Dimensional stability formalization

Minato, K., Yasuda, R. and Yano, H. (1990a). Improvement of dimensional stability and acoustic properties of wood for musical instruments with cychc oxymethylenes. I. Formalization with trioxane. Mokuzai Gakkaishi, 36(10), 860-866. 

In essence, Eqns. (2.3.20) and (2.3.23) are identical - expressed for different parameters, where the parameters are related via Eqn. (2.3.22). The mean flow U is real and unchanged and if a and (3 are real, then a three-dimensional stability problem at a Reynolds number Re has been reduced to a two-dimensional problem at the lower Reynolds number Re. This is known as the Squire s theorem, and formally stated as ... 

Wood has been treated with trioxane (cyclic trimer of FA) (31) and tetraox-ane (cyclic tetramer of FA) (32) in the presence of SO2. The S02-catalyzed formalization with tetraoxane was the most effective among the various formalization methods for improvement of dimensional stability and retention of strength (32). 

Formfestigkeit/ Formanderungsfestigkeit dimensional stability resistance to deformation Formbestandigkeitstemperatur/ Formbestandigkeit in der Warme heat distortion temperature (HDT) Formal formula... 

The pyramidal silicon capped cation 63a is a potential three-dimensional 6 r-electron aromatic system763, where the formal coordination number of the silicon is live (as in 59). The interest in 63a results from the detection of a C5SiH5+ fragment in the gas phase76 5. The crucial question is the stability of the pyramidal ion 63a relative to other possible C5SiH5+ isomers, such as 64a and 65a. A comparison with the analogous CgH5+ isomers is of interest. 

Earlier, a similar instanton analysis for a PES with two transition states was performed by Ivlev and Ovchinnikov [1987], in connection with tunneling in Josephson junctions. In the language of stability parameters introduced in Section 4.1, the appearance of two-dimensional tunneling paths is signaled by vanishing of the stability parameter. As follows from (4.24), the one-dimensional tunneling path formally becomes infinitely... 

Linear Stability Analysis. Patterns can be studied in the integral operator formalism. Here we demonstrate a stability analysis on an infinite two dimensional tissue. Under homogeneous culture conditions the system has a uniform steady state ch, Vh given by... 

The theory of adsorption equilibrium on homogeneous surfaces is so formalized as to be considered a set of statistico-mechanical exercises [15]. When the adsorbed molecules can be considered as structureless particles, practically all models consider the adsorbed phase as a sequence of layers, each stabilized by the adsorption field generated by the underlying one and described either as a two-dimensional (2D) lattice or as a 2D van der Waals gas. 

Mathematical formalism has been developed using semi-empirical considerations [36, 37]. Computer simulation smdies show that resulting equation predicts oscillations. Attempt has been made to provide justification on the bases of Navier-Stokes equation but it is open to question. Dimensional analysis has recently been employed for investigating the phenomena [31]. Flow dynamics and stability in a density oscillator have been examined by Steinbock and co-workers [38], They have related it to Rayleigh-Taylor instability of two different dense viscous liquids. A theoretical description has been presented which is based on a one-fluid model and a steady state approximation for a two-dimensional flow using Navier-Stokes equation. However, the treatment is quite complex and cannot explain the generation of electric potential oscillations. 

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