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A related concept is the isolating language, one in which there is only one, or on average close to one, morpheme per word. Not all analytic languages are isolating; for example, Chinese and English possess many compound words, but contain few inflections for them.
The second reason for considering only square-free polynomials is that the fastest root-isolation algorithms do not work in the case of multiple roots. For root isolation, one requires a procedure for counting the real roots of a polynomial in an interval without having to compute them, or, at least a procedure for deciding whether an interval ...
An isolating language is a type of language with a morpheme per word ratio close to one, and with no inflectional morphology whatsoever. In the extreme case, each word contains a single morpheme. Examples of widely spoken isolating languages are Yoruba [1] in West Africa and Vietnamese [2] [3] (especially its colloquial register) in Southeast Asia.
A typical example is a language that has nominative-accusative marking on verbs and ergative–absolutive case marking on nouns. Georgian has an ergative alignment, but the agent is only marked with the ergative case in the perfective aspect (also known as the "aorist screeve ").
In his fundamental papers, [1] [2] [3] Vincent presented examples that show precisely how to use his theorem to isolate real roots of polynomials with continued fractions. However the resulting method had exponential computing time, a fact that mathematicians must have realized then, as was realized by Uspensky [ 8 ] p. 136, a century later.
In theoretical computer science, the term isolation lemma (or isolating lemma) refers to randomized algorithms that reduce the number of solutions to a problem to one, should a solution exist. This is achieved by constructing random constraints such that, with non-negligible probability, exactly one solution satisfies these additional ...
In complex analysis, a branch of mathematics, an isolated singularity is one that has no other singularities close to it. In other words, a complex number z 0 is an isolated singularity of a function f if there exists an open disk D centered at z 0 such that f is holomorphic on D \ {z 0}, that is, on the set obtained from D by taking z 0 out.
For example, Proto-Indo-European had much more complex grammatical conjugation, grammatical genders, dual number and inflections for eight or nine cases in its nouns, pronouns, adjectives, numerals, participles, postpositions and determiners, Standard English has lost nearly all of them (except for three modified cases for pronouns) along with ...
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