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The cube-connected cycles of order n is the Cayley graph of a group that acts on binary words of length n by rotation and flipping bits of the word. [1] The generators used to form this Cayley graph from the group are the group elements that act by rotating the word one position left, rotating it one position right, or flipping its first bit.
A cyclic compound (or ring compound) is a term for a compound in the field of chemistry in which one or more series of atoms in the compound is connected to form a ring. Rings may vary in size from three to many atoms, and include examples where all the atoms are carbon (i.e., are carbocycles), none of the atoms are carbon (inorganic cyclic ...
In continuum mechanics, stress is a physical quantity that describes forces present during deformation. For example, an object being pulled apart, such as a stretched elastic band, is subject to tensile stress and may undergo elongation. An object being pushed together, such as a crumpled sponge, is subject to compressive stress and may undergo ...
Chemical cycling describes systems of repeated circulation of chemicals between other compounds, states and materials, and back to their original state, that occurs in space, and on many objects in space including the Earth. Active chemical cycling is known to occur in stars, many planets and natural satellites.
Heterocyclic organic chemistry is the branch of organic chemistry dealing with the synthesis, properties, and applications of organic heterocycles. [2] Examples of heterocyclic compounds include all of the nucleic acids, the majority of drugs, most biomass (cellulose and related materials), and many natural and synthetic dyes. More than half of ...
Spiro compound. Structure of C 17 H 20, which contains seven spiro atoms and eight cyclopropane rings [1] In organic chemistry, spiro compounds are compounds that have at least two molecular rings sharing one common atom. Simple spiro compounds are bicyclic (having just two rings). [2]: SP-0 [3]: 653, 839 The presence of only one common atom ...
A bicyclic molecule (from bi 'two' and cycle 'ring') is a molecule that features two joined rings. [1] Bicyclic structures occur widely, for example in many biologically important molecules like α-thujene and camphor. A bicyclic compound can be carbocyclic (all of the ring atoms are carbons), or heterocyclic (the rings' atoms consist of at ...
Definition and first properties. The symmetric group on a finite set is the group whose elements are all bijective functions from to and whose group operation is that of function composition. [1] For finite sets, "permutations" and "bijective functions" refer to the same operation, namely rearrangement. The symmetric group of degree is the ...