hyperlinearとは 意味・読み方・使い方

形容詞

hyperlinear ‎(comparative more hyperlinear, superlative most hyperlinear)

1. (dermatology) Having unusually pronounced creases marking the skin.
   • 2015, Thomas P. Habif, Clinical Dermatology, ISBN 032326607X, page 165:

     Atopic patients with ichthyosis vulgaris often have keratosis pilaris and hyperlinear, exaggerated palm creases.

2. (mathematics, of groups) Displaying a generalization of sofic that applies to finite-dimensional Hilbert spaces.
   • 2010, Tullio Ceccherini-Silberstein, & ‎Michel Coornaert, Cellular Automata and Groups, ISBN 3642140343, page 277:

     Indeed, by a profound result of E. Kirchberg, F. Radulescu and N. Ozawa, a group is hyperlinear if and only if it satisfies the Connes embedding conjecture for groups, that is, if and only if its von Neumann algebra embeds into an ultrapower of the hyperfinite II₁ factor R.

3. (mathematics, of a function of hyperreals) Both additive and homogeneous for hyperreal scalars.
   • 1986, Functiones Et Approximatio Commentarii Mathematici:

     We say that a hyperlinear fuzzy function, f say, strictly separates two fuzzy subsets A and B iff the fuzzy hyperplane determined by f and some point x₀ ϵ X strictly separates A and B

4. (mathematics, of a sequence) Converging very quickly to a limit so that the ratio of adjacent terms tends to zero.
   • 2007, William H. Press, Numerical Recipes 3rd Edition: The Art of Scientific Computing, ISBN 0521880688:

     We see that hyperlinear convergence doesn't necessarily imply that the series is easy to evaluate for all values of x.

5. (mathematics, curve fitting) Increasing exponentially or as a higher polynomial power.
   • 1981, Doklady: Proceedings of the Academy of Sciences of the USSR:

     It has been shown in [3] that, at low excitation intensities, the dependence of the emission intensity from a single crystal of AgBr(I) on the excitation intensity is linear while, at high excitation intensities, it becomes hyperlinear.