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Fuchsian groups are, by definition, discrete subgroups of the isometry group of the hyperbolic plane. A Fuchsian group that preserves orientation and acts on the upper half-plane model of the hyperbolic plane is a discrete subgroup of the Lie group PSL(2, R ), the group of orientation preserving isometries of the upper half-plane model of the ...
An advantage of overlapping generations can be found in the different experience levels of generations in a population. The younger age group will be able to acquire social information from the older and more experienced age groups. [3] Overlapping generations can, similarly, promote altruistic behaviour. [4]
This glossary of biology terms is a list of definitions of fundamental terms and concepts used in biology, the study of life and of living organisms.It is intended as introductory material for novices; for more specific and technical definitions from sub-disciplines and related fields, see Glossary of cell biology, Glossary of genetics, Glossary of evolutionary biology, Glossary of ecology ...
Many commonly named groups – rodents and insects, for example – are clades because, in each case, the group consists of a common ancestor with all its descendant branches. Rodents, for example, are a branch of mammals that split off after the end of the period when the clade Dinosauria stopped being the dominant terrestrial vertebrates 66 ...
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A whole set of terms including taxonomy, systematic biology, systematics, scientific classification, biological classification, and phylogenetics have at times had overlapping meanings – sometimes the same, sometimes slightly different, but always related and intersecting. [1] [11] The broadest meaning of "taxonomy" is used here.
The definition of amenability is simpler in the case of a discrete group, [4] i.e. a group equipped with the discrete topology. [5] Definition. A discrete group G is amenable if there is a finitely additive measure (also called a mean)—a function that assigns to each subset of G a number from 0 to 1—such that
A discrete subgroup of a topological group G is a subgroup H whose relative topology is the discrete one. For example, the integers, Z, form a discrete subgroup of the reals, R (with the standard metric topology), but the rational numbers, Q, do not. A lattice in a locally compact topological group is a discrete subgroup with the property that ...
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