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ROOT

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ATOMIC AND MOLECULAR PHYSICS

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Atomic properties and interactions with photons

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Category information

Cluster information:

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

Definitions:


Algebraic geometry

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Foundations

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Category information

Cluster information:

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

Definitions:

  • : galois extension (4.848)
  • : number field (4.256)
  • : field (mathematics) (3.517)
  • : plus construction (3.454)
  • : exact category (2.701)
  • : fields (2.665)
  • : galois group (2.647)
  • : valuation (2.642)
  • : decomposition group (2.530)
  • : cyclic group (2.481)
  • : steinberg group (2.317)
  • : galois extension (2.295)
  • : module (1.939)
  • : rational numbers (1.939)
  • : module (1.882)
  • : multiplicities (1.875)
  • : functor (1.728)
  • : irreducible element (1.726)
  • : multiplicities (1.691)
  • : finite extension (1.681)
  • : prime ideal (1.664)
  • : ring homomorphism (1.663)
  • : properties (1.489)


Surfaces and higher-dimensional varieties

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Category information

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:

  • : dimensional torus (4.230)
  • : k3 surface (3.473)
  • : radius (3.376)
  • : lattice (group) (3.257)
  • : hyperbolic paraboloid (2.764)
  • : circle (2.737)
  • : torus (2.597)
  • : automorphism (2.278)
  • : canonical line bundle (1.875)
  • : 0-cell (1.834)
  • : 2-torus (1.738)
  • : base space (1.701)
  • : 1-cells (1.685)
  • : bottle (1.465)


Computational aspects in algebraic geometry

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Category information

Cluster information:

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

Definitions:


Algebraic topology

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Fiber spaces and bundles

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Category information

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:

  • : topological space (6.620)
  • : vector bundle (6.029)
  • : tangent bundle (5.859)
  • : bundles (3.438)
  • : vector bundle (3.432)
  • : vector space (3.357)
  • : vector bundle (2.573)
  • : ∈ gl (1.848)
  • : frame (1.847)
  • : dual vector space (1.838)
  • : rank (1.823)
  • : continuous maps (1.800)
  • : principal fiber bundle (1.715)
  • : structures (1.662)
  • : open neighborhood (1.653)
  • : homeomorphism (1.625)


Astronomy and astrophysics

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Computational methods

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Category information

Cluster information:

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

Definitions:

  • : black body (5.297)
  • : temperature (3.670)
  • : radius (2.749)
  • : distance (1.789)


Biology and other natural sciences

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Physiological, cellular and medical topics

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Category information

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:

  • : velocity (8.716)
  • : electric field (7.522)
  • : magnetic flux (7.368)
  • : magnetic field (6.691)
  • : electric charge (5.029)
  • : direction (4.239)
  • : force (3.736)
  • : direction (3.493)
  • : speed of light (3.226)
  • : velocity (2.806)
  • : directions (2.762)
  • : time (2.595)
  • : magnetic field (2.527)
  • : position vector (1.847)
  • : position (1.845)
  • : mass (1.793)
  • : electromotive force (1.778)
  • : electric field (1.750)
  • : identical turns (1.714)
  • : proper time (1.712)
  • : vector area (1.531)
  • : magnetic induction (1.459)


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

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

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Category information

Cluster information:

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

Definitions:

  • : voltage (3.355)
  • : resistance (1.833)
  • : resistance (1.664)
  • : high precision (1.586)


Superconductivity

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Category information

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:

  • : uperconductor (4.900)
  • : uperconductor (3.371)
  • : josephson phase (2.657)
  • : josephson phase (2.644)
  • : josephson (2.597)
  • : time (1.974)
  • : inductance (1.939)
  • : supercurrent (1.882)
  • : junction (1.719)


Magnetic properties and materials

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Category information

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:


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

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Category information

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:

  • : angular frequency (1.845)
  • : permittivity (1.544)


CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES

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Mechanical and acoustical properties of condensed matter

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Category information

Cluster information:

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

Definitions:

  • : teeth (8.677)
  • : input gear (7.375)
  • : teeth (5.890)
  • : output gear (5.869)
  • : gear ratio (5.232)
  • : input gear (4.000)
  • : velocity (3.755)
  • : input gear (3.713)
  • : output gear (3.639)
  • : output torque (3.415)
  • : input gear (3.216)
  • : input torque (2.803)
  • : force (2.496)
  • : pitch radius (1.974)
  • : distance (1.842)
  • : rope sections (1.666)


Category theory; homological algebra

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General theory of categories and functors

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Category information

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:

  • : subcategory (6.987)
  • : functor (5.058)
  • : functor (4.953)
  • : contravariant functor (4.555)
  • : object (4.359)
  • : categories (4.132)
  • : functor (3.776)
  • : object (3.210)
  • : isomorphisms (2.595)
  • : small category (2.582)
  • : field (mathematics) (1.858)
  • : subset (1.775)
  • : ring (1.766)
  • : natural transformation (1.756)
  • : generator (1.746)
  • : morphism (1.629)
  • : object (1.628)
  • : objects (1.499)


Categories with structure

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Category information

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:

  • : monoidal category (6.125)
  • : category of sets (4.992)
  • : objects (4.915)
  • : commutativity constraint (2.705)
  • : fold tensor product factors (1.865)
  • : tensor product (1.774)


Categories and geometry

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Category information

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:


Homological algebra

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Category information

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:

  • : finitely generated module (21.818)
  • : module (19.662)
  • : module (17.887)
  • : group ring (10.747)
  • : ideal (ring theory) (8.643)
  • : field (mathematics) (7.863)
  • : module (7.513)
  • : module (7.511)
  • : polynomial ring (7.283)
  • : field (6.502)
  • : modules (5.827)
  • : module (4.475)
  • : modules (4.265)
  • : polynomial ring (3.905)
  • : module (3.639)
  • : surjective module homomorphism (3.627)
  • : linear map (3.605)
  • : multiplicatively closed subset (3.599)
  • : codimension (3.406)
  • : submodules (3.400)
  • : matrix (mathematics) (3.154)
  • : polynomial ring (3.100)
  • : ideal (ring theory) (2.798)
  • : lie algebra (2.711)
  • : ring (2.608)
  • : dense right ideal (2.571)
  • : nonzero (2.532)
  • : prime ideal (2.485)
  • : module homomorphism (1.950)
  • : chain (1.882)
  • : category (1.848)
  • : many copies (1.829)
  • : homomorphism (1.824)
  • : zariski (1.810)
  • : open subsets (1.810)
  • : module (1.774)
  • : module (1.725)
  • : modules (1.600)
  • : subject (1.598)
  • : zero-divisor (1.591)


Classical thermodynamics, heat transfer

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Thermodynamics and heat transfer

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Category information

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:

  • : temperature (18.171)
  • : volume (thermodynamics) (9.787)
  • : internal energy (8.118)
  • : heat (7.410)
  • : state (7.151)
  • : entropy (6.168)
  • : pressure (5.985)
  • : state (5.840)
  • : time (4.645)
  • : pressure (4.500)
  • : state (3.565)
  • : volume (3.523)
  • : volume (3.438)
  • : volume (2.761)
  • : work (thermodynamics) (2.735)
  • : energy (2.562)
  • : state (1.937)
  • : arbitrary state (1.907)
  • : volume (1.902)
  • : time (1.816)
  • : molar mass (1.779)
  • : heat (1.723)
  • : mass (1.688)
  • : exact differential (1.621)
  • : total energy (1.574)
  • : new system (1.476)


Combinatorics

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Graph theory

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Category information

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:

  • : vertices (19.811)
  • : graph (mathematics) (18.075)
  • : glossary of graph theory (17.852)
  • : complete graph (15.524)
  • : complete bipartite graph (9.558)
  • : vertex (graph theory) (8.425)
  • : vertices (7.720)
  • : cycle graph (7.051)
  • : series (7.009)
  • : glossary of graph theory (6.870)
  • : edges (5.725)
  • : vertex (5.393)
  • : complete graph (3.913)
  • : degree (graph theory) (3.842)
  • : color (3.635)
  • : graph isomorphism (3.485)
  • : edge (2.776)
  • : neighbourhood (graph theory) (2.731)
  • : edges (2.486)
  • : graph (2.441)
  • : vertices (2.221)
  • : vertices (1.950)
  • : vertex cover (1.939)
  • : complexity (1.939)
  • : graph (1.937)
  • : running time (1.866)
  • : finite set (1.848)
  • : sequence (1.847)
  • : vertex (1.816)
  • : first color (1.779)
  • : vertex (1.712)
  • : edges (1.708)
  • : wheel graph (1.690)
  • : graph (1.687)
  • : chromatic number (1.659)
  • : vertex (1.657)
  • : chromatic roots (1.524)


Computer science

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Theory of data

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Category information

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:

  • : rate (7.323)
  • : length (7.223)
  • : code (6.108)
  • : message (5.399)
  • : minimum distance (5.171)
  • : code (4.310)
  • : random variable (3.685)
  • : word (3.630)
  • : relative distance (3.555)
  • : arbitrary probability distribution (3.494)
  • : probability distribution (3.484)
  • : message length (3.372)
  • : information (3.253)
  • : radius (2.926)
  • : entropy (2.889)
  • : temperature (2.776)
  • : alphabet (2.670)
  • : conditional probability (2.650)
  • : likelihood function (2.604)
  • : codeword (2.406)
  • : entropy (2.288)
  • : function (1.974)
  • : codewords (1.939)
  • : estimator (1.891)
  • : codewords (1.882)
  • : function (1.858)
  • : codewords (1.754)
  • : code (1.659)
  • : code (1.563)
  • : nformation (1.524)


Discrete mathematics in relation to computer science

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Category information

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:

  • : context-sensitive grammar (7.034)
  • : time (4.738)
  • : convex function (3.659)
  • : function (3.656)
  • : function (3.172)
  • : tuple (1.891)
  • : tuple (1.817)
  • : successor function (1.791)
  • : nspace (1.754)
  • : induction step (1.738)
  • : acceptance set (1.609)
  • : middle term (1.587)
  • : natural numbers (1.495)


Artificial intelligence

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Category information

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:

  • : linear map (2.767)
  • : function (2.561)
  • : function (2.550)
  • : commodities (2.492)
  • : functions (2.481)
  • : time (2.250)
  • : cardinal (1.845)
  • : state (1.812)
  • : differential d (1.761)
  • : functions (1.719)
  • : derivative (1.707)
  • : jacobian matrix (1.664)
  • : state diagram (1.863)
  • : input variables (1.583)
  • : functions (1.430)


Computing methodologies and applications

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Category information

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:

  • : scale (6.939)
  • : integration scale parameter (4.427)
  • : binary image (3.724)
  • : direction (3.608)
  • : scale space (3.602)
  • : origin (3.496)
  • : structuring element (3.477)
  • : grayscale dilation (3.282)
  • : dimension (2.961)
  • : grayscale dilation (2.850)
  • : matrix (2.815)
  • : collection (2.685)
  • : scale (2.560)
  • : euclidean space (2.214)
  • : euclidean space (1.974)
  • : radius (1.950)
  • : dimensions (1.939)
  • : direction (1.902)
  • : erosion (1.902)
  • : dimensional ridge (1.900)
  • : matrix (1.847)
  • : covariance matrices (1.810)
  • : partial derivatives (1.790)
  • : translation (1.790)
  • : covariance matrices (1.781)
  • : dilation (1.781)
  • : image (1.690)
  • : direction (1.641)
  • : tangent lines (1.621)
  • : dilation (1.618)
  • : square (1.581)
  • : positive value (1.563)
  • : partial derivatives (1.524)
  • : pixels (1.488)


Algorithms

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Category information

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:

  • : sequence (4.369)
  • : multiplicity (1.974)
  • : finite field (1.891)
  • : tuple (1.864)
  • : real numbers (1.810)
  • : polynomial (1.800)


Computing methodologies

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Machine learning

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Category information

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:

  • : concept class (7.638)
  • : concept (3.624)
  • : concept class (3.183)
  • : distribution (2.707)
  • : classifier (1.939)
  • : partial approximation (1.902)
  • : labels (1.845)
  • : probability distribution (1.781)
  • : loss function (1.688)


Differential geometry

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Classical differential geometry

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Category information

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:

  • : differentiable manifold (5.972)
  • : function (3.502)
  • : structure group (2.961)
  • : lower-case index (2.810)
  • : scalar functions (2.571)
  • : − div (2.514)
  • : fiber (2.435)
  • : gaussian curvature (2.339)
  • : vector field (1.939)
  • : coordinate system (1.889)
  • : rational number (1.865)
  • : fiber (1.823)
  • : particular point (1.816)
  • : laplace (1.754)
  • : gaussian curvature (1.688)
  • : continuous (topology) (1.632)
  • : infinite area (1.628)
  • : unit sphere (1.591)
  • : unit sphere (1.583)


Dynamical systems and ergodic theory

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Applications

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Category information

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:

  • : volume (6.980)
  • : internal energy (2.749)
  • : absolute temperature (2.678)
  • : gas constant (2.595)
  • : pressure (2.570)
  • : proper convex function (2.450)
  • : volume (1.865)
  • : volume (1.865)
  • : vector space (1.858)
  • : specific volume (1.779)
  • : volume (1.756)
  • : pressure (1.752)
  • : partial pressure (1.726)
  • : gas mixture (1.717)
  • : chaotic behavior (1.632)


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

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Acoustics

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Category information

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:

  • : wave (6.764)
  • : particle velocity (2.677)
  • : sound intensity (2.593)
  • : distance (2.524)
  • : sound energy density (2.473)
  • : frequency (1.882)
  • : metre (1.876)
  • : watt (1.865)
  • : sound intensity (1.790)
  • : area (1.787)
  • : sound intensity (1.779)
  • : acoustic intensity (1.591)
  • : density (1.441)


Classical mechanics of discrete systems

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Category information

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:

  • : force (21.736)
  • : mass (21.105)
  • : velocity (21.053)
  • : time (17.001)
  • : momentum (14.082)
  • : angular momentum (13.398)
  • : particle (12.579)
  • : acceleration (12.473)
  • : position (vector) (10.802)
  • : moment of inertia (10.035)
  • : kinetic energy (7.861)
  • : velocity (7.840)
  • : effective exhaust velocity (7.699)
  • : rigid body (7.097)
  • : distance (6.877)
  • : particle (4.549)
  • : direction vector (4.526)
  • : mass (4.464)
  • : velocity (4.380)
  • : volume integral (3.731)
  • : velocity (3.661)
  • : particles (3.660)
  • : moment of inertia tensor (3.635)
  • : angular momentum (3.633)
  • : unit vector (3.626)
  • : acceleration (3.595)
  • : center of mass (3.583)
  • : magnitude (3.565)
  • : displacement (vector) (3.565)
  • : speed of light (3.394)
  • : rotation (3.369)
  • : kinetic energy (3.316)
  • : angular velocity (2.869)
  • : length (2.771)
  • : pivot point (2.728)
  • : gravitational acceleration (2.725)
  • : unit vector (2.682)
  • : rotation matrix (2.670)
  • : generalized coordinates (2.627)
  • : spring (2.602)
  • : reference point (2.597)
  • : gravitational constant (2.587)
  • : force (2.575)
  • : local acceleration (2.543)
  • : electric charge (2.467)
  • : body (2.292)
  • : curved path (1.950)
  • : angle (1.950)
  • : unit vector (1.907)
  • : frequency (1.882)
  • : masses (1.882)
  • : total work (1.881)
  • : frame (1.872)
  • : skew-symmetric matrix (1.865)
  • : mass (1.865)
  • : rotation (1.852)
  • : unit vector (1.845)
  • : weight (1.833)
  • : unit vector (1.789)
  • : orbital (1.752)
  • : direction vector (1.749)
  • : moment (1.744)
  • : electric field (1.724)
  • : torque (1.724)
  • : body (1.718)
  • : initial positions (1.718)
  • : canonical momentum (1.714)
  • : torque (1.701)
  • : similar objects (1.664)
  • : momentum operator (1.591)
  • : potential energy (1.576)
  • : polar coordinate system (1.540)
  • : direction (1.439)


Continuum mechanics of solids

[edit]

Category information

Cluster information:

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

Definitions:

  • : surface (5.460)
  • : time (4.609)
  • : position vector (4.360)
  • : vector field (2.791)
  • : material time derivative (2.755)
  • : material time derivative (2.661)
  • : position (2.652)
  • : material time derivative (2.638)
  • : flux (2.603)
  • : velocity (2.583)
  • : heat (2.548)
  • : mapping function (1.939)
  • : normal vector (1.939)
  • : surface forces (1.937)
  • : internal surface area (1.891)
  • : shear viscosity (1.845)
  • : body forces (1.816)
  • : particle velocity (1.813)
  • : particle (1.790)
  • : elastic strain (1.779)
  • : unit mass (1.766)
  • : material time derivative (1.766)
  • : velocity (1.745)
  • : region (1.689)
  • : continuum (1.662)
  • : components (1.640)
  • : position vector (1.591)


Field theory and polynomials

[edit]

Differential and difference algebra

[edit]

Category information

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:

  • : polynomial (17.140)
  • : module (mathematics) (16.749)
  • : field (mathematics) (15.345)
  • : field (mathematics) (13.863)
  • : local field (12.146)
  • : module (11.938)
  • : frobenius algebra (11.268)
  • : extension field (10.984)
  • : degree (10.686)
  • : vector space (9.943)
  • : finite field (8.287)
  • : length (6.994)
  • : division algebra (6.752)
  • : module (6.405)
  • : complex number (6.386)
  • : field (6.032)
  • : valuation (5.397)
  • : field (5.381)
  • : local field (5.259)
  • : field (5.180)
  • : quaternion (4.593)
  • : real number (4.559)
  • : linear operator (4.474)
  • : field (3.587)
  • : submodule (3.572)
  • : field (mathematics) (3.566)
  • : form (3.528)
  • : polynomial (3.462)
  • : symmetric matrix (3.432)
  • : generating set of a group (3.420)
  • : basis (3.326)
  • : matrix (2.799)
  • : column (2.450)
  • : polynomial (2.435)
  • : polynomial sequence (2.398)
  • : quadratic polynomial (1.904)
  • : polynomials (1.900)
  • : sequence (1.891)
  • : symmetric bilinear form (1.882)
  • : maximal ideal (1.790)
  • : quotient ring (1.774)
  • : character module (1.757)
  • : polynomial (1.757)
  • : subgroup (1.738)
  • : roots (1.714)
  • : segment (1.691)
  • : univariate polynomial (1.681)
  • : weight (1.659)
  • : valuation ring (1.657)
  • : basis (1.657)
  • : difference operator (1.640)
  • : hyperreal number (1.556)
  • : coordinate tuples (1.530)


Fluid mechanics

[edit]

Foundations, constitutive equations, rheology

[edit]

Category information

Cluster information:

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

Definitions:

  • : time (4.699)
  • : time (3.889)
  • : young's modulus (3.349)
  • : stress (1.974)
  • : viscosity (1.882)
  • : time (1.865)
  • : shear rate (1.845)
  • : total stress (1.845)
  • : strain rate (1.786)
  • : storage modulus (1.724)
  • : stress (physics) (1.651)


Turbulence

[edit]

Category information

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:

  • : velocity (1.974)
  • : energy dissipation (1.902)
  • : diffusive body-vortex interaction fluid velocity (1.866)
  • : constants (1.847)
  • : diffusion velocity (1.845)
  • : characteristic length (1.784)
  • : kinematic viscosity (1.779)
  • : fluxes (1.610)
  • : diffusive body-vortex interaction fluid velocity (1.591)
  • : large scales (1.556)
  • : fourier (1.556)


Compressible fluids and gas dynamics, general

[edit]

Category information

Cluster information:

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

Definitions:


Biological fluid mechanics

[edit]

Category information

Cluster information:

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

Definitions:

  • : dynamic viscosity (2.483)
  • : surface tension (1.816)
  • : viscosity (1.805)
  • : density (1.805)
  • : stokes radius (1.641)
  • : momentum diffusivity (1.600)


Fourier analysis

[edit]

Fourier analysis in several variables

[edit]

Category information

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:

  • : function (7.003)
  • : periodic function (6.900)
  • : reciprocal lattice (4.226)
  • : reciprocal lattice (3.473)
  • : integrable function (2.707)
  • : operator (2.660)
  • : norm (2.610)
  • : borel measure (1.939)
  • : weight vector (1.939)
  • : hexagonal sampling lattice (1.891)
  • : operator (1.882)
  • : norm (1.865)
  • : flip operator (1.847)
  • : samples (1.846)
  • : time (1.811)
  • : spectrum (1.704)
  • : lomb (1.657)
  • : matrix (1.657)
  • : dominant component (1.645)
  • : figure (1.625)
  • : window (1.562)


Functional analysis

[edit]

Nonlinear functional analysis

[edit]

Category information

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:

  • : bounded linear operator (6.085)
  • : hilbert (4.995)
  • : space (2.869)
  • : banach (2.688)
  • : operator (2.641)
  • : class (2.604)
  • : subset (2.565)
  • : bounded linear operator (2.450)
  • : space (1.950)
  • : space (1.937)
  • : diagonal matrix (1.762)
  • : complex number (1.732)
  • : class (1.719)
  • : vector space (1.700)
  • : span (1.641)


Functions of a complex variable

[edit]

Miscellaneous topics of analysis in the complex domain

[edit]

Category information

Cluster information:

  • cluster id: [2838, 9700]
  • matching score: 0.398631949552
  • purity: 1.0
  • matching keywords: [u'analytic', u'functions', u'complex', u'analysis']

Definitions:


GEOPHYSICS, ASTRONOMY, AND ASTROPHYSICS

[edit]

Solid Earth physics

[edit]

Category information

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:

  • : book (2.563)
  • : attenuation (1.659)


Hydrospheric and atmospheric geophysics

[edit]

Category information

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:

  • : mass (9.619)
  • : volume (6.751)
  • : constituent (6.485)
  • : mass fraction (chemistry) (5.721)
  • : mass concentration (chemistry) (5.470)
  • : molar mass (5.278)
  • : molar mass (4.941)
  • : mole fraction (4.898)
  • : molar concentration (4.784)
  • : density (3.584)
  • : molar mass (3.448)
  • : host (2.707)
  • : mass ratio (2.699)
  • : nucleus (2.649)
  • : adt matrix (2.619)
  • : volume (2.585)
  • : binding (2.561)
  • : constituent (1.950)
  • : elec (1.942)
  • : contour (1.939)
  • : mole ratio (1.937)
  • : matrix elements (1.900)
  • : reference temperature (1.900)
  • : electronic wave functions (1.891)
  • : positions (1.812)
  • : angle (1.811)
  • : molality (1.793)
  • : equation (1.744)
  • : equation (1.712)
  • : mass ratio (1.665)
  • : nuclear positions (1.653)
  • : integration (1.497)


Physics of the ionosphere and magnetosphere

[edit]

Category information

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:

  • : magnetic field (3.422)
  • : mass (3.315)
  • : average velocity (2.725)
  • : magnetic field (2.657)
  • : momentum (2.555)
  • : gyroradius (2.434)
  • : species (1.974)
  • : particle density (1.902)
  • : time (1.891)
  • : gyroradius (1.845)
  • : electric potential (1.797)
  • : velocity component (1.723)
  • : mass (1.677)
  • : velocity vector (1.621)


Stars

[edit]

Category information

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:

  • : star (43.305)
  • : radius (31.929)
  • : radius (3.705)
  • : effective surface temperature (3.705)
  • : luminosity (3.484)
  • : tauri (1.939)
  • : radial velocity (1.845)


Game theory, economics, social and behavioral sciences

[edit]

Mathematical economics

[edit]

Category information

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:

  • : total consumption (5.700)
  • : utility (4.233)
  • : consumption function (3.336)
  • : change (2.977)
  • : income (2.868)
  • : total consumption (2.850)
  • : marginal propensity to consume (2.685)
  • : price level (1.926)
  • : utility level (1.847)
  • : payments (1.790)
  • : disposable income (1.779)


Other social and behavioral sciences (mathematical treatment)

[edit]

Category information

Cluster information:

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

Definitions:

  • : player (9.955)
  • : player (5.852)
  • : machine (4.463)
  • : players (3.651)
  • : machine (2.768)
  • : flow (2.672)
  • : strategy (2.501)
  • : solution concept (1.887)
  • : flow (1.848)
  • : type (1.810)
  • : action (1.688)
  • : flows (1.677)
  • : player (1.677)
  • : player (1.588)
  • : paths (1.471)


General topology

[edit]

Generalities

[edit]

Category information

Cluster information:

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

Definitions:

  • : topological space (7.000)
  • : topological space (5.935)
  • : subspace (4.260)
  • : basis (topology) (4.164)
  • : subset (3.527)
  • : function (2.695)
  • : subspace (2.674)
  • : topology (2.642)
  • : continuous (topology) (2.562)
  • : topological space (1.882)
  • : subspace topology (1.744)
  • : rational number (1.702)


Geometry

[edit]

Analytic and descriptive geometry

[edit]

Category information

Cluster information:

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

Definitions:

  • : plane curve (8.757)
  • : tangent (7.168)
  • : plane curve (6.130)
  • : tangential trapezoid (5.174)
  • : area (4.535)
  • : bases (3.051)
  • : =-lrb- (2.855)
  • : vertex angle (2.573)
  • : polar coordinate system (2.550)
  • : pedal point (2.531)
  • : consecutive sides (2.527)
  • : polar angle (1.878)
  • : distance (1.824)
  • : lengths (1.790)
  • : specific values (1.774)
  • : curve (1.714)
  • : side (1.657)
  • : =-lrb- (1.600)
  • : height (1.598)
  • : perpendicular distance (1.585)
  • : polar coordinate system (1.576)
  • : tangent (1.562)


Group theory and generalizations

[edit]

Connections with homological algebra and category theory

[edit]

Category information

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:


Hardware

[edit]

Power and energy

[edit]

Category information

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:

  • : electrical impedance (8.909)
  • : shunt (7.073)
  • : position (6.383)
  • : charges (5.442)
  • : test charge (5.062)
  • : filter half-section (4.865)
  • : electric potential energy (4.738)
  • : electric charge (4.681)
  • : test charge (4.450)
  • : electric field (4.171)
  • : electrostatic force (3.769)
  • : electric charge (3.461)
  • : half-sections (2.937)
  • : electric field (2.865)
  • : complex exponentials (2.787)
  • : displacement vector (2.532)
  • : farad (2.523)
  • : potential energy (2.433)
  • : customers (2.286)
  • : nominal impedance (1.939)
  • : filters (1.939)
  • : energy density (1.937)
  • : customers (1.900)
  • : positions (1.865)
  • : electric potential (1.847)
  • : charge (1.845)
  • : propagation constant (1.821)
  • : characteristic impedance (1.783)
  • : potential energy (1.776)
  • : distance (1.766)
  • : different values (1.758)
  • : propagation constant (1.724)
  • : electrical conductance (1.722)
  • : electric displacement field (1.718)
  • : source point (1.681)
  • : field point (1.677)
  • : volume element (1.655)
  • : displacement vector (1.552)


[edit]

Physical chemistry and chemical physics

[edit]

Category information

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:


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

[edit]

Category information

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:

  • : diameter (4.901)
  • : diameter (3.405)
  • : power level (3.318)
  • : frequency (2.746)
  • : speed of light (2.553)
  • : length (1.937)
  • : relative permeability (1.793)
  • : characteristic impedance (1.714)
  • : insulator (1.689)
  • : dielectric constant (1.677)


Other areas of applied and interdisciplinary physics

[edit]

Category information

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:

  • : direction (3.623)
  • : equation (2.665)
  • : wave vector (2.640)
  • : atomic number density (2.625)
  • : dependence (2.619)
  • : specific heat capacity (2.600)
  • : atomic mass (2.521)
  • : atom (2.492)
  • : atom (2.452)
  • : type materials (2.417)
  • : limit (1.939)
  • : direction (1.937)
  • : partition function (statistical mechanics) (1.902)
  • : carrier density (1.902)
  • : time (1.902)
  • : long wavelength limit (1.865)
  • : distance (1.865)
  • : drift velocity (1.858)
  • : electric field (1.848)
  • : density of states (1.834)
  • : equilibrium distribution (1.811)
  • : spin (1.810)
  • : group velocity (1.810)
  • : concentration (1.810)
  • : elementary charge (1.790)
  • : length (1.749)
  • : radiation intensity (1.744)
  • : temperature (1.742)
  • : slope (1.714)
  • : momentum (1.696)
  • : electrolyte (1.688)
  • : unit vector (1.677)
  • : drift velocity (1.664)
  • : electron hole concentration (1.657)
  • : electron hole concentration (1.657)
  • : film2 (1.657)
  • : velocity (1.653)
  • : displacement vector (1.592)
  • : phonon velocity (1.574)
  • : film2 (1.524)
  • : electron (1.490)
  • : inverse screening length (1.489)


Information and communication, circuits

[edit]

Communication, information

[edit]

Category information

Cluster information:

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

Definitions:

  • : length (10.082)
  • : hamming weight (9.143)
  • : block code (4.437)
  • : hamming distance (2.771)
  • : codeword (2.688)
  • : ary code (2.662)
  • : errors (1.939)
  • : relation (1.719)
  • : error (1.598)


Circuits, networks

[edit]

Category information

Cluster information:

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

Definitions:

  • : circuit (3.294)
  • : closed circuit (1.939)
  • : impedance (1.847)
  • : total number (1.754)
  • : δ circuit (1.524)


Information systems

[edit]

Data management systems

[edit]

Category information

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:

  • : schedule (1.974)
  • : original value (1.865)


K-theory

[edit]

Whitehead groups and K_1

[edit]

Category information

Cluster information:

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

Definitions:


Manifolds and cell complexes

[edit]

Topological manifolds

[edit]

Category information

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:

  • : sphere (3.729)
  • : manifold (2.675)
  • : embedding (2.458)
  • : circles (1.926)
  • : boundary (1.811)
  • : boundary (1.533)
  • : 3-sphere (1.497)


Mathematical logic and foundations

[edit]

General logic

[edit]

Category information

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:

  • : statement (5.991)
  • : statement (5.452)
  • : statement (3.564)
  • : truth (1.657)
  • : truth (1.625)


Set theory

[edit]

Category information

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:


Mechanics of deformable solids

[edit]

Special subfields of solid mechanics

[edit]

Category information

Cluster information:

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

Definitions:

  • : mass (5.535)
  • : eccentricity (3.380)
  • : energy (2.869)
  • : radius (2.768)
  • : tensile stress (2.499)
  • : order (1.812)
  • : function (1.775)
  • : equation (1.738)
  • : notation (1.724)
  • : plane (1.707)
  • : yield strength (1.671)
  • : change (1.524)


Mechanics of particles and systems

[edit]

Kinematics

[edit]

Category information

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:

  • : freedom (5.343)
  • : joints (3.849)
  • : links (3.808)
  • : constraints (2.961)
  • : freedom (2.961)
  • : degree-of-freedom (2.941)
  • : fixed link (2.531)
  • : freedom (2.488)


Dynamics of a system of particles, including celestial mechanics

[edit]

Category information

Cluster information:

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

Definitions:

  • : world manifold (5.701)
  • : gravitational constant (4.191)
  • : time (3.635)
  • : linear connection (2.811)
  • : time (2.649)
  • : structure group (2.621)
  • : mean motion (2.516)
  • : spatial distributions (1.939)
  • : structure group (1.915)
  • : gravitational constant (1.900)
  • : hours (1.812)
  • : mass (1.724)
  • : distortion (1.654)
  • : time (1.556)


NUCLEAR PHYSICS

[edit]

Nuclear structure

[edit]

Category information

Cluster information:

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

Definitions:

  • : initial concentration (5.369)
  • : initial concentration (5.125)
  • : concentration (3.662)
  • : 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)

[edit]

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:

  • : electric charge (15.630)
  • : magnetic field (13.834)
  • : electric charge (11.565)
  • : speed of light (9.225)
  • : electric field (9.034)
  • : baryon number (8.185)
  • : coordinate time (7.233)
  • : magnetic potential (6.897)
  • : velocity (6.333)
  • : subatomic particle (5.922)
  • : rest mass (5.253)
  • : hypercharge (5.186)
  • : electromagnetic tensor (5.147)
  • : % 20mechanics (5.088)
  • : strangeness (4.699)
  • : kinetic energy (4.620)
  • : total angular momentum quantum number (4.580)
  • : energy (4.532)
  • : lepton number (4.524)
  • : speed (4.374)
  • : direction (4.287)
  • : weak isospin (4.261)
  • : potential energy (4.258)
  • : magnetic dipole (4.197)
  • : position vector (3.784)
  • : magnetic charge (3.667)
  • : dimensions (3.531)
  • : manifold (3.404)
  • : kinetic momentum (3.362)
  • : up quark (3.213)
  • : parity (3.142)
  • : isospin (2.830)
  • : physics (2.803)
  • : current density (2.803)
  • : weak hypercharge (2.762)
  • : up quark (2.744)
  • : electric potential (2.685)
  • : gauge covariant derivative (2.676)
  • : space (2.615)
  • : field (2.595)
  • : probability current (2.578)
  • : third component (2.555)
  • : fields (2.543)
  • : position (2.479)
  • : form (2.472)
  • : electric displacement (1.942)
  • : metric tensor (1.939)
  • : closed loop (1.891)
  • : lorentz force (1.858)
  • : momentum component (1.858)
  • : magnetization (1.850)
  • : direction (1.779)
  • : direction (1.779)
  • : momentum operator (1.766)
  • : charm (quantum number) (1.756)
  • : surface (1.749)
  • : direction (1.749)
  • : gravitational acceleration (1.724)
  • : four momentum (1.717)
  • : cartesian coordinate (1.689)
  • : velocities (1.677)
  • : smooth function (1.621)
  • : invariant mass (1.621)
  • : direction (1.564)
  • : lorentz factor (1.532)
  • : mmj2ubwoeev70gxo14dyaw (1.532)


Networks

[edit]

Network protocols

[edit]

Category information

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:

  • : antennas (8.788)
  • : antennas (5.391)
  • : session key (5.126)
  • : server (4.412)
  • : channel matrix (4.110)
  • : identities (3.513)
  • : symmetric key (2.637)
  • : spatial correlation matrix (2.513)
  • : signal covariance (1.939)
  • : spatial correlation matrix (1.872)
  • : cryptographic nonce (1.837)
  • : session (1.814)
  • : channel matrix (1.790)
  • : antenna (1.790)
  • : network (1.736)
  • : alice (1.712)
  • : permanent (1.654)
  • : timestamp (1.635)
  • : message (1.621)
  • : cryptographic nonce (1.603)


Nonassociative rings and algebras

[edit]

General nonassociative rings

[edit]

Category information

Cluster information:

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

Definitions:


Number theory

[edit]

Sequences and sets

[edit]

Category information

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:

  • : prime number (13.232)
  • : prime number (6.160)
  • : sequences (5.232)
  • : natural number (4.160)
  • : triangular number (2.669)
  • : real numbers (2.619)
  • : estimate (2.471)
  • : lucas sequence (2.263)
  • : sequences (1.939)
  • : irrational number (1.939)
  • : real number (1.939)
  • : pseudoprime (1.900)
  • : fibonacci number (1.891)
  • : sequence (1.812)
  • : natural number (1.799)
  • : sequences (1.754)
  • : conventions (1.712)
  • : lower triangular matrix (1.529)
  • : integer sequence (1.513)


Algebraic number theory: local and p-adic fields

[edit]

Category information

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:


Connections with logic

[edit]

Category information

Cluster information:

  • cluster id: [8638]
  • matching score: 0.501027191748
  • purity: 1.0
  • matching keywords: [u'number', u'arithmetic']

Definitions:


Numerical analysis

[edit]

Numerical linear algebra

[edit]

Category information

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:

  • : symmetric matrix (14.671)
  • : triangular matrix (8.400)
  • : skew-hermitian matrix (5.940)
  • : matrix (5.320)
  • : triangular matrix (4.422)
  • : diagonal matrix (3.654)
  • : triangular matrix (3.572)
  • : computation (2.781)
  • : right hand side (2.323)
  • : initial guess (1.903)
  • : ω output (1.895)
  • : loop (1.852)
  • : loop (1.817)
  • : diagonal matrix (1.816)
  • : iteration (1.765)
  • : matrix (1.677)
  • : iteration (1.659)
  • : error end (1.623)


Mathematical programming, optimization and variational techniques

[edit]

Category information

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:

  • : internal function (3.409)
  • : euclidean space (2.835)
  • : hardy space (2.798)
  • : euclidean space (2.783)
  • : outer distortion (2.736)
  • : outer distortion (2.583)
  • : function (2.560)
  • : function (2.434)
  • : open set (1.937)


Integral equations, integral transforms

[edit]

Category information

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:

  • : stochastic process (3.452)
  • : stochastic process (1.939)
  • : flow (1.900)
  • : bounded linear operator (1.865)
  • : wiener process (1.744)
  • : cell centres (1.663)
  • : action (1.657)
  • : distribution (1.654)
  • : dimensional case (1.648)


Numerical methods in Fourier analysis

[edit]

Category information

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:

  • : signal (5.495)
  • : filter coefficients (1.891)
  • : filter (1.882)
  • : admissibility (1.754)
  • : period (1.690)
  • : period (1.586)


Computer aspects of numerical algorithms

[edit]

Category information

Cluster information:

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

Definitions:

  • : domain of a function (7.203)
  • : lipschitz continuity (3.389)
  • : function values (2.590)
  • : initial values (2.586)
  • : mean value (2.297)
  • : initial values (1.663)
  • : fixed-point iteration (1.628)
  • : secant method (1.563)


OTHER

[edit]

Miscellaneous topics in measure theory

[edit]

Category information

Cluster information:

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

Definitions:


Data management systems

[edit]

Category information

Cluster information:

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

Definitions:


Phase transformations in solids

[edit]

Category information

Cluster information:

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

Definitions:

  • : edge length (3.727)
  • : johnson solid (3.626)
  • : decagon (1.476)
  • : octagon (1.468)


Geophysical observations, instrumentation, and techniques

[edit]

Category information

Cluster information:

  • cluster id: [2035]
  • matching score: 0.0738295007636
  • purity: 1.0
  • matching keywords: [u'new', u'national']

Definitions:

  • : note1 (7.299)
  • : % note1 (6.653)
  • : note1 (5.567)
  • : note1 (5.487)
  • : note1 (4.557)
  • : charter member (1.854)
  • : note1 (1.812)


Randomness, geometry and discrete structures

[edit]

Category information

Cluster information:

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


General

[edit]

Category information

Cluster information:

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

Definitions:

  • : radius (3.479)


Low-dimensional topology

[edit]

Category information

Cluster information:

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


Basic methods

[edit]

Category information

Cluster information:

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

Definitions:

  • : gain (4.934)
  • : base station antenna height (4.338)
  • : path loss (3.335)
  • : wavelength (1.900)
  • : frequency (1.900)
  • : slope (1.790)
  • : distance (1.790)
  • : adjustment (1.742)


Algebraic combinatorics

[edit]

Category information

Cluster information:

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

Definitions:

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


Algebraic combinatorics

[edit]

Category information

Cluster information:

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


Computer graphics

[edit]

Category information

Cluster information:

  • cluster id: [9126]
  • matching score: 0.161404183301
  • purity: 1.0
  • matching keywords: [u'graphics']

Definitions:


Interaction design

[edit]

Category information

Cluster information:

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

Definitions:

  • : order (4.474)
  • : cutoff frequency (3.641)
  • : gain (2.830)
  • : gain (2.608)
  • : complex frequency space (2.585)
  • : transfer function (2.487)
  • : poles (1.939)
  • : frequency (1.939)
  • : shunt (1.779)
  • : filter (signal processing) (1.742)
  • : shunt (1.712)
  • : ripple factor (1.673)


Low-dimensional topology

[edit]

Category information

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)

[edit]

Category information

Cluster information:

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

Definitions:

  • : resistor load (8.064)
  • : resistance (2.937)
  • : early voltage (1.974)
  • : series resistance (1.891)
  • : signal source (1.891)
  • : current source (1.882)
  • : active load (1.850)
  • : norton's theorem (1.845)
  • : boltzmann constant (1.766)
  • : output (1.712)
  • : output resistance (1.712)
  • : resistor load (1.676)
  • : gain (1.636)
  • : norton's theorem (1.628)
  • : discharge (1.593)


Graphical methods

[edit]

Category information

Cluster information:

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

Definitions:

  • : hit (baseball) (2.850)
  • : poor (2.696)


Stochastic systems and control

[edit]

Category information

Cluster information:

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

Definitions:

  • : chart (7.054)
  • : shewhart (3.520)
  • : chart (3.468)

Randomness, geometry and discrete structures

[edit]

Category information

Cluster information:

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

Definitions:

  • : latitude (7.113)
  • : latitude (4.498)
  • : longitude (1.845)


Probability theory on algebraic and topological structures

[edit]

Category information

Cluster information:

  • cluster id: [3822]
  • matching score: 0.631482808408
  • purity: 1.0
  • matching keywords: [u'probability']

Definitions:

  • : random variable (5.253)
  • : probability (3.419)
  • : discrete random variable (2.675)
  • : probability-generating function (2.558)
  • : thinsp ;-rrb- (2.394)
  • : factorial (1.863)
  • : complex number (1.830)
  • : probability (1.556)


Connections with logic

[edit]

Category information

Cluster information:

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

Definitions:

  • : polynomials (2.639)
  • : polynomials (2.487)
  • : integral polynomial (1.939)
  • : prime number (1.910)
  • : positive integer (1.867)
  • : proof (1.688)
  • : 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)

[edit]

Category information

Cluster information:

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

Definitions:


Computational methods

[edit]

Category information

Cluster information:

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

Definitions:


Decision theory

[edit]

Category information

Cluster information:

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

Definitions:


Physical chemistry and chemical physics

[edit]

Category information

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:

  • : type (2.735)
  • : agcl (1.868)


Close-to-elliptic equations

[edit]

Category information

Cluster information:

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

Definitions:

  • : path loss (3.544)
  • : depth (1.766)
  • : path loss exponent (1.724)


Mechanical and acoustical properties of condensed matter

[edit]

Category information

Cluster information:

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

Definitions:

  • : major diameter (7.944)
  • : pitch (6.967)
  • : height (3.877)


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

[edit]

Category information

Cluster information:

  • cluster id: [6094]
  • matching score: 0.115373534547
  • purity: 1.0
  • matching keywords: [u'astronomical', u'astronomy', u'objects']

Definitions:


Physical chemistry and chemical physics

[edit]

Category information

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:

Computing methodologies and applications

[edit]

Category information

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:

  • : first-order hold (2.799)
  • : dirac delta function (2.554)
  • : gain (1.939)
  • : dirac delta function (1.797)
  • : signal (1.764)
  • : gain (1.754)
  • : octave (1.724)
  • : dirac delta function (1.424)


Computational methods

[edit]

Category information

Cluster information:

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

Definitions:

  • : mass (5.160)
  • : black hole (2.843)
  • : angular momentum (2.201)
  • : temporal component (1.939)
  • : solution (1.724)
  • : quantity (1.610)
  • : body (1.505)


Homological algebra

[edit]

Category information

Cluster information:

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

Definitions:

  • : dimensions (4.319)
  • : rational functions (2.571)
  • : basis vectors (1.743)
  • : euclidean space (1.733)
  • : basis vectors (1.714)
  • : mapping vectors (1.710)


Hamilton-Jacobi theories, including dynamic programming

[edit]

Category information

Cluster information:

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

Definitions:

  • : vector operator (6.317)
  • : velocity field (5.444)
  • : vector field (4.221)
  • : vector area (3.661)
  • : direction (3.348)
  • : volume form (3.019)
  • : time (2.799)
  • : function (2.766)
  • : smooth function (2.708)
  • : vector fields (2.615)
  • : vector element (2.547)
  • : density on a manifold (2.535)
  • : vector element (2.508)
  • : form (2.475)
  • : vector field (2.412)
  • : volume (1.865)
  • : source-free part (1.865)
  • : vector area (1.847)
  • : vector field (1.847)
  • : electric field (1.824)
  • : scalar-valued function (1.714)
  • : unit vector (1.707)
  • : direction (1.690)
  • : unit vector (1.659)
  • : tensor (1.657)
  • : field (1.641)
  • : tangent vector (1.550)
  • : 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)

[edit]

Category information

Cluster information:

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

Definitions:

  • : effective mass (solid-state physics) (3.656)
  • : time (3.419)
  • : region (2.799)
  • : region (2.799)
  • : region (2.576)
  • : solutions (2.465)
  • : momentum (2.421)
  • : position (2.367)
  • : wave vector (1.939)
  • : discrete components (1.937)
  • : particles (1.848)
  • : wavefunction (1.847)
  • : ball (1.815)
  • : total volume (1.754)
  • : potential barrier (1.754)
  • : volume (1.754)
  • : resonance frequency (1.749)
  • : scalar multiplication (1.742)
  • : wave vector (1.659)
  • : classical mechanics (1.645)
  • : dispersion relation (1.628)
  • : wave (1.618)
  • : position vector (1.604)
  • : spin (physics) (1.600)


Nuclear engineering and nuclear power studies

[edit]

Category information

Cluster information:

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

Definitions:

  • : rocket (4.071)
  • : mass (3.560)
  • : total mass (3.245)
  • : effective exhaust velocity (3.160)
  • : direction (2.777)
  • : mass (2.758)
  • : mass (2.726)
  • : effective exhaust velocity (2.679)
  • : mass (2.676)
  • : specific impulse (2.508)
  • : rocket engine (2.402)
  • : external forces (1.865)
  • : equation (1.779)
  • : lorentz factor (1.720)
  • : velocity (1.689)
  • : speed of light (1.665)
  • : equation (1.557)


Operator theory

[edit]

Other (nonclassical) types of operator theory

[edit]

Category information

Cluster information:

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

Definitions:

  • : hilbert space (8.983)
  • : linear operator (4.387)
  • : linear operator (4.181)
  • : operator (3.199)
  • : orthogonal projection (2.702)
  • : dilation (1.939)
  • : operator (1.749)
  • : normal operator (1.696)


Optics, electromagnetic theory

[edit]

General

[edit]

Category information

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:

  • : direction (8.647)
  • : angle (6.736)
  • : speed of light (6.072)
  • : angle (5.655)
  • : refractive index (4.457)
  • : refraction (4.085)
  • : wavenumber (3.579)
  • : electric field (3.427)
  • : angle (3.425)
  • : speed of light (3.157)
  • : angle (2.799)
  • : refractive indices (2.741)
  • : refractive index (2.697)
  • : vacuum permittivity (2.685)
  • : electric field (2.649)
  • : right (2.635)
  • : wavelength (2.491)
  • : unit vectors (2.445)
  • : circular polarization (2.390)
  • : circular polarization (2.338)
  • : radians (1.974)
  • : incidence (1.939)
  • : wavelength (1.882)
  • : state (1.865)
  • : absolute value (1.865)
  • : operator (physics) (1.848)
  • : normal vector (1.847)
  • : refractive index (1.847)
  • : angle (1.816)
  • : transmittance (1.800)
  • : radii (1.799)
  • : state (1.787)
  • : fig. (1.781)
  • : light (1.778)
  • : integer (1.725)
  • : light vector (1.701)
  • : fraction (1.683)
  • : radians (1.659)
  • : light (1.621)
  • : absorption (1.558)
  • : radians (1.524)
  • : colors (1.515)
  • : angle (1.441)


Ordinary differential equations

[edit]

General theory

[edit]

Category information

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:

  • : system (3.216)
  • : eigenvalue (2.683)
  • : function (mathematics) (1.913)
  • : fiber bundle (1.766)
  • : function (1.718)
  • : tangent bundle (1.689)


PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES

[edit]

Physics of plasmas and electric discharges

[edit]

Category information

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:


Partial differential equations

[edit]

Close-to-elliptic equations

[edit]

Category information

Cluster information:

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

Definitions:

  • : electric field (7.113)
  • : magnetic field (4.360)
  • : current density (4.341)
  • : magnetic field (4.115)
  • : unknown coefficients (3.785)
  • : electric displacement field (3.702)
  • : field (3.581)
  • : differential operator (3.571)
  • : field (2.780)
  • : unit normal (2.765)
  • : frequency (2.763)
  • : wavenumber (2.718)
  • : density (2.504)
  • : magnetization (2.504)
  • : electric field (2.242)
  • : angle (1.939)
  • : charge (1.926)
  • : differential operator (1.900)
  • : computational domain (1.900)
  • : wave vector (1.900)
  • : surface area (1.882)
  • : time (1.868)
  • : density (1.864)
  • : speed of light (1.826)
  • : density (1.823)
  • : dirichlet (1.790)
  • : general solution (1.790)
  • : electrical potential (1.774)
  • : ricci calculus (1.762)
  • : electric field (1.750)
  • : direction (1.746)
  • : differential (infinitesimal) (1.712)
  • : vector area (1.690)
  • : slab (1.657)
  • : nabla (1.628)
  • : material (1.598)
  • : frequency (1.591)
  • : nabla (1.506)
  • : charge (1.476)


Probability theory and stochastic processes

[edit]

Foundations of probability theory

[edit]

Category information

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:

  • : stochastic process (8.994)
  • : time (6.933)
  • : state (5.402)
  • : stochastic process (4.099)
  • : measurable space (3.889)
  • : state (3.385)
  • : equilibrium distribution (3.293)
  • : time (3.250)
  • : time (2.869)
  • : probability measure (2.644)
  • : transition rate matrix (1.974)
  • : transition matrix (1.939)
  • : martingale (probability theory) (1.816)
  • : a.s. (1.815)
  • : variance (1.749)
  • : condition (1.627)


Probability theory on algebraic and topological structures

[edit]

Category information

Cluster information:

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

Definitions:


Distribution theory

[edit]

Category information

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:

  • : probability distribution (34.317)
  • : triangular distribution (9.286)
  • : random variables (6.777)
  • : degrees of freedom (statistics) (4.065)
  • : location parameter (3.971)
  • : matrix inverse (3.648)
  • : noncentrality parameter (3.567)
  • : constants (3.548)
  • : interval (3.348)
  • : posterior distribution (3.233)
  • : uniform distribution (continuous) (3.077)
  • : shape parameters (2.540)
  • : scale parameter (2.533)
  • : uniform distribution (continuous) (2.530)
  • : scale (2.467)
  • : scale matrix (2.417)
  • : scale matrix (2.417)
  • : thinsp (1.900)
  • : positive constants (1.882)
  • : heaviside step function (1.865)
  • : chi-squared distribution (1.840)
  • : l-kurtosis (1.781)
  • : continuous distributions (1.743)
  • : uniform distribution (continuous) (1.739)
  • : incomplete gamma function (1.724)
  • : positive-definite matrix (1.707)
  • : positive constants (1.707)
  • : f-distribution (1.689)
  • : rayleigh distribution (1.677)
  • : covariance matrix (1.653)
  • : laplace distribution (1.653)
  • : relation (1.590)
  • : scale matrix (1.589)
  • : scale matrix (1.589)
  • : constants (1.497)


Stochastic analysis

[edit]

Category information

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:

  • : stochastic differential equation (8.347)
  • : compact support (5.321)
  • : domain (4.611)
  • : initial datum (4.605)
  • : initial datum (4.595)
  • : functions (4.414)
  • : time (4.393)
  • : brownian motion (4.288)
  • : borel (4.127)
  • : differential equation (3.820)
  • : brownian motion (3.741)
  • : expectation (3.648)
  • : operator (3.447)
  • : observations (2.799)
  • : characteristic operator (2.797)
  • : brownian motion (2.625)
  • : itō diffusion (2.492)
  • : expectation (2.453)
  • : measurable space (1.974)
  • : natural filtration (1.915)
  • : euclidean space (1.910)
  • : state (1.891)
  • : observations (1.865)
  • : sets (1.848)
  • : sequences (1.810)
  • : operator (1.781)
  • : natural number (1.779)
  • : space (1.666)
  • : green's function (1.621)
  • : first exit time (1.591)


Quantum theory

[edit]

General mathematical topics and methods in quantum theory

[edit]

Category information

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:

  • : operator (mathematics) (4.668)
  • : measure (mathematics) (3.439)
  • : magnetic quantum number (3.112)
  • : space (2.835)
  • : electrostatic (2.644)
  • : state (2.635)
  • : measurable space (2.182)
  • : time (1.974)
  • : pure state (1.939)
  • : energy (1.937)
  • : basis (1.915)
  • : simple proof (1.882)
  • : state (1.858)
  • : degenerate energy (1.845)
  • : potential (1.812)
  • : current densities (1.812)
  • : target state (1.812)
  • : operators (1.811)
  • : operators (1.810)
  • : function (1.800)
  • : radiation field (1.790)
  • : scalar potential (1.756)
  • : sigma algebra (1.708)
  • : states (1.698)
  • : unitary operator (1.690)
  • : systems (1.689)
  • : hilbert space (1.657)
  • : fidelity (1.618)
  • : degenerate energy (1.524)


[edit]

Category information

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:

  • : tensor rank (5.360)
  • : field (4.726)
  • : % 20tensor (3.800)
  • : generating functional (3.661)
  • : mass (3.566)
  • : action (physics) (2.741)
  • : tensor (2.586)
  • : metric tensor (1.974)
  • : closed loop (1.939)
  • : operator (physics) (1.882)
  • : spin connection (1.845)
  • : time ordering (1.790)
  • : source field (1.757)
  • : determinant (1.754)
  • : electromagnetic tensor (1.744)
  • : particle green (1.696)
  • : theory (1.659)
  • : speed of light (1.659)
  • : mass (1.657)
  • : equations (1.654)
  • : covariant derivative (1.629)
  • : perturbation theory (quantum mechanics) (1.527)


Real functions

[edit]

Functions of one variable

[edit]

Category information

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:

  • : list (5.816)
  • : nonzero (1.790)


Miscellaneous topics

[edit]

Category information

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:

  • : function (mathematics) (24.187)
  • : function (mathematics) (11.764)
  • : sinc function (5.240)
  • : polynomial function (5.049)
  • : metric spaces (5.004)
  • : sequence (4.713)
  • : euler's totient function (4.294)
  • : continuous function (4.132)
  • : function (4.073)
  • : function (3.850)
  • : real number (3.664)
  • : degree (3.559)
  • : function (3.478)
  • : final topology (3.402)
  • : function (3.275)
  • : distribution (2.799)
  • : key length (2.799)
  • : continuity (2.685)
  • : neighbourhood (mathematics) (2.677)
  • : continuous function (2.627)
  • : normed vector space (2.595)
  • : open set (2.551)
  • : positive number (1.950)
  • : ball (1.939)
  • : open interval (1.915)
  • : poly (1.903)
  • : neighborhood (1.900)
  • : domain (1.790)
  • : möbius function (1.766)
  • : function (1.712)
  • : approaches (1.657)
  • : function (1.591)
  • : continuous function (1.588)
  • : open interval (1.588)


Relativity and gravitational theory

[edit]

Computational methods

[edit]

Category information

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:

  • : speed of light (7.772)
  • : position (6.931)
  • : mass (6.302)
  • : black hole (5.922)
  • : time (5.601)
  • : initial rest length (5.482)
  • : relative velocity (4.254)
  • : electric potential (3.679)
  • : electric potential (3.539)
  • : proper length (3.359)
  • : position (3.289)
  • : distance (2.728)
  • : electric charge (2.688)
  • : gravitational constant (2.649)
  • : angular momentum (2.642)
  • : endpoints (2.368)
  • : dimensions (1.907)
  • : electric field (1.889)
  • : distance (1.875)
  • : total energy (1.858)
  • : proper time (1.848)
  • : electric current density (1.845)
  • : black hole (1.812)
  • : time (1.793)
  • : event (1.781)
  • : event (1.781)
  • : boltzmann constant (1.779)
  • : magnetic field (1.769)
  • : schwarzschild radius (1.749)
  • : hendrik lorentz (1.732)
  • : harmonic function (1.724)
  • : infinity (1.723)
  • : initial mass (1.707)
  • : acceleration (1.524)


Unified, higher-dimensional and super field theories

[edit]

Category information

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:

  • : dimensions (2.536)

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

[edit]

Elementary classical functions

[edit]

Category information

Cluster information:

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

Definitions:


Hypergeometric functions

[edit]

Category information

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:


Other special functions

[edit]

Category information

Cluster information:

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

Definitions:


Statistics

[edit]

Parametric inference

[edit]

Category information

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:

  • : hypothesis tests (9.682)
  • : type i and type ii errors (6.550)
  • : statistic (5.426)
  • : type i and type ii errors (4.687)
  • : type i and type ii errors (4.687)
  • : statistics (4.295)
  • : type i and type ii errors (3.725)
  • : level (3.694)
  • : alternative hypothesis (3.643)
  • : mean (2.799)
  • : test (2.741)
  • : parameter vector (2.652)
  • : random variable (2.616)
  • : null hypotheses (2.565)
  • : pareto distribution (2.469)
  • : random parameter (1.939)
  • : hypothesis (1.939)
  • : independent comparisons (1.939)
  • : samples (1.900)
  • : weight (1.882)
  • : function (1.834)
  • : quantiles (1.816)
  • : well-behaved statistic (1.751)
  • : confidence intervals (1.738)
  • : bernoulli distribution (1.700)
  • : discoveries (1.677)
  • : pareto distribution (1.673)
  • : random vector (1.666)
  • : intersection hypothesis (1.544)
  • : null hypotheses (1.524)


Multivariate analysis

[edit]

Category information

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:

  • : moran (7.965)
  • : geary (4.327)
  • : random variables (3.589)
  • : functions (3.510)
  • : observation (3.495)
  • : mean (3.435)
  • : random sample (3.420)
  • : sample variance (3.401)
  • : pearson product-moment correlation coefficient (3.227)
  • : variance (2.833)
  • : distribution (2.802)
  • : observation (2.800)
  • : correlation (2.791)
  • : estimator (2.552)
  • : rank (2.536)
  • : standard deviation (2.429)
  • : weight vector (1.939)
  • : regressor (1.926)
  • : unknown parameter (1.907)
  • : interest (1.900)
  • : constants (1.900)
  • : variance (1.865)
  • : measure (1.855)
  • : independent variables (1.845)
  • : dependent variable (1.833)
  • : sample covariance matrix (1.817)
  • : distribution (1.810)
  • : week (1.774)
  • : matrix (1.749)
  • : mean (1.724)
  • : correlation (1.701)
  • : function (1.701)
  • : iq (1.627)
  • : observations (1.611)
  • : data points (1.610)
  • : standard deviation (1.591)
  • : mean (1.591)
  • : functions (1.524)
  • : constants (1.524)


Linear inference, regression

[edit]

Category information

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:

  • : observation (6.257)
  • : observations (5.196)
  • : explanatory variable (4.712)
  • : design matrix (3.317)
  • : model (2.961)
  • : study (2.799)
  • : coefficient (2.725)
  • : data (2.672)
  • : matrix (2.593)
  • : matrix (2.527)
  • : model (2.448)
  • : residual vector (1.974)
  • : data matrix (1.939)
  • : effect size (1.915)
  • : matrix (1.897)
  • : rank (matrix theory) (1.882)
  • : variance (1.876)
  • : columns (1.865)
  • : pcr estimator (1.812)
  • : explanators (1.793)
  • : posterior mean (1.781)
  • : squares (1.779)
  • : moore–penrose_pseudoinverse (1.724)
  • : true coefficients (1.718)
  • : probability distribution (1.689)
  • : bias of an estimator (1.520)


Systems theory; control

[edit]

General

[edit]

Category information

Cluster information:

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

Definitions:

  • : coordinate system (7.644)
  • : differential operators (4.439)
  • : direction (3.729)
  • : form (2.926)
  • : form (2.926)
  • : moon (2.894)
  • : black sphere (2.286)
  • : mcgraw-hill (1.926)
  • : cartesian coordinates (1.579)
  • : cartesian coordinate system (1.556)


Stochastic systems and control

[edit]

Category information

Cluster information:

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

Definitions:

Theory of computation

[edit]

Design and analysis of algorithms

[edit]

Category information

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:

  • : complexity class (7.405)
  • : self (6.937)
  • : dspace (6.799)
  • : space (6.224)
  • : state (5.292)
  • : state (5.084)
  • : deterministic turing machine (4.549)
  • : linear bounded automaton (4.456)
  • : length (4.283)
  • : call position (3.887)
  • : gödel numbering (3.732)
  • : state (3.510)
  • : transition relation (3.178)
  • : symbol (2.961)
  • : state (2.799)
  • : alphabet (computer science) (2.727)
  • : word (2.674)
  • : finite set (2.661)
  • : complexity measure (2.485)
  • : state (2.266)
  • : pushdown automaton (1.974)
  • : initial state (1.974)
  • : states (1.974)
  • : function (1.974)
  • : formal language (1.939)
  • : input (1.939)
  • : alphabet (1.891)
  • : partial computable function (1.882)
  • : empty word (1.858)
  • : symbol (1.847)
  • : hash (1.843)
  • : context-free grammar (1.824)
  • : program (1.790)
  • : domain (mathematics) (1.774)
  • : disjoint (1.774)
  • : function (1.757)
  • : computer science (1.757)
  • : state (1.749)
  • : position (1.688)
  • : alphabet (1.675)
  • : state (1.665)
  • : state (1.623)
  • : right multiplication (1.576)


Topological groups, Lie groups

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Lie groups

[edit]

Category information

Cluster information:

  • cluster id: [450, 1494, 3819, 8632, 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:

  • : lie algebra (16.000)
  • : subgroup (11.003)
  • : weyl group (7.311)
  • : weight (representation theory) (7.243)
  • : symbol (5.392)
  • : weyl group (4.243)
  • : subgroup (3.732)
  • : root (3.630)
  • : representation of a lie algebra (3.623)
  • : dominant weight (2.751)
  • : holomorphic line bundle (2.736)
  • : complex semisimple lie group (2.628)
  • : 1-dimensional lie algebra (2.596)
  • : borel subgroup (2.563)
  • : vector space (2.366)
  • : edge lengths (1.875)
  • : angular momenta (1.875)
  • : inner product (1.845)
  • : semisimple lie algebra (1.834)
  • : edge lengths (1.801)
  • : module (mathematics) (1.779)
  • : field (1.756)
  • : commute (1.756)
  • : coroot (1.749)
  • : operators ad (1.749)
  • : semisimple lie algebra (1.746)
  • : weight_(representation_theory) (1.724)
  • : homomorphism (1.724)
  • : module (mathematics) (1.723)
  • : abelian lie algebra (1.701)
  • : angular momenta (1.691)
  • : root reflection (1.689)
  • : weight vector (1.659)
  • : symmetric operators (1.657)
  • : compact subgroup (1.641)
  • : global minimum (1.618)
  • : modules (1.599)