Run 10953593

Paper: https://arxiv.org/abs/1404.6919

Formulas:

1-

H = ℏ ω (a^{†} a + \frac{1}{2}) = \frac{ℏ ω}{2} (a^{†} a + a a^{†})

2-

H = ℏ ω a^{†} a .

3-

F_{3 D} = \frac{π^{2} ℏ c}{240} \frac{A}{L^{4}} .

4-

(\begin{matrix} b^{+} \\ a^{-} \end{matrix}) = 𝖲 (\begin{matrix} a^{+} \\ b^{-} \end{matrix}) .

5-

𝖲 = (\begin{matrix} t & \bar{r} \\ r & \bar{t} \end{matrix}),

6-

(a^{-}, b^{+})

7-

𝖲^{†} 𝖲 = 𝟣 .

8-

{| t |}^{2} + {| r |}^{2} = {| \bar{t} |}^{2} + {| \bar{r} |}^{2}

9-

r {\bar{t}}^{*} + t {\bar{r}}^{*}

10-

det (𝖲) = - \frac{r}{{\bar{r}}^{*}} = - \frac{\bar{r}}{r^{*}} .

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1202.2065

Formulas:

1-

100 < m_{H} < 200 GeV / c^{2}

2-

W H \to l ν b \bar{b}

3-

V H \to E_{T} b \bar{b}

4-

Z H \to l^{+} l^{-} b \bar{b}

5-

V H \to j j b \bar{b}

6-

H \to W^{+} W^{-}

7-

H \to τ^{+} τ^{-} j j

8-

H \to Z Z \to l l l l

9-

t \bar{t} H

10-

m_{H} = 115 GeV / c^{2}

Formulas (html):

Correct Categorie: hep-ex

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1801.01044

Formulas:

1-

\frac{1}{2} [110]

2-

\frac{1}{2} [110]

3-

- \frac{1}{2} [201]

4-

E_{t o t} = J_{0} N + \sum_{n = 1}^{M} \sum_{i = 1}^{N} J_{n} σ_{i} σ_{i + n},

5-

E_{t o t}

6-

σ_{1} = σ_{N + 1}

7-

E_{f} (SF)

8-

E_{f} (SF) = \frac{E_{t o t} (SF)}{A} - \frac{N E_{t o t} (0)}{A},

9-

E_{t o t} (0)

10-

\bar{V (z_{0})} = \frac{\int_{z_{0} - τ / 2}^{z_{0} + τ / 2} \int \int V (x, y, z) 𝑑 x 𝑑 y 𝑑 z}{τ \int \int 𝑑 x 𝑑 y},

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/9905291

Formulas:

1-

ρ (x, y, z)

2-

τ_{h o m}

3-

g = ⟨ \cos θ ⟩ = 0.6

4-

τ_{h o m}

5-

τ_{h o m} = 1

6-

τ_{h o m} = 10

7-

τ_{h o m}

8-

τ_{h o m}

9-

τ_{e f f} = - \ln (L_{e s c a p e} / L_{e m i t})

10-

τ_{e f f}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/cond-mat/0410502

Formulas:

1-

ρ_{a b} (T)

2-

Δ ρ_{a b}

3-

\ln (T_{c 0} / T_{c}) = Ψ (1 / 2 + 1 / 2 π T_{c} τ) - Ψ (1 / 2)

4-

τ^{- 1} \propto x_{d} \propto Δ ρ_{a b}

5-

T_{c} (Δ ρ_{a b})

6-

\ln (T_{c 0} / T_{c}) = (1 - χ) [Ψ (1 / 2 + 1 / 2 π T_{c} τ_{m}) - Ψ (1 / 2)] + χ [Ψ (1 / 2 + 1 / 4 π T_{c} τ_{n} + 1 / 4 π T_{c} τ_{m}) - Ψ (1 / 2)]

7-

χ = 1 - {⟨ Δ (𝐩) ⟩}_{F S}^{2} / {⟨ Δ^{2} (𝐩) ⟩}_{F S}

8-

T_{c} / T_{c 0}

9-

Δ ρ_{a b}

10-

α = τ_{m}^{- 1} / (τ_{n}^{- 1} + τ_{m}^{- 1})

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/hep-th/0007182

Formulas:

1-

\int 𝒟 [\bar{Ψ}, Ψ, A] 𝒪 [\bar{Ψ}, Ψ, A] e^{- S_{QCD} [\bar{Ψ}, Ψ, A]} .

2-

γ_{m} (α)

3-

α = \frac{4}{3} (1 + γ_{m}^{var}) \cot \frac{π / 2}{1 + γ_{m}^{var}} .

4-

γ_{m} (α)

5-

γ_{m} (α)

6-

N_{n} = \frac{(2 n)!}{2^{n} n!} = (2 n - 1)!! \overset{n \to \infty}{⟶} 2^{n + 1 / 2} e^{- n} n^{n}

7-

{lim}_{n \to \infty} {| N_{n} |}^{- 1 / n}

8-

γ_{m}^{DS} = 1 - \sqrt{1 - \frac{3}{π} α}

9-

α_{c o n}^{DS} = α_{c r}

10-

α_{c o n}^{DS}

Formulas (html):

Correct Categorie: hep-th

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1509.06531

Formulas:

1-

_{d u s t}

2-

_{h a l o}

3-

_{i n n e r d i s k / h a l o}

4-

_{w a l l}

5-

2.1 < F_{30} / F_{13.5} < 5.1

6-

F_{30} / F_{13.5} ⩽ 2.1

7-

2.1 < F_{30} / F_{13.5} < 5.1

8-

F_{30} / F_{13.5} ⩾ 5.1

9-

s h \propto r^{s h p o w}

10-

s h p o w

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1502.01543

Formulas:

1-

1 \leq k \leq n - 1

2-

w = w_{1} w_{2} \dots w_{n}

3-

w_{i_{1}} \dots w_{i_{s}}

4-

w_{i_{1}} > w_{i_{2}} < w_{i_{3}} \dots

5-

| w_{i_{j}} - w_{i_{j + 1}} | \geq k

6-

a s_{k} (w)

7-

E_{n} (a s_{k})

8-

E_{n} (a s_{k}) = \frac{1}{n!} \sum_{w \in 𝔖_{n}} a s_{k} (w)

9-

n \geq k + 1 \geq 2

10-

E_{n} (a s_{k}) = \frac{4 (n - k) + 5}{6} .

Formulas (html):

Correct Categorie: math

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/0108209

Formulas:

1-

\frac{\partial R (x, t)}{\partial t} = - \frac{\partial}{\partial x} [v R (x, t)] + \frac{\partial}{\partial x} [D \frac{\partial R (x, t)}{\partial x}] + Γ (R, \tilde{h}),

2-

Γ (R, \tilde{h}) = - R (x, t) [γ \frac{\partial \tilde{h} (x, t)}{\partial x} + κ \frac{\partial^{2} \tilde{h} (x, t)}{\partial x^{2}}] = - \frac{\partial \tilde{h} (x, t)}{\partial t},

3-

\tilde{h} = h + x \tan θ_{r}, θ_{r}

4-

x_{o} + δ x

5-

δ m_{r} = \int_{x_{o}}^{x_{o} + δ x} [\int_{h (x, t)}^{h (x, t) + r (x, t)} ρ_{r} (x, y, t) 𝑑 y] 𝑑 x,

6-

h (x, t)

7-

height of the static phase in a point x at time t,

8-

r (x, t)

9-

height of the rolling phase in a point x at a time t .

10-

R (x_{o}, t) = lim_{δ x \to 0} \frac{δ m_{r}}{δ x} = lim_{δ x \to 0} \frac{1}{δ x} \int_{x_{o}}^{x_{o} + δ x} [\int_{h (x, t)}^{h (x, t) + r (x, t)} ρ_{r} (x, y, t) 𝑑 y] 𝑑 x .

Formulas (html):

<math><mrow id="S1.E1.m1.10.10" xref="S1.E1.m1.10.10.cmml"><mfrac id="S1.E1.m1.2.2" xref="S1.E1.m1.2.2.cmml"><mrow id="S1.E1.m1.2.2.2" xref="S1.E1.m1.2.2.2.cmml"><mrow id="S1.E1.m1.2.2.2.4" xref="S1.E1.m1.2.2.2.4.cmml"><mo id="S1.E1.m1.2.2.2.4.1" xref="S1.E1.m1.2.2.2.4.1.cmml">∂</mo><mo id="S1.E1.m1.2.2.2.4a" xref="S1.E1.m1.2.2.2.4.cmml">⁡</mo><mpadded width="-1.7pt" id="S1.E1.m1.2.2.2.4.2" xref="S1.E1.m1.2.2.2.4.2.cmml"><mi id="S1.E1.m1.2.2.2.4.2a" xref="S1.E1.m1.2.2.2.4.2.cmml">R</mi></mpadded></mrow><mo id="S1.E1.m1.2.2.2.3" xref="S1.E1.m1.2.2.2.3.cmml">⁢</mo><mrow id="S1.E1.m1.2.2.2.5.2" xref="S1.E1.m1.2.2.2.5.1.cmml"><mo id="S1.E1.m1.2.2.2.5.2.1" xref="S1.E1.m1.2.2.2.5.1.cmml">(</mo><mi id="S1.E1.m1.1.1.1.1" xref="S1.E1.m1.1.1.1.1.cmml">x</mi><mo id="S1.E1.m1.2.2.2.5.2.2" xref="S1.E1.m1.2.2.2.5.1.cmml">,</mo><mi id="S1.E1.m1.2.2.2.2" xref="S1.E1.m1.2.2.2.2.cmml">t</mi><mo id="S1.E1.m1.2.2.2.5.2.3" xref="S1.E1.m1.2.2.2.5.1.cmml">)</mo></mrow></mrow><mrow id="S1.E1.m1.2.2.4" xref="S1.E1.m1.2.2.4.cmml"><mo id="S1.E1.m1.2.2.4.1" xref="S1.E1.m1.2.2.4.1.cmml">∂</mo><mo id="S1.E1.m1.2.2.4a" xref="S1.E1.m1.2.2.4.cmml">⁡</mo><mi id="S1.E1.m1.2.2.4.2" xref="S1.E1.m1.2.2.4.2.cmml">t</mi></mrow></mfrac><mo id="S1.E1.m1.10.10.3" xref="S1.E1.m1.10.10.3.cmml">=</mo><mrow id="S1.E1.m1.10.10.2" xref="S1.E1.m1.10.10.2.cmml"><mrow id="S1.E1.m1.9.9.1.1" xref="S1.E1.m1.9.9.1.1.cmml"><mo id="S1.E1.m1.9.9.1.1.2" xref="S1.E1.m1.9.9.1.1.2.cmml">-</mo><mrow id="S1.E1.m1.9.9.1.1.1" xref="S1.E1.m1.9.9.1.1.1.cmml"><mfrac id="S1.E1.m1.9.9.1.1.1.3" xref="S1.E1.m1.9.9.1.1.1.3.cmml"><mo id="S1.E1.m1.9.9.1.1.1.3.2" xref="S1.E1.m1.9.9.1.1.1.3.2.cmml">∂</mo><mrow id="S1.E1.m1.9.9.1.1.1.3.3" xref="S1.E1.m1.9.9.1.1.1.3.3.cmml"><mo id="S1.E1.m1.9.9.1.1.1.3.3.1" xref="S1.E1.m1.9.9.1.1.1.3.3.1.cmml">∂</mo><mo id="S1.E1.m1.9.9.1.1.1.3.3a" xref="S1.E1.m1.9.9.1.1.1.3.3.cmml">⁡</mo><mi id="S1.E1.m1.9.9.1.1.1.3.3.2" xref="S1.E1.m1.9.9.1.1.1.3.3.2.cmml">x</mi></mrow></mfrac><mo id="S1.E1.m1.9.9.1.1.1.2" xref="S1.E1.m1.9.9.1.1.1.2.cmml">⁢</mo><mrow id="S1.E1.m1.9.9.1.1.1.1.1" xref="S1.E1.m1.9.9.1.1.1.1.2.cmml"><mo id="S1.E1.m1.9.9.1.1.1.1.1.2" xref="S1.E1.m1.9.9.1.1.1.1.2.1.cmml">[</mo><mrow id="S1.E1.m1.9.9.1.1.1.1.1.1" xref="S1.E1.m1.9.9.1.1.1.1.1.1.cmml"><mi id="S1.E1.m1.9.9.1.1.1.1.1.1.2" xref="S1.E1.m1.9.9.1.1.1.1.1.1.2.cmml">v</mi><mo id="S1.E1.m1.9.9.1.1.1.1.1.1.1" xref="S1.E1.m1.9.9.1.1.1.1.1.1.1.cmml">⁢</mo><mi id="S1.E1.m1.9.9.1.1.1.1.1.1.3" xref="S1.E1.m1.9.9.1.1.1.1.1.1.3.cmml">R</mi><mo id="S1.E1.m1.9.9.1.1.1.1.1.1.1a" xref="S1.E1.m1.9.9.1.1.1.1.1.1.1.cmml">⁢</mo><mrow id="S1.E1.m1.9.9.1.1.1.1.1.1.4.2" xref="S1.E1.m1.9.9.1.1.1.1.1.1.4.1.cmml"><mo stretchy="false" id="S1.E1.m1.9.9.1.1.1.1.1.1.4.2.1" xref="S1.E1.m1.9.9.1.1.1.1.1.1.4.1.cmml">(</mo><mi id="S1.E1.m1.5.5" xref="S1.E1.m1.5.5.cmml">x</mi><mo id="S1.E1.m1.9.9.1.1.1.1.1.1.4.2.2" xref="S1.E1.m1.9.9.1.1.1.1.1.1.4.1.cmml">,</mo><mi id="S1.E1.m1.6.6" xref="S1.E1.m1.6.6.cmml">t</mi><mo stretchy="false" id="S1.E1.m1.9.9.1.1.1.1.1.1.4.2.3" xref="S1.E1.m1.9.9.1.1.1.1.1.1.4.1.cmml">)</mo></mrow></mrow><mo id="S1.E1.m1.9.9.1.1.1.1.1.3" xref="S1.E1.m1.9.9.1.1.1.1.2.1.cmml">]</mo></mrow></mrow></mrow><mo id="S1.E1.m1.10.10.2.3" xref="S1.E1.m1.10.10.2.3.cmml">+</mo><mrow id="S1.E1.m1.10.10.2.2" xref="S1.E1.m1.10.10.2.2.cmml"><mfrac id="S1.E1.m1.10.10.2.2.3" xref="S1.E1.m1.10.10.2.2.3.cmml"><mo id="S1.E1.m1.10.10.2.2.3.2" xref="S1.E1.m1.10.10.2.2.3.2.cmml">∂</mo><mrow id="S1.E1.m1.10.10.2.2.3.3" xref="S1.E1.m1.10.10.2.2.3.3.cmml"><mo id="S1.E1.m1.10.10.2.2.3.3.1" xref="S1.E1.m1.10.10.2.2.3.3.1.cmml">∂</mo><mo id="S1.E1.m1.10.10.2.2.3.3a" xref="S1.E1.m1.10.10.2.2.3.3.cmml">⁡</mo><mi id="S1.E1.m1.10.10.2.2.3.3.2" xref="S1.E1.m1.10.10.2.2.3.3.2.cmml">x</mi></mrow></mfrac><mo id="S1.E1.m1.10.10.2.2.2" xref="S1.E1.m1.10.10.2.2.2.cmml">⁢</mo><mrow id="S1.E1.m1.10.10.2.2.1.1" xref="S1.E1.m1.10.10.2.2.1.2.cmml"><mo id="S1.E1.m1.10.10.2.2.1.1.2" xref="S1.E1.m1.10.10.2.2.1.2.1.cmml">[</mo><mrow id="S1.E1.m1.10.10.2.2.1.1.1" xref="S1.E1.m1.10.10.2.2.1.1.1.cmml"><mi id="S1.E1.m1.10.10.2.2.1.1.1.2" xref="S1.E1.m1.10.10.2.2.1.1.1.2.cmml">D</mi><mo id="S1.E1.m1.10.10.2.2.1.1.1.1" xref="S1.E1.m1.10.10.2.2.1.1.1.1.cmml">⁢</mo><mfrac id="S1.E1.m1.4.4" xref="S1.E1.m1.4.4.cmml"><mrow id="S1.E1.m1.4.4.2" xref="S1.E1.m1.4.4.2.cmml"><mrow id="S1.E1.m1.4.4.2.4" xref="S1.E1.m1.4.4.2.4.cmml"><mo id="S1.E1.m1.4.4.2.4.1" xref="S1.E1.m1.4.4.2.4.1.cmml">∂</mo><mo id="S1.E1.m1.4.4.2.4a" xref="S1.E1.m1.4.4.2.4.cmml">⁡</mo><mi id="S1.E1.m1.4.4.2.4.2" xref="S1.E1.m1.4.4.2.4.2.cmml">R</mi></mrow><mo id="S1.E1.m1.4.4.2.3" xref="S1.E1.m1.4.4.2.3.cmml">⁢</mo><mrow id="S1.E1.m1.4.4.2.5.2" xref="S1.E1.m1.4.4.2.5.1.cmml"><mo stretchy="false" id="S1.E1.m1.4.4.2.5.2.1" xref="S1.E1.m1.4.4.2.5.1.cmml">(</mo><mi id="S1.E1.m1.3.3.1.1" xref="S1.E1.m1.3.3.1.1.cmml">x</mi><mo id="S1.E1.m1.4.4.2.5.2.2" xref="S1.E1.m1.4.4.2.5.1.cmml">,</mo><mi id="S1.E1.m1.4.4.2.2" xref="S1.E1.m1.4.4.2.2.cmml">t</mi><mo stretchy="false" id="S1.E1.m1.4.4.2.5.2.3" xref="S1.E1.m1.4.4.2.5.1.cmml">)</mo></mrow></mrow><mrow id="S1.E1.m1.4.4.4" xref="S1.E1.m1.4.4.4.cmml"><mo id="S1.E1.m1.4.4.4.1" xref="S1.E1.m1.4.4.4.1.cmml">∂</mo><mo id="S1.E1.m1.4.4.4a" xref="S1.E1.m1.4.4.4.cmml">⁡</mo><mi id="S1.E1.m1.4.4.4.2" xref="S1.E1.m1.4.4.4.2.cmml">x</mi></mrow></mfrac></mrow><mo id="S1.E1.m1.10.10.2.2.1.1.3" xref="S1.E1.m1.10.10.2.2.1.2.1.cmml">]</mo></mrow></mrow><mo id="S1.E1.m1.10.10.2.3a" xref="S1.E1.m1.10.10.2.3.cmml">+</mo><mrow id="S1.E1.m1.10.10.2.4" xref="S1.E1.m1.10.10.2.4.cmml"><mpadded width="-1.7pt" id="S1.E1.m1.10.10.2.4.2" xref="S1.E1.m1.10.10.2.4.2.cmml"><mi mathvariant="normal" id="S1.E1.m1.10.10.2.4.2a" xref="S1.E1.m1.10.10.2.4.2.cmml">Γ</mi></mpadded><mo id="S1.E1.m1.10.10.2.4.1" xref="S1.E1.m1.10.10.2.4.1.cmml">⁢</mo><mrow id="S1.E1.m1.10.10.2.4.3.2" xref="S1.E1.m1.10.10.2.4.3.1.cmml"><mo id="S1.E1.m1.10.10.2.4.3.2.1" xref="S1.E1.m1.10.10.2.4.3.1.cmml">(</mo><mi id="S1.E1.m1.7.7" xref="S1.E1.m1.7.7.cmml">R</mi><mo id="S1.E1.m1.10.10.2.4.3.2.2" xref="S1.E1.m1.10.10.2.4.3.1.cmml">,</mo><mover accent="true" id="S1.E1.m1.8.8" xref="S1.E1.m1.8.8.cmml"><mi id="S1.E1.m1.8.8.2" xref="S1.E1.m1.8.8.2.cmml">h</mi><mo stretchy="false" id="S1.E1.m1.8.8.1" xref="S1.E1.m1.8.8.1.cmml">~</mo></mover><mo id="S1.E1.m1.10.10.2.4.3.2.3" xref="S1.E1.m1.10.10.2.4.3.1.cmml">)</mo></mrow><mo id="S1.E1.m1.10.10.2.4.1a" xref="S1.E1.m1.10.10.2.4.1.cmml">⁢</mo><mtext id="S1.E1.m1.10.10.2.4.4" xref="S1.E1.m1.10.10.2.4.4a.cmml">,</mtext></mrow></mrow></mrow></math>, <math><mrow id="S1.E2.m1.11.11" xref="S1.E2.m1.11.11.cmml"><mrow id="S1.E2.m1.11.11.3" xref="S1.E2.m1.11.11.3.cmml"><mi mathvariant="normal" id="S1.E2.m1.11.11.3.2" xref="S1.E2.m1.11.11.3.2.cmml">Γ</mi><mo id="S1.E2.m1.11.11.3.1" xref="S1.E2.m1.11.11.3.1.cmml">⁢</mo><mrow id="S1.E2.m1.11.11.3.3.2" xref="S1.E2.m1.11.11.3.3.1.cmml"><mo id="S1.E2.m1.11.11.3.3.2.1" xref="S1.E2.m1.11.11.3.3.1.cmml">(</mo><mi id="S1.E2.m1.7.7" xref="S1.E2.m1.7.7.cmml">R</mi><mo id="S1.E2.m1.11.11.3.3.2.2" xref="S1.E2.m1.11.11.3.3.1.cmml">,</mo><mover accent="true" id="S1.E2.m1.8.8" xref="S1.E2.m1.8.8.cmml"><mi id="S1.E2.m1.8.8.2" xref="S1.E2.m1.8.8.2.cmml">h</mi><mo stretchy="false" id="S1.E2.m1.8.8.1" xref="S1.E2.m1.8.8.1.cmml">~</mo></mover><mo id="S1.E2.m1.11.11.3.3.2.3" xref="S1.E2.m1.11.11.3.3.1.cmml">)</mo></mrow></mrow><mo id="S1.E2.m1.11.11.4" xref="S1.E2.m1.11.11.4.cmml">=</mo><mrow id="S1.E2.m1.11.11.1" xref="S1.E2.m1.11.11.1.cmml"><mo id="S1.E2.m1.11.11.1.2" xref="S1.E2.m1.11.11.1.2.cmml">-</mo><mrow id="S1.E2.m1.11.11.1.1" xref="S1.E2.m1.11.11.1.1.cmml"><mi id="S1.E2.m1.11.11.1.1.3" xref="S1.E2.m1.11.11.1.1.3.cmml">R</mi><mo id="S1.E2.m1.11.11.1.1.2" xref="S1.E2.m1.11.11.1.1.2.cmml">⁢</mo><mrow id="S1.E2.m1.11.11.1.1.4.2" xref="S1.E2.m1.11.11.1.1.4.1.cmml"><mo id="S1.E2.m1.11.11.1.1.4.2.1" xref="S1.E2.m1.11.11.1.1.4.1.cmml">(</mo><mi id="S1.E2.m1.9.9" xref="S1.E2.m1.9.9.cmml">x</mi><mo id="S1.E2.m1.11.11.1.1.4.2.2" xref="S1.E2.m1.11.11.1.1.4.1.cmml">,</mo><mi id="S1.E2.m1.10.10" xref="S1.E2.m1.10.10.cmml">t</mi><mo id="S1.E2.m1.11.11.1.1.4.2.3" xref="S1.E2.m1.11.11.1.1.4.1.cmml">)</mo></mrow><mo id="S1.E2.m1.11.11.1.1.2a" xref="S1.E2.m1.11.11.1.1.2.cmml">⁢</mo><mrow id="S1.E2.m1.11.11.1.1.1.1" xref="S1.E2.m1.11.11.1.1.1.2.cmml"><mo id="S1.E2.m1.11.11.1.1.1.1.2" xref="S1.E2.m1.11.11.1.1.1.2.1.cmml">[</mo><mrow id="S1.E2.m1.11.11.1.1.1.1.1" xref="S1.E2.m1.11.11.1.1.1.1.1.cmml"><mrow id="S1.E2.m1.11.11.1.1.1.1.1.2" xref="S1.E2.m1.11.11.1.1.1.1.1.2.cmml"><mi id="S1.E2.m1.11.11.1.1.1.1.1.2.2" xref="S1.E2.m1.11.11.1.1.1.1.1.2.2.cmml">γ</mi><mo id="S1.E2.m1.11.11.1.1.1.1.1.2.1" xref="S1.E2.m1.11.11.1.1.1.1.1.2.1.cmml">⁢</mo><mfrac id="S1.E2.m1.2.2" xref="S1.E2.m1.2.2.cmml"><mrow id="S1.E2.m1.2.2.2" xref="S1.E2.m1.2.2.2.cmml"><mrow id="S1.E2.m1.2.2.2.4" xref="S1.E2.m1.2.2.2.4.cmml"><mo id="S1.E2.m1.2.2.2.4.1" xref="S1.E2.m1.2.2.2.4.1.cmml">∂</mo><mo id="S1.E2.m1.2.2.2.4a" xref="S1.E2.m1.2.2.2.4.cmml">⁡</mo><mover accent="true" id="S1.E2.m1.2.2.2.4.2" xref="S1.E2.m1.2.2.2.4.2.cmml"><mi id="S1.E2.m1.2.2.2.4.2.2" xref="S1.E2.m1.2.2.2.4.2.2.cmml">h</mi><mo stretchy="false" id="S1.E2.m1.2.2.2.4.2.1" xref="S1.E2.m1.2.2.2.4.2.1.cmml">~</mo></mover></mrow><mo id="S1.E2.m1.2.2.2.3" xref="S1.E2.m1.2.2.2.3.cmml">⁢</mo><mrow id="S1.E2.m1.2.2.2.5.2" xref="S1.E2.m1.2.2.2.5.1.cmml"><mo id="S1.E2.m1.2.2.2.5.2.1" xref="S1.E2.m1.2.2.2.5.1.cmml">(</mo><mi id="S1.E2.m1.1.1.1.1" xref="S1.E2.m1.1.1.1.1.cmml">x</mi><mo id="S1.E2.m1.2.2.2.5.2.2" xref="S1.E2.m1.2.2.2.5.1.cmml">,</mo><mi id="S1.E2.m1.2.2.2.2" xref="S1.E2.m1.2.2.2.2.cmml">t</mi><mo id="S1.E2.m1.2.2.2.5.2.3" xref="S1.E2.m1.2.2.2.5.1.cmml">)</mo></mrow></mrow><mrow id="S1.E2.m1.2.2.4" xref="S1.E2.m1.2.2.4.cmml"><mo id="S1.E2.m1.2.2.4.1" xref="S1.E2.m1.2.2.4.1.cmml">∂</mo><mo id="S1.E2.m1.2.2.4a" xref="S1.E2.m1.2.2.4.cmml">⁡</mo><mi id="S1.E2.m1.2.2.4.2" xref="S1.E2.m1.2.2.4.2.cmml">x</mi></mrow></mfrac></mrow><mo id="S1.E2.m1.11.11.1.1.1.1.1.1" xref="S1.E2.m1.11.11.1.1.1.1.1.1.cmml">+</mo><mrow id="S1.E2.m1.11.11.1.1.1.1.1.3" xref="S1.E2.m1.11.11.1.1.1.1.1.3.cmml"><mpadded width="+1.7pt" id="S1.E2.m1.11.11.1.1.1.1.1.3.2" xref="S1.E2.m1.11.11.1.1.1.1.1.3.2.cmml"><mi id="S1.E2.m1.11.11.1.1.1.1.1.3.2a" xref="S1.E2.m1.11.11.1.1.1.1.1.3.2.cmml">κ</mi></mpadded><mo id="S1.E2.m1.11.11.1.1.1.1.1.3.1" xref="S1.E2.m1.11.11.1.1.1.1.1.3.1.cmml">⁢</mo><mfrac id="S1.E2.m1.4.4" xref="S1.E2.m1.4.4.cmml"><mrow id="S1.E2.m1.4.4.2" xref="S1.E2.m1.4.4.2.cmml"><mrow id="S1.E2.m1.4.4.2.4" xref="S1.E2.m1.4.4.2.4.cmml"><msup id="S1.E2.m1.4.4.2.4.1" xref="S1.E2.m1.4.4.2.4.1.cmml"><mo id="S1.E2.m1.4.4.2.4.1.2" xref="S1.E2.m1.4.4.2.4.1.2.cmml">∂</mo><mn id="S1.E2.m1.4.4.2.4.1.3" xref="S1.E2.m1.4.4.2.4.1.3.cmml">2</mn></msup><mo id="S1.E2.m1.4.4.2.4a" xref="S1.E2.m1.4.4.2.4.cmml">⁡</mo><mover accent="true" id="S1.E2.m1.4.4.2.4.2" xref="S1.E2.m1.4.4.2.4.2.cmml"><mi id="S1.E2.m1.4.4.2.4.2.2" xref="S1.E2.m1.4.4.2.4.2.2.cmml">h</mi><mo stretchy="false" id="S1.E2.m1.4.4.2.4.2.1" xref="S1.E2.m1.4.4.2.4.2.1.cmml">~</mo></mover></mrow><mo id="S1.E2.m1.4.4.2.3" xref="S1.E2.m1.4.4.2.3.cmml">⁢</mo><mrow id="S1.E2.m1.4.4.2.5.2" xref="S1.E2.m1.4.4.2.5.1.cmml"><mo id="S1.E2.m1.4.4.2.5.2.1" xref="S1.E2.m1.4.4.2.5.1.cmml">(</mo><mi id="S1.E2.m1.3.3.1.1" xref="S1.E2.m1.3.3.1.1.cmml">x</mi><mo id="S1.E2.m1.4.4.2.5.2.2" xref="S1.E2.m1.4.4.2.5.1.cmml">,</mo><mi id="S1.E2.m1.4.4.2.2" xref="S1.E2.m1.4.4.2.2.cmml">t</mi><mo id="S1.E2.m1.4.4.2.5.2.3" xref="S1.E2.m1.4.4.2.5.1.cmml">)</mo></mrow></mrow><mrow id="S1.E2.m1.4.4.4" xref="S1.E2.m1.4.4.4.cmml"><mo id="S1.E2.m1.4.4.4.1" xref="S1.E2.m1.4.4.4.1.cmml">∂</mo><mo id="S1.E2.m1.4.4.4a" xref="S1.E2.m1.4.4.4.cmml">⁡</mo><msup id="S1.E2.m1.4.4.4.2" xref="S1.E2.m1.4.4.4.2.cmml"><mi id="S1.E2.m1.4.4.4.2.2" xref="S1.E2.m1.4.4.4.2.2.cmml">x</mi><mn id="S1.E2.m1.4.4.4.2.3" xref="S1.E2.m1.4.4.4.2.3.cmml">2</mn></msup></mrow></mfrac></mrow></mrow><mo id="S1.E2.m1.11.11.1.1.1.1.3" xref="S1.E2.m1.11.11.1.1.1.2.1.cmml">]</mo></mrow></mrow></mrow><mo id="S1.E2.m1.11.11.5" xref="S1.E2.m1.11.11.5.cmml">=</mo><mrow id="S1.E2.m1.11.11.6" xref="S1.E2.m1.11.11.6.cmml"><mo id="S1.E2.m1.11.11.6.1" xref="S1.E2.m1.11.11.6.1.cmml">-</mo><mrow id="S1.E2.m1.11.11.6.2" xref="S1.E2.m1.11.11.6.2.cmml"><mfrac id="S1.E2.m1.6.6" xref="S1.E2.m1.6.6.cmml"><mrow id="S1.E2.m1.6.6.2" xref="S1.E2.m1.6.6.2.cmml"><mrow id="S1.E2.m1.6.6.2.4" xref="S1.E2.m1.6.6.2.4.cmml"><mo id="S1.E2.m1.6.6.2.4.1" xref="S1.E2.m1.6.6.2.4.1.cmml">∂</mo><mo id="S1.E2.m1.6.6.2.4a" xref="S1.E2.m1.6.6.2.4.cmml">⁡</mo><mover accent="true" id="S1.E2.m1.6.6.2.4.2" xref="S1.E2.m1.6.6.2.4.2.cmml"><mi id="S1.E2.m1.6.6.2.4.2.2" xref="S1.E2.m1.6.6.2.4.2.2.cmml">h</mi><mo stretchy="false" id="S1.E2.m1.6.6.2.4.2.1" xref="S1.E2.m1.6.6.2.4.2.1.cmml">~</mo></mover></mrow><mo id="S1.E2.m1.6.6.2.3" xref="S1.E2.m1.6.6.2.3.cmml">⁢</mo><mrow id="S1.E2.m1.6.6.2.5.2" xref="S1.E2.m1.6.6.2.5.1.cmml"><mo id="S1.E2.m1.6.6.2.5.2.1" xref="S1.E2.m1.6.6.2.5.1.cmml">(</mo><mi id="S1.E2.m1.5.5.1.1" xref="S1.E2.m1.5.5.1.1.cmml">x</mi><mo id="S1.E2.m1.6.6.2.5.2.2" xref="S1.E2.m1.6.6.2.5.1.cmml">,</mo><mi id="S1.E2.m1.6.6.2.2" xref="S1.E2.m1.6.6.2.2.cmml">t</mi><mo id="S1.E2.m1.6.6.2.5.2.3" xref="S1.E2.m1.6.6.2.5.1.cmml">)</mo></mrow></mrow><mrow id="S1.E2.m1.6.6.4" xref="S1.E2.m1.6.6.4.cmml"><mo id="S1.E2.m1.6.6.4.1" xref="S1.E2.m1.6.6.4.1.cmml">∂</mo><mo id="S1.E2.m1.6.6.4a" xref="S1.E2.m1.6.6.4.cmml">⁡</mo><mi id="S1.E2.m1.6.6.4.2" xref="S1.E2.m1.6.6.4.2.cmml">t</mi></mrow></mfrac><mo id="S1.E2.m1.11.11.6.2.1" xref="S1.E2.m1.11.11.6.2.1.cmml">⁢</mo><mtext id="S1.E2.m1.11.11.6.2.2" xref="S1.E2.m1.11.11.6.2.2a.cmml">,</mtext></mrow></mrow></mrow></math>, <math><mrow id="S1.p6.2.m2.2.2" xref="S1.p6.2.m2.2.2.cmml"><mpadded lspace="1.7pt" width="+1.7pt" id="S1.p6.2.m2.2.2.4" xref="S1.p6.2.m2.2.2.4.cmml"><mover accent="true" id="S1.p6.2.m2.2.2.4a" xref="S1.p6.2.m2.2.2.4.cmml"><mi id="S1.p6.2.m2.2.2.4.2" xref="S1.p6.2.m2.2.2.4.2.cmml">h</mi><mo stretchy="false" id="S1.p6.2.m2.2.2.4.1" xref="S1.p6.2.m2.2.2.4.1.cmml">~</mo></mover></mpadded><mo id="S1.p6.2.m2.2.2.3" xref="S1.p6.2.m2.2.2.3.cmml">=</mo><mrow id="S1.p6.2.m2.2.2.2.2" xref="S1.p6.2.m2.2.2.2.3.cmml"><mrow id="S1.p6.2.m2.1.1.1.1.1" xref="S1.p6.2.m2.1.1.1.1.1.cmml"><mi id="S1.p6.2.m2.1.1.1.1.1.2" xref="S1.p6.2.m2.1.1.1.1.1.2.cmml">h</mi><mo id="S1.p6.2.m2.1.1.1.1.1.1" xref="S1.p6.2.m2.1.1.1.1.1.1.cmml">+</mo><mrow id="S1.p6.2.m2.1.1.1.1.1.3" xref="S1.p6.2.m2.1.1.1.1.1.3.cmml"><mi id="S1.p6.2.m2.1.1.1.1.1.3.2" xref="S1.p6.2.m2.1.1.1.1.1.3.2.cmml">x</mi><mo id="S1.p6.2.m2.1.1.1.1.1.3.1" xref="S1.p6.2.m2.1.1.1.1.1.3.1.cmml">⁢</mo><mrow id="S1.p6.2.m2.1.1.1.1.1.3.3" xref="S1.p6.2.m2.1.1.1.1.1.3.3.cmml"><mi id="S1.p6.2.m2.1.1.1.1.1.3.3.1" xref="S1.p6.2.m2.1.1.1.1.1.3.3.1.cmml">tan</mi><mo id="S1.p6.2.m2.1.1.1.1.1.3.3a" xref="S1.p6.2.m2.1.1.1.1.1.3.3.cmml">⁡</mo><msub id="S1.p6.2.m2.1.1.1.1.1.3.3.2" xref="S1.p6.2.m2.1.1.1.1.1.3.3.2.cmml"><mi id="S1.p6.2.m2.1.1.1.1.1.3.3.2.2" xref="S1.p6.2.m2.1.1.1.1.1.3.3.2.2.cmml">θ</mi><mi id="S1.p6.2.m2.1.1.1.1.1.3.3.2.3" xref="S1.p6.2.m2.1.1.1.1.1.3.3.2.3.cmml">r</mi></msub></mrow></mrow></mrow><mo rspace="9.7pt" id="S1.p6.2.m2.2.2.2.2.3" xref="S1.p6.2.m2.2.2.2.3.cmml">,</mo><msub id="S1.p6.2.m2.2.2.2.2.2" xref="S1.p6.2.m2.2.2.2.2.2.cmml"><mi id="S1.p6.2.m2.2.2.2.2.2.2" xref="S1.p6.2.m2.2.2.2.2.2.2.cmml">θ</mi><mi id="S1.p6.2.m2.2.2.2.2.2.3" xref="S1.p6.2.m2.2.2.2.2.2.3.cmml">r</mi></msub></mrow></mrow></math>, <math><mrow id="S2.p1.3.m3.1.1" xref="S2.p1.3.m3.1.1.cmml"><msub id="S2.p1.3.m3.1.1.2" xref="S2.p1.3.m3.1.1.2.cmml"><mi id="S2.p1.3.m3.1.1.2.2" xref="S2.p1.3.m3.1.1.2.2.cmml">x</mi><mi id="S2.p1.3.m3.1.1.2.3" xref="S2.p1.3.m3.1.1.2.3.cmml">o</mi></msub><mo id="S2.p1.3.m3.1.1.1" xref="S2.p1.3.m3.1.1.1.cmml">+</mo><mrow id="S2.p1.3.m3.1.1.3" xref="S2.p1.3.m3.1.1.3.cmml"><mi id="S2.p1.3.m3.1.1.3.2" xref="S2.p1.3.m3.1.1.3.2.cmml">δ</mi><mo id="S2.p1.3.m3.1.1.3.1" xref="S2.p1.3.m3.1.1.3.1.cmml">⁢</mo><mi id="S2.p1.3.m3.1.1.3.3" xref="S2.p1.3.m3.1.1.3.3.cmml">x</mi></mrow></mrow></math>, <math><mrow id="S2.Ex1.m1.10.10" xref="S2.Ex1.m1.10.10.cmml"><mrow id="S2.Ex1.m1.10.10.3" xref="S2.Ex1.m1.10.10.3.cmml"><mi id="S2.Ex1.m1.10.10.3.2" xref="S2.Ex1.m1.10.10.3.2.cmml">δ</mi><mo id="S2.Ex1.m1.10.10.3.1" xref="S2.Ex1.m1.10.10.3.1.cmml">⁢</mo><msub id="S2.Ex1.m1.10.10.3.3" xref="S2.Ex1.m1.10.10.3.3.cmml"><mi id="S2.Ex1.m1.10.10.3.3.2" xref="S2.Ex1.m1.10.10.3.3.2.cmml">m</mi><mi id="S2.Ex1.m1.10.10.3.3.3" xref="S2.Ex1.m1.10.10.3.3.3.cmml">r</mi></msub></mrow><mo id="S2.Ex1.m1.10.10.2" xref="S2.Ex1.m1.10.10.2.cmml">=</mo><mrow id="S2.Ex1.m1.10.10.1" xref="S2.Ex1.m1.10.10.1.cmml"><munderover id="S2.Ex1.m1.10.10.1.2" xref="S2.Ex1.m1.10.10.1.2.cmml"><mo largeop="true" movablelimits="false" symmetric="true" id="S2.Ex1.m1.10.10.1.2.2.2" xref="S2.Ex1.m1.10.10.1.2.2.2.cmml">∫</mo><msub id="S2.Ex1.m1.10.10.1.2.2.3" xref="S2.Ex1.m1.10.10.1.2.2.3.cmml"><mi id="S2.Ex1.m1.10.10.1.2.2.3.2" xref="S2.Ex1.m1.10.10.1.2.2.3.2.cmml">x</mi><mi id="S2.Ex1.m1.10.10.1.2.2.3.3" xref="S2.Ex1.m1.10.10.1.2.2.3.3.cmml">o</mi></msub><mrow id="S2.Ex1.m1.10.10.1.2.3" xref="S2.Ex1.m1.10.10.1.2.3.cmml"><msub id="S2.Ex1.m1.10.10.1.2.3.2" xref="S2.Ex1.m1.10.10.1.2.3.2.cmml"><mi id="S2.Ex1.m1.10.10.1.2.3.2.2" xref="S2.Ex1.m1.10.10.1.2.3.2.2.cmml">x</mi><mi id="S2.Ex1.m1.10.10.1.2.3.2.3" xref="S2.Ex1.m1.10.10.1.2.3.2.3.cmml">o</mi></msub><mo id="S2.Ex1.m1.10.10.1.2.3.1" xref="S2.Ex1.m1.10.10.1.2.3.1.cmml">+</mo><mrow id="S2.Ex1.m1.10.10.1.2.3.3" xref="S2.Ex1.m1.10.10.1.2.3.3.cmml"><mi id="S2.Ex1.m1.10.10.1.2.3.3.2" xref="S2.Ex1.m1.10.10.1.2.3.3.2.cmml">δ</mi><mo id="S2.Ex1.m1.10.10.1.2.3.3.1" xref="S2.Ex1.m1.10.10.1.2.3.3.1.cmml">⁢</mo><mi id="S2.Ex1.m1.10.10.1.2.3.3.3" xref="S2.Ex1.m1.10.10.1.2.3.3.3.cmml">x</mi></mrow></mrow></munderover><mrow id="S2.Ex1.m1.10.10.1.1" xref="S2.Ex1.m1.10.10.1.1.cmml"><mrow id="S2.Ex1.m1.10.10.1.1.1.1" xref="S2.Ex1.m1.10.10.1.1.1.2.cmml"><mo id="S2.Ex1.m1.10.10.1.1.1.1.2" xref="S2.Ex1.m1.10.10.1.1.1.2.1.cmml">[</mo><mrow id="S2.Ex1.m1.10.10.1.1.1.1.1" xref="S2.Ex1.m1.10.10.1.1.1.1.1.cmml"><munderover id="S2.Ex1.m1.10.10.1.1.1.1.1.1" xref="S2.Ex1.m1.10.10.1.1.1.1.1.1.cmml"><mo largeop="true" movablelimits="false" symmetric="true" id="S2.Ex1.m1.10.10.1.1.1.1.1.1.2.2" xref="S2.Ex1.m1.10.10.1.1.1.1.1.1.2.2.cmml">∫</mo><mrow id="S2.Ex1.m1.2.2.2" xref="S2.Ex1.m1.2.2.2.cmml"><mi id="S2.Ex1.m1.2.2.2.4" xref="S2.Ex1.m1.2.2.2.4.cmml">h</mi><mo id="S2.Ex1.m1.2.2.2.3" xref="S2.Ex1.m1.2.2.2.3.cmml">⁢</mo><mrow id="S2.Ex1.m1.2.2.2.5.2" xref="S2.Ex1.m1.2.2.2.5.1.cmml"><mo id="S2.Ex1.m1.2.2.2.5.2.1" xref="S2.Ex1.m1.2.2.2.5.1.cmml">(</mo><mi id="S2.Ex1.m1.1.1.1.1" xref="S2.Ex1.m1.1.1.1.1.cmml">x</mi><mo id="S2.Ex1.m1.2.2.2.5.2.2" xref="S2.Ex1.m1.2.2.2.5.1.cmml">,</mo><mi id="S2.Ex1.m1.2.2.2.2" xref="S2.Ex1.m1.2.2.2.2.cmml">t</mi><mo id="S2.Ex1.m1.2.2.2.5.2.3" xref="S2.Ex1.m1.2.2.2.5.1.cmml">)</mo></mrow></mrow><mrow id="S2.Ex1.m1.6.6.4" xref="S2.Ex1.m1.6.6.4.cmml"><mrow id="S2.Ex1.m1.6.6.4.6" xref="S2.Ex1.m1.6.6.4.6.cmml"><mi id="S2.Ex1.m1.6.6.4.6.2" xref="S2.Ex1.m1.6.6.4.6.2.cmml">h</mi><mo id="S2.Ex1.m1.6.6.4.6.1" xref="S2.Ex1.m1.6.6.4.6.1.cmml">⁢</mo><mrow id="S2.Ex1.m1.6.6.4.6.3.2" xref="S2.Ex1.m1.6.6.4.6.3.1.cmml"><mo id="S2.Ex1.m1.6.6.4.6.3.2.1" xref="S2.Ex1.m1.6.6.4.6.3.1.cmml">(</mo><mi id="S2.Ex1.m1.3.3.1.1" xref="S2.Ex1.m1.3.3.1.1.cmml">x</mi><mo id="S2.Ex1.m1.6.6.4.6.3.2.2" xref="S2.Ex1.m1.6.6.4.6.3.1.cmml">,</mo><mi id="S2.Ex1.m1.4.4.2.2" xref="S2.Ex1.m1.4.4.2.2.cmml">t</mi><mo id="S2.Ex1.m1.6.6.4.6.3.2.3" xref="S2.Ex1.m1.6.6.4.6.3.1.cmml">)</mo></mrow></mrow><mo id="S2.Ex1.m1.6.6.4.5" xref="S2.Ex1.m1.6.6.4.5.cmml">+</mo><mrow id="S2.Ex1.m1.6.6.4.7" xref="S2.Ex1.m1.6.6.4.7.cmml"><mi id="S2.Ex1.m1.6.6.4.7.2" xref="S2.Ex1.m1.6.6.4.7.2.cmml">r</mi><mo id="S2.Ex1.m1.6.6.4.7.1" xref="S2.Ex1.m1.6.6.4.7.1.cmml">⁢</mo><mrow id="S2.Ex1.m1.6.6.4.7.3.2" xref="S2.Ex1.m1.6.6.4.7.3.1.cmml"><mo id="S2.Ex1.m1.6.6.4.7.3.2.1" xref="S2.Ex1.m1.6.6.4.7.3.1.cmml">(</mo><mi id="S2.Ex1.m1.5.5.3.3" xref="S2.Ex1.m1.5.5.3.3.cmml">x</mi><mo id="S2.Ex1.m1.6.6.4.7.3.2.2" xref="S2.Ex1.m1.6.6.4.7.3.1.cmml">,</mo><mi id="S2.Ex1.m1.6.6.4.4" xref="S2.Ex1.m1.6.6.4.4.cmml">t</mi><mo id="S2.Ex1.m1.6.6.4.7.3.2.3" xref="S2.Ex1.m1.6.6.4.7.3.1.cmml">)</mo></mrow></mrow></mrow></munderover><mrow id="S2.Ex1.m1.10.10.1.1.1.1.1.2" xref="S2.Ex1.m1.10.10.1.1.1.1.1.2.cmml"><msub id="S2.Ex1.m1.10.10.1.1.1.1.1.2.2" xref="S2.Ex1.m1.10.10.1.1.1.1.1.2.2.cmml"><mi id="S2.Ex1.m1.10.10.1.1.1.1.1.2.2.2" xref="S2.Ex1.m1.10.10.1.1.1.1.1.2.2.2.cmml">ρ</mi><mi id="S2.Ex1.m1.10.10.1.1.1.1.1.2.2.3" xref="S2.Ex1.m1.10.10.1.1.1.1.1.2.2.3.cmml">r</mi></msub><mo id="S2.Ex1.m1.10.10.1.1.1.1.1.2.1" xref="S2.Ex1.m1.10.10.1.1.1.1.1.2.1.cmml">⁢</mo><mrow id="S2.Ex1.m1.10.10.1.1.1.1.1.2.3.2" xref="S2.Ex1.m1.10.10.1.1.1.1.1.2.3.1.cmml"><mo id="S2.Ex1.m1.10.10.1.1.1.1.1.2.3.2.1" xref="S2.Ex1.m1.10.10.1.1.1.1.1.2.3.1.cmml">(</mo><mi id="S2.Ex1.m1.7.7" xref="S2.Ex1.m1.7.7.cmml">x</mi><mo id="S2.Ex1.m1.10.10.1.1.1.1.1.2.3.2.2" xref="S2.Ex1.m1.10.10.1.1.1.1.1.2.3.1.cmml">,</mo><mi id="S2.Ex1.m1.8.8" xref="S2.Ex1.m1.8.8.cmml">y</mi><mo id="S2.Ex1.m1.10.10.1.1.1.1.1.2.3.2.3" xref="S2.Ex1.m1.10.10.1.1.1.1.1.2.3.1.cmml">,</mo><mi id="S2.Ex1.m1.9.9" xref="S2.Ex1.m1.9.9.cmml">t</mi><mo id="S2.Ex1.m1.10.10.1.1.1.1.1.2.3.2.4" xref="S2.Ex1.m1.10.10.1.1.1.1.1.2.3.1.cmml">)</mo></mrow><mo id="S2.Ex1.m1.10.10.1.1.1.1.1.2.1a" xref="S2.Ex1.m1.10.10.1.1.1.1.1.2.1.cmml">⁢</mo><mrow id="S2.Ex1.m1.10.10.1.1.1.1.1.2.4" xref="S2.Ex1.m1.10.10.1.1.1.1.1.2.4.cmml"><mo rspace="0pt" id="S2.Ex1.m1.10.10.1.1.1.1.1.2.4.1" xref="S2.Ex1.m1.10.10.1.1.1.1.1.2.4.1.cmml">𝑑</mo><mi id="S2.Ex1.m1.10.10.1.1.1.1.1.2.4.2" xref="S2.Ex1.m1.10.10.1.1.1.1.1.2.4.2.cmml">y</mi></mrow></mrow></mrow><mo id="S2.Ex1.m1.10.10.1.1.1.1.3" xref="S2.Ex1.m1.10.10.1.1.1.2.1.cmml">]</mo></mrow><mo id="S2.Ex1.m1.10.10.1.1.2" xref="S2.Ex1.m1.10.10.1.1.2.cmml">⁢</mo><mrow id="S2.Ex1.m1.10.10.1.1.3" xref="S2.Ex1.m1.10.10.1.1.3.cmml"><mo rspace="0pt" id="S2.Ex1.m1.10.10.1.1.3.1" xref="S2.Ex1.m1.10.10.1.1.3.1.cmml">𝑑</mo><mi id="S2.Ex1.m1.10.10.1.1.3.2" xref="S2.Ex1.m1.10.10.1.1.3.2.cmml">x</mi></mrow><mo id="S2.Ex1.m1.10.10.1.1.2a" xref="S2.Ex1.m1.10.10.1.1.2.cmml">⁢</mo><mtext id="S2.Ex1.m1.10.10.1.1.4" xref="S2.Ex1.m1.10.10.1.1.4a.cmml">,</mtext></mrow></mrow></mrow></math>, <math><mrow id="S2.Ex2.m1.2.3" xref="S2.Ex2.m1.2.3.cmml"><mi id="S2.Ex2.m1.2.3.2" xref="S2.Ex2.m1.2.3.2.cmml">h</mi><mo id="S2.Ex2.m1.2.3.1" xref="S2.Ex2.m1.2.3.1.cmml">⁢</mo><mrow id="S2.Ex2.m1.2.3.3.2" xref="S2.Ex2.m1.2.3.3.1.cmml"><mo id="S2.Ex2.m1.2.3.3.2.1" xref="S2.Ex2.m1.2.3.3.1.cmml">(</mo><mi id="S2.Ex2.m1.1.1" xref="S2.Ex2.m1.1.1.cmml">x</mi><mo id="S2.Ex2.m1.2.3.3.2.2" xref="S2.Ex2.m1.2.3.3.1.cmml">,</mo><mi id="S2.Ex2.m1.2.2" xref="S2.Ex2.m1.2.2.cmml">t</mi><mo id="S2.Ex2.m1.2.3.3.2.3" xref="S2.Ex2.m1.2.3.3.1.cmml">)</mo></mrow></mrow></math>, <math><mrow id="S2.Ex2.m3.1.1" xref="S2.Ex2.m3.1.1.cmml"><mtext id="S2.Ex2.m3.1.1.2" xref="S2.Ex2.m3.1.1.2a.cmml">height of the static phase in a point </mtext><mo id="S2.Ex2.m3.1.1.1" xref="S2.Ex2.m3.1.1.1.cmml">⁢</mo><mi id="S2.Ex2.m3.1.1.3" xref="S2.Ex2.m3.1.1.3.cmml">x</mi><mo id="S2.Ex2.m3.1.1.1a" xref="S2.Ex2.m3.1.1.1.cmml">⁢</mo><mtext id="S2.Ex2.m3.1.1.4" xref="S2.Ex2.m3.1.1.4a.cmml"> at time </mtext><mo id="S2.Ex2.m3.1.1.1b" xref="S2.Ex2.m3.1.1.1.cmml">⁢</mo><mi id="S2.Ex2.m3.1.1.5" xref="S2.Ex2.m3.1.1.5.cmml">t</mi><mo id="S2.Ex2.m3.1.1.1c" xref="S2.Ex2.m3.1.1.1.cmml">⁢</mo><mtext id="S2.Ex2.m3.1.1.6" xref="S2.Ex2.m3.1.1.6a.cmml">,</mtext></mrow></math>, <math><mrow id="S2.Ex3.m1.2.3" xref="S2.Ex3.m1.2.3.cmml"><mi id="S2.Ex3.m1.2.3.2" xref="S2.Ex3.m1.2.3.2.cmml">r</mi><mo id="S2.Ex3.m1.2.3.1" xref="S2.Ex3.m1.2.3.1.cmml">⁢</mo><mrow id="S2.Ex3.m1.2.3.3.2" xref="S2.Ex3.m1.2.3.3.1.cmml"><mo id="S2.Ex3.m1.2.3.3.2.1" xref="S2.Ex3.m1.2.3.3.1.cmml">(</mo><mi id="S2.Ex3.m1.1.1" xref="S2.Ex3.m1.1.1.cmml">x</mi><mo id="S2.Ex3.m1.2.3.3.2.2" xref="S2.Ex3.m1.2.3.3.1.cmml">,</mo><mi id="S2.Ex3.m1.2.2" xref="S2.Ex3.m1.2.2.cmml">t</mi><mo id="S2.Ex3.m1.2.3.3.2.3" xref="S2.Ex3.m1.2.3.3.1.cmml">)</mo></mrow></mrow></math>, <math><mrow id="S2.Ex3.m3.1.1" xref="S2.Ex3.m3.1.1.cmml"><mtext id="S2.Ex3.m3.1.1.2" xref="S2.Ex3.m3.1.1.2a.cmml">height of the rolling phase in a point </mtext><mo id="S2.Ex3.m3.1.1.1" xref="S2.Ex3.m3.1.1.1.cmml">⁢</mo><mi id="S2.Ex3.m3.1.1.3" xref="S2.Ex3.m3.1.1.3.cmml">x</mi><mo id="S2.Ex3.m3.1.1.1a" xref="S2.Ex3.m3.1.1.1.cmml">⁢</mo><mtext id="S2.Ex3.m3.1.1.4" xref="S2.Ex3.m3.1.1.4a.cmml"> at a time </mtext><mo id="S2.Ex3.m3.1.1.1b" xref="S2.Ex3.m3.1.1.1.cmml">⁢</mo><mi id="S2.Ex3.m3.1.1.5" xref="S2.Ex3.m3.1.1.5.cmml">t</mi><mo id="S2.Ex3.m3.1.1.1c" xref="S2.Ex3.m3.1.1.1.cmml">⁢</mo><mtext id="S2.Ex3.m3.1.1.6" xref="S2.Ex3.m3.1.1.6a.cmml">.</mtext></mrow></math>, <math><mrow id="S2.E3.m1.12.12" xref="S2.E3.m1.12.12.cmml"><mrow id="S2.E3.m1.11.11.1" xref="S2.E3.m1.11.11.1.cmml"><mi id="S2.E3.m1.11.11.1.3" xref="S2.E3.m1.11.11.1.3.cmml">R</mi><mo id="S2.E3.m1.11.11.1.2" xref="S2.E3.m1.11.11.1.2.cmml">⁢</mo><mrow id="S2.E3.m1.11.11.1.1.1" xref="S2.E3.m1.11.11.1.1.2.cmml"><mo id="S2.E3.m1.11.11.1.1.1.2" xref="S2.E3.m1.11.11.1.1.2.cmml">(</mo><msub id="S2.E3.m1.11.11.1.1.1.1" xref="S2.E3.m1.11.11.1.1.1.1.cmml"><mi id="S2.E3.m1.11.11.1.1.1.1.2" xref="S2.E3.m1.11.11.1.1.1.1.2.cmml">x</mi><mi id="S2.E3.m1.11.11.1.1.1.1.3" xref="S2.E3.m1.11.11.1.1.1.1.3.cmml">o</mi></msub><mo id="S2.E3.m1.11.11.1.1.1.3" xref="S2.E3.m1.11.11.1.1.2.cmml">,</mo><mi id="S2.E3.m1.7.7" xref="S2.E3.m1.7.7.cmml">t</mi><mo id="S2.E3.m1.11.11.1.1.1.4" xref="S2.E3.m1.11.11.1.1.2.cmml">)</mo></mrow></mrow><mo id="S2.E3.m1.12.12.4" xref="S2.E3.m1.12.12.4.cmml">=</mo><mrow id="S2.E3.m1.12.12.5" xref="S2.E3.m1.12.12.5.cmml"><munder id="S2.E3.m1.12.12.5.1" xref="S2.E3.m1.12.12.5.1.cmml"><mo movablelimits="false" id="S2.E3.m1.12.12.5.1.2" xref="S2.E3.m1.12.12.5.1.2.cmml">lim</mo><mrow id="S2.E3.m1.12.12.5.1.3" xref="S2.E3.m1.12.12.5.1.3.cmml"><mrow id="S2.E3.m1.12.12.5.1.3.2" xref="S2.E3.m1.12.12.5.1.3.2.cmml"><mi id="S2.E3.m1.12.12.5.1.3.2.2" xref="S2.E3.m1.12.12.5.1.3.2.2.cmml">δ</mi><mo id="S2.E3.m1.12.12.5.1.3.2.1" xref="S2.E3.m1.12.12.5.1.3.2.1.cmml">⁢</mo><mi id="S2.E3.m1.12.12.5.1.3.2.3" xref="S2.E3.m1.12.12.5.1.3.2.3.cmml">x</mi></mrow><mo id="S2.E3.m1.12.12.5.1.3.1" xref="S2.E3.m1.12.12.5.1.3.1.cmml">→</mo><mn id="S2.E3.m1.12.12.5.1.3.3" xref="S2.E3.m1.12.12.5.1.3.3.cmml">0</mn></mrow></munder><mo id="S2.E3.m1.12.12.5a" xref="S2.E3.m1.12.12.5.cmml">⁡</mo><mfrac id="S2.E3.m1.12.12.5.2" xref="S2.E3.m1.12.12.5.2.cmml"><mrow id="S2.E3.m1.12.12.5.2.2" xref="S2.E3.m1.12.12.5.2.2.cmml"><mi id="S2.E3.m1.12.12.5.2.2.2" xref="S2.E3.m1.12.12.5.2.2.2.cmml">δ</mi><mo id="S2.E3.m1.12.12.5.2.2.1" xref="S2.E3.m1.12.12.5.2.2.1.cmml">⁢</mo><msub id="S2.E3.m1.12.12.5.2.2.3" xref="S2.E3.m1.12.12.5.2.2.3.cmml"><mi id="S2.E3.m1.12.12.5.2.2.3.2" xref="S2.E3.m1.12.12.5.2.2.3.2.cmml">m</mi><mi id="S2.E3.m1.12.12.5.2.2.3.3" xref="S2.E3.m1.12.12.5.2.2.3.3.cmml">r</mi></msub></mrow><mrow id="S2.E3.m1.12.12.5.2.3" xref="S2.E3.m1.12.12.5.2.3.cmml"><mi id="S2.E3.m1.12.12.5.2.3.2" xref="S2.E3.m1.12.12.5.2.3.2.cmml">δ</mi><mo id="S2.E3.m1.12.12.5.2.3.1" xref="S2.E3.m1.12.12.5.2.3.1.cmml">⁢</mo><mi id="S2.E3.m1.12.12.5.2.3.3" xref="S2.E3.m1.12.12.5.2.3.3.cmml">x</mi></mrow></mfrac></mrow><mo id="S2.E3.m1.12.12.6" xref="S2.E3.m1.12.12.6.cmml">=</mo><mrow id="S2.E3.m1.12.12.2" xref="S2.E3.m1.12.12.2.cmml"><munder id="S2.E3.m1.12.12.2.2" xref="S2.E3.m1.12.12.2.2.cmml"><mo movablelimits="false" id="S2.E3.m1.12.12.2.2.2" xref="S2.E3.m1.12.12.2.2.2.cmml">lim</mo><mrow id="S2.E3.m1.12.12.2.2.3" xref="S2.E3.m1.12.12.2.2.3.cmml"><mrow id="S2.E3.m1.12.12.2.2.3.2" xref="S2.E3.m1.12.12.2.2.3.2.cmml"><mi id="S2.E3.m1.12.12.2.2.3.2.2" xref="S2.E3.m1.12.12.2.2.3.2.2.cmml">δ</mi><mo id="S2.E3.m1.12.12.2.2.3.2.1" xref="S2.E3.m1.12.12.2.2.3.2.1.cmml">⁢</mo><mi id="S2.E3.m1.12.12.2.2.3.2.3" xref="S2.E3.m1.12.12.2.2.3.2.3.cmml">x</mi></mrow><mo id="S2.E3.m1.12.12.2.2.3.1" xref="S2.E3.m1.12.12.2.2.3.1.cmml">→</mo><mn id="S2.E3.m1.12.12.2.2.3.3" xref="S2.E3.m1.12.12.2.2.3.3.cmml">0</mn></mrow></munder><mo id="S2.E3.m1.12.12.2a" xref="S2.E3.m1.12.12.2.cmml">⁡</mo><mrow id="S2.E3.m1.12.12.2.1" xref="S2.E3.m1.12.12.2.1.cmml"><mfrac id="S2.E3.m1.12.12.2.1.3" xref="S2.E3.m1.12.12.2.1.3.cmml"><mn id="S2.E3.m1.12.12.2.1.3.2" xref="S2.E3.m1.12.12.2.1.3.2.cmml">1</mn><mrow id="S2.E3.m1.12.12.2.1.3.3" xref="S2.E3.m1.12.12.2.1.3.3.cmml"><mi id="S2.E3.m1.12.12.2.1.3.3.2" xref="S2.E3.m1.12.12.2.1.3.3.2.cmml">δ</mi><mo id="S2.E3.m1.12.12.2.1.3.3.1" xref="S2.E3.m1.12.12.2.1.3.3.1.cmml">⁢</mo><mi id="S2.E3.m1.12.12.2.1.3.3.3" xref="S2.E3.m1.12.12.2.1.3.3.3.cmml">x</mi></mrow></mfrac><mo id="S2.E3.m1.12.12.2.1.2" xref="S2.E3.m1.12.12.2.1.2.cmml">⁢</mo><mrow id="S2.E3.m1.12.12.2.1.1" xref="S2.E3.m1.12.12.2.1.1.cmml"><munderover id="S2.E3.m1.12.12.2.1.1.2" xref="S2.E3.m1.12.12.2.1.1.2.cmml"><mo largeop="true" movablelimits="false" symmetric="true" id="S2.E3.m1.12.12.2.1.1.2.2.2" xref="S2.E3.m1.12.12.2.1.1.2.2.2.cmml">∫</mo><msub id="S2.E3.m1.12.12.2.1.1.2.2.3" xref="S2.E3.m1.12.12.2.1.1.2.2.3.cmml"><mi id="S2.E3.m1.12.12.2.1.1.2.2.3.2" xref="S2.E3.m1.12.12.2.1.1.2.2.3.2.cmml">x</mi><mi id="S2.E3.m1.12.12.2.1.1.2.2.3.3" xref="S2.E3.m1.12.12.2.1.1.2.2.3.3.cmml">o</mi></msub><mrow id="S2.E3.m1.12.12.2.1.1.2.3" xref="S2.E3.m1.12.12.2.1.1.2.3.cmml"><msub id="S2.E3.m1.12.12.2.1.1.2.3.2" xref="S2.E3.m1.12.12.2.1.1.2.3.2.cmml"><mi id="S2.E3.m1.12.12.2.1.1.2.3.2.2" xref="S2.E3.m1.12.12.2.1.1.2.3.2.2.cmml">x</mi><mi id="S2.E3.m1.12.12.2.1.1.2.3.2.3" xref="S2.E3.m1.12.12.2.1.1.2.3.2.3.cmml">o</mi></msub><mo id="S2.E3.m1.12.12.2.1.1.2.3.1" xref="S2.E3.m1.12.12.2.1.1.2.3.1.cmml">+</mo><mrow id="S2.E3.m1.12.12.2.1.1.2.3.3" xref="S2.E3.m1.12.12.2.1.1.2.3.3.cmml"><mi id="S2.E3.m1.12.12.2.1.1.2.3.3.2" xref="S2.E3.m1.12.12.2.1.1.2.3.3.2.cmml">δ</mi><mo id="S2.E3.m1.12.12.2.1.1.2.3.3.1" xref="S2.E3.m1.12.12.2.1.1.2.3.3.1.cmml">⁢</mo><mi id="S2.E3.m1.12.12.2.1.1.2.3.3.3" xref="S2.E3.m1.12.12.2.1.1.2.3.3.3.cmml">x</mi></mrow></mrow></munderover><mrow id="S2.E3.m1.12.12.2.1.1.1" xref="S2.E3.m1.12.12.2.1.1.1.cmml"><mrow id="S2.E3.m1.12.12.2.1.1.1.1.1" xref="S2.E3.m1.12.12.2.1.1.1.1.2.cmml"><mo id="S2.E3.m1.12.12.2.1.1.1.1.1.2" xref="S2.E3.m1.12.12.2.1.1.1.1.2.1.cmml">[</mo><mrow id="S2.E3.m1.12.12.2.1.1.1.1.1.1" xref="S2.E3.m1.12.12.2.1.1.1.1.1.1.cmml"><munderover id="S2.E3.m1.12.12.2.1.1.1.1.1.1.1" xref="S2.E3.m1.12.12.2.1.1.1.1.1.1.1.cmml"><mo largeop="true" movablelimits="false" symmetric="true" id="S2.E3.m1.12.12.2.1.1.1.1.1.1.1.2.2" xref="S2.E3.m1.12.12.2.1.1.1.1.1.1.1.2.2.cmml">∫</mo><mrow id="S2.E3.m1.2.2.2" xref="S2.E3.m1.2.2.2.cmml"><mi id="S2.E3.m1.2.2.2.4" xref="S2.E3.m1.2.2.2.4.cmml">h</mi><mo id="S2.E3.m1.2.2.2.3" xref="S2.E3.m1.2.2.2.3.cmml">⁢</mo><mrow id="S2.E3.m1.2.2.2.5.2" xref="S2.E3.m1.2.2.2.5.1.cmml"><mo id="S2.E3.m1.2.2.2.5.2.1" xref="S2.E3.m1.2.2.2.5.1.cmml">(</mo><mi id="S2.E3.m1.1.1.1.1" xref="S2.E3.m1.1.1.1.1.cmml">x</mi><mo id="S2.E3.m1.2.2.2.5.2.2" xref="S2.E3.m1.2.2.2.5.1.cmml">,</mo><mi id="S2.E3.m1.2.2.2.2" xref="S2.E3.m1.2.2.2.2.cmml">t</mi><mo id="S2.E3.m1.2.2.2.5.2.3" xref="S2.E3.m1.2.2.2.5.1.cmml">)</mo></mrow></mrow><mrow id="S2.E3.m1.6.6.4" xref="S2.E3.m1.6.6.4.cmml"><mrow id="S2.E3.m1.6.6.4.6" xref="S2.E3.m1.6.6.4.6.cmml"><mi id="S2.E3.m1.6.6.4.6.2" xref="S2.E3.m1.6.6.4.6.2.cmml">h</mi><mo id="S2.E3.m1.6.6.4.6.1" xref="S2.E3.m1.6.6.4.6.1.cmml">⁢</mo><mrow id="S2.E3.m1.6.6.4.6.3.2" xref="S2.E3.m1.6.6.4.6.3.1.cmml"><mo id="S2.E3.m1.6.6.4.6.3.2.1" xref="S2.E3.m1.6.6.4.6.3.1.cmml">(</mo><mi id="S2.E3.m1.3.3.1.1" xref="S2.E3.m1.3.3.1.1.cmml">x</mi><mo id="S2.E3.m1.6.6.4.6.3.2.2" xref="S2.E3.m1.6.6.4.6.3.1.cmml">,</mo><mi id="S2.E3.m1.4.4.2.2" xref="S2.E3.m1.4.4.2.2.cmml">t</mi><mo id="S2.E3.m1.6.6.4.6.3.2.3" xref="S2.E3.m1.6.6.4.6.3.1.cmml">)</mo></mrow></mrow><mo id="S2.E3.m1.6.6.4.5" xref="S2.E3.m1.6.6.4.5.cmml">+</mo><mrow id="S2.E3.m1.6.6.4.7" xref="S2.E3.m1.6.6.4.7.cmml"><mi id="S2.E3.m1.6.6.4.7.2" xref="S2.E3.m1.6.6.4.7.2.cmml">r</mi><mo id="S2.E3.m1.6.6.4.7.1" xref="S2.E3.m1.6.6.4.7.1.cmml">⁢</mo><mrow id="S2.E3.m1.6.6.4.7.3.2" xref="S2.E3.m1.6.6.4.7.3.1.cmml"><mo id="S2.E3.m1.6.6.4.7.3.2.1" xref="S2.E3.m1.6.6.4.7.3.1.cmml">(</mo><mi id="S2.E3.m1.5.5.3.3" xref="S2.E3.m1.5.5.3.3.cmml">x</mi><mo id="S2.E3.m1.6.6.4.7.3.2.2" xref="S2.E3.m1.6.6.4.7.3.1.cmml">,</mo><mi id="S2.E3.m1.6.6.4.4" xref="S2.E3.m1.6.6.4.4.cmml">t</mi><mo id="S2.E3.m1.6.6.4.7.3.2.3" xref="S2.E3.m1.6.6.4.7.3.1.cmml">)</mo></mrow></mrow></mrow></munderover><mrow id="S2.E3.m1.12.12.2.1.1.1.1.1.1.2" xref="S2.E3.m1.12.12.2.1.1.1.1.1.1.2.cmml"><msub id="S2.E3.m1.12.12.2.1.1.1.1.1.1.2.2" xref="S2.E3.m1.12.12.2.1.1.1.1.1.1.2.2.cmml"><mi id="S2.E3.m1.12.12.2.1.1.1.1.1.1.2.2.2" xref="S2.E3.m1.12.12.2.1.1.1.1.1.1.2.2.2.cmml">ρ</mi><mi id="S2.E3.m1.12.12.2.1.1.1.1.1.1.2.2.3" xref="S2.E3.m1.12.12.2.1.1.1.1.1.1.2.2.3.cmml">r</mi></msub><mo id="S2.E3.m1.12.12.2.1.1.1.1.1.1.2.1" xref="S2.E3.m1.12.12.2.1.1.1.1.1.1.2.1.cmml">⁢</mo><mrow id="S2.E3.m1.12.12.2.1.1.1.1.1.1.2.3.2" xref="S2.E3.m1.12.12.2.1.1.1.1.1.1.2.3.1.cmml"><mo id="S2.E3.m1.12.12.2.1.1.1.1.1.1.2.3.2.1" xref="S2.E3.m1.12.12.2.1.1.1.1.1.1.2.3.1.cmml">(</mo><mi id="S2.E3.m1.8.8" xref="S2.E3.m1.8.8.cmml">x</mi><mo id="S2.E3.m1.12.12.2.1.1.1.1.1.1.2.3.2.2" xref="S2.E3.m1.12.12.2.1.1.1.1.1.1.2.3.1.cmml">,</mo><mi id="S2.E3.m1.9.9" xref="S2.E3.m1.9.9.cmml">y</mi><mo id="S2.E3.m1.12.12.2.1.1.1.1.1.1.2.3.2.3" xref="S2.E3.m1.12.12.2.1.1.1.1.1.1.2.3.1.cmml">,</mo><mi id="S2.E3.m1.10.10" xref="S2.E3.m1.10.10.cmml">t</mi><mo id="S2.E3.m1.12.12.2.1.1.1.1.1.1.2.3.2.4" xref="S2.E3.m1.12.12.2.1.1.1.1.1.1.2.3.1.cmml">)</mo></mrow><mo id="S2.E3.m1.12.12.2.1.1.1.1.1.1.2.1a" xref="S2.E3.m1.12.12.2.1.1.1.1.1.1.2.1.cmml">⁢</mo><mrow id="S2.E3.m1.12.12.2.1.1.1.1.1.1.2.4" xref="S2.E3.m1.12.12.2.1.1.1.1.1.1.2.4.cmml"><mo rspace="0pt" id="S2.E3.m1.12.12.2.1.1.1.1.1.1.2.4.1" xref="S2.E3.m1.12.12.2.1.1.1.1.1.1.2.4.1.cmml">𝑑</mo><mi id="S2.E3.m1.12.12.2.1.1.1.1.1.1.2.4.2" xref="S2.E3.m1.12.12.2.1.1.1.1.1.1.2.4.2.cmml">y</mi></mrow></mrow></mrow><mo id="S2.E3.m1.12.12.2.1.1.1.1.1.3" xref="S2.E3.m1.12.12.2.1.1.1.1.2.1.cmml">]</mo></mrow><mo id="S2.E3.m1.12.12.2.1.1.1.2" xref="S2.E3.m1.12.12.2.1.1.1.2.cmml">⁢</mo><mrow id="S2.E3.m1.12.12.2.1.1.1.3" xref="S2.E3.m1.12.12.2.1.1.1.3.cmml"><mo rspace="0pt" id="S2.E3.m1.12.12.2.1.1.1.3.1" xref="S2.E3.m1.12.12.2.1.1.1.3.1.cmml">𝑑</mo><mi id="S2.E3.m1.12.12.2.1.1.1.3.2" xref="S2.E3.m1.12.12.2.1.1.1.3.2.cmml">x</mi></mrow><mo id="S2.E3.m1.12.12.2.1.1.1.2a" xref="S2.E3.m1.12.12.2.1.1.1.2.cmml">⁢</mo><mtext id="S2.E3.m1.12.12.2.1.1.1.4" xref="S2.E3.m1.12.12.2.1.1.1.4a.cmml">.</mtext></mrow></mrow></mrow></mrow></mrow></math>

Correct Categorie: cond-mat

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/physics/0006063

Formulas:

1-

\bar{μ} (z) = E (z) / E_{0} (z),

2-

E_{0} (z)

3-

{\bar{μ}}_{d} (z) = E_{d} / E_{0}

4-

K (z) = - 1 / E (z) d E (z) / d z

5-

d E (z) / d z = - a (z) E_{0} (z)

6-

\bar{μ} (z) = a (z) / K (z)

7-

\bar{μ} (z)

8-

a = 0.1801 m^{- 1}

9-

b = 1.2525 m^{- 1}

10-

10 m g m^{- 3}

Formulas (html):

Correct Categorie: physics

Guessed Categorie: physics

Result: correct

Paper: https://arxiv.org/abs/2010.08971

Formulas:

1-

\hat{H} = e^{- γ t} \frac{{\hat{p}}^{2}}{2 m} + \frac{1}{2} e^{γ t} m [ω_{0}^{2} {\hat{q}}^{2} - 2 f (t) \hat{q}],

2-

f (t) = 0

3-

Q (t) = Q_{h} (t) + Q_{p} (t)

4-

Q_{h} (t)

5-

Q_{p} (t)

6-

Q_{h} (t)

7-

Q_{0} e^{- γ t / 2} \cos (ω t + φ),

8-

Q_{p} (t)

9-

\int_{0}^{t} [f (t^{'}) / ω] e^{- γ (t - t^{'}) / 2} \sin [ω (t - t^{'})] 𝑑 t^{'},

10-

ω = {(ω_{0}^{2} - γ^{2} / 4)}^{1 / 2}

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/0708.0097

Formulas:

1-

i = 83^{\circ} .63 \pm 0^{\circ} .05

2-

M_{w} = 0.90 \pm 0.01 M_{☉}

3-

M_{r} = 0.056 \pm 0.001 M_{☉}

4-

R_{r} = 0.096 \pm 0.001 R_{☉}

5-

u^{'} g^{'} r^{'}

6-

u^{'} g^{'} r^{'}

7-

T_{mid} = (T_{we} + T_{wi}) / 2

8-

\begin{matrix} H J D & = & 2453798.738844 & + & 0.04625829 & E . \\ 2 & \pm & 3 \end{matrix}

9-

u^{'} g^{'} r^{'}

10-

q = M_{r} / M_{w}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1810.01287

Formulas:

1-

D_{A} (z)

2-

D_{A} (z_{1}, z_{2}) = \frac{c_{z_{s}}}{H_{0} (1 + z_{2})} \int_{z_{1}}^{z_{2}} \frac{d z^{'}}{E (z^{'})},

3-

Δ t_{i, j} = \frac{D_{Δ t} (1 + z_{l})}{c_{z_{s}}} Δ ϕ_{i, j},

4-

Δ ϕ_{i, j} = [{(𝜽_{i} - 𝜷)}^{2} / 2 - ψ (𝜽_{i}) - {(𝜽_{j} - 𝜷)}^{2} / 2 + ψ (𝜽_{j})]

5-

\nabla^{2} ψ = 2 κ

6-

D_{Δ t} = \frac{D_{l} D_{s}}{D_{ls}} .

7-

D_{A} (z_{1}, z_{2}) = D_{P} (z_{1}, z_{2}) / (1 + z_{2})

8-

D_{l s} / D_{s}

9-

\frac{D_{l s}}{D_{s}} = 1 - \frac{1 + z_{l}}{1 + z_{s}} \frac{D_{l}}{D_{s}}

10-

c_{z_{s}} = \frac{D_{l} (1 + z_{l}) D_{s} (1 + z_{s})}{(1 + z_{s}) D_{s} - (1 + z_{l}) D_{l}} \frac{1}{Δ t_{i, j}} Δ ϕ_{i, j},

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1705.10644

Formulas:

1-

ψ_{α} (k_{VBM})

2-

ξ_{X ϕ} = {char}_{X ϕ} [ψ_{α} (Γ)] \times \frac{1}{2},

3-

{char}_{X ϕ} [ψ (k)]

4-

ζ_{X ϕ} = {char}_{X ϕ} [ψ_{β} (Γ)] \times \frac{1}{2} .

5-

\sum_{X ϕ} ξ_{X ϕ} = \sum_{X ϕ} ζ_{X ϕ} = \frac{1}{2} .

6-

V_{S, α}^{X ϕ}

7-

= V_{X} (f_{0}) - V_{X} (f_{0} - ξ_{X ϕ})

8-

V_{S, β}^{X ϕ}

9-

= - [V_{X} (f_{0}) - V_{X} (f_{0} - ζ_{X ϕ})],

10-

V_{X} (f)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/2009.11299

Formulas:

1-

M_{⊙} {yr}^{- 1}

2-

\frac{1}{R} \frac{\partial}{\partial R} (R \frac{\partial Φ_{tot}}{\partial R}) + \frac{\partial^{2} Φ_{tot}}{\partial z^{2}} = 4 π G (\sum_{i = 1}^{3} ρ_{i} + ρ_{h})

3-

\frac{\partial}{\partial z} (ρ_{i} {⟨ σ_{z}^{2} ⟩}_{i}) + ρ_{i} \frac{\partial Φ_{tot}}{\partial z} = 0

4-

\begin{matrix} {⟨ σ_{z}^{2} ⟩}_{i} \frac{\partial}{\partial z} (\frac{1}{ρ_{i}} \frac{\partial ρ_{i}}{\partial z}) & = \\ - 4 π G (ρ_{s} + ρ_{HI} + ρ_{H2} + ρ_{h}) \\ + \frac{1}{R} \frac{\partial}{\partial R} (R \frac{\partial Φ_{tot}}{\partial R}) \end{matrix}

5-

{(R \frac{\partial Φ_{tot}}{\partial R})}_{R, z} = {(v_{rot}^{2})}_{R, z}

6-

\begin{matrix} {⟨ σ_{z}^{2} ⟩}_{i} \frac{\partial}{\partial z} (\frac{1}{ρ_{i}} \frac{\partial ρ_{i}}{\partial z}) & = \\ - 4 π G (ρ_{s} + ρ_{HI} + ρ_{H2} + ρ_{h}) \\ + \frac{1}{R} \frac{\partial}{\partial R} (v_{rot}^{2}) \end{matrix}

7-

ρ_{s} (z)

8-

ρ_{H2} (z)

9-

ρ_{HI} (z)

10-

ρ_{h} (R) = \frac{ρ_{0}}{\frac{R}{R_{s}} {(1 + \frac{R}{R_{s}})}^{2}}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/0907.5131

Formulas:

1-

(2, 0, 0)

2-

(3 / 2, \sqrt{3} / 2, 0)

3-

(- 1, 0, 0)

4-

(3 / 2, 1 / 2, - 1 / 2)

5-

(1 / 2, 1 / 2, 0)

6-

(- 2.01059, 5.93236, 0)

7-

(1, \sqrt{3}, 0)

8-

(3 / 2, 3 \sqrt{3} / 2, 0)

9-

(1 / 2, \sqrt{3} / 2, \sqrt{8 / 3})

10-

(1 / 2, 3 / 2, 1 / 2)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/2010.05065

Formulas:

1-

t (G) = \min {\frac{| S |}{c (G - S)}}

2-

S \subset V (G)

3-

c (G - S) > 1

4-

c (G - S)

5-

t (G) > \frac{1}{3} (\frac{d^{2}}{d λ + λ^{2}} - 1)

6-

t (G) > \frac{d}{λ} - 2

7-

t (G) \geq \frac{d}{λ} - 1

8-

λ_{i} (G)

9-

i = 1, 2, \dots, n

10-

| λ_{i} | \leq λ_{1}

Formulas (html):

Correct Categorie: math

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/quant-ph/0403234

Formulas:

1-

x = a + a^{†}

2-

p = (a - a^{†}) / i

3-

[x, p] = 2 i

4-

γ = (\begin{matrix} ⟨ x^{2} ⟩ & \frac{1}{2} ⟨ x p + p x ⟩ \\ \frac{1}{2} ⟨ x p + p x ⟩ & ⟨ p^{2} ⟩ \end{matrix}) .

5-

⟨ x ⟩ = ⟨ p ⟩ = 0

6-

\frac{1}{\sqrt{G}} (\sqrt{H} x_{vac} + \sqrt{H - 1} x_{anc}),

7-

\sqrt{G} (\sqrt{H} p_{vac} - \sqrt{H - 1} p_{anc}),

8-

(2 H - 1) / G,

9-

(2 H - 1) G .

10-

V_{\min} + V_{\max},

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: quant-ph

Result: correct

Paper: https://arxiv.org/abs/0902.0642

Formulas:

1-

κ = \sum_{λ} κ_{λ}

2-

κ_{λ} = \sum_{𝐪} {(𝐯 (𝐪) \cdot 𝐭)}^{2} τ (𝐪) C_{p h} (ω)

3-

C_{p h} (ω)

4-

C_{p h} (ω) = ℏ ω \frac{d N^{0}}{d T} = \frac{{(ℏ ω)}^{2}}{k_{B} T^{2}} \frac{\exp (ℏ ω / k_{B} T)}{{[\exp (ℏ ω / k_{B} T) - 1]}^{2}}

5-

2 / {⟨ v ⟩}^{2} = 1 / {⟨ v_{L A} ⟩}^{2} + 1 / {⟨ v_{T A} ⟩}^{2}

6-

k_{B} T = ℏ ω

7-

\frac{1}{τ_{λ}} = 2 γ_{λ}^{2} \frac{k_{B} T}{M v^{2}} \frac{ω^{2}}{ω_{m}}

8-

γ_{λ} = - [a / 2 ω_{λ} (𝐪)] [d ω_{λ} (𝐪) / d a]

9-

ω_{Z A, Z O^{'}}

10-

κ / τ = 4.78 \times 10^{13} W m^{- 1} s^{- 1}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1109.1833

Formulas:

1-

E_{peak} (t) - L_{iso} (t)

2-

E_{peak}^{obs} (t) - P (t)

3-

E_{peak}^{obs} (t) - P (t)

4-

E_{peak}^{obs} (t) \propto P {(t)}^{a}

5-

E_{peak}^{obs} (t) - P (t)

6-

E_{peak}^{obs} (t) \propto P {(t)}^{a}

7-

E_{peak}^{obs} (t) - P (t)

8-

E_{peak}^{obs} (t) - P (t)

9-

E_{peak} (t) - L_{iso} (t)

10-

E_{peak}^{obs} (t) - P (t)

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1103.0161

Formulas:

1-

a_{M n S i} = 4.56

2-

E_{q} = D q^{2}

3-

S (q, E) = \frac{q_{d}^{2}}{κ_{1}^{2} + q^{2}} \frac{1}{2 π} \frac{E Γ}{{(E - E_{q})}^{2} + Γ^{2}} ⟨ n + 1 ⟩

4-

Γ = A q^{2.5}

5-

E_{q} = D q^{2}

6-

D_{s f} = 35

7-

D_{s w} = 23.5

8-

D_{n s f} = 0

9-

A_{n s f} = 44

10-

A_{n s f}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1007.0003

Formulas:

1-

Δ z \approx 0.5 - 1

2-

P (< δ R) \sim 0.1

3-

δ R \sim 10 ″

4-

z = 0.111, 0.473, 0.403

5-

m_{AB} (F606W) ≳ 28.5

6-

5' \times 5'

7-

⟨ r_{AB} ⟩ = 23.0 \pm 1.3

8-

⟨ r_{AB} ⟩ = 24.4 \pm 1.4

9-

N (γ) \propto γ^{- p}

10-

ν_{m} < ν_{opt} < ν_{c}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1010.0772

Formulas:

1-

𝒫 = {x_{1}, \dots, x_{m}} \subset 𝒳

2-

𝒰 = {x_{m + 1}, \dots, x_{n}}

3-

| 𝒫 | << | 𝒰 |

4-

h_{u} = γ h_{+} + (1 - γ) h_{-} .

5-

\frac{h_{u} (x)}{h_{+} (x)} = γ + (1 - γ) \frac{h_{-} (x)}{h_{+} (x)},

6-

\sim B (K, \hat{γ})

7-

𝔼 ({\hat{γ}}_{t}) = \hat{γ} and 𝕍 ({\hat{γ}}_{t}) = \frac{1}{K} \hat{γ} (1 - \hat{γ}) .

8-

f = \frac{1}{T} \sum_{t = 1}^{T} f_{t}

9-

\forall x \in 𝒰, n (x) \leftarrow 0, f (x) \leftarrow 0

10-

x \in 𝒰 ∖ 𝒰_{t}

Formulas (html):

Correct Categorie: stat

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/0812.4863

Formulas:

1-

| F = 1, m = \pm 1 ⟩

2-

\begin{matrix} {\hat{J}}_{0} & = \frac{1}{2} \hat{N_{a}}, \\ {\hat{J}}_{𝐱} & = \frac{1}{2} \sum_{k} ({\hat{F}}_{x, k}^{2} - {\hat{F}}_{y, k}^{2}), \\ {\hat{J}}_{𝐲} & = \frac{1}{2} \sum_{k} ({\hat{F}}_{x, k} {\hat{F}}_{y, k} + {\hat{F}}_{y, k} {\hat{F}}_{x, k}), \\ {\hat{J}}_{𝐳} & = \frac{1}{2} \sum_{k} {\hat{F}}_{z, k}, \end{matrix}

3-

\begin{matrix} {\hat{S}}_{0} & = \frac{1}{2} ({\hat{a}}_{+}^{†} {\hat{a}}_{+} + {\hat{a}}_{-}^{†} {\hat{a}}_{-}), \\ {\hat{S}}_{𝐱} & = \frac{1}{2} ({\hat{a}}_{-}^{†} {\hat{a}}_{+} + {\hat{a}}_{+}^{†} {\hat{a}}_{-}), \\ {\hat{S}}_{𝐲} & = \frac{i}{2} ({\hat{a}}_{-}^{†} {\hat{a}}_{+} - {\hat{a}}_{+}^{†} {\hat{a}}_{-}), \\ {\hat{S}}_{𝐳} & = \frac{1}{2} ({\hat{a}}_{+}^{†} {\hat{a}}_{+} - {\hat{a}}_{-}^{†} {\hat{a}}_{-}), \end{matrix}

4-

{𝐱, 𝐲, 𝐳}

5-

F = 1 \to F^{'}

6-

{\hat{H}}_{I} = ℏ \frac{G}{τ} {\hat{S}}_{z} {\hat{J}}_{z},

7-

G (Δ, A) = \frac{1}{A} \frac{Γ λ^{2}}{16 π} (- 4 δ_{0} (Δ) - 5 δ_{1} (Δ) + 5 δ_{2} (Δ)) .

8-

δ_{F^{'}} (Δ) = {(Δ + Δ_{0, F^{'}})}^{- 1}

9-

F^{'} = 1, 2

10-

\begin{matrix} {\hat{S}}_{𝐲}^{(out)} & \approx {\hat{S}}_{𝐲}^{(in)} + G {\hat{J}}_{𝐳}^{(in)} {\hat{S}}_{𝐱}^{(in)}, \\ {\hat{S}}_{𝐳}^{(out)} & = {\hat{S}}_{𝐳}^{(in)}, \\ {\hat{J}}_{𝐲}^{(out)} & \approx {\hat{J}}_{𝐲}^{(in)} + G {\hat{S}}_{𝐳}^{(in)} {\hat{J}}_{𝐱}^{(in)}, \\ {\hat{J}}_{𝐳}^{(out)} & = {\hat{J}}_{𝐳}^{(in)}, \end{matrix}

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/1807.03894

Formulas:

1-

M_{WD} \sim 0.6 M_{☉}

2-

M_{WD} \sim 0.82 M_{☉}

3-

M_{WD} ≳ 0.8 M_{☉}

4-

M_{WD} ≳ 1.10 M_{☉}

5-

9.0 \leq M_{ZAMS} / M_{☉} \leq 10.5

6-

Γ = \frac{e^{2}}{k_{B} a_{e} T} Z^{5 / 3}

7-

a_{e} = {(\frac{3}{4 π n_{e}})}^{1 / 3}

8-

Γ_{O} = \frac{e^{2}}{k_{B} a_{e} T} 8^{5 / 3}

9-

Γ = \frac{e^{2}}{k_{B} a_{e} T} Z_{mixture}^{5 / 3}

10-

Γ_{O} = (e^{2} / k_{B} a_{e} T) 8^{5 / 3}

Formulas (html):

<math><mrow id="S1.p2.1.m1.1.1" xref="S1.p2.1.m1.1.1.cmml"><msub id="S1.p2.1.m1.1.1.2" xref="S1.p2.1.m1.1.1.2.cmml"><mi id="S1.p2.1.m1.1.1.2.2" xref="S1.p2.1.m1.1.1.2.2.cmml">M</mi><mi id="S1.p2.1.m1.1.1.2.3" xref="S1.p2.1.m1.1.1.2.3.cmml">WD</mi></msub><mo id="S1.p2.1.m1.1.1.1" xref="S1.p2.1.m1.1.1.1.cmml">∼</mo><mrow id="S1.p2.1.m1.1.1.3" xref="S1.p2.1.m1.1.1.3.cmml"><mn id="S1.p2.1.m1.1.1.3.2" xref="S1.p2.1.m1.1.1.3.2.cmml">0.6</mn><mo id="S1.p2.1.m1.1.1.3.1" xref="S1.p2.1.m1.1.1.3.1.cmml">⁢</mo><msub id="S1.p2.1.m1.1.1.3.3" xref="S1.p2.1.m1.1.1.3.3.cmml"><mi id="S1.p2.1.m1.1.1.3.3.2" xref="S1.p2.1.m1.1.1.3.3.2.cmml">M</mi><mi mathvariant="normal" id="S1.p2.1.m1.1.1.3.3.3" xref="S1.p2.1.m1.1.1.3.3.3.cmml">☉</mi></msub></mrow></mrow></math>, <math><mrow id="S1.p2.2.m2.1.1" xref="S1.p2.2.m2.1.1.cmml"><msub id="S1.p2.2.m2.1.1.2" xref="S1.p2.2.m2.1.1.2.cmml"><mi id="S1.p2.2.m2.1.1.2.2" xref="S1.p2.2.m2.1.1.2.2.cmml">M</mi><mi id="S1.p2.2.m2.1.1.2.3" xref="S1.p2.2.m2.1.1.2.3.cmml">WD</mi></msub><mo id="S1.p2.2.m2.1.1.1" xref="S1.p2.2.m2.1.1.1.cmml">∼</mo><mrow id="S1.p2.2.m2.1.1.3" xref="S1.p2.2.m2.1.1.3.cmml"><mn id="S1.p2.2.m2.1.1.3.2" xref="S1.p2.2.m2.1.1.3.2.cmml">0.82</mn><mo id="S1.p2.2.m2.1.1.3.1" xref="S1.p2.2.m2.1.1.3.1.cmml">⁢</mo><msub id="S1.p2.2.m2.1.1.3.3" xref="S1.p2.2.m2.1.1.3.3.cmml"><mi id="S1.p2.2.m2.1.1.3.3.2" xref="S1.p2.2.m2.1.1.3.3.2.cmml">M</mi><mi mathvariant="normal" id="S1.p2.2.m2.1.1.3.3.3" xref="S1.p2.2.m2.1.1.3.3.3.cmml">☉</mi></msub></mrow></mrow></math>, <math><mrow id="S1.p2.3.m3.1.1" xref="S1.p2.3.m3.1.1.cmml"><msub id="S1.p2.3.m3.1.1.2" xref="S1.p2.3.m3.1.1.2.cmml"><mi id="S1.p2.3.m3.1.1.2.2" xref="S1.p2.3.m3.1.1.2.2.cmml">M</mi><mi id="S1.p2.3.m3.1.1.2.3" xref="S1.p2.3.m3.1.1.2.3.cmml">WD</mi></msub><mo id="S1.p2.3.m3.1.1.1" xref="S1.p2.3.m3.1.1.1.cmml">≳</mo><mrow id="S1.p2.3.m3.1.1.3" xref="S1.p2.3.m3.1.1.3.cmml"><mn id="S1.p2.3.m3.1.1.3.2" xref="S1.p2.3.m3.1.1.3.2.cmml">0.8</mn><mo id="S1.p2.3.m3.1.1.3.1" xref="S1.p2.3.m3.1.1.3.1.cmml">⁢</mo><msub id="S1.p2.3.m3.1.1.3.3" xref="S1.p2.3.m3.1.1.3.3.cmml"><mi id="S1.p2.3.m3.1.1.3.3.2" xref="S1.p2.3.m3.1.1.3.3.2.cmml">M</mi><mi mathvariant="normal" id="S1.p2.3.m3.1.1.3.3.3" xref="S1.p2.3.m3.1.1.3.3.3.cmml">☉</mi></msub></mrow></mrow></math>, <math><mrow id="S1.p2.4.m4.1.1" xref="S1.p2.4.m4.1.1.cmml"><msub id="S1.p2.4.m4.1.1.2" xref="S1.p2.4.m4.1.1.2.cmml"><mi id="S1.p2.4.m4.1.1.2.2" xref="S1.p2.4.m4.1.1.2.2.cmml">M</mi><mi id="S1.p2.4.m4.1.1.2.3" xref="S1.p2.4.m4.1.1.2.3.cmml">WD</mi></msub><mo id="S1.p2.4.m4.1.1.1" xref="S1.p2.4.m4.1.1.1.cmml">≳</mo><mrow id="S1.p2.4.m4.1.1.3" xref="S1.p2.4.m4.1.1.3.cmml"><mn id="S1.p2.4.m4.1.1.3.2" xref="S1.p2.4.m4.1.1.3.2.cmml">1.10</mn><mo id="S1.p2.4.m4.1.1.3.1" xref="S1.p2.4.m4.1.1.3.1.cmml">⁢</mo><msub id="S1.p2.4.m4.1.1.3.3" xref="S1.p2.4.m4.1.1.3.3.cmml"><mi id="S1.p2.4.m4.1.1.3.3.2" xref="S1.p2.4.m4.1.1.3.3.2.cmml">M</mi><mi mathvariant="normal" id="S1.p2.4.m4.1.1.3.3.3" xref="S1.p2.4.m4.1.1.3.3.3.cmml">☉</mi></msub></mrow></mrow></math>, <math><mrow id="S1.p7.1.m1.1.1" xref="S1.p7.1.m1.1.1.cmml"><mn id="S1.p7.1.m1.1.1.2" xref="S1.p7.1.m1.1.1.2.cmml">9.0</mn><mo id="S1.p7.1.m1.1.1.3" xref="S1.p7.1.m1.1.1.3.cmml">≤</mo><mrow id="S1.p7.1.m1.1.1.4" xref="S1.p7.1.m1.1.1.4.cmml"><msub id="S1.p7.1.m1.1.1.4.2" xref="S1.p7.1.m1.1.1.4.2.cmml"><mi id="S1.p7.1.m1.1.1.4.2.2" xref="S1.p7.1.m1.1.1.4.2.2.cmml">M</mi><mi id="S1.p7.1.m1.1.1.4.2.3" xref="S1.p7.1.m1.1.1.4.2.3.cmml">ZAMS</mi></msub><mo id="S1.p7.1.m1.1.1.4.1" xref="S1.p7.1.m1.1.1.4.1.cmml">/</mo><msub id="S1.p7.1.m1.1.1.4.3" xref="S1.p7.1.m1.1.1.4.3.cmml"><mi id="S1.p7.1.m1.1.1.4.3.2" xref="S1.p7.1.m1.1.1.4.3.2.cmml">M</mi><mi mathvariant="normal" id="S1.p7.1.m1.1.1.4.3.3" xref="S1.p7.1.m1.1.1.4.3.3.cmml">☉</mi></msub></mrow><mo id="S1.p7.1.m1.1.1.5" xref="S1.p7.1.m1.1.1.5.cmml">≤</mo><mn id="S1.p7.1.m1.1.1.6" xref="S1.p7.1.m1.1.1.6.cmml">10.5</mn></mrow></math>, <math><mrow id="S2.SS1.p1.8.m8.1.1" xref="S2.SS1.p1.8.m8.1.1.cmml"><mi mathvariant="normal" id="S2.SS1.p1.8.m8.1.1.2" xref="S2.SS1.p1.8.m8.1.1.2.cmml">Γ</mi><mo id="S2.SS1.p1.8.m8.1.1.1" xref="S2.SS1.p1.8.m8.1.1.1.cmml">=</mo><mrow id="S2.SS1.p1.8.m8.1.1.3" xref="S2.SS1.p1.8.m8.1.1.3.cmml"><mfrac id="S2.SS1.p1.8.m8.1.1.3.2" xref="S2.SS1.p1.8.m8.1.1.3.2.cmml"><msup id="S2.SS1.p1.8.m8.1.1.3.2.2" xref="S2.SS1.p1.8.m8.1.1.3.2.2.cmml"><mi mathvariant="normal" id="S2.SS1.p1.8.m8.1.1.3.2.2.2" xref="S2.SS1.p1.8.m8.1.1.3.2.2.2.cmml">e</mi><mn id="S2.SS1.p1.8.m8.1.1.3.2.2.3" xref="S2.SS1.p1.8.m8.1.1.3.2.2.3.cmml">2</mn></msup><mrow id="S2.SS1.p1.8.m8.1.1.3.2.3" xref="S2.SS1.p1.8.m8.1.1.3.2.3.cmml"><msub id="S2.SS1.p1.8.m8.1.1.3.2.3.2" xref="S2.SS1.p1.8.m8.1.1.3.2.3.2.cmml"><mi mathvariant="normal" id="S2.SS1.p1.8.m8.1.1.3.2.3.2.2" xref="S2.SS1.p1.8.m8.1.1.3.2.3.2.2.cmml">k</mi><mi mathvariant="normal" id="S2.SS1.p1.8.m8.1.1.3.2.3.2.3" xref="S2.SS1.p1.8.m8.1.1.3.2.3.2.3.cmml">B</mi></msub><mo id="S2.SS1.p1.8.m8.1.1.3.2.3.1" xref="S2.SS1.p1.8.m8.1.1.3.2.3.1.cmml">⁢</mo><msub id="S2.SS1.p1.8.m8.1.1.3.2.3.3" xref="S2.SS1.p1.8.m8.1.1.3.2.3.3.cmml"><mi mathvariant="normal" id="S2.SS1.p1.8.m8.1.1.3.2.3.3.2" xref="S2.SS1.p1.8.m8.1.1.3.2.3.3.2.cmml">a</mi><mi mathvariant="normal" id="S2.SS1.p1.8.m8.1.1.3.2.3.3.3" xref="S2.SS1.p1.8.m8.1.1.3.2.3.3.3.cmml">e</mi></msub><mo id="S2.SS1.p1.8.m8.1.1.3.2.3.1a" xref="S2.SS1.p1.8.m8.1.1.3.2.3.1.cmml">⁢</mo><mi id="S2.SS1.p1.8.m8.1.1.3.2.3.4" xref="S2.SS1.p1.8.m8.1.1.3.2.3.4.cmml">T</mi></mrow></mfrac><mo id="S2.SS1.p1.8.m8.1.1.3.1" xref="S2.SS1.p1.8.m8.1.1.3.1.cmml">⁢</mo><msup id="S2.SS1.p1.8.m8.1.1.3.3" xref="S2.SS1.p1.8.m8.1.1.3.3.cmml"><mi id="S2.SS1.p1.8.m8.1.1.3.3.2" xref="S2.SS1.p1.8.m8.1.1.3.3.2.cmml">Z</mi><mrow id="S2.SS1.p1.8.m8.1.1.3.3.3" xref="S2.SS1.p1.8.m8.1.1.3.3.3.cmml"><mn id="S2.SS1.p1.8.m8.1.1.3.3.3.2" xref="S2.SS1.p1.8.m8.1.1.3.3.3.2.cmml">5</mn><mo id="S2.SS1.p1.8.m8.1.1.3.3.3.1" xref="S2.SS1.p1.8.m8.1.1.3.3.3.1.cmml">/</mo><mn id="S2.SS1.p1.8.m8.1.1.3.3.3.3" xref="S2.SS1.p1.8.m8.1.1.3.3.3.3.cmml">3</mn></mrow></msup></mrow></mrow></math>, <math><mrow id="S2.SS1.p1.9.m9.1.2" xref="S2.SS1.p1.9.m9.1.2.cmml"><msub id="S2.SS1.p1.9.m9.1.2.2" xref="S2.SS1.p1.9.m9.1.2.2.cmml"><mi mathvariant="normal" id="S2.SS1.p1.9.m9.1.2.2.2" xref="S2.SS1.p1.9.m9.1.2.2.2.cmml">a</mi><mi mathvariant="normal" id="S2.SS1.p1.9.m9.1.2.2.3" xref="S2.SS1.p1.9.m9.1.2.2.3.cmml">e</mi></msub><mo id="S2.SS1.p1.9.m9.1.2.1" xref="S2.SS1.p1.9.m9.1.2.1.cmml">=</mo><msup id="S2.SS1.p1.9.m9.1.2.3" xref="S2.SS1.p1.9.m9.1.2.3.cmml"><mrow id="S2.SS1.p1.9.m9.1.2.3.2.2" xref="S2.SS1.p1.9.m9.1.1.cmml"><mo id="S2.SS1.p1.9.m9.1.2.3.2.2.1" xref="S2.SS1.p1.9.m9.1.1.cmml">(</mo><mfrac id="S2.SS1.p1.9.m9.1.1" xref="S2.SS1.p1.9.m9.1.1.cmml"><mn id="S2.SS1.p1.9.m9.1.1.2" xref="S2.SS1.p1.9.m9.1.1.2.cmml">3</mn><mrow id="S2.SS1.p1.9.m9.1.1.3" xref="S2.SS1.p1.9.m9.1.1.3.cmml"><mn id="S2.SS1.p1.9.m9.1.1.3.2" xref="S2.SS1.p1.9.m9.1.1.3.2.cmml">4</mn><mo id="S2.SS1.p1.9.m9.1.1.3.1" xref="S2.SS1.p1.9.m9.1.1.3.1.cmml">⁢</mo><mi id="S2.SS1.p1.9.m9.1.1.3.3" xref="S2.SS1.p1.9.m9.1.1.3.3.cmml">π</mi><mo id="S2.SS1.p1.9.m9.1.1.3.1a" xref="S2.SS1.p1.9.m9.1.1.3.1.cmml">⁢</mo><msub id="S2.SS1.p1.9.m9.1.1.3.4" xref="S2.SS1.p1.9.m9.1.1.3.4.cmml"><mi mathvariant="normal" id="S2.SS1.p1.9.m9.1.1.3.4.2" xref="S2.SS1.p1.9.m9.1.1.3.4.2.cmml">n</mi><mi mathvariant="normal" id="S2.SS1.p1.9.m9.1.1.3.4.3" xref="S2.SS1.p1.9.m9.1.1.3.4.3.cmml">e</mi></msub></mrow></mfrac><mo id="S2.SS1.p1.9.m9.1.2.3.2.2.2" xref="S2.SS1.p1.9.m9.1.1.cmml">)</mo></mrow><mrow id="S2.SS1.p1.9.m9.1.2.3.3" xref="S2.SS1.p1.9.m9.1.2.3.3.cmml"><mn id="S2.SS1.p1.9.m9.1.2.3.3.2" xref="S2.SS1.p1.9.m9.1.2.3.3.2.cmml">1</mn><mo id="S2.SS1.p1.9.m9.1.2.3.3.1" xref="S2.SS1.p1.9.m9.1.2.3.3.1.cmml">/</mo><mn id="S2.SS1.p1.9.m9.1.2.3.3.3" xref="S2.SS1.p1.9.m9.1.2.3.3.3.cmml">3</mn></mrow></msup></mrow></math>, <math><mrow id="S2.SS1.p1.14.m14.1.1" xref="S2.SS1.p1.14.m14.1.1.cmml"><msub id="S2.SS1.p1.14.m14.1.1.2" xref="S2.SS1.p1.14.m14.1.1.2.cmml"><mi mathvariant="normal" id="S2.SS1.p1.14.m14.1.1.2.2" xref="S2.SS1.p1.14.m14.1.1.2.2.cmml">Γ</mi><mi mathvariant="normal" id="S2.SS1.p1.14.m14.1.1.2.3" xref="S2.SS1.p1.14.m14.1.1.2.3.cmml">O</mi></msub><mo id="S2.SS1.p1.14.m14.1.1.1" xref="S2.SS1.p1.14.m14.1.1.1.cmml">=</mo><mrow id="S2.SS1.p1.14.m14.1.1.3" xref="S2.SS1.p1.14.m14.1.1.3.cmml"><mfrac id="S2.SS1.p1.14.m14.1.1.3.2" xref="S2.SS1.p1.14.m14.1.1.3.2.cmml"><msup id="S2.SS1.p1.14.m14.1.1.3.2.2" xref="S2.SS1.p1.14.m14.1.1.3.2.2.cmml"><mi mathvariant="normal" id="S2.SS1.p1.14.m14.1.1.3.2.2.2" xref="S2.SS1.p1.14.m14.1.1.3.2.2.2.cmml">e</mi><mn id="S2.SS1.p1.14.m14.1.1.3.2.2.3" xref="S2.SS1.p1.14.m14.1.1.3.2.2.3.cmml">2</mn></msup><mrow id="S2.SS1.p1.14.m14.1.1.3.2.3" xref="S2.SS1.p1.14.m14.1.1.3.2.3.cmml"><msub id="S2.SS1.p1.14.m14.1.1.3.2.3.2" xref="S2.SS1.p1.14.m14.1.1.3.2.3.2.cmml"><mi mathvariant="normal" id="S2.SS1.p1.14.m14.1.1.3.2.3.2.2" xref="S2.SS1.p1.14.m14.1.1.3.2.3.2.2.cmml">k</mi><mi mathvariant="normal" id="S2.SS1.p1.14.m14.1.1.3.2.3.2.3" xref="S2.SS1.p1.14.m14.1.1.3.2.3.2.3.cmml">B</mi></msub><mo id="S2.SS1.p1.14.m14.1.1.3.2.3.1" xref="S2.SS1.p1.14.m14.1.1.3.2.3.1.cmml">⁢</mo><msub id="S2.SS1.p1.14.m14.1.1.3.2.3.3" xref="S2.SS1.p1.14.m14.1.1.3.2.3.3.cmml"><mi mathvariant="normal" id="S2.SS1.p1.14.m14.1.1.3.2.3.3.2" xref="S2.SS1.p1.14.m14.1.1.3.2.3.3.2.cmml">a</mi><mi mathvariant="normal" id="S2.SS1.p1.14.m14.1.1.3.2.3.3.3" xref="S2.SS1.p1.14.m14.1.1.3.2.3.3.3.cmml">e</mi></msub><mo id="S2.SS1.p1.14.m14.1.1.3.2.3.1a" xref="S2.SS1.p1.14.m14.1.1.3.2.3.1.cmml">⁢</mo><mi id="S2.SS1.p1.14.m14.1.1.3.2.3.4" xref="S2.SS1.p1.14.m14.1.1.3.2.3.4.cmml">T</mi></mrow></mfrac><mo id="S2.SS1.p1.14.m14.1.1.3.1" xref="S2.SS1.p1.14.m14.1.1.3.1.cmml">⁢</mo><msup id="S2.SS1.p1.14.m14.1.1.3.3" xref="S2.SS1.p1.14.m14.1.1.3.3.cmml"><mn id="S2.SS1.p1.14.m14.1.1.3.3.2" xref="S2.SS1.p1.14.m14.1.1.3.3.2.cmml">8</mn><mrow id="S2.SS1.p1.14.m14.1.1.3.3.3" xref="S2.SS1.p1.14.m14.1.1.3.3.3.cmml"><mn id="S2.SS1.p1.14.m14.1.1.3.3.3.2" xref="S2.SS1.p1.14.m14.1.1.3.3.3.2.cmml">5</mn><mo id="S2.SS1.p1.14.m14.1.1.3.3.3.1" xref="S2.SS1.p1.14.m14.1.1.3.3.3.1.cmml">/</mo><mn id="S2.SS1.p1.14.m14.1.1.3.3.3.3" xref="S2.SS1.p1.14.m14.1.1.3.3.3.3.cmml">3</mn></mrow></msup></mrow></mrow></math>, <math><mrow id="S2.SS1.p1.19.m19.1.1" xref="S2.SS1.p1.19.m19.1.1.cmml"><mi mathvariant="normal" id="S2.SS1.p1.19.m19.1.1.2" xref="S2.SS1.p1.19.m19.1.1.2.cmml">Γ</mi><mo id="S2.SS1.p1.19.m19.1.1.1" xref="S2.SS1.p1.19.m19.1.1.1.cmml">=</mo><mrow id="S2.SS1.p1.19.m19.1.1.3" xref="S2.SS1.p1.19.m19.1.1.3.cmml"><mfrac id="S2.SS1.p1.19.m19.1.1.3.2" xref="S2.SS1.p1.19.m19.1.1.3.2.cmml"><msup id="S2.SS1.p1.19.m19.1.1.3.2.2" xref="S2.SS1.p1.19.m19.1.1.3.2.2.cmml"><mi mathvariant="normal" id="S2.SS1.p1.19.m19.1.1.3.2.2.2" xref="S2.SS1.p1.19.m19.1.1.3.2.2.2.cmml">e</mi><mn id="S2.SS1.p1.19.m19.1.1.3.2.2.3" xref="S2.SS1.p1.19.m19.1.1.3.2.2.3.cmml">2</mn></msup><mrow id="S2.SS1.p1.19.m19.1.1.3.2.3" xref="S2.SS1.p1.19.m19.1.1.3.2.3.cmml"><msub id="S2.SS1.p1.19.m19.1.1.3.2.3.2" xref="S2.SS1.p1.19.m19.1.1.3.2.3.2.cmml"><mi mathvariant="normal" id="S2.SS1.p1.19.m19.1.1.3.2.3.2.2" xref="S2.SS1.p1.19.m19.1.1.3.2.3.2.2.cmml">k</mi><mi mathvariant="normal" id="S2.SS1.p1.19.m19.1.1.3.2.3.2.3" xref="S2.SS1.p1.19.m19.1.1.3.2.3.2.3.cmml">B</mi></msub><mo id="S2.SS1.p1.19.m19.1.1.3.2.3.1" xref="S2.SS1.p1.19.m19.1.1.3.2.3.1.cmml">⁢</mo><msub id="S2.SS1.p1.19.m19.1.1.3.2.3.3" xref="S2.SS1.p1.19.m19.1.1.3.2.3.3.cmml"><mi mathvariant="normal" id="S2.SS1.p1.19.m19.1.1.3.2.3.3.2" xref="S2.SS1.p1.19.m19.1.1.3.2.3.3.2.cmml">a</mi><mi mathvariant="normal" id="S2.SS1.p1.19.m19.1.1.3.2.3.3.3" xref="S2.SS1.p1.19.m19.1.1.3.2.3.3.3.cmml">e</mi></msub><mo id="S2.SS1.p1.19.m19.1.1.3.2.3.1a" xref="S2.SS1.p1.19.m19.1.1.3.2.3.1.cmml">⁢</mo><mi id="S2.SS1.p1.19.m19.1.1.3.2.3.4" xref="S2.SS1.p1.19.m19.1.1.3.2.3.4.cmml">T</mi></mrow></mfrac><mo id="S2.SS1.p1.19.m19.1.1.3.1" xref="S2.SS1.p1.19.m19.1.1.3.1.cmml">⁢</mo><msubsup id="S2.SS1.p1.19.m19.1.1.3.3" xref="S2.SS1.p1.19.m19.1.1.3.3.cmml"><mi id="S2.SS1.p1.19.m19.1.1.3.3.2.2" xref="S2.SS1.p1.19.m19.1.1.3.3.2.2.cmml">Z</mi><mi id="S2.SS1.p1.19.m19.1.1.3.3.2.3" xref="S2.SS1.p1.19.m19.1.1.3.3.2.3.cmml">mixture</mi><mrow id="S2.SS1.p1.19.m19.1.1.3.3.3" xref="S2.SS1.p1.19.m19.1.1.3.3.3.cmml"><mn id="S2.SS1.p1.19.m19.1.1.3.3.3.2" xref="S2.SS1.p1.19.m19.1.1.3.3.3.2.cmml">5</mn><mo id="S2.SS1.p1.19.m19.1.1.3.3.3.1" xref="S2.SS1.p1.19.m19.1.1.3.3.3.1.cmml">/</mo><mn id="S2.SS1.p1.19.m19.1.1.3.3.3.3" xref="S2.SS1.p1.19.m19.1.1.3.3.3.3.cmml">3</mn></mrow></msubsup></mrow></mrow></math>, <math><mrow id="S2.F1.14.m7.1.1" xref="S2.F1.14.m7.1.1.cmml"><msub id="S2.F1.14.m7.1.1.3" xref="S2.F1.14.m7.1.1.3.cmml"><mi mathvariant="normal" id="S2.F1.14.m7.1.1.3.2" xref="S2.F1.14.m7.1.1.3.2.cmml">Γ</mi><mi mathvariant="normal" id="S2.F1.14.m7.1.1.3.3" xref="S2.F1.14.m7.1.1.3.3.cmml">O</mi></msub><mo mathvariant="normal" id="S2.F1.14.m7.1.1.2" xref="S2.F1.14.m7.1.1.2.cmml">=</mo><mrow id="S2.F1.14.m7.1.1.1" xref="S2.F1.14.m7.1.1.1.cmml"><mrow id="S2.F1.14.m7.1.1.1.1.1" xref="S2.F1.14.m7.1.1.1.1.1.1.cmml"><mo mathvariant="normal" stretchy="false" id="S2.F1.14.m7.1.1.1.1.1.2" xref="S2.F1.14.m7.1.1.1.1.1.1.cmml">(</mo><mrow id="S2.F1.14.m7.1.1.1.1.1.1" xref="S2.F1.14.m7.1.1.1.1.1.1.cmml"><mrow id="S2.F1.14.m7.1.1.1.1.1.1.2" xref="S2.F1.14.m7.1.1.1.1.1.1.2.cmml"><msup id="S2.F1.14.m7.1.1.1.1.1.1.2.2" xref="S2.F1.14.m7.1.1.1.1.1.1.2.2.cmml"><mi id="S2.F1.14.m7.1.1.1.1.1.1.2.2.2" xref="S2.F1.14.m7.1.1.1.1.1.1.2.2.2.cmml">e</mi><mn mathvariant="normal" id="S2.F1.14.m7.1.1.1.1.1.1.2.2.3" xref="S2.F1.14.m7.1.1.1.1.1.1.2.2.3.cmml">2</mn></msup><mo mathvariant="normal" id="S2.F1.14.m7.1.1.1.1.1.1.2.1" xref="S2.F1.14.m7.1.1.1.1.1.1.2.1.cmml">/</mo><msub id="S2.F1.14.m7.1.1.1.1.1.1.2.3" xref="S2.F1.14.m7.1.1.1.1.1.1.2.3.cmml"><mi mathvariant="normal" id="S2.F1.14.m7.1.1.1.1.1.1.2.3.2" xref="S2.F1.14.m7.1.1.1.1.1.1.2.3.2.cmml">k</mi><mi mathvariant="normal" id="S2.F1.14.m7.1.1.1.1.1.1.2.3.3" xref="S2.F1.14.m7.1.1.1.1.1.1.2.3.3.cmml">B</mi></msub></mrow><mo mathvariant="bold-sans-serif" id="S2.F1.14.m7.1.1.1.1.1.1.1" xref="S2.F1.14.m7.1.1.1.1.1.1.1.cmml">⁢</mo><msub id="S2.F1.14.m7.1.1.1.1.1.1.3" xref="S2.F1.14.m7.1.1.1.1.1.1.3.cmml"><mi mathvariant="normal" id="S2.F1.14.m7.1.1.1.1.1.1.3.2" xref="S2.F1.14.m7.1.1.1.1.1.1.3.2.cmml">a</mi><mi mathvariant="normal" id="S2.F1.14.m7.1.1.1.1.1.1.3.3" xref="S2.F1.14.m7.1.1.1.1.1.1.3.3.cmml">e</mi></msub><mo mathvariant="bold-sans-serif" id="S2.F1.14.m7.1.1.1.1.1.1.1b" xref="S2.F1.14.m7.1.1.1.1.1.1.1.cmml">⁢</mo><mi mathvariant="normal" id="S2.F1.14.m7.1.1.1.1.1.1.4" xref="S2.F1.14.m7.1.1.1.1.1.1.4.cmml">T</mi></mrow><mo mathvariant="normal" stretchy="false" id="S2.F1.14.m7.1.1.1.1.1.3" xref="S2.F1.14.m7.1.1.1.1.1.1.cmml">)</mo></mrow><mo mathvariant="bold-sans-serif" id="S2.F1.14.m7.1.1.1.2" xref="S2.F1.14.m7.1.1.1.2.cmml">⁢</mo><msup id="S2.F1.14.m7.1.1.1.3" xref="S2.F1.14.m7.1.1.1.3.cmml"><mn mathvariant="normal" id="S2.F1.14.m7.1.1.1.3.2" xref="S2.F1.14.m7.1.1.1.3.2.cmml">8</mn><mrow id="S2.F1.14.m7.1.1.1.3.3" xref="S2.F1.14.m7.1.1.1.3.3.cmml"><mn mathvariant="normal" id="S2.F1.14.m7.1.1.1.3.3.2" xref="S2.F1.14.m7.1.1.1.3.3.2.cmml">5</mn><mo mathvariant="normal" id="S2.F1.14.m7.1.1.1.3.3.1" xref="S2.F1.14.m7.1.1.1.3.3.1.cmml">/</mo><mn mathvariant="normal" id="S2.F1.14.m7.1.1.1.3.3.3" xref="S2.F1.14.m7.1.1.1.3.3.3.cmml">3</mn></mrow></msup></mrow></mrow></math>

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1101.2643

Formulas:

1-

(v_{x}, v_{y})

2-

⟨ T ⟩ = {⟨ T^{4} ⟩}^{1 / 4}

3-

χ_{exc} [e V]

4-

\frac{n_{A} n_{B}}{n_{A B}} = {(\frac{2 π m_{A B} k T}{h^{2}})}^{3 / 2} e^{- D / k T} [\frac{U_{A} (T) U_{B} (T)}{Q_{A B} (T)}] = Φ (T),

5-

n_{A, B, A B}

6-

⟨ \frac{n_{A} n_{B}}{n_{A B}} ⟩ \neq Φ (< T >),

7-

n_{A B} ≪ n_{A}, n_{B}

8-

C {(\frac{D}{k T})}^{3 / 2} e^{D / k T} \equiv C ϕ (T)

9-

n_{A} n_{B} {(\frac{h^{2}}{2 π m_{A B} D})}^{3 / 2} [\frac{Q_{A B}}{U_{A} U_{B}}] .

10-

⟨ n_{A B} (T) ⟩

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/1807.09255

Formulas:

1-

ϵ = 1 - \frac{ω_{p}^{2}}{ω^{2}}

2-

ω_{n}^{T O} = ω_{p} \sqrt{e^{- n s} \sinh (n s)}, n = 1, 2, 3, \dots,

3-

\sinh^{2} s = (δ / R) (1 + δ / 4 R)

4-

| ω_{n}^{T O} ⟩

5-

(B_{1}, B_{2})

6-

(B_{2}, B_{3})

7-

(B_{1}, B_{2})

8-

(B_{2}, B_{3})

9-

(a_{n}, b_{n})

10-

a_{n} | ω_{n}^{T O} (B_{1}, B_{2}) ⟩ + b_{n} | ω_{n}^{T O} (B_{2}, B_{3}) ⟩

Formulas (html):

Correct Categorie: physics

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/0909.5576

Formulas:

1-

{(g - 2)}_{μ}

2-

(m_{1 / 2} / m_{0})

3-

(m_{1 / 2} / m_{0})

4-

{(g - 2)}_{μ}

5-

m_{{\tilde{l}}_{L}} - m_{χ_{1}^{0}}

6-

m_{\tilde{g}} - m_{χ_{1}^{0}}

7-

m_{{\tilde{q}}_{R}} - m_{χ_{1}^{0}}

8-

m_{\tilde{g}} - m_{{\tilde{b}}_{1}}

9-

m_{\tilde{g}} - m_{{\tilde{b}}_{2}}

10-

m_{l l q}^{\max}

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1706.02849

Formulas:

1-

\sim \exp (- c o n s t | ϕ |)

2-

ω << ω_{c i}

3-

T_{i} / T_{e} << 1

4-

\frac{\partial n}{\partial t}

5-

- κ \frac{\partial ϕ}{\partial y} + α (\tilde{ϕ} - \tilde{n}) + [n, ϕ] + D \nabla^{2} n

6-

\frac{\partial}{\partial t} \nabla^{2} ϕ

7-

α (\tilde{ϕ} - \tilde{n}) + [\nabla^{2} ϕ, ϕ] + μ \nabla^{2} (\nabla^{2} ϕ),

8-

n = \tilde{n} + ⟨ n ⟩

9-

ϕ = \tilde{ϕ} + ⟨ ϕ ⟩

10-

⟨ f ⟩ = \frac{1}{L_{y}} \int_{0}^{L_{y}} f 𝑑 y .

Formulas (html):

Correct Categorie: physics

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1908.04908

Formulas:

1-

χ^{2} / d o f = 1139.0 / 1045

2-

χ^{2} / d o f = 1105.7 / 1042

3-

χ^{2} / d o f = 1047.8 / 1040

4-

n H = {0.07}_{- 0.02}^{+ 0.03} \times 10^{22}

5-

k T_{apec} = {0.96}_{- 0.09}^{+ 0.08}

6-

N o r m_{apec} = {6.4}_{- 2.1}^{+ 2.0}

7-

k T_{BB}^{low} = {0.22}_{- 0.02}^{+ 0.03}

8-

N o r m_{BB}^{low} = {86.3}_{- 47.8}^{+ 90.4}

9-

Γ = {0.73}_{- 0.02}^{+ 0.02}

10-

N o r m_{PL} = {2.66}_{- 0.09}^{+ 0.09} \times 10^{- 3}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/nlin/0607049

Formulas:

1-

\bar{X} (n) = (X (n), Y (n))

2-

X (n + 1)

3-

= Y (n) + a (1 - b Y {(n)}^{2}) Y (n) + f (X (n)) .

4-

Y (n + 1)

5-

= - X (n) + f (X (n + 1)) .

6-

f (X (n)) = μ X (n) + \frac{2 (1 - μ) X^{2} (n)}{1 + X^{2} (n)}

7-

{\bar{X}}_{d r} (t) = F ({\bar{X}}_{d} (t))

8-

X_{a} (t)

9-

X_{d r} (t)

10-

X_{a} (t)

Formulas (html):

Correct Categorie: nlin

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/0911.2437

Formulas:

1-

2.39 \begin{matrix} + 0.42 \\ - 0.33 \end{matrix} \times 10^{- 3} {eV}^{2},

2-

7.67 \begin{matrix} + 0.52 \\ - 0.53 \end{matrix} \times 10^{- 5} {eV}^{2},

3-

0.466 \begin{matrix} + 0.178 \\ - 0.135 \end{matrix},

4-

0.312 \begin{matrix} + 0.063 \\ - 0.049 \end{matrix},

5-

0.046, (0.016 \pm 0.010),

6-

U_{P M N S} = (\begin{matrix} 2 / \sqrt{6} & 1 / \sqrt{3} & 0 \\ - 1 / \sqrt{6} & 1 / \sqrt{3} & - 1 / \sqrt{2} \\ - 1 / \sqrt{6} & 1 / \sqrt{3} & 1 / \sqrt{2} \end{matrix}),

7-

\sin^{2} θ_{23} = 0.5, \sin^{2} θ_{12} = 0.33

8-

\sin^{2} θ_{13} = 0

9-

\sum_{i} m_{i} \leq 0.17 - 1.2 eV,

10-

B (ν_{α L}, N_{α L}^{c})

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/0312647

Formulas:

1-

H_{C 2} (0)

2-

H_{C 2} (T)

3-

H \sim 1.1 H_{C 2} (0)

4-

H_{C 2} (0)

5-

Δ M (T, H)

6-

H_{C 2} (0)

7-

Δ M (T, H)

8-

1.1 H_{C 2} (0)

9-

Δ M (T, H)

10-

H ≫ H_{C 2} (0)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1904.04893

Formulas:

1-

Δ t = t_{2} - t_{1}

2-

φ_{1} = 20 μ

3-

φ_{2} = 8 μ

4-

Δ t = 3, 2.5, 2

5-

φ_{1} / φ_{2} = 2.5, 2.8, 3

6-

φ_{1} / φ_{2} = 2.5

7-

φ_{1} / φ_{2} = 2.8

8-

φ_{1} / φ_{2} = 3

9-

φ_{1} / φ_{2} = 2.5

10-

\frac{\partial 𝑩}{\partial t} = η \nabla \times 𝒋_{𝒃} + \nabla (η) \times 𝒋_{𝒃} + \frac{η}{μ_{0}} \nabla^{2} 𝑩 - \frac{1}{μ_{0}} \nabla (η) \times 𝑩

Formulas (html):

Correct Categorie: physics

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/0104377

Formulas:

1-

f (x, t) + g (x) η (t)

2-

- \frac{1}{τ} \frac{d}{d η} V_{q} (η) + \frac{1}{τ} ξ (t)

3-

< ξ (t) ξ (t^{'}) > = 2 D δ (t - t^{'})

4-

V_{q} (η)

5-

V_{q} (η) = \frac{1}{β (q - 1)} \ln [1 + β (q - 1) \frac{η^{2}}{2}]

6-

f (x, t)

7-

U (x, t)

8-

S (t) \sim F \cos (ω t)

9-

f (x, t) = - \frac{\partial U}{\partial x} = - U_{0}^{'} + S (t)

10-

U_{0} (x)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1612.05034

Formulas:

1-

S U_{q} (2, 2)

2-

G L (4)

3-

U (g l (4))

4-

S L (4)

5-

U (s l (4))

6-

S L (4)

7-

S U (2, 2)

8-

U_{q} (s l (m))

9-

U_{q} (s l (4))

10-

S L_{q} (m)

Formulas (html):

Correct Categorie: math

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0510823

Formulas:

1-

S A L I (t) = m i n {∥ \frac{v_{1} (t)}{∥ v_{1} (t) ∥} + \frac{v_{2} (t)}{∥ v_{2} (t) ∥} ∥, ∥ \frac{v_{1} (t)}{∥ v_{1} (t) ∥} - \frac{v_{2} (t)}{∥ v_{2} (t) ∥} ∥} .

2-

H = \frac{1}{2} (p_{x}^{2} + p_{y}^{2} + p_{z}^{2}) + V (x, y, z) - Ω_{b} (x p_{y} - y p_{x}) .

3-

(x, y, p_{x}, p_{y}) = (1.5, 0, p_{x} (H), 0)

4-

(x, y, p_{x}, p_{y}) = (- 0.9, 0, p_{x} (H), 0)

5-

(x, \dot{x})

6-

M_{b a r}

7-

(x, p_{y}, z)

8-

(y, p_{x}, p_{z}) = (0, 0, 0)

9-

(x, p_{y}, p_{z})

10-

(y, z, p_{z}) = (0, 0, 0)

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/0709.4150

Formulas:

1-

v (r_{ij}) = v_{0} ϵ [{(\frac{σ}{r_{ij}})}^{a} - {(\frac{σ}{r_{ij}})}^{b}],

2-

ρ σ^{2} ≃ 1.16

3-

v_{0} ϵ {(σ / z_{i})}^{a}

4-

δ t = 0.0005 t_{0}

5-

t_{0} = \sqrt{ϵ σ^{2} / m}

6-

N (s) = \frac{1}{s} \int_{s}^{\infty} n (s^{'}) 𝑑 s^{'} .

7-

n (s) \sim s^{- τ}

8-

m_{2} = \sum_{s} s^{2} n (s),

9-

τ = α \ln V + β,

10-

V_{t} \leq V \leq 3

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1804.09398

Formulas:

1-

ψ_{k, 3} (x_{A})

2-

ψ_{k, 4} (x_{A})

3-

ψ_{k, b} (x_{k})

4-

ψ_{k, b} (x_{k}) = \max {0, 1 - | x_{k} - μ_{k, b} | \times w_{k, b}},

5-

\max {\cdot, \cdot}

6-

[μ_{b} - w_{k, b}, μ_{b} + w_{k, b}]

7-

ψ_{k, b} (x_{k})

8-

ψ_{k, 3} (x_{A})

9-

ψ_{k, 3} (x_{A})

10-

\frac{\partial E}{\partial w_{k, b}} = {\begin{matrix} | x_{k} - μ_{k, b} |, & ψ_{k, b} (x_{k}) > 0, \\ 0, & otherwise. \end{matrix}

Formulas (html):

<math><mrow id="S3.F3.20.m8.3.3" xref="S3.F3.20.m8.3.3.cmml"><msub id="S3.F3.20.m8.3.3.3" xref="S3.F3.20.m8.3.3.3.cmml"><mi id="S3.F3.20.m8.3.3.3.2" xref="S3.F3.20.m8.3.3.3.2.cmml">ψ</mi><mrow id="S3.F3.20.m8.2.2.2.4" xref="S3.F3.20.m8.2.2.2.3.cmml"><mi id="S3.F3.20.m8.1.1.1.1" xref="S3.F3.20.m8.1.1.1.1.cmml">k</mi><mo id="S3.F3.20.m8.2.2.2.4.1" xref="S3.F3.20.m8.2.2.2.3.cmml">,</mo><mn id="S3.F3.20.m8.2.2.2.2" xref="S3.F3.20.m8.2.2.2.2.cmml">3</mn></mrow></msub><mo id="S3.F3.20.m8.3.3.2" xref="S3.F3.20.m8.3.3.2.cmml">⁢</mo><mrow id="S3.F3.20.m8.3.3.1.1" xref="S3.F3.20.m8.3.3.1.1.1.cmml"><mo stretchy="false" id="S3.F3.20.m8.3.3.1.1.2" xref="S3.F3.20.m8.3.3.1.1.1.cmml">(</mo><msub id="S3.F3.20.m8.3.3.1.1.1" xref="S3.F3.20.m8.3.3.1.1.1.cmml"><mi id="S3.F3.20.m8.3.3.1.1.1.2" xref="S3.F3.20.m8.3.3.1.1.1.2.cmml">x</mi><mi id="S3.F3.20.m8.3.3.1.1.1.3" xref="S3.F3.20.m8.3.3.1.1.1.3.cmml">A</mi></msub><mo stretchy="false" id="S3.F3.20.m8.3.3.1.1.3" xref="S3.F3.20.m8.3.3.1.1.1.cmml">)</mo></mrow></mrow></math>, <math><mrow id="S3.F3.21.m9.3.3" xref="S3.F3.21.m9.3.3.cmml"><msub id="S3.F3.21.m9.3.3.3" xref="S3.F3.21.m9.3.3.3.cmml"><mi id="S3.F3.21.m9.3.3.3.2" xref="S3.F3.21.m9.3.3.3.2.cmml">ψ</mi><mrow id="S3.F3.21.m9.2.2.2.4" xref="S3.F3.21.m9.2.2.2.3.cmml"><mi id="S3.F3.21.m9.1.1.1.1" xref="S3.F3.21.m9.1.1.1.1.cmml">k</mi><mo id="S3.F3.21.m9.2.2.2.4.1" xref="S3.F3.21.m9.2.2.2.3.cmml">,</mo><mn id="S3.F3.21.m9.2.2.2.2" xref="S3.F3.21.m9.2.2.2.2.cmml">4</mn></mrow></msub><mo id="S3.F3.21.m9.3.3.2" xref="S3.F3.21.m9.3.3.2.cmml">⁢</mo><mrow id="S3.F3.21.m9.3.3.1.1" xref="S3.F3.21.m9.3.3.1.1.1.cmml"><mo stretchy="false" id="S3.F3.21.m9.3.3.1.1.2" xref="S3.F3.21.m9.3.3.1.1.1.cmml">(</mo><msub id="S3.F3.21.m9.3.3.1.1.1" xref="S3.F3.21.m9.3.3.1.1.1.cmml"><mi id="S3.F3.21.m9.3.3.1.1.1.2" xref="S3.F3.21.m9.3.3.1.1.1.2.cmml">x</mi><mi id="S3.F3.21.m9.3.3.1.1.1.3" xref="S3.F3.21.m9.3.3.1.1.1.3.cmml">A</mi></msub><mo stretchy="false" id="S3.F3.21.m9.3.3.1.1.3" xref="S3.F3.21.m9.3.3.1.1.1.cmml">)</mo></mrow></mrow></math>, <math><mrow id="S3.SS2.SSS2.p2.3.m3.3.3" xref="S3.SS2.SSS2.p2.3.m3.3.3.cmml"><msub id="S3.SS2.SSS2.p2.3.m3.3.3.3" xref="S3.SS2.SSS2.p2.3.m3.3.3.3.cmml"><mi id="S3.SS2.SSS2.p2.3.m3.3.3.3.2" xref="S3.SS2.SSS2.p2.3.m3.3.3.3.2.cmml">ψ</mi><mrow id="S3.SS2.SSS2.p2.3.m3.2.2.2.4" xref="S3.SS2.SSS2.p2.3.m3.2.2.2.3.cmml"><mi id="S3.SS2.SSS2.p2.3.m3.1.1.1.1" xref="S3.SS2.SSS2.p2.3.m3.1.1.1.1.cmml">k</mi><mo id="S3.SS2.SSS2.p2.3.m3.2.2.2.4.1" xref="S3.SS2.SSS2.p2.3.m3.2.2.2.3.cmml">,</mo><mi id="S3.SS2.SSS2.p2.3.m3.2.2.2.2" xref="S3.SS2.SSS2.p2.3.m3.2.2.2.2.cmml">b</mi></mrow></msub><mo id="S3.SS2.SSS2.p2.3.m3.3.3.2" xref="S3.SS2.SSS2.p2.3.m3.3.3.2.cmml">⁢</mo><mrow id="S3.SS2.SSS2.p2.3.m3.3.3.1.1" xref="S3.SS2.SSS2.p2.3.m3.3.3.1.1.1.cmml"><mo stretchy="false" id="S3.SS2.SSS2.p2.3.m3.3.3.1.1.2" xref="S3.SS2.SSS2.p2.3.m3.3.3.1.1.1.cmml">(</mo><msub id="S3.SS2.SSS2.p2.3.m3.3.3.1.1.1" xref="S3.SS2.SSS2.p2.3.m3.3.3.1.1.1.cmml"><mi id="S3.SS2.SSS2.p2.3.m3.3.3.1.1.1.2" xref="S3.SS2.SSS2.p2.3.m3.3.3.1.1.1.2.cmml">x</mi><mi id="S3.SS2.SSS2.p2.3.m3.3.3.1.1.1.3" xref="S3.SS2.SSS2.p2.3.m3.3.3.1.1.1.3.cmml">k</mi></msub><mo stretchy="false" id="S3.SS2.SSS2.p2.3.m3.3.3.1.1.3" xref="S3.SS2.SSS2.p2.3.m3.3.3.1.1.1.cmml">)</mo></mrow></mrow></math>, <math><mrow id="S3.E1.m1.9.9.1" xref="S3.E1.m1.9.9.1.1.cmml"><mrow id="S3.E1.m1.9.9.1.1" xref="S3.E1.m1.9.9.1.1.cmml"><mrow id="S3.E1.m1.9.9.1.1.1" xref="S3.E1.m1.9.9.1.1.1.cmml"><msub id="S3.E1.m1.9.9.1.1.1.3" xref="S3.E1.m1.9.9.1.1.1.3.cmml"><mi id="S3.E1.m1.9.9.1.1.1.3.2" xref="S3.E1.m1.9.9.1.1.1.3.2.cmml">ψ</mi><mrow id="S3.E1.m1.2.2.2.4" xref="S3.E1.m1.2.2.2.3.cmml"><mi id="S3.E1.m1.1.1.1.1" xref="S3.E1.m1.1.1.1.1.cmml">k</mi><mo id="S3.E1.m1.2.2.2.4.1" xref="S3.E1.m1.2.2.2.3.cmml">,</mo><mi id="S3.E1.m1.2.2.2.2" xref="S3.E1.m1.2.2.2.2.cmml">b</mi></mrow></msub><mo id="S3.E1.m1.9.9.1.1.1.2" xref="S3.E1.m1.9.9.1.1.1.2.cmml">⁢</mo><mrow id="S3.E1.m1.9.9.1.1.1.1.1" xref="S3.E1.m1.9.9.1.1.1.1.1.1.cmml"><mo stretchy="false" id="S3.E1.m1.9.9.1.1.1.1.1.2" xref="S3.E1.m1.9.9.1.1.1.1.1.1.cmml">(</mo><msub id="S3.E1.m1.9.9.1.1.1.1.1.1" xref="S3.E1.m1.9.9.1.1.1.1.1.1.cmml"><mi id="S3.E1.m1.9.9.1.1.1.1.1.1.2" xref="S3.E1.m1.9.9.1.1.1.1.1.1.2.cmml">x</mi><mi id="S3.E1.m1.9.9.1.1.1.1.1.1.3" xref="S3.E1.m1.9.9.1.1.1.1.1.1.3.cmml">k</mi></msub><mo stretchy="false" id="S3.E1.m1.9.9.1.1.1.1.1.3" xref="S3.E1.m1.9.9.1.1.1.1.1.1.cmml">)</mo></mrow></mrow><mo id="S3.E1.m1.9.9.1.1.3" xref="S3.E1.m1.9.9.1.1.3.cmml">=</mo><mrow id="S3.E1.m1.9.9.1.1.2.1" xref="S3.E1.m1.9.9.1.1.2.2.cmml"><mi id="S3.E1.m1.7.7" xref="S3.E1.m1.7.7.cmml">max</mi><mo id="S3.E1.m1.9.9.1.1.2.1a" xref="S3.E1.m1.9.9.1.1.2.2.cmml">⁡</mo><mrow id="S3.E1.m1.9.9.1.1.2.1.1" xref="S3.E1.m1.9.9.1.1.2.2.cmml"><mo id="S3.E1.m1.9.9.1.1.2.1.1.2" xref="S3.E1.m1.9.9.1.1.2.2.cmml">{</mo><mn id="S3.E1.m1.8.8" xref="S3.E1.m1.8.8.cmml">0</mn><mo id="S3.E1.m1.9.9.1.1.2.1.1.3" xref="S3.E1.m1.9.9.1.1.2.2.cmml">,</mo><mrow id="S3.E1.m1.9.9.1.1.2.1.1.1" xref="S3.E1.m1.9.9.1.1.2.1.1.1.cmml"><mn id="S3.E1.m1.9.9.1.1.2.1.1.1.3" xref="S3.E1.m1.9.9.1.1.2.1.1.1.3.cmml">1</mn><mo id="S3.E1.m1.9.9.1.1.2.1.1.1.2" xref="S3.E1.m1.9.9.1.1.2.1.1.1.2.cmml">-</mo><mrow id="S3.E1.m1.9.9.1.1.2.1.1.1.1" xref="S3.E1.m1.9.9.1.1.2.1.1.1.1.cmml"><mrow id="S3.E1.m1.9.9.1.1.2.1.1.1.1.1.1" xref="S3.E1.m1.9.9.1.1.2.1.1.1.1.1.2.cmml"><mo stretchy="false" id="S3.E1.m1.9.9.1.1.2.1.1.1.1.1.1.2" xref="S3.E1.m1.9.9.1.1.2.1.1.1.1.1.2.1.cmml">|</mo><mrow id="S3.E1.m1.9.9.1.1.2.1.1.1.1.1.1.1" xref="S3.E1.m1.9.9.1.1.2.1.1.1.1.1.1.1.cmml"><msub id="S3.E1.m1.9.9.1.1.2.1.1.1.1.1.1.1.2" xref="S3.E1.m1.9.9.1.1.2.1.1.1.1.1.1.1.2.cmml"><mi id="S3.E1.m1.9.9.1.1.2.1.1.1.1.1.1.1.2.2" xref="S3.E1.m1.9.9.1.1.2.1.1.1.1.1.1.1.2.2.cmml">x</mi><mi id="S3.E1.m1.9.9.1.1.2.1.1.1.1.1.1.1.2.3" xref="S3.E1.m1.9.9.1.1.2.1.1.1.1.1.1.1.2.3.cmml">k</mi></msub><mo id="S3.E1.m1.9.9.1.1.2.1.1.1.1.1.1.1.1" xref="S3.E1.m1.9.9.1.1.2.1.1.1.1.1.1.1.1.cmml">-</mo><msub id="S3.E1.m1.9.9.1.1.2.1.1.1.1.1.1.1.3" xref="S3.E1.m1.9.9.1.1.2.1.1.1.1.1.1.1.3.cmml"><mi id="S3.E1.m1.9.9.1.1.2.1.1.1.1.1.1.1.3.2" xref="S3.E1.m1.9.9.1.1.2.1.1.1.1.1.1.1.3.2.cmml">μ</mi><mrow id="S3.E1.m1.4.4.2.4" xref="S3.E1.m1.4.4.2.3.cmml"><mi id="S3.E1.m1.3.3.1.1" xref="S3.E1.m1.3.3.1.1.cmml">k</mi><mo id="S3.E1.m1.4.4.2.4.1" xref="S3.E1.m1.4.4.2.3.cmml">,</mo><mi id="S3.E1.m1.4.4.2.2" xref="S3.E1.m1.4.4.2.2.cmml">b</mi></mrow></msub></mrow><mo stretchy="false" id="S3.E1.m1.9.9.1.1.2.1.1.1.1.1.1.3" xref="S3.E1.m1.9.9.1.1.2.1.1.1.1.1.2.1.cmml">|</mo></mrow><mo id="S3.E1.m1.9.9.1.1.2.1.1.1.1.2" xref="S3.E1.m1.9.9.1.1.2.1.1.1.1.2.cmml">×</mo><msub id="S3.E1.m1.9.9.1.1.2.1.1.1.1.3" xref="S3.E1.m1.9.9.1.1.2.1.1.1.1.3.cmml"><mi id="S3.E1.m1.9.9.1.1.2.1.1.1.1.3.2" xref="S3.E1.m1.9.9.1.1.2.1.1.1.1.3.2.cmml">w</mi><mrow id="S3.E1.m1.6.6.2.4" xref="S3.E1.m1.6.6.2.3.cmml"><mi id="S3.E1.m1.5.5.1.1" xref="S3.E1.m1.5.5.1.1.cmml">k</mi><mo id="S3.E1.m1.6.6.2.4.1" xref="S3.E1.m1.6.6.2.3.cmml">,</mo><mi id="S3.E1.m1.6.6.2.2" xref="S3.E1.m1.6.6.2.2.cmml">b</mi></mrow></msub></mrow></mrow><mo id="S3.E1.m1.9.9.1.1.2.1.1.4" xref="S3.E1.m1.9.9.1.1.2.2.cmml">}</mo></mrow></mrow></mrow><mo id="S3.E1.m1.9.9.1.2" xref="S3.E1.m1.9.9.1.1.cmml">,</mo></mrow></math>, <math><mrow id="S3.SS2.SSS2.p2.8.m5.3.4.2" xref="S3.SS2.SSS2.p2.8.m5.3.4.1.cmml"><mi id="S3.SS2.SSS2.p2.8.m5.1.1" xref="S3.SS2.SSS2.p2.8.m5.1.1.cmml">max</mi><mo id="S3.SS2.SSS2.p2.8.m5.3.4.2a" xref="S3.SS2.SSS2.p2.8.m5.3.4.1.cmml">⁡</mo><mrow id="S3.SS2.SSS2.p2.8.m5.3.4.2.1" xref="S3.SS2.SSS2.p2.8.m5.3.4.1.cmml"><mo stretchy="false" id="S3.SS2.SSS2.p2.8.m5.3.4.2.1.1" xref="S3.SS2.SSS2.p2.8.m5.3.4.1.cmml">{</mo><mo id="S3.SS2.SSS2.p2.8.m5.2.2" xref="S3.SS2.SSS2.p2.8.m5.2.2.cmml">⋅</mo><mo id="S3.SS2.SSS2.p2.8.m5.3.4.2.1.2" xref="S3.SS2.SSS2.p2.8.m5.3.4.1.cmml">,</mo><mo id="S3.SS2.SSS2.p2.8.m5.3.3" xref="S3.SS2.SSS2.p2.8.m5.3.3.cmml">⋅</mo><mo stretchy="false" id="S3.SS2.SSS2.p2.8.m5.3.4.2.1.3" xref="S3.SS2.SSS2.p2.8.m5.3.4.1.cmml">}</mo></mrow></mrow></math>, <math><mrow id="S3.SS2.SSS2.p2.14.m11.6.6.2" xref="S3.SS2.SSS2.p2.14.m11.6.6.3.cmml"><mo stretchy="false" id="S3.SS2.SSS2.p2.14.m11.6.6.2.3" xref="S3.SS2.SSS2.p2.14.m11.6.6.3.cmml">[</mo><mrow id="S3.SS2.SSS2.p2.14.m11.5.5.1.1" xref="S3.SS2.SSS2.p2.14.m11.5.5.1.1.cmml"><msub id="S3.SS2.SSS2.p2.14.m11.5.5.1.1.2" xref="S3.SS2.SSS2.p2.14.m11.5.5.1.1.2.cmml"><mi id="S3.SS2.SSS2.p2.14.m11.5.5.1.1.2.2" xref="S3.SS2.SSS2.p2.14.m11.5.5.1.1.2.2.cmml">μ</mi><mi id="S3.SS2.SSS2.p2.14.m11.5.5.1.1.2.3" xref="S3.SS2.SSS2.p2.14.m11.5.5.1.1.2.3.cmml">b</mi></msub><mo id="S3.SS2.SSS2.p2.14.m11.5.5.1.1.1" xref="S3.SS2.SSS2.p2.14.m11.5.5.1.1.1.cmml">-</mo><msub id="S3.SS2.SSS2.p2.14.m11.5.5.1.1.3" xref="S3.SS2.SSS2.p2.14.m11.5.5.1.1.3.cmml"><mi id="S3.SS2.SSS2.p2.14.m11.5.5.1.1.3.2" xref="S3.SS2.SSS2.p2.14.m11.5.5.1.1.3.2.cmml">w</mi><mrow id="S3.SS2.SSS2.p2.14.m11.2.2.2.4" xref="S3.SS2.SSS2.p2.14.m11.2.2.2.3.cmml"><mi id="S3.SS2.SSS2.p2.14.m11.1.1.1.1" xref="S3.SS2.SSS2.p2.14.m11.1.1.1.1.cmml">k</mi><mo id="S3.SS2.SSS2.p2.14.m11.2.2.2.4.1" xref="S3.SS2.SSS2.p2.14.m11.2.2.2.3.cmml">,</mo><mi id="S3.SS2.SSS2.p2.14.m11.2.2.2.2" xref="S3.SS2.SSS2.p2.14.m11.2.2.2.2.cmml">b</mi></mrow></msub></mrow><mo id="S3.SS2.SSS2.p2.14.m11.6.6.2.4" xref="S3.SS2.SSS2.p2.14.m11.6.6.3.cmml">,</mo><mrow id="S3.SS2.SSS2.p2.14.m11.6.6.2.2" xref="S3.SS2.SSS2.p2.14.m11.6.6.2.2.cmml"><msub id="S3.SS2.SSS2.p2.14.m11.6.6.2.2.2" xref="S3.SS2.SSS2.p2.14.m11.6.6.2.2.2.cmml"><mi id="S3.SS2.SSS2.p2.14.m11.6.6.2.2.2.2" xref="S3.SS2.SSS2.p2.14.m11.6.6.2.2.2.2.cmml">μ</mi><mi id="S3.SS2.SSS2.p2.14.m11.6.6.2.2.2.3" xref="S3.SS2.SSS2.p2.14.m11.6.6.2.2.2.3.cmml">b</mi></msub><mo id="S3.SS2.SSS2.p2.14.m11.6.6.2.2.1" xref="S3.SS2.SSS2.p2.14.m11.6.6.2.2.1.cmml">+</mo><msub id="S3.SS2.SSS2.p2.14.m11.6.6.2.2.3" xref="S3.SS2.SSS2.p2.14.m11.6.6.2.2.3.cmml"><mi id="S3.SS2.SSS2.p2.14.m11.6.6.2.2.3.2" xref="S3.SS2.SSS2.p2.14.m11.6.6.2.2.3.2.cmml">w</mi><mrow id="S3.SS2.SSS2.p2.14.m11.4.4.2.4" xref="S3.SS2.SSS2.p2.14.m11.4.4.2.3.cmml"><mi id="S3.SS2.SSS2.p2.14.m11.3.3.1.1" xref="S3.SS2.SSS2.p2.14.m11.3.3.1.1.cmml">k</mi><mo id="S3.SS2.SSS2.p2.14.m11.4.4.2.4.1" xref="S3.SS2.SSS2.p2.14.m11.4.4.2.3.cmml">,</mo><mi id="S3.SS2.SSS2.p2.14.m11.4.4.2.2" xref="S3.SS2.SSS2.p2.14.m11.4.4.2.2.cmml">b</mi></mrow></msub></mrow><mo stretchy="false" id="S3.SS2.SSS2.p2.14.m11.6.6.2.5" xref="S3.SS2.SSS2.p2.14.m11.6.6.3.cmml">]</mo></mrow></math>, <math><mrow id="S3.SS2.SSS2.p2.16.m13.3.3" xref="S3.SS2.SSS2.p2.16.m13.3.3.cmml"><msub id="S3.SS2.SSS2.p2.16.m13.3.3.3" xref="S3.SS2.SSS2.p2.16.m13.3.3.3.cmml"><mi id="S3.SS2.SSS2.p2.16.m13.3.3.3.2" xref="S3.SS2.SSS2.p2.16.m13.3.3.3.2.cmml">ψ</mi><mrow id="S3.SS2.SSS2.p2.16.m13.2.2.2.4" xref="S3.SS2.SSS2.p2.16.m13.2.2.2.3.cmml"><mi id="S3.SS2.SSS2.p2.16.m13.1.1.1.1" xref="S3.SS2.SSS2.p2.16.m13.1.1.1.1.cmml">k</mi><mo id="S3.SS2.SSS2.p2.16.m13.2.2.2.4.1" xref="S3.SS2.SSS2.p2.16.m13.2.2.2.3.cmml">,</mo><mi id="S3.SS2.SSS2.p2.16.m13.2.2.2.2" xref="S3.SS2.SSS2.p2.16.m13.2.2.2.2.cmml">b</mi></mrow></msub><mo id="S3.SS2.SSS2.p2.16.m13.3.3.2" xref="S3.SS2.SSS2.p2.16.m13.3.3.2.cmml">⁢</mo><mrow id="S3.SS2.SSS2.p2.16.m13.3.3.1.1" xref="S3.SS2.SSS2.p2.16.m13.3.3.1.1.1.cmml"><mo stretchy="false" id="S3.SS2.SSS2.p2.16.m13.3.3.1.1.2" xref="S3.SS2.SSS2.p2.16.m13.3.3.1.1.1.cmml">(</mo><msub id="S3.SS2.SSS2.p2.16.m13.3.3.1.1.1" xref="S3.SS2.SSS2.p2.16.m13.3.3.1.1.1.cmml"><mi id="S3.SS2.SSS2.p2.16.m13.3.3.1.1.1.2" xref="S3.SS2.SSS2.p2.16.m13.3.3.1.1.1.2.cmml">x</mi><mi id="S3.SS2.SSS2.p2.16.m13.3.3.1.1.1.3" xref="S3.SS2.SSS2.p2.16.m13.3.3.1.1.1.3.cmml">k</mi></msub><mo stretchy="false" id="S3.SS2.SSS2.p2.16.m13.3.3.1.1.3" xref="S3.SS2.SSS2.p2.16.m13.3.3.1.1.1.cmml">)</mo></mrow></mrow></math>, <math><mrow id="S3.SS2.SSS2.p2.23.m20.3.3" xref="S3.SS2.SSS2.p2.23.m20.3.3.cmml"><msub id="S3.SS2.SSS2.p2.23.m20.3.3.3" xref="S3.SS2.SSS2.p2.23.m20.3.3.3.cmml"><mi id="S3.SS2.SSS2.p2.23.m20.3.3.3.2" xref="S3.SS2.SSS2.p2.23.m20.3.3.3.2.cmml">ψ</mi><mrow id="S3.SS2.SSS2.p2.23.m20.2.2.2.4" xref="S3.SS2.SSS2.p2.23.m20.2.2.2.3.cmml"><mi id="S3.SS2.SSS2.p2.23.m20.1.1.1.1" xref="S3.SS2.SSS2.p2.23.m20.1.1.1.1.cmml">k</mi><mo id="S3.SS2.SSS2.p2.23.m20.2.2.2.4.1" xref="S3.SS2.SSS2.p2.23.m20.2.2.2.3.cmml">,</mo><mn id="S3.SS2.SSS2.p2.23.m20.2.2.2.2" xref="S3.SS2.SSS2.p2.23.m20.2.2.2.2.cmml">3</mn></mrow></msub><mo id="S3.SS2.SSS2.p2.23.m20.3.3.2" xref="S3.SS2.SSS2.p2.23.m20.3.3.2.cmml">⁢</mo><mrow id="S3.SS2.SSS2.p2.23.m20.3.3.1.1" xref="S3.SS2.SSS2.p2.23.m20.3.3.1.1.1.cmml"><mo stretchy="false" id="S3.SS2.SSS2.p2.23.m20.3.3.1.1.2" xref="S3.SS2.SSS2.p2.23.m20.3.3.1.1.1.cmml">(</mo><msub id="S3.SS2.SSS2.p2.23.m20.3.3.1.1.1" xref="S3.SS2.SSS2.p2.23.m20.3.3.1.1.1.cmml"><mi id="S3.SS2.SSS2.p2.23.m20.3.3.1.1.1.2" xref="S3.SS2.SSS2.p2.23.m20.3.3.1.1.1.2.cmml">x</mi><mi id="S3.SS2.SSS2.p2.23.m20.3.3.1.1.1.3" xref="S3.SS2.SSS2.p2.23.m20.3.3.1.1.1.3.cmml">A</mi></msub><mo stretchy="false" id="S3.SS2.SSS2.p2.23.m20.3.3.1.1.3" xref="S3.SS2.SSS2.p2.23.m20.3.3.1.1.1.cmml">)</mo></mrow></mrow></math>, <math><mrow id="S3.SS2.SSS2.p2.24.m21.3.3" xref="S3.SS2.SSS2.p2.24.m21.3.3.cmml"><msub id="S3.SS2.SSS2.p2.24.m21.3.3.3" xref="S3.SS2.SSS2.p2.24.m21.3.3.3.cmml"><mi id="S3.SS2.SSS2.p2.24.m21.3.3.3.2" xref="S3.SS2.SSS2.p2.24.m21.3.3.3.2.cmml">ψ</mi><mrow id="S3.SS2.SSS2.p2.24.m21.2.2.2.4" xref="S3.SS2.SSS2.p2.24.m21.2.2.2.3.cmml"><mi id="S3.SS2.SSS2.p2.24.m21.1.1.1.1" xref="S3.SS2.SSS2.p2.24.m21.1.1.1.1.cmml">k</mi><mo id="S3.SS2.SSS2.p2.24.m21.2.2.2.4.1" xref="S3.SS2.SSS2.p2.24.m21.2.2.2.3.cmml">,</mo><mn id="S3.SS2.SSS2.p2.24.m21.2.2.2.2" xref="S3.SS2.SSS2.p2.24.m21.2.2.2.2.cmml">3</mn></mrow></msub><mo id="S3.SS2.SSS2.p2.24.m21.3.3.2" xref="S3.SS2.SSS2.p2.24.m21.3.3.2.cmml">⁢</mo><mrow id="S3.SS2.SSS2.p2.24.m21.3.3.1.1" xref="S3.SS2.SSS2.p2.24.m21.3.3.1.1.1.cmml"><mo stretchy="false" id="S3.SS2.SSS2.p2.24.m21.3.3.1.1.2" xref="S3.SS2.SSS2.p2.24.m21.3.3.1.1.1.cmml">(</mo><msub id="S3.SS2.SSS2.p2.24.m21.3.3.1.1.1" xref="S3.SS2.SSS2.p2.24.m21.3.3.1.1.1.cmml"><mi id="S3.SS2.SSS2.p2.24.m21.3.3.1.1.1.2" xref="S3.SS2.SSS2.p2.24.m21.3.3.1.1.1.2.cmml">x</mi><mi id="S3.SS2.SSS2.p2.24.m21.3.3.1.1.1.3" xref="S3.SS2.SSS2.p2.24.m21.3.3.1.1.1.3.cmml">A</mi></msub><mo stretchy="false" id="S3.SS2.SSS2.p2.24.m21.3.3.1.1.3" xref="S3.SS2.SSS2.p2.24.m21.3.3.1.1.1.cmml">)</mo></mrow></mrow></math>, <math><mrow id="S3.E2.m1.6.7" xref="S3.E2.m1.6.7.cmml"><mstyle displaystyle="true" id="S3.E2.m1.6.6" xref="S3.E2.m1.6.6.cmml"><mfrac id="S3.E2.m1.6.6a" xref="S3.E2.m1.6.6.cmml"><mrow id="S3.E2.m1.6.6.4" xref="S3.E2.m1.6.6.4.cmml"><mo id="S3.E2.m1.6.6.4.1" xref="S3.E2.m1.6.6.4.1.cmml">∂</mo><mo id="S3.E2.m1.6.6.4a" xref="S3.E2.m1.6.6.4.cmml">⁡</mo><mi id="S3.E2.m1.6.6.4.2" xref="S3.E2.m1.6.6.4.2.cmml">E</mi></mrow><mrow id="S3.E2.m1.6.6.2" xref="S3.E2.m1.6.6.2.cmml"><mo id="S3.E2.m1.6.6.2.3" xref="S3.E2.m1.6.6.2.3.cmml">∂</mo><mo id="S3.E2.m1.6.6.2a" xref="S3.E2.m1.6.6.2.cmml">⁡</mo><msub id="S3.E2.m1.6.6.2.4" xref="S3.E2.m1.6.6.2.4.cmml"><mi id="S3.E2.m1.6.6.2.4.2" xref="S3.E2.m1.6.6.2.4.2.cmml">w</mi><mrow id="S3.E2.m1.6.6.2.2.2.4" xref="S3.E2.m1.6.6.2.2.2.3.cmml"><mi id="S3.E2.m1.5.5.1.1.1.1" xref="S3.E2.m1.5.5.1.1.1.1.cmml">k</mi><mo id="S3.E2.m1.6.6.2.2.2.4.1" xref="S3.E2.m1.6.6.2.2.2.3.cmml">,</mo><mi id="S3.E2.m1.6.6.2.2.2.2" xref="S3.E2.m1.6.6.2.2.2.2.cmml">b</mi></mrow></msub></mrow></mfrac></mstyle><mo id="S3.E2.m1.6.7.1" xref="S3.E2.m1.6.7.1.cmml">=</mo><mrow id="S3.E2.m1.4.4a" xref="S3.E2.m1.6.7.2.1.cmml"><mo id="S3.E2.m1.4.4a.5" xref="S3.E2.m1.6.7.2.1.1.cmml">{</mo><mtable columnspacing="5pt" rowspacing="0pt" id="S3.E2.m1.4.4.4a" xref="S3.E2.m1.6.7.2.1.cmml"><mtr id="S3.E2.m1.4.4.4aa" xref="S3.E2.m1.6.7.2.1.cmml"><mtd columnalign="left" id="S3.E2.m1.4.4.4ab" xref="S3.E2.m1.6.7.2.1.cmml"><mrow id="S3.E2.m1.1.1.1.1.1.1.3" xref="S3.E2.m1.6.7.2.1.cmml"><mrow id="S3.E2.m1.1.1.1.1.1.1.3.1.1" xref="S3.E2.m1.1.1.1.1.1.1.3.1.2.cmml"><mo stretchy="false" id="S3.E2.m1.1.1.1.1.1.1.3.1.1.2" xref="S3.E2.m1.1.1.1.1.1.1.3.1.2.1.cmml">|</mo><mrow id="S3.E2.m1.1.1.1.1.1.1.3.1.1.1" xref="S3.E2.m1.1.1.1.1.1.1.3.1.1.1.cmml"><msub id="S3.E2.m1.1.1.1.1.1.1.3.1.1.1.2" xref="S3.E2.m1.1.1.1.1.1.1.3.1.1.1.2.cmml"><mi id="S3.E2.m1.1.1.1.1.1.1.3.1.1.1.2.2" xref="S3.E2.m1.1.1.1.1.1.1.3.1.1.1.2.2.cmml">x</mi><mi id="S3.E2.m1.1.1.1.1.1.1.3.1.1.1.2.3" xref="S3.E2.m1.1.1.1.1.1.1.3.1.1.1.2.3.cmml">k</mi></msub><mo id="S3.E2.m1.1.1.1.1.1.1.3.1.1.1.1" xref="S3.E2.m1.1.1.1.1.1.1.3.1.1.1.1.cmml">-</mo><msub id="S3.E2.m1.1.1.1.1.1.1.3.1.1.1.3" xref="S3.E2.m1.1.1.1.1.1.1.3.1.1.1.3.cmml"><mi id="S3.E2.m1.1.1.1.1.1.1.3.1.1.1.3.2" xref="S3.E2.m1.1.1.1.1.1.1.3.1.1.1.3.2.cmml">μ</mi><mrow id="S3.E2.m1.1.1.1.1.1.1.2.2.4" xref="S3.E2.m1.1.1.1.1.1.1.2.2.3.cmml"><mi id="S3.E2.m1.1.1.1.1.1.1.1.1.1" xref="S3.E2.m1.1.1.1.1.1.1.1.1.1.cmml">k</mi><mo id="S3.E2.m1.1.1.1.1.1.1.2.2.4.1" xref="S3.E2.m1.1.1.1.1.1.1.2.2.3.cmml">,</mo><mi id="S3.E2.m1.1.1.1.1.1.1.2.2.2" xref="S3.E2.m1.1.1.1.1.1.1.2.2.2.cmml">b</mi></mrow></msub></mrow><mo stretchy="false" id="S3.E2.m1.1.1.1.1.1.1.3.1.1.3" xref="S3.E2.m1.1.1.1.1.1.1.3.1.2.1.cmml">|</mo></mrow><mo id="S3.E2.m1.1.1.1.1.1.1.3.2" xref="S3.E2.m1.6.7.2.1.cmml">,</mo></mrow></mtd><mtd columnalign="left" id="S3.E2.m1.4.4.4ac" xref="S3.E2.m1.6.7.2.1.cmml"><mrow id="S3.E2.m1.2.2.2.2.2.1.3" xref="S3.E2.m1.2.2.2.2.2.1.3.1.cmml"><mrow id="S3.E2.m1.2.2.2.2.2.1.3.1" xref="S3.E2.m1.2.2.2.2.2.1.3.1.cmml"><mrow id="S3.E2.m1.2.2.2.2.2.1.3.1.1" xref="S3.E2.m1.2.2.2.2.2.1.3.1.1.cmml"><msub id="S3.E2.m1.2.2.2.2.2.1.3.1.1.3" xref="S3.E2.m1.2.2.2.2.2.1.3.1.1.3.cmml"><mi id="S3.E2.m1.2.2.2.2.2.1.3.1.1.3.2" xref="S3.E2.m1.2.2.2.2.2.1.3.1.1.3.2.cmml">ψ</mi><mrow id="S3.E2.m1.2.2.2.2.2.1.2.2.4" xref="S3.E2.m1.2.2.2.2.2.1.2.2.3.cmml"><mi id="S3.E2.m1.2.2.2.2.2.1.1.1.1" xref="S3.E2.m1.2.2.2.2.2.1.1.1.1.cmml">k</mi><mo id="S3.E2.m1.2.2.2.2.2.1.2.2.4.1" xref="S3.E2.m1.2.2.2.2.2.1.2.2.3.cmml">,</mo><mi id="S3.E2.m1.2.2.2.2.2.1.2.2.2" xref="S3.E2.m1.2.2.2.2.2.1.2.2.2.cmml">b</mi></mrow></msub><mo id="S3.E2.m1.2.2.2.2.2.1.3.1.1.2" xref="S3.E2.m1.2.2.2.2.2.1.3.1.1.2.cmml">⁢</mo><mrow id="S3.E2.m1.2.2.2.2.2.1.3.1.1.1.1" xref="S3.E2.m1.2.2.2.2.2.1.3.1.1.1.1.1.cmml"><mo stretchy="false" id="S3.E2.m1.2.2.2.2.2.1.3.1.1.1.1.2" xref="S3.E2.m1.2.2.2.2.2.1.3.1.1.1.1.1.cmml">(</mo><msub id="S3.E2.m1.2.2.2.2.2.1.3.1.1.1.1.1" xref="S3.E2.m1.2.2.2.2.2.1.3.1.1.1.1.1.cmml"><mi id="S3.E2.m1.2.2.2.2.2.1.3.1.1.1.1.1.2" xref="S3.E2.m1.2.2.2.2.2.1.3.1.1.1.1.1.2.cmml">x</mi><mi id="S3.E2.m1.2.2.2.2.2.1.3.1.1.1.1.1.3" xref="S3.E2.m1.2.2.2.2.2.1.3.1.1.1.1.1.3.cmml">k</mi></msub><mo stretchy="false" id="S3.E2.m1.2.2.2.2.2.1.3.1.1.1.1.3" xref="S3.E2.m1.2.2.2.2.2.1.3.1.1.1.1.1.cmml">)</mo></mrow></mrow><mo id="S3.E2.m1.2.2.2.2.2.1.3.1.2" xref="S3.E2.m1.2.2.2.2.2.1.3.1.2.cmml">></mo><mn id="S3.E2.m1.2.2.2.2.2.1.3.1.3" xref="S3.E2.m1.2.2.2.2.2.1.3.1.3.cmml">0</mn></mrow><mo id="S3.E2.m1.2.2.2.2.2.1.3.2" xref="S3.E2.m1.2.2.2.2.2.1.3.1.cmml">,</mo></mrow></mtd></mtr><mtr id="S3.E2.m1.4.4.4ad" xref="S3.E2.m1.6.7.2.1.cmml"><mtd columnalign="left" id="S3.E2.m1.4.4.4ae" xref="S3.E2.m1.6.7.2.1.cmml"><mrow id="S3.E2.m1.3.3.3.3.1.1.3" xref="S3.E2.m1.6.7.2.1.cmml"><mn id="S3.E2.m1.3.3.3.3.1.1.1" xref="S3.E2.m1.3.3.3.3.1.1.1.cmml">0</mn><mo id="S3.E2.m1.3.3.3.3.1.1.3.1" xref="S3.E2.m1.6.7.2.1.cmml">,</mo></mrow></mtd><mtd columnalign="left" id="S3.E2.m1.4.4.4af" xref="S3.E2.m1.6.7.2.1.cmml"><mtext id="S3.E2.m1.4.4.4.4.2.1" xref="S3.E2.m1.4.4.4.4.2.1a.cmml">otherwise.</mtext></mtd></mtr></mtable></mrow></mrow></math>

Correct Categorie: cs

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1506.08889

Formulas:

1-

n = c / c_{0}

2-

n - 1 = G (λ) ρ

3-

\frac{d^{2} x}{d z^{2}} = \frac{1}{n} \frac{\partial n}{\partial x} \frac{d^{2} y}{d z^{2}} = \frac{1}{n} \frac{\partial n}{\partial y}

4-

\tan α_{x} = \frac{d x}{d z} = \int_{0}^{H} \frac{1}{n} \frac{\partial n}{\partial x} 𝑑 z \tan α_{y} = \frac{d y}{d z} = \int_{0}^{H} \frac{1}{n} \frac{\partial n}{\partial y} 𝑑 z

5-

Δ x_{i} = \int_{0}^{H_{i}} [\int_{0}^{H_{i}} \frac{1}{n_{i}} \frac{\partial n_{i}}{\partial x} 𝑑 z] 𝑑 z = H_{i}^{2} \frac{1}{n_{i}} \frac{\partial n}{\partial x}

6-

Δ x, Δ y

7-

Δ x = \sum_{i = 1}^{N} H_{i}^{2} \frac{1}{n_{i}} \frac{\partial n}{\partial x} Δ y = \sum_{i = 1}^{N} H_{i}^{2} \frac{1}{n_{i}} \frac{\partial n}{\partial y}

8-

Δ n = \frac{\partial^{2} n}{\partial x^{2}} + \frac{\partial^{2} n}{\partial y^{2}} = K [\frac{\partial}{\partial x} Δ x + \frac{\partial}{\partial y} Δ y]

9-

K = {[2 \sum_{i = 1}^{N} \frac{H_{i}^{2}}{n_{i}}]}^{- 1}

10-

Δ x, Δ y

Formulas (html):

Correct Categorie: physics

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1709.07462

Formulas:

1-

M_{b a r y}^{c o l d}

2-

M_{h a l o}

3-

M_{b a r y}^{c o l d}

4-

M_{b a r y}^{c o l d}

5-

M_{b a r y}^{c o l d}

6-

M_{r, t o t}

7-

M_{r, t o t}

8-

u g r i z

9-

M_{s t a r}

10-

M_{r, t o t}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1809.07967

Formulas:

1-

\dot{M} (R_{ν})

2-

\dot{M} (R_{ν}) = 0.015 {(\frac{R_{in}}{R_{s}})}^{1.2} {(1 + \frac{R_{ν}}{10 R_{in}})}^{2} M_{⊙} s^{- 1},

3-

R_{in} ≃ 3 R_{s}

4-

{\dot{M}}_{w} (t)

5-

\dot{M} (R_{ν})

6-

\frac{\dot{M} (R_{ν})}{0.015 M_{⊙} s^{- 1}} (\frac{3 M_{⊙}}{M_{B H}}) = {(\frac{R_{in}}{R_{s}})}^{1.2} {(1 + \frac{R_{ν}}{10 R_{in}})}^{2} .

7-

\dot{M} (R_{ν})

8-

{(α / 0.1)}^{5 / 3}

9-

R_{in} < R_{ν} < R_{d}

10-

\dot{M} (R) = {\dot{M}}_{d} {(\frac{R}{R_{d}})}^{s},

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0209227

Formulas:

1-

\frac{\partial 𝐯}{\partial t} + 𝐯 \cdot \nabla 𝐯

2-

- g \nabla h - f 𝐤 \times 𝐯 + ℱ_{a},

3-

\frac{\partial h}{\partial t} + 𝐯 \cdot \nabla h

4-

- 𝒦 h \nabla \cdot 𝐯 + ℱ_{d},

5-

𝐯 = 𝐯 (λ, φ, t)

6-

h = h (λ, φ, t)

7-

f = 2 Ω \sin φ

8-

ℱ_{a} = - g \nabla η (1 - \exp {- t / τ_{a}}) \cos (φ) \cos (λ)

9-

ℱ_{d} = - (h - h_{E}) / τ_{d}

10-

h_{E} = H + η \cos (φ) \cos (λ)

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1310.2591

Formulas:

1-

κ r^{2} / 2

2-

𝑳_{m e c h} = 𝒓 \times m \dot{𝒓}

3-

𝑳_{m e c h}

4-

\frac{d}{d t} (m \dot{𝑹}) = q (𝑬 + \dot{𝑹} \times 𝑩)

5-

𝑹 = 𝒓 + (E / B) t 𝒖

6-

𝒖 = 𝑩 \times 𝑬 / (B E)

7-

\frac{d}{d t} (m \dot{𝒓}) = q \dot{𝒓} \times 𝑩 .

8-

(E / B) t 𝒖

9-

\ddot{r} - r {\dot{θ}}^{2}

10-

r \dot{θ} ω,

Formulas (html):

Correct Categorie: physics

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/physics/0211014

Formulas:

1-

δ = k_{L} (v \pm v_{R})

2-

| 2, 0, δ_{S} / k_{L} - v_{R} ⟩

3-

| 3, 0, δ_{S} / k_{L} + v_{R} ⟩

4-

| F, m_{F}, v ⟩

5-

| 3, 0, δ_{A} / k_{L} + v_{R} ⟩

6-

| 2, 0, δ_{A} / k_{L} - v_{R} ⟩

7-

2 k_{L} σ_{v} \approx 2 π / τ

8-

2 k_{L} σ_{v} = 2 π \times 7.7

9-

σ_{v} = 0.50 v_{R} = 3.0

10-

U (x, z) = U_{0} e^{- 2 κ z} (1 + ϵ \cos (2 k_{x} x)),

Formulas (html):

Correct Categorie: physics

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/hep-ex/0202030

Formulas:

1-

c m^{- 2} s^{- 1}

2-

V_{d r i f t} ≃

3-

μ m / n s

4-

x = c o n s t

5-

V_{d r i f t}

6-

m m / μ s

7-

∣ \cos θ ∣ <

8-

σ_{v t x} =

9-

\pm V_{d r i f t} \times Δ t

10-

\pm V_{d r i f t} \times Δ t

Formulas (html):

Correct Categorie: hep-ex

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1301.0998

Formulas:

1-

I_{m}, I_{n} ϵ I

2-

2 r \times 2 r

3-

η ϵ [0, min (m_{1}, n_{1})]

4-

γ_{k} = (ϕ_{j} - Θ_{i})

5-

n o b i n s

6-

n o b i n s

7-

R i n t e r

8-

γ = (ϕ_{j} - θ_{i}) mod 360 °

9-

ψ = \frac{d_{2}}{d_{1}}

10-

R i n t e r \subseteq R

Formulas (html):

Correct Categorie: cs

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/1202.0161

Formulas:

1-

l_{η} \sim η^{1 / 2}

2-

x = L \hat{x}, y = L \hat{y}, 𝐁 = B_{n} \hat{𝐁}, ρ = ρ_{n} \hat{ρ},

3-

p_{n} = \frac{B_{n}^{2}}{μ}, ϵ_{n} = \frac{B_{n}^{2}}{μ ρ_{n}}, j_{n} = \frac{B_{n}}{μ L} and v_{n} = \frac{B_{n}}{\sqrt{μ ρ_{n}}} .

4-

β = \frac{2 \hat{p}}{{\hat{B}}^{2}} .

5-

\frac{\partial ρ}{\partial t} + \nabla \cdot (ρ 𝐯)

6-

ρ \frac{\partial 𝐯}{\partial t} + ρ (𝐯 \cdot \nabla) 𝐯

7-

- \nabla p + (\nabla \times 𝐁) \times 𝐁 + 𝐅_{ν},

8-

\frac{\partial p}{\partial t} + 𝐯 \cdot \nabla p

9-

- γ p \nabla \cdot 𝐯 + H_{ν} + \frac{j^{2}}{σ},

10-

\frac{\partial 𝐁}{\partial t}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1009.3202

Formulas:

1-

M_{I} (l i m) = - 2.5

2-

{(m - M)}_{0} = 31.12 \pm 0.14

3-

d (M 87) = (16.4 \pm 0.5)

4-

I_{T R G B} ≃ 27.0

5-

12 30^{'} {58.576}^{''}

6-

+ 12^{\circ} 24^{'} {39.00}^{''}

7-

97^{''} - 105^{''}, 105^{''} - 115^{''}, 115^{''} - 125^{''},

8-

F 606 W, F 814 W

9-

F 606 W = - 2.5 \log (f_{V}) + 26.421

10-

F 814 W = - 2.5 \log (f_{I}) + 25.536

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0402430

Formulas:

1-

t, ϕ, r, θ

2-

d s^{2} = (β^{2} - α^{2}) d p t^{2} + 2 β_{i} d x^{i} d t + γ_{i j} d x^{i} d x^{j},

3-

γ_{i j} = (\begin{matrix} Σ \sin^{2} θ / κ^{2} & - a \sin^{2} θ (1 + Z) & 0 \\ - a \sin^{2} θ (1 + Z) & 1 + Z & 0 \\ 0 & 0 & κ^{2} \end{matrix}),

4-

α = 1 / \sqrt{1 + Z},

5-

β^{i} = (0, \frac{Z}{1 + Z}, 0) .

6-

r^{2} + a^{2} \cos^{2} θ,

7-

2 r / κ^{2},

8-

{(r^{2} + a^{2})}^{2} - a^{2} Δ \sin^{2} θ,

9-

r^{2} + a^{2} - 2 r .

10-

G = M = c = 1

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Run 10953593 (Agent054)