symplecticadj.n.

/sɪmˈplɛktɪk/

Etymology: < Greek συμπλεκτικός twining or plaiting together, copulative, < σύν sym- prefix + πλέκειν to twine, plait, weave: see -ic suffix.

A. adj.

1. Anatomy and Zoology. Epithet of a bone of the suspensorium in the skull of fishes, between the hyomandibular and the quadrate bones.

ΚΠ

1839–47 Todd's Cycl. Anat. & Physiol. III. 833/1 The symplectic bones seem to be peculiar to Fishes.

2. Geology. Of a rock or its texture: exhibiting an intimate intergrowth of two different minerals, esp. one where one mineral has a vermicular habit within the other as a result of secondary action. [ < German symplektisch (C. F. Naumann Lehrb. der Geognosie (1850) I. 667.]

ΘΚΠ

the world > the earth > minerals > mineral structure or appearance > [adjective] > intergrowth

symplectic1916

symplectitic1979

the world > the earth > structure of the earth > constituent materials > rock > texture or colour > [adjective] > texture > symplectic

symplectic1916

symplectitic1979

1916 J. J. Sederholm in Bull. de la Comm. Géol. de la Finlande No. 48. 46 I..take the liberty of proposing that the term symplektic, or symplektitic should be used preferably as a designation of secondary intergrowths of two different minerals.

1949 F. H. Hatch et al. Petrol. Igneous Rocks (ed. 10) iv. 281 A characteristic feature of certain noritic rocks is the development of symplectic intergrowths along intercrystal boundaries.

1971 Nature 3 Dec. 251/3 The decomposition of a fayalitic olivine (Fe₂SiO₄) to symplectic metallic iron and cristobalite provides confirmation of a very low oxygen fugacity.

B. n.

Anatomy and Zoology. The symplectic bone.

ΘΚΠ

the world > animals > fish > parts of fish > [noun] > bones (various types of)

grate1481

pharyngeal1791

suboperculum1818

supratemporal1834

shackle-joint1837

mastoid1840

wrist1840

mastoid bone1841

subopercular1841

mesotympanic1846

suprascapula1846

hypobranchials1848

hypotympanic1848

urohyal1848

radius1854

epicentral1866

pterotic1866

mesocoracoid1868

supraclavicle1868

precoracoid1869

symplectic1870

hypural1871

mesopterygoid1871

post-temporal1871

postclavicle1872

brachial1873

urostyle1875

hypercoracoid1876

admaxillary1885

intercalarium1887

palatopterygoquadrate1888

subtectal1888

Weberian apparatus1889

Weberian ossicles1889

radial1890

supracleithrum1903

1870 G. Rolleston Forms Animal Life 44 The synchondrosis between the hyomandibular and the symplectic.

1880 A. Günther Introd. Study of Fishes 55 The mesotympanic or symplectic appears as a styliform prolongation of the lower part of the hyomandibular.

Derivatives

symˈplectite n. an intergrowth of two different minerals.

ΘΚΠ

the world > the earth > minerals > mineral structure or appearance > [noun] > intergrowth

symplectite1916

1916 J. J. Sederholm in Bull. de la Comm. Géol. de la Finlande No. 48. 46, I..propose to use for these intergrowths of two minerals plaited together, and generally of second origin, the common designation symplektites (or symplectites).

1949 F. H. Hatch et al. Petrol. Igneous Rocks (ed. 10) iv. 282 (caption) Myrmekite-like symplectites of orthopyroxene and plagioclase are lobed into the labradorite.

1976 Nature 22 Apr. 673/2 Rare symplectites of spinel and pyroxene may result from the dehydration of amphibole.

symplecˈtitic adj.

ΘΚΠ

the world > the earth > minerals > mineral structure or appearance > [adjective] > intergrowth

symplectic1916

symplectitic1979

the world > the earth > structure of the earth > constituent materials > rock > texture or colour > [adjective] > texture > symplectic

symplectic1916

symplectitic1979

1979 Nature 5 Apr. 512/2 Symplectitic diopside is not different from coarser, recrystallised diopside.

Draft additions 1993

Mathematics. Involving, belonging to, or designating the symplectic group of linear transformations (or their matrix equivalents) under which a given non-degenerate skew-symmetric bilinear form is invariant. Also used, by extension, in Hamiltonian mechanics with reference to such forms acting on manifolds and vector spaces.

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

1939 H. Weyl Classical Groups vi. 165 The study of the symplectic group, which has a close analogy to the orthogonal group. [Note] The name ‘complex group’ formerly proposed by me..has become more and more embarrassing through collision with the word ‘complex’ in the connotation of complex number. I therefore propose to replace it by the corresponding Greek adjective ‘symplectic’.

1939 H. Weyl Classical Groups vi. 169 The analogues of the real orthogonal transformations are in many respects the unitary rather than the real symplectic transformations.

1959 Amer. Jrnl. Math. 81 846 Let Sp (n, R) be the group of 2n × 2n real symplectic matrices.

1965 Proc. Amer. Math. Soc. 16 393 Let Σ_G denote the group of all bicontinuous symplectic automorphisms of A.

1975 Jrnl. Math. Physics 16 1697/2 The explicit time dependence of the symplectic algebra depends on the chosen Hamiltonian.

1980 N. Woodhouse Geometric Quantization i. 1 The basic object in the geometric formulation of Hamiltonian mechanics is the symplectic manifold.

1989 Physical Rev. A. 40 2840/1 The symplectic structure of the collective manifold is defined only when one takes into account the dynamically generated effective gauge field on the collective phase space.

Draft additions 1993

symˈplectically adv. in a symplectic manner; with respect to symplectic properties.

ΘΚΠ

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

alternately1570

homographically1859

birationally1915

homoeomorphically1927

homotopically1930

isomorphically1935

homomorphically1941

isometrically1959

symplectically1959

1959 Amer. Jrnl. Math. 81 848  is a normal representation of  by 2m × 2m matrices A such that ^tA is symplectically self-adjoint.

1987 Nature 3 Sept. 18/1 Mathematicians are only beginning to learn how to think symplectically.

This entry has not yet been fully updated (first published 1919; most recently modified version published online June 2022).

单词	symplectic
释义	symplecticadj.n. /sɪmˈplɛktɪk/ Etymology: < Greek συμπλεκτικός twining or plaiting together, copulative, < σύν sym- prefix + πλέκειν to twine, plait, weave: see -ic suffix. A. adj. 1. Anatomy and Zoology. Epithet of a bone of the suspensorium in the skull of fishes, between the hyomandibular and the quadrate bones. ΚΠ 1839–47 Todd's Cycl. Anat. & Physiol. III. 833/1 The symplectic bones seem to be peculiar to Fishes. 2. Geology. Of a rock or its texture: exhibiting an intimate intergrowth of two different minerals, esp. one where one mineral has a vermicular habit within the other as a result of secondary action. [ < German symplektisch (C. F. Naumann Lehrb. der Geognosie (1850) I. 667.] ΘΚΠ the world > the earth > minerals > mineral structure or appearance > [adjective] > intergrowth symplectic1916 symplectitic1979 the world > the earth > structure of the earth > constituent materials > rock > texture or colour > [adjective] > texture > symplectic symplectic1916 symplectitic1979 1916 J. J. Sederholm in Bull. de la Comm. Géol. de la Finlande No. 48. 46 I..take the liberty of proposing that the term symplektic, or symplektitic should be used preferably as a designation of secondary intergrowths of two different minerals. 1949 F. H. Hatch et al. Petrol. Igneous Rocks (ed. 10) iv. 281 A characteristic feature of certain noritic rocks is the development of symplectic intergrowths along intercrystal boundaries. 1971 Nature 3 Dec. 251/3 The decomposition of a fayalitic olivine (Fe₂SiO₄) to symplectic metallic iron and cristobalite provides confirmation of a very low oxygen fugacity. B. n. Anatomy and Zoology. The symplectic bone. ΘΚΠ the world > animals > fish > parts of fish > [noun] > bones (various types of) grate1481 pharyngeal1791 suboperculum1818 supratemporal1834 shackle-joint1837 mastoid1840 wrist1840 mastoid bone1841 subopercular1841 mesotympanic1846 suprascapula1846 hypobranchials1848 hypotympanic1848 urohyal1848 radius1854 epicentral1866 pterotic1866 mesocoracoid1868 supraclavicle1868 precoracoid1869 symplectic1870 hypural1871 mesopterygoid1871 post-temporal1871 postclavicle1872 brachial1873 urostyle1875 hypercoracoid1876 admaxillary1885 intercalarium1887 palatopterygoquadrate1888 subtectal1888 Weberian apparatus1889 Weberian ossicles1889 radial1890 supracleithrum1903 1870 G. Rolleston Forms Animal Life 44 The synchondrosis between the hyomandibular and the symplectic. 1880 A. Günther Introd. Study of Fishes 55 The mesotympanic or symplectic appears as a styliform prolongation of the lower part of the hyomandibular. Derivatives symˈplectite n. an intergrowth of two different minerals. ΘΚΠ the world > the earth > minerals > mineral structure or appearance > [noun] > intergrowth symplectite1916 1916 J. J. Sederholm in Bull. de la Comm. Géol. de la Finlande No. 48. 46, I..propose to use for these intergrowths of two minerals plaited together, and generally of second origin, the common designation symplektites (or symplectites). 1949 F. H. Hatch et al. Petrol. Igneous Rocks (ed. 10) iv. 282 (caption) Myrmekite-like symplectites of orthopyroxene and plagioclase are lobed into the labradorite. 1976 Nature 22 Apr. 673/2 Rare symplectites of spinel and pyroxene may result from the dehydration of amphibole. symplecˈtitic adj. ΘΚΠ the world > the earth > minerals > mineral structure or appearance > [adjective] > intergrowth symplectic1916 symplectitic1979 the world > the earth > structure of the earth > constituent materials > rock > texture or colour > [adjective] > texture > symplectic symplectic1916 symplectitic1979 1979 Nature 5 Apr. 512/2 Symplectitic diopside is not different from coarser, recrystallised diopside. Draft additions 1993 Mathematics. Involving, belonging to, or designating the symplectic group of linear transformations (or their matrix equivalents) under which a given non-degenerate skew-symmetric bilinear form is invariant. Also used, by extension, in Hamiltonian mechanics with reference to such forms acting on manifolds and vector spaces. 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 1939 H. Weyl Classical Groups vi. 165 The study of the symplectic group, which has a close analogy to the orthogonal group. [Note] The name ‘complex group’ formerly proposed by me..has become more and more embarrassing through collision with the word ‘complex’ in the connotation of complex number. I therefore propose to replace it by the corresponding Greek adjective ‘symplectic’. 1939 H. Weyl Classical Groups vi. 169 The analogues of the real orthogonal transformations are in many respects the unitary rather than the real symplectic transformations. 1959 Amer. Jrnl. Math. 81 846 Let Sp (n, R) be the group of 2n × 2n real symplectic matrices. 1965 Proc. Amer. Math. Soc. 16 393 Let Σ_G denote the group of all bicontinuous symplectic automorphisms of A. 1975 Jrnl. Math. Physics 16 1697/2 The explicit time dependence of the symplectic algebra depends on the chosen Hamiltonian. 1980 N. Woodhouse Geometric Quantization i. 1 The basic object in the geometric formulation of Hamiltonian mechanics is the symplectic manifold. 1989 Physical Rev. A. 40 2840/1 The symplectic structure of the collective manifold is defined only when one takes into account the dynamically generated effective gauge field on the collective phase space. Draft additions 1993 symˈplectically adv. in a symplectic manner; with respect to symplectic properties. ΘΚΠ the world > relative properties > number > arithmetic or algebraic operations > transformation > [adverb] alternately1570 homographically1859 birationally1915 homoeomorphically1927 homotopically1930 isomorphically1935 homomorphically1941 isometrically1959 symplectically1959 1959 Amer. Jrnl. Math. 81 848  is a normal representation of  by 2m × 2m matrices A such that ^tA is symplectically self-adjoint. 1987 Nature 3 Sept. 18/1 Mathematicians are only beginning to learn how to think symplectically. This entry has not yet been fully updated (first published 1919; most recently modified version published online June 2022). < adj.n.1839
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