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Mathematical model in nuclear physics
In nuclear physics, the Bateman equation is a mathematical model describing abundances and activities in a decay chain as a function of time, based on
Bateman_equation
British-American mathematician
Harry Bateman FRS (29 May 1882 – 21 January 1946) was an English mathematician with a specialty in differential equations of mathematical physics. With
Harry_Bateman
half-lives, on average. The activity of the daughter is given by the Bateman equation: A d = A P ( 0 ) λ d λ d − λ P × ( e − λ P t − e − λ d t ) × B R +
Transient_equilibrium
Partial differential equation
Burgers' equation or Bateman–Burgers equation is a fundamental partial differential equation and convection–diffusion equation occurring in various areas
Burgers'_equation
Decrease in value at a rate proportional to the current value
means of an exponential process. These systems are solved using the Bateman equation. In the pharmacology setting, some ingested substances might be absorbed
Exponential_decay
Series of radioactive decays
the universe: tellurium-128 has a half-life of 2.2×1024 years. The Bateman equation predicts the relative quantities of all the isotopes that compose a
Decay_chain
Emissions from unstable atomic nuclei
general solution to the recursive problem is given by Bateman's equations: 'Bateman's equations' N D = N 1 ( 0 ) λ D ∑ i = 1 D λ i c i e − λ i t c i =
Radioactive_decay
New Zealand physicist and chemist (1871–1937)
Elements" Harper's Monthly Magazine, January 1904, pages 279 to 284. Bateman equation Hydrophone Magnetic detector Neutron generator Royal Society of New
Ernest_Rutherford
Branch of pharmacology
lethal dose and other factors are the main focus of Ecotoxicology. Bateman equation Blood alcohol concentration Biological half-life Bioavailability Cooperstown
Pharmacokinetics
Method for solving the Laplace equation in four dimensions
partial differential equations, the Bateman transform is a method for solving the Laplace equation in four dimensions and wave equation in three by using
Bateman_transform
Second-order partial differential equation
In mathematics and physics, Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace, who first studied its
Laplace's_equation
Situation in which the quantity of a radioactive isotope remains constant
\lambda _{A}t\ll 1} and the exponential can be approximated as 1. Bateman equation Transient equilibrium Velikyan, Irina (2015-07-16). "68Ga-Based Radiopharmaceuticals:
Secular_equilibrium
Non-linear partial differential equation
1921. Bateman, Harry. "Partial differential equations of mathematical physics." Partial Differential Equations of Mathematical Physics, by H. Bateman, Cambridge
Liouville–Bratu–Gelfand equation
Liouville–Bratu–Gelfand_equation
This is a list of scientific equations named after people (eponymous equations). Contents A B C D E F G H I J K L M N O P R S T V W Y Z See also References
List of scientific equations named after people
List_of_scientific_equations_named_after_people
Math equation
{b^{2}}{1-t^{2}}})\,S=0} Wave equation see Abramowitz and Stegun, page 722 see Bateman, page 442 Bibliography M. Abramowitz and I. Stegun
Spheroidal_wave_equation
Differential equation for the description of waves or standing wave
Acoustic wave equation Bateman transform Electromagnetic wave equation Helmholtz equation Inhomogeneous electromagnetic wave equation Laplace operator
Wave_equation
Biological principle about the differential reproductive success in males versus females
Bateman's principle, in evolutionary biology, states that the variability in reproductive success (or reproductive variance) is greater in males than
Bateman's_principle
Equations with an unknown function under an integral sign
integral equations are equations in which an unknown function appears under an integral sign. In mathematical notation, integral equations may thus be
Integral_equation
This article summarizes equations in the theory of nuclear physics and particle physics. The following apply for the nuclear reaction: a + b ↔ R → c in
List of equations in nuclear and particle physics
List_of_equations_in_nuclear_and_particle_physics
Equations modelling predator–prey cycles
Lotka–Volterra equations, also known as the Lotka–Volterra predator–prey model, are a pair of first-order nonlinear differential equations, frequently used
Lotka–Volterra_equations
)\,d\theta .} Bateman discovered this function, when Theodore von Kármán asked for the solution of the following differential equation which appeared
Bateman_function
The Bateman Manuscript Project was a major effort at collation and encyclopedic compilation of the mathematical theory of special functions. It resulted
Bateman_Manuscript_Project
Solutions of Lamé's equation
solution of Lamé's equation, a second-order ordinary differential equation. It was introduced in the paper (Gabriel Lamé 1837). Lamé's equation appears in the
Lamé_function
See also Nonlinear partial differential equation, List of partial differential equation topics and List of nonlinear ordinary differential equations.
List of nonlinear partial differential equations
List_of_nonlinear_partial_differential_equations
Mapping involving integration between function spaces
operator or the Fredholm kernel. Bateman transform Convolution kernel Circular convolution Circulant matrix Differential equations Kernel method List of transforms
Integral_transform
In physics, solution to Schrödinger equation
mathematics, a Coulomb wave function is a solution of the Coulomb wave equation, named after Charles-Augustin de Coulomb. They are used to describe the
Coulomb_wave_function
In mathematics, the Bateman polynomials are a family Fn of orthogonal polynomials introduced by Harry Bateman (1933). The Bateman–Pasternack polynomials
Bateman_polynomials
Biological process to convert light into chemical energy
the equation for this process is: CO2carbon dioxide + 2H2Owater + photonslight energy → [CH2O]carbohydrate + O2oxygen + H2Owater This equation emphasizes
Photosynthesis
British mathematician (1885–1977)
worked on topics relating to analysis, number theory, and differential equations and had lengthy collaborations with G. H. Hardy, Srinivasa Ramanujan and
John_Edensor_Littlewood
In mathematics, a solution to a modified form of the confluent hypergeometric equation
function is a special solution of Whittaker's equation, a modified form of the confluent hypergeometric equation introduced by Whittaker (1903) to make the
Whittaker_function
Mathematical problem in number theory
Archimedis) is a problem in Diophantine analysis, the study of polynomial equations with integer solutions. Attributed to Archimedes, the problem involves
Archimedes's_cattle_problem
Solution of a confluent hypergeometric equation
solution of a confluent hypergeometric equation, which is a degenerate form of a hypergeometric differential equation where two of the three regular singularities
Confluent hypergeometric function
Confluent_hypergeometric_function
Mathematical function that preserves angles
maps for relating solutions of Maxwell's equations was identified by Ebenezer Cunningham (1908) and Harry Bateman (1910). Their training at Cambridge University
Conformal_map
American mathematician (1903–1961)
in mathematics and physics there in 1925 under the supervision of Harry Bateman, writing "On Dynamical Space-Times Which Contain a Conformal Euclidean
Howard_P._Robertson
tensors, and the basic equations of fluid mechanics, Prentice-Hall, OCLC 299650765 Bateman, H. (1929), "Notes on a differential equation which occurs in the
Clebsch_representation
Theorem In probability theory and statistics
point process arose as a solution to a family of differential equations by Harry Bateman. In Campbell's work, he presents the moments and generating functions
Campbell's theorem (probability)
Campbell's_theorem_(probability)
Mutually beneficial interaction between species
of species j on species i. Mutualism is in essence the logistic growth equation modified for mutualistic interaction. The mutualistic interaction term
Mutualism_(biology)
2014 film by Alex Garland
for a one-week visit to the luxurious, isolated home of the CEO, Nathan Bateman. Nathan lives there with an unspeaking servant named Kyoko, who, according
Ex_Machina_(film)
American actor (born 1998)
Wyatt Langmore in the Netflix crime drama series Ozark, alongside Jason Bateman, Laura Linney, and Julia Garner. Ozark received positive reviews from critics
Charlie_Tahan
Fluid dynamics problem
simplest unsteady problems that have an exact solution for the Navier-Stokes equations. The impulse movement of semi-infinite plate was studied by Keith Stewartson
Rayleigh_problem
Model in theoretical ecology and statistical mechanics
set of coupled ordinary differential equations where the parameters of the generalized Lotka–Volterra equation are sampled from a probability distribution
Random generalized Lotka–Volterra model
Random_generalized_Lotka–Volterra_model
Extension of the factorial function
the Hadamard function. A more restrictive requirement is the functional equation that interpolates the shifted factorial f ( n ) = ( n − 1 ) ! {\displaystyle
Gamma_function
German-American mathematician
Göttingen. In 1948, he emigrated to the United States to collaborate on the Bateman Manuscript Project as a co-editor while a visiting professor at the California
Wilhelm_Magnus
American mathematician (1927–2010)
Acta Arith. 49 (5): 507–523. doi:10.4064/aa-49-5-507-523. MR 0967334. Bateman, P. T.; Selfridge, J. L.; Wagstaff, S. S. (1989). "The New Mersenne conjecture"
John_Selfridge
Musical by Madness
Peter Darling Orchestrations – Steve Sidwell Musical Director – Philip Bateman ‡ Song originally by Labi Siffre The recorded original production was telecast
Our_House_(musical)
Root-finding algorithm
doi:10.1515/jnma-2015-0026. S2CID 10356202. Bateman, Harry (January 1938). "Halley's methods for solving equations". The American Mathematical Monthly. 45
Halley's_method
Class of ecological models
consumer-resource model is described by the system of coupled ordinary differential equations, d N i d t = N i g i ( R 1 , … , R M ) , i = 1 , … , S , d R α d t = f
Consumer-resource_model
Extension to the Poincaré group
one for a dilation. Harry Bateman and Ebenezer Cunningham were the first to study the conformal symmetry of Maxwell's equations. They called a generic expression
Conformal_symmetry
Mathematical function, inverse of an exponential function
scientific formulas, such as the Tsiolkovsky rocket equation, the Fenske equation, or the Nernst equation. Scientific quantities are often expressed as logarithms
Logarithm
Airstrikes and capture of Nicolás Maduro
2026. Retrieved 8 January 2026. Goodwin, Grace Eliza; Vasquez, Cristobal; Bateman, Tom (4 January 2026). "Venezuelans react to US Maduro arrest with hope
2026 United States intervention in Venezuela
2026_United_States_intervention_in_Venezuela
Species of bird
Savannas Preserve State Park. Florida Atlantic University. Balda, R. P., & Bateman, G. C. (1971). Flocking and annual cycle of the pinon jay, Gymnorhinus
Cooper's_hawk
Process that leads to chemical changes
change to the elements present), and can often be described by a chemical equation. Nuclear chemistry is a sub-discipline of chemistry that involves the chemical
Chemical_reaction
frequently in the study of differential equations. For instance, one might study solutions of the heat equation in an idealised semi-infinite metal bar
Semi-infinite
Extinct giant shark species
northern range limit of Otodus megalodon is underestimated: comment on Bateman and Larsson (2025)". Canadian Journal of Earth Sciences. 63: 1–2. doi:10
Megalodon
Mathematics of surface waves on a fluid
Harry Bateman. Variation with respect to the velocity potential Φ(x,z,t) and free-moving surfaces like z = η(x,t) results in the Laplace equation for the
Luke's_variational_principle
Predator at the top of a food chain
dynamics Population modeling Population size Predator–prey (Lotka–Volterra) equations Recruitment Small population size Stability Resilience Resistance Random
Apex_predator
Mathematical transformation
frames. They were defined between 1908 and 1909 by Harry Bateman and Ebenezer Cunningham, with Bateman giving the transformation its name. They correspond
Spherical_wave_transformation
2023 maritime disaster
Cavitation to Astrophysics: Explicit Solution of the Spherical Collapse Equation". Phys. Rev. E. 109 (6) 065102. arXiv:2401.05445. Bibcode:2024PhRvE.109f5102O
Titan_submersible_implosion
2014 American film
surgery on a little girl named Kayla who recites a complex mathematical equation before dying during the operation. Based on what he saw with Kayla, Dr
The_Hive_(2014_film)
is a list of transforms in mathematics. Abel transform Aboodh transform Bateman transform Fourier transform Fourier cosine transform Fourier sine transform
List_of_transforms
Dutch physicist (1895–1981)
Ehrenfest, where he obtained his PhD in 1918. He is known for the Burgers' equation, the Burgers vector in dislocation theory and the Burgers material in viscoelasticity
Jan_Burgers
American physiologist (1904–2004)
(2): 352–363. doi:10.1007/BF00339114. S2CID 28971898. Keys, Ancel; J.B. Bateman (1932). "Branchial Responses to Adrenaline and to Pitressin in the eel"
Ancel_Keys
Describes approximate behavior of a function
as two volumes in one by Chelsea, 1974, with an appendix by Dr. Paul T. Bateman. pp. 59–63. Cormen, Thomas H.; Leiserson, Charles E.; Rivest, Ronald L
Big_O_notation
original on April 18, 2026. Retrieved April 19, 2026. Booty, Natasha; Bateman, Tom; Usher, Barbara Plett (November 13, 2025). "US calls for international
Foreign policy of the second Trump administration
Foreign_policy_of_the_second_Trump_administration
Pair of polynomial sequences
thesis). p. 70. Archived from the original (PDF) on 2 July 2007. Bateman & Bateman Manuscript Project 1953, p. 184, eqs. 3–4. Beckenbach, E. F.; Seidel
Chebyshev_polynomials
Beneficial symbiosis between species
dynamics Population modeling Population size Predator–prey (Lotka–Volterra) equations Recruitment Small population size Stability Resilience Resistance Random
Commensalism
Development of linear transformations forming the Lorentz group
1112/plms/s2-8.1.223. Bateman, Harry (1912) [1910]. "Some geometrical theorems connected with Laplace's equation and the equation of wave motion". American
History of Lorentz transformations
History_of_Lorentz_transformations
Animal that can eat and survive on both plants and animals
dynamics Population modeling Population size Predator–prey (Lotka–Volterra) equations Recruitment Small population size Stability Resilience Resistance Random
Omnivore
2024 bridge collapse near Baltimore, Maryland, US
Retrieved March 28, 2024 – via www.youtube.com. Debusmann Jr, Bernd; Bateman, Tom (March 26, 2024). "Lost power, a mayday call and the crash that brought
Francis Scott Key Bridge collapse
Francis_Scott_Key_Bridge_collapse
Species with a large effect on its environment
dynamics Population modeling Population size Predator–prey (Lotka–Volterra) equations Recruitment Small population size Stability Resilience Resistance Random
Keystone_species
American physicist, author, and inventor (1927–1992)
in space with his parents, and in college he enjoyed working on rocket equations. However, he did not see space science as an option for a career path
Gerard_K._O'Neill
Hardy–Littlewood conjecture Hardy–Littlewood circle method Schinzel's hypothesis H Bateman–Horn conjecture Waring's problem Brahmagupta–Fibonacci identity Euler's
List_of_number_theory_topics
cancer. Volodymyr Marchenko, 103, Ukrainian mathematician (Marchenko equation, Marchenko–Pastur distribution). Hélio Mauro, 83, Brazilian politician
Deaths_in_January_2026
Organism that eats mostly or exclusively animal tissue
dynamics Population modeling Population size Predator–prey (Lotka–Volterra) equations Recruitment Small population size Stability Resilience Resistance Random
Carnivore
Virus that infects bacteria
dynamics Population modeling Population size Predator–prey (Lotka–Volterra) equations Recruitment Small population size Stability Resilience Resistance Random
Bacteriophage
American mathematician (1933–2019)
differential equation is the hypergeometric equation with the three singularities moved to the three given points. Differential equations with four or
Richard_Askey
Type of heterotrophic nutrition based on decayed organic matter
dynamics Population modeling Population size Predator–prey (Lotka–Volterra) equations Recruitment Small population size Stability Resilience Resistance Random
Saprotroph
Aspect of ecosystems
dynamics Population modeling Population size Predator–prey (Lotka–Volterra) equations Recruitment Small population size Stability Resilience Resistance Random
Food_chain
Number divisible only by 1 and itself
extended to multivariable polynomials in Dickson's conjecture and then Bateman–Horn conjecture. One of the most famous unsolved questions in mathematics
Prime_number
Species introduced by human activity
dynamics Population modeling Population size Predator–prey (Lotka–Volterra) equations Recruitment Small population size Stability Resilience Resistance Random
Introduced_species
Family of power series in mathematics
(1945). "The contiguous function relations for pFq with application to Bateman's J and Rice's H". Bull. Amer. Math. Soc. 51 (10): 714–723. doi:10
Generalized hypergeometric function
Generalized_hypergeometric_function
Obsolete postulated medium for the propagation of light
electromotive force equation (the precursor of the Lorentz force equation), he derived a wave equation from a set of eight equations which appeared in the
Luminiferous_aether
Ecological theory concerning the selection of life history traits
respect to time t) is the rate of change in population with time. Thus, the equation relates the growth rate of the population N to the current population size
R/K_selection_theory
(2): 123–138. doi:10.1080/02614367.2010.541481. S2CID 144386213. Anthony Bateman (2008). "Sporting Sounds: Relationships Between Sport and Music", p. 186
Culture_of_the_United_Kingdom
Position of an organism in a food chain
dynamics Population modeling Population size Predator–prey (Lotka–Volterra) equations Recruitment Small population size Stability Resilience Resistance Random
Trophic_level
Collection of random variables
their work, Harry Bateman studied the counting problem and derived Poisson probabilities as a solution to a family of differential equations, resulting in
Stochastic_process
Animal that feeds on decomposing plant and animal parts as well as faeces
dynamics Population modeling Population size Predator–prey (Lotka–Volterra) equations Recruitment Small population size Stability Resilience Resistance Random
Detritivore
Personality disorder
Dependence. 49 (3): 217–23. doi:10.1016/S0376-8716(98)00015-5. PMID 9571386. Bateman AW (23 March 2022). "Mentalizing and Group Psychotherapy: A Novel Treatment
Antisocial personality disorder
Antisocial_personality_disorder
Geometric shell bounded by two concentric, similar ellipses or ellipsoids
II, Cambridge University Press, Cambridge (1882) Harry Bateman. "Partial differential equations of mathematical physics.", Cambridge, UK: Cambridge University
Homoeoid_and_focaloid
Ecological communities abruptly losing biodiversity, often irreversibly
dynamics Population modeling Population size Predator–prey (Lotka–Volterra) equations Recruitment Small population size Stability Resilience Resistance Random
Ecosystem_collapse
Approximate power law relating animal metabolic rate to mass
"Energy metabolism and body size I. Is the 0.75 mass exponent of Kleiber's equation a statistical artifact?". Respiration Physiology. 48 (1): 1–12. doi:10
Kleiber's_law
Geographical area in which a species can be found
dynamics Population modeling Population size Predator–prey (Lotka–Volterra) equations Recruitment Small population size Stability Resilience Resistance Random
Species_distribution
the equation he needed to stabilize said ping-pong ball. 39 16 "The Duck Knight Returns!" Tanner Johnson Story by : Francisco Angones, Madison Bateman, Colleen
List of DuckTales (2017 TV series) episodes
List_of_DuckTales_(2017_TV_series)_episodes
Community of living organisms together with the nonliving components of their environment
dynamics Population modeling Population size Predator–prey (Lotka–Volterra) equations Recruitment Small population size Stability Resilience Resistance Random
Ecosystem
Type of environment in which an organism lives
dynamics Population modeling Population size Predator–prey (Lotka–Volterra) equations Recruitment Small population size Stability Resilience Resistance Random
Habitat
Non-living factors that affect organisms and ecosystems
dynamics Population modeling Population size Predator–prey (Lotka–Volterra) equations Recruitment Small population size Stability Resilience Resistance Random
Abiotic_component
Behavior characterized by activity during the night and sleeping during the day
dynamics Population modeling Population size Predator–prey (Lotka–Volterra) equations Recruitment Small population size Stability Resilience Resistance Random
Nocturnal_animal
Hypothesis that predators are the primary regulators of ecosystems
dynamics Population modeling Population size Predator–prey (Lotka–Volterra) equations Recruitment Small population size Stability Resilience Resistance Random
Green_world_hypothesis
Organism type
dynamics Population modeling Population size Predator–prey (Lotka–Volterra) equations Recruitment Small population size Stability Resilience Resistance Random
Autotroph
Hypothesis about plant resource use competition in community ecology
dynamics Population modeling Population size Predator–prey (Lotka–Volterra) equations Recruitment Small population size Stability Resilience Resistance Random
R*_rule_(ecology)
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