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, 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 generally, if the numbers are, the geometric mean satisfies

More important to them than their own fates was that of Opel, for its collapse would mean the loss of the most important employer for the people of Rüsselsheim, who were finding their way home from the chaos of war.

More Probability density function | probability density will be found the closer one gets to the expected ( mean ) value in a normal distribution.

This testimony was extremely dubious: witnesses Richard Southwell and Mr. Palmer both denied having heard the details of the reported conversation, and as More himself pointed out :< Blockquote > " Can it therefore seem likely to your Lordships, that I should in so weighty an Affair as this, act so unadvisedly, as to trust Mr. Rich, a Man I had always so mean an Opinion of, in reference to his Truth and Honesty, ... that I should only impart to Mr. Rich the Secrets of my Conscience in respect to the King's Supremacy, the particular Secrets, and only Point about which I have been so long pressed to explain my self?

More broadly, the term cohabitation can mean any number of people living together.

More precisely, it states that as n gets larger, the distribution of the difference between the sample average S < sub > n </ sub > and its limit µ, when blown up by the factor ( that is ), approximates the normal distribution with mean 0 and variance σ < sup > 2 </ sup >.

More roads add on to car-dependence, which can mean that a new road brings only short-term mitigation of traffic congestion.

( More precisely, the king is set up as a winner, but that doesn't mean it will necessarily take a trick.

More clearly, D ' Souza states, " Today courts wrongly interpret separation of church and state to mean that religion has no place in the public arena, or that morality derived from religion should not be permitted to shape our laws.

More recently, critical theorists such as Nikolas Kompridis have voiced opposition to Habermas, claiming that he has undermined the aspirations for social change which originally gave purpose to critical theory's various projects — for example the problem of what reason should mean, the analysis and enlargement of " conditions of possibility " for social emancipation, and the critique of modern capitalism.

More recent measurements seem to point to more encouraging values for the α-sticking probability, finding the α-sticking probability to be about 0. 5 % ( or perhaps even about 0. 4 % or 0. 3 %), which could mean as many as about 200 ( or perhaps even about 250 or about 333 ) muon-catalyzed d-t fusions per muon.

More specialised decision making structures mean councillors are expected to perform a range of different roles, such as ; policy overview & scrutiny, executive decision making, political leadership, determining planning applications and community representation.

More recently, IBM defined an XCOFF64 version supporting 64-bit AIX, and used XCOFF32 to mean the original file format.

More supersymmetries would mean the particles would have superpartners with spins higher than 2.

More simply, in general computer terminology, it can mean simply the total number of instructions executed from point A to point B in a program-Instruction path length.

More specifically, a vector field can mean a section of the tangent bundle.

) More commonly, however, the expected value ( mean or average ) of the sampled values is chosen ; this is a Bayes estimator that takes advantage of the additional data about the entire distribution that is available from Bayesian sampling, whereas a maximization algorithm such as expectation maximization ( EM ) is capable of only returning a single point from the distribution.

More generally, rates on a long-term instrument are equal to the geometric mean of the yield on a series of short-term instruments.

More recently the term has come to mean 1st person RPGs, particularly ones which are aligned to a grid system and can be mapped on graph paper.

More generally, for a hypersurface the mean curvature is given as

More importantly one must study the values of different people to understand what situations would have meant to people, that in the actor's own culture might mean nothing.

More money for the fort will also mean it is able to stay open longer.

More recently, the first year results from the SMART Study ( Stabilizing Myopia by Accelerated Reshaping Technique ) – a five-year longitudinal study currently underway in the Greater Chicago area – show a statistically significant difference for children in the treatment group wearing orthokeratology lenses who exhibited no overall prescription change against children in the control group wearing conventional soft contact lenses for whom there was a mean increase in myopia of 0. 40 diopters.

More humorously, the 1911 edition of the Encyclopædia Britannica suggested another perfectly logical English version, " Your Transparency ", based on a literal translation of German " durch ", which can also mean " through ", or " more thoroughly ", and "- laucht ", as in " Erlaucht " ( illustrious ), meaning radiant — in other words, something that lets light through: something transparent.