Results for medial
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medial

  (mē'dē-əl) pronunciation
adj.
  1. Relating to, situated in, or extending toward the middle; median.
  2. Linguistics. Being a sound, syllable, or letter occurring between the initial and final positions in a word or morpheme.
  3. Mathematics. Being or relating to an average or a mean.
  4. Average; ordinary.
n. Linguistics.
  1. A voiced stop, such as (b), (d), or (g). Also called media.
  2. A sound, letter, or form of a letter that is neither initial nor final.

[Late Latin mediālis, from Latin medius, middle.]

medially me'di·al·ly adv.
 
 
Thesaurus: medial

adjective

  1. At, in, near, or being the center: center, central, median, mid, middle. See edge/center.
  2. Not extreme: central, intermediate, mean3, median, mid, middle, middle-of-the-road, midway. See edge/center.

 
Dental Dictionary: medial
(me'de-əl)
adj

Located in or directed toward the middle; closer to the body’s midline.

 
Sports Science and Medicine: medial

Toward the midline of the body.

 
Veterinary Dictionary: medial

Pertaining to or situated toward the midline.

  • m. nasal process — one of the frontal processes derived from frontonasal mesenchyme and forming part of the border of the nasal pits, the future nostrils.
  • m. palatine process — see palatine process.
  • m. patellar ligament — in the species in which the tendon is trifurcated (horse, cattle), the largest and most medial of the three patellar ligaments.
 
Wikipedia: medial
This article is about medial in mathematics. For other uses, see medial (disambiguation).

In abstract algebra, a medial magma (or medial groupoid) is a set with a binary operation which satisfies the identity

(x \cdot y) \cdot (u \cdot z) = (x \cdot u) \cdot (y \cdot z), or more simply, xy\cdot uz = xu\cdot yz

using the convention that juxtaposition has higher precedence. This identity has been variously called medial, abelian, alternation, transposition, bi-commutative, bisymmetric, surcommutative, entropic, etc.[1]

Any commutative semigroup is a medial magma, and a medial magma has an identity element if and only if it is a commutative monoid. An elementary example of a nonassociative medial quasigroup can be constructed as follows: take an abelian group (written additively) and define a new operation by x * y = (− x) + (− y).

A magma M is medial if and only if its binary operation is a homomorphism from the Cartesian square M x M to M. This can easily be expressed in terms of a commutative diagram, and thus leads to the notion of a medial magma object in a category with a cartesian product. (See the discussion in auto magma object.)

If f and g are endomorphisms of a medial magma, then the mapping f.g defined by pointwise multiplication

(f\cdot g)(x) = f(x)\cdot g(x)

is itself an endomorphism.

See also

External links

  1. ^ Historical comments J.Jezek and T.Kepka: Medial groupoids Rozpravy CSAV, Rada mat. a prir. ved 93/2 (1983), 93 pp

This entry is from Wikipedia, the leading user-contributed encyclopedia. It may not have been reviewed by professional editors (see full disclaimer)

 
Translations: Translations for: Medial

Dansk (Danish)
adj. - midt-, midter-, i midten, middelstor
n. - medial (fonetisk)

Nederlands (Dutch)
middel-, midden-, gemiddeld, mediaal

Français (French)
adj. - (Ling) médial, médian (position), (Math) moyen
n. - (Phon) médiale

Deutsch (German)
adj. - mittler, medial
n. - Media

Ελληνική (Greek)
adj. - διάμεσος, μεσαίος, μέσος
n. - μεσαίο γράμμα

Italiano (Italian)
medio, mediano

Português (Portuguese)
adj. - mediano
n. - letra média (f) (Gram.)

Русский (Russian)
средний, медиальный

Español (Spanish)
adj. - central, medial
n. - letra del medio, letra interna

Svenska (Swedish)
adj. - medial, mitt-, genomsnitts-
n. - inljud

中文（简体） (Chinese (Simplified))
中间的, 普通的, 平均的, 中间字母

中文（繁體） (Chinese (Traditional))
adj. - 中間的, 普通的, 平均的
n. - 中間字母

한국어 (Korean)
adj. - 중앙의, 일반적인, 기준의
n. - 중간, 평균

日本語 (Japanese)
adj. - 中間の, 平均の, 中央の, 語中の

العربيه (Arabic)
‏(صفه) توسطي (الاسم) متوسط‏

עברית (Hebrew)
adj. - ‮ממוצע, תיכון, אמצעי‬
n. - ‮ממוצע, צליל אמצעי (פונטיקה)‬

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Copyrights:

Dictionary. The American Heritage® Dictionary of the English Language, Fourth Edition Copyright © 2007, 2000 by Houghton Mifflin Company. Updated in 2007. Published by Houghton Mifflin Company. All rights reserved.  Read more
Thesaurus. Roget's II: The New Thesaurus, Third Edition by the Editors of the American Heritage® Dictionary Copyright © 1995 by Houghton Mifflin Company. Published by Houghton Mifflin Company. All rights reserved.  Read more
Dental Dictionary. Mosby's Dental Dictionary. Copyright © 2004 by Elsevier, Inc. All rights reserved.  Read more
Sports Science and Medicine. The Oxford Dictionary of Sports Science & Medicine. Copyright © Michael Kent 1998, 2006, 2007. All rights reserved.  Read more
Veterinary Dictionary. Saunders Comprehensive Veterinary Dictionary 3rd Edition. Copyright © 2007 by D.C. Blood, V.P. Studdert and C.C. Gay, Elsevier. All rights reserved.  Read more
Wikipedia. This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Medial".  Read more
Translations. Copyright © 2007, WizCom Technologies Ltd. All rights reserved.  Read more

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