User:Physikerwelt

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)
• $M\_\{J\}$: 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)
• $M\_\{L\}$: microstates (1.437)

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)
• $\backslash mathbf\{Q\}$: rational numbers (1.939)
• $M\_\{\backslash mathfrak\{p\}\}$: module (1.882)
• $e$: multiplicities (1.875)
• $K\_\{0\}$: 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)

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)
• $\backslash mathbf\{Z\}$: 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)
• $\backslash mathbf\{T\}$: 2-torus (1.738)
• $B$: base space (1.701)
• $C$: 1-cells (1.685)
• $\backslash mathbf\{R\}$: bottle (1.465)

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)

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)
• $E\_\{x\}$: 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)
• $\backslash mathbf\{R\}$: homeomorphism (1.625)

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)

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:

• $\backslash mathbf\{v\}$: velocity (8.716)
• $\backslash mathbf\{E\}$: electric field (7.522)
• $B$: magnetic flux (7.368)
• $\backslash mathbf\{B\}$: magnetic field (6.691)
• $q$: electric charge (5.029)
• $x$: direction (4.239)
• $\backslash mathbf\{F\}$: 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)
• $\backslash mathbf\{r\}$: position vector (1.847)
• $\backslash mathbf\{x\}$: position (1.845)
• $m$: mass (1.793)
• $\backslash mathcal\{E\}$: electromotive force (1.778)
• $E$: electric field (1.750)
• $N$: identical turns (1.714)
• $\backslash tau$: proper time (1.712)
• $\backslash mathbf\{A\}$: vector area (1.531)
• $d$: magnetic induction (1.459)

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:

• $V\_\{G\}$: voltage (3.355)
• $R\_\{G\}$: resistance (1.833)
• $R\_\{2\}$: resistance (1.664)
• $R\_\{x\}$: high precision (1.586)

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:

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

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:

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

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:

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

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:

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

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)
• $\backslash eta$: natural transformation (1.756)
• $y$: generator (1.746)
• $f$: morphism (1.629)
• $\backslash mathbf\{C\}$: object (1.628)
• $R$: objects (1.499)

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:

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

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)
• $\backslash mathbf\{C\}$: category (2.665)
• $Y$: function (mathematics) (2.460)
• $a$: diagram (category theory) (1.852)
• $\backslash mathbf\{A\}$: exact functor (1.845)
• $F$: exact functor (1.793)
• $M$: ring (mathematics) (1.664)
• $k$: one-dimensional vector space (1.641)

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)
• $\backslash mathbf\{Z\}$: 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)
• $N\_\{i\}$: submodules (3.400)
• $m$: matrix (mathematics) (3.154)
• $x$: polynomial ring (3.100)
• $\backslash mathfrak\{m\}$: ideal (ring theory) (2.798)
• $\backslash mathfrak\{g\}$: lie algebra (2.711)
• $\backslash mathbf\{Q\}$: ring (2.608)
• $B$: dense right ideal (2.571)
• $b$: nonzero (2.532)
• $p$: prime ideal (2.485)
• $g$: module homomorphism (1.950)
• $\backslash mathfrak\{p\}\_\{i\}$: chain (1.882)
• $C$: category (1.848)
• $\backslash mathbf\{F\}$: many copies (1.829)
• $h$: homomorphism (1.824)
• $U$: zariski (1.810)
• $\backslash mathbf\{R\}$: open subsets (1.810)
• $R\_\{\backslash mathfrak\{p\}\}$: module (1.774)
• $Q$: module (1.725)
• $O$: modules (1.600)
• $s$: subject (1.598)
• $x\_\{i\}$: zero-divisor (1.591)

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)
• $V\_\{b\}$: volume (3.523)
• $V\_\{a\}$: volume (3.438)
• $V\_\{c\}$: volume (2.761)
• $W$: work (thermodynamics) (2.735)
• $a$: energy (2.562)
• $A$: state (1.937)
• $X$: arbitrary state (1.907)
• $V\_\{d\}$: volume (1.902)
• $t\_\{1\}$: time (1.816)
• $M$: molar mass (1.779)
• $q$: heat (1.723)
• $u\text{'}$: mass (1.688)
• $d$: exact differential (1.621)
• $E$: total energy (1.574)
• $U\_\{2\}$: new system (1.476)

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)
• $v\_\{i\}$: vertex (5.393)
• $K\_\{n\}$: complete graph (3.913)
• $d$: degree (graph theory) (3.842)
• $i$: color (3.635)
• $f$: graph isomorphism (3.485)
• $e$: edge (2.776)
• $N\_\{i\}$: neighbourhood (graph theory) (2.731)
• $w$: edges (2.486)
• $W$: graph (2.441)
• $k\_\{i\}$: vertices (2.221)
• $V$: vertices (1.950)
• $C$: vertex cover (1.939)
• $r$: complexity (1.939)
• $K\_\{6\}$: graph (1.937)
• $O$: running time (1.866)
• $X$: finite set (1.848)
• $Q$: sequence (1.847)
• $v\_\{j\}$: vertex (1.816)
• $m\_\{2\}$: first color (1.779)
• $e\_\{ij\}$: vertex (1.712)
• $E$: edges (1.708)
• $W\_\{n\}$: wheel graph (1.690)
• $F$: graph (1.687)
• $K\_\{n,n\}$: chromatic number (1.659)
• $c$: vertex (1.657)
• $\backslash phi$: chromatic roots (1.524)

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)
• $\backslash mathcal\{C\}$: 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)
• $\backslash delta$: 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)
• $\backslash Sigma$: 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)
• $c\_\{1\}$: codewords (1.939)
• $B$: estimator (1.891)
• $M$: codewords (1.882)
• $h$: function (1.858)
• $c\_\{2\}$: codewords (1.754)
• $C\_\{i\}$: code (1.659)
• $L$: code (1.563)
• $S$: nformation (1.524)

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)
• $\backslash mathbf\{x\}$: tuple (1.891)
• $k$: tuple (1.817)
• $S$: successor function (1.791)
• $O$: nspace (1.754)
• $h$: induction step (1.738)
• $A\_\{t\}$: acceptance set (1.609)
• $v$: middle term (1.587)
• $A$: natural numbers (1.495)

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:

• $\backslash mathbf\{R\}$: linear map (2.767)
• $a$: function (2.561)
• $f$: function (2.550)
• $n$: commodities (2.492)
• $j$: functions (2.481)
• $p\_\{i\}$: 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)

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)
• $X\_\{i\}$: collection (2.685)
• $\backslash sigma\_\{I\}$: scale (2.560)
• $\backslash mathbb\{R\}$: euclidean space (2.214)
• $R$: euclidean space (1.974)
• $r$: radius (1.950)
• $N$: dimensions (1.939)
• $L\_\{v\}$: direction (1.902)
• $\backslash varepsilon$: erosion (1.902)
• $k$: dimensional ridge (1.900)
• $\backslash mu$: matrix (1.847)
• $\backslash Sigma\_\{D\}$: covariance matrices (1.810)
• $I\_\{y\}$: partial derivatives (1.790)
• $z$: translation (1.790)
• $\backslash Sigma\_\{I\}$: covariance matrices (1.781)
• $\backslash delta$: dilation (1.781)
• $I$: image (1.690)
• $\backslash mathbf\{x\}$: direction (1.641)
• $\backslash mathbf\{x\}\_\{0\}$: tangent lines (1.621)
• $a$: dilation (1.618)
• $\backslash gamma$: square (1.581)
• $\backslash lambda\_\{2\}$: positive value (1.563)
• $I\_\{x\}$: partial derivatives (1.524)
• $n$: pixels (1.488)

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)
• $\backslash mathbb\{F\}\_\{q\}$: finite field (1.891)
• $s$: tuple (1.864)
• $b$: real numbers (1.810)
• $p$: polynomial (1.800)

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)
• $D\_\{t\}$: distribution (2.707)
• $h\_\{t\}$: classifier (1.939)
• $S$: partial approximation (1.902)
• $y\_\{i\}$: labels (1.845)
• $D\_\{t+1\}$: probability distribution (1.781)
• $\backslash mathcal\{H\}$: loss function (1.688)

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)
• $\backslash Delta\_\{\backslash xi\}$: laplace (1.754)
• $K$: gaussian curvature (1.688)
• $B$: continuous (topology) (1.632)
• $H$: infinite area (1.628)
• $\backslash mathbf\{R\}$: unit sphere (1.591)
• $n$: unit sphere (1.583)

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)
• $\backslash nu$: specific volume (1.779)
• $n$: volume (1.756)
• $p$: pressure (1.752)
• $P\_\{tot\}$: partial pressure (1.726)
• $P\_\{x\}$: gas mixture (1.717)
• $a$: chaotic behavior (1.632)

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)
• $r\_\{1\}$: sound intensity (1.790)
• $A$: area (1.787)
• $I\_\{2\}$: sound intensity (1.779)
• $\backslash mathbf\{I\}$: acoustic intensity (1.591)
• $w$: density (1.441)

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:

• $\backslash mathbf\{F\}$: force (21.736)
• $m$: mass (21.105)
• $\backslash mathbf\{v\}$: velocity (21.053)
• $t$: time (17.001)
• $\backslash mathbf\{p\}$: momentum (14.082)
• $\backslash mathbf\{L\}$: angular momentum (13.398)
• $i$: particle (12.579)
• $\backslash mathbf\{a\}$: acceleration (12.473)
• $\backslash mathbf\{r\}$: position (vector) (10.802)
• $I$: moment of inertia (10.035)
• $E$: kinetic energy (7.861)
• $\backslash mathbf\{V\}$: 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)
• $\backslash mathbf\{u\}$: velocity (3.661)
• $N$: particles (3.660)
• $\backslash mathbf\{I\}$: moment of inertia tensor (3.635)
• $\backslash mathbf\{S\}$: angular momentum (3.633)
• $\backslash mathbf\{e\}$: unit vector (3.626)
• $\backslash mathbf\{A\}$: acceleration (3.595)
• $\backslash mathbf\{C\}$: 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)
• $\backslash omega$: angular velocity (2.869)
• $L$: length (2.771)
• $P$: pivot point (2.728)
• $\backslash mathbf\{g\}$: gravitational acceleration (2.725)
• $\backslash mathbf\{n\}$: unit vector (2.682)
• $Q$: rotation matrix (2.670)
• $\backslash mathbf\{q\}$: generalized coordinates (2.627)
• $k$: spring (2.602)
• $\backslash mathbf\{R\}$: 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)
• $\backslash phi$: angle (1.950)
• $\backslash mathbf\{t\}$: unit vector (1.907)
• $f$: frequency (1.882)
• $m\_\{i\}$: masses (1.882)
• $W$: total work (1.881)
• $S$: frame (1.872)
• $B$: skew-symmetric matrix (1.865)
• $I\_\{C\}$: mass (1.865)
• $\backslash mathbf\{\backslash hat\{e\}\}\_\{r\}$: rotation (1.852)
• $\backslash mathbf\{\backslash hat\{e\}\}\_\{\backslash theta\}$: unit vector (1.845)
• $\backslash mathbf\{W\}$: weight (1.833)
• $\backslash hat\{u\}\_\{R\}$: unit vector (1.789)
• $\backslash mathbf\{J\}$: orbital (1.752)
• $y$: direction vector (1.749)
• $A$: moment (1.744)
• $\backslash mathbf\{D\}$: electric field (1.724)
• $\backslash mathbf\{r\}\_\{1\}$: torque (1.724)
• $m\_\{B\}$: body (1.718)
• $\backslash mathbf\{x\}$: initial positions (1.718)
• $\backslash mathbf\{P\}$: canonical momentum (1.714)
• $\backslash mathbf\{M\}$: torque (1.701)
• $n$: similar objects (1.664)
• $r\_\{z\}$: momentum operator (1.591)
• $p$: potential energy (1.576)
• $R$: polar coordinate system (1.540)
• $\backslash hat\{u\}\_\{\backslash theta\}$: direction (1.439)

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:

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

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)
• $\backslash mathbf\{Z\}$: module (6.405)
• $\backslash mathbf\{C\}$: complex number (6.386)
• $T$: field (6.032)
• $v$: valuation (5.397)
• $k$: field (5.381)
• $\backslash mathbf\{Q\}$: local field (5.259)
• $E$: field (5.180)
• $\backslash mathbf\{H\}$: quaternion (4.593)
• $\backslash mathbf\{R\}$: real number (4.559)
• $Q$: linear operator (4.474)
• $\backslash mathbf\{K\}$: 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)
• $\backslash mathbf\{t\}$: 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)
• $\backslash mathbf\{a\}$: 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)
• $\backslash mathbb\{Z\}$: subgroup (1.738)
• $r$: roots (1.714)
• $\backslash Gamma$: segment (1.691)
• $Y$: univariate polynomial (1.681)
• $a\_\{i\}$: weight (1.659)
• $\backslash mathbb\{Z\}\_\{p\}$: valuation ring (1.657)
• $\backslash mathbf\{f\}$: basis (1.657)
• $and$: difference operator (1.640)
• $\backslash mathbf\{F\}$: hyperreal number (1.556)
• $\backslash mathbf\{y\}$: coordinate tuples (1.530)

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

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:

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

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)

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:

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

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

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)
• $\backslash mathbf\{H\}$: space (2.869)
• $E$: banach (2.688)
• $\backslash mathbf\{T\}$: operator (2.641)
• $C$: class (2.604)
• $i$: subset (2.565)
• $U$: bounded linear operator (2.450)
• $H\_\{i\}$: 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)

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)
• $\backslash mathbf\{C\}$: complex plane (2.845)
• $\backslash gamma$: curve (1.974)
• $z$: zero (1.900)
• $K$: kernel (1.812)
• $f\_\{c\}$: critical point (mathematics) (1.762)
• $c$: change (1.623)
• $n$: iterated function (1.598)

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)

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:

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

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

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)
• $T\_\{\backslash mathrm\{eff\}\}$: radius (3.705)
• $\backslash sigma$: effective surface temperature (3.705)
• $L$: luminosity (3.484)
• $T$: tauri (1.939)
• $V\_\{t\}$: radial velocity (1.845)

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:

• $c\_\{0\}$: 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)
• $c\_\{1\}$: marginal propensity to consume (2.685)
• $p$: price level (1.926)
• $\backslash bar\{u\}$: utility level (1.847)
• $Y$: payments (1.790)
• $Y\_\{d\}$: disposable income (1.779)

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)
• $f\_\{\backslash Gamma,R\}$: flow (2.672)
• $A$: strategy (2.501)
• $a$: solution concept (1.887)
• $f$: flow (1.848)
• $T\_\{i\}$: type (1.810)
• $A\_\{i\}$: action (1.688)
• $G$: flows (1.677)
• $S\_\{i\}$: player (1.677)
• $U$: player (1.588)
• $s\_\{i\}$: paths (1.471)

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)
• $\backslash mathbf\{R\}$: 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)

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)
• $\backslash psi$: vertex angle (2.573)
• $f$: polar coordinate system (2.550)
• $P$: pedal point (2.531)
• $c$: consecutive sides (2.527)
• $\backslash theta$: 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)

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)

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

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)

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)
• $\backslash mu\_\{r\}$: relative permeability (1.793)
• $Z\_\{0\}$: characteristic impedance (1.714)
• $S$: insulator (1.689)
• $\backslash epsilon$: dielectric constant (1.677)

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)
• $\backslash mathbf\{j\}$: equation (2.665)
• $\backslash mathbf\{q\}$: wave vector (2.640)
• $n$: atomic number density (2.625)
• $k$: dependence (2.619)
• $c\_\{v,p\}$: specific heat capacity (2.600)
• $m$: atomic mass (2.521)
• $i$: atom (2.492)
• $j$: atom (2.452)
• $p$: type materials (2.417)
• $\backslash delta$: limit (1.939)
• $z$: direction (1.937)
• $Z\_\{f\}$: partition function (statistical mechanics) (1.902)
• $n\_\{e,c\}$: 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)
• $D\_\{p\}$: density of states (1.834)
• $f\_\{ph\}$: equilibrium distribution (1.811)
• $S$: spin (1.810)
• $\backslash tau$: group velocity (1.810)
• $c$: concentration (1.810)
• $e$: elementary charge (1.790)
• $L$: length (1.749)
• $I\_\{ph,\}$: radiation intensity (1.744)
• $T$: temperature (1.742)
• $d\_\{p\}$: slope (1.714)
• $\backslash mathbf\{p\}$: momentum (1.696)
• $A$: electrolyte (1.688)
• $\backslash mathbf\{s\}$: unit vector (1.677)
• $v\_\{d\}$: drift velocity (1.664)
• $n\_\{i\}$: electron hole concentration (1.657)
• $p\_\{0\}$: electron hole concentration (1.657)
• $v\_\{1\}$: film2 (1.657)
• $\backslash mathbf\{u\}$: velocity (1.653)
• $\backslash mathbf\{d\}$: displacement vector (1.592)
• $v\_\{z\}$: phonon velocity (1.574)
• $v\_\{2\}$: film2 (1.524)
• $a$: electron (1.490)
• $\backslash kappa$: inverse screening length (1.489)

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)

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)
• $R\_\{\backslash Delta\}$: impedance (1.847)
• $n$: total number (1.754)
• $R\text{'}\text{'}$: δ circuit (1.524)

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)

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)

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)
• $\backslash mathbf\{R\}$: 3-sphere (1.497)

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)

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)
• $\backslash kappa$: cardinal number (4.692)
• $\backslash aleph\_\{\backslash omega\}$: cardinal number (4.375)
• $G$: domain (3.577)
• $B$: subset (3.482)
• $\backslash mathbf\{N\}$: natural number (3.396)
• $\backslash aleph\_\{\backslash lambda\}$: successor ordinal (3.316)
• $\backslash aleph\_\{0\}$: cardinality (3.231)
• $N$: transitive class (2.787)
• $\backslash aleph\_\{\backslash alpha\}$: cardinal number (2.741)
• $\backslash mathbf\{M\}$: 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)
• $\backslash omega$: ordinals (2.469)
• $\backslash beth\_\{2\}$: cardinality of the continuum (2.414)
• $\backslash alpha$: ordinals (1.939)
• $\backslash mathbf\{Q\}$: rational number (1.933)
• $\backslash mathbf\{R\}$: real number (1.855)
• $\backslash beth\_\{\backslash alpha\}$: cardinality (1.847)
• $\backslash aleph\_\{1\}$: successor cardinal (1.790)
• $\backslash lambda$: successor ordinal (1.754)
• $\backslash mathbf\{C\}$: complex number (1.740)
• $X$: measure theory (1.698)
• $x$: integer (1.648)
• $i$: sets (1.548)

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)
• $\backslash sigma\_\{v\}$: tensile stress (2.499)
• $h$: order (1.812)
• $J$: function (1.775)
• $u$: equation (1.738)
• $\backslash mathbf\{MandelVoigtnotation\}$: notation (1.724)
• $\backslash sigma\_\{3\}$: plane (1.707)
• $\backslash sigma\_\{y\}$: yield strength (1.671)
• $t$: change (1.524)

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)
• $f\_\{i\}$: freedom (2.961)
• $M$: degree-of-freedom (2.941)
• $N$: fixed link (2.531)
• $i$: freedom (2.488)

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

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)
• $C\_\{0\}$: initial concentration (5.125)
• $C\_\{t\}$: concentration (3.662)
• $k\_\{e\}$: elimination rate (1.754)

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)
• $\backslash mathbf\{B\}$: magnetic field (13.834)
• $Q$: electric charge (11.565)
• $c$: speed of light (9.225)
• $\backslash mathbf\{E\}$: electric field (9.034)
• $B$: baryon number (8.185)
• $t$: coordinate time (7.233)
• $\backslash mathbf\{A\}$: magnetic potential (6.897)
• $\backslash mathbf\{v\}$: 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)
• $T\_\{3\}$: weak isospin (4.261)
• $V$: potential energy (4.258)
• $A$: magnetic dipole (4.197)
• $\backslash mathbf\{r\}$: position vector (3.784)
• $e$: magnetic charge (3.667)
• $d$: dimensions (3.531)
• $M$: manifold (3.404)
• $\backslash mathbf\{p\}$: kinetic momentum (3.362)
• $u$: up quark (3.213)
• $P$: parity (3.142)
• $I\_\{3\}$: isospin (2.830)
• $G$: physics (2.803)
• $\backslash mathbf\{J\}$: current density (2.803)
• $Y\_\{W\}$: weak hypercharge (2.762)
• $n$: up quark (2.744)
• $\backslash varphi$: electric potential (2.685)
• $D$: gauge covariant derivative (2.676)
• $\backslash mathbf\{R\}$: space (2.615)
• $s$: field (2.595)
• $\backslash mathbf\{j\}$: probability current (2.578)
• $I$: third component (2.555)
• $\backslash mathbf\{H\}$: fields (2.543)
• $x$: position (2.479)
• $p$: form (2.472)
• $\backslash mathbf\{D\}$: electric displacement (1.942)
• $g$: metric tensor (1.939)
• $\backslash gamma$: closed loop (1.891)
• $\backslash mathbf\{f\}$: lorentz force (1.858)
• $p\_\{i\}$: momentum component (1.858)
• $\backslash mathbf\{M\}$: magnetization (1.850)
• $v\_\{y\}$: direction (1.779)
• $v\_\{z\}$: direction (1.779)
• $\backslash mathbf\{S\}$: momentum operator (1.766)
• $C$: charm (quantum number) (1.756)
• $\backslash sigma$: surface (1.749)
• $y$: direction (1.749)
• $\backslash mathbf\{g\}$: gravitational acceleration (1.724)
• $\backslash mathbf\{P\}$: four momentum (1.717)
• $q\_\{i\}$: cartesian coordinate (1.689)
• $u\_\{1\}$: velocities (1.677)
• $\backslash mathcal\{C\}$: smooth function (1.621)
• $m\_\{0\}$: invariant mass (1.621)
• $i$: direction (1.564)
• $\backslash mathbf\{u\}$: lorentz factor (1.532)
• $X$: mmj2ubwoeev70gxo14dyaw (1.532)

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:

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

Category information

• reference category: General nonassociative rings
• code: 17Axx (MSC)
• wiki categories: [(:Category:Algebras, 3), (:Category:Algebraic structures, 2), (:Category:Representation theory, 2)]

Cluster information:

• cluster id: [7971]
• matching score: 0.383603283984
• purity: 1.0
• matching keywords: [u'algebras', u'nonassociative']

Definitions:

• $a$: unital algebra (5.875)
• $N$: 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)
• $\backslash mathbf\{R\}$: octonion algebra (1.865)
• $\backslash mathbb\{Q\}\_\{\backslash nu\}$: quaternion algebra (1.659)
• $B$: algebra over a field (1.655)

Category information

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

Cluster information:

• cluster id: [589, 2465, 3238, 4338, 6820]
• matching score: 0.450480059793
• purity: 1.0
• matching keywords: [u'functions', u'lucas', u'stirling', u'number', u'binomial', u'numbers', u'sequences', u'arithmetic', u'fibonacci']

Definitions:

• $n$: prime number (13.232)
• $p$: 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)
• $\backslash mathcal\{B\}\_\{r\}$: sequences (1.939)
• $r$: irrational number (1.939)
• $x$: real number (1.939)
• $s$: pseudoprime (1.900)
• $V\_\{n\}$: fibonacci number (1.891)
• $V$: sequence (1.812)
• $m$: natural number (1.799)
• $\backslash mathcal\{B\}\_\{s\}$: sequences (1.754)
• $L$: conventions (1.712)
• $S$: lower triangular matrix (1.529)
• $Q$: integer sequence (1.513)

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:

• cluster id: [7565]
• matching score: 0.513512645652
• purity: 1.0
• matching keywords: [u'field', u'number', u'class', u'galois', u'algebraic']

Definitions:

• $a$: g-module (5.129)
• $K$: brauer group (4.785)
• $G$: galois group (4.459)
• $v$: discrete valuation (4.071)
• $L$: abelian extension (3.565)
• $p$: prime number (2.753)
• $\backslash mathbf\{Z\}$: projective module (2.636)
• $\backslash mathbf\{R\}$: trivial extension (1.834)
• $O\_\{K\}$: galois (1.790)
• $\backslash mathfrak\{m\}\_\{K\}$: field norm (1.790)
• $A$: galois (1.787)
• $w$: extension of a valuation (1.749)
• $\backslash mathbf\{Q\}$: field (1.725)
• $X$: smooth morphism (1.677)

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:

• cluster id: [5948]
• matching score: 0.501027191748
• purity: 1.0
• matching keywords: [u'number', u'arithmetic']

Definitions:

• $a$: field (mathematics) (4.389)
• $\backslash mathbf\{C\}$: p-adic number (4.367)
• $\backslash mathbf\{Q\}$: field (mathematics) (4.365)
• $F$: field (3.392)
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• $p$: adic numbers (3.162)
• $L$: dirichlet l-function (2.725)
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• $E$: 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)
• $\backslash mathbf\{K\}$: field (mathematics) (1.939)
• $v$: ultrametric place (1.848)
• $\backslash mathbf\{Q\}\_\{p\}$: galois extension (1.845)
• $c$: choice (1.810)
• $\backslash mathbf\{R\}$: real number (1.739)
• $G$: absolute galois group (1.688)
• $D$: prime ideal (1.683)
• $n$: root (1.672)
• $P$: prime ideal (1.666)
• $A$: field (1.642)
• $N$: morphism (1.632)
• $i$: gaussian rational (1.629)
• $g$: valuation (1.623)
• $\backslash mathbf\{Z\}$: ring (1.577)

Category information

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

Cluster information:

• cluster id: [474, 2843, 8509]
• matching score: 0.462938101673
• purity: 1.0
• matching keywords: [u'linear', u'algebra', u'numerical', u'iterative', u'analysis', u'sparse', u'matrices', u'matrix']

Definitions:

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• $a$: triangular matrix (8.400)
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• $\backslash Lambda$: diagonal matrix (1.816)
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• $s$: matrix (1.677)
• $\backslash omega$: iteration (1.659)
• $e$: error end (1.623)

Category information

• reference category: Mathematical programming, optimization and variational techniques
• code: 65Kxx (MSC)
• wiki categories: [(:Category:Mathematical analysis, 6), (:Category:Fields of mathematics, 4), (:Category:Analysis, 2)]

Cluster information:

• cluster id: [6109, 9711]
• matching score: 0.35403960571
• purity: 1.0
• matching keywords: [u'mathematical', u'numerical', u'variational', u'optimization', u'analysis']

Definitions:

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

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:

• cluster id: [9609]
• 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)
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• $\backslash mathbf\{R\}$: wiener process (1.744)
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• $P$: distribution (1.654)
• $d$: dimensional case (1.648)

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:

• cluster id: [4521, 8900]
• matching score: 0.303644398062
• purity: 1.0
• matching keywords: [u'numerical', u'wavelets', u'analysis', u'transforms', u'fourier']

Definitions:

• $a$: signal (5.495)
• $H$: filter coefficients (1.891)
• $h$: filter (1.882)
• $\backslash hat\{\backslash psi\}$: admissibility (1.754)
• $\backslash pi$: period (1.690)
• $y$: period (1.586)

Category information

• reference category: Computer aspects of numerical algorithms
• code: 65Yxx (MSC)
• wiki categories: [(:Category:Numerical analysis, 5), (:Category:Zero, 3), (:Category:Algorithms, 3)]

Cluster information:

• cluster id: [3003]
• matching score: 0.535513837448
• purity: 1.0
• matching keywords: [u'numerical', u'algorithms', u'analysis']

Definitions:

• $f$: domain of a function (7.203)
• $L$: lipschitz continuity (3.389)
• $n$: function values (2.590)
• $x\_\{0\}$: initial values (2.586)
• $x$: mean value (2.297)
• $x\_\{1\}$: initial values (1.663)
• $a$: fixed-point iteration (1.628)
• $x\_\{n\}$: secant method (1.563)

Category information

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

Cluster information:

• cluster id: [469]
• matching score: 0.805389122876
• purity: 1.0
• matching keywords: [u'measure']

Definitions:

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

Category information

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

Cluster information:

• cluster id: [8220]
• matching score: 0.297866726589
• purity: 1.0
• matching keywords: [u'data']

Definitions:

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

Category information

• reference category: NO_REFERENCE_CATEGORY
• code: NO_CODE (NO_SCHEMA)
• wiki categories: [(:Category:Polyhedra, 4), (:Category:Johnson solids, 4), (:Category:Prismatoid polyhedra, 2)]

Cluster information:

• cluster id: [5716]
• matching score: 0.180265473142
• purity: 1.0
• matching keywords: [u'solids']

Definitions:

• $a$: edge length (3.727)
• $J$: johnson solid (3.626)
• $C\_\{5v\}$: decagon (1.476)
• $C\_\{4v\}$: octagon (1.468)

Category information

• reference category: NO_REFERENCE_CATEGORY
• code: NO_CODE (NO_SCHEMA)
• wiki categories: [(:Category:Lists of NFL head coaches by team, 3), (:Category:NFL lists, 3), (:Category:NFL head coaches by team, 3)]

Cluster information:

• cluster id: [2035]
• matching score: 0.0738290007636
• purity: 1.0
• matching keywords: [u'new', u'national']

Definitions:

• $e$: note1 (7.299)
• $b$: % note1 (6.653)
• $f$: note1 (5.567)
• $c$: note1 (5.487)
• $d$: note1 (4.557)
• $a$: charter member (1.854)
• $g$: note1 (1.812)

Category information

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

Cluster information:

• cluster id: [7597]
• matching score: 0.135198347331
• purity: 1.0
• matching keywords: [u'projections']

Category information

• reference category: NO_REFERENCE_CATEGORY
• code: NO_CODE (NO_SCHEMA)
• wiki categories: [(:Category:Coordinate systems, 4), (:Category:Cartography, 4), (:Category:Cartographic projections, 4)]

Cluster information:

• cluster id: [9660]
• matching score: 0.140056702345
• purity: 1.0
• matching keywords: [u'systems']

Definitions:

• $R$: radius (3.479)

Category information

• reference category: NO_REFERENCE_CATEGORY
• code: NO_CODE (NO_SCHEMA)
• wiki categories: [(:Category:Knot theory, 4), (:Category:Surfaces, 2), (:Category:Torus knots, 2)]

Cluster information:

• cluster id: [6000]
• matching score: 0.19018451167
• purity: 1.0
• matching keywords: [u'surfaces', u'knots']

Category information

• reference category: NO_REFERENCE_CATEGORY
• code: NO_CODE (NO_SCHEMA)
• wiki categories: [(:Category:Wireless, 3), (:Category:Radio technology, 3), (:Category:Radio frequency propagation, 3)]

Cluster information:

• cluster id: [7678]
• matching score: 0.0970316339844
• purity: 1.0
• matching keywords: [u'electromagnetic']

Definitions:

• $G$: gain (4.934)
• $h$: base station antenna height (4.338)
• $L$: path loss (3.335)
• $\backslash lambda$: wavelength (1.900)
• $f$: frequency (1.900)
• $\backslash gamma$: slope (1.790)
• $d$: distance (1.790)
• $F$: adjustment (1.742)

Category information

• reference category: NO_REFERENCE_CATEGORY
• code: NO_CODE (NO_SCHEMA)
• wiki categories: [(:Category:National Basketball Association seasons, 6), (:Category:National Basketball Association seasons by team, 6), (:Category:National Basketball Association lists, 2)]

Cluster information:

• cluster id: [2044, 9746]
• matching score: 0.100187378156
• purity: 1.0
• matching keywords: [u'association']

Definitions:

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

Category information

• reference category: NO_REFERENCE_CATEGORY
• 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:

• cluster id: [7982]
• matching score: 0.101694565889
• purity: 1.0
• matching keywords: [u'association']

Category information

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

Cluster information:

• cluster id: [9126]
• matching score: 0.161404183301
• 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)

Category information

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

Cluster information:

• cluster id: [8646]
• matching score: 0.306093112328
• purity: 1.0
• matching keywords: [u'design']

Definitions:

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

Category information

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

Cluster information:

• cluster id: [2680]
• matching score: 0.188257495156
• purity: 1.0
• matching keywords: [u'surfaces', u'knots', u'geometric', u'topology']

Category information

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

Cluster information:

• cluster id: [2156]
• matching score: 0.0941993903914
• purity: 1.0
• matching keywords: [u'electronic']

Definitions:

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

Category information

• reference category: NO_REFERENCE_CATEGORY
• code: NO_CODE (NO_SCHEMA)
• wiki categories: [(:Category:Baseball statistics, 5), (:Category:Batting statistics, 4), (:Category:Batting (baseball), 4)]

Cluster information:

• cluster id: [7094]
• matching score: 0.747742788884
• purity: 1.0
• matching keywords: [u'statistics']

Definitions:

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

Category information

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

Cluster information:

• cluster id: [5332]
• matching score: 0.197741178813
• purity: 1.0
• matching keywords: [u'control']

Definitions:

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

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:

• cluster id: [6375]
• matching score: 0.132670227656
• purity: 1.0
• matching keywords: [u'projections']

Definitions:

• $\backslash varphi$: latitude (7.113)
• $\backslash lambda$: latitude (4.498)
• $\backslash lambda\_\{0\}$: longitude (1.845)

Category information

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

Cluster information:

• cluster id: [3822]
• matching score: 0.631482808408
• purity: 1.0
• 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)

Category information

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

Cluster information:

• cluster id: [9112]
• matching score: 0.373216933738
• purity: 1.0
• matching keywords: [u'number']

Definitions:

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

Category information

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

Cluster information:

• cluster id: [2076]
• matching score: 0.276097133578
• purity: 1.0
• matching keywords: [u'physics']

Definitions:

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

Category information

• reference category: NO_REFERENCE_CATEGORY
• code: NO_CODE (NO_SCHEMA)
• wiki categories: [(:Category:Tensors, 3), (:Category:Mathematical methods in general relativity, 2), (:Category:Tensors in general relativity, 2)]

Cluster information:

• cluster id: [3608]
• matching score: 0.331350124557
• purity: 1.0
• matching keywords: [u'relativity']

Definitions:

• $a$: tensor rank (5.498)
• $C\_\{abcd\}$: weyl tensor (1.882)

Category information

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

Cluster information:

• cluster id: [2215]
• matching score: 0.241447787175
• purity: 1.0
• matching keywords: [u'procedures']

Definitions:

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

Category information

• reference category: NO_REFERENCE_CATEGORY
• code: NO_CODE (NO_SCHEMA)
• wiki categories: [(:Category:Electrodes, 4), (:Category:Electricity, 4), (:Category:Electrochemistry, 4)]

Cluster information:

• cluster id: [9596]
• matching score: 0.126858336587
• purity: 1.0
• 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)
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Category information

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

Cluster information:

• cluster id: [4928]
• matching score: 0.125097921763
• purity: 1.0
• matching keywords: [u'equations', u'differential', u'partial']

Definitions:

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

Category information

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

Cluster information:

• cluster id: [7570]
• matching score: 0.302754171352
• purity: 1.0
• matching keywords: [u'mechanical']

Definitions:

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

Category information

• reference category: NO_REFERENCE_CATEGORY
• code: NO_CODE (NO_SCHEMA)
• wiki categories: [(:Category:Northern constellations, 3), (:Category:Extrasolar planets, 3), (:Category:Exoplanets discovered by year, 3)]

Cluster information:

• cluster id: [6094]
• matching score: 0.115373534547
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• matching keywords: [u'astronomical', u'astronomy', u'objects']

Definitions:

• $a$: jupiter mass (5.811)

Category information

• reference category: NO_REFERENCE_CATEGORY
• code: NO_CODE (NO_SCHEMA)
• wiki categories: [(:Category:Physical quantities, 3), (:Category:Physical constants, 3), (:Category:Constants, 3)]

Cluster information:

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• matching score: 0.156645730378
• purity: 1.0
• matching keywords: [u'energy', u'matter', u'electron', u'mass', u'spectroscopy', u'molecular', u'physics', u'constants', u'physical']

Definitions:

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Category information

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• code: NO_CODE (NO_SCHEMA)
• wiki categories: [(:Category:Telecommunications engineering, 3), (:Category:Applied mathematics, 3), (:Category:Electrical engineering, 3)]

Cluster information:

• cluster id: [8027]
• matching score: 0.191024375397
• purity: 1.0
• 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)
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• $t$: dirac delta function (1.424)

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)
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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:

• cluster id: [2513]
• matching score: 0.234530365211
• purity: 1.0
• matching keywords: [u'algebra']

Definitions:

• $n$: dimensions (4.319)
• $z\_\{i\}$: rational functions (2.571)
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• $\backslash mathbf\{x\}$: mapping vectors (1.710)

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:

• cluster id: [7471]
• matching score: 0.251226310938
• purity: 1.0
• matching keywords: [u'calculus']

Definitions:

• $a$: vector operator (6.317)
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• $\backslash varphi$: scalar-valued function (1.714)
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• $q$: tensor (1.657)
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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:

• cluster id: [5231]
• matching score: 0.248183919026
• purity: 1.0
• matching keywords: [u'physics']

Definitions:

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• $t$: time (3.419)
• $R$: region (2.799)
• $R\_\{2\}$: region (2.799)
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• $n$: solutions (2.465)
• $p$: momentum (2.421)
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• $\backslash mathbf\{k\}$: wave vector (1.939)
• $A\_\{k\}$: discrete components (1.937)
• $N$: particles (1.848)
• $\backslash Psi$: wavefunction (1.847)
• $a$: ball (1.815)
• $V$: total volume (1.754)
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• $\backslash Omega\_\{r\}$: volume (1.754)
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• $A$: classical mechanics (1.645)
• $\backslash boldsymbol\{q\}$: dispersion relation (1.628)
• $s$: wave (1.618)
• $\backslash mathbf\{r\}$: position vector (1.604)
• $s\_\{z\}$: spin (physics) (1.600)

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)
• $m\_\{0\}$: mass (3.560)
• $m\_\{1\}$: total mass (3.245)
• $v\_\{e\}$: 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)
• $I\_\{sp\}$: specific impulse (2.508)
• $a$: rocket engine (2.402)
• $F\_\{i\}$: external forces (1.865)
• $I$: equation (1.779)
• $\backslash gamma$: lorentz factor (1.720)
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• $c$: speed of light (1.665)
• $\backslash eta$: equation (1.557)

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:

• $H$: hilbert space (8.983)
• $T$: linear operator (4.387)
• $N$: linear operator (4.181)
• $K$: operator (3.199)
• $V$: orthogonal projection (2.702)
• $X$: dilation (1.939)
• $D\_\{T\}$: operator (1.749)
• $A$: normal operator (1.696)

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

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:

• cluster id: [5986, 6541]
• 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)
• $\backslash lambda$: eigenvalue (2.683)
• $u$: function (mathematics) (1.913)
• $\backslash mathbb\{R\}$: fiber bundle (1.766)
• $t$: function (1.718)
• $Q$: tangent bundle (1.689)

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:

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

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:

• $\backslash mathbf\{E\}$: electric field (7.113)
• $\backslash mathbf\{H\}$: magnetic field (4.360)
• $\backslash mathbf\{J\}$: current density (4.341)
• $\backslash mathbf\{B\}$: magnetic field (4.115)
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• $\backslash mathbf\{F\}$: field (3.581)
• $L$: differential operator (3.571)
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• $\backslash mathbf\{k\}$: wave vector (1.900)
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• $\backslash rho$: density (1.823)
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• $\backslash mathbf\{A\}$: electrical potential (1.774)
• $\backslash alpha$: ricci calculus (1.762)
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• $\backslash mathbf\{S\}$: vector area (1.690)
• $\backslash rho\_\{1\}$: slab (1.657)
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• $\backslash mathbf\{P\}$: material (1.598)
• $f$: frequency (1.591)
• $v$: nabla (1.506)
• $I$: charge (1.476)

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)
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• $i$: state (5.402)
• $X$: stochastic process (4.099)
• $S$: measurable space (3.889)
• $j$: state (3.385)
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• $c$: a.s. (1.815)
• $C$: variance (1.749)
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Category information

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

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)
• $\backslash mathbf\{M\}$: location parameter (3.971)
• $\backslash mathbf\{X\}$: matrix inverse (3.648)
• $\backslash lambda$: noncentrality parameter (3.567)
• $c$: constants (3.548)
• $b$: interval (3.348)
• $p$: posterior distribution (3.233)
• $X\_\{i\}$: uniform distribution (continuous) (3.077)
• $\backslash beta$: shape parameters (2.540)
• $\backslash mu$: scale parameter (2.533)
• $U$: uniform distribution (continuous) (2.530)
• $x$: scale (2.467)
• $\backslash boldsymbol\{\backslash Omega\}$: scale matrix (2.417)
• $\backslash boldsymbol\{\backslash Sigma\}$: 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)
• $\backslash tau\_\{4\}$: l-kurtosis (1.781)
• $\backslash mathbf\{R\}$: continuous distributions (1.743)
• $\backslash chi$: uniform distribution (continuous) (1.739)
• $\backslash gamma$: incomplete gamma function (1.724)
• $\backslash mathbf\{\backslash Psi\}$: positive-definite matrix (1.707)
• $r$: positive constants (1.707)
• $F$: f-distribution (1.689)
• $\backslash sigma$: rayleigh distribution (1.677)
• $\backslash mathbf\{\backslash Sigma\}$: covariance matrix (1.653)
• $Y$: laplace distribution (1.653)
• $T$: relation (1.590)
• $\backslash mathbf\{U\}$: scale matrix (1.589)
• $\backslash mathbf\{V\}$: scale matrix (1.589)
• $j$: constants (1.497)

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)
• $\backslash mathbf\{E\}$: expectation (3.648)
• $A$: operator (3.447)
• $Z$: observations (2.799)
• $\backslash mathcal\{A\}$: characteristic operator (2.797)
• $m$: brownian motion (2.625)
• $n$: itō diffusion (2.492)
• $\backslash mathbf\{P\}$: expectation (2.453)
• $S$: measurable space (1.974)
• $F$: natural filtration (1.915)
• $\backslash mathbf\{R\}$: euclidean space (1.910)
• $Y$: state (1.891)
• $s$: observations (1.865)
• $U$: sets (1.848)
• $U\_\{k\}$: sequences (1.810)
• $L$: operator (1.781)
• $\backslash mathbf\{N\}$: natural number (1.779)
• $K$: space (1.666)
• $y$: green's function (1.621)
• $r$: first exit time (1.591)

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:

• $F\_\{i\}$: operator (mathematics) (4.668)
• $a$: measure (mathematics) (3.439)
• $n$: magnetic quantum number (3.112)
• $H\_\{A\}$: space (2.835)
• $V$: electrostatic (2.644)
• $\backslash psi$: 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)
• $\backslash phi$: state (1.858)
• $K$: degenerate energy (1.845)
• $KS$: potential (1.812)
• $\backslash mathbf\{j\}$: current densities (1.812)
• $\backslash psi\_\{tar\}$: target state (1.812)
• $\backslash hat\{a\}\_\{i\}$: operators (1.811)
• $\backslash hat\{a\}\_\{j\}$: operators (1.810)
• $F$: function (1.800)
• $\backslash mathbf\{r\}$: radiation field (1.790)
• $v$: scalar potential (1.756)
• $M$: sigma algebra (1.708)
• $\backslash ell$: states (1.698)
• $U$: unitary operator (1.690)
• $\backslash mathbf\{V\}$: systems (1.689)
• $N$: hilbert space (1.657)
• $p$: fidelity (1.618)
• $J$: degenerate energy (1.524)

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)
• $\backslash phi$: 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)
• $g\_\{\backslash mu\backslash nu\}$: metric tensor (1.974)
• $W$: closed loop (1.939)
• $K$: operator (physics) (1.882)
• $\backslash omega\_\{\backslash mu\backslash nu\backslash rho\}$: spin connection (1.845)
• $\backslash mathcal\{T\}$: 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)
• $\backslash mathbf\{SchwingerDysonequations\}$: equations (1.654)
• $\backslash mu$: covariant derivative (1.629)
• $E$: perturbation theory (quantum mechanics) (1.527)

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)

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)
• $x\_\{n\}$: sequence (4.713)
• $\backslash varphi$: euler's totient function (4.294)
• $x$: continuous function (4.132)
• $\backslash mathbf\{R\}$: function (4.073)
• $d$: function (3.850)
• $\backslash epsilon$: 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)
• $\backslash delta$: positive number (1.950)
• $B\_\{x\}$: ball (1.939)
• $I$: open interval (1.915)
• $N$: poly (1.903)
• $R$: neighborhood (1.900)
• $c$: domain (1.790)
• $\backslash mu$: möbius function (1.766)
• $\backslash varphi\_\{\backslash epsilon\}$: function (1.712)
• $P$: approaches (1.657)
• $Y$: function (1.591)
• $r$: continuous function (1.588)
• $b$: open interval (1.588)

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)
• $\backslash varphi$: electric potential (3.679)
• $\backslash mathbf\{A\}$: electric potential (3.539)
• $L\_\{0\}$: 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)
• $\backslash mathbf\{E\}$: electric field (1.889)
• $d$: distance (1.875)
• $E$: total energy (1.858)
• $T\_\{0\}$: proper time (1.848)
• $\backslash mathbf\{J\}$: 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)
• $\backslash mathbf\{B\}$: magnetic field (1.769)
• $r\_\{s\}$: schwarzschild radius (1.749)
• $\backslash mathbf\{LorentzFitzGeraldcontraction\}$: hendrik lorentz (1.732)
• $f$: harmonic function (1.724)
• $r$: infinity (1.723)
• $M\_\{0\}$: initial mass (1.707)
• $L\text{'}$: acceleration (1.524)

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)

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)
• $\backslash Gamma$: gamma function (1.845)
• $\backslash mathcal\{L\}\_\{k\}$: transfer operator (1.816)

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)
• $\backslash mathbf\{q\}$: 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)
• $a\_\{j\}$: order (1.525)

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)

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)
• $\backslash alpha$: level (3.694)
• $V$: alternative hypothesis (3.643)
• $M$: mean (2.799)
• $H\_\{i\}$: test (2.741)
• $\backslash boldsymbol\{\backslash theta\}$: parameter vector (2.652)
• $X$: random variable (2.616)
• $m\_\{0\}$: null hypotheses (2.565)
• $k$: pareto distribution (2.469)
• $\backslash mathbf\{\backslash Theta\}$: random parameter (1.939)
• $i$: hypothesis (1.939)
• $n$: independent comparisons (1.939)
• $Z$: samples (1.900)
• $w\_\{i\}$: weight (1.882)
• $g\_\{\backslash boldsymbol\{\backslash theta\}\}$: function (1.834)
• $\backslash delta$: quantiles (1.816)
• $A$: well-behaved statistic (1.751)
• $\backslash mu$: confidence intervals (1.738)
• $p$: bernoulli distribution (1.700)
• $Q$: discoveries (1.677)
• $K$: pareto distribution (1.673)
• $\backslash boldsymbol\{\backslash Theta\}$: random vector (1.666)
• $c\_\{i\}$: intersection hypothesis (1.544)
• $H$: null hypotheses (1.524)

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)
• $f\_\{j\}$: 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)
• $\backslash sigma$: variance (2.833)
• $N$: distribution (2.802)
• $j$: observation (2.800)
• $x$: correlation (2.791)
• $\backslash hat\{\backslash theta\}$: estimator (2.552)
• $x\_\{i\}$: rank (2.536)
• $y$: standard deviation (2.429)
• $w$: weight vector (1.939)
• $p$: regressor (1.926)
• $\backslash theta$: unknown parameter (1.907)
• $\backslash bar\{X\}$: interest (1.900)
• $d$: constants (1.900)
• $\backslash mu$: variance (1.865)
• $a$: measure (1.855)
• $m$: independent variables (1.845)
• $y\_\{i\}$: dependent variable (1.833)
• $T$: sample covariance matrix (1.817)
• $z$: distribution (1.810)
• $Y\_\{i\}$: week (1.774)
• $W$: matrix (1.749)
• $t$: mean (1.724)
• $\backslash rho$: correlation (1.701)
• $f$: function (1.701)
• $X\_\{i\}$: iq (1.627)
• $r\_\{t\}$: observations (1.611)
• $k$: data points (1.610)
• $s\_\{y\}$: standard deviation (1.591)
• $w\_\{ij\}$: mean (1.591)
• $\backslash beta\_\{j\}$: functions (1.524)
• $c$: constants (1.524)

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

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

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)

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)
• $\backslash ell$: length (4.283)
• $i$: call position (3.887)
• $\backslash varphi$: gödel numbering (3.732)
• $q\_\{i\}$: state (3.510)
• $\backslash delta$: transition relation (3.178)
• $\backslash mathbf\{a\}$: symbol (2.961)
• $p\_\{i\}$: state (2.799)
• $\backslash Sigma$: alphabet (computer science) (2.727)
• $w$: word (2.674)
• $Q$: finite set (2.661)
• $\backslash Phi$: complexity measure (2.485)
• $M\_\{i\}$: state (2.266)
• $M\text{'}$: pushdown automaton (1.974)
• $q\_\{0\}$: initial state (1.974)
• $s$: states (1.974)
• $t$: function (1.974)
• $L$: formal language (1.939)
• $x$: input (1.939)
• $\backslash Gamma$: alphabet (1.891)
• $\backslash mathbf\{P\}$: partial computable function (1.882)
• $\backslash varepsilon$: empty word (1.858)
• $Z$: symbol (1.847)
• $h$: hash (1.843)
• $G$: context-free grammar (1.824)
• $g$: program (1.790)
• $\backslash varphi\_\{i\}$: 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)
• $\backslash hat\{\backslash Sigma\}$: alphabet (1.675)
• $w\_\{j\}$: state (1.665)
• $\backslash gamma\_\{i\}$: state (1.623)
• $\backslash mu$: right multiplication (1.576)

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:

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