The following table shows where isomorphism may be generally expected.
It is not the quantity but the quality of the anatomical and bionomic characters which determines their taxonomic value, and a few fundamental characters are better indications of the affinities of given groups of birds than a great number of agreements if these can be shown to be cases of isomorphism or heterophyletic, convergent analogy.
To these results he was aided by the law of isomorphism formulated by E.
The chlorine is not completely precipitated by silver nitrate in nitric acid solution, the ionization apparently not proceeding to all the chlorine atoms. Thallic iodide, T11 3, is interesting on account of its isomorphism with rubidium and caesium tri-iodides, a resemblance which suggests the formula T11 (12) for the salt, in which the metal is obviously monovalent.
Mitscherlich, who also observed the similarity of the crystallographic characters of selenates and sulphates, which afforded valuable corroboration of his doctrine of isomorphism.
The development of the theory of crystal structure, and the fundamental principles on which is based the classification of crystal forms, are treated in the article Crystallography; in the same place will be found an account of the doctrine of isomorphism, polymorphism and morphotropy.
Isomorphism may be defined as the existence of two or more different substances in the same crystal form and structure, polymorphism as the existence of the same substance in two or more crystal modifications, and morphotropy (after P. von Groth) as the change in crystal form due to alterations in the molecule of closely (chemically) related substances.
Mitscherlich, in the case of the acid phosphate and acid arsenate of potassium, KH 2 P(As)04, who adopted the term isomorphism, and regarded phosphorus and arsenic as isomorphously related elements.
Identity, or approximate identity, of crystal form is not in itself sufficient to establish true isomorphism.
von Hauer has investigated a number of cases in which salts exhibiting episomorphism have different colours, thereby clearly demonstrating this property of isomorphism.
Isomorphism is most clearly discerned between elements of analogous chemical properties; and from the wide generality of such observations attempts have been made to form a classification of elements based on isomorphous replacements.
In 1858 he pointed out the isomorphism of the fluostannates and the fluosilicates, thus settling the then vexed question of the composition of silicic acid; and subsequently he studied the fluosalts of zirconium, boron, tungsten, &c., and prepared silicotungstic acid, one of the first examples of the complex inorganic acids.
Berzelius as to their composition; and his observation that corresponding phosphates and arsenates crystallize in the same form was the germ from which grew the theory of isomorphism which he communicated to the Berlin Academy in December 1819.
Other instances of the isomorphism of thallous with potassium salts are the nitrates, phosphates, hydrazoates, sulphates, chromates, selenates, and the analogously constituted double salts, and also the oxalates, racemates and picrates.
However, the groups have gone through the random isomorphism test and hence it is likely that they are not isomorphic.
IsomorphismFpGroup returns an isomorphismFpGroup returns an isomorphism to this new group, given by the preimages of the new generators.
This module contains an algorithm to test isomorphism of pc groups using a random method.
As long as t y never equals 1 this defines a unique order isomorphism from X into [0,1] .
isomorphism between language and reality.
The case study was guided by the social science concepts of institutional isomorphism and resource dependency.
This relation can, first of all, be characterized in terms of the notion of partial isomorphism.
isomorphism theorem was first proved in Karp ; see also Barwise  .
isomorphism algorithm for ordered graphs, which performs well on the TOPS descriptions of protein structure.
isomorphism type of the group defined by P.
isomorphism problem, involves trying to decide whether two graphs are the same.
isomorphism tests, Calculation of all subgroups, Calculations with finitely presented structures.
We have developed a subgraph isomorphism algorithm for ordered graphs, which performs well on the TOPS descriptions of protein structure.
The retrieval searches for graph isomorphism among these attribute graphs.
isomorphism of pc groups using a random method.
isomorphism of thought and the object of thought.
Identification of tertiary structure resemblance in proteins using a maximal common subgraph isomorphism algorithm.
resemblance in proteins using a maximal common subgraph isomorphism algorithm.
Karp's partial isomorphism theorem was first proved in Karp ; see also Barwise  .
well-ordered subsets of R and [a ], [b] for their isomorphism classes.
The elements are arranged in eleven series, and the series are subdivided (as indicated by semicolons) into groups; these groups exhibit partial isomorphism with the other groups of the same series (see W.
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