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Index of articles associated with the same name
Holmgren's uniqueness theorem for linear partial differential equations with real analytic coefficients. Picard–Lindelöf theorem, the uniqueness of solutions
Uniqueness_theorem
Integers have unique prime factorizations
mathematics, the fundamental theorem of arithmetic, also called the unique factorization theorem and prime factorization theorem, states that every integer
Fundamental theorem of arithmetic
Fundamental_theorem_of_arithmetic
Black holes are characterized only by mass, charge, and spin
The no-hair theorem, also known as the black hole uniqueness theorem, states that all stationary black hole solutions of the Einstein–Maxwell equations
No-hair_theorem
Existence and uniqueness of solutions to initial value problems
known as Picard's existence theorem, the Cauchy–Lipschitz theorem, or the existence and uniqueness theorem. The theorem is named after Émile Picard,
Picard–Lindelöf_theorem
Logical quantifier
. Essentially unique Extension by definition One-hot Singleton (mathematics) Uniqueness theorem Weisstein, Eric W. "Uniqueness Theorem". mathworld.wolfram
Uniqueness_quantification
Existence and uniqueness theorem for certain partial differential equations
the Cauchy–Kovalevskaya theorem (also written as the Cauchy–Kowalevski theorem) is the main local existence and uniqueness theorem for analytic partial differential
Cauchy–Kovalevskaya_theorem
Uniqueness for linear partial differential equations with real analytic coefficients
Holmgren's uniqueness theorem, or simply Holmgren's theorem, named after the Swedish mathematician Erik Albert Holmgren (1873–1943), is a uniqueness result
Holmgren's_uniqueness_theorem
Providing boundary conditions for Maxwell's equations uniquely fixes a solution
The electromagnetism uniqueness theorem states the uniqueness (but not necessarily the existence) of a solution to Maxwell's equations, if the boundary
Electromagnetism uniqueness theorem
Electromagnetism_uniqueness_theorem
For a large class of boundary conditions, all solutions have the same gradient
The uniqueness theorem for Poisson's equation states that, for a large class of boundary conditions, the equation may have many solutions, but the gradient
Uniqueness theorem for Poisson's equation
Uniqueness_theorem_for_Poisson's_equation
Theorem about metric spaces
Banach fixed-point theorem (also known as the contraction mapping theorem or contractive mapping theorem or Banach–Caccioppoli theorem) is an important
Banach_fixed-point_theorem
Differential equation containing derivatives with respect to only one variable
non-Lipschitz functions at their ending time, they are not included in the uniqueness theorem of solutions of Lipschitz differential equations. As example, the
Ordinary differential equation
Ordinary_differential_equation
Uniqueness theorem in complex analysis
In mathematics, in the area of complex analysis, Carlson's theorem is a uniqueness theorem which was discovered by Fritz David Carlson. Informally, it
Carlson's_theorem
Theorem in stochastic calculus
decomposition theorem is a theorem in stochastic calculus stating the conditions under which a submartingale may be decomposed in a unique way as the sum
Doob–Meyer decomposition theorem
Doob–Meyer_decomposition_theorem
Polyhedra are determined by surface distance
earliest existence and uniqueness theorems for convex polyhedra is Cauchy's theorem, which states that a convex polyhedron is uniquely determined by the shape
Alexandrov's theorem on polyhedra
Alexandrov's_theorem_on_polyhedra
On certain subgroups of a minimal simple finite group of odd order
original uniqueness theorem (Feit & Thompson 1963, theorems 24.5 and 25.2) states that in a minimal simple finite group of odd order there is a unique maximal
Thompson_uniqueness_theorem
Theorem classifying finite simple groups
odd prime (classified by the Gilman–Griess theorem and work by several others), and groups of uniqueness type, where a result of Aschbacher implies that
Classification of finite simple groups
Classification_of_finite_simple_groups
Mathematical transform
equations as well as a version of the classical uniqueness theorem, strengthening the Cauchy–Kowalevski theorem, due to the Swedish mathematician Erik Albert
Fourier–Bros–Iagolnitzer transform
Fourier–Bros–Iagolnitzer_transform
Division with remainder of integers
named after Euclid, it seems that he did not know the existence and uniqueness theorem, and that the only computation method that he knew was the division
Euclidean_division
Theorem in calculus relating line and double integrals
the uniqueness theorem (derived from Green's theorem) Shoelace formula – A special case of Green's theorem for simple polygons Bendixson-Dulac theorem –
Green's_theorem
However, this version of the theorem does not generalize to higher dimensions. Alexandrov's uniqueness theorem Cauchy's theorem (geometry) Klain, Daniel A
Minkowski problem for polytopes
Minkowski_problem_for_polytopes
Type of differential equation
and uniqueness theorems are usually important organizational principles. In many introductory textbooks, the role of existence and uniqueness theorems for
Partial_differential_equation
Mathematical theorem
theoretical physics, the Stone–von Neumann theorem refers to any one of a number of different formulations of the uniqueness of the canonical commutation relations
Stone–von_Neumann_theorem
Foundational law of electromagnetism relating electric field and charge distributions
as Gauss's flux theorem or sometimes Gauss's theorem, is one of Maxwell's equations. It is an application of the divergence theorem, and it relates the
Gauss's_law
mathematical theory of differential equations the Chaplygin Theorem states about the existence and uniqueness of the solution to an initial value problem for the
Chaplygin's Theorem and Method for Solving ODE
Chaplygin's_Theorem_and_Method_for_Solving_ODE
the proof of the odd order theorem by Feit and Thompson (1963), where it was used to prove the Thompson uniqueness theorem. Suppose that G is a finite
Thompson_transitivity_theorem
Part of the mathematical subject of group theory
result is also known as the structure theorem. One of the immediate consequences is the classic Kurosh subgroup theorem describing the algebraic structure
Bass–Serre_theory
Partial differential equation
topology as t {\displaystyle t} decreases to 0. He showed the following uniqueness theorem: If { g t : t ∈ ( 0 , T ) } {\displaystyle \{g_{t}:t\in (0,T)\}} and
Ricci_flow
Rigidity theorem for convex polyhedra
surface. The analogous uniqueness theorem for smooth surfaces was proved by Cohn-Vossen in 1927. Pogorelov's uniqueness theorem is a result by Pogorelov
Cauchy's_theorem_(geometry)
Viviani's theorem (Euclidean geometry) Alexandrov's uniqueness theorem (discrete geometry) Balinski's theorem (combinatorics) Bang's theorem (geometry)
List_of_theorems
Directed path algebra
gauge-invariant uniqueness theorem and Cuntz-Krieger uniqueness theorem for graph C*-algebras. Formal statements of the uniqueness theorems are as follows:
Leavitt_path_algebra
Mathematics of real numbers and real functions
supplies the basic existence and uniqueness theorem for solutions of ordinary differential equations – the Picard existence theorem – as well as a method for
Real_analysis
Theorem which asserts the existence of an object
proof Constructivism (philosophy of mathematics) Uniqueness theorem "Definition of existence theorem | Dictionary.com". www.dictionary.com. Retrieved
Existence_theorem
Nondeterministic Newtonian mechanical system
function of the particle's trajectory—this allows evasion of the local uniqueness theorem for solutions of ordinary differential equations), or in violation
Norton's_dome
Representation of modular integers by "small" fractions
root of m, but the general form is sometimes useful, and makes the uniqueness theorem (below) easier to state. The first known proof is attributed to Axel
Thue's_lemma
Theorem in electromagnetism
imaginary surface currents are enforced by the uniqueness theorem in electromagnetism, which dictates that a unique solution can be determined by fixing a boundary
Surface_equivalence_principle
Generalization of the standard Boltzmann–Gibbs entropy
statistics apply, the following ones can be selected: Anomalous diffusion. Uniqueness theorem. Sensitivity to initial conditions and entropy production at the edge
Tsallis_entropy
C*-algebras: the gauge-invariant uniqueness theorem and the Cuntz-Krieger uniqueness theorem. The uniqueness theorems are fundamental results in the study
Graph_C*-algebra
Mathematical rule for inverting probabilities
Bayes' theorem determines the posterior distribution from the prior distribution. Uniqueness requires continuity assumptions. Bayes' theorem can be generalized
Bayes'_theorem
Expressing a measure as an integral of another
\\0&{\text{otherwise,}}\end{cases}}} then f has the desired properties. Uniqueness As for the uniqueness, let f, g : X → [0, ∞) be measurable functions satisfying
Radon–Nikodym_theorem
Result about when a matrix can be diagonalized
In linear algebra and functional analysis, a spectral theorem is a result about when a linear operator or matrix can be diagonalized (that is, represented
Spectral_theorem
Topics referred to by the same term
Tutte's theorem on perfect matchings, a characterization of the graphs having perfect matchings Tutte's spring theorem, on the planarity and uniqueness of
Tutte's_theorem
Calculation technique for classical electrostatics
charges rests upon a corollary of the uniqueness theorem, which states that the electric potential in a volume V is uniquely determined if both the charge density
Method_of_image_charges
Mathematical theorem
ISSN 0012-7094. Mattner, Lutz (1993). "Bernstein's theorem, inversion formula of Post and Widder, and the uniqueness theorem for Laplace transforms" (PDF). Expositiones
Bernstein's theorem on monotone functions
Bernstein's_theorem_on_monotone_functions
Classification theorem in group theory
the proof of the odd-order theorem takes over 100 journal pages. A key step is the proof of the Thompson uniqueness theorem, stating that abelian subgroups
Feit–Thompson_theorem
Equations with an unknown function under an integral sign
and uniqueness theorem for the semi-linear Hammerstein integral equation. Theorem—Suppose that the semi-linear Hammerstein equation has a unique solution
Integral_equation
About simultaneous modular congruences
existence and the uniqueness of the solution may be proven independently. However, the first proof of existence, given below, uses this uniqueness. Suppose that
Chinese_remainder_theorem
On tangency patterns of circles
generalized the uniqueness of circle packings to certain packings of infinitely many circles on a sphere or open disk. His uniqueness theorem applies to circle
Circle_packing_theorem
Theorem extending pre-measures to measures
In measure theory, Carathéodory's extension theorem (named after the mathematician Constantin Carathéodory) states that any pre-measure defined on a given
Carathéodory's extension theorem
Carathéodory's_extension_theorem
Summation method for divergent series
region. Watson's theorem and Carleman's theorem show that Borel summation produces such a best possible sum of the series. Watson's theorem gives conditions
Borel_summation
Theorem in functional analysis
functional analysis, Fichera's existence principle is an existence and uniqueness theorem for solution of functional equations, proved by Gaetano Fichera in
Fichera's_existence_principle
17th-century conjecture proved by Andrew Wiles in 1994
In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that there are no positive integers a
Fermat's_Last_Theorem
Differential equations involving stochastic processes
has a solution, and whether or not it is unique. The following is a typical existence and uniqueness theorem for Itô SDEs taking values in n-dimensional
Stochastic differential equation
Stochastic_differential_equation
Arithmetic operation
exist at integer values of its argument. Hooshmand derived another uniqueness theorem for it which states: If f : ( − 2 , + ∞ ) → R {\displaystyle f:(-2
Tetration
Property of mathematical objects
combinatorial adjacency rules. Alexandrov's uniqueness theorem states that a convex polyhedron in three dimensions is uniquely determined by the metric space of
Rigidity_(mathematics)
Theorem regarding the existence of a solution to a differential equation
Peano existence theorem, Peano theorem or Cauchy–Peano theorem, named after Giuseppe Peano and Augustin-Louis Cauchy, is a fundamental theorem which guarantees
Peano_existence_theorem
all of their Bell series are equal; this is sometimes called the uniqueness theorem: given multiplicative functions f {\displaystyle f} and g {\displaystyle
Bell_series
Process of simplifying circuit solutions
be derived from the uniqueness theorem. In the present context, it implies that a black box with two terminals must have a unique well-defined relation
Source_transformation
Edge-joined polygons which fold into a polyhedron
exactly one polyhedron that can be folded from it; this is Alexandrov's uniqueness theorem. However, the polyhedron formed in this way may have different faces
Net_(polyhedron)
Extension of the domain of an analytic function (mathematics)
corresponding to it. This is the sheaf of the logarithm function. The uniqueness theorem for analytic functions also extends to sheaves of analytic functions:
Analytic_continuation
Soviet and Russian mathematician
and on the foundations of geometry. Pogorelov's uniqueness theorem and the Alexandrov–Pogorelov theorem are named after him. He was born in Korocha in
Aleksei_Pogorelov
American mathematician (1943–2024)
prove a general existence and uniqueness theorem for geometric evolution equations; the standard implicit function theorem does not often apply in such
Richard_S._Hamilton
Georgian and Soviet mathematician
theory of fluid motion. In particular he rediscovered an important uniqueness theorem for the classical solutions to the Navier–Stokes equations for an
David_Dolidze
Mathematical structure
the maximal atlas contains a C∞−atlas on the same underlying set by a theorem due to Hassler Whitney. It has also been shown that any maximal Ck−atlas
Differential_structure
Theorem on extension of bounded linear functionals
In functional analysis, the Hahn–Banach theorem is a central result that allows the extension of bounded linear functionals defined on a vector subspace
Hahn–Banach_theorem
Elliptic partial differential equation
Discrete Poisson equation Poisson–Boltzmann equation Helmholtz equation Uniqueness theorem for Poisson's equation Weak formulation Harmonic function Heat equation
Poisson's_equation
incompatibility (help) Alexandrov, Alexander Danilovich (1962). "Uniqueness theorem for surfaces in the large". American Mathematical Society Translations
Alexandrov's soap bubble theorem
Alexandrov's_soap_bubble_theorem
Relation between sides of a right triangle
In mathematics, the Pythagorean theorem or Pythagoras's theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle
Pythagorean_theorem
Product of numbers from 1 to n
the factorials and obeys the same functional equation. A related uniqueness theorem of Helmut Wielandt states that the complex gamma function and its
Factorial
Sufficiency theorem for reconstructing signals from samples
The Nyquist–Shannon sampling theorem is a theorem in the field of signal processing which serves as a fundamental bridge between continuous-time signals
Nyquist–Shannon sampling theorem
Nyquist–Shannon_sampling_theorem
Swedish mathematician
known for contributions to partial differential equations. Holmgren's uniqueness theorem is named after him. Torsten Carleman was one of his students. His
Erik_Albert_Holmgren
Conditions for switching order of integration in calculus
Fubini's theorem gives the conditions under which a double integral can be computed as an iterated integral, i.e. by integrating in one variable at a
Fubini's_theorem
Result in combinatorics and graph theory
mathematics, Hall's marriage theorem, proved by Philip Hall (1935), is a theorem with two equivalent formulations. In each case, the theorem gives a necessary and
Hall's_marriage_theorem
Type of calculus problem
there is no guarantee of uniqueness. The result may be found in Coddington & Levinson (1955, Theorem 1.3) or Robinson (2001, Theorem 2.6). An even more general
Initial_value_problem
Classification of semi-simple rings and algebras
algebra, the Wedderburn–Artin theorem is a classification theorem for semisimple rings and semisimple algebras. The theorem states that a(n Artinian) semisimple
Wedderburn–Artin_theorem
The unique homomorphic extension theorem is a result in mathematical logic which formalizes the intuition that the truth or falsity of a statement can
Unique homomorphic extension theorem
Unique_homomorphic_extension_theorem
Cauchy–Kovalevskaya theorem In mathematics, the Cauchy–Kowalevski theorem (also written as the Cauchy–Kovalevskaya theorem) is the main local existence and uniqueness theorem
List of inventions and discoveries by women
List_of_inventions_and_discoveries_by_women
theory, the uniqueness case is one of the three possibilities for groups of characteristic 2 type given by the trichotomy theorem. The uniqueness case covers
Uniqueness_case
On the unique representation of integers as sums of non-consecutive Fibonacci numbers
21 + 8 + 2. Zeckendorf's theorem has two parts: Existence: every positive integer n has a Zeckendorf representation. Uniqueness: no positive integer n has
Zeckendorf's_theorem
Well-quasi-ordering of finite trees
In mathematics, Kruskal's tree theorem states that the set of finite trees over a well-quasi-ordered set of labels is itself well-quasi-ordered under
Kruskal's_tree_theorem
Theorem that any three objects in space can be simultaneously bisected by a plane
mathematical measure theory, for every positive integer n the ham sandwich theorem states that given n measurable "objects" in n-dimensional Euclidean space
Ham_sandwich_theorem
Topics referred to by the same term
result by Joyal on uniqueness of composition law This disambiguation page lists articles associated with the title Joyal's theorem. If an internal link
Joyal's_theorem
Functional analysis theorem
famous Lax–Milgram theorem, which gives conditions under which a bilinear function can be "inverted" to show the existence and uniqueness of a weak solution
Lions–Lax–Milgram_theorem
Existence and cardinality of models of logical theories
In mathematical logic, the Löwenheim–Skolem theorem is a theorem on the existence and cardinality of models, named after Leopold Löwenheim and Thoralf
Löwenheim–Skolem_theorem
Japanese mathematician (1905–1948)
Hirosi OKAMURA, nekrologo (E-e) George, John H. (1967), "On Okamura's uniqueness theorem" (PDF), Proceedings of the American Mathematical Society, 18 (4):
Hiroshi_Okamura
Theorem in probability theory
solution with pathwise uniqueness implies a strong solution and uniqueness in distribution. In its original form, the theorem was stated for n {\displaystyle
Yamada–Watanabe_theorem
Polish mathematician (1890–1940)
probability. In mathematics, there are such concepts as the Rajchman global uniqueness theorem, Rajchman measures, Rajchman collection, Rajchman algebras, Rajchman
Aleksander_Rajchman
Straight path on a curved surface or a Riemannian manifold
existence and uniqueness theorem for geodesics states that geodesics on a smooth manifold with an affine connection exist, and are unique. More precisely:
Geodesic
On converting relations to functions of several real variables
In multivariable calculus, the implicit function theorem is a theorem that provides sufficient conditions under which a planar curve specified by F ( x
Implicit_function_theorem
American mathematician (born 1940)
in the monograph. The uniqueness theorems for model inverse problems of geophysics have been proved, examples of non-uniqueness were constructed, the
Alexander_Ramm
Theorem in mathematical economics
choice variable, and uniqueness and interiority of the optimum. We can get the same monotone comparative static using Topkis's theorem by assuming directly
Topkis's_theorem
Ornamental pincushion
pattern of a biscornu will form the boundary of a unique convex polyhedron, by Alexandrov's uniqueness theorem. In the case of a biscornu, this polyhedron is
Biscornu
Inverse of a finite difference
following uniqueness theorem, their method requiring the solution to be eventually p {\displaystyle p} -convex or p {\displaystyle p} -concave. Theorem. Let
Indefinite_sum
On triangles inscribed in a circle with a diameter as an edge
In geometry, Thales's theorem states that if A, B, and C are distinct points on a circle where the line AC is a diameter, the angle ∠ ABC is a right angle
Thales's_theorem
1950 book on geometry by Aleksandr Danilovich Aleksandrov
Shor, including a simplified proof of Pogorelov's theorems generalizing Alexandrov's uniqueness theorem to non-polyhedral convex surfaces. Robert Connelly
Convex_Polyhedra_(book)
In algebra, expression of an ideal as the intersection of ideals of a specific type
series of exercises. There is the following uniqueness theorem for an ideal having a primary decomposition. Theorem—Let R {\displaystyle R} be a commutative
Primary_decomposition
Theory of gravitation as curved spacetime
and location at a specified time. This is stated by the black hole uniqueness theorem: "black holes have no hair", that is, no distinguishing marks like
General_relativity
American mathematician
several advances in the 1930s: In 1930, he proved the Stone–von Neumann uniqueness theorem. In 1932, he published a 662 page long monograph titled Linear transformations
Marshall_H._Stone
Area of functional analysis and convex analysis
given point c, one might also consider the uniqueness of such measures. It is easy to see that uniqueness does not hold even in the finite dimensional
Choquet_theory
French mathematical physicist (1923–2025)
of uniqueness. With a two-page argument in point-set topology using Zorn's lemma, they showed that Choquet-Bruhat's above existence and uniqueness theorems
Yvonne_Choquet-Bruhat
Theorem in network theory
current law, KCL) and the uniqueness of the potentials at the network nodes (Kirchhoff's voltage law, KVL). The Tellegen theorem provides a useful tool to
Tellegen's_theorem
UNIQUENESS THEOREM
UNIQUENESS THEOREM
Boy/Male
Arabic
Rarity; Uniqueness
Girl/Female
Hindu, Indian, Traditional
Propounder of the Uniqueness of the Absolute
Boy/Male
Arabic
Uniqueness of Religion
UNIQUENESS THEOREM
UNIQUENESS THEOREM
Girl/Female
Hindu
Boy/Male
Indian
Attractive, Beloved, Mistress, Soothing heart, Mind
Boy/Male
Hindu
The person who inspires to think, An ancient scholar
Boy/Male
Indian, Punjabi, Sikh
Lamp of Air
Female
Hebrew
(×ï‹×¨Ö¸×”-לִי) Hebrew name ORALEE means "my light." Compare with another form of Oralee.
Girl/Female
Sikh
A women with a beautiful eyes, Fish eyed
Boy/Male
Hindu, Indian, Marathi
Wonderful; Admirable
Boy/Male
Indian, Sanskrit
Ever Faithful; Constant
Boy/Male
Indian, Punjabi, Sikh
Formless Being
Girl/Female
Arabic Muslim Native American
Desire.
UNIQUENESS THEOREM
UNIQUENESS THEOREM
UNIQUENESS THEOREM
UNIQUENESS THEOREM
UNIQUENESS THEOREM
n.
A statement of a principle to be demonstrated.
a.
Containing many names or terms; multinominal; as, the polynomial theorem.
n.
The quality or state of being unique; uniqueness.
n.
One who constructs theorems.
n.
A theorem or proposition so easy of demonstration as to be almost self-evident.
n.
The quality of being undue.
n.
That which is considered and established as a principle; hence, sometimes, a rule.
a.
Alt. of Theorematical
a.
Of or pertaining to a theorem or theorems; comprised in a theorem; consisting of theorems.
n.
The quality of being antique; an appearance of ancient origin and workmanship.
v. t.
To formulate into a theorem.
n.
A numerical coefficient in any particular case of the binomial theorem.
a.
Theorematic.
n.
The enunciation of a self-evident problem, in distinction from an axiom, which is the enunciation of a self-evident theorem.