Equivalence of functional-differential equations of neutral type and abstract Cauchy problems

Equivalence of functional-differential equations of neutral type to well-posed abstract Cauchy problems in the state spaces ⁿ }L ^p ,L ^p resp.C is investigated. The assumptions allow non-atomic difference operators.This work was supported by the Fonds zur Förderung der wissenschaftlichen Forschung (Austria) under Grant No. P4534.Work done by this author was done during a stay at the University of Graz from October 1981 till April 1984.     

Low temperature Mössbauer spectra and magnetic ordering of lithiated ferric molybdate: Li2Fe2(MoO4)3

Powder x-ray diffraction, variable temperature magnetic susceptibility, and zero field Mössbauer spectroscopy measurements were used to characterize the new phase Li₂Fe₂ (MoO₄)₃. This material is obtained topochemically simply by the mixing of solutions of lithium iodide in acetonitrile with solid Fe₂(MoO₄)₃ at ambient temperature. Li₂Fe₂(MoO₄)₃ possesses the high temperature orthorhombic ferric molybdate $$\begin{gathered} Fe_2 (MoO_4 )_3 + 2LiI\xrightarrow{{CH_3 CN}}Li_2 Fe_2 (MoO_4 )_3 + I_2 \hfill \\ (solid)(solution)(solid)(solution) \hfill \\ \end{gathered}$$ structure. Guinier photographs were completely indexed in space group Pnca. Magnetic hyperfine splitting of the zero field Mössbauer spectrum below 12.5 K indicates a three-dimensional magnetically ordered state which susceptibility results show to be weakly ferromagnetic owing to probable canting of antiferromagnetically coupled sublattices.     

On the low temperature magnetic properties of some sulfites of divalent iron

Zero field Mössbauer spectra and powder susceptibility measurements show that the condensed, hydrogen bonded network compound FeSO₃ 3H₂O orders antiferromagnetically (T_Néel 9.5 K). The related anhydrous material FeSO₃ also shows antiferromagnetic exchange but no evidence of long range three-dimenstional magnetic order to as low as 1.4 K.Supported by the U.S. National Science Foundation Division of Materials Research—Solid State Chemistry Program Grant No. DMR 8313710.     

Pore Structure Analysis of Porous Particles by Equivalent Model

Starting from Wheeler's composite theory, which takes both the multilayer adsorption and the capillary condensation into consideration, and assuming the equivalent cylindrical model, we have deduced a strict and relatively simpler formula for the calculation of pore size distribution by solving the integral equation directly. The formula is more convenient for application because of its recursion form. Following the same line of reasoning and using the mean value theorem of definite integrals under different conditions, we have unified the equations of Barrett-Joyner-Halenda, Dubinin, Cranston-Inkley, Dollimore-Heal and Roberts. A table of parameters which is required in the calculation is given. Besides the adsorption of nitrogen, the adsorption with water vapor as the adsorbate is investigated and the corresponding empirical equation of adsorption thickness is given.     

Synthesis, band structure, and optical properties of Ba2ZnV2O8

A novel compound Ba₂ZnV₂O₈ has been synthesized in high temperature solution reaction and its crystal structure has been characterized by means of single crystal X-ray diffraction analysis. It crystallizes in monoclinic system and belongs to space group P2₁/c with a=7.9050(16), b=16.149(3), , β=90.49(3). It builds up from 1-D branchy chains of [ZnV₂O₈⁴⁻]_∞, and the Ba²⁺ cations are located in the space among these chains. The IR spectrum, ultraviolet-visible diffuse reflection integral spectrum and fluorescent spectra of this compound have been investigated. The calculated results of energy band structure by the density functional theory method show that the solid-state compound of Ba₂ZnV₂O₈ is an insulator with direct band gap of 3.48 eV. The calculated total and partial density of states indicate that the top valence bands are contributions from the mixings of O-2p, V-3d, and Zn-3d states and low conduction bands mostly originate from unoccupied antibonding states between the V-3d and O-2p states. The V-O bonds are mostly covalence characters and Zn-O bonds are mostly ionic interactions, and the ionic interaction strength is stronger between the Ba-O than between the Zn-O. The refractive index of n_x, n_y, and n_z is estimated to be 1.7453, 1.7469, and 1.7126, respectively, at wavelength of 1060 nm for Ba₂ZnV₂O₈ crystal.     

Further explorations on bridged 1,2,4-trioxanes

Three new bicyclo[3.2.1]-type 1,2,4-trioxanes have been designed and synthesized. One of them demonstrates better tolerance of the intramolecular hemiketals to steric crowding in hydroperoxidation. The other represents a prototype for possible manipulation of the transient radicals generated in cleavage reactions. A new substitution pattern in the bridged system is explored through synthesis of the third molecule. The configurations of all stereogenic centers in the bridged system can be effectively controlled by the chirality of the allyl alcohol as illustrated by the enantioselective synthesis of the fourth molecule. Finally, similar bicyclo[3.3.1]-type 1,2,4-trioxanes are shown very difficult to be synthesized because of the involvement of a conformer with two substituents at axial positions at the same time.