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,

More abstractly, it means that the cohomology class in the classifying space for pulls back from the cohomology class in under the inclusion ( which corresponds to the inclusion and similar ).

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, " 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 conceptually, this rule expresses the fact that a change in the x < sub > i </ sub > direction may change all of g < sub > 1 </ sub > through g < sub > k </ sub >, and any of these changes may affect f.

Retrieved at < http :// books. google. com / books? id = NztlWQeXf2IC & printsec = frontcover & dq = zhou + enlai & hl = en & ei = wBkuTdKyB4H_8AaJucigAQ & sa = X & oi = book_result & ct = result & resnum = 2 & ved = 0CCsQ6AEwAQ # v = onepage & q & f = false > on March 12, 2011. p. 38 </ ref > More liberal estimates regarding the White Terror in China, estimate it took millions of lives, most of them in the rural areas.

More precisely, if R and S are rings, then a ring homomorphism is a function f: R → S such that

More generally, a twice-differentiable real function f on n real variables has an isolated local minimum at arguments if its gradient is zero and its Hessian ( the matrix of all second derivatives ) is positive definite at that point.

More generally, a function f defined on X is said to be Hölder continuous or to satisfy a Hölder condition of order α > 0 on X if there exists a constant M > 0 such that

More explicitly, an injective continuous map f: X → Y between topological spaces X and Y is a topological embedding if f yields a homeomorphism between X and f ( X ) ( where f ( X ) carries the subspace topology inherited from Y ).

More precisely, the Roche limit is determined by the fact that the function f, which can be regarded as a nonlinear measure of the force squeezing the ellipsoid towards a spherical shape, is bounded so that there is an eccentricity at which this contracting force becomes maximal.

More formally: f ( f ( x )) = f ( x ) for all x.

More generally, if g is an extended real-valued measurable function, nonnegative and nondecreasing on the range of f, then

More precisely, this means to leave f unchanged initially on C < sub > 0 </ sub > := A

) More generally, if f is monotonic, then the least fixpoint of f is the stationary limit of f < sup > α </ sup >( 0 ), taking α over the ordinals, where f < sup > α </ sup > is defined by transfinite induction: f < sup > α + 1 </ sup > = f ( f < sup > α </ sup >) and f < sup > γ </ sup > for a limit ordinal γ is the least upper bound of the f < sup > β </ sup > for all β ordinals less than γ.

More commonly, a function is defined by a formula, or ( more generally ) an algorithm — a recipe that tells how to compute the value of f ( x ) given any x in the domain.

More profound and more disturbing, however, is the moral isolation of Raymond Chandler's Philip Marlowe.

More important is the simple human point that all men suffer, and that it is a kind of anthropological-religious pride on the part of the Jew to believe that his suffering is more poignant than mine or anyone else's.

More than that, Sam Rayburn is the very living symbol of an iron-clad integrity so powerful in his nature and so constantly demonstrated that he can count some of his best friends in the opposition.

More than 50% of all lumber is unitized ; ;

More unitized lumber is being shipped on flat cars, and NLRDA studies show that flat cars loaded with the new Type 6-B floating-load method can be unloaded for as little as $.054/mbf.

More than anything, it is the therapist's intuitive sensing of these latent meanings in the stereotype which helps these meanings to become revealed, something like a spread-out deck of cards, on sporadic occasions over the passage of the patient's and his months of work together.

But to return to the main line of our inquiry, it is doubtful that Utopia is still widely read because More was medieval or even because he was a martyr -- indeed, it is likely that these days many who read Utopia with interest do not even know that its author was a martyr.

Utopia is still widely read because in a sense More stood on the margin of modernity.

we are concerned with Utopian communism -- that is, simply communism as it appears in the imaginary commonwealth of Utopia, as More conceived it.

More rarely, the hymen is so sturdy that it does not yield to penetration.

More typical is the case of a suburban Long Island housewife described by a marriage counselor.

More often, though, he is so accustomed to submitting to authority on the job without argument that he lives by the same rule at home.

More than 10 companies maintain facilities in Dallas and one large manufacturer is located to the north at Sherman.

More than 700 employees make gin machinery that's sold anywhere cotton is grown.

More than 200 are expected at the autumn event which is matched in the spring.

More than 300 teenagers last Sunday proved there is and as many more are expected to prove it again for Jim Kern and his wife Lynn from 4 to 8 p.m. Sunday at First Presbyterian Church.

More than a beautiful visualization of the illustrious adventures and escapades of the tragi-comic knight-errant and his squire, Sancho Panza, in seventeenth-century Spain, this inevitably abbreviated rendering of the classic satire on chivalry is an affectingly warm and human exposition of character.

More recently, Alasdair MacIntyre has attempted to reform what he calls the Aristotelian tradition in a way that is anti-elitist and capable of disputing the claims of both liberals and Nietzscheans.

More rarely, a script may have separate letters for tones, as is the case for Hmong and Zhuang.

More precisely, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function.

More explicitly, it is stating that for every indexed family of nonempty sets there exists an indexed family of elements such that for every.