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Mathematical theorem using Laplace transform
In mathematical analysis, the initial value theorem is a theorem used to relate frequency domain expressions to the time domain behavior as time approaches
Initial_value_theorem
Existence and uniqueness of solutions to initial value problems
equations, the Picard–Lindelöf theorem gives a set of sufficient (but not necessary) conditions under which an initial value problem has a unique solution
Picard–Lindelöf_theorem
Type of calculus problem
calculus, an initial value problem (IVP) is an ordinary differential equation together with an initial condition which specifies the value of the unknown
Initial_value_problem
Relation between frequency- and time-domain behavior at large time
In mathematical analysis, the final value theorem (FVT) is one of several similar theorems used to relate frequency domain expressions to the time domain
Final_value_theorem
Theorem in probability theory
theorem (or sometimes Doob's optional sampling theorem, for American probabilist Joseph Doob) says that, under certain conditions, the expected value
Optional_stopping_theorem
Theorem regarding the existence of a solution to a differential equation
guarantees the existence of solutions to certain initial value problems. Peano first published the theorem in 1886 with an incorrect proof. In 1890 he published
Peano_existence_theorem
Existence and uniqueness theorem for certain partial differential equations
Cauchy initial value problems. A special case was proven by Augustin Cauchy (1842), and the full result by Sofya Kovalevskaya (1874). This theorem is about
Cauchy–Kovalevskaya_theorem
Final value theorem (mathematical analysis) Initial value theorem (integral transform) Mellin inversion theorem (complex analysis) Stahl's theorem (matrix
List_of_theorems
Matrix decomposition
{T}}\mathbf {M} \mathbf {x} \end{aligned}}\right\}.} By the extreme value theorem, this continuous function attains a maximum at some u {\displaystyle
Singular_value_decomposition
About simultaneous modular congruences
In mathematics, the Chinese remainder theorem states that if one knows the remainders of the Euclidean division of an integer n by several integers, then
Chinese_remainder_theorem
Mathematical rule for inverting probabilities
Bayes' theorem (alternatively Bayes' law or Bayes' rule), named after Thomas Bayes (/beɪz/), gives a mathematical rule for inverting conditional probabilities
Bayes'_theorem
Theorem in economics
which they value something more once they actually have possession of it. Thus, the Coase theorem would not always work in practice because initial allocations
Coase_theorem
Integral transform useful in probability theory, physics, and engineering
transform: Initial value theorem f ( 0 + ) = lim s → ∞ s F ( s ) . {\displaystyle f(0^{+})=\lim _{s\to \infty }{sF(s)}.} Final value theorem f ( ∞ )
Laplace_transform
Statement on solutions to ordinary differential equations
solution to the initial value problem. Mathematics portal Picard–Lindelöf theorem Cauchy–Kowalevski theorem Coddington & Levinson (1955), Theorem 1.2 of Chapter
Carathéodory's existence theorem
Carathéodory's_existence_theorem
Relation between sides of a right triangle
In mathematics, the Pythagorean theorem or Pythagoras's theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle
Pythagorean_theorem
Index of articles associated with the same name
Cauchy–Kowalevski theorem is the main local existence and uniqueness theorem for analytic partial differential equations associated with Cauchy initial value problems
Uniqueness_theorem
Theorem in topology
Brouwer's fixed-point theorem is a fixed-point theorem in topology, named after L. E. J. (Bertus) Brouwer. It states that for any continuous function f
Brouwer_fixed-point_theorem
Thermodynamic theorem
thermodynamics, albeit under the assumption of low-entropy initial conditions. The H-theorem is a natural consequence of the kinetic equation derived by
H-theorem
Theorem in statistical mathematics
The fluctuation theorem (FT), which originated from statistical mechanics, deals with the relative probability that the entropy of a system which is currently
Fluctuation_theorem
Theorem in mathematics
the multiplicative inverse of the derivative of f. The theorem applies verbatim to complex-valued functions of a complex variable. It generalizes to functions
Inverse_function_theorem
17th-century conjecture proved by Andrew Wiles in 1994
In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that there are no positive integers a
Fermat's_Last_Theorem
Parameter in differential equations and dynamical systems
In mathematics and particularly in dynamical systems, an initial condition is the initial value (often at time t = 0 {\displaystyle t=0} ) of a differential
Initial_condition
Theorem in numerical analysis
for a well-posed linear initial value problem, the method is convergent if and only if it is stable. The importance of the theorem is that while the convergence
Lax_equivalence_theorem
second theorem of DFT states that the energy functional for the Hamiltonian [i.e., the energy content of the Hamiltonian] reaches its minimum value (i.e
Rayleigh theorem for eigenvalues
Rayleigh_theorem_for_eigenvalues
Complete, full information, perfectly competitive markets are Pareto efficient
else nothing). The second theorem states that any Pareto optimum can be supported as a competitive equilibrium for some initial set of endowments. The implication
Fundamental theorems of welfare economics
Fundamental_theorems_of_welfare_economics
Topics referred to by the same term
virtualization Intermediate value theorem, a theorem in mathematical analysis Initial value theorem, a mathematical theorem using Laplace transform Integrated
IVT
differential equations the Chaplygin Theorem states about the existence and uniqueness of the solution to an initial value problem for the first order explicit
Chaplygin's Theorem and Method for Solving ODE
Chaplygin's_Theorem_and_Method_for_Solving_ODE
Theorem in quantum information science
In physics, the no-cloning theorem states that it is impossible to create an independent and identical copy of an arbitrary unknown quantum state, a statement
No-cloning_theorem
Root-finding algorithm
mathematics, an iterative method is a mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class
Fixed-point_iteration
Partial results found before the complete proof
descent. Fermat's Last Theorem states that no three positive integers (a, b, c) can satisfy the equation an + bn = cn for any integer value of n greater than
Proof of Fermat's Last Theorem for specific exponents
Proof_of_Fermat's_Last_Theorem_for_specific_exponents
Type of problem involving ODEs or PDEs
thus the term "initial" value). A boundary value is a data value that corresponds to a minimum or maximum input, internal, or output value specified for
Boundary_value_problem
Statement on the gravitational attraction of spherical bodies
shell theorem gives gravitational simplifications that can be applied to objects inside or outside a spherically symmetric body. This theorem has particular
Shell_theorem
Used in the summation of divergent series
In mathematics, Abelian and Tauberian theorems are theorems giving conditions for two methods of summing divergent series to give the same result, named
Abelian and Tauberian theorems
Abelian_and_Tauberian_theorems
Decision rule used for minimizing the possible loss for a worst-case scenario
values are very important in the theory of repeated games. One of the central theorems in this theory, the folk theorem, relies on the minimax values
Minimax
Limitative results in mathematical logic
Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories
Gödel's incompleteness theorems
Gödel's_incompleteness_theorems
Linear transform from the time domain to the frequency domain
_{C}X_{1}(v)X_{2}^{*}({\tfrac {1}{v^{*}}})v^{-1}\mathrm {d} v} Initial value theorem : If x [ n ] {\displaystyle x[n]} is causal, then x [ 0 ] = lim
Z-transform
Theorem in quantum mechanics
The Ehrenfest theorem, named after Austrian theoretical physicist Paul Ehrenfest, relates the time derivative of the expectation values of the position
Ehrenfest_theorem
Theorem in electrical circuit analysis
organization. Thévenin's theorem and its dual, Norton's theorem, are widely used to make circuit analysis simpler and to study a circuit's initial-condition and
Thévenin's_theorem
2.71828...; base of natural logarithms
Mathematics. Dover. pp. 44–48. A standard calculus exercise using the mean value theorem; see for example Apostol (1967) Calculus, § 6.17.41. Sloane, N. J. A
E_(mathematical_constant)
Combinatorial game theory theorem
In combinatorial game theory, the Sprague–Grundy theorem states that every impartial game under the normal play convention is equivalent to a one-heap
Sprague–Grundy_theorem
Class of ordinary differential equations
continuous function we have u ( c ) = 0 {\textstyle u(c)=0} . By The Mean Value Theorem we have that for all h > 0 {\textstyle h>0} there exists some θ ∈ [
Sturm–Liouville_theory
Construction on any polygon that yields a regular polygon with the same number of sides
yields a regular polygon having the same number of sides as the initial polygon. The theorem was first published by Karel Petr (1868–1950) of Prague in 1905
Petr–Douglas–Neumann_theorem
On converting relations to functions of several real variables
In multivariable calculus, the implicit function theorem is a theorem that provides sufficient conditions under which a planar curve specified by F ( x
Implicit_function_theorem
Property of a partially ordered set
such as the intermediate value theorem, the Bolzano–Weierstrass theorem, the extreme value theorem, and the Heine–Borel theorem. It is usually taken as
Least-upper-bound_property
Mathematical theorem
the existence of solutions of certain initial values problems with continuous right hand side, H. Kneser's theorem deals with the topology of the set of
Kneser's theorem (differential equations)
Kneser's_theorem_(differential_equations)
Theorem in statistics and econometrics
the theorem is sometimes called the regression anatomy theorem. An initial version of the theorem was introduced by Udny Yule in 1907, though it was not
Frisch–Waugh–Lovell_theorem
Strong form of uniform continuity
condition of the Picard–Lindelöf theorem which guarantees the existence and uniqueness of the solution to an initial value problem. A special type of Lipschitz
Lipschitz_continuity
A rigid body with 3 distinct axes of inertia is unstable rotating about the middle axis
The tennis racket theorem, or intermediate axis theorem, is a kinetic phenomenon of classical mechanics which describes the movement of a rigid body with
Tennis_racket_theorem
1995 publication in mathematics
Together with Ribet's theorem, it provides a proof for Fermat's Last Theorem. Both Fermat's Last Theorem and the modularity theorem were believed to be
Wiles's proof of Fermat's Last Theorem
Wiles's_proof_of_Fermat's_Last_Theorem
Theory of speed in physics
The mean speed theorem, also known as the Merton rule of uniform acceleration, was discovered in the 14th century by the Oxford Calculators of Merton
Mean_speed_theorem
Expressing a measure as an integral of another
In mathematics, the Radon–Nikodym theorem, named after Johann Radon and Otto M. Nikodym, is a result in measure theory that expresses the relationship
Radon–Nikodym_theorem
Theorem in linear algebra
controlled by the eigenvalue of A with the largest absolute value (modulus). The Perron–Frobenius theorem describes the properties of the leading eigenvalue and
Perron–Frobenius_theorem
Reformulation of general relativity
The initial value formulation of general relativity is a reformulation of Albert Einstein's theory of general relativity that describes a universe evolving
Initial value formulation (general relativity)
Initial_value_formulation_(general_relativity)
Concept in probability theory and gambling
This is a corollary of a general theorem by Christiaan Huygens, which is also known as gambler's ruin. That theorem shows how to compute the probability
Gambler's_ruin
Concept in quantum mechanics
The adiabatic theorem is a concept in quantum mechanics. Its original form, due to Max Born and Vladimir Fock (1928), was stated as follows: A physical
Adiabatic_theorem
Key results in general relativity on gravitational singularities
when gravitation produces singularities. The Penrose singularity theorem is a theorem in semi-Riemannian geometry and its general relativistic interpretation
Penrose–Hawking singularity theorems
Penrose–Hawking_singularity_theorems
Theorem in classical statistical mechanics
mechanics, the equipartition theorem relates the temperature of a system to its average energies. The equipartition theorem is also known as the law of
Equipartition_theorem
Problem in computer science
the standard form of Gödel's First Incompleteness Theorem is completely unconcerned with the truth value of a statement, but only concerns the issue of whether
Halting_problem
Initial estimate or framework to the solution of a mathematical problem
equation(s), the theorem(s), or the value(s) describing a mathematical or physical problem or solution. It typically provides an initial estimate or framework
Ansatz
Theorem in mathematical logic
compactness theorem states that a set of first-order sentences has a model if and only if every finite subset of it has a model. This theorem is an important
Compactness_theorem
Property of differential equations describing physical phenomena
results on this topic. For example, the Cauchy–Kowalevski theorem for Cauchy initial value problems essentially states that if the terms in a partial
Well-posed_problem
Problem of constructing equal-area shapes
area; this principle can be seen as a form of the modern intermediate value theorem. The more general goal of carrying out all geometric constructions using
Squaring_the_circle
Key result in Hamiltonian mechanics and statistical mechanics
In physics, Liouville's theorem, named after the French mathematician Joseph Liouville, is a key theorem in classical statistical and Hamiltonian mechanics
Liouville's theorem (Hamiltonian)
Liouville's_theorem_(Hamiltonian)
Generalized function whose value is zero everywhere except at zero
Sokhotski–Plemelj theorem, important in quantum mechanics, relates the delta function to the distribution p.v. 1/x, the Cauchy principal value of the function
Dirac_delta_function
In differential calculus, the domain-straightening theorem states that, given a vector field X {\displaystyle X} on a manifold, there exist local coordinates
Straightening theorem for vector fields
Straightening_theorem_for_vector_fields
Branch of ordinary differential equations
defines the state of the stability of solutions. The main theorem of Floquet theory, Floquet's theorem, due to Gaston Floquet (1883), gives a canonical form
Floquet_theory
Measure of algorithmic complexity
theorem, and Turing's halting problem. In particular, no program P computing a lower bound for each text's Kolmogorov complexity can return a value essentially
Kolmogorov_complexity
Bound on eigenvalues
In mathematics, the Gershgorin circle theorem (also called sometimes Gershgorin Disk Theorem) may be used to bound the spectrum of a square matrix. It
Gershgorin_circle_theorem
Subfield of automated reasoning and mathematical logic
Automated theorem proving (also known as ATP or automated deduction) is a subfield of automated reasoning and mathematical logic dealing with proving
Automated_theorem_proving
differential equation is a solution that is singular or one for which the initial value problem (also called the Cauchy problem by some authors) fails to have
Singular_solution
functional theory, the Runge–Gross theorem (RG theorem) shows that for a many-body system evolving from a given initial wavefunction, there exists a one-to-one
Runge–Gross_theorem
Maximized objective function of an optimization problem
conditions for the differentiability of the value function, which in turn allows an application of the envelope theorem, see Benveniste, L. M.; Scheinkman, J
Value_function
Algorithm for finding zeros of functions
zeroes) of a real-valued function. The most basic version starts with a real-valued function f, its derivative f′, and an initial guess x0 for a root
Newton's_method
Equations of degree 5 or higher cannot be solved by radicals
In mathematics, the Abel–Ruffini theorem (also known as Abel's impossibility theorem) states that there is no solution in radicals to general polynomial
Abel–Ruffini_theorem
Square matrices satisfy their characteristic equation
In linear algebra, the Cayley–Hamilton theorem (named after the mathematicians Arthur Cayley and William Rowan Hamilton) states that every square matrix
Cayley–Hamilton_theorem
Theorem in relativistic quantum mechanics
positive-operator valued measures that are compatible with the restrictions imposed by the Hegerfeldt theorem. Specifically, Hegerfeldt's theorem refers to a
Hegerfeldt's_theorem
Concept in statistics
uniformly distributed random phase. Where applicable, the central limit theorem dictates that at any point, the sum of these individual plane-wave contributions
Gaussian_random_field
Statistical theorem
then evaluate that conditional expected value to get an estimator that is in various senses optimal. The theorem is named after C.R. Rao and David Blackwell
Rao–Blackwell_theorem
Hypothetical self-improving program
theorem into proof, thus trivializing proof verification. Appends the n-th axiom as a theorem to the current theorem sequence. Below is the initial axiom
Gödel_machine
Statistical measures of whether a finding is likely to be true
PPV and NPV can be derived using Bayes' theorem. Although sometimes used synonymously, a positive predictive value generally refers to what is established
Positive and negative predictive values
Positive_and_negative_predictive_values
Approach to finding numerical solutions of ordinary differential equations
procedure for solving ordinary differential equations (ODEs) with a given initial value. It is the most basic explicit method for numerical integration of ordinary
Euler_method
Relation between deterministic and nondeterministic space complexity
In computational complexity theory, Savitch's theorem, proved by Walter Savitch in 1970, gives a relationship between deterministic and non-deterministic
Savitch's_theorem
Pictorial representation of the behavior of subatomic particles
interpretation of Wick's theorem is that each field insertion can be thought of as a dangling line, and the expectation value is calculated by linking
Feynman_diagram
Mathematically obvious
shows that the theorem is true for a particular initial value (such as n = 0 or n = 1), and the inductive step which shows that if the theorem is true for
Triviality_(mathematics)
Theorem on extension of bounded linear functionals
Hahn–Banach theorem can be deduced from the above theorem. If X {\displaystyle X} is reflexive then this theorem solves the vector problem. A real-valued function
Hahn–Banach_theorem
Valuation in finance
typically has a positive NPV when the present value of its expected future benefits exceeds its initial cost, indicating that it is likely to be financially
Net_present_value
Power series with rational exponents
all possible initial terms of Puiseux series that are solutions of P ( y ) = 0. {\displaystyle P(y)=0.} The proof of Newton–Puiseux theorem will consist
Puiseux_series
Acquisition of a company using a significant proportion of borrowed money
used. The LBO (or leveraged buyout) valuation model estimates the current value of a business to a "financial buyer", based on the business's forecast financial
Leveraged_buyout
Instrument of indebtedness
and the amount of cash flow provided varies, depending on the economic value that is emphasized upon, thus giving rise to different types of bonds. The
Bond_(finance)
American diversified financial services company
independently after the transition. In October 2013, the firm filed for an initial public offering, which was offered the subsequent month. The company was
J.G._Wentworth
American mathematician (1943–2024)
implicit function theorem, and many authors have attempted to put the logic of the proof into the setting of a general theorem. Such theorems are now known
Richard_S._Hamilton
Equation in statistical mechanics
experiments with biomolecules to numerical simulations. The Crooks fluctuation theorem, proved two years later, leads immediately to the Jarzynski equality. Many
Jarzynski_equality
Condition under which an odd prime is a sum of two squares
In additive number theory, Fermat's theorem on sums of two squares states that an odd prime p can be expressed as: p = x 2 + y 2 , {\displaystyle p=x^{2}+y^{2}
Fermat's theorem on sums of two squares
Fermat's_theorem_on_sums_of_two_squares
Stochastic process modeling random walk with friction
equation with initial condition P ( x , t 0 ) = δ ( x − x 0 ) {\displaystyle P(x,t_{0})=\delta (x-x_{0})} . Conditioned on a particular value of x 0 {\displaystyle
Ornstein–Uhlenbeck_process
Result on periodic sequences
Wilf's theorem refines this result only by bounding the length of the sequence ( a n ) {\displaystyle (a_{n})} to some large-enough finite value such that
Fine_and_Wilf's_theorem
American mathematician
condition for solutions of ordinary initial value problems to be unique and to depend on a class C1 manner on the initial conditions for solutions. He died
Philip_Hartman
Quantity in quantum mechanics
is the initial or preselection state and | ψ f ⟩ {\displaystyle |\psi _{f}\rangle } is the final or postselection state. The nth order weak value, A w n
Weak_value
Theorem on genetic algorithms
Holland's schema theorem, also called the fundamental theorem of genetic algorithms, is an inequality that results from coarse-graining an equation for
Holland's_schema_theorem
On the existence of arithmetic progressions in subsets of the natural numbers
Roth's theorem on arithmetic progressions is a result in additive combinatorics concerning the existence of arithmetic progressions in subsets of the
Roth's theorem on arithmetic progressions
Roth's_theorem_on_arithmetic_progressions
Mathematical proposition equivalent to the axiom of choice
the proofs of several theorems of crucial importance, for instance the Hahn–Banach theorem in functional analysis, the theorem that every vector space
Zorn's_lemma
INITIAL VALUE-THEOREM
INITIAL VALUE-THEOREM
Girl/Female
Arabic, Muslim
Superiority; Attribute; Value
Boy/Male
Arabic
Value
Boy/Male
Indian
Value, Price
Girl/Female
American, British, English
Of High Value
Surname or Lastname
English
English : topographic name for someone who lived in a valley, Middle English vale (Old French val, from Latin vallis). The surname is now also common in Ireland, where it has been Gaelicized as de Bhál.Galician and Aragonese : topographic name from val ‘valley’, or habitational name from any of the places named with this word.
Girl/Female
Muslim/Islamic
Value Worth
Boy/Male
Anglo, British, English, Finnish, Swedish
Valley; Usually with a Stream; From the Glen
Girl/Female
American, British, English, Italian
Of High Value
Girl/Female
Tamil
The initial reality
Boy/Male
Australian, Finnish, Swedish
Value; Worth; Benefit
Boy/Male
Australian, Finnish
Rule
Girl/Female
Indian
The initial reality
Girl/Female
Arabic, Indian, Muslim, Parsi, Sindhi
Value; Price; Worth
Boy/Male
Arabic, Hindu, Indian, Marathi, Muslim
Powerful; Don; Value
Boy/Male
Arabic, Muslim
Destiny; Dignity; Value
Boy/Male
Muslim
Value, Price
Boy/Male
Hindu, Indian
Value
Boy/Male
Hindu, Indian
The Sprout; Initial
Boy/Male
Gujarati, Hindu, Indian
Value; Inside Trueness
Girl/Female
Arabic
Value; Price
INITIAL VALUE-THEOREM
INITIAL VALUE-THEOREM
Girl/Female
Hindu
Sweet Basil, Sweet smelling plant
Girl/Female
Indian
Lucky (Daughter of a king, Queen of iran)
Boy/Male
Muslim/Islamic
King's son
Boy/Male
Gujarati, Hindu, Indian, Kannada, Telugu
Creator; Creative; Birth
Girl/Female
Indian
Goddess Saraswati, India
Boy/Male
African, Basque, Finnish, French, German, Ghana, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Oriya, Sanskrit, Sindhi, Tamil, Telugu
Original Man; Letter; Founder Father of Human Beings; Born Second
Boy/Male
Hindu, Indian
Succsesor
Girl/Female
Muslim
Pure, Honest
Girl/Female
Muslim
Princess
Girl/Female
Indian
Gracious
INITIAL VALUE-THEOREM
INITIAL VALUE-THEOREM
INITIAL VALUE-THEOREM
INITIAL VALUE-THEOREM
INITIAL VALUE-THEOREM
n.
Precise signification; import; as, the value of a word; the value of a legal instrument
v. t.
To estimate the value, or worth, of; to rate at a certain price; to appraise; to reckon with respect to number, power, importance, etc.
adv.
In an initial or incipient manner or degree; at the beginning.
a.
Placed at the beginning; standing at the head, as of a list or series; as, the initial letters of a name.
p. pr. & vb. n.
of Initial
imp. & p. p.
of Value
a.
Of or pertaining to the beginning; marking the commencement; incipient; commencing; as, the initial symptoms of a disease.
a.
Not prized or valued; being without value.
v. t.
To rate highly; to have in high esteem; to hold in respect and estimation; to appreciate; to prize; as, to value one for his works or his virtues.
v. i.
Unsettled; unfixed; undetermined; indefinite; ambiguous; as, a vague idea; a vague proposition.
v. t.
To raise to estimation; to cause to have value, either real or apparent; to enhance in value.
v. t.
To be worth; to be equal to in value.
v. i.
Proceeding from no known authority; unauthenticated; uncertain; flying; as, a vague report.
imp. & p. p.
of Initial
a.
Highly regarded; esteemed; prized; as, a valued contributor; a valued friend.
n.
The relative length or duration of a tone or note, answering to quantity in prosody; thus, a quarter note [/] has the value of two eighth notes [/].
n.
One who values; an appraiser.
v. t.
To put an initial to; to mark with an initial of initials.
n.
Value.