General stability condition

While inequality 35 is the evolution criterion for systems near equilibrium, the reverse inequality, together with Equation 37, can be regarded as a generalized stability condition ... 

The p-stability condition. A more general definition of stability with respect to the initial data became rather urgent and extremely important. 

Stability and convergence. The general stability theory for two-layer schemes applies equally well to the stability analysis of the weighted scheme (7). With this aim, the appropriate difference scheme with the homogeneous boundary conditions comes first ... 

The general stability theory outlined in Chapter 6 asserts that scheme (20) is stable under the condition... 

Along these lines, it is worth noting that we are still in the framework of the general stability theory outlined in Chapter 6, Section 2 for difference schemes like (22) asserting that a necessary and sufficient condition for the estimate < pWllkWo valid for any 0 < / < 1 and any operator... 

The book includes many good examples illustrating the practical use of general stability theory with regard to particular schemes to assist the users in subsequent implementations. Stability is probably the most pressing problem in any algorithm, since it is a necessary rather than a sufficient condition for accuracy. 

Quite diverse reaction conditions have been used for the final step in the synthesis of different heterophanes, demonstrating the general stability of the multicyclic systems. Heterophanes do undergo reactions, some that are typical of the structural fragments and some that are probably more characteristic of the phane structure itself or the strain associated with it. Some reactions of heterophanes are included in Section 5.22.2. 

In accordance with the general stability of alkylthio groups in heteroaromatic systems, 3-alkylthio groups in 1,2,4-thiadiazoles are not easily replaced.Thus, 3-alkylthio-1,2,4-thiadiazoles resist theaction of aniline at 100°, ammonia at 120°, or molten urea or ammonium acetate.99 On the other hand, hydrazine attacks 3-methylthio-l,2,4-thiadiazole under restrained conditions, with formation of 3-amino-... 

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