ROOT

ATOMIC AND MOLECULAR PHYSICS

Atomic properties and interactions with photons

Category information

reference category: Atomic properties and interactions with photons
code: 32.00.00 (PACS)
wiki categories: [(Category:Atomic physics, 3), (Category:Quantum mechanics, 3), (Category:Chemistry, 3)]

Cluster information:

cluster id: [5737]
matching score: 0.261742084319
purity: 1.0
matching keywords: [u'molecular', u'optical', u'physics', u'atomic']

Definitions:

$S$ : spin quantum number (3.354)
${\displaystyle M_{J))$ : quantum state (2.361)
$L$ : total angular momentum quantum number (1.779)
$z$ : component (1.648)
$J$ : total angular momentum quantum number (1.628)
$l$ : orbital quantum number (1.562)
${\displaystyle M_{L))$ : microstates (1.437)

Algebraic geometry

Foundations

Category information

reference category: Foundations
code: 14Axx (MSC)
wiki categories: [(Category:Abstract algebra, 3), (Category:Field theory, 2), (Category:Geometry, 2)]

Cluster information:

cluster id: [5411]
matching score: 0.459044613144
purity: 1.0
matching keywords: [u'geometry', u'algebraic', u'algebra']

Definitions:

$L$ : galois extension (4.848)
$a$ : number field (4.256)
$k$ : field (mathematics) (3.517)
$Q$ : plus construction (3.454)
$P$ : exact category (2.701)
$F$ : fields (2.665)
$G$ : galois group (2.647)
$A$ : valuation (2.642)
$D$ : decomposition group (2.530)
$m$ : cyclic group (2.481)
$X$ : steinberg group (2.317)
$K$ : galois extension (2.295)
$M$ : module (1.939)
$\mathbf {Q}$ : rational numbers (1.939)
$M_{\mathfrak {p))$ : module (1.882)
$e$ : multiplicities (1.875)
${\displaystyle K_{0))$ : functor (1.728)
$R$ : irreducible element (1.726)
$j$ : multiplicities (1.691)
$w$ : finite extension (1.681)
$O$ : prime ideal (1.664)
$B$ : ring homomorphism (1.663)
$b$ : properties (1.489)

Surfaces and higher-dimensional varieties

Category information

reference category: Surfaces and higher-dimensional varieties
code: 14Jxx (MSC)
wiki categories: [(Category:Surfaces, 6), (Category:Differential geometry of surfaces, 4), (Category:Geometric shapes, 4)]

Cluster information:

cluster id: [1101, 8567]
matching score: 0.588221516182
purity: 1.0
matching keywords: [u'surfaces', u'varieties', u'geometry', u'enriques', u'algebraic', u'manifolds', u'topology']

Definitions:

$n$ : dimensional torus (4.230)
$a$ : k3 surface (3.473)
$r$ : radius (3.376)
$\mathbf {Z}$ : lattice (group) (3.257)
$z$ : hyperbolic paraboloid (2.764)
$S$ : circle (2.737)
$A$ : torus (2.597)
$T$ : automorphism (2.278)
$K$ : canonical line bundle (1.875)
$P$ : 0-cell (1.834)
$\mathbf {T}$ : 2-torus (1.738)
$B$ : base space (1.701)
$C$ : 1-cells (1.685)
$\mathbf {R}$ : bottle (1.465)

Computational aspects in algebraic geometry

Category information

reference category: Computational aspects in algebraic geometry
code: 14Qxx (MSC)
wiki categories: [(Category:Algebraic curves, 3), (Category:Algebraic geometry, 2), (Category:Geometric shapes, 2)]

Cluster information:

cluster id: [8798]
matching score: 0.68798842196
purity: 1.0
matching keywords: [u'geometry', u'algebraic', u'varieties', u'curves']

Definitions:

$a$ : algebraic curve (5.224)
$x$ : complex projective plane (1.671)

Algebraic topology

Fiber spaces and bundles

Category information

reference category: Fiber spaces and bundles
code: 55Rxx (MSC)
wiki categories: [(Category:Topology, 3), (Category:Differential geometry, 2), (Category:Mathematical analysis, 2)]

Cluster information:

cluster id: [9434]
matching score: 0.44889498643
purity: 1.0
matching keywords: [u'vector', u'algebraic', u'fiber', u'space', u'bundles', u'homotopy', u'topology']

Definitions:

$X$ : topological space (6.620)
$E$ : vector bundle (6.029)
$M$ : tangent bundle (5.859)
$C$ : bundles (3.438)
$n$ : vector bundle (3.432)
$x$ : vector space (3.357)
$V$ : vector bundle (2.573)
$g$ : ∈ gl (1.848)
$p$ : frame (1.847)
${\displaystyle E_{x))$ : dual vector space (1.838)
$k$ : rank (1.823)
$f$ : continuous maps (1.800)
$F$ : principal fiber bundle (1.715)
$G$ : structures (1.662)
$U$ : open neighborhood (1.653)
$\mathbf {R}$ : homeomorphism (1.625)

Astronomy and astrophysics

Computational methods

Category information

reference category: Computational methods
code: 85-08 (MSC)
wiki categories: [(Category:Stellar astronomy, 3), (Category:Thermodynamics, 2), (Category:Stars, 2)]

Cluster information:

cluster id: [5300]
matching score: 0.339870022404
purity: 1.0
matching keywords: [u'stellar', u'planetary', u'astronomy']

Definitions:

$a$ : black body (5.297)
$T$ : temperature (3.670)
$r$ : radius (2.749)
$D$ : distance (1.789)

Biology and other natural sciences

Physiological, cellular and medical topics

Category information

reference category: Physiological, cellular and medical topics
code: 92Cxx (MSC)
wiki categories: [(Category:Physics, 4), (Category:Electromagnetism, 3), (Category:Force, 2)]

Cluster information:

cluster id: [1727]
matching score: 0.233071320342
purity: 1.0
matching keywords: [u'cell', u'biochemistry', u'biology', u'molecular', u'biophysics']

Definitions:

$\mathbf {v}$ : velocity (8.716)
$\mathbf {E}$ : electric field (7.522)
$B$ : magnetic flux (7.368)
$\mathbf {B}$ : magnetic field (6.691)
$q$ : electric charge (5.029)
$x$ : direction (4.239)
$\mathbf {F}$ : force (3.736)
$y$ : direction (3.493)
$c$ : speed of light (3.226)
$v$ : velocity (2.806)
$z$ : directions (2.762)
$t$ : time (2.595)
$a$ : magnetic field (2.527)
$\mathbf {r}$ : position vector (1.847)
$\mathbf {x}$ : position (1.845)
$m$ : mass (1.793)
${\mathcal {E))$ : electromotive force (1.778)
$E$ : electric field (1.750)
$N$ : identical turns (1.714)
$\tau$ : proper time (1.712)
$\mathbf {A}$ : vector area (1.531)
$d$ : magnetic induction (1.459)

CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES

Electronic structure and electrical properties of surfaces, interfaces, thin films, and low-dimensional structures

Category information

reference category: Electronic structure and electrical properties of surfaces, interfaces, thin films, and low-dimensional structures
code: 73.00.00 (PACS)
wiki categories: [(Category:Electrical circuits, 3), (Category:Electrical engineering, 3), (Category:Electronic engineering, 3)]

Cluster information:

cluster id: [9388]
matching score: 0.212394161612
purity: 1.0
matching keywords: [u'electronic', u'electrical', u'systems']

Definitions:

${\displaystyle V_{G))$ : voltage (3.355)
${\displaystyle R_{G))$ : resistance (1.833)
${\displaystyle R_{2))$ : resistance (1.664)
${\displaystyle R_{x))$ : high precision (1.586)

Superconductivity

Category information

reference category: Superconductivity
code: 74.00.00 (PACS)
wiki categories: [(Category:Materials science, 3), (Category:Condensed matter physics, 3), (Category:Superconductivity, 3)]

Cluster information:

cluster id: [4010]
matching score: 0.248358724836
purity: 1.0
matching keywords: [u'phases', u'junction', u'josephson', u'superconductivity', u'condensed', u'effect', u'matter', u'materials']

Definitions:

$\mathbf {S}$ : uperconductor (4.900)
$\mathbf {F}$ : uperconductor (3.371)
$a$ : josephson phase (2.657)
$\phi$ : josephson phase (2.644)
$\pi$ : josephson (2.597)
$t$ : time (1.974)
$L$ : inductance (1.939)
${\displaystyle I_{s))$ : supercurrent (1.882)
${\displaystyle \phi _{0))$ : junction (1.719)

Magnetic properties and materials

Category information

reference category: Magnetic properties and materials
code: 75.00.00 (PACS)
wiki categories: [(Category:Electromagnetism, 6), (Category:Condensed matter physics, 5), (Category:Materials science, 5)]

Cluster information:

cluster id: [4670, 5925]
matching score: 0.257194208697
purity: 1.0
matching keywords: [u'susceptibility', u'condensed', u'magnetization', u'magnetic', u'matter', u'magnetism', u'materials', u'systems']

Definitions:

$\mathbf {E}$ : electric field (10.805)
$\mathbf {P}$ : polarization (electrostatics) (7.511)
$\mathbf {D}$ : electric displacement (4.694)
$\mathbf {J}$ : current density (3.716)
$\chi$ : susceptibility (3.583)
$\mathbf {M}$ : magnetization (3.428)
$\mathbf {H}$ : effective magnetic field (3.214)
$\rho$ : density (1.937)
$\mathbf {B}$ : magnetic field (1.882)
$d$ : thickness (1.858)
$M$ : molar mass (1.817)
$N$ : volume (1.790)
${\displaystyle \varepsilon _{0))$ : vacuum permittivity (1.790)
$f$ : frequency (1.707)
$j$ : direction (1.665)
${\displaystyle \chi _{v))$ : permeability (electromagnetism) (1.581)

Optical properties, condensed-matter spectroscopy and other interactions of radiation and particles with condensed matter

Category information

reference category: Optical properties, condensed-matter spectroscopy and other interactions of radiation and particles with condensed matter
code: 78.00.00 (PACS)
wiki categories: [(Category:Materials science, 3), (Category:Condensed matter physics, 3), (Category:Chemical physics, 2)]

Cluster information:

cluster id: [1207]
matching score: 0.268363578666
purity: 1.0
matching keywords: [u'matter', u'condensed', u'materials', u'solid', u'magnetic', u'state']

Definitions:

$\tau$ : angular frequency (1.845)
$\varepsilon$ : permittivity (1.544)

CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES

Mechanical and acoustical properties of condensed matter

Category information

reference category: Mechanical and acoustical properties of condensed matter
code: 62.00.00 (PACS)
wiki categories: [(Category:Mechanical engineering, 3), (Category:Kinematics, 3), (Category:Technology systems, 3)]

Cluster information:

cluster id: [8170]
matching score: 0.252663411967
purity: 1.0
matching keywords: [u'ratio', u'systems', u'mechanical']

Definitions:

${\displaystyle N_{B))$ : teeth (8.677)
$G$ : input gear (7.375)
${\displaystyle N_{A))$ : teeth (5.890)
$B$ : output gear (5.869)
$R$ : gear ratio (5.232)
${\displaystyle r_{A))$ : input gear (4.000)
$v$ : velocity (3.755)
${\displaystyle G_{A))$ : input gear (3.713)
${\displaystyle G_{B))$ : output gear (3.639)
$T$ : output torque (3.415)
$A$ : input gear (3.216)
${\displaystyle T_{A))$ : input torque (2.803)
$F$ : force (2.496)
${\displaystyle r_{B))$ : pitch radius (1.974)
$b$ : distance (1.842)
$n$ : rope sections (1.666)

Category theory; homological algebra

General theory of categories and functors

Category information

reference category: General theory of categories and functors
code: 18Axx (MSC)
wiki categories: [(Category:Functors, 3), (Category:Duality theories, 1), (Category:Adjoint functors, 1)]

Cluster information:

cluster id: [325]
matching score: 0.35211595218
purity: 1.0
matching keywords: [u'functors', u'category', u'adjoint', u'natural', u'functor']

Definitions:

$C$ : subcategory (6.987)
$F$ : functor (5.058)
$a$ : functor (4.953)
$G$ : contravariant functor (4.555)
$X$ : object (4.359)
$D$ : categories (4.132)
$A$ : functor (3.776)
$Y$ : object (3.210)
$T$ : isomorphisms (2.595)
$I$ : small category (2.582)
$K$ : field (mathematics) (1.858)
$S$ : subset (1.775)
$r$ : ring (1.766)
$\eta$ : natural transformation (1.756)
$y$ : generator (1.746)
$f$ : morphism (1.629)
$\mathbf {C}$ : object (1.628)
$R$ : objects (1.499)

Categories with structure

Category information

reference category: Categories with structure
code: 18Dxx (MSC)
wiki categories: [(Category:Multilinear algebra, 3), (Category:Category theory, 3), (Category:Monoidal categories, 3)]

Cluster information:

cluster id: [8097]
matching score: 0.69065621336
purity: 1.0
matching keywords: [u'category', u'monoidal', u'closed', u'algebra', u'categories', u'braided']

Definitions:

${\mathcal {C))$ : monoidal category (6.125)
$A$ : category of sets (4.992)
$B$ : objects (4.915)
$\gamma$ : commutativity constraint (2.705)
$N$ : fold tensor product factors (1.865)
$C$ : tensor product (1.774)

Categories and geometry

Category information

reference category: Categories and geometry
code: 18Fxx (MSC)
wiki categories: [(Category:Category theory, 6), (Category:Functions and mappings, 4), (Category:Mathematical structures, 3)]

Cluster information:

cluster id: [4101, 8374]
matching score: 0.557360171149
purity: 1.0
matching keywords: [u'category', u'functors', u'homological', u'geometry', u'abstract', u'algebra', u'categories', u'manifolds']

Definitions:

$C$ : opposite category (8.085)
$A$ : object (7.286)
$f$ : morphism (5.536)
$X$ : morphism (3.906)
$R$ : module (mathematics) (3.734)
$V$ : categories (3.392)
$B$ : objects (3.248)
$\mathbf {C}$ : category (2.665)
$Y$ : function (mathematics) (2.460)
$a$ : diagram (category theory) (1.852)
$\mathbf {A}$ : exact functor (1.845)
$F$ : exact functor (1.793)
$M$ : ring (mathematics) (1.664)
$k$ : one-dimensional vector space (1.641)

Homological algebra

Category information

reference category: Homological algebra
code: 18Gxx (MSC)
wiki categories: [(Category:Abstract algebra, 20), (Category:Ring theory, 11), (Category:Commutative algebra, 8)]

Cluster information:

cluster id: [1028, 2631, 4007, 6860]
matching score: 0.411389729336
purity: 1.0
matching keywords: [u'category', u'homology', u'homological', u'algebra', u'theories', u'relative', u'objects', u'projective', u'dimension']

Definitions:

$a$ : finitely generated module (21.818)
$M$ : module (19.662)
$R$ : module (17.887)
$\mathbf {Z}$ : group ring (10.747)
$I$ : ideal (ring theory) (8.643)
$K$ : field (mathematics) (7.863)
$N$ : module (7.513)
$A$ : module (7.511)
$X$ : polynomial ring (7.283)
$k$ : field (6.502)
$i$ : modules (5.827)
$P$ : module (4.475)
$E$ : modules (4.265)
$n$ : polynomial ring (3.905)
$F$ : module (3.639)
$f$ : surjective module homomorphism (3.627)
$V$ : linear map (3.605)
$S$ : multiplicatively closed subset (3.599)
$W$ : codimension (3.406)
${\displaystyle N_{i))$ : submodules (3.400)
$m$ : matrix (mathematics) (3.154)
$x$ : polynomial ring (3.100)
${\mathfrak {m))$ : ideal (ring theory) (2.798)
${\mathfrak {g))$ : lie algebra (2.711)
$\mathbf {Q}$ : ring (2.608)
$B$ : dense right ideal (2.571)
$b$ : nonzero (2.532)
$p$ : prime ideal (2.485)
$g$ : module homomorphism (1.950)
${\displaystyle {\mathfrak {p))_{i))$ : chain (1.882)
$C$ : category (1.848)
$\mathbf {F}$ : many copies (1.829)
$h$ : homomorphism (1.824)
$U$ : zariski (1.810)
$\mathbf {R}$ : open subsets (1.810)
$R_{\mathfrak {p))$ : module (1.774)
$Q$ : module (1.725)
$O$ : modules (1.600)
$s$ : subject (1.598)
${\displaystyle x_{i))$ : zero-divisor (1.591)

Classical thermodynamics, heat transfer

Thermodynamics and heat transfer

Category information

reference category: Thermodynamics and heat transfer
code: 80Axx (MSC)
wiki categories: [(Category:Thermodynamics, 10), (Category:Empirical laws, 4), (Category:Physics, 4)]

Cluster information:

cluster id: [6386, 7746, 9950]
matching score: 0.399318825195
purity: 1.0
matching keywords: [u'transfer', u'chemical', u'thermodynamics', u'heat', u'chemistry']

Definitions:

$T$ : temperature (18.171)
$V$ : volume (thermodynamics) (9.787)
$U$ : internal energy (8.118)
$Q$ : heat (7.410)
$O$ : state (7.151)
$S$ : entropy (6.168)
$P$ : pressure (5.985)
$Y$ : state (5.840)
$t$ : time (4.645)
$p$ : pressure (4.500)
$B$ : state (3.565)
${\displaystyle V_{b))$ : volume (3.523)
${\displaystyle V_{a))$ : volume (3.438)
${\displaystyle V_{c))$ : volume (2.761)
$W$ : work (thermodynamics) (2.735)
$a$ : energy (2.562)
$A$ : state (1.937)
$X$ : arbitrary state (1.907)
${\displaystyle V_{d))$ : volume (1.902)
${\displaystyle t_{1))$ : time (1.816)
$M$ : molar mass (1.779)
$q$ : heat (1.723)
$u'$ : mass (1.688)
$d$ : exact differential (1.621)
$E$ : total energy (1.574)
${\displaystyle U_{2))$ : new system (1.476)

Combinatorics

Graph theory

Category information

reference category: Graph theory
code: 05Cxx (MSC)
wiki categories: [(Category:Graph theory, 14), (Category:Graph theory objects, 6), (Category:Graph invariants, 5)]

Cluster information:

cluster id: [758, 3372, 3998, 5175, 6657]
matching score: 0.462997559186
purity: 1.0
matching keywords: [u'perfect', u'paths', u'isomorphism', u'degree', u'hamiltonian', u'combinatorics', u'graph', u'topological', u'graphs', u'connectivity', u'coloring', u'algorithms', u'geometric', u'cycles', u'matrices']

Definitions:

$n$ : vertices (19.811)
$a$ : graph (mathematics) (18.075)
$G$ : glossary of graph theory (17.852)
$k$ : complete graph (15.524)
$K$ : complete bipartite graph (9.558)
$v$ : vertex (graph theory) (8.425)
$u$ : vertices (7.720)
$A$ : cycle graph (7.051)
$B$ : series (7.009)
$H$ : glossary of graph theory (6.870)
$m$ : edges (5.725)
${\displaystyle v_{i))$ : vertex (5.393)
${\displaystyle K_{n))$ : complete graph (3.913)
$d$ : degree (graph theory) (3.842)
$i$ : color (3.635)
$f$ : graph isomorphism (3.485)
$e$ : edge (2.776)
${\displaystyle N_{i))$ : neighbourhood (graph theory) (2.731)
$w$ : edges (2.486)
$W$ : graph (2.441)
${\displaystyle k_{i))$ : vertices (2.221)
$V$ : vertices (1.950)
$C$ : vertex cover (1.939)
$r$ : complexity (1.939)
${\displaystyle K_{6))$ : graph (1.937)
$O$ : running time (1.866)
$X$ : finite set (1.848)
$Q$ : sequence (1.847)
${\displaystyle v_{j))$ : vertex (1.816)
${\displaystyle m_{2))$ : first color (1.779)
${\displaystyle e_{ij))$ : vertex (1.712)
$E$ : edges (1.708)
${\displaystyle W_{n))$ : wheel graph (1.690)
$F$ : graph (1.687)
${\displaystyle K_{n,n))$ : chromatic number (1.659)
$c$ : vertex (1.657)
$\phi$ : chromatic roots (1.524)

Computer science

Theory of data

Category information

reference category: Theory of data
code: 68Pxx (MSC)
wiki categories: [(Category:Information theory, 7), (Category:Statistical theory, 6), (Category:Theoretical computer science, 5)]

Cluster information:

cluster id: [5498, 7294, 8316]
matching score: 0.338922814986
purity: 1.0
matching keywords: [u'information', u'science', u'coding', u'computer', u'communication', u'data']

Definitions:

$R$ : rate (7.323)
$n$ : length (7.223)
${\mathcal {C))$ : code (6.108)
$m$ : message (5.399)
$d$ : minimum distance (5.171)
$C$ : code (4.310)
$X$ : random variable (3.685)
$y$ : word (3.630)
$\delta$ : relative distance (3.555)
$q$ : arbitrary probability distribution (3.494)
$p$ : probability distribution (3.484)
$k$ : message length (3.372)
$a$ : information (3.253)
$e$ : radius (2.926)
$H$ : entropy (2.889)
$T$ : temperature (2.776)
$\Sigma$ : alphabet (2.670)
$x$ : conditional probability (2.650)
$f$ : likelihood function (2.604)
$c$ : codeword (2.406)
$Y$ : entropy (2.288)
$g$ : function (1.974)
${\displaystyle c_{1))$ : codewords (1.939)
$B$ : estimator (1.891)
$M$ : codewords (1.882)
$h$ : function (1.858)
${\displaystyle c_{2))$ : codewords (1.754)
${\displaystyle C_{i))$ : code (1.659)
$L$ : code (1.563)
$S$ : nformation (1.524)

Discrete mathematics in relation to computer science

Category information

reference category: Discrete mathematics in relation to computer science
code: 68Rxx (MSC)
wiki categories: [(Category:Theoretical computer science, 5), (Category:Mathematical science occupations, 3), (Category:Fields of finance, 3)]

Cluster information:

cluster id: [2172, 7093, 8197]
matching score: 0.349110770367
purity: 1.0
matching keywords: [u'computer', u'words', u'mathematics', u'combinatorics', u'science']

Definitions:

$a$ : context-sensitive grammar (7.034)
$t$ : time (4.738)
$g$ : convex function (3.659)
$f$ : function (3.656)
$n$ : function (3.172)
$\mathbf {x}$ : tuple (1.891)
$k$ : tuple (1.817)
$S$ : successor function (1.791)
$O$ : nspace (1.754)
$h$ : induction step (1.738)
${\displaystyle A_{t))$ : acceptance set (1.609)
$v$ : middle term (1.587)
$A$ : natural numbers (1.495)

Artificial intelligence

Category information

reference category: Artificial intelligence
code: 68Txx (MSC)
wiki categories: [(Category:Fields of mathematics, 3), (Category:Calculus, 2), (Category:Mathematical analysis, 2)]

Cluster information:

cluster id: [2670]
matching score: 0.243265095288
purity: 1.0
matching keywords: [u'solving', u'knowledge', u'intelligence', u'processing', u'artificial', u'systems', u'uncertainty', u'representation', u'science']

Definitions:

$\mathbf {R}$ : linear map (2.767)
$a$ : function (2.561)
$f$ : function (2.550)
$n$ : commodities (2.492)
$j$ : functions (2.481)
${\displaystyle p_{i))$ : time (2.250)
$U$ : cardinal (1.845)
$S$ : state (1.812)
$x$ : differential d (1.761)
$I$ : functions (1.719)
$y$ : derivative (1.707)
$m$ : jacobian matrix (1.664)
$M$ : state diagram (1.594)
$t$ : input variables (1.583)
$p$ : functions (1.430)

Computing methodologies and applications

Category information

reference category: Computing methodologies and applications
code: 68Uxx (MSC)
wiki categories: [(Category:Computer graphics, 6), (Category:Computer vision, 6), (Category:Image processing, 6)]

Cluster information:

cluster id: [831, 1622]
matching score: 0.402364510194
purity: 1.0
matching keywords: [u'mathematical', u'geometry', u'image', u'processing', u'computer', u'graphics']

Definitions:

$t$ : scale (6.939)
$s$ : integration scale parameter (4.427)
$A$ : binary image (3.724)
$v$ : direction (3.608)
$L$ : scale space (3.602)
$E$ : origin (3.496)
$B$ : structuring element (3.477)
$b$ : grayscale dilation (3.282)
$d$ : dimension (2.961)
$f$ : grayscale dilation (2.850)
$x$ : matrix (2.815)
${\displaystyle X_{i))$ : collection (2.685)
${\displaystyle \sigma _{I))$ : scale (2.560)
$\mathbb {R}$ : euclidean space (2.214)
$R$ : euclidean space (1.974)
$r$ : radius (1.950)
$N$ : dimensions (1.939)
${\displaystyle L_{v))$ : direction (1.902)
$\varepsilon$ : erosion (1.902)
$k$ : dimensional ridge (1.900)
$\mu$ : matrix (1.847)
${\displaystyle \Sigma _{D))$ : covariance matrices (1.810)
${\displaystyle I_{y))$ : partial derivatives (1.790)
$z$ : translation (1.790)
${\displaystyle \Sigma _{I))$ : covariance matrices (1.781)
$\delta$ : dilation (1.781)
$I$ : image (1.690)
$\mathbf {x}$ : direction (1.641)
${\displaystyle \mathbf {x} _{0))$ : tangent lines (1.621)
$a$ : dilation (1.618)
$\gamma$ : square (1.581)
${\displaystyle \lambda _{2))$ : positive value (1.563)
${\displaystyle I_{x))$ : partial derivatives (1.524)
$n$ : pixels (1.488)

Algorithms

Category information

reference category: Algorithms
code: 68Wxx (MSC)
wiki categories: [(Category:Algorithms, 3), (Category:Algebra, 2), (Category:Computational science, 2)]

Cluster information:

cluster id: [6563]
matching score: 0.397769173482
purity: 1.0
matching keywords: [u'algebraic', u'computer', u'algorithms', u'analysis', u'science']

Definitions:

$a$ : sequence (4.369)
$k$ : multiplicity (1.974)
${\displaystyle \mathbb {F} _{q))$ : finite field (1.891)
$s$ : tuple (1.864)
$b$ : real numbers (1.810)
$p$ : polynomial (1.800)

Computing methodologies

Machine learning

Category information

reference category: Machine learning
code: NO_CODE (ACM)
wiki categories: [(Category:Machine learning, 6), (Category:Computational learning theory, 3), (Category:Theoretical computer science, 3)]

Cluster information:

cluster id: [4551, 8206]
matching score: 0.649404202935
purity: 1.0
matching keywords: [u'kernel', u'regularization', u'statistical', u'classification', u'support', u'analysis', u'machine', u'vector', u'algorithms', u'learning', u'ensemble', u'machines']

Definitions:

$C$ : concept class (7.638)
$c$ : concept (3.624)
$X$ : concept class (3.183)
${\displaystyle D_{t))$ : distribution (2.707)
${\displaystyle h_{t))$ : classifier (1.939)
$S$ : partial approximation (1.902)
${\displaystyle y_{i))$ : labels (1.845)
${\displaystyle D_{t+1))$ : probability distribution (1.781)
${\mathcal {H))$ : loss function (1.688)

Differential geometry

Classical differential geometry

Category information

reference category: Classical differential geometry
code: 53Axx (MSC)
wiki categories: [(Category:Differential geometry, 5), (Category:Differential equations, 3), (Category:Topology, 3)]

Cluster information:

cluster id: [6805, 9370]
matching score: 0.477953735166
purity: 1.0
matching keywords: [u'surfaces', u'objects', u'classical', u'geometry', u'geometric', u'differential', u'analysis']

Definitions:

$a$ : differentiable manifold (5.972)
$f$ : function (3.502)
$G$ : structure group (2.961)
$i$ : lower-case index (2.810)
$h$ : scalar functions (2.571)
$d$ : − div (2.514)
$E$ : fiber (2.435)
$S$ : gaussian curvature (2.339)
$X$ : vector field (1.939)
$x$ : coordinate system (1.889)
$k$ : rational number (1.865)
$F$ : fiber (1.823)
$p$ : particular point (1.816)
${\displaystyle \Delta _{\xi ))$ : laplace (1.754)
$K$ : gaussian curvature (1.688)
$B$ : continuous (topology) (1.632)
$H$ : infinite area (1.628)
$\mathbf {R}$ : unit sphere (1.591)
$n$ : unit sphere (1.583)

Dynamical systems and ergodic theory

Applications

Category information

reference category: Applications
code: 37Nxx (MSC)
wiki categories: [(Category:Dynamical systems, 8), (Category:Functions and mappings, 4), (Category:Physical systems, 4)]

Cluster information:

cluster id: [2297, 8165, 9135]
matching score: 0.330787405056
purity: 1.0
matching keywords: [u'mechanics', u'control', u'meteorology', u'branches', u'dynamical', u'solid', u'economics', u'analysis', u'optimization', u'systems', u'quantum', u'physics']

Definitions:

$V$ : volume (6.980)
$U$ : internal energy (2.749)
$T$ : absolute temperature (2.678)
$R$ : gas constant (2.595)
$P$ : pressure (2.570)
$f$ : proper convex function (2.450)
$i$ : volume (1.865)
$m$ : volume (1.865)
$X$ : vector space (1.858)
$\nu$ : specific volume (1.779)
$n$ : volume (1.756)
$p$ : pressure (1.752)
${\displaystyle P_{tot))$ : partial pressure (1.726)
${\displaystyle P_{x))$ : gas mixture (1.717)
$a$ : chaotic behavior (1.632)

ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS

Acoustics

Category information

reference category: Acoustics
code: 43.00.00 (PACS)
wiki categories: [(Category:Physical quantities, 4), (Category:Acoustics, 4), (Category:Sound measurements, 4)]

Cluster information:

cluster id: [5274]
matching score: 0.456310006196
purity: 1.0
matching keywords: [u'sound', u'mechanics', u'acoustics', u'dynamics', u'measurements', u'fluid', u'physical']

Definitions:

$a$ : wave (6.764)
$v$ : particle velocity (2.677)
$I$ : sound intensity (2.593)
$r$ : distance (2.524)
$E$ : sound energy density (2.473)
$f$ : frequency (1.882)
$m$ : metre (1.876)
$W$ : watt (1.865)
${\displaystyle r_{1))$ : sound intensity (1.790)
$A$ : area (1.787)
${\displaystyle I_{2))$ : sound intensity (1.779)
$\mathbf {I}$ : acoustic intensity (1.591)
$w$ : density (1.441)

Classical mechanics of discrete systems

Category information

reference category: Classical mechanics of discrete systems
code: 45.00.00 (PACS)
wiki categories: [(Category:Physics, 16), (Category:Mechanics, 14), (Category:Classical mechanics, 14)]

Cluster information:

cluster id: [5683, 6742, 8032, 8640, 8940]
matching score: 0.314862814041
purity: 1.0
matching keywords: [u'mechanics', u'computational', u'power', u'energy', u'fluid', u'celestial', u'rigid', u'dynamics', u'newtonian', u'classical', u'system', u'motion', u'conservation', u'kinematics', u'momentum', u'forces', u'mechanical', u'bodies']

Definitions:

$\mathbf {F}$ : force (21.736)
$m$ : mass (21.105)
$\mathbf {v}$ : velocity (21.053)
$t$ : time (17.001)
$\mathbf {p}$ : momentum (14.082)
$\mathbf {L}$ : angular momentum (13.398)
$i$ : particle (12.579)
$\mathbf {a}$ : acceleration (12.473)
$\mathbf {r}$ : position (vector) (10.802)
$I$ : moment of inertia (10.035)
$E$ : kinetic energy (7.861)
$\mathbf {V}$ : velocity (7.840)
$v$ : effective exhaust velocity (7.699)
$a$ : rigid body (7.097)
$r$ : distance (6.877)
$j$ : particle (4.549)
$x$ : direction vector (4.526)
$M$ : mass (4.464)
$u$ : velocity (4.380)
$V$ : volume integral (3.731)
$\mathbf {u}$ : velocity (3.661)
$N$ : particles (3.660)
$\mathbf {I}$ : moment of inertia tensor (3.635)
$\mathbf {S}$ : angular momentum (3.633)
$\mathbf {e}$ : unit vector (3.626)
$\mathbf {A}$ : acceleration (3.595)
$\mathbf {C}$ : center of mass (3.583)
$d$ : magnitude (3.565)
$s$ : displacement (vector) (3.565)
$c$ : speed of light (3.394)
$T$ : rotation (3.369)
$U$ : kinetic energy (3.316)
$\omega$ : angular velocity (2.869)
$L$ : length (2.771)
$P$ : pivot point (2.728)
$\mathbf {g}$ : gravitational acceleration (2.725)
$\mathbf {n}$ : unit vector (2.682)
$Q$ : rotation matrix (2.670)
$\mathbf {q}$ : generalized coordinates (2.627)
$k$ : spring (2.602)
$\mathbf {R}$ : reference point (2.597)
$G$ : gravitational constant (2.587)
$F$ : force (2.575)
$g$ : local acceleration (2.543)
$q$ : electric charge (2.467)
$K$ : body (2.292)
$C$ : curved path (1.950)
$\phi$ : angle (1.950)
$\mathbf {t}$ : unit vector (1.907)
$f$ : frequency (1.882)
${\displaystyle m_{i))$ : masses (1.882)
$W$ : total work (1.881)
$S$ : frame (1.872)
$B$ : skew-symmetric matrix (1.865)
${\displaystyle I_{C))$ : mass (1.865)
${\displaystyle \mathbf {\hat {e)) _{r))$ : rotation (1.852)
${\displaystyle \mathbf {\hat {e)) _{\theta ))$ : unit vector (1.845)
$\mathbf {W}$ : weight (1.833)
${\displaystyle {\hat {u))_{R))$ : unit vector (1.789)
$\mathbf {J}$ : orbital (1.752)
$y$ : direction vector (1.749)
$A$ : moment (1.744)
$\mathbf {D}$ : electric field (1.724)
${\displaystyle \mathbf {r} _{1))$ : torque (1.724)
${\displaystyle m_{B))$ : body (1.718)
$\mathbf {x}$ : initial positions (1.718)
$\mathbf {P}$ : canonical momentum (1.714)
$\mathbf {M}$ : torque (1.701)
$n$ : similar objects (1.664)
${\displaystyle r_{z))$ : momentum operator (1.591)
$p$ : potential energy (1.576)
$R$ : polar coordinate system (1.540)
${\displaystyle {\hat {u))_{\theta ))$ : direction (1.439)

Continuum mechanics of solids

Category information

reference category: Continuum mechanics of solids
code: 46.00.00 (PACS)
wiki categories: [(Category:Mechanics, 3), (Category:Materials science, 3), (Category:Continuum mechanics, 3)]

Cluster information:

cluster id: [2450]
matching score: 0.54066037904
purity: 1.0
matching keywords: [u'mechanics', u'continuum', u'classical', u'plasticity']

Definitions:

$\Omega$ : surface (5.460)
$t$ : time (4.609)
$\mathbf {X}$ : position vector (4.360)
${\boldsymbol {S))$ : vector field (2.791)
$\rho$ : material time derivative (2.755)
${\dot {e))$ : material time derivative (2.661)
$\mathbf {x}$ : position (2.652)
$e$ : material time derivative (2.638)
$s$ : flux (2.603)
$\mathbf {v}$ : velocity (2.583)
$\mathbf {q}$ : heat (2.548)
$\chi$ : mapping function (1.939)
$\mathbf {n}$ : normal vector (1.939)
${\displaystyle \mathbf {F} _{C))$ : surface forces (1.937)
$S$ : internal surface area (1.891)
$\lambda$ : shear viscosity (1.845)
${\displaystyle \mathbf {F} _{B))$ : body forces (1.816)
${\dot {\mathbf {v} ))$ : particle velocity (1.813)
$\mathbf {u}$ : particle (1.790)
${\displaystyle \varepsilon _{e))$ : elastic strain (1.779)
$T$ : unit mass (1.766)
${\dot {\rho ))$ : material time derivative (1.766)
${\displaystyle u_{n))$ : velocity (1.745)
$\eta$ : region (1.689)
$a$ : continuum (1.662)
${\displaystyle \mathbf {e} _{i))$ : components (1.640)
$X$ : position vector (1.591)

Field theory and polynomials

Differential and difference algebra

Category information

reference category: Differential and difference algebra
code: 12Hxx (MSC)
wiki categories: [(Category:Abstract algebra, 31), (Category:Ring theory, 20), (Category:Algebra, 18)]

Cluster information:

cluster id: [2012, 2090, 3378, 3397, 5021, 5579, 6946, 7439, 8428]
matching score: 0.422155362999
purity: 1.0
matching keywords: [u'field', u'algebra', u'abstract', u'differential', u'polynomials']

Definitions:

$x$ : polynomial (17.140)
$R$ : module (mathematics) (16.749)
$a$ : field (mathematics) (15.345)
$F$ : field (mathematics) (13.594)
$K$ : local field (12.146)
$M$ : module (11.938)
$A$ : frobenius algebra (11.268)
$L$ : extension field (10.984)
$n$ : degree (10.686)
$V$ : vector space (9.943)
$p$ : finite field (8.287)
$N$ : length (6.994)
$D$ : division algebra (6.752)
$\mathbf {Z}$ : module (6.405)
$\mathbf {C}$ : complex number (6.386)
$T$ : field (6.032)
$v$ : valuation (5.397)
$k$ : field (5.381)
$\mathbf {Q}$ : local field (5.259)
$E$ : field (5.180)
$\mathbf {H}$ : quaternion (4.593)
$\mathbf {R}$ : real number (4.559)
$Q$ : linear operator (4.474)
$\mathbf {K}$ : field (3.587)
$I$ : submodule (3.572)
$G$ : field (mathematics) (3.566)
$t$ : form (3.528)
$X$ : polynomial (3.462)
$S$ : symmetric matrix (3.432)
$u$ : generating set of a group (3.420)
$W$ : basis (3.326)
$\mathbf {t}$ : matrix (2.799)
$j$ : column (2.450)
$f$ : polynomial (2.435)
$q$ : polynomial sequence (2.398)
$P$ : quadratic polynomial (1.904)
$s$ : polynomials (1.900)
$\mathbf {a}$ : sequence (1.891)
$B$ : symmetric bilinear form (1.882)
$m$ : maximal ideal (1.790)
$i$ : quotient ring (1.774)
$H$ : character module (1.757)
$g$ : polynomial (1.757)
$\mathbb {Z}$ : subgroup (1.738)
$r$ : roots (1.714)
$\Gamma$ : segment (1.691)
$Y$ : univariate polynomial (1.681)
${\displaystyle a_{i))$ : weight (1.659)
${\displaystyle \mathbb {Z} _{p))$ : valuation ring (1.657)
$\mathbf {f}$ : basis (1.657)
$and$ : difference operator (1.640)
$\mathbf {F}$ : hyperreal number (1.556)
$\mathbf {y}$ : coordinate tuples (1.530)

Fluid mechanics

Foundations, constitutive equations, rheology

Category information

reference category: Foundations, constitutive equations, rheology
code: 76Axx (MSC)
wiki categories: [(Category:Non-Newtonian fluids, 7), (Category:Liquids, 7), (Category:Fluid mechanics, 7)]

Cluster information:

cluster id: [3030, 5890]
matching score: 0.53559712298
purity: 1.0
matching keywords: [u'mechanics', u'classical', u'fluids', u'fluid']

Definitions:

$t$ : time (4.699)
${\displaystyle t_{1))$ : time (3.889)
$E$ : young's modulus (3.349)
${\displaystyle \sigma _{0))$ : stress (1.974)
$\eta$ : viscosity (1.882)
$\lambda$ : time (1.865)
${\dot {\gamma ))$ : shear rate (1.845)
${\displaystyle \sigma _{\mathrm {Total} ))$ : total stress (1.845)
$\varepsilon$ : strain rate (1.786)
$G''$ : storage modulus (1.724)
$a$ : stress (physics) (1.651)

Turbulence

Category information

reference category: Turbulence
code: 76Fxx (MSC)
wiki categories: [(Category:Fluid dynamics, 3), (Category:Physics, 2), (Category:Aerodynamics, 2)]

Cluster information:

cluster id: [5342]
matching score: 0.407243228585
purity: 1.0
matching keywords: [u'mechanics', u'dynamical', u'turbulence', u'aerodynamics', u'fluid', u'transport', u'systems']

Definitions:

$\mathbf {u}$ : velocity (1.974)
$\varepsilon$ : energy dissipation (1.902)
$\mathbf {V}$ : diffusive body-vortex interaction fluid velocity (1.866)
${\displaystyle C_{n))$ : constants (1.847)
$d$ : diffusion velocity (1.845)
$r$ : characteristic length (1.784)
$\nu$ : kinematic viscosity (1.779)
$\Pi$ : fluxes (1.610)
$\mathbf {r}$ : diffusive body-vortex interaction fluid velocity (1.591)
$L$ : large scales (1.556)
$\mathbf {k}$ : fourier (1.556)

Compressible fluids and gas dynamics, general

Category information

reference category: Compressible fluids and gas dynamics, general
code: 76Nxx (MSC)
wiki categories: [(Category:Gases, 4), (Category:Thermodynamics, 3), (Category:Gas technologies, 3)]

Cluster information:

cluster id: [1166]
matching score: 0.381402182058
purity: 1.0
matching keywords: [u'mechanics', u'dynamics', u'gas', u'fluid']

Definitions:

$V$ : volume (6.958)
$T$ : temperature (5.072)
$P$ : pressure (4.230)
$n$ : volume (3.550)
$R$ : universal gas constant (2.685)
$Z$ : compressibility factor (1.854)
$p$ : pressure (1.821)
$k$ : heat capacity ratio (1.810)
$a$ : volume (1.623)

Biological fluid mechanics

Category information

reference category: Biological fluid mechanics
code: 76Zxx (MSC)
wiki categories: [(Category:Fluid mechanics, 6), (Category:Fluid dynamics, 5), (Category:Dynamics, 5)]

Cluster information:

cluster id: [3743, 6074]
matching score: 0.590251215805
purity: 1.0
matching keywords: [u'mechanics', u'fluid']

Definitions:

$\eta$ : dynamic viscosity (2.483)
$L$ : surface tension (1.816)
$\nu$ : viscosity (1.805)
$\rho$ : density (1.805)
$r$ : stokes radius (1.641)
$\mathrm {Pr}$ : momentum diffusivity (1.600)

Fourier analysis

Fourier analysis in several variables

Category information

reference category: Fourier analysis in several variables
code: 42Bxx (MSC)
wiki categories: [(Category:Fourier analysis, 7), (Category:Signal processing, 5), (Category:Mathematical analysis, 5)]

Cluster information:

cluster id: [719, 2145, 5631]
matching score: 0.473693116456
purity: 1.0
matching keywords: [u'function', u'functions', u'series', u'harmonic', u'analysis', u'transforms', u'fourier']

Definitions:

$f$ : function (7.003)
$a$ : periodic function (6.900)
$\Gamma$ : reciprocal lattice (4.226)
$\Lambda$ : reciprocal lattice (3.473)
$g$ : integrable function (2.707)
$T$ : operator (2.660)
$L$ : norm (2.610)
${\displaystyle \nu _{x))$ : borel measure (1.939)
$x$ : weight vector (1.939)
$A$ : hexagonal sampling lattice (1.891)
$C$ : operator (1.882)
$\ell$ : norm (1.865)
$R$ : flip operator (1.847)
$N$ : samples (1.846)
$t$ : time (1.811)
${\displaystyle {\hat {f))_{s))$ : spectrum (1.704)
$\mathbf {LombScarglemethod}$ : lomb (1.657)
${\displaystyle v_{i))$ : matrix (1.657)
${\displaystyle \omega _{0))$ : dominant component (1.645)
$u$ : figure (1.625)
$w$ : window (1.562)

Functional analysis

Nonlinear functional analysis

Category information

reference category: Nonlinear functional analysis
code: 46Txx (MSC)
wiki categories: [(Category:Functional analysis, 3), (Category:Operator theory, 2), (Category:Theoretical physics, 2)]

Cluster information:

cluster id: [1]
matching score: 0.411485246068
purity: 1.0
matching keywords: [u'analysis', u'spaces', u'nonlinear', u'manifolds', u'functional']

Definitions:

$a$ : bounded linear operator (6.085)
$H$ : hilbert (4.995)
$\mathbf {H}$ : space (2.869)
$E$ : banach (2.688)
$\mathbf {T}$ : operator (2.641)
$C$ : class (2.604)
$i$ : subset (2.565)
$U$ : bounded linear operator (2.450)
${\displaystyle H_{i))$ : space (1.950)
$K$ : space (1.937)
$D$ : diagonal matrix (1.762)
$V$ : complex number (1.732)
$r$ : class (1.719)
$y$ : vector space (1.700)
$e$ : span (1.641)

Functions of a complex variable

Miscellaneous topics of analysis in the complex domain

Category information

reference category: Miscellaneous topics of analysis in the complex domain
code: 30Exx (MSC)
wiki categories: [(Category:Complex analysis, 7), (Category:Theorems in complex analysis, 3), (Category:Theorems in analysis, 3)]

Cluster information:

cluster id: [2838, 9700]
matching score: 0.395941949552
purity: 1.0
matching keywords: [u'analytic', u'functions', u'complex', u'analysis']

Definitions:

$f$ : analytic function (7.907)
$a$ : holomorphic function (7.846)
$D$ : holomorphic function (4.860)
$\mathbf {C}$ : complex plane (2.845)
$\gamma$ : curve (1.974)
$z$ : zero (1.900)
$K$ : kernel (1.812)
${\displaystyle f_{c))$ : critical point (mathematics) (1.762)
$c$ : change (1.623)
$n$ : iterated function (1.598)

GEOPHYSICS, ASTRONOMY, AND ASTROPHYSICS

Solid Earth physics

Category information

reference category: Solid Earth physics
code: 91.00.00 (PACS)
wiki categories: [(Category:Subfields of geology, 4), (Category:Seismology, 4), (Category:Seismology measurement, 4)]

Cluster information:

cluster id: [1041]
matching score: 0.294063392018
purity: 1.0
matching keywords: [u'attenuation', u'geophysics', u'seismology', u'geology', u'solid', u'earth', u'physics']

Definitions:

$a$ : book (2.563)
$w$ : attenuation (1.659)

Hydrospheric and atmospheric geophysics

Category information

reference category: Hydrospheric and atmospheric geophysics
code: 92.00.00 (PACS)
wiki categories: [(Category:Chemistry, 9), (Category:Chemical properties, 6), (Category:Analytical chemistry, 4)]

Cluster information:

cluster id: [212, 1751, 7409]
matching score: 0.241404318401
purity: 1.0
matching keywords: [u'mechanics', u'biology', u'analysis', u'chemical', u'mixing', u'analytical', u'chemistry', u'physics', u'properties', u'physical']

Definitions:

${\displaystyle m_{i))$ : mass (9.619)
$V$ : volume (6.751)
${\displaystyle n_{i))$ : constituent (6.485)
${\displaystyle w_{i))$ : mass fraction (chemistry) (5.721)
${\displaystyle \rho _{i))$ : mass concentration (chemistry) (5.470)
${\displaystyle M_{i))$ : molar mass (5.278)
$M$ : molar mass (4.941)
${\displaystyle x_{i))$ : mole fraction (4.898)
${\displaystyle c_{i))$ : molar concentration (4.784)
$\rho$ : density (3.584)
$i$ : molar mass (3.448)
$a$ : host (2.707)
${\displaystyle \zeta _{i))$ : mass ratio (2.699)
$A$ : nucleus (2.649)
$\mathbf {A}$ : adt matrix (2.619)
${\displaystyle V_{i))$ : volume (2.585)
$B$ : binding (2.561)
${\displaystyle N_{i))$ : constituent (1.950)
$m$ : elec (1.942)
$\Gamma$ : contour (1.939)
${\displaystyle r_{i))$ : mole ratio (1.937)
$T_{\textrm {n))$ : matrix elements (1.900)
$\alpha$ : reference temperature (1.900)
${\displaystyle \chi _{k))$ : electronic wave functions (1.891)
$\mathbf {R}$ : positions (1.812)
$\gamma$ : angle (1.811)
${\displaystyle b_{i))$ : molality (1.793)
$c$ : equation (1.744)
$t$ : equation (1.712)
${\displaystyle m_{\mathrm {tot} ))$ : mass ratio (1.665)
$e$ : nuclear positions (1.653)
$\mathbf {r}$ : integration (1.497)

Physics of the ionosphere and magnetosphere

Category information

reference category: Physics of the ionosphere and magnetosphere
code: 94.00.00 (PACS)
wiki categories: [(Category:Physics, 4), (Category:Astrophysics, 3), (Category:Plasma physics, 3)]

Cluster information:

cluster id: [2908]
matching score: 0.289974051297
purity: 1.0
matching keywords: [u'motion', u'systems', u'astrophysics', u'plasma', u'dynamics', u'physics', u'experimental']

Definitions:

$B$ : magnetic field (3.422)
$m$ : mass (3.315)
$\mathbf {u}$ : average velocity (2.725)
$q$ : magnetic field (2.657)
${\vec {r))$ : momentum (2.555)
${\displaystyle r_{g))$ : gyroradius (2.434)
$\alpha$ : species (1.974)
$n$ : particle density (1.902)
$t$ : time (1.891)
$R$ : gyroradius (1.845)
$\rho$ : electric potential (1.797)
$v$ : velocity component (1.723)
${\displaystyle m_{\alpha ))$ : mass (1.677)
${\vec {v))$ : velocity vector (1.621)

Stars

Category information

reference category: Stars
code: 97.00.00 (PACS)
wiki categories: [(Category:Astronomical catalogues, 31), (Category:Constellations, 31), (Category:Bayer objects, 27)]

Cluster information:

cluster id: [1182, 4734, 4891, 5812, 7129, 8964, 9590]
matching score: 0.604734859715
purity: 1.0
matching keywords: [u'planetary', u'planets', u'sequence', u'variables', u'degenerate', u'proper', u'multiple', u'ceti', u'spectral', u'binary', u'giant', u'cygni', u'systems', u'stars', u'white', u'majoris', u'star', u'dwarf', u'spectroscopic', u'beta', u'objects', u'variable', u'alpha', u'class', u'types', u'supernovae', u'g', u'luminosity', u'lyrae', u'cataclysmic', u'binaries']

Definitions:

$a$ : star (43.305)
$R$ : radius (31.929)
${\displaystyle T_{\mathrm {eff} ))$ : radius (3.705)
$\sigma$ : effective surface temperature (3.705)
$L$ : luminosity (3.484)
$T$ : tauri (1.939)
${\displaystyle V_{t))$ : radial velocity (1.845)

Game theory, economics, social and behavioral sciences

Mathematical economics

Category information

reference category: Mathematical economics
code: 91Bxx (MSC)
wiki categories: [(Category:Consumer theory, 5), (Category:Consumerism, 4), (Category:Economic theories, 4)]

Cluster information:

cluster id: [3248, 9819]
matching score: 0.438017007388
purity: 1.0
matching keywords: [u'mathematical', u'decision', u'economics', u'monetary', u'economic', u'behavior', u'demand', u'consumer', u'utility']

Definitions:

${\displaystyle c_{0))$ : total consumption (5.700)
$u$ : utility (4.233)
$a$ : consumption function (3.336)
$i$ : change (2.977)
$w$ : income (2.868)
$C$ : total consumption (2.850)
${\displaystyle c_{1))$ : marginal propensity to consume (2.685)
$p$ : price level (1.926)
${\bar {u))$ : utility level (1.847)
$Y$ : payments (1.790)
${\displaystyle Y_{d))$ : disposable income (1.779)

Other social and behavioral sciences (mathematical treatment)

Category information

reference category: Other social and behavioral sciences (mathematical treatment)
code: 91Fxx (MSC)
wiki categories: [(Category:Gaming, 3), (Category:Formal sciences, 3), (Category:Decision theory, 3)]

Cluster information:

cluster id: [8680]
matching score: 0.402049421229
purity: 1.0
matching keywords: [u'mathematical', u'sciences', u'game', u'economics']

Definitions:

$i$ : player (9.955)
$D$ : player (5.852)
$j$ : machine (4.463)
$N$ : players (3.651)
$k$ : machine (2.768)
${\displaystyle f_{\Gamma ,R))$ : flow (2.672)
$A$ : strategy (2.501)
$a$ : solution concept (1.887)
$f$ : flow (1.848)
${\displaystyle T_{i))$ : type (1.810)
${\displaystyle A_{i))$ : action (1.688)
$G$ : flows (1.677)
${\displaystyle S_{i))$ : player (1.677)
$U$ : player (1.588)
${\displaystyle s_{i))$ : paths (1.471)

General topology

Generalities

Category information

reference category: Generalities
code: 54Axx (MSC)
wiki categories: [(Category:General topology, 3), (Category:Topology, 3), (Category:Mathematical structures, 2)]

Cluster information:

cluster id: [3399]
matching score: 0.474817002951
purity: 1.0
matching keywords: [u'general', u'structures', u'topology']

Definitions:

$a$ : topological space (7.000)
$X$ : topological space (5.935)
$\mathbf {R}$ : subspace (4.260)
$B$ : basis (topology) (4.164)
$S$ : subset (3.527)
$f$ : function (2.695)
$A$ : subspace (2.674)
$T$ : topology (2.642)
$i$ : continuous (topology) (2.562)
$Z$ : topological space (1.882)
$Y$ : subspace topology (1.744)
$b$ : rational number (1.702)

Geometry

Analytic and descriptive geometry

Category information

reference category: Analytic and descriptive geometry
code: 51Nxx (MSC)
wiki categories: [(Category:Quadrilaterals, 3), (Category:Analytic geometry, 3), (Category:Geometric shapes, 3)]

Cluster information:

cluster id: [4774, 6224]
matching score: 0.494281227371
purity: 1.0
matching keywords: [u'geometry', u'analytic', u'physics', u'euclidean']

Definitions:

$a$ : plane curve (8.757)
$T$ : tangent (7.168)
$C$ : plane curve (6.130)
$A$ : tangential trapezoid (5.174)
$K$ : area (4.535)
$b$ : bases (3.051)
$x$ : =-lrb- (2.855)
$\psi$ : vertex angle (2.573)
$f$ : polar coordinate system (2.550)
$P$ : pedal point (2.531)
$c$ : consecutive sides (2.527)
$\theta$ : polar angle (1.878)
$O$ : distance (1.824)
$q$ : lengths (1.790)
$n$ : specific values (1.774)
$R$ : curve (1.714)
$G$ : side (1.657)
$y$ : =-lrb- (1.600)
$h$ : height (1.598)
$p$ : perpendicular distance (1.585)
$r$ : polar coordinate system (1.576)
$X$ : tangent (1.562)

Group theory and generalizations

Connections with homological algebra and category theory

Category information

reference category: Connections with homological algebra and category theory
code: 20Jxx (MSC)
wiki categories: [(Category:Group theory, 10), (Category:Abstract algebra, 7), (Category:Metric geometry, 6)]

Cluster information:

cluster id: [4138, 5935, 8793]
matching score: 0.379961219218
purity: 1.0
matching keywords: [u'group', u'groups', u'algebra', u'cohomology']

Definitions:

$G$ : group action (7.766)
$a$ : cyclic group (6.241)
$H$ : normal subgroup (5.197)
$N$ : normal subgroup (4.376)
$p$ : order (4.137)
$A$ : complement (group theory) (3.460)
$L$ : field (2.800)
$n$ : order (1.950)
$V$ : basis (linear algebra) (1.865)
$u$ : generator (1.781)
$K$ : field extension (1.722)
$c$ : factor system (1.714)
$g$ : basis (1.623)

Hardware

Power and energy

Category information

reference category: Power and energy
code: NO_CODE (ACM)
wiki categories: [(Category:Electronic engineering, 6), (Category:Electronic circuits, 5), (Category:Electrical engineering, 5)]

Cluster information:

cluster id: [1337, 2980, 4546, 9432]
matching score: 0.282528098133
purity: 1.0
matching keywords: [u'power', u'circuits', u'communication', u'energy', u'processing', u'hardware', u'design', u'systems', u'digital', u'distribution', u'signal', u'analog']

Definitions:

$Z$ : electrical impedance (8.909)
$Y$ : shunt (7.073)
$\mathbf {r}$ : position (6.383)
$N$ : charges (5.442)
$q$ : test charge (5.062)
$L$ : filter half-section (4.865)
$U$ : electric potential energy (4.738)
${\displaystyle Q_{i))$ : electric charge (4.681)
$Q$ : test charge (4.450)
$\mathbf {E}$ : electric field (4.171)
$\mathbf {F}$ : electrostatic force (3.769)
$i$ : electric charge (3.461)
$n$ : half-sections (2.937)
$E$ : electric field (2.865)
$p$ : complex exponentials (2.787)
$\mathbf {s}$ : displacement vector (2.532)
$C$ : farad (2.523)
${\displaystyle U_{E))$ : potential energy (2.433)
${\displaystyle N_{i))$ : customers (2.286)
$R$ : nominal impedance (1.939)
$k$ : filters (1.939)
$u$ : energy density (1.937)
${\displaystyle U_{i))$ : customers (1.900)
${\displaystyle q_{N))$ : positions (1.865)
$\Phi$ : electric potential (1.847)
$e$ : charge (1.845)
$\gamma$ : propagation constant (1.821)
${\displaystyle Z_{0))$ : characteristic impedance (1.783)
$a$ : potential energy (1.776)
$r$ : distance (1.766)
$m$ : different values (1.758)
$\gamma '$ : propagation constant (1.724)
$G$ : electrical conductance (1.722)
$\mathbf {D}$ : electric displacement field (1.718)
${\displaystyle {\vec {r))_{i))$ : source point (1.681)
${\vec {r))$ : field point (1.677)
$V$ : volume element (1.655)
$d$ : displacement vector (1.552)

INTERDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY

Physical chemistry and chemical physics

Category information

reference category: Physical chemistry and chemical physics
code: 82.00.00 (PACS)
wiki categories: [(Category:Physical chemistry, 3), (Category:Chemical kinetics, 2), (Category:Fluid dynamics, 1)]

Cluster information:

cluster id: [7453]
matching score: 0.209100203938
purity: 1.0
matching keywords: [u'applied', u'atmospheric', u'interdisciplinary', u'kinetics', u'chemical', u'thermodynamics', u'engineering', u'materials', u'systems', u'statistical', u'dynamics', u'chemistry', u'physics', u'physical']

Definitions:

$R$ : gas constant (2.558)
$T$ : gas constant (1.900)
$K$ : equilibrium (1.790)
$F$ : absolute pressure (1.552)
$C$ : kelvin (1.546)

Electronics; radiowave and microwave technology; direct energy conversion and storage

Category information

reference category: Electronics; radiowave and microwave technology; direct energy conversion and storage
code: 84.00.00 (PACS)
wiki categories: [(Category:Radio technology, 5), (Category:Telecommunications, 4), (Category:Signal cables, 2)]

Cluster information:

cluster id: [428, 1471]
matching score: 0.240137596747
purity: 1.0
matching keywords: [u'technology', u'circuits', u'communication', u'signal', u'lines', u'cables', u'transmission', u'connectors', u'components', u'antennas', u'electronics', u'electronic', u'telecommunications']

Definitions:

$d$ : diameter (4.901)
$D$ : diameter (3.405)
$P$ : power level (3.318)
$f$ : frequency (2.746)
$c$ : speed of light (2.553)
$C$ : length (1.937)
${\displaystyle \mu _{r))$ : relative permeability (1.793)
${\displaystyle Z_{0))$ : characteristic impedance (1.714)
$S$ : insulator (1.689)
$\epsilon$ : dielectric constant (1.677)

Other areas of applied and interdisciplinary physics

Category information

reference category: Other areas of applied and interdisciplinary physics
code: 89.00.00 (PACS)
wiki categories: [(Category:Physics, 6), (Category:Condensed matter physics, 5), (Category:Materials science, 5)]

Cluster information:

cluster id: [3258, 7353]
matching score: 0.246735933334
purity: 1.0
matching keywords: [u'applied', u'industrial', u'interdisciplinary', u'science', u'energy', u'engineering', u'systems', u'technology', u'physics']

Definitions:

$y$ : direction (3.623)
$\mathbf {j}$ : equation (2.665)
$\mathbf {q}$ : wave vector (2.640)
$n$ : atomic number density (2.625)
$k$ : dependence (2.619)
${\displaystyle c_{v,p))$ : specific heat capacity (2.600)
$m$ : atomic mass (2.521)
$i$ : atom (2.492)
$j$ : atom (2.452)
$p$ : type materials (2.417)
$\delta$ : limit (1.939)
$z$ : direction (1.937)
${\displaystyle Z_{f))$ : partition function (statistical mechanics) (1.902)
${\displaystyle n_{e,c))$ : carrier density (1.902)
$t$ : time (1.902)
$q$ : long wavelength limit (1.865)
$r$ : distance (1.865)
$v$ : drift velocity (1.858)
$E$ : electric field (1.848)
${\displaystyle D_{p))$ : density of states (1.834)
${\displaystyle f_{ph))$ : equilibrium distribution (1.811)
$S$ : spin (1.810)
$\tau$ : group velocity (1.810)
$c$ : concentration (1.810)
$e$ : elementary charge (1.790)
$L$ : length (1.749)
${\displaystyle I_{ph,))$ : radiation intensity (1.744)
$T$ : temperature (1.742)
${\displaystyle d_{p))$ : slope (1.714)
$\mathbf {p}$ : momentum (1.696)
$A$ : electrolyte (1.688)
$\mathbf {s}$ : unit vector (1.677)
${\displaystyle v_{d))$ : drift velocity (1.664)
${\displaystyle n_{i))$ : electron hole concentration (1.657)
${\displaystyle p_{0))$ : electron hole concentration (1.657)
${\displaystyle v_{1))$ : film2 (1.657)
$\mathbf {u}$ : velocity (1.653)
$\mathbf {d}$ : displacement vector (1.592)
${\displaystyle v_{z))$ : phonon velocity (1.574)
${\displaystyle v_{2))$ : film2 (1.524)
$a$ : electron (1.490)
$\kappa$ : inverse screening length (1.489)

Information and communication, circuits

Communication, information

Category information

reference category: Communication, information
code: 94Axx (MSC)
wiki categories: [(Category:Discrete mathematics, 4), (Category:Coding theory, 4), (Category:Encodings, 4)]

Cluster information:

cluster id: [9339]
matching score: 0.291389710465
purity: 1.0
matching keywords: [u'information', u'theorems', u'coding']

Definitions:

$n$ : length (10.082)
$d$ : hamming weight (9.143)
$C$ : block code (4.437)
$x$ : hamming distance (2.771)
$y$ : codeword (2.688)
$q$ : ary code (2.662)
$t$ : errors (1.939)
$e$ : relation (1.719)
$p$ : error (1.598)

Circuits, networks

Category information

reference category: Circuits, networks
code: 94Cxx (MSC)
wiki categories: [(Category:Electronic circuits, 3), (Category:Circuit theorems, 2), (Category:Electronic engineering, 2)]

Cluster information:

cluster id: [8217]
matching score: 0.350636813123
purity: 1.0
matching keywords: [u'circuits', u'graph', u'circuit']

Definitions:

$Y$ : circuit (3.294)
$s$ : closed circuit (1.939)
${\displaystyle R_{\Delta ))$ : impedance (1.847)
$n$ : total number (1.754)
$R''$ : δ circuit (1.524)

Information systems

Data management systems

Category information

reference category: Data management systems
code: NO_CODE (ACM)
wiki categories: [(Category:Databases, 4), (Category:Information technology management, 3), (Category:Computer data, 3)]

Cluster information:

cluster id: [3792]
matching score: 0.456086633014
purity: 1.0
matching keywords: [u'information', u'management', u'database', u'processing', u'system', u'transaction', u'systems', u'databases', u'data']

Definitions:

$S$ : schedule (1.974)
$A$ : original value (1.865)

K-theory

Whitehead groups and K_1

Category information

reference category: Whitehead groups and K_1
code: 19Bxx (MSC)
wiki categories: [(Category:Group theory, 6), (Category:Subgroup properties, 6), (Category:Metric geometry, 2)]

Cluster information:

cluster id: [4366, 5999]
matching score: 0.372728245829
purity: 1.0
matching keywords: [u'group', u'subgroup']

Definitions:

$H$ : subgroup (11.404)
$G$ : group (mathematics) (6.319)
$K$ : subgroup (1.974)

Manifolds and cell complexes

Topological manifolds

Category information

reference category: Topological manifolds
code: 57Nxx (MSC)
wiki categories: [(Category:Geometric topology, 3), (Category:Differential geometry, 2), (Category:Differential topology, 2)]

Cluster information:

cluster id: [5957]
matching score: 0.454491410648
purity: 1.0
matching keywords: [u'algebraic', u'spaces', u'manifolds', u'geometric', u'structures', u'topological', u'topology']

Definitions:

$n$ : sphere (3.729)
$N$ : manifold (2.675)
$M$ : embedding (2.458)
$S$ : circles (1.926)
$X$ : boundary (1.811)
$I$ : boundary (1.533)
$\mathbf {R}$ : 3-sphere (1.497)

Mathematical logic and foundations

General logic

Category information

reference category: General logic
code: 03Bxx (MSC)
wiki categories: [(Category:Proof theory, 7), (Category:Propositional calculus, 7), (Category:Inference, 6)]

Cluster information:

cluster id: [4081, 9697]
matching score: 0.408926723256
purity: 1.0
matching keywords: [u'mathematical', u'calculus', u'classical', u'logical', u'systems', u'logic', u'propositional', u'paraconsistent']

Definitions:

$Q$ : statement (5.991)
$P$ : statement (5.452)
$R$ : statement (3.564)
$B$ : truth (1.657)
$A$ : truth (1.625)

Set theory

Category information

reference category: Set theory
code: 03Exx (MSC)
wiki categories: [(Category:Cardinal numbers, 16), (Category:Infinity, 16), (Category:Set theory, 14)]

Cluster information:

cluster id: [963, 2347, 3838, 4965, 6276]
matching score: 0.418232115185
purity: 1.0
matching keywords: [u'ordinal', u'mathematical', u'set', u'determinacy', u'descriptive', u'algebra', u'sets', u'cardinals', u'large', u'cardinal', u'numbers', u'logic', u'hypothesis', u'forcing', u'foundations']

Definitions:

$j$ : elementary embedding (8.989)
$V$ : elementary embedding (8.788)
$A$ : sets (6.874)
$M$ : critical point (set theory) (6.212)
$\kappa$ : cardinal number (4.692)
${\displaystyle \aleph _{\omega ))$ : cardinal number (4.375)
$G$ : domain (3.577)
$B$ : subset (3.482)
$\mathbf {N}$ : natural number (3.396)
${\displaystyle \aleph _{\lambda ))$ : successor ordinal (3.316)
${\displaystyle \aleph _{0))$ : cardinality (3.231)
$N$ : transitive class (2.787)
${\displaystyle \aleph _{\alpha ))$ : cardinal number (2.741)
$\mathbf {M}$ : union (2.688)
$n$ : power set (2.682)
$I$ : index set (2.657)
$a$ : critical point (set theory) (2.526)
$U$ : normal measure (2.501)
$\omega$ : ordinals (2.469)
${\displaystyle \beth _{2))$ : cardinality of the continuum (2.414)
$\alpha$ : ordinals (1.939)
$\mathbf {Q}$ : rational number (1.933)
$\mathbf {R}$ : real number (1.855)
${\displaystyle \beth _{\alpha ))$ : cardinality (1.847)
${\displaystyle \aleph _{1))$ : successor cardinal (1.790)
$\lambda$ : successor ordinal (1.754)
$\mathbf {C}$ : complex number (1.740)
$X$ : measure theory (1.698)
$x$ : integer (1.648)
$i$ : sets (1.548)

Mechanics of deformable solids

Special subfields of solid mechanics

Category information

reference category: Special subfields of solid mechanics
code: 74Lxx (MSC)
wiki categories: [(Category:Mechanics, 5), (Category:Physics, 3), (Category:Solid mechanics, 3)]

Cluster information:

cluster id: [2527, 7115]
matching score: 0.410678810296
purity: 1.0
matching keywords: [u'mechanics', u'solid']

Definitions:

$m$ : mass (5.535)
$e$ : eccentricity (3.380)
$E$ : energy (2.869)
$r$ : radius (2.768)
${\displaystyle \sigma _{v))$ : tensile stress (2.499)
$h$ : order (1.812)
$J$ : function (1.775)
$u$ : equation (1.738)
$\mathbf {MandelVoigtnotation}$ : notation (1.724)
${\displaystyle \sigma _{3))$ : plane (1.707)
${\displaystyle \sigma _{y))$ : yield strength (1.671)
$t$ : change (1.524)

Mechanics of particles and systems

Kinematics

Category information

reference category: Kinematics
code: 70Bxx (MSC)
wiki categories: [(Category:Robot control, 3), (Category:Mechanics, 3), (Category:Mechanical engineering, 2)]

Cluster information:

cluster id: [6703]
matching score: 0.338562777169
purity: 1.0
matching keywords: [u'mechanics', u'mechanisms', u'statics', u'rigid', u'kinematics']

Definitions:

$f$ : freedom (5.343)
$j$ : joints (3.849)
$n$ : links (3.808)
$c$ : constraints (2.961)
${\displaystyle f_{i))$ : freedom (2.961)
$M$ : degree-of-freedom (2.941)
$N$ : fixed link (2.531)
$i$ : freedom (2.488)

Dynamics of a system of particles, including celestial mechanics

Category information

reference category: Dynamics of a system of particles, including celestial mechanics
code: 70Fxx (MSC)
wiki categories: [(Category:Gravitation, 6), (Category:Celestial mechanics, 6), (Category:Statics, 3)]

Cluster information:

cluster id: [2239, 4273]
matching score: 0.264334861599
purity: 1.0
matching keywords: [u'mechanics', u'celestial', u'dynamics', u'system']

Definitions:

$X$ : world manifold (5.701)
$G$ : gravitational constant (4.191)
$a$ : time (3.635)
$\Gamma$ : linear connection (2.811)
$\mathbf {t}$ : time (2.649)
$P$ : structure group (2.621)
$n$ : mean motion (2.516)
${\mathfrak {F))$ : spatial distributions (1.939)
$H$ : structure group (1.915)
$M$ : gravitational constant (1.900)
$T$ : hours (1.812)
$m$ : mass (1.724)
$\Theta$ : distortion (1.654)
$d$ : time (1.556)

NUCLEAR PHYSICS

Nuclear structure

Category information

reference category: Nuclear structure
code: 21.00.00 (PACS)
wiki categories: [(Category:Pharmacology, 3), (Category:Pharmacokinetics, 2), (Category:Pharmaceutics, 2)]

Cluster information:

cluster id: [4433]
matching score: 0.232017461777
purity: 1.0
matching keywords: [u'nuclear', u'physics']

Definitions:

$t$ : initial concentration (5.369)
${\displaystyle C_{0))$ : initial concentration (5.125)
${\displaystyle C_{t))$ : concentration (3.662)
${\displaystyle k_{e))$ : elimination rate (1.754)

Properties of specific nuclei listed by mass ranges (an additional heading must be chosen with these entries, where the given mass number limits are, to some degree, arbitrary)

Category information

reference category: Properties of specific nuclei listed by mass ranges (an additional heading must be chosen with these entries, where the given mass number limits are, to some degree, arbitrary)
code: 27.00.00 (PACS)
wiki categories: [(Category:Physics, 14), (Category:Particle physics, 9), (Category:Force, 7)]

Cluster information:

cluster id: [6221, 6623, 8187]
matching score: 0.286862684549
purity: 1.0
matching keywords: [u'mass', u'nuclear', u'physics', u'number']

Definitions:

$q$ : electric charge (15.630)
$\mathbf {B}$ : magnetic field (13.834)
$Q$ : electric charge (11.565)
$c$ : speed of light (9.225)
$\mathbf {E}$ : electric field (9.034)
$B$ : baryon number (8.185)
$t$ : coordinate time (7.233)
$\mathbf {A}$ : magnetic potential (6.897)
$\mathbf {v}$ : velocity (6.333)
$a$ : subatomic particle (5.922)
$m$ : rest mass (5.253)
$Y$ : hypercharge (5.186)
$F$ : electromagnetic tensor (5.147)
$f$ : % 20mechanics (5.088)
$S$ : strangeness (4.699)
$T$ : kinetic energy (4.620)
$J$ : total angular momentum quantum number (4.580)
$E$ : energy (4.532)
$L$ : lepton number (4.524)
$v$ : speed (4.374)
$z$ : direction (4.287)
${\displaystyle T_{3))$ : weak isospin (4.261)
$V$ : potential energy (4.258)
$A$ : magnetic dipole (4.197)
$\mathbf {r}$ : position vector (3.784)
$e$ : magnetic charge (3.667)
$d$ : dimensions (3.531)
$M$ : manifold (3.404)
$\mathbf {p}$ : kinetic momentum (3.362)
$u$ : up quark (3.213)
$P$ : parity (3.142)
${\displaystyle I_{3))$ : isospin (2.830)
$G$ : physics (2.803)
$\mathbf {J}$ : current density (2.803)
${\displaystyle Y_{W))$ : weak hypercharge (2.762)
$n$ : up quark (2.744)
$\varphi$ : electric potential (2.685)
$D$ : gauge covariant derivative (2.676)
$\mathbf {R}$ : space (2.615)
$s$ : field (2.595)
$\mathbf {j}$ : probability current (2.578)
$I$ : third component (2.555)
$\mathbf {H}$ : fields (2.543)
$x$ : position (2.479)
$p$ : form (2.472)
$\mathbf {D}$ : electric displacement (1.942)
$g$ : metric tensor (1.939)
$\gamma$ : closed loop (1.891)
$\mathbf {f}$ : lorentz force (1.858)
${\displaystyle p_{i))$ : momentum component (1.858)
$\mathbf {M}$ : magnetization (1.850)
${\displaystyle v_{y))$ : direction (1.779)
${\displaystyle v_{z))$ : direction (1.779)
$\mathbf {S}$ : momentum operator (1.766)
$C$ : charm (quantum number) (1.756)
$\sigma$ : surface (1.749)
$y$ : direction (1.749)
$\mathbf {g}$ : gravitational acceleration (1.724)
$\mathbf {P}$ : four momentum (1.717)
${\displaystyle q_{i))$ : cartesian coordinate (1.689)
${\displaystyle u_{1))$ : velocities (1.677)
${\mathcal {C))$ : smooth function (1.621)
${\displaystyle m_{0))$ : invariant mass (1.621)
$i$ : direction (1.564)
$\mathbf {u}$ : lorentz factor (1.532)
$X$ : mmj2ubwoeev70gxo14dyaw (1.532)

Networks

Network protocols

Category information

reference category: Network protocols
code: NO_CODE (ACM)
wiki categories: [(Category:Authentication methods, 4), (Category:Computer access control, 4), (Category:Telecommunications engineering, 4)]

Cluster information:

cluster id: [472, 7073]
matching score: 0.51438647157
purity: 1.0
matching keywords: [u'layer', u'protocol', u'network', u'transport', u'protocols', u'formal']

Definitions:

${\displaystyle N_{r))$ : antennas (8.788)
${\displaystyle N_{t))$ : antennas (5.391)
$A$ : session key (5.126)
$S$ : server (4.412)
$\mathbf {H}$ : channel matrix (4.110)
$B$ : identities (3.513)
${\displaystyle K_{AS))$ : symmetric key (2.637)
${\displaystyle \mathbf {R} _{R))$ : spatial correlation matrix (2.513)
$\mathbf {Q}$ : signal covariance (1.939)
${\displaystyle \mathbf {R} _{T))$ : spatial correlation matrix (1.872)
${\displaystyle N_{B))$ : cryptographic nonce (1.837)
${\displaystyle K_{AB))$ : session (1.814)
$\mathbf {n}$ : channel matrix (1.790)
$i$ : antenna (1.790)
$a$ : network (1.736)
${\displaystyle K_{BS))$ : alice (1.712)
$\mathbf {G}$ : permanent (1.654)
${\displaystyle T_{A))$ : timestamp (1.635)
$I$ : message (1.621)
${\displaystyle N_{A))$ : cryptographic nonce (1.603)

Nonassociative rings and algebras

General nonassociative rings

Category information

reference category: General nonassociative rings
code: 17Axx (MSC)
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Cluster information:

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Definitions:

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$N$ : quadratic form (5.707)
$F$ : composition algebra (3.985)
$A$ : algebra over a field (3.469)
$K$ : matrix algebra (2.591)
$p$ : hamilton (2.523)
$\mathbf {R}$ : octonion algebra (1.865)
${\displaystyle \mathbb {Q} _{\nu ))$ : quaternion algebra (1.659)
$B$ : algebra over a field (1.655)

Number theory

Sequences and sets

Category information

reference category: Sequences and sets
code: 11Bxx (MSC)
wiki categories: [(Category:Integer sequences, 16), (Category:Numbers, 14), (Category:Combinatorics, 11)]

Cluster information:

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matching keywords: [u'functions', u'lucas', u'stirling', u'number', u'binomial', u'numbers', u'sequences', u'arithmetic', u'fibonacci']

Definitions:

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$p$ : prime number (6.160)
$U$ : sequences (5.232)
$a$ : natural number (4.160)
$k$ : triangular number (2.669)
$q$ : real numbers (2.619)
$F$ : estimate (2.471)
$P$ : lucas sequence (2.263)
${\displaystyle {\mathcal {B))_{r))$ : sequences (1.939)
$r$ : irrational number (1.939)
$x$ : real number (1.939)
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${\displaystyle V_{n))$ : fibonacci number (1.891)
$V$ : sequence (1.812)
$m$ : natural number (1.799)
${\displaystyle {\mathcal {B))_{s))$ : sequences (1.754)
$L$ : conventions (1.712)
$S$ : lower triangular matrix (1.529)
$Q$ : integer sequence (1.513)

Algebraic number theory: local and p-adic fields

Category information

reference category: Algebraic number theory: local and p-adic fields
code: 11Sxx (MSC)
wiki categories: [(Category:Field theory, 4), (Category:Algebraic number theory, 4), (Category:Group theory, 2)]

Cluster information:

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matching keywords: [u'field', u'number', u'class', u'galois', u'algebraic']

Definitions:

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$K$ : brauer group (4.785)
$G$ : galois group (4.459)
$v$ : discrete valuation (4.071)
$L$ : abelian extension (3.565)
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$A$ : galois (1.787)
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$\mathbf {Q}$ : field (1.725)
$X$ : smooth morphism (1.677)

Connections with logic

Category information

reference category: Connections with logic
code: 11Uxx (MSC)
wiki categories: [(Category:Number theory, 4), (Category:Abstract algebra, 3), (Category:Field theory, 3)]

Cluster information:

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matching keywords: [u'number', u'arithmetic']

Definitions:

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$\mathbf {C}$ : p-adic number (4.367)
$\mathbf {Q}$ : field (mathematics) (4.365)
$F$ : field (3.392)
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$p$ : adic numbers (3.162)
$L$ : dirichlet l-function (2.725)
$x$ : rational number (2.506)
$E$ : algebraic field extension (2.500)
$s$ : dedekind zeta function (2.487)
$d$ : quadratic field (2.466)
$O$ : ring (mathematics) (2.417)
$f$ : algebraic field extension (2.320)
$\mathbf {K}$ : field (mathematics) (1.939)
$v$ : ultrametric place (1.848)
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$c$ : choice (1.810)
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$P$ : prime ideal (1.666)
$A$ : field (1.642)
$N$ : morphism (1.632)
$i$ : gaussian rational (1.629)
$g$ : valuation (1.623)
$\mathbf {Z}$ : ring (1.577)

Numerical analysis

Numerical linear algebra

Category information

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code: 65Fxx (MSC)
wiki categories: [(Category:Linear algebra, 8), (Category:Matrices, 6), (Category:Mathematical objects, 5)]

Cluster information:

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Definitions:

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$B$ : skew-hermitian matrix (5.940)
$n$ : matrix (5.320)
$L$ : triangular matrix (4.422)
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$U$ : triangular matrix (3.572)
$x$ : computation (2.781)
$\mathbf {x}$ : right hand side (2.323)
$\phi$ : initial guess (1.903)
$b$ : ω output (1.895)
$j$ : loop (1.852)
$i$ : loop (1.817)
$\Lambda$ : diagonal matrix (1.816)
$k$ : iteration (1.765)
$s$ : matrix (1.677)
$\omega$ : iteration (1.659)
$e$ : error end (1.623)

Mathematical programming, optimization and variational techniques

Category information

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code: 65Kxx (MSC)
wiki categories: [(Category:Mathematical analysis, 6), (Category:Fields of mathematics, 4), (Category:Analysis, 2)]

Cluster information:

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purity: 1.0
matching keywords: [u'mathematical', u'numerical', u'variational', u'optimization', u'analysis']

Definitions:

$f$ : internal function (3.409)
$\mathbf {R}$ : euclidean space (2.835)
$a$ : hardy space (2.798)
$n$ : euclidean space (2.783)
$O$ : outer distortion (2.736)
$K$ : outer distortion (2.583)
$\mathbb {R}$ : function (2.560)
$x$ : function (2.434)
$X$ : open set (1.937)

Integral equations, integral transforms

Category information

reference category: Integral equations, integral transforms
code: 65Rxx (MSC)
wiki categories: [(Category:Mathematical analysis, 3), (Category:Functional analysis, 2), (Category:Functions and mappings, 2)]

Cluster information:

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matching score: 0.400436391948
purity: 1.0
matching keywords: [u'integral', u'numerical', u'equations', u'transforms', u'analysis']

Definitions:

$a$ : stochastic process (3.452)
$X$ : stochastic process (1.939)
$f$ : flow (1.900)
$L$ : bounded linear operator (1.865)
$\mathbf {R}$ : wiener process (1.744)
$i$ : cell centres (1.663)
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$P$ : distribution (1.654)
$d$ : dimensional case (1.648)

Numerical methods in Fourier analysis

Category information

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code: 65Txx (MSC)
wiki categories: [(Category:Functional analysis, 6), (Category:Numerical analysis, 5), (Category:Signal processing, 5)]

Cluster information:

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matching keywords: [u'numerical', u'wavelets', u'analysis', u'transforms', u'fourier']

Definitions:

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$H$ : filter coefficients (1.891)
$h$ : filter (1.882)
${\hat {\psi ))$ : admissibility (1.754)
$\pi$ : period (1.690)
$y$ : period (1.586)

Computer aspects of numerical algorithms

Category information

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code: 65Yxx (MSC)
wiki categories: [(Category:Numerical analysis, 5), (Category:Zero, 3), (Category:Algorithms, 3)]

Cluster information:

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matching keywords: [u'numerical', u'algorithms', u'analysis']

Definitions:

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$L$ : lipschitz continuity (3.389)
$n$ : function values (2.590)
${\displaystyle x_{0))$ : initial values (2.586)
$x$ : mean value (2.297)
${\displaystyle x_{1))$ : initial values (1.663)
$a$ : fixed-point iteration (1.628)
${\displaystyle x_{n))$ : secant method (1.563)

OTHER

Miscellaneous topics in measure theory

Category information

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code: NO_CODE (NO_SCHEMA)
wiki categories: [(Category:Measures (measure theory), 4), (Category:Measure theory, 4)]

Cluster information:

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Definitions:

$X$ : borel sigma algebra (6.504)
$T$ : topology (4.742)
$\mathbf {R}$ : real line (2.905)
$n$ : euclidean space (1.629)

Data management systems

Category information

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code: NO_CODE (NO_SCHEMA)
wiki categories: [(Category:Chemical data pages, 3), (Category:Chemical properties, 3), (Category:Chemistry, 3)]

Cluster information:

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Definitions:

$S$ : standard molar entropy (14.455)
$H$ : standard enthalpy change of fusion (14.263)
${\displaystyle c_{p))$ : heat capacity (8.065)
$P$ : mmhg (3.347)
$n$ : index of refraction (2.850)

Phase transformations in solids

Category information

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Cluster information:

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matching keywords: [u'solids']

Definitions:

$a$ : edge length (3.727)
$J$ : johnson solid (3.626)
${\displaystyle C_{5v))$ : decagon (1.476)
${\displaystyle C_{4v))$ : octagon (1.468)

Geophysical observations, instrumentation, and techniques

Category information

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wiki categories: [(Category:Lists of head coaches by National Football League team, 3), (Category:National Football League lists, 3), (Category:National Football League head coaches by team, 3)]

Cluster information:

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Definitions:

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$b$ : % note1 (6.653)
$f$ : note1 (5.567)
$c$ : note1 (5.487)
$d$ : note1 (4.557)
$a$ : charter member (1.854)
$g$ : note1 (1.812)

Randomness, geometry and discrete structures

Category information

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code: NO_CODE (NO_SCHEMA)
wiki categories: [(Category:Coordinate systems, 3), (Category:Cartography, 3), (Category:Cartographic projections, 3)]

Cluster information:

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matching keywords: [u'projections']

General

Category information

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wiki categories: [(Category:Coordinate systems, 4), (Category:Cartography, 4), (Category:Cartographic projections, 4)]

Cluster information:

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Definitions:

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Low-dimensional topology

Category information

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wiki categories: [(Category:Knot theory, 4), (Category:Surfaces, 2), (Category:Torus knots, 2)]

Cluster information:

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Basic methods

Category information

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Cluster information:

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matching keywords: [u'electromagnetic']

Definitions:

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$h$ : base station antenna height (4.338)
$L$ : path loss (3.335)
$\lambda$ : wavelength (1.900)
$f$ : frequency (1.900)
$\gamma$ : slope (1.790)
$d$ : distance (1.790)
$F$ : adjustment (1.742)

Algebraic combinatorics

Category information

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wiki categories: [(Category:National Basketball Association seasons, 6), (Category:National Basketball Association seasons by team, 6), (Category:National Basketball Association lists, 2)]

Cluster information:

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Definitions:

$a$ : basketball (5.457)
$c$ : table.lower-alphanote _ (3.948)

Algebraic combinatorics

Category information

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code: NO_CODE (NO_SCHEMA)
wiki categories: [(Category:National Basketball Association seasons, 4), (Category:National Basketball Association seasons by team, 4), (Category:National Basketball Association lists, 1)]

Cluster information:

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matching score: 0.101694565889
purity: 1.0
matching keywords: [u'association']

Computer graphics

Category information

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code: NO_CODE (NO_SCHEMA)
wiki categories: [(Category:Enzyme kinetics, 3), (Category:Enzymes, 3), (Category:Plots (graphics), 2)]

Cluster information:

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purity: 1.0
matching keywords: [u'graphics']

Definitions:

$V$ : maximum reaction velocity (3.269)
$S$ : reaction velocity (2.488)
$v$ : reaction velocity (1.793)
$i$ : inhibitor (1.766)
$K$ : reaction rate (1.746)
$m$ : michaelis–menten constant (1.691)

Interaction design

Category information

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code: NO_CODE (NO_SCHEMA)
wiki categories: [(Category:Electronic engineering, 3), (Category:Design, 3), (Category:Network synthesis filters, 3)]

Cluster information:

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Definitions:

$n$ : order (4.474)
${\displaystyle \omega _{0))$ : cutoff frequency (3.641)
$G$ : gain (2.830)
${\displaystyle G_{0))$ : gain (2.608)
$s$ : complex frequency space (2.585)
$H$ : transfer function (2.487)
${\displaystyle \omega _{pm))$ : poles (1.939)
$f$ : frequency (1.939)
$L$ : shunt (1.779)
$a$ : filter (signal processing) (1.742)
$C$ : shunt (1.712)
$\varepsilon$ : ripple factor (1.673)

Low-dimensional topology

Category information

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code: NO_CODE (NO_SCHEMA)
wiki categories: [(Category:Knot theory, 3), (Category:Surfaces, 1), (Category:Knots, 1)]

Cluster information:

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matching keywords: [u'surfaces', u'knots', u'geometric', u'topology']

Electronic structure of bulk materials (see section 73 for electronic structure of surfaces, interfaces, low-dimensional structures, and nanomaterials; for electronic structure of superconductors, see 74.25.Jb)

Category information

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code: NO_CODE (NO_SCHEMA)
wiki categories: [(Category:Transistors, 4), (Category:Electronic amplifiers, 4), (Category:Single-stage transistor amplifiers, 2)]

Cluster information:

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purity: 1.0
matching keywords: [u'electronic']

Definitions:

${\displaystyle R_{L))$ : resistor load (8.064)
${\displaystyle R_{S))$ : resistance (2.937)
${\displaystyle V_{A))$ : early voltage (1.974)
${\displaystyle R_{A))$ : series resistance (1.891)
$V$ : signal source (1.891)
${\displaystyle I_{E))$ : current source (1.882)
${\displaystyle I_{C))$ : active load (1.850)
${\displaystyle I_{S))$ : norton's theorem (1.845)
${\displaystyle V_{T))$ : boltzmann constant (1.766)
${\displaystyle V_{out))$ : output (1.712)
${\displaystyle i_{x))$ : output resistance (1.712)
${\displaystyle R_{C))$ : resistor load (1.676)
${\displaystyle R_{out))$ : gain (1.636)
${\displaystyle I_{A))$ : norton's theorem (1.628)
${\displaystyle C_{dg))$ : discharge (1.593)

Graphical methods

Category information

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wiki categories: [(Category:Baseball statistics, 5), (Category:Batting statistics, 4), (Category:Batting (baseball), 4)]

Cluster information:

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matching score: 0.747742788884
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matching keywords: [u'statistics']

Definitions:

$H$ : hit (baseball) (2.850)
$F$ : poor (2.696)

Stochastic systems and control

Category information

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code: NO_CODE (NO_SCHEMA)
wiki categories: [(Category:Statistics, 4), (Category:Charts, 4), (Category:Images of graphs, 4)]

Cluster information:

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matching score: 0.197741178813
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matching keywords: [u'control']

Definitions:

$s$ : chart (7.054)
$n$ : shewhart (3.520)
${\bar {x))$ : chart (3.468)

Randomness, geometry and discrete structures

Category information

reference category: NO_REFERENCE_CATEGORY
code: NO_CODE (NO_SCHEMA)
wiki categories: [(Category:Cartographic projections, 6), (Category:Cartography, 5), (Category:Coordinate systems, 5)]

Cluster information:

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matching score: 0.132670227656
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matching keywords: [u'projections']

Definitions:

$\varphi$ : latitude (7.113)
$\lambda$ : latitude (4.498)
${\displaystyle \lambda _{0))$ : longitude (1.845)

Probability theory on algebraic and topological structures

Category information

reference category: NO_REFERENCE_CATEGORY
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wiki categories: [(Category:Theory of probability distributions, 3), (Category:Probability distributions, 3), (Category:Probability theory, 3)]

Cluster information:

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matching keywords: [u'probability']

Definitions:

$X$ : random variable (5.253)
$p$ : probability (3.419)
$a$ : discrete random variable (2.675)
$N$ : probability-generating function (2.558)
$d$ : thinsp ;-rrb- (2.394)
$n$ : factorial (1.863)
$z$ : complex number (1.830)
$r$ : probability (1.556)

Connections with logic

Category information

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code: NO_CODE (NO_SCHEMA)
wiki categories: [(Category:Analytic number theory, 3), (Category:Number theory, 3), (Category:Conjectures, 2)]

Cluster information:

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matching keywords: [u'number']

Definitions:

$i$ : polynomials (2.639)
$F$ : polynomials (2.487)
${\displaystyle f_{i))$ : integral polynomial (1.939)
$p$ : prime number (1.910)
$n$ : positive integer (1.867)
$a$ : proof (1.688)
$u$ : polynomial ring (1.665)

Properties of specific nuclei listed by mass ranges (an additional heading must be chosen with these entries, where the given mass number limits are, to some degree, arbitrary)

Category information

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code: NO_CODE (NO_SCHEMA)
wiki categories: [(Category:Physics, 4), (Category:Particle physics, 4), (Category:Aesthetics, 1)]

Cluster information:

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Definitions:

${\bar {4))$ : representations of lie groups/algebras (2.613)
$U$ : weak hypercharge (1.781)
$H$ : higgs (1.659)

Computational methods

Category information

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wiki categories: [(Category:Tensors, 3), (Category:Mathematical methods in general relativity, 2), (Category:Tensors in general relativity, 2)]

Cluster information:

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matching keywords: [u'relativity']

Definitions:

$a$ : tensor rank (5.498)
${\displaystyle C_{abcd))$ : weyl tensor (1.882)

Decision theory

Category information

reference category: NO_REFERENCE_CATEGORY
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wiki categories: [(Category:Thyroid, 3), (Category:Endocrine procedures, 3), (Category:Biochemistry, 3)]

Cluster information:

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matching score: 0.241447787175
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matching keywords: [u'procedures']

Definitions:

$K$ : dissociation constant (6.925)
${\displaystyle \alpha _{31))$ : dilution (1.900)
${\displaystyle \beta _{31))$ : clearance (medicine) (1.900)
$D$ : l/mol (1.876)
$T$ : ec50 (1.876)
${\displaystyle \alpha _{T))$ : dilution (1.876)
${\displaystyle \beta _{T))$ : clearance (medicine) (1.876)
$M$ : dissociation constant (1.790)

Physical chemistry and chemical physics

Category information

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wiki categories: [(Category:Electrodes, 4), (Category:Electricity, 4), (Category:Electrochemistry, 4)]

Cluster information:

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matching keywords: [u'electrodes', u'technology', u'energy', u'devices', u'electroanalytical', u'applications', u'electrochemistry', u'chemistry', u'hydrogen']

Definitions:

$a$ : type (2.735)
$s$ : agcl (1.868)

Close-to-elliptic equations

Category information

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code: NO_CODE (NO_SCHEMA)
wiki categories: [(Category:Wireless, 3), (Category:Radio frequency propagation, 3), (Category:Amateur radio, 3)]

Cluster information:

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matching keywords: [u'equations', u'differential', u'partial']

Definitions:

$L$ : path loss (3.544)
$d$ : depth (1.766)
$n$ : path loss exponent (1.724)

Mechanical and acoustical properties of condensed matter

Category information

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code: NO_CODE (NO_SCHEMA)
wiki categories: [(Category:Threaded fasteners, 3), (Category:Standards by type, 3), (Category:Mechanical engineering, 3)]

Cluster information:

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matching keywords: [u'mechanical']

Definitions:

$D$ : major diameter (7.944)
$P$ : pitch (6.967)
$H$ : height (3.877)

Fundamental astronomy and astrophysics; instrumentation, techniques, and astronomical observations

Category information

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wiki categories: [(Category:Northern constellations, 3), (Category:Extrasolar planets, 3), (Category:Exoplanets discovered by year, 3)]

Cluster information:

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matching keywords: [u'astronomical', u'astronomy', u'objects']

Definitions:

$a$ : jupiter mass (5.811)

Physical chemistry and chemical physics

Category information

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wiki categories: [(Category:Physical quantities, 3), (Category:Physical constants, 3), (Category:Constants, 3)]

Cluster information:

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matching keywords: [u'energy', u'matter', u'electron', u'mass', u'spectroscopy', u'molecular', u'physics', u'constants', u'physical']

Definitions:

$h$ : planck constant (5.294)
$c$ : planck constant (3.579)
$Z$ : atomic number (3.489)
$R$ : rydberg constant (2.554)
$m$ : rest mass (2.453)
$e$ : electron (1.845)
$X$ : atomic number (1.810)
$E$ : codata (1.497)

Computing methodologies and applications

Category information

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wiki categories: [(Category:Telecommunications engineering, 3), (Category:Applied mathematics, 3), (Category:Electrical engineering, 3)]

Cluster information:

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matching keywords: [u'image', u'computer', u'systems', u'processing', u'graphics']

Definitions:

$h$ : first-order hold (2.799)
$s$ : dirac delta function (2.554)
$H$ : gain (1.939)
$x$ : dirac delta function (1.797)
$a$ : signal (1.764)
$z$ : gain (1.754)
$n$ : octave (1.724)
$t$ : dirac delta function (1.424)

Computational methods

Category information

reference category: NO_REFERENCE_CATEGORY
code: NO_CODE (NO_SCHEMA)
wiki categories: [(Category:General relativity, 3), (Category:Density, 2), (Category:Unsolved problems in physics, 2)]

Cluster information:

cluster id: [6305]
matching score: 0.382049687457
purity: 1.0
matching keywords: [u'relativity']

Definitions:

$M$ : mass (5.160)
$a$ : black hole (2.843)
$J$ : angular momentum (2.201)
${\displaystyle g_{tt))$ : temporal component (1.939)
$\mathbf {KerrNewmanmetric}$ : solution (1.724)
$r$ : quantity (1.610)
$Q$ : body (1.505)

Homological algebra

Category information

reference category: NO_REFERENCE_CATEGORY
code: NO_CODE (NO_SCHEMA)
wiki categories: [(Category:Algebra, 3), (Category:Analytic number theory, 2), (Category:Complex analysis, 2)]

Cluster information:

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matching score: 0.234530365211
purity: 1.0
matching keywords: [u'algebra']

Definitions:

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${\displaystyle z_{i))$ : rational functions (2.571)
$\mathbf {y}$ : basis vectors (1.743)
$V$ : euclidean space (1.733)
$\mathbf {e}$ : basis vectors (1.714)
$\mathbf {x}$ : mapping vectors (1.710)

Hamilton-Jacobi theories, including dynamic programming

Category information

reference category: NO_REFERENCE_CATEGORY
code: NO_CODE (NO_SCHEMA)
wiki categories: [(Category:Multivariable calculus, 4), (Category:Vectors, 3), (Category:Vector calculus, 3)]

Cluster information:

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matching score: 0.251226310938
purity: 1.0
matching keywords: [u'calculus']

Definitions:

$a$ : vector operator (6.317)
$\mathbf {v}$ : velocity field (5.444)
$\mathbf {F}$ : vector field (4.221)
$\mathbf {A}$ : vector area (3.661)
$z$ : direction (3.348)
$n$ : volume form (3.019)
$t$ : time (2.799)
$f$ : function (2.766)
$\mathbf {R}$ : smooth function (2.708)
$\mathbf {G}$ : vector fields (2.615)
$d$ : vector element (2.547)
$\mu$ : density on a manifold (2.535)
$\mathbf {s}$ : vector element (2.508)
$k$ : form (2.475)
$\mathbf {r}$ : vector field (2.412)
$V$ : volume (1.865)
$\mathbf {B}$ : source-free part (1.865)
$A$ : vector area (1.847)
$X$ : vector field (1.847)
$\mathbf {E}$ : electric field (1.824)
$\varphi$ : scalar-valued function (1.714)
$\mathbf {\hat {n))$ : unit vector (1.707)
$x$ : direction (1.690)
$\mathbf {e}$ : unit vector (1.659)
$q$ : tensor (1.657)
$curl$ : field (1.641)
$C$ : tangent vector (1.550)
$p$ : contravariant vector (1.483)

Properties of specific nuclei listed by mass ranges (an additional heading must be chosen with these entries, where the given mass number limits are, to some degree, arbitrary)

Category information

reference category: NO_REFERENCE_CATEGORY
code: NO_CODE (NO_SCHEMA)
wiki categories: [(Category:Physics, 3), (Category:Solid state engineering, 3), (Category:Condensed matter physics, 2)]

Cluster information:

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matching score: 0.248183919026
purity: 1.0
matching keywords: [u'physics']

Definitions:

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$t$ : time (3.419)
$R$ : region (2.799)
${\displaystyle R_{2))$ : region (2.799)
${\displaystyle R_{1))$ : region (2.576)
$n$ : solutions (2.465)
$p$ : momentum (2.421)
$x$ : position (2.367)
$\mathbf {k}$ : wave vector (1.939)
${\displaystyle A_{k))$ : discrete components (1.937)
$N$ : particles (1.848)
$\Psi$ : wavefunction (1.847)
$a$ : ball (1.815)
$V$ : total volume (1.754)
${\displaystyle V_{0))$ : potential barrier (1.754)
${\displaystyle \Omega _{r))$ : volume (1.754)
${\displaystyle \omega _{p))$ : resonance frequency (1.749)
${\displaystyle a_{n))$ : scalar multiplication (1.742)
${\displaystyle k_{F))$ : wave vector (1.659)
$A$ : classical mechanics (1.645)
${\boldsymbol {q))$ : dispersion relation (1.628)
$s$ : wave (1.618)
$\mathbf {r}$ : position vector (1.604)
${\displaystyle s_{z))$ : spin (physics) (1.600)

Nuclear engineering and nuclear power studies

Category information

reference category: NO_REFERENCE_CATEGORY
code: NO_CODE (NO_SCHEMA)
wiki categories: [(Category:Spacecraft propulsion, 3), (Category:Astrodynamics, 3), (Category:Propulsion, 2)]

Cluster information:

cluster id: [6288]
matching score: 0.0689655757804
purity: 1.0
matching keywords: [u'propulsion', u'engineering', u'types', u'components']

Definitions:

$t$ : rocket (4.071)
${\displaystyle m_{0))$ : mass (3.560)
${\displaystyle m_{1))$ : total mass (3.245)
${\displaystyle v_{e))$ : effective exhaust velocity (3.160)
$x$ : direction (2.777)
$m$ : mass (2.758)
$M$ : mass (2.726)
$v$ : effective exhaust velocity (2.679)
$P$ : mass (2.676)
${\displaystyle I_{sp))$ : specific impulse (2.508)
$a$ : rocket engine (2.402)
${\displaystyle F_{i))$ : external forces (1.865)
$I$ : equation (1.779)
$\gamma$ : lorentz factor (1.720)
${\displaystyle V_{e))$ : velocity (1.689)
$c$ : speed of light (1.665)
$\eta$ : equation (1.557)

Operator theory

Other (nonclassical) types of operator theory

Category information

reference category: Other (nonclassical) types of operator theory
code: 47Sxx (MSC)
wiki categories: [(Category:Functional analysis, 3), (Category:Theoretical physics, 2), (Category:Operator theory, 2)]

Cluster information:

cluster id: [6996]
matching score: 0.493677166448
purity: 1.0
matching keywords: [u'operator', u'linear']

Definitions:

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$T$ : linear operator (4.387)
$N$ : linear operator (4.181)
$K$ : operator (3.199)
$V$ : orthogonal projection (2.702)
$X$ : dilation (1.939)
${\displaystyle D_{T))$ : operator (1.749)
$A$ : normal operator (1.696)

Optics, electromagnetic theory

General

Category information

reference category: General
code: 78Axx (MSC)
wiki categories: [(Category:Electromagnetic radiation, 10), (Category:Optics, 7), (Category:Physical optics, 6)]

Cluster information:

cluster id: [336, 4142, 5562]
matching score: 0.411635379213
purity: 1.0
matching keywords: [u'electromagnetic', u'radiation', u'optical', u'waves', u'antennas', u'optics', u'physical']

Definitions:

$z$ : direction (8.647)
${\displaystyle \theta _{2))$ : angle (6.736)
$c$ : speed of light (6.072)
$\theta$ : angle (5.655)
$n$ : refractive index (4.457)
$a$ : refraction (4.085)
$k$ : wavenumber (3.579)
$\mathbf {E}$ : electric field (3.427)
${\displaystyle \theta _{1))$ : angle (3.425)
$v$ : speed of light (3.157)
$u$ : angle (2.799)
${\displaystyle n_{2))$ : refractive indices (2.741)
${\displaystyle n_{1))$ : refractive index (2.697)
${\displaystyle \epsilon _{0))$ : vacuum permittivity (2.685)
$\mathbf {A}$ : electric field (2.649)
$R$ : right (2.635)
${\displaystyle \lambda _{0))$ : wavelength (2.491)
$x$ : unit vectors (2.445)
$q$ : circular polarization (2.390)
$y$ : circular polarization (2.338)
$\pi$ : radians (1.974)
$h$ : incidence (1.939)
$\lambda$ : wavelength (1.882)
$M$ : state (1.865)
$g$ : absolute value (1.865)
$U$ : operator (physics) (1.848)
$\mathbf {n}$ : normal vector (1.847)
${\displaystyle n_{o))$ : refractive index (1.847)
$\phi$ : angle (1.816)
$T$ : transmittance (1.800)
$r$ : radii (1.799)
$L$ : state (1.787)
$S$ : fig. (1.781)
$A$ : light (1.778)
$m$ : integer (1.725)
$\mathbf {l}$ : light vector (1.701)
$p$ : fraction (1.683)
${\displaystyle \alpha _{x))$ : radians (1.659)
$s$ : light (1.621)
$\kappa$ : absorption (1.558)
${\displaystyle \alpha _{y))$ : radians (1.524)
$b$ : colors (1.515)
$\rho$ : angle (1.441)

Ordinary differential equations

General theory

Category information

reference category: General theory
code: 34Axx (MSC)
wiki categories: [(Category:Differential equations, 5), (Category:Theoretical physics, 5), (Category:Differential calculus, 4)]

Cluster information:

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matching score: 0.366427384013
purity: 1.0
matching keywords: [u'calculus', u'inverse', u'linear', u'differential', u'transforms', u'equations', u'theoretical', u'systems']

Definitions:

$a$ : system (3.216)
$\lambda$ : eigenvalue (2.683)
$u$ : function (mathematics) (1.913)
$\mathbb {R}$ : fiber bundle (1.766)
$t$ : function (1.718)
$Q$ : tangent bundle (1.689)

PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES

Physics of plasmas and electric discharges

Category information

reference category: Physics of plasmas and electric discharges
code: 52.00.00 (PACS)
wiki categories: [(Category:Plasma physics, 3), (Category:Waves in plasmas, 3), (Category:Waves, 3)]

Cluster information:

cluster id: [4193]
matching score: 0.615388778637
purity: 1.0
matching keywords: [u'upper', u'electromagnetic', u'hybrid', u'wave', u'electron', u'waves', u'plasmas', u'physics', u'plasma']

Definitions:

${\displaystyle \omega _{p))$ : plasma frequency (2.674)
${\displaystyle \Omega _{c))$ : plasma parameters (1.900)
${\displaystyle \omega _{i))$ : plasma frequency (1.845)
${\displaystyle {\vec {B))_{0))$ : light wave (1.845)
$A$ : plasma (physics) (1.816)
${\displaystyle \omega _{c))$ : plasma frequency (1.779)
$or$ : plasma (physics) (1.566)

Partial differential equations

Close-to-elliptic equations

Category information

reference category: Close-to-elliptic equations
code: 35Hxx (MSC)
wiki categories: [(Category:Differential equations, 7), (Category:Partial differential equations, 6), (Category:Dynamical systems, 4)]

Cluster information:

cluster id: [5574, 6687, 6816]
matching score: 0.441596749631
purity: 1.0
matching keywords: [u'partial', u'differential', u'equations']

Definitions:

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$\mathbf {H}$ : magnetic field (4.360)
$\mathbf {J}$ : current density (4.341)
$\mathbf {B}$ : magnetic field (4.115)
${\displaystyle \alpha _{i))$ : unknown coefficients (3.785)
$\mathbf {D}$ : electric displacement field (3.702)
$\mathbf {F}$ : field (3.581)
$L$ : differential operator (3.571)
$H$ : field (2.780)
$\mathbf {n}$ : unit normal (2.765)
$\omega$ : frequency (2.763)
$k$ : wavenumber (2.718)
$u$ : density (2.504)
$\mathbf {M}$ : magnetization (2.504)
$a$ : electric field (2.242)
$\Theta$ : angle (1.939)
$Q$ : charge (1.926)
$\Omega$ : differential operator (1.900)
${\displaystyle \Omega _{D))$ : computational domain (1.900)
$\mathbf {k}$ : wave vector (1.900)
$S$ : surface area (1.882)
$t$ : time (1.868)
$p$ : density (1.864)
$c$ : speed of light (1.826)
$\rho$ : density (1.823)
${\displaystyle \Omega _{N))$ : dirichlet (1.790)
$\phi$ : general solution (1.790)
$\mathbf {A}$ : electrical potential (1.774)
$\alpha$ : ricci calculus (1.762)
$E$ : electric field (1.750)
$z$ : direction (1.746)
$d$ : differential (infinitesimal) (1.712)
$\mathbf {S}$ : vector area (1.690)
${\displaystyle \rho _{1))$ : slab (1.657)
$B$ : nabla (1.628)
$\mathbf {P}$ : material (1.598)
$f$ : frequency (1.591)
$v$ : nabla (1.506)
$I$ : charge (1.476)

Probability theory and stochastic processes

Foundations of probability theory

Category information

reference category: Foundations of probability theory
code: 60Axx (MSC)
wiki categories: [(Category:Stochastic processes, 10), (Category:Probability theory, 8), (Category:Statistics, 7)]

Cluster information:

cluster id: [1139, 2659, 4671]
matching score: 0.495918534389
purity: 1.0
matching keywords: [u'processes', u'probability', u'stochastic', u'probabilistic']

Definitions:

$a$ : stochastic process (8.994)
$t$ : time (6.933)
$i$ : state (5.402)
$X$ : stochastic process (4.099)
$S$ : measurable space (3.889)
$j$ : state (3.385)
$\pi$ : equilibrium distribution (3.293)
$T$ : time (3.250)
$s$ : time (2.869)
$\mathbf {P}$ : probability measure (2.644)
$Q$ : transition rate matrix (1.974)
$P$ : transition matrix (1.939)
${\displaystyle Y_{n))$ : martingale (probability theory) (1.816)
$c$ : a.s. (1.815)
$C$ : variance (1.749)
$b$ : condition (1.627)

Probability theory on algebraic and topological structures

Category information

reference category: Probability theory on algebraic and topological structures
code: 60Bxx (MSC)
wiki categories: [(Category:Theory of probability distributions, 3), (Category:Inequalities, 3), (Category:Probability theorems, 3)]

Cluster information:

cluster id: [1952]
matching score: 0.635883377417
purity: 1.0
matching keywords: [u'stochastic', u'processes', u'theorems', u'probability']

Definitions:

$n$ : random variable (2.458)
$X$ : random variable (1.556)

Distribution theory

Category information

reference category: Distribution theory
code: 60Exx (MSC)
wiki categories: [(Category:Continuous distributions, 14), (Category:Probability distributions, 14), (Category:Exponential family distributions, 5)]

Cluster information:

cluster id: [1276, 3197, 5086, 9107]
matching score: 0.548760421665
purity: 1.0
matching keywords: [u'processes', u'probability', u'infinitely', u'divisible', u'functions', u'stochastic', u'distribution', u'distributions']

Definitions:

$a$ : probability distribution (34.317)
$X$ : triangular distribution (9.286)
$n$ : random variables (6.777)
$k$ : degrees of freedom (statistics) (4.065)
$\mathbf {M}$ : location parameter (3.971)
$\mathbf {X}$ : matrix inverse (3.648)
$\lambda$ : noncentrality parameter (3.567)
$c$ : constants (3.548)
$b$ : interval (3.348)
$p$ : posterior distribution (3.233)
${\displaystyle X_{i))$ : uniform distribution (continuous) (3.077)
$\beta$ : shape parameters (2.540)
$\mu$ : scale parameter (2.533)
$U$ : uniform distribution (continuous) (2.530)
$x$ : scale (2.467)
${\boldsymbol {\Omega ))$ : scale matrix (2.417)
${\boldsymbol {\Sigma ))$ : scale matrix (2.417)
$t$ : thinsp (1.900)
$C$ : positive constants (1.882)
$H$ : heaviside step function (1.865)
$A$ : chi-squared distribution (1.840)
${\displaystyle \tau _{4))$ : l-kurtosis (1.781)
$\mathbf {R}$ : continuous distributions (1.743)
$\chi$ : uniform distribution (continuous) (1.739)
$\gamma$ : incomplete gamma function (1.724)
$\mathbf {\Psi }$ : positive-definite matrix (1.707)
$r$ : positive constants (1.707)
$F$ : f-distribution (1.689)
$\sigma$ : rayleigh distribution (1.677)
$\mathbf {\Sigma }$ : covariance matrix (1.653)
$Y$ : laplace distribution (1.653)
$T$ : relation (1.590)
$\mathbf {U}$ : scale matrix (1.589)
$\mathbf {V}$ : scale matrix (1.589)
$j$ : constants (1.497)

Stochastic analysis

Category information

reference category: Stochastic analysis
code: 60Hxx (MSC)
wiki categories: [(Category:Stochastic processes, 7), (Category:Stochastic differential equations, 6), (Category:Differential equations, 6)]

Cluster information:

cluster id: [5052, 6063]
matching score: 0.721419164148
purity: 1.0
matching keywords: [u'calculus', u'processes', u'partial', u'probability', u'differential', u'stochastic', u'equations']

Definitions:

$a$ : stochastic differential equation (8.347)
$C$ : compact support (5.321)
$D$ : domain (4.611)
$X$ : initial datum (4.605)
$x$ : initial datum (4.595)
$f$ : functions (4.414)
$t$ : time (4.393)
$B$ : brownian motion (4.288)
$H$ : borel (4.127)
$d$ : differential equation (3.820)
$b$ : brownian motion (3.741)
$\mathbf {E}$ : expectation (3.648)
$A$ : operator (3.447)
$Z$ : observations (2.799)
${\mathcal {A))$ : characteristic operator (2.797)
$m$ : brownian motion (2.625)
$n$ : itō diffusion (2.492)
$\mathbf {P}$ : expectation (2.453)
$S$ : measurable space (1.974)
$F$ : natural filtration (1.915)
$\mathbf {R}$ : euclidean space (1.910)
$Y$ : state (1.891)
$s$ : observations (1.865)
$U$ : sets (1.848)
${\displaystyle U_{k))$ : sequences (1.810)
$L$ : operator (1.781)
$\mathbf {N}$ : natural number (1.779)
$K$ : space (1.666)
$y$ : green's function (1.621)
$r$ : first exit time (1.591)

Quantum theory

General mathematical topics and methods in quantum theory

Category information

reference category: General mathematical topics and methods in quantum theory
code: 81Qxx (MSC)
wiki categories: [(Category:Quantum mechanics, 11), (Category:Quantum chemistry, 5), (Category:Electronic structure methods, 5)]

Cluster information:

cluster id: [2350, 6498, 8945]
matching score: 0.349509741883
purity: 1.0
matching keywords: [u'mechanics', u'mathematical', u'quantum', u'equations', u'analysis', u'techniques']

Definitions:

${\displaystyle F_{i))$ : operator (mathematics) (4.668)
$a$ : measure (mathematics) (3.439)
$n$ : magnetic quantum number (3.112)
${\displaystyle H_{A))$ : space (2.835)
$V$ : electrostatic (2.644)
$\psi$ : state (2.635)
$X$ : measurable space (2.182)
$t$ : time (1.974)
$B$ : pure state (1.939)
$E$ : energy (1.937)
$i$ : basis (1.915)
$A$ : simple proof (1.882)
$\phi$ : state (1.858)
$K$ : degenerate energy (1.845)
$KS$ : potential (1.812)
$\mathbf {j}$ : current densities (1.812)
${\displaystyle \psi _{tar))$ : target state (1.812)
${\displaystyle {\hat {a))_{i))$ : operators (1.811)
${\displaystyle {\hat {a))_{j))$ : operators (1.810)
$F$ : function (1.800)
$\mathbf {r}$ : radiation field (1.790)
$v$ : scalar potential (1.756)
$M$ : sigma algebra (1.708)
$\ell$ : states (1.698)
$U$ : unitary operator (1.690)
$\mathbf {V}$ : systems (1.689)
$N$ : hilbert space (1.657)
$p$ : fidelity (1.618)
$J$ : degenerate energy (1.524)

Quantum field theory; related classical field theories

Category information

reference category: Quantum field theory; related classical field theories
code: 81Txx (MSC)
wiki categories: [(Category:Theoretical physics, 14), (Category:Particle physics, 14), (Category:Quantum mechanics, 13)]

Cluster information:

cluster id: [1274, 2256, 2454, 2667]
matching score: 0.437921005826
purity: 1.0
matching keywords: [u'group', u'string', u'geometry', u'theories', u'field', u'objects', u'quantum', u'conformal', u'renormalization']

Definitions:

$a$ : tensor rank (5.360)
$\phi$ : field (4.726)
$f$ : % 20tensor (3.800)
$Z$ : generating functional (3.661)
$M$ : mass (3.566)
$S$ : action (physics) (2.741)
$G$ : tensor (2.586)
${\displaystyle g_{\mu \nu ))$ : metric tensor (1.974)
$W$ : closed loop (1.939)
$K$ : operator (physics) (1.882)
${\displaystyle \omega _{\mu \nu \rho ))$ : spin connection (1.845)
${\mathcal {T))$ : time ordering (1.790)
$J$ : source field (1.757)
$g$ : determinant (1.754)
$F$ : electromagnetic tensor (1.744)
$n$ : particle green (1.696)
$O$ : theory (1.659)
$c$ : speed of light (1.659)
$m$ : mass (1.657)
$\mathbf {SchwingerDysonequations}$ : equations (1.654)
$\mu$ : covariant derivative (1.629)
$E$ : perturbation theory (quantum mechanics) (1.527)

Real functions

Functions of one variable

Category information

reference category: Functions of one variable
code: 26Axx (MSC)
wiki categories: [(Category:Science-related lists, 3), (Category:Mathematics-related lists, 3), (Category:Integrals, 3)]

Cluster information:

cluster id: [4190]
matching score: 0.256862861669
purity: 1.0
matching keywords: [u'calculus', u'elementary', u'functions', u'integrals', u'special']

Definitions:

$a$ : list (5.816)
$C$ : nonzero (1.790)

Miscellaneous topics

Category information

reference category: Miscellaneous topics
code: 26Exx (MSC)
wiki categories: [(Category:Mathematical analysis, 9), (Category:Functions and mappings, 8), (Category:Fields of mathematics, 6)]

Cluster information:

cluster id: [388, 5516, 9677]
matching score: 0.437176523568
purity: 1.0
matching keywords: [u'real', u'calculus', u'functions', u'analysis']

Definitions:

$a$ : function (mathematics) (24.187)
$f$ : function (mathematics) (11.764)
$g$ : sinc function (5.240)
$A$ : polynomial function (5.049)
$X$ : metric spaces (5.004)
${\displaystyle x_{n))$ : sequence (4.713)
$\varphi$ : euler's totient function (4.294)
$x$ : continuous function (4.132)
$\mathbf {R}$ : function (4.073)
$d$ : function (3.850)
$\epsilon$ : real number (3.664)
$q$ : degree (3.559)
$L$ : function (3.478)
$S$ : final topology (3.402)
$t$ : function (3.275)
$T$ : distribution (2.799)
$n$ : key length (2.799)
$G$ : continuity (2.685)
$V$ : neighbourhood (mathematics) (2.677)
$M$ : continuous function (2.627)
$W$ : normed vector space (2.595)
$U$ : open set (2.551)
$\delta$ : positive number (1.950)
${\displaystyle B_{x))$ : ball (1.939)
$I$ : open interval (1.915)
$N$ : poly (1.903)
$R$ : neighborhood (1.900)
$c$ : domain (1.790)
$\mu$ : möbius function (1.766)
${\displaystyle \varphi _{\epsilon ))$ : function (1.712)
$P$ : approaches (1.657)
$Y$ : function (1.591)
$r$ : continuous function (1.588)
$b$ : open interval (1.588)

Relativity and gravitational theory

Computational methods

Category information

reference category: Computational methods
code: 83-08 (MSC)
wiki categories: [(Category:Special relativity, 9), (Category:Theory of relativity, 9), (Category:Theoretical physics, 9)]

Cluster information:

cluster id: [551, 3157, 4809, 6387]
matching score: 0.384375861751
purity: 1.0
matching keywords: [u'gravitational', u'relativity', u'special', u'experimental']

Definitions:

$c$ : speed of light (7.772)
$x$ : position (6.931)
$M$ : mass (6.302)
$a$ : black hole (5.922)
$t$ : time (5.601)
$L$ : initial rest length (5.482)
$v$ : relative velocity (4.254)
$\varphi$ : electric potential (3.679)
$\mathbf {A}$ : electric potential (3.539)
${\displaystyle L_{0))$ : proper length (3.359)
$0$ : position (3.289)
$S$ : distance (2.728)
$Q$ : electric charge (2.688)
$G$ : gravitational constant (2.649)
$J$ : angular momentum (2.642)
$B$ : endpoints (2.368)
$D$ : dimensions (1.907)
$\mathbf {E}$ : electric field (1.889)
$d$ : distance (1.875)
$E$ : total energy (1.858)
${\displaystyle T_{0))$ : proper time (1.848)
$\mathbf {J}$ : electric current density (1.845)
$A$ : black hole (1.812)
$T$ : time (1.793)
$N$ : event (1.781)
$O$ : event (1.781)
$k$ : boltzmann constant (1.779)
$\mathbf {B}$ : magnetic field (1.769)
${\displaystyle r_{s))$ : schwarzschild radius (1.749)
$\mathbf {LorentzFitzGeraldcontraction}$ : hendrik lorentz (1.732)
$f$ : harmonic function (1.724)
$r$ : infinity (1.723)
${\displaystyle M_{0))$ : initial mass (1.707)
$L'$ : acceleration (1.524)

Unified, higher-dimensional and super field theories

Category information

reference category: Unified, higher-dimensional and super field theories
code: 83Exx (MSC)
wiki categories: [(Category:Theoretical physics, 3), (Category:Theory of relativity, 2), (Category:Theories of gravity, 2)]

Cluster information:

cluster id: [9582]
matching score: 0.326339668235
purity: 1.0
matching keywords: [u'theories', u'field', u'relativity', u'string', u'cosmology']

Definitions:

$D$ : dimensions (2.536)

Special functions (33-XX deals with the properties of functions as functions)

Elementary classical functions

Category information

reference category: Elementary classical functions
code: 33Bxx (MSC)
wiki categories: [(Category:Special functions, 3), (Category:Analytic number theory, 2), (Category:Complex analysis, 2)]

Cluster information:

cluster id: [1444]
matching score: 0.423177481488
purity: 1.0
matching keywords: [u'functions', u'polygamma', u'gamma', u'special']

Definitions:

$z$ : digamma function (2.385)
$m$ : order (1.939)
$\Gamma$ : gamma function (1.845)
${\displaystyle {\mathcal {L))_{k))$ : transfer operator (1.816)

Hypergeometric functions

Category information

reference category: Hypergeometric functions
code: 33Cxx (MSC)
wiki categories: [(Category:Hypergeometric functions, 15), (Category:Special functions, 15), (Category:Combinatorics, 11)]

Cluster information:

cluster id: [1054, 2545, 3844]
matching score: 0.719389899667
purity: 1.0
matching keywords: [u'functions', u'groups', u'orthogonal', u'series', u'topics', u'hypergeometric', u'polynomials', u'generalized', u'elliptic', u'special']

Definitions:

$a$ : rational function (12.878)
$n$ : dual hahn polynomials (9.838)
$q$ : q-hahn polynomials (8.534)
$x$ : dual hahn polynomials (7.191)
$F$ : generalized hypergeometric function (5.528)
$R$ : dual hahn polynomials (3.633)
$f$ : suitable function (2.739)
$l$ : constants (2.688)
$g$ : function (2.683)
$\mathbf {q}$ : mathematics (2.464)
$Q$ : q-hahn polynomials (1.974)
$A$ : series (1.950)
$p$ : hypergeometric series (1.939)
$C$ : type (1.865)
$h$ : power (1.758)
$j$ : special case (1.754)
$S$ : continuous dual hahn polynomials (1.749)
$P$ : polynomials (1.712)
$z$ : generalized hypergeometric function (1.677)
$N$ : continuous hahn polynomials (1.659)
$i$ : simple poles (1.657)
${\displaystyle a_{j))$ : order (1.525)

Other special functions

Category information

reference category: Other special functions
code: 33Exx (MSC)
wiki categories: [(Category:Combinatorics, 3), (Category:Complex analysis, 3), (Category:Special functions, 3)]

Cluster information:

cluster id: [5023]
matching score: 0.464915805598
purity: 1.0
matching keywords: [u'functions', u'special']

Definitions:

$z$ : bessel function (1.654)

Statistics

Parametric inference

Category information

reference category: Parametric inference
code: 62Fxx (MSC)
wiki categories: [(Category:Statistical inference, 7), (Category:Hypothesis testing, 4), (Category:Statistics, 3)]

Cluster information:

cluster id: [2861, 9920]
matching score: 0.396066953603
purity: 1.0
matching keywords: [u'tests', u'statistics', u'inference', u'testing', u'hypothesis', u'resampling']

Definitions:

$m$ : hypothesis tests (9.682)
$U$ : type i and type ii errors (6.550)
$s$ : statistic (5.426)
$S$ : type i and type ii errors (4.687)
$T$ : type i and type ii errors (4.687)
$a$ : statistics (4.295)
$R$ : type i and type ii errors (3.725)
$\alpha$ : level (3.694)
$V$ : alternative hypothesis (3.643)
$M$ : mean (2.799)
${\displaystyle H_{i))$ : test (2.741)
${\boldsymbol {\theta ))$ : parameter vector (2.652)
$X$ : random variable (2.616)
${\displaystyle m_{0))$ : null hypotheses (2.565)
$k$ : pareto distribution (2.469)
$\mathbf {\Theta }$ : random parameter (1.939)
$i$ : hypothesis (1.939)
$n$ : independent comparisons (1.939)
$Z$ : samples (1.900)
${\displaystyle w_{i))$ : weight (1.882)
$g_{\boldsymbol {\theta ))$ : function (1.834)
$\delta$ : quantiles (1.816)
$A$ : well-behaved statistic (1.751)
$\mu$ : confidence intervals (1.738)
$p$ : bernoulli distribution (1.700)
$Q$ : discoveries (1.677)
$K$ : pareto distribution (1.673)
${\boldsymbol {\Theta ))$ : random vector (1.666)
${\displaystyle c_{i))$ : intersection hypothesis (1.544)
$H$ : null hypotheses (1.524)

Multivariate analysis

Category information

reference category: Multivariate analysis
code: 62Hxx (MSC)
wiki categories: [(Category:Statistics, 14), (Category:Statistical data types, 8), (Category:Data analysis, 8)]

Cluster information:

cluster id: [819, 5240, 7893]
matching score: 0.364025347619
purity: 1.0
matching keywords: [u'statistics', u'spatial', u'analysis', u'testing', u'correlation', u'hypothesis', u'estimation', u'data', u'association']

Definitions:

$I$ : moran (7.965)
$C$ : geary (4.327)
$X$ : random variables (3.589)
${\displaystyle f_{j))$ : functions (3.510)
$i$ : observation (3.495)
$E$ : mean (3.435)
$n$ : random sample (3.420)
$Y$ : sample variance (3.401)
$r$ : pearson product-moment correlation coefficient (3.227)
$\sigma$ : variance (2.833)
$N$ : distribution (2.802)
$j$ : observation (2.800)
$x$ : correlation (2.791)
${\hat {\theta ))$ : estimator (2.552)
${\displaystyle x_{i))$ : rank (2.536)
$y$ : standard deviation (2.429)
$w$ : weight vector (1.939)
$p$ : regressor (1.926)
$\theta$ : unknown parameter (1.907)
${\bar {X))$ : interest (1.900)
$d$ : constants (1.900)
$\mu$ : variance (1.865)
$a$ : measure (1.855)
$m$ : independent variables (1.845)
${\displaystyle y_{i))$ : dependent variable (1.833)
$T$ : sample covariance matrix (1.817)
$z$ : distribution (1.810)
${\displaystyle Y_{i))$ : week (1.774)
$W$ : matrix (1.749)
$t$ : mean (1.724)
$\rho$ : correlation (1.701)
$f$ : function (1.701)
${\displaystyle X_{i))$ : iq (1.627)
${\displaystyle r_{t))$ : observations (1.611)
$k$ : data points (1.610)
${\displaystyle s_{y))$ : standard deviation (1.591)
${\displaystyle w_{ij))$ : mean (1.591)
${\displaystyle \beta _{j))$ : functions (1.524)
$c$ : constants (1.524)

Linear inference, regression

Category information

reference category: Linear inference, regression
code: 62Jxx (MSC)
wiki categories: [(Category:Statistics, 9), (Category:Regression analysis, 9), (Category:Statistical models, 8)]

Cluster information:

cluster id: [692, 4261, 5405]
matching score: 0.426251280322
purity: 1.0
matching keywords: [u'statistics', u'inference', u'linear', u'analysis', u'diagnostics', u'variance', u'regression']

Definitions:

$i$ : observation (6.257)
$n$ : observations (5.196)
$k$ : explanatory variable (4.712)
$\mathbf {X}$ : design matrix (3.317)
$M$ : model (2.961)
$j$ : study (2.799)
$b$ : coefficient (2.725)
$x$ : data (2.672)
$p$ : matrix (2.593)
$\mathbf {B}$ : matrix (2.527)
$a$ : model (2.448)
${\hat {e))$ : residual vector (1.974)
${\displaystyle W_{k))$ : data matrix (1.939)
$\theta$ : effect size (1.915)
$X$ : matrix (1.897)
$q$ : rank (matrix theory) (1.882)
$\sigma$ : variance (1.876)
$V$ : columns (1.865)
${\displaystyle {\widehat {\boldsymbol {\beta ))}_{k))$ : pcr estimator (1.812)
$\beta$ : explanators (1.793)
${\displaystyle {\boldsymbol {\mu ))_{n))$ : posterior mean (1.781)
$\mathbf {E}$ : squares (1.779)
${\hat {\mathbf {B} ))$ : moore–penrose_pseudoinverse (1.724)
$e$ : true coefficients (1.718)
$S$ : probability distribution (1.689)
${\boldsymbol {\beta ))$ : bias of an estimator (1.520)

Systems theory; control

General

Category information

reference category: General
code: 93Axx (MSC)
wiki categories: [(Category:Coordinate systems, 4), (Category:Cartography, 4), (Category:Systems, 4)]

Cluster information:

cluster id: [3434]
matching score: 0.295205721387
purity: 1.0
matching keywords: [u'mathematical', u'systems']

Definitions:

$a$ : coordinate system (7.644)
$\mathbf {F}$ : differential operators (4.439)
$z$ : direction (3.729)
$\sigma$ : form (2.926)
$\tau$ : form (2.926)
$P$ : moon (2.894)
$\mathbf {P}$ : black sphere (2.286)
$I$ : mcgraw-hill (1.926)
$x$ : cartesian coordinates (1.579)
$y$ : cartesian coordinate system (1.556)

Stochastic systems and control

Category information

reference category: Stochastic systems and control
code: 93Exx (MSC)
wiki categories: [(Category:Control theory, 3), (Category:Cybernetics, 3), (Category:Systems theory, 3)]

Cluster information:

cluster id: [6439]
matching score: 0.67363017829
purity: 1.0
matching keywords: [u'control', u'stochastic', u'systems']

Definitions:

$t$ : nonsingular (1.724)
$A$ : eigenvalues (1.677)

Theory of computation

Design and analysis of algorithms

Category information

reference category: Design and analysis of algorithms
code: NO_CODE (ACM)
wiki categories: [(Category:Computational complexity theory, 6), (Category:Structural complexity theory, 5), (Category:Theory of computation, 4)]

Cluster information:

cluster id: [1477, 4240, 8631, 9087]
matching score: 0.575616074441
purity: 1.0
matching keywords: [u'computational', u'language', u'data', u'automata', u'tree', u'searching', u'languages', u'complexity', u'classes', u'algorithms', u'systems', u'computation', u'logic', u'infinite', u'formal', u'structures', u'hashing']

Definitions:

$f$ : complexity class (7.405)
$k$ : self (6.937)
$O$ : dspace (6.799)
$n$ : space (6.224)
$q$ : state (5.292)
$p$ : state (5.084)
$M$ : deterministic turing machine (4.549)
$A$ : linear bounded automaton (4.456)
$\ell$ : length (4.283)
$i$ : call position (3.887)
$\varphi$ : gödel numbering (3.732)
${\displaystyle q_{i))$ : state (3.510)
$\delta$ : transition relation (3.178)
$\mathbf {a}$ : symbol (2.961)
${\displaystyle p_{i))$ : state (2.799)
$\Sigma$ : alphabet (computer science) (2.727)
$w$ : word (2.674)
$Q$ : finite set (2.661)
$\Phi$ : complexity measure (2.485)
${\displaystyle M_{i))$ : state (2.266)
$M'$ : pushdown automaton (1.974)
${\displaystyle q_{0))$ : initial state (1.974)
$s$ : states (1.974)
$t$ : function (1.974)
$L$ : formal language (1.939)
$x$ : input (1.939)
$\Gamma$ : alphabet (1.891)
$\mathbf {P}$ : partial computable function (1.882)
$\varepsilon$ : empty word (1.858)
$Z$ : symbol (1.847)
$h$ : hash (1.843)
$G$ : context-free grammar (1.824)
$g$ : program (1.790)
${\displaystyle \varphi _{i))$ : domain (mathematics) (1.774)
$V$ : disjoint (1.774)
$T$ : function (1.757)
$a$ : computer science (1.757)
$r$ : state (1.749)
$j$ : position (1.688)
${\hat {\Sigma ))$ : alphabet (1.675)
${\displaystyle w_{j))$ : state (1.665)
${\displaystyle \gamma _{i))$ : state (1.623)
$\mu$ : right multiplication (1.576)

Topological groups, Lie groups

Lie groups

Category information

reference category: Lie groups
code: 22Exx (MSC)
wiki categories: [(Category:Lie algebras, 10), (Category:Lie groups, 8), (Category:Representation theory of Lie groups, 7)]

Cluster information:

cluster id: [450, 1494, 3819, 5942, 6342]
matching score: 0.628314735831
purity: 1.0
matching keywords: [u'lie', u'group', u'linear', u'nilpotent', u'verma', u'topological', u'algebraic', u'analysis', u'groups', u'representation', u'algebras', u'physics', u'properties', u'semisimple']

Definitions:

${\mathfrak {g))$ : lie algebra (16.000)
$a$ : subgroup (11.003)
$W$ : weyl group (7.311)
$\lambda$ : weight (representation theory) (7.243)
$j$ : symbol (5.392)
$w$ : weyl group (4.243)
$K$ : subgroup (3.732)
$\alpha$ : root (3.630)
$V$ : representation of a lie algebra (3.623)
${\tilde {\lambda ))$ : dominant weight (2.751)
$L$ : holomorphic line bundle (2.736)
$G$ : complex semisimple lie group (2.628)
${\mathfrak {k))$ : 1-dimensional lie algebra (2.596)
$B$ : borel subgroup (2.563)
$n$ : vector space (2.366)
$J$ : edge lengths (1.875)
${\displaystyle \mathbf {j} _{1))$ : angular momenta (1.875)
$H$ : inner product (1.845)
${\mathfrak {s))$ : semisimple lie algebra (1.834)
$i$ : edge lengths (1.801)
${\displaystyle {\mathfrak {g))_{0))$ : module (mathematics) (1.779)
$F$ : field (1.756)
$s$ : commute (1.756)
${\displaystyle \gamma _{i))$ : coroot (1.749)
$p$ : operators ad (1.749)
${\mathfrak {p))$ : semisimple lie algebra (1.746)
${\displaystyle M_{\lambda ))$ : weight_(representation_theory) (1.724)
$f$ : homomorphism (1.724)
${\mathfrak {b))$ : module (mathematics) (1.723)
${\mathfrak {a))$ : abelian lie algebra (1.701)
${\displaystyle \mathbf {j} _{2))$ : angular momenta (1.691)
${\displaystyle s_{\alpha ))$ : root reflection (1.689)
${\displaystyle v_{\lambda ))$ : weight vector (1.659)
$P$ : symmetric operators (1.657)
$A$ : compact subgroup (1.641)
$Y$ : global minimum (1.618)
${\displaystyle M_{\mu ))$ : modules (1.599)

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