s
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o
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996 values
p
stringlengths
7
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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