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Topics referred to by the same term
Phase integral may refer to: Phase integral, in statistical mechanics, a classical analog to the partition function. Phase integral, in astronomy, a concept
Phase_integral
Fraction of incident light reflected by an astronomical body
{\displaystyle A=pq} where q is termed the phase integral and is given in terms of the directional scattered flux I(α) into phase angle α (averaged over all wavelengths
Bond_albedo
Space of all possible states that a system can take
classical analog to the partition function (sum over states) known as the phase integral. Instead of summing the Boltzmann factor over discretely spaced energy
Phase_space
Measure of the luminosity of celestial objects
\alpha } is the phase angle, the angle between the body-Sun and body–observer lines. q ( α ) {\displaystyle q(\alpha )} is the phase integral (the integration
Absolute_magnitude
Formulation of quantum mechanics
second-order phase transition. The Schrödinger equation is a diffusion equation with an imaginary diffusion constant, and the path integral is an analytic
Path_integral_formulation
Vietnamese mathematician
Multidimensional Phase Integrals (Russian: Асимптотика многомерных фазовых интегралов). Her other works on mathematical physics include: On Fourier Integral Operators
Lê_Vũ_Anh
Magnetic resonance imaging sequence
accomplished by refocusing the phase-encoding gradient in each repetition interval in order to keep the phase integral (or gradient moment) constant.
Steady-state free precession imaging
Steady-state_free_precession_imaging
albedo and scattering properties, such as the geometric albedo, the phase integral, and the Bond albedo. The Hapke model has been criticized for having
Hapke_parameters
Exoplanet in the constellation Draco, known for being the "Darkest Exoplanet"
1051/0004-6361/200810988. ISSN 0004-6361. S2CID 9893376. Assuming the phase integral is 3/2, the Bond Albedo is measured as 0.0204. Angerhausen, Daniel;
TrES-2b
American-German physicist, engineer (1927–1999)
NASA IBM Thesis Phase Integral Approximations in Wave Mechanics: I. Reflections in One-Dimensional Wave Mechanics. II. Phase Integral Approximations in
Rolf_Landauer
In nonlinear optics, B-Integral is a measure of the nonlinear optics phase shift of light. It calculates the exponential growth of the least stable spatial
B_Integral
Type of MRI sequence
accomplished by refocusing the phase-encoding gradient in each repetition interval in order to keep the phase integral (or gradient moment) constant.
Gradient_echo
Notation for conserved quantities in physics and chemistry
atomic model added a second quantum number and the concept of quantized phase integrals to justify them. Sommerfeld's model was still essentially two dimensional
Quantum_number
Electronic method of transmitting information with a carrier wave
of the message signal changes, the phase of the carrier changes correspondingly. Phase modulation is an integral part of many digital transmission coding
Phase_modulation
Control loop feedback mechanism
A proportional–integral–derivative (PID) controller, or three-term controller, is a feedback-based control loop mechanism commonly used to manage machines
PID_controller
Type of distribution in mathematical analysis
oscillatory integral is a type of distribution. Oscillatory integrals make rigorous many arguments that, on a naive level, appear to use divergent integrals. It
Oscillatory_integral
2016–2019 group of superhero films
Phase Three of the Marvel Cinematic Universe (MCU) is a group of American superhero films produced by Marvel Studios based on characters that appear in
Marvel Cinematic Universe: Phase Three
Marvel_Cinematic_Universe:_Phase_Three
French physicist (1889–1969)
approximation, also known as the WKB method, classical approach, and phase integral method. In 1928, after the Institut Henri Poincaré was established,
Léon_Brillouin
Electronic control system
A phase-locked loop (PLL) is a control system that generates an output signal whose phase is fixed relative to the phase of an input signal. Keeping the
Phase-locked_loop
Frequency domain representation of random fluctuations in the phase of a waveform
Spreading of the spectrum line caused by phase noise is characterized by the fundamental linewidth and the integral linewidth. The fundamental linewidth,
Phase_noise
Nonlinear phase response to filters
the phase-frequency characteristic is not 0 or an integral multiple of 2π radians. Grossly changed phase relationships, without changing amplitudes, can
Phase_distortion
Physical process of transition between basic states of matter
Topology Change and Path Integrals, Berlin: Springer, ISBN 978-3-540-79356-4, retrieved 14 March 2013 M.R. Khoshbin-e-Khoshnazar, Ice Phase Transition as a sample
Phase_transition
Asymptotic analysis used when integrating rapidly-varying complex exponentials
the formula, the stationary phase approximation is a first-order approximation of the asymptotic behavior of the integral. The lower-order terms can be
Stationary phase approximation
Stationary_phase_approximation
Physical quantity of dimension energy × time
the path integral formulation of quantum mechanics makes use of the concept—where a physical system explores all possible paths, with the phase of the probability
Action_(physics)
ν {\displaystyle p_{\nu }} is the geometric albedo, q = 0.8 is the phase integral, and r {\displaystyle r} is the distance from the Sun in AU. This formula
List of gravitationally rounded objects of the Solar System
List_of_gravitationally_rounded_objects_of_the_Solar_System
Mathematical transform that expresses a function of time as a function of frequency
In mathematics, the Fourier transform (FT) is an integral transform that takes a function as input and outputs another function that describes the extent
Fourier_transform
Method for modulation of data
modulated signal. The integral located inside of the cosine's argument is what gives the CPFSK signal its continuous phase; an integral over any finitely
Continuous_phase_modulation
Extension of Laplace's method for approximating integrals
phase. The saddle-point approximation is used with integrals in the complex plane, whereas Laplace’s method is used with real integrals. The integral
Method_of_steepest_descent
European space telescope for observing gamma rays
In March 2023, INTEGRAL science operations were extended to the end of 2024, which will be followed by a two-year post-operations phase and further monitoring
INTEGRAL
Approach emphasizing human and social dimensions
new geobiological period is the condition for the integral functioning of the planet in all phases of its activities, whether these be biological, ecological
Integral_ecology
Integral used in physics
Stratonovich integral or Fisk–Stratonovich integral (developed simultaneously by Ruslan Stratonovich and Donald Fisk) is a stochastic integral, the most
Stratonovich_integral
Phase of a cycle
mechanics, the geometric phase (also known as the Pancharatnam–Berry phase, Pancharatnam phase, or Berry phase) is a phase difference acquired over the
Geometric_phase
Phenomenon resulting from the superposition of two waves
lower amplitude (destructive interference) if the two waves are in phase or out of phase, respectively. Interference effects can be observed with all types
Wave_interference
Integral expressing the amount of overlap of one function as it is shifted over another
{\displaystyle g} that produces a third function f ∗ g {\displaystyle f*g} , as the integral of the product of the two functions after one is reflected about the y-axis
Convolution
Model of rotating physical systems
can be rewritten to the following expression, which is needed in the phase integral arising in the classical statistical mechanics of rigid rotors, T =
Rigid_rotor
Near-field diffraction
validity of the Fresnel diffraction integral is deduced by the approximations derived below. Specifically, the phase terms of third order and higher must
Fresnel_diffraction
Substance with high latent heat of melting or solidifying
A phase-change material (PCM) is a substance which releases/absorbs sufficient energy at phase transition to provide useful heat or cooling. Generally
Phase-change_material
Topics referred to by the same term
phase approximation in the evaluation of integrals in mathematics This disambiguation page lists articles associated with the title Stationary phase.
Stationary_phase
Formulation of quantum mechanics
means of formal phase-space trajectories, the time evolution problem of the Wigner function can be rigorously solved using the path-integral method and the
Phase-space_formulation
MR 0378683, S2CID 120940116 Ursell, H. D. (1927), "The evaluation of Gibbs phase-integral for imperfect gases", Proc. Cambridge Philos. Soc., 23 (6): 685–697
Ursell_function
Plot of a dynamical system's trajectories in phase space
In mathematics, a phase portrait is a geometric representation of the orbits of a dynamical system in the phase plane. Each set of initial conditions
Phase_portrait
Moldovan football's second-tier league
scored; 8) Least red cards; 9) Least yellow cards. Notes: Ineligible for Phase II Group 1 Source: FMF (in Romanian) Legend: Blue = home team win; Yellow
2025–26_Moldovan_Liga_1
Wigner distribution function in physics as opposed to in signal processing
the integral representation of ⋆ {\displaystyle \star } -products, successive operations by them have been adapted to a phase-space path integral, to
Wigner quasiprobability distribution
Wigner_quasiprobability_distribution
Complex number representing a particular sine wave
diagram below from the previous Phase Difference tutorial. The time derivative or integral of a phasor produces another phasor. For example: Re ( d d t (
Phasor
Fundamental mechanical principles
action, all possible paths add (the integral over xk), weighted by a complex probability amplitude eiS⁄ħ. The phase of the amplitude is given by the action
Action_principles
German physicist (1898–1978)
approximation, also known as the WKB approximation, classical approach, and phase integral method. Wentzel is also known for his contributions to photoemission
Gregor_Wentzel
enclosures that can be welded to become an integral part of the isolated-phase bus system. Isolated-phase bus is usually custom manufactured for a particular
Isolated-phase_bus
Fourier integral operators, and quantization conditions in classical and quantum mechanics. In the theory of Fourier integral operators, phase functions
Maslov_index
Oscillator with frequency controlled by a voltage input
modulation (FM) or phase modulation (PM) by applying a modulating signal to the control input. A VCO is also an integral part of a phase-locked loop. VCOs
Voltage-controlled_oscillator
Mathematical theorem about functions
i(x-y)\cdot \xi }\,f(y)\,dy\,d\xi .} This last equation is called the Fourier integral theorem. Another way to state the theorem is that if R {\displaystyle R}
Fourier_inversion_theorem
Concept in physics
)} can never be physically observable. However, its integral along a closed path, the Berry phase γ n {\displaystyle \gamma _{n}} , is gauge-invariant
Berry connection and curvature
Berry_connection_and_curvature
Theorem in calculus
the surface integral of a vector field over a closed surface, which is called the "flux" through the surface, is equal to the volume integral of the divergence
Divergence_theorem
Frequency of a chirp pulse
the Fourier integral is difficult to evaluate. In such cases, it is possible to resort to an approximation method such as the stationary phase approximation
Chirp_spectrum
Class of integral and differential operator
mathematics, in the field of harmonic analysis, an oscillatory integral operator is an integral operator of the form T λ u ( x ) = ∫ R n e i λ S ( x , y )
Oscillatory_integral_operator
Enthalpy change from diluting a substance in solution
dilution can be defined from two perspectives: the differential heat and the integral heat. The differential heat of dilution is viewed on a micro scale, which
Heat_of_dilution
Molecular dynamics simulations augmented with quantum mechanics
path integral Monte Carlo (PIMC). There are two ways to calculate the dynamics calculations of PIMD. The first one is the non-Hamiltonian phase space
Path integral molecular dynamics
Path_integral_molecular_dynamics
Framework to describe phase transitions
superconductivity, superfluidity, topological phase transition, wetting as well as non-equilibrium phase transitions. A SFT is any model in statistical
Statistical_field_theory
State in southern India
components and automobile output, earning the nickname "Detroit of India". The Integral Coach Factory in Chennai manufactures railway coaches and other rolling
Tamil_Nadu
Type of AC motor
reversing magnetic field. Because of hysteresis the phase of the magnetization lags behind the phase of the applied field. Thus the axis of the magnetic
Synchronous_motor
Physical quantity conserved throughout a motion
the constants of motion are the integrals of motion, or first integrals, defined as any functions of only the phase-space coordinates that are constant
Constant_of_motion
woodwork and ""crackle-coat"" wallpaper, while Glenn Bowman routes out an integral drainboard in the kitchen's soapstone countertop. Upstairs, we see the
List of This Old House episodes (seasons 11–20)
List_of_This_Old_House_episodes_(seasons_11–20)
Internet protocol for HTTP payments
maintains full HTTP compatibility while introducing payment negotiation as an integral part of the request–response cycle. A client makes a standard HTTP request
X402
In chaos theory, the correlation integral is the mean probability that the states at two different times are close: C ( ε ) = lim N → ∞ 1 N 2 ∑ i ≠ j i
Correlation_integral
Topics referred to by the same term
area of a given plane figure, drawing a square with the same area, an integral or integration Squaring the circle Quadrature of the Parabola Quadrature
Quadrature
Equations describing classical electromagnetism
magnetic field corresponds to the negative curl of an electric field. In integral form, it states that the work per unit charge required to move a charge
Maxwell's_equations
Quantum mechanical phenomenon
(2012). Introduction To Quantum Mechanics: Schrodinger Equation And Path Integral (2nd ed.). Singapore: World Scientific Publishing Company. ISBN 978-981-4397-76-6
Quantum_tunnelling
Lake in Burundi
hectares (52 acres). Lake Gitama is protected as an "Integral Zone", where human presence will be phased out. Buffer zones, or belts of land at least 50 metres
Lake_Gitamo
Measure of sustained displacement of an object from its initial position
constant as the object resides at the initial position. It is the first time-integral of the displacement (i.e. absement is the area under a displacement vs
Absement
Methods of calculating definite integrals
family of algorithms for calculating the numerical value of a definite integral. The term numerical quadrature (often abbreviated to quadrature) is more
Numerical_integration
Short "burst" or "envelope" of restricted wave action that travels as a unit
carrier waves, phase velocity, and group velocity – date from the mid-1800s. The idea of a group velocity distinct from a wave's phase velocity was first
Wave_packet
Pseudo-digital circuit
oscillator. The control signal impacts the oscillator's frequency, and phase is the integral of frequency, so a second integration is unavoidably performed by
Delay-locked_loop
Human development theory
of Integral Consciousness, Culture, and Science. 1. Retrieved 12 Aug 2020. Visser, Frank (May 2017). "A More Adequate Spectrum of Colors?". Integral World
Graves's emergent cyclical levels of existence
Graves's_emergent_cyclical_levels_of_existence
Mathematical identities
The following are important identities involving derivatives and integrals in vector calculus. For a function f ( x , y , z ) {\displaystyle f(x,y,z)}
Vector_calculus_identities
Force resulting from the quantisation of a field
turn the double integral into a single integral. The q in front is the Jacobian, and the 2π comes from the angular integration. The integral converges if
Casimir_effect
Relativistic wave equation in quantum mechanics
{\mathcal {L}}} is the Lagrangian. The conserved charges are given by the integral of the zeroth component of the current over all space. In this case the
Klein–Gordon_equation
Rapid transit system in India serving Delhi NCR
December 2004. The network was developed in phases. Phase I was completed by 2006, followed by Phase II in 2011. Phase III was mostly complete in 2021, except
Delhi_Metro
monkeys on Madagascar; Colin Tudge believed that mass extinctions were integral to evolution; Lystrosaurus lasted for ten million years. Narrated by Roger
List_of_Equinox_episodes
function, integrals of loop diagrams, etc. The following Gaussian integrals are useful in calculating path integrals appearing in path integral formulation
Common integrals in quantum field theory
Common_integrals_in_quantum_field_theory
Integral transform and linear operator
mathematics and signal processing, the Hilbert transform is a specific singular integral that takes a function, u(t) of a real variable and produces another function
Hilbert_transform
Example of a phase-space star product in mathematics
Heisenberg algebra and its envelope, the Weyl algebra. Inside a phase-space integral, just one star product of the Moyal type may be dropped, resulting
Moyal_product
Spanish footballer (born 2007)
to the best young player in the world. In the following season, he was integral to Barcelona winning a domestic treble of the La Liga title, the Copa del
Lamine_Yamal
Rapid transit system in Bengaluru, Karnataka, India
(77 mi) Phase 3 was initially proposed in May 2016. Certain significant sections that were proposed for Phase 3 were included in Phase 2 as Phase 2A and
Namma_Metro
Differential equations involving stochastic processes
Stratonovich, leading to what is known as the Stratonovich integral. The Itô integral and Stratonovich integral are related, but different, objects and the choice
Stochastic differential equation
Stochastic_differential_equation
Marine radar capability
This of course was not the ideal situation and eventually it was the integral ARPA that replaced the stand-alone unit. The majority of ARPAs manufactured
Automatic_radar_plotting_aid
Phase shift torque measurement involves the use of a shaft, which is either an integral part of the rotating machine under test - such as a turbine, compressor
Phase shift torque measurement
Phase_shift_torque_measurement
Scientific theory
{\displaystyle M=1} . Path integral formulation comes from quantum mechanics. But for a Langevin SDE we can also induce a corresponding path integral. Considering the
Langevin_dynamics
Integral transform useful in probability theory, physics, and engineering
Laplace transform, named after Pierre-Simon Laplace (/ləˈplɑːs/), is an integral transform that converts a function of a real variable (usually t {\displaystyle
Laplace_transform
Device to determine relative phase shift
Mach–Zehnder interferometer is a device used to determine the relative phase shift variations between two collimated beams derived by splitting light
Mach–Zehnder_interferometer
Integral transform
Hamiltonian mechanics, the linear canonical transformation (LCT) is a family of integral transforms that generalizes many classical transforms. It has 4 parameters
Linear canonical transformation
Linear_canonical_transformation
Human resource and accounting systems company
deprecated archival service (link) "Integral Systems Inc. Awarded Contract Options to Begin Development of the Next Phase of the RAIDRS Program". Space Newsfeed
Integral_Systems
Generalized function whose value is zero everywhere except at zero
value is zero everywhere except at zero, where it is infinite, and whose integral over the entire real line is equal to one. Thus it can be represented heuristically
Dirac_delta_function
Upcoming Marvel Studios film
Secret Wars, were announced in July 2022 as the conclusion of the MCU's Phase Six and "The Multiverse Saga". Jonathan Majors was set to reprise his MCU
Avengers:_Doomsday
Systematic procedure of turning a classical theory into a quantum one
is based upon a classical action, but is different from the functional integral approach. The method does not apply to all possible actions (for instance
Quantization_(physics)
Indian expressway connecting Bengaluru and Chennai
acting as a crucial artery among other expressways. The expressway is an integral core part of the larger and broader project of Bengaluru-Chennai Economic
Bengaluru–Chennai_Expressway
Two-dimensional state of matter
The hexatic phase is a state of matter that is between the solid and the isotropic liquid phases in two dimensional systems of particles. It is characterized
Hexatic_phase
Control system component
discretization of the derivatives and integrals. The reason for expressing the transfer function as an integral equation is that differentiating signals
Lead–lag_compensator
female enslaved people and previously owned single slaves. Ferries were an integral aspect of the development of the city of Camden as they lead to the formation
History_of_Camden,_New_Jersey
Product of geometric length and refractive index
inhomogeneous optical media, the product above is generalized as a path integral as part of the ray tracing procedure. A difference in OPL between two paths
Optical_path_length
Metro line in Thane, India
design phase". Hindustan Times. 3 September 2024. Archived from the original on 3 September 2024. Retrieved 19 May 2025. "Cabinet approves Thane integral Ring
Thane_Metro
Portuguese footballer (born 1985)
with Manchester United in 2003. He gradually established himself as an integral player for the club, and won three consecutive Premier League titles, the
Cristiano_Ronaldo
PHASE INTEGRAL
PHASE INTEGRAL
Girl/Female
Hindu
Art, Phases of Moon
Girl/Female
Tamil
Kala Devi | கலா தேவீ
Art, Phases of Moon
Kala Devi | கலா தேவீ
Girl/Female
Indian
Phases of Quran
Boy/Male
German
Chase; Hunt
Boy/Male
Hindu, Indian
Gods Prayer; Sanskrit Phrase
Girl/Female
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sindhi, Telugu
Phase; Time of Day
Girl/Female
Indian, Telugu
Phrase of Music
Girl/Female
Hindu
Phases of Moon
Girl/Female
Hindu
Art, Phases of Moon
Girl/Female
Tamil
Shashikala | ஷஷிகலா
Phases of Moon
Shashikala | ஷஷிகலா
Surname or Lastname
English
English : metonymic occupational name for a huntsman, or rather a nickname for an exceptionally skilled huntsman, from Middle English chase ‘hunt’ (Old French chasse, from chasser ‘to hunt’, Latin captare).Southern French : topographic name for someone who lived in or by a house, probably the occupier of the most distinguished house in the village, from a southern derivative of Latin casa ‘hut’, ‘cottage’, ‘cabin’.Thomas Chase came to MA from Chesham, Buckinghamshire, England, in the 1640s, and had many prominent descendants. Samuel Chase, born in Somerset Co., MD, in 1741, was one of the first members of the U.S. Supreme Court; Philander Chase, born in Cornish, NH, in 1741 was a prominent Episcopal clergyman, and his nephew Salmon Portland Chase (1808–73), also born in Cornish, was governor of OH, a U.S. senator, and secretary of the U.S. Treasury during the Civil War.
Girl/Female
Tamil
Art, Phases of Moon
Male
English
Middle English surname (of Norman French origin) transferred to forename use, CHASE means "hunter."Â
Girl/Female
Indian, Telugu
A Phase of Life; Childhood
Surname or Lastname
English
English : from Middle English pese ‘pea’, hence a metonymic occupational name for a grower or seller of peas, or a nickname for a small and insignificant person. The word was originally a collective singular (Old English peose, pise, from Latin pisa) from which the modern English vocabulary word pea is derived by folk etymology, the singular having been taken as a plural.Robert and John Pease came from Great Baddow, Essex, England, to Salem, MA, in 1634. In 1644 Robert died, leaving a son (also called Robert) who was apprenticed as a weaver in Salem. By 1646 John Pease was living on Martha’s Vineyard.
Surname or Lastname
German
German : nickname for a swift runner or a timorous person, from Middle High German, Middle Low German hase ‘hare’.Jewish (Ashkenazic) : ornamental name from German Hase ‘hare’.English : from a Middle English nickname, Hase, from Old English hÄs ‘harsh, raucous, or hoarse voice’.Japanese : usually written with characters meaning ‘long valley’; habitational name from a place in Yamato (now Nara prefecture). Listed in the Shinsen shÅjiroku. Some bearers are descended from the Taira clan; they are found mainly in eastern Japan. Also pronounced Nagaya and Nagatani; the original pronunciation was Hatsuse, meaning ‘beginning of the strait’.
Girl/Female
Tamil
Phase, Time of day
Male
French
French form of Latin Stephanus, STÉPHANE means "crown."
Boy/Male
American, Australian, British, Chinese, Christian, English, French
Huntsman; Hunter
Boy/Male
English American
Huntsman.
PHASE INTEGRAL
PHASE INTEGRAL
Boy/Male
Hindu
The one who bestows protection to anyone who comes seeking it. the word Sharan in Sanskrit means protection. and the one who bestows it is Sharanyan
Boy/Male
Hindu
Cowherd
Girl/Female
African, American, Australian, British, English
Blend of Nichole and Michelle
Female
Hawaiian
Hawaiian form of Old German Adala, AKELA means "noble."
Girl/Female
Indian
Placid
Boy/Male
Tamil
Prajjwal | பà¯à®°à®œà¯à®œà¯à®µà®¾à®²
Bright light
Surname or Lastname
English
English : habitational name from any of various minor places, for example in Staffordshire, so named from Old English grēne ‘green’ + lēah ‘woodland clearing’.
Girl/Female
English
White.
Girl/Female
Gujarati, Hindu, Indian, Sanskrit
Right Thing to do
Male
Welsh
Variant spelling of Welsh Owen, OWIN means "born of yew."
PHASE INTEGRAL
PHASE INTEGRAL
PHASE INTEGRAL
PHASE INTEGRAL
PHASE INTEGRAL
n.
Pulse; pease.
a.
Resembling prase.
a.
Without a phase, or visible form.
n.
That which is exhibited to the eye; the appearance which anything manifests, especially any one among different and varying appearances of the same object.
n.
Any appearance or aspect of an object of mental apprehension or view; as, the problem has many phases.
pl.
of Phase
v. t.
To chase.
v. t.
To follow as if to catch; to pursue; to compel to move on; to drive by following; to cause to fly; -- often with away or off; as, to chase the hens away.
n.
A particular appearance or state in a regularly recurring cycle of changes with respect to quantity of illumination or form of enlightened disk; as, the phases of the moon or planets. See Illust. under Moon.
n.
See Phase.
pl.
of Pease
pl.
of Pease
n.
A brief expression, sometimes a single word, but usually two or more words forming an expression by themselves, or being a portion of a sentence; as, an adverbial phrase.
p. pr. & vb. n.
of Chase
imp. & p. p.
of Phrase
p. pr. & vb. n.
of Phrase
n.
The liberty or franchise of having a chase; free chase.
v. i.
To group notes into phrases; as, he phrases well. See Phrase, n., 4.
n.
Any one point or portion in a recurring series of changes, as in the changes of motion of one of the particles constituting a wave or vibration; one portion of a series of such changes, in distinction from a contrasted portion, as the portion on one side of a position of equilibrium, in contrast with that on the opposite side.
v. i.
To give chase; to hunt; as, to chase around after a doctor.