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Mathematical function
In mathematics, Landau's function g(n), named after Edmund Landau, is defined for every natural number n to be the largest order of an element of the
Landau's_function
Describes approximate behavior of a function
size of a function on a domain. Big O is a member of a family of notations invented by the German mathematicians Paul Bachmann and Edmund Landau and expanded
Big_O_notation
German mathematician (1877–1938)
ISBN 0-8218-2004-4. Landau's function Landau prime ideal theorem Landau's problems Landau's symbol (Big O notation) Landau–Kolmogorov inequality Landau–Ramanujan
Edmund_Landau
Luxury four-wheeled open carriage
The French-style canoe-shaped landaus may be called canoe, gondola or Sefton landaus. English-style angular landaus may be called angular, square, or
Landau_(carriage)
Conjecture on zeros of the zeta function
Unsolved problem in mathematics Do all non-trivial zeros of the Riemann zeta function have a real part equal to one half? More unsolved problems in mathematics
Riemann_hypothesis
Quantization of cyclotron orbits
Under strong magnetic fields, Landau quantization leads to oscillations in electronic properties of materials as a function of the applied magnetic field
Landau_levels
Thermodynamic potential used in statistical mechanics
processes in open systems. The grand potential is the characteristic state function for the grand canonical ensemble. The grand potential is defined by Φ G
Grand_potential
Theory of continuous phase transitions
temperature T c {\displaystyle T_{c}} . In Landau theory, one considers a free energy functional that is an analytic function of the order parameter. In many systems
Landau_theory
Mathematical description of quantum state
In quantum mechanics, a wave function (or wavefunction) is a mathematical description of the quantum state of an isolated quantum system. The most common
Wave_function
Mathematical theorem
holomorphic function in the unit disk with the property |f′(0)| = 1, then let Lf be the radius of the largest disk contained in the image of f. Landau's theorem
Bloch's theorem (complex analysis)
Bloch's_theorem_(complex_analysis)
Ewens's sampling formula Ferrers graph Glaisher's theorem Landau's function Partition function (number theory) Pentagonal number theorem Plane partition
List_of_partition_topics
Effect in physics
In physics, Landau damping is a mechanism by which oscillations in a charged medium (typically a plasma) are damped by non-collisional interactions with
Landau_damping
Number of integers coprime to and less than n
( x ) {\displaystyle \log _{e}(x)} . In number theory, Euler's totient function counts the positive integers up to a given integer n {\displaystyle n}
Euler's_totient_function
Coupling constant divergence at high energies
nonperturbative existence of the Landau pole becomes questionable. The actual behavior of the charge g(μ) as a function of the momentum scale μ is determined
Landau_pole
Probability distribution
case of stable distribution. The probability density function, as written originally by Landau, is defined by the complex integral: p ( x ) = 1 2 π i
Landau_distribution
Superconductivity theory
In physics, Ginzburg–Landau theory, often called Landau–Ginzburg theory, named after Vitaly Ginzburg and Lev Landau, is a mathematical physical theory
Ginzburg–Landau_theory
Simpler variant of the Riemann zeta function
lower-case "xi"-function, ξ {\displaystyle \xi } was renamed with a Ξ {\displaystyle \Xi } (Greek uppercase letter "xi") by Edmund Landau. Landau's ξ {\displaystyle
Riemann_xi_function
Function in thermodynamics and statistical physics
partition function describes the statistical properties of a system in thermodynamic equilibrium.[citation needed] Partition functions are functions of the
Partition function (statistical mechanics)
Partition_function_(statistical_mechanics)
Formula for the probability that a system will change between two energy states
as the Landau–Zener approximation. The simplifications are as follows: The perturbation parameter in the Hamiltonian is a known, linear function of time
Landau–Zener_formula
American manufacturing company
German-born chemist Alfred Landau, who had been making batteries in Europe. The Ramsay collective invested in Landau's functioning low-profile Columbia Dry
Spectrum_Brands
Potential counterexample to the generalized Riemann hypothesis
analytic number theory, a Landau–Siegel zero or simply Siegel zero, also known as an exceptional zero, named after Edmund Landau and Carl Ludwig Siegel,
Siegel_zero
function 1, −24, 252, −1472, 4830, −6048, −16744, 84480, −113643, ... Values of the Ramanujan tau function, τ(n) at n = 1, 2, 3, ... A000594 Landau's
List_of_integer_sequences
function Liouville function Partition function (number theory) Integer partition Bell numbers Landau's function Pentagonal number theorem Bell series
List_of_number_theory_topics
Frobenius group Galois group of a polynomial Jucys–Murphy element Landau's function Oligomorphic group O'Nan–Scott theorem Parker vector Permutation group
List_of_permutation_topics
Multiplicative function in number theory
The Möbius function μ ( n ) {\displaystyle \mu (n)} is a multiplicative function in number theory introduced by the German mathematician August Ferdinand
Möbius_function
Type of group in abstract algebra
(equivalently, the largest possible order of an element in Sn) is given by Landau's function. For n ≠ 2, 6, Sn is a complete group: its center and outer automorphism
Symmetric_group
Process by which a quantum system takes on a definitive state
interpretations of quantum mechanics, wave function collapse, also called reduction of the state vector, occurs when a wave function—initially in a superposition of
Wave_function_collapse
Monte Carlo method for density of states
(or energy) function. For instance, it has been applied to the solution of numerical integrals and the folding of proteins. The Wang–Landau sampling is
Wang_and_Landau_algorithm
Equation in fluid dynamics
The Ginzburg–Landau equation, named after Vitaly Ginzburg and Lev Landau, describes the nonlinear evolution of small disturbances near a finite wavelength
Ginzburg–Landau_equation
Special functions of several complex variables
mathematics, theta functions are special functions of several complex variables. Fundamentally, they are a family of continuous functions which encode the
Theta_function
Topics referred to by the same term
also called Landau notation or Bachmann-Landau notation, a mathematical notation describing the limiting behaviour of a function Landau quantization
Landau_(disambiguation)
Four basic unsolved problems about prime numbers
At the 1912 International Congress of Mathematicians, Edmund Landau listed four basic problems about prime numbers. These problems were characterised in
Landau's_problems
n ln n ) {\displaystyle g(n)=e^{\Theta ({\sqrt {n\ln n}})}} be Landau's function. For a one-letter alphabet, transformations between different types
State_complexity
Electromagnetic effect in physics
the gaussian function in x {\displaystyle x} , which are the wavefunctions of a harmonic oscillator. From the expression for the Landau levels one notices
Quantum_Hall_effect
Meromorphic function on the complex plane
An L-function is a meromorphic function on the complex plane, and one out of several categories of mathematical objects studied in analytic number theory
L-function
Branch of mathematics
of the function near that point. By finding the derivative of a function at every point in its domain, it is possible to produce a new function, called
Calculus
Function in analytic number theory
function is analytic and finite there. The problem of proving this without defining the zeta function first was signaled and left open by E. Landau in
Dirichlet_eta_function
Function whose domain is the positive integers
prime-counting functions. This article provides links to functions of both classes. An example of an arithmetic function is the divisor function whose value
Arithmetic_function
Arithmetic function
theory, the totient summatory function Φ ( n ) {\displaystyle \Phi (n)} is a summatory function of Euler's totient function defined by Φ ( n ) := ∑ k =
Totient_summatory_function
Function on an integer n which is log(p) if n equals p^k and zero otherwise
Mangoldt function is an arithmetic function named after German mathematician Hans von Mangoldt. It is an example of an important arithmetic function that
Von_Mangoldt_function
Description of the dynamics of magnetization in a solid
dissipation function. It is shown that viscous damping of the magnetization fields leads to an equation of motion which reduces to the Landau-Lifshitz equation
Landau–Lifshitz–Gilbert equation
Landau–Lifshitz–Gilbert_equation
mathematics, the notions of an absolutely monotonic function and a completely monotonic function are two very closely related concepts. Both imply very
Absolutely and completely monotonic functions and sequences
Absolutely_and_completely_monotonic_functions_and_sequences
In solid-state physics, the Landau–Lifshitz equation (LLE), named for Lev Landau and Evgeny Lifshitz, is a partial differential equation describing time
Landau–Lifshitz_model
The Landau kinetic equation is a transport equation of weakly coupled charged particles performing Coulomb collisions in a plasma. The equation was derived
Landau_kinetic_equation
Summatory function of the Möbius function
In number theory, the Mertens function is defined for all positive integers n as M ( n ) = ∑ k = 1 n μ ( k ) , {\displaystyle M(n)=\sum _{k=1}^{n}\mu (k)
Mertens_function
Mathematical function
Slepian functions are a class of spatio-spectrally concentrated functions that form an orthogonal basis for bandlimited or spacelimited spaces. That is
Slepian_function
Collective excitation in a Fermi liquid
time of the quasiparticles' momentum distribution function. As the shape of Fermi distribution function changes slightly (or largely), zero sound propagates
Zero_sound
Phenomenon in physics
practice that are subject to Landau–Peierls instability. Consider a one-dimensionally ordered crystal in 3D space. The density function is then given by ρ = ρ
Landau–Peierls_instability
Mathematical function
algebraic function. Basic examples of algebraic functions are polynomial functions, rational functions, the nth root function, and functions obtained from
Algebraic_function
function, as seen in the image, where the following functions are plotted. Some general properties of the Landau kernel is that it is nonnegative and continuous
Landau_kernel
Statistical description for the behavior of fermions
Parastatistics Logistic function Sigmoid function The F–D distribution is a type of mathematical function called a logistic function or sigmoid function. Note that
Fermi–Dirac_statistics
Mathematical family of interpolation inequalities
Arbitrary Function on an Infinite Interval". Amer. Math. Soc. Transl. 1–2: 233–243. Schoenberg, I.J. (1973). "The Elementary Case of Landau's Problem of
Landau–Kolmogorov_inequality
Museum in Lisbon, Portugal
landaus, sedans, carriages, baby carriages, litters, chairs, phaetons, milords, victorias, child carriages, charabancs, hunting carriages, landaus, and
National Coach Museum (Portugal)
National_Coach_Museum_(Portugal)
Equation relating to oscillating systems
Stuart–Landau equation describes the behavior of a nonlinear oscillating system near the Hopf bifurcation, named after John Trevor Stuart and Lev Landau. In
Stuart–Landau_equation
Function that encodes the dependence of a coupling parameter on the energy scale
theoretical physics, specifically quantum field theory, a beta function or Gell-Mann–Low function, β(g), encodes the dependence of a coupling parameter, g,
Beta_function_(physics)
Theoretical model in physics
Fermi liquid theory (also known as Landau's Fermi-liquid theory) is a theoretical model of interacting fermions that describes the normal state of the
Fermi_liquid_theory
Theorem bounding the growth rate of analytic functions
the idea of a function of exponential type. Classification of growth rates based on type help provide a finer tool than big O or Landau notation, since
Nachbin's_theorem
Formulation of classical mechanics using momenta
a characteristic function. Printed by P.D. Hardy. OCLC 68159539.{{cite book}}: CS1 maint: multiple names: authors list (link) Landau & Lifshitz 1976,
Hamiltonian_mechanics
Israeli sculptor, video and installation artist (born 1969)
function as hills. Landau represented Israel at the Venice Biennale in 1997 and again in 2011. She exhibited at Documenta X in 1997. In 1999 Landau exhibited
Sigalit_Landau
On the distribution of prime numbers
different problems: the original Riemann hypothesis for the Riemann zeta function the solvability of two-variable, linear, diophantine equations in prime
Hilbert's_eighth_problem
Integral transform useful in probability theory, physics, and engineering
transform that converts a function of a real variable (usually t {\displaystyle t} , in the time domain) to a function of a complex variable s {\displaystyle
Laplace_transform
Defunct German university
University of Koblenz and Landau (German: Universität Koblenz-Landau) was a German public university located in Koblenz and Landau, Rhineland-Palatinate,
University of Koblenz and Landau
University_of_Koblenz_and_Landau
American mathematician
Henry Jacob Landau was an American mathematician known for his contributions to information theory, including the theory of bandlimited functions and on moment
Henry_Landau
Formulation of classical mechanics
system of particles at coordinates q {\displaystyle \mathbf {q} } . The function H {\displaystyle H} is the system's Hamiltonian giving the system's energy
Hamilton–Jacobi_equation
Sufficiency theorem for reconstructing signals from samples
Academic/Plenum Publishers. Landau, H. J. (1967). "Necessary density conditions for sampling and interpolation of certain entire functions". Acta Mathematica.
Nyquist–Shannon sampling theorem
Nyquist–Shannon_sampling_theorem
In physics, solution to Schrödinger equation
In mathematics, a Coulomb wave function is a solution of the Coulomb wave equation, named after Charles-Augustin de Coulomb. They are used to describe
Coulomb_wave_function
Parameter describing the strength of a force
phenomenon was first noted by Lev Landau, and is called the Landau pole. However, one cannot expect the perturbative beta function to give accurate results at
Coupling_constant
Formula in calculus
that expresses the derivative of the composition of two differentiable functions z and y in terms of the derivatives of z and y. More precisely, if h =
Chain_rule
Theorem about the range of an analytic function
theorems about the range of an analytic function. They are named after Émile Picard. Little Picard Theorem: If a function f : C → C {\textstyle f:\mathbb {C}
Picard_theorem
Function in quantum field theory showing probability amplitudes of moving particles
In quantum mechanics and quantum field theory, the propagator is a function that specifies the probability amplitude for a particle to travel from one
Propagator
Concept in computer science
logically reversible if the transition function that maps old computational states to new ones is a one-to-one function; i.e. the output logical states uniquely
Reversible_computing
Topics referred to by the same term
algorithm, a polynomial time lattice reduction algorithm Lowest Landau level, wave functions in quantum mechanics Lovász local lemma, a lemma in probability
LLL
Average uncertainty in variable's states
the states of individual molecules; but, as Landauer (from 1961) and co-workers have shown, to function the demon himself must increase thermodynamic
Entropy_(information_theory)
Schweiger Action thriller The Adventures of Pinocchio Steve Barron Martin Landau, Udo Kier, Rob Schneider, Geneviève Bujold Family American-Czech-German-British-French
List of German films of the 1990s
List_of_German_films_of_the_1990s
Possible outcome of renormalization in physics
existence of the “Landau pole" in Eq.(2) has no physical sense. The actual behavior of the charge g ( μ ) {\displaystyle g(\mu )} as a function of the momentum
Quantum_triviality
Country in Eastern Europe and North Asia
(2015). Russia's constitutional structure: Federal in form, unitary in function: In depth analysis. Publications Office. doi:10.2861/664907. ISBN 978-92-823-8022-2
Russia
Magnetic property of ordinary materials
oscillates as a function of the field strength, a phenomenon known as the De Haas–Van Alphen effect, also first described theoretically by Landau. Antiferromagnetism
Diamagnetism
Tabular arrangement of the chemical elements
properties and atomic structures of the chemical elements are a periodic function of their atomic number. Elements are placed in the periodic table according
Periodic_table
Provides an asymptotic formula for counting the number of prime ideals of a number field
theorem is dominated by the ideals of norm a prime number. As Edmund Landau proved in Landau 1903, for norm at most X the same asymptotic formula X log X
Landau_prime_ideal_theorem
Gradient flow of the Yang–Mills–Higgs action functional
\varphi )\colon I\rightarrow \mathbb {R} } is a monotonically decreasing function. Since the Yang–Mills–Higgs action functional is always positive, a Yang–Mills–Higgs
Yang–Mills–Higgs_flow
Grade I listed stables and carriage house attached to Buckingham Palace
Coach Several landau carriages including: the 1902 State Landau, seven other state landaus, five semi-state landaus, and five Ascot landaus Barouches and
Royal_Mews
System where changes of output are not proportional to changes of input
unknown functions in the case of differential equations) appear as variables of a polynomial of degree higher than one or in the argument of a function which
Nonlinear_system
Physics of many interacting particles
probability density function is proportional to some function of the ensemble parameters and random variables. Thermodynamic state functions are described by
Statistical_mechanics
Herbert Knaup, Eisi Gulp [de] Biography, Sport a.k.a. Landauer – Der Präsident a.k.a. Kurt Landauer The Limits of Patience [de] Christian Wagner Martina
List of German films of the 2010s
List_of_German_films_of_the_2010s
Special type of functions in mathematics
In mathematics, prolate spheroidal wave functions (PSWFs) are eigenfunctions of the Laplacian in prolate spheroidal coordinates, adapted to boundary conditions
Prolate spheroidal wave function
Prolate_spheroidal_wave_function
Motion of charged particles
properties of materials as a function of the applied magnetic field known as the De Haas–Van Alphen and Shubnikov–de Haas effects. Landau quantization is a key
Cyclotron_motion
Number, approximately 3.14
Baltzer and popularized by Edmund Landau, is the following: π is twice the smallest positive number at which the cosine function equals 0. π is also the smallest
Pi
Geometric analogue of the Dirac equation
theoretical physics, the Dirac–Kähler equation, also known as the Ivanenko–Landau–Kähler equation, is the geometric analogue of the Dirac equation that can
Dirac–Kähler_equation
Physics of heat, work, and temperature
of heat added or removed and work performed on or by the system. As a function of state, the internal energy does not depend on the manner, or on the
Thermodynamics
German economist (born 1949)
David Folkerts-Landau (born May 21, 1949) is a German born economist. He became member of the Deutsche Bank Group Executive Committee in 2012 and was named
David_Folkerts-Landau
normalized pair correlation function between pairs of zeros of the Riemann zeta function is the same as the pair correlation function of random Hermitian matrices
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Japanese mathematician
zeta function on the line Re s = 1 (as the 1908 proof of Edmund Landau), also appealed to some bound on the order of growth of the zeta function on this
Shikao_Ikehara
Indian mathematician (1887–1920)
such as the Ramanujan prime, the Ramanujan theta function, partition formulae and mock theta functions, have opened entire new areas of work and inspired
Srinivasa_Ramanujan
the University of Bristol; Roger Mathias of Plessey Radar and the Multi-function Electronically Scanned Adaptive Radar (MESAR), began in 1982; Henry Thompson
List_of_Equinox_episodes
Description of the time-evolution of plasma
differential equation describing the time evolution of the distribution function of a collisionless plasma consisting of charged particles with long-range
Vlasov_equation
Relationship between the concepts of thermodynamic entropy and information entropy
probability density function is proportional to some function of the ensemble parameters and random variables. Thermodynamic state functions are described by
Entropy in thermodynamics and information theory
Entropy_in_thermodynamics_and_information_theory
Special functions in mathematics
are poles), but which are not generally solvable in terms of elementary functions. They were discovered by Émile Picard (1889), Paul Painlevé (1900, 1902)
Painlevé_transcendents
Russian physicist (1919–2021)
SSSR. 95: 497–500. Landau, L.D.; Abrikosov, A.A.; Khalatnikov, I.M. (1954). "An asymptotic expression for the photon Green function in quantum electrodynamics"
Isaak_Khalatnikov
In fluid dynamics, Landau–Squire jet or Submerged Landau jet describes a round submerged jet issued from a point source of momentum into an infinite fluid
Landau–Squire_jet
Computer program for working with tabular data
pre-programmed function in a formula. Spreadsheet programs also provide conditional expressions, functions to convert between text and numbers, and functions that
Spreadsheet
LANDAUS FUNCTION
LANDAUS FUNCTION
Male
Arthurian
, the Red Knight of the Red Lands.
Girl/Female
Indian, Sanskrit, Tamil
Mother of Lands
Boy/Male
Latin Greek Shakespearean
A Trojan soldier.
Girl/Female
Arabic, Basque, Greek, Muslim, Spanish
Reference to the Virgin Mary
Girl/Female
Tamil
Mirthika | மீரà¯à®¤à¯€à®•à®¾
Mother of lands
Mirthika | மீரà¯à®¤à¯€à®•à®¾
Boy/Male
Christian & English(British/American/Australian)
From the Flat Lands
Boy/Male
Australian, Finnish
Man; Warrior
Boy/Male
Irish
Steward of church lands.
Girl/Female
Hindu, Indian
Wife of Pandavs
Boy/Male
Australian, Greek, Latin
King and Father of the Danaides in Ancient Greek Mythology
Boy/Male
Australian, British, English, French
Form of Landry; Rough Land; From the Grassy Plain
Surname or Lastname
English
English : variant of Andrews.William Andrus came to Boston in 1635 and moved to New Haven in 1639, where he died in 1676.
Girl/Female
Celtic American Scottish
From the plain lands.
Surname or Lastname
English
English : variant of Land.
Boy/Male
French
From the grassy plain.
Girl/Female
Bengali, Finnish, Indian, Swedish, Telugu
Wends; Vandals
Boy/Male
American, British, English
From the Grassy Plain
Girl/Female
Hindu, Indian
Awesome Queen that Rules All Lands
Boy/Male
French
From the grassy plain.
Surname or Lastname
English
English : unexplained.
LANDAUS FUNCTION
LANDAUS FUNCTION
Surname or Lastname
English
English : probably a variant spelling of Champness, a variant of Champney.
Boy/Male
Tamil
Gurudas | கà¯à®°à¯à®¤à®¾à®¸
Servant to the enlightener, Servant of the Guru
Boy/Male
Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Gentle
Boy/Male
Indian, Sanskrit, Telugu
Goodness
Boy/Male
Hindu
Forest
Boy/Male
British, English
Wealthy Protector
Boy/Male
Tamil
One who conquered the mind
Girl/Female
English
Birdlike.
Boy/Male
Muslim/Islamic
Fortunate of good fortune
Girl/Female
Hindu
Truth, Morality, Justice, Good behavior
LANDAUS FUNCTION
LANDAUS FUNCTION
LANDAUS FUNCTION
LANDAUS FUNCTION
LANDAUS FUNCTION
n.
Exchange; barter; -- used commonly of lands.
n.
The act of pulling off the shoes or sandals.
n.
One who holds lands by emphyteusis.
n.
A genus of endogenous plants. See Screw pine.
n.
A long, narrow spade for stony lands.
a.
Of or pertaining to the Vandals; resembling the Vandals in barbarism and destructiveness.
n.
An officer appointed to procession lands.
n.
A small landau.
n.
Church lands.
v. t.
To deprive of lands.
n.
An estate in lands; a fief.
n.
A writ issued by a superior court and directed to some inferior tribunal, or to some corporation or person exercising authority, commanding the performance of some specified duty.
n.
Lands recovered from the sea.
n.
Swampy or wet lands overgrown with bushes.
n.
The pagan lands; pagans, collectively; paganism.
n.
A four-wheeled covered vehicle, the top of which is divided into two sections which can be let down, or thrown back, in such a manner as to make an open carriage.
a.
Wearing sandals.
v. t.
To pull off shoes or sandals from.
a.
Deprived off shoes or sandals; unshod; discalced.