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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
X | k | urn:hailstone:economics:structural_equation[12e545522d57] | 1 | structural_equation | 5 | arxiv.q-fin.MF.2410.15824v2.eq_1721 | X\stackrel{d}{=}AX+B,\,\, X\perp\!\!\!\perp (A, B) | arxiv_extracted | ["a", "t", "X", "s", "c", "k"] | arxiv | arxiv | arxiv:q-fin.MF:2410.15824v2 | cross_domain_amplification | |
T | n | urn:hailstone:economics:structural_equation[bb184e9bcfd3] | 1 | structural_equation | 5 | arxiv.q-fin.MF.2406.09488v2.eq_1722 | ). The central equation presented in this analysis is: \begin{equation*} F_a(0;T_s,T_e)=\frac{1}{τ(T_s,T_e)}\sum_{k=1}^K τ_k \mathcal{A}_k F_k\,, \end{equation*} with | arxiv_extracted | ["e", "h", "c", "n", "T"] | arxiv | arxiv | arxiv:q-fin.MF:2406.09488v2 | cross_domain_amplification | |
t | m | urn:hailstone:economics:structural_equation[5c235bffa5a2] | 1 | structural_equation | 5 | arxiv.q-fin.MF.2406.09488v2.eq_1723 | \{\tilde{\mathcal{A}}_k\}_{k=1}^K | arxiv_extracted | ["e", "t", "m", "i", "d", "l"] | arxiv | arxiv | arxiv:q-fin.MF:2406.09488v2 | cross_domain_amplification | |
X_t | t | urn:hailstone:economics:structural_equation[ede5ef3e0edf] | 1 | structural_equation | 5 | arxiv.q-fin.MF.2403.13791v1.eq_1724 | X_t =\int_0^t Ψ_{t,s}dS_s, t \geq0, | arxiv_extracted | ["t_0", "t", "i", "X_t", "n"] | arxiv | arxiv | arxiv:q-fin.MF:2403.13791v1 | cross_domain_amplification | |
d | t | urn:hailstone:economics:structural_equation[65dc8bc1722b] | 1 | structural_equation | 5 | arxiv.q-fin.MF.2402.07503v1.eq_1725 | dR(r)=F(R(t))dt+\sum_{i=1}^{d}G_i(R(t-))dZ_i(t), \quad R(0)=r_0\geq 0, \quad t>0, \quad (1) | arxiv_extracted | ["F", "t", "R", "r", "d"] | arxiv | arxiv | arxiv:q-fin.MF:2402.07503v1 | cross_domain_amplification | |
d | Z_t | urn:hailstone:economics:structural_equation[dc2e1cda3237] | 1 | structural_equation | 5 | arxiv.q-fin.MF.2312.06690v1.eq_1726 | -dY_t = f(t,Y_t,Z_t)dt - Z_t^*dW_t;\ Y_T = ξ | arxiv_extracted | ["f", "t", "Y_t", "Z_t", "d"] | arxiv | arxiv | arxiv:q-fin.MF:2312.06690v1 | cross_domain_amplification | |
c | p | urn:hailstone:economics:structural_equation[1cfdb557513e] | 1 | structural_equation | 5 | arxiv.q-fin.MF.2309.15044v1.eq_1727 | {\cal S}(T) \propto a(H) T^{b\cdot (H-1/2)}, \, b = const | arxiv_extracted | ["a", "T", "S", "p", "c", "l"] | arxiv | arxiv | arxiv:q-fin.MF:2309.15044v1 | cross_domain_amplification | |
T | P_{0T} | urn:hailstone:economics:structural_equation[b990ae06f41b] | 1 | structural_equation | 5 | arxiv.q-fin.MF.2305.10239v2.eq_1728 | Π_{0T}(\hat X_T) = P_{0T}\,{\rm tr} ( \hat q \hat X_T) | arxiv_extracted | ["a", "t", "h", "P_{0T}", "T", "X_T"] | arxiv | arxiv | arxiv:q-fin.MF:2305.10239v2 | cross_domain_amplification | |
l | e | urn:hailstone:economics:structural_equation[d46189aa958c] | 1 | structural_equation | 5 | arxiv.q-fin.MF.2305.10239v2.eq_1729 | \langle \bar ξ| \hat p | ξ\rangle = 0 | arxiv_extracted | ["e", "g", "a", "n", "l"] | arxiv | arxiv | arxiv:q-fin.MF:2305.10239v2 | cross_domain_amplification | |
l | e | urn:hailstone:economics:structural_equation[05bdb908c3c4] | 1 | structural_equation | 5 | arxiv.q-fin.MF.2305.10239v2.eq_1730 | \langle \bar ξ| \hat q | ξ\rangle = 0 | arxiv_extracted | ["e", "g", "a", "n", "l"] | arxiv | arxiv | arxiv:q-fin.MF:2305.10239v2 | cross_domain_amplification | |
d | t | urn:hailstone:economics:structural_equation[00edecbd9c7b] | 1 | structural_equation | 5 | arxiv.q-fin.MF.2303.08477v1.eq_1731 | dR(t)=F(R(t))dt+\sum_{i=1}^{d}G_i(R(t-))dZ_i(t), \quad R(0)=x\geq 0, \quad t>0, | arxiv_extracted | ["t", "d", "R", "F"] | arxiv | arxiv | arxiv:q-fin.MF:2303.08477v1 | cross_domain_amplification | |
d | e | urn:hailstone:economics:structural_equation[92a17bb62d04] | 1 | structural_equation | 5 | arxiv.q-fin.MF.2207.01235v3.eq_1732 | define the cost functionals \begin{align*} C(μ,ρ):=\sup_{π\in Π(μ,ρ)} \int \langle x,y\rangle\, π(dx,dy),\quad C(ν,ρ):=\sup_{π\in Π(ν,ρ)} \int \langle x,y\rangle\, π(dx,dy), \end{align*} where | arxiv_extracted | ["e", "f", "i", "n", "d"] | arxiv | arxiv | arxiv:q-fin.MF:2207.01235v3 | cross_domain_amplification | |
l | m | urn:hailstone:economics:structural_equation[a12aef340fa4] | 1 | structural_equation | 5 | arxiv.q-fin.MF.2203.06865v4.eq_1733 | σ_{loc}(t,S_t)^2 = \mathbb{E}[σ_t^2|S_t] | arxiv_extracted | ["S_t", "t", "m", "o", "c", "l"] | arxiv | arxiv | arxiv:q-fin.MF:2203.06865v4 | cross_domain_amplification | |
V | i | urn:hailstone:economics:structural_equation[ea56e3d182a8] | 1 | structural_equation | 5 | arxiv.q-fin.MF.2107.12439v2.eq_1734 | V(T) = \int_{0}^\infty e^{-\frac{u^2}{2T}} g(u) du | arxiv_extracted | ["V", "t_{0}", "i", "n", "T"] | arxiv | arxiv | arxiv:q-fin.MF:2107.12439v2 | cross_domain_amplification | |
l | a | urn:hailstone:economics:structural_equation[2f35360c87a6] | 1 | structural_equation | 5 | arxiv.q-fin.MF.2107.08109v2.eq_1735 | \lim_n\|X\mathbf{1}_{\{X\leq -n\}}\|=0 | arxiv_extracted | ["a", "m_n", "m", "i", "X", "l"] | arxiv | arxiv | arxiv:q-fin.MF:2107.08109v2 | cross_domain_amplification | |
m | m | urn:hailstone:economics:structural_equation[eebe84a13710] | 1 | structural_equation | 5 | arxiv.q-fin.MF.2107.08109v2.eq_1736 | \mathrm{d}(\mathcal{CL}(X),\mathcal{X}_a) =0 | arxiv_extracted | ["a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:q-fin.MF:2107.08109v2 | cross_domain_amplification | |
m | a | urn:hailstone:economics:structural_equation[8b31c1a0b651] | 1 | structural_equation | 5 | arxiv.q-fin.MF.2107.08109v2.eq_1737 | \mathcal{X}_a=\{X\in\mathcal{X}:\lim_n \|X\mathbf{1}_{ \{|X|\geq n\} }\| =0\} | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:q-fin.MF:2107.08109v2 | cross_domain_amplification | |
A_N | T | urn:hailstone:economics:structural_equation[81fa4ae2c300] | 1 | structural_equation | 5 | arxiv.q-fin.MF.2104.10187v1.eq_1738 | A_N(T) = 0 | arxiv_extracted | ["A_N", "T"] | arxiv | arxiv | arxiv:q-fin.MF:2104.10187v1 | cross_domain_amplification | |
r | A_N | urn:hailstone:economics:structural_equation[380bc90751e1] | 1 | structural_equation | 5 | arxiv.q-fin.MF.2104.10187v1.eq_1739 | r(τ) = r + (1/τ) A_N(τ) | arxiv_extracted | ["A_N", "r"] | arxiv | arxiv | arxiv:q-fin.MF:2104.10187v1 | cross_domain_amplification | |
t | K | urn:hailstone:economics:structural_equation[70fcd0b0a7ea] | 1 | structural_equation | 5 | arxiv.q-fin.MF.2104.10187v1.eq_1740 | \tilde{K} = K e^{-A_N(T)} | arxiv_extracted | ["e", "t", "i", "K", "d", "l"] | arxiv | arxiv | arxiv:q-fin.MF:2104.10187v1 | cross_domain_amplification | |
S_t | s | urn:hailstone:economics:structural_equation[a6e3f4075b4d] | 1 | structural_equation | 5 | arxiv.q-fin.MF.2103.02948v1.eq_1741 | S_t = s e^{ζt + σB_t - \sum_{i=1}^{N_t} Y_i} | arxiv_extracted | ["e", "S_t", "t", "B_t", "s"] | arxiv | arxiv | arxiv:q-fin.MF:2103.02948v1 | cross_domain_amplification | |
u | m | urn:hailstone:economics:structural_equation[20d2931ac3fd] | 1 | structural_equation | 5 | arxiv.q-fin.MF.2012.10847v1.eq_1742 | u(x) = \int_{\mathbb{I}} \frac{x^{1-γ}}{1-γ}ν(\mathrm{d} γ) | arxiv_extracted | ["t", "m", "i", "u", "n", "x"] | arxiv | arxiv | arxiv:q-fin.MF:2012.10847v1 | cross_domain_amplification | |
X | m | urn:hailstone:economics:structural_equation[30ca771ad2bc] | 1 | structural_equation | 5 | arxiv.q-fin.MF.2010.14646v3.eq_1743 | X(t) = X(0) + B(t) - α\mathbb{P}(τ\le t) | arxiv_extracted | ["X", "t", "m", "B"] | arxiv | arxiv | arxiv:q-fin.MF:2010.14646v3 | cross_domain_amplification | |
X | t | urn:hailstone:economics:structural_equation[6155ee68f3c3] | 1 | structural_equation | 5 | arxiv.q-fin.MF.2010.14646v3.eq_1744 | X(t) = X(0) + βt + B(t) + α\log \mathbb{P}(τ> t) | arxiv_extracted | ["X", "t", "B"] | arxiv | arxiv | arxiv:q-fin.MF:2010.14646v3 | cross_domain_amplification | |
X | r | urn:hailstone:economics:structural_equation[d7d35f045ad9] | 1 | structural_equation | 5 | arxiv.q-fin.MF.2008.01385v1.eq_1745 | X^{H}(x) = Γ(H)^{\frac{1}{2}} \left( B^{H}(x) - \int_{\mathbb{R}^{d}} B^{H}(u) ψ(u, x)du\right), | arxiv_extracted | ["f", "H", "X", "r", "x"] | arxiv | arxiv | arxiv:q-fin.MF:2008.01385v1 | cross_domain_amplification | |
M | X | urn:hailstone:economics:structural_equation[1bdb1ddde2e1] | 1 | structural_equation | 5 | arxiv.q-fin.MF.2008.01385v1.eq_1746 | M^{H}_γ(dx) = e^{γX^{H}(x) - \frac{γ^{2}}{2} E[X^{H}(x)^{2}] }dx, | arxiv_extracted | ["e", "M", "H", "X", "d", "x"] | arxiv | arxiv | arxiv:q-fin.MF:2008.01385v1 | cross_domain_amplification | |
V | s | urn:hailstone:economics:structural_equation[d871406b03ca] | 1 | structural_equation | 5 | arxiv.q-fin.MF.2007.09419v2.eq_1747 | V^ω_{\rm A}(s) = \sup_{τ\in\mathcal{T}} \mathbb{E}_{s}[e^{-\int_0^τω(S_w) dw} g(S_τ)], | arxiv_extracted | ["V", "m", "A", "r", "s"] | arxiv | arxiv | arxiv:q-fin.MF:2007.09419v2 | cross_domain_amplification | |
S_{T | H_T | urn:hailstone:economics:structural_equation[efa6be2e8572] | 1 | structural_equation | 5 | arxiv.q-fin.MF.2003.07967v2.eq_1748 | S_{T^-} = H_T | arxiv_extracted | ["S_{T", "H_T"] | arxiv | arxiv | arxiv:q-fin.MF:2003.07967v2 | cross_domain_amplification | |
m | a | urn:hailstone:economics:structural_equation[21b746e9645a] | 1 | structural_equation | 5 | arxiv.q-fin.MF.2002.06253v1.eq_1749 | \mathcal{L} = \wp\{1,\dots,m\} | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:q-fin.MF:2002.06253v1 | cross_domain_amplification | |
A | t | urn:hailstone:economics:structural_equation[4b8448255858] | 1 | structural_equation | 5 | arxiv.q-fin.MF.1911.12944v2.eq_1750 | σ_{A}(T):=\sqrt{\frac{1}{T^3}\int_0^Tσ^2(t,S_0)(T-t)^2\,dt}\,, | arxiv_extracted | ["q", "t", "A", "r", "s", "T"] | arxiv | arxiv | arxiv:q-fin.MF:1911.12944v2 | cross_domain_amplification | |
b | x | urn:hailstone:economics:structural_equation[388728010db4] | 1 | structural_equation | 5 | arxiv.q-fin.MF.1906.02216v2.eq_1751 | b^*=c^*=Σ^{-1}(μ-r\textbf{1}) | arxiv_extracted | ["e", "t", "r", "b", "c", "x"] | arxiv | arxiv | arxiv:q-fin.MF:1906.02216v2 | cross_domain_amplification | |
r_L | r | urn:hailstone:economics:structural_equation[1a80deaf5905] | 1 | structural_equation | 5 | arxiv.q-fin.MF.1904.06628v2.eq_1752 | r_L^*=(3/4)r+(1/4)(ν-σ^2/2) | arxiv_extracted | ["r_L", "r"] | arxiv | arxiv | arxiv:q-fin.MF:1904.06628v2 | cross_domain_amplification | |
c | y | urn:hailstone:economics:structural_equation[c70e229a42bd] | 1 | structural_equation | 5 | arxiv.q-fin.MF.1812.00032v4.eq_1753 | c(x,y)= Ψ(x-y) | arxiv_extracted | ["c", "y", "x"] | arxiv | arxiv | arxiv:q-fin.MF:1812.00032v4 | cross_domain_amplification | |
t | a | urn:hailstone:economics:structural_equation[36ee84435215] | 1 | structural_equation | 5 | arxiv.q-fin.MF.1811.07220v2.eq_1754 | ψ(α) = t^{-1}\log \mathbb E(\rm e^{αξ_t}) | arxiv_extracted | ["g", "a", "t", "m", "o", "l"] | arxiv | arxiv | arxiv:q-fin.MF:1811.07220v2 | cross_domain_amplification | |
C | r | urn:hailstone:economics:structural_equation[f4c20aa22c25] | 1 | structural_equation | 5 | arxiv.q-fin.MF.1810.02485v2.eq_1755 | C(S,t)=\sqrt{T/t}\cdot\,\exp\{rt+σ^2b(S,t)^2\cdot t/2\} | arxiv_extracted | ["q", "t", "S", "r", "s", "C"] | arxiv | arxiv | arxiv:q-fin.MF:1810.02485v2 | cross_domain_amplification | |
C | n | urn:hailstone:economics:structural_equation[85cd481aa3a3] | 1 | structural_equation | 5 | arxiv.q-fin.MF.1810.02485v2.eq_1756 | C(S,t)=(T/t)^{n/2}\exp(rt+b'Σb\cdot t/2) | arxiv_extracted | ["t", "S", "n", "T", "C"] | arxiv | arxiv | arxiv:q-fin.MF:1810.02485v2 | cross_domain_amplification | |
m | l | urn:hailstone:economics:structural_equation[11ceef7372c9] | 1 | structural_equation | 5 | arxiv.q-fin.MF.1801.03720v1.eq_1757 | modelled by \begin{align}\label{eq0.1} \begin{cases} dX(t)&=π(t)X(t)[α(t)dt+β(t)dB(t)]; \quad t\in[0, T] X(0)&=x_0>0, \end{cases} \end{align} where | arxiv_extracted | ["e", "m", "o", "d", "l"] | arxiv | arxiv | arxiv:q-fin.MF:1801.03720v1 | cross_domain_amplification | |
s | e | urn:hailstone:economics:structural_equation[a7a8bd035b44] | 1 | structural_equation | 5 | arxiv.q-fin.MF.1801.03720v1.eq_1758 | \sup_πJ(π)= J(π^{*}), \text {where } J(π)= \mathbb{E}[\log(X^π(T))]. | arxiv_extracted | ["e", "t", "u", "J", "s", "p_\u03c0J"] | arxiv | arxiv | arxiv:q-fin.MF:1801.03720v1 | cross_domain_amplification | |
i | r | urn:hailstone:economics:structural_equation[bc3045cb3570] | 1 | structural_equation | 5 | arxiv.q-fin.MF.1801.03720v1.eq_1759 | \int_0^T\frac{1}{\varepsilon_t}dt=\infty, | arxiv_extracted | ["f", "t_0", "i", "r", "n", "T"] | arxiv | arxiv | arxiv:q-fin.MF:1801.03720v1 | cross_domain_amplification | |
l | e | urn:hailstone:economics:structural_equation[322237cc33b6] | 1 | structural_equation | 5 | arxiv.q-fin.MF.1801.03720v1.eq_1760 | \label{eq0.2} \mathbb{H}=\{\mathcal{H}_t\}_{t\in[0.T]},\quad \mathcal{H}_t=\mathcal{F}_t\veeσ(B(t+ε_t+r),0\leq r \leq ε_0-t-ε_t), \forall t\in [0,T]. | arxiv_extracted | ["e", "b", "l", "a"] | arxiv | arxiv | arxiv:q-fin.MF:1801.03720v1 | cross_domain_amplification | |
l | e | urn:hailstone:economics:structural_equation[84503d319ba3] | 1 | structural_equation | 5 | arxiv.q-fin.MF.1801.03720v1.eq_1761 | \label{eq0.1} \begin{cases} dX(t)&=π(t)X(t)[α(t)dt+β(t)dB(t)]; \quad t\in[0, T] X(0)&=x_0>0, \end{cases} | arxiv_extracted | ["e", "b", "l", "a"] | arxiv | arxiv | arxiv:q-fin.MF:1801.03720v1 | cross_domain_amplification | |
S | b | urn:hailstone:economics:structural_equation[9d5c4806734d] | 1 | structural_equation | 5 | arxiv.q-fin.MF.1709.07329v2.eq_1762 | S^{\mathbb{Q}}_t=\mathbb{E}^{\mathbb{Q}}\left[ψ\lvert\mathcal{F}_{t}\right] | arxiv_extracted | ["a", "t", "m", "h", "S", "b"] | arxiv | arxiv | arxiv:q-fin.MF:1709.07329v2 | cross_domain_amplification | |
S_t | h | urn:hailstone:economics:structural_equation[af43cb18401b] | 1 | structural_equation | 5 | arxiv.q-fin.MF.1709.07329v2.eq_1763 | S_t(x) = \mathbb{E}^{\mathbb{Q}(x)}\left[ψ(x)\lvert\mathcal{F}_{t}\right] | arxiv_extracted | ["a", "S_t", "t", "m", "h", "x"] | arxiv | arxiv | arxiv:q-fin.MF:1709.07329v2 | cross_domain_amplification | |
d | W_t | urn:hailstone:economics:structural_equation[d225167e1afc] | 1 | structural_equation | 5 | arxiv.q-fin.MF.1707.00899v1.eq_1764 | dS_t = σ_t S_t dW_t,dσ_t = ωσ_t dZ_t | arxiv_extracted | ["t", "d", "S_t", "W_t"] | arxiv | arxiv | arxiv:q-fin.MF:1707.00899v1 | cross_domain_amplification | |
z | q | urn:hailstone:economics:structural_equation[cbf93af63e13] | 1 | structural_equation | 5 | arxiv.q-fin.MF.1705.05934v1.eq_1765 | ψ(z) = q | arxiv_extracted | ["q", "z"] | arxiv | arxiv | arxiv:q-fin.MF:1705.05934v1 | cross_domain_amplification | |
l | q | urn:hailstone:economics:structural_equation[a4261fa29df8] | 1 | structural_equation | 5 | arxiv.q-fin.MF.1611.06218v2.eq_1766 | [-ζ,ζ]=\{ξ: -ζ\leq ξ\leqζ\} | arxiv_extracted | ["e", "q", "l"] | arxiv | arxiv | arxiv:q-fin.MF:1611.06218v2 | cross_domain_amplification | |
s | n | urn:hailstone:economics:structural_equation[eb86b3ed7fb0] | 1 | structural_equation | 5 | arxiv.q-fin.MF.1608.06121v1.eq_1767 | \sum_{i=1}^d \int_0^\cdot μ_i (t) \mathrm{d} \langle \log μ_i \rangle (t) | arxiv_extracted | ["m_{i", "i", "u", "s", "n", "d"] | arxiv | arxiv | arxiv:q-fin.MF:1608.06121v1 | cross_domain_amplification | |
x | x | urn:hailstone:economics:structural_equation[c222b0d0a55f] | 1 | structural_equation | 5 | arxiv.q-fin.MF.1607.01317v1.eq_1768 | Ψ(x,t) = e^{iS(x,t)} | arxiv_extracted | ["e", "t", "S", "i", "x"] | arxiv | arxiv | arxiv:q-fin.MF:1607.01317v1 | cross_domain_amplification | |
p | a | urn:hailstone:economics:structural_equation[276d92c96abf] | 1 | structural_equation | 5 | arxiv.q-fin.MF.1605.03097v1.eq_1769 | \partial_t u - L_0 u = 0 | arxiv_extracted | ["a", "t", "i", "p", "r"] | arxiv | arxiv | arxiv:q-fin.MF:1605.03097v1 | cross_domain_amplification | |
d | t | urn:hailstone:economics:structural_equation[94963c50ffef] | 1 | structural_equation | 5 | arxiv.q-fin.MF.1605.01028v1.eq_1770 | dX(t)= (1+f(X(t))dt+ f(X(t))dW(t) | arxiv_extracted | ["X", "f", "t", "d"] | arxiv | arxiv | arxiv:q-fin.MF:1605.01028v1 | cross_domain_amplification | |
s | c_i | urn:hailstone:economics:structural_equation[d13b14ce0f8f] | 1 | structural_equation | 5 | arxiv.q-fin.MF.1604.04608v2.eq_1771 | \sum_i c_i=1 | arxiv_extracted | ["s", "u", "c_i", "m_i"] | arxiv | arxiv | arxiv:q-fin.MF:1604.04608v2 | cross_domain_amplification | |
t | y | urn:hailstone:economics:structural_equation[aced705faafd] | 1 | structural_equation | 5 | arxiv.q-fin.MF.1603.07488v1.eq_1772 | σ(t,y)=g(t)h(y) | arxiv_extracted | ["t", "g", "y", "h"] | arxiv | arxiv | arxiv:q-fin.MF:1603.07488v1 | cross_domain_amplification | |
s | m | urn:hailstone:economics:structural_equation[3c9ab3780a9c] | 1 | structural_equation | 5 | arxiv.q-fin.MF.1601.08099v2.eq_1773 | (1-\sum\limits_{j=1}^q β_j L^j)σ_{t}^2 = ω+(1-\sum\limits_{j=1}^q β_j L^j - (\sum\limits_{k=1}^p \varphi_k L^k) (1-L)^d) u_t^2 | arxiv_extracted | ["m", "i", "u", "s", "l"] | arxiv | arxiv | arxiv:q-fin.MF:1601.08099v2 | cross_domain_amplification | |
u_t | x | urn:hailstone:economics:structural_equation[e2f3f13e7db8] | 1 | structural_equation | 5 | arxiv.q-fin.MF.1512.06151v2.eq_1774 | u_t+ax^2u_{xx}+bx^3u_{xx}^2+c(xu_x-u)=0,\quad a,b>0,\ c\geq0. | arxiv_extracted | ["u_t", "a", "u_{xx}", "b", "x"] | arxiv | arxiv | arxiv:q-fin.MF:1512.06151v2 | cross_domain_amplification | |
u_t | u_x | urn:hailstone:economics:structural_equation[6a293cab00db] | 1 | structural_equation | 5 | arxiv.q-fin.MF.1512.06151v2.eq_1775 | u_t+(u_{xx}+u_x)^2=0 | arxiv_extracted | ["u_{xx}", "u_x", "u_t"] | arxiv | arxiv | arxiv:q-fin.MF:1512.06151v2 | cross_domain_amplification | |
S | X_t | urn:hailstone:economics:structural_equation[5a7d777a1fe6] | 1 | structural_equation | 5 | arxiv.q-fin.MF.1506.00188v1.eq_1776 | S^F_t = f(X_t) | arxiv_extracted | ["f", "F_t", "X_t", "S"] | arxiv | arxiv | arxiv:q-fin.MF:1506.00188v1 | cross_domain_amplification | |
S | h | urn:hailstone:economics:structural_equation[5731d2c8e416] | 1 | structural_equation | 5 | arxiv.q-fin.MF.1506.00188v1.eq_1777 | S^B_t:=\mathbb{E}[g(X_1) | \mathcal{F}_t] | arxiv_extracted | ["a", "t", "m", "S", "h", "B_t"] | arxiv | arxiv | arxiv:q-fin.MF:1506.00188v1 | cross_domain_amplification | |
m | a | urn:hailstone:economics:structural_equation[09f2b890f333] | 1 | structural_equation | 5 | arxiv.q-fin.MF.1408.3692v3.eq_1778 | (Ω,\mathcal{F},P,\mathbb{F}=(\mathcal{F}_t)_{t=0,\dotso,T}) | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:q-fin.MF:1408.3692v3 | cross_domain_amplification | |
o | i | urn:hailstone:economics:structural_equation[4dfdbf8c1f36] | 1 | structural_equation | 5 | arxiv.q-fin.MF.1408.3692v3.eq_1779 | \overline V:=\inf_{\Rho\in\bT^{ii}}\sup_{τ\in\T}\E[U(\Rho(τ),τ)] | arxiv_extracted | ["e", "o", "i", "r", "l", "v"] | arxiv | arxiv | arxiv:q-fin.MF:1408.3692v3 | cross_domain_amplification | |
u | l | urn:hailstone:economics:structural_equation[273d694f5fea] | 1 | structural_equation | 5 | arxiv.q-fin.MF.1408.3692v3.eq_1780 | \underline V:=\sup_{\Tau\in\bT^i}\inf_{ρ\in\T}\E[U(\Rho(τ),τ)] | arxiv_extracted | ["e", "u", "r", "n", "d", "l"] | arxiv | arxiv | arxiv:q-fin.MF:1408.3692v3 | cross_domain_amplification | |
o | i | urn:hailstone:economics:structural_equation[738037317ee7] | 1 | structural_equation | 5 | arxiv.q-fin.MF.1408.3692v3.eq_1781 | \overline V=\underline V=V | arxiv_extracted | ["e", "o", "i", "r", "l", "v"] | arxiv | arxiv | arxiv:q-fin.MF:1408.3692v3 | cross_domain_amplification | |
d | x_{t} | urn:hailstone:economics:structural_equation[4fa3167ef613] | 1 | structural_equation | 5 | arxiv.q-fin.MF.1405.4537v1.eq_1782 | dy_{t}=f(y_{t})dx_{t} | arxiv_extracted | ["f", "y_{t}", "d", "x_{t}"] | arxiv | arxiv | arxiv:q-fin.MF:1405.4537v1 | cross_domain_amplification | |
y_{0} | a | urn:hailstone:economics:structural_equation[24b4690b038a] | 1 | structural_equation | 5 | arxiv.q-fin.MF.1405.4537v1.eq_1783 | y_{0}=a | arxiv_extracted | ["y_{0}", "a"] | arxiv | arxiv | arxiv:q-fin.MF:1405.4537v1 | cross_domain_amplification | |
n | t | urn:hailstone:math:structural_equation[f1642c02a141] | 1 | structural_equation | 4 | arxiv.nlin.CD.2604.19317v1.eq_1784 | α\not =1 | arxiv_extracted | ["t", "n", "o"] | arxiv | arxiv | arxiv:nlin.CD:2604.19317v1 | cross_domain_amplification | |
x_0 | t | urn:hailstone:math:structural_equation[8e43c20fde2b] | 1 | structural_equation | 4 | arxiv.nlin.CD.2604.19317v1.eq_1785 | x_0\not =0 | arxiv_extracted | ["t", "n", "x_0", "o"] | arxiv | arxiv | arxiv:nlin.CD:2604.19317v1 | cross_domain_amplification | |
h | m | urn:hailstone:math:structural_equation[5e11cea8766a] | 1 | structural_equation | 4 | arxiv.nlin.CD.2604.12745v1.eq_1786 | \hbar_{\rm eff}=1/N \to 0 | arxiv_extracted | ["a", "m", "h", "r", "b"] | arxiv | arxiv | arxiv:nlin.CD:2604.12745v1 | cross_domain_amplification | |
m | a | urn:hailstone:math:structural_equation[0afb643df3c0] | 1 | structural_equation | 4 | arxiv.nlin.CD.2604.03281v2.eq_1787 | \mathcal{N} = \mathcal A/δ_L^2 | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:nlin.CD:2604.03281v2 | cross_domain_amplification | |
L | m | urn:hailstone:math:structural_equation[3e52cd3a78cc] | 1 | structural_equation | 4 | arxiv.nlin.CD.2603.19125v2.eq_1788 | Lη_{h,pav}^{-1} = \mathit{Re}^{1/(1+h)} | arxiv_extracted | ["a", "m", "h", "p", "L", "v"] | arxiv | arxiv | arxiv:nlin.CD:2603.19125v2 | cross_domain_amplification | |
a | D | urn:hailstone:math:structural_equation[b04bed5626bd] | 1 | structural_equation | 4 | arxiv.nlin.CD.2603.17509v1.eq_1789 | (a,d,q)(n)=2\,(A,D,Q)(n)-n | arxiv_extracted | ["D", "q", "a", "A", "n", "d"] | arxiv | arxiv | arxiv:nlin.CD:2603.17509v1 | cross_domain_amplification | |
t | e | urn:hailstone:math:structural_equation[b4ccf6da90b6] | 1 | structural_equation | 4 | arxiv.nlin.CD.2602.17810v1.eq_1790 | \tildeα=0.507(2) | arxiv_extracted | ["e", "t", "i", "d", "l"] | arxiv | arxiv | arxiv:nlin.CD:2602.17810v1 | cross_domain_amplification | |
C_T | g | urn:hailstone:math:structural_equation[299a4d6db06c] | 1 | structural_equation | 4 | arxiv.nlin.CD.2602.05322v1.eq_1791 | C_T(t) = -\langle [x(t), p]^2 \rangle_β | arxiv_extracted | ["g", "a", "t", "C_T", "n", "l"] | arxiv | arxiv | arxiv:nlin.CD:2602.05322v1 | cross_domain_amplification | |
h | r | urn:hailstone:math:structural_equation[e759b2589462] | 1 | structural_equation | 4 | arxiv.nlin.CD.2602.04793v2.eq_1792 | \hbar=0 | arxiv_extracted | ["b", "r", "h", "a"] | arxiv | arxiv | arxiv:nlin.CD:2602.04793v2 | cross_domain_amplification | |
s | o | urn:hailstone:math:structural_equation[a55ba3f20a7b] | 1 | structural_equation | 4 | arxiv.nlin.CD.2601.14899v1.eq_1793 | ω_1/ω_2=5\sqrt{2}/7=1.010\dots | arxiv_extracted | ["q", "t", "o", "r", "s", "d"] | arxiv | arxiv | arxiv:nlin.CD:2601.14899v1 | cross_domain_amplification | |
m | b | urn:hailstone:math:structural_equation[7c84badb9f5f] | 1 | structural_equation | 4 | arxiv.nlin.CD.2601.00638v1.eq_1794 | \mathbb{H}=(L^2(Ω))^N | arxiv_extracted | ["a", "t", "m", "h", "b"] | arxiv | arxiv | arxiv:nlin.CD:2601.00638v1 | cross_domain_amplification | |
m | m | urn:hailstone:math:structural_equation[ede2fab78518] | 1 | structural_equation | 4 | arxiv.nlin.CD.2512.20390v3.eq_1795 | \mathrm{AUC} = 0.9995 | arxiv_extracted | ["a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:nlin.CD:2512.20390v3 | cross_domain_amplification | |
L | r | urn:hailstone:math:structural_equation[6af1b457d94d] | 1 | structural_equation | 4 | arxiv.nlin.CD.2511.03843v3.eq_1796 | λ_L^{\rm forward} = λ_L^{\rm backward} | arxiv_extracted | ["f", "m", "o", "L", "r"] | arxiv | arxiv | arxiv:nlin.CD:2511.03843v3 | cross_domain_amplification | |
s | l | urn:hailstone:math:structural_equation[4a5eb347f429] | 1 | structural_equation | 4 | arxiv.nlin.CD.2510.08321v1.eq_1797 | \sqrt{N}\{\langle \varphi^{(j)}|\operatorname{Op}_{k,\ell}(a)|\varphi^{(j)}\rangle-\int_{\mathbb{T}^2}a\}_{j=1}^{N} | arxiv_extracted | ["q", "t", "r", "s", "l", "N"] | arxiv | arxiv | arxiv:nlin.CD:2510.08321v1 | cross_domain_amplification | |
v | i | urn:hailstone:math:structural_equation[608b801ad0a6] | 1 | structural_equation | 4 | arxiv.nlin.CD.2510.08321v1.eq_1798 | \{\varphi^{(j)}\}_{j=1}^{N} | arxiv_extracted | ["a", "h", "i", "p", "r", "v"] | arxiv | arxiv | arxiv:nlin.CD:2510.08321v1 | cross_domain_amplification | |
t | m | urn:hailstone:math:structural_equation[e130d6fe9fac] | 1 | structural_equation | 4 | arxiv.nlin.CD.2510.03968v2.eq_1799 | \textrm{Re}_λ=O(10^2) | arxiv_extracted | ["e", "t", "m", "r", "x"] | arxiv | arxiv | arxiv:nlin.CD:2510.03968v2 | cross_domain_amplification | |
m_{1} | m_{2} | urn:hailstone:math:structural_equation[e5d871ad3924] | 1 | structural_equation | 4 | arxiv.nlin.CD.2508.08568v1.eq_1800 | m_{1}=m_{2}=1 | arxiv_extracted | ["m_{2}", "m_{1}"] | arxiv | arxiv | arxiv:nlin.CD:2508.08568v1 | cross_domain_amplification | |
m_{3} | n | urn:hailstone:math:structural_equation[50dfec6cce3c] | 1 | structural_equation | 4 | arxiv.nlin.CD.2508.08568v1.eq_1801 | m_{3}=0.1n | arxiv_extracted | ["n", "m_{3}"] | arxiv | arxiv | arxiv:nlin.CD:2508.08568v1 | cross_domain_amplification | |
m_{1} | m_{2} | urn:hailstone:math:structural_equation[e5d871ad3924] | 1 | structural_equation | 4 | arxiv.nlin.CD.2508.08568v1.eq_1802 | m_{1}=m_{2}=1 | arxiv_extracted | ["m_{2}", "m_{1}"] | arxiv | arxiv | arxiv:nlin.CD:2508.08568v1 | cross_domain_amplification | |
L_{z} | N | urn:hailstone:math:structural_equation[85ed7caee83f] | 1 | structural_equation | 4 | arxiv.nlin.CD.2508.01729v2.eq_1803 | L_{z}=N | arxiv_extracted | ["N", "L_{z}"] | arxiv | arxiv | arxiv:nlin.CD:2508.01729v2 | cross_domain_amplification | |
L_{z} | N | urn:hailstone:math:structural_equation[17801dc5c9a4] | 1 | structural_equation | 4 | arxiv.nlin.CD.2508.01729v2.eq_1804 | L_{z}=2N | arxiv_extracted | ["N", "L_{z}"] | arxiv | arxiv | arxiv:nlin.CD:2508.01729v2 | cross_domain_amplification | |
L_{z} | N | urn:hailstone:math:structural_equation[33146afe693c] | 1 | structural_equation | 4 | arxiv.nlin.CD.2508.01729v2.eq_1805 | L_{z}=3N | arxiv_extracted | ["N", "L_{z}"] | arxiv | arxiv | arxiv:nlin.CD:2508.01729v2 | cross_domain_amplification | |
L_{z} | N | urn:hailstone:math:structural_equation[02caa1e36c3e] | 1 | structural_equation | 4 | arxiv.nlin.CD.2508.01729v2.eq_1806 | L_{z} = N | arxiv_extracted | ["N", "L_{z}"] | arxiv | arxiv | arxiv:nlin.CD:2508.01729v2 | cross_domain_amplification | |
L_{z} | N | urn:hailstone:math:structural_equation[02caa1e36c3e] | 1 | structural_equation | 4 | arxiv.nlin.CD.2508.01729v2.eq_1807 | L_{z} = N | arxiv_extracted | ["N", "L_{z}"] | arxiv | arxiv | arxiv:nlin.CD:2508.01729v2 | cross_domain_amplification | |
d | i | urn:hailstone:math:structural_equation[700cf95e0c36] | 1 | structural_equation | 4 | arxiv.nlin.CD.2507.19053v2.eq_1808 | {dα/dt} = λ(t)\sin 2(α- φ(t)) | arxiv_extracted | ["t", "d", "s", "i"] | arxiv | arxiv | arxiv:nlin.CD:2507.19053v2 | cross_domain_amplification | |
t | t | urn:hailstone:math:structural_equation[a6b773ba25a8] | 1 | structural_equation | 4 | arxiv.nlin.CD.2507.19053v2.eq_1809 | λ(t) = \cos(ω_1 t) | arxiv_extracted | ["t", "c", "s", "o"] | arxiv | arxiv | arxiv:nlin.CD:2507.19053v2 | cross_domain_amplification | |
t | t | urn:hailstone:math:structural_equation[f6ca2b4b99d2] | 1 | structural_equation | 4 | arxiv.nlin.CD.2507.19053v2.eq_1810 | φ(t) = ω_2 t | arxiv_extracted | ["t"] | arxiv | arxiv | arxiv:nlin.CD:2507.19053v2 | cross_domain_amplification | |
x | m | urn:hailstone:math:structural_equation[1df2344d529b] | 1 | structural_equation | 4 | arxiv.nlin.CD.2507.10863v7.eq_1811 | (x,y) = (\pm 1, \pm 1) | arxiv_extracted | ["p", "m", "y", "x"] | arxiv | arxiv | arxiv:nlin.CD:2507.10863v7 | cross_domain_amplification | |
f | x_{i | urn:hailstone:math:structural_equation[bb26befb9a04] | 1 | structural_equation | 4 | arxiv.nlin.CD.2507.04780v2.eq_1812 | f(x_i)=x_{i+1} | arxiv_extracted | ["f", "x_{i", "x_i"] | arxiv | arxiv | arxiv:nlin.CD:2507.04780v2 | cross_domain_amplification | |
x_{t | f | urn:hailstone:math:structural_equation[83b7b73c37ac] | 1 | structural_equation | 4 | arxiv.nlin.CD.2505.15709v2.eq_1813 | x_{t+1} = f_L(x_t)x_t^{-α} - \lfloor f_L(x_t)x_t^{-α} \rfloor | arxiv_extracted | ["f", "x_{t", "f_L", "x_t", "l"] | arxiv | arxiv | arxiv:nlin.CD:2505.15709v2 | cross_domain_amplification | |
f_L | x_t | urn:hailstone:math:structural_equation[7d7874480aab] | 1 | structural_equation | 4 | arxiv.nlin.CD.2505.15709v2.eq_1814 | f_L(x_t) = r x_t (1-x_t) | arxiv_extracted | ["f_L", "x_t", "r"] | arxiv | arxiv | arxiv:nlin.CD:2505.15709v2 | cross_domain_amplification | |
v | y | urn:hailstone:math:structural_equation[579feda2449d] | 1 | structural_equation | 4 | arxiv.nlin.CD.2506.01996v2.eq_1815 | v_\infty = v_0 \left( 1 + \mathcal{G}(K) \right) | arxiv_extracted | ["f", "t", "y", "i", "n", "v"] | arxiv | arxiv | arxiv:nlin.CD:2506.01996v2 | cross_domain_amplification | |
A | g | urn:hailstone:math:structural_equation[cbc139d511ee] | 1 | structural_equation | 4 | arxiv.nlin.CD.2505.09225v2.eq_1816 | A = \sum_{n=1}^N g(\textbf{x}_n) | arxiv_extracted | ["g", "m_{n", "u", "A", "s", "N"] | arxiv | arxiv | arxiv:nlin.CD:2505.09225v2 | cross_domain_amplification | |
m | a | urn:hailstone:math:structural_equation[69159b65f5d4] | 1 | structural_equation | 4 | arxiv.nlin.CD.2504.10729v2.eq_1817 | \mathcal{N} = \mathcal{J} \mathcal{R} + \mathcal{R} \mathcal{J} | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:nlin.CD:2504.10729v2 | cross_domain_amplification | |
d_s | q | urn:hailstone:math:structural_equation[8c6e861d6554] | 1 | structural_equation | 4 | arxiv.nlin.CD.2503.20708v1.eq_1818 | d_s \simeq 2 < d_c=4 | arxiv_extracted | ["e", "q", "d_s", "m", "i", "s"] | arxiv | arxiv | arxiv:nlin.CD:2503.20708v1 | cross_domain_amplification | |
m | m | urn:hailstone:math:structural_equation[4fe97afb57d2] | 1 | structural_equation | 4 | arxiv.nlin.CD.2503.11799v1.eq_1819 | \mathrm{Pr} = 0.1 | arxiv_extracted | ["a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:nlin.CD:2503.11799v1 | cross_domain_amplification | |
x | g | urn:hailstone:math:structural_equation[fca21d8d87bd] | 1 | structural_equation | 4 | arxiv.nlin.CD.2503.06939v3.eq_1820 | (x',y')=(f(x,y),g(x,y)) | arxiv_extracted | ["f", "g", "y", "x"] | arxiv | arxiv | arxiv:nlin.CD:2503.06939v3 | cross_domain_amplification |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.