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where b is the number base (10 for decimal), and p is a prime that does not divide b. (Primes p that give cyclic numbers in base b are called full reptend primes or long primes in base b). For example, the case b = 10, p = 7 gives the cyclic number 142857, and the case b = 12, p = 5 gives the cyclic number 2497.
Because of the tremendous diversity allowed, in combination, by the valences of common atoms and their ability to form rings, the number of possible cyclic structures, even of small size (e.g., < 17 total atoms) numbers in the many billions. Cyclic compound examples: All-carbon (carbocyclic) and more complex natural cyclic compounds
4-Cyano-4'-pentylbiphenyl is a commonly used nematic liquid crystal with the chemical formula C 18 H 19 N. It frequently goes by the common name 5CB. 5CB was first synthesized by George William Gray, Ken Harrison, and J.A. Nash at the University of Hull in 1972 and at the time it was the first member of the cyanobiphenyls.
If p is a prime number, then any group with p elements is isomorphic to the simple group Z/pZ. A number n is called a cyclic number if Z/nZ is the only group of order n, which is true exactly when gcd(n, φ(n)) = 1. [13] The sequence of cyclic numbers include all primes, but some are composite such as 15. However, all cyclic numbers are odd ...
Clar's rule states that for a benzenoid polycyclic aromatic hydrocarbon (i.e. one with only hexagonal rings), the resonance structure with the largest number of disjoint aromatic π-sextets is the most important to characterize its chemical and physical properties. Such a resonance structure is called a Clar structure. In other words, a ...
In organic chemistry, the phenyl group, or phenyl ring, is a cyclic group of atoms with the formula C6H5, and is often represented by the symbol Ph (archaically φ) or Ø. The phenyl group is closely related to benzene and can be viewed as a benzene ring, minus a hydrogen, which may be replaced by some other element or compound to serve as a ...
A large number of organoboron compounds, species with B-C bonds, are known. Many organoboron compounds are produced from hydroboration, the addition of B-H bonds to C=C and C≡C bonds. [62] Diborane is traditionally used for such reactions, as illustrated by the preparation of trioctylborane: [63] B 2 H 6 + 6 H 2 C=CH(CH 2) 5 CH 3 → 2 B((CH ...
The number of pi electrons in borazine obeys the 4n + 2 rule, and the B-N bond lengths are equal, which suggests the compound may be aromatic. The electronegativity difference between boron and nitrogen, however, creates an unequal sharing of charge which results in bonds with greater ionic character, and thus it is expected to have poorer ...