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Topics referred to by the same term
The phrase limiting case has several different meanings in: Limiting case (mathematics) Limiting case (philosophy of science) This disambiguation page
Limiting_case
Special case which arises when input values are at their extremes
In mathematics, a limiting case of a mathematical object is a special case that arises when one or more components of the object take on their most extreme
Limiting_case_(mathematics)
limiting case theory is an earlier theory which becomes incorporated into a later, usually broader theory; that is to say, the earlier (limiting case)
Limiting case (philosophy of science)
Limiting_case_(philosophy_of_science)
Limiting case which is different from the rest of the class
In mathematics, a degenerate case is a limiting case of a class of objects which appears to be qualitatively different from (and usually simpler than)
Degeneracy_(mathematics)
Simple curve of Euclidean geometry
AE (corollary of the chord theorem). A tangent can be considered a limiting case of a secant whose ends are coincident. If a tangent from an external
Circle
Plane curve
ranging from e = 0 {\displaystyle e=0} (the limiting case of a circle) to e = 1 {\displaystyle e=1} (the limiting case of infinite elongation, no longer an ellipse
Ellipse
Specific, usually well-known application of a mathematical rule or law
versa, or equivalently, if B is a generalization of A. A limiting case is a type of special case which is arrived at by taking some aspect of the concept
Special_case
Property of an electrical circuit
\over 4}+{Z \over Y}}}\ } For a transmission line, it can be seen as a limiting case of an infinite ladder network with infinitesimal impedance and admittance
Characteristic_impedance
Nondeterministic Newtonian mechanical system
mechanics. It was devised by John D. Norton in 2003. It is a special limiting case of a more general class of examples from 1997 by Sanjay Bhat and Dennis
Norton's_dome
Topics referred to by the same term
organisation in the United Kingdom Limiting case (mathematics), a special case with one or more extreme parameter values Limiting case (philosophy of science),
Case
Polyhedron with 12 faces
has tetrahedral symmetry. The rhombic dodecahedron can be seen as a limiting case of the pyritohedron, and it has octahedral symmetry. The elongated dodecahedron
Dodecahedron
Equation characterising electrochemical kinetics
{\displaystyle \alpha _{\rm {a}}=1-\alpha _{\rm {c}}} . There are two limiting cases of the Butler–Volmer equation: the low overpotential region (called
Butler–Volmer_equation
Faintest item observable by an instrument
astronomy, limiting magnitude is the faintest apparent magnitude of a celestial body that is detectable or detected by a given instrument. In some cases, limiting
Limiting_magnitude
Method of generating random small-world graphs
(0)\approx N/2K\gg 1} and scales linearly with the system size. In the limiting case of β → 1 {\displaystyle \beta \rightarrow 1} , the graph approaches
Watts–Strogatz_model
Illusionary dark gray color
luminances below approximately 10− 5 cd m−2 (25.08 mag arcsec−2). This is a limiting case of Ricco's law. Researchers noticed as early as 1860 that the shape
Eigengrau
Polarization state
left-hand sense. Circular polarization is a limiting case of elliptical polarization. The other special case is the easier-to-understand linear polarization
Circular_polarization
Difference between phase angles
angular frequency of ω. The limiting case of c2 = 0 corresponds to a "fixed end" that doesn't move, whereas the limiting case of c2 → ∞ corresponds to a
Reflection_phase_change
Differential equation important in physics
angular frequency of ω. The limiting case of c2 = 0 corresponds to a "fixed end" that does not move, whereas the limiting case of c2 → ∞ corresponds to a
Wave_equation
Topics referred to by the same term
between sets of points in geometry Infinitesimal transformation, a limiting case of a geometrical transformation Chemical transformation Phase transformation
Transformation
Theory of subatomic structure
before it was conjectured in the mid-1990s that they were all different limiting cases of a single theory in eleven dimensions known as M-theory. In late 1997
String_theory
Concept in economics
preserve mathematical consistency with the limiting case of ln ( c ) {\displaystyle \ln(c)} ; see Special cases below). Since the family contains both power
Isoelastic_utility
Function in economics
Leontief and represents a limiting case of the constant elasticity of substitution production function. For the simple case of a good that is produced
Leontief_production_function
Catalan solid with 12 faces
and (0, 0, ±2). The rhombic dodecahedron can be seen as a degenerate limiting case of a pyritohedron, with permutation of coordinates (±1, ±1, ±1) and
Rhombic_dodecahedron
Vector representing the energy passing through a given area per unit time
To define the heat flux at a certain point in space, one takes the limiting case where the size of the surface becomes infinitesimally small. Heat flux
Heat_flux
Observational basis of thermodynamics
While reversible processes are a useful and convenient theoretical limiting case, all natural processes are irreversible. A prime example of this irreversibility
Laws_of_thermodynamics
Framework of superstring theory
all of these.) Each of these five string theories arises as a special limiting case of M-theory. This theory, like its string theory predecessors, is an
M-theory
Candidate unified theory of physics
of classical field theory. Moreover, it gives quantum mechanics as a limiting case and has revealed close connections to quantum field theory. Therefore
Causal_fermion_systems
Limiting the data rate on network controllers
In computer networks, rate limiting is used to control the rate of requests sent or received by a network interface controller. It can be used to prevent
Rate_limiting
Mathematical metric
the Moore neighborhood of that point. The Chebyshev distance is the limiting case of the order- p {\displaystyle p} Minkowski distance, when p {\displaystyle
Chebyshev_distance
Geometry problem of a coin rolling around another
+ r/r = R/r + 1 times its own radius (or circumference). In the limiting case when R = 0, the coin with radius r makes 0/r + 1 = 1 simple rotation
Coin_rotation_paradox
Concept in physics
justified in the present case"). Einstein revisited the problem in 1919 ("It is by no means settled a priori that a limiting transition of this kind has
Postulates of special relativity
Postulates_of_special_relativity
Construct all the circles that are tangent to three given circles
a line (denoted CCL, generally 8 solutions) In a different type of limiting case, the three given geometrical elements may have a special arrangement
Special cases of Apollonius' problem
Special_cases_of_Apollonius'_problem
Scale-free network generation algorithm
analytic result for the density of nodes with h-index 1 can be obtained in the case where m 0 = 1 {\displaystyle m_{0}=1} H ( 1 ) | m 0 = 1 = 4 − π {\displaystyle
Barabási–Albert_model
Topics referred to by the same term
Welcome "DEGENERATE", a 2024 song by Starset Degeneracy (mathematics), a limiting case in which a class of object changes its nature so as to belong to another
Degeneracy
Description of large objects' physics
Galilean transform). This group is a limiting case of the Poincaré group used in special relativity. The limiting case applies when the velocity u is very
Classical_mechanics
SI unit of apparent power in an electrical circuit
the real power as voltage and current are no longer in phase. In the limiting case of a purely reactive load, current is drawn but no power is dissipated
Volt-ampere
Measure of a channel flow efficiency
= 4 R H , {\displaystyle D_{\text{H}}=4R_{\text{H}},} Note that for the case of a circular pipe, D H = 4 π R 2 2 π R = 2 R {\displaystyle D_{\text{H}}={\frac
Hydraulic_diameter
State of gravitational equilibrium between Earth's crust and mantle
responds to loads in many different ways, isostasy describes the important limiting case in which crust and mantle are in static equilibrium. Certain areas (such
Isostasy
Probability distribution
parameters, including more than thirty named distributions as limiting or special cases. A fifth parameter for scaling is sometimes included, while a
Generalized_beta_distribution
Safety feature in electrical engineering
Current limiting is the practice of imposing a limit on the current that may be delivered to a load to protect the circuit generating or transmitting the
Current_limiting
2.71828...; base of natural logarithms
exponential for which the inequality ax ≥ x + 1 holds for all x. This is a limiting case of Bernoulli's inequality. Steiner's problem asks to find the global
E_(mathematical_constant)
Form of artificial neural network
neuron selects the state that has the lowest of the two energies. In the limiting case when the non-linear energy function is quadratic F ( x ) = x 2 {\displaystyle
Hopfield_network
Model of an energy potential in quantum mechanics
be approximated by a delta potential. The delta potential well is a limiting case of the finite potential well, which is obtained if one maintains the
Delta_potential
Analytic solution of the nonlinear Schrödinger equation
limiting case of the space-periodic Akhmediev breather when the period tends to infinity. The Peregrine soliton can also be seen as the limiting case
Peregrine_soliton
Three-dimensional coordinate system
coordinates. Prolate spheroidal coordinates can also be considered as a limiting case of ellipsoidal coordinates in which the two smallest principal axes
Prolate spheroidal coordinates
Prolate_spheroidal_coordinates
Family of probability distributions
q-distribution is a family of probability distributions that includes, as limiting cases, the uniform distribution and the normal (Gaussian) distribution. It
Gaussian_q-distribution
Geometry problem about finding touching circles
François Viète found a straightedge and compass solution by exploiting limiting cases: any of the three given circles can be shrunk to zero radius (a point)
Problem_of_Apollonius
Passage of a system from an initial to a final state of thermodynamic equilibrium
progress. As a useful theoretical but not actually physically realizable limiting case, a process may be imagined to take place practically infinitely slowly
Thermodynamic_process
Probability distribution
distribution and geometric distribution as special cases and the Bernoulli distribution as a limiting case. The CMP distribution was originally proposed by
Conway–Maxwell–Poisson distribution
Conway–Maxwell–Poisson_distribution
Feature of artificial neural networks
Theoretical analysis of artificial neural networks sometimes considers the limiting case that layer width becomes large or infinite. This limit enables simple
Large width limits of neural networks
Large_width_limits_of_neural_networks
Characteristic of conic sections
eccentricity for parabolas is not defined). A parabola can be treated as a limiting case of an ellipse or a hyperbola with one focal point at infinity. The eccentricity
Eccentricity_(mathematics)
Vector distance function
Manhattan distance and the Euclidean distance, respectively. In the limiting case of p {\displaystyle p} approaching infinity, we obtain the Chebyshev
Minkowski_distance
Generates a forecast of future values of a time series
{\displaystyle \alpha } actually reduce the level of smoothing, and in the limiting case with α {\displaystyle \alpha } = 1 the smoothing output series is just
Exponential_smoothing
Discrete population dynamics model
patches linked by density-dependent dispersal. The Ricker model is a limiting case of the Hassell model which takes the form N t + 1 = k 1 N t ( 1 + k
Ricker_model
Complete reflection of a wave
above. Obviously the angle of refraction cannot exceed 90°. In the limiting case, we put θ2 = 90° and θ1 = θc in Eq. (1), and solve for the critical
Total_internal_reflection
In physics, two bodies contacting each other
inelastic" collision (also called a "perfectly plastic" collision) is a limiting case of inelastic collision in which the two bodies coalesce after impact
Collision
Neural networks
neuron selects the state that has the lowest of the two energies. In the limiting case when the non-linear energy function is quadratic F ( x ) = x 2 {\displaystyle
Modern_Hopfield_network
Mathematical problem
had considered finds its application in hypersonic flow theory as a limiting case. In Proposition 34 of Book 2 of the Principia, Newton wrote: "If in
Newton's minimal resistance problem
Newton's_minimal_resistance_problem
Probability distribution
for n = 1, 2, 3 gives 15/24, 315/480, 9009/13440; rapidly approaching a limiting value of 1 / 2 = 0.70710678 … {\displaystyle 1/{\sqrt {2}}=0.70710678\ldots
Beta_distribution
Intersection of a sphere and cone emanating from its center
direction to the middle of the cap as seen from the sphere center. The limiting case is for φ approaching 180 degrees, which then describes a complete sphere
Spherical_sector
Medical condition with dark feces
self-limiting case of melena can occur in newborns two to three days after delivery, due to swallowed maternal blood.[citation needed] In acute cases, with
Melena
System where only the inputs and outputs can be viewed, and not its implementation
receiving the black box typically is hands-off. In mathematical modeling, a limiting case. In neural networking or heuristic algorithms (computer terms generally
Black_box
Solution of Einstein field equations
be seen to reduce to other exact solutions in general relativity in limiting cases. It reduces to the Kerr metric as the charge Q goes to zero; the Reissner–Nordström
Kerr–Newman_metric
Concept in differential equation mathematics
regular singular points, and the Bessel equation which is in a sense a limiting case, but where the analytic properties are substantially different. More
Regular_singular_point
Output of a dynamic system when given a brief input
function for discrete-time systems. The Dirac delta represents the limiting case of a pulse made very short in time while maintaining its area or integral
Impulse_response
Geometry theorem
case of Pascal's theorem for a conic—the limiting case when the conic degenerates into 2 straight lines. Pascal's theorem is in turn a special case of
Pappus's_hexagon_theorem
Type of enzyme inhibition
and in practice uncompetitive inhibition is mainly encountered as a limiting case of inhibition in two-substrate reactions in which one substrate concentration
Uncompetitive_inhibition
Deficiency of amniotic fluid in the amniotic sac
fluid that surrounds the fetus in the abdomen, in the amniotic sac. The limiting case is anhydramnios, where there is a complete absence of amniotic fluid
Oligohydramnios
Doughnut-shaped surface of revolution
equivalent to a sphere – by adding one additional point that represents the limiting case as a rectangular torus approaches an aspect ratio of 0 in the limit
Torus
in depth: see the two left pictures. In the third picture, Panum's limiting case, AB and CD coincide. With even greater rotation (right picture), C and
Double-nail_illusion
Gradual loss of flux intensity through a medium
Indeed, one emerging school of thought is that a glass is simply the limiting case of a polycrystalline solid. Within this framework, "domains" exhibiting
Attenuation
Cylindrical conformal map projection
well have been based on the similar central cylindrical projection, a limiting case of the gnomonic projection, which is the basis for a sundial. Snyder
Mercator_projection
Buoyancy principle in fluid dynamics
cubes is decreased, the precision of the approximation increases. The limiting case for infinitely small cubes is the exact equivalence. Angled surfaces
Archimedes'_principle
Reduced pressure caused by a flow restriction in a tube or pipe
with the small tube end face parallel with the flow direction. The limiting case of the Venturi effect is when a fluid reaches the state of choked flow
Venturi_effect
Mathematical equation describing the motion of a rocket
{m_{0}}{m_{f}}}\right).} The rocket equation can also be derived as the limiting case of the speed change for a rocket that expels its fuel in the form of
Tsiolkovsky_rocket_equation
Application of Zipf's law to publications by field
_{x=1}^{\infty }{\frac {1}{x^{s}}}} is the Riemann zeta function. It is the limiting case of Zipf's law where an individual's maximum number of publications is
Lotka's_law
Fluid dynamics study of flow distribution in parallel channels
recurrence and iteration method for a manifold. It is clear that Eq.2a is limiting case of Eq.2b when ∆X → 0. Eq.2a is simplified to Eq.1 Bernoulli equation
Flow distribution in manifolds
Flow_distribution_in_manifolds
Set of quantities in probability theory
p = μ·n−1 gives K '(t) = ((μ−1 − n−1)·e−t + n−1)−1 and κ1 = μ. The limiting case n → +∞ is a Poisson distribution. The negative binomial distributions
Cumulant
Geometric object moved along a path to generate a shape
resulting shape is a circular cone. The generatrix of a cylinder, a limiting case of a cone, is a line that is kept parallel to some axis. Surface of
Generatrix
Line which touches a circle at exactly one point
limiting cases of a family of circles which are internally or externally tangent to both circles, while the internal tangent lines are limiting cases
Tangent_lines_to_circles
Fluid flow revolving around an axis of rotation
the axis of rotation. The axis itself is one of the vortex lines, a limiting case of a vortex tube with zero diameter. According to Helmholtz's theorems
Vortex
Function defined by a hypergeometric series
hypergeometric series, that includes many other special functions as specific or limiting cases. It is a solution of a second-order linear ordinary differential equation
Hypergeometric_function
Three-dimensional solid
cylindrical conics. A solid circular cylinder can be regarded as the limiting case of a n-gonal prism as n approaches infinity. Because of this close relationship
Cylinder
Upward force that opposes the weight of an object immersed in fluid
cube is decreased, the precision of the approximation increases. The limiting case for infinitely small cubes is the exact equivalence. Angled surfaces
Buoyancy
using standard geometrical techniques along with some assumptions about limiting cases. There are two different ways to execute TMA: manual and automated.
Target_Motion_Analysis
Simple model of topological insulator
Hamiltonian analytically in the finite case due to the lack of translational symmetry. There exist two limiting cases for the finite chain, either v = 0 {\displaystyle
Su–Schrieffer–Heeger_model
Rule in geometry of individual molecules
lone pair (an occupied nonbonding orbital) can be thought of as the limiting case of an electropositive substituent, with electron density completely
Bent's_rule
Probability distribution
the mean or variance is finite. Except for the Gaussian which is a limiting case, all stable distributions have heavy tails and infinite variance. It
Normal_distribution
Neoclassical economic model
obtained conditions similar to what he finds. Cass also considers the limiting case where the discount rate goes to zero in his paper. For his part, Cass
Ramsey–Cass–Koopmans_model
Probability distribution
X\sim {\textrm {Laplace}}(0,\lambda )} . The Laplace distribution is a limiting case of the hyperbolic distribution. If X | Y ∼ N ( μ , Y 2 ) {\displaystyle
Laplace_distribution
Theory of interpersonal relationships
ranking, equality matching and market pricing (to these are added the limiting cases of asocial and null interactions, whereby people do not coordinate with
Relational_models_theory
Branch of physics
supersedes an older one, it almost always contains the older theory as a limiting case. This is sometimes called the correspondence principle. The predictions
Theoretical_physics
Concept in astrophysics
ellipse is increasingly off-center with increasing ellipticity. In the limiting case of a degenerate ellipse with an eccentricity of 1, the largest diameter
Free-fall_time
Surface drawn by a moving line passing through a fixed point
is a developable surface. A cylindrical surface can be viewed as a limiting case of a conical surface whose apex is moved off to infinity in a particular
Conical_surface
Hedge fund investment strategy
market and sector moves. Market neutral strategies can be seen as the limiting case of equity long/short, in which the long and short portfolios of the
Long/short_equity
Type of nonlinear wave in physics
for values of the modulation parameter b less than √2. Note that a limiting case of the breather solution is the Peregrine soliton. Breather surface
Breather
Thermodynamic process that is reversible and adiabatic
seventh edition, North Holland, Amsterdam, ISBN 0444869514, p. 12: "As a limiting case between natural and unnatural processes[,] we have reversible processes
Isentropic_process
Geometric point from which certain types of curves are constructed
having a fixed ratio of distances to the two foci. A parabola is a limiting case of an ellipse in which one of the foci is a point at infinity. A hyperbola
Focus_(geometry)
Natural limits on organisms or medical conditions
population. In some cases, the self-limiting nature of a colony may be advantageous to the continued survival of the colony, such as in the case of parasites
Self-limiting_(biology)
Discrete probability distribution
appendix of Kamath et al. The Poisson distribution can be derived as a limiting case to the binomial distribution as the number of trials goes to infinity
Poisson_distribution
LIMITING CASE
LIMITING CASE
Girl/Female
Latin
Protectress of the dead.
Boy/Male
Arabic
Lighting
Girl/Female
Hindu, Indian
Lighting
Girl/Female
Arabic, Muslim
Visiting; Returning
Girl/Female
British, Gujarati, Hindu, Indian, Muslim, Pakistani
God's Lighting
Girl/Female
Assamese, Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Oriya, Tamil, Telugu
Lighting; Bright
Boy/Male
Indian, Tamil
Lighting
Boy/Male
Hindu, Indian
Lighting
Girl/Female
Indian
Lighting
Girl/Female
Tamil
Ujvalitha | உஜà¯à®µà®²à¯€à®¤à®¾
Lighting
Ujvalitha | உஜà¯à®µà®²à¯€à®¤à®¾
Girl/Female
Hindu
Lighting
Boy/Male
Tamil
Vishwdeep | விஷà¯à®µà®¤à¯€à®ªÂ
Big lighting
Vishwdeep | விஷà¯à®µà®¤à¯€à®ªÂ
Boy/Male
Hindu, Indian
Lighting
Boy/Male
Gujarati, Hindu, Indian
Lighting
Girl/Female
Indian
Visiting, Returning
Girl/Female
Tamil
Restless, Lighting
Boy/Male
Hindu, Indian
Lighting
Boy/Male
Hindu
Big lighting
Boy/Male
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Lighting
Girl/Female
Muslim
Visiting, Returning
LIMITING CASE
LIMITING CASE
Girl/Female
Indian
Free, Princess
Girl/Female
Tamil
Manideepa | மநிதீபா
A lamp of precious stones
Boy/Male
Australian, German, Greek
Vigilant
Girl/Female
Hindu, Indian, Tamil, Traditional
One who Increases Happiness
Boy/Male
Tamil
Mahaketu | மஹாகேதà¯
Lord Shiva
Boy/Male
Indian, Tamil
King
Boy/Male
Indian, Punjabi, Sanskrit, Sikh
Blessing; Gift from God
Girl/Female
Indian
The earth
Girl/Female
Hindu
From the word of Nishkarsh
Boy/Male
German
Yew Wood; Archer; Yew Wood was Used for Bows
LIMITING CASE
LIMITING CASE
LIMITING CASE
LIMITING CASE
LIMITING CASE
n.
A vomiting of blood.
n.
That which causes vomiting.
a.
Involving a limit; as, a limitive law, one designed to limit existing powers.
n.
A vomiting.
p. pr. & vb. n.
of Limit
a.
Causing vomiting; emetic; vomitive.
a.
Having power to determine; limiting; shaping; directing; conclusive.
n.
A limiting element or quality.
n.
The act or process of one who lists (in any sense of the verb); as, the listing of a door; the listing of a stock at the Stock Exchange.
a.
Limiting; determining; as, a definitive word.
vb. n.
Visiting slums.
a.
Vomiting fire.
n.
A case for visiting cards.
a.
Piteous; lamentable; eliciting compassion.
a.
Used in, or for, or by, lifting.
a.
Limping.
a.
Qualifying; limiting.
v. t.
Limiting, or tending to limit; restrictive.
a.
Visiting.