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To get a definition you can go to Google.com and type in the words define isomorphism or whatever you want defined. isomorphismA map or function taking a structure A (such as a group, ring, field, etc.) exactly onto another similar structure B , so that both A (considered as a substructure of B ) and B look exactly the same. In other words, an isomorphism is an embedding that is surjective as well as injective.
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Identical atoms of other elements.
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Is the problem of subgraph isomorphism being NP-complete?
Yes, the problem of subgraph isomorphism is NP-complete.
What is a balanced category?
A balanced category is a category in which every bimorphism is an isomorphism.
What is an automorphism?
An automorphism is an isomorphism of a mathematical object or system of objects onto itself.
How many abelian groups up to isomorphism are there of order 32?
7 groups, use the structure theorem
What is the significance of the graph isomorphism problem in the field of computer science and mathematics?
The graph isomorphism problem is significant in computer science and mathematics because it involves determining if two graphs are structurally identical. Solving this problem efficiently has implications for cryptography, network analysis, and algorithm design.
What are the current challenges and advancements in solving the subgraph isomorphism problem?
The current challenges in solving the subgraph isomorphism problem include the exponential growth of possible subgraph combinations and the need for efficient algorithms to find matches. Advancements in this area include the development of faster algorithms, improved heuristics, and the use of parallel computing to speed up the process.
Why ionic compounds show isomorphism?
Ionic compounds show isomorphism because different cations can occupy the same crystal lattice sites in the crystal structure, resulting in similar crystal shapes and properties despite having different chemical formulas. This occurs when cations have similar sizes and charges, allowing them to substitute for each other in the crystal lattice.
What has the author Harold Simmons written?
Harold Simmons has written: 'Derivation and computation' -- subject(s): Curry-Howard isomorphism, Lambda calculus, Proof theory, Type theory
How to determine the number of group of order 10 upto isomorphism?
10 = 2*5, a product of 2 primes, and 2 divides (5-1). So there are only two groups.
What are the examples of isomorphism of ionic crystals?
Compounds are said to be isomorphic when the crystals have the same form. In crystallographic terms this means having the same space group. The best known examples are perhaps the alums and the double sulfates, Tutton's salts. The crystals of the different compounds are very similar.
What are the examples of isomorphic minerals?
Examples of isomorphic minerals include olivine, pyroxene, amphibole, garnet, and feldspar. These minerals have similar crystal structures but different chemical compositions, resulting in isomorphism.
What is the number of groups of order 8 upto isomorphisms?
There are 5 groups of order 8 up to isomorphism. 3 abelian ones (C8, C4xC2, C2xC2xC2) and 2 non-abelian ones (dihedral group D8 and quaternion group Q)
