Congruent

Hence, the evaporation rate of each element will only be in die proportion of the alloy composition at one composition, die congruently vaporizing composition. If drere is a large difference between the vapour pressures of the elements then the element having the higher vapour pressure could be completely evaporated hrst. 

In the case of TiC, preferential evaporation of titanium leads to a change in the stoichiometry of the compound towards the carbon-rich end, the excess carbon being left diffuses into the carbide phase, and so the flux ratio of the two elements changes widi time until congruent vaporization is achieved. 

To return to die problem of die vaporization of die tantalum silicides, which could be transported as the tetraiodide of each element, but not as the elementary species. From these data it can be concluded that whatever die starting point in the composition range, the composition of the surface phase will tend towards Tag Sis, which is die most nearly congruently vaporizing composition. 

The implementation strategy should be congruent with the objective of the project and the company organization and culture. The plan should be presented in a clear and succinct manner so that all those involved can follow it and progress against the plan can be monitored. 

Addition of the appropriate amount of water to anhydrous H3PO4, or crystallization from a concentrated aqueous solution of syrupy phosphoric acid, yields the hemihydrale 2H3PO4.H2O as a congruently melting compound (mp 29.3 "). The crystal structure shows the presence of 2 similar H3P()4 molecules which, together with the H2O molecule, are linked into... 

In congruent circles, if two chords are congruent, so are the corresponding minor arcs. 

Maximumtotal alkalinity consistentwith acceptable steam purity. If necessary, the limitation on total alkalinity should override conductance as the control parameter. If make-up is demineralized waterat 600-1000 Ib/in g, boiler wateralkalinity and conductance should be shown in the table for the 1001 -1500 Ib/in g range. NS (not specified) in these cases refers to free sodium- or potassium-hydroxide alkalinity. Some small variable amount of total alkalinity will be present, and measurable with the assumed congruent control or volatile treatment employed at these high-pressure ranges. 

For both coordinated and congruent control, the pH depends upon the phosphate concentration and the sodium to phosphate ratio. Generally, however, phosphates are unsuitable for use at boiler pressures above 100 bar as their low solubility and high concentration factors developed lead to corrosive conditions. 

Notice that this reduction forces every dipolynomial to be congruent to a unique conventional polynomial with degree d< N. 

Let G and C7 be two graphs. The vertices of both are partitioned into species, the edges of all coronas are numbered, for each k k 1, 2,. ..) a group is given, associated with the coronas of degree k. The graphs G and G are congruent if and only if there exists a one-to-one correspondence between G and G by which... 

The last two conditions will be dealt with below in more detail. We call a mapping of G onto C7 satisfying these four conditions a congruent mapping. Two elements which can be mapped onto each other may be called congruent in this sense [(I), (II)] one may say ... 

Any two edges are congruent to each other. Vertices of the same species are congruent, vertices of different species noncongruent. 

If the cyclic group 2 is associated with the coronas of order k k 1, 2,. ..) then two graphs which are congruent according to the definition of Sec. 34 are called "planar nondistinct", while jf they are noncongruent in this sense they are called "planar distinct". 

I claim that one can find a planted tree S which is congruent to S and whose principal branches are numbered 1, 2,. .., k - 1. This is a consequence of the transitivity of the group Gj. This group contains a permutation which maps the number assigned in the corona of K to the stem of S into k. Subject the corona of K to this permutation and leave everything else unchanged. The resulting planted tree S has the desired properties (cf. Sec. 34, in particular (IV)). 

The name "configuration" has here the same connotation as in Sec. 11. Congruent principal branches are considered equivalent, non-... 

Two planted trees whose principal branches form the same configuration are certainly congruent in the sense of Sec. 34. Is it possible that different configurations of the principal branches belong to congruent planted trees ... 

Reading the deductions in reverse order, we conclude two planted trees are congruent to each other if and only if they have the same number of principal branches and the configurations of the principal branches are equivalent with respect to the associated subgroup. Depending on the associated groups A 4, H j, the associated subgroups are A3 H3, and respectively. These... 

For a proof of this statement, one has to consider two planted trees, S and 5 , whose principal branches, numbered in the same way, are congruent with each other. The k - 1 congruent mappings of the principal branches are used to construct a congruent mapping from. S to. S. The details are left to the reader. 

Similar arguments as in Sec. 39 lead to the following result Two centric trees are congruent if and only if the same number of branches originates from their centers and the configurations of these branches are equivalent with respect to the group associated with the corona of the center. 

Two pictures of two spatial (three-dimensional) models can represent the same structural formula without representing the same stereoformula they describe the same structural formula if they exhibit the same relationships (if they are topologically congruent, i.e., they satisfy conditions (I), (II), (III)). In order to describe the same stereoformula they must display the same relationships and the same spatial orientation [they satisfy (I), (II), (III), and in addition (IV) (with A ), that is, be spatially congruent]. If two formulas viewed as stereoformulas are equal then they are certainly equal when they are treated as structural formulas. Consequently there are at least as many stereoisomers as there are structural isomers. This fact is reflected by (2.8). It is true particularly for paraffins and monosubstituted paraffins. 

---