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A cyclic pattern, or simply a cycle, occurs when the data exhibit rises and falls in other periods, i.e., much longer (e.g., decadal) or much shorter (e.g., weekly) than seasonal. A quasiperiodicity is a more general, irregular periodicity.
Some free-by-cyclic groups are hyperbolic relative to free-abelian subgroups. More generally, all free-by-cyclic groups are hyperbolic relative to a collection of subgroups that are free-by-cyclic for an automorphism of polynomial growth. [3] [4] Any finitely generated subgroup of a free-by-cyclic group is finitely presented (Feighn and Handel ...
Cyclic sediments (also called rhythmic sediments [1]) are sequences of sedimentary rocks that are characterised by repetitive patterns of different rock types or facies within the sequence. Processes that generate sedimentary cyclicity can be either autocyclic or allocyclic, and can result in piles of sedimentary cycles hundreds or even ...
Equivalently, a group G is polycyclic if and only if it admits a subnormal series with cyclic factors, that is a finite set of subgroups, let's say G 0, ..., G n such that G n coincides with G; G 0 is the trivial subgroup; G i is a normal subgroup of G i+1 (for every i between 0 and n - 1) and the quotient group G i+1 / G i is a cyclic group ...
A link that is fixed in place relative to the viewer is called a ground link. A link connecting to the ground by a revolute joint that can perform a complete revolution is called a crank link. A link connecting to the ground by a revolute joint that cannot perform a complete revolution is called a rocker link.
A heterocyclic compound or ring structure is a cyclic compound that has atoms of at least two different elements as members of its ring(s). [1] Heterocyclic organic chemistry is the branch of organic chemistry dealing with the synthesis, properties, and applications of organic heterocycles .
Suppose a function f(x, y, z) = 0, where x, y, and z are functions of each other. Write the total differentials of the variables = + = + Substitute dy into dx = [() + ()] + By using the chain rule one can show the coefficient of dx on the right hand side is equal to one, thus the coefficient of dz must be zero () + = Subtracting the second term and multiplying by its inverse gives the triple ...
Connes later found a more categorical approach to cyclic homology using a notion of cyclic object in an abelian category, which is analogous to the notion of simplicial object. In this way, cyclic homology (and cohomology) may be interpreted as a derived functor, which can be explicitly computed by the means of the (b, B)-bicomplex.