The direct product permuting matrices

A new matrix product is defined and its properties are investigated. The commutatuion matrix which flips a left direct product of two matrices into a right direct one is derived as a composition of two identity matrices. The communication matrix is a special case of the direct product permuting matrices defined in this paper which are matrix representations of the permutation operators on tensor spaces i e. the linear mappings which permute the order of the vectors in a direct product of them. Explicit expressions for these matrices are given. properties of the matrices are investigated and it is shown how these matrices, act on various representations of tensor spaces.     

Lorenz-Mie Theory for Spheres Immersed in an absorbing host medium

Light scattering by particles is often used to determine velocities or concentrations of particles in gaseous or liquid streams. Within the Lorenz-Mie theory, light scattering is well understood both for a single compact spherical particle and a single multilayered particle in a non-absorbing surrounding medium. However, in some cases of practical importance the Lorenz-Mie theory in its present form may fail to describe the scattering because the host medium is absorbing (e.g. water droplets in oil). In this case, a new treatment of the scattering theory is required. In previous work, solutions were obtained in the far-field of the scattering sphere. In this paper, a rigorous solution is derived from the calculation of the total absorption rate of the particle in the host medium, which is valid for all distances from the surface of the encapsulated particle. It is shown that it is necessary to consider finite sizes R of the integrating sphere when dealing with absorbing host media. Cross-sections are defined which are characteristic quantities not only for the particle, depending on the size of a conceptual sphere around the scatterer and the imaginary part of the refractive index of the host medium. The results obtained are discussed for the case of non-absorbing host media and in the far-field approximation. Some numerical examples are given which are also related to experimental results.     

Towards a more general notion of Gelfand-Kirillov dimension

Gelfand-Kirillov dimension (GK) has proved to be a useful invariant for algebras over fields. In this paper we generalize the notion of GK to algebras over commutative Noetherian rings by replacing vector space dimension with reduced rank. It turns out that most results about GK have analogues for the new GK.     

Velocity distribution in horizontal slug flow

An experimental device for measurement of the velocity distribution in a two-phase slug is developed. Velocity profiles both in the film and the liquid slug besides velocity variation along the pipe bottom (at a distance of 1 mm) through the slug front are presented.     

Advances in photolithographically fabricated ENFET membranes

A photolithographically fabricated membrane for enzyme immobilisation based on an Ion Sensitive Field Effect Transistor (ISFET) is described. The preparation of an Enzyme-FET (ENFET) containing urease was successful. The ENFET has been used for the determination of urea and pesticides; this depends on the chosen enzyme level in the membrane and can be employed in a flow-injection system. The urea sensitive sensor (high enzyme load) has a wide linear range (1–500 mmol/l) a fast response (t₉₅=20 s) and a lifetime greater than 30 days. The application of this sensor to the determination of urea in the waste water from a fertilizer plant and in blood serum is discussed. The second sensor (low enzyme level) was able to detect pesticides in water based on the inhibition of urease. The detection limit was found to be 0.1 µg/l for Carbofuran (10 minutes incubation time, without preconcentration).     

Ising models with two- and three-spin interactions: Mean field equation of state

The Ising model with pair and triplet interactions on the triangular lattice is solved in the mean-field approximation. With a sufficiently strong triplet interaction two first-order transitions take place at low temperature, and at intermediate temperatures one transition, terminating in a critical point. For J₂ > 0.75J₃ only the latter transition remains.     

Determination of the enantiomers of indoprofen in blood plasma by high-performance liquid chromatography after rapid derivatization by means of ethyl chloroformate

A rapid method for the determination of (+)- and (-)-indoprofen in blood plasma has been developed and applied to pharmacokinetic work. By means of ethyl chloroformate, indoprofen is coupled to leucinamide, a reaction which is complete in less than 3 min at room temperature. The diastereoisomeric derivatives are then separated by reversed-phase high-performance liquid chromatography. In two surgical patients given racemic indoprofen intravenously, the pharmacologically active (+)-enantiomer had a lower clearance and a lower distribution volume than the (-)-enantiomer, which gave it a slightly longer half-life.     

Correlation of gas solubilities in water and methanol at high pressure

A random—nonrandom—mixture equation for the Helmholtz energy of a fluid mixture is shown to correlate the solubility of inert and acidic gases in water and methanol quite accurately at pressures up to 300 bar. Further, the calculated Henry's law constants of the gases in water show good agreement with experimental data.The gas solubility models is a modification of our previous model. It contains three binary interaction parameters, one in the reduced density term and two in the attractive terms. When the nonrandom parameter vanishes the model reduces to the classical mixing rule. The model correlates vapour—liquid equilibria in binary and ternary hydrocarbon—methanol systems quite accurately.The results of the correlation are compared with results obtained using the classical van der Waals quadratic mixing rule. The random—nonrandom model is, in all cases, superior to the van der Waals model. Finally, a comparison of computer time consumption for the two models is given.     

Potentiometric studies on the formation of metal complexes with trans-1,2- diaminocyclohexane-N,N,N',N'-tetra-acetic acid--I: protonation of the ligand

The protonation of trans-1,2-diaminocyclohexane-N,N, N',N'-tetraacetic acid is studied potentiometrically with the hydrogen electrode. The formation constants have been re-evaluated at 25.0 degrees at an ionic strength of 3.0 (NaClO(4)), with a least-squares treatment of the data. The potentiometric data are explained from the law of mass action, using a model which assumes five different ligands to be present in the solution; the logarithmic stepwise stability constants are then 9.90, 6.72, 3.65 and 3.21 for the mono-, di-, tri- and tetra-protonated ligand respectively.