An Etymological Dictionary of Astronomy and Astrophysics

فرهنگ ریشه شناختی اخترشناسی-اخترفیزیک

M. Heydari-Malayeri    -    Paris Observatory



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Number of Results: 23 Search : tensor
absolute tensor
  تانسور ِ اوست   
tânsor-e avast

Fr.: tenseur absolu   

A → tensor of → weight  → zero.

absolute; → tensor.

calculus of tensors
  افماریک ِ تانسورها   
afmârik-e tânsorhâ

Fr.: calcul tensoriel   

The branch of mathematics dealing with the differentiation of tensors.

calculus; → tensor.

Afmârik, → calculus; → tensor.

contravariant tensor
  تانسور ِ پادورتا   
tânsor-e pâdvartâ

Fr.: tenseur contravariant   

A tensor whose components are distinguished by → superscript indices.

contra-; + variant; → variance; → tensor.

covariant tensor
  تانسر ِ هم‌ورتا   
tânsor-e hamvartâ

Fr.: tenseur covariant   

A tensor whose components are distinguished by → subscript indices.

covariant; → tensor.

Einstein tensor
  تانسور ِ اینشتین   
tânsor-e Einstein (#)

Fr.: tenseur d'Einstein   

A mathematical entity describing the → curvature of → space-time in → Einstein's field equations, according to the theory of → general relativity. It is expressed by Gμν = Rμν - (1/2) gμνR, where Rμν is the Ricci tensor, gμν is the → metric tensor, and R the scalar curvature. This tensor is both symmetric and divergence free.

Named after Albert Einstein (1879-1955); → tensor.

energy-momentum tensor
  تانسور ِ کاروژ-جنباک   
tânsor-e kâruž-jonbâk

Fr.: tenseur énergie-quantité de mouvement   

A tensor (Tμν) related to the → Einstein tensor through → Einstein's field equations. The energy-momentum tensor depends upon the distribution of the → energy and → matter in the space.

energy; → momentum; → tensor.

metric tensor
  تانسور ِ متریک   
tânsor-e metrik

Fr.: tenseur métrique   

The abstract tensor operation which is computed in a particular → reference frame using the → metric components. The metric tensor defines magnitude and direction of vectors about a point.

metric; → tensor.

order of a tensor
  رایه‌ی ِ تانسور   
râye-ye tânsor

Fr.: ordre de tenseur   

The maximum number of the indices (→ index) of a tensor.

order; → tensor.

relative tensor
  تانسور ِ بازانی   
tânsor-e bâzâni

Fr.: tenseur relatif   

A generalized tensor concept that is characterized by a → Jacobian matrix of transformation raised to a power called → weight of a tensor density. In practice, only relative tensors of weight 1 or -1 are used. The product of a relative tensor of weight -1 by another tensor of weight 1 is an → absolute tensor. Same as → tensor density.

relative; → tensor.

Ricci tensor
  تانسور ِ ریتچی   
tânsor-e Ricci

Fr.: tenseur de Ricci   

A → rank 2, → symmetric tensor Rμν that is a contraction of the → Riemann curvature tensor Rλμνλ. More specifically, Rμν ≡ Σ (λ) Rλμνκ = Rλμνκ. Closely related to the Ricci tensor is the → Einstein tensor, which plays an important role in the theory of → general relativity.

Named after the Italian mathematician Gregorio Ricci-Curbastro (1853-1925); → tensor.

Riemann curvature tensor
  تانسور ِ خمیدگی ِ ریمان   
tânsor-e xamidegi-ye Riemann

Fr.: tenseur de courbure de Riemann   

A 4th → rank tensor that characterizes the deviation of the geometry of space from the Euclidean type. The curvature tensor Rλμνκ is defined through the → Christoffel symbols Γλμν as follows: Rλμνκ = (∂Γλμκ)/(∂xν) - (∂Γλμν)/(∂xκ) + ΓημκΓλην - ΓημνΓληκ.

Riemannian geometry; → curvature; → tensor.

scalar-tensor theory
  نگره‌ی ِ مرپلی-تانسوری   
negare-ye marpel-tânsori

Fr.: théorie scalaire-tensorielle   

An alternative to the standard → general relativity of gravity that contains not only the → tensor field (or → metric), but also a → scalar field. In this formalism, the → gravitational constant is considered to vary over time. As a consequence, the measured strength of the gravitational interaction is a function of time. Same as → Jordan-Brans-Dicke theory.

scalar; → tensor; → theory.

skew-symmetric tensor
  تانسور ِ پاد-همامون   
tânsor-e pâdhamâmun

Fr.: tenseur antisymétrique   

A tensor that is the negative of its → transpose. For example, a second-order covariant tensor Ajk if its components satisfy the equality: Ajk = - Akj. Also called antisymmetric tensor.

skew; → symmetric; → tensor.

Tânsor, → tensor; pâd-, → anti-; hamâmun, → symmetric.

symmetric tensor
  تانسور ِ همامون   
tânsor-e hamâmun

Fr.: tenseur symétrique   

A tensor that is → invariant under any → permutation of its indices (→ index). In other words, a tensor that equals its → transpose. For example, a second-order → covariant tensor Ajk if its components satisfy the equality: Ajk = Akj.

symmetric; → tensor.

  تانسور، تانگر   
tânsor, tângar

Fr.: tenseur   

A system of numbers or functions where components obey a certain law of transformation when the variables undergo a linear transformation. A tensor may consist of a single number, in which case it is referred to as a tensor of order zero, or simply a → scalar. The tensor of order one represents a → vector. Similarly there will be tensors of order two, three, and so on.
See also:
absolute tensor, → calculus of tensors, → contravariant tensor, → covariant tensor, → Einstein tensor, → energy-momentum tensor, → metric tensor, → order of a tensor, → relative tensor, → Ricci tensor, → Riemann curvature tensor, → scalar-tensor theory, → skew-symmetric tensor, → symmetric tensor, → tensor analysis, → tensor contraction, → tensor density, → tensor field, → tensor perturbation, → tensor rank, → tensor-vector-scalar (TeVeS) theory, → weight of a tensor.

Agent noun of tense (v.) → tension.

tensor analysis
  آ نالس ِ تانسوری، ~ ِ تانگری   
ânâlas-e tânsori

Fr.: analyse tensorielle   

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

tensor; → analysis.

tensor contraction
  ترنگش ِ تانسور   
terengeš-e tânsor

Fr.: contraction de tenseur   

An operation of tensor algebra that is obtained by setting unlike indices equal and summing according to a summation convention.

contraction; → tensor.

tensor density
  چگالی ِ تانسور   
cagâli-ye tânsor

Fr.: densité de tenseur   

A generalization of the tensor concept that like a tensor transforms, except for the appearance of an extra factor, which is the → Jacobian matrix of the transformation of the coordinates, raised to some power, in transformation law. The exponent, which is a positive or negative integer, is called the weight of the tensor density. → weight of a tensor density. Ordinary tensors are tensor densities of weight 0. Tensor density is also called → relative tensor.

tensor; → density.

tensor field
  میدان ِ تانسوری   
meydân-e tânsori

Fr.: champ tensoriel   

A field of space and time each point of which has multiple directionality, and is describable by a tensor function.

tensor; → field.

tensor perturbation
  پرتورش ِ تانسوری   
partureš-e tânsori

Fr.: perturbation tensorielle   

The perturbation in the → primordial Universe plasma caused by → gravitational waves. These waves stretch and squeeze space in orthogonal directions and bring about → quadrupole anisotropy in incoming radiation temperature.

tensor; → perturbation.

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