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Mapping involving integration between function spaces
In mathematics, an integral transform is a type of transformation that maps a function from its original function space into another function space via
Integral_transform
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
Probability theory operation
In probability theory, the probability integral transform (also known as universality of the uniform) relates to the result that data values that are modeled
Probability integral transform
Probability_integral_transform
Integral transform useful in probability theory, physics, and engineering
In mathematics, the Laplace transform, named after Pierre-Simon Laplace (/ləˈplɑːs/), is an integral transform that converts a function of a real variable
Laplace_transform
In mathematics, Legendre transform is an integral transform named after the mathematician Adrien-Marie Legendre, which uses Legendre polynomials P n (
Legendre transform (integral transform)
Legendre_transform_(integral_transform)
Mathematical operation
of the scaling factor k constitutes the transformed function. The Hankel transform is an integral transform and was first developed by the mathematician
Hankel_transform
Integral transform and linear operator
In mathematics and signal processing, the Hilbert transform is a specific singular integral that takes a function, u(t) of a real variable and produces
Hilbert_transform
Mathematical operation
for analysing linear dynamical systems. There is an integral formula for the inverse Laplace transform, called the Mellin's inversion formula. It was popularized
Inverse_Laplace_transform
Framework for integrating diverse theories
Integral theory as developed by Ken Wilber is a synthetic metatheory aiming to unify a broad spectrum of Western theories and models and Eastern meditative
Integral_theory
Operation in mathematical calculus
common ways of calculating definite integrals; for instance, Parseval's identity can be used to transform an integral over a rectangular region into an
Integral
Integral transform in mathematics
In mathematics, the Radon transform is the integral transform which takes a function f defined on the plane to a function Rf defined on the (two-dimensional)
Radon_transform
Hankel transform Hartley transform Hermite transform Hilbert transform Hilbert–Schmidt integral operator Jacobi transform Laguerre transform Laplace
List_of_transforms
Integral of sin(x)/x from 0 to infinity
be determined in several ways: the Laplace transform, double integration, differentiating under the integral sign, contour integration, and the Dirichlet
Dirichlet_integral
transforms include: Two-sided Laplace transform Mellin transform, another closely related integral transform Laplace transform: the Fourier transform
List of Fourier-related transforms
List_of_Fourier-related_transforms
"Smoothing" integral transform
Gaussian will have a total integral of 1, with the consequence that constant functions are not changed by the Weierstrass transform. Instead of F ( x ) {\displaystyle
Weierstrass_transform
Mathematical technique used in data compression and analysis
mathematical definition of an orthonormal wavelet and of the integral wavelet transform. A function ψ ∈ L 2 ( R ) {\displaystyle \psi \,\in \,L^{2}(\mathbb
Wavelet_transform
Integral transform used in various branches of mathematics
In mathematics, the Abel transform, named for Niels Henrik Abel, is an integral transform often used in the analysis of spherically symmetric or axially
Abel_transform
Basic method for pseudo-random number sampling
Inverse transform sampling (also known as inversion sampling, the inverse probability integral transform, the inverse transformation method, or the Smirnov
Inverse_transform_sampling
Mathematical operation
Mellin transform is an integral transform that may be regarded as the multiplicative version of the two-sided Laplace transform. This integral transform is
Mellin_transform
Branch of mathematics
differential calculus and integral calculus. Differential calculus studies instantaneous rates of change and slopes of curves; integral calculus studies accumulation
Calculus
Integral transform
of integral geometry, the Funk transform (also known as Minkowski–Funk transform, Funk–Radon transform or spherical Radon transform) is an integral transform
Funk_transform
Mathematical theorem about functions
Fourier transform is also integrable. The most common statement of the Fourier inversion theorem is to state the inverse transform as an integral. For any
Fourier_inversion_theorem
Type of differential equation
higher dimensions, one may find characteristic surfaces. An integral transform may transform the PDE to a simpler one, in particular, a separable PDE. This
Partial_differential_equation
Integration over a non-flat region in 3D space
calculus, a surface integral is a generalization of multiple integrals to integration over surfaces. It can be thought of as the double integral analogue of the
Surface_integral
Integral expressing the amount of overlap of one function as it is shifted over another
latter integral is preferred over the former. On locally compact abelian groups, a version of the convolution theorem holds: the Fourier transform of a
Convolution
Concept in mathematics
limit of integrals of simple functions. The Bochner integral provides the mathematical foundation for extensions of basic integral transforms into more
Bochner_integral
Integral transform
In mathematics, the Riemann–Liouville integral associates with a real function f : R → R {\displaystyle f:\mathbb {R} \rightarrow \mathbb {R} } another
Riemann–Liouville_integral
delta function Distribution Oscillatory integral Laplace transform Discrete Hartley transform List of transforms Dirichlet kernel Fejér kernel Convolution
List of Fourier analysis topics
List_of_Fourier_analysis_topics
Mathematical operation
In mathematics, the two-sided Laplace transform or bilateral Laplace transform is an integral transform equivalent to probability's moment-generating
Two-sided_Laplace_transform
Definite integral of a scalar or vector field along a path
mathematics, a line integral is an integral where the function to be integrated is evaluated along a curve. The terms path integral, curve integral, and curvilinear
Line_integral
Type o integral transform in mathematics
In mathematics, a Hilbert–Schmidt integral operator is a type of integral transform. Specifically, given a domain Ω in Rn, any k : Ω × Ω → C such that
Hilbert–Schmidt integral operator
Hilbert–Schmidt_integral_operator
Generalization of the hypergeometric function
another G-function, and generalizations of integral transforms like the Hankel transform and the Laplace transform and their inverses result when suitable
Meijer_G-function
In mathematics, the Hermite transform is an integral transform named after the mathematician Charles Hermite that uses Hermite polynomials H n ( x ) {\displaystyle
Hermite_transform
Topics referred to by the same term
to themselves Transform theory, theory of integral transforms List of transforms, a list of mathematical transforms Integral transform, a type of mathematical
Transform
In mathematics, Laguerre transform is an integral transform named after the mathematician Edmond Laguerre, which uses generalized Laguerre polynomials
Laguerre_transform
Differentiation under the integral sign formula
variation of the Laplace transform, which can be differentiated to generate the moments of a random variable. Whether Leibniz's integral rule applies is essentially
Leibniz_integral_rule
Basic integral in elementary calculus
analysis, the Riemann integral is a rigorous definition of the integral of a function on an interval. It defines the integral by approximating the region
Riemann_integral
Branch of mathematics
{\displaystyle \int _{P}} is the integral over any interval of length P {\displaystyle P} ). The inverse transform, known as Fourier series, is a representation
Fourier_analysis
Method of evaluating certain integrals along paths in the complex plane
the contour. The inverse Laplace transform is defined by a complex contour integral known as the Bromwich integral: f ( t ) = 1 2 π i ∫ γ − i ∞ γ + i
Contour_integration
Mathematical theorem, used in calculus
In mathematics, integrals of inverse functions can be computed by means of a formula that expresses the antiderivatives of the inverse f − 1 {\displaystyle
Integral_of_inverse_functions
Instantaneous rate of change (mathematics)
way to define the basic concepts of calculus such as the derivative and integral in terms of infinitesimals, thereby giving a precise meaning to the d {\displaystyle
Derivative
Integral transform type in mathematics
In mathematics, an orbital integral is an integral transform that generalizes the spherical mean operator to homogeneous spaces. Instead of integrating
Orbital_integral
Laplace–Stieltjes transform, named for Pierre-Simon Laplace and Thomas Joannes Stieltjes, is an integral transform similar to the Laplace transform. For real-valued
Laplace–Stieltjes_transform
Integral over a 3-D domain
calculus), a volume integral (∭) is an integral over a 3-dimensional domain; that is, it is a special case of multiple integrals. Volume integrals are especially
Volume_integral
Generalization of definite integrals to functions of multiple variables
calculus), a multiple integral is a definite integral of a function of several real variables, for instance, f(x, y) or f(x, y, z). Integrals of a function of
Multiple_integral
Integral transform
In mathematics, the continuous wavelet transform (CWT) is a formal (i.e., non-numerical) tool that provides an overcomplete representation of a signal
Continuous_wavelet_transform
Variant Fourier transforms
In mathematics, the Fourier sine and cosine transforms are integral equations that decompose arbitrary functions into a sum of sine waves representing
Sine_and_cosine_transforms
Mathematical operation
Fourier transform (FRFT) is a family of linear transformations generalizing the Fourier transform. It can be thought of as the Fourier transform to the
Fractional_Fourier_transform
Manuscript are specific to integral transforms. There are several web sites which have tables of integrals and integrals on demand. Wolfram Alpha can
Lists_of_integrals
Integral transform closely related to the Fourier transform
mathematics, the Hartley transform (HT) is an integral transform closely related to the Fourier transform (FT), but which transforms real-valued functions
Hartley_transform
Integral transform generalizing both Laplace and Sumudu transforms
mathematics, the Shehu transform is an integral transform which generalizes both the Laplace transform and the Sumudu integral transform. It was introduced
Shehu_transform
Multivariate derivative (mathematics)
p} gives the direction and the rate of fastest increase. The gradient transforms like a vector under change of basis of the space of variables of f {\displaystyle
Gradient
Concept in mathematics
transformations often take the form of integral transforms such as the Radon transform and its generalizations. Integral geometry as such first emerged as
Integral_geometry
Matrix of partial derivatives of a vector-valued function
\end{bmatrix}}} The Jacobian determinant is equal to r. This can be used to transform integrals between the two coordinate systems: ∬ F ( A ) f ( x , y ) d x d y
Jacobian matrix and determinant
Jacobian_matrix_and_determinant
Valuation in finance
present value can be regarded as Laplace- respectively Z-transformed cash flow with the integral operator including the complex number s which resembles
Net_present_value
Conditions for switching order of integration in calculus
theorem gives the conditions under which a double integral can be computed as an iterated integral, i.e. by integrating in one variable at a time. Intuitively
Fubini's_theorem
Method for partial-fraction expansion
In integral calculus we would want to write a fractional algebraic expression as the sum of its partial fractions in order to take the integral of each
Heaviside_cover-up_method
Mathematical integral transform
In mathematics, the Kontorovich–Lebedev transform is an integral transform which uses a Macdonald function (modified Bessel function of the second kind)
Kontorovich–Lebedev_transform
Mathematical integral
resemblance of the Nørlund–Rice integral to the Mellin transform is not accidental, but is related by means of the binomial transform and the Newton series. In
Nørlund–Rice_integral
Statistical physics approach
Kaniadakis Laplace transform (or κ-Laplace transform) is a κ-deformed integral transform of the ordinary Laplace transform. The κ-Laplace transform converts a
Kaniadakis_statistics
Number, approximately 3.14
hence the Hilbert transform are associated with the asymptotics of the Poisson kernel. The Hilbert transform H is the integral transform given by the Cauchy
Pi
Integral transform
In mathematics, the X-ray transform (also called ray transform or John transform) is an integral transform introduced by Fritz John in 1938 that is one
X-ray_transform
is a list of Laplace transforms for many common functions of a single variable. The Laplace transform is an integral transform that takes a function
List_of_Laplace_transforms
Branch of mathematical analysis
by means of the Fourier or Mellin integral transforms.[citation needed] The Erdélyi–Kober operator is an integral operator introduced by Arthur Erdélyi
Fractional_calculus
3D generalization of the Leibniz integral rule
Reynolds (1842–1912), is a three-dimensional generalization of the Leibniz integral rule. It is used to recast time derivatives of integrated quantities and
Reynolds_transport_theorem
Formulation of quantum mechanics
The path-integral formulation of quantum mechanics generalizes the action principle of classical mechanics. It replaces the classical notion of a single
Path-integral_formulation
Integral transform
canonical transformation (LCT) is a family of integral transforms that generalizes many classical transforms. It has 4 parameters and 1 constraint, so it
Linear canonical transformation
Linear_canonical_transformation
In mathematics, Jacobi transform is an integral transform named after the mathematician Carl Gustav Jacob Jacobi, which uses Jacobi polynomials P n α
Jacobi_transform
Wikidata]; Stampfel, Rosemarie (1954). Erdélyi, Arthur (ed.). Tables of Integral Transforms - Volume I - Based, in part, on notes left by Harry Bateman (PDF)
Bateman_Manuscript_Project
Method for solving linear differential equations using the Laplace transform
the Laplace transform is a powerful integral transform used to switch a function from the time domain to the s-domain. The Laplace transform can be used
Laplace transform applied to differential equations
Laplace_transform_applied_to_differential_equations
Integrals not expressible in closed-form from elementary functions
antiderivative of a given elementary function is an antiderivative (or indefinite integral) that is, itself, not an elementary function. A theorem by Liouville in
Nonelementary_integral
Mathematical transformation
→ 0 + {\displaystyle \varepsilon \to 0^{+}} of the integral diverges, and the Stieltjes transform S μ {\displaystyle S_{\mu }} has a pole at x {\displaystyle
Stieltjes_transformation
Special case of the short-time Fourier transform
The Gabor transform, named after Dennis Gabor, is a special case of the short-time Fourier transform. It is used to determine the sinusoidal frequency
Gabor_transform
Indicator function of positive numbers
ds} . The limit appearing in the integral is also taken in the sense of (tempered) distributions. The Laplace transform of the Heaviside step function is
Heaviside_step_function
Tent function, often used in signal processing
idealized signals, and the triangular function specifically as an integral transform kernel function from which more realistic signals can be derived,
Triangular_function
Relationship between derivatives and integrals
continuous function f , an antiderivative or indefinite integral F can be obtained as the integral of f over an interval with a variable upper bound. Conversely
Fundamental theorem of calculus
Fundamental_theorem_of_calculus
Theorem in mathematics
theorem, in integral form, as an instant reflex but this use requires the continuity of the derivative. If one uses the Henstock–Kurzweil integral one can
Mean_value_theorem
Concept in mathematical analysis
improper integral is an extension of the notion of a definite integral to cases that violate the usual assumptions for that kind of integral. In the context
Improper_integral
Mathematical method in calculus
integral of a product of functions in terms of the integral of the product of their derivative and antiderivative. It is frequently used to transform
Integration_by_parts
Mathematical algorithm
The chirp Z-transform (CZT) is a generalization of the discrete Fourier transform (DFT). While the DFT samples the Z plane at uniformly-spaced points
Chirp_Z-transform
Indefinite integral
antiderivative, inverse derivative, primitive function, primitive integral or indefinite integral of a function f is a differentiable function F whose derivative
Antiderivative
Method of mathematical integration
Fourier transforms, and other topics. The Lebesgue integral describes better how and when it is possible to take limits under the integral sign (via
Lebesgue_integral
Theorem in vector calculus
vector field, the theorem relates the integral of the curl of the vector field over some surface, to the line integral of the vector field around the boundary
Stokes'_theorem
Academic journal
Integral Transforms and Special Functions is a monthly peer-reviewed scientific journal published by Taylor & Francis. It was established by A. P. Prudnikov
Integral Transforms and Special Functions
Integral_Transforms_and_Special_Functions
Mathematical analysis of frequency content of signals
more dimensions. One of the more popular multidimensional transforms is the Fourier transform, which converts a signal from a time/space domain representation
Multidimensional_transform
Operator that involves integration
integral symbol Integral linear operators, which are linear operators induced by bilinear forms involving integrals Integral transforms, which are maps
Integral_operator
Variant of the Laplace integral transform
Laplace–Carson transform, named for Pierre Simon Laplace and John Renshaw Carson, is an integral transform closely related to the standard Laplace transform. It
Laplace–Carson_transform
transforms that are both well known and widely applicable include integral transforms such as the Fourier transform, the fractional Fourier Transform
Transform_theory
Vector operator in vector calculus
F(x) at a point x0 is defined as the limit of the ratio of the surface integral of F out of the closed surface of a volume V enclosing x0 to the volume
Divergence
transform ΦK is a functor between derived categories of coherent sheaves D(X) → D(Y) for schemes X and Y, which is, in a sense, an integral transform
Fourier–Mukai_transform
the integral sign Trigonometric substitution Partial fractions in integration Quadratic integral Proof that 22/7 exceeds π Trapezium rule Integral of the
List_of_calculus_topics
Mathematical notion of infinitesimal difference
integrator in a Stieltjes integral is represented as the differential of a function. Formally, the differential appearing under the integral behaves exactly as
Differential_(mathematics)
Statement relating differentiable symmetries to conserved quantities
mathematician Emmy Noether in 1918. The action of a physical system is the integral over time of a Lagrangian function, from which the system's behavior can
Noether's_theorem
Convergence test for infinite series
→ 2 n f ( 2 n ) {\textstyle f(n)\rightarrow 2^{n}f(2^{n})} recalls the integral variable substitution x → e x {\textstyle x\rightarrow e^{x}} yielding
Cauchy_condensation_test
Integral transform introduced in 1990
The Sumudu transform is an integral transform introduced in 1990 by G K Watagala. It is defined over the set of functions A = { f ( t ) :∋ M , p , q >
Sumudu_transform
Circulation density in a vector field
is Stokes' theorem, which relates the surface integral of the curl of a vector field to the line integral of the vector field around the boundary curve
Curl_(mathematics)
Theorem in complex analysis
{\displaystyle f(x)} as defined by the inversion integral exists and is continuous; moreover the Mellin transform of f {\displaystyle f} is φ {\displaystyle
Mellin_inversion_theorem
Formula in calculus
Integration by substitution – Technique in integral evaluation Leibniz integral rule – Differentiation under the integral sign formula Product rule – Formula
Chain_rule
Any sheaf whose value is based on an eigenfunction
object that is a tensor-multiple of itself when formed under the integral transform of a Hecke correspondence. Hecke eigensheaves are part of the geometric
Hecke_eigensheaf
Notation of differential calculus
second integral, f ( − 3 ) ( x ) {\displaystyle f^{(-3)}(x)} for the third integral, and f ( − n ) ( x ) {\displaystyle f^{(-n)}(x)} for the nth integral. Dxy
Notation_for_differentiation
INTEGRAL TRANSFORM
INTEGRAL TRANSFORM
Girl/Female
Greek
Most beautiful. Calista was a Mythological Arcadian who transformed into a she-bear, then into...
Boy/Male
Indian
Internal Cleanliness
Surname or Lastname
Irish
Irish : reduced Anglicized form of either of two Gaelic names, Ó DuibhÃn ‘descendant of DuibhÃn’, a byname meaning ‘little black one’, or Ó DaimhÃn ‘descendant of DaimhÃn’, a byname meaning ‘fawn’, ‘little stag’. These are attenuated versions of Ó Dubháin and Ó Damháin, and are the phonetic origin of Anglicizations with an internal v (as opposed to w, as in Dewan, or monosyllabic forms with an o or u) (see Doane).English and French : nickname, of literal or ironic application, from Middle English, Old French devin, divin ‘excellent’, ‘perfect’ (Latin divinus ‘divine’).
Girl/Female
American, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sindhi, Tamil, Telugu
Plucked Flower; Voice of Heart; Woman; Intellect; Behold of Any Beautiful Scene; Internal Beauty
Girl/Female
Israeli
The laurel tree. The mythological virtuous Daphne was transformed into a laurel tree to protect...
Girl/Female
Greek
Most beautiful. In Mythology the Arcadian nymph Calista transformed into a she-bear; then into...
Girl/Female
Greek American
Bee. Famous bearer: Melissa, Mythological princess of Crete transformed to a bee after learning...
Girl/Female
Greek
Bee. Famous bearer: Melissa, Mythological princess of Crete transformed to a bee after learning...
Girl/Female
Latin
or Selena. One of seven mythological daughters of Atlas transformed by Zeus into stars of the...
Girl/Female
Greek
Bee. Famous bearer: Melissa, Mythological princess of Crete transformed to a bee after learning...
Girl/Female
Latin
or Selena. One of seven mythological daughters of Atlas transformed by Zeus into stars of the...
Girl/Female
Latin
or Selena. One of seven mythological daughters of Atlas transformed by Zeus into stars of the...
Girl/Female
Arabic, Bengali, Gujarati, Hindu, Indian, Kannada, Marathi, Muslim, Punjabi, Sikh, Sindhi, Telugu
Heart; Inner Beauty; Fame; Internal Nature; Wisdom
Girl/Female
Greek American
Bee. Famous bearer: Melissa, Mythological princess of Crete transformed to a bee after learning...
Girl/Female
Greek
Bee. Famous bearer: Melissa, Mythological princess of Crete transformed to a bee after learning...
Surname or Lastname
English and French
English and French : regional name from Old French Poitevin, denoting someone from Poitou in western France. The form Potvin has long been established in England and was brought to the U.S. from there. However, French bearers of the surname Poitevin also came to the New World, where their surname underwent a similar transformation on arrival in New England.
Surname or Lastname
English and French
English and French : nickname for a handsome man (perhaps also ironically for an ugly one), from Old French beu, bel ‘fair’, ‘lovely’ (Late Latin bellus).Hungarian (Bél) : from the old secular Hungarian name Bél, or alternatively from bél ‘internal part’, probably an occupational name for a servant who worked in the household.Czech (BÄ›l) from Czech bÃlý ‘white’.
Girl/Female
Greek
Bee. Famous bearer: Melissa, Mythological princess of Crete transformed to a bee after learning...
Girl/Female
Greek
The laurel tree. The mythological virtuous Daphne was transformed into a laurel tree to protect...
Surname or Lastname
English
English : habitational name from Lichfield in Staffordshire. The first element preserves a British name recorded as Letocetum during the Romano-British period. This means ‘gray wood’, from words which are the ancestors of Welsh llŵyd ‘gray’ and coed ‘wood’. By the Old English period this had been reduced to Licced, and the element feld ‘pasture’, ‘open country’ was added to describe a patch of cleared land within the ancient wood.English : habitational name from Litchfield in Hampshire, recorded in Domesday Book as Liveselle. This is probably from an Old English hlīf ‘shelter’ + Old English scylf ‘shelf’, ‘ledge’. The subsequent transformation of the place name may be the result of folk etymological association with Old English hlið, hlid ‘slope’ + feld ‘open country’.
INTEGRAL TRANSFORM
INTEGRAL TRANSFORM
Male
Turkish
Turkish unisex form of Persian Darya, DERYA means "ocean."
Boy/Male
Indian, Kannada
Equal to Lord Indra
Boy/Male
Tamil
Mirror
Girl/Female
Tamil
Surname or Lastname
English (Kent)
English (Kent) : of uncertain origin. Reaney suggests that it may be a metonymic occupational name for a fish seller or a baker, from Middle English fagge, Old English facg, which denoted a kind of flatfish, and perhaps also a flat loaf. Another Middle English word fagge apparently denoted a fault in the weave of a piece of cloth.
Girl/Female
Tamil
Bitter
Female
Scottish
Possibly a modern variant spelling of Scottish Gaelic Aithbhreac, OIGHRIG means "new speckled one."
Girl/Female
Hindu, Indian
Greedy
Girl/Female
English
which is a.
Girl/Female
Tamil
Lucky
INTEGRAL TRANSFORM
INTEGRAL TRANSFORM
INTEGRAL TRANSFORM
INTEGRAL TRANSFORM
INTEGRAL TRANSFORM
a.
Derived from, or dependent on, the thing itself; inherent; as, the internal evidence of the divine origin of the Scriptures.
a.
Inward; interior; being within any limit or surface; inclosed; -- opposed to external; as, the internal parts of a body, or of the earth.
a.
Making part of a whole; necessary to constitute an entire thing; integral.
n.
A brief space of time between the recurrence of similar conditions or states; as, the interval between paroxysms of pain; intervals of sanity or delirium.
n.
A space between things; a void space intervening between any two objects; as, an interval between two houses or hills.
a.
Pertaining to, or proceeding by, integration; as, the integral calculus.
n.
An interval.
a.
Pertaining to its own affairs or interests; especially, (said of a country) domestic, as opposed to foreign; as, internal trade; internal troubles or war.
adv.
In an integral manner; wholly; completely; also, by integration.
a.
Lacking nothing of completeness; complete; perfect; uninjured; whole; entire.
a.
Of, pertaining to, or being, a whole number or undivided quantity; not fractional.
v. t.
To subject to the operation of integration; to find the integral of.
a.
Essential to completeness; constituent, as a part; pertaining to, or serving to form, an integer; integrant.
n.
A whole; an entire thing; a whole number; an individual.
a.
Internal.
n.
An expression which, being differentiated, will produce a given differential. See differential Differential, and Integration. Cf. Fluent.
n.
Interval; intermission.
p. pr. & vb. n.
of Integrate
imp. & p. p.
of Integrate
n.
Space of time between any two points or events; as, the interval between the death of Charles I. of England, and the accession of Charles II.