Search results
Results from the WOW.Com Content Network
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.
A cyclic number [1] [2] is a natural number n such that n and φ(n) are coprime. Here φ is Euler's totient function. An equivalent definition is that a number n is cyclic if and only if any group of order n is cyclic. [3] Any prime number is clearly cyclic. All cyclic numbers are square-free. [4] Let n = p 1 p 2 …
A heterocyclic compound is a cyclic compound that has atoms of at least two different elements as members of its ring(s). [5] Cyclic compounds that have both carbon and non-carbon atoms present are heterocyclic carbon compounds, and the name refers to inorganic cyclic compounds as well (e.g., siloxanes, which contain only silicon and oxygen in ...
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 ...
3,5-dimethylene-1-cyclopentene 3,5-dimethylene-1-cyclopentene Consider 3,5-dimethylene-1-cyclopentene as an example. Transition electric dipole, magnetic dipole and electric quadrupole moments interactions result in optical rotation(OR), which can be described by both tensor components and chemical geometries.
The first number in a crown ether's name refers to the number of atoms in the cycle, and the second number refers to the number of those atoms that are oxygen. Crown ethers are much broader than the oligomers of ethylene oxide; an important group are derived from catechol. Crown ethers strongly bind certain cations, forming complexes. The ...
A homocycle or homocyclic ring is a ring in which all atoms are of the same chemical element. [1] A heterocycle or heterocyclic ring is a ring containing atoms of at least two different elements, i.e. a non-homocyclic ring. [2] A carbocycle or carbocyclic ring is a homocyclic ring in which all of the atoms are carbon. [3]
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 ...