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Concept in the solution of linear partial differential equations
In mathematics, a fundamental solution for a linear partial differential operator L is a formulation in the language of distribution theory of the older
Fundamental_solution
Type of Diophantine equation
that every solution is a Pell multiple of a solution from that set. In particular, if ( u , v ) {\displaystyle (u,v)} is the fundamental solution to u 2 −
Pell's_equation
Partial differential equation describing the evolution of temperature in a region
(\mathbf {x} )\end{cases}}} The n-variable fundamental solution is the product of the fundamental solutions in each variable; i.e., Φ ( x , t ) = Φ ( x
Heat_equation
Type of differential equation
navigate through the plethora of different solutions at hand. For this reason, they are also fundamental when carrying out a purely numerical simulation
Partial_differential_equation
Second-order partial differential equation
particle), which is the solution of the Euler equations in two-dimensional incompressible flow. A Green's function is a fundamental solution that also satisfies
Laplace's_equation
the method of fundamental solutions (MFS) is a technique for solving partial differential equations based on using the fundamental solution as a basis function
Method of fundamental solutions
Method_of_fundamental_solutions
Concept in the solution of linear partial differential equations
differential equations (PDEs), a parametrix is an approximation to a fundamental solution of a PDE, and is essentially an approximate inverse to a differential
Parametrix
Generalized function whose value is zero everywhere except at zero
is a differential operator on Rn, is to seek first a fundamental solution, which is a solution of the equation L [ u ] = δ . {\displaystyle L[u]=\delta
Dirac_delta_function
Matrix consisting of linearly independent solutions to a linear differential equation
(t)=\Psi _{0}(t)C} is also a fundamental matrix. In particular, if Ψ 0 {\displaystyle \Psi _{0}} is any fixed fundamental solution for a given equation, then
Fundamental matrix (linear differential equation)
Fundamental_matrix_(linear_differential_equation)
Group in group theory and physics
The sub-Laplacian also has an explicit fundamental solution, analogous to the Euclidean fundamental solution of the ordinary Laplacian. In complex coordinates
Heisenberg_group
Mathematical problem set on a chessboard
the puzzle has 12 solutions. These are called fundamental solutions; representatives of each are shown below. A fundamental solution usually has eight
Eight_queens_puzzle
Formulae for viscous and incompressible fluid flow at small Reynolds numbers
Source: The fundamental solution due to a singular point force embedded in an Oseen flow is the Oseenlet. The closed-form fundamental solutions for the generalized
Oseen_equations
Provides integral formulas for all derivatives of a holomorphic function
value. The second conclusion asserts that the Cauchy kernel is a fundamental solution of the Cauchy–Riemann equations. Note that for smooth complex-valued
Cauchy's_integral_formula
Branch of ordinary differential equations
solution if the columns form a basis of the solution set. A matrix Φ ( t ) {\displaystyle \Phi (t)} is called a principal fundamental matrix solution
Floquet_theory
Method of solution to differential equations
For this reason, the Green's function is also sometimes called the fundamental solution associated to the operator L. Not every operator L {\displaystyle
Green's_function
Elliptic partial differential equation
electrolyte solutions. Using a Green's function, the potential at distance r from a central point charge Q (i.e., the fundamental solution) is φ ( r )
Poisson's_equation
Fundamental solution to the heat equation, given boundary values
mathematical study of heat conduction and diffusion, a heat kernel is the fundamental solution to the heat equation on a specified domain with appropriate boundary
Heat_kernel
Probability distribution
mathematics, it is closely related to the Poisson kernel, which is the fundamental solution for the Laplace equation in the upper half-plane. It is one of the
Cauchy_distribution
Topics referred to by the same term
two variables that defines an integral transform Heat kernel, the fundamental solution to the heat equation on a specified domain Convolution kernel Stochastic
Kernel
integral transforms and infinite series, or by employing appropriate fundamental solutions. For example, the Dirichlet problem of the heat equation on the
Fokas_method
Number, approximately 3.14
1/2\pi } is necessary to ensure that Φ {\displaystyle \Phi } is the fundamental solution of the Poisson equation in R 2 {\displaystyle \mathbb {R} ^{2}} :
Pi
Computational method for solving partial differential equations
function, satisfy the governing equation and are often fundamental solution or general solution of governing equation. Consequently, only boundary discretization
Kansa_method
Property of vector fields in mathematics
\cdot )\to f,&{\text{as }}t\to 0;\end{cases}}} to have a smooth fundamental solution, i.e. a real-valued function p (0, +∞) × R2d → R such that p(t, ·
Hörmander's_condition
Green's function for Laplacian
origin, the Newtonian kernel Γ {\displaystyle \Gamma } which is the fundamental solution of the Laplace equation. It is named for Isaac Newton, who first
Newtonian_potential
Partial differential equations
In physics, the Green's function (or fundamental solution) for the Laplacian (or Laplace operator) in three variables is used to describe the response
Green's function for the three-variable Laplace equation
Green's_function_for_the_three-variable_Laplace_equation
Relationship of a signal transducer
see also transfer function. The concept of a Green's function or fundamental solution of an ordinary differential equation is closely related. Denote the
Linear_response_function
Output of a dynamic system when given a brief input
Dirac's delta function under the transformation, analogous to the fundamental solution of a partial differential operator. It is usually easier to analyze
Impulse_response
Mathematical problem in number theory
{609\times 7766}},} where ( u , v ) {\displaystyle (u,v)} is the fundamental solution of the Pell equation u 2 − ( 609 × 7766 ) v 2 = 1. {\displaystyle
Archimedes's_cattle_problem
Type of fluid flow
point force embedded in a Stokes flow. From its derivatives, other fundamental solutions can be obtained. The Stokeslet was first derived by Carl Wilhelm
Stokes_flow
Certain vector fields are the sum of an irrotational and a solenoidal vector field
physics and mathematics, the Helmholtz decomposition theorem or the fundamental theorem of vector calculus states that certain differentiable vector
Helmholtz_decomposition
Procedure for solving differential equations
variation of parameters usually involves the fundamental solution of the homogeneous problem, the infinitesimal solutions x s {\displaystyle x_{s}} then being
Variation_of_parameters
Complex-valued function
_{n=0}^{\infty }(1-e^{-t})e^{-nt}~h_{n}(x)h_{n}(y)} In physics, the fundamental solution, (Green's function), or propagator of the Hamiltonian for the quantum
Mehler_kernel
Mathematical descriptions of molecular diffusion
law has the same mathematical form as the Heat equation and its fundamental solution is the same as the Heat kernel, except switching thermal conductivity
Fick's_laws_of_diffusion
Study of the deformation of bodies in the presence of frictional effects
classical contribution by Heinrich Hertz stands out. Further the fundamental solutions by Boussinesq and Cerruti are of primary importance for the investigation
Frictional_contact_mechanics
manifold. The quantization of the geodesic flow is given by the fundamental solution of the Schrödinger equation U t = exp ( i t Δ ) {\displaystyle
Quantum_ergodicity
Solution exhibiting thermodynamic properties analogous to an ideal gas
ideality) is equal to one for each component. The concept of an ideal solution is fundamental to both thermodynamics and chemical thermodynamics and their applications
Ideal_solution
Probability distribution
physics of heat conduction, the folded normal distribution is a fundamental solution of the heat equation on the half space; it corresponds to having
Folded_normal_distribution
Partial differential equations describing diffusion
{\displaystyle D=\sigma ^{2}/2.} Define the transition density (or fundamental solution) p ( t , x ; T , y ) {\displaystyle p(t,x;\,T,y)} by p ( t , x ;
Kolmogorov backward equations (diffusion)
Kolmogorov_backward_equations_(diffusion)
Concept in dynamical systems
rix}}=A{\begin{bmatrix}z_{1}\\z_{2}\end{bmatrix}}} which has the fundamental solution Φ ( t ) = e A t {\displaystyle \Phi (t)=e^{At}} corresponding to
Method_of_averaging
Expression in differential equations
complex entries. Let Φ denote a matrix-valued solution on I, meaning that Φ(t) is the so-called fundamental matrix, a square matrix of dimension n with
Liouville's_formula
Quantum mechanical model
performing calculations, by bypassing clutter. For example, the fundamental solution (propagator) of H − i∂t, the time-dependent Schrödinger operator
Quantum_harmonic_oscillator
Concept in statistics
equivalent to the amount of heat generated when heat kernels (the fundamental solution to the heat equation) are placed at each data point locations xi
Kernel_density_estimation
Method of solving linear partial differential equations
matrix. The Green's functions, or fundamental solutions, are often problematic to integrate as they are based on a solution of the system equations subject
Boundary_element_method
is used to uniquely categorize certain fundamental solutions of the heat equation to make existing solutions easier to identify, store, and retrieve
Green's_function_number
Functions in mathematics
which is less singular at x 0 {\displaystyle x_{0}} than the fundamental solution (for n > 2 {\displaystyle n>2} ), that is f ( x ) = o ( | x −
Harmonic_function
Feature enhancement algorithm in imaging science
that the family of Gaussians Φ t {\displaystyle \Phi _{t}} is the fundamental solution of the heat equation ∂ t Φ t ( x ) = 1 2 Δ Φ t ( x ) . {\displaystyle
Difference_of_Gaussians
the other methods based on the fundamental solutions, such as boundary element method, method of fundamental solutions and singular boundary method in
Boundary_knot_method
Class of ordinary differential equations
{\displaystyle y_{n}=y_{n}(x)} (up to constant multiple), called the nth fundamental solution. The normalized eigenfunctions y n {\displaystyle y_{n}} form an
Sturm–Liouville_theory
Every polynomial has a real or complex root
problem of finding a constructive proof of the fundamental theorem of algebra. He presented his solution, which amounts in modern terms to a combination
Fundamental theorem of algebra
Fundamental_theorem_of_algebra
Comune in Lombardy, Italy
This was considered a fundamental solution to increase traffic on the road, as transport by water was a much easier solution to transport big amounts
Rho,_Lombardy
F {\displaystyle G(\cdot ,z)*F} is the convolution of F with the fundamental solution G: ( G ( ⋅ , z ) ∗ F ) ( x ) = ∫ R G ( x − y ; z ) F ( y ) d y ,
Limiting_absorption_principle
D^{2}=-\Delta _{n}} where Δn is the Laplacian in n-euclidean space. The fundamental solution to the euclidean Dirac operator is G ( x − y ) := 1 ω n x − y ‖ x
Clifford_analysis
Type of energy healing
that is, elimination of defilement in the spirit, results in the fundamental solution of any type of illness and leads to true happiness. This is similar
Johrei
combination of a harmonic function in the unpunctured domain with a scaled fundamental solution for the Laplacian in that domain. Marden's theorem Axler, Sheldon;
Bôcher's_theorem
Vector calculus formulas relating the bulk with the boundary of a region
identity by choosing φ = G, where Green's function G is taken to be a fundamental solution of the Laplace operator, ∆. This means that: Δ G ( x , η ) = δ (
Green's_identities
Describes state evolution of a linear system
n\times n} matrix U ( t ) {\displaystyle \mathbf {U} (t)} is the fundamental solution matrix that satisfies U ˙ ( t ) = A ( t ) U ( t ) {\displaystyle
State-transition_matrix
Integral used in the theory of vibrations
{dx}{dt}}\right|_{t=0}=0} , then by solving the differential equation one can get a fundamental solution (known as a unit-impulse response function) h ( t ) = { 1 m ω d e
Duhamel's_integral
Astronomical catalogues of stars
Jährling, R. (1999). "Sixth Catalogue of Fundamental Stars (FK6): Part I: Basic Fundamental Stars with Direct Solutions" (PDF). Veröffentlichungen Astronomisches
Catalogues of Fundamental Stars
Catalogues_of_Fundamental_Stars
Short "burst" or "envelope" of restricted wave action that travels as a unit
it}}}e^{i(x-y)^{2}/2t}dy\,.} Thus, this is a formal way to express the fundamental solution or general solution. The interpretation of this expression is that the amplitude
Wave_packet
Theorem in geometric topology
have the same Betti numbers but distinct fundamental groups. He posed the question of whether the fundamental group is sufficient to topologically characterize
Poincaré_conjecture
method designed to solve certain partial differential equations whose fundamental solution is explicitly known. The RMM is a strong-form collocation method
Regularized_meshless_method
Modular arithmetic concept
language primitive root of unity modulo n, emphasizing its role as a fundamental solution of the roots of unity polynomial equations Xm − 1 in the ring Z n
Primitive_root_modulo_n
Function defined by a hypergeometric series
singularity of 2F1, the value of the solutions at the endpoint will differ from the starting point. Two fundamental solutions of the hypergeometric equation
Hypergeometric_function
Japanese mathematician
pseudo-differential operators. Its work contributed to the construction of the fundamental solution of a first order hyperbolic partial differential equation. His treatise
Hitoshi_Kumano-Go
meshless boundary collocation techniques which include the method of fundamental solutions (MFS), boundary knot method (BKM), regularized meshless method (RMM)
Singular_boundary_method
Technique for computing light scattering by nonspherical particles
scattering. They are the fundamental solutions of the vector Helmholtz equation and can be generated from the scalar fundamental solutions in spherical coordinates
T-matrix_method
Study of groundwater's movement and distribution
which is another common method for deriving the Theis solution — from the fundamental solution to the diffusion equation in free space. No matter which
Hydrogeology
Method for solving partial differential equations
with a fundamental solution. In semigroup theory, the integral formula supplied by Duhamel's principle is also used to define a mild solution. If A {\displaystyle
Duhamel's_principle
Short story by James Tiptree Jr.
"The Screwfly Solution" is a 1977 science fiction novella by Raccoona Sheldon, a pen name for American psychologist Alice Sheldon, who also wrote as James
The_Screwfly_Solution
+\lambda _{j}\eta )}}{P(i\xi +\lambda _{j}\eta )}}\right)} is a fundamental solution of P ( ∂ ) {\displaystyle P(\partial )} , i.e., P ( ∂ ) E = δ {\displaystyle
Malgrange–Ehrenpreis_theorem
Process by which heat is transferred within an object
y^{2}}}+{\frac {\partial ^{2}T}{\partial z^{2}}}\right)} with a fundamental solution famously known as the heat kernel. By integrating the differential
Thermal_conduction
and Leonidas Guibas. It is based on the heat kernel, which is a fundamental solution to the heat equation. HKS is one of the many recently introduced
Heat_kernel_signature
then the fundamental unit is ε = a + b Δ 2 {\displaystyle \varepsilon ={\frac {a+b{\sqrt {\Delta }}}{2}}} where (a, b) is the smallest solution to x 2 −
Fundamental unit (number theory)
Fundamental_unit_(number_theory)
Multivalued function in mathematics
function provides an exact solution to the quantum-mechanical double-well Dirac delta function model for equal charges—a fundamental problem in physics. Prompted
Lambert_W_function
Solution of Einstein field equations
The Gödel metric, also known as the Gödel solution or Gödel universe, is an exact solution, found in 1949 by Kurt Gödel, of the Einstein field equations
Gödel_metric
Type of differential operator
elliptic operator is hypoelliptic. The property also means that every fundamental solution of an elliptic operator is infinitely differentiable in any neighborhood
Elliptic_operator
Aqueous solution of a weak acid and its conjugate base
A buffer solution is a solution where the pH does not change significantly on dilution or if an acid or base is added at constant temperature. Its pH changes
Buffer_solution
Pair of polynomial sequences
the standard technique for Pell equations of taking powers of a fundamental solution: T n ( x ) + U n − 1 ( x ) x 2 − 1 = ( x + x 2 − 1 ) n . {\displaystyle
Chebyshev_polynomials
Aqueous solution of iodine and potassium iodide
Lugol's iodine, also known as aqueous iodine and strong iodine solution, is a solution of potassium iodide with iodine in water. It is a medication and
Lugol's_iodine
Non-self-adjoint compact operator used to solve boundary value problems for the Laplacian
_{n}u\right|\leq 2\pi CR^{-1},}} so the integral over ∂Ω must vanish. The fundamental solution of the Laplacian is given by E ( z ) = − 1 2 π log | z | . {\displaystyle
Neumann–Poincaré_operator
Helmholtz, Poisson and plate bending problems, the high-order fundamental solution or general solution, harmonic function or Trefftz function (T-complete functions)
Boundary_particle_method
Solitons in Euclidean spacetime
a solution as long as ρ : R 4 → R {\displaystyle \rho :\mathbb {R} ^{4}\rightarrow \mathbb {R} } is harmonic. In four dimensions, the fundamental solution
Instanton
Scientific journal on solution chemistry
Journal of Solution Chemistry is a peer-reviewed scientific journal published monthly by Springer. It covers fundamental and applied research in physical
Journal_of_Solution_Chemistry
Field-equations in general relativity
of nonlinear partial differential equations when used in this way. The solutions of the EFE are the components of the metric tensor. The inertial trajectories
Einstein_field_equations
Solvable quantum mechanics potential
Laplace–Beltrami equation on S 3 {\displaystyle S^{3}} , it represents a fundamental solution on S 3 {\displaystyle S^{3}} , a reason for which Schrödinger considered
Trigonometric Rosen–Morse potential
Trigonometric_Rosen–Morse_potential
Theory of fundamental physics
elementary particle with predefined mass) alone is not the most fundamental solution of the mass generation problem but only its reformulation ad infinitum
Superfluid_vacuum_theory
Linear optimal control technique
part of the solution to the LQG (linear–quadratic–Gaussian) problem. Like the LQR problem itself, the LQG problem is one of the most fundamental problems
Linear–quadratic_regulator
Compact astronomical body
In 1916, the first solution of general relativity that would characterise a black hole was found. By the late 1950s, this solution began to be interpreted
Black_hole
τ ≤ t ≤ T {\displaystyle 0\leq \tau \leq t\leq T} , is called a fundamental solution of the time-dependent problem if: the partial derivative δ U ( t
Abstract differential equation
Abstract_differential_equation
Physics Textbook by Halliday, Resnick, Walker
nuclear physics and cosmology. A solutions manual and a study guide are also available. Physics education "Fundamentals of Physics 12th Edition Extended"
Fundamentals_of_Physics
Co-founder of the Chinese Communist Party (1888–1927)
Li Dazhao countered that problems could not be solved without a "fundamental solution" to the political structure as a whole. "Isms", he argued, were necessary
Li_Dazhao
Partial differential equation
{z}})=f_{z},} where the subscripts denote complex partial derivatives. The fundamental solution of the operator D = ∂ z ¯ {\displaystyle D=\partial _{\overline {z}}}
Beltrami_equation
government engaged in the embankment works of the Watarase River, no fundamental solution of the problem was achieved. Current Japanese environmental policy
Environmental_issues_in_Japan
the Russian mathematician I. G. Petrovsky, is a region where the fundamental solution of a linear hyperbolic partial differential equation vanishes. They
Petrovsky_lacuna
Generating function in integrable systems
isomonodromic τ {\displaystyle \tau } -function associated to the fundamental solution Ψ {\displaystyle \Psi } of the system (6), (7). Defining the Lie
Tau function (integrable systems)
Tau_function_(integrable_systems)
Theorem of analytic continuations
that ( π z ) − 1 {\displaystyle (\pi z)^{-1}} is known to provide a fundamental solution for the Cauchy–Riemann operator ∂ / ∂ z ¯ {\displaystyle \partial
Edge-of-the-wedge_theorem
mathematical analysis, Ehrenpreis's fundamental principle, introduced by Leon Ehrenpreis, states: Every solution of a system (in general, overdetermined)
Ehrenpreis's fundamental principle
Ehrenpreis's_fundamental_principle
Function with a repeating pattern
called the fundamental period (also primitive period or basic period). Often, "the" period of a function is used to refer to its fundamental period. Geometrically
Periodic_function
Monochrome light beam whose amplitude envelope is a Gaussian function
above. In seeking paraxial solutions, and in particular ones that would describe laser radiation that is not in the fundamental Gaussian mode, we will look
Gaussian_beam
French mathematician (born 1958)
studied the behavior of diffusion processes on manifolds and their fundamental solutions, in connection to the geometry of the underlying spaces. He also
Laurent_Saloff-Coste
FUNDAMENTAL SOLUTION
FUNDAMENTAL SOLUTION
Surname or Lastname
English
English : from an Old English byname, Budde, which was applied to a thickset or plump person. By the Middle English period it had become a common personal name, with derivatives formed with hypocoristic suffixes, Budecok and Budekin. Reaney derives it from Old English budda ‘beetle’.Shortened form of German Budde.John Budd was one of the free planters who assented to the ‘Fundamental Agreement’ of the New Haven Colony on June 4, 1639.
Boy/Male
Gujarati, Hindu, Indian, Sanskrit
Space; God of Tech; Bliss Solutions; Wise
Girl/Female
Gujarati, Hindu, Indian, Kannada, Tamil
Trick; Power; Strategy; Solution by Logic; By Reasoning
Girl/Female
Tamil
Good or Happy condition, Solution
Girl/Female
Hindu
Good or Happy condition, Solution
Girl/Female
Tamil
Trick, Power, Strategy, Solution by logic, By reasoning
Surname or Lastname
English
English : from a pet form of the Middle English personal name Boye.Jarvis Boykin was one of the free planters who assented to the ‘Fundamental Agreement’ of the New Haven Colony on June 4, 1639.
Surname or Lastname
English
English : occupational name for a merchant or trader, Middle English chapman, Old English cēapmann, a compound of cēap ‘barter’, ‘bargain’, ‘price’, ‘property’ + mann ‘man’.This name was brought independently to North America from England by numerous different bearers from the 17th century onward. John Chapmen (sic) was one of the free planters who assented to the ‘Fundamental Agreement’ of the New Haven Colony on June 4, 1639.
Surname or Lastname
English
English : from the Middle English and Old English personal name Brūning, originally a patronymic from the byname Brūn (see Brown).This name was brought independently to North America from England by numerous different bearers from the 17th century onward. William Browning was one of the free planters who assented to the ‘Fundamental Agreement’ of the New Haven Colony on June 4, 1639.
Girl/Female
Hindu
Good or Happy condition, Solution, Fortune
Boy/Male
Arabic, Muslim
Testimony; Evidence; Fundamental Belief in Islam; Witness
Male
Turkish
Turkish name TEMEL means "basic, fundamental."
Surname or Lastname
English
English : habitational name from a place in Berkshire named with the Old English personal name Benna + Old English hamm ‘river meadow’.John Benham was one of the free planters who assented to the ‘Fundamental Agreement’ of the New Haven Colony on June 4, 1639.
Girl/Female
Hindu
Trick, Power, Strategy, Solution by logic, By reasoning
Surname or Lastname
English
English : habitational name from any of the various places, in Kent, Oxfordshire, and Sussex, named Beckley, from the Old English byname Becca (see Beck 4) + Old English lēah ‘woodland clearing’.Altered spelling of the South German and Swiss topographic names Bächle, Bächli (see Bach 1).Richard Beckley was one of the free planters who assented to the ‘Fundamental Agreement’ of the New Haven Colony on June 4, 1639.
Girl/Female
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Sindhi, Telugu
Strategy; Idea; Trick; Solution; A Device; Planning
Girl/Female
Tamil
Good or Happy condition, Solution, Fortune
Girl/Female
Tamil
Trick, Power, Strategy, Solution by logic, By reasoning
FUNDAMENTAL SOLUTION
FUNDAMENTAL SOLUTION
Female
Chinese
joy, satisfaction.
Boy/Male
Latin Basque
Beyond praise.
Boy/Male
Arabic
Successful.
Girl/Female
Arabic
Beautiful Woman
Boy/Male
Hindu, Indian, Marathi
Luminous
Boy/Male
Indian
Orator, Preacher, Religious minister
Girl/Female
Arabic, Australian, German, Muslim
Delicate; Frail
Girl/Female
Indian
Guiding light lighthouse
Girl/Female
Hindu, Indian, Malayalam, Marathi
Sweet Person
Surname or Lastname
English and Irish of uncertain origin
English and Irish of uncertain origin : of uncertain origin: perhaps from a Norman nickname for a stubborn person, from Old French tirel, used of an animal which pulls on the reins, a derivative of tirer ‘to pull’.English and Irish of uncertain origin : Woulfe suggests that it may be from the personal name Thurold, Old Norse Thorvaldr, composed of the elements þórr, name of the Norse god of thunder (see Thor) + valdr ‘rule’.
FUNDAMENTAL SOLUTION
FUNDAMENTAL SOLUTION
FUNDAMENTAL SOLUTION
FUNDAMENTAL SOLUTION
FUNDAMENTAL SOLUTION
a.
First in order of time or development or in intention; primitive; fundamental; original.
n. pl.
First principles; fundamental beginnings; elements; as. Newton's Principia.
v. t.
The fundamental material of which anything is made up; elemental part; essence.
n.
Original or fundamental signification.
n.
A thing of chief or prime importance; something fundamental or especially conspicuous.
a.
Pertaining to the foundation or basis; serving for the foundation. Hence: Essential, as an element, principle, or law; important; original; elementary; as, a fundamental truth; a fundamental axiom.
n.
The ground work the first or fundamental principle; that which supports.
n.
The fundament; the buttocks.
n.
A leading or primary principle, rule, law, or article, which serves as the groundwork of a system; essential part, as, the fundamentals of the Christian faith.
adv.
Primarily; originally; essentially; radically; at the foundation; in origin or constituents.
n.
Fundamental principle; axiom; maxim.
n.
Fig.: The fundamental or essential part of a thing; the essential principle; a groundwork.
a.
Necessarily assumed by the mind as fundamental to all other knowledge; furnishing fundamental principles; as, the regulative principles, or principles a priori; the regulative faculty.
a.
Earliest formed; fundamental.
n.
Foundation.
n.
The part of the body on which one sits; the buttocks; specifically (Anat.), the anus.
a.
Of fundamental importance; preeminent; superior; chief; principal.
n.
Fundamental principle; basis; plan; -- used only in the singular.
n.
A characteristic, essential, and fundamental constituent of any compound; hence, sometimes, an atom.