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Topics referred to by the same term
exponential map is a generalization of the ordinary exponential function of mathematical analysis. Important special cases include: exponential map (Riemannian
Exponential_map
Map from a Lie algebra to its Lie group
In the theory of Lie groups, the exponential map is a map from the Lie algebra g {\displaystyle {\mathfrak {g}}} of a Lie group G {\displaystyle G} to
Exponential_map_(Lie_theory)
Map from tangent space to the manifold
In Riemannian geometry, an exponential map is a map from a subset of a tangent space TpM of a Riemannian manifold (or pseudo-Riemannian manifold) M to
Exponential map (Riemannian geometry)
Exponential_map_(Riemannian_geometry)
Formula in Lie group theory
groups, the exponential map is a map from the Lie algebra g of a Lie group G into G. In case G is a matrix Lie group, the exponential map reduces to the
Derivative of the exponential map
Derivative_of_the_exponential_map
Topics referred to by the same term
function's current value Exponential map (Riemannian geometry), in Riemannian geometry Exponential map (Lie theory), in Lie theory Exponential notation, also known
Exponential
Mathematical function, denoted exp(x) or e^x
In mathematics, the exponential function is the unique real function which maps zero to one and has a derivative everywhere equal to its value. It is
Exponential_function
systems, the exponential map can be used as the evolution function of the discrete nonlinear dynamical system. The family of exponential functions is
Exponential map (discrete dynamical systems)
Exponential_map_(discrete_dynamical_systems)
Group of rotations in 3 dimensions
one-parameter subgroup follows directly from properties of the exponential map. The exponential map provides a diffeomorphism between a neighborhood of the origin
3D_rotation_group
Parameterization of a rotation into a unit vector and angle
inverting the exponential map, that is, when finding a rotation vector that corresponds to a given rotation matrix. The exponential map is onto but not
Axis–angle_representation
Type of matrix
the Lie algebra to the Lie group is the exponential map, which is defined using the standard matrix exponential series for exp(A) For any skew-symmetric
Infinitesimal_rotation_matrix
Group that is also a differentiable manifold with group operations that are smooth
, then the exponential map takes the Lie algebra of G {\displaystyle G} into G {\displaystyle G} ; thus, we have an exponential map for all matrix
Lie_group
Mathematics of smooth surfaces
The map from tangent vectors to endpoints smoothly sweeps out a neighbourhood of the base point and defines what is called the exponential map, defining
Differential geometry of surfaces
Differential_geometry_of_surfaces
Azimuthal equidistant map projection
that all points on the map are at the correct azimuth (direction) from the center point — that is, it is the exponential map on a sphere. A useful application
Azimuthal equidistant projection
Azimuthal_equidistant_projection
Exponential hierarchy Exponential integral Exponential integrator Exponential map (Lie theory) Exponential map (Riemannian geometry) Exponential map (discrete dynamical
List_of_exponential_topics
Matrix representing a Euclidean rotation
Cayley map specifies the same rotation matrix through the map exp(2 artanh A). For a detailed derivation, see Derivative of the exponential map. Issues
Rotation_matrix
Matrix operation generalizing exponentiation of scalar numbers
differential equations. In the theory of Lie groups, the matrix exponential gives the exponential map between a matrix Lie algebra and the corresponding Lie group
Matrix_exponential
Theorem in manifold theory
equipped with its Levi-Civita connection, and p a point of M. The exponential map is a mapping from the tangent space at p to M: e x p : T p M → M {\displaystyle
Gauss's lemma (Riemannian geometry)
Gauss's_lemma_(Riemannian_geometry)
Arithmetic operation
general knowledge of complex dynamics and specific research of the exponential map.[citation needed] Tetration can be extended to infinite heights; i
Tetration
Group in group theory and physics
Heisenberg group H has the special property that the exponential map is a one-to-one and onto map from the Lie algebra h {\displaystyle {\mathfrak {h}}}
Heisenberg_group
Special coordinate system in differential geometry
coordinate system in a neighborhood of p obtained by applying the exponential map to the tangent space at p. In a normal coordinate system, the Christoffel
Normal_coordinates
Type of transfinite numbers
points of an exponential map. Consequently, they are not reachable from 0 via a finite series of applications of the chosen exponential map and of "weaker"
Epsilon_number
Sum of directed areas in exterior algebra
orthogonal matrices with determinant 1 through the exponential map. In particular, applying the exponential map to a bivector that is associated with a rotation
Bivector
Function acting on the space of physical states in physics
recovered, under normal circumstances, from the generators, via the exponential map. In the case of the translations the idea works like this. The translation
Operator_(physics)
Vector formula for a rotation in space, given its axis
theory, the Rodrigues' formula provides an algorithm to compute the exponential map from the Lie algebra so(3) to its Lie group SO(3). This formula is
Rodrigues'_rotation_formula
Form of a matrix
exponential of the skew-symmetric matrix Q Σ Q T {\displaystyle Q\Sigma Q^{\textsf {T}}} . Conversely, the surjectivity of the exponential map, together
Skew-symmetric_matrix
Set of points where the shortest paths from a specific starting point cease to be unique
T p M {\displaystyle T_{p}M} , the curve defined by the Riemannian exponential map, γ ( t ) = exp p ( t v ) {\displaystyle \gamma (t)=\exp _{p}(tv)}
Cut_locus
Mathematical term
{\displaystyle {\mathfrak {g}}} consists of matrices and the exponential map is the matrix exponential exp ( X ) = e X {\displaystyle \operatorname {exp} (X)=e^{X}}
Adjoint_representation
Algorithms and methods of plotting the Mandelbrot set on a computing device
the exponentially mapped and cyclic method above, we can take the result of that into the Luma and Chroma channels. We can also exponentially map the
Plotting algorithms for the Mandelbrot set
Plotting_algorithms_for_the_Mandelbrot_set
No complete regular surface of constant negative gaussian curvature immerses in R3
The exponential map exp p : T p ( S ) ⟶ S {\displaystyle \exp _{p}:T_{p}(S)\longrightarrow S} is a local diffeomorphism (in fact a covering map, by Cartan-Hadamard
Hilbert's theorem (differential geometry)
Hilbert's_theorem_(differential_geometry)
Formula in Lie theory
Let exp : g → G {\displaystyle \exp :{\mathfrak {g}}\to G} be the exponential map. The following general combinatorial formula was introduced by Eugene
Baker–Campbell–Hausdorff formula
Baker–Campbell–Hausdorff_formula
On the structure of complete Riemannian manifolds of non-positive sectional curvature
cover of such a manifold is diffeomorphic to a Euclidean space via the exponential map at any point. It was first proved by Hans Carl Friedrich von Mangoldt
Cartan–Hadamard_theorem
Concepts in mathematics
by X. The exponential map is smooth. For a fixed X, the map t ↦ exp(tX) is the one-parameter subgroup of G generated by X. The exponential map restricts
Vector_flow
Categorical generalization of a function space in set theory
In mathematics, specifically in category theory, an exponential object or map object is the categorical generalization of a function space in set theory
Exponential_object
Mathematical operation on invertible matrices
mathematics, a logarithm of a matrix is another matrix such that the matrix exponential of the latter matrix equals the original matrix. It is thus a generalization
Logarithm_of_a_matrix
Family of linear transformations
the case of the Lorentz group, the exponential map is just the matrix exponential. Globally, the exponential map is not one-to-one, but in the case of
Lorentz_transformation
Square matrices satisfy their characteristic equation
of such usage is the exponential map from the Lie algebra of a matrix Lie group into the group. It is given by a matrix exponential, exp : g → G ; t X ↦
Cayley–Hamilton_theorem
Algebraic structure used in analysis
infinite-dimensional Lie algebras, Lie theory works less well. The exponential map need not be a local homeomorphism (for example, in the diffeomorphism
Lie_algebra
Correspondence between topics in Lie theory
{\displaystyle \exp(df(X))=f(\exp(X))} for all X in Lie(G), where "exp" is the exponential map Lie ( ker ( f ) ) = ker ( d f ) {\displaystyle \operatorname
Lie group–Lie algebra correspondence
Lie_group–Lie_algebra_correspondence
Concept in group theory (mathematics)
The invariant decomposition therefore gives a closed form formula for exponentials, since each F i {\displaystyle F_{i}} squares to a scalar and thus follows
Invariant_decomposition
Mathematical object
different way to think of the one-point compactification is via the exponential map. Returning to our picture of the unit two-sphere sitting on the Euclidean
3-sphere
Mathematical group
2 n , C ) {\displaystyle {\mathfrak {sp}}(2n,\mathbb {C} )} . The exponential map from s p ( 2 n , R ) {\displaystyle {\mathfrak {sp}}(2n,\mathbb {R}
Symplectic_group
{O}}_{M}\to {\mathcal {O}}_{M}^{*}\to 0.} The exponential mapping here is not always a surjective map on sections; this can be seen for example when
Exponential_sheaf_sequence
Study of Lie groups, Lie algebras and differential equations
Wilhelm Killing and Élie Cartan. The foundation of Lie theory is the exponential map relating Lie algebras to Lie groups which is called the Lie group–Lie
Lie_theory
Extension of the domain of an analytic function (mathematics)
exponential map, but we would discover that they are all represented by some germ in S. In that sense, S is the "one true inverse" of the exponential
Analytic_continuation
Metric on a smooth statistical manifold
With some additional abuse of language, one notes that the exponential map provides a map from vectors in a tangent space to points in an underlying manifold
Fisher_information_metric
Topological group with compact topology
a well-defined map of T into S 1 {\displaystyle S^{1}} . Rather, let Γ {\displaystyle \Gamma } denote the kernel of the exponential map: Γ = { H ∈ t ∣
Compact_group
Topics referred to by the same term
in differential in geometrical, local coordinates obtained from the exponential map (Riemannian geometry) Normal distribution, the Gaussian continuous
Normal
Branch of mathematics that studies abstract algebraic structures
Lie) algebra A {\displaystyle A} on a vector space V {\displaystyle V} is a map Φ : G × V → V or Φ : A × V → V {\displaystyle \Phi \colon G\times V\to V\quad
Representation_theory
Feature of systems that defy description
easy. For example, some difficult problems need algorithms that take an exponential amount of time in terms of the size of the problem to solve. Take the
Complexity
Mathematical function between groups that preserves multiplication structure
= a u {\displaystyle f_{u}(a)=a^{u}} is a group homomorphism. The exponential map yields a group homomorphism from the group of real numbers R with addition
Group_homomorphism
Group theory theorem
U of the origin in g {\displaystyle {\mathfrak {g}}} such that the exponential map sends U diffeomorphically onto some neighborhood V {\displaystyle V}
Closed-subgroup_theorem
connection Einstein manifold Euclidean geometry Exponential map Exponential map (Lie theory), Exponential map (Riemannian geometry) Finsler metric A generalization
Glossary of Riemannian and metric geometry
Glossary_of_Riemannian_and_metric_geometry
Geometric space with six dimensions
1 {\displaystyle \mathbb {R} ^{3,1}} through the exponential map (e.g. applying the exponential map of all bivectors in Λ 2 R 4 {\displaystyle \Lambda
Six-dimensional_space
Riemannian manifold in which geodesics extend infinitely in all directions
(geodesically) complete if for all points p ∈ M {\displaystyle p\in M} , the exponential map at p {\displaystyle p} is defined on T p M {\displaystyle T_{p}M}
Complete_manifold
Approach to general relativity
{\displaystyle X} can be taken to be an element of the algebra, the exponential is the exponential map of a Lie group, and group elements correspond to the geodesics
Tetrad_formalism
Description in Riemannian geometry
other words, the image of σ p {\displaystyle \sigma _{p}} under the exponential map at p {\displaystyle p} ). The sectional curvature is a real-valued
Sectional_curvature
Space which has no holes through it
be simply connected. Take for example the complex plane under the exponential map: the image is C ∖ { 0 } , {\displaystyle \mathbb {C} \setminus \{0\}
Simply_connected_space
Generalized matrix decomposition for Lie groups and Lie algebras
exponential map is a diffeomorphism from p {\displaystyle {\mathfrak {p}}} onto the space of positive definite matrices. Up to this exponential map,
Cartan_decomposition
Element of interest in an algebraic structure
of it, by means of integration. The general concept is of using the exponential map to take the vectors in the tangent space and extend them, as geodesics
Generator_(mathematics)
Representation of the symmetry group of spacetime in special relativity
are 6-dimensional, the kernel must be 0-dimensional, hence {0}. The exponential map is one-to-one in a neighborhood of the identity in SL ( 2 , C ) , {\displaystyle
Representation theory of the Lorentz group
Representation_theory_of_the_Lorentz_group
Topics referred to by the same term
notation EXP, a building located at Northeastern University in Boston Exponential map (disambiguation) This disambiguation page lists articles associated
Exp
Group representation
X\in V} . That is, the exponential map has a local inverse. In most groups, this is only local; that is, the exponential map is typically neither one-to-one
Representation_of_a_Lie_group
Quadratic polynomial
"Julia and Mandelbrot sets, alternate planes". aleph0.clarku.edu. "Exponential Map, Mu-Ency at MROB". mrob.com. Trees of visible components in the Mandelbrot
Complex_quadratic_polynomial
coadjoint orbits, weighted by the square-root of the Jacobian of the exponential map, denoted by j {\displaystyle j} . It does not apply to all Lie groups
Kirillov_character_formula
Universal construction of a complex Lie group from a real Lie group
connected subgroups of N± and subalgebras of their Lie algebras. The exponential map is onto in each case, since the polynomial function log ( eA eB ) lies
Complexification_(Lie_group)
Function used in computer graphics
space at any point on a quaternion slerp curve, the inverse of the exponential map transforms the curve into a line segment. Slerp curves not extending
Spherical linear interpolation
Spherical_linear_interpolation
Condition on transcendence of numbers
In mathematics, specifically transcendental number theory, the six exponentials theorem is a result that, given the right conditions on the exponents,
Six_exponentials_theorem
Real numbers adjoined with a nil-squaring element
}{\frac {\left(b\varepsilon \right)^{n}}{n!}}=1+b\varepsilon ,} so the exponential map applied to the ε-axis covers only half the "circle". Let z = a + bε
Dual_number
Representation of a quantum mechanical system
the (real) dimension of U(n) is n2. This is easy to see since the exponential map A ↦ e i A {\displaystyle A\mapsto e^{iA}} is a local homeomorphism
Bloch_sphere
Mathematical function, inverse of an exponential function
analogous to the real case. In the context of differential geometry, the exponential map maps the tangent space at a point of a manifold to a neighborhood of that
Logarithm
Möbius transformation generalized to rings other than the complex numbers
numbers as rings that express angle and "rotation". In each case the exponential map applied to the imaginary axis produces an isomorphism between one-parameter
Linear fractional transformation
Linear_fractional_transformation
Complex exponential in terms of sine and cosine
fundamental relationship between the trigonometric functions and the complex exponential function. Euler's formula states that, for any real number x, one has
Euler's_formula
Family of probability distributions related to the normal distribution
In probability and statistics, an exponential family is a parametric set of probability distributions of a certain form, specified below. This special
Exponential_family
Branch of differential geometry
is diffeomorphic to the Euclidean space Rn with n = dim M via the exponential map at any point. It implies that any two points of a simply connected
Riemannian_geometry
Algebraic generalization of the derivative
Hasse derivative p-derivation Wirtinger derivatives Derivative of the exponential map Bourbaki, Nicolas (1989), Algebra I, Elements of mathematics, Springer-Verlag
Derivation (differential algebra)
Derivation_(differential_algebra)
In mathematics, a chaotic map is a map (an evolution function) that exhibits some sort of chaotic behavior. Maps may be parameterized by a discrete-time
List_of_chaotic_maps
Major unsolved problem in transcendental number theory
iterated exponential identities for exponential constants, and the exponential subring of the real numbers generated by 1 is the free exponential ring on
Schanuel's_conjecture
One-dimensional complex manifold
is hyperbolic – compare pair of pants. One can map from one puncture to two, via the exponential map (which is entire and has an essential singularity
Riemann_surface
Invariance of operations under geometric translation
Diffeomorphism Loop Euclidean Lie algebras Lie group–Lie algebra correspondence Exponential map Adjoint representation Killing form Index Simple Lie algebra Loop algebra
Translational_symmetry
Straight path on a curved surface or a Riemannian manifold
G t ( V ) = exp ( t V ) {\displaystyle G^{t}(V)=\exp(tV)} is the exponential map of the vector tV. A closed orbit of the geodesic flow corresponds to
Geodesic
Mathematical field with an extra operation
In mathematics, an exponential field is a field with a further unary operation that is a homomorphism from the field's additive group to its multiplicative
Exponential_field
Algebraic term
the exponential map takes any nilpotent square matrix to a unipotent matrix. Moreover, if U is a commutative unipotent group, the exponential map induces
Unipotent
Graphical method to simplify Boolean expressions
A Karnaugh map (KM or K-map) is a diagram that can be used to simplify a Boolean algebra expression. Maurice Karnaugh introduced the technique in 1953
Karnaugh_map
Assignment of a vector to each point in a subset of Euclidean space
pathline in fluid, geodesic flow, and one-parameter subgroups and the exponential map in Lie groups. By definition, a vector field on M {\displaystyle M}
Vector_field
Assignment of vector fields to manifolds
Coordinate-induced basis Cotangent space Differential geometry of curves Exponential map Vector space do Carmo, Manfredo P. (1976). Differential Geometry of
Tangent_space
Creating a "larger" Lie algebra from a smaller one, in one of several ways
extensions. Notational abuse to be found below includes eX for the exponential map exp given an argument, writing g for the element (g, eH) in a direct
Lie_algebra_extension
Exponential representation for differential equations
Magnus expansion, named after Wilhelm Magnus (1907–1990), provides an exponential representation of the product integral solution of a first-order homogeneous
Magnus_expansion
Tool in symplectic geometry
where exp : g → G {\displaystyle \exp :{\mathfrak {g}}\to G} is the exponential map and ⋅ {\displaystyle \cdot } denotes the G {\displaystyle G} -action
Momentum_map
Group of unitary complex matrices with determinant of 1
can be mapped to the quaternion a 1 ^ + b i ^ + c j ^ + d k ^ {\displaystyle a\,{\hat {1}}+b\,{\hat {i}}+c\,{\hat {j}}+d\,{\hat {k}}} This map is in fact
Special_unitary_group
Mathematical transformation in physics
Diffeomorphism Loop Euclidean Lie algebras Lie group–Lie algebra correspondence Exponential map Adjoint representation Killing form Index Simple Lie algebra Loop algebra
Time-translation_symmetry
Group of flat spacetime symmetries
Diffeomorphism Loop Euclidean Lie algebras Lie group–Lie algebra correspondence Exponential map Adjoint representation Killing form Index Simple Lie algebra Loop algebra
Poincaré_group
abelian group G, and is the universal ring R such that there is an exponential map from G to the group of the formal power series in R[[t]] with constant
Exp_algebra
Isomorphism of differentiable manifolds
by fixing a Riemannian metric on M {\displaystyle M} and using the exponential map for that metric. If r {\displaystyle r} is finite and the manifold
Diffeomorphism
Theory in physics and mathematics
space X is the phase space of the dynamical system. A transformation (a map) τ : X → X {\displaystyle \tau :X\to X} is said to be Σ-measurable if and
Conservative_system
English mathematician, philosopher, and engineer (1791–1871)
(in which Δ and D were related by the simple additive case of the exponential map). But via Herschel he was influenced by Arbogast's ideas in the matter
Charles_Babbage
Group of matrices with determinant 1
determinant and having positive eigenvalues can be uniquely expressed as the exponential of a traceless Hermitian matrix, and therefore the topology of this is
Special_linear_group
Mathematical matrix
of a symplectic matrix is not necessarily Hamiltonian because the exponential map from the Lie algebra to the group is not surjective. The characteristic
Hamiltonian_matrix
Gives equivalent statements about the geodesic completeness of Riemannian manifolds
geodesically complete; that is, for every p ∈ M , {\displaystyle p\in M,} the exponential map expp is defined on the entire tangent space T p M . {\displaystyle
Hopf–Rinow_theorem
{\displaystyle {\mathfrak {g}}'} . exponential map The exponential map for a Lie group G with g {\displaystyle {\mathfrak {g}}} is a map g → G {\displaystyle {\mathfrak
Glossary of Lie groups and Lie algebras
Glossary_of_Lie_groups_and_Lie_algebras
Mathematical concept
Using this integrability condition, it is possible to define the exponential map of the Lie algebra and in this way obtain, locally, a group action
Maurer–Cartan_form
EXPONENTIAL MAP
EXPONENTIAL MAP
Boy/Male
Hindu
King of stars, Map
Boy/Male
Anglo Saxon
God of youth and music.
Surname or Lastname
German
German : nickname for someone with boils or lumpy skin, or perhaps for a hunchback, from Middle High German maser ‘lump’, ‘protuberance’.German and English : from Middle High Germanmaser, Middle English maser ‘maple-wood bowl’ (Old French masere, of Germanic origin), hence a metonymic occupational name for a wood-turner producing such ware.English : variant spelling of Macer, an occupational name for a mace-bearer, from Old French maissier, massier, a derivative of Old French masse ‘mace’.German (Maaser) : pet form of Thomas.
Surname or Lastname
English
English : variant spelling of Maple.
Surname or Lastname
English
English : variant of Maple.
Surname or Lastname
English
English : metronymic from the medieval female personal name Mab(be) (see Mapp).
Surname or Lastname
English (Norfolk)
English (Norfolk) : metronymic from the medieval female personal name Mab(be) (see Mapp 1).
Surname or Lastname
English
English : from a short form of the female personal name Mabel (see Mapp).
Surname or Lastname
English
English : topographic name for someone who lived by a maple tree, Middle English mapel (Old English mapul).French : from Latin mapula, a diminutive of mappa ‘piece of cloth’, ‘napkin’, presumably a metonymic occupational name for a cloth merchant or a weaver.
Girl/Female
Indian, Marathi
Star; Map
Girl/Female
Hindu
King of stars, Map
Surname or Lastname
English
English : of uncertain origin, perhaps, as Reaney suggests, from a pet form of the Old English personal name Wippa, or perhaps a topographic name for someone who lived by a whipple tree, whatever that may have been. Chaucer lists whippletree (probably a kind of dogwood) along with maple, thorn, beech, hazel, and yew.Matthew Whipple came from England to Ipswich, MA, in about 1638. His descendent William Whipple (1730–85) born in Kittery, ME, was a signer of the Declaration of Independence.
Girl/Female
Hindu, Indian
Maple Tree
Girl/Female
Tamil
King of stars, Map
Surname or Lastname
English and French
English and French : from the medieval personal name Masselin. This originated as an Old French pet form of Germanic names with the first element mathal ‘speech’, ‘counsel’. However, it was later used as a pet form of Matthew. Compare Mace. A feminine form, Mazelina, was probably originally a pet form of Matilda.English and French : possibly a metonymic occupational name for a maker of wooden bowls, from Middle English, Old French maselin ‘bowl or goblet of maple wood’ (a diminutive of Old French masere ‘maple wood’, of Germanic origin). In some cases it may derive from the homonymous dialect terms maslin, one of which means ‘brass’ (Old English mæslen, mæstling), the other ‘mixed grain’ (Old French mesteillon).
Female
Native American
Native American Sioux name MAPIYA means "sky."
Surname or Lastname
English
English : from a variant of the medieval female personal name Mab(be), a short form of Middle English, Old French Amabel (from Latin amabilis ‘loveable’). This has survived into the 20th century in the short form Mabel.English : possibly from an unattested Old English male personal name, Mappa.English : from Old Welsh map, mab ‘son’, which was used as a distinguishing epithet.
Boy/Male
Tamil
King of stars, Map
Surname or Lastname
English
English : habitational name from Great and Little Linford in Buckinghamshire or Lynford in Norfolk. The former may have Old English hlyn ‘maple’ as its first element; the latter is more likely to contain līn ‘flax’. The second element in each case is Old English ford ‘ford’.
Surname or Lastname
English (Somerset and Gloucester)
English (Somerset and Gloucester) : unexplained. Perhaps a habitational name from a lost or unidentified place.
EXPONENTIAL MAP
EXPONENTIAL MAP
Boy/Male
Muslim
Lover
Girl/Female
Hindu
Who protect
Girl/Female
Hindu, Indian
With Many Forms
Boy/Male
Indian
Girl/Female
British, Hindu, Indian, Russian
Compassionate; Brightness
Girl/Female
Tamil
Goddess Lakshmi
Boy/Male
British, English, Hindu, Indian
Listening
Male
Basque
, Jehovah's gift or grace.
Girl/Female
Spanish
of Mars. Mars was the mythological Roman god of fertility for whom the month March was named;...
Girl/Female
Indian, Tamil
Sure
EXPONENTIAL MAP
EXPONENTIAL MAP
EXPONENTIAL MAP
EXPONENTIAL MAP
EXPONENTIAL MAP
a.
Having or consisting of lines resembling a map; as, the maplike figures in which certain lichens grow.
n.
Thick sirup made by boiling down the sap of the sugar maple, and then cooling.
n.
Relative dimensions, without difference in proportion of parts; size or degree of the parts or components in any complex thing, compared with other like things; especially, the relative proportion of the linear dimensions of the parts of a drawing, map, model, etc., to the dimensions of the corresponding parts of the object that is represented; as, a map on a scale of an inch to a mile.
n.
The making, or study, of maps.
n.
A zodiacal constellation, represented on maps and globes as a centaur shooting an arrow.
n.
A series of spaces marked by lines, and representing proportionately larger distances; as, a scale of miles, yards, feet, etc., for a map or plan.
n.
Anything which represents graphically a succession of events, states, or acts; as, an historical map.
a.
Of or pertaining to an order of trees and shrubs (Sapindaceae), including the (typical) genus Sapindus, the maples, the margosa, and about seventy other genera.
a.
Pertaining to exponents; involving variable exponents; as, an exponential expression; exponential calculus; an exponential function.
v. t.
To represent by a map; -- often with out; as, to survey and map, or map out, a county. Hence, figuratively: To represent or indicate systematically and clearly; to sketch; to plan; as, to map, or map out, a journey; to map out business.
n.
A tree of the genus Acer, including about fifty species. A. saccharinum is the rock maple, or sugar maple, from the sap of which sugar is made, in the United States, in great quantities, by evaporation; the red or swamp maple is A. rubrum; the silver maple, A. dasycarpum, having fruit wooly when young; the striped maple, A. Pennsylvanium, called also moosewood. The common maple of Europe is A. campestre, the sycamore maple is A. Pseudo-platanus, and the Norway maple is A. platanoides.
imp. & p. p.
of Map
n.
An expression of the condition of equality between two algebraic quantities or sets of quantities, the sign = being placed between them; as, a binomial equation; a quadratic equation; an algebraic equation; a transcendental equation; an exponential equation; a logarithmic equation; a differential equation, etc.
p. pr. & vb. n.
of Map
n.
The moosewood, or striped maple. See Maple.
n.
A description or plan of the heavens and the heavenly bodies; the construction of celestial maps, globes, etc.; uranology.
n.
That which runs or flows in the course of a certain operation, or during a certain time; as, a run of must in wine making; the first run of sap in a maple orchard.
n.
A dry, indehiscent, usually one-seeded, winged fruit, as that of the ash, maple, and elm; a key or key fruit.