Run 16446905

Paper: https://arxiv.org/abs/hep-th/9905126

Formulas:

1-

(ℱ_{i}) {(ℱ_{k})}^{- 1} (ℱ_{j}) = (ℱ_{j}) {(ℱ_{k})}^{- 1} (ℱ_{i}),

2-

{(ℱ_{i})}_{j k} := \partial^{3} ℱ / \partial a_{i} \partial a_{j} \partial a_{k}

3-

a_{D_{j}} := \partial ℱ / a_{j}

4-

S := (\begin{matrix} 0 & I \\ - I & 0 \end{matrix}),

5-

(\begin{matrix} a_{D_{i}} \\ a_{j} \end{matrix}) ⟶ (\begin{matrix} {\tilde{a}}_{D_{i}} \\ {\tilde{a}}_{j} \end{matrix}) := S (\begin{matrix} a_{D_{i}} \\ a_{j} \end{matrix}) .

6-

τ_{i j} := \frac{\partial a_{D_{i}}}{\partial a_{j}} = \frac{\partial^{2} ℱ}{\partial a_{i} \partial a_{j}} ⟶ τ_{D_{i j}} := \frac{\partial {\tilde{a}}_{D_{i}}}{\partial {\tilde{a}}_{j}} = - \frac{1}{\frac{\partial a_{D_{j}}}{\partial a_{i}}} = - \frac{1}{τ_{i j}},

7-

\frac{\partial τ_{D_{i j}}}{\partial {\tilde{a}}_{k}} = \sum_{l = 1}^{r} \frac{\partial}{\partial a_{l}} (- \frac{1}{τ_{i j}}) \frac{\partial a_{l}}{\partial {\tilde{a}}_{k}} = \sum_{l = 1}^{r} \frac{{(ℱ_{i})}_{j l}}{τ_{i j}^{2}} τ_{D_{l k}} .

8-

{\tilde{a}}_{D_{i}} := \frac{\partial ℱ_{D}}{\partial {\tilde{a}}_{i}} = - \frac{\partial ℱ_{D}}{\partial a_{D_{i}}} .

9-

{(ℱ_{D_{i}})}_{j k} = \sum_{l = 1}^{r} {(ℱ_{i})}_{j l} {(τ_{D})}_{l k},

10-

{(ℱ_{D_{i}})}_{j k} := \frac{\partial^{3} ℱ_{D}}{\partial {\tilde{a}}_{i} \partial {\tilde{a}}_{j} \partial {\tilde{a}}_{k}} = - \frac{\partial^{3} ℱ_{D}}{\partial a_{D_{i}} \partial a_{D_{j}} \partial a_{D_{k}}}

Formulas (html):

Correct Categorie: hep-th

Guessed Categorie: math

Result: incorrect

Paper: https://arxiv.org/abs/1008.4381

Formulas:

1-

𝐕 = 𝐯_{n} - 𝐯_{s}

2-

𝐬 (ξ, t)

3-

𝐯_{L} = 𝐯_{s l} + α 𝐬^{'} \times (𝐕 - 𝐯_{𝐢}) - α^{'} 𝐬^{'} \times [𝐬^{'} \times (𝐕 - 𝐯_{𝐢})],

4-

𝐯_{s l} = 𝐯_{s} + 𝐯_{𝐢}

5-

s^{'} \equiv \partial s / \partial ξ

6-

𝐯_{𝐢}^{(l o c)} = \tilde{β} {[𝐬^{'} \times 𝐬^{''}]}_{s = s_{0}}, with \tilde{β} = \frac{κ}{4 π} \ln (\frac{c}{a_{0} L^{1 / 2}}),

7-

𝐬^{''} = \partial^{2} s / \partial ξ^{2}

8-

| 𝐯_{𝐢} | = \tilde{β} / R

9-

ϵ_{V} = ρ_{s} κ \tilde{β}

10-

𝐯_{L} = (1 - α^{'}) \tilde{β} 𝐬^{'} \times 𝐬^{''} + α \tilde{β} 𝐬^{''} + 𝐯_{s} + α 𝐬^{'} \times 𝐕 - α^{'} 𝐬^{'} \times (𝐬^{'} \times 𝐕) .

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1803.08907

Formulas:

1-

v \sim Λ_{QCD} \sim 100

2-

y_{t}^{6} h^{6} / M_{P}^{2}

3-

\frac{ℒ_{ϕ, g}}{\sqrt{- g}} = G_{4} (| ϕ |) R + G_{2} (| ϕ |, {| \partial ϕ |}^{2}),

4-

{| \partial ϕ |}^{2} \equiv \nabla_{μ} ϕ \nabla^{μ} ϕ^{*}

5-

⟨ φ ⟩ \sim \int 𝒟 𝒜 𝒟 φ 𝒟 g_{μ ν} φ e^{- S_{E}} .

6-

g_{μ ν} = δ_{μ ν}

7-

S_{E} = \int d^{4} x ℒ_{φ, g}

8-

\frac{ℒ_{φ, g}}{\sqrt{g}} = - \frac{1}{2} (M_{P}^{2} + ξ φ^{2}) R + \frac{1}{2} {(\partial φ)}^{2} + V (φ)

9-

V (φ) = \frac{λ}{4} φ^{4}

10-

| φ | ≫ M_{P} / \sqrt{ξ}

Formulas (html):

Correct Categorie: hep-th

Guessed Categorie: hep-th

Result: correct

Paper: https://arxiv.org/abs/1805.03254

Formulas:

1-

M ≳ 10^{9} M_{⊙}

2-

N ≳ 10^{- 6.8} {(h^{- 1} Mpc)}^{- 3}

3-

\log_{10} (M / M_{⊙}) ≲ 9.7

4-

\log_{10} (M / M_{⊙}) ≳ 9.3

5-

\log_{10} (M_{thr} / M_{⊙}) = 9.4

6-

0.025 / 0.5 \sim 5 %

7-

x_{α} / (1 + x_{α})

8-

\log_{10} (M / M_{⊙}) ≳ 9.3

9-

\log_{10} (M / M_{⊙}) ≲ 9.7

10-

9.3 ≲ \log_{10} (M / M_{⊙}) ≲ 9.7

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0605297

Formulas:

1-

A_{v} \sim 50 magnitudes

2-

N_{H} = 1.33 \times 10^{22} {cm}^{- 2}

3-

1.6 \times 10^{- 9} {erg cm}^{- 2} 𝘀^{- 1}

4-

1.6 μ 𝗺

5-

e x t_{B} = 0.214

6-

e x t_{V} = 0.125

7-

e x t_{R} = 0.091

8-

e x t_{I} = 0.051

9-

e x t_{J} = 0.08

10-

e x t_{H} = 0.03

Formulas (html):

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xref="S2.p4.3.3.m3.1.1.2.1.cmml">⁢</mo><msub id="S2.p4.3.3.m3.1.1.2.4" xref="S2.p4.3.3.m3.1.1.2.4.cmml"><mi id="S2.p4.3.3.m3.1.1.2.4.2" xref="S2.p4.3.3.m3.1.1.2.4.2.cmml">t</mi><mi id="S2.p4.3.3.m3.1.1.2.4.3" xref="S2.p4.3.3.m3.1.1.2.4.3.cmml">R</mi></msub></mrow><mo id="S2.p4.3.3.m3.1.1.1" xref="S2.p4.3.3.m3.1.1.1.cmml">=</mo><mn id="S2.p4.3.3.m3.1.1.3" xref="S2.p4.3.3.m3.1.1.3.cmml">0.091</mn></mrow></math>, <math><mrow id="S2.p4.4.4.m4.1.1" xref="S2.p4.4.4.m4.1.1.cmml"><mrow id="S2.p4.4.4.m4.1.1.2" xref="S2.p4.4.4.m4.1.1.2.cmml"><mi id="S2.p4.4.4.m4.1.1.2.2" xref="S2.p4.4.4.m4.1.1.2.2.cmml">e</mi><mo id="S2.p4.4.4.m4.1.1.2.1" xref="S2.p4.4.4.m4.1.1.2.1.cmml">⁢</mo><mi id="S2.p4.4.4.m4.1.1.2.3" xref="S2.p4.4.4.m4.1.1.2.3.cmml">x</mi><mo id="S2.p4.4.4.m4.1.1.2.1a" xref="S2.p4.4.4.m4.1.1.2.1.cmml">⁢</mo><msub id="S2.p4.4.4.m4.1.1.2.4" xref="S2.p4.4.4.m4.1.1.2.4.cmml"><mi id="S2.p4.4.4.m4.1.1.2.4.2" xref="S2.p4.4.4.m4.1.1.2.4.2.cmml">t</mi><mi id="S2.p4.4.4.m4.1.1.2.4.3" xref="S2.p4.4.4.m4.1.1.2.4.3.cmml">I</mi></msub></mrow><mo id="S2.p4.4.4.m4.1.1.1" xref="S2.p4.4.4.m4.1.1.1.cmml">=</mo><mn id="S2.p4.4.4.m4.1.1.3" xref="S2.p4.4.4.m4.1.1.3.cmml">0.051</mn></mrow></math>, <math><mrow id="S2.p4.5.5.m5.1.1" xref="S2.p4.5.5.m5.1.1.cmml"><mrow id="S2.p4.5.5.m5.1.1.2" xref="S2.p4.5.5.m5.1.1.2.cmml"><mi id="S2.p4.5.5.m5.1.1.2.2" xref="S2.p4.5.5.m5.1.1.2.2.cmml">e</mi><mo id="S2.p4.5.5.m5.1.1.2.1" xref="S2.p4.5.5.m5.1.1.2.1.cmml">⁢</mo><mi id="S2.p4.5.5.m5.1.1.2.3" xref="S2.p4.5.5.m5.1.1.2.3.cmml">x</mi><mo id="S2.p4.5.5.m5.1.1.2.1a" xref="S2.p4.5.5.m5.1.1.2.1.cmml">⁢</mo><msub id="S2.p4.5.5.m5.1.1.2.4" xref="S2.p4.5.5.m5.1.1.2.4.cmml"><mi id="S2.p4.5.5.m5.1.1.2.4.2" xref="S2.p4.5.5.m5.1.1.2.4.2.cmml">t</mi><mi id="S2.p4.5.5.m5.1.1.2.4.3" xref="S2.p4.5.5.m5.1.1.2.4.3.cmml">J</mi></msub></mrow><mo id="S2.p4.5.5.m5.1.1.1" xref="S2.p4.5.5.m5.1.1.1.cmml">=</mo><mn id="S2.p4.5.5.m5.1.1.3" xref="S2.p4.5.5.m5.1.1.3.cmml">0.08</mn></mrow></math>, <math><mrow id="S2.p4.6.6.m6.1.1" xref="S2.p4.6.6.m6.1.1.cmml"><mrow id="S2.p4.6.6.m6.1.1.2" xref="S2.p4.6.6.m6.1.1.2.cmml"><mi id="S2.p4.6.6.m6.1.1.2.2" xref="S2.p4.6.6.m6.1.1.2.2.cmml">e</mi><mo id="S2.p4.6.6.m6.1.1.2.1" xref="S2.p4.6.6.m6.1.1.2.1.cmml">⁢</mo><mi id="S2.p4.6.6.m6.1.1.2.3" xref="S2.p4.6.6.m6.1.1.2.3.cmml">x</mi><mo id="S2.p4.6.6.m6.1.1.2.1a" xref="S2.p4.6.6.m6.1.1.2.1.cmml">⁢</mo><msub id="S2.p4.6.6.m6.1.1.2.4" xref="S2.p4.6.6.m6.1.1.2.4.cmml"><mi id="S2.p4.6.6.m6.1.1.2.4.2" xref="S2.p4.6.6.m6.1.1.2.4.2.cmml">t</mi><mi id="S2.p4.6.6.m6.1.1.2.4.3" xref="S2.p4.6.6.m6.1.1.2.4.3.cmml">H</mi></msub></mrow><mo id="S2.p4.6.6.m6.1.1.1" xref="S2.p4.6.6.m6.1.1.1.cmml">=</mo><mn id="S2.p4.6.6.m6.1.1.3" xref="S2.p4.6.6.m6.1.1.3.cmml">0.03</mn></mrow></math>

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1103.2170

Formulas:

1-

\sim 7^{\circ} \times 7^{\circ}

2-

F_{ν}^{ns} (7.9 μ m) = F_{ν} (7.9 μ m) - 0.232 F_{ν} (3.6 μ m)

3-

F_{ν}^{ns} (24 μ m) = F_{ν} (24 μ m) - 0.032 F_{ν} (3.6 μ m),

4-

\frac{ν F_{ν}^{ns} (7.9 μ m)}{ν F_{ν} (71 μ m) + ν F_{ν} (160 μ m)},

5-

\frac{ν F_{ν}^{ns} (24 μ m)}{ν F_{ν} (71 μ m) + ν F_{ν} (160 μ m)},

6-

R_{71} = \frac{ν F_{ν} (71 μ m)}{ν F_{ν} (160 μ m)} .

7-

ν F_{ν} (71 μ m) + ν F_{ν} (160 μ m)

8-

ν F_{ν} (71 μ m) + ν F_{ν} (160 μ m)

9-

P_{24} - 0.14 P_{7.9}

10-

\int_{0}^{\infty} C_{a b s} (a, λ) u_{λ} 𝑑 λ = \frac{4 π}{c} \int_{0}^{\infty} C_{a b s} (a, λ) B_{λ} (T) 𝑑 λ,

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1512.06350

Formulas:

1-

\sim 150 h^{- 1} Mpc

2-

150 h^{- 1} Mpc

3-

70 - 150 h^{- 1} Mpc

4-

100 h^{- 1} Mpc

5-

≳ 300 h^{- 1} Mpc

6-

120 h^{- 1} Mpc

7-

120 - 130 h^{- 1} Mpc

8-

120 h^{- 1} Mpc

9-

240 h^{- 1} Mpc

10-

120 h^{- 1} Mpc

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1510.08464

Formulas:

1-

J - K_{s} = 2.62 \pm 0.15

2-

16 \overset{''}{.} 5

3-

1 \overset{''}{.} 5

4-

z_{e r r}

5-

1 \overset{''}{.} 3

6-

z - J > - 0.75 (J - K_{s}) + 3.8

7-

16 \overset{''}{.} 5

8-

1 \overset{''}{.} 3

9-

K_{s} - W 1

10-

16 \overset{''}{.} 5

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1801.02524

Formulas:

1-

θ_{SH} = j_{s} / j

2-

θ_{SH} = {\tilde{σ}}_{SH} ρ_{x x} + b

3-

θ_{SH} = {\tilde{σ}}_{SH} / σ_{x x}

4-

W_{x} {Hf}_{1 - x}

5-

2 \times 10^{- 3} mbar

6-

5 \times 10^{- 9} mbar

7-

ρ_{x x}^{ML} = \frac{π}{\ln 2} \frac{U}{I} (t_{W_{x} {Hf}_{1 - x}} + t_{CFB})

8-

ρ_{CFB} = 175 \times 10^{- 8} Ω m

9-

w = 16 μ m

10-

l = 48 μ m

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/hep-ph/9808233

Formulas:

1-

C = P = + 1

2-

γ (q_{1}) + γ (q_{2}) ⟶ V_{1} (p_{1}) + V_{2} (p_{2})

3-

V_{1}, V_{2} = ρ^{0}, ω, ϕ, J / ψ \dots .

4-

| q_{1}^{2} |, | q_{2}^{2} |

5-

V_{1} = V_{2} = ρ^{0}

6-

C = P = + 1

7-

α_{l P} (t) = 1

8-

C = P = - 1

9-

C = P = - 1

10-

α_{𝕆} (0)

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: hep-ph

Result: correct

Paper: https://arxiv.org/abs/gr-qc/0601135

Formulas:

1-

I_{E H} = \int_{ℳ} R^{a b} \land e^{c} \land e^{d} ε_{a b c d},

2-

R^{a b} = d ω^{a b} + ω_{c}^{a} \land ω^{c b} = \frac{1}{2} R_{c d}^{a b} e^{c} \land e^{d},

3-

R_{c d}^{a b}

4-

ε_{a b c d} = \pm 1, 0

5-

R^{a b} \land e^{c} ε_{a b c d} = 0,

6-

δ ω^{a b}

7-

T^{c} \land e^{d} ε_{a b c d} = 0,

8-

T^{a} = d e^{a} + ω_{b}^{a} \land e^{b} = \frac{1}{2} T_{b c}^{a} e^{b} \land e^{c}

9-

T_{c d}^{a} = 0

10-

A^{A B} \sim [\begin{matrix} ω^{a b} & e^{a} \\ - e^{b} & 0 \end{matrix}] .

Formulas (html):

Correct Categorie: gr-qc

Guessed Categorie: hep-th

Result: incorrect

Paper: https://arxiv.org/abs/0710.1033

Formulas:

1-

L \propto t^{- 3 / 2}

2-

ϵ = ν^{'} {(κ L)}^{2} \propto t^{- 3}

3-

ν^{'} = 0.003 κ

4-

ℓ \equiv L^{- 1 / 2}

5-

ϵ = ν^{'} {(κ L)}^{2},

6-

L (t) \propto ν^{', - 1 / 2} t^{- 3 / 2}

7-

E \approx u^{2} / 2

8-

ϵ = - \dot{E} \sim u^{3} / d \sim - E^{3 / 2} / d

9-

E \sim d^{2} {(t + t^{*})}^{- 2}

10-

ϵ \sim d^{2} {(t + t^{*})}^{- 3}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1907.13185

Formulas:

1-

𝒔_{d} = {[x_{d}, y_{d}]}^{⊤}

2-

𝒔_{u} = {[x_{u}, y_{u}]}^{⊤} = f (𝒔_{d}; 𝜽) 𝒔_{d}

3-

f (𝒔_{d}; 𝜽)

4-

f (𝒔_{d}; 𝜽)

5-

f (𝒔_{d}; λ) = \frac{1}{1 + λ r^{2}}

6-

f (𝒔_{d}; λ) = 1 + λ r^{2}

7-

r = \sqrt{x_{d}^{2} + y_{d}^{2}}

8-

f (𝒔_{d}; 𝜽)

9-

𝑺_{1} = {[X_{1}, Y_{1}, Z_{1}]}^{⊤}

10-

𝑺_{2} = {[X_{2}, Y_{2}, Z_{2}]}^{⊤}

Formulas (html):

Correct Categorie: cs

Guessed Categorie: cs

Result: correct

Paper: https://arxiv.org/abs/hep-ex/0206029

Formulas:

1-

E_{T}^{2} / Q^{2}

2-

Q^{2} \sim > 150 {GeV}^{2}

3-

𝒪 (α_{s}^{2})

4-

η_{lab} = - \ln \tan (θ / 2)

5-

E_{T}^{2} > Q^{2}

6-

Q^{2} < 11 {GeV}^{2}

7-

Q^{2} < 10 {GeV}^{2}

8-

M_{j j} < 25 GeV

9-

E_{T} < 20 GeV

10-

2 x \vec{p} + \vec{q} = 0

Formulas (html):

Correct Categorie: hep-ex

Guessed Categorie: hep-ex

Result: correct

Paper: https://arxiv.org/abs/hep-ph/9304211

Formulas:

1-

K^{0} - {\bar{K}}^{0}

2-

D^{0} - {\bar{D}}^{0}

3-

B^{0} - {\bar{B}}^{0}

4-

D^{0} - {\bar{D}}^{0}

5-

K^{0} - {\bar{K}}^{0}

6-

B^{0} - {\bar{B}}^{0}

7-

M \sim > 200

8-

ℒ = {\bar{l} [g_{L}^{d} P_{L} + g_{R}^{d} P_{R}] d + \bar{l} [g_{L}^{s} P_{L} + g_{R}^{s} P_{R}] s},

9-

K^{0} - {\bar{K}}^{0}

10-

Δ M_{12} = \frac{1}{192 π^{2} M_{L Q}^{2}} | {(a_{L}^{K})}^{2} + {(a_{R}^{K})}^{2} - (E_{K} + \frac{3}{2}) a_{L}^{K} a_{R}^{K} | f_{K}^{2} M_{K},

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: hep-ph

Result: correct

Paper: https://arxiv.org/abs/1210.6640

Formulas:

1-

\sqrt{s_{N N}} = 200

2-

\sqrt{s_{N N}} = 200

3-

\equiv ⟨ ⟨ 2 ⟩ ⟩ \equiv v (η_{α}) v (η_{β}) + σ (η_{α}) σ (η_{β}) + σ^{'} (Δ η) + δ (Δ η),

4-

\equiv \sqrt{2 {⟨ ⟨ 2 ⟩ ⟩}^{2} - ⟨ ⟨ 4 ⟩ ⟩} \approx v (η_{α}) v (η_{β}) - σ (η_{α}) σ (η_{β}) - σ^{'} (Δ η),

5-

Δ η = η_{β} - η_{α}

6-

η_{α} < η_{β} < 0

7-

V_{n} {2}

8-

(η_{α}, η_{β})

9-

(η_{α}, - η_{β})

10-

V_{n} {4}

Formulas (html):

Correct Categorie: nucl-ex

Guessed Categorie: nucl-ex

Result: correct

Paper: https://arxiv.org/abs/1902.03748

Formulas:

1-

T_{o b s}

2-

T_{o b s + 1}

3-

T_{p r e d}

4-

T_{p r e d}

5-

T_{o b s} \times d

6-

T_{o b s} \times d

7-

T_{o b s} \times h \times w

8-

ℝ^{T_{o b s} \times C}

9-

ℝ^{T_{o b s} \times d}

10-

(x_{b}, y_{b}, w_{b}, h_{b})

Formulas (html):

Correct Categorie: cs

Guessed Categorie: cs

Result: correct

Paper: https://arxiv.org/abs/1705.10759

Formulas:

1-

- \nabla^{2} h + h = C,

2-

h (ρ, φ)

3-

0 < φ < 2 π

4-

h = C + R (ρ) Φ (φ)

5-

h (ρ, φ) = C + \sum_{m = 0}^{\infty} (A_{m} \cos m φ + B_{m} \sin m φ) J_{m} (ρ),

6-

J_{m} (ρ)

7-

h (ρ, φ) \approx C + A_{0} J_{0} (ρ) + A_{2} J_{2} (ρ) \cos 2 φ + A_{4} J_{4} (ρ) \cos 4 φ + A_{6} J_{6} (ρ) \cos 6 φ,

8-

(C, A_{0}, A_{2}, A_{4}, A_{6})

9-

h_{m a x}

10-

h (\frac{w_{x}}{2}, 0) = 0, h (\frac{w_{y}}{2}, \frac{π}{2}) = 0, h (0, 0) = h_{m a x}, \frac{\partial h}{\partial x} (\frac{w_{x}}{2}, 0) = θ_{r}, \frac{\partial h}{\partial y} (\frac{w_{y}}{2}, \frac{π}{2}) = θ_{a},

Formulas (html):

Correct Categorie: physics

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/hep-th/9809023

Formulas:

1-

{(n p)}^{- α}, α \geq 1

2-

S_{gf} = \frac{1}{2} \int d^{d} x n_{μ} A_{μ}^{a} \frac{1}{ξ n^{2}} n_{ν} A_{ν}^{a}

3-

\frac{1}{4} \int d^{d} x F_{μ ν}^{a} F_{μ ν}^{a}

4-

\partial_{μ} A_{ν}^{a} - \partial_{ν} A_{μ}^{a} + g f_{b c}^{a} A_{μ}^{b} A^{c}_{ν}

5-

δ^{a b} \partial_{μ} + g f^{a c b} A_{μ}^{c}, [t^{b}, t^{c}] = f_{a}^{b c} t^{a} .

6-

a_{1} \frac{δ_{μ ν}}{p^{2}} + a_{2} \frac{p_{μ} p_{ν}}{p^{4}} + a_{3} \frac{n_{μ} p_{ν} + n_{ν} p_{μ}}{p^{2} (n p)} + a_{4} \frac{n_{μ} n_{ν}}{n^{2} p^{2}} .

7-

a_{1, \dots, 4}

8-

S = S_{A} + S_{gf}

9-

(1 + ξ p^{2}) / s^{2}

10-

{(n p)}^{2} / n^{2} p^{2} .

Formulas (html):

Correct Categorie: hep-th

Guessed Categorie: hep-th

Result: correct

Paper: https://arxiv.org/abs/hep-ph/9305283

Formulas:

1-

λ_{1} + λ_{2} = \pm 1

2-

λ_{1} + λ_{2} = 0

3-

λ_{1} + λ_{2} = \pm 1

4-

λ_{1} + λ_{2} = 0

5-

λ_{1} + λ_{2} = \pm 1

6-

λ_{1} + λ_{2} = \pm 1

7-

λ_{1} + λ_{2} = \pm 1

8-

λ_{1} + λ_{2} = 0

9-

λ_{1} + λ_{2} = \pm 1

10-

{\vec{q}}_{1} + {\vec{q}}_{2} = 0

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/9806093

Formulas:

1-

\log N - \log S

2-

14 \pm 3 \times 10^{- 9} {Wm}^{- 2} {ster}^{- 1}

3-

25 \pm 7 \times 10^{- 9} {Wm}^{- 2} {ster}^{- 1}

4-

S_{FIR} = 1.15 \pm 0.20 \times 10^{- 20}

5-

{Wm}^{- 2} {ster}^{- 1} {Hz}^{- 1}

6-

\frac{S_{80 μ m}}{S_{20 cm}} = 10^{2.34},

7-

S_{40 cm}^{*} = 10^{- 2.34} S_{FIR} ≃ 5300

8-

T_{40 cm}^{*} = 0.31

9-

S_{ν} \propto ν^{- α}

10-

T_{170 cm}^{*} \sim 15

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/2008.12797

Formulas:

1-

\log (L / L_{⊙}) \approx 5.4

2-

\approx 3 \times 10^{- 5} M_{⊙} {yr}^{- 1}

3-

280 \pm 50 km s^{- 1}

4-

2.9 \pm 0.5 M_{⊙}

5-

11^{h} 54^{m} 43 \overset{s}{.} 54

6-

- 63 ° 13' 31 \overset{''}{.} 1

7-

- 1 \overset{\circ}{.} 0534

8-

E (B - V)

9-

f (r) = \bar{ρ} / ρ (r)

10-

f (r) = f_{\infty} + (1 - f_{\infty}) \exp (- v (r) / v_{cl})

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1212.3460

Formulas:

1-

𝐱 = x^{1}, \dots, x^{r}

2-

𝐲 = y^{1}, \dots, y^{s}

3-

X_{dk} (𝐱, 𝐲)

4-

d σ / d 𝐱 d 𝐲

5-

X_{dk} (𝐱, 𝐲)

6-

W_{max} (X)

7-

X_{dk} (𝐱, 𝐲)

8-

\frac{d σ}{d 𝐱 d 𝐲} (X_{dk} (𝐱, 𝐲)) > r W_{max} (X)

9-

X_{dk} (𝐱, 𝐲)

10-

W_{max} (X)

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: cs

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/9811241

Formulas:

1-

Δ Mg b / Mg b

2-

Δ v \equiv c Δ z = c (10^{Δ \log λ} - 1)

3-

(k_{1}, k_{2}, k_{3}, k_{4})

4-

N_{p i x}

5-

N_{p i x}

6-

N_{p i x}

7-

N_{p i x}

8-

λ_{m i n}

9-

λ_{m a x}

10-

0.01 (N_{m a x} - N_{m i n})

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/nucl-ex/0606003

Formulas:

1-

\sqrt{s_{_{N N}}} = 200

2-

\sqrt{s_{_{N N}}} = 200

3-

p (\bar{p})

4-

d E / d x

5-

2.5 \leq p_{T} \leq 12

6-

- 1 < η < 0

7-

d E / d x

8-

0.3 \leq p_{T} \leq 12

9-

d E / d x

10-

d E / d x

Formulas (html):

Correct Categorie: nucl-ex

Guessed Categorie: nucl-ex

Result: correct

Paper: https://arxiv.org/abs/1105.5029

Formulas:

1-

I = 1 / 2, 3 / 2

2-

J^{P} = 1 / 2^{+}, 3 / 2^{+}

3-

N \bar{K} K

4-

γ p \to K^{+} K^{-} p

5-

f_{2} (1270)

6-

ρ_{3} (1690)

7-

f_{4} (2050)

8-

ρ_{5} (2350)

9-

f_{6} (2510)

10-

K_{2}^{*} (1430)

Formulas (html):

Correct Categorie: nucl-th

Guessed Categorie: nucl-th

Result: correct

Paper: https://arxiv.org/abs/cond-mat/0603171

Formulas:

1-

\dot{γ} (x)

2-

σ (x) = \frac{Γ}{2 π h r^{2}} and \dot{γ} (x) = - r \frac{\partial}{\partial x} \frac{v (x)}{r},

3-

r = R_{1} + x

4-

\dot{γ} (x)

5-

\dot{γ} (x)

6-

σ (x) = σ_{0} + A \dot{γ} {(x)}^{n},

7-

\frac{v (x)}{R_{1} + x} = \frac{v_{2}}{R_{2}} + \int_{R_{1} + x}^{R_{2}} \frac{d r}{r} {[\frac{Γ / (2 π h r^{2}) - σ_{0}}{A}]}^{1 / n},

8-

R_{2} = R_{1} + e

9-

\dot{γ} (x)

10-

\dot{γ} (x) = 2

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1306.0680

Formulas:

1-

U_{b h} / u_{τ}

2-

τ_{c} U_{b H} / H

3-

h = H - 0.8 D

4-

R e_{b} = U_{b H} H / ν

5-

R e_{τ} = u_{τ} h / ν

6-

D^{+} = D u_{τ} / ν

7-

ϕ (𝐱, t)

8-

ϕ^{'} (𝐱, t) = ϕ (𝐱, t) - ⟨ ϕ ⟩ (y)

9-

y_{0} = 0.8 D

10-

h = H - y_{0}

Formulas (html):

Correct Categorie: physics

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/1404.1195

Formulas:

1-

T_{i r r}

2-

T_{i r r}

3-

T_{i r r}

4-

T_{i r r}

5-

M_{F C}^{r e f}

6-

M_{Z F C}^{r e f}

7-

M_{Z F C}^{s t o p}

8-

M_{F C}^{r e f}

9-

M_{Z F C}^{r e f}

10-

M_{Z F C}^{s t o p}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0505588

Formulas:

1-

d s^{2} = a^{2} (τ) [d τ^{2} - (δ_{i j} + h_{i j}) d x^{i} d x^{j}],

2-

\partial_{i} h^{i j} = 0

3-

δ^{i j} h_{i j} = 0 .

4-

| h_{i j} | ≪ 1

5-

\partial_{μ} (\sqrt{- g} \partial^{μ} h_{i j} (𝐱, τ)) = 0 .

6-

h_{i j} (𝐱, τ) = \frac{\sqrt{16 π} l_{P l}}{{(2 π)}^{\frac{3}{2}}} \sum_{λ = 1}^{2} \int_{- \infty}^{\infty} d^{3} 𝐤 ϵ_{i j}^{(λ)} (𝐤) \frac{1}{\sqrt{2 k}} [a_{k}^{(λ)} h_{k}^{(λ)} (τ) e^{i 𝐤 \cdot 𝐱} + a_{k}^{† (λ)} h_{k}^{(λ), *} (τ) e^{- i 𝐤 \cdot 𝐱}],

7-

l_{P l} = \sqrt{G}

8-

ϵ_{i j}^{(λ)} (𝐤)

9-

k^{i} ϵ_{i j}^{(λ)} (𝐤) = 0

10-

δ^{i j} ϵ_{i j}^{(λ)} (𝐤) = 0

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: gr-qc

Result: incorrect

Paper: https://arxiv.org/abs/1510.07904

Formulas:

1-

E_{g} = ⟨ Φ (𝐪) | E_{g} (𝐪) | Φ (𝐪) ⟩,

2-

E_{g} (𝐪)

3-

E_{g} = E_{g} (𝟎) + \sum_{n, 𝐤} a_{n 𝐤}^{(2)} ⟨ Φ_{n 𝐤} | q_{n 𝐤}^{2} | Φ_{n 𝐤} ⟩ + 𝒪 (q^{4}),

4-

a_{n 𝐤}^{(2)}

5-

a_{n 𝐤}^{(2)}

6-

Δ q_{n 𝐤}

7-

a_{n 𝐤}^{(2)} = (E_{g} (Δ q_{n 𝐤}) + E_{g} (- Δ q_{n 𝐤})) / 2 Δ q_{n 𝐤}^{2}

8-

a_{n 𝐤}^{(2)}

9-

Δ q_{n 𝐤}

10-

\sqrt{⟨ q^{2} ⟩} = 1 / \sqrt{2 ω}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/astro-ph/9812002

Formulas:

1-

4 h^{- 1} Mpc

2-

h \equiv H_{0} / 100 km s^{- 1} {Mpc}^{- 1}

3-

δ_{g} = b δ_{m}

4-

δ_{m} \equiv ρ / \bar{ρ} - 1

5-

δ_{g} = b δ_{m}

6-

δ_{m, \min} < - 1 / b

7-

ξ_{g} (r) = b^{2} (r) ξ_{m} (r)

8-

ξ (r) ≪ 1

9-

ρ_{g} / {\bar{ρ}}_{g} ≲ 100

10-

ρ_{g} / {\bar{ρ}}_{g} ≳ 10^{5}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0308366

Formulas:

1-

L_{dust} / L_{FUV} \propto e^{- τ_{K} (α + 0.62)} L_{K}^{0.62}

2-

L_{dust} / L_{FUV} \propto L_{K}^{δ}

3-

δ = 0.61 - 0.02 α

4-

e^{- τ_{K}} \propto L_{K}^{- 0.02}

5-

\log L_{dust} / L_{FUV}^{obs}

6-

km s^{- 1} {Mpc}^{- 1}

7-

L_{dust} / L_{FUV}^{obs}

8-

K^{'} - K = 0

9-

K_{s} - K = 0

10-

L_{dust} / L_{FUV}^{obs}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/astro-ph/9607086

Formulas:

1-

B (r, θ) = B_{0} (r) \cos (θ - β \ln \frac{r}{r_{0}}),

2-

β = 1 / \tan p

3-

B (r, θ) = B_{0} (r) | \cos (θ - β \ln \frac{r}{r_{0}}) |,

4-

B_{θ} = B (r, θ) \cos p, B_{r} = B (r, θ) \sin p .

5-

B_{0} (r)

6-

| B (r, θ, z) | = | B (r, θ) | \exp (z / z_{0})

7-

l_{t r u e}

8-

b_{t r u e}

9-

Δ Ψ_{R M S}

10-

Δ Ψ_{R M S}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/0905.1496

Formulas:

1-

E_{n} = (n + \frac{1}{2}) ℏ ω_{c}

2-

n = 0, 1, 2, \dots

3-

ℏ ω_{c} = e B / m^{*}

4-

- \frac{ℏ^{2}}{2 m^{*}} \frac{d^{2} ψ_{σ_{z}} (z)}{d z^{2}} + U_{σ_{z}} (z) ψ_{σ_{z}} (z) = E_{z} ψ_{σ_{z}} (z),

5-

U_{σ_{z}} (z)

6-

U_{σ_{z}} (z) = V_{s} + U_{0} - e V_{a} z / L

7-

0 < z < L_{1}

8-

L_{1} + L_{2} < z < L

9-

U_{σ_{z}} (z) = V_{s} + V_{x} (z) + V_{σ_{z}} (z) - e V_{a} z / L

10-

L_{1} < z < L_{1} + L_{2}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1412.2766

Formulas:

1-

{(2 π)}^{2} / A_{k}

2-

h / | e B |

3-

= v \hat{𝒏} (- i \nabla \times 𝝈)

4-

𝝈 = (σ_{x}, σ_{y}, σ_{z})

5-

= \frac{v}{R} (σ_{x} Λ_{θ} + σ_{y} Λ_{φ})

6-

𝚲 = - i [𝒆_{φ} \frac{\partial}{\partial θ} - 𝒆_{θ} \frac{1}{\sin θ} (\frac{\partial}{\partial φ} - \frac{i}{2} σ_{z} \cos θ)]

7-

2 π σ_{z}

8-

(r, θ, φ)

9-

σ_{x}, σ_{y}, σ_{z}

10-

𝒆_{φ}, - 𝒆_{θ}, 𝒆_{r}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1505.06592

Formulas:

1-

u n i f o r m

2-

Y_{tot} = t d ρ_{s}^{HOMO} = L^{2 - d} \frac{⟨ 𝑾^{2} ⟩}{β},

3-

Y_{tot} = \sum_{x} Y (x) .

4-

ρ_{s} (x)

5-

ρ_{s} (x) = \frac{Y (x)}{t d} .

6-

ρ_{s} (x)

7-

ρ_{s} (x)

8-

𝑾 = \sum_{x} 𝒘 (x) .

9-

w_{x} (x)

10-

w_{α} (x)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: hep-lat

Result: incorrect

Paper: https://arxiv.org/abs/1602.04659

Formulas:

1-

- 29 ≲ M_{1450} ≲ - 26.4

2-

W 1 - W 2

3-

H_{0} = 70 km s^{- 1} {Mpc}^{- 1}

4-

W 1 - W 2 > 0.57

5-

W I S E

6-

z_{A B} = z_{S D S S} + 0.02

7-

W 1 - W 2

8-

W 1 - W 2 > 0.5

9-

W 1 - W 2 > 0.57

10-

W 1 - W 2

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0612664

Formulas:

1-

B ≲ 10^{14} G

2-

1 M_{☉} s^{- 1}

3-

v_{A} = B / {(4 π ρ)}^{1 / 2}

4-

λ \sim v_{A} / Ω

5-

R e \equiv \frac{L U}{ν} = \frac{v_{A}^{2}}{ν Ω} ≳ 1,

6-

τ_{abs} ≃ 4.5 \times 10^{- 39} T^{2} X_{nuc} ρ H

7-

τ_{sc} = 3 ρ κ_{sc} H ≃ 8.1 \times 10^{- 39} T^{2} ρ H

8-

τ_{tot} = τ_{abs} + τ_{sc} = 1.3 \times 10^{- 38} T^{2} ρ H .

9-

τ_{tot} > 2 / 3

10-

⟨ λ ⟩ = H / τ_{tot}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1108.3200

Formulas:

1-

| ψ (- T) ⟩

2-

| ψ (0) ⟩

3-

N = 16, 32, 64, 80

4-

| ψ_{i n} ⟩

5-

[- T, 0]

6-

i ℏ | \dot{ψ} (t) ⟩ = H (t) | ψ (t) ⟩

7-

H (t) = H [\tilde{Γ}]

8-

1 - {| ⟨ ψ (t) | ψ (t + d t) ⟩ |}^{2} = Δ {\tilde{E}}^{2} d t^{2} / ℏ^{2} + O (d t^{3}),

9-

Δ \tilde{E} = \sqrt{⟨ ψ (t) | H^{2} [\tilde{Γ}] | ψ (t) ⟩ - {\tilde{E}}^{2}}

10-

\tilde{E} = ⟨ ψ (t) | H [\tilde{Γ}] | ψ (t) ⟩

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: quant-ph

Result: correct

Paper: https://arxiv.org/abs/1903.09129

Formulas:

1-

r_{in} = 6 r_{g}

2-

r_{g} = G M / c^{2}

3-

r_{in} = 1.23 r_{g}

4-

r < 6 r_{g}

5-

r > 6 r_{g}

6-

\sim 150 e V

7-

\sim 1 k e V

8-

r < 6 r_{g}

9-

r_{in} = 1.23 r_{g}

10-

r > 6 r_{g}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1908.05282

Formulas:

1-

ν_{n l m}

2-

ν_{n l m}

3-

ν_{n l m} = ν_{n l} + \sum_{j = 1}^{j_{\max}} c_{j}^{(n, l)} 𝒫_{j}^{l} (m),

4-

ν_{n l m}

5-

δ v_{ϕ} = v_{ϕ} (r, θ, t) - ⟨ v_{ϕ} (r, θ, t) ⟩,

6-

v_{ϕ} (r, θ, t) \equiv Ω (r, θ, t) r \cos θ

7-

δ Ω_{r} \equiv \partial δ Ω / \partial r

8-

δ Ω_{θ} \equiv (1 / r) \partial δ Ω / \partial | θ |

9-

r = 0.90 R_{⊙}

10-

(1 / r) (\partial δ Ω / \partial | θ |) \cos θ

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1802.05018

Formulas:

1-

θ_{s t a r t}

2-

θ_{s t a r t}

3-

μ_{s} = \cos α_{s}

4-

μ_{s} = \max (0, μ_{0} \cos θ + \sqrt{1 - μ_{0}^{2}} \sin θ \cos (ξ - ξ_{0}))

5-

I = D + R + S

6-

k \frac{\partial^{2} T (t, h)}{\partial h^{2}} - \frac{\partial q_{r} (t, h)}{\partial h} = ρ C \frac{\partial T (t, h)}{\partial t}

7-

T (t, h)

8-

\dot{M} = P_{a v g} A \sqrt{\frac{m}{2 k_{B} T}} (\frac{L_{r}}{L_{x}} \frac{Δ T}{T_{a v g}} Q_{T} - \frac{L_{r}}{L_{x}} \frac{Δ P}{P_{a v g}} Q_{P})

9-

P_{a v g}

10-

T_{a v g}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/1606.01207

Formulas:

1-

H_{0} = 70.5 km s^{- 1} {Mpc}^{- 1}

2-

Ω_{Λ} = 1 - Ω_{m}

3-

{}^{T R G B}_{I}

4-

_{p e a k}

5-

_{p e a k}

6-

_{p e a k}

7-

_{t o t, 1 / 2}

8-

{(m - M)}_{0}

9-

σ_{[F e / H]}

10-

{(m - M)}_{0}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/2001.12000

Formulas:

1-

\frac{d A}{d t} = σ A - l {| A |}^{2} A,

2-

R e = 5.62 \times 10^{4}

3-

\frac{d A}{d t} = σ A - l {| A |}^{2} A + g (A, F), F (t) = F (t + 2 π / ω_{f}),

4-

g (A, F)

5-

g (A, F)

6-

S t = ω_{0} H / 2 π U_{\infty} = 0.23

7-

c_{μ} = 2 \frac{h}{H} \frac{U_{jet}^{2}}{U_{\infty}^{2}},

8-

x_{H} (t)

9-

A (t) = (x + i x_{H}) (t)

10-

Ω = ω_{f} \pm ω

Formulas (html):

Correct Categorie: physics

Guessed Categorie: nlin

Result: incorrect

Paper: https://arxiv.org/abs/1107.4482

Formulas:

1-

Ω = \sqrt{Q / R^{3}}

2-

I = 7 \times 10^{14}

3-

Y \propto K^{3 / 2}

4-

Y \propto K^{3 / 2}

5-

R_{+ +} = \sqrt{q_{Xe} K / E_{bs2}}

6-

N_{+ +} = 4 π ρ_{He} R_{+ +}^{3} / 3 = 4 π ρ_{He} {(q_{Xe} K / E_{bs2})}^{3 / 2} / 3

7-

Y = (N_{+} + 2 N_{+ +}) / N_{He}

8-

Y (K) = \frac{4 π ρ_{He}}{3 N_{He}} (E_{bs1}^{- 3 / 2} + E_{bs2}^{- 3 / 2}) q_{Xe}^{3 / 2} K^{3 / 2},

9-

Y \propto K^{3 / 2}

10-

Y^{''} (K_{cr}) = 0

Formulas (html):

Correct Categorie: physics

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1210.4522

Formulas:

1-

| M | \geq α q^{r (M)}

2-

| M | \geq α q^{r (M)}

3-

AG (n, q)

4-

U_{2, q + 2}

5-

| M | \geq α q^{r (M)}

6-

AG (n, q)

7-

U_{2, q + 2}

8-

| M | \leq c_{ℳ} r (M)

9-

| M | \leq c_{ℳ} r {(M)}^{2}

10-

| M | \leq c_{ℳ} q^{r (M)}

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/nucl-th/0107046

Formulas:

1-

N^{*} (1520) - h

2-

π π \to π π

3-

(I, J) = (1, 1)

4-

\frac{1}{2} | π^{+} π^{-} - π^{-} π^{+} ⟩

5-

| K \bar{K} ⟩

6-

\frac{1}{\sqrt{2}} | K^{+} K^{-} - K^{0} {\bar{K}}^{0} ⟩ .

7-

T (s) = {[I + K (s) \cdot G (s)]}^{- 1} \cdot K (s),

8-

G_{i}^{D} (s) = \frac{1}{16 π^{2}} [- 2 + d_{i} + σ_{i} (s) \log \frac{σ_{i} (s) + 1}{σ_{i} (s) - 1}],

9-

σ_{i} (s) = \sqrt{1 - 4 m_{i}^{2} / s}

10-

π π \to π π

Formulas (html):

Correct Categorie: nucl-th

Guessed Categorie: hep-ph

Result: incorrect

Paper: https://arxiv.org/abs/hep-th/9605093

Formulas:

1-

(x_{q}, 0, 0)

2-

𝐇 = \frac{1}{c} 𝐕 \times 𝐄

3-

𝐄 = (1 - β^{2}) \frac{q 𝐑}{R^{3} {(1 - β^{2} \sin^{2} θ)}^{3 / 2}}

4-

R = {[X {(t)}^{2} + y^{2} + z^{2}]}^{1 / 2}

5-

X (t) = x - x_{q} (t)

6-

c u r l 𝐇 = \frac{4 π}{c} 𝐣

7-

d i v 𝐄 = 4 π ϱ

8-

c u r l 𝐇 = \frac{1}{c} 𝐕 (d i v 𝐄) = \frac{1}{c} c u r l (𝐕 \times 𝐄) + \frac{1}{c} (𝐕 \cdot \nabla) 𝐄

9-

d i v 𝐕 = (𝐄 \cdot \nabla) 𝐕 = 0

10-

c u r l 𝐇 = \frac{1}{c} c u r l (𝐕 \times 𝐄)

Formulas (html):

Correct Categorie: hep-th

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/2001.04442

Formulas:

1-

{\dot{E}}_{R} = κ {\dot{N}}_{GJ} m_{e} c^{2} Γ_{wind} (1 + \frac{ξ m_{i}}{κ m_{e}}) (1 + σ),

2-

{\dot{N}}_{GJ} = 3 \times 10^{30} μ_{30} P^{- 2}

3-

σ = B^{2} / (4 π n_{e} m_{e} Γ^{2} c^{2}),

4-

10^{4} < Γ_{wind} < 10^{7}

5-

10^{3} < κ < 10^{6}

6-

σ = 3 \times 10^{- 3}

7-

10^{3} < Γ_{w} < 10^{7}

8-

δ B / B ≫ 1

9-

λ / (r_{L} σ) ≳

10-

λ = 2 π R_{LC}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Run 16446905 (Agent672)