Isomorph

Definitions

  • Webster's Revised Unabridged Dictionary
    • Isomorph A substance which is similar to another in crystalline form and composition.
    • Isomorph (Biol) An animal, plant, or group having superficial similarity to another, although phylogenetically different.
    • ***
Century Dictionary and Cyclopedia
    • n isomorph A substance which exhibits isomorphism.
    • n isomorph In zoology, an organism which has the same form as another, and thus resembles it, though belonging to a different group.
    • ***

Etymology

Webster's Revised Unabridged Dictionary
See Isomorphous

Usage

In literature:

Its salts are isomorphous with those of alumina and sesquioxide of iron.
"Scientific American Supplement, No. 401, September 8, 1883" by Various
Being isomorphous with aragonite, it crystallizes in the orthorhombic system, but simple crystals are not known.
"Encyclopaedia Britannica, 11th Edition, Volume 4, Part 3" by Various
It is rhombohedral in crystallization and isomorphous with calcite and chalybite.
"Encyclopaedia Britannica, 11th Edition, Volume 4, Part 4" by Various
Isomorphous: having the same form, appearance or construction.
"Explanation of Terms Used in Entomology" by John. B. Smith
When both the crystal form and structure are retained, the substances are said to be isomorphous.
"Encyclopaedia Britannica, 11th Edition, Volume 6, Slice 1" by Various
The alkaline perchlorates are isomorphous with the permanganates.
"Encyclopaedia Britannica, 11th Edition, Volume 6, Slice 3" by Various
It forms dark red crystals isomorphous with ferrous sulphate, and readily soluble in water.
"Encyclopaedia Britannica, 11th Edition, Volume 6, Slice 5" by Various
Celestine crystallizes in the orthorhombic system, being isomorphous with barytes (q.v.).
"Encyclopaedia Britannica, 11th Edition, Volume 5, Slice 5" by Various
It crystallizes in the orthorhombic system and is isomorphous with stibnite (Sb2S3), which it closely resembles in appearance.
"Encyclopaedia Britannica, 11th Edition, Volume 4, Slice 1" by Various
Ni3(AsO4)2 + 8H2O, crystallizing in the monoclinic system and isomorphous with vivianite and erythrite.
"Encyclopaedia Britannica, 11th Edition, Volume 2, Slice 2" by Various
Isomorphism, theory of, 370.
"A Manual of Elementary Geology" by Charles Lyell
Formation of mixed crystals of isomorphous substances, 182.
"The Phase Rule and Its Applications" by Alexander Findlay
Isomorphous with greenockite is the hexagonal zinc sulphide (ZnS) known as wurtzite.
"Encyclopaedia Britannica, 11th Edition, Volume 12, Slice 5" by Various
An isomorphism of the group with itself, established in this way, is called an inner isomorphism.
"Encyclopaedia Britannica, 11th Edition, Volume 12, Slice 6" by Various
Haematite crystallizes in the rhombohedral system, and is isomorphous with corundum (Al2O3).
"Encyclopaedia Britannica, 11th Edition, Volume 12, Slice 7" by Various
Isomorphous with heulandite is the strontium and barium zeolite brewsterite, named after Sir David Brewster.
"Encyclopaedia Britannica, 11th Edition, Volume 13, Slice 4" by Various
***

In science:

Theorem 2.3 (D’Andrea and Kac, [DK]). A simple conformal algebra of finite type is either isomorphic to RW or isomorphic to R(G ) for some finite-dimensional simple Lie algebra G .
Simple Conformal Algebras Generated by Jordan Algebras
To check condition (2) of Theorem 1.4, let H ′ be a subgroup of An which is isomorphic to H and denote by α : H → H ′ an isomorphism.
Finite simple groups and localization
Two formal distribution Lie superalgebras (g, F ) and (g1 , F1 ) are called isomorphic if there exists an isomorphism ϕ : g → g1 such that ϕ(F ) = F1 .
Classification of finite simple Lie conformal superalgebras
Suppose we are given a line bundle L on X and for every H ∈ H an isomorphism L(H ) ⊗ OH ∼= OH , or equivalently, an isomorphism between the normal bundle νH/X and the coherent restriction of L∗ to H .
Compactifications defined by arrangements I: the ball quotient case
We shall want these isomorphisms to satisfy a normal triviality condition which roughly says that if L is any connected component of an intersection of members of H, then these isomorphisms trivialize the pro jectivized normal bundle of L.
Compactifications defined by arrangements I: the ball quotient case
Moreover, the isomorphism G\U ∼= X ◦ extends to an isomorphism G\\Y ss ∼= ˆX H .
Compactifications defined by arrangements I: the ball quotient case
This induces an isomorphism between the underlying pro j’s and so we obtain an isomorphism G\\Y ss ∼= ˆX H , as stated.
Compactifications defined by arrangements I: the ball quotient case
The last isomorphism is covered by an isomorphism of orbiline bundles G\\η → L|X − Dh and so Theorem 7.1 applies with U = Y ss : we find that the period map extends to an isomorphism G\\Y ss ∼= ˆX Hh .
Compactifications defined by arrangements I: the ball quotient case
This isomorphism is covered by an isomorphism of orbifold line bundles: G\η⊗6 is isomorphic to the pull-back of the L12 .
Compactifications defined by arrangements I: the ball quotient case
The chain map ǫ• is a quasi-isomorphism iff it induces an isomorphism H•(ǫ• ) in homology.
The nonabelian bar resolution
Consequently, Σ is isomorphic to the powerset of Ω, and Ω itself is isomorphic to the powerset of E.
The temporal calculus of conditional objects and conditional events
In this general situation we would assume the existence of a natural isomorphism θ : Ke −→ tKe in addition to the isomorphism σ : ⊗ −→ t⊗.
The categorical theory of relations and quantizations
If Q is any nonzero finitely generated pro jective right R-module, Lemma 1.4 implies that Q is isomorphic to a direct summand of eR, and so Q is isomorphic to some nonzero right ideal I ⊆ R.
$K_0$ of purely infinite simple regular rings
In terms of isomorphism classes of finitely generated pro jective modules A and B , we have [A] ≤ [B ] if and only if A is isomorphic to a direct summand of B .
$K_0$ of purely infinite simple regular rings
In particular, any nonzero finitely generated projective R-modules which are stably isomorphic must be isomorphic.
$K_0$ of purely infinite simple regular rings
***