Zero-divisor graphs, von Neumann regular rings, and Boolean algebras

For a commutative ring R with set of zero-divisors Z(R), the zero-divisor graph of R is Γ(R)=Z(R)−{0}, with distinct vertices x and y adjacent if and only if xy=0. In this paper, we show that Γ(T(R)) and Γ(R) are isomorphic as graphs, where T(R) is the total quotient ring of R, and that Γ(R) is uniquely complemented if and only if either T(R) is von Neumann regular or Γ(R) is a star graph. We also investigate which cardinal numbers can arise as orders of equivalence classes (related to annihilator conditions) in a von Neumann regular ring.     

A Mossbauer study of the magnetic coupling in iron phosphorous trisulfides

The polycrystalline sample of layered compound FePS_3 has been investigated by using M?ssbauer spectroscopy (12K to 300K), magnetic susceptibility measurements, x-ray diffraction and FTIR spectroscopy. The antiferromagnetic order exists below T_N=120.5±1K. The M?ssbauer spectra below T_N indicate that the magnetization axis is perpendicular to the layer of FePS_3, and the divalent iron cations are in their high spin configurations. By fitting the hyperfine field parameters near the Néel temperature, we obtain information on the nature of magnetic interactions in the material. The results show that the magnetic coupling can be treated by the two-dimensional Ising model, and it can be interpreted on the basis of a crystal-field effect.     

Approximation of a laminated microstructure for a rotationally invariant,double well energy density

Summary. We give error estimates for the approximation of a laminated microstructure which minimizes the energy for a rotationally invariant, double well energy density . We present error estimates for the convergence of the deformation in the convergence of directional derivatives of the deformation in the “twin planes,” the weak convergence of the deformation gradient, the convergence of the microstructure (or Young measure) of the deformation gradients, and the convergence of nonlinear integrals of the deformation gradient. Received July 25, 1995 / Revised version received November 20, 1995     

Discontinuous Galerkin method with a posterioriL_p(0,t_i) error estimate for second-kind Volterra problems

Summary. We consider a discontinuous Galerkin finite element method applied in time to a model Volterra equation of the second kind. A residual-based computable Galerkin-error estimate is derived for . This estimate does not explicitly contain the time step and therefore the time step control must be based on a heuristic criterion, the estimate can then be used to demonstrate the integrity, or otherwise, of the finite element solution. After performing some numerical experiments we conclude that this approach is at least competetive with classical discretizations since it is computationally simple to implement, but has the added advantage of reliable error feedback. Received June 25, 1995     

Third order nonoscillatory central scheme for hyperbolic conservation laws

Summary. A third-order accurate Godunov-type scheme for the approximate solution of hyperbolic systems of conservation laws is presented. Its two main ingredients include: 1. A non-oscillatory piecewise-quadratic reconstruction of pointvalues from their given cell averages; and 2. A central differencing based on staggered evolution of the reconstructed cell averages. This results in a third-order central scheme, an extension along the lines of the second-order central scheme of Nessyahu and Tadmor \cite{NT}. The scalar scheme is non-oscillatory (and hence – convergent), in the sense that it does not increase the number of initial extrema (– as does the exact entropy solution operator). Extension to systems is carried out by componentwise application of the scalar framework. In particular, we have the advantage that, unlike upwind schemes, no (approximate) Riemann solvers, field-by-field characteristic decompositions, etc., are required. Numerical experiments confirm the high-resolution content of the proposed scheme. Thus, a considerable amount of simplicity and robustness is gained while retaining the expected third-order resolution. Received April 10, 1996 / Revised version received January 20, 1997     

Mössbauer study on LiFePO4 cathode material for lithium ion batteries

Crystalline LiFePO₄ has been synthesized using solid-state, spray pyrolysis, and wet chemical methods. The crystal parameters were obtained from Rietveld’s refinement methods of the X-ray diffraction patterns. A detailed investigation of the Fe valency carried out using Mössbauer spectroscopy at room temperature indicates that Fe is predominantly present in its bivalent state.     

FULL DISCRETE NONLINEAR GALERKIN METHOD FOR THE NAVIER-STOKES EQUATIONS

This paper deals with the inertial manifold and the approximate inertial manifold concepts of the Navier-Stokes equations with nonhomogeneous boundary conditions and inertial algorithm. Furtheremore, we provide the error estimates of the approximate solutions of the Navier-Stokes Equations.     

Mechanosynthesis of YIG and GdIG: A Structural and Mössbauer Study

We have investigated the mechanosynthesis of gadolinium and yttrium iron garnets by high-energy ball-milling of α-Fe₂O₃ and Gd₂O₃ or α-Fe₂O₃ and Y₂O₃, respectively, followed by short thermal annealings conducted at moderate temperatures. The samples were characterized by X-ray diffraction and Mössbauer spectroscopy, in order to determine the influence of the milling time and annealing conditions on the final products. For as-milled samples of each rare-earth system, the results revealed the formation of perovskite phases, in relative amounts that depend on the milling time. The formation of garnet phases was observed in as-annealed samples treated at 1000°C for 2 h or 1100°C for 3 h, i.e., at very modest annealing requirements when compared with ordinary solid-state-reaction processes performed without previous high-energy milling. Also, the occurrence was verified of a milling time for which the relative amount of garnet phases formed by annealing was maximized. This time depends on the rare-earth composing the garnet phase and on the annealing temperature.     

Mössbauer study of nanodimensional nickel ferrite – mechanochemical synthesis and catalytic properties

Iron–nickel spinel oxide NiFe₂O₄ nanoparticles have been prepared by the combination of chemical precipitation and subsequent mechanical milling. For comparison, their analogue obtained by thermal synthesis is also studied. Phase composition and structural properties of iron–nickel oxides are investigated by X-ray diffraction and Mössbauer spectroscopy. Their catalytic behavior in methanol decomposition to CO and methane is tested. An influence of the preparation method on the reduction and catalytic properties of iron–nickel samples is established.