User:Physikerwelt

= ROOT =

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

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

Definitions:
 * $$S$$: spin quantum number (3.354)
 * $$M_{J}$$: 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)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Definitions:
 * $$V_{G}$$: voltage (3.355)
 * $$R_{G}$$: resistance (1.833)
 * $$R_{2}$$: resistance (1.664)
 * $$R_{x}$$: high precision (1.586)

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

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

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

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

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

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

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

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

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

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

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

Definitions:
 * $$N_{B}$$: 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)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Definitions:
 * $$T$$: temperature (18.171)
 * $$V$$: volume (thermodynamics) (9.787)
 * $$U$$: internal energy (8.118)
 * $$Q$$: heat (7.410)
 * $$O$$: state (7.151)
 * $$S$$: entropy (6.168)
 * $$P$$: pressure (5.985)
 * $$Y$$: state (5.840)
 * $$t$$: time (4.645)
 * $$p$$: pressure (4.500)
 * $$B$$: state (3.565)
 * $$V_{b}$$: 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)
 * $$u'$$: mass (1.688)
 * $$d$$: exact differential (1.621)
 * $$E$$: total energy (1.574)
 * $$U_{2}$$: new system (1.476)

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

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

Definitions:
 * $$n$$: vertices (19.811)
 * $$a$$: graph (mathematics) (18.075)
 * $$G$$: glossary of graph theory (17.852)
 * $$k$$: complete graph (15.524)
 * $$K$$: complete bipartite graph (9.558)
 * $$v$$: vertex (graph theory) (8.425)
 * $$u$$: vertices (7.720)
 * $$A$$: cycle graph (7.051)
 * $$B$$: series (7.009)
 * $$H$$: glossary of graph theory (6.870)
 * $$m$$: edges (5.725)
 * $$v_{i}$$: 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)
 * $$\phi$$: chromatic roots (1.524)

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

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

Definitions:
 * $$R$$: rate (7.323)
 * $$n$$: length (7.223)
 * $$\mathcal{C}$$: code (6.108)
 * $$m$$: message (5.399)
 * $$d$$: minimum distance (5.171)
 * $$C$$: code (4.310)
 * $$X$$: random variable (3.685)
 * $$y$$: word (3.630)
 * $$\delta$$: relative distance (3.555)
 * $$q$$: arbitrary probability distribution (3.494)
 * $$p$$: probability distribution (3.484)
 * $$k$$: message length (3.372)
 * $$a$$: information (3.253)
 * $$e$$: radius (2.926)
 * $$H$$: entropy (2.889)
 * $$T$$: temperature (2.776)
 * $$\Sigma$$: alphabet (2.670)
 * $$x$$: conditional probability (2.650)
 * $$f$$: likelihood function (2.604)
 * $$c$$: codeword (2.406)
 * $$Y$$: entropy (2.288)
 * $$g$$: function (1.974)
 * $$c_{1}$$: 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)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Definitions:
 * $$C$$: concept class (7.638)
 * $$c$$: concept (3.624)
 * $$X$$: concept class (3.183)
 * $$D_{t}$$: 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)
 * $$\mathcal{H}$$: loss function (1.688)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Definitions:
 * $$a$$: bounded linear operator (6.085)
 * $$H$$: hilbert (4.995)
 * $$\mathbf{H}$$: space (2.869)
 * $$E$$: banach (2.688)
 * $$\mathbf{T}$$: operator (2.641)
 * $$C$$: class (2.604)
 * $$i$$: subset (2.565)
 * $$U$$: bounded linear operator (2.450)
 * $$H_{i}$$: 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)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Definitions:
 * $$c_{0}$$: 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)
 * $$\bar{u}$$: utility level (1.847)
 * $$Y$$: payments (1.790)
 * $$Y_{d}$$: disposable income (1.779)

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

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

Definitions:
 * $$i$$: player (9.955)
 * $$D$$: player (5.852)
 * $$j$$: machine (4.463)
 * $$N$$: players (3.651)
 * $$k$$: machine (2.768)
 * $$f_{\Gamma,R}$$: 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)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Definitions:
 * $$y$$: direction (3.623)
 * $$\mathbf{j}$$: equation (2.665)
 * $$\mathbf{q}$$: wave vector (2.640)
 * $$n$$: atomic number density (2.625)
 * $$k$$: dependence (2.619)
 * $$c_{v,p}$$: specific heat capacity (2.600)
 * $$m$$: atomic mass (2.521)
 * $$i$$: atom (2.492)
 * $$j$$: atom (2.452)
 * $$p$$: type materials (2.417)
 * $$\delta$$: limit (1.939)
 * $$z$$: direction (1.937)
 * $$Z_{f}$$: 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)
 * $$\tau$$: 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)
 * $$\mathbf{p}$$: momentum (1.696)
 * $$A$$: electrolyte (1.688)
 * $$\mathbf{s}$$: 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)
 * $$\mathbf{u}$$: velocity (1.653)
 * $$\mathbf{d}$$: displacement vector (1.592)
 * $$v_{z}$$: phonon velocity (1.574)
 * $$v_{2}$$: film2 (1.524)
 * $$a$$: electron (1.490)
 * $$\kappa$$: inverse screening length (1.489)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Definitions:
 * $$t$$: initial concentration (5.369)
 * $$C_{0}$$: initial concentration (5.125)
 * $$C_{t}$$: concentration (3.662)
 * $$k_{e}$$: elimination rate (1.754)

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

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

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

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

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

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

General nonassociative rings
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)
 * $$\mathbf{R}$$: octonion algebra (1.865)
 * $$\mathbb{Q}_{\nu}$$: quaternion algebra (1.659)
 * $$B$$: algebra over a field (1.655)

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

Cluster information:
 * 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)
 * $$\mathcal{B}_{r}$$: 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)
 * $$\mathcal{B}_{s}$$: sequences (1.754)
 * $$L$$: conventions (1.712)
 * $$S$$: lower triangular matrix (1.529)
 * $$Q$$: integer sequence (1.513)

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

Cluster information:
 * 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)
 * $$\mathbf{Z}$$: projective module (2.636)
 * $$\mathbf{R}$$: trivial extension (1.834)
 * $$O_{K}$$: galois (1.790)
 * $$\mathfrak{m}_{K}$$: field norm (1.790)
 * $$A$$: galois (1.787)
 * $$w$$: extension of a valuation (1.749)
 * $$\mathbf{Q}$$: field (1.725)
 * $$X$$: smooth morphism (1.677)

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

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

Definitions:
 * $$a$$: field (mathematics) (4.389)
 * $$\mathbf{C}$$: p-adic number (4.367)
 * $$\mathbf{Q}$$: field (mathematics) (4.365)
 * $$F$$: field (3.392)
 * $$\mathbf{P}$$: preperiodic points (3.168)
 * $$p$$: adic numbers (3.162)
 * $$L$$: dirichlet l-function (2.725)
 * $$x$$: rational number (2.506)
 * $$E$$: algebraic field extension (2.500)
 * $$s$$: dedekind zeta function (2.487)
 * $$d$$: quadratic field (2.466)
 * $$O$$: ring (mathematics) (2.417)
 * $$f$$: algebraic field extension (2.320)
 * $$\mathbf{K}$$: field (mathematics) (1.939)
 * $$v$$: ultrametric place (1.848)
 * $$\mathbf{Q}_{p}$$: galois extension (1.845)
 * $$c$$: choice (1.810)
 * $$\mathbf{R}$$: 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)
 * $$\mathbf{Z}$$: ring (1.577)

Numerical linear algebra
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:
 * $$A$$: symmetric matrix (14.671)
 * $$a$$: triangular matrix (8.400)
 * $$B$$: skew-hermitian matrix (5.940)
 * $$n$$: matrix (5.320)
 * $$L$$: triangular matrix (4.422)
 * $$D$$: diagonal matrix (3.654)
 * $$U$$: triangular matrix (3.572)
 * $$x$$: computation (2.781)
 * $$\mathbf{x}$$: right hand side (2.323)
 * $$\phi$$: initial guess (1.903)
 * $$b$$: ω output (1.895)
 * $$j$$: loop (1.852)
 * $$i$$: loop (1.817)
 * $$\Lambda$$: diagonal matrix (1.816)
 * $$k$$: iteration (1.765)
 * $$s$$: matrix (1.677)
 * $$\omega$$: iteration (1.659)
 * $$e$$: error end (1.623)

Mathematical programming, optimization and variational techniques
Category information
 * 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)
 * $$\mathbf{R}$$: euclidean space (2.835)
 * $$a$$: hardy space (2.798)
 * $$n$$: euclidean space (2.783)
 * $$O$$: outer distortion (2.736)
 * $$K$$: outer distortion (2.583)
 * $$\mathbb{R}$$: function (2.560)
 * $$x$$: function (2.434)
 * $$X$$: open set (1.937)

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

Cluster information:
 * 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)
 * $$L$$: bounded linear operator (1.865)
 * $$\mathbf{R}$$: wiener process (1.744)
 * $$i$$: cell centres (1.663)
 * $$s$$: action (1.657)
 * $$P$$: distribution (1.654)
 * $$d$$: dimensional case (1.648)

Numerical methods in Fourier analysis
Category information
 * reference category: Numerical methods in Fourier analysis
 * 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)
 * $$\hat{\psi}$$: admissibility (1.754)
 * $$\pi$$: period (1.690)
 * $$y$$: period (1.586)

Computer aspects of numerical algorithms
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)

Miscellaneous topics in measure theory
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)
 * $$\mathbf{R}$$: real line (2.905)
 * $$n$$: euclidean space (1.629)

Data management systems
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)

Phase transformations in solids
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)

Geophysical observations, instrumentation, and techniques
Category information
 * reference category: NO_REFERENCE_CATEGORY
 * code: NO_CODE (NO_SCHEMA)
 * wiki categories: [(Category:Lists of head coaches by National Football League team, 3), (Category:National Football League lists, 3), (Category:National Football League head coaches by team, 3)]

Cluster information:
 * 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)

Randomness, geometry and discrete structures
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']

General
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)

Low-dimensional topology
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']

Basic methods
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)
 * $$\lambda$$: wavelength (1.900)
 * $$f$$: frequency (1.900)
 * $$\gamma$$: slope (1.790)
 * $$d$$: distance (1.790)
 * $$F$$: adjustment (1.742)

Algebraic combinatorics
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)

Algebraic combinatorics
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']

Computer graphics
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)

Interaction design
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)
 * $$\omega_{0}$$: cutoff frequency (3.641)
 * $$G$$: gain (2.830)
 * $$G_{0}$$: gain (2.608)
 * $$s$$: complex frequency space (2.585)
 * $$H$$: transfer function (2.487)
 * $$\omega_{pm}$$: poles (1.939)
 * $$f$$: frequency (1.939)
 * $$L$$: shunt (1.779)
 * $$a$$: filter (signal processing) (1.742)
 * $$C$$: shunt (1.712)
 * $$\varepsilon$$: ripple factor (1.673)

Low-dimensional topology
Category information
 * 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']

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

Graphical methods
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)

Stochastic systems and control
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)
 * $$\bar{x}$$: chart (3.468)

Randomness, geometry and discrete structures
Category information
 * reference category: NO_REFERENCE_CATEGORY
 * code: NO_CODE (NO_SCHEMA)
 * wiki categories: [(Category:Cartographic projections, 6), (Category:Cartography, 5), (Category:Coordinate systems, 5)]

Cluster information:
 * cluster id: [6375]
 * matching score: 0.132670227656
 * purity: 1.0
 * matching keywords: [u'projections']

Definitions:
 * $$\varphi$$: latitude (7.113)
 * $$\lambda$$: latitude (4.498)
 * $$\lambda_{0}$$: longitude (1.845)

Probability theory on algebraic and topological structures
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)

Connections with logic
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)

Properties of specific nuclei listed by mass ranges (an additional heading must be chosen with these entries, where the given mass number limits are, to some degree, arbitrary)
Category information
 * reference category: NO_REFERENCE_CATEGORY
 * code: NO_CODE (NO_SCHEMA)
 * wiki categories: [(Category:Physics, 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:
 * $$\bar{4}$$: representations of lie groups/algebras (2.613)
 * $$U$$: weak hypercharge (1.781)
 * $$H$$: higgs (1.659)

Computational methods
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)

Decision theory
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)
 * $$\alpha_{31}$$: dilution (1.900)
 * $$\beta_{31}$$: clearance (medicine) (1.900)
 * $$D$$: l/mol (1.876)
 * $$T$$: ec50 (1.876)
 * $$\alpha_{T}$$: dilution (1.876)
 * $$\beta_{T}$$: clearance (medicine) (1.876)
 * $$M$$: dissociation constant (1.790)

Physical chemistry and chemical physics
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)
 * $$s$$: agcl (1.868)

Close-to-elliptic equations
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)

Mechanical and acoustical properties of condensed matter
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)

Fundamental astronomy and astrophysics; instrumentation, techniques, and astronomical observations
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
 * purity: 1.0
 * matching keywords: [u'astronomical', u'astronomy', u'objects']

Definitions:
 * $$a$$: jupiter mass (5.811)

Physical chemistry and chemical physics
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:
 * cluster id: [4766]
 * 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:
 * $$h$$: planck constant (5.294)
 * $$c$$: planck constant (3.579)
 * $$Z$$: atomic number (3.489)
 * $$R$$: rydberg constant (2.554)
 * $$m$$: rest mass (2.453)
 * $$e$$: electron (1.845)
 * $$X$$: atomic number (1.810)
 * $$E$$: codata (1.497)

Computing methodologies and applications
Category information
 * reference category: NO_REFERENCE_CATEGORY
 * 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)
 * $$a$$: signal (1.764)
 * $$z$$: gain (1.754)
 * $$n$$: octave (1.724)
 * $$t$$: dirac delta function (1.424)

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

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

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

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

Cluster information:
 * 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)
 * $$\mathbf{y}$$: basis vectors (1.743)
 * $$V$$: euclidean space (1.733)
 * $$\mathbf{e}$$: basis vectors (1.714)
 * $$\mathbf{x}$$: mapping vectors (1.710)

Hamilton-Jacobi theories, including dynamic programming
Category information
 * reference category: NO_REFERENCE_CATEGORY
 * code: NO_CODE (NO_SCHEMA)
 * wiki categories: [(Category:Multivariable calculus, 4), (Category:Vectors, 3), (Category:Vector calculus, 3)]

Cluster information:
 * cluster id: [7471]
 * matching score: 0.251226310938
 * purity: 1.0
 * matching keywords: [u'calculus']

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

Properties of specific nuclei listed by mass ranges (an additional heading must be chosen with these entries, where the given mass number limits are, to some degree, arbitrary)
Category information
 * reference category: NO_REFERENCE_CATEGORY
 * code: NO_CODE (NO_SCHEMA)
 * wiki categories: [(Category:Physics, 3), (Category:Solid state engineering, 3), (Category:Condensed matter physics, 2)]

Cluster information:
 * cluster id: [5231]
 * matching score: 0.248183919026
 * purity: 1.0
 * matching keywords: [u'physics']

Definitions:
 * $$m$$: effective mass (solid-state physics) (3.656)
 * $$t$$: time (3.419)
 * $$R$$: region (2.799)
 * $$R_{2}$$: region (2.799)
 * $$R_{1}$$: region (2.576)
 * $$n$$: solutions (2.465)
 * $$p$$: momentum (2.421)
 * $$x$$: position (2.367)
 * $$\mathbf{k}$$: wave vector (1.939)
 * $$A_{k}$$: discrete components (1.937)
 * $$N$$: particles (1.848)
 * $$\Psi$$: wavefunction (1.847)
 * $$a$$: ball (1.815)
 * $$V$$: total volume (1.754)
 * $$V_{0}$$: potential barrier (1.754)
 * $$\Omega_{r}$$: volume (1.754)
 * $$\omega_{p}$$: resonance frequency (1.749)
 * $$a_{n}$$: scalar multiplication (1.742)
 * $$k_{F}$$: wave vector (1.659)
 * $$A$$: classical mechanics (1.645)
 * $$\boldsymbol{q}$$: dispersion relation (1.628)
 * $$s$$: wave (1.618)
 * $$\mathbf{r}$$: position vector (1.604)
 * $$s_{z}$$: spin (physics) (1.600)

Nuclear engineering and nuclear power studies
Category information
 * reference category: NO_REFERENCE_CATEGORY
 * code: NO_CODE (NO_SCHEMA)
 * wiki categories: [(Category:Spacecraft propulsion, 3), (Category:Astrodynamics, 3), (Category:Propulsion, 2)]

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

Definitions:
 * $$t$$: rocket (4.071)
 * $$m_{0}$$: 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)
 * $$\gamma$$: lorentz factor (1.720)
 * $$V_{e}$$: velocity (1.689)
 * $$c$$: speed of light (1.665)
 * $$\eta$$: equation (1.557)

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

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

Definitions:
 * $$H$$: 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)

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

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

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

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

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

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

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

Definitions:
 * $$\omega_{p}$$: plasma frequency (2.674)
 * $$\Omega_{c}$$: plasma parameters (1.900)
 * $$\omega_{i}$$: plasma frequency (1.845)
 * $$\vec{B}_{0}$$: light wave (1.845)
 * $$A$$: plasma (physics) (1.816)
 * $$\omega_{c}$$: plasma frequency (1.779)
 * $$or$$: plasma (physics) (1.566)

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

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

Definitions:
 * $$\mathbf{E}$$: electric field (7.113)
 * $$\mathbf{H}$$: magnetic field (4.360)
 * $$\mathbf{J}$$: current density (4.341)
 * $$\mathbf{B}$$: magnetic field (4.115)
 * $$\alpha_{i}$$: unknown coefficients (3.785)
 * $$\mathbf{D}$$: electric displacement field (3.702)
 * $$\mathbf{F}$$: field (3.581)
 * $$L$$: differential operator (3.571)
 * $$H$$: field (2.780)
 * $$\mathbf{n}$$: unit normal (2.765)
 * $$\omega$$: frequency (2.763)
 * $$k$$: wavenumber (2.718)
 * $$u$$: density (2.504)
 * $$\mathbf{M}$$: magnetization (2.504)
 * $$a$$: electric field (2.242)
 * $$\Theta$$: angle (1.939)
 * $$Q$$: charge (1.926)
 * $$\Omega$$: differential operator (1.900)
 * $$\Omega_{D}$$: computational domain (1.900)
 * $$\mathbf{k}$$: wave vector (1.900)
 * $$S$$: surface area (1.882)
 * $$t$$: time (1.868)
 * $$p$$: density (1.864)
 * $$c$$: speed of light (1.826)
 * $$\rho$$: density (1.823)
 * $$\Omega_{N}$$: dirichlet (1.790)
 * $$\phi$$: general solution (1.790)
 * $$\mathbf{A}$$: electrical potential (1.774)
 * $$\alpha$$: ricci calculus (1.762)
 * $$E$$: electric field (1.750)
 * $$z$$: direction (1.746)
 * $$d$$: differential (infinitesimal) (1.712)
 * $$\mathbf{S}$$: vector area (1.690)
 * $$\rho_{1}$$: slab (1.657)
 * $$B$$: nabla (1.628)
 * $$\mathbf{P}$$: material (1.598)
 * $$f$$: frequency (1.591)
 * $$v$$: nabla (1.506)
 * $$I$$: charge (1.476)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Definitions:
 * $$D$$: dimensions (2.536)

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

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

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

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

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

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

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

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

Definitions:
 * $$z$$: bessel function (1.654)

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

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

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

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

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

Definitions:
 * $$I$$: moran (7.965)
 * $$C$$: geary (4.327)
 * $$X$$: random variables (3.589)
 * $$f_{j}$$: functions (3.510)
 * $$i$$: observation (3.495)
 * $$E$$: mean (3.435)
 * $$n$$: random sample (3.420)
 * $$Y$$: sample variance (3.401)
 * $$r$$: pearson product-moment correlation coefficient (3.227)
 * $$\sigma$$: variance (2.833)
 * $$N$$: distribution (2.802)
 * $$j$$: observation (2.800)
 * $$x$$: correlation (2.791)
 * $$\hat{\theta}$$: estimator (2.552)
 * $$x_{i}$$: rank (2.536)
 * $$y$$: standard deviation (2.429)
 * $$w$$: weight vector (1.939)
 * $$p$$: regressor (1.926)
 * $$\theta$$: unknown parameter (1.907)
 * $$\bar{X}$$: interest (1.900)
 * $$d$$: constants (1.900)
 * $$\mu$$: variance (1.865)
 * $$a$$: measure (1.855)
 * $$m$$: independent variables (1.845)
 * $$y_{i}$$: 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)
 * $$\rho$$: 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)
 * $$\beta_{j}$$: functions (1.524)
 * $$c$$: constants (1.524)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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