Second proving

A second proving takes place when the piece is ready for assembling. 

For this reason a second test was carried out in Southern Bohemia in 1981, and again in spring, 1983. The first experiment was more succesful, some results of the second proved... 

There are no official specifications for obtaining a minimum level of engine cleanliness from a fuel. However, all additives in France are subject to approval by the Direction des Carburants (DHYCA), with the objective of having data that prove, first of all, the product to be harmless, and second, the product s effectiveness. Likewise, the automotive manufacturers, in establishing their specifications, set the minimum performance to be obtained by the fuel with regard to engine cleanliness. 

It will be recognized that this generalizes the result proved by Baer in [72]. Though that work did establish the validity of the curl condition for the derivative operator as long as some 25 years ago and the validity is nearly trivial for the second term taken separately, the same result is not self-evident for the combination of the two teiins, due to the nonlinearity of F X). An important special case is when G(R) = R /2. Then... 

C2H5ONO + NaOH C2H5OH + NaNOa sodium nitrite. The second compound is nitroethane, C,H NO, of b.p. 114° its identity is clearly shown by the action of reducing agents, which convert it into ethylamiiie, CjHjNHj, thus proving the presence of a nitrogen carbon... 

Treating 5.5 g of 2-amino-4,5-dimethylthiazole HCl with 0.66 g of solid sodium hydroxide 15 min at 220°C yields 53% of 4.4. 5.5 -tetramethyT 2,2 -dithiazolylamine, whose structure w as proved by identification with the produa obtained from the reaction between dithiobiuret and 3-bromo-2-butanone (467). This result is comparable to the reaction between 2-aminopyridine and its hydrochloride to yield bis(pyridyl-2)amine (468). Gronowitz applied this reaction to 2-aminothiazole, refluxing it with its hydrochloride 4 hr in benzene and obtained the dimeric 2-aminothiazole (236). He proposed a mechanism (Scheme 143) that involves the addition of a proton to the 5-position of the ring to give 234. The carbocation formed then reacts on the 5-position of a second... 

A second form of desolvation chamber relies on diffusion of small vapor molecules through pores in a Teflon membrane in preference to the much larger droplets (molecular agglomerations), which are held back. These devices have proved popular with thermospray and ultrasonic nebulizers, both of which produce large quantities of solvent and droplets in a short space of time. Bundles of heated hollow polyimide or Naflon fibers have been introduced as short, high-surface-area membranes for efficient desolvation. 

The "overlap" information allows the original protein sequence to be generated. In this example, the sequence D-E-F-G in the fourth peptide proves that the first and second peptides must have been joined originaliy at E,F and not A,H. 

Therefore, (2.170) implies the second assertion of Theorem 2.19 on strong convergence. The theorem is proved. 

Besides, the property p[w] = [w] has already been proved. Let us consider the second (dual) problem in (3.226). We assume that qG K is a parameter and seek the solution w G of the following problem,... 

Proof. We consider a parabolic regularization of the problem approximating (5.68)-(5.72). The auxiliary boundary value problem will contain two positive parameters a, 5. The first parameter is responsible for the parabolic regularization and the second one characterizes the penalty approach. Our aim is first to prove an existence of solutions for the fixed parameters a, 5 and second to justify a passage to limits as a, d —> 0. A priori estimates uniform with respect to a, 5 are needed to analyse the passage to the limits, and we shall obtain all necessary estimates while the theorem of existence is proved. 

The inclusion m G K can be proved by standard arguments. Note that the second boundary condition (5.142) and the conditions (5.143) are included in the identity (5.145). This means that it is possible to obtain these conditions by integrating by parts provided that the solution is sufficiently smooth. Actually, we can prove that the second condition (5.142) holds in the sense 77 / (F), but the arguments are omitted here. The theorem is proved. 

The second boundary condition (5.214) and the conditions (5.215) are involved in (5.218). This means that those conditions hold at any point of r, r, respectively, provided the solution v, rriij is smooth enough. The statement can be verified by integrating by parts. Theorem 5.7 is proved. 

We have to stress that the analysed problems prove to be free boundary problems. Mathematically, the existence of free boundaries for the models concerned, as a rule, is due to the available inequality restrictions imposed on a solution. As to all contact problems, this is a nonpenetration condition of two bodies. The given condition is of a geometric nature and should be met for any constitutive law. The second class of restrictions is defined by the constitutive law and has a physical nature. Such restrictions are typical for elastoplastic models. Some problems of the elasticity theory discussed in the book have generally allowable variational formulation... 

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