s
stringlengths
1
39
o
stringclasses
996 values
p
stringlengths
7
77
confidence
float64
0.4
1
predicate_class
stringclasses
2 values
community
int64
0
14
equation_name
stringlengths
14
73
equation_latex
stringlengths
5
217
equation_sympy
stringclasses
617 values
equation_form
stringclasses
472 values
variables
stringlengths
2
85
domain
stringclasses
119 values
scm_name
stringclasses
165 values
source
stringlengths
9
50
extraction_method
stringclasses
8 values
F
f
urn:hailstone:math:structural_equation[3fd61b676cc0]
1
structural_equation
4
arxiv.nlin.CD.2503.02411v1.eq_1821
F(x,y)=\left(|x| - y + a, x - |y| + b\right),
arxiv_extracted
["e", "f", "F", "y", "l", "x"]
arxiv
arxiv
arxiv:nlin.CD:2503.02411v1
cross_domain_amplification
T_{ω
t
urn:hailstone:math:structural_equation[bcefa39ff4ab]
1
structural_equation
4
arxiv.nlin.CD.2502.20614v2.eq_1822
T_{ω,λ}=2π/\sqrt{ω^{2}-λ^{2}}
arxiv_extracted
["q", "t", "T_{\u03c9", "r", "s"]
arxiv
arxiv
arxiv:nlin.CD:2502.20614v2
cross_domain_amplification
m
a
urn:hailstone:math:structural_equation[03ba6f3e3e6a]
1
structural_equation
4
arxiv.nlin.CD.2502.04152v1.eq_1823
\mathcal{T}^2=1
arxiv_extracted
["a", "t", "m", "h", "c"]
arxiv
arxiv
arxiv:nlin.CD:2502.04152v1
cross_domain_amplification
m
a
urn:hailstone:math:structural_equation[03ba6f3e3e6a]
1
structural_equation
4
arxiv.nlin.CD.2502.04152v1.eq_1824
\mathcal{T}^2=1
arxiv_extracted
["a", "t", "m", "h", "c"]
arxiv
arxiv
arxiv:nlin.CD:2502.04152v1
cross_domain_amplification
m
a
urn:hailstone:math:structural_equation[f108db837f3f]
1
structural_equation
4
arxiv.nlin.CD.2502.04152v1.eq_1825
\mathcal{T}^2=-1
arxiv_extracted
["a", "t", "m", "h", "c"]
arxiv
arxiv
arxiv:nlin.CD:2502.04152v1
cross_domain_amplification
q_{0}
t
urn:hailstone:math:structural_equation[bf56090c0d8c]
1
structural_equation
4
arxiv.nlin.CD.2501.17990v1.eq_1826
q_{0}=q(\textbf{x},\,0)
arxiv_extracted
["e", "q", "t", "q_{0}", "x"]
arxiv
arxiv
arxiv:nlin.CD:2501.17990v1
cross_domain_amplification
x_{t
x_t
urn:hailstone:math:structural_equation[9477eb018152]
1
structural_equation
4
arxiv.nlin.CD.2411.13629v1.eq_1827
x_{t+1}=\frac{1}{x_t^α} - \Bigl[\frac{1}{x_t^α} \Bigr]
arxiv_extracted
["f", "a", "x_{t", "r", "x_t", "c"]
arxiv
arxiv
arxiv:nlin.CD:2411.13629v1
cross_domain_amplification
H
c
urn:hailstone:math:structural_equation[edea105a3c31]
1
structural_equation
4
arxiv.nlin.CD.2411.02641v1.eq_1828
H(O) = c
arxiv_extracted
["O", "H", "c"]
arxiv
arxiv
arxiv:nlin.CD:2411.02641v1
cross_domain_amplification
x_{t
d
urn:hailstone:math:structural_equation[057527e39232]
1
structural_equation
4
arxiv.nlin.CD.2409.19999v2.eq_1829
x_{t+1}=2 x_t [mod 1]
arxiv_extracted
["m", "x_{t", "o", "x_t", "d"]
arxiv
arxiv
arxiv:nlin.CD:2409.19999v2
cross_domain_amplification
x_{t
x_t}
urn:hailstone:math:structural_equation[440d4e414274]
1
structural_equation
4
arxiv.nlin.CD.2409.19999v2.eq_1830
x_{t+1}=\frac{x_t}{2}
arxiv_extracted
["f", "a", "x_t}", "x_{t", "r", "c"]
arxiv
arxiv
arxiv:nlin.CD:2409.19999v2
cross_domain_amplification
x_t
n
urn:hailstone:math:structural_equation[81e63c9da121]
1
structural_equation
4
arxiv.nlin.CD.2409.19999v2.eq_1831
x_t = \sum_{l=1}^{+\infty} \frac{σ_l (t)}{2^l}
arxiv_extracted
["m_{l", "i", "u", "s", "n", "x_t"]
arxiv
arxiv
arxiv:nlin.CD:2409.19999v2
cross_domain_amplification
z_{τ
z_τ
urn:hailstone:math:structural_equation[0c031e29a63d]
1
structural_equation
4
arxiv.nlin.CD.2409.19999v2.eq_1832
z_{τ+1}=0=z_τ
arxiv_extracted
["z_{\u03c4", "z_\u03c4"]
arxiv
arxiv
arxiv:nlin.CD:2409.19999v2
cross_domain_amplification
x
r
urn:hailstone:math:structural_equation[5ed7ab42e2ee]
1
structural_equation
4
arxiv.nlin.CD.2407.16632v1.eq_1833
φ(x) = d(x,x_0)^{-\frac{1}α}
arxiv_extracted
["f", "x_0", "r", "d", "x"]
arxiv
arxiv
arxiv:nlin.CD:2407.16632v1
cross_domain_amplification
m
m
urn:hailstone:math:structural_equation[ea8b95507041]
1
structural_equation
4
arxiv.nlin.CD.2404.08481v1.eq_1834
\mathrm{Pr}= 0.025
arxiv_extracted
["a", "t", "m", "h", "r"]
arxiv
arxiv
arxiv:nlin.CD:2404.08481v1
cross_domain_amplification
u
s
urn:hailstone:math:structural_equation[22dffea0841b]
1
structural_equation
4
arxiv.nlin.CD.2404.03241v3.eq_1835
\underset{r\rightarrow 0}{\lim }\frac{\log τ_{r}(x,y)}{-\log r}% =d_{μ}(y).
arxiv_extracted
["e", "u", "r", "s", "n", "d"]
arxiv
arxiv
arxiv:nlin.CD:2404.03241v3
cross_domain_amplification
v
a
urn:hailstone:math:structural_equation[cec414ea1cab]
1
structural_equation
4
arxiv.nlin.CD.2401.16943v2.eq_1836
||\vec{y}-\hat{\vec{y}}||^2_{M^{-1}} = (\vec{y}-\hat{\vec{y}})^\top {M^{-1}} (\vec{y}-\hat{\vec{y}})
arxiv_extracted
["e", "a", "y", "h", "c", "v"]
arxiv
arxiv
arxiv:nlin.CD:2401.16943v2
cross_domain_amplification
g
t
urn:hailstone:math:structural_equation[135d491b9fb0]
1
structural_equation
4
arxiv.nlin.CD.2406.12852v2.eq_1837
g(u) = 1 - \left( \frac{\sin(πu)}{πu} \right)^2 + δ(u)
arxiv_extracted
["e", "f", "g", "t", "u", "l"]
arxiv
arxiv
arxiv:nlin.CD:2406.12852v2
cross_domain_amplification
x_{n
f
urn:hailstone:math:structural_equation[aee6f31aeb9d]
1
structural_equation
4
arxiv.nlin.CD.2406.12852v2.eq_1838
x_{n+1} = 1 - \left( \frac{\sin(π/x_n)}{π/x_n} \right)^2 + \frac{1}{x_n}
arxiv_extracted
["e", "f", "t", "x_{n", "l"]
arxiv
arxiv
arxiv:nlin.CD:2406.12852v2
cross_domain_amplification
f
x
urn:hailstone:math:structural_equation[f022f8af83bc]
1
structural_equation
4
arxiv.nlin.CD.2406.12852v2.eq_1839
f(x) = 1 - π^2 x^2
arxiv_extracted
["f", "x"]
arxiv
arxiv
arxiv:nlin.CD:2406.12852v2
cross_domain_amplification
V
x
urn:hailstone:math:structural_equation[7c46614716d2]
1
structural_equation
4
arxiv.nlin.CD.2406.12852v2.eq_1840
V(x) = C_1 e^{-π^2 x^3/3}
arxiv_extracted
["e", "V", "C_1", "x"]
arxiv
arxiv
arxiv:nlin.CD:2406.12852v2
cross_domain_amplification
x_{t
t
urn:hailstone:math:structural_equation[4665510d62a5]
1
structural_equation
4
arxiv.nlin.CD.2311.00593v2.eq_1841
x_{t+1} = 2 x_t [\text{mod} 1]
arxiv_extracted
["e", "t", "x_{t", "x_t", "x"]
arxiv
arxiv
arxiv:nlin.CD:2311.00593v2
cross_domain_amplification
x
n
urn:hailstone:math:structural_equation[89d6709df4cb]
1
structural_equation
4
arxiv.nlin.CD.2311.00593v2.eq_1842
x= \sum_{l=1}^{+\infty} \frac{σ_l}{2^l}
arxiv_extracted
["m_{l", "i", "u", "s", "n", "x"]
arxiv
arxiv
arxiv:nlin.CD:2311.00593v2
cross_domain_amplification
t
t
urn:hailstone:math:structural_equation[ac9b8f600a18]
1
structural_equation
4
arxiv.nlin.CD.2310.03053v1.eq_1843
ρ(t) = \exp \{ - i t H / \hbar \} ρ(0) \exp \{ i H t / \hbar \}
arxiv_extracted
["e", "t", "i", "p", "x"]
arxiv
arxiv
arxiv:nlin.CD:2310.03053v1
cross_domain_amplification
w
a
urn:hailstone:math:structural_equation[458f2ffa310f]
1
structural_equation
4
arxiv.nlin.CD.2309.14179v1.eq_1844
\widehat{=}
arxiv_extracted
["e", "w", "a", "h", "i", "d"]
arxiv
arxiv
arxiv:nlin.CD:2309.14179v1
cross_domain_amplification
w
a
urn:hailstone:math:structural_equation[458f2ffa310f]
1
structural_equation
4
arxiv.nlin.CD.2309.14179v1.eq_1845
\widehat{=}
arxiv_extracted
["e", "w", "a", "h", "i", "d"]
arxiv
arxiv
arxiv:nlin.CD:2309.14179v1
cross_domain_amplification
p
r
urn:hailstone:math:structural_equation[a8c740742974]
1
structural_equation
4
arxiv.nlin.CD.2309.04520v1.eq_1846
p_\mathrm{ent} = p_\mathrm{ctrl}
arxiv_extracted
["a", "t", "m", "h", "p", "r"]
arxiv
arxiv
arxiv:nlin.CD:2309.04520v1
cross_domain_amplification
T
q
urn:hailstone:math:structural_equation[d00dbbe81a1b]
1
structural_equation
4
arxiv.nlin.CD.2309.03358v1.eq_1847
ν_{T}=0.55l(x,t)\sqrt{k(x,t)}
arxiv_extracted
["q", "t", "s", "T", "l", "x"]
arxiv
arxiv
arxiv:nlin.CD:2309.03358v1
cross_domain_amplification
z_2
w
urn:hailstone:math:structural_equation[0da0f1a88337]
1
structural_equation
4
arxiv.nlin.CD.2308.16179v2.eq_1848
z_2(w)= z_2(w=1)
arxiv_extracted
["z_2", "w"]
arxiv
arxiv
arxiv:nlin.CD:2308.16179v2
cross_domain_amplification
T
E
urn:hailstone:math:structural_equation[0055bc233daf]
1
structural_equation
4
arxiv.nlin.CD.2308.16159v1.eq_1849
T^{*}=T|E|^{3/2}<80
arxiv_extracted
["E", "T"]
arxiv
arxiv
arxiv:nlin.CD:2308.16159v1
cross_domain_amplification
t
t
urn:hailstone:math:structural_equation[cff32be7093f]
1
structural_equation
4
arxiv.nlin.CD.2308.13555v1.eq_1850
κ_γ(t)=κ_0(E(t))
arxiv_extracted
["t", "E"]
arxiv
arxiv
arxiv:nlin.CD:2308.13555v1
cross_domain_amplification
f
P_{in}
urn:hailstone:math:structural_equation[2bc462b0904a]
1
structural_equation
4
arxiv.nlin.CD.2309.00633v2.eq_1851
\frac{P_{out}}{P_{in}} = 3.71 \times 10^{-8}
arxiv_extracted
["f", "a", "P_{in}", "r", "P_{out}", "c"]
arxiv
arxiv
arxiv:nlin.CD:2309.00633v2
cross_domain_amplification
R_{n
n
urn:hailstone:math:structural_equation[9ad5b3569c58]
1
structural_equation
4
arxiv.nlin.CD.2308.08835v1.eq_1852
R_{n,a,c}(z)=z^n+\frac{a}{z^n}+c
arxiv_extracted
["z", "a", "R_{n", "n", "c"]
arxiv
arxiv
arxiv:nlin.CD:2308.08835v1
cross_domain_amplification
x_{t
x_t
urn:hailstone:math:structural_equation[3eafd808ec8d]
1
structural_equation
4
arxiv.nlin.CD.2306.13608v1.eq_1853
x_{t+1}=1-ax_t^2
arxiv_extracted
["x_t", "x_{t", "a"]
arxiv
arxiv
arxiv:nlin.CD:2306.13608v1
cross_domain_amplification
R
a_c
urn:hailstone:math:structural_equation[d34bfb26937d]
1
structural_equation
4
arxiv.nlin.CD.2306.09952v2.eq_1854
Ra_c = (2π)^4
arxiv_extracted
["R", "a_c"]
arxiv
arxiv
arxiv:nlin.CD:2306.09952v2
cross_domain_amplification
v
i
urn:hailstone:math:structural_equation[b3222a393ce0]
1
structural_equation
4
arxiv.nlin.CD.2305.14085v1.eq_1855
\varphi=0.5
arxiv_extracted
["a", "h", "i", "p", "r", "v"]
arxiv
arxiv
arxiv:nlin.CD:2305.14085v1
cross_domain_amplification
s
s
urn:hailstone:math:structural_equation[4c89e1abcd57]
1
structural_equation
4
arxiv.nlin.CD.2303.07780v2.eq_1856
ν_{s} = νL^{2(s-1)}
arxiv_extracted
["s", "L"]
arxiv
arxiv
arxiv:nlin.CD:2303.07780v2
cross_domain_amplification
n
t
urn:hailstone:math:structural_equation[b7015013beea]
1
structural_equation
4
arxiv.nlin.CD.2302.13008v3.eq_1857
n_{\text{typ}}=\exp\langle \ln n \rangle \propto (h/K)^2
arxiv_extracted
["t", "n", "e", "x"]
arxiv
arxiv
arxiv:nlin.CD:2302.13008v3
cross_domain_amplification
v
s
urn:hailstone:math:structural_equation[1a3b98944599]
1
structural_equation
4
arxiv.nlin.CD.2302.01284v1.eq_1858
\varepsilon(t) = \varepsilon_{0} \exp(κ\,t)
arxiv_extracted
["e", "a", "p", "r", "s", "v"]
arxiv
arxiv
arxiv:nlin.CD:2302.01284v1
cross_domain_amplification
I
o
urn:hailstone:math:structural_equation[1b8a19b8890b]
1
structural_equation
4
arxiv.nlin.CD.2301.09441v2.eq_1859
δI^j_k={\rm cov}(s_j, s_{j+k})
arxiv_extracted
["m", "o", "j_k", "r", "c", "I"]
arxiv
arxiv
arxiv:nlin.CD:2301.09441v2
cross_domain_amplification
m
f
urn:hailstone:math:structural_equation[d1e5e2a41a4e]
1
structural_equation
4
arxiv.nlin.CD.2212.06617v1.eq_1860
\mathbf{v}_{d}=\mathbf{v-\mathbf{v}}_{RB}
arxiv_extracted
["f", "a", "t", "m", "h", "b"]
arxiv
arxiv
arxiv:nlin.CD:2212.06617v1
cross_domain_amplification
d_l
O
urn:hailstone:math:structural_equation[9c1b633fb137]
1
structural_equation
4
arxiv.nlin.CD.2211.15497v1.eq_1861
d_l^O=2
arxiv_extracted
["O", "d_l"]
arxiv
arxiv
arxiv:nlin.CD:2211.15497v1
cross_domain_amplification
d_l
R
urn:hailstone:math:structural_equation[ba4907fc2585]
1
structural_equation
4
arxiv.nlin.CD.2211.15497v1.eq_1862
d_l^R=4
arxiv_extracted
["d_l", "R"]
arxiv
arxiv
arxiv:nlin.CD:2211.15497v1
cross_domain_amplification
t
m
urn:hailstone:math:structural_equation[3ae9dcf00256]
1
structural_equation
4
arxiv.nlin.CD.2211.12147v2.eq_1863
2λ_{\textrm{q}}=aλ_{\textrm{L}}+bλ_{\textrm{loc}}
arxiv_extracted
["e", "t", "m", "r", "x"]
arxiv
arxiv
arxiv:nlin.CD:2211.12147v2
cross_domain_amplification
e
l
urn:hailstone:math:structural_equation[9d7c77eaaf6e]
1
structural_equation
4
arxiv.nlin.CD.2210.14695v2.eq_1864
α_{el}=1/137
arxiv_extracted
["e", "l"]
arxiv
arxiv
arxiv:nlin.CD:2210.14695v2
cross_domain_amplification
J_{i_1
s
urn:hailstone:math:structural_equation[fa4ef4792ed3]
1
structural_equation
4
arxiv.nlin.CD.2210.13123v2.eq_1865
J_{i_1\cdots i_q}^{(L)}=J_{i_1\cdots i_q}^{(R)}
arxiv_extracted
["t", "J_{i_1", "d", "o", "s", "c"]
arxiv
arxiv
arxiv:nlin.CD:2210.13123v2
cross_domain_amplification
t
e
urn:hailstone:math:structural_equation[5724b9d33c5e]
1
structural_equation
4
arxiv.nlin.CD.2209.02945v3.eq_1866
\text{Re}_τ^2 \text{Nu} = f(\text{Pr}) \text{Pr}^{-1} \text{Ra}
arxiv_extracted
["t", "R", "e", "x"]
arxiv
arxiv
arxiv:nlin.CD:2209.02945v3
cross_domain_amplification
v
s
urn:hailstone:math:structural_equation[15746744b9de]
1
structural_equation
4
arxiv.nlin.CD.2209.02945v3.eq_1867
\varepsilon=1/3
arxiv_extracted
["e", "a", "p", "r", "s", "v"]
arxiv
arxiv
arxiv:nlin.CD:2209.02945v3
cross_domain_amplification
v
s
urn:hailstone:math:structural_equation[fdd3e680af27]
1
structural_equation
4
arxiv.nlin.CD.2209.02945v3.eq_1868
\varepsilon=1
arxiv_extracted
["e", "a", "p", "r", "s", "v"]
arxiv
arxiv
arxiv:nlin.CD:2209.02945v3
cross_domain_amplification
m
f
urn:hailstone:math:structural_equation[751bb780c280]
1
structural_equation
4
arxiv.nlin.CD.2207.02758v5.eq_1869
\mathbf{k}=\mathbf{p}+\mathbf{q}
arxiv_extracted
["f", "a", "t", "m", "h", "b"]
arxiv
arxiv
arxiv:nlin.CD:2207.02758v5
cross_domain_amplification
m
f
urn:hailstone:math:structural_equation[1db4b61f69c9]
1
structural_equation
4
arxiv.nlin.CD.2207.02758v5.eq_1870
ω_{\mathbf{k}}=|ω_{\mathbf{p}}\pmω_{\mathbf{q}}|
arxiv_extracted
["f", "a", "t", "m", "h", "b"]
arxiv
arxiv
arxiv:nlin.CD:2207.02758v5
cross_domain_amplification
n
g
urn:hailstone:math:structural_equation[1450e9c8b9d8]
1
structural_equation
4
arxiv.nlin.CD.2205.09475v1.eq_1871
τ_n^g(G)=τ_n(τ_n^{g-1}(G))
arxiv_extracted
["n", "g", "G"]
arxiv
arxiv
arxiv:nlin.CD:2205.09475v1
cross_domain_amplification
n
G
urn:hailstone:math:structural_equation[6bbb850fd6c9]
1
structural_equation
4
arxiv.nlin.CD.2205.09475v1.eq_1872
τ_n^0(G)=G
arxiv_extracted
["n", "G"]
arxiv
arxiv
arxiv:nlin.CD:2205.09475v1
cross_domain_amplification
k
n
urn:hailstone:math:structural_equation[490cb1085ba4]
1
structural_equation
4
arxiv.nlin.CD.2205.06080v2.eq_1873
k_{\sf in}=1
arxiv_extracted
["f", "i", "s", "n", "k"]
arxiv
arxiv
arxiv:nlin.CD:2205.06080v2
cross_domain_amplification
h
r
urn:hailstone:math:structural_equation[cb427e7e0aaa]
1
structural_equation
4
arxiv.nlin.CD.2205.02867v2.eq_1874
\hbar_{eff} = 1/N \rightarrow 0
arxiv_extracted
["a", "h", "r", "r_{eff}", "b", "N"]
arxiv
arxiv
arxiv:nlin.CD:2205.02867v2
cross_domain_amplification
E
r
urn:hailstone:math:structural_equation[3410180f11a5]
1
structural_equation
4
arxiv.nlin.CD.2203.12484v2.eq_1875
α_{E1}=1+2/(D_V+2)=(13/9)\approx 1.44
arxiv_extracted
["a", "p", "r", "E", "D_V"]
arxiv
arxiv
arxiv:nlin.CD:2203.12484v2
cross_domain_amplification
E
r
urn:hailstone:math:structural_equation[fb9d44003205]
1
structural_equation
4
arxiv.nlin.CD.2203.12484v2.eq_1876
α_{E2}=1+2/D_A=(7/3)\approx 2.33
arxiv_extracted
["a", "D_A", "p", "r", "E"]
arxiv
arxiv
arxiv:nlin.CD:2203.12484v2
cross_domain_amplification
E
r
urn:hailstone:math:structural_equation[58e358f2f588]
1
structural_equation
4
arxiv.nlin.CD.2203.12484v2.eq_1877
α_{E3}=1+2/D_V=(9/5)\approx 1.80
arxiv_extracted
["a", "p", "r", "E", "D_V"]
arxiv
arxiv
arxiv:nlin.CD:2203.12484v2
cross_domain_amplification
E
m
urn:hailstone:math:structural_equation[26b4f3dc7def]
1
structural_equation
4
arxiv.nlin.CD.2203.12484v2.eq_1878
α_{E1}=1.47 \pm 0.07
arxiv_extracted
["p", "E", "m"]
arxiv
arxiv
arxiv:nlin.CD:2203.12484v2
cross_domain_amplification
E
m
urn:hailstone:math:structural_equation[6456caf34929]
1
structural_equation
4
arxiv.nlin.CD.2203.12484v2.eq_1879
α_{E2}=2.38 \pm 0.09
arxiv_extracted
["p", "E", "m"]
arxiv
arxiv
arxiv:nlin.CD:2203.12484v2
cross_domain_amplification
E
m
urn:hailstone:math:structural_equation[75b86840920d]
1
structural_equation
4
arxiv.nlin.CD.2203.12484v2.eq_1880
α_{E3}=1.80 \pm 0.18
arxiv_extracted
["p", "E", "m"]
arxiv
arxiv
arxiv:nlin.CD:2203.12484v2
cross_domain_amplification
m
a
urn:hailstone:math:structural_equation[d3e208066318]
1
structural_equation
4
arxiv.nlin.CD.2202.12075v1.eq_1881
\mathcal{N}=4
arxiv_extracted
["a", "t", "m", "h", "c"]
arxiv
arxiv
arxiv:nlin.CD:2202.12075v1
cross_domain_amplification
m
a
urn:hailstone:math:structural_equation[4f0f44984d77]
1
structural_equation
4
arxiv.nlin.CD.2202.12075v1.eq_1882
\mathcal{N}=1
arxiv_extracted
["a", "t", "m", "h", "c"]
arxiv
arxiv
arxiv:nlin.CD:2202.12075v1
cross_domain_amplification
m
a
urn:hailstone:math:structural_equation[d3e208066318]
1
structural_equation
4
arxiv.nlin.CD.2202.12075v1.eq_1883
\mathcal{N}=4
arxiv_extracted
["a", "t", "m", "h", "c"]
arxiv
arxiv
arxiv:nlin.CD:2202.12075v1
cross_domain_amplification
m
a
urn:hailstone:math:structural_equation[d3e208066318]
1
structural_equation
4
arxiv.nlin.CD.2202.12075v1.eq_1884
\mathcal{N}=4
arxiv_extracted
["a", "t", "m", "h", "c"]
arxiv
arxiv
arxiv:nlin.CD:2202.12075v1
cross_domain_amplification
n
V_2
urn:hailstone:math:structural_equation[4ed86d5a5217]
1
structural_equation
4
arxiv.nlin.CD.2201.11180v4.eq_1885
nV_1 = -mV_2
arxiv_extracted
["V_2", "n", "m", "V_1"]
arxiv
arxiv
arxiv:nlin.CD:2201.11180v4
cross_domain_amplification
q
i
urn:hailstone:math:structural_equation[f3268bf76848]
1
structural_equation
4
arxiv.nlin.CD.2111.00305v1.eq_1886
q_{\rm{crit}}=a_{\rm{N}}\,\big(\ln((24^2/5)\,(m_{\rm{N}}/M_{\odot})\,(a/a_{\rm{N}})^{5/2})\big)^{1/2}
arxiv_extracted
["q", "m", "i", "r", "c"]
arxiv
arxiv
arxiv:nlin.CD:2111.00305v1
cross_domain_amplification
t_{n}
p
urn:hailstone:math:structural_equation[4173e47bdb7d]
1
structural_equation
4
arxiv.nlin.CD.2109.10694v1.eq_1887
t_{n} =\varepsilon^{n}t, \ n\rightarrow\infty, \ \varepsilon<1
arxiv_extracted
["e", "a", "p", "r", "t_{n}", "v"]
arxiv
arxiv
arxiv:nlin.CD:2109.10694v1
cross_domain_amplification
T_{n}
t_{n}
urn:hailstone:math:structural_equation[c3c8353a40cf]
1
structural_equation
4
arxiv.nlin.CD.2109.10694v1.eq_1888
T_{n}=t_{n}σ(t_{n})
arxiv_extracted
["T_{n}", "t_{n}"]
arxiv
arxiv
arxiv:nlin.CD:2109.10694v1
cross_domain_amplification
V
x
urn:hailstone:math:structural_equation[d1ded0474a36]
1
structural_equation
4
arxiv.nlin.CD.2108.13924v1.eq_1889
V\left( x\right) =\frac{1}{2}ω^{2}Q\left( x\right) x^{2}
arxiv_extracted
["e", "V", "f", "t", "l", "x"]
arxiv
arxiv
arxiv:nlin.CD:2108.13924v1
cross_domain_amplification
m
a
urn:hailstone:math:structural_equation[e47039dc834e]
1
structural_equation
4
arxiv.nlin.CD.2108.13924v1.eq_1890
\mathcal{R}\left( x,\dot{x}\right) =\frac{1}{2}b\,m\left( x\right) \dot{x}^{2}
arxiv_extracted
["a", "t", "m", "h", "c"]
arxiv
arxiv
arxiv:nlin.CD:2108.13924v1
cross_domain_amplification
F
t
urn:hailstone:math:structural_equation[af89a3db5f50]
1
structural_equation
4
arxiv.nlin.CD.2108.13924v1.eq_1891
F\left( t\right) =F_{\circ }\,\cos \left( Ωt\right)
arxiv_extracted
["e", "f", "F", "t", "l"]
arxiv
arxiv
arxiv:nlin.CD:2108.13924v1
cross_domain_amplification
q
x
urn:hailstone:math:structural_equation[b14064e99c68]
1
structural_equation
4
arxiv.nlin.CD.2108.13924v1.eq_1892
q\left( x\right) =\int \sqrt{m\left( x\right) }dx=\sqrt{% Q\left( x\right) }x
arxiv_extracted
["e", "f", "q", "t", "l", "x"]
arxiv
arxiv
arxiv:nlin.CD:2108.13924v1
cross_domain_amplification
S_{eq}
T
urn:hailstone:math:structural_equation[ce0815b07430]
1
structural_equation
4
arxiv.nlin.CD.2107.01300v1.eq_1893
S_{eq} πT =\sum_{λ>0}2 πT
arxiv_extracted
["S_{eq}", "m_{\u03bb", "u", "s", "T"]
arxiv
arxiv
arxiv:nlin.CD:2107.01300v1
cross_domain_amplification
m
a
urn:hailstone:math:structural_equation[d3e208066318]
1
structural_equation
4
arxiv.nlin.CD.2107.01300v1.eq_1894
\mathcal{N}=4
arxiv_extracted
["a", "t", "m", "h", "c"]
arxiv
arxiv
arxiv:nlin.CD:2107.01300v1
cross_domain_amplification
f
B
urn:hailstone:math:structural_equation[65ec63bef403]
1
structural_equation
4
arxiv.nlin.CD.2106.14067v1.eq_1895
α= γ, \fracαβ = 1, A = B = C
arxiv_extracted
["f", "a", "B", "A", "r", "c"]
arxiv
arxiv
arxiv:nlin.CD:2106.14067v1
cross_domain_amplification
f
r
urn:hailstone:math:structural_equation[47bb7a1d6f7d]
1
structural_equation
4
arxiv.nlin.CD.2106.14067v1.eq_1896
α= γ, \fracαβ = \frac{1}{6}, A = C
arxiv_extracted
["f", "c", "r", "a"]
arxiv
arxiv
arxiv:nlin.CD:2106.14067v1
cross_domain_amplification
f
r
urn:hailstone:math:structural_equation[89ca2d092618]
1
structural_equation
4
arxiv.nlin.CD.2106.14067v1.eq_1897
α= γ, \fracαβ = \frac{1}{16}, A = C, \frac{A}{B} = \frac{1}{16}
arxiv_extracted
["f", "c", "r", "a"]
arxiv
arxiv
arxiv:nlin.CD:2106.14067v1
cross_domain_amplification
u_x
l
urn:hailstone:math:structural_equation[806207763eee]
1
structural_equation
4
arxiv.nlin.CD.2106.10788v4.eq_1898
u_x = \langle \ \dot x \ \rangle = \dot εy
arxiv_extracted
["g", "a", "u_x", "n", "l"]
arxiv
arxiv
arxiv:nlin.CD:2106.10788v4
cross_domain_amplification
r
r
urn:hailstone:math:structural_equation[81daa24633c9]
1
structural_equation
4
arxiv.nlin.CD.2106.10788v4.eq_1899
φ(r<2) = (2-r)^6 - 2(2-r)^3
arxiv_extracted
["r"]
arxiv
arxiv
arxiv:nlin.CD:2106.10788v4
cross_domain_amplification
d
o
urn:hailstone:math:structural_equation[2d4a49146853]
1
structural_equation
4
arxiv.nlin.CD.2106.10788v4.eq_1900
(du_x/dy) = \dot ε
arxiv_extracted
["d", "y", "u_x", "o"]
arxiv
arxiv
arxiv:nlin.CD:2106.10788v4
cross_domain_amplification
v
t
urn:hailstone:math:structural_equation[ed21d44c8c69]
1
structural_equation
4
arxiv.nlin.CD.2106.08268v1.eq_1901
\vec{\mathrm B} = 0
arxiv_extracted
["e", "a", "t", "m", "c", "v"]
arxiv
arxiv
arxiv:nlin.CD:2106.08268v1
cross_domain_amplification
U
c
urn:hailstone:math:structural_equation[b8bed98000c5]
1
structural_equation
4
arxiv.nlin.CD.2106.08268v1.eq_1902
U(ρ,s) = \frac{1}{2}ρs
arxiv_extracted
["f", "a", "r", "s", "U", "c"]
arxiv
arxiv
arxiv:nlin.CD:2106.08268v1
cross_domain_amplification
t
h
urn:hailstone:math:structural_equation[d9e3f7e03ddd]
1
structural_equation
4
arxiv.nlin.CD.2105.13097v2.eq_1903
to each other. The resulting horizontal surface flow has a stripe-like spatial structure. The width of the stripes L =
arxiv_extracted
["e", "a", "t", "h", "o", "c"]
arxiv
arxiv
arxiv:nlin.CD:2105.13097v2
cross_domain_amplification
e
l
urn:hailstone:chemistry_physics:structural_equation[97a1a1146cf5]
1
structural_equation
2
arxiv.quant-ph.2605.13271v1.eq_1904
θ_\ell=\ellπ/\ell_{\max}
arxiv_extracted
["e", "l"]
arxiv
arxiv
arxiv:quant-ph:2605.13271v1
cross_domain_amplification
m
a
urn:hailstone:chemistry_physics:structural_equation[26b83f5dd0d1]
1
structural_equation
2
arxiv.quant-ph.2605.13271v1.eq_1905
\mathcal{C}=\mathcal{F}_Q\cdot(-\ln P_{\rm err})
arxiv_extracted
["a", "t", "m", "h", "c"]
arxiv
arxiv
arxiv:quant-ph:2605.13271v1
cross_domain_amplification
v
s
urn:hailstone:chemistry_physics:structural_equation[92ad0753f3b8]
1
structural_equation
2
arxiv.quant-ph.2605.13066v1.eq_1906
\varepsilon = 0
arxiv_extracted
["e", "a", "p", "r", "s", "v"]
arxiv
arxiv
arxiv:quant-ph:2605.13066v1
cross_domain_amplification
v
s
urn:hailstone:chemistry_physics:structural_equation[c82e742e677f]
1
structural_equation
2
arxiv.quant-ph.2605.13066v1.eq_1907
\varepsilon = Ω/2
arxiv_extracted
["e", "a", "p", "r", "s", "v"]
arxiv
arxiv
arxiv:quant-ph:2605.13066v1
cross_domain_amplification
x
x
urn:hailstone:chemistry_physics:structural_equation[f6ce5d3cc614]
1
structural_equation
2
arxiv.quant-ph.2605.12828v1.eq_1908
x^2-2x-4=0
arxiv_extracted
["x"]
arxiv
arxiv
arxiv:quant-ph:2605.12828v1
cross_domain_amplification
H
r
urn:hailstone:chemistry_physics:structural_equation[6e4c820992f1]
1
structural_equation
2
arxiv.quant-ph.2605.12450v1.eq_1909
H_{\mathrm{eff}} = H_R + iH_I
arxiv_extracted
["a", "t", "m", "H", "h", "r"]
arxiv
arxiv
arxiv:quant-ph:2605.12450v1
cross_domain_amplification
p
n
urn:hailstone:chemistry_physics:structural_equation[89668cd4db2e]
1
structural_equation
2
arxiv.quant-ph.2605.12044v1.eq_1910
p_{\rm win}=1/2+S(P)/8
arxiv_extracted
["w", "m", "i", "p", "r", "n"]
arxiv
arxiv
arxiv:quant-ph:2605.12044v1
cross_domain_amplification
e
h
urn:hailstone:chemistry_physics:structural_equation[6124be56b2e0]
1
structural_equation
2
arxiv.quant-ph.2605.11895v1.eq_1911
\ell^2(t) = C\hbar t/m
arxiv_extracted
["e", "t", "h", "l", "C"]
arxiv
arxiv
arxiv:quant-ph:2605.11895v1
cross_domain_amplification
V
d
urn:hailstone:chemistry_physics:structural_equation[95e617262af8]
1
structural_equation
2
arxiv.quant-ph.2605.11557v1.eq_1912
\Var[X] = Θ(d^{-2})
arxiv_extracted
["V", "a", "X", "r", "d"]
arxiv
arxiv
arxiv:quant-ph:2605.11557v1
cross_domain_amplification
b
c
urn:hailstone:chemistry_physics:structural_equation[77fdbf9a1cf2]
1
structural_equation
2
arxiv.quant-ph.2605.11230v1.eq_1913
\bar{n}_c = 1250
arxiv_extracted
["a", "r", "n", "b", "c"]
arxiv
arxiv
arxiv:quant-ph:2605.11230v1
cross_domain_amplification
b
c
urn:hailstone:chemistry_physics:structural_equation[408465521027]
1
structural_equation
2
arxiv.quant-ph.2605.11230v1.eq_1914
\bar{n}_c/2 = 625
arxiv_extracted
["a", "r", "n", "b", "c"]
arxiv
arxiv
arxiv:quant-ph:2605.11230v1
cross_domain_amplification
v
e
urn:hailstone:chemistry_physics:structural_equation[a2af19cce8b7]
1
structural_equation
2
arxiv.quant-ph.2605.10250v1.eq_1915
\vartheta_{\mathrm{eff}} =\vartheta_0/(1 -\vartheta_0 B_0/\hbar_0)
arxiv_extracted
["e", "a", "t", "h", "r", "v"]
arxiv
arxiv
arxiv:quant-ph:2605.10250v1
cross_domain_amplification
E
x
urn:hailstone:chemistry_physics:structural_equation[7d67cb245457]
1
structural_equation
2
arxiv.quant-ph.2605.09149v1.eq_1916
E[W_{\rm ext}] = Δ\left(\frac12+\frac{S(P)}{8}\right)
arxiv_extracted
["e", "W", "m", "r", "E", "x"]
arxiv
arxiv
arxiv:quant-ph:2605.09149v1
cross_domain_amplification
E
x
urn:hailstone:chemistry_physics:structural_equation[e0f8dc1644fe]
1
structural_equation
2
arxiv.quant-ph.2605.09149v1.eq_1917
E[W_{\rm ext}]=Δ
arxiv_extracted
["e", "W", "m", "r", "E", "x"]
arxiv
arxiv
arxiv:quant-ph:2605.09149v1
cross_domain_amplification
E
h
urn:hailstone:chemistry_physics:structural_equation[9c869451ef06]
1
structural_equation
2
arxiv.quant-ph.2605.09149v1.eq_1918
E[Q_{\mathrm{reset}}] \ge k_B T \ln 2 \, h_2(p_{\mathrm{win}}), \qquad p_{\mathrm{win}} = \frac{1}{2} + \frac{S(P)}{8}.
arxiv_extracted
["Q", "a", "t", "m", "h", "E"]
arxiv
arxiv
arxiv:quant-ph:2605.09149v1
cross_domain_amplification
m
a
urn:hailstone:chemistry_physics:structural_equation[9206dea25fe6]
1
structural_equation
2
arxiv.quant-ph.2605.08829v1.eq_1919
\mathcal{R}(φ(A))=A
arxiv_extracted
["a", "t", "m", "h", "c"]
arxiv
arxiv
arxiv:quant-ph:2605.08829v1
cross_domain_amplification
m
m
urn:hailstone:chemistry_physics:structural_equation[bde2da215bee]
1
structural_equation
2
arxiv.quant-ph.2605.07405v1.eq_1920
\mathrm{tr}(ρ_1^2ρ_2^2) = \mathrm{tr}(ρ_1 ρ_2 ρ_1 ρ_2)
arxiv_extracted
["a", "t", "m", "h", "r"]
arxiv
arxiv
arxiv:quant-ph:2605.07405v1
cross_domain_amplification