Definitions for acnode
ac·n·ode

WiktionaryRate this definition:0.0 / 0 votes

1. acnodenoun

   An isolated point not upon a curve, but whose coordinates satisfy the equation of the curve so that it is considered as belonging to the curve.

2. Etymology: acus + nodus

WikipediaRate this definition:0.0 / 0 votes

1. Acnode

   An acnode is an isolated point in the solution set of a polynomial equation in two real variables. Equivalent terms are "isolated point or hermit point".For example the equation f ( x , y ) = y 2 + x 2 − x 3 = 0 {\displaystyle f(x,y)=y^{2}+x^{2}-x^{3}=0} has an acnode at the origin, because it is equivalent to y 2 = x 2 ( x − 1 ) {\displaystyle y^{2}=x^{2}(x-1)} and x 2 ( x − 1 ) {\displaystyle x^{2}(x-1)} is non-negative only when x {\displaystyle x} ≥ 1 or x = 0 {\displaystyle x=0} . Thus, over the real numbers the equation has no solutions for x < 1 {\displaystyle x<1} except for (0, 0). In contrast, over the complex numbers the origin is not isolated since square roots of negative real numbers exist. In fact, the complex solution set of a polynomial equation in two complex variables can never have an isolated point. An acnode is a critical point, or singularity, of the defining polynomial function, in the sense that both partial derivatives ∂ f ∂ x {\displaystyle \partial f \over \partial x} and ∂ f ∂ y {\displaystyle \partial f \over \partial y} vanish. Further the Hessian matrix of second derivatives will be positive definite or negative definite, since the function must have a local minimum or a local maximum at the singularity.

Webster DictionaryRate this definition:0.0 / 0 votes

1. Acnodenoun

   an isolated point not upon a curve, but whose coordinates satisfy the equation of the curve so that it is considered as belonging to the curve

2. Etymology: [L. acus needle + E. node.]

WikidataRate this definition:0.0 / 0 votes

1. Acnode

   An acnode is an isolated point not on a curve, but whose coordinates satisfy the equation of the curve. The term "isolated point" or "hermit point" is an equivalent term. Acnodes commonly occur when studying algebraic curves over fields which are not algebraically closed, defined as the zero set of a polynomial of two variables. For example the equation has an acnode at the origin of, because it is equivalent to and is non-negative when ≥ 1 and when . Thus, over the real numbers the equation has no solutions for except for. In contrast, over the complex numbers the origin is not isolated since square roots of negative real numbers exist. An acnode is a singularity of the function, where both partial derivatives and vanish. Further the Hessian matrix of second derivatives will be positive definite or negative definite. Hence the function has a local minimum or a local maximum.

Anagrams for acnode »

1. canoed

2. deacon

How to pronounce acnode?

1. Alex

   US English

   David

   US English

   Mark

   US English

   Daniel

   British

   Libby

   British

   Mia

   British

   Karen

   Australian

   Hayley

   Australian

   Natasha

   Australian

   Veena

   Indian

   Priya

   Indian

   Neerja

   Indian

   Zira

   US English

   Oliver

   British

   Wendy

   British

   Fred

   US English

   Tessa

   South African

How to say acnode in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of acnode in Chaldean Numerology is: 7

2. Pythagorean Numerology

   The numerical value of acnode in Pythagorean Numerology is: 6

References

1. ^ Wiktionary
   https://en.wiktionary.org/wiki/Acnode
2. ^ Wikipedia
   https://en.wikipedia.org/wiki/Acnode
3. ^ Webster Dictionary
   https://www.merriam-webster.com/dictionary/acnode
4. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=acnode