P stable

Scheme (4) is said to be p-stable with respect to the initial data if estimate (5) is valid. An estimate of the form (3) is admissible for the solution of problem (4) when p < 1. 

Stabiiity Very stable, even at the m.p. Stable in aqueous alkali... 

From Figure 7 it is deduced that the number of the equilibrium states depends on the number of points where the straight line yo = constant intersects with the curve defined by Eq.(13). With a value of yo 0.025, there are three equilibrium points Pi, P2, P3, being P stable, P2 unstable and P3 can be stable or unstable depending on the real part of the eigenvalues of the linearized system at this point. When the line yo = constant is tangent to the curve yo = fiy ) (be. point M) a new behavior of the reactor appears, which can be characterized from dyo/dy = 0 in Eq.(13) as follows ... 

Remark 2 If A = A, B = B > 0 and conditions (36) are satisfied, then scheme (1) is p-stable in the space Hg with respect to the initial data, that is, a solution of problem (la) satisfies the inequality... 

Fig. 4.11 Two-dimensional lattices (a) stable, six-coordinate, closest packed lattice of uncharged atoms (b) unstable, six-coordinate lattice of charged ions (p) stable, four-coordinate lattice of charged ions.

The arguments just presented suggest that all n-type semiconductor photoanodes which resist corrosion under conditions of H2O to O2 oxidation must have (a) stable elemental component(s) at low pH. Moreover, since the oxide dissolution reaction is associated with essentially the same H+/0= interactions, the low pH stability limit will be at approximately the same value (P stable 3). 

If xecw(x), the x-motion is called P+-stable (positively Poisson-stable). 

If the x-motion is whole, not P+ -stable [x ca(x)] and a(x) (°) co(x) 4>> then the x-trajectory will be called a loop. An example of a loop on the plane is a loop of the sepatrix that is a trajectory going from a singular point and back to it. Another example is a homoclinic trajectory for which the same saddle limit cycle is both a a-limit and an co-limit set. 

For t3, tj3 slow relaxations, the necessary and sufficient conditions have been obtained in terms of the limit behaviour of dynamic systems. Note that the (x, -motion is called positively Poisson-stable (P+-stable) if xeco(x, k). 

Bottom Pinned I-. AP stable I+. P stable Consistent with spin transfer mechanisms... 

Fig. 4. Nucleosynthesis of superheavy nuclei in the r-process rapid neutron capture alternating with IT-transilions during a supernova explosion. Shown in the Z-N plane is the r-process path of very neutron-rich nuclei extending to ZA100, from where p -decay chains directed towards the belt of p-stable nuclei would lead to Z 114, N=184 nuclei (dots). From D.N. Schramm and W.A. Fowler [28], reprinted with permission from Nature, Copyright (2002) Macmillan Magazines Limited.

Angst, J., Scheidegger, P., Stabl, M. 1993, Efficacy of moclobemide in different patient groups. Results of new subscales of the Hamilton Depression Rating Scale, Clin.Neuropharmacol., vol. 16, suppl. 2, pp. S55-S62. 

M. Shen, C. Beguin, A. Golbraikh, J. P. Stables, H. Kohn and A. Tropsha, Application of predictive QSAR models to database mining identification and experimental validation of novel anticonvulsant compounds., J. Med. Chem., 2004, 47, 2356-2364. 

The P-stable Exponentially Fitted Method developed by Kalogiratou and Simos"" (which is indicated as Method III)... 

In this part of the paper we present the study of the stabilization of the multistep exponentially-fitted methods. More specifically we present a family of singularly P-stable exponentially-fitted four-step methods and a family of six-step exponentially-fitted methods for the numerical solution of the radial Schrodinger equation. 

In order the new method to be P-stable we require the characteristic eqn (79) to have the following roots ... 

Definition 2. A method is called singularly P-stable if its interval of periodicity is equal to (0,oo) only when the frequency of the exponential fitting is the same as the frequency of the scalar test equation, i.e. H = w. 

Definition 4. A method is called P-stable if its interval of periodicity is equal to... 

If the frequency of the exponential fitting is different from the frequency of the scalar test equation the method is not P-stable i.e. there are areas in the Fig. 28 that are white and in which the conditions of P-stability are not satisfied). 

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