isomorphicadj.

1862 H. Holland Mod. Chem. in Ess. 444 This peculiar isomorphic relation between various chemical substances, having in themselves other singular resemblances.

1894 Thinker 5 435 This statement is not vitiated by the existence of such phenomena as those of pleomorphism and of isomorphic replacement.

1892 F. N. Cole tr. E. Netto Theory Substitutions iv. 83 If to every substitution of G correspond q substitutions of , and to every substitution of  p substitutions of G, then G and  are said to be (p-q)-fold isomorphic, or if p and q are not specified, manifold isomorphic. If p = q = 1, the groups are said to be simply isomorphic.

1897 W. Burnside Theory Groups of Finite Order 21 If a correspondence can be established between the operations of G and G′, so that to every operation of G there corresponds a single operation of G′,..while to the product AB of any two operations of G there corresponds the product A′B′ of the two corresponding operations of G′, the groups G and G′ are said to be simply isomorphic.

1900 Ann. Math. 2 48 Two abstract groups G, H which are 1–1 isomorphic are evidently, as far as structure goes, not distinct.

1934 J. A. Eldridge Physical Basis of Things xxviii. 372 The scientist studies the infinite variety of nature's processes, acquaints himself with nature's group of operations, and then attempts to find a representation, in models or symbols, which is isomorphic therewith.

1937 A. Smeaton tr. R. Carnap Logical Syntax Lang. iv. 224 If S₁ is reversibly transformable in S₂ in respect of symbols, then S₁ and S₂ are called isomorphic.

1952 H. B. Veatch Intentional Logic i. iii. 36 Whether it is necessary and proper that the structure of logical entities should correspond to, or be isomorphic with, or be similar to the structure of the facts which they are supposed to signify or represent.

1962 C. O. Frake in J. A. Fishman Readings Sociol. of Lang. (1968) 437 The items and arrangements of a structural description of the language code need not be isomorphic with the categories and propositions of the message.

1965 E. M. Patterson & D. E. Rutherford Elem. Abstr. Algebra ii. 51 In other words, G₂ is isomorphic to G₁ if G₁ is isomorphic to G₂.

1968 J. Lyons Introd. Theoret. Linguistics ii. 55 To the degree that the meanings of one language can be brought into one-to-one correspondence with those of another we will say that the two languages are semantically isomorphic (have the same semantic structure).

1971 Nature 22 Jan. 233/2 We can imagine the state of the whole system described by the states S₁, S₂,... S_n of its S_n components. These values will determine a unique point in the n dimensional phase-space S such that there is an isomorphic correspondence between points in the space and the states of the system.

1973 J. Hintikka Logic, Lang.-games & Information ii. 28 In order for anything to be an isomorphic representation of anything else, they must both have a certain structure.

1888 Nature 20 Dec. 180/1 Dicholophus..has assumed peculiar Raptorial characters isomorphic with those of Gypogeranus, which is a true bird of prey.

1935 F. E. Fritsch Struct. & Reprod. Algae I. 52 Isomorphic (homologous) alternation occurs in each of the three largest classes of the Algae.

1951 M. O. P. Ivengar in G. M. Smith Man. Phycology iii. 59 In the third type of life-cycle [of Chlorophyta], there is an alternation of two generations both externally similar... This kind of alternation has been called by Fritsch isomorphic alternation.

1951 M. O. P. Ivengar in G. M. Smith Man. Phycology iii. 60 Isomorphic types very probably originated from haploid types.

1964 E. J. H. Corner Life of Plants vi. 93 Their [sc. slender brown seaweeds'] life-cycle is an isomorphic alternation of diploid sporophyte with haploid gametophyte.

1964 J. S. Karling Synchytrium iii. 51 In 1905 Lowenthal described fusion of two motile isomorphic cells in S[ynchytrium] taraxaci and illustrated what appears to be a binucleate zygote.

1970 P. H. Raven & H. Curtis Biol. Plants vi. 438/2 In Ulva, the alternation is isomorphic—that is, the mature sporophytes are morphologically identical to mature gametophytes.

1950 Language Learning III. iii. 93 The presentation of such items seems to be indicated in terms of lists the members of which are isomorphic (i.e. show similar differences between morpheme alternants).

1954 M. A. Pei & F. Gaynor Dict. Linguistics 107 Isomorphic lines, lines on a linguistic map, indicating the approximate boundaries of the speech-areas in which a uniformity in grammatical forms, inflections, etc. can be observed.

1957 S. Potter Mod. Ling. vi. 134 On more detailed [linguistic] maps we might construct different kinds of lines called isophonic, isotonic, isomorphic, or isosyntagmic, which would record differentiating features of sound, tone, word-form and clause-structure respectively.

1935 Amer. Jrnl. Math. 57 434 By means of P_i → P*_i we thus map the algebra 11 reduced modulo (1 − u) isomorphically upon itself.

1960 Brown & Gilman in T. A. Sebeok Style in Lang. 267 There are a large number of expressions of subordination which are patterned isomorphically with T [sc. a familiar pronoun such as tu] and V [sc. a polite pronoun such as vous].

1971 E. C. Dade in M. P. Powell & G. Higman Finite Simple Groups viii. 258 R_i sends the algebra A_i isomorphically onto Hom_F (I_i, I_i) for all i = 1,…, k.