Run 11277718

Paper: https://arxiv.org/abs/1609.02843

Formulas:

1-

n = 2.5 \cdot 10^{20}

2-

ℏ ω_{P} = {(ℏ^{2} e^{2} n / ε_{0} m_{e})}^{\frac{1}{2}}

3-

Im ϵ^{- 1} (𝐪, ω)

4-

ϵ^{- 1} (𝐪, ω)

5-

n = 2.5 \cdot 10^{19}

6-

n = 2.5 \cdot 10^{20}

7-

q_{c} = k_{F} [{(1 + ℏ ω_{P} / ε_{F})}^{1 / 2} - 1]

8-

ϵ^{- 1} (𝐪, ω)

9-

ϵ_{P} (𝐪 + 𝐆, ω) = {\frac{\partial ϵ_{M}}{\partial ω} |}_{ω = ω_{P} (𝐪)} [ω - ω_{P} (𝐪)] + i η

10-

ω_{P} (𝐪)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1712.06827

Formulas:

1-

σ = \sqrt{2 T^{'} d t}

2-

T^{'} = k_{B} T / 3 π η d

3-

v (r) = v_{m} (1 - {(\frac{r}{R})}^{2}),

4-

τ_{B} = d^{2} / D_{0}

5-

U_{H S} = {\begin{matrix} 4 ϵ [{(\frac{d}{r})}^{24} - {(\frac{d}{r})}^{12} + \frac{1}{4}] & , r \leq 2^{\frac{1}{12}} d \\ 0 & , r > 2^{\frac{1}{12}} d \end{matrix}

6-

d t = 2 \times 10^{- 5}

7-

P e = (v_{m} d^{2}) / (R D_{0})

8-

L_{x} = 10 d

9-

L_{y} = 20 d

10-

L_{z} = 13.09 d

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/nucl-th/9707008

Formulas:

1-

γ ℏ c / R \approx 3

2-

γ ℏ c / R

3-

q \bar{q} g

4-

e^{+} e^{-} \to γ γ

5-

p_{⟂} < ℏ c / R

6-

2 R_{A} + 2 R_{P} > b > 2 R_{A}

7-

γ P \to V \to e^{+} e^{-}

8-

γ γ \to e^{+} e^{-}

9-

2.5 < | η | < 4

10-

d E / d x

Formulas (html):

Correct Categorie: nucl-th

Guessed Categorie: hep-ph

Result: incorrect

Paper: https://arxiv.org/abs/1701.02328

Formulas:

1-

f_{agn} = 50 - 100 %

2-

λ_{i} = ρ_{agn} V_{i}

3-

ℬ_{i} (N_{agn, i}) = Poiss (N_{agn, i}, ρ_{agn} V_{i}) .

4-

𝒮_{i} (N_{agn, i}) = Poiss (N_{agn, i} - 1, ρ_{agn} V_{i}) .

5-

(1 - f_{agn})

6-

ℒ (f_{agn}) = \prod_{i} [f_{agn} 𝒮_{i} + (1 - f_{agn}) ℬ_{i}]

7-

ℒ (f_{agn})

8-

λ = 2 \log [\frac{ℒ (f_{agn})}{ℒ (0)}]

9-

P_{bg} (λ)

10-

N_{gw, 3 σ} (f_{agn})

Formulas (html):

<math><mrow id="id1.1.m1.1.1" xref="id1.1.m1.1.1.cmml"><msub id="id1.1.m1.1.1.2" xref="id1.1.m1.1.1.2.cmml"><mi id="id1.1.m1.1.1.2.2" xref="id1.1.m1.1.1.2.2.cmml">f</mi><mi id="id1.1.m1.1.1.2.3" xref="id1.1.m1.1.1.2.3.cmml">agn</mi></msub><mo id="id1.1.m1.1.1.1" xref="id1.1.m1.1.1.1.cmml">=</mo><mrow id="id1.1.m1.1.1.3" xref="id1.1.m1.1.1.3.cmml"><mn id="id1.1.m1.1.1.3.2" xref="id1.1.m1.1.1.3.2.cmml">50</mn><mo id="id1.1.m1.1.1.3.1" xref="id1.1.m1.1.1.3.1.cmml">-</mo><mrow id="id1.1.m1.1.1.3.3" xref="id1.1.m1.1.1.3.3.cmml"><mn id="id1.1.m1.1.1.3.3.2" xref="id1.1.m1.1.1.3.3.2.cmml">100</mn><mo id="id1.1.m1.1.1.3.3.1" xref="id1.1.m1.1.1.3.3.1.cmml">%</mo></mrow></mrow></mrow></math>, <math><mrow id="S2.p4.4.m4.1.1" xref="S2.p4.4.m4.1.1.cmml"><msub id="S2.p4.4.m4.1.1.2" xref="S2.p4.4.m4.1.1.2.cmml"><mi id="S2.p4.4.m4.1.1.2.2" xref="S2.p4.4.m4.1.1.2.2.cmml">λ</mi><mi id="S2.p4.4.m4.1.1.2.3" xref="S2.p4.4.m4.1.1.2.3.cmml">i</mi></msub><mo id="S2.p4.4.m4.1.1.1" xref="S2.p4.4.m4.1.1.1.cmml">=</mo><mrow id="S2.p4.4.m4.1.1.3" xref="S2.p4.4.m4.1.1.3.cmml"><msub id="S2.p4.4.m4.1.1.3.2" xref="S2.p4.4.m4.1.1.3.2.cmml"><mi id="S2.p4.4.m4.1.1.3.2.2" xref="S2.p4.4.m4.1.1.3.2.2.cmml">ρ</mi><mi id="S2.p4.4.m4.1.1.3.2.3" xref="S2.p4.4.m4.1.1.3.2.3.cmml">agn</mi></msub><mo id="S2.p4.4.m4.1.1.3.1" xref="S2.p4.4.m4.1.1.3.1.cmml">⁢</mo><msub id="S2.p4.4.m4.1.1.3.3" xref="S2.p4.4.m4.1.1.3.3.cmml"><mi id="S2.p4.4.m4.1.1.3.3.2" xref="S2.p4.4.m4.1.1.3.3.2.cmml">V</mi><mi id="S2.p4.4.m4.1.1.3.3.3" xref="S2.p4.4.m4.1.1.3.3.3.cmml">i</mi></msub></mrow></mrow></math>, <math><mrow id="S2.E1.m1.5.5.1" xref="S2.E1.m1.5.5.1.1.cmml"><mrow id="S2.E1.m1.5.5.1.1" xref="S2.E1.m1.5.5.1.1.cmml"><mrow id="S2.E1.m1.5.5.1.1.1" xref="S2.E1.m1.5.5.1.1.1.cmml"><msub id="S2.E1.m1.5.5.1.1.1.3" xref="S2.E1.m1.5.5.1.1.1.3.cmml"><mi class="ltx_font_mathcaligraphic" id="S2.E1.m1.5.5.1.1.1.3.2" xref="S2.E1.m1.5.5.1.1.1.3.2.cmml">ℬ</mi><mi id="S2.E1.m1.5.5.1.1.1.3.3" xref="S2.E1.m1.5.5.1.1.1.3.3.cmml">i</mi></msub><mo id="S2.E1.m1.5.5.1.1.1.2" xref="S2.E1.m1.5.5.1.1.1.2.cmml">⁢</mo><mrow id="S2.E1.m1.5.5.1.1.1.1.1" xref="S2.E1.m1.5.5.1.1.1.1.1.1.cmml"><mo stretchy="false" id="S2.E1.m1.5.5.1.1.1.1.1.2" xref="S2.E1.m1.5.5.1.1.1.1.1.1.cmml">(</mo><msub id="S2.E1.m1.5.5.1.1.1.1.1.1" xref="S2.E1.m1.5.5.1.1.1.1.1.1.cmml"><mi id="S2.E1.m1.5.5.1.1.1.1.1.1.2" xref="S2.E1.m1.5.5.1.1.1.1.1.1.2.cmml">N</mi><mrow id="S2.E1.m1.2.2.2.4" xref="S2.E1.m1.2.2.2.3.cmml"><mi id="S2.E1.m1.1.1.1.1" xref="S2.E1.m1.1.1.1.1.cmml">agn</mi><mo id="S2.E1.m1.2.2.2.4.1" xref="S2.E1.m1.2.2.2.3.cmml">,</mo><mi mathvariant="normal" id="S2.E1.m1.2.2.2.2" xref="S2.E1.m1.2.2.2.2.cmml">i</mi></mrow></msub><mo stretchy="false" id="S2.E1.m1.5.5.1.1.1.1.1.3" xref="S2.E1.m1.5.5.1.1.1.1.1.1.cmml">)</mo></mrow></mrow><mo id="S2.E1.m1.5.5.1.1.4" xref="S2.E1.m1.5.5.1.1.4.cmml">=</mo><mrow id="S2.E1.m1.5.5.1.1.3" xref="S2.E1.m1.5.5.1.1.3.cmml"><mtext id="S2.E1.m1.5.5.1.1.3.4" xref="S2.E1.m1.5.5.1.1.3.4a.cmml">Poiss</mtext><mo id="S2.E1.m1.5.5.1.1.3.3" xref="S2.E1.m1.5.5.1.1.3.3.cmml">⁢</mo><mrow id="S2.E1.m1.5.5.1.1.3.2.2" xref="S2.E1.m1.5.5.1.1.3.2.3.cmml"><mo stretchy="false" id="S2.E1.m1.5.5.1.1.3.2.2.3" xref="S2.E1.m1.5.5.1.1.3.2.3.cmml">(</mo><msub id="S2.E1.m1.5.5.1.1.2.1.1.1" xref="S2.E1.m1.5.5.1.1.2.1.1.1.cmml"><mi id="S2.E1.m1.5.5.1.1.2.1.1.1.2" xref="S2.E1.m1.5.5.1.1.2.1.1.1.2.cmml">N</mi><mrow id="S2.E1.m1.4.4.2.4" xref="S2.E1.m1.4.4.2.3.cmml"><mi id="S2.E1.m1.3.3.1.1" xref="S2.E1.m1.3.3.1.1.cmml">agn</mi><mo id="S2.E1.m1.4.4.2.4.1" xref="S2.E1.m1.4.4.2.3.cmml">,</mo><mi mathvariant="normal" id="S2.E1.m1.4.4.2.2" xref="S2.E1.m1.4.4.2.2.cmml">i</mi></mrow></msub><mo id="S2.E1.m1.5.5.1.1.3.2.2.4" xref="S2.E1.m1.5.5.1.1.3.2.3.cmml">,</mo><mrow id="S2.E1.m1.5.5.1.1.3.2.2.2" xref="S2.E1.m1.5.5.1.1.3.2.2.2.cmml"><msub id="S2.E1.m1.5.5.1.1.3.2.2.2.2" xref="S2.E1.m1.5.5.1.1.3.2.2.2.2.cmml"><mi id="S2.E1.m1.5.5.1.1.3.2.2.2.2.2" xref="S2.E1.m1.5.5.1.1.3.2.2.2.2.2.cmml">ρ</mi><mi id="S2.E1.m1.5.5.1.1.3.2.2.2.2.3" xref="S2.E1.m1.5.5.1.1.3.2.2.2.2.3.cmml">agn</mi></msub><mo id="S2.E1.m1.5.5.1.1.3.2.2.2.1" xref="S2.E1.m1.5.5.1.1.3.2.2.2.1.cmml">⁢</mo><msub id="S2.E1.m1.5.5.1.1.3.2.2.2.3" xref="S2.E1.m1.5.5.1.1.3.2.2.2.3.cmml"><mi id="S2.E1.m1.5.5.1.1.3.2.2.2.3.2" xref="S2.E1.m1.5.5.1.1.3.2.2.2.3.2.cmml">V</mi><mi id="S2.E1.m1.5.5.1.1.3.2.2.2.3.3" xref="S2.E1.m1.5.5.1.1.3.2.2.2.3.3.cmml">i</mi></msub></mrow><mo stretchy="false" id="S2.E1.m1.5.5.1.1.3.2.2.5" xref="S2.E1.m1.5.5.1.1.3.2.3.cmml">)</mo></mrow></mrow></mrow><mo id="S2.E1.m1.5.5.1.2" xref="S2.E1.m1.5.5.1.1.cmml">.</mo></mrow></math>, <math><mrow id="S2.E2.m1.5.5.1" xref="S2.E2.m1.5.5.1.1.cmml"><mrow id="S2.E2.m1.5.5.1.1" xref="S2.E2.m1.5.5.1.1.cmml"><mrow id="S2.E2.m1.5.5.1.1.1" xref="S2.E2.m1.5.5.1.1.1.cmml"><msub id="S2.E2.m1.5.5.1.1.1.3" xref="S2.E2.m1.5.5.1.1.1.3.cmml"><mi class="ltx_font_mathcaligraphic" id="S2.E2.m1.5.5.1.1.1.3.2" xref="S2.E2.m1.5.5.1.1.1.3.2.cmml">𝒮</mi><mi id="S2.E2.m1.5.5.1.1.1.3.3" xref="S2.E2.m1.5.5.1.1.1.3.3.cmml">i</mi></msub><mo id="S2.E2.m1.5.5.1.1.1.2" xref="S2.E2.m1.5.5.1.1.1.2.cmml">⁢</mo><mrow id="S2.E2.m1.5.5.1.1.1.1.1" xref="S2.E2.m1.5.5.1.1.1.1.1.1.cmml"><mo stretchy="false" id="S2.E2.m1.5.5.1.1.1.1.1.2" xref="S2.E2.m1.5.5.1.1.1.1.1.1.cmml">(</mo><msub id="S2.E2.m1.5.5.1.1.1.1.1.1" xref="S2.E2.m1.5.5.1.1.1.1.1.1.cmml"><mi id="S2.E2.m1.5.5.1.1.1.1.1.1.2" xref="S2.E2.m1.5.5.1.1.1.1.1.1.2.cmml">N</mi><mrow id="S2.E2.m1.2.2.2.4" xref="S2.E2.m1.2.2.2.3.cmml"><mi id="S2.E2.m1.1.1.1.1" xref="S2.E2.m1.1.1.1.1.cmml">agn</mi><mo id="S2.E2.m1.2.2.2.4.1" xref="S2.E2.m1.2.2.2.3.cmml">,</mo><mi mathvariant="normal" id="S2.E2.m1.2.2.2.2" xref="S2.E2.m1.2.2.2.2.cmml">i</mi></mrow></msub><mo stretchy="false" id="S2.E2.m1.5.5.1.1.1.1.1.3" xref="S2.E2.m1.5.5.1.1.1.1.1.1.cmml">)</mo></mrow></mrow><mo id="S2.E2.m1.5.5.1.1.4" xref="S2.E2.m1.5.5.1.1.4.cmml">=</mo><mrow id="S2.E2.m1.5.5.1.1.3" xref="S2.E2.m1.5.5.1.1.3.cmml"><mtext id="S2.E2.m1.5.5.1.1.3.4" xref="S2.E2.m1.5.5.1.1.3.4a.cmml">Poiss</mtext><mo id="S2.E2.m1.5.5.1.1.3.3" xref="S2.E2.m1.5.5.1.1.3.3.cmml">⁢</mo><mrow id="S2.E2.m1.5.5.1.1.3.2.2" xref="S2.E2.m1.5.5.1.1.3.2.3.cmml"><mo stretchy="false" id="S2.E2.m1.5.5.1.1.3.2.2.3" xref="S2.E2.m1.5.5.1.1.3.2.3.cmml">(</mo><mrow id="S2.E2.m1.5.5.1.1.2.1.1.1" xref="S2.E2.m1.5.5.1.1.2.1.1.1.cmml"><msub id="S2.E2.m1.5.5.1.1.2.1.1.1.2" xref="S2.E2.m1.5.5.1.1.2.1.1.1.2.cmml"><mi id="S2.E2.m1.5.5.1.1.2.1.1.1.2.2" xref="S2.E2.m1.5.5.1.1.2.1.1.1.2.2.cmml">N</mi><mrow id="S2.E2.m1.4.4.2.4" xref="S2.E2.m1.4.4.2.3.cmml"><mi id="S2.E2.m1.3.3.1.1" xref="S2.E2.m1.3.3.1.1.cmml">agn</mi><mo id="S2.E2.m1.4.4.2.4.1" xref="S2.E2.m1.4.4.2.3.cmml">,</mo><mi mathvariant="normal" id="S2.E2.m1.4.4.2.2" xref="S2.E2.m1.4.4.2.2.cmml">i</mi></mrow></msub><mo id="S2.E2.m1.5.5.1.1.2.1.1.1.1" xref="S2.E2.m1.5.5.1.1.2.1.1.1.1.cmml">-</mo><mn id="S2.E2.m1.5.5.1.1.2.1.1.1.3" xref="S2.E2.m1.5.5.1.1.2.1.1.1.3.cmml">1</mn></mrow><mo id="S2.E2.m1.5.5.1.1.3.2.2.4" xref="S2.E2.m1.5.5.1.1.3.2.3.cmml">,</mo><mrow id="S2.E2.m1.5.5.1.1.3.2.2.2" xref="S2.E2.m1.5.5.1.1.3.2.2.2.cmml"><msub id="S2.E2.m1.5.5.1.1.3.2.2.2.2" xref="S2.E2.m1.5.5.1.1.3.2.2.2.2.cmml"><mi id="S2.E2.m1.5.5.1.1.3.2.2.2.2.2" xref="S2.E2.m1.5.5.1.1.3.2.2.2.2.2.cmml">ρ</mi><mi id="S2.E2.m1.5.5.1.1.3.2.2.2.2.3" xref="S2.E2.m1.5.5.1.1.3.2.2.2.2.3.cmml">agn</mi></msub><mo id="S2.E2.m1.5.5.1.1.3.2.2.2.1" xref="S2.E2.m1.5.5.1.1.3.2.2.2.1.cmml">⁢</mo><msub id="S2.E2.m1.5.5.1.1.3.2.2.2.3" xref="S2.E2.m1.5.5.1.1.3.2.2.2.3.cmml"><mi id="S2.E2.m1.5.5.1.1.3.2.2.2.3.2" xref="S2.E2.m1.5.5.1.1.3.2.2.2.3.2.cmml">V</mi><mi id="S2.E2.m1.5.5.1.1.3.2.2.2.3.3" xref="S2.E2.m1.5.5.1.1.3.2.2.2.3.3.cmml">i</mi></msub></mrow><mo stretchy="false" id="S2.E2.m1.5.5.1.1.3.2.2.5" xref="S2.E2.m1.5.5.1.1.3.2.3.cmml">)</mo></mrow></mrow></mrow><mo id="S2.E2.m1.5.5.1.2" xref="S2.E2.m1.5.5.1.1.cmml">.</mo></mrow></math>, <math><mrow id="S2.p5.2.m2.1.1.1" xref="S2.p5.2.m2.1.1.1.1.cmml"><mo stretchy="false" id="S2.p5.2.m2.1.1.1.2" xref="S2.p5.2.m2.1.1.1.1.cmml">(</mo><mrow id="S2.p5.2.m2.1.1.1.1" xref="S2.p5.2.m2.1.1.1.1.cmml"><mn id="S2.p5.2.m2.1.1.1.1.2" xref="S2.p5.2.m2.1.1.1.1.2.cmml">1</mn><mo id="S2.p5.2.m2.1.1.1.1.1" xref="S2.p5.2.m2.1.1.1.1.1.cmml">-</mo><msub id="S2.p5.2.m2.1.1.1.1.3" xref="S2.p5.2.m2.1.1.1.1.3.cmml"><mi mathvariant="normal" id="S2.p5.2.m2.1.1.1.1.3.2" xref="S2.p5.2.m2.1.1.1.1.3.2.cmml">f</mi><mi id="S2.p5.2.m2.1.1.1.1.3.3" xref="S2.p5.2.m2.1.1.1.1.3.3.cmml">agn</mi></msub></mrow><mo stretchy="false" id="S2.p5.2.m2.1.1.1.3" xref="S2.p5.2.m2.1.1.1.1.cmml">)</mo></mrow></math>, <math><mrow id="S2.E3.m1.2.2" xref="S2.E3.m1.2.2.cmml"><mrow id="S2.E3.m1.1.1.1" xref="S2.E3.m1.1.1.1.cmml"><mi class="ltx_font_mathcaligraphic" id="S2.E3.m1.1.1.1.3" xref="S2.E3.m1.1.1.1.3.cmml">ℒ</mi><mo id="S2.E3.m1.1.1.1.2" xref="S2.E3.m1.1.1.1.2.cmml">⁢</mo><mrow id="S2.E3.m1.1.1.1.1.1" xref="S2.E3.m1.1.1.1.1.1.1.cmml"><mo stretchy="false" id="S2.E3.m1.1.1.1.1.1.2" xref="S2.E3.m1.1.1.1.1.1.1.cmml">(</mo><msub id="S2.E3.m1.1.1.1.1.1.1" xref="S2.E3.m1.1.1.1.1.1.1.cmml"><mi mathvariant="normal" id="S2.E3.m1.1.1.1.1.1.1.2" xref="S2.E3.m1.1.1.1.1.1.1.2.cmml">f</mi><mi id="S2.E3.m1.1.1.1.1.1.1.3" xref="S2.E3.m1.1.1.1.1.1.1.3.cmml">agn</mi></msub><mo stretchy="false" id="S2.E3.m1.1.1.1.1.1.3" xref="S2.E3.m1.1.1.1.1.1.1.cmml">)</mo></mrow></mrow><mo id="S2.E3.m1.2.2.3" xref="S2.E3.m1.2.2.3.cmml">=</mo><mrow id="S2.E3.m1.2.2.2" xref="S2.E3.m1.2.2.2.cmml"><munder id="S2.E3.m1.2.2.2.2" xref="S2.E3.m1.2.2.2.2.cmml"><mo largeop="true" movablelimits="false" symmetric="true" id="S2.E3.m1.2.2.2.2.2" xref="S2.E3.m1.2.2.2.2.2.cmml">∏</mo><mi id="S2.E3.m1.2.2.2.2.3" xref="S2.E3.m1.2.2.2.2.3.cmml">i</mi></munder><mrow id="S2.E3.m1.2.2.2.1.1" xref="S2.E3.m1.2.2.2.1.2.cmml"><mo id="S2.E3.m1.2.2.2.1.1.2" xref="S2.E3.m1.2.2.2.1.2.1.cmml">[</mo><mrow id="S2.E3.m1.2.2.2.1.1.1" xref="S2.E3.m1.2.2.2.1.1.1.cmml"><mrow id="S2.E3.m1.2.2.2.1.1.1.3" xref="S2.E3.m1.2.2.2.1.1.1.3.cmml"><msub id="S2.E3.m1.2.2.2.1.1.1.3.2" xref="S2.E3.m1.2.2.2.1.1.1.3.2.cmml"><mi mathvariant="normal" id="S2.E3.m1.2.2.2.1.1.1.3.2.2" xref="S2.E3.m1.2.2.2.1.1.1.3.2.2.cmml">f</mi><mi id="S2.E3.m1.2.2.2.1.1.1.3.2.3" xref="S2.E3.m1.2.2.2.1.1.1.3.2.3.cmml">agn</mi></msub><mo id="S2.E3.m1.2.2.2.1.1.1.3.1" xref="S2.E3.m1.2.2.2.1.1.1.3.1.cmml">⁢</mo><msub id="S2.E3.m1.2.2.2.1.1.1.3.3" xref="S2.E3.m1.2.2.2.1.1.1.3.3.cmml"><mi class="ltx_font_mathcaligraphic" id="S2.E3.m1.2.2.2.1.1.1.3.3.2" xref="S2.E3.m1.2.2.2.1.1.1.3.3.2.cmml">𝒮</mi><mi id="S2.E3.m1.2.2.2.1.1.1.3.3.3" xref="S2.E3.m1.2.2.2.1.1.1.3.3.3.cmml">i</mi></msub></mrow><mo id="S2.E3.m1.2.2.2.1.1.1.2" xref="S2.E3.m1.2.2.2.1.1.1.2.cmml">+</mo><mrow id="S2.E3.m1.2.2.2.1.1.1.1" xref="S2.E3.m1.2.2.2.1.1.1.1.cmml"><mrow id="S2.E3.m1.2.2.2.1.1.1.1.1.1" xref="S2.E3.m1.2.2.2.1.1.1.1.1.1.1.cmml"><mo stretchy="false" id="S2.E3.m1.2.2.2.1.1.1.1.1.1.2" xref="S2.E3.m1.2.2.2.1.1.1.1.1.1.1.cmml">(</mo><mrow id="S2.E3.m1.2.2.2.1.1.1.1.1.1.1" xref="S2.E3.m1.2.2.2.1.1.1.1.1.1.1.cmml"><mn id="S2.E3.m1.2.2.2.1.1.1.1.1.1.1.2" xref="S2.E3.m1.2.2.2.1.1.1.1.1.1.1.2.cmml">1</mn><mo id="S2.E3.m1.2.2.2.1.1.1.1.1.1.1.1" xref="S2.E3.m1.2.2.2.1.1.1.1.1.1.1.1.cmml">-</mo><msub id="S2.E3.m1.2.2.2.1.1.1.1.1.1.1.3" xref="S2.E3.m1.2.2.2.1.1.1.1.1.1.1.3.cmml"><mi mathvariant="normal" id="S2.E3.m1.2.2.2.1.1.1.1.1.1.1.3.2" xref="S2.E3.m1.2.2.2.1.1.1.1.1.1.1.3.2.cmml">f</mi><mi id="S2.E3.m1.2.2.2.1.1.1.1.1.1.1.3.3" xref="S2.E3.m1.2.2.2.1.1.1.1.1.1.1.3.3.cmml">agn</mi></msub></mrow><mo stretchy="false" id="S2.E3.m1.2.2.2.1.1.1.1.1.1.3" xref="S2.E3.m1.2.2.2.1.1.1.1.1.1.1.cmml">)</mo></mrow><mo id="S2.E3.m1.2.2.2.1.1.1.1.2" xref="S2.E3.m1.2.2.2.1.1.1.1.2.cmml">⁢</mo><msub id="S2.E3.m1.2.2.2.1.1.1.1.3" xref="S2.E3.m1.2.2.2.1.1.1.1.3.cmml"><mi class="ltx_font_mathcaligraphic" id="S2.E3.m1.2.2.2.1.1.1.1.3.2" xref="S2.E3.m1.2.2.2.1.1.1.1.3.2.cmml">ℬ</mi><mi id="S2.E3.m1.2.2.2.1.1.1.1.3.3" xref="S2.E3.m1.2.2.2.1.1.1.1.3.3.cmml">i</mi></msub></mrow></mrow><mo id="S2.E3.m1.2.2.2.1.1.3" xref="S2.E3.m1.2.2.2.1.2.1.cmml">]</mo></mrow></mrow></mrow></math>, <math><mrow id="S2.p6.3.m3.1.1" xref="S2.p6.3.m3.1.1.cmml"><mi class="ltx_font_mathcaligraphic" id="S2.p6.3.m3.1.1.3" xref="S2.p6.3.m3.1.1.3.cmml">ℒ</mi><mo id="S2.p6.3.m3.1.1.2" xref="S2.p6.3.m3.1.1.2.cmml">⁢</mo><mrow id="S2.p6.3.m3.1.1.1.1" xref="S2.p6.3.m3.1.1.1.1.1.cmml"><mo stretchy="false" id="S2.p6.3.m3.1.1.1.1.2" xref="S2.p6.3.m3.1.1.1.1.1.cmml">(</mo><msub id="S2.p6.3.m3.1.1.1.1.1" xref="S2.p6.3.m3.1.1.1.1.1.cmml"><mi mathvariant="normal" id="S2.p6.3.m3.1.1.1.1.1.2" xref="S2.p6.3.m3.1.1.1.1.1.2.cmml">f</mi><mi id="S2.p6.3.m3.1.1.1.1.1.3" xref="S2.p6.3.m3.1.1.1.1.1.3.cmml">agn</mi></msub><mo stretchy="false" id="S2.p6.3.m3.1.1.1.1.3" xref="S2.p6.3.m3.1.1.1.1.1.cmml">)</mo></mrow></mrow></math>, <math><mrow id="S2.E4.m1.3.4" xref="S2.E4.m1.3.4.cmml"><mi id="S2.E4.m1.3.4.2" xref="S2.E4.m1.3.4.2.cmml">λ</mi><mo id="S2.E4.m1.3.4.1" xref="S2.E4.m1.3.4.1.cmml">=</mo><mrow id="S2.E4.m1.3.4.3" xref="S2.E4.m1.3.4.3.cmml"><mn id="S2.E4.m1.3.4.3.2" xref="S2.E4.m1.3.4.3.2.cmml">2</mn><mo id="S2.E4.m1.3.4.3.1" xref="S2.E4.m1.3.4.3.1.cmml">⁢</mo><mrow id="S2.E4.m1.3.4.3.3.2" xref="S2.E4.m1.3.4.3.3.1.cmml"><mi id="S2.E4.m1.3.3" xref="S2.E4.m1.3.3.cmml">log</mi><mo id="S2.E4.m1.3.4.3.3.2a" xref="S2.E4.m1.3.4.3.3.1.cmml">⁡</mo><mrow id="S2.E4.m1.3.4.3.3.2.1" xref="S2.E4.m1.3.4.3.3.1.cmml"><mo id="S2.E4.m1.3.4.3.3.2.1.1" xref="S2.E4.m1.3.4.3.3.1.cmml">[</mo><mfrac id="S2.E4.m1.2.2" xref="S2.E4.m1.2.2.cmml"><mrow id="S2.E4.m1.1.1.1" xref="S2.E4.m1.1.1.1.cmml"><mi class="ltx_font_mathcaligraphic" id="S2.E4.m1.1.1.1.3" xref="S2.E4.m1.1.1.1.3.cmml">ℒ</mi><mo id="S2.E4.m1.1.1.1.2" xref="S2.E4.m1.1.1.1.2.cmml">⁢</mo><mrow id="S2.E4.m1.1.1.1.1.1" xref="S2.E4.m1.1.1.1.1.1.1.cmml"><mo stretchy="false" id="S2.E4.m1.1.1.1.1.1.2" xref="S2.E4.m1.1.1.1.1.1.1.cmml">(</mo><msub id="S2.E4.m1.1.1.1.1.1.1" xref="S2.E4.m1.1.1.1.1.1.1.cmml"><mi mathvariant="normal" id="S2.E4.m1.1.1.1.1.1.1.2" xref="S2.E4.m1.1.1.1.1.1.1.2.cmml">f</mi><mi id="S2.E4.m1.1.1.1.1.1.1.3" xref="S2.E4.m1.1.1.1.1.1.1.3.cmml">agn</mi></msub><mo stretchy="false" id="S2.E4.m1.1.1.1.1.1.3" xref="S2.E4.m1.1.1.1.1.1.1.cmml">)</mo></mrow></mrow><mrow id="S2.E4.m1.2.2.2" xref="S2.E4.m1.2.2.2.cmml"><mi class="ltx_font_mathcaligraphic" id="S2.E4.m1.2.2.2.3" xref="S2.E4.m1.2.2.2.3.cmml">ℒ</mi><mo id="S2.E4.m1.2.2.2.2" xref="S2.E4.m1.2.2.2.2.cmml">⁢</mo><mrow id="S2.E4.m1.2.2.2.4.2" xref="S2.E4.m1.2.2.2.cmml"><mo stretchy="false" id="S2.E4.m1.2.2.2.4.2.1" xref="S2.E4.m1.2.2.2.cmml">(</mo><mn id="S2.E4.m1.2.2.2.1" xref="S2.E4.m1.2.2.2.1.cmml">0</mn><mo stretchy="false" id="S2.E4.m1.2.2.2.4.2.2" xref="S2.E4.m1.2.2.2.cmml">)</mo></mrow></mrow></mfrac><mo id="S2.E4.m1.3.4.3.3.2.1.2" xref="S2.E4.m1.3.4.3.3.1.cmml">]</mo></mrow></mrow></mrow></mrow></math>, <math><mrow id="S2.p7.3.m3.1.2" xref="S2.p7.3.m3.1.2.cmml"><msub id="S2.p7.3.m3.1.2.2" xref="S2.p7.3.m3.1.2.2.cmml"><mi id="S2.p7.3.m3.1.2.2.2" xref="S2.p7.3.m3.1.2.2.2.cmml">P</mi><mi id="S2.p7.3.m3.1.2.2.3" xref="S2.p7.3.m3.1.2.2.3.cmml">bg</mi></msub><mo id="S2.p7.3.m3.1.2.1" xref="S2.p7.3.m3.1.2.1.cmml">⁢</mo><mrow id="S2.p7.3.m3.1.2.3.2" xref="S2.p7.3.m3.1.2.cmml"><mo stretchy="false" id="S2.p7.3.m3.1.2.3.2.1" xref="S2.p7.3.m3.1.2.cmml">(</mo><mi id="S2.p7.3.m3.1.1" xref="S2.p7.3.m3.1.1.cmml">λ</mi><mo stretchy="false" id="S2.p7.3.m3.1.2.3.2.2" xref="S2.p7.3.m3.1.2.cmml">)</mo></mrow></mrow></math>, <math><mrow id="S2.p8.3.m3.3.3" xref="S2.p8.3.m3.3.3.cmml"><msub id="S2.p8.3.m3.3.3.3" xref="S2.p8.3.m3.3.3.3.cmml"><mi id="S2.p8.3.m3.3.3.3.2" xref="S2.p8.3.m3.3.3.3.2.cmml">N</mi><mrow id="S2.p8.3.m3.2.2.2.2" xref="S2.p8.3.m3.2.2.2.3.cmml"><mi id="S2.p8.3.m3.1.1.1.1" xref="S2.p8.3.m3.1.1.1.1.cmml">gw</mi><mo id="S2.p8.3.m3.2.2.2.2.2" xref="S2.p8.3.m3.2.2.2.3.cmml">,</mo><mrow id="S2.p8.3.m3.2.2.2.2.1" xref="S2.p8.3.m3.2.2.2.2.1.cmml"><mn id="S2.p8.3.m3.2.2.2.2.1.2" xref="S2.p8.3.m3.2.2.2.2.1.2.cmml">3</mn><mo id="S2.p8.3.m3.2.2.2.2.1.1" xref="S2.p8.3.m3.2.2.2.2.1.1.cmml">⁢</mo><mi id="S2.p8.3.m3.2.2.2.2.1.3" xref="S2.p8.3.m3.2.2.2.2.1.3.cmml">σ</mi></mrow></mrow></msub><mo id="S2.p8.3.m3.3.3.2" xref="S2.p8.3.m3.3.3.2.cmml">⁢</mo><mrow id="S2.p8.3.m3.3.3.1.1" xref="S2.p8.3.m3.3.3.1.1.1.cmml"><mo stretchy="false" id="S2.p8.3.m3.3.3.1.1.2" xref="S2.p8.3.m3.3.3.1.1.1.cmml">(</mo><msub id="S2.p8.3.m3.3.3.1.1.1" xref="S2.p8.3.m3.3.3.1.1.1.cmml"><mi mathvariant="normal" id="S2.p8.3.m3.3.3.1.1.1.2" xref="S2.p8.3.m3.3.3.1.1.1.2.cmml">f</mi><mi id="S2.p8.3.m3.3.3.1.1.1.3" xref="S2.p8.3.m3.3.3.1.1.1.3.cmml">agn</mi></msub><mo stretchy="false" id="S2.p8.3.m3.3.3.1.1.3" xref="S2.p8.3.m3.3.3.1.1.1.cmml">)</mo></mrow></mrow></math>

Correct Categorie: astro-ph

Guessed Categorie: stat

Result: incorrect

Paper: https://arxiv.org/abs/quant-ph/0103070

Formulas:

1-

H = ω (| 0 ⟩ ⟨ 0 | - | 1 ⟩ ⟨ 1 |)

2-

{| Ψ (0) ⟩}_{A B} = \frac{1}{\sqrt{2}} (| 01 ⟩ - | 10 ⟩) .

3-

{| Ψ (t) ⟩}_{A B}

4-

\frac{1}{\sqrt{2}} (e^{i ω t} | 01 ⟩ - e^{- i ω t} | 10 ⟩)

5-

| + ⟩ | ψ^{+} (t) ⟩ - | - ⟩ | ψ^{-} (t) ⟩,

6-

| \pm ⟩ \equiv (1 / \sqrt{2}) (| 0 ⟩ \pm | 1 ⟩)

7-

| ψ^{\pm} (t) ⟩ \equiv \pm i \sin ω t | \pm ⟩ \mp \cos ω t | \mp ⟩

8-

P (+, +)

9-

P (-, -) = \frac{1}{2} \sin^{2} ω t_{a},

10-

P (+, -)

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: quant-ph

Result: correct

Paper: https://arxiv.org/abs/cond-mat/9612048

Formulas:

1-

\exp (- E / 2)

2-

\exp (E / 2)

3-

E = \frac{\sqrt{2} a q E_{f}}{k T},

4-

150 \times 1.6 \times 10^{- 19}

5-

E \sim 10^{- 3} E_{f}

6-

1 / (3 N^{2})

7-

v = \frac{1}{N} \sum_{i} (ⅇ^{E / 2} r_{i} - ⅇ^{- E / 2} s_{i}) p_{i},

8-

D = lim_{E \to 0} \frac{v}{N E}

9-

p_{i} = 3^{- (N - 1)}

10-

p_{i} = \frac{1}{3^{N - 1}} [1 + \frac{1}{2} a_{i} E + O (E^{2})] .

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: q-bio

Result: incorrect

Paper: https://arxiv.org/abs/0912.4643

Formulas:

1-

S_{l}^{⟂} = \sqrt{{(S_{l}^{x})}^{2} + {(S_{l}^{y})}^{2}}

2-

l / ξ_{s} = 10

3-

l / ξ_{s} = 30

4-

l / ξ_{s} = 10

5-

l / ξ_{s} = 10

6-

L / ξ_{s} = 200, K_{s} = 20

7-

S_{l}^{⟂} = \sqrt{{(S_{l}^{x})}^{2} + {(S_{l}^{y})}^{2}}

8-

l_{0} = \frac{π^{2} l}{4 K_{s} ξ_{s}}

9-

g_{↓ ↓} = g_{↑ ↑}

10-

| F = 1, m_{F} = - 1 ⟩

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0006048

Formulas:

1-

39^{\circ} \leq i \leq 80^{\circ}

2-

H_{0} = 75 km s^{- 1} {Mpc}^{- 1}

3-

14^{''} \times 14^{''} / \sin δ

4-

Σ_{HI} (R) = Σ_{0} {(\frac{R}{R_{1}})}^{β} e^{- R / R_{1}} + f Σ_{0} e^{- {((R - R_{2}) / σ)}^{2}} .

5-

ρ^{*} (R, z) = ρ_{0}^{*} \exp (- R / R_{d}) {sech}^{2} (z / z_{0})

6-

z_{0} = R_{d} / 6

7-

ρ (r) = \frac{ρ_{0}}{{(r / r_{s})}^{α} {(1 + r / r_{s})}^{3 - α}},

8-

c = r_{200} / r_{s}

9-

\frac{r_{200}}{h^{- 1} kpc} = \frac{V_{200}}{km s^{- 1}} .

10-

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

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0405493

Formulas:

1-

H_{0} = 50 {km s}^{- 1} {Mpc}^{- 1}

2-

ρ (0) = 4.05 \times 10^{- 3} {𝗰𝗺}^{- 3}

3-

L_{X} \sim 6.8 \times 10^{43}

4-

ρ (0) = 2 \times 10^{- 3} {𝗰𝗺}^{- 3}

5-

L_{X} \sim 1.4 \times 10^{43}

6-

\sim 2.4 \times 10^{9} M_{☉}

7-

\sim 1.4 \times 10^{9} M_{☉}

8-

H_{SN} (r) = \frac{H_{SN} (0)}{{[1 + {(r / r_{c})}^{2}]}^{3 β_{SN} / 2}}

9-

H_{SN} (r)

10-

t_{cool, SN} (r) = \frac{E_{th} (r)}{L_{X} (r) - H_{SN} (r)}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/hep-ph/0212127

Formulas:

1-

ν_{e} \to ν_{μ, τ}

2-

(δ m^{2}, θ_{12})

3-

Δ m^{2} ≫ δ m^{2}

4-

(m_{1}^{2}, m_{2}^{2}, m_{3}^{2}) = (- δ m^{2} / 2, + δ m^{2}, \pm Δ m^{2})

5-

(δ m^{2}, θ_{12}, θ_{13})

6-

E = E_{ν} - (M_{n} - M_{p}) + m_{e} ≃ E_{ν} - 0.8

7-

7.5 % / E^{1 / 2}

8-

(i = 1, \dots, 13)

9-

N_{i}^{osc} \to N_{i}^{theo} = N_{i}^{osc} (1 + \sum_{k} c_{i}^{k} ξ_{k})

10-

χ_{KL}^{2} = \min_{{ξ_{k}}} [\sum_{i = 1}^{13} 2 (N_{i}^{theo} - N_{i}^{\exp} + N_{i}^{\exp} \ln \frac{N_{i}^{\exp}}{N_{i}^{theo}}) + \sum_{k = 1, 2} ξ_{k}^{2}],

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0503368

Formulas:

1-

ρ (r) = \frac{1}{r}

2-

r \geq 20 U A

3-

a = 8.74 \pm 1.33 \times 10^{- 8} \frac{cm}{s^{2}},

4-

Λ = 3 Ω_{D E} {(\frac{H_{0}}{c})}^{2}

5-

Ω_{D E} = 0.7

6-

Λ = 1.2 h \times 10^{- 56} {cm}^{- 2}

7-

a_{Λ} = c^{2} \sqrt{Λ} = 9.79 \times 10^{- 8} \frac{cm}{s^{2}}

8-

ρ (r) \propto \frac{1}{r}

9-

ρ (\vec{r})

10-

\vec{\nabla} \cdot \vec{a} = - 4 π G ρ (\vec{r}),

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/quant-ph/0105043

Formulas:

1-

F_{L} = F_{U} = 1

2-

Λ_{a} \equiv | 2 ⟩ \leftrightarrow | 4 ⟩ \leftrightarrow | 1 ⟩

3-

Λ_{b} \equiv | 2 ⟩ \leftrightarrow | 6 ⟩ \leftrightarrow | 3 ⟩

4-

| 1 ⟩ \to | 5 ⟩

5-

| 3 ⟩ \to | 5 ⟩

6-

F_{L} = F_{U} = 1

7-

Λ_{a} \equiv | 2 ⟩ \leftrightarrow | 4 ⟩ \leftrightarrow | 1 ⟩

8-

Λ_{b} \equiv | 2 ⟩ \leftrightarrow | 6 ⟩ \leftrightarrow | 3 ⟩

9-

Δ_{L, U} = (μ_{B} / ℏ) M_{L, U} g_{L, U} B

10-

Δ M = \pm 1

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: quant-ph

Result: correct

Paper: https://arxiv.org/abs/1911.06418

Formulas:

1-

58 m e V

2-

d I / d V_{S D}

3-

| e V_{S D} | > E_{O R B}

4-

d I / d V_{S D}

5-

e V_{S D} = \pm E_{O R B}

6-

d I / d V_{S D}

7-

V_{G} = 510.5 m V

8-

d I / d V_{S D}

9-

d I / d V_{S D}

10-

V_{G} = 528.3 m V

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/cond-mat/0103303

Formulas:

1-

F \equiv π R^{2} / λ L

2-

u (\vec{r}, t) \equiv < σ^{-} (\vec{r}, t) >, s (\vec{r}, t) \equiv < σ^{z} (\vec{r}, t) >,

3-

f \equiv f_{0} + f_{r a d}

4-

f_{0} \equiv - i \vec{d} \cdot {\vec{E}}_{0}

5-

f_{r a d} (\vec{r}, t) \equiv - \frac{3}{4} i γ ρ \int [φ (\vec{r} - {\vec{r}}^{'}) u ({\vec{r}}^{'}, t) - {\vec{e_{d}}}^{2} φ^{*} (\vec{r} - {\vec{r}}^{'}) u^{*} ({\vec{r}}^{'}, t)] 𝑑 {\vec{r}}^{'}

6-

\vec{d} \equiv d_{0} {\vec{e}}_{d}

7-

φ (\vec{r}) \equiv \exp (i k_{0} | \vec{r} |) / k_{0} | \vec{r} |

8-

k_{0} \equiv ω_{0} / c

9-

γ \equiv 4 k_{0}^{3} d_{0}^{2} / 3

10-

{\vec{E}}_{0} = {\vec{E}}_{1} e^{i (k z - ω t)} + {\vec{E}}_{1}^{*} e^{- i (k z - ω t)} .

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/1803.02064

Formulas:

1-

C_{1 - x} C o_{x}

2-

Δ R (T, H) = R (T, H) - R (T, 0)

3-

Δ R (T, H)

4-

M (T, H)

5-

C_{1 - x} C o_{x}

6-

C_{1 - x} C o_{x}

7-

S i (100)

8-

5 \times 5 m m^{2}

9-

λ = 248 n m

10-

I = 100 μ A

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1708.08942

Formulas:

1-

\tilde{ζ} \equiv ζ_{X} / n_{H}

2-

n (m^{+})

3-

n (M^{+})

4-

ζ_{X} n_{H} = (k n_{M} + β n_{e} + k_{d} n_{d}) n (m^{+}),

5-

k_{ce} n_{M} n (m^{+}) = (α n_{e} + k_{d} n_{d}) n (M^{+}) .

6-

k = k_{ce} + k_{pt}

7-

α = 2 \times 10^{- 10} T^{- 2 / 3} {cm}^{3} s^{- 1}, β = 1.2 \times 10^{- 7} T^{- 3 / 4} {cm}^{3} s^{- 1} .

8-

k_{ce} = k_{pt} = 5 \times 10^{- 10} {cm}^{3} s^{- 1} .

9-

τ = \frac{a k_{B} T}{e^{2}} = 59.9 (\frac{a}{10 μ m}) (\frac{T}{100 K}),

10-

μ_{i} \equiv {(\frac{n_{e}}{n_{i}})}^{2} (\frac{m_{i}}{m_{H}}),

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/2002.07360

Formulas:

1-

{}^{13}C (α, n)

2-

{}^{13}C (α, n)

3-

{}^{13}C (α, n)

4-

{}^{13}C (α, n)

5-

{}^{13}C (α, n)

6-

{}^{13}C (α, n)

7-

{}^{13}C (α, n)

8-

{}^{13}C (α, n)

9-

{}^{13}C (α, n)

10-

{}^{13}C (α, n)

Formulas (html):

Correct Categorie: nucl-ex

Guessed Categorie: nucl-ex

Result: correct

Paper: https://arxiv.org/abs/1106.5510

Formulas:

1-

M_{p} = {8.40}_{- 0.18}^{+ 0.19} M_{J}

2-

R_{p} = {1.136}_{- 0.054}^{+ 0.073} R_{J}

3-

ρ_{p} = 7.1 \pm 1.1 g {cm}^{- 3}

4-

19^{h} 10^{m} 50 \overset{s}{.} 12

5-

+ 47^{\circ} 19^{'} 58 \overset{''}{.} 98

6-

Δ_{m a g}

7-

2 ″ \times 2 ″

8-

2.4 ″ \times 2.4 ″

9-

λ_{0} = 1.25 μ

10-

λ_{0} = 2.145 μ

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1108.3929

Formulas:

1-

I = I_{0} ξ_{R - S} t ξ_{S - R}

2-

I^{^{'}} = I_{0} ξ_{R - S}^{^{'}} t ξ_{S - R}^{^{'}}

3-

ξ_{R - S} ξ_{S - R} ≢ ξ_{R - S}^{^{'}} ξ_{S - R}^{^{'}}

4-

0.8 % ¡ « 1.4 %

5-

0.4 % ¡ « 0.8 %

6-

T_{12} = T_{21} = T_{1} T_{2}

7-

2 m i n

8-

2 h o u r s

9-

82 M H z

10-

ρ > 3000 Ω \cdot c m

Formulas (html):

Correct Categorie: physics

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/2010.11877

Formulas:

1-

(M, g, J)

2-

ω (X, Y) = g (X, J Y)

3-

J T_{p} N = ν_{p} M

4-

ℂ H^{n} ≅ 𝖲𝖴 (1, n) / 𝖴 (n)

5-

K ≅ 𝖴 (n)

6-

G = 𝖲𝖴 (1, n)

7-

𝔤 = 𝔰 𝔲 (1, n)

8-

𝔨 ≅ 𝔲 (n)

9-

𝔤 = 𝔤_{- 2 α} \oplus 𝔤_{- α} \oplus 𝔤_{0} \oplus 𝔤_{α} \oplus 𝔤_{2 α}

10-

𝔥 = 𝔩 \oplus 𝔤_{2 α}

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0106507

Formulas:

1-

\frac{1}{a} \log \frac{D_{ref} (b)}{D}

2-

A_{B} \times \frac{A_{V}}{A_{B}} = A_{B} \times \frac{R_{V}}{1 + R_{V}}

3-

\log D_{ref} (b)

4-

\log D_{ref} = β + α \times b

5-

A_{V} (SFD98) - A_{V} (starcount) \approx 0.20 - {7.3 10}^{- 3} \times b

6-

Δ A_{V} = \pm_{0.23}^{0.29}

7-

U B V R I

8-

P = B_{ν} (T) \times {(λ / λ_{0})}^{- 2}

9-

R (λ, 60)

10-

I_{ν} (λ) / I_{ν} (60)

Formulas (html):

<math><mrow id="S2.E1.m3.1.2" xref="S2.E1.m3.1.2.cmml"><mstyle displaystyle="true" id="S2.E1.m3.1.2.2" xref="S2.E1.m3.1.2.2.cmml"><mfrac id="S2.E1.m3.1.2.2a" xref="S2.E1.m3.1.2.2.cmml"><mn id="S2.E1.m3.1.2.2.2" xref="S2.E1.m3.1.2.2.2.cmml">1</mn><mi id="S2.E1.m3.1.2.2.3" xref="S2.E1.m3.1.2.2.3.cmml">a</mi></mfrac></mstyle><mo id="S2.E1.m3.1.2.1" xref="S2.E1.m3.1.2.1.cmml">⁢</mo><mrow id="S2.E1.m3.1.2.3" xref="S2.E1.m3.1.2.3.cmml"><mi id="S2.E1.m3.1.2.3.1" xref="S2.E1.m3.1.2.3.1.cmml">log</mi><mo id="S2.E1.m3.1.2.3a" xref="S2.E1.m3.1.2.3.cmml">⁡</mo><mstyle displaystyle="true" id="S2.E1.m3.1.1" xref="S2.E1.m3.1.1.cmml"><mfrac id="S2.E1.m3.1.1a" xref="S2.E1.m3.1.1.cmml"><mrow id="S2.E1.m3.1.1.1" xref="S2.E1.m3.1.1.1.cmml"><msub id="S2.E1.m3.1.1.1.3" xref="S2.E1.m3.1.1.1.3.cmml"><mi id="S2.E1.m3.1.1.1.3.2" xref="S2.E1.m3.1.1.1.3.2.cmml">D</mi><mi id="S2.E1.m3.1.1.1.3.3" xref="S2.E1.m3.1.1.1.3.3.cmml">ref</mi></msub><mo id="S2.E1.m3.1.1.1.2" xref="S2.E1.m3.1.1.1.2.cmml">⁢</mo><mrow id="S2.E1.m3.1.1.1.4.2" xref="S2.E1.m3.1.1.1.cmml"><mo stretchy="false" id="S2.E1.m3.1.1.1.4.2.1" xref="S2.E1.m3.1.1.1.cmml">(</mo><mi id="S2.E1.m3.1.1.1.1" xref="S2.E1.m3.1.1.1.1.cmml">b</mi><mo stretchy="false" id="S2.E1.m3.1.1.1.4.2.2" xref="S2.E1.m3.1.1.1.cmml">)</mo></mrow></mrow><mi id="S2.E1.m3.1.1.3" xref="S2.E1.m3.1.1.3.cmml">D</mi></mfrac></mstyle></mrow></mrow></math>, <math><mrow id="S2.E2.m3.1.1" xref="S2.E2.m3.1.1.cmml"><mrow id="S2.E2.m3.1.1.2" xref="S2.E2.m3.1.1.2.cmml"><msub id="S2.E2.m3.1.1.2.2" xref="S2.E2.m3.1.1.2.2.cmml"><mi id="S2.E2.m3.1.1.2.2.2" xref="S2.E2.m3.1.1.2.2.2.cmml">A</mi><mi id="S2.E2.m3.1.1.2.2.3" xref="S2.E2.m3.1.1.2.2.3.cmml">B</mi></msub><mo id="S2.E2.m3.1.1.2.1" xref="S2.E2.m3.1.1.2.1.cmml">×</mo><mstyle displaystyle="true" id="S2.E2.m3.1.1.2.3" xref="S2.E2.m3.1.1.2.3.cmml"><mfrac id="S2.E2.m3.1.1.2.3a" xref="S2.E2.m3.1.1.2.3.cmml"><msub id="S2.E2.m3.1.1.2.3.2" xref="S2.E2.m3.1.1.2.3.2.cmml"><mi id="S2.E2.m3.1.1.2.3.2.2" xref="S2.E2.m3.1.1.2.3.2.2.cmml">A</mi><mi id="S2.E2.m3.1.1.2.3.2.3" xref="S2.E2.m3.1.1.2.3.2.3.cmml">V</mi></msub><msub id="S2.E2.m3.1.1.2.3.3" xref="S2.E2.m3.1.1.2.3.3.cmml"><mi id="S2.E2.m3.1.1.2.3.3.2" xref="S2.E2.m3.1.1.2.3.3.2.cmml">A</mi><mi id="S2.E2.m3.1.1.2.3.3.3" xref="S2.E2.m3.1.1.2.3.3.3.cmml">B</mi></msub></mfrac></mstyle></mrow><mo id="S2.E2.m3.1.1.1" xref="S2.E2.m3.1.1.1.cmml">=</mo><mrow id="S2.E2.m3.1.1.3" xref="S2.E2.m3.1.1.3.cmml"><msub id="S2.E2.m3.1.1.3.2" xref="S2.E2.m3.1.1.3.2.cmml"><mi id="S2.E2.m3.1.1.3.2.2" xref="S2.E2.m3.1.1.3.2.2.cmml">A</mi><mi id="S2.E2.m3.1.1.3.2.3" xref="S2.E2.m3.1.1.3.2.3.cmml">B</mi></msub><mo id="S2.E2.m3.1.1.3.1" xref="S2.E2.m3.1.1.3.1.cmml">×</mo><mstyle displaystyle="true" id="S2.E2.m3.1.1.3.3" xref="S2.E2.m3.1.1.3.3.cmml"><mfrac id="S2.E2.m3.1.1.3.3a" xref="S2.E2.m3.1.1.3.3.cmml"><msub id="S2.E2.m3.1.1.3.3.2" xref="S2.E2.m3.1.1.3.3.2.cmml"><mi id="S2.E2.m3.1.1.3.3.2.2" xref="S2.E2.m3.1.1.3.3.2.2.cmml">R</mi><mi id="S2.E2.m3.1.1.3.3.2.3" xref="S2.E2.m3.1.1.3.3.2.3.cmml">V</mi></msub><mrow id="S2.E2.m3.1.1.3.3.3" xref="S2.E2.m3.1.1.3.3.3.cmml"><mn id="S2.E2.m3.1.1.3.3.3.2" xref="S2.E2.m3.1.1.3.3.3.2.cmml">1</mn><mo id="S2.E2.m3.1.1.3.3.3.1" xref="S2.E2.m3.1.1.3.3.3.1.cmml">+</mo><msub id="S2.E2.m3.1.1.3.3.3.3" xref="S2.E2.m3.1.1.3.3.3.3.cmml"><mi id="S2.E2.m3.1.1.3.3.3.3.2" xref="S2.E2.m3.1.1.3.3.3.3.2.cmml">R</mi><mi id="S2.E2.m3.1.1.3.3.3.3.3" xref="S2.E2.m3.1.1.3.3.3.3.3.cmml">V</mi></msub></mrow></mfrac></mstyle></mrow></mrow></math>, <math><mrow id="S2.SS1.p2.1.m1.1.2" xref="S2.SS1.p2.1.m1.1.2.cmml"><mrow id="S2.SS1.p2.1.m1.1.2.2" xref="S2.SS1.p2.1.m1.1.2.2.cmml"><mi id="S2.SS1.p2.1.m1.1.2.2.1" xref="S2.SS1.p2.1.m1.1.2.2.1.cmml">log</mi><mo id="S2.SS1.p2.1.m1.1.2.2a" xref="S2.SS1.p2.1.m1.1.2.2.cmml">⁡</mo><msub id="S2.SS1.p2.1.m1.1.2.2.2" xref="S2.SS1.p2.1.m1.1.2.2.2.cmml"><mi id="S2.SS1.p2.1.m1.1.2.2.2.2" xref="S2.SS1.p2.1.m1.1.2.2.2.2.cmml">D</mi><mi id="S2.SS1.p2.1.m1.1.2.2.2.3" xref="S2.SS1.p2.1.m1.1.2.2.2.3.cmml">ref</mi></msub></mrow><mo id="S2.SS1.p2.1.m1.1.2.1" xref="S2.SS1.p2.1.m1.1.2.1.cmml">⁢</mo><mrow id="S2.SS1.p2.1.m1.1.2.3.2" xref="S2.SS1.p2.1.m1.1.2.cmml"><mo stretchy="false" id="S2.SS1.p2.1.m1.1.2.3.2.1" xref="S2.SS1.p2.1.m1.1.2.cmml">(</mo><mi id="S2.SS1.p2.1.m1.1.1" xref="S2.SS1.p2.1.m1.1.1.cmml">b</mi><mo stretchy="false" id="S2.SS1.p2.1.m1.1.2.3.2.2" xref="S2.SS1.p2.1.m1.1.2.cmml">)</mo></mrow></mrow></math>, <math><mrow id="S2.SS1.p2.4.m4.1.1" xref="S2.SS1.p2.4.m4.1.1.cmml"><mrow id="S2.SS1.p2.4.m4.1.1.2" xref="S2.SS1.p2.4.m4.1.1.2.cmml"><mi id="S2.SS1.p2.4.m4.1.1.2.1" xref="S2.SS1.p2.4.m4.1.1.2.1.cmml">log</mi><mo id="S2.SS1.p2.4.m4.1.1.2a" xref="S2.SS1.p2.4.m4.1.1.2.cmml">⁡</mo><msub id="S2.SS1.p2.4.m4.1.1.2.2" xref="S2.SS1.p2.4.m4.1.1.2.2.cmml"><mi id="S2.SS1.p2.4.m4.1.1.2.2.2" xref="S2.SS1.p2.4.m4.1.1.2.2.2.cmml">D</mi><mi id="S2.SS1.p2.4.m4.1.1.2.2.3" xref="S2.SS1.p2.4.m4.1.1.2.2.3.cmml">ref</mi></msub></mrow><mo id="S2.SS1.p2.4.m4.1.1.1" xref="S2.SS1.p2.4.m4.1.1.1.cmml">=</mo><mrow id="S2.SS1.p2.4.m4.1.1.3" xref="S2.SS1.p2.4.m4.1.1.3.cmml"><mi id="S2.SS1.p2.4.m4.1.1.3.2" xref="S2.SS1.p2.4.m4.1.1.3.2.cmml">β</mi><mo id="S2.SS1.p2.4.m4.1.1.3.1" xref="S2.SS1.p2.4.m4.1.1.3.1.cmml">+</mo><mrow id="S2.SS1.p2.4.m4.1.1.3.3" xref="S2.SS1.p2.4.m4.1.1.3.3.cmml"><mi id="S2.SS1.p2.4.m4.1.1.3.3.2" xref="S2.SS1.p2.4.m4.1.1.3.3.2.cmml">α</mi><mo id="S2.SS1.p2.4.m4.1.1.3.3.1" xref="S2.SS1.p2.4.m4.1.1.3.3.1.cmml">×</mo><mi id="S2.SS1.p2.4.m4.1.1.3.3.3" xref="S2.SS1.p2.4.m4.1.1.3.3.3.cmml">b</mi></mrow></mrow></mrow></math>, <math><mrow id="S2.SS1.p2.12.m12.2.3" xref="S2.SS1.p2.12.m12.2.3.cmml"><mrow id="S2.SS1.p2.12.m12.2.3.2" xref="S2.SS1.p2.12.m12.2.3.2.cmml"><mrow id="S2.SS1.p2.12.m12.2.3.2.2" xref="S2.SS1.p2.12.m12.2.3.2.2.cmml"><msub id="S2.SS1.p2.12.m12.2.3.2.2.2" xref="S2.SS1.p2.12.m12.2.3.2.2.2.cmml"><mi id="S2.SS1.p2.12.m12.2.3.2.2.2.2" xref="S2.SS1.p2.12.m12.2.3.2.2.2.2.cmml">A</mi><mi id="S2.SS1.p2.12.m12.2.3.2.2.2.3" xref="S2.SS1.p2.12.m12.2.3.2.2.2.3.cmml">V</mi></msub><mo id="S2.SS1.p2.12.m12.2.3.2.2.1" xref="S2.SS1.p2.12.m12.2.3.2.2.1.cmml">⁢</mo><mrow id="S2.SS1.p2.12.m12.2.3.2.2.3.2" xref="S2.SS1.p2.12.m12.2.3.2.2.cmml"><mo stretchy="false" id="S2.SS1.p2.12.m12.2.3.2.2.3.2.1" xref="S2.SS1.p2.12.m12.2.3.2.2.cmml">(</mo><mi id="S2.SS1.p2.12.m12.1.1" xref="S2.SS1.p2.12.m12.1.1.cmml">SFD98</mi><mo stretchy="false" id="S2.SS1.p2.12.m12.2.3.2.2.3.2.2" xref="S2.SS1.p2.12.m12.2.3.2.2.cmml">)</mo></mrow></mrow><mo id="S2.SS1.p2.12.m12.2.3.2.1" xref="S2.SS1.p2.12.m12.2.3.2.1.cmml">-</mo><mrow id="S2.SS1.p2.12.m12.2.3.2.3" xref="S2.SS1.p2.12.m12.2.3.2.3.cmml"><msub id="S2.SS1.p2.12.m12.2.3.2.3.2" xref="S2.SS1.p2.12.m12.2.3.2.3.2.cmml"><mi id="S2.SS1.p2.12.m12.2.3.2.3.2.2" xref="S2.SS1.p2.12.m12.2.3.2.3.2.2.cmml">A</mi><mi id="S2.SS1.p2.12.m12.2.3.2.3.2.3" xref="S2.SS1.p2.12.m12.2.3.2.3.2.3.cmml">V</mi></msub><mo id="S2.SS1.p2.12.m12.2.3.2.3.1" xref="S2.SS1.p2.12.m12.2.3.2.3.1.cmml">⁢</mo><mrow id="S2.SS1.p2.12.m12.2.3.2.3.3.2" xref="S2.SS1.p2.12.m12.2.3.2.3.cmml"><mo stretchy="false" id="S2.SS1.p2.12.m12.2.3.2.3.3.2.1" xref="S2.SS1.p2.12.m12.2.3.2.3.cmml">(</mo><mi id="S2.SS1.p2.12.m12.2.2" xref="S2.SS1.p2.12.m12.2.2.cmml">starcount</mi><mo stretchy="false" id="S2.SS1.p2.12.m12.2.3.2.3.3.2.2" xref="S2.SS1.p2.12.m12.2.3.2.3.cmml">)</mo></mrow></mrow></mrow><mo id="S2.SS1.p2.12.m12.2.3.1" xref="S2.SS1.p2.12.m12.2.3.1.cmml">≈</mo><mrow id="S2.SS1.p2.12.m12.2.3.3" xref="S2.SS1.p2.12.m12.2.3.3.cmml"><mn id="S2.SS1.p2.12.m12.2.3.3.2" xref="S2.SS1.p2.12.m12.2.3.3.2.cmml">0.20</mn><mo id="S2.SS1.p2.12.m12.2.3.3.1" xref="S2.SS1.p2.12.m12.2.3.3.1.cmml">-</mo><mrow id="S2.SS1.p2.12.m12.2.3.3.3" xref="S2.SS1.p2.12.m12.2.3.3.3.cmml"><msup id="S2.SS1.p2.12.m12.2.3.3.3.2" xref="S2.SS1.p2.12.m12.2.3.3.3.2.cmml"><mn id="S2.SS1.p2.12.m12.2.3.3.3.2.2" xref="S2.SS1.p2.12.m12.2.3.3.3.2.2.cmml">7.3 10</mn><mrow id="S2.SS1.p2.12.m12.2.3.3.3.2.3" xref="S2.SS1.p2.12.m12.2.3.3.3.2.3.cmml"><mo id="S2.SS1.p2.12.m12.2.3.3.3.2.3.1" xref="S2.SS1.p2.12.m12.2.3.3.3.2.3.1.cmml">-</mo><mn id="S2.SS1.p2.12.m12.2.3.3.3.2.3.2" xref="S2.SS1.p2.12.m12.2.3.3.3.2.3.2.cmml">3</mn></mrow></msup><mo id="S2.SS1.p2.12.m12.2.3.3.3.1" xref="S2.SS1.p2.12.m12.2.3.3.3.1.cmml">×</mo><mi id="S2.SS1.p2.12.m12.2.3.3.3.3" xref="S2.SS1.p2.12.m12.2.3.3.3.3.cmml">b</mi></mrow></mrow></mrow></math>, <math><mrow id="S2.SS1.p3.4.m4.1.1" xref="S2.SS1.p3.4.m4.1.1.cmml"><mrow id="S2.SS1.p3.4.m4.1.1.2" xref="S2.SS1.p3.4.m4.1.1.2.cmml"><mi mathvariant="normal" id="S2.SS1.p3.4.m4.1.1.2.2" xref="S2.SS1.p3.4.m4.1.1.2.2.cmml">Δ</mi><mo id="S2.SS1.p3.4.m4.1.1.2.1" xref="S2.SS1.p3.4.m4.1.1.2.1.cmml">⁢</mo><msub id="S2.SS1.p3.4.m4.1.1.2.3" xref="S2.SS1.p3.4.m4.1.1.2.3.cmml"><mi id="S2.SS1.p3.4.m4.1.1.2.3.2" xref="S2.SS1.p3.4.m4.1.1.2.3.2.cmml">A</mi><mi id="S2.SS1.p3.4.m4.1.1.2.3.3" xref="S2.SS1.p3.4.m4.1.1.2.3.3.cmml">V</mi></msub></mrow><mo id="S2.SS1.p3.4.m4.1.1.1" xref="S2.SS1.p3.4.m4.1.1.1.cmml">=</mo><msubsup id="S2.SS1.p3.4.m4.1.1.3" xref="S2.SS1.p3.4.m4.1.1.3.cmml"><mo id="S2.SS1.p3.4.m4.1.1.3.2.2" xref="S2.SS1.p3.4.m4.1.1.3.2.2.cmml">±</mo><mn id="S2.SS1.p3.4.m4.1.1.3.3" xref="S2.SS1.p3.4.m4.1.1.3.3.cmml">0.23</mn><mn id="S2.SS1.p3.4.m4.1.1.3.2.3" xref="S2.SS1.p3.4.m4.1.1.3.2.3.cmml">0.29</mn></msubsup></mrow></math>, <math><mrow id="S2.SS2.p2.2.m2.1.1" xref="S2.SS2.p2.2.m2.1.1.cmml"><mi id="S2.SS2.p2.2.m2.1.1.2" xref="S2.SS2.p2.2.m2.1.1.2.cmml">U</mi><mo id="S2.SS2.p2.2.m2.1.1.1" xref="S2.SS2.p2.2.m2.1.1.1.cmml">⁢</mo><mi id="S2.SS2.p2.2.m2.1.1.3" xref="S2.SS2.p2.2.m2.1.1.3.cmml">B</mi><mo id="S2.SS2.p2.2.m2.1.1.1a" xref="S2.SS2.p2.2.m2.1.1.1.cmml">⁢</mo><mi id="S2.SS2.p2.2.m2.1.1.4" xref="S2.SS2.p2.2.m2.1.1.4.cmml">V</mi><mo id="S2.SS2.p2.2.m2.1.1.1b" xref="S2.SS2.p2.2.m2.1.1.1.cmml">⁢</mo><mi id="S2.SS2.p2.2.m2.1.1.5" xref="S2.SS2.p2.2.m2.1.1.5.cmml">R</mi><mo id="S2.SS2.p2.2.m2.1.1.1c" xref="S2.SS2.p2.2.m2.1.1.1.cmml">⁢</mo><mi id="S2.SS2.p2.2.m2.1.1.6" xref="S2.SS2.p2.2.m2.1.1.6.cmml">I</mi></mrow></math>, <math><mrow id="S2.F4.4.m1.2.2" xref="S2.F4.4.m1.2.2.cmml"><mi id="S2.F4.4.m1.2.2.3" xref="S2.F4.4.m1.2.2.3.cmml">P</mi><mo mathvariant="normal" id="S2.F4.4.m1.2.2.2" xref="S2.F4.4.m1.2.2.2.cmml">=</mo><mrow id="S2.F4.4.m1.2.2.1" xref="S2.F4.4.m1.2.2.1.cmml"><mrow id="S2.F4.4.m1.2.2.1.3" xref="S2.F4.4.m1.2.2.1.3.cmml"><msub id="S2.F4.4.m1.2.2.1.3.2" xref="S2.F4.4.m1.2.2.1.3.2.cmml"><mi id="S2.F4.4.m1.2.2.1.3.2.2" xref="S2.F4.4.m1.2.2.1.3.2.2.cmml">B</mi><mi id="S2.F4.4.m1.2.2.1.3.2.3" xref="S2.F4.4.m1.2.2.1.3.2.3.cmml">ν</mi></msub><mo mathvariant="bold-sans-serif" id="S2.F4.4.m1.2.2.1.3.1" xref="S2.F4.4.m1.2.2.1.3.1.cmml">⁢</mo><mrow id="S2.F4.4.m1.2.2.1.3.3.2" xref="S2.F4.4.m1.2.2.1.3.cmml"><mo mathvariant="normal" stretchy="false" id="S2.F4.4.m1.2.2.1.3.3.2.1" xref="S2.F4.4.m1.2.2.1.3.cmml">(</mo><mi id="S2.F4.4.m1.1.1" xref="S2.F4.4.m1.1.1.cmml">T</mi><mo mathvariant="normal" stretchy="false" id="S2.F4.4.m1.2.2.1.3.3.2.2" xref="S2.F4.4.m1.2.2.1.3.cmml">)</mo></mrow></mrow><mo mathvariant="normal" id="S2.F4.4.m1.2.2.1.2" xref="S2.F4.4.m1.2.2.1.2.cmml">×</mo><msup id="S2.F4.4.m1.2.2.1.1" xref="S2.F4.4.m1.2.2.1.1.cmml"><mrow id="S2.F4.4.m1.2.2.1.1.1.1" xref="S2.F4.4.m1.2.2.1.1.1.1.1.cmml"><mo mathvariant="normal" stretchy="false" id="S2.F4.4.m1.2.2.1.1.1.1.2" xref="S2.F4.4.m1.2.2.1.1.1.1.1.cmml">(</mo><mrow id="S2.F4.4.m1.2.2.1.1.1.1.1" xref="S2.F4.4.m1.2.2.1.1.1.1.1.cmml"><mi id="S2.F4.4.m1.2.2.1.1.1.1.1.2" xref="S2.F4.4.m1.2.2.1.1.1.1.1.2.cmml">λ</mi><mo mathvariant="normal" id="S2.F4.4.m1.2.2.1.1.1.1.1.1" xref="S2.F4.4.m1.2.2.1.1.1.1.1.1.cmml">/</mo><msub id="S2.F4.4.m1.2.2.1.1.1.1.1.3" xref="S2.F4.4.m1.2.2.1.1.1.1.1.3.cmml"><mi id="S2.F4.4.m1.2.2.1.1.1.1.1.3.2" xref="S2.F4.4.m1.2.2.1.1.1.1.1.3.2.cmml">λ</mi><mn mathvariant="normal" id="S2.F4.4.m1.2.2.1.1.1.1.1.3.3" xref="S2.F4.4.m1.2.2.1.1.1.1.1.3.3.cmml">0</mn></msub></mrow><mo mathvariant="normal" stretchy="false" id="S2.F4.4.m1.2.2.1.1.1.1.3" xref="S2.F4.4.m1.2.2.1.1.1.1.1.cmml">)</mo></mrow><mrow id="S2.F4.4.m1.2.2.1.1.3" xref="S2.F4.4.m1.2.2.1.1.3.cmml"><mo mathvariant="normal" id="S2.F4.4.m1.2.2.1.1.3.1" xref="S2.F4.4.m1.2.2.1.1.3.1.cmml">-</mo><mn mathvariant="normal" id="S2.F4.4.m1.2.2.1.1.3.2" xref="S2.F4.4.m1.2.2.1.1.3.2.cmml">2</mn></mrow></msup></mrow></mrow></math>, <math><mrow id="S3.SS2.p1.5.m5.2.3" xref="S3.SS2.p1.5.m5.2.3.cmml"><mi id="S3.SS2.p1.5.m5.2.3.2" xref="S3.SS2.p1.5.m5.2.3.2.cmml">R</mi><mo id="S3.SS2.p1.5.m5.2.3.1" xref="S3.SS2.p1.5.m5.2.3.1.cmml">⁢</mo><mrow id="S3.SS2.p1.5.m5.2.3.3.2" xref="S3.SS2.p1.5.m5.2.3.3.1.cmml"><mo stretchy="false" id="S3.SS2.p1.5.m5.2.3.3.2.1" xref="S3.SS2.p1.5.m5.2.3.3.1.cmml">(</mo><mi id="S3.SS2.p1.5.m5.1.1" xref="S3.SS2.p1.5.m5.1.1.cmml">λ</mi><mo id="S3.SS2.p1.5.m5.2.3.3.2.2" xref="S3.SS2.p1.5.m5.2.3.3.1.cmml">,</mo><mn id="S3.SS2.p1.5.m5.2.2" xref="S3.SS2.p1.5.m5.2.2.cmml">60</mn><mo stretchy="false" id="S3.SS2.p1.5.m5.2.3.3.2.3" xref="S3.SS2.p1.5.m5.2.3.3.1.cmml">)</mo></mrow></mrow></math>, <math><mrow id="S3.SS2.p1.6.m6.2.3" xref="S3.SS2.p1.6.m6.2.3.cmml"><mrow id="S3.SS2.p1.6.m6.2.3.2" xref="S3.SS2.p1.6.m6.2.3.2.cmml"><mrow id="S3.SS2.p1.6.m6.2.3.2.2" xref="S3.SS2.p1.6.m6.2.3.2.2.cmml"><msub id="S3.SS2.p1.6.m6.2.3.2.2.2" xref="S3.SS2.p1.6.m6.2.3.2.2.2.cmml"><mi id="S3.SS2.p1.6.m6.2.3.2.2.2.2" xref="S3.SS2.p1.6.m6.2.3.2.2.2.2.cmml">I</mi><mi id="S3.SS2.p1.6.m6.2.3.2.2.2.3" xref="S3.SS2.p1.6.m6.2.3.2.2.2.3.cmml">ν</mi></msub><mo id="S3.SS2.p1.6.m6.2.3.2.2.1" xref="S3.SS2.p1.6.m6.2.3.2.2.1.cmml">⁢</mo><mrow id="S3.SS2.p1.6.m6.2.3.2.2.3.2" xref="S3.SS2.p1.6.m6.2.3.2.2.cmml"><mo stretchy="false" id="S3.SS2.p1.6.m6.2.3.2.2.3.2.1" xref="S3.SS2.p1.6.m6.2.3.2.2.cmml">(</mo><mi id="S3.SS2.p1.6.m6.1.1" xref="S3.SS2.p1.6.m6.1.1.cmml">λ</mi><mo stretchy="false" id="S3.SS2.p1.6.m6.2.3.2.2.3.2.2" xref="S3.SS2.p1.6.m6.2.3.2.2.cmml">)</mo></mrow></mrow><mo id="S3.SS2.p1.6.m6.2.3.2.1" xref="S3.SS2.p1.6.m6.2.3.2.1.cmml">/</mo><msub id="S3.SS2.p1.6.m6.2.3.2.3" xref="S3.SS2.p1.6.m6.2.3.2.3.cmml"><mi id="S3.SS2.p1.6.m6.2.3.2.3.2" xref="S3.SS2.p1.6.m6.2.3.2.3.2.cmml">I</mi><mi id="S3.SS2.p1.6.m6.2.3.2.3.3" xref="S3.SS2.p1.6.m6.2.3.2.3.3.cmml">ν</mi></msub></mrow><mo id="S3.SS2.p1.6.m6.2.3.1" xref="S3.SS2.p1.6.m6.2.3.1.cmml">⁢</mo><mrow id="S3.SS2.p1.6.m6.2.3.3.2" xref="S3.SS2.p1.6.m6.2.3.cmml"><mo stretchy="false" id="S3.SS2.p1.6.m6.2.3.3.2.1" xref="S3.SS2.p1.6.m6.2.3.cmml">(</mo><mn id="S3.SS2.p1.6.m6.2.2" xref="S3.SS2.p1.6.m6.2.2.cmml">60</mn><mo stretchy="false" id="S3.SS2.p1.6.m6.2.3.3.2.2" xref="S3.SS2.p1.6.m6.2.3.cmml">)</mo></mrow></mrow></math>

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/0812.3467

Formulas:

1-

ρ (r) = c_{k} r^{n_{k}}

2-

ρ (r) = c r^{- 3}

3-

ρ (r) \sim c_{l} r^{n_{l}}

4-

ρ (r) \sim c_{h} r^{n_{h}}

5-

ρ (r) = [\frac{c}{R_{0}^{3}}] {[\frac{r}{R_{0}}]}^{n_{k}},

6-

R_{0} ≃ 6.96 \times 10^{10}

7-

ρ (r) = [\frac{c_{0}}{R_{0}^{3}}] [\frac{c}{c_{0}}] {[\frac{r}{R_{0}}]}^{n_{k}},

8-

c_{0} / R_{0}^{3}

9-

ρ (r) = c r^{- 3}

10-

10^{31} g < c < 15 \times 10^{31} g

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1210.3942

Formulas:

1-

f : I \to ℝ,

2-

a, b \in I^{\circ}

3-

| f^{'} (x) | \leq M

4-

x \in [a, b]

5-

| f (x) - \frac{1}{b - a} \int_{a}^{b} f (t) 𝑑 t | \leq M (b - a) [\frac{1}{4} + \frac{{(x - \frac{a + b}{2})}^{2}}{{(b - a)}^{2}}], \forall x \in [a, b] .

6-

\frac{1}{(b - a)} \int_{a}^{b} f (t) 𝑑 t

7-

x \in [a, b] .

8-

t \in (0, 1)

9-

f (t x + (1 - t) y) \leq \frac{f (x)}{t} + \frac{f (y)}{1 - t} .

10-

f : I \subseteq ℝ \to ℝ

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/0711.3640

Formulas:

1-

Ω_{m} = {0.218}_{- 0.037}^{+ 0.047}

2-

Ω_{b} = {0.047}_{- 0.016}^{+ 0.016}

3-

40 < s < 200 h^{- 1} Mpc

4-

Ω_{b} h^{2} = 0.024

5-

Ω_{DE} = {0.770}_{- 0.040}^{+ 0.051}

6-

w = - {0.93}_{- 0.35}^{+ 0.45}

7-

β ≃ Ω_{m}^{0.6} / b

8-

100 h^{- 1} Mpc

9-

- 23.2 < M_{g} < - 21.2

10-

H_{0} = 100 {km s}^{- 1} {Mpc}^{- 1}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1105.6318

Formulas:

1-

| S C_{8} ⟩ = \frac{1}{\sqrt{2}} ({| H ⟩}^{\otimes 8} + {| V ⟩}^{\otimes 8}) .

2-

| φ^{+} ⟩ = (| H ⟩ | H ⟩ + | V ⟩ | V ⟩) / \sqrt{2}

3-

| + ⟩ = (| H ⟩ + | V ⟩) / \sqrt{2}

4-

{(p \times ξ)}^{4}

5-

\sim 2.8 \times 10^{- 5}

6-

(| H ⟩ | V ⟩ + | V ⟩ | H ⟩) / \sqrt{2}

7-

| H ⟩ | H ⟩

8-

| V ⟩ | V ⟩

9-

| φ^{+} ⟩ = (| H ⟩ | H ⟩ + | V ⟩ | V ⟩) / \sqrt{2}

10-

| H H H H ⟩

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: quant-ph

Result: correct

Paper: https://arxiv.org/abs/1803.07145

Formulas:

1-

\approx 5 L_{UV, z \sim 4}^{*}

2-

M_{star} \sim M_{z \sim 4}^{*}

3-

(Ω, Ω_{Λ}, σ_{8}, h) = (0.27, 0.73, 0.8, 0.7)

4-

R Y K_{S}

5-

> 10^{15} M_{⊙}

6-

B_{W} R I Y

7-

B_{W} R I Y

8-

B_{W} R I

9-

B_{W} - R ≳ 3.2

10-

R - I = 0.18 \pm 0.14

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1607.07244

Formulas:

1-

100 n g . {mL}^{- 1}

2-

10^{6} cells . {mL}^{- 1}

3-

1 n g . {mL}^{- 1}

4-

100 n g . {mL}^{- 1}

5-

= \frac{1}{1 + I / (1 - β)} \times \frac{1}{1 + {(K_{T} / L)}^{n_{T}}},

6-

= \frac{1 - α + α T}{1 + {(K_{I} / L)}^{n_{I}}},

7-

= \frac{1}{1 + {(\frac{K_{C}}{L + θ T})}^{n_{C}}},

8-

= \frac{B}{1 + I},

9-

k_{abs} = 4 π D R^{2} κ / (D + R κ c)

10-

κ = k_{on} N_{R} / 4 π R^{2}

Formulas (html):

<math><mrow id="S2.F1.6.m2.2.2.2" xref="S2.F1.6.m2.2.2.3.cmml"><mrow id="S2.F1.6.m2.1.1.1.1" xref="S2.F1.6.m2.1.1.1.1.cmml"><mn id="S2.F1.6.m2.1.1.1.1.2" xref="S2.F1.6.m2.1.1.1.1.2.cmml">100</mn><mo id="S2.F1.6.m2.1.1.1.1.1" xref="S2.F1.6.m2.1.1.1.1.1.cmml">⁢</mo><mi mathvariant="normal" id="S2.F1.6.m2.1.1.1.1.3" xref="S2.F1.6.m2.1.1.1.1.3.cmml">n</mi><mo id="S2.F1.6.m2.1.1.1.1.1b" xref="S2.F1.6.m2.1.1.1.1.1.cmml">⁢</mo><mi mathvariant="normal" id="S2.F1.6.m2.1.1.1.1.4" xref="S2.F1.6.m2.1.1.1.1.4.cmml">g</mi></mrow><mo id="S2.F1.6.m2.2.2.2.3" xref="S2.F1.6.m2.2.2.3a.cmml">.</mo><msup id="S2.F1.6.m2.2.2.2.2" xref="S2.F1.6.m2.2.2.2.2.cmml"><mi id="S2.F1.6.m2.2.2.2.2.2" xref="S2.F1.6.m2.2.2.2.2.2.cmml">mL</mi><mrow id="S2.F1.6.m2.2.2.2.2.3" xref="S2.F1.6.m2.2.2.2.2.3.cmml"><mo id="S2.F1.6.m2.2.2.2.2.3.1" xref="S2.F1.6.m2.2.2.2.2.3.1.cmml">-</mo><mn id="S2.F1.6.m2.2.2.2.2.3.2" xref="S2.F1.6.m2.2.2.2.2.3.2.cmml">1</mn></mrow></msup></mrow></math>, <math><mrow id="S2.SS4.p3.1.m1.2.2.2" xref="S2.SS4.p3.1.m1.2.2.3.cmml"><mrow id="S2.SS4.p3.1.m1.1.1.1.1" xref="S2.SS4.p3.1.m1.1.1.1.1.cmml"><msup id="S2.SS4.p3.1.m1.1.1.1.1.2" xref="S2.SS4.p3.1.m1.1.1.1.1.2.cmml"><mn id="S2.SS4.p3.1.m1.1.1.1.1.2.2" xref="S2.SS4.p3.1.m1.1.1.1.1.2.2.cmml">10</mn><mn id="S2.SS4.p3.1.m1.1.1.1.1.2.3" xref="S2.SS4.p3.1.m1.1.1.1.1.2.3.cmml">6</mn></msup><mo id="S2.SS4.p3.1.m1.1.1.1.1.1" xref="S2.SS4.p3.1.m1.1.1.1.1.1.cmml">⁢</mo><mi id="S2.SS4.p3.1.m1.1.1.1.1.3" xref="S2.SS4.p3.1.m1.1.1.1.1.3.cmml">cells</mi></mrow><mo id="S2.SS4.p3.1.m1.2.2.2.3" xref="S2.SS4.p3.1.m1.2.2.3a.cmml">.</mo><msup id="S2.SS4.p3.1.m1.2.2.2.2" xref="S2.SS4.p3.1.m1.2.2.2.2.cmml"><mi id="S2.SS4.p3.1.m1.2.2.2.2.2" xref="S2.SS4.p3.1.m1.2.2.2.2.2.cmml">mL</mi><mrow id="S2.SS4.p3.1.m1.2.2.2.2.3" xref="S2.SS4.p3.1.m1.2.2.2.2.3.cmml"><mo id="S2.SS4.p3.1.m1.2.2.2.2.3.1" xref="S2.SS4.p3.1.m1.2.2.2.2.3.1.cmml">-</mo><mn id="S2.SS4.p3.1.m1.2.2.2.2.3.2" xref="S2.SS4.p3.1.m1.2.2.2.2.3.2.cmml">1</mn></mrow></msup></mrow></math>, <math><mrow id="S2.F5.3.m1.2.2.2" xref="S2.F5.3.m1.2.2.3.cmml"><mrow id="S2.F5.3.m1.1.1.1.1" xref="S2.F5.3.m1.1.1.1.1.cmml"><mn id="S2.F5.3.m1.1.1.1.1.2" xref="S2.F5.3.m1.1.1.1.1.2.cmml">1</mn><mo id="S2.F5.3.m1.1.1.1.1.1" xref="S2.F5.3.m1.1.1.1.1.1.cmml">⁢</mo><mi mathvariant="normal" id="S2.F5.3.m1.1.1.1.1.3" xref="S2.F5.3.m1.1.1.1.1.3.cmml">n</mi><mo id="S2.F5.3.m1.1.1.1.1.1b" xref="S2.F5.3.m1.1.1.1.1.1.cmml">⁢</mo><mi mathvariant="normal" id="S2.F5.3.m1.1.1.1.1.4" xref="S2.F5.3.m1.1.1.1.1.4.cmml">g</mi></mrow><mo id="S2.F5.3.m1.2.2.2.3" xref="S2.F5.3.m1.2.2.3a.cmml">.</mo><msup id="S2.F5.3.m1.2.2.2.2" xref="S2.F5.3.m1.2.2.2.2.cmml"><mi id="S2.F5.3.m1.2.2.2.2.2" xref="S2.F5.3.m1.2.2.2.2.2.cmml">mL</mi><mrow id="S2.F5.3.m1.2.2.2.2.3" xref="S2.F5.3.m1.2.2.2.2.3.cmml"><mo id="S2.F5.3.m1.2.2.2.2.3.1" xref="S2.F5.3.m1.2.2.2.2.3.1.cmml">-</mo><mn id="S2.F5.3.m1.2.2.2.2.3.2" xref="S2.F5.3.m1.2.2.2.2.3.2.cmml">1</mn></mrow></msup></mrow></math>, <math><mrow id="S2.F5.4.m2.2.2.2" xref="S2.F5.4.m2.2.2.3.cmml"><mrow id="S2.F5.4.m2.1.1.1.1" xref="S2.F5.4.m2.1.1.1.1.cmml"><mn id="S2.F5.4.m2.1.1.1.1.2" xref="S2.F5.4.m2.1.1.1.1.2.cmml">100</mn><mo id="S2.F5.4.m2.1.1.1.1.1" xref="S2.F5.4.m2.1.1.1.1.1.cmml">⁢</mo><mi mathvariant="normal" id="S2.F5.4.m2.1.1.1.1.3" xref="S2.F5.4.m2.1.1.1.1.3.cmml">n</mi><mo id="S2.F5.4.m2.1.1.1.1.1b" xref="S2.F5.4.m2.1.1.1.1.1.cmml">⁢</mo><mi mathvariant="normal" id="S2.F5.4.m2.1.1.1.1.4" xref="S2.F5.4.m2.1.1.1.1.4.cmml">g</mi></mrow><mo id="S2.F5.4.m2.2.2.2.3" xref="S2.F5.4.m2.2.2.3a.cmml">.</mo><msup id="S2.F5.4.m2.2.2.2.2" xref="S2.F5.4.m2.2.2.2.2.cmml"><mi id="S2.F5.4.m2.2.2.2.2.2" xref="S2.F5.4.m2.2.2.2.2.2.cmml">mL</mi><mrow id="S2.F5.4.m2.2.2.2.2.3" xref="S2.F5.4.m2.2.2.2.2.3.cmml"><mo id="S2.F5.4.m2.2.2.2.2.3.1" xref="S2.F5.4.m2.2.2.2.2.3.1.cmml">-</mo><mn id="S2.F5.4.m2.2.2.2.2.3.2" xref="S2.F5.4.m2.2.2.2.2.3.2.cmml">1</mn></mrow></msup></mrow></math>, <math><mrow id="S4.E1.m2.3.3.1" xref="S4.E1.m2.3.3.1.1.cmml"><mrow id="S4.E1.m2.3.3.1.1" xref="S4.E1.m2.3.3.1.1.cmml"><mi id="S4.E1.m2.3.3.1.1.2" xref="S4.E1.m2.3.3.1.1.2.cmml"/><mo id="S4.E1.m2.3.3.1.1.1" xref="S4.E1.m2.3.3.1.1.1.cmml">=</mo><mrow id="S4.E1.m2.3.3.1.1.3" xref="S4.E1.m2.3.3.1.1.3.cmml"><mstyle displaystyle="true" id="S4.E1.m2.1.1" xref="S4.E1.m2.1.1.cmml"><mfrac id="S4.E1.m2.1.1a" xref="S4.E1.m2.1.1.cmml"><mn id="S4.E1.m2.1.1.3" xref="S4.E1.m2.1.1.3.cmml">1</mn><mrow id="S4.E1.m2.1.1.1" xref="S4.E1.m2.1.1.1.cmml"><mn id="S4.E1.m2.1.1.1.3" xref="S4.E1.m2.1.1.1.3.cmml">1</mn><mo id="S4.E1.m2.1.1.1.2" xref="S4.E1.m2.1.1.1.2.cmml">+</mo><mrow id="S4.E1.m2.1.1.1.1" xref="S4.E1.m2.1.1.1.1.cmml"><mi id="S4.E1.m2.1.1.1.1.3" xref="S4.E1.m2.1.1.1.1.3.cmml">I</mi><mo id="S4.E1.m2.1.1.1.1.2" xref="S4.E1.m2.1.1.1.1.2.cmml">/</mo><mrow id="S4.E1.m2.1.1.1.1.1.1" xref="S4.E1.m2.1.1.1.1.1.1.1.cmml"><mo stretchy="false" id="S4.E1.m2.1.1.1.1.1.1.2" xref="S4.E1.m2.1.1.1.1.1.1.1.cmml">(</mo><mrow id="S4.E1.m2.1.1.1.1.1.1.1" xref="S4.E1.m2.1.1.1.1.1.1.1.cmml"><mn id="S4.E1.m2.1.1.1.1.1.1.1.2" xref="S4.E1.m2.1.1.1.1.1.1.1.2.cmml">1</mn><mo id="S4.E1.m2.1.1.1.1.1.1.1.1" xref="S4.E1.m2.1.1.1.1.1.1.1.1.cmml">-</mo><mi id="S4.E1.m2.1.1.1.1.1.1.1.3" xref="S4.E1.m2.1.1.1.1.1.1.1.3.cmml">β</mi></mrow><mo stretchy="false" id="S4.E1.m2.1.1.1.1.1.1.3" xref="S4.E1.m2.1.1.1.1.1.1.1.cmml">)</mo></mrow></mrow></mrow></mfrac></mstyle><mo id="S4.E1.m2.3.3.1.1.3.1" xref="S4.E1.m2.3.3.1.1.3.1.cmml">×</mo><mstyle displaystyle="true" id="S4.E1.m2.2.2" xref="S4.E1.m2.2.2.cmml"><mfrac id="S4.E1.m2.2.2a" xref="S4.E1.m2.2.2.cmml"><mn id="S4.E1.m2.2.2.3" xref="S4.E1.m2.2.2.3.cmml">1</mn><mrow id="S4.E1.m2.2.2.1" xref="S4.E1.m2.2.2.1.cmml"><mn id="S4.E1.m2.2.2.1.3" xref="S4.E1.m2.2.2.1.3.cmml">1</mn><mo id="S4.E1.m2.2.2.1.2" xref="S4.E1.m2.2.2.1.2.cmml">+</mo><msup id="S4.E1.m2.2.2.1.1" xref="S4.E1.m2.2.2.1.1.cmml"><mrow id="S4.E1.m2.2.2.1.1.1.1" xref="S4.E1.m2.2.2.1.1.1.1.1.cmml"><mo stretchy="false" id="S4.E1.m2.2.2.1.1.1.1.2" xref="S4.E1.m2.2.2.1.1.1.1.1.cmml">(</mo><mrow id="S4.E1.m2.2.2.1.1.1.1.1" xref="S4.E1.m2.2.2.1.1.1.1.1.cmml"><msub id="S4.E1.m2.2.2.1.1.1.1.1.2" xref="S4.E1.m2.2.2.1.1.1.1.1.2.cmml"><mi id="S4.E1.m2.2.2.1.1.1.1.1.2.2" xref="S4.E1.m2.2.2.1.1.1.1.1.2.2.cmml">K</mi><mi id="S4.E1.m2.2.2.1.1.1.1.1.2.3" xref="S4.E1.m2.2.2.1.1.1.1.1.2.3.cmml">T</mi></msub><mo id="S4.E1.m2.2.2.1.1.1.1.1.1" xref="S4.E1.m2.2.2.1.1.1.1.1.1.cmml">/</mo><mi id="S4.E1.m2.2.2.1.1.1.1.1.3" xref="S4.E1.m2.2.2.1.1.1.1.1.3.cmml">L</mi></mrow><mo stretchy="false" id="S4.E1.m2.2.2.1.1.1.1.3" xref="S4.E1.m2.2.2.1.1.1.1.1.cmml">)</mo></mrow><msub id="S4.E1.m2.2.2.1.1.3" xref="S4.E1.m2.2.2.1.1.3.cmml"><mi id="S4.E1.m2.2.2.1.1.3.2" xref="S4.E1.m2.2.2.1.1.3.2.cmml">n</mi><mi id="S4.E1.m2.2.2.1.1.3.3" xref="S4.E1.m2.2.2.1.1.3.3.cmml">T</mi></msub></msup></mrow></mfrac></mstyle></mrow></mrow><mo id="S4.E1.m2.3.3.1.2" xref="S4.E1.m2.3.3.1.1.cmml">,</mo></mrow></math>, <math><mrow id="S4.E2.m2.2.2.1" xref="S4.E2.m2.2.2.1.1.cmml"><mrow id="S4.E2.m2.2.2.1.1" xref="S4.E2.m2.2.2.1.1.cmml"><mi id="S4.E2.m2.2.2.1.1.2" xref="S4.E2.m2.2.2.1.1.2.cmml"/><mo id="S4.E2.m2.2.2.1.1.1" xref="S4.E2.m2.2.2.1.1.1.cmml">=</mo><mstyle displaystyle="true" id="S4.E2.m2.1.1" xref="S4.E2.m2.1.1.cmml"><mfrac id="S4.E2.m2.1.1a" xref="S4.E2.m2.1.1.cmml"><mrow id="S4.E2.m2.1.1.3" xref="S4.E2.m2.1.1.3.cmml"><mrow id="S4.E2.m2.1.1.3.2" xref="S4.E2.m2.1.1.3.2.cmml"><mn id="S4.E2.m2.1.1.3.2.2" xref="S4.E2.m2.1.1.3.2.2.cmml">1</mn><mo id="S4.E2.m2.1.1.3.2.1" xref="S4.E2.m2.1.1.3.2.1.cmml">-</mo><mi id="S4.E2.m2.1.1.3.2.3" xref="S4.E2.m2.1.1.3.2.3.cmml">α</mi></mrow><mo id="S4.E2.m2.1.1.3.1" xref="S4.E2.m2.1.1.3.1.cmml">+</mo><mrow id="S4.E2.m2.1.1.3.3" xref="S4.E2.m2.1.1.3.3.cmml"><mi id="S4.E2.m2.1.1.3.3.2" xref="S4.E2.m2.1.1.3.3.2.cmml">α</mi><mo id="S4.E2.m2.1.1.3.3.1" xref="S4.E2.m2.1.1.3.3.1.cmml">⁢</mo><mi id="S4.E2.m2.1.1.3.3.3" xref="S4.E2.m2.1.1.3.3.3.cmml">T</mi></mrow></mrow><mrow id="S4.E2.m2.1.1.1" xref="S4.E2.m2.1.1.1.cmml"><mn id="S4.E2.m2.1.1.1.3" xref="S4.E2.m2.1.1.1.3.cmml">1</mn><mo id="S4.E2.m2.1.1.1.2" xref="S4.E2.m2.1.1.1.2.cmml">+</mo><msup id="S4.E2.m2.1.1.1.1" xref="S4.E2.m2.1.1.1.1.cmml"><mrow id="S4.E2.m2.1.1.1.1.1.1" xref="S4.E2.m2.1.1.1.1.1.1.1.cmml"><mo stretchy="false" id="S4.E2.m2.1.1.1.1.1.1.2" xref="S4.E2.m2.1.1.1.1.1.1.1.cmml">(</mo><mrow id="S4.E2.m2.1.1.1.1.1.1.1" xref="S4.E2.m2.1.1.1.1.1.1.1.cmml"><msub id="S4.E2.m2.1.1.1.1.1.1.1.2" xref="S4.E2.m2.1.1.1.1.1.1.1.2.cmml"><mi id="S4.E2.m2.1.1.1.1.1.1.1.2.2" xref="S4.E2.m2.1.1.1.1.1.1.1.2.2.cmml">K</mi><mi id="S4.E2.m2.1.1.1.1.1.1.1.2.3" xref="S4.E2.m2.1.1.1.1.1.1.1.2.3.cmml">I</mi></msub><mo id="S4.E2.m2.1.1.1.1.1.1.1.1" xref="S4.E2.m2.1.1.1.1.1.1.1.1.cmml">/</mo><mi id="S4.E2.m2.1.1.1.1.1.1.1.3" xref="S4.E2.m2.1.1.1.1.1.1.1.3.cmml">L</mi></mrow><mo stretchy="false" id="S4.E2.m2.1.1.1.1.1.1.3" xref="S4.E2.m2.1.1.1.1.1.1.1.cmml">)</mo></mrow><msub id="S4.E2.m2.1.1.1.1.3" xref="S4.E2.m2.1.1.1.1.3.cmml"><mi id="S4.E2.m2.1.1.1.1.3.2" xref="S4.E2.m2.1.1.1.1.3.2.cmml">n</mi><mi id="S4.E2.m2.1.1.1.1.3.3" xref="S4.E2.m2.1.1.1.1.3.3.cmml">I</mi></msub></msup></mrow></mfrac></mstyle></mrow><mo id="S4.E2.m2.2.2.1.2" xref="S4.E2.m2.2.2.1.1.cmml">,</mo></mrow></math>, <math><mrow id="S4.E3.m2.2.2.1" xref="S4.E3.m2.2.2.1.1.cmml"><mrow id="S4.E3.m2.2.2.1.1" xref="S4.E3.m2.2.2.1.1.cmml"><mi id="S4.E3.m2.2.2.1.1.2" xref="S4.E3.m2.2.2.1.1.2.cmml"/><mo id="S4.E3.m2.2.2.1.1.1" xref="S4.E3.m2.2.2.1.1.1.cmml">=</mo><mstyle displaystyle="true" id="S4.E3.m2.1.1" xref="S4.E3.m2.1.1.cmml"><mfrac id="S4.E3.m2.1.1a" xref="S4.E3.m2.1.1.cmml"><mn id="S4.E3.m2.1.1.3" xref="S4.E3.m2.1.1.3.cmml">1</mn><mrow id="S4.E3.m2.1.1.1" xref="S4.E3.m2.1.1.1.cmml"><mn id="S4.E3.m2.1.1.1.3" xref="S4.E3.m2.1.1.1.3.cmml">1</mn><mo id="S4.E3.m2.1.1.1.2" xref="S4.E3.m2.1.1.1.2.cmml">+</mo><msup id="S4.E3.m2.1.1.1.4" xref="S4.E3.m2.1.1.1.4.cmml"><mrow id="S4.E3.m2.1.1.1.4.2.2" xref="S4.E3.m2.1.1.1.1.cmml"><mo id="S4.E3.m2.1.1.1.4.2.2.1" xref="S4.E3.m2.1.1.1.1.cmml">(</mo><mfrac id="S4.E3.m2.1.1.1.1" xref="S4.E3.m2.1.1.1.1.cmml"><msub id="S4.E3.m2.1.1.1.1.2" xref="S4.E3.m2.1.1.1.1.2.cmml"><mi id="S4.E3.m2.1.1.1.1.2.2" xref="S4.E3.m2.1.1.1.1.2.2.cmml">K</mi><mi id="S4.E3.m2.1.1.1.1.2.3" xref="S4.E3.m2.1.1.1.1.2.3.cmml">C</mi></msub><mrow id="S4.E3.m2.1.1.1.1.3" xref="S4.E3.m2.1.1.1.1.3.cmml"><mi id="S4.E3.m2.1.1.1.1.3.2" xref="S4.E3.m2.1.1.1.1.3.2.cmml">L</mi><mo id="S4.E3.m2.1.1.1.1.3.1" xref="S4.E3.m2.1.1.1.1.3.1.cmml">+</mo><mrow id="S4.E3.m2.1.1.1.1.3.3" xref="S4.E3.m2.1.1.1.1.3.3.cmml"><mi id="S4.E3.m2.1.1.1.1.3.3.2" xref="S4.E3.m2.1.1.1.1.3.3.2.cmml">θ</mi><mo id="S4.E3.m2.1.1.1.1.3.3.1" xref="S4.E3.m2.1.1.1.1.3.3.1.cmml">⁢</mo><mi id="S4.E3.m2.1.1.1.1.3.3.3" xref="S4.E3.m2.1.1.1.1.3.3.3.cmml">T</mi></mrow></mrow></mfrac><mo id="S4.E3.m2.1.1.1.4.2.2.2" xref="S4.E3.m2.1.1.1.1.cmml">)</mo></mrow><msub id="S4.E3.m2.1.1.1.4.3" xref="S4.E3.m2.1.1.1.4.3.cmml"><mi id="S4.E3.m2.1.1.1.4.3.2" xref="S4.E3.m2.1.1.1.4.3.2.cmml">n</mi><mi id="S4.E3.m2.1.1.1.4.3.3" xref="S4.E3.m2.1.1.1.4.3.3.cmml">C</mi></msub></msup></mrow></mfrac></mstyle></mrow><mo id="S4.E3.m2.2.2.1.2" xref="S4.E3.m2.2.2.1.1.cmml">,</mo></mrow></math>, <math><mrow id="S4.E4.m2.1.1.1" xref="S4.E4.m2.1.1.1.1.cmml"><mrow id="S4.E4.m2.1.1.1.1" xref="S4.E4.m2.1.1.1.1.cmml"><mi id="S4.E4.m2.1.1.1.1.2" xref="S4.E4.m2.1.1.1.1.2.cmml"/><mo id="S4.E4.m2.1.1.1.1.1" xref="S4.E4.m2.1.1.1.1.1.cmml">=</mo><mstyle displaystyle="true" id="S4.E4.m2.1.1.1.1.3" xref="S4.E4.m2.1.1.1.1.3.cmml"><mfrac id="S4.E4.m2.1.1.1.1.3a" xref="S4.E4.m2.1.1.1.1.3.cmml"><mi id="S4.E4.m2.1.1.1.1.3.2" xref="S4.E4.m2.1.1.1.1.3.2.cmml">B</mi><mrow id="S4.E4.m2.1.1.1.1.3.3" xref="S4.E4.m2.1.1.1.1.3.3.cmml"><mn id="S4.E4.m2.1.1.1.1.3.3.2" xref="S4.E4.m2.1.1.1.1.3.3.2.cmml">1</mn><mo id="S4.E4.m2.1.1.1.1.3.3.1" xref="S4.E4.m2.1.1.1.1.3.3.1.cmml">+</mo><mi id="S4.E4.m2.1.1.1.1.3.3.3" xref="S4.E4.m2.1.1.1.1.3.3.3.cmml">I</mi></mrow></mfrac></mstyle></mrow><mo id="S4.E4.m2.1.1.1.2" xref="S4.E4.m2.1.1.1.1.cmml">,</mo></mrow></math>, <math><mrow id="S4.SS4.p2.1.m1.1.1" xref="S4.SS4.p2.1.m1.1.1.cmml"><msub id="S4.SS4.p2.1.m1.1.1.3" xref="S4.SS4.p2.1.m1.1.1.3.cmml"><mi id="S4.SS4.p2.1.m1.1.1.3.2" xref="S4.SS4.p2.1.m1.1.1.3.2.cmml">k</mi><mi id="S4.SS4.p2.1.m1.1.1.3.3" xref="S4.SS4.p2.1.m1.1.1.3.3.cmml">abs</mi></msub><mo id="S4.SS4.p2.1.m1.1.1.2" xref="S4.SS4.p2.1.m1.1.1.2.cmml">=</mo><mrow id="S4.SS4.p2.1.m1.1.1.1" xref="S4.SS4.p2.1.m1.1.1.1.cmml"><mrow id="S4.SS4.p2.1.m1.1.1.1.3" xref="S4.SS4.p2.1.m1.1.1.1.3.cmml"><mn id="S4.SS4.p2.1.m1.1.1.1.3.2" xref="S4.SS4.p2.1.m1.1.1.1.3.2.cmml">4</mn><mo id="S4.SS4.p2.1.m1.1.1.1.3.1" xref="S4.SS4.p2.1.m1.1.1.1.3.1.cmml">⁢</mo><mi id="S4.SS4.p2.1.m1.1.1.1.3.3" xref="S4.SS4.p2.1.m1.1.1.1.3.3.cmml">π</mi><mo id="S4.SS4.p2.1.m1.1.1.1.3.1a" xref="S4.SS4.p2.1.m1.1.1.1.3.1.cmml">⁢</mo><mi id="S4.SS4.p2.1.m1.1.1.1.3.4" xref="S4.SS4.p2.1.m1.1.1.1.3.4.cmml">D</mi><mo id="S4.SS4.p2.1.m1.1.1.1.3.1b" xref="S4.SS4.p2.1.m1.1.1.1.3.1.cmml">⁢</mo><msup id="S4.SS4.p2.1.m1.1.1.1.3.5" xref="S4.SS4.p2.1.m1.1.1.1.3.5.cmml"><mi id="S4.SS4.p2.1.m1.1.1.1.3.5.2" xref="S4.SS4.p2.1.m1.1.1.1.3.5.2.cmml">R</mi><mn id="S4.SS4.p2.1.m1.1.1.1.3.5.3" xref="S4.SS4.p2.1.m1.1.1.1.3.5.3.cmml">2</mn></msup><mo id="S4.SS4.p2.1.m1.1.1.1.3.1c" xref="S4.SS4.p2.1.m1.1.1.1.3.1.cmml">⁢</mo><mi id="S4.SS4.p2.1.m1.1.1.1.3.6" xref="S4.SS4.p2.1.m1.1.1.1.3.6.cmml">κ</mi></mrow><mo id="S4.SS4.p2.1.m1.1.1.1.2" xref="S4.SS4.p2.1.m1.1.1.1.2.cmml">/</mo><mrow id="S4.SS4.p2.1.m1.1.1.1.1.1" xref="S4.SS4.p2.1.m1.1.1.1.1.1.1.cmml"><mo stretchy="false" id="S4.SS4.p2.1.m1.1.1.1.1.1.2" xref="S4.SS4.p2.1.m1.1.1.1.1.1.1.cmml">(</mo><mrow id="S4.SS4.p2.1.m1.1.1.1.1.1.1" xref="S4.SS4.p2.1.m1.1.1.1.1.1.1.cmml"><mi id="S4.SS4.p2.1.m1.1.1.1.1.1.1.2" xref="S4.SS4.p2.1.m1.1.1.1.1.1.1.2.cmml">D</mi><mo id="S4.SS4.p2.1.m1.1.1.1.1.1.1.1" xref="S4.SS4.p2.1.m1.1.1.1.1.1.1.1.cmml">+</mo><mrow id="S4.SS4.p2.1.m1.1.1.1.1.1.1.3" xref="S4.SS4.p2.1.m1.1.1.1.1.1.1.3.cmml"><mi id="S4.SS4.p2.1.m1.1.1.1.1.1.1.3.2" xref="S4.SS4.p2.1.m1.1.1.1.1.1.1.3.2.cmml">R</mi><mo id="S4.SS4.p2.1.m1.1.1.1.1.1.1.3.1" xref="S4.SS4.p2.1.m1.1.1.1.1.1.1.3.1.cmml">⁢</mo><mi id="S4.SS4.p2.1.m1.1.1.1.1.1.1.3.3" xref="S4.SS4.p2.1.m1.1.1.1.1.1.1.3.3.cmml">κ</mi><mo id="S4.SS4.p2.1.m1.1.1.1.1.1.1.3.1a" xref="S4.SS4.p2.1.m1.1.1.1.1.1.1.3.1.cmml">⁢</mo><mi id="S4.SS4.p2.1.m1.1.1.1.1.1.1.3.4" xref="S4.SS4.p2.1.m1.1.1.1.1.1.1.3.4.cmml">c</mi></mrow></mrow><mo stretchy="false" id="S4.SS4.p2.1.m1.1.1.1.1.1.3" xref="S4.SS4.p2.1.m1.1.1.1.1.1.1.cmml">)</mo></mrow></mrow></mrow></math>, <math><mrow id="S4.SS4.p2.4.m4.1.1" xref="S4.SS4.p2.4.m4.1.1.cmml"><mi id="S4.SS4.p2.4.m4.1.1.2" xref="S4.SS4.p2.4.m4.1.1.2.cmml">κ</mi><mo id="S4.SS4.p2.4.m4.1.1.1" xref="S4.SS4.p2.4.m4.1.1.1.cmml">=</mo><mrow id="S4.SS4.p2.4.m4.1.1.3" xref="S4.SS4.p2.4.m4.1.1.3.cmml"><mrow id="S4.SS4.p2.4.m4.1.1.3.2" xref="S4.SS4.p2.4.m4.1.1.3.2.cmml"><mrow id="S4.SS4.p2.4.m4.1.1.3.2.2" xref="S4.SS4.p2.4.m4.1.1.3.2.2.cmml"><msub id="S4.SS4.p2.4.m4.1.1.3.2.2.2" xref="S4.SS4.p2.4.m4.1.1.3.2.2.2.cmml"><mi id="S4.SS4.p2.4.m4.1.1.3.2.2.2.2" xref="S4.SS4.p2.4.m4.1.1.3.2.2.2.2.cmml">k</mi><mi id="S4.SS4.p2.4.m4.1.1.3.2.2.2.3" xref="S4.SS4.p2.4.m4.1.1.3.2.2.2.3.cmml">on</mi></msub><mo id="S4.SS4.p2.4.m4.1.1.3.2.2.1" xref="S4.SS4.p2.4.m4.1.1.3.2.2.1.cmml">⁢</mo><msub id="S4.SS4.p2.4.m4.1.1.3.2.2.3" xref="S4.SS4.p2.4.m4.1.1.3.2.2.3.cmml"><mi id="S4.SS4.p2.4.m4.1.1.3.2.2.3.2" xref="S4.SS4.p2.4.m4.1.1.3.2.2.3.2.cmml">N</mi><mi id="S4.SS4.p2.4.m4.1.1.3.2.2.3.3" xref="S4.SS4.p2.4.m4.1.1.3.2.2.3.3.cmml">R</mi></msub></mrow><mo id="S4.SS4.p2.4.m4.1.1.3.2.1" xref="S4.SS4.p2.4.m4.1.1.3.2.1.cmml">/</mo><mn id="S4.SS4.p2.4.m4.1.1.3.2.3" xref="S4.SS4.p2.4.m4.1.1.3.2.3.cmml">4</mn></mrow><mo id="S4.SS4.p2.4.m4.1.1.3.1" xref="S4.SS4.p2.4.m4.1.1.3.1.cmml">⁢</mo><mi id="S4.SS4.p2.4.m4.1.1.3.3" xref="S4.SS4.p2.4.m4.1.1.3.3.cmml">π</mi><mo id="S4.SS4.p2.4.m4.1.1.3.1a" xref="S4.SS4.p2.4.m4.1.1.3.1.cmml">⁢</mo><msup id="S4.SS4.p2.4.m4.1.1.3.4" xref="S4.SS4.p2.4.m4.1.1.3.4.cmml"><mi id="S4.SS4.p2.4.m4.1.1.3.4.2" xref="S4.SS4.p2.4.m4.1.1.3.4.2.cmml">R</mi><mn id="S4.SS4.p2.4.m4.1.1.3.4.3" xref="S4.SS4.p2.4.m4.1.1.3.4.3.cmml">2</mn></msup></mrow></mrow></math>

Correct Categorie: q-bio

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1703.06636

Formulas:

1-

T_{c} = 97 \pm 6

2-

H = - \sum_{\begin{matrix} i, j \end{matrix}} J (r_{i j}) 𝐒_{i} 𝐒_{j} .

3-

J (r_{i j})

4-

J (r) = J_{0} e^{- r / l} r^{- 4} (sin (2 k_{F} r) - 2 k_{F} r cos (2 k_{F} r)) .

5-

k_{F} = {(\frac{3}{2} π^{2} n_{c})}^{1 / 3}

6-

\sim π / k_{F} \approx 1.37

7-

𝐪 = [0, 0, 0]

8-

𝐪_{𝟏} = [\frac{2 π}{L}, 0, 0]

9-

ξ = \frac{1}{| 𝐪_{𝟏} |} \sqrt{\frac{S (𝐪)}{S (𝐪_{𝟏})} - 1},

10-

S (𝐪) = \sum_{𝐫} cos (𝐪 \cdot 𝐫) C (𝐫),

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0503090

Formulas:

1-

- 69^{°} 34^{'} {31.75}^{''}

2-

V_{M A C H O} + 24.22 - 0.1804 (V_{M A C H O} - R_{M A C H O})

3-

R_{M A C H O} + 23.98 + 0.1825 (V_{M A C H O} - R_{M A C H O}) .

4-

7 - 5.6 M_{⊙}

5-

4.9 - 4.3 R_{⊙}

6-

T_{e f f} = 19300 - 16000 K

7-

Δ (V R) / Δ t

8-

Δ (V R) \geq

9-

I_{D I A}

10-

v = 2 π R / P \sim 120

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/0904.2979

Formulas:

1-

{}_{- 0.16}^{+ 0.21}R_{\oplus}

2-

M < 10 M_{\oplus}

3-

\frac{\partial r}{\partial M_{r}} = \frac{1}{4 π r^{2} ρ}

4-

\frac{\partial P}{\partial M_{r}} = - \frac{G M_{r}}{4 π r^{4}}

5-

M_{d i s k} \propto M_{s t a r}^{β}

6-

M_{s t a r}

7-

M_{d i s k}

8-

M_{s t a r}

9-

M_{s t a r}

10-

{}_{- 0.16}^{+ 0.21}R_{\oplus}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/0812.0775

Formulas:

1-

{q_{i}, q_{j}} = 0

2-

{q_{i}, p_{j}} = δ_{i j}

3-

H (q_{i}, p_{i}) = λ_{j} C^{j} (q_{i}, p_{i}) = 0

4-

H (q_{i}, p_{i}) = λ C (q_{i}, p_{i}) = 0

5-

{O, C} = f C

6-

{O, C} = 0

7-

{\frac{d}{d τ} α^{τ} (\cdot) |}_{τ = 0} = {C, \cdot}

8-

C = p_{t} + \frac{1}{2} p_{x}^{2}

9-

{q_{i} |}_{q_{j} = β} = \int α^{τ} (q_{i}) {C, α^{τ} (q_{j})} δ (α^{τ} (q_{j}) - β) 𝑑 τ

10-

{x |}_{t = β} = x + p_{x} (β - t)

Formulas (html):

Correct Categorie: gr-qc

Guessed Categorie: gr-qc

Result: correct

Paper: https://arxiv.org/abs/math/0412242

Formulas:

1-

e_{(p + 1) / 2}

2-

ℚ (ζ_{p})

3-

ℚ (ζ_{p})

4-

p (q - 1) | q^{n} - 1

5-

f = (q^{n} - 1) / p

6-

e = (p - 1) / n

7-

ℤ [ζ_{p}]

8-

𝔽 = ℤ [ζ_{p}] / Q

9-

α \in ℤ [ζ_{p}]

10-

α^{f} \equiv ζ_{p} mod Q

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/1608.07088

Formulas:

1-

164 \pm 10 km s^{- 1}

2-

\sim 1000 km s^{- 1}

3-

10 km s^{- 1}

4-

164 \pm 10 km s^{- 1}

5-

\sim 150 \pm 70 km s^{- 1}

6-

M_{⊙} {yr}^{- 1}

7-

8 \times 10^{7} yr

8-

164 km s^{- 1}

9-

700 km s^{- 1}

10-

\sim 1000 km s^{- 1}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/cond-mat/0112364

Formulas:

1-

T < T_{c M}

2-

T > T_{c M}

3-

T < T_{c S}

4-

T > T_{c S}

5-

H (t) \propto I (t),

6-

B (t) = B [I (t)]

7-

\begin{matrix} V = V_{S} + V_{M} \\ V_{M} = \frac{d Φ [B]}{d t} \propto \frac{d B (t)}{d t} = \frac{d B [I (t)]}{d t} \end{matrix}

8-

B [I (t)]

9-

B (t) = B [I (t)]

10-

T < T_{c M}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/astro-ph/9705078

Formulas:

1-

k_{c r i t} = κ^{2} / (2 π G Σ)

2-

k_{c r i t} r ≫ 1

3-

k_{c r i t} r

4-

0.1 r_{m a x}

5-

r_{m a x}

6-

k_{c r i t} r \approx 2 π

7-

(k_{r}) \approx 1.85 k_{c r i t}

8-

(k_{r}) \approx 0.9 k_{c r i t}

9-

§ § 2 - 4

10-

ω_{i} \approx 0.14 Ω

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1207.5984

Formulas:

1-

ω_{j} (k)

2-

| ψ_{j} (k) ⟩

3-

| ψ_{i} (k_{0}) ⟩

4-

ρ_{i} (ω, δ k) = \sum_{j} {| ⟨ ψ_{j} (k) | ψ_{i} (k_{0}) ⟩ |}^{2} δ (ω - ω_{i j} (k, k_{0})),

5-

ω_{i j} (k, k_{0}) = ω_{i} (k_{0}) - ω_{j} (k)

6-

δ k \equiv k - k_{0}

7-

| ψ_{i} (k_{0}) ⟩

8-

ρ_{i} (ω, δ k) = ℱ [⟨ ψ_{i} (k_{0}) | e^{i H (k) t / ℏ} e^{- i H (k_{0}) t / ℏ} | ψ_{i} (k_{0}) ⟩] .

9-

[\begin{matrix} q^{^{'}} \\ p^{^{'}} \end{matrix}] = G [\begin{matrix} q \\ p \end{matrix}] + [\begin{matrix} 0 \\ 1 \end{matrix}] ϵ (q, k) (m o d 1),

10-

T r (G) > 2

Formulas (html):

Correct Categorie: nlin

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1612.04903

Formulas:

1-

T_{eff} (K)

2-

{(Z / X)}_{s}

3-

T_{eff}, [Fe/H], log g

4-

ν mod Δ ν

5-

\frac{d^{2} ψ}{d τ^{2}} + (ω^{2} - U^{2}) ψ = 0,

6-

τ = \int_{r}^{R} \frac{d r}{c}

7-

U^{2} (τ)

8-

ψ = r {(ρ c)}^{\frac{1}{2}} ξ

9-

U^{2} (τ) = \frac{g}{c} (\frac{g}{c} - \frac{d \ln h}{d τ}) + {[\frac{1}{2} \frac{d \ln ζ}{d τ}]}^{2} - \frac{1}{2} \frac{d^{2} \ln ζ}{d τ^{2}}

10-

ζ = \frac{r^{2} h}{c}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/1810.03790

Formulas:

1-

k_{G I S T}

2-

k_{L D B}

3-

k_{B o W}

4-

k = k_{G I S T} + k_{B o W} + k_{L D B}

5-

k_{G I S T} = k_{B o W} = k_{L D B} = 5

6-

P r e c i s i o n = \frac{T P}{T P + F P}

7-

R e c a l l = \frac{T P}{T P + F N}

8-

k_{G I S T}

9-

k_{L D B}

10-

k_{B o W}

Formulas (html):

Correct Categorie: cs

Guessed Categorie: cs

Result: correct

Paper: https://arxiv.org/abs/1104.2778

Formulas:

1-

D 𝐏 \cdot (𝐩_{𝐞} \times 𝐩_{𝐯})

2-

D = (- 0.96 \pm 1.89 (s t a t) \pm 1.01 (s y s)) \times 10^{- 4}

3-

ϕ_{A V} = {180.013}^{\circ} \pm {0.028}^{\circ}

4-

d W \propto 1 + a \frac{𝐩_{e} \cdot 𝐩_{ν}}{E_{e} E_{ν}} + b \frac{m_{e}}{E_{e}} +

5-

𝐏 \cdot (A \frac{𝐩_{e}}{E_{e}} + B \frac{𝐩_{ν}}{E_{ν}} + D \frac{𝐩_{e} \times 𝐩_{ν}}{E_{e} E_{ν}}) .

6-

D 𝐏 \cdot (𝐩_{e} \times 𝐩_{ν})

7-

D = (- 4 \pm 6) \times 10^{- 4}

8-

D 𝐏 \cdot (𝐩_{p} \times 𝐩_{e})

9-

w^{p_{i} e_{j}} = \frac{N_{+}^{p_{i} e_{j}} - N_{-}^{p_{i} e_{j}}}{N_{+}^{p_{i} e_{j}} + N_{-}^{p_{i} e_{j}}},

10-

N_{+}^{p_{i} e_{j}}

Formulas (html):

Correct Categorie: nucl-ex

Guessed Categorie: nucl-ex

Result: correct

Paper: https://arxiv.org/abs/hep-th/9310079

Formulas:

1-

\ln Z = N^{2} (\int 𝑑 λ 𝑑 μ ρ (λ) ρ (μ) \ln ∣ λ - μ ∣ - \int 𝑑 λ ρ (λ) W (λ))

2-

Γ (λ_{f}) = δ \ln Z = N^{2} \int 𝑑 λ δ ρ (λ) (2 \int 𝑑 μ ρ (μ) \ln ∣ λ - μ ∣ - W (λ))

3-

δ ρ (λ) = N^{- 1} {δ (λ - λ_{f}) - δ (λ - λ_{i})}

4-

Γ (λ_{f})

5-

Γ (λ_{f})

6-

N \int_{λ_{i}}^{λ_{f}} 𝑑 λ (2 \int 𝑑 μ \frac{ρ (μ)}{λ - μ} - W^{'} (λ))

7-

- 2 N \int_{λ_{i}}^{λ_{f}} 𝑑 λ U (λ) \sqrt{λ^{2} - a^{2}}

8-

Γ (λ_{f})

9-

Γ (λ_{f})

10-

ρ (λ) = U (λ) \sqrt{a^{2} - λ^{2}}, λ \in (- a, a)

Formulas (html):

Correct Categorie: hep-th

Guessed Categorie: gr-qc

Result: incorrect

Paper: https://arxiv.org/abs/1508.07152

Formulas:

1-

f = ω_{d} / (2 π)

2-

\ddot{θ} + (\frac{γ_{1}}{I}) \dot{θ} + ω_{0}^{2} \sin θ + F ω_{d}^{2} \cos (ω_{d} t) \cos θ = 0,

3-

I = M L^{2} + \frac{1}{3} m L^{2}

4-

F = A ω_{0}^{2} / g

5-

ω_{0}^{2} = \frac{1}{I} (m g L / 2 + M g L)

6-

{\ddot{θ}}_{n} + ω_{0}^{2} \sin θ_{n} - (\frac{β}{I}) Δ_{2} θ_{n} + (\frac{γ_{1}}{I}) {\dot{θ}}_{n}

7-

- \frac{γ_{2}}{I} Δ_{2} {\dot{θ}}_{n} + F ω_{d}^{2} \cos (ω_{d} t) \cos θ_{n}

8-

ω = ω_{d} / ω_{0}

9-

C = β / I ω_{0}^{2}

10-

α_{1} = γ_{1} / I ω_{0}

Formulas (html):

Correct Categorie: nlin

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/0906.3719

Formulas:

1-

ρ (m) \propto \exp (m / T_{0}) / m^{α}

2-

p_{r} = B + p_{k} (V, T),

3-

(ε - 3 p_{k}) / T^{4}

4-

s / T^{3} \equiv (ε + p_{k}) / T^{4}

5-

1 \leq α \leq 5 / 2

6-

(ε - 3 p_{k}) / T^{4}

7-

p_{k} (\infty, T) / T^{4}

8-

1 \leq α \leq 5 / 2

9-

⟨ n ⟩ = ⟨ N ⟩ / V

10-

α_{0} < α \leq 5 / 2

Formulas (html):

Correct Categorie: nucl-th

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/1702.05507

Formulas:

1-

E \approx 1.5 \times 10^{52} M_{☉} R_{10}^{2} P_{0}^{- 2} erg,

2-

v_{ph} ≳ 20, 000

3-

⟨ v^{2} ⟩ = 3 / 5 v_{ph}^{2}

4-

E_{k} = \frac{3}{10} M_{ej} v_{ph}^{2} \sim 7 \times 10^{51}

5-

E_{γ, iso} = (5.7 \pm 0.7) \times 10^{53}

6-

E = (1 - \cos θ) E_{iso} erg,

7-

b_{f} = {(1 - \cos θ)}^{- 1}

8-

t_{j} = 10 \times (1 + z) {(\frac{θ_{0}}{0.2})}^{4} η^{- 1} E_{γ, iso, 53} A_{*}^{- 1} days,

9-

E_{γ, iso, 53}

10-

A = {\dot{M}}_{w} / 4 π V_{w} = 5 \times 10^{11} A_{*}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/0802.1339

Formulas:

1-

S (ν) = \frac{S_{0} \cdot ν^{a}}{(1 + {(\frac{ν}{ν_{b}})}^{b}) (1 + {(\frac{ν}{ν_{c}})}^{c})} .

2-

τ_{e} \sim 10^{- 10}

3-

Φ (t) = Φ_{0} \cdot e^{- t / τ_{e}}

4-

S (ω) = \frac{S_{0}}{1 + ω^{2} τ_{e}^{2}},

5-

Φ (t) = Φ_{0} {(\frac{τ_{0}}{τ + τ_{0}})}^{n} \cdot e^{- t / τ_{e}}

6-

n = \frac{σ_{c} τ_{0} c}{π δ r_{0}^{2}}

7-

S (ω) = S_{0} {(\frac{1 + ω^{2} τ_{e}^{2}}{τ_{e}^{2}})}^{n - 1} \cdot e^{- i (n - 1) \cdot a t a n (ω τ_{e})} .

8-

S_{ν} (ν) = \frac{S_{0}}{1 + {(2 π ν)}^{2} τ_{e}^{2}}

9-

0.1 ns < τ_{e} < 2.0 ns

10-

S = 0.5 \pm 0.2 mJy

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/cond-mat/0606618

Formulas:

1-

N_{m a x}

2-

σ_{S i S i} \equiv σ

3-

σ_{O O} = 1.6 σ

4-

σ_{S i O} = σ

5-

S_{1} \hat{C} S_{2}

6-

u_{S W} = - u_{0} r < δ

7-

= 0 r > δ,

8-

δ = (1 - \sqrt{3} / 2) σ \approx 0.134 σ

9-

0.5 (\sqrt{5 - 2 \sqrt{3}} - 1) σ \approx 0.119 σ

10-

E_{g s} = - 4

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/2005.05718

Formulas:

1-

V_{ho} (𝐫) = \frac{1}{2} m (ω_{x}^{2} x^{2} + ω_{x}^{2} y^{2} + ω_{z}^{2} z^{2})

2-

Ψ (𝐫, t)

3-

i ℏ \frac{\partial}{\partial t} Ψ (𝐫, t) = ℋ (𝐫) Ψ (𝐫, t),

4-

ℋ (𝐫) = -

5-

\frac{ℏ^{2}}{2 m} \nabla^{2} + V_{ho} (𝐫) + g {| Ψ (𝐫, t) |}^{2} + γ (ε_{d d}) {| Ψ (𝐫, t) |}^{3}

6-

\int 𝑑 𝐫^{'} V_{d d} (𝐫 - 𝐫^{'}) {| Ψ (𝐫^{'}, t) |}^{2},

7-

g = 4 π ℏ^{2} a / m

8-

V_{d d} (𝐫_{i} - 𝐫_{j}) = \frac{μ_{0} μ^{2}}{4 π} \frac{1 - 3 \cos^{2} θ}{{| 𝐫_{i} - 𝐫_{j} |}^{3}}

9-

ε_{d d} = μ_{0} μ^{2} / (3 g) = a_{d d} / a

10-

a_{d d} = 131 a_{B}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/2010.00259

Formulas:

1-

\hat{ρ} = 𝒩 {\hat{a}}^{†} {\hat{ρ}}_{th} \hat{a}

2-

{\hat{ρ}}_{th} = 1 / (\bar{n} + 1) \sum_{k = 0}^{\infty} {[\bar{n} / (\bar{n} + 1)]}^{k} | k ⟩ ⟨ k |

3-

W (α_{1}) W (α_{2}) - e^{- {| α_{2} - α_{1} |}^{2}} W {[(α_{1} + α_{2}) / 2]}^{2} < 0 .

4-

W (α) - 2 π Q {(α)}^{2} < 0 .

5-

\bar{n} < 1 / \sqrt{2}

6-

\bar{n} = 0.98 \pm 0.02

7-

(η, \bar{n})

8-

(\bar{n} = 0.98)

9-

(η, \bar{n})

10-

W (0) - 2 π Q {(0)}^{2}

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: quant-ph

Result: correct

Paper: https://arxiv.org/abs/0704.0206

Formulas:

1-

{\dot{E}}_{+} = \frac{1}{2} [(1 + i α) g_{+} - 1] E_{+} + \sqrt{2 D_{s p} N} ξ_{+}

2-

{\dot{E}}_{-} = \frac{1}{2} [(1 + i α) g_{-} - 1] E_{-} + \sqrt{2 D_{s p} N} ξ_{-}

3-

\dot{N} = γ [J (t) - N - g_{+} {| E_{+} |}^{2} - g_{-} {| E_{-} |}^{2}]

4-

g_{\pm} = \frac{N \pm ε (N - N_{c})}{1 + s {| E_{\pm} |}^{2} + c {| E_{\mp} |}^{2}},

5-

⟨ ξ_{\pm} (t) ⟩ = 0

6-

⟨ ξ_{i} (t) ξ_{j}^{*} (t^{'}) ⟩ = δ_{i j} δ (t - t^{'})

7-

J (t) = J_{0}

8-

D_{s p} = 0

9-

E_{+} \neq 0, E_{-} = 0

10-

D_{s p} > 0

Formulas (html):

Correct Categorie: physics

Guessed Categorie: nucl-th

Result: incorrect

Paper: https://arxiv.org/abs/q-bio/0403027

Formulas:

1-

\begin{matrix} \dot{R} = f (T) - b_{1} R \\ \dot{L} = g_{1} R - b_{2} L \\ \dot{T} = g_{2} L (t - τ) - b_{3} T \end{matrix}

2-

b_{1}, b_{2}, b_{3}, g_{1}, g_{2}

3-

f (x) = A / (K + x)

4-

f (T) - \frac{b_{1} b_{2} b_{3} T}{g_{1} g_{2}} = 0

5-

L_{0} = \frac{b_{3} T_{0}}{g_{2}}, R_{0} = \frac{b_{3} b_{2} T_{0}}{g_{1} g_{2}}, T_{0}

6-

\begin{matrix} \dot{x} = f^{'} (T_{0}) z - b_{1} x \\ \dot{y} = g_{1} x - b_{2} y \\ \dot{z} = g_{2} y (t - τ) - b_{3} z \end{matrix}

7-

𝐯 (t) = 𝐯_{𝟎} e^{λ t}

8-

(λ + b_{1}) (λ + b_{2}) (λ + b_{3}) + d e^{- λ τ} = 0, d = - f^{'} (T_{0}) g_{1} g_{2} > 0

9-

b_{1}, b_{2}, b_{3}, g_{1}, g_{2}, τ

10-

f (x) = A / (K + x)

Formulas (html):

Correct Categorie: q-bio

Guessed Categorie: q-bio

Result: correct

Paper: https://arxiv.org/abs/0911.2987

Formulas:

1-

Q^{2} = 10 G e V^{2}

2-

l n^{2} (E / E_{0})

3-

ρ = \frac{d N}{d y d^{2} p_{T} d^{2} x_{T}}

4-

E = - κ ρ + κ^{'} α_{S} ρ^{2}

5-

ρ \sim 1 / α_{S}

6-

\frac{d N}{d y} = \int d^{2} x_{T} \int d^{2} q_{T} ρ \sim \frac{1}{α_{S}} π R^{2} Q_{s a t}^{2}

7-

Q_{s a t}

8-

ρ \sim 1 / α_{S}

9-

R \sim 1 / Q_{s a t}

10-

1 / Q_{s a t}

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: hep-ex

Result: incorrect

Run 11277718 (Agent950)