In literature:
The story is in the Cyclic writers.
"Hesiod, The Homeric Hymns, and Homerica" by Homer and Hesiod
Thus 6, which is the first perfect or cyclical number, = 1 + 2 + 3.
"The Republic" by Plato
He adopted Hwang-che for the style of his reign in 399, and the cyclical name of that year was Kang-tsze.
"Record of Buddhistic Kingdoms" by Fa-Hsien
And Nature with her quaint irony began working in him one of her strange revolutions, following her cyclic laws into the depths of his heart.
"The Forsyte Saga, Volume I." by John Galsworthy
He became Marshal of the Empire in the cyclic year 2496.
"Myths and Legends of China" by E. T. C. Werner
What is the relation of rhyme to the cyclic movement of the unit group and of the verse?
"Harvard Psychological Studies, Volume 1" by Various
Any of the half-hours here assigned to the constellation-seasons may be taken first, and the rest in seasonal or cyclic order.
"Half-hours with the Telescope" by Richard A. Proctor
The world was on the eve of one of its cyclic changes, and unrest seemed to make the air murky.
"The Half-Hearted" by John Buchan
Life is monotonous and cyclical, and yet it is more than that.
"Thoughts on religion at the front" by Neville Stuart Talbot
A vast preponderance of all the action that takes place around us is cyclical action.
"Selections from Previous Worksand Remarks on Romanes' Mental Evolution in Animals" by Samuel Butler
Such motion may be called cyclical.
"Encyclopaedia Britannica, 11th Edition, Volume 4, Part 4" by Various
Another fact strikes the observer: the cyclic march of evolution.
"Reincarnation" by Th. Pascal
Rather should all this be regarded as part of the great cyclic process in obedience to the eternal law.
"The Story of Atlantis and the Lost Lemuria" by W. Scott-Elliot
The law of Cyclic change follows us relentlessly even in the realm of thought.
"Sir Jagadis Chunder Bose" by Sir Jagadis Chunder Bose
Somehow it transforms electric fields cyclically into magnetic fields and back again.
"The Ultimate Weapon" by John Wood Campbell
This cyclical festival was celebrated with great festivity.
"Cleopatra's Needle" by James King
The atmospheric changes may have been either progressive or cyclic, or both.
"Climatic Changes" by Ellsworth Huntington
Nay, we have but to cast our eyes over the rest of the world and cyclical change presents itself on all sides.
"Aphorisms and Reflections from the Works of T. H. Huxley" by T. H. Huxley
In these dates we seem to be dealing with certain cyclic periods.
"The History of Antiquity" by Max Duncker
For a single parameter there is, of course, only one type of group, which has been called cyclical.
"Encyclopaedia Britannica, 11th Edition, Volume 12, Slice 6" by Various
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In poetry:
He perfumes from my women's gowns
Their tainted makers' shame;
In Glory cyclic Wrong he drowns,
And Treachery in Fame.
"Prosperity" by Bernard O Dowd
From seas whose cyclic ebb and sweep,
Unseen to Life's oblivious hours,
Are ostent of the changeless Pow'rs
That hold dominion of the Deep.
"The Testimony of the Suns" by George Sterling
In news:
In the cyclical time of the Hindu world, history moves drowsily through the ordered, unchanging world of rituals and festivals, and a God who pervades everything and must be propitiated for everything.
Many practicing landmen are lawyers, but employment is cyclical with boom and bust trends in energy exploration.
ART, like nature, is cyclical.
NAR said the time is now in the range of historic norms for a balanced market, well below the cyclical peak reached in 2009.
Consultants who worked for the Reagan-Bush campaigns, however, have solved the cyclical nature of the game by merging it with the influence- peddling business.
The University of Idaho is reviving a group to fight a cyclical bacterial invasion that's attacked the state's potato fields with a ferocity not seen in a decade.
Prospering in cyclical markets and surviving a recession starts with recognizing what will happen when a market softens.
"Things are cyclical and you have to shore up when it becomes more difficult," said Caroline Farrar.
The products contain intelligent microcapsule technology, based on betacyclodextrin, a cyclic molecule that traps and locks away bad odors as they occur and at the same time releases fresh fragrance from the perfumes loaded within it.
Industry profit margins are cyclical too.
Some say fashion is cyclical, others see it as a constant reinvention of taste.
The trend of opening branch campuses overseas is cyclical.
Brett Duke/The Times-Picayune LSU baseball coach Paul Mainieri says of the SEC: 'The reality is the league is so balanced, and it seems somewhat cyclical.
Hyundai coupe joins a crowd Like clothing fashion, automotive style is a cyclical thing.
"We think this slow global trade is cyclical and it will come back," he said.
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In science:
Suppose as before (and again this is not obvious) one can replace element cn,1 by a uniform random cyclic element, so the walk-segment corresponds asymptotically to the walk-segment ending at the ﬁrst time of reaching 0 after visiting U ∗ |Cn | cyclic vertices, where U ∗ has uniform[0, 1] distribution.
Two recursive decompositions of Brownian bridge
Di ˚Rj k = λxxiy(j zk) + (cyclic), where (cyclic) means cyclic permutations of (x, y , z ), and λxλy λz 6= 0. (This ansatz is general enough to lead to the required result, and simple enough so that the calculations are manageable.
KIDs are non-generic
Sometimes, the set of deﬁning words of a presentation will be assumed symmetrized. A cyclic word is the set of all cyclic shifts of some word.
Diagrams with Selection and Method for Constructing Boundedly Generated and Boundedly Simple Groups
Furthermore, the cyclic order of the restrictions of all blocks to the interval [1, n] must be the inversion of the cyclic order of the restrictions of all blocks to the interval [n + 1, n + m].
Second Order Freeness and Fluctuations of Random Matrices: I. Gaussian and Wishart matrices and Cyclic Fock spaces
Since the ﬂuctuations are given by taking inner products in cyclic Fock space, we can achieve such a diagonalization by taking functions of our operators which yield elementary tensors in cyclic Fock space.
Second Order Freeness and Fluctuations of Random Matrices: I. Gaussian and Wishart matrices and Cyclic Fock spaces
The generator of the cyclic group shifts cyclically the order by one.
Moduli spaces of convex projective structures on surfaces
Then any mapping φ : T → Q assigning the labels to actual elements of Q, naturally induces a map from the set of cyclic words to L as follows: Let W be the set of cyclic words in T that have distinct labels (i.e. each label in T can appear at most once in each word w ∈ W ).
A Hopf algebra quantizing a necklace Lie algebra canonically associated to a quiver
Here a cyclic word is a word deﬁned up to cyclic permutations of the letters, i.e. ef g = f ge = gef , the same meaning we used earlier in deﬁning “cyclic” noncommutative monomials.
A Hopf algebra quantizing a necklace Lie algebra canonically associated to a quiver
Suppose that G is not cyclic or that G is cyclic of order divisible by the characteristic of K .
Fields of moduli of hyperelliptic curves
Since the base ﬁeld k admits cyclic extensions of any given degree, there exists a map ρ1 from Gal(k/k) to W whose image is the cyclic subgroup generated by w.
Arithmetic of algebraic groups
Now the cyclic ordering of half-edges at each vertex is speciﬁed by a 3-cycle, and a collection of all cyclic orders on the half-edges yields a permutation of H consisting of the product of 3-cycles.
Poisson--Dirichlet distribution for random Belyi surfaces
Note that ˆΩ inherits a cyclic ordering from the cyclic ordering of Q ∪ {∞} induced from the standard embedding into R ∪ {∞} ∼= S 1 .
Generalized Markoff Maps and McShane's Identity
These representatives are essentially the cyclically reduced words, and conjugates of the cyclically reduced word by the elements of the commutator subgroup.
Generalized Markoff Maps and McShane's Identity
G/K is an inﬁnite cyclic group, so therefore G is an extension of a residually solvable group by an inﬁnite cyclic group, and thus G is residually solvable.
On the residual solvability of generalized free products of finitely generated nilpotent groups
Since the vector z r r+1 pro jects to a cyclic vector of its generalized eigenspace in Mπ ⊗R F , we ﬁnd that Ψ(z r r+1) = −ar w−r,−r−1 − a−r wr,−r−1 is a cyclic vector of P .
Representations of quantum groups defined over commutative rings II
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