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 |
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