bipy), 4,4'-di-tert-butyl-2,2'-bipyridine (4,4'-dtbipy), or 4,4'-di-methyl-2,2'-bipyridine (4,4'-dmbipy) affords compounds of the general formula cis-[V(IV)O(OH)(L(NN))(2)]Y [where L(NN) = bipy, Y = BF(4)(-) (1), L(NN) = 4,4'-dtbipy, Y = BF(4)(-) (2.1.2H(2)O), L(NN) = 4,4'-dmbipy, Y = BF(4)(-) (3.2H(2)O), and L(NN) = 4,4'-dtbipy, Y = SbF(6)(-) (4)]. Sequential addition of 1 equiv of Ba(ClO(4))(2) and then of 2 equiv of bipy to an aqueous solution containing 1 equiv of V(IV)OSO(4).5H(2)O yields cis-[V(IV)O(OH)(bipy)(2)]ClO(4) (5). The monomeric compounds 1-5 contain the cis-[V(IV)O(OH)](+) structural unit. Reaction of 1 equiv of V(IV)OSO(4).5H(2)O in water and of 1 equiv of [V(IV)OCl(2)(THF)(2)] in ethanol with 2 equiv of bipy gives the compounds cis-[V(IV)O(OSO(3))(bipy)(2)].CH(3)OH.1.5H(2)O (6.CH(3)OH.1.5H(2)O) and cis-[V(IV)OCl(bipy)(2)]Cl (7), respectively, while reaction of 1 equiv of [V(IV)OCl(2)(THF)(2)] in CH(2)Cl(2) with 2 equiv of 4,4'-dtbipy gives the compound cis-[V(IV)OCl(4,4'-dtbipy)(2)]Cl.0.5CH(2)Cl(2) (8.0.5CH(2)Cl(2)). Compounds cis-[V(IV)O(BF(4))(4,4'-dtbipy)(2)]BF(4) (9), cis-[V(IV)O(BF(4))(4,4'-dmbipy)(2)]BF(4) (10), and cis-[V(IV)O(SbF(6))(4,4'-dtbipy)(2)]SbF(6) (11) were synthesized by sequential addition of 2 equiv of 4,4'-dtbipy or 4,4'-dmbipy and 2 equiv of AgBF(4) or AgSbF(6) to a dichloromethane solution containing 1 equiv of [V(IV)OCl(2)(THF)(2)]. The crystal structures of 2.1.2H(2)O, 6.CH(3)OH.1.5H(2)O, and 8.0.5CH(2)Cl(2) were demonstrated by X-ray diffraction analysis. Crystal data are as follows: Compound 2.1.2H(2)O crystallizes in the orthorhombic space group Pbca with (at 298 K) a = 21.62(1) A, b = 13.33(1) A, c = 27.25(2) A, V = 7851(2) A(3), Z = 8. Compound 6.CH(3)OH.1.5H(2)O crystallizes in the monoclinic space group P2(1)/a with (at 298 K) a = 12.581(4) A, b = 14.204(5) A, c = 14.613(6) A, beta = 114.88(1) degrees, V = 2369(1), Z = 4. Compound 8.0.5CH(2)Cl(2) crystallizes in the orthorhombic space group Pca2(1) with (at 298 K) a = 23.072(2) A, b = 24.176(2) A, c = 13.676(1) A, V = 7628(2) A(3), Z = 8 with two crystallographically independent molecules per asymmetric unit. In addition to the synthesis and crystallographic studies, we report the optical, infrared, magnetic, conductivity, and CW EPR properties of these oxovanadium(IV) compounds as well as theoretical studies on [V(IV)O(bipy)(2)](2+) and [V(IV)OX(bipy)(2)](+/0) species (X = OH(-), SO(4)(2)(-), Cl(-)).     

Coordination complexes of l-azetidine-2-carboxylic acid with platinum(II) and palladium(II)

Summary The complexes K[Pt(l-aze)Cl₂, [Pt(l-aze)₂] and [Pd(l-aze)₂] (l-aze = l-azetidine-2-carboxylate) were prepared. X-ray structures show that [Pt(l-aze)₂] and [Pd(l-aze)₂] are isomorphous, having a planar tetragonal geometry with a trans configuration around the Pt and Pd atoms. Slight puckerings of the MN(1)N(11)O(11) chelate ring (M = Pt or Pd) and the azetidine ring were observed. The circular dichroism (c.d.) spectra of the complexes in aqueous solution agree with the structures found in the solid state as far as the hexadecant rule is concerned, giving, for the trans configuration of [M(l-ia)₂] (where ia = imino acid), the profile of the c.d. signs for the three predominant d-d transitions as: +,-,-. I.r., conductivity and n.m.r. measurements are also reported and are in accord with the proposed structures.     

Synthesis of a Novel Chitosan/Basil Oil Blend and Development of Novel Low Density Poly Ethylene/Chitosan/Basil Oil Active Packaging Films Following a Melt-Extrusion Process for Enhancing Chicken Breast Fillets Shelf-Life

An innovative process for the adsorption of the hydrophobic Basil-Oil (BO) into the hydrophilic food byproduct chitosan (CS) and the development of an advanced low-density polyethylene/chitosan/basil-oil (LDPE/CS_BO) active packaging film was investigated in this work. The idea of this study was the use of the BO as both a bioactive agent and a compatibilizer. The CS was modified to a CS_BO hydrophobic blend via a green evaporation/adsorption process. This blend was incorporated directly in the LDPE to produce films with advanced properties. All the obtained composite films exhibited improved packaging properties. The film with 10% CS_BO content exhibited the best packaging properties, i.e., 33.0% higher tensile stress, 31.0% higher water barrier, 54.3% higher oxygen barrier, and 12.3% higher antioxidant activity values compared to the corresponding values of the LDPE films. The lipid oxidation values of chicken breast fillets which were packaged under vacuum using this film were measured after seven and after fourteen days of storage. These values were found to be lower by around 41% and 45%, respectively, compared with the corresponding lipid oxidation values of pure LDPE film.