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ROOT
Information
ATOMIC AND MOLECULAR PHYSICS
Atomic properties and interactions with photons
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
Foundations
Category information
Cluster information:
cluster id: [5411]
matching score: 0.459044613144
purity: 1.0
matching keywords: [u'geometry', u'algebraic', u'algebra']
Definitions:
L
{\displaystyle L}
:
galois extension (4.848)
a
{\displaystyle a}
:
number field (4.256)
k
{\displaystyle k}
:
field (mathematics) (3.517)
Q
{\displaystyle Q}
:
plus construction (3.454)
P
{\displaystyle P}
:
exact category (2.701)
F
{\displaystyle F}
: fields (2.665)
G
{\displaystyle G}
:
galois group (2.647)
A
{\displaystyle A}
: valuation (2.642)
D
{\displaystyle D}
: decomposition group (2.530)
m
{\displaystyle m}
:
cyclic group (2.481)
X
{\displaystyle X}
:
steinberg group (2.317)
K
{\displaystyle K}
:
galois extension (2.295)
M
{\displaystyle M}
: module (1.939)
Q
{\displaystyle \mathbf {Q} }
:
rational numbers (1.939)
M
p
{\displaystyle M_{\mathfrak {p}}}
: module (1.882)
e
{\displaystyle e}
: multiplicities (1.875)
K
0
{\displaystyle K_{0}}
: functor (1.728)
R
{\displaystyle R}
:
irreducible element (1.726)
j
{\displaystyle j}
: multiplicities (1.691)
w
{\displaystyle w}
:
finite extension (1.681)
O
{\displaystyle O}
:
prime ideal (1.664)
B
{\displaystyle B}
: ring homomorphism (1.663)
b
{\displaystyle b}
: properties (1.489)
Surfaces and higher-dimensional varieties
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:
n
{\displaystyle n}
: dimensional torus (4.230)
a
{\displaystyle a}
:
k3 surface (3.473)
r
{\displaystyle r}
: radius (3.376)
Z
{\displaystyle \mathbf {Z} }
:
lattice (group) (3.257)
z
{\displaystyle z}
:
hyperbolic paraboloid (2.764)
S
{\displaystyle S}
:
circle (2.737)
A
{\displaystyle A}
: torus (2.597)
T
{\displaystyle T}
: automorphism (2.278)
K
{\displaystyle K}
: canonical line bundle (1.875)
P
{\displaystyle P}
: 0-cell (1.834)
T
{\displaystyle \mathbf {T} }
: 2-torus (1.738)
B
{\displaystyle B}
: base space (1.701)
C
{\displaystyle C}
: 1-cells (1.685)
R
{\displaystyle \mathbf {R} }
: bottle (1.465)
Computational aspects in algebraic geometry
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
Fiber spaces and bundles
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:
X
{\displaystyle X}
:
topological space (6.620)
E
{\displaystyle E}
:
vector bundle (6.029)
M
{\displaystyle M}
:
tangent bundle (5.859)
C
{\displaystyle C}
: bundles (3.438)
n
{\displaystyle n}
: vector bundle (3.432)
x
{\displaystyle x}
: vector space (3.357)
V
{\displaystyle V}
:
vector bundle (2.573)
g
{\displaystyle g}
: ∈ gl (1.848)
p
{\displaystyle p}
: frame (1.847)
E
x
{\displaystyle E_{x}}
:
dual vector space (1.838)
k
{\displaystyle k}
: rank (1.823)
f
{\displaystyle f}
: continuous maps (1.800)
F
{\displaystyle F}
:
principal fiber bundle (1.715)
G
{\displaystyle G}
: structures (1.662)
U
{\displaystyle U}
: open neighborhood (1.653)
R
{\displaystyle \mathbf {R} }
:
homeomorphism (1.625)
Astronomy and astrophysics
Computational methods
Category information
Cluster information:
cluster id: [5300]
matching score: 0.339870022404
purity: 1.0
matching keywords: [u'stellar', u'planetary', u'astronomy']
Definitions:
a
{\displaystyle a}
:
black body (5.297)
T
{\displaystyle T}
: temperature (3.670)
r
{\displaystyle r}
: radius (2.749)
D
{\displaystyle D}
: distance (1.789)
Biology and other natural sciences
Physiological, cellular and medical topics
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:
v
{\displaystyle \mathbf {v} }
:
velocity (8.716)
E
{\displaystyle \mathbf {E} }
:
electric field (7.522)
B
{\displaystyle B}
:
magnetic flux (7.368)
B
{\displaystyle \mathbf {B} }
:
magnetic field (6.691)
q
{\displaystyle q}
:
electric charge (5.029)
x
{\displaystyle x}
: direction (4.239)
F
{\displaystyle \mathbf {F} }
:
force (3.736)
y
{\displaystyle y}
: direction (3.493)
c
{\displaystyle c}
:
speed of light (3.226)
v
{\displaystyle v}
: velocity (2.806)
z
{\displaystyle z}
: directions (2.762)
t
{\displaystyle t}
: time (2.595)
a
{\displaystyle a}
:
magnetic field (2.527)
r
{\displaystyle \mathbf {r} }
:
position vector (1.847)
x
{\displaystyle \mathbf {x} }
: position (1.845)
m
{\displaystyle m}
:
mass (1.793)
E
{\displaystyle {\mathcal {E}}}
:
electromotive force (1.778)
E
{\displaystyle E}
: electric field (1.750)
N
{\displaystyle N}
: identical turns (1.714)
τ
{\displaystyle \tau }
:
proper time (1.712)
A
{\displaystyle \mathbf {A} }
:
vector area (1.531)
d
{\displaystyle d}
: magnetic induction (1.459)
CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES
Electronic structure and electrical properties of surfaces, interfaces, thin films, and low-dimensional structures
Category information
Cluster information:
cluster id: [9388]
matching score: 0.212394161612
purity: 1.0
matching keywords: [u'electronic', u'electrical', u'systems']
Definitions:
V
G
{\displaystyle V_{G}}
: voltage (3.355)
R
G
{\displaystyle R_{G}}
: resistance (1.833)
R
2
{\displaystyle R_{2}}
: resistance (1.664)
R
x
{\displaystyle R_{x}}
: high precision (1.586)
Superconductivity
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:
S
{\displaystyle \mathbf {S} }
: uperconductor (4.900)
F
{\displaystyle \mathbf {F} }
: uperconductor (3.371)
a
{\displaystyle a}
:
josephson phase (2.657)
ϕ
{\displaystyle \phi }
:
josephson phase (2.644)
π
{\displaystyle \pi }
: josephson (2.597)
t
{\displaystyle t}
: time (1.974)
L
{\displaystyle L}
: inductance (1.939)
I
s
{\displaystyle I_{s}}
:
supercurrent (1.882)
ϕ
0
{\displaystyle \phi _{0}}
: junction (1.719)
Magnetic properties and materials
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
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:
τ
{\displaystyle \tau }
:
angular frequency (1.845)
ε
{\displaystyle \varepsilon }
: permittivity (1.544)
CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES
Mechanical and acoustical properties of condensed matter
Category information
Cluster information:
cluster id: [8170]
matching score: 0.252663411967
purity: 1.0
matching keywords: [u'ratio', u'systems', u'mechanical']
Definitions:
N
B
{\displaystyle N_{B}}
: teeth (8.677)
G
{\displaystyle G}
: input gear (7.375)
N
A
{\displaystyle N_{A}}
: teeth (5.890)
B
{\displaystyle B}
: output gear (5.869)
R
{\displaystyle R}
:
gear ratio (5.232)
r
A
{\displaystyle r_{A}}
: input gear (4.000)
v
{\displaystyle v}
: velocity (3.755)
G
A
{\displaystyle G_{A}}
: input gear (3.713)
G
B
{\displaystyle G_{B}}
: output gear (3.639)
T
{\displaystyle T}
: output torque (3.415)
A
{\displaystyle A}
: input gear (3.216)
T
A
{\displaystyle T_{A}}
: input torque (2.803)
F
{\displaystyle F}
: force (2.496)
r
B
{\displaystyle r_{B}}
: pitch radius (1.974)
b
{\displaystyle b}
: distance (1.842)
n
{\displaystyle n}
: rope sections (1.666)
Category theory; homological algebra
General theory of categories and functors
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:
C
{\displaystyle C}
:
subcategory (6.987)
F
{\displaystyle F}
:
functor (5.058)
a
{\displaystyle a}
:
functor (4.953)
G
{\displaystyle G}
:
contravariant functor (4.555)
X
{\displaystyle X}
: object (4.359)
D
{\displaystyle D}
: categories (4.132)
A
{\displaystyle A}
:
functor (3.776)
Y
{\displaystyle Y}
: object (3.210)
T
{\displaystyle T}
: isomorphisms (2.595)
I
{\displaystyle I}
:
small category (2.582)
K
{\displaystyle K}
:
field (mathematics) (1.858)
S
{\displaystyle S}
: subset (1.775)
r
{\displaystyle r}
: ring (1.766)
η
{\displaystyle \eta }
: natural transformation (1.756)
y
{\displaystyle y}
: generator (1.746)
f
{\displaystyle f}
:
morphism (1.629)
C
{\displaystyle \mathbf {C} }
: object (1.628)
R
{\displaystyle R}
: objects (1.499)
Categories with structure
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:
C
{\displaystyle {\mathcal {C}}}
:
monoidal category (6.125)
A
{\displaystyle A}
:
category of sets (4.992)
B
{\displaystyle B}
: objects (4.915)
γ
{\displaystyle \gamma }
: commutativity constraint (2.705)
N
{\displaystyle N}
: fold tensor product factors (1.865)
C
{\displaystyle C}
: tensor product (1.774)
Categories and geometry
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
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:
a
{\displaystyle a}
:
finitely generated module (21.818)
M
{\displaystyle M}
: module (19.662)
R
{\displaystyle R}
: module (17.887)
Z
{\displaystyle \mathbf {Z} }
:
group ring (10.747)
I
{\displaystyle I}
:
ideal (ring theory) (8.643)
K
{\displaystyle K}
:
field (mathematics) (7.863)
N
{\displaystyle N}
: module (7.513)
A
{\displaystyle A}
: module (7.511)
X
{\displaystyle X}
:
polynomial ring (7.283)
k
{\displaystyle k}
: field (6.502)
i
{\displaystyle i}
: modules (5.827)
P
{\displaystyle P}
: module (4.475)
E
{\displaystyle E}
: modules (4.265)
n
{\displaystyle n}
:
polynomial ring (3.905)
F
{\displaystyle F}
: module (3.639)
f
{\displaystyle f}
: surjective module homomorphism (3.627)
V
{\displaystyle V}
:
linear map (3.605)
S
{\displaystyle S}
:
multiplicatively closed subset (3.599)
W
{\displaystyle W}
: codimension (3.406)
N
i
{\displaystyle N_{i}}
: submodules (3.400)
m
{\displaystyle m}
:
matrix (mathematics) (3.154)
x
{\displaystyle x}
:
polynomial ring (3.100)
m
{\displaystyle {\mathfrak {m}}}
:
ideal (ring theory) (2.798)
g
{\displaystyle {\mathfrak {g}}}
: lie algebra (2.711)
Q
{\displaystyle \mathbf {Q} }
: ring (2.608)
B
{\displaystyle B}
: dense right ideal (2.571)
b
{\displaystyle b}
: nonzero (2.532)
p
{\displaystyle p}
:
prime ideal (2.485)
g
{\displaystyle g}
: module homomorphism (1.950)
p
i
{\displaystyle {\mathfrak {p}}_{i}}
: chain (1.882)
C
{\displaystyle C}
: category (1.848)
F
{\displaystyle \mathbf {F} }
: many copies (1.829)
h
{\displaystyle h}
: homomorphism (1.824)
U
{\displaystyle U}
: zariski (1.810)
R
{\displaystyle \mathbf {R} }
: open subsets (1.810)
R
p
{\displaystyle R_{\mathfrak {p}}}
: module (1.774)
Q
{\displaystyle Q}
: module (1.725)
O
{\displaystyle O}
: modules (1.600)
s
{\displaystyle s}
: subject (1.598)
x
i
{\displaystyle x_{i}}
: zero-divisor (1.591)
Classical thermodynamics, heat transfer
Thermodynamics and heat transfer
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:
T
{\displaystyle T}
:
temperature (18.171)
V
{\displaystyle V}
:
volume (thermodynamics) (9.787)
U
{\displaystyle U}
:
internal energy (8.118)
Q
{\displaystyle Q}
:
heat (7.410)
O
{\displaystyle O}
: state (7.151)
S
{\displaystyle S}
:
entropy (6.168)
P
{\displaystyle P}
:
pressure (5.985)
Y
{\displaystyle Y}
: state (5.840)
t
{\displaystyle t}
: time (4.645)
p
{\displaystyle p}
: pressure (4.500)
B
{\displaystyle B}
: state (3.565)
V
b
{\displaystyle V_{b}}
: volume (3.523)
V
a
{\displaystyle V_{a}}
: volume (3.438)
V
c
{\displaystyle V_{c}}
: volume (2.761)
W
{\displaystyle W}
:
work (thermodynamics) (2.735)
a
{\displaystyle a}
: energy (2.562)
A
{\displaystyle A}
: state (1.937)
X
{\displaystyle X}
: arbitrary state (1.907)
V
d
{\displaystyle V_{d}}
: volume (1.902)
t
1
{\displaystyle t_{1}}
: time (1.816)
M
{\displaystyle M}
:
molar mass (1.779)
q
{\displaystyle q}
: heat (1.723)
u
′
{\displaystyle u'}
: mass (1.688)
d
{\displaystyle d}
:
exact differential (1.621)
E
{\displaystyle E}
: total energy (1.574)
U
2
{\displaystyle U_{2}}
: new system (1.476)
Combinatorics
Graph theory
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:
n
{\displaystyle n}
: vertices (19.811)
a
{\displaystyle a}
:
graph (mathematics) (18.075)
G
{\displaystyle G}
:
glossary of graph theory (17.852)
k
{\displaystyle k}
:
complete graph (15.524)
K
{\displaystyle K}
:
complete bipartite graph (9.558)
v
{\displaystyle v}
:
vertex (graph theory) (8.425)
u
{\displaystyle u}
: vertices (7.720)
A
{\displaystyle A}
:
cycle graph (7.051)
B
{\displaystyle B}
: series (7.009)
H
{\displaystyle H}
:
glossary of graph theory (6.870)
m
{\displaystyle m}
: edges (5.725)
v
i
{\displaystyle v_{i}}
: vertex (5.393)
K
n
{\displaystyle K_{n}}
:
complete graph (3.913)
d
{\displaystyle d}
:
degree (graph theory) (3.842)
i
{\displaystyle i}
: color (3.635)
f
{\displaystyle f}
:
graph isomorphism (3.485)
e
{\displaystyle e}
: edge (2.776)
N
i
{\displaystyle N_{i}}
:
neighbourhood (graph theory) (2.731)
w
{\displaystyle w}
: edges (2.486)
W
{\displaystyle W}
: graph (2.441)
k
i
{\displaystyle k_{i}}
: vertices (2.221)
V
{\displaystyle V}
: vertices (1.950)
C
{\displaystyle C}
: vertex cover (1.939)
r
{\displaystyle r}
: complexity (1.939)
K
6
{\displaystyle K_{6}}
: graph (1.937)
O
{\displaystyle O}
: running time (1.866)
X
{\displaystyle X}
: finite set (1.848)
Q
{\displaystyle Q}
: sequence (1.847)
v
j
{\displaystyle v_{j}}
: vertex (1.816)
m
2
{\displaystyle m_{2}}
: first color (1.779)
e
i
j
{\displaystyle e_{ij}}
: vertex (1.712)
E
{\displaystyle E}
: edges (1.708)
W
n
{\displaystyle W_{n}}
: wheel graph (1.690)
F
{\displaystyle F}
: graph (1.687)
K
n
,
n
{\displaystyle K_{n,n}}
: chromatic number (1.659)
c
{\displaystyle c}
: vertex (1.657)
ϕ
{\displaystyle \phi }
: chromatic roots (1.524)
Computer science
Theory of data
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:
R
{\displaystyle R}
: rate (7.323)
n
{\displaystyle n}
: length (7.223)
C
{\displaystyle {\mathcal {C}}}
: code (6.108)
m
{\displaystyle m}
: message (5.399)
d
{\displaystyle d}
: minimum distance (5.171)
C
{\displaystyle C}
: code (4.310)
X
{\displaystyle X}
:
random variable (3.685)
y
{\displaystyle y}
: word (3.630)
δ
{\displaystyle \delta }
: relative distance (3.555)
q
{\displaystyle q}
: arbitrary probability distribution (3.494)
p
{\displaystyle p}
:
probability distribution (3.484)
k
{\displaystyle k}
: message length (3.372)
a
{\displaystyle a}
: information (3.253)
e
{\displaystyle e}
: radius (2.926)
H
{\displaystyle H}
: entropy (2.889)
T
{\displaystyle T}
:
temperature (2.776)
Σ
{\displaystyle \Sigma }
: alphabet (2.670)
x
{\displaystyle x}
:
conditional probability (2.650)
f
{\displaystyle f}
:
likelihood function (2.604)
c
{\displaystyle c}
: codeword (2.406)
Y
{\displaystyle Y}
: entropy (2.288)
g
{\displaystyle g}
: function (1.974)
c
1
{\displaystyle c_{1}}
: codewords (1.939)
B
{\displaystyle B}
:
estimator (1.891)
M
{\displaystyle M}
: codewords (1.882)
h
{\displaystyle h}
: function (1.858)
c
2
{\displaystyle c_{2}}
: codewords (1.754)
C
i
{\displaystyle C_{i}}
: code (1.659)
L
{\displaystyle L}
: code (1.563)
S
{\displaystyle S}
: nformation (1.524)
Discrete mathematics in relation to computer science
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:
a
{\displaystyle a}
:
context-sensitive grammar (7.034)
t
{\displaystyle t}
: time (4.738)
g
{\displaystyle g}
:
convex function (3.659)
f
{\displaystyle f}
: function (3.656)
n
{\displaystyle n}
: function (3.172)
x
{\displaystyle \mathbf {x} }
: tuple (1.891)
k
{\displaystyle k}
: tuple (1.817)
S
{\displaystyle S}
: successor function (1.791)
O
{\displaystyle O}
: nspace (1.754)
h
{\displaystyle h}
: induction step (1.738)
A
t
{\displaystyle A_{t}}
:
acceptance set (1.609)
v
{\displaystyle v}
: middle term (1.587)
A
{\displaystyle A}
: natural numbers (1.495)
Artificial intelligence
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:
R
{\displaystyle \mathbf {R} }
: linear map (2.767)
a
{\displaystyle a}
: function (2.561)
f
{\displaystyle f}
: function (2.550)
n
{\displaystyle n}
: commodities (2.492)
j
{\displaystyle j}
: functions (2.481)
p
i
{\displaystyle p_{i}}
: time (2.250)
U
{\displaystyle U}
: cardinal (1.845)
S
{\displaystyle S}
: state (1.812)
x
{\displaystyle x}
: differential d (1.761)
I
{\displaystyle I}
: functions (1.719)
y
{\displaystyle y}
:
derivative (1.707)
m
{\displaystyle m}
:
jacobian matrix (1.664)
M
{\displaystyle M}
:
state diagram (1.594)
t
{\displaystyle t}
: input variables (1.583)
p
{\displaystyle p}
: functions (1.430)
Computing methodologies and applications
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:
t
{\displaystyle t}
: scale (6.939)
s
{\displaystyle s}
: integration scale parameter (4.427)
A
{\displaystyle A}
: binary image (3.724)
v
{\displaystyle v}
: direction (3.608)
L
{\displaystyle L}
:
scale space (3.602)
E
{\displaystyle E}
: origin (3.496)
B
{\displaystyle B}
: structuring element (3.477)
b
{\displaystyle b}
: grayscale dilation (3.282)
d
{\displaystyle d}
: dimension (2.961)
f
{\displaystyle f}
: grayscale dilation (2.850)
x
{\displaystyle x}
: matrix (2.815)
X
i
{\displaystyle X_{i}}
: collection (2.685)
σ
I
{\displaystyle \sigma _{I}}
: scale (2.560)
R
{\displaystyle \mathbb {R} }
:
euclidean space (2.214)
R
{\displaystyle R}
:
euclidean space (1.974)
r
{\displaystyle r}
: radius (1.950)
N
{\displaystyle N}
: dimensions (1.939)
L
v
{\displaystyle L_{v}}
: direction (1.902)
ε
{\displaystyle \varepsilon }
: erosion (1.902)
k
{\displaystyle k}
: dimensional ridge (1.900)
μ
{\displaystyle \mu }
: matrix (1.847)
Σ
D
{\displaystyle \Sigma _{D}}
: covariance matrices (1.810)
I
y
{\displaystyle I_{y}}
:
partial derivatives (1.790)
z
{\displaystyle z}
: translation (1.790)
Σ
I
{\displaystyle \Sigma _{I}}
: covariance matrices (1.781)
δ
{\displaystyle \delta }
: dilation (1.781)
I
{\displaystyle I}
: image (1.690)
x
{\displaystyle \mathbf {x} }
: direction (1.641)
x
0
{\displaystyle \mathbf {x} _{0}}
: tangent lines (1.621)
a
{\displaystyle a}
: dilation (1.618)
γ
{\displaystyle \gamma }
: square (1.581)
λ
2
{\displaystyle \lambda _{2}}
: positive value (1.563)
I
x
{\displaystyle I_{x}}
:
partial derivatives (1.524)
n
{\displaystyle n}
: pixels (1.488)
Algorithms
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:
a
{\displaystyle a}
: sequence (4.369)
k
{\displaystyle k}
: multiplicity (1.974)
F
q
{\displaystyle \mathbb {F} _{q}}
: finite field (1.891)
s
{\displaystyle s}
: tuple (1.864)
b
{\displaystyle b}
: real numbers (1.810)
p
{\displaystyle p}
:
polynomial (1.800)
Computing methodologies
Machine learning
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:
C
{\displaystyle C}
:
concept class (7.638)
c
{\displaystyle c}
: concept (3.624)
X
{\displaystyle X}
:
concept class (3.183)
D
t
{\displaystyle D_{t}}
: distribution (2.707)
h
t
{\displaystyle h_{t}}
: classifier (1.939)
S
{\displaystyle S}
: partial approximation (1.902)
y
i
{\displaystyle y_{i}}
: labels (1.845)
D
t
+
1
{\displaystyle D_{t+1}}
:
probability distribution (1.781)
H
{\displaystyle {\mathcal {H}}}
: loss function (1.688)
Differential geometry
Classical differential geometry
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:
a
{\displaystyle a}
:
differentiable manifold (5.972)
f
{\displaystyle f}
: function (3.502)
G
{\displaystyle G}
:
structure group (2.961)
i
{\displaystyle i}
: lower-case index (2.810)
h
{\displaystyle h}
: scalar functions (2.571)
d
{\displaystyle d}
: − div (2.514)
E
{\displaystyle E}
: fiber (2.435)
S
{\displaystyle S}
:
gaussian curvature (2.339)
X
{\displaystyle X}
:
vector field (1.939)
x
{\displaystyle x}
: coordinate system (1.889)
k
{\displaystyle k}
:
rational number (1.865)
F
{\displaystyle F}
: fiber (1.823)
p
{\displaystyle p}
: particular point (1.816)
Δ
ξ
{\displaystyle \Delta _{\xi }}
: laplace (1.754)
K
{\displaystyle K}
:
gaussian curvature (1.688)
B
{\displaystyle B}
:
continuous (topology) (1.632)
H
{\displaystyle H}
: infinite area (1.628)
R
{\displaystyle \mathbf {R} }
: unit sphere (1.591)
n
{\displaystyle n}
: unit sphere (1.583)
Dynamical systems and ergodic theory
Applications
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:
V
{\displaystyle V}
: volume (6.980)
U
{\displaystyle U}
:
internal energy (2.749)
T
{\displaystyle T}
:
absolute temperature (2.678)
R
{\displaystyle R}
:
gas constant (2.595)
P
{\displaystyle P}
: pressure (2.570)
f
{\displaystyle f}
:
proper convex function (2.450)
i
{\displaystyle i}
: volume (1.865)
m
{\displaystyle m}
: volume (1.865)
X
{\displaystyle X}
:
vector space (1.858)
ν
{\displaystyle \nu }
:
specific volume (1.779)
n
{\displaystyle n}
: volume (1.756)
p
{\displaystyle p}
: pressure (1.752)
P
t
o
t
{\displaystyle P_{tot}}
:
partial pressure (1.726)
P
x
{\displaystyle P_{x}}
: gas mixture (1.717)
a
{\displaystyle a}
: chaotic behavior (1.632)
ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS
Acoustics
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:
a
{\displaystyle a}
:
wave (6.764)
v
{\displaystyle v}
: particle velocity (2.677)
I
{\displaystyle I}
:
sound intensity (2.593)
r
{\displaystyle r}
: distance (2.524)
E
{\displaystyle E}
: sound energy density (2.473)
f
{\displaystyle f}
: frequency (1.882)
m
{\displaystyle m}
:
metre (1.876)
W
{\displaystyle W}
:
watt (1.865)
r
1
{\displaystyle r_{1}}
: sound intensity (1.790)
A
{\displaystyle A}
: area (1.787)
I
2
{\displaystyle I_{2}}
: sound intensity (1.779)
I
{\displaystyle \mathbf {I} }
:
acoustic intensity (1.591)
w
{\displaystyle w}
: density (1.441)
Classical mechanics of discrete systems
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:
F
{\displaystyle \mathbf {F} }
:
force (21.736)
m
{\displaystyle m}
:
mass (21.105)
v
{\displaystyle \mathbf {v} }
:
velocity (21.053)
t
{\displaystyle t}
:
time (17.001)
p
{\displaystyle \mathbf {p} }
:
momentum (14.082)
L
{\displaystyle \mathbf {L} }
:
angular momentum (13.398)
i
{\displaystyle i}
: particle (12.579)
a
{\displaystyle \mathbf {a} }
:
acceleration (12.473)
r
{\displaystyle \mathbf {r} }
:
position (vector) (10.802)
I
{\displaystyle I}
:
moment of inertia (10.035)
E
{\displaystyle E}
:
kinetic energy (7.861)
V
{\displaystyle \mathbf {V} }
: velocity (7.840)
v
{\displaystyle v}
:
effective exhaust velocity (7.699)
a
{\displaystyle a}
:
rigid body (7.097)
r
{\displaystyle r}
: distance (6.877)
j
{\displaystyle j}
: particle (4.549)
x
{\displaystyle x}
:
direction vector (4.526)
M
{\displaystyle M}
: mass (4.464)
u
{\displaystyle u}
:
velocity (4.380)
V
{\displaystyle V}
:
volume integral (3.731)
u
{\displaystyle \mathbf {u} }
: velocity (3.661)
N
{\displaystyle N}
: particles (3.660)
I
{\displaystyle \mathbf {I} }
:
moment of inertia tensor (3.635)
S
{\displaystyle \mathbf {S} }
: angular momentum (3.633)
e
{\displaystyle \mathbf {e} }
:
unit vector (3.626)
A
{\displaystyle \mathbf {A} }
: acceleration (3.595)
C
{\displaystyle \mathbf {C} }
:
center of mass (3.583)
d
{\displaystyle d}
: magnitude (3.565)
s
{\displaystyle s}
:
displacement (vector) (3.565)
c
{\displaystyle c}
:
speed of light (3.394)
T
{\displaystyle T}
: rotation (3.369)
U
{\displaystyle U}
: kinetic energy (3.316)
ω
{\displaystyle \omega }
:
angular velocity (2.869)
L
{\displaystyle L}
: length (2.771)
P
{\displaystyle P}
: pivot point (2.728)
g
{\displaystyle \mathbf {g} }
:
gravitational acceleration (2.725)
n
{\displaystyle \mathbf {n} }
:
unit vector (2.682)
Q
{\displaystyle Q}
: rotation matrix (2.670)
q
{\displaystyle \mathbf {q} }
:
generalized coordinates (2.627)
k
{\displaystyle k}
: spring (2.602)
R
{\displaystyle \mathbf {R} }
: reference point (2.597)
G
{\displaystyle G}
:
gravitational constant (2.587)
F
{\displaystyle F}
:
force (2.575)
g
{\displaystyle g}
: local acceleration (2.543)
q
{\displaystyle q}
:
electric charge (2.467)
K
{\displaystyle K}
: body (2.292)
C
{\displaystyle C}
: curved path (1.950)
ϕ
{\displaystyle \phi }
: angle (1.950)
t
{\displaystyle \mathbf {t} }
: unit vector (1.907)
f
{\displaystyle f}
:
frequency (1.882)
m
i
{\displaystyle m_{i}}
: masses (1.882)
W
{\displaystyle W}
: total work (1.881)
S
{\displaystyle S}
: frame (1.872)
B
{\displaystyle B}
: skew-symmetric matrix (1.865)
I
C
{\displaystyle I_{C}}
: mass (1.865)
e
^
r
{\displaystyle \mathbf {\hat {e}} _{r}}
: rotation (1.852)
e
^
θ
{\displaystyle \mathbf {\hat {e}} _{\theta }}
: unit vector (1.845)
W
{\displaystyle \mathbf {W} }
: weight (1.833)
u
^
R
{\displaystyle {\hat {u}}_{R}}
: unit vector (1.789)
J
{\displaystyle \mathbf {J} }
: orbital (1.752)
y
{\displaystyle y}
:
direction vector (1.749)
A
{\displaystyle A}
: moment (1.744)
D
{\displaystyle \mathbf {D} }
:
electric field (1.724)
r
1
{\displaystyle \mathbf {r} _{1}}
: torque (1.724)
m
B
{\displaystyle m_{B}}
: body (1.718)
x
{\displaystyle \mathbf {x} }
: initial positions (1.718)
P
{\displaystyle \mathbf {P} }
:
canonical momentum (1.714)
M
{\displaystyle \mathbf {M} }
: torque (1.701)
n
{\displaystyle n}
: similar objects (1.664)
r
z
{\displaystyle r_{z}}
:
momentum operator (1.591)
p
{\displaystyle p}
:
potential energy (1.576)
R
{\displaystyle R}
:
polar coordinate system (1.540)
u
^
θ
{\displaystyle {\hat {u}}_{\theta }}
: direction (1.439)
Continuum mechanics of solids
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:
Ω
{\displaystyle \Omega }
: surface (5.460)
t
{\displaystyle t}
: time (4.609)
X
{\displaystyle \mathbf {X} }
: position vector (4.360)
S
{\displaystyle {\boldsymbol {S}}}
: vector field (2.791)
ρ
{\displaystyle \rho }
:
material time derivative (2.755)
e
˙
{\displaystyle {\dot {e}}}
: material time derivative (2.661)
x
{\displaystyle \mathbf {x} }
: position (2.652)
e
{\displaystyle e}
: material time derivative (2.638)
s
{\displaystyle s}
:
flux (2.603)
v
{\displaystyle \mathbf {v} }
:
velocity (2.583)
q
{\displaystyle \mathbf {q} }
:
heat (2.548)
χ
{\displaystyle \chi }
: mapping function (1.939)
n
{\displaystyle \mathbf {n} }
: normal vector (1.939)
F
C
{\displaystyle \mathbf {F} _{C}}
: surface forces (1.937)
S
{\displaystyle S}
: internal surface area (1.891)
λ
{\displaystyle \lambda }
:
shear viscosity (1.845)
F
B
{\displaystyle \mathbf {F} _{B}}
: body forces (1.816)
v
˙
{\displaystyle {\dot {\mathbf {v} }}}
: particle velocity (1.813)
u
{\displaystyle \mathbf {u} }
: particle (1.790)
ε
e
{\displaystyle \varepsilon _{e}}
: elastic strain (1.779)
T
{\displaystyle T}
: unit mass (1.766)
ρ
˙
{\displaystyle {\dot {\rho }}}
:
material time derivative (1.766)
u
n
{\displaystyle u_{n}}
: velocity (1.745)
η
{\displaystyle \eta }
: region (1.689)
a
{\displaystyle a}
: continuum (1.662)
e
i
{\displaystyle \mathbf {e} _{i}}
: components (1.640)
X
{\displaystyle X}
: position vector (1.591)
Field theory and polynomials
Differential and difference algebra
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:
x
{\displaystyle x}
:
polynomial (17.140)
R
{\displaystyle R}
:
module (mathematics) (16.749)
a
{\displaystyle a}
:
field (mathematics) (15.345)
F
{\displaystyle F}
:
field (mathematics) (13.594)
K
{\displaystyle K}
:
local field (12.146)
M
{\displaystyle M}
: module (11.938)
A
{\displaystyle A}
:
frobenius algebra (11.268)
L
{\displaystyle L}
:
extension field (10.984)
n
{\displaystyle n}
: degree (10.686)
V
{\displaystyle V}
:
vector space (9.943)
p
{\displaystyle p}
:
finite field (8.287)
N
{\displaystyle N}
: length (6.994)
D
{\displaystyle D}
:
division algebra (6.752)
Z
{\displaystyle \mathbf {Z} }
: module (6.405)
C
{\displaystyle \mathbf {C} }
:
complex number (6.386)
T
{\displaystyle T}
: field (6.032)
v
{\displaystyle v}
: valuation (5.397)
k
{\displaystyle k}
: field (5.381)
Q
{\displaystyle \mathbf {Q} }
:
local field (5.259)
E
{\displaystyle E}
: field (5.180)
H
{\displaystyle \mathbf {H} }
:
quaternion (4.593)
R
{\displaystyle \mathbf {R} }
:
real number (4.559)
Q
{\displaystyle Q}
: linear operator (4.474)
K
{\displaystyle \mathbf {K} }
: field (3.587)
I
{\displaystyle I}
:
submodule (3.572)
G
{\displaystyle G}
:
field (mathematics) (3.566)
t
{\displaystyle t}
: form (3.528)
X
{\displaystyle X}
:
polynomial (3.462)
S
{\displaystyle S}
:
symmetric matrix (3.432)
u
{\displaystyle u}
:
generating set of a group (3.420)
W
{\displaystyle W}
: basis (3.326)
t
{\displaystyle \mathbf {t} }
: matrix (2.799)
j
{\displaystyle j}
: column (2.450)
f
{\displaystyle f}
:
polynomial (2.435)
q
{\displaystyle q}
: polynomial sequence (2.398)
P
{\displaystyle P}
:
quadratic polynomial (1.904)
s
{\displaystyle s}
: polynomials (1.900)
a
{\displaystyle \mathbf {a} }
: sequence (1.891)
B
{\displaystyle B}
:
symmetric bilinear form (1.882)
m
{\displaystyle m}
:
maximal ideal (1.790)
i
{\displaystyle i}
:
quotient ring (1.774)
H
{\displaystyle H}
: character module (1.757)
g
{\displaystyle g}
:
polynomial (1.757)
Z
{\displaystyle \mathbb {Z} }
: subgroup (1.738)
r
{\displaystyle r}
: roots (1.714)
Γ
{\displaystyle \Gamma }
: segment (1.691)
Y
{\displaystyle Y}
: univariate polynomial (1.681)
a
i
{\displaystyle a_{i}}
: weight (1.659)
Z
p
{\displaystyle \mathbb {Z} _{p}}
: valuation ring (1.657)
f
{\displaystyle \mathbf {f} }
: basis (1.657)
a
n
d
{\displaystyle and}
:
difference operator (1.640)
F
{\displaystyle \mathbf {F} }
:
hyperreal number (1.556)
y
{\displaystyle \mathbf {y} }
: coordinate tuples (1.530)
Fluid mechanics
Foundations, constitutive equations, rheology
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:
t
{\displaystyle t}
:
time (4.699)
t
1
{\displaystyle t_{1}}
: time (3.889)
E
{\displaystyle E}
:
young's modulus (3.349)
σ
0
{\displaystyle \sigma _{0}}
: stress (1.974)
η
{\displaystyle \eta }
:
viscosity (1.882)
λ
{\displaystyle \lambda }
: time (1.865)
γ
˙
{\displaystyle {\dot {\gamma }}}
:
shear rate (1.845)
σ
T
o
t
a
l
{\displaystyle \sigma _{\mathrm {Total} }}
: total stress (1.845)
ε
{\displaystyle \varepsilon }
: strain rate (1.786)
G
″
{\displaystyle G''}
: storage modulus (1.724)
a
{\displaystyle a}
:
stress (physics) (1.651)
Turbulence
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:
u
{\displaystyle \mathbf {u} }
: velocity (1.974)
ε
{\displaystyle \varepsilon }
: energy dissipation (1.902)
V
{\displaystyle \mathbf {V} }
: diffusive body-vortex interaction fluid velocity (1.866)
C
n
{\displaystyle C_{n}}
: constants (1.847)
d
{\displaystyle d}
: diffusion velocity (1.845)
r
{\displaystyle r}
: characteristic length (1.784)
ν
{\displaystyle \nu }
:
kinematic viscosity (1.779)
Π
{\displaystyle \Pi }
: fluxes (1.610)
r
{\displaystyle \mathbf {r} }
: diffusive body-vortex interaction fluid velocity (1.591)
L
{\displaystyle L}
: large scales (1.556)
k
{\displaystyle \mathbf {k} }
: fourier (1.556)
Compressible fluids and gas dynamics, general
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
Category information
Cluster information:
cluster id: [3743, 6074]
matching score: 0.590251215805
purity: 1.0
matching keywords: [u'mechanics', u'fluid']
Definitions:
η
{\displaystyle \eta }
: dynamic viscosity (2.483)
L
{\displaystyle L}
:
surface tension (1.816)
ν
{\displaystyle \nu }
:
viscosity (1.805)
ρ
{\displaystyle \rho }
:
density (1.805)
r
{\displaystyle r}
:
stokes radius (1.641)
P
r
{\displaystyle \mathrm {Pr} }
: momentum diffusivity (1.600)
Fourier analysis
Fourier analysis in several variables
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:
f
{\displaystyle f}
: function (7.003)
a
{\displaystyle a}
:
periodic function (6.900)
Γ
{\displaystyle \Gamma }
:
reciprocal lattice (4.226)
Λ
{\displaystyle \Lambda }
:
reciprocal lattice (3.473)
g
{\displaystyle g}
: integrable function (2.707)
T
{\displaystyle T}
: operator (2.660)
L
{\displaystyle L}
: norm (2.610)
ν
x
{\displaystyle \nu _{x}}
:
borel measure (1.939)
x
{\displaystyle x}
: weight vector (1.939)
A
{\displaystyle A}
: hexagonal sampling lattice (1.891)
C
{\displaystyle C}
: operator (1.882)
ℓ
{\displaystyle \ell }
: norm (1.865)
R
{\displaystyle R}
: flip operator (1.847)
N
{\displaystyle N}
: samples (1.846)
t
{\displaystyle t}
: time (1.811)
f
^
s
{\displaystyle {\hat {f}}_{s}}
: spectrum (1.704)
L
o
m
b
S
c
a
r
g
l
e
m
e
t
h
o
d
{\displaystyle \mathbf {LombScarglemethod} }
: lomb (1.657)
v
i
{\displaystyle v_{i}}
: matrix (1.657)
ω
0
{\displaystyle \omega _{0}}
: dominant component (1.645)
u
{\displaystyle u}
: figure (1.625)
w
{\displaystyle w}
: window (1.562)
Functional analysis
Nonlinear functional analysis
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:
a
{\displaystyle a}
:
bounded linear operator (6.085)
H
{\displaystyle H}
: hilbert (4.995)
H
{\displaystyle \mathbf {H} }
: space (2.869)
E
{\displaystyle E}
: banach (2.688)
T
{\displaystyle \mathbf {T} }
: operator (2.641)
C
{\displaystyle C}
: class (2.604)
i
{\displaystyle i}
:
subset (2.565)
U
{\displaystyle U}
:
bounded linear operator (2.450)
H
i
{\displaystyle H_{i}}
: space (1.950)
K
{\displaystyle K}
: space (1.937)
D
{\displaystyle D}
:
diagonal matrix (1.762)
V
{\displaystyle V}
:
complex number (1.732)
r
{\displaystyle r}
: class (1.719)
y
{\displaystyle y}
:
vector space (1.700)
e
{\displaystyle e}
: span (1.641)
Functions of a complex variable
Miscellaneous topics of analysis in the complex domain
Category information
Cluster information:
cluster id: [2838, 9700]
matching score: 0.395941949552
purity: 1.0
matching keywords: [u'analytic', u'functions', u'complex', u'analysis']
Definitions:
GEOPHYSICS, ASTRONOMY, AND ASTROPHYSICS
Solid Earth physics
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:
a
{\displaystyle a}
: book (2.563)
w
{\displaystyle w}
: attenuation (1.659)
Hydrospheric and atmospheric geophysics
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:
m
i
{\displaystyle m_{i}}
:
mass (9.619)
V
{\displaystyle V}
:
volume (6.751)
n
i
{\displaystyle n_{i}}
: constituent (6.485)
w
i
{\displaystyle w_{i}}
:
mass fraction (chemistry) (5.721)
ρ
i
{\displaystyle \rho _{i}}
:
mass concentration (chemistry) (5.470)
M
i
{\displaystyle M_{i}}
:
molar mass (5.278)
M
{\displaystyle M}
:
molar mass (4.941)
x
i
{\displaystyle x_{i}}
:
mole fraction (4.898)
c
i
{\displaystyle c_{i}}
:
molar concentration (4.784)
ρ
{\displaystyle \rho }
:
density (3.584)
i
{\displaystyle i}
:
molar mass (3.448)
a
{\displaystyle a}
: host (2.707)
ζ
i
{\displaystyle \zeta _{i}}
: mass ratio (2.699)
A
{\displaystyle A}
: nucleus (2.649)
A
{\displaystyle \mathbf {A} }
: adt matrix (2.619)
V
i
{\displaystyle V_{i}}
: volume (2.585)
B
{\displaystyle B}
: binding (2.561)
N
i
{\displaystyle N_{i}}
: constituent (1.950)
m
{\displaystyle m}
: elec (1.942)
Γ
{\displaystyle \Gamma }
: contour (1.939)
r
i
{\displaystyle r_{i}}
: mole ratio (1.937)
T
n
{\displaystyle T_{\textrm {n}}}
: matrix elements (1.900)
α
{\displaystyle \alpha }
: reference temperature (1.900)
χ
k
{\displaystyle \chi _{k}}
: electronic wave functions (1.891)
R
{\displaystyle \mathbf {R} }
: positions (1.812)
γ
{\displaystyle \gamma }
: angle (1.811)
b
i
{\displaystyle b_{i}}
:
molality (1.793)
c
{\displaystyle c}
: equation (1.744)
t
{\displaystyle t}
: equation (1.712)
m
t
o
t
{\displaystyle m_{\mathrm {tot} }}
: mass ratio (1.665)
e
{\displaystyle e}
: nuclear positions (1.653)
r
{\displaystyle \mathbf {r} }
: integration (1.497)
Physics of the ionosphere and magnetosphere
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:
B
{\displaystyle B}
: magnetic field (3.422)
m
{\displaystyle m}
:
mass (3.315)
u
{\displaystyle \mathbf {u} }
: average velocity (2.725)
q
{\displaystyle q}
: magnetic field (2.657)
r
→
{\displaystyle {\vec {r}}}
:
momentum (2.555)
r
g
{\displaystyle r_{g}}
: gyroradius (2.434)
α
{\displaystyle \alpha }
: species (1.974)
n
{\displaystyle n}
: particle density (1.902)
t
{\displaystyle t}
: time (1.891)
R
{\displaystyle R}
:
gyroradius (1.845)
ρ
{\displaystyle \rho }
:
electric potential (1.797)
v
{\displaystyle v}
: velocity component (1.723)
m
α
{\displaystyle m_{\alpha }}
: mass (1.677)
v
→
{\displaystyle {\vec {v}}}
: velocity vector (1.621)
Stars
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:
a
{\displaystyle a}
:
star (43.305)
R
{\displaystyle R}
: radius (31.929)
T
e
f
f
{\displaystyle T_{\mathrm {eff} }}
: radius (3.705)
σ
{\displaystyle \sigma }
: effective surface temperature (3.705)
L
{\displaystyle L}
: luminosity (3.484)
T
{\displaystyle T}
: tauri (1.939)
V
t
{\displaystyle V_{t}}
: radial velocity (1.845)
Game theory, economics, social and behavioral sciences
Mathematical economics
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:
c
0
{\displaystyle c_{0}}
: total consumption (5.700)
u
{\displaystyle u}
: utility (4.233)
a
{\displaystyle a}
: consumption function (3.336)
i
{\displaystyle i}
: change (2.977)
w
{\displaystyle w}
:
income (2.868)
C
{\displaystyle C}
: total consumption (2.850)
c
1
{\displaystyle c_{1}}
:
marginal propensity to consume (2.685)
p
{\displaystyle p}
:
price level (1.926)
u
¯
{\displaystyle {\bar {u}}}
: utility level (1.847)
Y
{\displaystyle Y}
: payments (1.790)
Y
d
{\displaystyle Y_{d}}
: disposable income (1.779)
Other social and behavioral sciences (mathematical treatment)
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:
i
{\displaystyle i}
: player (9.955)
D
{\displaystyle D}
: player (5.852)
j
{\displaystyle j}
: machine (4.463)
N
{\displaystyle N}
: players (3.651)
k
{\displaystyle k}
: machine (2.768)
f
Γ
,
R
{\displaystyle f_{\Gamma ,R}}
: flow (2.672)
A
{\displaystyle A}
: strategy (2.501)
a
{\displaystyle a}
:
solution concept (1.887)
f
{\displaystyle f}
: flow (1.848)
T
i
{\displaystyle T_{i}}
: type (1.810)
A
i
{\displaystyle A_{i}}
: action (1.688)
G
{\displaystyle G}
: flows (1.677)
S
i
{\displaystyle S_{i}}
: player (1.677)
U
{\displaystyle U}
: player (1.588)
s
i
{\displaystyle s_{i}}
: paths (1.471)
General topology
Generalities
Category information
Cluster information:
cluster id: [3399]
matching score: 0.474817002951
purity: 1.0
matching keywords: [u'general', u'structures', u'topology']
Definitions:
a
{\displaystyle a}
:
topological space (7.000)
X
{\displaystyle X}
:
topological space (5.935)
R
{\displaystyle \mathbf {R} }
: subspace (4.260)
B
{\displaystyle B}
:
basis (topology) (4.164)
S
{\displaystyle S}
:
subset (3.527)
f
{\displaystyle f}
: function (2.695)
A
{\displaystyle A}
: subspace (2.674)
T
{\displaystyle T}
: topology (2.642)
i
{\displaystyle i}
:
continuous (topology) (2.562)
Z
{\displaystyle Z}
: topological space (1.882)
Y
{\displaystyle Y}
: subspace topology (1.744)
b
{\displaystyle b}
:
rational number (1.702)
Geometry
Analytic and descriptive geometry
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:
a
{\displaystyle a}
:
plane curve (8.757)
T
{\displaystyle T}
:
tangent (7.168)
C
{\displaystyle C}
:
plane curve (6.130)
A
{\displaystyle A}
: tangential trapezoid (5.174)
K
{\displaystyle K}
: area (4.535)
b
{\displaystyle b}
: bases (3.051)
x
{\displaystyle x}
: =-lrb- (2.855)
ψ
{\displaystyle \psi }
: vertex angle (2.573)
f
{\displaystyle f}
:
polar coordinate system (2.550)
P
{\displaystyle P}
: pedal point (2.531)
c
{\displaystyle c}
: consecutive sides (2.527)
θ
{\displaystyle \theta }
: polar angle (1.878)
O
{\displaystyle O}
: distance (1.824)
q
{\displaystyle q}
: lengths (1.790)
n
{\displaystyle n}
: specific values (1.774)
R
{\displaystyle R}
: curve (1.714)
G
{\displaystyle G}
: side (1.657)
y
{\displaystyle y}
: =-lrb- (1.600)
h
{\displaystyle h}
: height (1.598)
p
{\displaystyle p}
: perpendicular distance (1.585)
r
{\displaystyle r}
:
polar coordinate system (1.576)
X
{\displaystyle X}
: tangent (1.562)
Group theory and generalizations
Connections with homological algebra and category theory
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
Power and energy
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:
Z
{\displaystyle Z}
:
electrical impedance (8.909)
Y
{\displaystyle Y}
: shunt (7.073)
r
{\displaystyle \mathbf {r} }
: position (6.383)
N
{\displaystyle N}
: charges (5.442)
q
{\displaystyle q}
:
test charge (5.062)
L
{\displaystyle L}
: filter half-section (4.865)
U
{\displaystyle U}
:
electric potential energy (4.738)
Q
i
{\displaystyle Q_{i}}
:
electric charge (4.681)
Q
{\displaystyle Q}
:
test charge (4.450)
E
{\displaystyle \mathbf {E} }
:
electric field (4.171)
F
{\displaystyle \mathbf {F} }
: electrostatic force (3.769)
i
{\displaystyle i}
:
electric charge (3.461)
n
{\displaystyle n}
: half-sections (2.937)
E
{\displaystyle E}
: electric field (2.865)
p
{\displaystyle p}
: complex exponentials (2.787)
s
{\displaystyle \mathbf {s} }
:
displacement vector (2.532)
C
{\displaystyle C}
:
farad (2.523)
U
E
{\displaystyle U_{E}}
: potential energy (2.433)
N
i
{\displaystyle N_{i}}
: customers (2.286)
R
{\displaystyle R}
: nominal impedance (1.939)
k
{\displaystyle k}
: filters (1.939)
u
{\displaystyle u}
: energy density (1.937)
U
i
{\displaystyle U_{i}}
: customers (1.900)
q
N
{\displaystyle q_{N}}
: positions (1.865)
Φ
{\displaystyle \Phi }
:
electric potential (1.847)
e
{\displaystyle e}
: charge (1.845)
γ
{\displaystyle \gamma }
:
propagation constant (1.821)
Z
0
{\displaystyle Z_{0}}
:
characteristic impedance (1.783)
a
{\displaystyle a}
:
potential energy (1.776)
r
{\displaystyle r}
: distance (1.766)
m
{\displaystyle m}
: different values (1.758)
γ
′
{\displaystyle \gamma '}
: propagation constant (1.724)
G
{\displaystyle G}
:
electrical conductance (1.722)
D
{\displaystyle \mathbf {D} }
:
electric displacement field (1.718)
r
→
i
{\displaystyle {\vec {r}}_{i}}
: source point (1.681)
r
→
{\displaystyle {\vec {r}}}
: field point (1.677)
V
{\displaystyle V}
:
volume element (1.655)
d
{\displaystyle d}
:
displacement vector (1.552)
INTERDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY
Physical chemistry and chemical physics
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
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:
d
{\displaystyle d}
: diameter (4.901)
D
{\displaystyle D}
: diameter (3.405)
P
{\displaystyle P}
: power level (3.318)
f
{\displaystyle f}
:
frequency (2.746)
c
{\displaystyle c}
:
speed of light (2.553)
C
{\displaystyle C}
: length (1.937)
μ
r
{\displaystyle \mu _{r}}
: relative permeability (1.793)
Z
0
{\displaystyle Z_{0}}
:
characteristic impedance (1.714)
S
{\displaystyle S}
: insulator (1.689)
ϵ
{\displaystyle \epsilon }
:
dielectric constant (1.677)
Other areas of applied and interdisciplinary physics
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:
y
{\displaystyle y}
: direction (3.623)
j
{\displaystyle \mathbf {j} }
: equation (2.665)
q
{\displaystyle \mathbf {q} }
: wave vector (2.640)
n
{\displaystyle n}
: atomic number density (2.625)
k
{\displaystyle k}
: dependence (2.619)
c
v
,
p
{\displaystyle c_{v,p}}
: specific heat capacity (2.600)
m
{\displaystyle m}
: atomic mass (2.521)
i
{\displaystyle i}
: atom (2.492)
j
{\displaystyle j}
: atom (2.452)
p
{\displaystyle p}
: type materials (2.417)
δ
{\displaystyle \delta }
: limit (1.939)
z
{\displaystyle z}
: direction (1.937)
Z
f
{\displaystyle Z_{f}}
:
partition function (statistical mechanics) (1.902)
n
e
,
c
{\displaystyle n_{e,c}}
: carrier density (1.902)
t
{\displaystyle t}
: time (1.902)
q
{\displaystyle q}
: long wavelength limit (1.865)
r
{\displaystyle r}
: distance (1.865)
v
{\displaystyle v}
: drift velocity (1.858)
E
{\displaystyle E}
: electric field (1.848)
D
p
{\displaystyle D_{p}}
:
density of states (1.834)
f
p
h
{\displaystyle f_{ph}}
: equilibrium distribution (1.811)
S
{\displaystyle S}
: spin (1.810)
τ
{\displaystyle \tau }
: group velocity (1.810)
c
{\displaystyle c}
: concentration (1.810)
e
{\displaystyle e}
:
elementary charge (1.790)
L
{\displaystyle L}
: length (1.749)
I
p
h
,
{\displaystyle I_{ph,}}
: radiation intensity (1.744)
T
{\displaystyle T}
: temperature (1.742)
d
p
{\displaystyle d_{p}}
: slope (1.714)
p
{\displaystyle \mathbf {p} }
: momentum (1.696)
A
{\displaystyle A}
: electrolyte (1.688)
s
{\displaystyle \mathbf {s} }
: unit vector (1.677)
v
d
{\displaystyle v_{d}}
:
drift velocity (1.664)
n
i
{\displaystyle n_{i}}
: electron hole concentration (1.657)
p
0
{\displaystyle p_{0}}
: electron hole concentration (1.657)
v
1
{\displaystyle v_{1}}
: film2 (1.657)
u
{\displaystyle \mathbf {u} }
: velocity (1.653)
d
{\displaystyle \mathbf {d} }
: displacement vector (1.592)
v
z
{\displaystyle v_{z}}
: phonon velocity (1.574)
v
2
{\displaystyle v_{2}}
: film2 (1.524)
a
{\displaystyle a}
:
electron (1.490)
κ
{\displaystyle \kappa }
: inverse screening length (1.489)
Information and communication, circuits
Communication, information
Category information
Cluster information:
cluster id: [9339]
matching score: 0.291389710465
purity: 1.0
matching keywords: [u'information', u'theorems', u'coding']
Definitions:
n
{\displaystyle n}
: length (10.082)
d
{\displaystyle d}
:
hamming weight (9.143)
C
{\displaystyle C}
:
block code (4.437)
x
{\displaystyle x}
:
hamming distance (2.771)
y
{\displaystyle y}
: codeword (2.688)
q
{\displaystyle q}
: ary code (2.662)
t
{\displaystyle t}
: errors (1.939)
e
{\displaystyle e}
: relation (1.719)
p
{\displaystyle p}
: error (1.598)
Circuits, networks
Category information
Cluster information:
cluster id: [8217]
matching score: 0.350636813123
purity: 1.0
matching keywords: [u'circuits', u'graph', u'circuit']
Definitions:
Y
{\displaystyle Y}
: circuit (3.294)
s
{\displaystyle s}
: closed circuit (1.939)
R
Δ
{\displaystyle R_{\Delta }}
: impedance (1.847)
n
{\displaystyle n}
: total number (1.754)
R
″
{\displaystyle R''}
: δ circuit (1.524)
Information systems
Data management systems
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:
S
{\displaystyle S}
: schedule (1.974)
A
{\displaystyle A}
: original value (1.865)
K-theory
Whitehead groups and K_1
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
Topological manifolds
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:
n
{\displaystyle n}
: sphere (3.729)
N
{\displaystyle N}
: manifold (2.675)
M
{\displaystyle M}
: embedding (2.458)
S
{\displaystyle S}
: circles (1.926)
X
{\displaystyle X}
: boundary (1.811)
I
{\displaystyle I}
: boundary (1.533)
R
{\displaystyle \mathbf {R} }
: 3-sphere (1.497)
Mathematical logic and foundations
General logic
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:
Q
{\displaystyle Q}
: statement (5.991)
P
{\displaystyle P}
: statement (5.452)
R
{\displaystyle R}
: statement (3.564)
B
{\displaystyle B}
: truth (1.657)
A
{\displaystyle A}
: truth (1.625)
Set theory
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
Special subfields of solid mechanics
Category information
Cluster information:
cluster id: [2527, 7115]
matching score: 0.410678810296
purity: 1.0
matching keywords: [u'mechanics', u'solid']
Definitions:
m
{\displaystyle m}
: mass (5.535)
e
{\displaystyle e}
: eccentricity (3.380)
E
{\displaystyle E}
:
energy (2.869)
r
{\displaystyle r}
: radius (2.768)
σ
v
{\displaystyle \sigma _{v}}
: tensile stress (2.499)
h
{\displaystyle h}
: order (1.812)
J
{\displaystyle J}
: function (1.775)
u
{\displaystyle u}
: equation (1.738)
M
a
n
d
e
l
V
o
i
g
t
n
o
t
a
t
i
o
n
{\displaystyle \mathbf {MandelVoigtnotation} }
: notation (1.724)
σ
3
{\displaystyle \sigma _{3}}
: plane (1.707)
σ
y
{\displaystyle \sigma _{y}}
:
yield strength (1.671)
t
{\displaystyle t}
: change (1.524)
Mechanics of particles and systems
Kinematics
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:
f
{\displaystyle f}
: freedom (5.343)
j
{\displaystyle j}
: joints (3.849)
n
{\displaystyle n}
: links (3.808)
c
{\displaystyle c}
: constraints (2.961)
f
i
{\displaystyle f_{i}}
: freedom (2.961)
M
{\displaystyle M}
: degree-of-freedom (2.941)
N
{\displaystyle N}
: fixed link (2.531)
i
{\displaystyle i}
: freedom (2.488)
Dynamics of a system of particles, including celestial mechanics
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:
X
{\displaystyle X}
:
world manifold (5.701)
G
{\displaystyle G}
:
gravitational constant (4.191)
a
{\displaystyle a}
: time (3.635)
Γ
{\displaystyle \Gamma }
:
linear connection (2.811)
t
{\displaystyle \mathbf {t} }
: time (2.649)
P
{\displaystyle P}
:
structure group (2.621)
n
{\displaystyle n}
:
mean motion (2.516)
F
{\displaystyle {\mathfrak {F}}}
: spatial distributions (1.939)
H
{\displaystyle H}
:
structure group (1.915)
M
{\displaystyle M}
:
gravitational constant (1.900)
T
{\displaystyle T}
: hours (1.812)
m
{\displaystyle m}
:
mass (1.724)
Θ
{\displaystyle \Theta }
: distortion (1.654)
d
{\displaystyle d}
: time (1.556)
NUCLEAR PHYSICS
Nuclear structure
Category information
Cluster information:
cluster id: [4433]
matching score: 0.232017461777
purity: 1.0
matching keywords: [u'nuclear', u'physics']
Definitions:
t
{\displaystyle t}
: initial concentration (5.369)
C
0
{\displaystyle C_{0}}
: initial concentration (5.125)
C
t
{\displaystyle C_{t}}
: concentration (3.662)
k
e
{\displaystyle k_{e}}
: elimination rate (1.754)
Properties of specific nuclei listed by mass ranges (an additional heading must be chosen with these entries, where the given mass number limits are, to some degree, arbitrary)
Category information
reference category: Properties of specific nuclei listed by mass ranges (an additional heading must be chosen with these entries, where the given mass number limits are, to some degree, arbitrary)
code: 27.00.00 (PACS)
wiki categories: [(
Category:Physics , 14), (
Category:Particle physics , 9), (
Category:Force , 7)]
Cluster information:
cluster id: [6221, 6623, 8187]
matching score: 0.286862684549
purity: 1.0
matching keywords: [u'mass', u'nuclear', u'physics', u'number']
Definitions:
q
{\displaystyle q}
:
electric charge (15.630)
B
{\displaystyle \mathbf {B} }
:
magnetic field (13.834)
Q
{\displaystyle Q}
:
electric charge (11.565)
c
{\displaystyle c}
:
speed of light (9.225)
E
{\displaystyle \mathbf {E} }
:
electric field (9.034)
B
{\displaystyle B}
:
baryon number (8.185)
t
{\displaystyle t}
:
coordinate time (7.233)
A
{\displaystyle \mathbf {A} }
:
magnetic potential (6.897)
v
{\displaystyle \mathbf {v} }
: velocity (6.333)
a
{\displaystyle a}
:
subatomic particle (5.922)
m
{\displaystyle m}
:
rest mass (5.253)
Y
{\displaystyle Y}
:
hypercharge (5.186)
F
{\displaystyle F}
:
electromagnetic tensor (5.147)
f
{\displaystyle f}
: % 20mechanics (5.088)
S
{\displaystyle S}
:
strangeness (4.699)
T
{\displaystyle T}
:
kinetic energy (4.620)
J
{\displaystyle J}
:
total angular momentum quantum number (4.580)
E
{\displaystyle E}
:
energy (4.532)
L
{\displaystyle L}
:
lepton number (4.524)
v
{\displaystyle v}
: speed (4.374)
z
{\displaystyle z}
: direction (4.287)
T
3
{\displaystyle T_{3}}
:
weak isospin (4.261)
V
{\displaystyle V}
:
potential energy (4.258)
A
{\displaystyle A}
:
magnetic dipole (4.197)
r
{\displaystyle \mathbf {r} }
:
position vector (3.784)
e
{\displaystyle e}
: magnetic charge (3.667)
d
{\displaystyle d}
: dimensions (3.531)
M
{\displaystyle M}
:
manifold (3.404)
p
{\displaystyle \mathbf {p} }
: kinetic momentum (3.362)
u
{\displaystyle u}
:
up quark (3.213)
P
{\displaystyle P}
: parity (3.142)
I
3
{\displaystyle I_{3}}
:
isospin (2.830)
G
{\displaystyle G}
: physics (2.803)
J
{\displaystyle \mathbf {J} }
:
current density (2.803)
Y
W
{\displaystyle Y_{W}}
:
weak hypercharge (2.762)
n
{\displaystyle n}
:
up quark (2.744)
φ
{\displaystyle \varphi }
:
electric potential (2.685)
D
{\displaystyle D}
:
gauge covariant derivative (2.676)
R
{\displaystyle \mathbf {R} }
: space (2.615)
s
{\displaystyle s}
: field (2.595)
j
{\displaystyle \mathbf {j} }
:
probability current (2.578)
I
{\displaystyle I}
: third component (2.555)
H
{\displaystyle \mathbf {H} }
: fields (2.543)
x
{\displaystyle x}
: position (2.479)
p
{\displaystyle p}
: form (2.472)
D
{\displaystyle \mathbf {D} }
:
electric displacement (1.942)
g
{\displaystyle g}
:
metric tensor (1.939)
γ
{\displaystyle \gamma }
: closed loop (1.891)
f
{\displaystyle \mathbf {f} }
:
lorentz force (1.858)
p
i
{\displaystyle p_{i}}
: momentum component (1.858)
M
{\displaystyle \mathbf {M} }
:
magnetization (1.850)
v
y
{\displaystyle v_{y}}
: direction (1.779)
v
z
{\displaystyle v_{z}}
: direction (1.779)
S
{\displaystyle \mathbf {S} }
: momentum operator (1.766)
C
{\displaystyle C}
:
charm (quantum number) (1.756)
σ
{\displaystyle \sigma }
: surface (1.749)
y
{\displaystyle y}
: direction (1.749)
g
{\displaystyle \mathbf {g} }
:
gravitational acceleration (1.724)
P
{\displaystyle \mathbf {P} }
:
four momentum (1.717)
q
i
{\displaystyle q_{i}}
: cartesian coordinate (1.689)
u
1
{\displaystyle u_{1}}
: velocities (1.677)
C
{\displaystyle {\mathcal {C}}}
:
smooth function (1.621)
m
0
{\displaystyle m_{0}}
:
invariant mass (1.621)
i
{\displaystyle i}
: direction (1.564)
u
{\displaystyle \mathbf {u} }
:
lorentz factor (1.532)
X
{\displaystyle X}
: mmj2ubwoeev70gxo14dyaw (1.532)
Networks
Network protocols
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:
N
r
{\displaystyle N_{r}}
: antennas (8.788)
N
t
{\displaystyle N_{t}}
: antennas (5.391)
A
{\displaystyle A}
:
session key (5.126)
S
{\displaystyle S}
: server (4.412)
H
{\displaystyle \mathbf {H} }
: channel matrix (4.110)
B
{\displaystyle B}
: identities (3.513)
K
A
S
{\displaystyle K_{AS}}
:
symmetric key (2.637)
R
R
{\displaystyle \mathbf {R} _{R}}
: spatial correlation matrix (2.513)
Q
{\displaystyle \mathbf {Q} }
: signal covariance (1.939)
R
T
{\displaystyle \mathbf {R} _{T}}
: spatial correlation matrix (1.872)
N
B
{\displaystyle N_{B}}
:
cryptographic nonce (1.837)
K
A
B
{\displaystyle K_{AB}}
: session (1.814)
n
{\displaystyle \mathbf {n} }
: channel matrix (1.790)
i
{\displaystyle i}
: antenna (1.790)
a
{\displaystyle a}
: network (1.736)
K
B
S
{\displaystyle K_{BS}}
: alice (1.712)
G
{\displaystyle \mathbf {G} }
:
permanent (1.654)
T
A
{\displaystyle T_{A}}
:
timestamp (1.635)
I
{\displaystyle I}
: message (1.621)
N
A
{\displaystyle N_{A}}
:
cryptographic nonce (1.603)
Nonassociative rings and algebras
General nonassociative rings
Category information
Cluster information:
cluster id: [7971]
matching score: 0.383603283984
purity: 1.0
matching keywords: [u'algebras', u'nonassociative']
Definitions:
Number theory
Sequences and sets
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:
n
{\displaystyle n}
:
prime number (13.232)
p
{\displaystyle p}
:
prime number (6.160)
U
{\displaystyle U}
: sequences (5.232)
a
{\displaystyle a}
:
natural number (4.160)
k
{\displaystyle k}
:
triangular number (2.669)
q
{\displaystyle q}
: real numbers (2.619)
F
{\displaystyle F}
: estimate (2.471)
P
{\displaystyle P}
:
lucas sequence (2.263)
B
r
{\displaystyle {\mathcal {B}}_{r}}
: sequences (1.939)
r
{\displaystyle r}
: irrational number (1.939)
x
{\displaystyle x}
: real number (1.939)
s
{\displaystyle s}
: pseudoprime (1.900)
V
n
{\displaystyle V_{n}}
:
fibonacci number (1.891)
V
{\displaystyle V}
: sequence (1.812)
m
{\displaystyle m}
: natural number (1.799)
B
s
{\displaystyle {\mathcal {B}}_{s}}
: sequences (1.754)
L
{\displaystyle L}
: conventions (1.712)
S
{\displaystyle S}
:
lower triangular matrix (1.529)
Q
{\displaystyle Q}
:
integer sequence (1.513)
Algebraic number theory: local and p-adic fields
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
Category information
Cluster information:
cluster id: [5948]
matching score: 0.501027191748
purity: 1.0
matching keywords: [u'number', u'arithmetic']
Definitions:
Numerical analysis
Numerical linear algebra
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:
A
{\displaystyle A}
:
symmetric matrix (14.671)
a
{\displaystyle a}
:
triangular matrix (8.400)
B
{\displaystyle B}
: skew-hermitian matrix (5.940)
n
{\displaystyle n}
: matrix (5.320)
L
{\displaystyle L}
:
triangular matrix (4.422)
D
{\displaystyle D}
:
diagonal matrix (3.654)
U
{\displaystyle U}
:
triangular matrix (3.572)
x
{\displaystyle x}
: computation (2.781)
x
{\displaystyle \mathbf {x} }
: right hand side (2.323)
ϕ
{\displaystyle \phi }
: initial guess (1.903)
b
{\displaystyle b}
: ω output (1.895)
j
{\displaystyle j}
: loop (1.852)
i
{\displaystyle i}
: loop (1.817)
Λ
{\displaystyle \Lambda }
: diagonal matrix (1.816)
k
{\displaystyle k}
: iteration (1.765)
s
{\displaystyle s}
: matrix (1.677)
ω
{\displaystyle \omega }
: iteration (1.659)
e
{\displaystyle e}
: error end (1.623)
Mathematical programming, optimization and variational techniques
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:
f
{\displaystyle f}
:
internal function (3.409)
R
{\displaystyle \mathbf {R} }
:
euclidean space (2.835)
a
{\displaystyle a}
:
hardy space (2.798)
n
{\displaystyle n}
:
euclidean space (2.783)
O
{\displaystyle O}
: outer distortion (2.736)
K
{\displaystyle K}
: outer distortion (2.583)
R
{\displaystyle \mathbb {R} }
: function (2.560)
x
{\displaystyle x}
: function (2.434)
X
{\displaystyle X}
:
open set (1.937)
Integral equations, integral transforms
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:
a
{\displaystyle a}
:
stochastic process (3.452)
X
{\displaystyle X}
: stochastic process (1.939)
f
{\displaystyle f}
: flow (1.900)
L
{\displaystyle L}
:
bounded linear operator (1.865)
R
{\displaystyle \mathbf {R} }
:
wiener process (1.744)
i
{\displaystyle i}
: cell centres (1.663)
s
{\displaystyle s}
: action (1.657)
P
{\displaystyle P}
: distribution (1.654)
d
{\displaystyle d}
: dimensional case (1.648)
Numerical methods in Fourier analysis
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:
a
{\displaystyle a}
: signal (5.495)
H
{\displaystyle H}
: filter coefficients (1.891)
h
{\displaystyle h}
: filter (1.882)
ψ
^
{\displaystyle {\hat {\psi }}}
: admissibility (1.754)
π
{\displaystyle \pi }
: period (1.690)
y
{\displaystyle y}
: period (1.586)
Computer aspects of numerical algorithms
Category information
Cluster information:
cluster id: [3003]
matching score: 0.535513837448
purity: 1.0
matching keywords: [u'numerical', u'algorithms', u'analysis']
Definitions:
f
{\displaystyle f}
:
domain of a function (7.203)
L
{\displaystyle L}
:
lipschitz continuity (3.389)
n
{\displaystyle n}
: function values (2.590)
x
0
{\displaystyle x_{0}}
: initial values (2.586)
x
{\displaystyle x}
: mean value (2.297)
x
1
{\displaystyle x_{1}}
: initial values (1.663)
a
{\displaystyle a}
: fixed-point iteration (1.628)
x
n
{\displaystyle x_{n}}
: secant method (1.563)
OTHER
Miscellaneous topics in measure theory
Category information
Cluster information:
cluster id: [469]
matching score: 0.805389122876
purity: 1.0
matching keywords: [u'measure']
Definitions:
Data management systems
Category information
Cluster information:
cluster id: [8220]
matching score: 0.297866726589
purity: 1.0
matching keywords: [u'data']
Definitions:
Phase transformations in solids
Category information
Cluster information:
cluster id: [5716]
matching score: 0.180265473142
purity: 1.0
matching keywords: [u'solids']
Definitions:
a
{\displaystyle a}
: edge length (3.727)
J
{\displaystyle J}
:
johnson solid (3.626)
C
5
v
{\displaystyle C_{5v}}
: decagon (1.476)
C
4
v
{\displaystyle C_{4v}}
: octagon (1.468)
Geophysical observations, instrumentation, and techniques
Category information
Cluster information:
cluster id: [2035]
matching score: 0.0738290007636
purity: 1.0
matching keywords: [u'new', u'national']
Definitions:
e
{\displaystyle e}
: note1 (7.299)
b
{\displaystyle b}
: % note1 (6.653)
f
{\displaystyle f}
: note1 (5.567)
c
{\displaystyle c}
: note1 (5.487)
d
{\displaystyle d}
: note1 (4.557)
a
{\displaystyle a}
: charter member (1.854)
g
{\displaystyle g}
: note1 (1.812)
Randomness, geometry and discrete structures
Category information
Cluster information:
cluster id: [7597]
matching score: 0.135198347331
purity: 1.0
matching keywords: [u'projections']
General
Category information
Cluster information:
cluster id: [9660]
matching score: 0.140056702345
purity: 1.0
matching keywords: [u'systems']
Definitions:
R
{\displaystyle R}
:
radius (3.479)
Low-dimensional topology
Category information
Cluster information:
cluster id: [6000]
matching score: 0.19018451167
purity: 1.0
matching keywords: [u'surfaces', u'knots']
Basic methods
Category information
Cluster information:
cluster id: [7678]
matching score: 0.0970316339844
purity: 1.0
matching keywords: [u'electromagnetic']
Definitions:
G
{\displaystyle G}
:
gain (4.934)
h
{\displaystyle h}
: base station antenna height (4.338)
L
{\displaystyle L}
:
path loss (3.335)
λ
{\displaystyle \lambda }
:
wavelength (1.900)
f
{\displaystyle f}
:
frequency (1.900)
γ
{\displaystyle \gamma }
:
slope (1.790)
d
{\displaystyle d}
:
distance (1.790)
F
{\displaystyle F}
: adjustment (1.742)
Algebraic combinatorics
Category information
Cluster information:
cluster id: [2044, 9746]
matching score: 0.100187378156
purity: 1.0
matching keywords: [u'association']
Definitions:
a
{\displaystyle a}
:
basketball (5.457)
c
{\displaystyle c}
: table.lower-alphanote _ (3.948)
Algebraic combinatorics
Category information
Cluster information:
cluster id: [7982]
matching score: 0.101694565889
purity: 1.0
matching keywords: [u'association']
Computer graphics
Category information
Cluster information:
cluster id: [9126]
matching score: 0.161404183301
purity: 1.0
matching keywords: [u'graphics']
Definitions:
Interaction design
Category information
Cluster information:
cluster id: [8646]
matching score: 0.306093112328
purity: 1.0
matching keywords: [u'design']
Definitions:
n
{\displaystyle n}
: order (4.474)
ω
0
{\displaystyle \omega _{0}}
:
cutoff frequency (3.641)
G
{\displaystyle G}
: gain (2.830)
G
0
{\displaystyle G_{0}}
: gain (2.608)
s
{\displaystyle s}
:
complex frequency space (2.585)
H
{\displaystyle H}
: transfer function (2.487)
ω
p
m
{\displaystyle \omega _{pm}}
: poles (1.939)
f
{\displaystyle f}
: frequency (1.939)
L
{\displaystyle L}
: shunt (1.779)
a
{\displaystyle a}
:
filter (signal processing) (1.742)
C
{\displaystyle C}
: shunt (1.712)
ε
{\displaystyle \varepsilon }
: ripple factor (1.673)
Low-dimensional topology
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)
Category information
Cluster information:
cluster id: [2156]
matching score: 0.0941993903914
purity: 1.0
matching keywords: [u'electronic']
Definitions:
R
L
{\displaystyle R_{L}}
: resistor load (8.064)
R
S
{\displaystyle R_{S}}
: resistance (2.937)
V
A
{\displaystyle V_{A}}
: early voltage (1.974)
R
A
{\displaystyle R_{A}}
: series resistance (1.891)
V
{\displaystyle V}
: signal source (1.891)
I
E
{\displaystyle I_{E}}
: current source (1.882)
I
C
{\displaystyle I_{C}}
: active load (1.850)
I
S
{\displaystyle I_{S}}
:
norton's theorem (1.845)
V
T
{\displaystyle V_{T}}
:
boltzmann constant (1.766)
V
o
u
t
{\displaystyle V_{out}}
: output (1.712)
i
x
{\displaystyle i_{x}}
:
output resistance (1.712)
R
C
{\displaystyle R_{C}}
: resistor load (1.676)
R
o
u
t
{\displaystyle R_{out}}
: gain (1.636)
I
A
{\displaystyle I_{A}}
:
norton's theorem (1.628)
C
d
g
{\displaystyle C_{dg}}
: discharge (1.593)
Graphical methods
Category information
Cluster information:
cluster id: [7094]
matching score: 0.747742788884
purity: 1.0
matching keywords: [u'statistics']
Definitions:
H
{\displaystyle H}
:
hit (baseball) (2.850)
F
{\displaystyle F}
: poor (2.696)
Stochastic systems and control
Category information
Cluster information:
cluster id: [5332]
matching score: 0.197741178813
purity: 1.0
matching keywords: [u'control']
Definitions:
s
{\displaystyle s}
: chart (7.054)
n
{\displaystyle n}
: shewhart (3.520)
x
¯
{\displaystyle {\bar {x}}}
: chart (3.468)
Randomness, geometry and discrete structures
Category information
Cluster information:
cluster id: [6375]
matching score: 0.132670227656
purity: 1.0
matching keywords: [u'projections']
Definitions:
φ
{\displaystyle \varphi }
:
latitude (7.113)
λ
{\displaystyle \lambda }
:
latitude (4.498)
λ
0
{\displaystyle \lambda _{0}}
:
longitude (1.845)
Probability theory on algebraic and topological structures
Category information
Cluster information:
cluster id: [3822]
matching score: 0.631482808408
purity: 1.0
matching keywords: [u'probability']
Definitions:
X
{\displaystyle X}
:
random variable (5.253)
p
{\displaystyle p}
: probability (3.419)
a
{\displaystyle a}
:
discrete random variable (2.675)
N
{\displaystyle N}
: probability-generating function (2.558)
d
{\displaystyle d}
: thinsp ;-rrb- (2.394)
n
{\displaystyle n}
: factorial (1.863)
z
{\displaystyle z}
:
complex number (1.830)
r
{\displaystyle r}
: probability (1.556)
Connections with logic
Category information
Cluster information:
cluster id: [9112]
matching score: 0.373216933738
purity: 1.0
matching keywords: [u'number']
Definitions:
i
{\displaystyle i}
: polynomials (2.639)
F
{\displaystyle F}
: polynomials (2.487)
f
i
{\displaystyle f_{i}}
:
integral polynomial (1.939)
p
{\displaystyle p}
:
prime number (1.910)
n
{\displaystyle n}
: positive integer (1.867)
a
{\displaystyle a}
: proof (1.688)
u
{\displaystyle 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
Cluster information:
cluster id: [2076]
matching score: 0.276097133578
purity: 1.0
matching keywords: [u'physics']
Definitions:
Computational methods
Category information
Cluster information:
cluster id: [3608]
matching score: 0.331350124557
purity: 1.0
matching keywords: [u'relativity']
Definitions:
Decision theory
Category information
Cluster information:
cluster id: [2215]
matching score: 0.241447787175
purity: 1.0
matching keywords: [u'procedures']
Definitions:
Physical chemistry and chemical physics
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:
a
{\displaystyle a}
: type (2.735)
s
{\displaystyle s}
: agcl (1.868)
Close-to-elliptic equations
Category information
Cluster information:
cluster id: [4928]
matching score: 0.125097921763
purity: 1.0
matching keywords: [u'equations', u'differential', u'partial']
Definitions:
L
{\displaystyle L}
: path loss (3.544)
d
{\displaystyle d}
: depth (1.766)
n
{\displaystyle n}
: path loss exponent (1.724)
Mechanical and acoustical properties of condensed matter
Category information
Cluster information:
cluster id: [7570]
matching score: 0.302754171352
purity: 1.0
matching keywords: [u'mechanical']
Definitions:
D
{\displaystyle D}
: major diameter (7.944)
P
{\displaystyle P}
: pitch (6.967)
H
{\displaystyle H}
: height (3.877)
Fundamental astronomy and astrophysics; instrumentation, techniques, and astronomical observations
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
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
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:
h
{\displaystyle h}
: first-order hold (2.799)
s
{\displaystyle s}
:
dirac delta function (2.554)
H
{\displaystyle H}
: gain (1.939)
x
{\displaystyle x}
:
dirac delta function (1.797)
a
{\displaystyle a}
: signal (1.764)
z
{\displaystyle z}
: gain (1.754)
n
{\displaystyle n}
: octave (1.724)
t
{\displaystyle t}
:
dirac delta function (1.424)
Computational methods
Category information
Cluster information:
cluster id: [6305]
matching score: 0.382049687457
purity: 1.0
matching keywords: [u'relativity']
Definitions:
M
{\displaystyle M}
: mass (5.160)
a
{\displaystyle a}
:
black hole (2.843)
J
{\displaystyle J}
:
angular momentum (2.201)
g
t
t
{\displaystyle g_{tt}}
: temporal component (1.939)
K
e
r
r
N
e
w
m
a
n
m
e
t
r
i
c
{\displaystyle \mathbf {KerrNewmanmetric} }
: solution (1.724)
r
{\displaystyle r}
: quantity (1.610)
Q
{\displaystyle Q}
: body (1.505)
Homological algebra
Category information
Cluster information:
cluster id: [2513]
matching score: 0.234530365211
purity: 1.0
matching keywords: [u'algebra']
Definitions:
n
{\displaystyle n}
: dimensions (4.319)
z
i
{\displaystyle z_{i}}
:
rational functions (2.571)
y
{\displaystyle \mathbf {y} }
: basis vectors (1.743)
V
{\displaystyle V}
:
euclidean space (1.733)
e
{\displaystyle \mathbf {e} }
: basis vectors (1.714)
x
{\displaystyle \mathbf {x} }
: mapping vectors (1.710)
Hamilton-Jacobi theories, including dynamic programming
Category information
Cluster information:
cluster id: [7471]
matching score: 0.251226310938
purity: 1.0
matching keywords: [u'calculus']
Definitions:
a
{\displaystyle a}
:
vector operator (6.317)
v
{\displaystyle \mathbf {v} }
:
velocity field (5.444)
F
{\displaystyle \mathbf {F} }
:
vector field (4.221)
A
{\displaystyle \mathbf {A} }
:
vector area (3.661)
z
{\displaystyle z}
: direction (3.348)
n
{\displaystyle n}
:
volume form (3.019)
t
{\displaystyle t}
: time (2.799)
f
{\displaystyle f}
: function (2.766)
R
{\displaystyle \mathbf {R} }
:
smooth function (2.708)
G
{\displaystyle \mathbf {G} }
: vector fields (2.615)
d
{\displaystyle d}
: vector element (2.547)
μ
{\displaystyle \mu }
:
density on a manifold (2.535)
s
{\displaystyle \mathbf {s} }
: vector element (2.508)
k
{\displaystyle k}
: form (2.475)
r
{\displaystyle \mathbf {r} }
: vector field (2.412)
V
{\displaystyle V}
: volume (1.865)
B
{\displaystyle \mathbf {B} }
: source-free part (1.865)
A
{\displaystyle A}
:
vector area (1.847)
X
{\displaystyle X}
: vector field (1.847)
E
{\displaystyle \mathbf {E} }
:
electric field (1.824)
φ
{\displaystyle \varphi }
: scalar-valued function (1.714)
n
^
{\displaystyle \mathbf {\hat {n}} }
:
unit vector (1.707)
x
{\displaystyle x}
: direction (1.690)
e
{\displaystyle \mathbf {e} }
: unit vector (1.659)
q
{\displaystyle q}
:
tensor (1.657)
c
u
r
l
{\displaystyle curl}
: field (1.641)
C
{\displaystyle C}
:
tangent vector (1.550)
p
{\displaystyle 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
Cluster information:
cluster id: [5231]
matching score: 0.248183919026
purity: 1.0
matching keywords: [u'physics']
Definitions:
m
{\displaystyle m}
:
effective mass (solid-state physics) (3.656)
t
{\displaystyle t}
: time (3.419)
R
{\displaystyle R}
: region (2.799)
R
2
{\displaystyle R_{2}}
: region (2.799)
R
1
{\displaystyle R_{1}}
: region (2.576)
n
{\displaystyle n}
: solutions (2.465)
p
{\displaystyle p}
:
momentum (2.421)
x
{\displaystyle x}
: position (2.367)
k
{\displaystyle \mathbf {k} }
:
wave vector (1.939)
A
k
{\displaystyle A_{k}}
: discrete components (1.937)
N
{\displaystyle N}
: particles (1.848)
Ψ
{\displaystyle \Psi }
:
wavefunction (1.847)
a
{\displaystyle a}
: ball (1.815)
V
{\displaystyle V}
: total volume (1.754)
V
0
{\displaystyle V_{0}}
: potential barrier (1.754)
Ω
r
{\displaystyle \Omega _{r}}
: volume (1.754)
ω
p
{\displaystyle \omega _{p}}
: resonance frequency (1.749)
a
n
{\displaystyle a_{n}}
:
scalar multiplication (1.742)
k
F
{\displaystyle k_{F}}
: wave vector (1.659)
A
{\displaystyle A}
:
classical mechanics (1.645)
q
{\displaystyle {\boldsymbol {q}}}
: dispersion relation (1.628)
s
{\displaystyle s}
: wave (1.618)
r
{\displaystyle \mathbf {r} }
:
position vector (1.604)
s
z
{\displaystyle s_{z}}
:
spin (physics) (1.600)
Nuclear engineering and nuclear power studies
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:
t
{\displaystyle t}
: rocket (4.071)
m
0
{\displaystyle m_{0}}
: mass (3.560)
m
1
{\displaystyle m_{1}}
: total mass (3.245)
v
e
{\displaystyle v_{e}}
:
effective exhaust velocity (3.160)
x
{\displaystyle x}
: direction (2.777)
m
{\displaystyle m}
: mass (2.758)
M
{\displaystyle M}
: mass (2.726)
v
{\displaystyle v}
:
effective exhaust velocity (2.679)
P
{\displaystyle P}
: mass (2.676)
I
s
p
{\displaystyle I_{sp}}
:
specific impulse (2.508)
a
{\displaystyle a}
:
rocket engine (2.402)
F
i
{\displaystyle F_{i}}
: external forces (1.865)
I
{\displaystyle I}
: equation (1.779)
γ
{\displaystyle \gamma }
:
lorentz factor (1.720)
V
e
{\displaystyle V_{e}}
: velocity (1.689)
c
{\displaystyle c}
:
speed of light (1.665)
η
{\displaystyle \eta }
: equation (1.557)
Operator theory
Other (nonclassical) types of operator theory
Category information
Cluster information:
cluster id: [6996]
matching score: 0.493677166448
purity: 1.0
matching keywords: [u'operator', u'linear']
Definitions:
H
{\displaystyle H}
:
hilbert space (8.983)
T
{\displaystyle T}
:
linear operator (4.387)
N
{\displaystyle N}
:
linear operator (4.181)
K
{\displaystyle K}
: operator (3.199)
V
{\displaystyle V}
: orthogonal projection (2.702)
X
{\displaystyle X}
: dilation (1.939)
D
T
{\displaystyle D_{T}}
: operator (1.749)
A
{\displaystyle A}
: normal operator (1.696)
Optics, electromagnetic theory
General
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:
z
{\displaystyle z}
: direction (8.647)
θ
2
{\displaystyle \theta _{2}}
: angle (6.736)
c
{\displaystyle c}
:
speed of light (6.072)
θ
{\displaystyle \theta }
: angle (5.655)
n
{\displaystyle n}
:
refractive index (4.457)
a
{\displaystyle a}
:
refraction (4.085)
k
{\displaystyle k}
:
wavenumber (3.579)
E
{\displaystyle \mathbf {E} }
:
electric field (3.427)
θ
1
{\displaystyle \theta _{1}}
: angle (3.425)
v
{\displaystyle v}
:
speed of light (3.157)
u
{\displaystyle u}
: angle (2.799)
n
2
{\displaystyle n_{2}}
: refractive indices (2.741)
n
1
{\displaystyle n_{1}}
: refractive index (2.697)
ϵ
0
{\displaystyle \epsilon _{0}}
:
vacuum permittivity (2.685)
A
{\displaystyle \mathbf {A} }
:
electric field (2.649)
R
{\displaystyle R}
: right (2.635)
λ
0
{\displaystyle \lambda _{0}}
: wavelength (2.491)
x
{\displaystyle x}
:
unit vectors (2.445)
q
{\displaystyle q}
: circular polarization (2.390)
y
{\displaystyle y}
:
circular polarization (2.338)
π
{\displaystyle \pi }
: radians (1.974)
h
{\displaystyle h}
: incidence (1.939)
λ
{\displaystyle \lambda }
:
wavelength (1.882)
M
{\displaystyle M}
: state (1.865)
g
{\displaystyle g}
: absolute value (1.865)
U
{\displaystyle U}
:
operator (physics) (1.848)
n
{\displaystyle \mathbf {n} }
: normal vector (1.847)
n
o
{\displaystyle n_{o}}
: refractive index (1.847)
ϕ
{\displaystyle \phi }
:
angle (1.816)
T
{\displaystyle T}
:
transmittance (1.800)
r
{\displaystyle r}
: radii (1.799)
L
{\displaystyle L}
: state (1.787)
S
{\displaystyle S}
: fig. (1.781)
A
{\displaystyle A}
: light (1.778)
m
{\displaystyle m}
:
integer (1.725)
l
{\displaystyle \mathbf {l} }
: light vector (1.701)
p
{\displaystyle p}
: fraction (1.683)
α
x
{\displaystyle \alpha _{x}}
: radians (1.659)
s
{\displaystyle s}
: light (1.621)
κ
{\displaystyle \kappa }
: absorption (1.558)
α
y
{\displaystyle \alpha _{y}}
: radians (1.524)
b
{\displaystyle b}
: colors (1.515)
ρ
{\displaystyle \rho }
:
angle (1.441)
Ordinary differential equations
General theory
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:
a
{\displaystyle a}
: system (3.216)
λ
{\displaystyle \lambda }
:
eigenvalue (2.683)
u
{\displaystyle u}
:
function (mathematics) (1.913)
R
{\displaystyle \mathbb {R} }
:
fiber bundle (1.766)
t
{\displaystyle t}
: function (1.718)
Q
{\displaystyle Q}
: tangent bundle (1.689)
PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES
Physics of plasmas and electric discharges
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
Close-to-elliptic equations
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:
E
{\displaystyle \mathbf {E} }
:
electric field (7.113)
H
{\displaystyle \mathbf {H} }
:
magnetic field (4.360)
J
{\displaystyle \mathbf {J} }
:
current density (4.341)
B
{\displaystyle \mathbf {B} }
:
magnetic field (4.115)
α
i
{\displaystyle \alpha _{i}}
: unknown coefficients (3.785)
D
{\displaystyle \mathbf {D} }
:
electric displacement field (3.702)
F
{\displaystyle \mathbf {F} }
: field (3.581)
L
{\displaystyle L}
: differential operator (3.571)
H
{\displaystyle H}
: field (2.780)
n
{\displaystyle \mathbf {n} }
:
unit normal (2.765)
ω
{\displaystyle \omega }
:
frequency (2.763)
k
{\displaystyle k}
:
wavenumber (2.718)
u
{\displaystyle u}
:
density (2.504)
M
{\displaystyle \mathbf {M} }
:
magnetization (2.504)
a
{\displaystyle a}
:
electric field (2.242)
Θ
{\displaystyle \Theta }
: angle (1.939)
Q
{\displaystyle Q}
: charge (1.926)
Ω
{\displaystyle \Omega }
: differential operator (1.900)
Ω
D
{\displaystyle \Omega _{D}}
: computational domain (1.900)
k
{\displaystyle \mathbf {k} }
:
wave vector (1.900)
S
{\displaystyle S}
: surface area (1.882)
t
{\displaystyle t}
: time (1.868)
p
{\displaystyle p}
:
density (1.864)
c
{\displaystyle c}
:
speed of light (1.826)
ρ
{\displaystyle \rho }
: density (1.823)
Ω
N
{\displaystyle \Omega _{N}}
: dirichlet (1.790)
ϕ
{\displaystyle \phi }
: general solution (1.790)
A
{\displaystyle \mathbf {A} }
:
electrical potential (1.774)
α
{\displaystyle \alpha }
:
ricci calculus (1.762)
E
{\displaystyle E}
: electric field (1.750)
z
{\displaystyle z}
: direction (1.746)
d
{\displaystyle d}
:
differential (infinitesimal) (1.712)
S
{\displaystyle \mathbf {S} }
:
vector area (1.690)
ρ
1
{\displaystyle \rho _{1}}
: slab (1.657)
B
{\displaystyle B}
: nabla (1.628)
P
{\displaystyle \mathbf {P} }
: material (1.598)
f
{\displaystyle f}
:
frequency (1.591)
v
{\displaystyle v}
: nabla (1.506)
I
{\displaystyle I}
: charge (1.476)
Probability theory and stochastic processes
Foundations of probability theory
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:
a
{\displaystyle a}
:
stochastic process (8.994)
t
{\displaystyle t}
: time (6.933)
i
{\displaystyle i}
: state (5.402)
X
{\displaystyle X}
:
stochastic process (4.099)
S
{\displaystyle S}
:
measurable space (3.889)
j
{\displaystyle j}
: state (3.385)
π
{\displaystyle \pi }
: equilibrium distribution (3.293)
T
{\displaystyle T}
: time (3.250)
s
{\displaystyle s}
: time (2.869)
P
{\displaystyle \mathbf {P} }
:
probability measure (2.644)
Q
{\displaystyle Q}
:
transition rate matrix (1.974)
P
{\displaystyle P}
: transition matrix (1.939)
Y
n
{\displaystyle Y_{n}}
:
martingale (probability theory) (1.816)
c
{\displaystyle c}
: a.s. (1.815)
C
{\displaystyle C}
:
variance (1.749)
b
{\displaystyle b}
: condition (1.627)
Probability theory on algebraic and topological structures
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
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:
a
{\displaystyle a}
:
probability distribution (34.317)
X
{\displaystyle X}
:
triangular distribution (9.286)
n
{\displaystyle n}
: random variables (6.777)
k
{\displaystyle k}
:
degrees of freedom (statistics) (4.065)
M
{\displaystyle \mathbf {M} }
: location parameter (3.971)
X
{\displaystyle \mathbf {X} }
:
matrix inverse (3.648)
λ
{\displaystyle \lambda }
:
noncentrality parameter (3.567)
c
{\displaystyle c}
: constants (3.548)
b
{\displaystyle b}
: interval (3.348)
p
{\displaystyle p}
:
posterior distribution (3.233)
X
i
{\displaystyle X_{i}}
:
uniform distribution (continuous) (3.077)
β
{\displaystyle \beta }
: shape parameters (2.540)
μ
{\displaystyle \mu }
: scale parameter (2.533)
U
{\displaystyle U}
:
uniform distribution (continuous) (2.530)
x
{\displaystyle x}
: scale (2.467)
Ω
{\displaystyle {\boldsymbol {\Omega }}}
: scale matrix (2.417)
Σ
{\displaystyle {\boldsymbol {\Sigma }}}
: scale matrix (2.417)
t
{\displaystyle t}
: thinsp (1.900)
C
{\displaystyle C}
: positive constants (1.882)
H
{\displaystyle H}
:
heaviside step function (1.865)
A
{\displaystyle A}
: chi-squared distribution (1.840)
τ
4
{\displaystyle \tau _{4}}
: l-kurtosis (1.781)
R
{\displaystyle \mathbf {R} }
: continuous distributions (1.743)
χ
{\displaystyle \chi }
:
uniform distribution (continuous) (1.739)
γ
{\displaystyle \gamma }
:
incomplete gamma function (1.724)
Ψ
{\displaystyle \mathbf {\Psi } }
:
positive-definite matrix (1.707)
r
{\displaystyle r}
: positive constants (1.707)
F
{\displaystyle F}
:
f-distribution (1.689)
σ
{\displaystyle \sigma }
:
rayleigh distribution (1.677)
Σ
{\displaystyle \mathbf {\Sigma } }
: covariance matrix (1.653)
Y
{\displaystyle Y}
:
laplace distribution (1.653)
T
{\displaystyle T}
: relation (1.590)
U
{\displaystyle \mathbf {U} }
: scale matrix (1.589)
V
{\displaystyle \mathbf {V} }
: scale matrix (1.589)
j
{\displaystyle j}
: constants (1.497)
Stochastic analysis
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:
a
{\displaystyle a}
:
stochastic differential equation (8.347)
C
{\displaystyle C}
:
compact support (5.321)
D
{\displaystyle D}
: domain (4.611)
X
{\displaystyle X}
: initial datum (4.605)
x
{\displaystyle x}
: initial datum (4.595)
f
{\displaystyle f}
: functions (4.414)
t
{\displaystyle t}
: time (4.393)
B
{\displaystyle B}
:
brownian motion (4.288)
H
{\displaystyle H}
: borel (4.127)
d
{\displaystyle d}
: differential equation (3.820)
b
{\displaystyle b}
:
brownian motion (3.741)
E
{\displaystyle \mathbf {E} }
: expectation (3.648)
A
{\displaystyle A}
: operator (3.447)
Z
{\displaystyle Z}
: observations (2.799)
A
{\displaystyle {\mathcal {A}}}
: characteristic operator (2.797)
m
{\displaystyle m}
:
brownian motion (2.625)
n
{\displaystyle n}
: itō diffusion (2.492)
P
{\displaystyle \mathbf {P} }
: expectation (2.453)
S
{\displaystyle S}
:
measurable space (1.974)
F
{\displaystyle F}
: natural filtration (1.915)
R
{\displaystyle \mathbf {R} }
:
euclidean space (1.910)
Y
{\displaystyle Y}
: state (1.891)
s
{\displaystyle s}
: observations (1.865)
U
{\displaystyle U}
: sets (1.848)
U
k
{\displaystyle U_{k}}
: sequences (1.810)
L
{\displaystyle L}
: operator (1.781)
N
{\displaystyle \mathbf {N} }
:
natural number (1.779)
K
{\displaystyle K}
: space (1.666)
y
{\displaystyle y}
:
green's function (1.621)
r
{\displaystyle r}
: first exit time (1.591)
Quantum theory
General mathematical topics and methods in quantum theory
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:
F
i
{\displaystyle F_{i}}
:
operator (mathematics) (4.668)
a
{\displaystyle a}
:
measure (mathematics) (3.439)
n
{\displaystyle n}
:
magnetic quantum number (3.112)
H
A
{\displaystyle H_{A}}
: space (2.835)
V
{\displaystyle V}
:
electrostatic (2.644)
ψ
{\displaystyle \psi }
: state (2.635)
X
{\displaystyle X}
:
measurable space (2.182)
t
{\displaystyle t}
: time (1.974)
B
{\displaystyle B}
: pure state (1.939)
E
{\displaystyle E}
: energy (1.937)
i
{\displaystyle i}
: basis (1.915)
A
{\displaystyle A}
: simple proof (1.882)
ϕ
{\displaystyle \phi }
: state (1.858)
K
{\displaystyle K}
: degenerate energy (1.845)
K
S
{\displaystyle KS}
: potential (1.812)
j
{\displaystyle \mathbf {j} }
: current densities (1.812)
ψ
t
a
r
{\displaystyle \psi _{tar}}
: target state (1.812)
a
^
i
{\displaystyle {\hat {a}}_{i}}
: operators (1.811)
a
^
j
{\displaystyle {\hat {a}}_{j}}
: operators (1.810)
F
{\displaystyle F}
: function (1.800)
r
{\displaystyle \mathbf {r} }
: radiation field (1.790)
v
{\displaystyle v}
:
scalar potential (1.756)
M
{\displaystyle M}
:
sigma algebra (1.708)
ℓ
{\displaystyle \ell }
: states (1.698)
U
{\displaystyle U}
: unitary operator (1.690)
V
{\displaystyle \mathbf {V} }
: systems (1.689)
N
{\displaystyle N}
:
hilbert space (1.657)
p
{\displaystyle p}
: fidelity (1.618)
J
{\displaystyle J}
: degenerate energy (1.524)
Quantum field theory; related classical field theories
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:
a
{\displaystyle a}
:
tensor rank (5.360)
ϕ
{\displaystyle \phi }
: field (4.726)
f
{\displaystyle f}
: % 20tensor (3.800)
Z
{\displaystyle Z}
:
generating functional (3.661)
M
{\displaystyle M}
: mass (3.566)
S
{\displaystyle S}
:
action (physics) (2.741)
G
{\displaystyle G}
: tensor (2.586)
g
μ
ν
{\displaystyle g_{\mu \nu }}
:
metric tensor (1.974)
W
{\displaystyle W}
: closed loop (1.939)
K
{\displaystyle K}
:
operator (physics) (1.882)
ω
μ
ν
ρ
{\displaystyle \omega _{\mu \nu \rho }}
:
spin connection (1.845)
T
{\displaystyle {\mathcal {T}}}
:
time ordering (1.790)
J
{\displaystyle J}
:
source field (1.757)
g
{\displaystyle g}
: determinant (1.754)
F
{\displaystyle F}
:
electromagnetic tensor (1.744)
n
{\displaystyle n}
: particle green (1.696)
O
{\displaystyle O}
: theory (1.659)
c
{\displaystyle c}
:
speed of light (1.659)
m
{\displaystyle m}
:
mass (1.657)
S
c
h
w
i
n
g
e
r
D
y
s
o
n
e
q
u
a
t
i
o
n
s
{\displaystyle \mathbf {SchwingerDysonequations} }
: equations (1.654)
μ
{\displaystyle \mu }
: covariant derivative (1.629)
E
{\displaystyle E}
:
perturbation theory (quantum mechanics) (1.527)
Real functions
Functions of one variable
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:
a
{\displaystyle a}
: list (5.816)
C
{\displaystyle C}
: nonzero (1.790)
Miscellaneous topics
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:
a
{\displaystyle a}
:
function (mathematics) (24.187)
f
{\displaystyle f}
:
function (mathematics) (11.764)
g
{\displaystyle g}
:
sinc function (5.240)
A
{\displaystyle A}
:
polynomial function (5.049)
X
{\displaystyle X}
:
metric spaces (5.004)
x
n
{\displaystyle x_{n}}
:
sequence (4.713)
φ
{\displaystyle \varphi }
:
euler's totient function (4.294)
x
{\displaystyle x}
:
continuous function (4.132)
R
{\displaystyle \mathbf {R} }
: function (4.073)
d
{\displaystyle d}
: function (3.850)
ϵ
{\displaystyle \epsilon }
:
real number (3.664)
q
{\displaystyle q}
: degree (3.559)
L
{\displaystyle L}
: function (3.478)
S
{\displaystyle S}
:
final topology (3.402)
t
{\displaystyle t}
: function (3.275)
T
{\displaystyle T}
: distribution (2.799)
n
{\displaystyle n}
: key length (2.799)
G
{\displaystyle G}
: continuity (2.685)
V
{\displaystyle V}
:
neighbourhood (mathematics) (2.677)
M
{\displaystyle M}
:
continuous function (2.627)
W
{\displaystyle W}
:
normed vector space (2.595)
U
{\displaystyle U}
:
open set (2.551)
δ
{\displaystyle \delta }
: positive number (1.950)
B
x
{\displaystyle B_{x}}
: ball (1.939)
I
{\displaystyle I}
:
open interval (1.915)
N
{\displaystyle N}
: poly (1.903)
R
{\displaystyle R}
: neighborhood (1.900)
c
{\displaystyle c}
: domain (1.790)
μ
{\displaystyle \mu }
: möbius function (1.766)
φ
ϵ
{\displaystyle \varphi _{\epsilon }}
: function (1.712)
P
{\displaystyle P}
: approaches (1.657)
Y
{\displaystyle Y}
: function (1.591)
r
{\displaystyle r}
:
continuous function (1.588)
b
{\displaystyle b}
:
open interval (1.588)
Relativity and gravitational theory
Computational methods
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:
c
{\displaystyle c}
:
speed of light (7.772)
x
{\displaystyle x}
: position (6.931)
M
{\displaystyle M}
:
mass (6.302)
a
{\displaystyle a}
:
black hole (5.922)
t
{\displaystyle t}
: time (5.601)
L
{\displaystyle L}
: initial rest length (5.482)
v
{\displaystyle v}
: relative velocity (4.254)
φ
{\displaystyle \varphi }
:
electric potential (3.679)
A
{\displaystyle \mathbf {A} }
:
electric potential (3.539)
L
0
{\displaystyle L_{0}}
:
proper length (3.359)
0
{\displaystyle 0}
: position (3.289)
S
{\displaystyle S}
: distance (2.728)
Q
{\displaystyle Q}
: electric charge (2.688)
G
{\displaystyle G}
:
gravitational constant (2.649)
J
{\displaystyle J}
:
angular momentum (2.642)
B
{\displaystyle B}
: endpoints (2.368)
D
{\displaystyle D}
: dimensions (1.907)
E
{\displaystyle \mathbf {E} }
:
electric field (1.889)
d
{\displaystyle d}
: distance (1.875)
E
{\displaystyle E}
: total energy (1.858)
T
0
{\displaystyle T_{0}}
:
proper time (1.848)
J
{\displaystyle \mathbf {J} }
:
electric current density (1.845)
A
{\displaystyle A}
: black hole (1.812)
T
{\displaystyle T}
: time (1.793)
N
{\displaystyle N}
: event (1.781)
O
{\displaystyle O}
: event (1.781)
k
{\displaystyle k}
:
boltzmann constant (1.779)
B
{\displaystyle \mathbf {B} }
:
magnetic field (1.769)
r
s
{\displaystyle r_{s}}
:
schwarzschild radius (1.749)
L
o
r
e
n
t
z
F
i
t
z
G
e
r
a
l
d
c
o
n
t
r
a
c
t
i
o
n
{\displaystyle \mathbf {LorentzFitzGeraldcontraction} }
:
hendrik lorentz (1.732)
f
{\displaystyle f}
:
harmonic function (1.724)
r
{\displaystyle r}
: infinity (1.723)
M
0
{\displaystyle M_{0}}
: initial mass (1.707)
L
′
{\displaystyle L'}
: acceleration (1.524)
Unified, higher-dimensional and super field theories
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:
D
{\displaystyle D}
: dimensions (2.536)
Special functions (33-XX deals with the properties of functions as functions)
Elementary classical functions
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
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
Category information
Cluster information:
cluster id: [5023]
matching score: 0.464915805598
purity: 1.0
matching keywords: [u'functions', u'special']
Definitions:
Statistics
Parametric inference
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:
m
{\displaystyle m}
: hypothesis tests (9.682)
U
{\displaystyle U}
:
type i and type ii errors (6.550)
s
{\displaystyle s}
: statistic (5.426)
S
{\displaystyle S}
:
type i and type ii errors (4.687)
T
{\displaystyle T}
:
type i and type ii errors (4.687)
a
{\displaystyle a}
:
statistics (4.295)
R
{\displaystyle R}
:
type i and type ii errors (3.725)
α
{\displaystyle \alpha }
: level (3.694)
V
{\displaystyle V}
:
alternative hypothesis (3.643)
M
{\displaystyle M}
: mean (2.799)
H
i
{\displaystyle H_{i}}
: test (2.741)
θ
{\displaystyle {\boldsymbol {\theta }}}
: parameter vector (2.652)
X
{\displaystyle X}
:
random variable (2.616)
m
0
{\displaystyle m_{0}}
: null hypotheses (2.565)
k
{\displaystyle k}
:
pareto distribution (2.469)
Θ
{\displaystyle \mathbf {\Theta } }
: random parameter (1.939)
i
{\displaystyle i}
: hypothesis (1.939)
n
{\displaystyle n}
: independent comparisons (1.939)
Z
{\displaystyle Z}
: samples (1.900)
w
i
{\displaystyle w_{i}}
: weight (1.882)
g
θ
{\displaystyle g_{\boldsymbol {\theta }}}
: function (1.834)
δ
{\displaystyle \delta }
: quantiles (1.816)
A
{\displaystyle A}
: well-behaved statistic (1.751)
μ
{\displaystyle \mu }
: confidence intervals (1.738)
p
{\displaystyle p}
:
bernoulli distribution (1.700)
Q
{\displaystyle Q}
: discoveries (1.677)
K
{\displaystyle K}
:
pareto distribution (1.673)
Θ
{\displaystyle {\boldsymbol {\Theta }}}
: random vector (1.666)
c
i
{\displaystyle c_{i}}
: intersection hypothesis (1.544)
H
{\displaystyle H}
: null hypotheses (1.524)
Multivariate analysis
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:
I
{\displaystyle I}
: moran (7.965)
C
{\displaystyle C}
: geary (4.327)
X
{\displaystyle X}
:
random variables (3.589)
f
j
{\displaystyle f_{j}}
: functions (3.510)
i
{\displaystyle i}
: observation (3.495)
E
{\displaystyle E}
:
mean (3.435)
n
{\displaystyle n}
: random sample (3.420)
Y
{\displaystyle Y}
:
sample variance (3.401)
r
{\displaystyle r}
:
pearson product-moment correlation coefficient (3.227)
σ
{\displaystyle \sigma }
: variance (2.833)
N
{\displaystyle N}
: distribution (2.802)
j
{\displaystyle j}
: observation (2.800)
x
{\displaystyle x}
:
correlation (2.791)
θ
^
{\displaystyle {\hat {\theta }}}
:
estimator (2.552)
x
i
{\displaystyle x_{i}}
: rank (2.536)
y
{\displaystyle y}
:
standard deviation (2.429)
w
{\displaystyle w}
: weight vector (1.939)
p
{\displaystyle p}
:
regressor (1.926)
θ
{\displaystyle \theta }
: unknown parameter (1.907)
X
¯
{\displaystyle {\bar {X}}}
: interest (1.900)
d
{\displaystyle d}
: constants (1.900)
μ
{\displaystyle \mu }
: variance (1.865)
a
{\displaystyle a}
: measure (1.855)
m
{\displaystyle m}
: independent variables (1.845)
y
i
{\displaystyle y_{i}}
: dependent variable (1.833)
T
{\displaystyle T}
: sample covariance matrix (1.817)
z
{\displaystyle z}
: distribution (1.810)
Y
i
{\displaystyle Y_{i}}
: week (1.774)
W
{\displaystyle W}
: matrix (1.749)
t
{\displaystyle t}
: mean (1.724)
ρ
{\displaystyle \rho }
:
correlation (1.701)
f
{\displaystyle f}
: function (1.701)
X
i
{\displaystyle X_{i}}
:
iq (1.627)
r
t
{\displaystyle r_{t}}
: observations (1.611)
k
{\displaystyle k}
: data points (1.610)
s
y
{\displaystyle s_{y}}
:
standard deviation (1.591)
w
i
j
{\displaystyle w_{ij}}
: mean (1.591)
β
j
{\displaystyle \beta _{j}}
: functions (1.524)
c
{\displaystyle c}
: constants (1.524)
Linear inference, regression
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:
i
{\displaystyle i}
: observation (6.257)
n
{\displaystyle n}
: observations (5.196)
k
{\displaystyle k}
:
explanatory variable (4.712)
X
{\displaystyle \mathbf {X} }
:
design matrix (3.317)
M
{\displaystyle M}
: model (2.961)
j
{\displaystyle j}
: study (2.799)
b
{\displaystyle b}
:
coefficient (2.725)
x
{\displaystyle x}
: data (2.672)
p
{\displaystyle p}
: matrix (2.593)
B
{\displaystyle \mathbf {B} }
: matrix (2.527)
a
{\displaystyle a}
: model (2.448)
e
^
{\displaystyle {\hat {e}}}
: residual vector (1.974)
W
k
{\displaystyle W_{k}}
: data matrix (1.939)
θ
{\displaystyle \theta }
: effect size (1.915)
X
{\displaystyle X}
: matrix (1.897)
q
{\displaystyle q}
:
rank (matrix theory) (1.882)
σ
{\displaystyle \sigma }
:
variance (1.876)
V
{\displaystyle V}
: columns (1.865)
β
^
k
{\displaystyle {\widehat {\boldsymbol {\beta }}}_{k}}
: pcr estimator (1.812)
β
{\displaystyle \beta }
: explanators (1.793)
μ
n
{\displaystyle {\boldsymbol {\mu }}_{n}}
: posterior mean (1.781)
E
{\displaystyle \mathbf {E} }
: squares (1.779)
B
^
{\displaystyle {\hat {\mathbf {B} }}}
:
moore–penrose_pseudoinverse (1.724)
e
{\displaystyle e}
: true coefficients (1.718)
S
{\displaystyle S}
: probability distribution (1.689)
β
{\displaystyle {\boldsymbol {\beta }}}
:
bias of an estimator (1.520)
Systems theory; control
General
Category information
Cluster information:
cluster id: [3434]
matching score: 0.295205721387
purity: 1.0
matching keywords: [u'mathematical', u'systems']
Definitions:
a
{\displaystyle a}
:
coordinate system (7.644)
F
{\displaystyle \mathbf {F} }
: differential operators (4.439)
z
{\displaystyle z}
: direction (3.729)
σ
{\displaystyle \sigma }
: form (2.926)
τ
{\displaystyle \tau }
: form (2.926)
P
{\displaystyle P}
: moon (2.894)
P
{\displaystyle \mathbf {P} }
: black sphere (2.286)
I
{\displaystyle I}
: mcgraw-hill (1.926)
x
{\displaystyle x}
:
cartesian coordinates (1.579)
y
{\displaystyle y}
:
cartesian coordinate system (1.556)
Stochastic systems and control
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
Design and analysis of algorithms
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:
f
{\displaystyle f}
:
complexity class (7.405)
k
{\displaystyle k}
: self (6.937)
O
{\displaystyle O}
: dspace (6.799)
n
{\displaystyle n}
: space (6.224)
q
{\displaystyle q}
: state (5.292)
p
{\displaystyle p}
: state (5.084)
M
{\displaystyle M}
:
deterministic turing machine (4.549)
A
{\displaystyle A}
:
linear bounded automaton (4.456)
ℓ
{\displaystyle \ell }
: length (4.283)
i
{\displaystyle i}
: call position (3.887)
φ
{\displaystyle \varphi }
:
gödel numbering (3.732)
q
i
{\displaystyle q_{i}}
: state (3.510)
δ
{\displaystyle \delta }
: transition relation (3.178)
a
{\displaystyle \mathbf {a} }
: symbol (2.961)
p
i
{\displaystyle p_{i}}
: state (2.799)
Σ
{\displaystyle \Sigma }
:
alphabet (computer science) (2.727)
w
{\displaystyle w}
: word (2.674)
Q
{\displaystyle Q}
: finite set (2.661)
Φ
{\displaystyle \Phi }
: complexity measure (2.485)
M
i
{\displaystyle M_{i}}
: state (2.266)
M
′
{\displaystyle M'}
: pushdown automaton (1.974)
q
0
{\displaystyle q_{0}}
: initial state (1.974)
s
{\displaystyle s}
: states (1.974)
t
{\displaystyle t}
: function (1.974)
L
{\displaystyle L}
:
formal language (1.939)
x
{\displaystyle x}
: input (1.939)
Γ
{\displaystyle \Gamma }
: alphabet (1.891)
P
{\displaystyle \mathbf {P} }
:
partial computable function (1.882)
ε
{\displaystyle \varepsilon }
:
empty word (1.858)
Z
{\displaystyle Z}
: symbol (1.847)
h
{\displaystyle h}
: hash (1.843)
G
{\displaystyle G}
: context-free grammar (1.824)
g
{\displaystyle g}
: program (1.790)
φ
i
{\displaystyle \varphi _{i}}
:
domain (mathematics) (1.774)
V
{\displaystyle V}
: disjoint (1.774)
T
{\displaystyle T}
: function (1.757)
a
{\displaystyle a}
:
computer science (1.757)
r
{\displaystyle r}
: state (1.749)
j
{\displaystyle j}
: position (1.688)
Σ
^
{\displaystyle {\hat {\Sigma }}}
: alphabet (1.675)
w
j
{\displaystyle w_{j}}
: state (1.665)
γ
i
{\displaystyle \gamma _{i}}
: state (1.623)
μ
{\displaystyle \mu }
: right multiplication (1.576)
Topological groups, Lie groups
Lie groups
Category information
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:
g
{\displaystyle {\mathfrak {g}}}
:
lie algebra (16.000)
a
{\displaystyle a}
:
subgroup (11.003)
W
{\displaystyle W}
:
weyl group (7.311)
λ
{\displaystyle \lambda }
:
weight (representation theory) (7.243)
j
{\displaystyle j}
: symbol (5.392)
w
{\displaystyle w}
:
weyl group (4.243)
K
{\displaystyle K}
:
subgroup (3.732)
α
{\displaystyle \alpha }
: root (3.630)
V
{\displaystyle V}
:
representation of a lie algebra (3.623)
λ
~
{\displaystyle {\tilde {\lambda }}}
:
dominant weight (2.751)
L
{\displaystyle L}
: holomorphic line bundle (2.736)
G
{\displaystyle G}
: complex semisimple lie group (2.628)
k
{\displaystyle {\mathfrak {k}}}
: 1-dimensional lie algebra (2.596)
B
{\displaystyle B}
:
borel subgroup (2.563)
n
{\displaystyle n}
:
vector space (2.366)
J
{\displaystyle J}
: edge lengths (1.875)
j
1
{\displaystyle \mathbf {j} _{1}}
: angular momenta (1.875)
H
{\displaystyle H}
: inner product (1.845)
s
{\displaystyle {\mathfrak {s}}}
: semisimple lie algebra (1.834)
i
{\displaystyle i}
: edge lengths (1.801)
g
0
{\displaystyle {\mathfrak {g}}_{0}}
:
module (mathematics) (1.779)
F
{\displaystyle F}
: field (1.756)
s
{\displaystyle s}
: commute (1.756)
γ
i
{\displaystyle \gamma _{i}}
:
coroot (1.749)
p
{\displaystyle p}
: operators ad (1.749)
p
{\displaystyle {\mathfrak {p}}}
:
semisimple lie algebra (1.746)
M
λ
{\displaystyle M_{\lambda }}
:
weight_(representation_theory) (1.724)
f
{\displaystyle f}
: homomorphism (1.724)
b
{\displaystyle {\mathfrak {b}}}
:
module (mathematics) (1.723)
a
{\displaystyle {\mathfrak {a}}}
: abelian lie algebra (1.701)
j
2
{\displaystyle \mathbf {j} _{2}}
: angular momenta (1.691)
s
α
{\displaystyle s_{\alpha }}
:
root reflection (1.689)
v
λ
{\displaystyle v_{\lambda }}
: weight vector (1.659)
P
{\displaystyle P}
: symmetric operators (1.657)
A
{\displaystyle A}
: compact subgroup (1.641)
Y
{\displaystyle Y}
: global minimum (1.618)
M
μ
{\displaystyle M_{\mu }}
: modules (1.599)