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: 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.

The same sort of thinking plays so large a part in both Babbitt and More, that we must examine it in some detail.

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.

The medieval was the most important to Chambers because he sought to place Thomas More, the author of Utopia, in some intelligible relation with St. Thomas More, the martyr.

More formally, the complexity of a string is the length of the shortest possible description of the string in some fixed universal description language ( the sensitivity of complexity relative to the choice of description language is discussed below ).

More significant was the discovery of fossilised bones of " some quadruped much larger than the ox or buffalo " in the Wellington Caves in mid-1830 by bushman George Rankin and later by Thomas Mitchell.

More commonly it is fired in a kiln of some sort to form a true ceramic.

More recently it has been used for fraternal associations of some sovereign nations.

More recently, personal symbols reflecting some aspect of their character have been used.

More commonly, and more pertinent to recent history, leaders merely claim some form of divine mandate, suggesting that their rule is in accordance with the will of God.

More at ease, the Emperor went to his desk to sign some decrees, where he was suddenly approached by Stephanus:

More than the name separates each church example :" Independent Christian Church " will not accept a woman as a minister when some of the " Disciples of Christ " congregation will.

More recently the Exile games have been remade as the Avernum series, which replaced the two-dimensional tile-based graphics system with an isometric one and made numerous changes to the RPG system and some changes to the content.

More often, however, players use the fourth valve in place of the first and third valve combination, which is somewhat sharp ( compensated for on trumpets and cornets and some three-valve flugelhorns by a slide for the first or third valve ).

More recently, dietary habits have been influenced by the concerns that some people have about possible impacts on health or the environment from genetically modified food.

They helped to make stars of actors like John Mills, Jack Hawkins and Kenneth More, and some of the most successful included The Cruel Sea ( 1953 ), The Dam Busters ( 1954 ), The Colditz Story ( 1955 ) and Reach for the Sky ( 1956 ).

* More ambitious 4GLs ( sometimes termed fourth generation environments ) attempt to automatically generate whole systems from the outputs of CASE tools, specifications of screens and reports, and possibly also the specification of some additional processing logic.

More controversially, some people define folk dancing as dancing for which there is no governing body or dancing for which there are no competitive or professional performances.

More are found in the surrounding countryside, some join with Xavier.

More popular in the United States is the landau style, with a heavily-padded leather or ( later ) vinyl roof, and long blind rear quarters, similarly covered, and decorated with large metal S-shaped bars designed to resemble those used to lower the tops on some horse-drawn coaches.

More severe withdrawal symptoms which occur can include seizures ( some of which can be fatal ), visual and auditory hallucinations, suicidal ideation, extremely severe panic attacks, depersonalization, tremors, delirium, delirium tremens and if not treated as an emergency by a proper medical staff death from a seizure can occur.

More typically the bottom is now heavier than the top ( but in some cases like the K Zildjian Steve Gadd Session Hats the pattern is reversed for a cleaner chick and cleaner sticking ), and may also be vented, this being one innovation to have caught on.

More broadly the term is used in a wide number of contexts for an image, picture, or representation ; it is a sign or likeness that stands for an object by signifying or representing it either concretely or by analogy, as in semiotics ; by extension, icon is also used, particularly in modern culture, in the general sense of symbol — i. e. a name, face, picture, edifice or even a person readily recognized as having some well-known significance or embodying certain qualities: one thing, an image or depiction, that represents something else of greater significance through literal or figurative meaning, usually associated with religious, cultural, political, or economic standing.

"</ ref > More recently, studies have suggested that sibling incest, particularly older brothers having sexual relations with younger siblings, is the most common form of incest, with some studies finding sibling incest occurring more frequently than other forms of incest.

More advanced statistical methods employed by some I – O psychologists include logistic regression, multivariate analysis of variance, structural equation modeling, and hierarchical linear modeling ( HLM ; also known as multilevel modeling ).