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 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.

If, at any time during the assignment pass, the compiler finds that there are no more index words available for assignment, the warning message `` No More Index Words Available '' will be placed in the object program listing, the table will be altered to show that index words 1 through 96 are available, and the assignment will continue as before.

If the compiler finds that there are no more electronic switches available for assignment, the warning message `` No More Electronic Switches Available '' will be placed in the object program listing, the table will be altered to show that electronic switches 1 through 30 are available, and assignment will continue as before.

More formally a k-combination of a set S is a subset of k distinct elements of S. If the set has n elements the number of k-combinations is equal to the binomial coefficient

These include " Seasons Change " by Exposé, " Thinking of You " by Sa-Fire, " One More Try " by Timmy T, " Because I Love You ( The Postman Song )" by Stevie B, and " If Wishes Came True " by Sweet Sensation.

* plus VII: A-Ha's " Take on Me ", Gordon Lightfoot's " If You Could Read My Mind ", Amy Grant's " Good For Me ", Aretha Franklin's "( You Make Me Feel Like ) A Natural Woman " ( also Carole King ), Elvis Costello and the Attractions ' " Everyday I Write The Book ", and the Traveling Wilburys ' " Not Alone Any More ".

Sabata and If You Meet Sartana Pray for Your Death, directed by Gianfranco Parolini introduces into similar betrayal environments a kind of hero molded on the Mortimer character from For a Few Dollars More, only without any vengeance motive and with more outrageous trick weapons.

More precisely, if A is a finite set of generators for G then the word problem is the membership problem for the formal language of all words in A and a formal set of inverses that map to the identity under the natural map from the free monoid with involution on A to the group G. If B is another finite generating set for G, then the word problem over the generating set B is equivalent to the word problem over the generating set A.

Peroutka's last drama was named Kdybych se ještě jednou narodil (" If I Was Born One More Time ").

): More What If?

More generally, it might be asked " If the world is completely in my head, how come I don't live the most fantastic life imaginable?

Songs covered by Lost Dogs on an album or in concert include Bob Dylan's " Lord, Protect My Child ," Leonard Cohen's " If It Be Your Will ," The Beatles ' " I'm A Loser ," " The Chipmunk Song ( Christmas Don't Be Late )", and Stephen Foster's " Hard Times, Come Again No More.

More importantly, If the pilum struck the shield of an enemy it would embed itself into the shield's fabric, and this along with the bending of the shank would cause the shield to become unwieldy, forcing the enemy to discard it or waste time trying to pull it out.

The group had a string of international hit singles including " I Ran ( So Far Away )", " Space Age Love Song ," " Wishing ( If I Had a Photograph of You )" and " The More You Live, the More You Love ", and became notable in the 1980s for their MTV video for the song " I Ran ( So Far Away )".

These include: Oleta Adams " Circle of One " album ( reaching No. 1 in the UK charts 1991 ); Marc Almond " Tenement Symphony " album which included the epic tracks " Jacky " and " The Days of Pearly Spencer "; The Associates " Wild and Lonely " album ; Rick Astley " Free " album ; B * Witched " Awake and Breathe " album ; Chris Botti " Slowing Down the World " album ; Boyzone " A Different Beat " album ; Cher " It's a Man's World " album ; Petula Clark " La Vie en Rose " track ; Lloyd Cole and the Commotions " Rattlesnakes " album ; Andrea Corr " Ten Feet High " album ; Cathy Dennis " Move to This " and " Into the Skyline " albums ; Electronic " Getting Away with It " single ( reaching No. 12 in the UK charts 1990 ); Frankie Goes to Hollywood " Welcome to the Pleasuredome " album which included their 2nd and 3rd No. 1s " Two Tribes " and " The Power of Love "; Elton John " The Big Picture " album ; Martyn Joseph " Being There " album ; Kingmaker " Sleepwalking " album ; Annie Lennox " Medusa " album ( No. 1 in the UK charts 1995 ); Let Loose " Best In Me " single ; Virginia MacNaughton " The Music " album ; Paul McCartney " Press to Play " album ; Malcolm McLaren " Duck Rock " album ; The Men They Couldn't Hang " A Map Of Morocco " single ; George Michael " Careless Whisper " single ( reaching No. 1 in 25 countries ); Liza Minnelli " Results " album ( reaching No. 6 in the UK charts 1989 ); The Moody Blues " Greatest Hits " album ; Moist " Gasoline " single ; Jimmy Nail " Crocodile Shoes " album ( reaching No. 2 in the UK charts 1994 ); The Painted Word " Lovelife " album ; Pet Shop Boys " Very " album ; Pulp " Different Class " and " This Is Hardcore " albums ( both reaching No. 1 ); Rialto " Monday Morning 5: 19 " single ; Frances Ruffelle " Stranger To The Rain " single ; S Club " 7 album " ( No. 1 in the UK charts 2000 ); Scarlet " Naked " album ; Seal first 3 albums " Seal " " Seal II " " Human Being "; Siphiwo " Hope " album ( featuring Nelson Mandela on the title track ); Wendy Stark " Stark " album ; Rod Stewart " A Spanner in the Works " album and " If We Fall in Love Tonight " album and the single " Downtown Train "; Suggs " The Lone Ranger " album ; Travis " More Than Us " EP featuring Anne on the title track ; Tina Turner " Wildest Dreams " album ; Wet Wet Wet " Holding Back the River " album ( reaching No. 2 in the UK charts 1989 ); Wham!

She performed three tracks solo (" Love Me No More ", " Stay With Me Till Dawn " and " If ( When You Go )") accompanied by a string quartet.

* If a hole card is exposed prior to the dealer announcing No More Bets, all hands shall be void.

If M is a differentiable manifold, a real or complex-valued function ƒ on M is said to be differentiable at a point p if it is differentiable with respect to some ( or any ) coordinate chart defined around p. More generally, if M and N are differentiable manifolds, a function ƒ: M → N is said to be differentiable at a point p if it is differentiable with respect to some ( or any ) coordinate charts defined around p and ƒ ( p ).

If the percentage is under 100 % then your economy is not going well ( More money going out than coming in ).

If you have exploited tragedy for its humor, how do you get around a happy ending ?... More than any other Simon play, ' God's Favorite ' depends heavily on its staging and setting.

* Dog Eat Dog covered " More Beer " on its extended play If These Are The Good Times.

If S is a polytope, then the k-extreme points are exactly the interior points of the k-dimensional faces of S. More generally, for any convex set S, the k-extreme points are partitioned into k-dimensional open faces.

This covariant derivative can be defined using the fact that the space of sections of over M is isomorphic to the space of G-equivariant W-valued functions on P. More generally, the space of k-forms with values in is identified with the space of G-equivariant and horizontal W-valued k-forms on P. If α is such a k-form, then its exterior derivative dα, although G-equivariant, is no longer horizontal.

More precisely, find necessary and sufficient conditions on the tuple ( x < sub > 1 </ sub >, ..., x < sub > n </ sub >) and ( y < sub > 1 </ sub >, ..., y < sub > n </ sub >) separately, so that there is an element of R with the property that x < sub > i </ sub >· r = y < sub > i </ sub > for all i. If D is the set of all R-module endomorphisms of U, then Schur's lemma asserts that D is a division ring, and the Jacobson density theorem answers the question on tuples in the affirmative, provided that the x's are linearly independent over D.

The pair also wrote the opening to the 2011 Emmy Awards, " TV Is a Vast Wonderland "; the opening (" What If Life Were More Like Theater?