Periodic function

Periodic function
Periodic Pe`ri*od"ic, Periodical Pe`ri*od"ic*al, a. [L. periodicus, Gr. ?: cf. F. p['e]riodique.] 1. Of or pertaining to a period or periods, or to division by periods. [1913 Webster]

The periodicaltimes of all the satellites. --Sir J. Herschel. [1913 Webster]

2. Performed in a period, or regular revolution; proceeding in a series of successive circuits; as, the periodical motion of the planets round the sun. [1913 Webster]

3. Happening, by revolution, at a stated time; returning regularly, after a certain period of time; acting, happening, or appearing, at fixed intervals; recurring; as, periodical epidemics. [1913 Webster]

The periodic return of a plant's flowering. --Henslow. [1913 Webster]

To influence opinion through the periodical press. --Courthope. [1913 Webster]

4. (Rhet.) Of or pertaining to a period; constituting a complete sentence. [1913 Webster]

{Periodic comet} (Astron.), a comet that moves about the sun in an elliptic orbit; a comet that has been seen at two of its approaches to the sun.

{Periodic function} (Math.), a function whose values recur at fixed intervals as the variable uniformly increases. The trigonomertic functions, as sin x, tan x, etc., are periodic functions. Exponential functions are also periodic, having an imaginary period, and the elliptic functions have not only a real but an imaginary period, and are hence called doubly periodic.

{Periodic law} (Chem.), the generalization that the properties of the chemical elements are periodic functions of their atomic wieghts. ``In other words, if the elements are grouped in the order of their atomic weights, it will be found that nearly the same properties recur periodically throughout the entire series.'' The following tabular arrangement of the atomic weights shows the regular recurrence of groups (under I., II., III., IV., etc.), each consisting of members of the same natural family. The gaps in the table indicate the probable existence of unknown elements. [1913 Webster] TABLE OF THE PERIODIC LAW OF THE CHEMICAL ELEMENTS (The vertical columns contain the periodic groups) Series1[ 2[ 3[ 4[ 5[ 6[ 7[ 8[ 9[ 10[ 11[ 12[ -------------------------------------------------------------- |I. II. III. IV. V. VI. VII. VIII. | RH4 RH3 RH3 RH |R2O RO R3O3 RO2 R2O5 RO3 R2O7 RO4 -------------------------------------------------------------- H 1 [1913 Webster] Li 7 [1913 Webster] Na 23 [1913 Webster] K 39 [1913 Webster] (Cu) 63 [1913 Webster] Rb 85.2 [1913 Webster] (Ag) (108) [1913 Webster] Cs 133 [1913 Webster] (-) [1913 Webster] (-) [1913 Webster] (Au) (197) [1913 Webster] (-) [1913 Webster]

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Note: A similar relation had been enunciated in a crude way by Newlands; but the law in its effective form was developed and elaborated by Mendelejeff, whence it is sometimes called {Mendelejeff's law}. Important extensions of it were also made by L. Meyer. By this means Mendelejeff predicted with remarkable accuracy the hypothetical elements ekaboron, ekaluminium, and ekasilicon, afterwards discovered and named respectively scandium, gallium, and germanium. [1913 Webster]

{Periodic star} (Astron.), a variable star whose changes of brightness recur at fixed periods.

{Periodic time of a heavenly body} (Astron.), the time of a complete revolution of the body about the sun, or of a satellite about its primary. [1913 Webster]

The Collaborative International Dictionary of English. 2000.

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  • Periodic function — Not to be confused with periodic mapping, a mapping whose nth iterate is the identity (see periodic point). In mathematics, a periodic function is a function that repeats its values in regular intervals or periods. The most important examples are …   Wikipedia

  • periodic function — periodinė funkcija statusas T sritis fizika atitikmenys: angl. periodic function vok. periodische Funktion, f rus. периодическая функция, f pranc. fonction périodique, f …   Fizikos terminų žodynas

  • periodic function — function that has identical images and sources with constant distances between them (for example sine) …   English contemporary dictionary

  • periodic function — /pear ee od ik, pear /, Math. a function of a real or complex variable that is periodic. Cf. periodic1 (def. 5). * * * …   Universalium

  • periodic function — noun Any function whose value repeats after the regular addition of a period to its independent variable; i.e. f(x+t) = f(x) for some t over all x …   Wiktionary

  • periodic function — noun Mathematics a function returning to the same value at regular intervals …   English new terms dictionary

  • periodic function — noun : a function any value of which recurs at regular intervals …   Useful english dictionary

  • Doubly-periodic function — In mathematics, a doubly periodic function is a function f defined at all points z in a plane and having two periods , which are linearly independent vectors u and v such that:f(z) = f(z + u) = f(z + v).,The doubly periodic function is thus a two …   Wikipedia

  • Doubly periodic function — In mathematics, a doubly periodic function is a function defined at all points on the complex plane and having two periods , which are complex numbers u and v that are linearly independent as vectors over the field of real numbers. That u and v… …   Wikipedia

  • Almost periodic function — In mathematics, almost periodic functions are functions of a real number that are periodic up to a small error, first studied by Harald Bohr. There are generalizations to almost periodic functions on locally compact abelian groups. Almost… …   Wikipedia

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