An Etymological Dictionary of Astronomy and Astrophysics
English-French-Persian

1) General: The separation of an intellectual or material whole into its constituent parts for individual study. The study of such constituent parts and their interrelationships in making up a whole (opposite of → synthesis).
2) Chemistry: The separation of a substance into its constituent elements to determine either their nature (qualitative analysis) or their proportions (quantitative analysis).
3) Mathematics: A branch of mathematics principally involving → differential and integral calculus, → sequences, and → series and concerned with → limits and → convergence.

From M.L. analysis, from Gk. analysis "a breaking up," from analyein "unloose," from ana- "up, throughout" + lysis "a loosening," from lyein "to loosen, release, untie". The L. cognate and counterpart of this Gk. word, i.e. luere has formed the words solve, dissolve, solution. The Skt. cognate lu, lunoti "to cut, sever, mow, pluck, tear asunder, destroy," lava "cutting, plucking; what is cut; fragment, piece;" PIE *leu- "to loosen, divide, cut apart". The Eng. lose, loose and Ger. los derive from this root.

Ânâlas, from ânâ-, → ana-, + las "loose" ([Mo'in], Gilaki, Tabari, Tâleši, Aftari). We do not know the Av./O.Pers. counterparts of these Gk. las, lysis, lyein, but we believe that las and the following words probably derive from the above-mentioned PIE *leu-:
lâ "slit, cut" (Tabari),
lâb, lâp, lib "slit, cut, piece, half" (Tabari),
lâpé "a cut piece of wood" [Mo'in],
lâpé kardan "to cut a timber along its length" [Mo'in],
lap "piece, big piece, big cut" [Mo'in]. This word was chosen by Farhangestân I for "lobe of the lung".
lâc "open, wide-open" (Tabari),
luš "torn" [Mo'in], also luš luš [Mo'in] "in pieces,"
lat "torn, piece" [Mo'in]. Compare with luta "cut, cut off" in Pali. Lat may also be a contraction of laxt.
lok "torn, piece" (Qâyeni),
lâš "slit" (Tabari),
lâš kardan "to pick, to pluck" [Mo'in],
latu "plough" (Tabari).
Ânâkâvidan, from ânâ- + kâvidan (kâftan) "to examine, investigate, search; dig," from kâv + infinitive suffix -idan; compare with Mod.Pres. kâvâk "hollow, empty," L. cavus "hollow" (E. derivatives: cavity, concave, cave, excavate), Gk. koilos "hollow."

The evaluation of reduced data; → data reduction.

→ data; → analysis.

A technique used in physics based on the fact that the various terms in a physical equation must have identical → dimensional formulae if the equation is to be true for all consistent systems of unit. Its main uses are:
a) To test the probable correctness of an equation between physical quantities.
b) To provide a safe method of changing the units in a physical quantity.
c) To solve partially a physical probable whose direct solution cannot be achieved by normal methods.

→ dimensional; → analysis.

The process of decomposing any function of time or space into a sum of sinusoidal functions using the → Fourier series and → Fourier transforms. In other words, any data analysis procedure that describes or measures the fluctuations in a time series by comparing them with sinusoids. Fourier analysis is an essential component of much of modern applied and pure mathematics. It forms an exceptionally powerful analytical tool for solving various problems in many areas of mathematics, physics, engineering, biology, finance, etc. and has opened up new realms of knowledge.

After the French mathematician Baron Jean Baptiste Joseph Fourier (1768-1830), whose work had a tremendous impact on the physical applications of mathematics; → analysis.

The study of methods for approximation of solutions of various classes of mathematical problems including error analysis.

→ numerical; → analysis.

The mathematical evaluation of an optical system to determine its basic optical properties and image quality characteristics.

→ optical; → analysis.

The analysis of a chemical sample to derive its precise percentage composition in terms of elements, radicals, or compounds.

→ quantitative; → analysis.

A statistical technique used to determine the values of parameters for a function that best fits a given set of data.

→ regression, → analysis.

The process of collecting, manipulating, analyzing, and interpreting quantitative data to uncover underlying causes, patterns, and relationships between variables.

→ statistical; → analysis.

A method of calculation in higher mathematics based on the properties of tensors.

→ tensor; → analysis.

The study of → vectors and → vector spaces.

→ vector; → analysis.

The resolution of a complex waveform into a sum of simple periodic waves, usually by computer means.

→ waveform; → analysis.