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English does not generally mark modifiers for restrictiveness, with the exception of relative clauses: non-restrictive ones are set off in speech through intonation (with a pause beforehand and an uninterrupted melody [dubious – discuss]) and in writing by using commas, whereas
For a function to have an inverse, it must be one-to-one.If a function is not one-to-one, it may be possible to define a partial inverse of by restricting the domain. For example, the function = defined on the whole of is not one-to-one since = for any .
English, unlike other West Germanic languages, has a zero relative pronoun (denoted below as ∅)—that is, the relative pronoun is implied and not explicitly written or spoken; it is "unvoiced". This measure is used in restrictive relative clauses (only) as an alternative to voicing that, which or who, whom, etc. in these clauses:
In mathematics, an analytic function is a function that is locally given by a convergent power series. There exist both real analytic functions and complex analytic functions . Functions of each type are infinitely differentiable , but complex analytic functions exhibit properties that do not generally hold for real analytic functions.
One of the earliest, and much studied, work of this genre is Flatland: A Romance of Many Dimensions, an 1884 satirical novella by the English schoolmaster Edwin Abbott Abbott. Mathematical fiction may have existed since ancient times, but it was recently rediscovered as a genre of literature; since then there has been a growing body of ...
The discipline of semantics studies the meaning of language. Formal semantics uses formal tools from the fields of symbolic logic and mathematics to give precise theories of the meaning of natural language expressions. It understands meaning usually in relation to truth conditions, i.e. it examines in which situations a sentence would be true ...
We can state β-acyclicity as the requirement that all subhypergraphs of the hypergraph are α-acyclic, which is equivalent [36] to an earlier definition by Graham. [33] The notion of γ-acyclicity is a more restrictive condition which is equivalent to several desirable properties of database schemas and is related to Bachman diagrams.
In linear algebra, the restricted isometry property (RIP) characterizes matrices which are nearly orthonormal, at least when operating on sparse vectors. The concept was introduced by Emmanuel Candès and Terence Tao [1] and is used to prove many theorems in the field of compressed sensing. [2]