Help


[permalink] [id link]
+
Page "Characteristic class" ¶ 22
from Wikipedia
Edit
Promote Demote Fragment Fix

Some Related Sentences

More and abstractly
More abstractly, one talks about the product in category theory, which formalizes these notions.
More abstractly, Campbell's idea that myths are how we shape our lives deeply informs the picture of life in Glorantha throughout the game world's publication history.
More abstractly, the convex-hull operator Conv () has the characteristic properties of a closure operator:
More abstractly, one can define the dicyclic group Dic < sub > n </ sub > as any group having the presentation
More abstractly, when using infix notation
More abstractly, the symplectic group can be defined as the set of linear transformations of a 2n-dimensional vector space over F that preserve a nondegenerate, skew-symmetric, bilinear form.
More abstractly, in classical mechanics phase space is the cotangent space of configuration space, and in this interpretaton the procedure above expresses that a choice of local coordinates on configuration space induces a choice of natural local Darboux coordinates for the standard symplectic structure on a cotangent space.
More abstractly and more precisely, it may be taken to ask whether specified axioms of Euclidean geometry concerning the existence of lines and circles entail the existence of such a square.
More abstractly, the integral can be written as the cap product of the homology class of Z and the cohomology class represented by α.
More abstractly, it can be defined as an incidence structure ( P, L, I ) consisting of a set P of points, a set L of lines, and an incidence relation I stating which points lie on which lines.
More generally and abstractly, given any group G and a representation of G on a vector space V,
so too is the dual group More abstractly, these are both examples of representable functors, being represented respectively by K and T.
The order of PSL ( n, q ) is the above, divided by, the number of scalar matrices with determinant 1 – or equivalently dividing by, the number of classes of element that have no nth root, or equivalently, dividing by the number of nth roots of unity in .< ref group =" note "> These are equal because they are the kernel and cokernel of the endomorphism formally, More abstractly, the first realizes PSL as SL / SZ, while the second realizes PSL as the kernel of
More abstractly, a conservative vector field is an exact 1-form.
More generally, if W is a linear subspace of a ( possibly infinite dimensional ) vector space V then the codimension of W in V is the dimension ( possibly infinite ) of the quotient space V / W, which is more abstractly known as the cokernel of the inclusion.
More abstractly, it studies how global properties of a graph influence local substructures of the graph.
More abstractly, the mean curvature is the trace of the second fundamental form divided by n ( or equivalently, the shape operator ).
More abstractly, some aspects of the narrative appear in the crucifixion story of Jesus found in the gospels.
More abstractly: If X < sub > 1 </ sub >, ..., X < sub > n + 1 </ sub > are conditionally independent random variables that each can assume the value 0 or 1, then, if we know nothing more about them,
More abstractly and generally, we note that the two quantities asserted to be equal count the subsets of size k and n − k, respectively, of any n-element set S. There is a simple bijection between the two families F < sub > k </ sub > and F < sub > n − k </ sub > of subsets of S: it associates every k-element subset with its complement, which contains precisely the remaining n − k elements of S. Since F < sub > k </ sub > and F < sub > n − k </ sub > have the same number of elements, the corresponding binomial coefficients must be equal.
More abstractly, the " pay-off set " ( i. e., the set of all plays in which the angel wins ) is a closed set ( in the natural topology on the set of all plays ), and it is known that such games are determined.
More abstractly, f is proper if for any space Z the map
More abstractly, " G-bundles over X " is a functor in G: given a map H → G, one gets a map from H-bundles to G-bundles by inducing ( as above ).
More abstractly, a natural class of objects to study in topology are objects that are homogeneous ( all points are topologically the same: the group of self-homeomorphisms acts transitively ) and " finite type " or " tame " ( to rule out spaces such as the Cantor set, where each open set contains uncountably many connected components ); more generally, a space of " finite type " where the self-homeomorphism group has finitely many orbits, forming the strata.

More and means
More formally, a " representation " means a homomorphism from the group to the automorphism group of an object.
More idealized motion in the " sublunary " realm could only be achieved through artifice, and prior to the 17th century, many did not view artificial experiments as a valid means of learning about the natural world.
More formally, if a, b, c, and d are all integers, then the fraction < sup > a </ sup >⁄< sub > b </ sub > is irreducible if and only if there is no other equal fraction < sup > c </ sup >⁄< sub > d </ sub > such that | c | < | a | or | d | < | b |, where | a | means the absolute value of a.
More specifically, a motion picture manuscript is called a screenplay ; a television manuscript, a teleplay ; a manuscript for the theatre, a stage play ; and a manuscript for audio-only performance is often called a radio play, even when the recorded performance is disseminated via non-radio means.
More used the novel describing an imaginary nation as a means of freely discussing contemporary controversial matters ; speculatively, he based Utopia on monastic communalism, based upon the biblical communalism in the Acts of the Apostles.
More than two teleprinters could be connected to the same wire circuit by means of a current loop.
More ecologically friendly means are being tested as an alternative to chemical treatments.
More sophisticated cryptographic systems, such as Anonymous Digital credentials, enable users to communicate pseudonymously ( i. e., by identifying themselves by means of pseudonyms ).
More eyes means better weight and stress distribution throughout the parabolic arc.
More generally, in the particular case of two planets, it means that they merely have the same right ascension ( and hence the same hour angle ).
More than one year later, all diplomatic means having been exhausted, on 10 July 1739 King George II authorized the Admiralty Board to seek maritime reprisals against Spain.
More complex means of measuring well-being must be employed to make such judgements, and these are very often political, thus controversial.
More drives in the array means higher bandwidth, but greater risk of data loss.
More recently, light therapy and melatonin administration have been explored by Dr. Alfred J. Lewy ( OHSU ), Dr. Josephine Arendt ( University of Surrey, UK ) and other researchers as a means to reset animal and human circadian rhythms.
: More typically, solving a game means providing an algorithm that secures a win for one player, or a draw for either, against any possible moves by the opponent, from the beginning of the game.
More and more PACS include web-based interfaces to utilize the internet or a Wide Area Network as their means of communication, usually via VPN ( Virtual Private Network ) or SSL ( Secure Sockets Layer ).
More modern spinning machines use a mechanical means to rotate the spindle, as well as an automatic method to draw out fibers, and devices to work many spindles together at speeds previously unattainable.
( More adjectives means the non-call was more questionable.
More advanced training consists of taking the attackers mind by means of pain through various techniques.
More often than not Sir Humphrey prevents him from achieving his goal while mollifying Hacker with some positive publicity or at least a means to cover up his failure.
More specifically, in musical notation, sharp means " higher in pitch by a semitone ( half step )," and has an associated symbol (), which may be found in key signatures or as an accidental, as may flats.
More specifically, in music notation, flat means, " lower in pitch by a semitone ( half step )," and has an associated symbol (), which is a stylised lowercase " b " that may be found in key signatures or as an accidental, as may sharps.
More important, because the presence of magnetite gives the basalt measurable magnetic properties, these magnetic variations have provided another means to study the deep ocean floor.
More common " base " metals can only be protected by more temporary means.
More directly, fornicatio means " done in the archway "; thus it originally referred to prostitution.

0.222 seconds.