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.     

Justification of the Shallow-Water Limit for a Rigid-Lid Flow with Bottom Topography

The so-called lake equations arise as the shallow-water limit of the rigid-lid equations—three-dimensional Euler equations with a rigid-lid upper boundary condition—in a horizontally periodic basin with bottom topography. We prove an a priori estimate in the Sobolev space H ^m for m≥ 3 which shows that a solution to the rigid-lid equations can be approximated by a solution of the lake equations for an interval of time which can be estimated in terms of the initial deviation from a columnar configuration and the magnitude of the initial data in H ^m , the gradient of the bottom topography in H ^m+1 , and the aspect ratio of the basin. In particular, any solution to the lake equations remains close to some solution of the rigid-lid equations for an interval of time that can be made arbitrarily large by choosing the aspect ratio of the basin small. Received 10 October 1996 and accepted 15 May 1997     

Consecutive reactions of diethoxydimethylsilane and triethoxymethylsilane with methoxide ions in methanol solution

The consecutive reactions of (CH₃)₂Si(OC₂H₅)₂ and CH₃Si(OC₂H₅)₃ with methoxide ions were investigated in methanol solutions. The reverse transesterification reactions with ethoxide ions could be neglected in both cases since the concentration of ethoxide in methanol solution was assumed to be low due to the fast equilibrium reaction C₂H₅O^? + CH₃OH ? C₂H₅OH + CH₃O^?. The progress of the reactions was followed by monitoring the formation of ethanol with a Fourier-transform infrared spectrometer. All rate constants were determined at 295 K. The reactions between the dialkoxydimethylsilanes and methoxide ions were assumed to consist of two consecutive steps that can be represented by the net reaction; (CH₃)₂Si(OC₂H₅)₂ + 2CH₃O^? → (CH₃)₂Si(OCH₃)₂ + 2C₂H₅O^?. The two consecutive rate constants were established as 1.93 ± 0.12M^?1s^?1 and 1.00 ± 0.12M^?1s^?1, respectively. The consecutive rate constants for the reactions between the trialkoxymethylsilanes and methoxide ions can be written according to the total reaction; CH₃Si(OC₂H₅)₃ + 3CH₃O^? → CH₃Si(OCH₃)₃ + 3C₂H₅O^?. The three rate constants corresponding to each consecutive step were established as 1.12 ± 0.09 M^?1s^?1, 0.82 ± 0.10 M^?1s^?1, and 0.51 ± 0.06 M^?1s^?1, respectively. © 1995 John Wiley & Sons, Inc.