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Concept in mathematics
on the tensor bundle a connection is needed, except for the special case of the exterior derivative of antisymmetric tensors. A tensor bundle is a fiber
Tensor_bundle
Assignment of a tensor continuously varying across a region of space
In mathematics and physics, a tensor field is a function assigning a tensor to each point of a region of a mathematical space (typically a Euclidean space
Tensor_field
Operation that pairs a left and a right R-module into an abelian group
universal property of the tensor product of vector spaces extends to more general situations in abstract algebra. The tensor product of an algebra and
Tensor_product_of_modules
Structure defining distance on a manifold
metric field on M consists of a metric tensor at each point p of M that varies smoothly with p. A metric tensor g is positive-definite if g ( v , v ) >
Metric_tensor
Universal construction in multilinear algebra
the tensor algebra of a vector space V, denoted T(V) or T•(V), is the algebra of tensors on V (of any order) with multiplication being the tensor product
Tensor_algebra
Manifold upon which it is possible to perform calculus
act as a multilinear operator on vector fields, or on other tensor fields. The tensor bundle is not a differentiable manifold in the traditional sense,
Differentiable_manifold
Tensor in differential geometry
converge. Formally, it is a symmetric rank-two tensor obtained by taking a trace of the Riemann curvature tensor of a Riemannian or pseudo-Riemannian metric
Ricci_curvature
Second-rank tensor in quantum chromodynamics
strength tensor is a rank-2 tensor field on the spacetime with values in the adjoint bundle of the chromodynamical SU(3) gauge group (see vector bundle for
Gluon_field_strength_tensor
Isomorphism between the tangent and cotangent bundles of a manifold
vector bundle endowed with a bundle metric and its dual. Given a (0, 2) tensor X = Xij ei ⊗ ej, we define the trace of X through the metric tensor g by
Musical_isomorphism
Mathematical operation
\mathbf {R} } be a multilinear form on W (also known as a tensor – not to be confused with a tensor field – of rank (0, s), where s is the number of factors
Pullback (differential geometry)
Pullback_(differential_geometry)
Mathematical operation on vector spaces
two vectors is sometimes called an elementary tensor or a decomposable tensor. The elementary tensors span V ⊗ W {\displaystyle V\otimes W} in the sense
Tensor_product
Tensor index notation for tensor-based calculations
notation and manipulation for tensors and tensor fields on a differentiable manifold, with or without a metric tensor or connection. It is also the modern
Ricci_calculus
Object in differential geometry
differential geometry, the torsion tensor is a tensor that is associated to any affine connection. The torsion tensor is a bilinear map of two input vectors
Torsion_tensor
Defines a notion of parallel transport on a bundle
the dual vector bundle E ∗ {\displaystyle E^{*}} , tensor powers E ⊗ k {\displaystyle E^{\otimes k}} , symmetric and antisymmetric tensor powers S k E
Connection_(vector_bundle)
Mathematical parametrization of vector spaces by another space
F is a vector bundle E ⊕ F over X whose fiber over x is the direct sum Ex ⊕ Fx of the vector spaces Ex and Fx. The tensor product bundle E ⊗ F is defined
Vector_bundle
Specification of a derivative along a tangent vector of a manifold
differentiation in general vector bundles which were, in contrast to the classical bundles of interest to geometers, not part of the tensor analysis of the manifold
Covariant_derivative
Generalization of tensor fields
differential geometry, a tensor density or relative tensor is a generalization of the tensor field concept. A tensor density transforms as a tensor field when passing
Tensor_density
Mathematical object that describes the electromagnetic field in spacetime
electromagnetic tensor or electromagnetic field tensor (sometimes called the field strength tensor, Faraday tensor or Maxwell bivector) is a tensor that describes
Electromagnetic_tensor
Covariant derivative of the metric tensor
In mathematics, the nonmetricity tensor in differential geometry is the covariant derivative of the metric tensor. It can be interpreted as the failure
Nonmetricity_tensor
Tensor describing energy momentum density in spacetime
stress-energy tensor The stress–energy tensor, sometimes called the stress–energy–momentum tensor or the energy–momentum tensor, is a tensor field quantity
Stress–energy_tensor
Measure of the curvature of a pseudo-Riemannian manifold
Riemann curvature tensor, the Weyl tensor expresses the tidal force that a body feels when moving along a geodesic. The Weyl tensor differs from the Riemann
Weyl_tensor
Tensor field in Riemannian geometry
mathematical field of differential geometry, the Riemann curvature tensor or Riemann–Christoffel tensor (after Bernhard Riemann and Elwin Bruno Christoffel) is the
Riemann_curvature_tensor
Continuous surjection satisfying a local triviality condition
In mathematics, and particularly topology, a fiber bundle (Commonwealth English: fibre bundle) is a space that is locally a product space, but globally
Fiber_bundle
Coordinate-free definition of a tensor
mathematics, the modern component-free approach to the theory of a tensor views a tensor as an abstract object, expressing some definite type of multilinear
Tensor_(intrinsic_definition)
tensor product of vector bundles E, F (over the same space X) is a vector bundle, denoted by E ⊗ F, whose fiber over each point x ∈ X is the tensor product
Tensor_product_bundle
Tensor invariant under permutations of vectors it acts on
In mathematics, a symmetric tensor is an unmixed tensor that is invariant under a permutation of its vector arguments: T ( v 1 , v 2 , … , v r ) = T (
Symmetric_tensor
Spinning motion in theoretical physics
theoretical physics, the spin tensor is a quantity used to describe the rotational motion of particles in spacetime. The spin tensor has application in general
Spin_tensor
Operation in mathematics
In multilinear algebra, a tensor contraction is an operation on a tensor that arises from the canonical pairing of a vector space and its dual. This example
Tensor_contraction
Tensor having both covariant and contravariant indices
In tensor analysis, a mixed tensor is a tensor which is neither strictly covariant nor strictly contravariant; at least one of the indices of a mixed
Mixed_tensor
Scalar measure of the rotational inertia with respect to a fixed axis of rotation
inertia tensor of a body calculated at its center of mass, and R {\displaystyle \mathbf {R} } be the displacement vector of the body. The inertia tensor of
Moment_of_inertia
Tensor used in general relativity
differential geometry, the Einstein tensor (named after Albert Einstein; also known as the trace-reversed Ricci tensor) is used to express the curvature
Einstein_tensor
Antisymmetric permutation object acting on tensors
independent of any metric tensor and coordinate system. Also, the specific term "symbol" emphasizes that it is not a tensor because of how it transforms
Levi-Civita_symbol
Algebraic object with geometric applications
(electromagnetic tensor, Maxwell tensor, permittivity, magnetic susceptibility, etc.), and general relativity (stress–energy tensor, curvature tensor, etc.). In
Tensor
one grand object called the tensor bundle. A tensor field is then defined as a map from the manifold to the tensor bundle, each point p {\displaystyle
Mathematics of general relativity
Mathematics_of_general_relativity
Tensor that describes the 4D geometry of spacetime
manifold M {\displaystyle M} and the metric tensor is given as a covariant, second-degree, symmetric tensor on M {\displaystyle M} , conventionally denoted
Metric tensor (general relativity)
Metric_tensor_(general_relativity)
Tensor equal to the negative of any of its transpositions
tensor is antisymmetric with respect to its first three indices. If a tensor changes sign under exchange of each pair of its indices, then the tensor
Antisymmetric_tensor
Array of numbers describing a metric connection
cotangent space by the metric tensor. Abstractly, one would say that the manifold has an associated (orthonormal) frame bundle, with each "frame" being a
Christoffel_symbols
Vector bundle of rank 1
global section, and its tensor powers with any real exponent may be defined and used to 'twist' any vector bundle by tensor product. The same construction
Line_bundle
Mathematical function of two variables; outputs 1 if they are equal, 0 otherwise
thought of as a tensor, and is written δ j i {\displaystyle \delta _{j}^{i}} . Sometimes the Kronecker delta is called the substitution tensor. For larger
Kronecker_delta
Decomposition in multilinear algebra
multilinear algebra, the tensor rank decomposition or rank-R decomposition is the decomposition of a tensor as a sum of R rank-1 tensors, where R is minimal
Tensor_rank_decomposition
Branch of mathematics
where N J {\displaystyle N_{J}} is a tensor of type (2, 1) related to J {\displaystyle J} , called the Nijenhuis tensor (or sometimes the torsion). An almost
Differential_geometry
of a metric tensor can be extended to an arbitrary vector bundle, and to some principal fiber bundles. This metric is often called a bundle metric, or
Bundle_metric
of tensor theory. For expositions of tensor theory from different points of view, see: Tensor Tensor (intrinsic definition) Application of tensor theory
Glossary_of_tensor_theory
Branch of mathematics
various areas, including: Classical treatment of tensors Dyadic tensor Glossary of tensor theory Metric tensor Bra–ket notation Multilinear subspace learning
Multilinear_algebra
Exterior algebraic map taking tensors from p forms to n-p forms
a differential form with values in the canonical line bundle. We compute in terms of tensor index notation with respect to a (not necessarily orthonormal)
Hodge_star_operator
Section of a certain line bundle
be made, since the density bundle is the tensor product of the orientation bundle of M and the n-th exterior product bundle of T∗M (see pseudotensor).
Density_on_a_manifold
{\displaystyle P_{ij}} is the Schouten tensor. A little work then shows that the sections of the tractor bundle (in a fixed Weyl gauge) can be represented
Tractor_bundle
Geometric structure
g ) , {\displaystyle (M,g),\,} one defines the spinor bundle to be the complex vector bundle π S : S → M {\displaystyle \pi _{\mathbf {S} }\colon {\mathbf
Spinor_bundle
Type of derivative in differential geometry
differentiable manifold. Functions, tensor fields and forms can be differentiated with respect to a vector field. If T is a tensor field and X is a vector field
Lie_derivative
Shorthand notation for tensor operations
the multiplication. Given a tensor, one can raise an index or lower an index by contracting the tensor with the metric tensor, g μ ν {\displaystyle g_{\mu
Einstein_notation
Graphical notation for multilinear algebra calculations
essentially the composition of functions. In the language of tensor algebra, a particular tensor is associated with a particular shape with many lines projecting
Penrose_graphical_notation
Abbreviation in the fields of special and general relativity
relativity, a four-tensor is an abbreviation for a tensor in a four-dimensional spacetime. General four-tensors are usually written in tensor index notation
Four-tensor
Concept in algebraic geometry
line bundle L is big if and only if it has a positive tensor power which is the tensor product of an ample line bundle A and an effective line bundle B (meaning
Ample_line_bundle
Topological space that locally resembles Euclidean space
and there is no intrinsic notion of a normal bundle, but instead there is an intrinsic stable normal bundle. The n-sphere Sn is a generalisation of the
Manifold
Expression that may be integrated over a region
covariant tensor field of rank k {\displaystyle k} . The differential forms on M {\displaystyle M} are in one-to-one correspondence with such tensor fields
Differential_form
Affine connection on the tangent bundle of a manifold
the Levi-Civita connection is the unique affine connection on the tangent bundle of a manifold that preserves the (pseudo-)Riemannian metric and is torsion-free
Levi-Civita_connection
Representation of mechanical stress at every point within a deformed 3D object
Cauchy stress tensor (symbol σ {\displaystyle {\boldsymbol {\sigma }}} , named after Augustin-Louis Cauchy), also called true stress tensor or simply stress
Cauchy_stress_tensor
Construct allowing differentiation of tangent vector fields of manifolds
differentiation of the sections of vector bundles. The notion of an affine connection has its roots in 19th-century geometry and tensor calculus, but was not fully
Affine_connection
Matrix operation which flips a matrix over its diagonal
coordinates Mixed tensor Antisymmetric tensor Symmetric tensor Tensor operator Tensor bundle Two-point tensor Operations Covariant derivative Exterior covariant
Transpose
Straight path on a curved surface or a Riemannian manifold
double tangent bundle TTM into horizontal and vertical bundles: T T M = H ⊕ V . {\displaystyle TTM=H\oplus V.} The double tangent bundle can be visualized
Geodesic
Second order tensor in vector algebra
mathematics, specifically multilinear algebra, a dyadic or dyadic tensor is a second order tensor, written in a notation that fits in with vector algebra. There
Dyadics
algebra bundle is a vector bundle. Examples include the tensor-algebra bundle, exterior bundle, and symmetric bundle associated to a given vector bundle, as
Algebra_bundle
Differential form of degree one or section of a cotangent bundle
cotangent bundle. Equivalently, a one-form on a manifold M {\displaystyle M} is a smooth mapping of the total space of the tangent bundle of M {\displaystyle
One-form
Conserved physical quantity; rotational analogue of linear momentum
fourth order tensor: L i j = I i j k ℓ ω k ℓ . {\displaystyle L_{ij}=I_{ijk\ell }\omega _{k\ell }\,.} Again, this equation in L and ω as tensors is true in
Angular_momentum
Property of a mathematical space
coordinates Mixed tensor Antisymmetric tensor Symmetric tensor Tensor operator Tensor bundle Two-point tensor Operations Covariant derivative Exterior covariant
Dimension
Algebra associated to any vector space
alternating tensor subspace. On the other hand, the image A ( T ( V ) ) {\displaystyle {\mathcal {A}}(\mathrm {T} (V))} is always the alternating tensor graded
Exterior_algebra
Theory of gravitation as curved spacetime
stress–energy tensor, which includes both energy and momentum densities as well as stress: pressure and shear. Using the equivalence principle, this tensor is readily
General_relativity
Tensor operator generalizes the notion of operators which are scalars and vectors
graphics, a tensor operator generalizes the notion of operators which are scalars and vectors. A special class of these are spherical tensor operators which
Tensor_operator
Method for specifying point positions
coordinates Mixed tensor Antisymmetric tensor Symmetric tensor Tensor operator Tensor bundle Two-point tensor Operations Covariant derivative Exterior covariant
Coordinate_system
Algebraic operation on coordinate vectors
(single-) dot product between a tensor of order n {\displaystyle n} and a tensor of order m {\displaystyle m} is a tensor of order n + m − 2 {\displaystyle
Dot_product
Construct in differenital geometry
the field strength tensor, a classical one using R as the curvature tensor, and the classical notation for the Riemann curvature tensor, most of which can
Metric_connection
field. Tensors also have extensive applications in physics: Electromagnetic tensor (or Faraday's tensor) in electromagnetism Finite deformation tensors for
Introduction to the mathematics of general relativity
Introduction_to_the_mathematics_of_general_relativity
Topics referred to by the same term
In differential geometry, the term curvature tensor may refer to: the Riemann curvature tensor of a Riemannian manifold — see also Curvature of Riemannian
Curvature_tensor
Differential form
cotangent bundle of the manifold. Here, | g | {\displaystyle |g|} is the absolute value of the determinant of the matrix representation of the metric tensor on
Volume_form
Mathematical notation for tensors and spinors
between tensor factors of type V {\displaystyle V} and those of type V ∗ {\displaystyle V^{*}} . A general homogeneous tensor is an element of a tensor product
Abstract_index_notation
Type of physical quantity
spacetime Tensor – Algebraic object with geometric applications Tensor density – Generalization of tensor fields Tensor field – Assignment of a tensor continuously
Pseudotensor
Tensorial object depending on two points in a manifold
{\displaystyle (r,s,r',s')} is defined as a section of the exterior tensor product bundle T s r M ⊠ T s ′ r ′ M {\displaystyle T_{s}^{r}M\boxtimes T_{s'}^{r'}M}
Bitensor
Mathematical Concept
notation is as follows: Write down the second order tensor in matrix form (in the example, the stress tensor) Strike out the diagonal Continue on the third
Voigt_notation
Theory of interwoven space and time by Albert Einstein
coordinates are divided by c or factors of c±2 are included in the metric tensor. These numerous conventions can be superseded by using natural units where
Special_relativity
Non-tensorial representation of the spin group
distinguished from the tensor representations given by Weyl's construction by the weights. Whereas the weights of the tensor representations are integer
Spinor
Elliptic differential operators in geometry mathematics
various tensor bundles of a manifold, defined in terms of a Riemannian- or pseudo-Riemannian metric. When applied to functions (i.e. tensors of rank 0)
Laplace operators in differential geometry
Laplace_operators_in_differential_geometry
Math/physics concept
the Riemann curvature tensor. The Levi-Civita connection is characterized as the unique metric connection in the tangent bundle with zero torsion. To
Connection_form
Vector behavior under coordinate changes
consequently a vector is called a contravariant tensor. A vector, which is an example of a contravariant tensor, has components that transform inversely to
Covariance and contravariance of vectors
Covariance_and_contravariance_of_vectors
Object in differential geometry
The contorsion tensor (or contortion tensor) in differential geometry is the difference between a connection with and without torsion in it. It commonly
Contorsion_tensor
Array of numbers
multiplication can be defined with entries objects of a category equipped with a "tensor product" similar to multiplication in a ring, having coproducts similar
Matrix_(mathematics)
Ways of writing certain laws of physics
t^{2}}-\nabla ^{2}.} The signs in the following tensor analysis depend on the convention used for the metric tensor. The convention used here is (+ − − −), corresponding
Covariant formulation of classical electromagnetism
Covariant_formulation_of_classical_electromagnetism
Curvilinear coordinates can be formulated in tensor calculus, with important applications in physics and engineering, particularly for describing transportation
Tensors in curvilinear coordinates
Tensors_in_curvilinear_coordinates
Mathematics concept
vertical bundle and the horizontal bundle are vector bundles associated to a smooth fiber bundle. More precisely, given a smooth fiber bundle π : E → B
Vertical and horizontal bundles
Vertical_and_horizontal_bundles
Function in mathematics
invariants, such as the curvature (see also curvature tensor and curvature form), and torsion tensor. Consider the following problem. Suppose that a tangent
Connection_(mathematics)
Term in differential geometry
form describes curvature of a connection on a principal bundle. The Riemann curvature tensor in Riemannian geometry can be considered as a special case
Curvature_form
Principal bundle associated to a vector bundle
In mathematics, a frame bundle is a principal fiber bundle F ( E ) {\displaystyle F(E)} associated with any vector bundle E {\displaystyle E} . The fiber
Frame_bundle
System of moving vectors in differential geometry
affine connection (a covariant derivative or connection on the tangent bundle), then this connection allows one to transport vectors of the manifold along
Parallel_transport
Branch of physics which studies the behavior of materials modeled as continuous media
stress tensor, and ρ 0 {\displaystyle \rho _{0}} is the mass density in the reference configuration. The first Piola-Kirchhoff stress tensor is related
Continuum_mechanics
that is 0 whenever arguments are linearly dependent Antisymmetric tensor – Tensor equal to the negative of any of its transpositions Hazewinkel (1990)
Symmetrization
Mathematics of smooth surfaces
to Élie Cartan. In the language of tensor calculus, making use of natural metrics and connections on tensor bundles, the Gauss equation can be written
Differential geometry of surfaces
Differential_geometry_of_surfaces
Set of vectors used to define coordinates
of redirect targets Spherical basis – Basis used to express spherical tensors Brown, William A. (1991). Matrices and vector spaces. New York: M. Dekker
Basis_(linear_algebra)
Operation on differential forms
{\displaystyle 1} -form d f {\displaystyle df} is a section of the cotangent bundle, that gives a local linear approximation to f {\displaystyle f} in the cotangent
Exterior_derivative
Representation of a tensor in Euclidean space
a Cartesian tensor uses an orthonormal basis to represent a tensor in a Euclidean space in the form of components. Converting a tensor's components from
Cartesian_tensor
manifold Tensor analysis Tangent vector Tangent space Tangent bundle Cotangent space Cotangent bundle Tensor Tensor bundle Vector field Tensor field Differential
List of differential geometry topics
List_of_differential_geometry_topics
Mathematical function, in linear algebra
linear maps are said to be 1-co- 1-contra-variant objects, or type (1, 1) tensors. A linear transformation between topological vector spaces, for example
Linear_map
TENSOR BUNDLE
TENSOR BUNDLE
Surname or Lastname
English
English : probably a variant of Manser.
Surname or Lastname
English
English : patronymic from Penn 3 or Paine 1.English : habitational name from Penson in Devon.
Surname or Lastname
English
English : variant of Tennyson.
Surname or Lastname
English
English : perhaps an altered spelling of Janson.Respelling of Danish, Norwegian, and North German Jensen.
Surname or Lastname
French
French : unexplained.English : unexplained.Possibly a respelling of Menter, an unexplained name of German origin.
Male
Greek
(ÎœÎντωÏ) Greek name derived from the word menos, MENTOR means "spirit." In mythology, this is the name of the son of Ãlkimos.
Surname or Lastname
German
German : variant of Tanner 2.English : from Old French teneor, teneur, tenor, ‘holder of a tenement’, hence an equivalent of Tennant.
Boy/Male
Muslim
Winner
Surname or Lastname
English
English : unexplained.
Male
English
English surname transferred to forename use, BENSON means "son of Ben."
Surname or Lastname
English
English : patronymic from the medieval personal name Benne, a pet form of Benedict (see Benn).English : habitational name from a place in Oxfordshire named Benson, from Old English Benesingtūn ‘settlement (Old English tūn) associated with Benesa’, a personal name of obscure origin, perhaps a derivative of Bana meaning ‘slayer’.Jewish (Ashkenazic) : patronymic composed of a pet form of the personal name Beniamin (see Bien, Benjamin) + German Sohn ‘son’.Scandinavian : altered form of such names as Bengtsson, Bendtsen, patronymics from Bengt, Bendt, etc., Scandinavian forms of Benedict.
Male
Scandinavian
Scandinavian form of Latin Theodorus, TEODOR means "gift of God."
Surname or Lastname
English (mainly Yorkshire)
English (mainly Yorkshire) : nickname for a peasant who gave himself airs and graces, from Anglo-Norman French segneur ‘lord’ (Latin senior ‘elder’).English and Dutch : distinguishing nickname for the elder of two bearers of the same personal name (for example, a father and son or two brothers), from Latin senior ‘elder’.
Surname or Lastname
English
English : patronymic from the personal name Henn(e), a short form of Henry 1, Hayne (see Hain 2), or Hendy.Irish : Anglicized form of Gaelic Ó hAmhsaigh (see Hampson 2).
Surname or Lastname
English
English : patronymic from a reduced form of the personal name Steven.English : habitational name from a place in Derbyshire, recorded in Domesday Book as Steintune, later as Steineston, from the Old Norse personal name Steinn (meaning ‘stone’) + Old English tūn ‘enclosure’, ‘settlement’.Variant of Steenson 2.
Boy/Male
French
Works in iron.
Surname or Lastname
English
English : habitational name for someone from Edensor in Derbyshire, which derives its name from the genitive case of the Old English personal name Ēadhūn (see Eden 1) + Old English ofer ‘ridge’.
Surname or Lastname
English
English : variant spelling of Ensor.
Surname or Lastname
English
English : variant of Windsor. This is the spelling used for places so named in Devon and Hampshire.Perhaps also an Americanized spelling of German Winzer.
Boy/Male
Polish Spanish
TENSOR BUNDLE
TENSOR BUNDLE
Girl/Female
Indian
Prostrate in worship, Bowing
Girl/Female
Tamil
Limitless, Boundless, Unmeasurable, Infinite, Eternal
Boy/Male
Greek
Brother of Helen.
Boy/Male
Gujarati, Hindu, Indian, Kannada, Marathi, Telugu, Traditional
The Sun
Boy/Male
Hindu
Boy/Male
Tamil
Complete
Boy/Male
Arabic, Muslim
One who Relies Upon Allah
Boy/Male
Gaelic
Free man.
Girl/Female
Indian
Pure gold
Boy/Male
Greek
Praising.
TENSOR BUNDLE
TENSOR BUNDLE
TENSOR BUNDLE
TENSOR BUNDLE
TENSOR BUNDLE
n.
Tension.
n.
A person who sings the tenor, or the instrument that play it.
n.
The ratio of one vector to another in length, no regard being had to the direction of the two vectors; -- so called because considered as a stretching factor in changing one vector into another. See Versor.
superl.
Adapted to excite feeling or sympathy; expressive of the softer passions; pathetic; as, tender expressions; tender expostulations; a tender strain.
n.
The quality or state of being tense, or strained to stiffness; tension; tenseness.
v. t.
To have a care of; to be tender toward; hence, to regard; to esteem; to value.
a.
Sensory; as, the sensor nerves.
superl.
Easily impressed, broken, bruised, or injured; not firm or hard; delicate; as, tender plants; tender flesh; tender fruit.
a.
The force by which a part is pulled when forming part of any system in equilibrium or in motion; as, the tension of a srting supporting a weight equals that weight.
a.
The act of stretching or straining; the state of being stretched or strained to stiffness; the state of being bent strained; as, the tension of the muscles, tension of the larynx.
n.
A muscle that stretches a part, or renders it tense.
n.
A machine or frame for stretching cloth by means of hooks, called tenter-hooks, so that it may dry even and square.
superl.
Apt to give pain; causing grief or pain; delicate; as, a tender subject.
n.
One in the fourth or final year of his collegiate course at an American college; -- originally called senior sophister; also, one in the last year of the course at a professional schools or at a seminary.
a.
Expansive force; the force with which the particles of a body, as a gas, tend to recede from each other and occupy a larger space; elastic force; elasticity; as, the tension of vapor; the tension of air.
n.
Any offer or proposal made for acceptance; as, a tender of a loan, of service, or of friendship; a tender of a bid for a contract.
a.
Stretched tightly; strained to stiffness; rigid; not lax; as, a tense fiber.
v. t.
To offer in payment or satisfaction of a demand, in order to save a penalty or forfeiture; as, to tender the amount of rent or debt.
a.
More advanced than another in age; prior in age; elder; hence, more advanced in dignity, rank, or office; superior; as, senior member; senior counsel.