Numerical solution of the three‐dimensional parabolic equation with an integral condition

Developement of numerical methods for obtaining approximate solutions to the three dimensional diffusion equation with an integral condition will be carried out. The numerical techniques discussed are based on the fully explicit (1,7) finite difference technique and the fully implicit (7,1) finite difference method and the (7,7) Crank‐Nicolson type finite difference formula. The new developed methods are tested on a problem. Truncation error analysis and numerical examples are used to illustrate the accuracy of the new algorithms. The results of numerical testing show that the numerical methods based on the finite difference techniques discussed in the present article produce good results. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 193–202, 2002; DOI 10.1002/num.1040     

Structural hierarchy of rock masses and the mechanisms of its formation

The formation mechanisms for the structural hierarchy in geological media are discussed. It is shown that the formation of such a hierarchy is caused by certain external and internal circumstances. The first ones consist in the fact that, because of external actions, the Earth’s poles continuously execute the translational and rotational motions responsible for a regular structure of rock fracture and for the appearance of the scale factor √2. The second ones consist in the fact that, under the action of many random factors and because of external actions, during the formation of geological media there appear dissipative structures and, hence, some self-similar fractal structures are formed.     

Reply to Nathan: How to reconstruct the causal argument

Nicholas Nathan tries to resist the current version of the causal argument for sense-data in two ways. First he suggests that, on what he considers to be the correct re-construction of the argument, it equivocates on the sense of proximate cause. Second he defends a form of disjunctivism, by claiming that there might be an extra mechanism involved in producing veridical hallucination, that is not present in perception. I argue that Nathan’s reconstruction of the argument is not the appropriate one, and that, properly interpreted, the argument does not equivocate on proximate cause. Furthermore, I claim that his postulation of a modified mechanism for hallucinations is implausibly ad hoc.     

Tetrakis(4-N,N-dimethylaminobenzene)porphyrinato]manganese(III) acetate as a novel carrier for a selective iodide PVC membrane electrode.

[5,10,15,20-Tetrakis(4-N,N-dimethylaminobenzene)porphyrinato]Mn(III) acetate (MnTDPAc) was applied as an ionophore for an iodide-selective PVC membrane electrode. The influences of the membrane composition, pH of the test solution and foreign ions on the electrode performance were investigated. The sensor exhibited not only excellent selectivity to iodide ion compared to Cl- and lipophilic anions such as ClO4- and salicylate, but also a Nernstian response with a slope of -59.4 +/- 1.2 mV per decade for iodide ions over a wide concentration range from 1.0 x 10(-2) to 7.5 x 10(-6) M at 25 degrees C. The potentiometric response was independent of the pH of the solution in the pH range of 2 - 8. The electrode could be used for at least 2 months without any considerable divergence in the potential. Good selectivity for iodide ion, a very short response time, simple preparation and relatively long-term stability were the silent characteristics of this electrode. It was successfully used as an indicator electrode in the potentiometric titration of iodide ions, and also in the determination of iodide from seawater samples and drug formulations.