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Attempt to explain drug bioavailability in humans
pH partition theory is a theory developed in the early 20th century as an attempt to explain drug bioavailability in humans. It describes the tendency
PH_partition_theory
Ratio of concentrations in a mixture at equilibrium
not be true for the aqueous phase. To measure the partition coefficient of ionizable solutes, the pH of the aqueous phase is adjusted such that the predominant
Partition_coefficient
Topological quantum field theory
the action. The action is gauge dependent, however the partition function of the quantum theory is well-defined when the level is an integer and the gauge
Chern–Simons_theory
Statistical mechanics model for phase transitions
the properties of small, finite-size systems. The theory revolves around the complex zeros of partition functions of finite-size systems and how these may
Lee–Yang_theory
Australian-born mathematician (born 1955)
specializes in number theory and combinatorics. He holds the position Professor of Mathematics at the University of Florida. He received his Ph.D. from Pennsylvania
Frank_Garvan
Method for recursively subdividing a space into two subsets using hyperplanes
In computer science, binary space partitioning (BSP) is a method for space partitioning which recursively subdivides a Euclidean space into two convex
Binary_space_partitioning
Theorem in arithmetic combinatorics on finite partitions of the natural numbers
arithmetic combinatorics and Ramsey theory. According to this theorem, whenever the natural numbers are partitioned into finitely many subsets, there exist
Folkman's_theorem
Partition of Bengal into East Bengal and West Bengal in 1947
The Partition of Bengal in 1947, also known as the Second Partition of Bengal, part of the Partition of India, divided the British Indian Bengal Province
Partition_of_Bengal_(1947)
Swedish political scientist and author (born 1947)
particularly the partition of India in 1947. His scholarly work examines the ideological foundations and consequences of the partition, with a focus on
Ishtiaq Ahmed (political scientist)
Ishtiaq_Ahmed_(political_scientist)
Biological process of energy distribution
Biomass partitioning is the process by which plants divide their energy among their leaves, stems, roots, and reproductive parts. These four main components
Biomass_partitioning
neutral or charged polymer system. It can be derived by transforming the partition function from its standard many-dimensional integral representation over
Polymer_field_theory
The nonequilibrium partition identity (NPI) is a remarkably simple and elegant consequence of the fluctuation theorem previously known as the Kawasaki
Nonequilibrium partition identity
Nonequilibrium_partition_identity
Swiss mathematician (1920–2011)
showing that certain types of hidden-variable theories are impossible. He also proved the ordinal partition relation ω2 → (ω2, 3)2, thereby solving a problem
Ernst_Specker
Physical theory with fields invariant under the action of local "gauge" Lie groups
In physics, a gauge theory is a type of field theory in which the Lagrangian, and hence the dynamics of the system itself, does not change under local
Gauge_theory
\mathbb {S} } . Ramsey theory is sometimes characterized as the study of which collections S {\displaystyle \mathbb {S} } are partition regular. The collection
Partition_regularity
Lattice formed by all integer partitions
partitions. It is named after Alfred Young, who, in a series of papers On quantitative substitutional analysis, developed the representation theory of
Young's_lattice
Concept in theoretical physics
distance behaviour in field theory and power counting". Communications in Mathematical Physics. 18 (3): 227–246. Bibcode:1970CMaPh..18..227S. doi:10.1007/BF01649434
Renormalization_group
Expectation value of time-ordered quantum operators
treated separately. Effective action Green's function (many-body theory) Partition function (mathematics) Source field The − i {\displaystyle -i} factor
Correlation function (quantum field theory)
Correlation_function_(quantum_field_theory)
Branch of logic
Finite model theory is a subarea of model theory. Model theory is the branch of logic which deals with the relation between a formal language (syntax)
Finite_model_theory
Israeli theoretical physicist
works on quantum field theory, including conformal field theories, gauge theories and supersymmetry. Komargodski received his Ph.D. from the Weizmann Institute
Zohar_Komargodski
Type of infinite structure
In mathematical logic, and more specifically in model theory, an infinite structure ( M , < , … ) {\displaystyle (M,<,\dots )} that is totally ordered
O-minimal_theory
British theoretical physicist and mathematician (1923–2020)
Eros to Gaia. Pantheon Books. 1992. arXiv:quant-ph/0608140. "Some Guesses in The Theory of Partitions". Selected Papers of Freeman Dyson with Commentary
Freeman_Dyson
Chinese American mathematician
张晨钟) was a mathematician who worked in model theory. Typically known by his initials "C.C." he obtained his PhD from Berkeley in 1955 on "Cardinal and Ordinal
Chen_Chung_Chang
Quantum field theory
Unsolved problem in physics Yang–Mills theory and the mass gap. Quantum particles described by the theory have mass but the classical waves of the field
Yang–Mills_theory
Method in ab initio Quantum Chemistry
perturbation theory: The new approach to multi-state multi-reference perturbation theory". J. Chem. Phys. 134 (21): 214113. Bibcode:2011JChPh.134u4113G.
Møller–Plesset perturbation theory
Møller–Plesset_perturbation_theory
Theory of stochastic partial differential equations
Supersymmetric theory of stochastic dynamics (STS) is a multidisciplinary approach to stochastic dynamics on the intersection of dynamical systems theory, topological
Supersymmetric theory of stochastic dynamics
Supersymmetric_theory_of_stochastic_dynamics
Mathematical models of strategic interactions
Game theory is the study of mathematical models of strategic interactions. It has applications in many fields of social science, and is used extensively
Game_theory
Field theory involving topological effects in physics
Another more famous example is Chern–Simons theory, which can be applied to knot invariants. In general, partition functions depend on a metric but the above
Topological quantum field theory
Topological_quantum_field_theory
Divide and conquer sorting algorithm
than or greater than the pivot. For this reason, it is sometimes called partition-exchange sort. The sub-arrays are then sorted recursively. This can be
Quicksort
Type theory in logic and mathematics
ω-Categories from Intensional Type Theory" (published 2009) and as part of his 2010 Ph.D. thesis "Higher Categories from Type Theories". The concept of a univalent
Homotopy_type_theory
Statistical mechanics simulation
statistical field theory, like e.g. a polymer field theory. A convenient possibility is to use Monte Carlo (MC) algorithms, to sample the full partition function
Field-theoretic_simulation
Theorem in statistical mechanics
mechanics, the Lee–Yang theorem states that if partition functions of certain models in statistical field theory with ferromagnetic interactions are considered
Lee–Yang_theorem
American mathematician and professor emeritus
"Finite Sums from Sequences Within Cells of a Partition of N". Gordon, C.; Hindman Neil. "Elementary Set Theory – Proof Techniques". Hafner Press, New York
Neil_Hindman
Theoretical framework in physics
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines field theory, special relativity and quantum mechanics. QFT
Quantum_field_theory
discrete and Euclidean geometries, graph theory, group theory, mathematical logic, number theory, set theory, Ramsey theory, dynamical systems, and partial differential
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
American mathematician
forcing and absoluteness. Galvin and Shelah also proved the square bracket partition relations ℵ 1 ↛ [ ℵ 1 ] 4 2 {\displaystyle \aleph _{1}\not \to [\aleph
Fred_Galvin
Complexity class used to classify decision problems
More unsolved problems in computer science In computational complexity theory, NP (nondeterministic polynomial time) is a complexity class used to classify
NP_(complexity)
Type of approximation to an underlying physical theory
effective field theory is a type of approximation, or effective theory, for an underlying physical theory, such as a quantum field theory or a statistical
Effective_field_theory
Theory in supersymmetric gauge theory
explicitly determine the instanton partition function of N = 2 {\displaystyle {\mathcal {N}}=2} super Yang–Mills theory. The Seiberg–Witten prepotential
Seiberg–Witten_theory
Theory of quantum gauge fields on a lattice
physics, lattice gauge theory is the study of gauge theories on a spacetime that has been discretized into a lattice. Gauge theories are important in particle
Lattice_gauge_theory
Entangled 3-qubit quantum state
N {\displaystyle N} parties is called biseparable, if one can find a partition of the parties in two disjoint subsets A {\displaystyle A} and B {\displaystyle
W_state
Yang–Mills theory in two dimensions with a well-defined measure
processes inspired by Yang–Mills theory and, indirectly, by Makeenko and Migdal in the physics literature. The Yang–Mills partition function is, formally, ∫ e
Two-dimensional Yang–Mills theory
Two-dimensional_Yang–Mills_theory
American mathematician (1904–1994)
1971. Foster's Ph.D. dissertation and his first few papers were in mathematical logic. From this point, he soon focused on the related theory of Boolean algebras
Alfred_Foster_(mathematician)
American musician
University specializing in number theory and combinatorics, particularly the theory of integer partitions and analytic number theory. After spending the first
Robert_Schneider
Dimensionless number that quantifies the strength of the electromagnetic interaction
from estimates of the constants that appear in any of its definitions, the theory of quantum electrodynamics (QED) provides a way to measure α directly using
Fine-structure_constant
In mathematics, variational perturbation theory (VPT) is a mathematical method to convert divergent power series in a small expansion parameter, say s
Variational perturbation theory
Variational_perturbation_theory
Mathematical theory of data types
In mathematical logic, and theoretical computer science, type theory is the study of formal systems that classify expressions or mathematical objects by
Type_theory
Theory of subatomic structure
described in terms of a higher dimensional black hole. Partition functions developed in bosonic string theory have also found applications in the study of tethered
String_theory
British-American mathematician
Atkin. Atkin is also known for his work on properties of the integer partition function and the monster module. He was a vocal fan of using computers
A._O._L._Atkin
American computer scientist and educator
contributions to algorithms for graph partitioning and for single- and multi-commodity flows. Rao received his PhD from the Massachusetts Institute of
Satish_B._Rao
Standard system of axiomatic set theory
In set theory, Zermelo–Fraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is an axiomatic system that was proposed in
Zermelo–Fraenkel_set_theory
American Jewish mathematician
prequantization has led to the theory of quantum Toda lattices. The Kostant partition function is named after him. With Gerhard Hochschild and Alex F. T. W
Bertram_Kostant
Quantum chromodynamics on a lattice
approach to solving the quantum chromodynamics (QCD) theory of quarks and gluons. It is a lattice gauge theory formulated on a grid or lattice of points in space
Lattice_QCD
American mathematician
far,” he said. Brenner, Charles Hallam (1984). Asymptotics of Partition Functions (Ph.D. thesis). UCLA. Brenner, Charles H. (November 1986). "Asymptotic
Charles Brenner (mathematician)
Charles_Brenner_(mathematician)
Computer science concept
In computational complexity theory, the polynomial hierarchy (sometimes called the polynomial-time hierarchy) is a hierarchy of complexity classes that
Polynomial_hierarchy
Microcanonic transition state theory of unimolecular reactions
are the molecular vibrational and external rotational partition functions. Transition state theory IUPAC, Compendium of Chemical Terminology, 5th ed. (the
RRKM_theory
Monster and modular connection
sectors of a conformal field theory with monster symmetry, and interpreted the functions f(g, h, τ) as genus one partition functions, where one forms a
Monstrous_moonshine
Asymmetry of classical and quantum action
anomalous symmetry in a quantum theory is a symmetry of the action, but not of the measure, and so not of the partition function as a whole. A global anomaly
Anomaly_(physics)
American mathematician (1916–2001)
scientist, cryptographer, and inventor known as the "father of information theory", and the man who laid the foundations of the Information Age. Shannon was
Claude_Shannon
Russian mathematical and theoretical physicist
His Ph.D. thesis on Four Dimensional Holomorphic Theories was defended in 1996. There he introduced a four dimensional variant of Chern-Simons theory, rediscovered
Nikita_Nekrasov
Mathematical limit applied in statistical physics
{\partial Z^{n}}{\partial n}}} where Z {\displaystyle Z} is most commonly the partition function, or a similar thermodynamic function. It is typically used to
Replica_trick
Theory of nationality in Ireland
variants of the theory gained renewed currency from the late 1960s when the onset of Northern Ireland Troubles called the 1921 partition settlement into
Two_nations_theory_(Ireland)
Indian mathematician (1887–1920)
algebraic expression given by Srinivasa Ramanujan Rank of a partition – Term in number theory and combinatorics Tamil: ஶ்ரீநிவாஸ ராமாநுஜையங்கார், romanized: Śrīnivāsa
Srinivasa_Ramanujan
Maximal subgraph whose vertices can reach each other
not part of any larger connected subgraph. The components of any graph partition its vertices into disjoint sets, and are the induced subgraphs of those
Component_(graph_theory)
Function that encodes the dependence of a coupling parameter on the energy scale
In theoretical physics, specifically quantum field theory, a beta function or Gell-Mann–Low function, β(g), encodes the dependence of a coupling parameter
Beta_function_(physics)
Hungarian set theorist
initiated Shelah's pcf theory. With James Earl Baumgartner he proved a result in infinite Ramsey theory, that for every partition of the vertices of a complete
András_Hajnal
Axiomatization of quantum field theory
"Quantum field theory cannot provide faster than light communication", Foundations of Physics Letters, 2 (2): 127–149, Bibcode:1989FoPhL...2..127E, doi:10
Wightman_axioms
German-born theoretical physicist (1879–1955)
physicist best known for developing the theory of relativity. Einstein also made important contributions to quantum theory. His mass–energy equivalence formula
Albert_Einstein
Relativistic wave equation describing massless fermions
In physics, particularly in quantum field theory, the Weyl equation (/vaɪl/ VILE) is a relativistic wave equation for describing massless spin-1/2 particles
Weyl_equation
Formal system of logic
"simple" indicates that the underlying type theory is the theory of simple types, also called the simple theory of types. Leon Chwistek and Frank P. Ramsey
Higher-order_logic
Theorem for reducing high-order derivatives
Italian physicist Gian Carlo Wick. It is used extensively in quantum field theory to reduce arbitrary products of creation and annihilation operators to sums
Wick's_theorem
American mathematician (born 1938)
Theory of Partitions is the standard reference on the subject of integer partitions. He has advanced mathematics in the theories of partitions and q-series
George Andrews (mathematician)
George_Andrews_(mathematician)
Graph with only one possible coloring
Equivalently, there is only one way to partition its vertices into k independent sets and there is no way to partition them into k − 1 independent sets. A
Uniquely_colorable_graph
On partitions into intersecting convex hulls
is the result that sufficiently many points in Euclidean space can be partitioned into subsets with intersecting convex hulls. Specifically, for any positive
Tverberg's_theorem
Israeli mathematician (born 1941)
contributions including introduction of Markov partitions (with Roy Adler), development of ergodic theory of amenable groups (with Don Ornstein), mean dimension
Benjamin_Weiss
Relationship between derivatives and integrals
as the largest of the partitions approaches zero in size, so that all other partitions are smaller and the number of partitions approaches infinity. So
Fundamental theorem of calculus
Fundamental_theorem_of_calculus
Japanese-born American theoretical physicist (1925–2023)
the University of Tokyo, earning his bachelor's degree in 1947 and then his PhD in 1952. Afterwards he spent two years as a postdoctoral researcher of the
Toichiro_Kinoshita
Physics of many interacting particles
techniques—such as mean-field theory, perturbation expansions, or Monte Carlo simulations—are employed to estimate the partition function and compute the average
Statistical_mechanics
Conformal field theory on a 2D spacetime
A two-dimensional conformal field theory is a quantum field theory on a Euclidean two-dimensional space, that is invariant under local conformal transformations
Two-dimensional conformal field theory
Two-dimensional_conformal_field_theory
Property of a mathematical space
two-dimensional region. The software is expected to use this boundary to partition 2-dimensional space into an interior and exterior. Surface (3-dimensional)
Dimension
Unstable configurations of atoms formed while a chemical reaction progresses
Error can arise from introducing symmetry numbers into the rotational partition functions for the reactants and activated complexes. To reduce errors
Activated_complex
Some remarkable congruences for the partition function
of general congruences. This was proved by his Ph.D. student Karl Mahlburg in his 2005 paper Partition Congruences and the Andrews–Garvan–Dyson Crank
Ramanujan's_congruences
Quantum field giving rise to gluons
generators of the SU(3) group, in the context of quantum mechanics and field theory; a generator can be viewed as an operator corresponding to a symmetry transformation
Gluon_field
Mathematical logic concept
Reflections on Skolem's Paradox (PDF) (Ph.D. thesis). UCLA Philosophy Department. Moore, A.W. (1985). "Set Theory, Skolem's Paradox and the Tractatus".
Skolem's_paradox
Thermal phase transition in AdS black holes
{\displaystyle T_{C}} , thermal AdS will become the dominant contribution to the partition function. The Hawking-Page phase transition between the unstable small
Hawking–Page_phase_transition
Paradox in set theory
mathematician, Bertrand Russell, in 1901. Russell's paradox shows that every set theory that contains an unrestricted comprehension principle leads to contradictions
Russell's_paradox
Isotope geochemistry modelling method
to the product of partition function ratios, namely the translational, rotational, vibrational, and sometimes electronic partition functions. Thus the
Urey–Bigeleisen–Mayer equation
Urey–Bigeleisen–Mayer_equation
Canadian mathematician
and probabilistic combinatorics, Ramsey theory, random polynomials and matrices, and combinatorial number theory. Sahasrabudhe grew up on Bowen Island,
Julian_Sahasrabudhe
Theory to explain the emergence of the classical world from the quantum world
arXiv:quant-ph/0405161. Bibcode:2005PhRvA..71e2105Z. doi:10.1103/PhysRevA.71.052105. S2CID 18210481. Wojciech Hubert Zurek (2018). "Quantum theory of the classical:
Quantum_Darwinism
Evolutionary equation under renormalization group flow
field theory and power counting". Communications in Mathematical Physics. 18 (3). Springer Science and Business Media LLC: 227–246. Bibcode:1970CMaPh..18
Callan–Symanzik_equation
Israeli theoretical physicist
Institute, Rehovot (Ph.D., 1985), where his graduate advisor was Yitzhak Frishman. His early work focused on non-perturbative quantum field theory in two space-time
Doron_Gepner
Conjecture in algebraic geometry
models of 2-dimensional quantum gravity should have the same partition function. The partition function for one of these models can be described in terms
Witten_conjecture
Mathematical subject
n_{k}} that sum up to | V ( G ) | {\displaystyle |V(G)|} , there exists a partition { V 1 , … , V k } {\displaystyle \{V_{1},\ldots ,V_{k}\}} of V ( G ) {\displaystyle
Topological_combinatorics
Understanding of gas properties in terms of molecular motion
Enskog theory for multicomponent mixtures. I. Linear transport theory". The Journal of Chemical Physics. 78 (5): 2746–2759. Bibcode:1983JChPh..78.2746L
Kinetic_theory_of_gases
Canadian-American mathematician
editor-in-chief of the Journal of Combinatorial Theory, Series A, from 2001 to 2009. Barcelo completed her Ph.D. from the University of California, San Diego
Hélène_Barcelo
Israeli encyclopedist and historian (1910–2012)
playwright. Benzion Mileikowsky (later Netanyahu) was born in Warsaw in partitioned Poland, which was under Russian control, to Sarah (Lurie) and writer
Benzion_Netanyahu
Technique in analytical chemistry
derived from two sets of chromatographic theory: plate theory (as part of partition chromatography), and the rate theory of chromatography / van Deemter equation
High-performance liquid chromatography
High-performance_liquid_chromatography
Fundamental theorem in mathematical logic
logic. The completeness theorem applies to any first-order theory: If T is such a theory, and φ is a sentence (in the same language) and every model
Gödel's_completeness_theorem
High-temperature expansion in statistical mechanics
expansion of the partition function of a statistical field theory around a model that is a union of non-interacting 0-dimensional field theories. Unlike the
Cluster_expansion
Iranian High Energy physicist
He is known for the proposal of the para-string theory, construction of modular invariant partition functions for WZNW models via the orbifold method
Farhad_Ardalan
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