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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
k | t | urn:hailstone:chemistry_physics:structural_equation[ab28a55e8c99] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2604.27525v1.eq_421 | Φ(θ) = 2k\,r(θ)\sqrt{1-β^2\sin^2θ}/(1-β^2) | arxiv_extracted | ["q", "t", "r", "s", "k"] | arxiv | arxiv | arxiv:physics.class-ph:2604.27525v1 | cross_domain_amplification | |
m | m | urn:hailstone:chemistry_physics:structural_equation[ef8e34effc3e] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2603.29035v1.eq_422 | χ^2/\mathrm{dof}=0.50 | arxiv_extracted | ["a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:physics.class-ph:2603.29035v1 | cross_domain_amplification | |
m | m | urn:hailstone:chemistry_physics:structural_equation[9474c4071f4d] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2603.19887v1.eq_423 | \mathrm{d}ΔT/\mathrm{d}t = -[γ_0 + \mathcal{M}Q(t)][ΔT - \mathcal{I}Q(t)] | arxiv_extracted | ["a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:physics.class-ph:2603.19887v1 | cross_domain_amplification | |
d | E | urn:hailstone:chemistry_physics:structural_equation[1383e09133db] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2602.07577v1.eq_424 | \dot{E}=0 | arxiv_extracted | ["t", "d", "E", "o"] | arxiv | arxiv | arxiv:physics.class-ph:2602.07577v1 | cross_domain_amplification | |
t | w | urn:hailstone:chemistry_physics:structural_equation[9e70faf653f1] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2602.03790v2.eq_425 | t_{\text{w}}=τ | arxiv_extracted | ["t", "w", "e", "x"] | arxiv | arxiv | arxiv:physics.class-ph:2602.03790v2 | cross_domain_amplification | |
a | m | urn:hailstone:chemistry_physics:structural_equation[aa6e35db5602] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2601.16325v1.eq_426 | Δa/g = κ(q/m) | arxiv_extracted | ["g", "m", "q", "a"] | arxiv | arxiv | arxiv:physics.class-ph:2601.16325v1 | cross_domain_amplification | |
m | f | urn:hailstone:chemistry_physics:structural_equation[3d221c96c754] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2512.22285v1.eq_427 | \mathbf{F}=\mathbf{F}^e\mathbf{F}^r_α\mathbf{F}^d_α | arxiv_extracted | ["f", "a", "t", "m", "h", "b"] | arxiv | arxiv | arxiv:physics.class-ph:2512.22285v1 | cross_domain_amplification | |
j | x | urn:hailstone:chemistry_physics:structural_equation[35ba436b5bc1] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2512.20123v1.eq_428 | j_{-1}(x) = \cos x / x | arxiv_extracted | ["j", "o", "s", "c", "x"] | arxiv | arxiv | arxiv:physics.class-ph:2512.20123v1 | cross_domain_amplification | |
b | y | urn:hailstone:chemistry_physics:structural_equation[f7419cfd31c1] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2510.25981v1.eq_429 | \boldsymbol{δF}=-γ_nv^{n-1}\boldsymbol{v} | arxiv_extracted | ["y", "o", "s", "b", "d", "l"] | arxiv | arxiv | arxiv:physics.class-ph:2510.25981v1 | cross_domain_amplification | |
m | f | urn:hailstone:chemistry_physics:structural_equation[cef8b1ebb29e] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2510.17750v4.eq_430 | \mathbf{k}_{\parallel} = \mathbf{0} | arxiv_extracted | ["f", "a", "t", "m", "h", "b"] | arxiv | arxiv | arxiv:physics.class-ph:2510.17750v4 | cross_domain_amplification | |
f | f | urn:hailstone:chemistry_physics:structural_equation[86757bd4a726] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2509.17821v2.eq_431 | f^N(q)=\pm\frac{q}{|q|^2} | arxiv_extracted | ["f", "q", "m", "p", "N"] | arxiv | arxiv | arxiv:physics.class-ph:2509.17821v2 | cross_domain_amplification | |
m | m | urn:hailstone:chemistry_physics:structural_equation[ccdd0a079c06] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2509.12601v1.eq_432 | Δ_{1} = 23~\mathrm{meV} | arxiv_extracted | ["a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:physics.class-ph:2509.12601v1 | cross_domain_amplification | |
m | m | urn:hailstone:chemistry_physics:structural_equation[7d97c9e2780b] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2509.12601v1.eq_433 | Δ_{2} = 6~\mathrm{meV} | arxiv_extracted | ["a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:physics.class-ph:2509.12601v1 | cross_domain_amplification | |
C | c | urn:hailstone:chemistry_physics:structural_equation[e5489f0c7607] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2509.09973v2.eq_434 | θ_{C}=60^{\circ} | arxiv_extracted | ["c", "r", "C", "i"] | arxiv | arxiv | arxiv:physics.class-ph:2509.09973v2 | cross_domain_amplification | |
m | f | urn:hailstone:chemistry_physics:structural_equation[6092da9843b3] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2508.16689v2.eq_435 | \mathbf{\nabla}\cdot{\bf B}=0 | arxiv_extracted | ["f", "a", "t", "m", "h", "b"] | arxiv | arxiv | arxiv:physics.class-ph:2508.16689v2 | cross_domain_amplification | |
s | y | urn:hailstone:chemistry_physics:structural_equation[66180ce23db5] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2507.20660v1.eq_436 | s_{\infty} = \ln (z) | arxiv_extracted | ["f", "t", "y", "i", "s", "n"] | arxiv | arxiv | arxiv:physics.class-ph:2507.20660v1 | cross_domain_amplification | |
S | r | urn:hailstone:chemistry_physics:structural_equation[c78cb90ba203] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2507.20660v1.eq_437 | S_{\mathrm{molar}} = R \ln 12 \approx 20.7 \, \mathrm{J/mol \cdot K} | arxiv_extracted | ["a", "t", "m", "h", "S", "r"] | arxiv | arxiv | arxiv:physics.class-ph:2507.20660v1 | cross_domain_amplification | |
v | p | urn:hailstone:chemistry_physics:structural_equation[62b3f8a6cbb6] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2506.08799v3.eq_438 | \varkappa=0 | arxiv_extracted | ["a", "p", "r", "k", "v"] | arxiv | arxiv | arxiv:physics.class-ph:2506.08799v3 | cross_domain_amplification | |
L | m | urn:hailstone:chemistry_physics:structural_equation[3ad72c29ae6f] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2505.12062v4.eq_439 | Δ_L(0) = 6.9 \pm 1.2 | arxiv_extracted | ["p", "m", "L"] | arxiv | arxiv | arxiv:physics.class-ph:2505.12062v4 | cross_domain_amplification | |
p | m | urn:hailstone:chemistry_physics:structural_equation[4e2f4d3a6c08] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2505.03551v4.eq_440 | p^μp_μ= m^2 | arxiv_extracted | ["m", "p", "p_\u03bc"] | arxiv | arxiv | arxiv:physics.class-ph:2505.03551v4 | cross_domain_amplification | |
f | f | urn:hailstone:chemistry_physics:structural_equation[574f57378102] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2504.01471v1.eq_441 | f^N(q)=\pm\frac{q}{|q|^3} | arxiv_extracted | ["f", "q", "m", "p", "N"] | arxiv | arxiv | arxiv:physics.class-ph:2504.01471v1 | cross_domain_amplification | |
e | m | urn:hailstone:chemistry_physics:structural_equation[e7ee346f3c11] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2503.19972v1.eq_442 | e_{\text{max}}^2-e^2=h=l\left(1-\cosθ\right) | arxiv_extracted | ["e", "t", "m", "x"] | arxiv | arxiv | arxiv:physics.class-ph:2503.19972v1 | cross_domain_amplification | |
b | y | urn:hailstone:chemistry_physics:structural_equation[1fb42cd11cd7] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2503.19972v1.eq_443 | \boldsymbolα=\textbf{j}+\textbf{e}, \boldsymbolβ=\textbf{j}-\textbf{e} | arxiv_extracted | ["y", "o", "s", "b", "d", "l"] | arxiv | arxiv | arxiv:physics.class-ph:2503.19972v1 | cross_domain_amplification | |
d | l | urn:hailstone:chemistry_physics:structural_equation[9d30e73163a7] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2503.19972v1.eq_444 | \dot{\boldsymbolα}=2\partial_{\boldsymbolα} φ\times \boldsymbolα | arxiv_extracted | ["t", "o", "b", "d", "l"] | arxiv | arxiv | arxiv:physics.class-ph:2503.19972v1 | cross_domain_amplification | |
d | l | urn:hailstone:chemistry_physics:structural_equation[748d6f62a483] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2503.19972v1.eq_445 | \dot{\boldsymbolβ}=2\partial_{\boldsymbolβ} φ\times \boldsymbolβ | arxiv_extracted | ["t", "o", "b", "d", "l"] | arxiv | arxiv | arxiv:physics.class-ph:2503.19972v1 | cross_domain_amplification | |
b | y | urn:hailstone:chemistry_physics:structural_equation[2c3d7bc8e1fa] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2503.19972v1.eq_446 | \boldsymbolα^2=\boldsymbolβ^2=1 | arxiv_extracted | ["y", "o", "s", "b", "d", "l"] | arxiv | arxiv | arxiv:physics.class-ph:2503.19972v1 | cross_domain_amplification | |
d | x | urn:hailstone:chemistry_physics:structural_equation[03714a48e9c5] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2501.08424v2.eq_447 | \ddot{x} - (1/2x) \dot{x}^2 + 2 ω^2 x - 1/8x = 0 | arxiv_extracted | ["t", "d", "x", "o"] | arxiv | arxiv | arxiv:physics.class-ph:2501.08424v2 | cross_domain_amplification | |
A | p | urn:hailstone:chemistry_physics:structural_equation[c2164e66457e] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2501.04743v1.eq_448 | A \frac{\partial {\bf q}}{\partial t}+\sum_{i=1}^n B_i \frac{\partial {\bf q}}{\partial x_i}=0, | arxiv_extracted | ["f", "a", "p", "A", "r", "c"] | arxiv | arxiv | arxiv:physics.class-ph:2501.04743v1 | cross_domain_amplification | |
h | a | urn:hailstone:chemistry_physics:structural_equation[e264ac0cfa34] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2501.01995v3.eq_449 | [\hat{x},\hat{k}]=i | arxiv_extracted | ["t", "x", "h", "a"] | arxiv | arxiv | arxiv:physics.class-ph:2501.01995v3 | cross_domain_amplification | |
h | a | urn:hailstone:chemistry_physics:structural_equation[38ffa4e68639] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2501.01995v3.eq_450 | [\hat{x},\hat{p}]=i\hbar | arxiv_extracted | ["t", "x", "h", "a"] | arxiv | arxiv | arxiv:physics.class-ph:2501.01995v3 | cross_domain_amplification | |
f | e | urn:hailstone:chemistry_physics:structural_equation[6811bf39fb32] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2412.13221v3.eq_451 | \frac{\text{d}}{\text{d}\text{t}}\oint_{s(t)}\vec{E}\cdot\text{d}\vec{s}(t)=\frac{I^{(s)}_{\text{in}}(t)}{ε_0} | arxiv_extracted | ["f", "e", "a", "t", "r", "c"] | arxiv | arxiv | arxiv:physics.class-ph:2412.13221v3 | cross_domain_amplification | |
d | k | urn:hailstone:chemistry_physics:structural_equation[57c817c72a25] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2412.09100v3.eq_452 | \ddot{x} + k x \dot{x} + ω^2 x + (k^2/9) x^3 = 0 | arxiv_extracted | ["t", "o", "d", "k", "x"] | arxiv | arxiv | arxiv:physics.class-ph:2412.09100v3 | cross_domain_amplification | |
d | J | urn:hailstone:chemistry_physics:structural_equation[893b57fd4a36] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2412.09100v3.eq_453 | \ddot{z} + J(z) \dot{z}^2 + F(z) \dot{z} + G(z) = 0 | arxiv_extracted | ["z", "t", "o", "J", "d"] | arxiv | arxiv | arxiv:physics.class-ph:2412.09100v3 | cross_domain_amplification | |
b | y | urn:hailstone:chemistry_physics:structural_equation[4010e9765416] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2412.10408v1.eq_454 | \boldsymbol{E}(\boldsymbol{r},t)=\nabla\times\boldsymbolΘ(\boldsymbol{r},t) | arxiv_extracted | ["y", "o", "s", "b", "d", "l"] | arxiv | arxiv | arxiv:physics.class-ph:2412.10408v1 | cross_domain_amplification | |
v | i | urn:hailstone:chemistry_physics:structural_equation[f5309d30f30a] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2410.00877v1.eq_455 | \varphi(x) = (\it{x/D})^{4/3} | arxiv_extracted | ["a", "h", "i", "p", "r", "v"] | arxiv | arxiv | arxiv:physics.class-ph:2410.00877v1 | cross_domain_amplification | |
v | i | urn:hailstone:chemistry_physics:structural_equation[187ee5957323] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2410.00877v1.eq_456 | \varphi(x) = (x/D)^{3/2} | arxiv_extracted | ["a", "h", "i", "p", "r", "v"] | arxiv | arxiv | arxiv:physics.class-ph:2410.00877v1 | cross_domain_amplification | |
v | i | urn:hailstone:chemistry_physics:structural_equation[0dac7ab6f832] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2410.00877v1.eq_457 | \varphi(x) = (x/D)^ξ | arxiv_extracted | ["a", "h", "i", "p", "r", "v"] | arxiv | arxiv | arxiv:physics.class-ph:2410.00877v1 | cross_domain_amplification | |
Q | r | urn:hailstone:chemistry_physics:structural_equation[3268215e1f1b] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2408.15773v2.eq_458 | δQ^\text{rev}/T = dS | arxiv_extracted | ["e", "Q", "t", "r", "x"] | arxiv | arxiv | arxiv:physics.class-ph:2408.15773v2 | cross_domain_amplification | |
n | c | urn:hailstone:chemistry_physics:structural_equation[b3e72424eb3d] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2407.09570v2.eq_459 | \nabla \cdot \vec{P}=-ρ, \ \partial \vec{P}/\partial t + c \nabla \times \vec{M} = \vec{J} | arxiv_extracted | ["a", "n", "b", "c", "l"] | arxiv | arxiv | arxiv:physics.class-ph:2407.09570v2 | cross_domain_amplification | |
m | c | urn:hailstone:chemistry_physics:structural_equation[8a4c9c8efd50] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2402.04047v2.eq_460 | {\mc E}=mc^2 | arxiv_extracted | ["E", "c", "m"] | arxiv | arxiv | arxiv:physics.class-ph:2402.04047v2 | cross_domain_amplification | |
T | E | urn:hailstone:chemistry_physics:structural_equation[0055bc233daf] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2308.16159v1.eq_461 | T^{*}=T|E|^{3/2}<80 | arxiv_extracted | ["E", "T"] | arxiv | arxiv | arxiv:physics.class-ph:2308.16159v1 | cross_domain_amplification | |
S | q | urn:hailstone:chemistry_physics:structural_equation[16e7e76350aa] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2308.15369v1.eq_462 | S(q',q'',T)=S(q',Q,t_1)+S(Q,q'',t_2) | arxiv_extracted | ["T", "q", "S"] | arxiv | arxiv | arxiv:physics.class-ph:2308.15369v1 | cross_domain_amplification | |
t_1 | T | urn:hailstone:chemistry_physics:structural_equation[a9de97357c87] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2308.15369v1.eq_463 | t_1+t_2=T | arxiv_extracted | ["t_2", "T", "t_1"] | arxiv | arxiv | arxiv:physics.class-ph:2308.15369v1 | cross_domain_amplification | |
v | i | urn:hailstone:chemistry_physics:structural_equation[053b2d1a4aed] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2307.04810v1.eq_464 | \vec{r}_i,\,i=1,2,3 | arxiv_extracted | ["e", "i", "r", "c", "v"] | arxiv | arxiv | arxiv:physics.class-ph:2307.04810v1 | cross_domain_amplification | |
v | h | urn:hailstone:chemistry_physics:structural_equation[54685b532a69] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2307.04810v1.eq_465 | \vec{f}_i=\hat{r}_i+\vec{e}_i | arxiv_extracted | ["e", "f", "h", "i", "c", "v"] | arxiv | arxiv | arxiv:physics.class-ph:2307.04810v1 | cross_domain_amplification | |
N | n | urn:hailstone:chemistry_physics:structural_equation[1cf753a70fa3] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2306.07897v1.eq_466 | N = 1, n = 2 | arxiv_extracted | ["n", "N"] | arxiv | arxiv | arxiv:physics.class-ph:2306.07897v1 | cross_domain_amplification | |
N | n | urn:hailstone:chemistry_physics:structural_equation[1cf753a70fa3] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2306.07897v1.eq_467 | N = 1, n = 2 | arxiv_extracted | ["n", "N"] | arxiv | arxiv | arxiv:physics.class-ph:2306.07897v1 | cross_domain_amplification | |
J_1 | x | urn:hailstone:chemistry_physics:structural_equation[0726822cb048] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2305.08869v1.eq_468 | J_1(x)=0 | arxiv_extracted | ["x", "J_1"] | arxiv | arxiv | arxiv:physics.class-ph:2305.08869v1 | cross_domain_amplification | |
J_0 | x | urn:hailstone:chemistry_physics:structural_equation[cefaab47906e] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2305.08869v1.eq_469 | J_0(x)=0 | arxiv_extracted | ["J_0", "x"] | arxiv | arxiv | arxiv:physics.class-ph:2305.08869v1 | cross_domain_amplification | |
J_1 | x | urn:hailstone:chemistry_physics:structural_equation[0726822cb048] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2305.08869v1.eq_470 | J_1(x)=0 | arxiv_extracted | ["x", "J_1"] | arxiv | arxiv | arxiv:physics.class-ph:2305.08869v1 | cross_domain_amplification | |
D | i | urn:hailstone:chemistry_physics:structural_equation[a1c3c45770de] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2305.04125v5.eq_471 | \Ddotθ + ω^{2} \sinθ = H\cos{ωt} | arxiv_extracted | ["D", "t", "o", "i", "s", "d"] | arxiv | arxiv | arxiv:physics.class-ph:2305.04125v5 | cross_domain_amplification | |
m | f | urn:hailstone:chemistry_physics:structural_equation[3eddb946f6bc] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2303.18204v1.eq_472 | {\mathbf q} = [{\mathbf q}_1, {\mathbf q}_2, \dots, {\mathbf q}_N] \in {\mathbb R}^{3N} | arxiv_extracted | ["f", "a", "t", "m", "h", "b"] | arxiv | arxiv | arxiv:physics.class-ph:2303.18204v1 | cross_domain_amplification | |
r_{ij} | b | urn:hailstone:chemistry_physics:structural_equation[7aaabf8d6184] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2303.18204v1.eq_473 | r_{ij} = |{\mathbf q}_i - {\mathbf q}_j | | arxiv_extracted | ["a", "r_{ij}", "t", "m", "h", "b"] | arxiv | arxiv | arxiv:physics.class-ph:2303.18204v1 | cross_domain_amplification | |
m | f | urn:hailstone:chemistry_physics:structural_equation[6e1a7dad139b] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2302.10224v1.eq_474 | ω\mathbf{A}_{0}=\mathbf{k}φ_{0} | arxiv_extracted | ["f", "a", "t", "m", "h", "b"] | arxiv | arxiv | arxiv:physics.class-ph:2302.10224v1 | cross_domain_amplification | |
c | v | urn:hailstone:chemistry_physics:structural_equation[c5f1a14d6022] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2302.10224v1.eq_475 | ω^{2}=c^{2}\left\vert \mathbf{k}\right\vert^{2} | arxiv_extracted | ["e", "f", "t", "c", "l", "v"] | arxiv | arxiv | arxiv:physics.class-ph:2302.10224v1 | cross_domain_amplification | |
c | r | urn:hailstone:chemistry_physics:structural_equation[e76d406e2050] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2301.10469v1.eq_476 | {\cal L}=1+\frac{n}{2} | arxiv_extracted | ["f", "a", "L", "r", "c", "l"] | arxiv | arxiv | arxiv:physics.class-ph:2301.10469v1 | cross_domain_amplification | |
c | L | urn:hailstone:chemistry_physics:structural_equation[439483270181] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2301.10469v1.eq_477 | {\cal L}=2,3 | arxiv_extracted | ["L", "c", "l", "a"] | arxiv | arxiv | arxiv:physics.class-ph:2301.10469v1 | cross_domain_amplification | |
R | s | urn:hailstone:chemistry_physics:structural_equation[bf2a9446d712] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2301.05360v2.eq_478 | Re[s]=1/2 | arxiv_extracted | ["e", "s", "R"] | arxiv | arxiv | arxiv:physics.class-ph:2301.05360v2 | cross_domain_amplification | |
a | a | urn:hailstone:chemistry_physics:structural_equation[4382fdb265a2] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2212.07005v1.eq_479 | a(x + y) = ax + ay | arxiv_extracted | ["y", "a", "x"] | arxiv | arxiv | arxiv:physics.class-ph:2212.07005v1 | cross_domain_amplification | |
o | t | urn:hailstone:chemistry_physics:structural_equation[d7455048f961] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2211.13213v2.eq_480 | \operatorname{curl} \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t} | arxiv_extracted | ["e", "a", "t", "o", "p", "r"] | arxiv | arxiv | arxiv:physics.class-ph:2211.13213v2 | cross_domain_amplification | |
o | t | urn:hailstone:chemistry_physics:structural_equation[06a28b0b1417] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2211.13213v2.eq_481 | \operatorname{curl} \mathbf{H} = \frac{\partial \mathbf{D}}{\partial t} + \mathbf{j} | arxiv_extracted | ["e", "a", "t", "o", "p", "r"] | arxiv | arxiv | arxiv:physics.class-ph:2211.13213v2 | cross_domain_amplification | |
o | t | urn:hailstone:chemistry_physics:structural_equation[417fd95441fe] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2211.13213v2.eq_482 | \operatorname{div} \mathbf{D} = \varrho | arxiv_extracted | ["e", "a", "t", "o", "p", "r"] | arxiv | arxiv | arxiv:physics.class-ph:2211.13213v2 | cross_domain_amplification | |
o | t | urn:hailstone:chemistry_physics:structural_equation[712f6ba86577] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2211.13213v2.eq_483 | \operatorname{div} \mathbf{B} = 0 | arxiv_extracted | ["e", "a", "t", "o", "p", "r"] | arxiv | arxiv | arxiv:physics.class-ph:2211.13213v2 | cross_domain_amplification | |
m | f | urn:hailstone:chemistry_physics:structural_equation[55e8ea8f21a9] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2211.13213v2.eq_484 | \mathbf{D} = \varepsilon_0 \mathbf{E} | arxiv_extracted | ["f", "a", "t", "m", "h", "b"] | arxiv | arxiv | arxiv:physics.class-ph:2211.13213v2 | cross_domain_amplification | |
m | f | urn:hailstone:chemistry_physics:structural_equation[6be6fb27d5d7] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2211.13213v2.eq_485 | \mathbf{B} = μ_0 \mathbf{H} | arxiv_extracted | ["f", "a", "t", "m", "h", "b"] | arxiv | arxiv | arxiv:physics.class-ph:2211.13213v2 | cross_domain_amplification | |
t | P | urn:hailstone:chemistry_physics:structural_equation[56d2b2193f40] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2210.05601v1.eq_486 | \tilde{P} = \boldsymbol{\tilde{p}} -\,\frac{1}{c}\,\boldsymbol{\tilde{M}} | arxiv_extracted | ["e", "t", "P", "i", "d", "l"] | arxiv | arxiv | arxiv:physics.class-ph:2210.05601v1 | cross_domain_amplification | |
t | J | urn:hailstone:chemistry_physics:structural_equation[f14f3ca3795b] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2210.05601v1.eq_487 | \tilde{J} = J -\,c\,\nabla\cdot\tilde{P} | arxiv_extracted | ["e", "t", "i", "J", "d", "l"] | arxiv | arxiv | arxiv:physics.class-ph:2210.05601v1 | cross_domain_amplification | |
d | e | urn:hailstone:chemistry_physics:structural_equation[3d2a9a493663] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2210.05601v1.eq_488 | \dot{T}\left(\dot{\nabla}\right) = \frac{1}{c}\,J \cdot F = f | arxiv_extracted | ["e", "t", "d", "o", "T", "l"] | arxiv | arxiv | arxiv:physics.class-ph:2210.05601v1 | cross_domain_amplification | |
v | s | urn:hailstone:chemistry_physics:structural_equation[be1899b61f6b] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2207.11508v1.eq_489 | \varepsilon(z) = 1 + αχ(z) | arxiv_extracted | ["e", "a", "p", "r", "s", "v"] | arxiv | arxiv | arxiv:physics.class-ph:2207.11508v1 | cross_domain_amplification | |
m | a | urn:hailstone:chemistry_physics:structural_equation[6729771ae87e] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2206.12996v2.eq_490 | \mathcal{N}=2 | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:physics.class-ph:2206.12996v2 | cross_domain_amplification | |
m | f | urn:hailstone:chemistry_physics:structural_equation[d6cfa03f8704] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2206.00764v3.eq_491 | \mathbf{V}= \sqrt{\mathbf{B}} | arxiv_extracted | ["f", "a", "t", "m", "h", "b"] | arxiv | arxiv | arxiv:physics.class-ph:2206.00764v3 | cross_domain_amplification | |
m | f | urn:hailstone:chemistry_physics:structural_equation[520707caa15a] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2206.00764v3.eq_492 | \mathbf{E}_{\text{Bell}} = \mathbf{V}-\mathbf{I} | arxiv_extracted | ["f", "a", "t", "m", "h", "b"] | arxiv | arxiv | arxiv:physics.class-ph:2206.00764v3 | cross_domain_amplification | |
r | T | urn:hailstone:chemistry_physics:structural_equation[3126280665e6] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2205.01832v1.eq_493 | ω_{\rm R} = 2π/T | arxiv_extracted | ["T", "m", "r", "R"] | arxiv | arxiv | arxiv:physics.class-ph:2205.01832v1 | cross_domain_amplification | |
b | A | urn:hailstone:chemistry_physics:structural_equation[2edeb438a643] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2204.03952v1.eq_494 | {\bf f}^{\rm Aterm} = [(\varepsilonμ-1)/c^2] \partial/\partial t ({\bf E}\times {\bf H}) | arxiv_extracted | ["f", "m", "A", "r", "b"] | arxiv | arxiv | arxiv:physics.class-ph:2204.03952v1 | cross_domain_amplification | |
v | e | urn:hailstone:chemistry_physics:structural_equation[fedfa7dfc248] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2203.05150v1.eq_495 | {\vec τ}=d{\vec L} / dt | arxiv_extracted | ["e", "c", "d", "v"] | arxiv | arxiv | arxiv:physics.class-ph:2203.05150v1 | cross_domain_amplification | |
v | t | urn:hailstone:chemistry_physics:structural_equation[f8b0cb615f6f] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2201.10856v4.eq_496 | \vec{\mathcal{E}}(x)=\vec{E}(Λ^{-1}x) | arxiv_extracted | ["e", "a", "t", "m", "c", "v"] | arxiv | arxiv | arxiv:physics.class-ph:2201.10856v4 | cross_domain_amplification | |
v | t | urn:hailstone:chemistry_physics:structural_equation[0cb8698b7934] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2201.10856v4.eq_497 | \vec{\mathcal{B}}(x)=\vec{B}(Λ^{-1}x) | arxiv_extracted | ["e", "a", "t", "m", "c", "v"] | arxiv | arxiv | arxiv:physics.class-ph:2201.10856v4 | cross_domain_amplification | |
R | R | urn:hailstone:chemistry_physics:structural_equation[aa26bdcca646] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2108.05070v1.eq_498 | R_\pm=\pm R | arxiv_extracted | ["p", "m", "R"] | arxiv | arxiv | arxiv:physics.class-ph:2108.05070v1 | cross_domain_amplification | |
T_c | m | urn:hailstone:chemistry_physics:structural_equation[96ca8f6af83b] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2108.02843v1.eq_499 | T_c^*=403 \pm 1 | arxiv_extracted | ["p", "m", "T_c"] | arxiv | arxiv | arxiv:physics.class-ph:2108.02843v1 | cross_domain_amplification | |
T_o | m | urn:hailstone:chemistry_physics:structural_equation[83ec0cf3b684] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2108.02843v1.eq_500 | T_o^*=373 \pm 1 | arxiv_extracted | ["p", "m", "T_o"] | arxiv | arxiv | arxiv:physics.class-ph:2108.02843v1 | cross_domain_amplification | |
X_t | N | urn:hailstone:chemistry_physics:structural_equation[4b97f2c4261c] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2103.15562v1.eq_501 | X_t^N = \sum_{i=1}^N ω_i Y_t^{x_i} | arxiv_extracted | ["m_{i", "u", "X_t", "s", "N"] | arxiv | arxiv | arxiv:physics.class-ph:2103.15562v1 | cross_domain_amplification | |
h | r | urn:hailstone:chemistry_physics:structural_equation[e41f6edde105] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2102.10857v1.eq_502 | \hbar = 1 | arxiv_extracted | ["b", "r", "h", "a"] | arxiv | arxiv | arxiv:physics.class-ph:2102.10857v1 | cross_domain_amplification | |
v | b | urn:hailstone:chemistry_physics:structural_equation[718e7bd58ffd] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2101.10118v1.eq_503 | \vec{\nabla}\cdot\vec{B}=0 | arxiv_extracted | ["e", "a", "n", "b", "c", "v"] | arxiv | arxiv | arxiv:physics.class-ph:2101.10118v1 | cross_domain_amplification | |
E_{vh} | C_VT | urn:hailstone:chemistry_physics:structural_equation[3dc052997e29] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2012.14787v1.eq_504 | E_{vh}=C_VT^2 /2 | arxiv_extracted | ["C_VT", "E_{vh}"] | arxiv | arxiv | arxiv:physics.class-ph:2012.14787v1 | cross_domain_amplification | |
U | t | urn:hailstone:chemistry_physics:structural_equation[b688c4a1ccd6] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2011.03412v1.eq_505 | . Using the height H of the fluid layer, we introduce the non-dimensional Biot number Bi* = | arxiv_extracted | ["g", "t", "n", "i", "s", "U"] | arxiv | arxiv | arxiv:physics.class-ph:2011.03412v1 | cross_domain_amplification | |
H | i | urn:hailstone:chemistry_physics:structural_equation[a78b51f1b710] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2011.03412v1.eq_506 | H. Varying Bi* allows us to transition from fixed temperature for Bi* = + | arxiv_extracted | ["V", "a", "H", "y", "i", "r"] | arxiv | arxiv | arxiv:physics.class-ph:2011.03412v1 | cross_domain_amplification | |
t | g | urn:hailstone:chemistry_physics:structural_equation[e74ff71b529a] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2010.15514v1.eq_507 | t(=τ_1+τ_2=τ_3=3/\sqrt{2g})=0.67 | arxiv_extracted | ["g", "q", "t", "r", "s"] | arxiv | arxiv | arxiv:physics.class-ph:2010.15514v1 | cross_domain_amplification | |
t | g | urn:hailstone:chemistry_physics:structural_equation[fc2ecfdeb8ea] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2010.15514v1.eq_508 | t(=τ_4=2/\sqrt{g})=0.63 | arxiv_extracted | ["g", "q", "t", "r", "s"] | arxiv | arxiv | arxiv:physics.class-ph:2010.15514v1 | cross_domain_amplification | |
t | B | urn:hailstone:chemistry_physics:structural_equation[a3d0a82c9ede] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2010.15514v1.eq_509 | t=τ_B=0.58 | arxiv_extracted | ["t", "B"] | arxiv | arxiv | arxiv:physics.class-ph:2010.15514v1 | cross_domain_amplification | |
i | c | urn:hailstone:chemistry_physics:structural_equation[f7d9d2ea008e] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2010.15514v1.eq_510 | ν\in (0, ν_c=0.09653) | arxiv_extracted | ["n", "c", "i"] | arxiv | arxiv | arxiv:physics.class-ph:2010.15514v1 | cross_domain_amplification | |
s | B | urn:hailstone:chemistry_physics:structural_equation[38ed572b9a91] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2010.15514v1.eq_511 | =1/\sqrt{2g}=τ_2) < τ_B | arxiv_extracted | ["g", "q", "B", "t", "r", "s"] | arxiv | arxiv | arxiv:physics.class-ph:2010.15514v1 | cross_domain_amplification | |
U_{rad} | t | urn:hailstone:chemistry_physics:structural_equation[e1445f1d13e5] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2009.05844v1.eq_512 | U_{rad}=const\timesω, | arxiv_extracted | ["s", "t", "o", "U_{rad}", "n", "c"] | arxiv | arxiv | arxiv:physics.class-ph:2009.05844v1 | cross_domain_amplification | |
r_{ij} | f | urn:hailstone:chemistry_physics:structural_equation[7108a74214b4] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2007.11959v5.eq_513 | r_{ij}=\mid {\bf r}_i - {\bf r}_j\mid | arxiv_extracted | ["f", "r_{ij}", "m", "i", "b", "d"] | arxiv | arxiv | arxiv:physics.class-ph:2007.11959v5 | cross_domain_amplification | |
i | r_{ij} | urn:hailstone:chemistry_physics:structural_equation[4e109b5f3eb1] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2007.11959v5.eq_514 | ρ_{ij}=r_{ij}^2 | arxiv_extracted | ["j", "r_{ij}", "i"] | arxiv | arxiv | arxiv:physics.class-ph:2007.11959v5 | cross_domain_amplification | |
b | B | urn:hailstone:chemistry_physics:structural_equation[b667fd6669b9] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2006.03162v2.eq_515 | {\bf A}=Γ_1{\bf B}Γ_1 | arxiv_extracted | ["f", "b", "A", "B"] | arxiv | arxiv | arxiv:physics.class-ph:2006.03162v2 | cross_domain_amplification | |
m_a | c | urn:hailstone:chemistry_physics:structural_equation[0a9d7094411f] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2006.03455v1.eq_516 | m_a/a=m_b/b=m_c/c=ρ | arxiv_extracted | ["a", "m_b", "m_c", "m_a", "b", "c"] | arxiv | arxiv | arxiv:physics.class-ph:2006.03455v1 | cross_domain_amplification | |
H_{0k} | p_{0k} | urn:hailstone:chemistry_physics:structural_equation[4c3f4393700a] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2006.00288v1.eq_517 | {H_{0k}} = n{p_{0k}}ω | arxiv_extracted | ["n", "H_{0k}", "p_{0k}"] | arxiv | arxiv | arxiv:physics.class-ph:2006.00288v1 | cross_domain_amplification | |
f | r | urn:hailstone:chemistry_physics:structural_equation[1f89084d1880] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2001.10375v2.eq_518 | \frac{d^2r(t)}{dt^2} = r^a | arxiv_extracted | ["f", "a", "d", "r", "c"] | arxiv | arxiv | arxiv:physics.class-ph:2001.10375v2 | cross_domain_amplification | |
r | t | urn:hailstone:chemistry_physics:structural_equation[7997b1af68e2] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2001.10375v2.eq_519 | r(t=0) =0 | arxiv_extracted | ["t", "r"] | arxiv | arxiv | arxiv:physics.class-ph:2001.10375v2 | cross_domain_amplification | |
f | r | urn:hailstone:chemistry_physics:structural_equation[038938f566c7] | 1 | structural_equation | 2 | arxiv.physics.class-ph.2001.10375v2.eq_520 | \frac{dr(t)}{dt}\mid_{r(t=0)} =0 | arxiv_extracted | ["f", "a", "d", "r", "c"] | arxiv | arxiv | arxiv:physics.class-ph:2001.10375v2 | cross_domain_amplification |
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