A → real number which cannot be exactly expressed as a
ratio ^{a}/_{b} of two integers.
Irrational numbers have decimal expansions that neither terminate nor become periodic.
Every → transcendental number
is irrational. The most famous irrational number is √ 2.

From ir- a prefix meaning "not," a variant of → in-,
+ → rational; → number.

operational

آپارشی

âpâreši

Fr.: opérationnel

Pertaining to a process or series of actions for achieving a result.

A method of mathematical analysis which in many cases makes
it possible to reduce the study of differential operators,
pseudo-differential operators and certain types of integral operators,
and the solution of equations containing them, to an
examination of simpler algebraic problems.
It is also known as operational analysis.

In the philosophy of science, the view that → concepts
are defined in terms of measuring operations
which determine their applicability. Same as operationism.

1) Having or exercising the ability to → reason.
2) Consistent with or based on reason; logical; in accordance with sound reasoning.
3) Math.: Capable of being expressed as a quotient of integers.

M.E. racional, from O.Fr. racionel,
from L. rationalis "of or belonging to reason,
reasonable," from ratio (genitive rationis) "reckoning, calculation, reason,"
from rat-, pp. stem of reri "to reckon,
calculate; consider, think."

1) Râyani, of or pertaining to râyan, → reason.
2) Xeradâné, xeradmandâné, of or pertaining to xerad
"understanding, judgement, intellect, wisdom;" Mid.Pers. xrad "reason, intellect,
intelligence, wisdom, understanding;" O.Pers. xraθu- "wisdom;"
Av. xratu- "intelligence, undestanding, wisdom; will, purpose, council;" cf.
Skt. krátu- "power, will-power;" Gk. kratos "power, strength."
3) vâbari, of or pertaining to vâbar, → ratio.

rational number

عدد ِ وابری

'adad-e vâbari

Fr.: nombre rationnel

Any number that can be expressed as a ratio of two integers, providing the second
number is not zero.

1) The fundamental reason or reasons serving to account for something.
2) A statement of reasons.
3) A reasoned exposition of principles (Dictionary.com).

A philosophical doctrine that holds that → reason
alone, unaided by experience, can arrive at basic truth regarding the world.

From → rational + -ism a Gk. suffix used in the formation of
nouns denoting action or practice, state or condition, principles, doctrines, and so forth.

Râyan, → reason; xerad,
→ rational; bâvari,
from bâvar
"belief" (Mid.Pers. wâbar "beleif;"
Proto-Iranian *uar- "to choose; to convince; to believe;" cf.
Av. var- "to choose; to convince" varəna-, varana-
"conviction, faith;" O.Pers. v(a)r- "to choose; to convince;"
Skt. vr- "to choose," vara- "choosing").

The energy due to the vibration of the molecules making up atoms
(→ molecular vibration). A molecule in space can
have energies in various forms: → rotational energy,
vibrational energy, or electronic energy. These energies of
molecules are → quantized and a particular molecule
can exist in different rotational and vibrational
→ energy levels. The molecules
can move from one level to another level only by a jump
involving a finite amount of energy. → Quantum mechanics
predicts that any molecule can never have zero vibrational energy,
that is atoms can never be completely at rest relative to each other.
The harmonically oscillating molecules can undergo vibrational changes
determined by simple selection rules obtained from
→ Schrödinger equation.

The frequency at which the atoms in a molecule vibrate. The frequencies of
→ molecular vibrations in diatomic molecules
are in the order of 10^{-12} to 10^{-14} Hz. In such molecules,
the only → vibrational mode available is along the bond.
More complicated molecules have many types of vibration and stretching modes.

Any of the ways in which a → molecule vibrates. Each
vibrational mode has a different → frequency
frequency. The number of vibrational modes of a molecule
is determined by the number of atoms in it. The number of vibrational modes for a
non-linear molecule is 3N - 6, where N is the number of atoms
making up the molecule. For a linear molecule it is 3N - 5.