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A cyclic group is a group which is equal to one of its cyclic subgroups: G = g for some element g, called a generator of G. For a finite cyclic group G of order n we have G = {e, g, g 2, ... , g n−1}, where e is the identity element and g i = g j whenever i ≡ j (mod n); in particular g n = g 0 = e, and g −1 = g n−1.
A cyclic permutation consisting of a single 8-cycle. There is not widespread consensus about the precise definition of a cyclic permutation. Some authors define a permutation σ of a set X to be cyclic if "successive application would take each object of the permuted set successively through the positions of all the other objects", [1] or, equivalently, if its representation in cycle notation ...
Cyclic stress is the distribution of forces (aka stresses) that change over time in a repetitive fashion. As an example, consider one of the large wheels used to drive an aerial lift such as a ski lift .
In geometry, a cyclic quadrilateral or inscribed quadrilateral is a quadrilateral (four-sided polygon) whose vertices all lie on a single circle, making the sides chords of the circle. This circle is called the circumcircle or circumscribed circle , and the vertices are said to be concyclic .
Cyclic history, a theory of history; Cyclical theory, a theory of American political history associated with Arthur Schlesinger, Sr. Social cycle, various cycles in social sciences Business cycle, the downward and upward movement of gross domestic product (GDP) around its ostensible, long-term growth trend
Cyclic is the maximum rate of fire given only mechanical function, not taking into account degradation of function due to heat, wear, or ammunition constraints. Sustained is the maximum efficient rate of fire given the time taken to load the weapon and keep it cool enough to operate.
These include simple cycle graph and cyclic graph, although the latter term is less often used, because it can also refer to graphs which are merely not acyclic. Among graph theorists, cycle , polygon , or n -gon are also often used.
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. [2]