alternation

Definitions

  • Repeated pattern, alternately reversed, forming a linear design
    Repeated pattern, alternately reversed, forming a linear design
  • WordNet 3.6
    • n alternation successive change from one thing or state to another and back again "a trill is a rapid alternation between the two notes"
    • ***

Additional illustrations & photos:

Blue Dogwood. Alternate-leaved Dogwood Blue Dogwood. Alternate-leaved Dogwood
Alternate leaves Alternate leaves

Webster's Revised Unabridged Dictionary
  • Interesting fact: Honorificabilitudinitatibus is the longest English word that consists strictly of alternating consonants and vowels
    • Alternation (Math) Permutation.
    • Alternation The reciprocal succession of things in time or place; the act of following and being followed by turns; alternate succession, performance, or occurrence; as, the alternation of day and night, cold and heat, summer and winter, hope and fear.
    • Alternation The response of the congregation speaking alternately with the minister.
    • ***
Century Dictionary and Cyclopedia
  • Interesting fact: Probably the best known multiple meaning is the hebrew word "SHALOM" which means, alternately, "hello", "good-bye", and "peace"
    • n alternation The act of alternating, or the state of being alternate; the reciprocal succession of things in time or place, or of states or actions; the act of following something and being in turn followed by it: as, the alternation of day and night, cold and heat, summer and winter.
    • n alternation Passage back and forth; repeated transition; the action of going from one state, condition, or point to another, and back again, indefinitely: as, alternation between states of mind or between places; his alternations from one point to the other were very frequent.
    • n alternation In mathematics: The different changes or alterations of order in numbers. More commonly called permutation.
    • n alternation Alternate proportion (which see, under alternate, a.).
    • n alternation In church ritual, the saying or reading of parts of a service by minister and congregation alternately.
    • n alternation In phytogeography, the discontinuous occurrence of a plant type due to local variations in the conditions. See the extract.
    • n alternation In electricity, the time of one reversal, or one half-wave of alternating current. One alternation therefore is one half-cycle. The frequency of an alternating current formerly was given in alternations per minute. See alternating.
    • ***
Chambers's Twentieth Century Dictionary
  • Interesting fact: The National Oceanic and Atmospheric Administration announced in 1978 that it would alternate men's and women's names in the naming of hurricanes. It was seen as an attempt at fair play. Hurricanes had been named for women for years, until NOAA succumbed to pressure from women's groups who were demanding that Atlantic storms be given unisex names.
    • Alternation the act of alternating: interchange: reading or singing antiphonally
    • ***

Quotations

  • Maurice Chevalier
    Maurice Chevalier
    “Old age isn't so bad when you consider the alternatives.”
  • Chinese Proverb
    Chinese Proverb
    “Of all the thirty-six alternatives, running away is best.”
  • Maya Angelou
    Maya%20Angelou
    “Children's talent to endure stems from their ignorance of alternatives.”
  • Doug Horton
    Doug%20Horton
    “It's not a question of happiness, it's a requirement. Consider the alternative.”
  • Henry Kissinger
    Henry%20Kissinger
    “Moderation is a virtue only in those who are thought to have an alternative.”
  • Ann Oakley
    Ann Oakley
    “Clearly, society has a tremendous stake in insisting on a woman's natural fitness for the career of mother: the alternatives are all too expensive.”

Etymology

Webster's Revised Unabridged Dictionary
L. alternatio,: cf. F. alternation,
Chambers's Twentieth Century Dictionary
L. alter, other.

Usage

In literature:

Frost and snow have alternated with periods of continuous rain.
"New York Times Current History: The European War, Vol 2, No. 1, April, 1915" by Various
The loss of the western approaches left General Kusmanek no alternative but to surrender.
"New York Times Current History; The European War, Vol 2, No. 2, May, 1915" by Various
We can grant alternate sections of land as we did for the Central Road, but not a dollar from the National Treasury.
"Stephen A. Douglas" by Allen Johnson
They were not alternating often.
"Matisse Picasso and Gertrude Stein" by Gertrude Stein
The disc was then displaced alternately upward and downward, and the judgment repeated.
"Harvard Psychological Studies, Volume 1" by Various
They, however, exist in two different, periodically alternating, conditions.
"The Vedanta-Sutras with the Commentary by Sankaracarya"
The second alternative was chosen.
"The Transvaal from Within" by J. P. Fitzpatrick
These alternative endings illustrate how we can create an alternative environment and make our dreams come true.
"Sequential Problem Solving" by Fredric Lozo
It is done by alternately knitting and purling two stitches.
"The Ladies' Work-Book" by Unknown
If the war is ended by additional tribute, they mean to offer us the same alternative.
"Memoir, Correspondence, And Miscellanies, From The Papers Of Thomas Jefferson" by Thomas Jefferson
Heading of leaf in alternate red and blue capitals.
"Catalogue of the William Loring Andrews Collection of Early Books in the Library of Yale University" by Anonymous
It is an excellent tool to use alternately with a spike or coulter-toothed harrow on lumpy soil.
"The First Book of Farming" by Charles L. Goodrich
A sudden horror ... followed by alternate shiverings, and flushings of heat ... immediately seized him.
"A Bibliographical, Antiquarian and Picturesque Tour in France and Germany, Volume Two" by Thomas Frognall Dibdin
For this last year I have suffered alternate hopes and fears.
"The Loyalists, Vol. 1-3" by Jane West
There was a third alternative to which hitherto he had given no attention.
"In the Roar of the Sea" by Sabine Baring-Gould
There is a reason for adopting the latter alternative.
"Essays in Experimental Logic" by John Dewey
Add the flour and milk alternately; that is, a quarter or third of the flour, then a portion of the milk, and so on.
"Foods and Household Management" by Helen Kinne
Abel Crew accepted the alternative meekly.
"Johnny Ludlow, Second Series" by Mrs. Henry Wood
They were mediators, though sometimes fighting on alternate sides, as interest or affront gave occasion.
"Wigwam and War-path; Or the Royal Chief in Chains" by A. B. (Alfred Benjamin) Meacham
There is an alternative to being penned in between these two theories.
"Human Nature and Conduct" by John Dewey
***

In poetry:

OH haste while roses bloom below,
Oh haste while pale and bright above
The sun and moon alternate glow,
To pluck the rose of love.
"Song I" by Mathilde Blind
Alas! how weather-like is life;
Eternal sunshine is unknown.
Our joys and sorrows room with strife,
And we alternate, laugh and mourn.
"Valedictory On Leaving San Francisco, California." by James Madison Bell
Yea, for its sake most noble deeds
And acts of damning, bitter sin,
Alternate fill the page of life,
For love is victor, love is king.
"Love Is Victor, Love Is King" by Robert C O Benjamin
Then haste while still the roses blow,
And pale and bright in heaven above
The sun and moon alternate glow,
Pluck, pluck the rose of love.
"Song I" by Mathilde Blind
"The sun is equal to thy chiefest nymph,
By virtue of the everlasting laws,
And pauses alternating,
Amongst my stars she's equal to the sun."
"The Heroic Enthusiasts - Part The Second =Fifth Dialogue=." by Giordano Bruno
Wild stared the minstrel's eyes of flame,
And high his sable locks arose,
And quick his colour went and came,
As fear and rage alternate rose.
"Glenfinlas; or, Lord Ronald's Coronach" by Sir Walter Scott

In news:

The US Coast Guard issues a policy letter describing procedures for obtaining an Alternative Management System (AMS) determination of a foreign type-approved ballast water management system (BWMS).
The Thorns Deep band formed in late 2010 and agreed to pursue alternative Christian music.
The nights leading up to Vault 350's Latin alternative mega-concert were all little deaths for Southland rockeros.
In an effort to wrest the ice-cream cake genre from the under-ten set, I offer this thoroughly grown-up rendition, a five-layer cake in which the three bands of chocolate ganache alternate with layers of raspberry ice cream.
When Banks Won't Lend, There Are Alternatives, Though Often Expensive.
Three companies find working capital from credit unions and other alternative sources.
Made with a mixture of lentils, chick peas and egg whites, Barilla Plus has been approved by the USDA Food & Nutrition Service to contribute 1 ounce of meat alternate and 2 servings of bread alternate in the.
Barnaby 's Alternative 5.
Barracuda offer an exhilarating alternative for skinny water anglers.
Spaniards turn to barter , alternative banks to alleviate economic pain.
Spanish institutions are in no shape to help struggling Spaniards, so they're turning to alternative banks and ways of exchanging goods to get by.
An Alternative to Cash, Beyond Banks or Barter .
Alternative forms of fitness seduce their way into mainstream.
Motorists who travel the Bayonne Bridge will need to find an alternate route for a few hours on Sunday.
Book your flights now, say experts, and look at alternate airports for lower fares.
***

In science:

It is always the case that the result of turning an m-tangle in a alternating diagram of an alternating link is again an alternating diagram of some alternating link.
Enumerating the Prime Alternating Links
They must be edges in the boundary walk of a face of the plane graph that is the reduced alternating diagram of the alternating link in question.
Enumerating the Prime Alternating Links
For example, in Figure 1, we turn a 6-tangle in a prime alternating knot and obtain an alternating knot which is the sum of two trefoils.
Enumerating the Prime Alternating Links
Let D be a reduced alternating diagram of an alternating prime link L, let T be a 2-edge-connected m-tangle of D with m ≤ 6, and let D ′ be the alternating diagram of an alternating link L′ that is obtained by turning T .
Enumerating the Prime Alternating Links
An application of either operator to an n-crossing reduced alternating diagram results in an n-crossing reduced alternating diagram.
Enumerating the Prime Alternating Links
Finally, since an OT S 6-tangle has no cut-edges, it follows from Proposition 1 that the result of applying OT S to an n-crossing prime (hence reduced) alternating diagram is again a prime alternating diagram.
Enumerating the Prime Alternating Links
Since a (sub)group does not contain any cut-edges, it follows from Proposition 1 that the result of applying T to an n-crossing reduced alternating diagram again an n-crossing reduced alternating diagram.
Enumerating the Prime Alternating Links
Let D be a reduced alternating diagram of an alternating link L, and let G be a (sub)group of D.
Enumerating the Prime Alternating Links
Let D ′ denote the reduced alternating diagram that results when T is applied to G, and let L′ denote the prime alternating link that is represented by D ′ .
Enumerating the Prime Alternating Links
This work relies on Theorem 5 of , a graph-theoretic result which is applicable to reduced alternating diagrams of prime alternating links as well as to those of prime alternating knots, as was the case in .
Enumerating the Prime Alternating Links
Let D be a reduced alternating diagram of a prime alternating link L, and let v be a component crossing of D.
Enumerating the Prime Alternating Links
The proof of the next result as presented in for prime alternating knots is actually valid for prime alternating links, with the modifications to the statement as shown below.
Enumerating the Prime Alternating Links
Let D be a reduced alternating diagram of a prime alternating link L.
Enumerating the Prime Alternating Links
Every reduced alternating diagram of a prime alternating link different from the unknot has a minimal 2-region.
Enumerating the Prime Alternating Links
The condensation of a reduced alternating diagram D of an alternating link L is the 4-regular plane graph G that is obtained from D by repeatedly replacing each group by a single crossing.
Enumerating the Prime Alternating Links
***