Dictionary

hyperlinear en · ADJ

Etymology

From hyper- + linear.

Meanings

1. Having unusually pronounced creases marking the skin.
   • Atopic patients with ichthyosis vulgaris often have keratosis pilaris and hyperlinear, exaggerated palm creases. 2015, Thomas P. Habif, Clinical Dermatology, →ISBN, page 165:
2. (of groups) Displaying a generalization of sofic that applies to finite-dimensional Hilbert spaces.
   • 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. 2010, Tullio Ceccherini-Silberstein, Michel Coornaert, Cellular Automata and Groups, →ISBN, page 277:
3. (of a function of hyperreals) Both additive and homogeneous for hyperreal scalars.
   • 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 1986, Functiones Et Approximatio Commentarii Mathematici:
4. (of a sequence) Converging very quickly to a limit so that the ratio of adjacent terms tends to zero.
   • We see that hyperlinear convergence doesn't necessarily imply that the series is easy to evaluate for all values of x. 2007, William H. Press, Numerical Recipes 3rd Edition: The Art of Scientific Computing, →ISBN:
5. (qualifier:curve fitting) Increasing exponentially or as a higher polynomial power.
   • 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. 1981, Doklady: Proceedings of the Academy of Sciences of the USSR:

Forms