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Algebro-geometric stability condition
geometry, K-stability is an algebro-geometric stability condition, for complex manifolds and complex algebraic varieties. The notion of K-stability was first
K-stability
algebraic geometry, K-stability is an algebro-geometric stability condition for projective algebraic varieties and complex manifolds. K-stability is of particular
K-stability_of_Fano_varieties
Topics referred to by the same term
Asymptotic stability Exponential stability Linear stability Lyapunov stability Marginal stability Orbital stability Structural stability Stability (probability)
Stability
Chinese mathematician (born 1958)
involving CM-stability. The first approach is now known to contain a gap. Specifically, Theorem 6.6 asserted that K-stability implies CM-stability. The proof
Tian_Gang
symplectic reduction. The Mabuchi functional appears in the theory of K-stability as an analytical functional which characterises the existence of constant
Mabuchi_functional
Prediction in nuclear physics
In nuclear physics, the island of stability is a predicted set of isotopes of superheavy elements that may have considerably longer half-lives than known
Island_of_stability
When a system's outputs are bounded for every bounded input
specifically control theory, bounded-input, bounded-output (BIBO) stability is a form of stability for signals and systems that take inputs. If a system is BIBO
BIBO_stability
Chinese mathematician
his work in birational geometry, the minimal model program, and the K-stability of Fano varieties. Xu graduated from Peking University with a Bachelor
Chenyang_Xu
Property of a dynamical system where solutions near an equilibrium point remain so
Various types of stability may be discussed for the solutions of differential equations or difference equations describing dynamical systems. The most
Lyapunov_stability
Type of metric in Riemannian geometry
case existence is equivalent to an algebro-geometric criterion called K-stability. Their proof appeared in a series of articles in the Journal of the American
Kähler–Einstein_metric
Hungarian mathematician
the supervision of Simon Donaldson with thesis Extremal metrics and K-stability. Székelyhidi was a postdoc at Harvard University and was from 2008 to
Gábor_Székelyhidi
Concept in algebraic geometry
the existence of Kähler–Einstein metrics on them through the study of K-stability of Fano varieties. The fundamental example of Fano varieties are the
Fano_variety
Problem in statistical physics
, K = − ∑ i = 1 N Δ x i 2 − ∑ k = 1 K Δ R k 2 M k − ∑ i = 1 N ∑ k = 1 K z k | x i − R k | + ∑ 1 ≤ i < j ≤ N 1 | x i − x j | + ∑ 1 ≤ k < m ≤ K z k z m
Stability_of_matter
Graphical method of determining the stability of a dynamical system
In control theory and stability theory, the Nyquist stability criterion or Strecker–Nyquist stability criterion, independently discovered by the German
Nyquist_stability_criterion
case of Fano or Calabi–Yau manifolds) the notions of K-stability and K-polystability coincide, cscK metrics are precisely Kähler-Einstein metrics and the
Constant scalar curvature Kähler metric
Constant_scalar_curvature_Kähler_metric
State of linear equations
linear stability does not automatically imply stability; in particular, when k = 2, the solitary waves are unstable. On the other hand, for 0 < k < 2, the
Linear_stability
French mathematician
to study Kähler manifolds have been very influential in the study of K-stability of Fano varieties. In 2014, the French Academy of Sciences awarded him
Sébastien_Boucksom
Field of algebraic geometry
Birational geometry has recently found important applications in the study of K-stability of Fano varieties through general existence results for Kähler–Einstein
Birational_geometry
English mathematician (born 1957)
of 4-dimensional manifolds and for the study of the relation between stability in algebraic geometry and in global differential geometry, both for bundles
Simon_Donaldson
Concept in algebraic geometry
Quantization commutes with reduction K-stability K-stability of Fano varieties Bridgeland stability condition Stability (algebraic geometry) Deligne, Pierre;
Geometric_invariant_theory
Swedish mathematical scientist
Gustafsson Prize in 2017. Berman is known for his constributions to the K-stability of Fano varieties. "Robert J. Berman". chalmers.se. Retrieved April 24
Robert_J._Berman
4007/annals.2010.172.673. Retrieved 29 September 2025. Liu, Yuchen (2022). "K-stability of cubic fourfolds". Journal für die reine und angewandte Mathematik
Cubic_fourfold
Stability conditions for triangulated cateogires
a Bridgeland stability condition is an algebro-geometric stability condition defined on elements of a triangulated category. Stability conditions serve
Bridgeland stability condition
Bridgeland_stability_condition
Study of complex manifolds and several complex variables
and for example recently the classification of Fano manifolds using K-stability has benefited tremendously both from techniques in analysis and in pure
Complex_geometry
Degree to which disturbing a plasma system at equilibrium will destabilize it
physics, plasma stability concerns the stability properties of a plasma in equilibrium and its behavior under small perturbations. The stability of the system
Plasma_stability
Computerized safety automotive technology
Electronic stability control (ESC), also referred to as electronic stability program (ESP) or dynamic stability control (DSC), is a computerized technology
Electronic_stability_control
Stability of soil or rock slopes
Slope stability refers to the condition of inclined soil or rock slopes to withstand or undergo movement; the opposite condition is called slope instability
Slope_stability
Chinese Communist Party political slogan
Stability maintenance (Chinese: 维稳; pinyin: Wéiwěn) is a term used by the Chinese Communist Party (CCP) to refer to all-round surveillance and control
Stability_maintenance
Theoretical model of shear fluid flow
Rayleigh's equation or Rayleigh stability equation is a linear ordinary differential equation to study the hydrodynamic stability of a parallel, incompressible
Rayleigh's equation (fluid dynamics)
Rayleigh's_equation_(fluid_dynamics)
States of matter for water as a solid
PMID 32461682. S2CID 218913209. Murray, B.J.; Bertram, A. K. (2006). "Formation and stability of cubic ice in water droplets". Phys. Chem. Chem. Phys.
Phases_of_ice
Method of determining if a discrete linear time-invariant system is stable
linear, time-invariant (LTI) system is stable proposed by Yuval Bistritz. Stability of a discrete LTI system requires that its characteristic polynomial D
Bistritz_stability_criterion
Characterization of nuclide stability
of stability (also called the belt of stability, nuclear valley, energy valley, or beta stability valley) is a characterization of the stability of nuclides
Valley_of_stability
Constants that describe stability of coordination complexes
In coordination chemistry, a stability constant (also called formation constant or binding constant) is an equilibrium constant for the formation of a
Stability constants of complexes
Stability_constants_of_complexes
Directional stability is the tendency of a vehicle or moving body to keep its orientation aligned with its direction of movement. When a car or an airplane
Directional_stability
Ability to manage financial crisis
Financial stability is the absence of system-wide episodes in which a financial crisis occurs and is characterised as an economy with low volatility.
Financial_stability
Type of mathematical theorem
138–140. doi:10.1007/bf01098313. Suslin, A. A. (1982), Stability in algebraic K-theory. Algebraic K-theory, Part I (Oberwolfach, 1980), Lecture Notes in
Homological_stability
Continuous-time linear system with only negative real parts
convergence is bounded by exponential decay. Exponential stability is a form of asymptotic stability, valid for more general dynamical systems. Consider the
Exponential_stability
and even the uniformization theorem. Gieseker stability Slope stability Bridgeland stability K-stability Mumford, D., Fogarty, J. and Kirwan, F., 1994
Stability (algebraic geometry)
Stability_(algebraic_geometry)
Vector bundles theorem
of stability should be an analogue of slope stability of vector bundles. Tian Gang gave a precise definition of such a stability notion, called K-stability
Kobayashi–Hitchin correspondence
Kobayashi–Hitchin_correspondence
Stability of an aircraft in the pitching plane
In flight dynamics, longitudinal stability is the stability of an aircraft in the longitudinal, or pitching, plane. This characteristic is important in
Longitudinal_stability
Stability notion for nonlinear control systems with external inputs
Input-to-state stability (ISS) is a stability notion widely used to study stability of nonlinear control systems with external inputs. Roughly speaking
Input-to-state_stability
Short science fiction story by Philip K. Dick (published 1987)
"Stability" is a short science fiction story by Philip K. Dick, first written around 1947, but not published until 1987 in Volume I of The Collected Stories
Stability_(short_story)
Aircraft with low or negative stability
aircraft is said to have relaxed stability if it has low or negative stability. An aircraft with negative stability will have a tendency to change its
Relaxed_stability
When an ecosystem does not drastically change over time even after perturbation
Although the terms community stability and ecological stability are sometimes used interchangeably, community stability refers only to the characteristics
Ecological_stability
Control loop feedback mechanism
( s ) = K p + K i s + K d s = K d s 2 + K p s + K i s {\displaystyle G(s)=K_{p}+{\frac {K_{i}}{s}}+K_{d}{s}={\frac {K_{d}{s^{2}}+K_{p}{s}+K_{i}}{s}}}
PID_controller
Numerical analysis procedure
analysis, von Neumann stability analysis (also known as Fourier stability analysis) is a procedure used to check the stability of finite difference schemes
Von Neumann stability analysis
Von_Neumann_stability_analysis
American science fiction author (1928–1982)
Philip K. Dick at LibriVox (public domain audiobooks) Philip K. Dick at IMDb Philip K. Dick at the Internet Speculative Fiction Database Philip K. Dick
Philip_K._Dick
Ability of a person to control the position and movement of their torso
In kinesiology, core stability is a person's ability to stabilize their core (all parts of the body that are not limbs). Stability, in this context, should
Core_stability
Riemannian manifold which satisfies vacuum Einstein equations
due to the existence results of Shing-Tung Yau, and the later study of K-stability especially in the case of Fano manifolds. Irreducible symmetric spaces
Einstein_manifold
Family of implicit and explicit iterative methods
using k 1 = f ( t n , y n ) , k 2 = f ( t n + h 2 , y n + k 1 h 2 ) , k 3 = f ( t n + h 2 , y n + k 2 h 2 ) , k 4 = f ( t n + h , y n + h k 3 )
Runge–Kutta_methods
Measurement of the initial static stability of a floating body
location must be found to calculate the ship's stability. It can be calculated using the formulae: K M = K B + B M {\displaystyle KM=KB+BM} B M = I V
Metacentric_height
Hyperspace in algebraic geometry
ISSN 0003-486X, JSTOR 1970801, MR 0302652 Liu, Yuchen; Xu, Chenyang (2019), "K-stability of cubic threefolds", Duke Math. J., 168 (11): 2029–2073 Murre, J. P
Cubic_threefold
Stability criterion for a dynamical system
Kharitonov's theorem is a result used in control theory to assess the stability of a dynamical system when the physical parameters of the system are not
Kharitonov's_theorem
are used in stability theory to characterize the stability properties of control systems as Lyapunov stability, uniform asymptotic stability etc. Let C
Comparison_function
Mass extinction event about 66 million years ago
The Cretaceous–Paleogene (K–Pg) extinction event, formerly known as the Cretaceous–Tertiary (K–T) extinction event, was a major mass extinction of three-quarters
Cretaceous–Paleogene extinction event
Cretaceous–Paleogene_extinction_event
stable if the master stability function is negative at σ λ k {\displaystyle \sigma \lambda _{k}} where λ k {\displaystyle \lambda _{k}} ranges over the eigenvalues
Master_stability_function
Science of air vehicle orientation and control in three dimensions
aircraft stability: speed stability, stick free static longitudinal stability, static lateral stability, directional stability, oscillatory stability, and
Aircraft_flight_dynamics
Characteristic polynomial whose associated linear system is stable
system, Schur stable for discrete-time). In practice, stability is tested via several stability criteria. The Routh–Hurwitz theorem provides an algorithm
Stable_polynomial
Type of Wilson tennis racquets
sweet spot. (K)ontour Yoke refers to the cross-sectional shape of the frame that enhances stiffness to increase stability of the racquet. (K)ompact Center
Wilson_K-Factor
Method for analyzing stability of slopes of soil or rock
Slope stability analysis is a static or dynamic, analytical or empirical method to evaluate the stability of slopes of soil- and rock-fill dams, embankments
Slope_stability_analysis
Cooperative international body on global financial system
The Financial Stability Board (FSB) is an international body that monitors and makes recommendations about the global financial system. It was established
Financial_Stability_Board
Country in Northwestern Europe
sterling maintains its high nominal value through both its long history of stability and by never undergoing formal redenomination. Since 2022 the UK has been
United_Kingdom
American author (1929–2018)
Retrieved September 28, 2018. Walton, Jo (April 29, 2009). "A new island of stability: Ursula Le Guin's Annals of the Western Shore". Tor.com. Archived from
Ursula_K._Le_Guin
Activity of the Installation Management Command-Korea (IMCOM-K)[link removed] The U.S. Army Stability Operations Field Manual The U.S. Army, with forewords by
Stability and support operations
Stability_and_support_operations
Mathematical theory
In mathematics, Reeb stability theorem, named after Georges Reeb, asserts that if one leaf of a codimension-one foliation is closed and has finite fundamental
Reeb_stability_theorem
fewer stable and long-lived nuclides. Island of stability Isotope § Nuclear properties and stability List of nuclides List of radioactive nuclides by
List of elements by stability of isotopes
List_of_elements_by_stability_of_isotopes
Potassium compound and alternative to salt
Sergey S.; Stavrou, Elissaios; Goncharov, Alexander F. (23 May 2016). "Stability of numerous novel potassium chlorides at high pressure". Sci Rep. 6 26265
Potassium_chloride
Notion in computational learning theory
Stability, also known as algorithmic stability, is a notion in computational learning theory of how a machine learning algorithm output is changed with
Stability_(learning_theory)
Ship response to disturbance from an upright condition
Ship stability is an area of naval architecture and ship design that deals with how a ship behaves at sea, both in still water and in waves, whether intact
Ship_stability
Matrix whose eigenvalues have negative real part
(1998). "A Note on Hurwitz Stability of Matrices". Automatica. 34 (4): 509–511. doi:10.1016/S0005-1098(97)00217-3. Khalil, Hassan K. (1996). Nonlinear Systems
Hurwitz-stable_matrix
In stability theory, hyperstability is a property of a system that requires the state vector to remain bounded if the inputs are restricted to belonging
Hyperstability
Indian mathematician (1931–2004)
Surindar Kumar Trehan (S.K. Trehan) was an Indian mathematician who specialised in non-linear stability in magnetohydrodynamics. He was awarded in 1976
Surindar_Kumar_Trehan
List of works by American science fiction, Philip K Dick
of Philip K. Dick includes 45 novels, 121 short stories, and 14 short story collections published by American science fiction author Philip K. Dick (December
Philip_K._Dick_bibliography
Monetary policy
Price stability occurs when average consumer prices for goods and services are constant over time, or when they are rising at a low and predictable rate
Price_stability
Ecological theory concerning the selection of life history traits
expendable nature of the offspring and parental commitment made. The stability of the environment can predict if many expendable offspring are made or
R/K_selection_theory
International organization
The Financial Stability Forum (FSF) was a group consisting of major national financial authorities such as finance ministries, central bankers, and international
Financial_Stability_Forum
Concerned with the notion of stability in model theory
theory is "neostability theory," which tries to generalize the concepts of stability theory to broader contexts, such as simple and NIP theories. A common
Stable_theory
Numerical method for solving ordinary differential equations
for a BDF can be written as ∑ k = 0 s a k y n + k = h β f ( t n + s , y n + s ) , {\displaystyle \sum _{k=0}^{s}a_{k}y_{n+k}=h\beta f(t_{n+s},y_{n+s}),}
Backward differentiation formula
Backward_differentiation_formula
Philip K. Dick was an American author known for his science fiction works, often with dystopian and drug-related themes. Some of his works have gone on
List of adaptations of works by Philip K. Dick
List_of_adaptations_of_works_by_Philip_K._Dick
Differential equation exhibiting high rate of dissipation
_{k=0}^{n-1}\left(1-h\lambda \right)^{k-n}h{\big (}{\dot {g}}(t_{k+1})-\lambda g(t_{k+1}){\big )}\,.} Here, the stability requirement is | 1 − h λ | − 1 ≤
Stiff_equation
engineering Finite element method Slope stability analysis Sarma S. K. (1968) Response characteristics and stability of earth dams during strong earthquakes
Sarma_method
Measurement related to thunderstorms
The K-Index or George's Index is a measure of thunderstorm potential in meteorology. According to the National Weather Service, the index harnesses measurements
K-index_(meteorology)
Series in chemistry
the relative stabilities of complexes formed by transition metals. In 1953 Harry Irving and Robert Williams observed that the stability of complexes formed
Irving–Williams_series
Chemical element with atomic number 118 (Og)
Bibcode:1989nufi.rept...16H. Oganessian, Yu. Ts.; Rykaczewski, K. P. (2015). "A beachhead on the island of stability". Physics Today. 68 (8): 32–38. Bibcode:2015PhT
Oganesson
to ensure the best product quality to the final consumer. “Dispersion stability refers to the ability of a dispersion to resist change in its properties
Dispersion_stability
In stability theory and nonlinear control, Massera's lemma, named after José Luis Massera, deals with the construction of the Lyapunov function to prove
Massera's_lemma
1968 science fiction novel by Philip K. Dick
printings) is a 1968 dystopian science fiction novel by American writer Philip K. Dick. It is set in a post-apocalyptic San Francisco, where Earth's life has
Do Androids Dream of Electric Sheep?
Do_Androids_Dream_of_Electric_Sheep?
Phenomenon of fluid mechanics
wavevector k = k x e x + k y e y {\displaystyle \mathbf {k} =k_{x}\mathbf {e} _{x}+k_{y}\mathbf {e} _{y}} . Since k x = k cos ϕ {\displaystyle k_{x}=k\cos
Kelvin–Helmholtz_instability
Italian sports car manufactured 2013–2018
rear. LaFerrari has several electronic controls including an electronic stability control, high-performance ABS/EBD (anti-lock braking system/electronic
LaFerrari
Concept in theory of differential equations
asymptotic stability of a simple system, the pendulum with friction. This system can be modeled with the differential equation m l θ ¨ = − m g sin θ − k l θ
LaSalle's invariance principle
LaSalle's_invariance_principle
The stability problem of functional equations originated from a question of Stanisław Ulam, posed in 1940, concerning the stability of group homomorphisms
Hyers–Ulam–Rassias_stability
Intermediate energetic state within a dynamical system
or reactive patterns with respect to the external influences defines stability and metastability (see brain metastability below). In these systems, the
Metastability
Economic policy regarding increases to the money supply
In macroeconomics, Friedman's k-percent rule (named for Milton Friedman) is the monetarist proposal that the money supply should be increased by the central
Friedman's_k-percent_rule
Nuclides predating the Earth's formation (found on Earth)
number is about 251. For a list, see the article list of elements by stability of isotopes. For a complete list noting which of the "stable" 251 nuclides
Primordial_nuclide
elements by stability of isotopes List of nuclides Orders of magnitude (time) Lists of isotopes, by element Reaching the limits of nuclear stability, M. Thoennessen
List of radioactive nuclides by half-life
List_of_radioactive_nuclides_by_half-life
British academic
Sarma S. K. (1973), Stability analysis of embankments and slopes. Geotechnique, 23, 423 - 433, ISSN 0016-8505 Sarma S. K. (1975), Seismic stability of earth
Sarada_K._Sarma
Discrete probability distribution
= k 1 , X 2 = k 2 ) = exp ( − λ 1 − λ 2 − λ 3 ) λ 1 k 1 k 1 ! λ 2 k 2 k 2 ! ∑ k = 0 min ( k 1 , k 2 ) ( k 1 k ) ( k 2 k ) k ! ( λ 3 λ 1 λ 2 ) k {\displaystyle
Poisson_distribution
Study of the physical care and treatment of photographic materials
varying degrees of stability. In addition, different materials may have dark-storage stability which differs from their stability in light. Kodachrome
Conservation and restoration of photographs
Conservation_and_restoration_of_photographs
Periodic table of the elements with eight or more periods
hypothesized to be within an island of stability that is resistant to fission but not to alpha decay. Other islands of stability beyond the known elements may
Extended_periodic_table
General-purpose programming language
may have been chosen over interpreted languages because of its speed, stability, and near-universal availability. It is no longer common practice for
C_(programming_language)
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