homomorphicadj.

/hɒməʊˈmɔːfɪk/

Etymology: formed as homomorph n. + -ic suffix.

1. Of the same or similar form. (In sense 1c opposed to homologous; in other senses opposed to heteromorphic.)

a. Entomology. Said of insects in which the larva more or less resembles the imago (Homomorpha); hemimetabolous or ametabolous.

ΘΚΠ

the world > animals > invertebrates > phylum Arthropoda > class Insecta > group Ametabola > [adjective]

ametabolous1828

ametabolian1840

ametabolic1844

homomorphous1854

homomorphic1874

the world > animals > invertebrates > phylum Arthropoda > class Insecta > subclass Pterygota > [adjective] > hemimetabolous

homomorphous1854

homomorphic1874

1874 J. Lubbock Orig. & Metamorphoses Insects i. 6 The Homomorphic insects do not pass through such striking changes of form as the Heteromorphic.

b. Botany. Applied to flowers or plants in which there is no difference in the relative length of the stamens and pistils; also to the self-fertilization of such flowers.

ΘΚΠ

the world > plants > part of plant > reproductive part(s) > flower or part containing reproductive organs > [adjective] > having or relating to parts > of or having stamens or pistils > characterized by relative length

homomorphous1854

thrum-eyed1861

trimorphic1866

dimorphic1870

homomorphic1873

heteromorphic1874

heterostyled1876

heterogone1877

heterogonous1877

homogone1877

homogonous1877

homostyled1877

homostylic1883

homostylous1886

heterostylous1887

1873 F. H. Hooker & J. D. Hooker tr. E. Le Maout & J. Decaisne Gen. Syst. Bot. 154 Heteromorphic unions produce considerably more capsules and good seeds than homomorphic unions.

1877 C. Darwin Different Forms Flowers i. 24 I formerly applied the term ‘heteromorphic’ to the legitimate unions; and ‘homomorphic’ to the illegitimate unions; but after discovering the existence of trimorphic plants..these two terms ceased to be applicable.

1896 G. Henslow How to study Wild Flowers 86 Every flower had become homomorphic and self-fertilizing.

c. Biology. Applied to organs or organisms showing an external resemblance, but not really related in structure or origin.

ΘΚΠ

the world > life > biology > physical aspects or shapes > shape > [adjective] > similar

homotypal1849

homotypical1870

homomorphic1872

homotypic1886

1872 H. A. Nicholson Introd. Study Biol. 50–1 Many examples are known, both in the animal and the vegetable kingdom, in which families widely removed from one another in their fundamental structure, nevertheless present a..close resemblance. For this phenomenon the term ‘homomorphism’ has been proposed, and such forms are said to be ‘homomorphic’.

d. Zoology. Applied to a colony in which all the constituent individuals are alike.

ΘΚΠ

the world > animals > invertebrates > colony or compound organism > [adjective] > in which all individuals are alike

homomorphic1875

1875 C. C. Blake Zoology 372 The nutritive zooids all resemble each other, or they are homomorphic.

1891 T. J. Parker Lessons Elem. Biol. xii. 137 There are no special reproductive individuals, so that the colony is homomorphic.

1931 W. C. Allee Animal Aggregations ii. 23 Homomorphic colonies have all the individuals morphologically similar and may be found among sponges and at certain times among hydroids and bryozoans.

e. Cytology. Applied to homologous chromosomes that do not differ in size or form.

ΘΚΠ

the world > life > biology > biological processes > genetic activity > genetic components > [adjective] > chromosome > chromosomes in respect of meiosis

non-homologous1883

quadrivalent1898

univalent1898

bivalent1899

plurivalent1901

homologous1903

heterotropic1905

monovalent1906

heteromorphic1917

homomorphic1917

trivalent1921

multivalent1929

sexivalent1931

nullisomic1932

quinquevalent1935

1917 E. E. Carothers in Jrnl. Morphol. 28 449 The unusual conditions of the chromosomes in this group have made advisable the introduction of four new terms. i. Homomorphic—used to designate those tetrads made up of morphologically similar homologues.

1925 E. B. Wilson Cell (ed. 3) xii. 937 Twenty-eight male offspring have thus been examined from five matings with especial reference to three chromosome-pairs..which may be either heteromorphic or homomorphic.

1968 J. A. Serra Mod. Genetics III. xxiii. 533 These bodies are homomorphic sex chromosomes..not heterochromosomes.

2. Mathematics. Related or produced by a homomorphism; giving rise to a second set under a homomorphism; that is a homomorphism.

ΘΚΠ

the world > relative properties > number > arithmetic or algebraic operations > transformation > [adjective] > having specific correspondence

orthogonal1852

permutational1888

isomorphic1892

birational1894

unary1931

homomorphic1935

symplectic1939

involutory1941

injective1952

monomorphic1958

bijective1962

surjective1964

1935 Proc. National Acad. Sci. U.S.A. 21 482 We define a continuous homomorphic mapping π_m of ℌp^m+1() into ℌp^m().

1939 Amer. Jrnl. Math. 61 783 Two homomorphic rings.

1941 G. Birkhoff & S. MacLane Surv. Mod. Algebra xiii. 350 This device for getting a field as a homomorphic image of a polynomial ring is important in the discussion of algebraic numbers.

1966 Math. Rev. 31 15/2 It is homomorphic to (i.e., can be contracted into, by identification of sets of connected vertices) the complete graph of order k.

1968 I. Adler Groups in New Math. xiii. 230 If there is a homomorphism that matches the members of one group with the members of another, we say that the first group is homomorphic to the second, and that the second group is a homomorphic image of the first group.

in extended use.1959 S. Beer Cybernetics & Managem. vi. 49 A black Box is homomorphic with a cybernetic system, because the latter has undergone a many-one simplifying transformation (which makes it tractable) without losing its key characteristic (of indefinability).

Derivatives

homoˈmorphically adv. Mathematics by a homomorphism.

ΘΚΠ

the world > relative properties > number > arithmetic or algebraic operations > transformation > [adverb]

alternately1570

homographically1859

birationally1915

homoeomorphically1927

homotopically1930

isomorphically1935

homomorphically1941

isometrically1959

symplectically1959

1941 G. Birkhoff & S. MacLane Surv. Mod. Algebra xiii. 350 The direct sum A + B of two rings A and B may be mapped homomorphically on the summand B by the correspondence (a, b) → b.

1952 S. Eilenberg & N. E. Steenrod Found. Algebraic Topol. i. 7 If G and H are groups, the notation ϕ: G→ H means that ϕ maps G homomorphically into H.

1971 M. Herzog in Powell & Higman Finite Simple Groups v. 200 G is p-solvable if and only if it can be mapped homomorphically on N_G(P)/W.

This entry has not yet been fully updated (first published 1899; most recently modified version published online June 2019).

单词	homomorphic
释义	homomorphicadj. /hɒməʊˈmɔːfɪk/ Etymology: formed as homomorph n. + -ic suffix. 1. Of the same or similar form. (In sense 1c opposed to homologous; in other senses opposed to heteromorphic.) a. Entomology. Said of insects in which the larva more or less resembles the imago (Homomorpha); hemimetabolous or ametabolous. ΘΚΠ the world > animals > invertebrates > phylum Arthropoda > class Insecta > group Ametabola > [adjective] ametabolous1828 ametabolian1840 ametabolic1844 homomorphous1854 homomorphic1874 the world > animals > invertebrates > phylum Arthropoda > class Insecta > subclass Pterygota > [adjective] > hemimetabolous homomorphous1854 homomorphic1874 1874 J. Lubbock Orig. & Metamorphoses Insects i. 6 The Homomorphic insects do not pass through such striking changes of form as the Heteromorphic. b. Botany. Applied to flowers or plants in which there is no difference in the relative length of the stamens and pistils; also to the self-fertilization of such flowers. ΘΚΠ the world > plants > part of plant > reproductive part(s) > flower or part containing reproductive organs > [adjective] > having or relating to parts > of or having stamens or pistils > characterized by relative length homomorphous1854 thrum-eyed1861 trimorphic1866 dimorphic1870 homomorphic1873 heteromorphic1874 heterostyled1876 heterogone1877 heterogonous1877 homogone1877 homogonous1877 homostyled1877 homostylic1883 homostylous1886 heterostylous1887 1873 F. H. Hooker & J. D. Hooker tr. E. Le Maout & J. Decaisne Gen. Syst. Bot. 154 Heteromorphic unions produce considerably more capsules and good seeds than homomorphic unions. 1877 C. Darwin Different Forms Flowers i. 24 I formerly applied the term ‘heteromorphic’ to the legitimate unions; and ‘homomorphic’ to the illegitimate unions; but after discovering the existence of trimorphic plants..these two terms ceased to be applicable. 1896 G. Henslow How to study Wild Flowers 86 Every flower had become homomorphic and self-fertilizing. c. Biology. Applied to organs or organisms showing an external resemblance, but not really related in structure or origin. ΘΚΠ the world > life > biology > physical aspects or shapes > shape > [adjective] > similar homotypal1849 homotypical1870 homomorphic1872 homotypic1886 1872 H. A. Nicholson Introd. Study Biol. 50–1 Many examples are known, both in the animal and the vegetable kingdom, in which families widely removed from one another in their fundamental structure, nevertheless present a..close resemblance. For this phenomenon the term ‘homomorphism’ has been proposed, and such forms are said to be ‘homomorphic’. d. Zoology. Applied to a colony in which all the constituent individuals are alike. ΘΚΠ the world > animals > invertebrates > colony or compound organism > [adjective] > in which all individuals are alike homomorphic1875 1875 C. C. Blake Zoology 372 The nutritive zooids all resemble each other, or they are homomorphic. 1891 T. J. Parker Lessons Elem. Biol. xii. 137 There are no special reproductive individuals, so that the colony is homomorphic. 1931 W. C. Allee Animal Aggregations ii. 23 Homomorphic colonies have all the individuals morphologically similar and may be found among sponges and at certain times among hydroids and bryozoans. e. Cytology. Applied to homologous chromosomes that do not differ in size or form. ΘΚΠ the world > life > biology > biological processes > genetic activity > genetic components > [adjective] > chromosome > chromosomes in respect of meiosis non-homologous1883 quadrivalent1898 univalent1898 bivalent1899 plurivalent1901 homologous1903 heterotropic1905 monovalent1906 heteromorphic1917 homomorphic1917 trivalent1921 multivalent1929 sexivalent1931 nullisomic1932 quinquevalent1935 1917 E. E. Carothers in Jrnl. Morphol. 28 449 The unusual conditions of the chromosomes in this group have made advisable the introduction of four new terms. i. Homomorphic—used to designate those tetrads made up of morphologically similar homologues. 1925 E. B. Wilson Cell (ed. 3) xii. 937 Twenty-eight male offspring have thus been examined from five matings with especial reference to three chromosome-pairs..which may be either heteromorphic or homomorphic. 1968 J. A. Serra Mod. Genetics III. xxiii. 533 These bodies are homomorphic sex chromosomes..not heterochromosomes. 2. Mathematics. Related or produced by a homomorphism; giving rise to a second set under a homomorphism; that is a homomorphism. ΘΚΠ the world > relative properties > number > arithmetic or algebraic operations > transformation > [adjective] > having specific correspondence orthogonal1852 permutational1888 isomorphic1892 birational1894 unary1931 homomorphic1935 symplectic1939 involutory1941 injective1952 monomorphic1958 bijective1962 surjective1964 1935 Proc. National Acad. Sci. U.S.A. 21 482 We define a continuous homomorphic mapping π_m of ℌp^m+1() into ℌp^m(). 1939 Amer. Jrnl. Math. 61 783 Two homomorphic rings. 1941 G. Birkhoff & S. MacLane Surv. Mod. Algebra xiii. 350 This device for getting a field as a homomorphic image of a polynomial ring is important in the discussion of algebraic numbers. 1966 Math. Rev. 31 15/2 It is homomorphic to (i.e., can be contracted into, by identification of sets of connected vertices) the complete graph of order k. 1968 I. Adler Groups in New Math. xiii. 230 If there is a homomorphism that matches the members of one group with the members of another, we say that the first group is homomorphic to the second, and that the second group is a homomorphic image of the first group. in extended use.1959 S. Beer Cybernetics & Managem. vi. 49 A black Box is homomorphic with a cybernetic system, because the latter has undergone a many-one simplifying transformation (which makes it tractable) without losing its key characteristic (of indefinability). Derivatives homoˈmorphically adv. Mathematics by a homomorphism. ΘΚΠ the world > relative properties > number > arithmetic or algebraic operations > transformation > [adverb] alternately1570 homographically1859 birationally1915 homoeomorphically1927 homotopically1930 isomorphically1935 homomorphically1941 isometrically1959 symplectically1959 1941 G. Birkhoff & S. MacLane Surv. Mod. Algebra xiii. 350 The direct sum A + B of two rings A and B may be mapped homomorphically on the summand B by the correspondence (a, b) → b. 1952 S. Eilenberg & N. E. Steenrod Found. Algebraic Topol. i. 7 If G and H are groups, the notation ϕ: G→ H means that ϕ maps G homomorphically into H. 1971 M. Herzog in Powell & Higman Finite Simple Groups v. 200 G is p-solvable if and only if it can be mapped homomorphically on N_G(P)/W. This entry has not yet been fully updated (first published 1899; most recently modified version published online June 2019). < adj.1872
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