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Type of surface singularity used in algebraic geometry
In algebraic geometry, an elliptic singularity of a surface, introduced by Philip Wagreich in 1970, is a surface singularity such that the arithmetic genus
Elliptic_singularity
Theory of a class of elliptic curves
the theory of elliptic curves E that have an endomorphism ring larger than the integers. Put another way, it contains the theory of elliptic functions with
Complex_multiplication
Algebraic curve in mathematics
general enough to include all non-singular cubic curves; see § Elliptic curves over a general field below.) An elliptic curve is an abelian variety – that
Elliptic_curve
Mathematical concept
that is), elliptic curves over number fields. The product of any elliptic curve with any curve is an elliptic surface (with no singular fibers). All
Elliptic_surface
Mathematical concept
nothing to do with singular points of curves, and all supersingular elliptic curves are non-singular. It comes from the phrase "singular values of the j
Supersingular_elliptic_curve
Val singularities. Elliptic singularity (Kollár & Mori 1998, Theorem 5.22.) (Artin 1966) Artin, Michael (1966), "On isolated rational singularities of
Rational_singularity
Kepler orbit with an eccentricity of less than one
In astrodynamics or celestial mechanics, an elliptical orbit or eccentric orbit is an orbit with an eccentricity of less than 1;[citation needed] this
Elliptic_orbit
Class of mathematical functions
In mathematics, the Weierstrass elliptic functions are elliptic functions that take a particularly simple form. They are named for Karl Weierstrass. This
Weierstrass_elliptic_function
Mathematical function
In mathematics, the Jacobi elliptic functions are a set of basic elliptic functions. They are found in the description of the motion of a pendulum, as
Jacobi_elliptic_functions
Techniques in mathematical analysis
pseudo-differential operators. It is concerned with elliptic regularity, propagation of singularities, Fourier integral operators, geometric optics, scattering
Microlocal_analysis
Mathematical result in differential geometry
proved by Michael Atiyah and Isadore Singer (1963), states that for an elliptic differential operator on a compact manifold, the analytical index (related
Atiyah–Singer_index_theorem
Algebraic curve
is called an elliptic curve. While this model is the simplest way to describe hyperelliptic curves, such an equation will have a singular point at infinity
Hyperelliptic_curve
American mathematician and businessman
two-dimensional singularities, Annals of Mathematics Studies, 71, Princeton University Press Laufer, Henry B. (1977), "On minimally elliptic singularities", American
Henry_Laufer
analysis) Residue (complex analysis) Isolated singularity Removable singularity Essential singularity Branch point Principal branch Weierstrass–Casorati
List of complex analysis topics
List_of_complex_analysis_topics
Class of partial differential equations
mathematics, an elliptic partial differential equation is a type of partial differential equation (PDE). In mathematical modeling, elliptic PDEs are frequently
Elliptic partial differential equation
Elliptic_partial_differential_equation
Mathematical functions
In mathematics, the lemniscate elliptic functions are elliptic functions related to the arc length of the lemniscate of Bernoulli. They were first studied
Lemniscate_elliptic_functions
Singularities of algebraic varieties
(1985) and Reid. In particular, a terminal 3-fold singularity is the quotient of a hypersurface singularity with multiplicity 2 by a finite cyclic group.
Canonical_singularity
Tate, John (1975), "Algorithm for determining the type of a singular fiber in an elliptic pencil", in Birch, B.J.; Kuyk, W. (eds.), Modular Functions
Semistable_abelian_variety
Partial differential equation
soliton The first two singularity models arise from Type I singularities, whereas the last one arises from a Type II singularity. In four dimensions very
Ricci_flow
Curve defined as zeros of polynomials
equations of the branches. For describing a singularity, it is worth to translate the curve for having the singularity at the origin. This consists of a change
Algebraic_curve
Theorem about the range of an analytic function
the unit disc. This function is explicitly constructed in the theory of elliptic functions. If f {\textstyle f} omits two values, then lifting f {\textstyle
Picard_theorem
Modular unit in mathematics
In mathematics, elliptic units are certain units of abelian extensions of imaginary quadratic fields constructed using singular values of modular functions
Elliptic_unit
Special function occurring in problems possessing elliptic symmetry
partial differential equation (PDE) boundary value problems possessing elliptic symmetry. In some usages, Mathieu function refers to solutions of the Mathieu
Mathieu_function
Analytic function on the upper half-plane with a certain behavior under the modular group
functions is to use elliptic curves: every lattice Λ determines an elliptic curve C/Λ over C; two lattices determine isomorphic elliptic curves if and only
Modular_form
Theorem in classical algebraic geometry
ordinary singularity of multiplicity r {\displaystyle r} decreases the genus by 1 2 r ( r − 1 ) {\displaystyle {\frac {1}{2}}r(r-1)} . Elliptic curves are
Genus–degree_formula
Partial differential operator
then P {\displaystyle P} is said to be analytically hypoelliptic. Every elliptic operator with C ∞ {\displaystyle C^{\infty }} coefficients is hypoelliptic
Hypoelliptic_operator
One-dimensional complex manifold
{\displaystyle \tau } is any complex non-real number. These are called elliptic curves. Important examples of non-compact Riemann surfaces are provided
Riemann_surface
Conformal map projection
transforming the stereographic projection with a pole at infinity, by means of an elliptic function". The Peirce quincuncial is really a projection of the hemisphere
Peirce_quincuncial_projection
Special mathematical function
In mathematics, specifically the theory of elliptic functions, the nome is a special function that belongs to the non-elementary functions. This function
Nome_(mathematics)
Celestial orbit whose trajectory is a conic section in the orbital plane
determined with the relation Note that the relations (53) and (54) has a singularity when V r = 0 {\displaystyle V_{r}=0} and V t = V 0 = α p = α ( r ⋅ V
Kepler_orbit
Number of "holes" of a surface
complex points). For example, the definition of elliptic curve from algebraic geometry is connected non-singular projective curve of genus 1 with a given rational
Genus_(mathematics)
theorem Twisted cubic Elliptic curve, cubic curve Elliptic function, Jacobi's elliptic functions, Weierstrass's elliptic functions Elliptic integral Complex
List of algebraic geometry topics
List_of_algebraic_geometry_topics
Modular function in mathematics
the j {\displaystyle j} -invariant was studied as a parameterization of elliptic curves over C {\displaystyle \mathbb {C} } , but it also has surprising
J-invariant
Mathematical concept
"supersingular" and "singular" do not indicate that the variety has singularities. The term "singular elliptic curve" (or "singular j-invariant") was originally
Supersingular_variety
equation of the curve into the above Hessian form. Theses curves are used in elliptic curve cryptography, because arithmetic in this curve representation is
Hessian form of an elliptic curve
Hessian_form_of_an_elliptic_curve
'leaf', folium, is neuter. In descriptions of a single leaf, the neuter singular ending of the adjective is used, e.g. folium lanceolatum 'lanceolate leaf'
Glossary_of_leaf_morphology
Functions in mathematics
harmonic function with the same singularity, so in this case the harmonic function is not determined by its singularities; however, we can make the solution
Harmonic_function
Asymptotically stable in the sense of geometric invariant theory
ordinary double points as singularities, and has finite automorphism group. For example, an elliptic curve (a non-singular genus 1 curve with 1 marked
Stable_curve
hyperelliptic surface, or bi-elliptic surface, is a minimal surface whose Albanese morphism is an elliptic fibration without singular fibres. Any such surface
Hyperelliptic_surface
Free swinging suspended body
ways to proceed to calculate the elliptic integral. Given Eq. 3 and the Legendre polynomial solution for the elliptic integral: K ( k ) = π 2 ∑ n = 0 ∞
Pendulum_(mechanics)
Theorem in complex analysis
{\displaystyle \mathbb {C} \cup \{\infty \}} . Viewed this way, the only possible singularity for entire functions, defined on C ⊂ C ∪ { ∞ } {\displaystyle \mathbb
Liouville's theorem (complex analysis)
Liouville's_theorem_(complex_analysis)
Right conoid ruled surface
however, the latter name is ambiguous, as "cylindroid" may also refer to an elliptic cylinder. Plücker's conoid is the surface defined by the function of two
Plücker's_conoid
Mathematical function associated to algebraic varieties
For an elliptic curve over a number field K, the Hasse–Weil zeta function is conjecturally related to the group of rational points of the elliptic curve
Hasse–Weil_zeta_function
In mathematics, the conductor of an elliptic curve over the field of rational numbers (or more generally a local or global field) is an integral ideal
Conductor of an elliptic curve
Conductor_of_an_elliptic_curve
Area of mathematics
dynamical systems; it is also a particular special case of more general singularity theory in geometry. Bifurcation theory studies and classifies phenomena
Catastrophe_theory
Special functions of several complex variables
{x^{n+2}+1}}}\,\mathrm {d} x} In the following some Elliptic Integral Singular Values are derived: The elliptic nome function has these important values: q (
Theta_function
introduction of the concept of the origin intensity factor, which isolates the singularity of the fundamental solutions. The SBM provides a significant and promising
Singular_boundary_method
Class of second-order linear partial differential equations
important for the study of the reflection of singularities of solutions to various other PDEs. Elliptic partial differential equation Hyperbolic partial
Parabolic partial differential equation
Parabolic_partial_differential_equation
Canadian-American mathematician (1925–2020)
previously understood for second-order elliptic partial differential equations, to the general setting of elliptic systems. With Basilis Gidas and Wei-Ming
Louis_Nirenberg
Topics referred to by the same term
constraints in Hamiltonian mechanics Regularity of an elliptic operator Regularity theory of elliptic partial differential equations Regular algebra, or
Regular
Algebraic surface with special triviality properties
quotient of a reduced singular Gorenstein surface by the group scheme α2. All Enriques surfaces are elliptic or quasi elliptic. A Reye congruence is the
Enriques_surface
Type of smooth complex surface of kodaira dimension 0
a continuous family of images of elliptic curves. (These curves are singular in X, unless X happens to be an elliptic K3 surface.) A stronger question
K3_surface
Italian mathematician
dimension of the singular sets of minimisers of vectorial integral functionals and the boundary singularities of solutions to nonlinear elliptic systems. This
Giuseppe_Mingione
back to the studies of Pierre de Fermat on what are now recognized as elliptic curves; and has become a very substantial area of arithmetic geometry both
Arithmetic of abelian varieties
Arithmetic_of_abelian_varieties
Components of the Fatou set
domain: these are "domains on which the iterates tend to an essential singularity (not possible for polynomials and rational functions)" one example of
Classification of Fatou components
Classification_of_Fatou_components
Type of differential operator
pseudo-differential operator. If a differential operator of order m is (uniformly) elliptic (of order m) and invertible, then its inverse is a pseudo-differential
Pseudo-differential_operator
Belgian scientist and Catholic priest (1894–1966)
espace elliptique ("Quaternions and elliptic space"). William Kingdon Clifford had introduced the concept of elliptic space in 1873. Lemaître developed
Georges_Lemaître
Riemannian manifold with SU(n) holonomy
Yat-Ming (2004), Desingularizations of Calabi-Yau 3-folds with a conical singularity, arXiv:math/0410260, Bibcode:2004math.....10260C Greene, Brian (1997)
Calabi–Yau_manifold
2D surface which extends indefinitely
intersect, so that every pair of lines intersects in exactly one point. The elliptic plane may be further defined by adding a metric to the real projective
Plane_(mathematics)
Mathematical study of illumination of rooms with mirrored walls
Roger Penrose's solution of the illumination problem using elliptical arcs (blue) and straight line segments (green), with 3 positions of the single light
Illumination_problem
Mathematical conjecture about elliptic curves
conjecture is a statistical statement about the family of elliptic curves Ep obtained from an elliptic curve E over the rational numbers by reduction modulo
Sato–Tate_conjecture
Cylindrical Compromise Google Variant of Mercator that ignores Earth's ellipticity for fast calculation, and clips latitudes to ~85.05° for square presentation
List_of_map_projections
Horizontal angle from north or other reference cardinal direction
Relative bearing Sextant Solar azimuth angle Sound Localization Zenith The singular form of the noun is Arabic: السَّمْت, romanized: as-samt, lit. 'the direction'
Azimuth
British mathematician (1903–1987)
differential geometry, and general relativity. The concept of Du Val singularity of an algebraic surface is named after him. Du Val was born in Cheadle
Patrick_du_Val
by Robert E. Stong, Princeton University Press (1968) ASIN B0006C2BN6 Elliptic Cohomology (University Series in Mathematics) by Charles B. Thomas, Springer;
List_of_cohomology_theories
prefigured by earlier results of Charles Morrey from 1938 on quasi-linear elliptic partial differential equations. The theorem of Ahlfors and Bers states
Measurable Riemann mapping theorem
Measurable_Riemann_mapping_theorem
Interpretation of sensory information
makes a circular image on the retina, but when held at angle it makes an elliptical image. In normal perception these are recognized as a single three-dimensional
Perception
Area of mathematical analysis
Riesz transforms, many convolution operators, and singular integral operators arising in elliptic and parabolic partial differential equations. Littlewood–Paley
Harmonic_analysis
Motion of a curve based on its curvature
so until reaching a singularity at which the curvature blows up. For a smooth curve without crossings, the only possible singularity happens when the curve
Curve-shortening_flow
Seven mathematical problems with a US$1 million prize for each solution
Swinnerton-Dyer, deals with certain types of equations: those defining elliptic curves over the rational numbers. The conjecture is that there is a simple
Millennium_Prize_Problems
Mathematical function often applied to matrices
coercive or monotone vector fields in nonlinear analysis, and strong ellipticity in differential operators on function spaces, subject to specific boundary
Logarithmic_norm
Theories about the end of the universe
of these solutions, the universe has been expanding from an initial singularity which was, essentially, the Big Bang. In 1929, Edwin Hubble published
Ultimate_fate_of_the_universe
Polyhedral conformal map projection
globe onto a tetrahedron using Dixon elliptic functions. It is conformal everywhere except for the four singularities at the vertices of the polyhedron.
Lee conformal world in a tetrahedron
Lee_conformal_world_in_a_tetrahedron
2-dimensional orthogonal coordinate system based on Apollonian circles
and never used for systems associated with those other curves, such as elliptic coordinates. The system is based on two foci F1 and F2. Referring to the
Bipolar_coordinates
negligible at large heights, this condition is necessary, if singularity of the elliptic pressure equation is to be avoided in view of the Neumann boundary
MEMO model (wind-flow simulation)
MEMO_model_(wind-flow_simulation)
American mathematician (born 1934)
conjecture for elliptic K3 surfaces and the pencil of elliptic curves over finite fields. He contributed to the theory of surface singularities which are both
Michael_Artin
Class of integer sequences in mathematics
In mathematics, an elliptic divisibility sequence (EDS) is a sequence of integers satisfying a nonlinear recursion relation arising from division polynomials
Elliptic divisibility sequence
Elliptic_divisibility_sequence
Distinguished surfaces of dynamic trajectories
therefore, (polar) elliptic LCSs are simply closed level curves of the PRA, which turn out to be objective. In three dimensions, (polar) elliptic LCSs are toroidal
Lagrangian_coherent_structure
American mathematician and Nobel Laureate (1928–2015)
methods, a body of results paving the way for a systematic understanding of elliptic and parabolic partial differential equations. Their De Giorgi–Nash theorem
John_Forbes_Nash_Jr.
Soviet, Canadian mathematician
with singular potentials" (PDF). Archived from the original (PDF) on 2012-05-23. Retrieved 2011-12-25. Precise Spectral Asymptotics for Elliptic Operators
Victor_Ivrii
Type of algebraic equation
of the term modular equation is in relation to the moduli problem for elliptic curves. In that case the moduli space itself is of dimension one. That
Modular_equation
Geometric space whose points represent algebro-geometric objects of some fixed kind
{M}}}_{1,1}} of genus 1 curves with one marked point. This is the stack of elliptic curves, and is the natural home of the much studied modular forms, which
Moduli_space
Scalar-valued bilinear function
\right\|.} Definition: A bilinear form on a normed vector space (V, ‖⋅‖) is elliptic, or coercive, if there is a constant c > 0 such that for all u ∈ V, B (
Bilinear_form
Type of vector space in math
equations. For many classes of partial differential equations, such as linear elliptic equations, it is possible to consider a generalized solution (known as
Hilbert_space
Geometric space
space of genus g = 1 {\displaystyle g=1} curves having a marked point (elliptic curve groups) is the (classical) modular curve. For g > 1 {\displaystyle
Moduli_of_algebraic_curves
Mathematical transform
It can also be used to prove the analyticity of solutions of analytic elliptic partial differential equations as well as a version of the classical uniqueness
Fourier–Bros–Iagolnitzer transform
Fourier–Bros–Iagolnitzer_transform
Family of elliptic curves used in cryptography
family of elliptic curves studied by Harold Edwards in 2007. The concept of elliptic curves over finite fields is widely used in elliptic curve cryptography
Edwards_curve
German mathematician (born 1958)
obtained by Wan-Xiong Shi for Ricci flow.[EH91] Given a finite-time singularity of the mean curvature flow, there are several ways to perform microscopic
Gerhard_Huisken
When there is a singularity in the function being integrated such that the antiderivative becomes undefined at some point (the singularity), then C does
Lists_of_integrals
System where changes of output are not proportional to changes of input
{C_{0}+2\cos(\theta )}}}=t+C_{1}} which is an implicit solution involving an elliptic integral. This "solution" generally does not have many uses because most
Nonlinear_system
Ancient Indo-Aryan language of South Asia, mainly Indian subcontinent
objects such as hands or eyes, extending to any collection of two. The elliptical dual is notable in the Vedic Sanskrit, according to Jamison, where a noun
Sanskrit
Physical presence of human activity in outer space
beyond them, with some understanding humanity's or life's presence as a singularity or one to be in isolation, pondering on the Fermi paradox. A diverse
Human_presence_in_space
Hungarian and American mathematician and physicist (1903–1957)
189–191. The Technological Singularity by Murray Shanahan, (MIT Press, 2015), page 233 Chalmers, David (2010). "The singularity: a philosophical analysis"
John_von_Neumann
Plane algebraic curve
elliptic curves over Q are modular. Mappings also arise in connection with X0(n) since points on it correspond to some n-isogenous pairs of elliptic curves
Classical_modular_curve
Branch of mathematics
function fields, and p-adic fields. A large part of singularity theory is devoted to the singularities of algebraic varieties. Computational algebraic geometry
Algebraic_geometry
Mathematical technique in aerodynamics
1} the PG transformation features a singularity. The singularity is also called the Prandtl–Glauert singularity, and the flow resistance is calculated
Prandtl–Glauert transformation
Prandtl–Glauert_transformation
Mathematical classification of surfaces
list of the possible singular fibers. The theory of elliptic surfaces is analogous to the theory of proper regular models of elliptic curves over discrete
Enriques–Kodaira classification
Enriques–Kodaira_classification
Method of approximating the properties of a composite material
abs(factor_denom) < small_number_cutoff disp('WARNING: the effective medium is singular!'); eps_mean = 0; else eps_mean = eps_base * factor_numer / factor_denom;
Effective medium approximations
Effective_medium_approximations
Mathematical concept
}}\,d\theta .} When r = 1, the integrand on the right-hand side has a singularity at θ = 0. The truncated Hilbert transform is defined by H ε f ( φ ) =
Singular integral operators of convolution type
Singular_integral_operators_of_convolution_type
French sociologist and philosopher (1929–2007)
representations, but I am interested in another kind of sign, which is elliptical, as in poetry, where the sign is fatal see here The Transparency of Evil
Jean_Baudrillard
ELLIPTIC SINGULARITY
ELLIPTIC SINGULARITY
Boy/Male
Indian
Singularity
Girl/Female
Arabic, Muslim, Sindhi
Singularity
Girl/Female
Muslim/Islamic
Singularity
Surname or Lastname
English
English : variant of Douthwaite, a habitational name from Dowthwaite in Cumbria or Dowthwaite Hall in North Yorkshire. The first is from the Old Norse personal name Dúfa + Old Norse þveit ‘clearing’; the second is from the Old Irish personal name Dubhan + Old Norse þveit. The elliptic form of the surname probably reflects the local pronunciation of the place names.
Boy/Male
Muslim
Singularity
Surname or Lastname
English
English : patronymic for the son of a vicar or, perhaps in most cases, an occupational name for the servant of a vicar (see Vicker). In many cases it may represent an elliptical form of a topographic name. Compare Parsons.
ELLIPTIC SINGULARITY
ELLIPTIC SINGULARITY
Girl/Female
Indian
Lovable; Sweet Person
Boy/Male
Teutonic
Rich.
Girl/Female
Indian
Fish which moves with ease everywhere bestowing Love and peace over her surroundings getting pride to all, Paradise, A gem, Precious stone
Boy/Male
Indian
Ardent, Longing, Forehead
Boy/Male
Tamil
Dwarkapati | தà¯à®µà®¾à®°à®•à®¾ பதி
Lord of dwarka
Girl/Female
Muslim
The utmost, Highest degree
Girl/Female
Hindu
Goddess Parvati
Surname or Lastname
English and Scottish
English and Scottish : from a diminutive of Biss.French : variant of Bisset.
Girl/Female
Indian
Ice, Cold like ice, Golden skinned
Boy/Male
German
Brave as a Bear
ELLIPTIC SINGULARITY
ELLIPTIC SINGULARITY
ELLIPTIC SINGULARITY
ELLIPTIC SINGULARITY
ELLIPTIC SINGULARITY
a.
Broadly elliptical.
a.
Having a form intermediate between elliptic and lanceolate.
n.
The angular distance of a heavenly body from the ecliptic.
a.
Pertaining to the ecliptic; as, the ecliptic way.
a.
Pertaining to an eclipse or to eclipses.
n.
The elliptical orbit of a planet.
a.
A great circle drawn on a terrestrial globe, making an angle of 23¡ 28' with the equator; -- used for illustrating and solving astronomical problems.
a.
Containing saccharine matter; marked by saccharine secretions; as, mellitic diabetes.
n.
A small shield, especially one of an approximately elliptic form, or crescent-shaped.
n.
Omission. See Ellipsis.
n.
A salt of mellitic acid.
a.
See Mellitic.
n.
An ellipse.
a.
Pertaining to, or derived from, the mineral mellite.
a.
Having a part omitted; as, an elliptical phrase.
n.
The twelfth part of the ecliptic or zodiac.
pl.
of Ellipsis
a.
Alt. of Elliptical
a.
A great circle of the celestial sphere, making an angle with the equinoctial of about 23¡ 28'. It is the apparent path of the sun, or the real path of the earth as seen from the sun.
a.
Of or pertaining to an ellipse; having the form of an ellipse; oblong, with rounded ends.