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Bound on eigenvalues
closed disc centered at a i i {\displaystyle a_{ii}} with radius R i {\displaystyle R_{i}} . Such a disc is called a Gershgorin disc. Theorem. Every eigenvalue
Gershgorin_circle_theorem
Two embeddings of a closed k-disc into a connected n-manifold are ambient isotopic
known as differential topology, the disc theorem of Palais (1960) states that two embeddings of a closed k-disc into a connected n-manifold are ambient
Disc_theorem
Statement on the gravitational attraction of spherical bodies
shell theorem gives gravitational simplifications that can be applied to objects inside or outside a spherically symmetric body. This theorem has particular
Shell_theorem
Theorem about the range of an analytic function
plane into the unit disc via a holomorphic function, which implies that f {\textstyle f} is constant by Liouville's theorem. This theorem is a significant
Picard_theorem
Theorem in differential geometry
In differential geometry, the Gauss–Bonnet theorem (or Gauss–Bonnet formula) is a fundamental formula which links the curvature of a surface to its underlying
Gauss–Bonnet_theorem
Theorem in vector calculus
theorem, also known as the Kelvin–Stokes theorem after Lord Kelvin and George Stokes, the fundamental theorem for curls, or simply the curl theorem,
Stokes'_theorem
Theorem in differential topology
assume this path bounds a disc, and provided 2m > 4 one can further assume (by the weak Whitney embedding theorem) that the disc is embedded in R 2 m {\displaystyle
Whitney_embedding_theorem
Theorem in calculus
In vector calculus, the divergence theorem, also known as Gauss's theorem or Ostrogradsky's theorem, is a theorem relating the flux of a vector field through
Divergence_theorem
Equality of areas of a sliced disk
geometry, the pizza theorem states the equality of two areas that arise when one partitions a disk in a certain way. The theorem is so called because
Pizza_theorem
Theorem in mathematics
In calculus and real analysis, the mean value theorem (or Lagrange's mean value theorem) is a theorem about differentiable functions, roughly stating
Mean_value_theorem
Set of points at distance less than one from a given point
In mathematics, the open unit disk (or disc) around P (where P is a given point in the plane), is the set of points whose distance from P is less than
Unit_disk
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
Statement in complex analysis
Schwarz–Pick theorem (after Georg Pick), characterizes the analytic automorphisms of the unit disc, i.e. bijective holomorphic mappings of the unit disc to itself:
Schwarz_lemma
Relationship between derivatives and integrals
The fundamental theorem of calculus is a theorem that links the concept of differentiating a function (calculating its slopes, or rate of change at every
Fundamental theorem of calculus
Fundamental_theorem_of_calculus
Theorem in calculus relating line and double integrals
In vector calculus, Green's theorem relates a line integral around a simple closed curve C to a double integral over the plane region D (surface in R
Green's_theorem
Way to join two given mathematical manifolds together
fact that this construction is well-defined depends crucially on the disc theorem, which is not at all obvious. For further details, see Kosinski, Differential
Connected_sum
Theorem in mathematics
In mathematical analysis, the inverse function theorem gives sufficient conditions for a function to have an inverse function. The essential idea is that
Inverse_function_theorem
Statement relating differentiable symmetries to conserved quantities
Noether's theorem states that every continuous symmetry of the action of a physical system with conservative forces has a corresponding conservation law
Noether's_theorem
Statement about integration on manifolds
generalized Stokes theorem (sometimes with apostrophe as Stokes' theorem or Stokes's theorem), also called the Stokes–Cartan theorem, is a statement about
Generalized_Stokes_theorem
Approximation of a function by a polynomial
In calculus, Taylor's theorem gives an approximation of a k {\textstyle k} -times differentiable function around a given point by a polynomial of degree
Taylor's_theorem
from the open unit disc D to any larger open set—not even to a single point on the boundary of D. Lacunary function Fabry gap theorem Krantz, Steven G.
Ostrowski–Hadamard gap theorem
Ostrowski–Hadamard_gap_theorem
Integral criterion for holomorphy
functions, converging uniformly to a continuous function f on an open disc. By Cauchy's theorem, we know that ∮ C f n ( z ) d z = 0 {\displaystyle \oint _{C}f_{n}(z)\
Morera's_theorem
In mathematics, the corona theorem is a result about the spectrum of the bounded holomorphic functions on the open unit disc, conjectured by Kakutani (1941)
Corona_theorem
Theorem in geometry
In mathematics, the Brunn–Minkowski theorem (or Brunn–Minkowski inequality) is an inequality relating the volumes (or more generally Lebesgue measures)
Brunn–Minkowski_theorem
Every polynomial has a real or complex root
The fundamental theorem of algebra, also called d'Alembert's theorem or the d'Alembert–Gauss theorem, states that every non-constant single-variable polynomial
Fundamental theorem of algebra
Fundamental_theorem_of_algebra
Theorem in topology
Brouwer's fixed-point theorem is a fixed-point theorem in topology, named after L. E. J. (Bertus) Brouwer. It states that for any continuous function f
Brouwer_fixed-point_theorem
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
Mathematical theorem in complex analysis
of an analytical function when the unit disc takes the same value no more than p times. Cartwright's theorem says that, for every integer p ≥ 1 {\displaystyle
Cartwright's_theorem
Inscribed clay disc found in Crete, Greece
Phaistos Disc Unicode characters. Without proper rendering support, you may see question marks, boxes, or other symbols instead of Phaistos Disc glyphs
Phaistos_Disc
Certain vector fields are the sum of an irrotational and a solenoidal vector field
In physics and mathematics, the Helmholtz decomposition theorem or the fundamental theorem of vector calculus states that certain differentiable vector
Helmholtz_decomposition
Limit of roots of sequence of functions
mathematics and in particular the field of complex analysis, Hurwitz's theorem is a theorem associating the zeroes of a sequence of holomorphic, compact locally
Hurwitz's theorem (complex analysis)
Hurwitz's_theorem_(complex_analysis)
Simple curve of Euclidean geometry
centre is called the diameter. A circle bounds a region of the plane called a disc. The circle has been known since before the beginning of recorded history
Circle
Description of degree sequences of graphs
The Erdős–Gallai theorem is a result in graph theory, a branch of combinatorial mathematics. It provides one of two known approaches to solving the graph
Erdős–Gallai_theorem
Theorem on edge-disjoint spanning trees
In graph theory, the Nash-Williams theorem is a tree-packing theorem that describes how many edge-disjoint spanning trees (and more generally forests)
Nash-Williams_theorem
Theorem in differential geometry
theorem expresses the Gaussian curvature of a surface in terms of the circumference of a geodesic circle, or the area of a geodesic disc. The theorem
Bertrand–Diguet–Puiseux theorem
Bertrand–Diguet–Puiseux_theorem
Theorem in political science
In political science and social choice, Black's median voter theorem says that if voters and candidates are distributed along a one-dimensional political
Median_voter_theorem
Theorem in dimensional analysis
Buckingham π theorem is a key theorem in dimensional analysis. It is a formalisation of Rayleigh's method of dimensional analysis. Loosely, the theorem states
Buckingham_pi_theorem
Mathematical theorem
function anywhere on the boundary of its disc of convergence. The theorem may be deduced from the first main theorem of Turán's method. Let 0 < p1 < p2 <
Fabry_gap_theorem
Operation in mathematical calculus
this case, they are also called indefinite integrals. The fundamental theorem of calculus relates definite integration to differentiation and provides
Integral
Mathematical theorem
for the symmetry to hold are given by Schwarz's theorem, also called Clairaut's theorem or Young's theorem. In the context of partial differential equations
Symmetry of second derivatives
Symmetry_of_second_derivatives
Theorem in transcendental number theory
Lindemann–Weierstrass theorem is a result that is very useful in establishing the transcendence of numbers. It states the following: Lindemann–Weierstrass theorem—if α1
Lindemann–Weierstrass_theorem
Evaluates a line integral through a gradient field using the original scalar field
The gradient theorem, also known as the fundamental theorem of calculus for line integrals, says that a line integral through a gradient field can be evaluated
Gradient_theorem
Area of mathematics
theorem. Many other Picard-type theorems can be derived from the Second Fundamental Theorem. As another corollary from the Second Fundamental Theorem
Nevanlinna_theory
Type of function in mathematics
of analytic functions are analytic is an easy consequence of Morera's theorem. The set A ∞ ( Ω ) {\displaystyle A_{\infty }(\Omega )} of all bounded
Analytic_function
Mathematical model in fluid dynamics
infinitely thin disc, inducing a constant velocity along the axis of rotation. The basic state of a helicopter is hovering. This disc creates a flow around
Momentum_theory
Integration method to calculate volume
Disc integration, also known in integral calculus as the disc method, is a method for calculating the volume of a solid of revolution of a solid-state
Disc_integration
Matrix of partial derivatives of a vector-valued function
generalization includes generalizations of the inverse function theorem and the implicit function theorem, where the non-nullity of the derivative is replaced by
Jacobian matrix and determinant
Jacobian_matrix_and_determinant
3D generalization of the Leibniz integral rule
calculus, the Reynolds transport theorem (also known as the Leibniz–Reynolds transport theorem), or simply the Reynolds theorem, named after Osborne Reynolds
Reynolds_transport_theorem
Mathematical theory in the field of algebraic geometry
algebro-geometric analogue of "small" disc around the s ∈ S {\displaystyle s\in S} , and the condition of the theorem states essentially that A {\displaystyle
Semistable_reduction_theorem
Every triangle-free planar graph is 3-colorable
Grötzsch's theorem is the statement that every triangle-free planar graph can be colored with only three colors. According to the four-color theorem, every
Grötzsch's_theorem
Point in the convex hull of a set P in Rd, is the convex combination of d+1 points in P
Carathéodory's theorem is a theorem in convex geometry. It states that if a point x {\displaystyle x} lies in the convex hull C o n v ( P ) {\displaystyle
Carathéodory's theorem (convex hull)
Carathéodory's_theorem_(convex_hull)
Perfect graphs have neither odd holes nor odd antiholes
In graph theory, the strong perfect graph theorem is a forbidden graph characterization of the perfect graphs as being exactly the graphs that have neither
Strong_perfect_graph_theorem
Condition under which an odd prime is a sum of two squares
In additive number theory, Fermat's theorem on sums of two squares states that an odd prime p can be expressed as: p = x 2 + y 2 , {\displaystyle p=x^{2}+y^{2}
Fermat's theorem on sums of two squares
Fermat's_theorem_on_sums_of_two_squares
Sufficient condition for a Hamiltonian cycle in a graph, based on its vertex's degrees
Discrete Mathematics, 311 (12): 897–907, doi:10.1016/j.disc.2011.02.023, MR 2787300 Weisstein, Eric W., "Pósa's Theorem", MathWorld About the Pósa theorem
Pósa's_theorem
Two tame knots with homeomorphic complements are the same or mirror images
In mathematics, the Gordon–Luecke theorem on knot complements states that if the complements of two tame knots are homeomorphic, then the knots are equivalent
Gordon–Luecke_theorem
Complex Analysis, Fixed-points and Iterations of Holomorphic Mappings
Denjoy–Wolff theorem is a theorem in complex analysis and dynamical systems concerning fixed points and iterations of holomorphic mappings of the unit disc in the
Denjoy–Wolff_theorem
Study of rates of change
Differential calculus and integral calculus are connected by the fundamental theorem of calculus, which states that differentiation and integration are inverse
Differential_calculus
Mathematical theorem
In mathematics, the Riesz–Fischer theorem in real analysis is any of a number of closely related results concerning the properties of the space L2 of
Riesz–Fischer_theorem
1968 film by Pier Paolo Pasolini
Teorema (English: "Theorem") is a 1968 Italian allegorical art film written and directed by Pier Paolo Pasolini. The film centers on an upper-class Milanese
Teorema
Differentiation under the integral sign formula
integral rule and can be derived using the fundamental theorem of calculus. The (first) fundamental theorem of calculus is just the particular case of the above
Leibniz_integral_rule
Branch of mathematics
curves. These two branches are related to each other by the fundamental theorem of calculus. Calculus uses convergence of infinite sequences and infinite
Calculus
Mathematical graph theorem
Petersen's theorem, named after Julius Petersen, is one of the earliest results in graph theory and can be stated as follows: Petersen's Theorem. Every cubic
Petersen's_theorem
Technique in integral evaluation
theorem. Alternatively, the requirement that det(Dφ) ≠ 0 can be eliminated by applying Sard's theorem. For Lebesgue measurable functions, the theorem
Integration_by_substitution
Theorem relating graph minors and topological embeddings
In mathematics, the graph structure theorem is a major result in the area of graph theory. The result establishes a deep and fundamental connection between
Graph_structure_theorem
Provides integral formulas for all derivatives of a holomorphic function
for smooth functions as well, as it is based on Stokes' theorem. Let D {\displaystyle D} be a disc in C {\displaystyle \mathbb {C} } and suppose that f {\displaystyle
Cauchy's_integral_formula
Theorem in hyperbolic geometry
they do not intersect and are not limiting parallel. The ultraparallel theorem states that every pair of (distinct) ultraparallel lines has a unique common
Ultraparallel_theorem
About the numbers of faces of different dimensions in an abstract simplicial complex
theorem gives a complete characterization of the f-vectors of abstract simplicial complexes. It includes as a special case the Erdős–Ko–Rado theorem and
Kruskal–Katona_theorem
Mathematical theory
main theorems implies Picard's theorem, and the Second main theorem of Nevanlinna theory. Many other important generalizations of Picard's theorem can
Ahlfors_theory
Generalization of the product rule in calculus
Leibniz rule bears a strong resemblance to the binomial theorem, and in fact the binomial theorem can be proven directly from the Leibniz rule by taking
General_Leibniz_rule
Topological mapping
theorem, where it is used to cancel the intersection points; and its failure in low dimensions corresponds to not being able to embed a Whitney disc.
Whitney_disk
Mathematical theorem
angle-preserving manner to the nice and regular unit disc seems counter-intuitive. The analog of the Riemann mapping theorem for more complicated domains is not true
Riemann_mapping_theorem
Vector calculus formulas relating the bulk with the boundary of a region
mathematician George Green, who discovered Green's theorem. This identity is derived from the divergence theorem applied to the vector field F = ψ ∇φ while using
Green's_identities
Two-dimensional manifold
not be surfaces in the extrinsic sense. However, the Whitney embedding theorem asserts every surface can in fact be embedded homeomorphically into Euclidean
Surface_(topology)
Generalization of definite integrals to functions of multiple variables
distribution. Main analysis theorems that relate multiple integrals: Divergence theorem Stokes' theorem Green's theorem Stewart, James (2008). Calculus:
Multiple_integral
Point to which functions converge in analysis
advantages of working with non-deleted limits is that they allow to state the theorem about limits of compositions without any constraints on the functions (other
Limit_of_a_function
Result in electrical engineering
Blondel's theorem, named after its discoverer, French electrical engineer André Blondel, is the result of his attempt to simplify both the measurement
Blondel's_theorem
On coloring infinite graphs
In graph theory, the De Bruijn–Erdős theorem relates graph coloring of an infinite graph to the same problem on its finite subgraphs. It states that,
De Bruijn–Erdős theorem (graph theory)
De_Bruijn–Erdős_theorem_(graph_theory)
Operation on differential forms
natural, metric-independent generalization of Stokes' theorem, Gauss's theorem, and Green's theorem from vector calculus. If a differential k {\displaystyle
Exterior_derivative
Mathematical theorem, used in calculus
continuous and invertible function. It follows from the intermediate value theorem that f {\displaystyle f} is strictly monotone. Consequently, f {\displaystyle
Integral_of_inverse_functions
Indefinite integral
Antiderivatives are related to definite integrals through the second fundamental theorem of calculus: the definite integral of a function over a closed interval
Antiderivative
measure on the circle. This result, the Herglotz-Riesz representation theorem, was proved independently by Gustav Herglotz and Frigyes Riesz in 1911
Positive_harmonic_function
Mathematical method in calculus
The discrete analogue for sequences is called summation by parts. The theorem can be derived as follows. For two continuously differentiable functions
Integration_by_parts
Theorem in complex analysis
In mathematics, the Borel–Carathéodory theorem in complex analysis shows that an analytic function may be bounded by its real part. It is an application
Borel–Carathéodory_theorem
Integrals not expressible in closed-form from elementary functions
elementary function. A theorem by Liouville in 1835 provided the first proof that nonelementary antiderivatives exist. This theorem also provides a basis
Nonelementary_integral
Method of evaluating certain integrals along paths in the complex plane
application of the Cauchy integral formula or residue theorem is possible application of Cauchy's integral theorem The integral is reduced to only an integration
Contour_integration
Integration over a non-flat region in 3D space
and vector calculus, such as the divergence theorem, magnetic flux, and its generalization, Stokes' theorem. Let us notice that we defined the surface
Surface_integral
Definite integral of a scalar or vector field along a path
quantum scattering theory. Divergence theorem Gradient theorem Methods of contour integration Nachbin's theorem Line element Surface integral Volume element
Line_integral
Basic concept of graph theory
generalization of Dirac's theorem on cycles through k vertices in k-connected graphs". Discrete Mathematics. 307 (7–8): 878–884. doi:10.1016/j.disc.2005.11.052. MR 2297171
Connectivity_(graph_theory)
Method of mathematical integration
under the integral sign (via the monotone convergence theorem and dominated convergence theorem). While the Riemann integral considers the area under
Lebesgue_integral
Theorem in graph theory
The Gale–Ryser theorem is a result in graph theory and combinatorial matrix theory, two branches of combinatorics. It provides one of two known approaches
Gale–Ryser_theorem
Vector operator in vector calculus
source density div v by the circulation density ∇ × v. This "decomposition theorem" is a by-product of the stationary case of electrodynamics. It is a special
Divergence
Circulation density in a vector field
vector fields. The corresponding form of the fundamental theorem of calculus is Stokes' theorem, which relates the surface integral of the curl of a vector
Curl_(mathematics)
Differential operator in mathematics
where n is the outward unit normal to the boundary of V. By the divergence theorem, ∫ V div ∇ u d V = ∫ S ∇ u ⋅ n d S = 0. {\displaystyle \int _{V}\operatorname
Laplace_operator
Formula in calculus
itself can be viewed as the polynomial remainder theorem (the little Bézout theorem, or factor theorem), generalized to an appropriate class of functions
Chain_rule
Function of the coefficients of a polynomial that gives information on its roots
numbers, where the fundamental theorem of algebra applies.) In terms of the roots, the discriminant is equal to Disc x ( A ) = a n 2 n − 2 ∏ i < j
Discriminant
In functional analysis, a Hilbert space
field of statistical learning theory because of the celebrated representer theorem which states that every function in an RKHS that minimises an empirical
Reproducing kernel Hilbert space
Reproducing_kernel_Hilbert_space
Mathematical identities
\varphi )} in a Cartesian coordinate system with Schwarz's theorem (also called Clairaut's theorem on equality of mixed partials). This result is a special
Vector_calculus_identities
z 0 ) = 0 {\displaystyle \phi (z_{0})=0} . Siegel's theorem proves the existence of Siegel discs for irrational numbers satisfying a strong irrationality
Siegel_disc
Theorem in group theory
mathematical subject of group theory, the Grushko theorem or the Grushko–Neumann theorem is a theorem stating that the rank (that is, the smallest cardinality
Grushko_theorem
connected compact topological 4-manifolds. In the proof of the h-cobordism theorem, the following construction is used. Given a circle in the boundary of
Casson_handle
DISC THEOREM
DISC THEOREM
Girl/Female
Arabic, Muslim
A Sweet Dish
Female
Norse
Old Norse name composed of the elements ey "island" and dis "goddess," hence "island goddess."
Girl/Female
Indian
Image, Reflection, Also referred to as the disk of brightness surrounding the Sun, Moon
Girl/Female
Norse Greek
Spirited.
Boy/Male
Australian, Egyptian
Sun Disk
Boy/Male
Indian, Sanskrit
The Disc of the Sun or the Moon; Lord of Images
Girl/Female
Australian, Danish, Greek, Norse, Scandinavian, Swedish
Active Spirit; Goddess; Double
Boy/Male
Indian, Sanskrit
Holding a Disc; Lord Vishnu
Male
Egyptian
, the most lovely Disk.
Male
Egyptian
, the spirit of Aton, or the Sun-disk.
Girl/Female
British, English
Direction
Girl/Female
Tamil
Image, Reflection, Also referred to as the disk of brightness surrounding the Sun, Moon
Girl/Female
Muslim
A sweet dish
Male
Egyptian
, glory of the Solar Disk.
Boy/Male
Latin
Hades.
Girl/Female
Norse
Spirited.
Male
Egyptian
, disk.
Surname or Lastname
English
English : habitational name from Diss in Suffolk, which gets its name from a Norman pronunciation of Middle English diche, Old English dīc ‘ditch’, ‘dike’ (see Dyke).German : habitational name from Dissen near the Teutoburg forest.
Male
Egyptian
, Horus, the winged disk of the sun.
Male
Egyptian
, the spirit of Aten, or the Sun-disk.
DISC THEOREM
DISC THEOREM
Boy/Male
Muslim
Schemer
Girl/Female
American, Australian, Celtic, Irish, Latin, Shakespearean
Little Ruler; Nobility; Child of the Small Ruler; Queen; Form of Regina; Regan is One of King Lear's Daughters
Boy/Male
Tamil
Karnajeet | கரà¯à®£à®œà¯€à®¤
Conqueror of Karna
Girl/Female
Assamese, Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu, Traditional
Pure; Name of a River
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Sindhi, Telugu
The Sun God
Girl/Female
Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
A Garland Made of Champa Flowers
Surname or Lastname
English
English : topographic name from Old English þel ‘footbridge’, or possibly a habitational name from a place named with this word, such as Theale in Berkshire or Somerset.
Boy/Male
Scottish
Son of the dark of peace.
Girl/Female
Hindu
Girl/Female
Tamil
Lovable, Passionate, A musical Raag
DISC THEOREM
DISC THEOREM
DISC THEOREM
DISC THEOREM
DISC THEOREM
v. t.
To put in a dish, ready for the table.
n.
A circular structure either in plants or animals; as, a blood disk; germinal disk, etc.
n.
A disk. See Disk.
n.
A flat round plate
n.
The state of being concave, or like a dish, or the degree of such concavity; as, the dish of a wheel.
imp. & p. p.
of Dish
n.
A large dish.
n.
The lower side of the body of some invertebrates, especially when used for locomotion, when it is often called a creeping disk.
a.
Dish-shaped; concave.
n.
The food served in a dish; hence, any particular kind of food; as, a cold dish; a warm dish; a delicious dish. "A dish fit for the gods."
n.
A circular structure either in plants or animals; as, a blood disc, a germinal disc, etc. Same as Disk.
n.
See Grail., a dish.
v. t.
To make concave, or depress in the middle, like a dish; as, to dish a wheel by inclining the spokes.
n.
A small dish.
a.
Disk-shaped; discoid.
n.
A cup or dish.
p. pr. & vb. n.
of Dish
n.
A public or state treasury.
n.
A flat, circular plate; as, a disk of metal or paper.