Crossword clues for graded
graded
Longman Dictionary of Contemporary English
The Collaborative International Dictionary
graded \graded\ adj.
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ordered by some quantitative ranking; as, Reading tests of graded difficulty.
Syn: ordered, ranked.
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leveled and drained but not paved; -- of roads.
Syn: graveled.
Wiktionary
Having been smoothed by a grader. v
(en-past of: grade)
WordNet
adj. arranged in a sequence of grades or ranks; "stratified areas of the distribution" [syn: ranked, stratified]
Wikipedia
In mathematics, the term “graded” has a number of meanings, mostly related:
In abstract algebra, it refers to a family of concepts:
- An algebraic structure X is said to be I-graded for an index set I if it has a gradation or grading, i.e. a decomposition into a direct sum X = ⊕ X of structures; the elements of X are said to be “homogeneous of degree i”.
- The index set I is most commonly N or Z, and may be required to have extra structure depending on the type of X.
- Grading by Z (i.e. Z/2Z) is also important.
- The trivial (Z- or N-) gradation has X = X, X = 0 for i ≠ 0 and a suitable trivial structure 0.
- An algebraic structure is said to be doubly graded if the index set is a direct product of sets; the pairs may be called “bidegrees” (e.g. see spectral sequence).
- A I- graded vector space or graded linear space is thus a vector space with a decomposition into a direct sum V = ⊕ V of spaces.
- A graded linear map is a map between graded vector spaces respecting their gradations.
- A graded ring is a ring that is a direct sum of abelian groups R such that RR ⊆ R, with i taken from some monoid, usually N or Z, or semigroup (for a ring without identity).
- The associated graded ring of a commutative ring R with respect to a proper ideal I is grR = ⊕ I/I.
- A graded module is left module M over a graded ring which is a direct sum ⊕ M of modules satisfying RM ⊆ M.
- The associated graded module of an R-module M with respect to a proper ideal I is grM = ⊕ IM/IM.
- A differential graded module , differential graded Z-module or DG-module is a graded module M with a differential d: M → M: M → M making M a chain complex, i.e. d ∘ d = 0 .
- A graded algebra is an algebra A over a ring R that is graded as a ring; if R is graded we also require AR ⊆ A ⊇ RA.
- The graded Leibniz rule for a map d: A → A on a graded algebra A specifies that d(a ⋅ b) = (da) ⋅ b + ( − 1)a ⋅ (db) .
- A differential graded algebra, DG-algebra or DGAlgebra is a graded algebra which is a differential graded module whose differential obeys the graded Leibniz rule.
- A homogeneous derivation on a graded algebra A is a homogeneous linear map of grade d = |D| on A such that D(ab) = D(a)b + ɛaD(b), ɛ = ± 1 acting on homogeneous elements of A.
- A graded derivation is a sum of homogeneous derivations with the same ɛ.
- A DGA is an augmented DG-algebra, or differential graded augmented algebra, (see differential graded algebra).
- A superalgebra is a Z-graded algebra.
- A graded-commutative superalgebra satisfies the “supercommutative” law yx = ( − 1)xy. for homogeneous x,y, where ∣a∣ represents the “parity” of a, i.e. 0 or 1 depending on the component in which it lies.
- CDGA may refer to the category of augmented differential graded commutative algebras.
- A graded Lie algebra is a Lie algebra which is graded as a vector space by a gradation compatible with its Lie bracket.
- A graded Lie superalgebra is a graded Lie algebra with the requirement for anticommutativity of its Lie bracket relaxed.
- A supergraded Lie superalgebra is a graded Lie superalgebra with an additional super Z-gradation.
- A Differential graded Lie algebra is a graded vector space over a field of characteristic zero together with a bilinear map [, ] : L ⊗ L → L and a differential d : L → L satisfying [x, y] = ( − 1)[y, x], for any homogeneous elements x, y in L, the “graded Jacobi identity” and the graded Leibniz rule.
- The Graded Brauer group is a synonym for the Brauer–Wall group BW(F) classifying finite-dimensional graded central division algebras over the field F.
- An A- graded category for a category A is a category C together with a functor F : C → A.
- A differential graded category or ' DG category' is a category whose morphism sets form differential graded Z-modules.
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Graded manifold – extension of the manifold concept based on ideas coming from supersymmetry and supercommutative algebra, including sections on
- Graded function
- Graded vector fields
- Graded exterior forms
- Graded differential geometry
- Graded differential calculus
In other areas of mathematics:
- Functionally graded elements are used in finite element analysis.
- A graded poset is a poset P with a rank function ρ: P → N compatible with the ordering (i.e. $\rho(x) < \rho(x) \implies x < y$) such that y covers $x \implies \rho(y)=\rho(x)+1$ .
Category:Linear algebra
Usage examples of "graded".
The scheme would work, eugenically, in proportion as it is discriminatory and graded.
The canyon floor is littered with lineated fill, frost-shattered from its walls and graded by water or ice flows.
Perry devotes himself mainly to the breeding of graded shorthorn bulls, which he sells when young for L6 per head.
Charlotte Graded School, which position he filled acceptably, until he resigned, during the same year, to accept the superintendency of the Industrial Department of Biddle University, Charlotte.
Man, therefore, lives in part under sensation, for he has the organs of sensation, and in large part even by the merely vegetative principle, for the body grows and propagates: all the graded phases are in a collaboration, but the entire form, man, takes rank by the dominant, and when the life-principle leaves the body it is what it is, what it most intensely lived.
This new wood was interrupted by small patches of rough meadowland and cut by two streams and a railbed that had been graded but never finished with ties and rails.
They are impoverished cultivators and herdsmen who have a strictly graded religiopolitical hierarchy and tend to maintain a more closed community than other ethnic or religious groups.
I introduced myself, and she responded, in a sort of cascade of words, that she was called Setsen, and she was of the Mongol tribe called Kerait, and she was a Nestorian Christian, all the Kerait having been converted, in a bunch, by some long-ago wandering Nestorian bishop, and she had never set foot outside her nameless village in the far-northern fur-trapping country of Tannu-Tuva until she was selected for concubinage and transported to a trading town called Urga, where, to her surprise and delight, the provincial Wang had graded her at twenty-four karats and sent her on south to Khanbalik.
Susan was lovely in her light curls and blue ribbons, and the becoming dress which could not help betraying the modestly emphasized crescendos and gently graded diminuendos of her figure.
They kept themselves back in the days of steamboating supremacy, by a system of wharfage-dues so stupidly graded as to prohibit what may be called small RETAIL traffic in freights and passengers.
Their old-fashioned outlook, their graded snobberies, their mixture of bawdiness and hypocrisy, their extreme gentleness, their deeply moral attitude to life, are all mirrored there.
The drive was graveled and graded smooth, and I shook my head, deciding that I should have asked for more for the chairs.
Big wooden tubs were lifted out and rushed up the beach to a kind of rickety market where, according to Tiger, the awabi were graded and priced.
The separating hedge ran almost beneath Bibbs's window--for this wing of the New House extended here almost to the edge of the lot--and, directly opposite the window, the Vertreeses' lawn had been graded so as to make a little knoll upon which stood a small rustic "summerhouse.
Tommy yanked the wheel to send the Radio Club van sloughing off the graded road onto the sand and gravel slope of the alluvial fan which spilled from the throat of Avalanche Gulch.