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Continuous vs Positone - What's the difference?

continuous | positone |

As adjectives the difference between continuous and positone

is that continuous is without break, cessation, or interruption; without intervening time while positone is (mathematics) of a particular kind of eigenvalue problem involving a nonlinear function on the reals that is continuous, positive, and monotone.

continuous

English

Adjective

(-)
  • Without break, cessation, or interruption; without intervening time.
    • a continuous current of electricity
  • * 1847 , , Ticknor and Fields (1854), page 90:
    • he can hear its continuous murmur
  • Without intervening space; continued; protracted; extended.
    • a continuous line of railroad
  • (botany) Not deviating or varying from uniformity; not interrupted; not joined or articulated.
  • (analysis, of a function) Such that, for every x'' in the domain, for each small open interval ''D'' about ''f''(''x''), there's an interval containing ''x'' whose image is in ''D .
  • (mathematics, more generally, of a function) Such that each open set in the range has an open preimage.
    • Each continuous function from the real line to the rationals is constant, since the rationals are totally disconnected.
  • (grammar) Expressing an ongoing action or state.

    • Usage notes

    *

    Synonyms

    * (without break, cessation, or interruption in time''): constant, continual (''but see usage notes above ), incessant, never-ending, ongoing, unbroken, unceasing, unending, uninterrupted * (without break, cessation, or interruption in space ): connected, unbroken * See also

    Antonyms

    * (without break, cessation, or interruption in time ): broken, discontinuous, discrete, intermittent, interrupted * (without break, cessation, or interruption in space ): broken, disconnected, disjoint, unbroken * (in mathematical analysis ): discontinuous, stepwise

    Derived terms

    * continuous brake * continuous impost * continuously * continuousness (in mathematics) * continuous distribution * continuous function * continuous group * continuous line illusion * continuous map * continuous mapping theorem * continuous space * continuous vector bundle * continuously differentiable function * uniformly continuous

    Related terms

    * continuity * continued * continuum

    See also

    * constant * contiguous

    References

    positone

    English

    Adjective

    (en adjective)
  • (mathematics) of a particular kind of eigenvalue problem involving a nonlinear function on the reals that is continuous, positive, and monotone.
  • * 2004 , Leszek Gasinski, Nikolaos S. Papageorgiou, Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems , CRC Press, 2004 ISBN 1420035037, page 704
    • Finally, we mention that several papers studied nonlinear eigenvalue problems of the form
  • *::
    • \begin{cases} -\Delta x(z) = \lambda f (x (z)) \text { for a.a. }z \in \Omega, \\ x, _{\partial \Omega},\ x \ge 0 \end{cases}
  • *:for \scriptstyle \lambda\ >\ 0 under the assumption that \scriptstyle f:\ \mathbb R\ \to\ \mathbb R is continuous, positive, monotone. For this reason such problems were named positone'' ... If the nonlinearity \scriptstyle f:\ \mathbb R\ \to\ \mathbb R is continuous, monotone and \scriptstyle f(0)\ <\ 0 ,...the the eigenvalue problem is called ''semipositone ...

    • Derived terms

    *semipositone