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

1) That conforms, especially to the shape of something.
2) Math.: Of, pertaining to, or specifying a mapping of a surface upon another surface so that all angles between intersecting curves remain unchanged.

→ con- + → form + → -al.

A mapping of an infinite → space-time onto a finite one that may make the far away parts of the former accessible to study. The technique invented by Penrose defines an equivalence class of → metrics, g_ab being equivalent to ĝ_ab = Ω²g_ab, where Ω is a positive scalar function of the space-time that modifies the distance scale making the asymptotics of the physical metric accessible to study.

→ conformal; → compactification.

A cosmological model developped by Roger Penrose and colleagues according which the Universe undergoes repeated cycles of expansion. Each cycle, referred to an aeon, starts from its own "→ big bang" and finally comes to a stage of accelerated expansion which continues indefinitely. There is no stage of contraction (to a "→ big crunch") in this model. Instead, each aeon of the universe, in a sense "forgets" how big it is, both at its big bang and in its very remote future where it becomes physically identical with the big bang of the next aeon, despite there being an infinite scale change involved, on passing from one aeon to the next. This model considers a conformal structure rather than a metric structure. Conformal structure may be viewed as family of metrics that are equivalent to one another via a scale change, which may vary from place to place. Thus, in conformal space-time geometry, there is not a particular metric g_ab, but an equivalence class of metrics where the metrics ğ_ab and g_ab are considered to be equivalent if there is a smooth positive scalar field Ω for which ğ_ab = Ω g_ab (R. Penrose, 2012, The Basic Ideas of Conformal Cyclic Cosmology).

→ conformal; → cyclic; → cosmology.

The study of the set of angle-preserving transformations on a space.

→ conformal; → geometry.

A continuous mapping u = f(x) of a domain D in an n-dimensional Euclidean space (n≥ 2) into the n-dimensional Euclidean space is called conformal at a point x₀∈ D if it has the properties of constancy of dilation and preservation of angles at this point.

→ conformal; → mapping.

1) According to, or following established or prescribed forms, conventions, etc.
2) Math., logic: Of a proof, in strict logical form with a justification for every step.
3) Math., logic: Of a calculation, correct in form; made with strict justification for every step; of or pertaining to manipulation of symbols without regard to their meaning.
4) → formal language.
5) → formal logic.

M.E. formal, formel, from L. formalis, from → form + → -al.

Diseyi, desevar, from dis, → form, + adj. suffixes -i and -var.

A language designed for use in situations in which natural language is unsuitable, as for example in → mathematics, → logic, or → computer  → programming. The symbols and formulas of such languages stand in precisely specified syntactic and semantic relations to one another (Dictionary.com).

→ formal; → language.

The traditional or → classical logic in which the → validity or → invalidity of a conclusion is deduced from two or more statements (→ premises). Based on Aristotle's (384-322 BC) theory of → syllogism, systematized in his book "Organon," its focus is not on what is stated (the content) but on the structure (form) of the → argument and the validity of the inference drawn from the premises of the argument; if the premises are true then the logical consequence must also be true. Formal logic is → bivalent, that is it recognizes only two → truth values: → true and → false. The basic principles of formal logic are: 1) → principle of identity, 2) → principle of excluded middle, and 3) → principle of non-contradiction. See also → symbolic logic, → fuzzy logic.

→ formal; → logic.

In logic and mathematics, a system in which statements can be constructed and manipulated with logical rules.

→ formal; → system.

A colorless gas with a pungent, suffocating odor used as an adhering component of glues in many wood products. Formaldehyde (H₂CO) is obtained most commonly by the oxidation of methanol or petroleum gases such as methane, ethane, etc.
In the → interstellar medium, formaldehyde is formed the surface of → dust grains. It is then converted into gas phase by → photodesorption. H₂CO was the first → organic molecule discovered in the ISM (Lewis E. Snyder et al. 1969, Phys. Rev. Lett., 22, 679).

From form(ic) acid, from Fr. formique, + → aldehyde.

1) Excessive adherence to prescribed forms.
2) Math., Logic: → Formalized expression of a set of elements; the nature of such expression.
3) A philosophical view of mathematics in which mathematics, including the logic used in proofs, can be based on the formal manipulation of symbols irrespective of their meaning.

From → formal + → -ism.

1) Condition or quality of being formal; accordance with required or traditional rules, procedures, etc.
2) Strict adherence to established rules and procedures (Dictionary.com).

→ formal; → -ity.

1) The act of giving something a form or structure by introducing rules and procedures.
2) The act of formalizing.

→ formalize; → -tion.

1) To state in symbolic form; to give a definite structure to.
2) To give something legal or formal status.

From → formal + → -ize.

Compound verb, from disevar, → formal, + kardan "to do, to make;" Mid.Pers. kardan; O.Pers./Av. kar- "to do, make, build;" Av. kərənaoiti "he makes;" cf. Skt. kr- "to do, to make," krnoti "he makes, he does," karoti "he makes, he does," karma "act, deed;" PIE base k^wer- "to do, to make."

A reformulation of classical mechanics that predicts the same outcomes as classical mechanics. → Hamiltonian dynamics.

→ Hamiltonian; → mechanics.

A reformulation of classical mechanics that describes the evolution of a physical system using → variational principle The formalism does not require the concept of force, which is replaced by the → Lagrangian function. The formalism makes the description of systems more simpler. Moreover, the passage from classical description to quantum description becomes natural. Same as → Lagrangian dynamics.

→ Lagrangian; → formalism.

An approximate version of → general relativity that applies when the → gravitational field is → weak, and the matter → velocity is → small. Post-Newtonian formalism successfully describes the gravitational field of the solar system. It can also be applied to situations involving compact bodies with strong internal gravity, provided that the mutual gravity between bodies is weak. It also provides a foundation to calculate the → gravitational waves emitted by → compact binary star systems, as well as their orbital evolution under radiative losses. The formalism proceeds from the Newtonian description and then, step by step, adds correction terms that take into account the effects of general relativity. The correction terms are ordered in a systematic way (from the largest effects to the smallest ones), and the progression of ever smaller corrections is called the → post-Newtonian expansion.

→ post-; → Newtonian; → formalism.

A mathematical analysis, based on → self-similarity, used to predict the → mass function of spherically collapsing → dark matter halos. The formalism assumes that the fraction of mass in halos more massive than M is related to the fraction of the volume in which the smoothed initial density field is above some threshold δ_cρ, where ρ is the average density of the Universe, with the volume encompassing a mass larger than M. A variety of smoothing → window functions and thresholds have been argued, but the most common is a top-hat window in real space and δ_c≅ 1.69. The Press-Schechter formalism provides a relatively good fit to the results of numerical simulations in cold dark matter theories.

First described by William H. Press and Paul Schechter's paper (1974, ApJ 187, 425); → formalism.