VECTOR FIELDS IN R2 WITH MAXIMAL INDEX

We consider the method of Poincaré to investigate thelocal index of vector fields in the plane. If m is the degreeof the first non-zero jet, X_m, of the vector field X at an isolatedzero, we explore the geometry of the pencil generated by thecoordinate functions of X_m when the absolute value of the indexof X, |ind (X)|, is m. We also find necessary and sufficientconditions for |ind (X)| to be m.     

Equilibrium distributions of stochastic networks without detailed balance

We present results for the determination of the equilibrium microstate probability distribution of a class of strongly interacting systems obeying stochastic dynamics but without the necessity of detailed balance. The specific case of Ising systems is highlighted, with applications to non-symmetric synaptic neural networks and more general recurrent Boolean networks.     

Substitution of calcium by strontium within selected calcium phosphates

Sr incorporation in the molecules of amorphous calcium phosphate, apatitic tricalcium phosphate, hydroxyapatite, octacalcium phosphate and dicalcium phosphate dihydrate was investigated. The concentration of Sr ranged from 225 to 1010 μ g / g, i.e. it overlapped with the physiological range of Sr concentrations in human bone. The leading experimental technique was extended X-ray absorption fine structure (EXAFS) at the Sr K edge. Results of these studies demonstrated the following: (1) Sr incorporation in the calcium phosphates is compound-dependent, (2) the coordination of incorporated Sr atoms in the Ca-P molecules is similar to that of Ca atoms, but interatomic distances are ≈0.015 nm larger, (3) in apatitic tricalcium phosphate, hydroxyapatite and octacalcium phosphate lattices Sr atoms may occupy selected Ca sites, which was not the case for dicalcium phosphate dihydrate, (4) in the apatite lattice Sr atoms are coordinated by 6 PO₄ tetrahedrals and (5) EXAFS spectra at the K edge of the incorporated Sr may be used to distinguish the structures of amorphous calcium phosphate, dicalcium phosphate dihydrate as well as apatite and its derivatives (apatitic tricalcium phosphate, octacalcium phosphate).     

A note on dephasing and pair-breaking

It is shown that the dephasing which suppresses the weak localization correction to the conductivity has the same physical origin than pair-breaking in superconductors and thus-following de Gennes-may be expressed in terms of the correlation function of the operator for time reversal.     

Unoccupied electronic states of epitaxial iron layers on Cu(100)

Inverse photoemission spectra were taken for thin epitaxial iron films on Cu(100). For a film thickness of eight monolayers the observed electronic states are characteristic for a fcc(100) surface. Thed-bands of iron show a ferromagnetic exchange splitting of 1.1 eV, considerably smaller than the bulk value of 1.8 eV, which we observe for film thicknesses above 18 monolayers.     

Flow and reactive transport in porous media induced by well injection: Similarity solution

The authors study concentration profiles of solutes undergoingequilibrium absorption in the vicinity of a water well. Forthe case of a contamination event, the limit problem of vanishingwell radius, which is of self-similar nature, is analysed indetail. Existence, uniqueness, and qualitative properties ofsolutions of the corresponding ordinary differential equationsare shown. Some numerical examples are also presented.     

Adaptation of an echelle spectrograph to a large CCD detector

A broad range echelle spectrograph with a CCD matrix detector is developed for different applications in atomic spectroscopy. The compact optical design in combination with a dispersive entrance slit illumination offers a low stray light level and high throughput in the UV spectral region comparable only with spectrographs of higher focal length. Ray tracing calculations for typical wavelengths and the multi-line spectrum of an iron arc show the excellent overall spectrum quality. The subtraction of two partial spectra of different steel alloys demonstrates the spectra evaluation possibilities of the CCD spectrograph.     

Matrix effects in the determination of butyltin compounds in environmental samples by GC AA after hydride generation

Experiments for the determination of mono-, di and tri-butyltin (MBT, DBT and TBT) by hydride generation/gas chromatography/atomic absorption spectrometry in various matrices (sediment, suspended matter, mussel, algae and water) have revealed that poor butyltin recoveries are obtained in sediments displaying high sulphur and hydrocarbon contents; very poor recoveries were also observed for TBT in sediments with high chlorophyll pigment contents as well as in algal samples. It was however not clear whether the hydride generatin was inhibited by these infering compounds, as was previously assumed in the case of hydrocarbons, or whether interferences affected the atomization rate. Further studies were performed to solve this problem in order to validate this method in the case of analyses of, for example, oil-contaminated sediment and algae. This paper presents the results obtained. It is concluded here that the poor recoveries were due to an inhibition of hydride generation rather than to interference at the atomization stage.     

Positive solutions and dynamics of a finite difference reaction–diffusion system

We investigate the dynamics and methods of computation for some nonlinear finite difference systems that are the discretized equations of a time-dependent and a steady-state reaction–diffusion problem. The formulation of the discrete equations for the time-dependent problem is based on the implicit method for parabolic equations, and the computational algorithm is based on the method of monotone iterations using upper and lower solutions as the initial iterations. The monotone iterative method yields improved upper and lower bounds of the solution in each iteration, and the sequence of iterations converges monotonically to a solution for both the time-dependent and the steady-state problems. An important consequence of this method is that it leads to a bifurcation point that determines the dynamic behavior of the time-dependent problem in relation to the corresponding steady-state problem. This bifurcation point also determines whether the steady-state problem has one or two non-negative solutions, and is explicitly given in terms of the physical parameters of the system and the type of boundary conditions. Numerical results are presented for both the time-dependent and the steady-state problems under various boundary conditions, including a test problem with known analytical solution. These numerical results exhibit the predicted dynamic behavior of the time-dependent solution given by the theoretical analysis. Also discussed are the numerical stability of the computational algorithm and the convergence of the finite difference solution to the corresponding continuous solution of the reaction–diffusion problem. © 1993 John Wiley & Sons, Inc.