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Examples ofinequivalent
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Moreover, the true vacuum of a field theory may be an overlap of several topologicallyinequivalentsectors, so called topological vacua.
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This example is from Wikipedia and may be reused under a CC BY-SA license.Spins that are chemically equivalent but are not indistinguishable (based on their coupling relationships) are termed magneticallyinequivalent.
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This example is from Wikipedia and may be reused under a CC BY-SA license.In technical terms, this comes about because the two vacua lead to unitarilyinequivalentrepresentations of the quantum field canonical commutation relations.
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This example is from Wikipedia and may be reused under a CC BY-SA license.Thus, while there is only one spin representation in odd dimensions, there are a pair ofinequivalentpin representations.
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This example is from Wikipedia and may be reused under a CC BY-SA license.There are 5inequivalentmatrices of order 16, 3 of order 20, 60 of order 24, and 487 of order 28.
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This example is from Wikipedia and may be reused under a CC BY-SA license.So far, we have only seen examples in which theinequivalentdiscrete symmetries form either a cyclic group or a direct product of such groups.
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Of course, there is no reason why this structure should be planar, since the two sides areinequivalentwith major and minor groove characteristics.
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We give examples of pairs of processes that are equivalent and of pairs that areinequivalent.
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The following two examples illustrate that to show that two processes are contextuallyinequivalent, it suffices to find a context that distinguishes them.
From theCambridge English Corpus
If the b-sheets are of the in-register, parallel type, the two opposite directions of interstrand hydrogen bonding within each b-sheet areinequivalent.
From theCambridge English Corpus
We shall consider equivalence under continuous symmetries with real-valued parameters; theinequivalentdiscrete symmetries may have a real or complex action on the variables (x, u).
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Are there essentially only a finite number ofinequivalentsuch f which give rise to the same zeta function?
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Hence, finding invariants or normal forms that distinguish betweeninequivalentsingularities is a major goal.
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Using the orthogonality relations derived above, we find that the q characters for the qinequivalentirreducible representations forms a basis set.
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This example is from Wikipedia and may be reused under a CC BY-SA license.The second factor sums over different values of f that areinequivalentgauge fixings.
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This example is from Wikipedia and may be reused under a CC BY-SA license.Mixtures of products may result from attack atinequivalent"ortho" or "para" positions.
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This example is from Wikipedia and may be reused under a CC BY-SA license.In higher dimensions the literature on algebraic geometry contains manyinequivalentdefinitions of ordinary singular points.
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This example is from Wikipedia and may be reused under a CC BY-SA license.The dual representation, which isinequivalent, is also 27-dimensional.
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This example is from Wikipedia and may be reused under a CC BY-SA license.Depending on the category of manifolds (differentiable, piecewise-linear, or topological), there are similarly defined, butinequivalent, concepts of normal maps and normal invariants.
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This example is from Wikipedia and may be reused under a CC BY-SA license.These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors.