Run 16403398

Paper: https://arxiv.org/abs/1602.08537

Formulas:

1-

(x_{c}, y_{c})

2-

({\dot{x}}_{c}, {\dot{y}}_{c})

3-

(x_{l}, y_{l})

4-

(x_{r}, y_{r})

5-

p (x, y)

6-

Δ p = p (x_{l}, y_{l}) - p (x_{r}, y_{r})

7-

R = (a + b) / 2

8-

z = x + i y

9-

z_{c} = x_{c} + i y_{c}

10-

z_{r} = x_{r} + i y_{r}

Formulas (html):

Correct Categorie: physics

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0610057

Formulas:

1-

z_{f} d d Final redshift of simulation.

2-

M ≲ 2 \times 10^{10} M_{⊙}

3-

M ≳ 1.28 \times 10^{9} M_{⊙}

4-

M ≳ 3.84 \times 10^{8} M_{⊙}

5-

d n / d L

6-

d n / d m

7-

L^{2} d n / d L

8-

10^{- 0.4 m} d n / d m

9-

27 ≲ z_{850} ≲ 29

10-

8 \times 10^{27} erg/s/Hz

Formulas (html):

<math><mrow id="S2.T1.4.4.4.m1.1.1" xref="S2.T1.4.4.4.m1.1.1.cmml"><msub id="S2.T1.4.4.4.m1.1.1.2" xref="S2.T1.4.4.4.m1.1.1.2.cmml"><mi id="S2.T1.4.4.4.m1.1.1.2.2" xref="S2.T1.4.4.4.m1.1.1.2.2.cmml">z</mi><mi id="S2.T1.4.4.4.m1.1.1.2.3" xref="S2.T1.4.4.4.m1.1.1.2.3.cmml">f</mi></msub><mo id="S2.T1.4.4.4.m1.1.1.1" xref="S2.T1.4.4.4.m1.1.1.1.cmml">⁢</mo><mtext id="S2.T1.4.4.4.m1.1.1.3" xref="S2.T1.4.4.4.m1.1.1.3b.cmml">ddFinal redshift of simulation.</mtext></mrow></math>, <math><mrow id="S3.SS1.p3.1.m1.1.1" xref="S3.SS1.p3.1.m1.1.1.cmml"><mi id="S3.SS1.p3.1.m1.1.1.2" xref="S3.SS1.p3.1.m1.1.1.2.cmml">M</mi><mo id="S3.SS1.p3.1.m1.1.1.1" xref="S3.SS1.p3.1.m1.1.1.1.cmml">≲</mo><mrow id="S3.SS1.p3.1.m1.1.1.3" xref="S3.SS1.p3.1.m1.1.1.3.cmml"><mrow id="S3.SS1.p3.1.m1.1.1.3.2" xref="S3.SS1.p3.1.m1.1.1.3.2.cmml"><mn id="S3.SS1.p3.1.m1.1.1.3.2.2" xref="S3.SS1.p3.1.m1.1.1.3.2.2.cmml">2</mn><mo id="S3.SS1.p3.1.m1.1.1.3.2.1" xref="S3.SS1.p3.1.m1.1.1.3.2.1.cmml">×</mo><msup id="S3.SS1.p3.1.m1.1.1.3.2.3" xref="S3.SS1.p3.1.m1.1.1.3.2.3.cmml"><mn id="S3.SS1.p3.1.m1.1.1.3.2.3.2" xref="S3.SS1.p3.1.m1.1.1.3.2.3.2.cmml">10</mn><mn id="S3.SS1.p3.1.m1.1.1.3.2.3.3" xref="S3.SS1.p3.1.m1.1.1.3.2.3.3.cmml">10</mn></msup></mrow><mo id="S3.SS1.p3.1.m1.1.1.3.1" xref="S3.SS1.p3.1.m1.1.1.3.1.cmml">⁢</mo><msub id="S3.SS1.p3.1.m1.1.1.3.3" xref="S3.SS1.p3.1.m1.1.1.3.3.cmml"><mtext id="S3.SS1.p3.1.m1.1.1.3.3.2" xref="S3.SS1.p3.1.m1.1.1.3.3.2a.cmml"> M</mtext><mo id="S3.SS1.p3.1.m1.1.1.3.3.3" xref="S3.SS1.p3.1.m1.1.1.3.3.3.cmml">⊙</mo></msub></mrow></mrow></math>, <math><mrow id="S3.F6.6.m2.1.1" xref="S3.F6.6.m2.1.1.cmml"><mi id="S3.F6.6.m2.1.1.2" xref="S3.F6.6.m2.1.1.2.cmml">M</mi><mo id="S3.F6.6.m2.1.1.1" xref="S3.F6.6.m2.1.1.1.cmml">≳</mo><mrow id="S3.F6.6.m2.1.1.3" xref="S3.F6.6.m2.1.1.3.cmml"><mrow id="S3.F6.6.m2.1.1.3.2" xref="S3.F6.6.m2.1.1.3.2.cmml"><mn id="S3.F6.6.m2.1.1.3.2.2" xref="S3.F6.6.m2.1.1.3.2.2.cmml">1.28</mn><mo id="S3.F6.6.m2.1.1.3.2.1" xref="S3.F6.6.m2.1.1.3.2.1.cmml">×</mo><msup id="S3.F6.6.m2.1.1.3.2.3" xref="S3.F6.6.m2.1.1.3.2.3.cmml"><mn id="S3.F6.6.m2.1.1.3.2.3.2" xref="S3.F6.6.m2.1.1.3.2.3.2.cmml">10</mn><mn id="S3.F6.6.m2.1.1.3.2.3.3" xref="S3.F6.6.m2.1.1.3.2.3.3.cmml">9</mn></msup></mrow><mo id="S3.F6.6.m2.1.1.3.1" xref="S3.F6.6.m2.1.1.3.1.cmml">⁢</mo><msub id="S3.F6.6.m2.1.1.3.3" xref="S3.F6.6.m2.1.1.3.3.cmml"><mtext id="S3.F6.6.m2.1.1.3.3.2" xref="S3.F6.6.m2.1.1.3.3.2a.cmml"> M</mtext><mo id="S3.F6.6.m2.1.1.3.3.3" xref="S3.F6.6.m2.1.1.3.3.3.cmml">⊙</mo></msub></mrow></mrow></math>, <math><mrow id="S3.F6.7.m3.1.1" xref="S3.F6.7.m3.1.1.cmml"><mi id="S3.F6.7.m3.1.1.2" xref="S3.F6.7.m3.1.1.2.cmml">M</mi><mo id="S3.F6.7.m3.1.1.1" xref="S3.F6.7.m3.1.1.1.cmml">≳</mo><mrow id="S3.F6.7.m3.1.1.3" xref="S3.F6.7.m3.1.1.3.cmml"><mrow id="S3.F6.7.m3.1.1.3.2" xref="S3.F6.7.m3.1.1.3.2.cmml"><mn id="S3.F6.7.m3.1.1.3.2.2" xref="S3.F6.7.m3.1.1.3.2.2.cmml">3.84</mn><mo id="S3.F6.7.m3.1.1.3.2.1" xref="S3.F6.7.m3.1.1.3.2.1.cmml">×</mo><msup id="S3.F6.7.m3.1.1.3.2.3" xref="S3.F6.7.m3.1.1.3.2.3.cmml"><mn id="S3.F6.7.m3.1.1.3.2.3.2" xref="S3.F6.7.m3.1.1.3.2.3.2.cmml">10</mn><mn id="S3.F6.7.m3.1.1.3.2.3.3" xref="S3.F6.7.m3.1.1.3.2.3.3.cmml">8</mn></msup></mrow><mo id="S3.F6.7.m3.1.1.3.1" xref="S3.F6.7.m3.1.1.3.1.cmml">⁢</mo><msub id="S3.F6.7.m3.1.1.3.3" xref="S3.F6.7.m3.1.1.3.3.cmml"><mtext id="S3.F6.7.m3.1.1.3.3.2" xref="S3.F6.7.m3.1.1.3.3.2a.cmml"> M</mtext><mo id="S3.F6.7.m3.1.1.3.3.3" xref="S3.F6.7.m3.1.1.3.3.3.cmml">⊙</mo></msub></mrow></mrow></math>, <math><mrow id="S3.SS3.p1.1.m1.1.1" xref="S3.SS3.p1.1.m1.1.1.cmml"><mrow id="S3.SS3.p1.1.m1.1.1.2" xref="S3.SS3.p1.1.m1.1.1.2.cmml"><mrow id="S3.SS3.p1.1.m1.1.1.2.2" xref="S3.SS3.p1.1.m1.1.1.2.2.cmml"><mi id="S3.SS3.p1.1.m1.1.1.2.2.2" xref="S3.SS3.p1.1.m1.1.1.2.2.2.cmml">d</mi><mo id="S3.SS3.p1.1.m1.1.1.2.2.1" xref="S3.SS3.p1.1.m1.1.1.2.2.1.cmml">⁢</mo><mi id="S3.SS3.p1.1.m1.1.1.2.2.3" xref="S3.SS3.p1.1.m1.1.1.2.2.3.cmml">n</mi></mrow><mo id="S3.SS3.p1.1.m1.1.1.2.1" xref="S3.SS3.p1.1.m1.1.1.2.1.cmml">/</mo><mi id="S3.SS3.p1.1.m1.1.1.2.3" xref="S3.SS3.p1.1.m1.1.1.2.3.cmml">d</mi></mrow><mo id="S3.SS3.p1.1.m1.1.1.1" xref="S3.SS3.p1.1.m1.1.1.1.cmml">⁢</mo><mi id="S3.SS3.p1.1.m1.1.1.3" xref="S3.SS3.p1.1.m1.1.1.3.cmml">L</mi></mrow></math>, <math><mrow id="S3.SS3.p1.2.m2.1.1" xref="S3.SS3.p1.2.m2.1.1.cmml"><mrow id="S3.SS3.p1.2.m2.1.1.2" xref="S3.SS3.p1.2.m2.1.1.2.cmml"><mrow id="S3.SS3.p1.2.m2.1.1.2.2" xref="S3.SS3.p1.2.m2.1.1.2.2.cmml"><mi id="S3.SS3.p1.2.m2.1.1.2.2.2" xref="S3.SS3.p1.2.m2.1.1.2.2.2.cmml">d</mi><mo id="S3.SS3.p1.2.m2.1.1.2.2.1" xref="S3.SS3.p1.2.m2.1.1.2.2.1.cmml">⁢</mo><mi id="S3.SS3.p1.2.m2.1.1.2.2.3" xref="S3.SS3.p1.2.m2.1.1.2.2.3.cmml">n</mi></mrow><mo id="S3.SS3.p1.2.m2.1.1.2.1" xref="S3.SS3.p1.2.m2.1.1.2.1.cmml">/</mo><mi id="S3.SS3.p1.2.m2.1.1.2.3" xref="S3.SS3.p1.2.m2.1.1.2.3.cmml">d</mi></mrow><mo id="S3.SS3.p1.2.m2.1.1.1" xref="S3.SS3.p1.2.m2.1.1.1.cmml">⁢</mo><mi id="S3.SS3.p1.2.m2.1.1.3" xref="S3.SS3.p1.2.m2.1.1.3.cmml">m</mi></mrow></math>, <math><mrow id="S3.SS3.p1.3.m3.1.1" xref="S3.SS3.p1.3.m3.1.1.cmml"><mrow id="S3.SS3.p1.3.m3.1.1.2" xref="S3.SS3.p1.3.m3.1.1.2.cmml"><mrow id="S3.SS3.p1.3.m3.1.1.2.2" xref="S3.SS3.p1.3.m3.1.1.2.2.cmml"><msup id="S3.SS3.p1.3.m3.1.1.2.2.2" xref="S3.SS3.p1.3.m3.1.1.2.2.2.cmml"><mi id="S3.SS3.p1.3.m3.1.1.2.2.2.2" xref="S3.SS3.p1.3.m3.1.1.2.2.2.2.cmml">L</mi><mn id="S3.SS3.p1.3.m3.1.1.2.2.2.3" xref="S3.SS3.p1.3.m3.1.1.2.2.2.3.cmml">2</mn></msup><mo id="S3.SS3.p1.3.m3.1.1.2.2.1" xref="S3.SS3.p1.3.m3.1.1.2.2.1.cmml">⁢</mo><mi id="S3.SS3.p1.3.m3.1.1.2.2.3" xref="S3.SS3.p1.3.m3.1.1.2.2.3.cmml">d</mi><mo id="S3.SS3.p1.3.m3.1.1.2.2.1a" xref="S3.SS3.p1.3.m3.1.1.2.2.1.cmml">⁢</mo><mi id="S3.SS3.p1.3.m3.1.1.2.2.4" xref="S3.SS3.p1.3.m3.1.1.2.2.4.cmml">n</mi></mrow><mo id="S3.SS3.p1.3.m3.1.1.2.1" xref="S3.SS3.p1.3.m3.1.1.2.1.cmml">/</mo><mi id="S3.SS3.p1.3.m3.1.1.2.3" xref="S3.SS3.p1.3.m3.1.1.2.3.cmml">d</mi></mrow><mo id="S3.SS3.p1.3.m3.1.1.1" xref="S3.SS3.p1.3.m3.1.1.1.cmml">⁢</mo><mi id="S3.SS3.p1.3.m3.1.1.3" xref="S3.SS3.p1.3.m3.1.1.3.cmml">L</mi></mrow></math>, <math><mrow id="S3.SS3.p1.4.m4.1.1" xref="S3.SS3.p1.4.m4.1.1.cmml"><mrow id="S3.SS3.p1.4.m4.1.1.2" xref="S3.SS3.p1.4.m4.1.1.2.cmml"><mrow id="S3.SS3.p1.4.m4.1.1.2.2" xref="S3.SS3.p1.4.m4.1.1.2.2.cmml"><msup id="S3.SS3.p1.4.m4.1.1.2.2.2" xref="S3.SS3.p1.4.m4.1.1.2.2.2.cmml"><mn id="S3.SS3.p1.4.m4.1.1.2.2.2.2" xref="S3.SS3.p1.4.m4.1.1.2.2.2.2.cmml">10</mn><mrow id="S3.SS3.p1.4.m4.1.1.2.2.2.3" xref="S3.SS3.p1.4.m4.1.1.2.2.2.3.cmml"><mo id="S3.SS3.p1.4.m4.1.1.2.2.2.3.1" xref="S3.SS3.p1.4.m4.1.1.2.2.2.3.1.cmml">-</mo><mrow id="S3.SS3.p1.4.m4.1.1.2.2.2.3.2" xref="S3.SS3.p1.4.m4.1.1.2.2.2.3.2.cmml"><mn id="S3.SS3.p1.4.m4.1.1.2.2.2.3.2.2" xref="S3.SS3.p1.4.m4.1.1.2.2.2.3.2.2.cmml">0.4</mn><mo id="S3.SS3.p1.4.m4.1.1.2.2.2.3.2.1" xref="S3.SS3.p1.4.m4.1.1.2.2.2.3.2.1.cmml">⁢</mo><mi id="S3.SS3.p1.4.m4.1.1.2.2.2.3.2.3" xref="S3.SS3.p1.4.m4.1.1.2.2.2.3.2.3.cmml">m</mi></mrow></mrow></msup><mo id="S3.SS3.p1.4.m4.1.1.2.2.1" xref="S3.SS3.p1.4.m4.1.1.2.2.1.cmml">⁢</mo><mi id="S3.SS3.p1.4.m4.1.1.2.2.3" xref="S3.SS3.p1.4.m4.1.1.2.2.3.cmml">d</mi><mo id="S3.SS3.p1.4.m4.1.1.2.2.1a" xref="S3.SS3.p1.4.m4.1.1.2.2.1.cmml">⁢</mo><mi id="S3.SS3.p1.4.m4.1.1.2.2.4" xref="S3.SS3.p1.4.m4.1.1.2.2.4.cmml">n</mi></mrow><mo id="S3.SS3.p1.4.m4.1.1.2.1" xref="S3.SS3.p1.4.m4.1.1.2.1.cmml">/</mo><mi id="S3.SS3.p1.4.m4.1.1.2.3" xref="S3.SS3.p1.4.m4.1.1.2.3.cmml">d</mi></mrow><mo id="S3.SS3.p1.4.m4.1.1.1" xref="S3.SS3.p1.4.m4.1.1.1.cmml">⁢</mo><mi id="S3.SS3.p1.4.m4.1.1.3" xref="S3.SS3.p1.4.m4.1.1.3.cmml">m</mi></mrow></math>, <math><mrow id="S3.SS3.p6.2.m2.1.2" xref="S3.SS3.p6.2.m2.1.2.cmml"><mn id="S3.SS3.p6.2.m2.1.2.2" xref="S3.SS3.p6.2.m2.1.2.2.cmml">27</mn><mo id="S3.SS3.p6.2.m2.1.2.3" xref="S3.SS3.p6.2.m2.1.2.3.cmml">≲</mo><mrow id="S3.SS3.p6.2.m2.1.1.1" xref="S3.SS3.p6.2.m2.1.1.1b.cmml"><mtext id="S3.SS3.p6.2.m2.1.1.1a" xref="S3.SS3.p6.2.m2.1.1.1b.cmml">z</mtext><msub id="S3.SS3.p6.2.m2.1.1.1.m1.1.1" xref="S3.SS3.p6.2.m2.1.1.1.m1.1.1.cmml"><mi id="S3.SS3.p6.2.m2.1.1.1.m1.1.1a" xref="S3.SS3.p6.2.m2.1.1.1.m1.1.1.cmml"/><mn id="S3.SS3.p6.2.m2.1.1.1.m1.1.1.1" xref="S3.SS3.p6.2.m2.1.1.1.m1.1.1.1.cmml">850</mn></msub></mrow><mo id="S3.SS3.p6.2.m2.1.2.4" xref="S3.SS3.p6.2.m2.1.2.4.cmml">≲</mo><mn id="S3.SS3.p6.2.m2.1.2.5" xref="S3.SS3.p6.2.m2.1.2.5.cmml">29</mn></mrow></math>, <math><mrow id="S3.SS3.p10.2.m2.1.1" xref="S3.SS3.p10.2.m2.1.1.cmml"><mrow id="S3.SS3.p10.2.m2.1.1.2" xref="S3.SS3.p10.2.m2.1.1.2.cmml"><mn id="S3.SS3.p10.2.m2.1.1.2.2" xref="S3.SS3.p10.2.m2.1.1.2.2.cmml">8</mn><mo id="S3.SS3.p10.2.m2.1.1.2.1" xref="S3.SS3.p10.2.m2.1.1.2.1.cmml">×</mo><msup id="S3.SS3.p10.2.m2.1.1.2.3" xref="S3.SS3.p10.2.m2.1.1.2.3.cmml"><mn id="S3.SS3.p10.2.m2.1.1.2.3.2" xref="S3.SS3.p10.2.m2.1.1.2.3.2.cmml">10</mn><mn id="S3.SS3.p10.2.m2.1.1.2.3.3" xref="S3.SS3.p10.2.m2.1.1.2.3.3.cmml">27</mn></msup></mrow><mo id="S3.SS3.p10.2.m2.1.1.1" xref="S3.SS3.p10.2.m2.1.1.1.cmml">⁢</mo><mtext id="S3.SS3.p10.2.m2.1.1.3" xref="S3.SS3.p10.2.m2.1.1.3a.cmml"> erg/s/Hz</mtext></mrow></math>

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1601.07605

Formulas:

1-

M = ρ_{g} U_{g}^{2} / ρ_{l} U_{l}^{2}

2-

α_{m a x}

3-

0.23 m s^{- 1}

4-

α_{m a x}

5-

0.23 m s^{- 1}

6-

α_{m a x}

7-

α_{m a x}

8-

α_{m a x}

9-

U_{l} = 0.23 m s^{- 1}

10-

U_{g} = 20 m s^{- 1}

Formulas (html):

Correct Categorie: physics

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1707.08395

Formulas:

1-

[NII] 6563 / H α NLR

2-

[OIII] 5007 / H β NLR

3-

F_{15 μ m} / F_{30 μ m}

4-

F_{15 μ m} / F_{30 μ m}

5-

F_{30 μ m} / F_{15 μ m}

6-

F_{30 μ m} / F_{15 μ m}

7-

z_{w a r n i n g}

8-

[OIII] 5007 / H β

9-

[OIII] 5007 / H β

10-

[OIII] 5007 / H β

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/hep-ex/0608032

Formulas:

1-

M_{t} = 171.4 \pm 1.2 (stat) \pm 1.8 (syst) GeV / c^{2}

2-

2.1 GeV / c^{2}

3-

t \bar{t} \to q q^{'} b q q^{'} \bar{b}

4-

t \bar{t} \to ℓ ν q q^{'} b \bar{b}

5-

t \bar{t} \to ℓ^{+} ν b ℓ^{-} \bar{ν} \bar{b}

6-

370 - 1000 {pb}^{- 1}

7-

170.9 \pm 2.5 GeV / c^{2}

8-

170.3 \pm 4.5 GeV / c^{2}

9-

W \to q q^{'}

10-

W \to q q^{'}

Formulas (html):

Correct Categorie: hep-ex

Guessed Categorie: hep-ex

Result: correct

Paper: https://arxiv.org/abs/1502.07725

Formulas:

1-

O^{*} ({3.188}^{k})

2-

G = (V, E)

3-

O^{*} (f (k))

4-

O^{*} (f (k))

5-

f (k) < 10^{20}

6-

O^{*} ((17 k^{4})!)

7-

O^{*} ({(2 k)}^{4 k})

8-

O^{*} ({14.23}^{k})

9-

O^{*} ({9.49}^{k})

10-

O^{*} ({8.12}^{k})

Formulas (html):

Correct Categorie: cs

Guessed Categorie: cs

Result: correct

Paper: https://arxiv.org/abs/1005.1474

Formulas:

1-

Δ_{0} / k_{B} = 16.5

2-

a l w a y s

3-

ℋ = J_{∥} \sum_{i, j = 1, 2} 𝐒_{i, j} 𝐒_{i + 1, j} + J_{⊥} \sum_{i} 𝐒_{i, 1} 𝐒_{i, 2} + ℋ_{δ},

4-

B_{c 1} \approx 6.8

5-

B_{c 2} \approx 13.8

6-

J_{⊥} / k_{B} \approx 12.7 - 13.3

7-

J_{∥} / k_{B} \approx 3.3 - 3.8

8-

c^{*} ⊥ a, b

9-

ℋ_{e f f} = D_{x} S_{x}^{2} + D_{y} S_{y}^{2} + D_{z} S_{z}^{2} - μ_{B} 𝐁 \hat{g} 𝐒,

10-

D^{'} = \frac{3}{2} D_{z}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/quant-ph/0111128

Formulas:

1-

A = a \sqrt{f (a^{†} a)}

2-

| ζ, f ⟩ = 𝒩 \sum_{n = 0}^{\infty} \frac{ζ^{n}}{\sqrt{{[n]}_{f}!}} | n ⟩, 𝒩 = {[\exp_{f} (ζ^{2})]}^{- 1 / 2},

3-

\exp_{f} (x) \equiv \sum_{n = 0}^{\infty} \frac{x^{n}}{{[n]}_{f}!},

4-

{[n]}_{f}! \equiv [n f (n)] \times [(n - 1) f (n - 1)] \times \dots [2 f (2)] \times [f (1)] \times [f (0)] .

5-

\exp_{f} (x) \exp_{f} (y) \neq \exp_{f} (x + y)

6-

𝒩_{+} (| ζ, f ⟩ + | - ζ, f ⟩), 𝒩_{+} = {[2 + 2 𝒩^{2} \exp_{f} (- ζ^{2})]}^{- 1 / 2},

7-

𝒩_{-} (| ζ, f ⟩ - | - ζ, f ⟩), 𝒩_{-} = {[2 - 2 𝒩^{2} \exp_{f} (- ζ^{2})]}^{- 1 / 2} .

8-

| Φ_{+} ⟩ = 𝒩_{+} (| ζ, f ⟩ + | - ζ, f ⟩),

9-

| Φ_{-} ⟩ = 𝒩_{-} (| ζ, f ⟩ - | - ζ, f ⟩) .

10-

Δ = \frac{| 𝒩_{+} - 𝒩_{-} |}{\min [𝒩_{+}, 𝒩_{-}]},

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: quant-ph

Result: correct

Paper: https://arxiv.org/abs/2002.09011

Formulas:

1-

ℳ_{⋆} ≲ 2 \times 10^{9} ℳ_{⊙}

2-

ℳ_{crit} \approx 2 \times 10^{11} ℳ_{⊙}

3-

10^{10.9} - 10^{11.5} ℳ_{⊙}

4-

(V / σ, ϵ)

5-

\sim 10^{9.5} ℳ_{⊙}

6-

H_{0} = 70 k m s^{- 1} M p c^{- 1}

7-

σ_{inst} \sim 72 km s^{- 1}

8-

A = π R_{e}^{2}

9-

{(1 - ϵ)}^{2} = q^{', 2} = \frac{⟨ y^{2} ⟩}{⟨ x^{2} ⟩} = \frac{\sum_{k = 1}^{P} F_{k} y_{k}^{2}}{\sum_{k = 1}^{P} F_{k} x_{k}^{2}}

10-

(x_{k}, y_{k})

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1712.07910

Formulas:

1-

B_{i} = - \sum_{α} p_{i}^{[α]} \log (p_{i}^{[α]}),

2-

p_{i}^{[α]} = \frac{n_{i}^{[α]}}{\sum_{β} n_{i}^{[β]}}

3-

S_{i} = - \sum_{α} q_{i}^{[α]} \log (q_{i}^{[α]}),

4-

B_{i} (t)

5-

S_{i} (t)

6-

{\tilde{N}}_{i}^{c i t} (t)

7-

{\tilde{N}}_{i}^{c i t} (t)

8-

{\tilde{N}}_{i}^{c i t} (t)

9-

B_{i} (5)

10-

S_{i} (5)

Formulas (html):

Correct Categorie: physics

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/1612.05718

Formulas:

1-

ζ = z - \frac{1}{\bar{z}},

2-

ζ = ξ + i η

3-

z = x + i y

4-

A_{j} = \frac{1}{\det J_{j}}; \det J_{j} = {| 1 - \frac{\partial ζ}{\partial \bar{z}} \frac{\partial \bar{ζ}}{\partial z} |}_{z = z_{j}},

5-

A = \sum_{i} A_{i}

6-

A = \frac{{| ζ |}^{2} + 2}{| ζ | \sqrt{{| ζ |}^{2} + 4}},

7-

| ζ | = (t - t_{0}) / t_{E} + i u_{0}

8-

ζ = z - \sum_{i = 1}^{N} \frac{ϵ_{i}}{\bar{z} - {\bar{z}}_{L, i}},

9-

ϵ_{i} = m_{i} / m_{tot}

10-

{(\sqrt[3]{ϵ_{1}} + \sqrt[3]{ϵ_{2}})}^{3 / 2}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/1710.09694

Formulas:

1-

ψ_{i}, ω_{i}, β_{i}

2-

ϕ (t) = \sum_{i = 1}^{n} α_{i} \exp (ϕ_{i} t), α_{i} = β_{i} \exp (𝚒 γ_{i}), ϕ_{i} = ψ_{i} + 𝚒 2 π ω_{i} .

3-

| ℑ (ϕ_{i}) | / (2 π) = | ω_{i} | < Ω / 2, i = 1, \dots, n,

4-

t_{j} = j Δ

5-

j = 0, 1, \dots, 2 n - 1, \dots

6-

f_{j} := ϕ (t_{j}), j = 0, 1, \dots, 2 n - 1, \dots

7-

ϕ_{1}, \dots, ϕ_{n}

8-

α_{1}, \dots, α_{n}

9-

f_{0}, \dots, f_{2 n}, \dots

10-

λ_{i} := \exp (ϕ_{i} Δ), i = 1, \dots, n .

Formulas (html):

Correct Categorie: math

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/0806.4978

Formulas:

1-

[Δ, 2 Δ]

2-

2 Δ ≃ 3 τ π / N

3-

H = - \sum_{i, j} τ_{i j} | i ⟩ ⟨ j | + \sum_{i} V (y_{i}) | i ⟩ ⟨ i |,

4-

τ_{i j} = τ

5-

τ_{i j} = 0

6-

V (y_{i})

7-

G = \frac{2 e^{2}}{h} \sum_{μ, ν} T (μ, ν), T (μ, ν) = {| t_{μ ν} |}^{2},

8-

T (μ, ν)

9-

T (K_{- 2}^{'}, K_{0})

10-

V_{0} Θ (y),

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1210.6588

Formulas:

1-

T^{μ ν} = ρ_{0} h u^{μ} u^{ν} + p g^{μ ν},

2-

h = 1 + ϵ + p / ρ_{0}

3-

p = ρ_{0} ϵ (Γ - 1),

4-

\nabla_{μ} (ρ_{0} u^{μ})

5-

\nabla_{μ} (T^{μ ν})

6-

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

7-

x^{μ} = (t, r, θ, ϕ)

8-

{(\frac{ϱ^{2} Δ}{Σ})}^{1 / 2},

9-

(0, 0, - \frac{2 M a r}{Σ}),

10-

(\begin{matrix} \frac{ϱ^{2}}{Δ} & 0 & 0 \\ 0 & ϱ^{2} & 0 \\ 0 & 0 & \frac{Σ}{ϱ^{2}} \sin^{2} θ \end{matrix}),

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: gr-qc

Result: incorrect

Paper: https://arxiv.org/abs/physics/0410182

Formulas:

1-

n_{0} = n_{e 0} = Z n_{i 0}

2-

𝐁_{0} = B_{0} {\hat{𝐞}}_{z} .

3-

\frac{\partial f_{a}}{\partial t} + v_{x} \frac{\partial f_{a}}{\partial x} - μ_{a} [E_{x}^{t o t} + v_{y} B_{z}] \frac{\partial f_{a}}{\partial v_{x}} - μ_{a} [E_{y}^{t o t} - v_{x} B_{z}^{t o t}] \frac{\partial f_{a}}{\partial v_{y}} = 0,

4-

μ_{i} = - Z m_{e} / m_{i}

5-

t \to t ω_{p e}

6-

x \to x / d_{e}

7-

E (B) \to e E (B) / m_{e} c ω_{p e}

8-

ω_{p e} = {(4 π n_{0} e^{2} / m_{e})}^{1 / 2}

9-

d_{e} = c / ω_{p e} .

10-

λ_{D} = v_{t h, e} / c

Formulas (html):

Correct Categorie: physics

Guessed Categorie: physics

Result: correct

Paper: https://arxiv.org/abs/1802.06200

Formulas:

1-

A \in ℬ (ℋ)

2-

⟨ A x, x ⟩ > 0

3-

⟨ A x, x ⟩ \geq 0

4-

𝒫 𝒮, 𝒫 \subset ℬ (ℋ)

5-

B \leq A ⟹ f (B) \leq f (A)

6-

A, B \in ℬ (ℋ)

7-

σ (A), σ (B) \in I

8-

X \in ℬ (ℋ)

9-

σ : 𝒫 𝒮^{2} \to 𝒫 𝒮

10-

σ (A, B) \leq σ (C, D)

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/2009.10981

Formulas:

1-

G = (V, E)

2-

Col = {1, 2, \dots, c}

3-

1 - 1 / n + O (n^{2})

4-

G = (V, E)

5-

Col = {1, 2, \dots, c}

6-

C = (v_{1}, v_{2}, \dots, v_{j})

7-

f^{'} (v_{i + 1}) = f (v_{i})

8-

f^{'} (v_{1}) = f (v_{j})

9-

f^{'} (v_{i}) = f (v_{i + 1})

10-

f^{'} (v_{j}) = f (v_{1})

Formulas (html):

Correct Categorie: cs

Guessed Categorie: cs

Result: correct

Paper: https://arxiv.org/abs/1805.05531

Formulas:

1-

Λ = 2 μ m

2-

E (r, t) = R e (\tilde{E} (r) e^{i ω t + λ z})

3-

λ = - (δ_{z} + i β)

4-

n_{eff} = i λ / k_{0}

5-

L_{c} = 20 \log 10 (e) Im (k_{0} n_{eff})

6-

S_{λ} (nm / RIU) = \frac{δ λ_{r e s}}{δ n_{a}}

7-

δ λ_{r e s}

8-

n_{a} = 1.33 / 1.34

9-

k_{s p p} = \frac{k}{c} \sqrt{\frac{ϵ_{A u} n_{a}^{2}}{ϵ_{A u} + n_{a}^{2}}}

10-

n_{spp} = \sqrt{\frac{ϵ_{A u} n_{a}^{2}}{ϵ_{A u} + n_{a}^{2}}}

Formulas (html):

Correct Categorie: physics

Guessed Categorie: physics

Result: correct

Paper: https://arxiv.org/abs/1308.5870

Formulas:

1-

\sum m_{ν} = (0.320 \pm 0.081) eV

2-

\sum m_{ν} = 0.06 eV

3-

m_{ν, sterile}^{eff} = (0.450 \pm 0.124) eV

4-

Δ N_{eff} = 0.45 \pm 0.23

5-

N_{eff} = 3.046 + Δ N_{eff}

6-

\sum m_{ν} < 0.248 eV

7-

m_{ν, sterile}^{eff} < 0.42 eV

8-

𝐩 = {Ω_{b} h^{2}, Ω_{c} h^{2}, θ_{MC}, A_{S}, n_{S}, τ}

9-

100 h km \sec^{- 1} {Mpc}^{- 1}

10-

Ω_{m} = Ω_{b} + Ω_{c}

Formulas (html):

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xref="id2.2.m2.1.1.3.3.cmml">eV</mi></mrow></mrow></math>, <math><mrow id="id3.3.m3.3.3" xref="id3.3.m3.3.3.cmml"><msubsup id="id3.3.m3.3.3.3" xref="id3.3.m3.3.3.3.cmml"><mi id="id3.3.m3.3.3.3.2.2" xref="id3.3.m3.3.3.3.2.2.cmml">m</mi><mrow id="id3.3.m3.2.2.2.4" xref="id3.3.m3.2.2.2.3.cmml"><mi id="id3.3.m3.1.1.1.1" xref="id3.3.m3.1.1.1.1.cmml">ν</mi><mo rspace="4.2pt" id="id3.3.m3.2.2.2.4.1" xref="id3.3.m3.2.2.2.3.cmml">,</mo><mi id="id3.3.m3.2.2.2.2" xref="id3.3.m3.2.2.2.2.cmml">sterile</mi></mrow><mi id="id3.3.m3.3.3.3.3" xref="id3.3.m3.3.3.3.3.cmml">eff</mi></msubsup><mo id="id3.3.m3.3.3.2" xref="id3.3.m3.3.3.2.cmml">=</mo><mrow id="id3.3.m3.3.3.1" xref="id3.3.m3.3.3.1.cmml"><mrow id="id3.3.m3.3.3.1.1.1" xref="id3.3.m3.3.3.1.1.1.1.cmml"><mo stretchy="false" id="id3.3.m3.3.3.1.1.1.2" xref="id3.3.m3.3.3.1.1.1.1.cmml">(</mo><mrow id="id3.3.m3.3.3.1.1.1.1" xref="id3.3.m3.3.3.1.1.1.1.cmml"><mn id="id3.3.m3.3.3.1.1.1.1.2" xref="id3.3.m3.3.3.1.1.1.1.2.cmml">0.450</mn><mo id="id3.3.m3.3.3.1.1.1.1.1" xref="id3.3.m3.3.3.1.1.1.1.1.cmml">±</mo><mn id="id3.3.m3.3.3.1.1.1.1.3" xref="id3.3.m3.3.3.1.1.1.1.3.cmml">0.124</mn></mrow><mo rspace="4.2pt" stretchy="false" id="id3.3.m3.3.3.1.1.1.3" xref="id3.3.m3.3.3.1.1.1.1.cmml">)</mo></mrow><mo id="id3.3.m3.3.3.1.2" xref="id3.3.m3.3.3.1.2.cmml">⁢</mo><mi id="id3.3.m3.3.3.1.3" xref="id3.3.m3.3.3.1.3.cmml">eV</mi></mrow></mrow></math>, <math><mrow id="id4.4.m4.1.1" xref="id4.4.m4.1.1.cmml"><mrow id="id4.4.m4.1.1.2" xref="id4.4.m4.1.1.2.cmml"><mi mathvariant="normal" id="id4.4.m4.1.1.2.2" xref="id4.4.m4.1.1.2.2.cmml">Δ</mi><mo id="id4.4.m4.1.1.2.1" xref="id4.4.m4.1.1.2.1.cmml">⁢</mo><msub id="id4.4.m4.1.1.2.3" xref="id4.4.m4.1.1.2.3.cmml"><mi id="id4.4.m4.1.1.2.3.2" xref="id4.4.m4.1.1.2.3.2.cmml">N</mi><mi id="id4.4.m4.1.1.2.3.3" xref="id4.4.m4.1.1.2.3.3.cmml">eff</mi></msub></mrow><mo id="id4.4.m4.1.1.1" xref="id4.4.m4.1.1.1.cmml">=</mo><mrow id="id4.4.m4.1.1.3" xref="id4.4.m4.1.1.3.cmml"><mn id="id4.4.m4.1.1.3.2" xref="id4.4.m4.1.1.3.2.cmml">0.45</mn><mo id="id4.4.m4.1.1.3.1" xref="id4.4.m4.1.1.3.1.cmml">±</mo><mn id="id4.4.m4.1.1.3.3" xref="id4.4.m4.1.1.3.3.cmml">0.23</mn></mrow></mrow></math>, <math><mrow id="p2.4.m4.1.1" xref="p2.4.m4.1.1.cmml"><msub id="p2.4.m4.1.1.2" xref="p2.4.m4.1.1.2.cmml"><mi id="p2.4.m4.1.1.2.2" xref="p2.4.m4.1.1.2.2.cmml">N</mi><mi id="p2.4.m4.1.1.2.3" xref="p2.4.m4.1.1.2.3.cmml">eff</mi></msub><mo id="p2.4.m4.1.1.1" xref="p2.4.m4.1.1.1.cmml">=</mo><mrow id="p2.4.m4.1.1.3" xref="p2.4.m4.1.1.3.cmml"><mn id="p2.4.m4.1.1.3.2" xref="p2.4.m4.1.1.3.2.cmml">3.046</mn><mo id="p2.4.m4.1.1.3.1" xref="p2.4.m4.1.1.3.1.cmml">+</mo><mrow id="p2.4.m4.1.1.3.3" xref="p2.4.m4.1.1.3.3.cmml"><mi mathvariant="normal" id="p2.4.m4.1.1.3.3.2" xref="p2.4.m4.1.1.3.3.2.cmml">Δ</mi><mo id="p2.4.m4.1.1.3.3.1" xref="p2.4.m4.1.1.3.3.1.cmml">⁢</mo><msub id="p2.4.m4.1.1.3.3.3" xref="p2.4.m4.1.1.3.3.3.cmml"><mi id="p2.4.m4.1.1.3.3.3.2" xref="p2.4.m4.1.1.3.3.3.2.cmml">N</mi><mi id="p2.4.m4.1.1.3.3.3.3" xref="p2.4.m4.1.1.3.3.3.3.cmml">eff</mi></msub></mrow></mrow></mrow></math>, <math><mrow id="p3.1.m1.1.1" xref="p3.1.m1.1.1.cmml"><mrow id="p3.1.m1.1.1.2" xref="p3.1.m1.1.1.2.cmml"><mo largeop="true" symmetric="true" id="p3.1.m1.1.1.2.1" xref="p3.1.m1.1.1.2.1.cmml">∑</mo><msub id="p3.1.m1.1.1.2.2" xref="p3.1.m1.1.1.2.2.cmml"><mi id="p3.1.m1.1.1.2.2.2" xref="p3.1.m1.1.1.2.2.2.cmml">m</mi><mi id="p3.1.m1.1.1.2.2.3" xref="p3.1.m1.1.1.2.2.3.cmml">ν</mi></msub></mrow><mo id="p3.1.m1.1.1.1" xref="p3.1.m1.1.1.1.cmml"><</mo><mrow id="p3.1.m1.1.1.3" xref="p3.1.m1.1.1.3.cmml"><mpadded width="+1.7pt" id="p3.1.m1.1.1.3.2" xref="p3.1.m1.1.1.3.2.cmml"><mn id="p3.1.m1.1.1.3.2a" xref="p3.1.m1.1.1.3.2.cmml">0.248</mn></mpadded><mo id="p3.1.m1.1.1.3.1" xref="p3.1.m1.1.1.3.1.cmml">⁢</mo><mi id="p3.1.m1.1.1.3.3" xref="p3.1.m1.1.1.3.3.cmml">eV</mi></mrow></mrow></math>, <math><mrow id="p3.3.m3.2.3" xref="p3.3.m3.2.3.cmml"><msubsup id="p3.3.m3.2.3.2" xref="p3.3.m3.2.3.2.cmml"><mi id="p3.3.m3.2.3.2.2.2" xref="p3.3.m3.2.3.2.2.2.cmml">m</mi><mrow id="p3.3.m3.2.2.2.4" xref="p3.3.m3.2.2.2.3.cmml"><mi id="p3.3.m3.1.1.1.1" xref="p3.3.m3.1.1.1.1.cmml">ν</mi><mo rspace="4.2pt" id="p3.3.m3.2.2.2.4.1" xref="p3.3.m3.2.2.2.3.cmml">,</mo><mi id="p3.3.m3.2.2.2.2" xref="p3.3.m3.2.2.2.2.cmml">sterile</mi></mrow><mi id="p3.3.m3.2.3.2.3" xref="p3.3.m3.2.3.2.3.cmml">eff</mi></msubsup><mo id="p3.3.m3.2.3.1" xref="p3.3.m3.2.3.1.cmml"><</mo><mrow id="p3.3.m3.2.3.3" xref="p3.3.m3.2.3.3.cmml"><mpadded width="+1.7pt" id="p3.3.m3.2.3.3.2" xref="p3.3.m3.2.3.3.2.cmml"><mn id="p3.3.m3.2.3.3.2a" xref="p3.3.m3.2.3.3.2.cmml">0.42</mn></mpadded><mo id="p3.3.m3.2.3.3.1" xref="p3.3.m3.2.3.3.1.cmml">⁢</mo><mi id="p3.3.m3.2.3.3.3" xref="p3.3.m3.2.3.3.3.cmml">eV</mi></mrow></mrow></math>, <math><mrow id="p3.8.m8.6.6" xref="p3.8.m8.6.6.cmml"><mi id="p3.8.m8.6.6.7" xref="p3.8.m8.6.6.7.cmml">𝐩</mi><mo id="p3.8.m8.6.6.6" xref="p3.8.m8.6.6.6.cmml">=</mo><mrow id="p3.8.m8.6.6.5.5" xref="p3.8.m8.6.6.5.6.cmml"><mo stretchy="false" id="p3.8.m8.6.6.5.5.6" xref="p3.8.m8.6.6.5.6.cmml">{</mo><mrow id="p3.8.m8.2.2.1.1.1" xref="p3.8.m8.2.2.1.1.1.cmml"><msub id="p3.8.m8.2.2.1.1.1.2" xref="p3.8.m8.2.2.1.1.1.2.cmml"><mi mathvariant="normal" id="p3.8.m8.2.2.1.1.1.2.2" xref="p3.8.m8.2.2.1.1.1.2.2.cmml">Ω</mi><mi mathvariant="normal" id="p3.8.m8.2.2.1.1.1.2.3" xref="p3.8.m8.2.2.1.1.1.2.3.cmml">b</mi></msub><mo id="p3.8.m8.2.2.1.1.1.1" xref="p3.8.m8.2.2.1.1.1.1.cmml">⁢</mo><msup id="p3.8.m8.2.2.1.1.1.3" xref="p3.8.m8.2.2.1.1.1.3.cmml"><mi id="p3.8.m8.2.2.1.1.1.3.2" xref="p3.8.m8.2.2.1.1.1.3.2.cmml">h</mi><mn id="p3.8.m8.2.2.1.1.1.3.3" xref="p3.8.m8.2.2.1.1.1.3.3.cmml">2</mn></msup></mrow><mo id="p3.8.m8.6.6.5.5.7" xref="p3.8.m8.6.6.5.6.cmml">,</mo><mrow id="p3.8.m8.3.3.2.2.2" xref="p3.8.m8.3.3.2.2.2.cmml"><msub id="p3.8.m8.3.3.2.2.2.2" xref="p3.8.m8.3.3.2.2.2.2.cmml"><mi mathvariant="normal" id="p3.8.m8.3.3.2.2.2.2.2" xref="p3.8.m8.3.3.2.2.2.2.2.cmml">Ω</mi><mi mathvariant="normal" id="p3.8.m8.3.3.2.2.2.2.3" xref="p3.8.m8.3.3.2.2.2.2.3.cmml">c</mi></msub><mo id="p3.8.m8.3.3.2.2.2.1" xref="p3.8.m8.3.3.2.2.2.1.cmml">⁢</mo><msup id="p3.8.m8.3.3.2.2.2.3" xref="p3.8.m8.3.3.2.2.2.3.cmml"><mi id="p3.8.m8.3.3.2.2.2.3.2" xref="p3.8.m8.3.3.2.2.2.3.2.cmml">h</mi><mn id="p3.8.m8.3.3.2.2.2.3.3" xref="p3.8.m8.3.3.2.2.2.3.3.cmml">2</mn></msup></mrow><mo id="p3.8.m8.6.6.5.5.8" xref="p3.8.m8.6.6.5.6.cmml">,</mo><msub id="p3.8.m8.4.4.3.3.3" xref="p3.8.m8.4.4.3.3.3.cmml"><mi id="p3.8.m8.4.4.3.3.3.2" xref="p3.8.m8.4.4.3.3.3.2.cmml">θ</mi><mi id="p3.8.m8.4.4.3.3.3.3" xref="p3.8.m8.4.4.3.3.3.3.cmml">MC</mi></msub><mo id="p3.8.m8.6.6.5.5.9" xref="p3.8.m8.6.6.5.6.cmml">,</mo><msub id="p3.8.m8.5.5.4.4.4" xref="p3.8.m8.5.5.4.4.4.cmml"><mi id="p3.8.m8.5.5.4.4.4.2" xref="p3.8.m8.5.5.4.4.4.2.cmml">A</mi><mi mathvariant="normal" id="p3.8.m8.5.5.4.4.4.3" xref="p3.8.m8.5.5.4.4.4.3.cmml">S</mi></msub><mo id="p3.8.m8.6.6.5.5.10" xref="p3.8.m8.6.6.5.6.cmml">,</mo><msub id="p3.8.m8.6.6.5.5.5" xref="p3.8.m8.6.6.5.5.5.cmml"><mi id="p3.8.m8.6.6.5.5.5.2" xref="p3.8.m8.6.6.5.5.5.2.cmml">n</mi><mi mathvariant="normal" id="p3.8.m8.6.6.5.5.5.3" xref="p3.8.m8.6.6.5.5.5.3.cmml">S</mi></msub><mo id="p3.8.m8.6.6.5.5.11" xref="p3.8.m8.6.6.5.6.cmml">,</mo><mi id="p3.8.m8.1.1" xref="p3.8.m8.1.1.cmml">τ</mi><mo stretchy="false" id="p3.8.m8.6.6.5.5.12" xref="p3.8.m8.6.6.5.6.cmml">}</mo></mrow></mrow></math>, <math><mrow id="p3.12.m12.1.1" xref="p3.12.m12.1.1.cmml"><mn id="p3.12.m12.1.1.2" xref="p3.12.m12.1.1.2.cmml">100</mn><mo id="p3.12.m12.1.1.1" xref="p3.12.m12.1.1.1.cmml">⁢</mo><mpadded width="+1.7pt" id="p3.12.m12.1.1.3" xref="p3.12.m12.1.1.3.cmml"><mi id="p3.12.m12.1.1.3a" xref="p3.12.m12.1.1.3.cmml">h</mi></mpadded><mo id="p3.12.m12.1.1.1a" xref="p3.12.m12.1.1.1.cmml">⁢</mo><mpadded width="+1.7pt" id="p3.12.m12.1.1.4" xref="p3.12.m12.1.1.4.cmml"><mi id="p3.12.m12.1.1.4a" xref="p3.12.m12.1.1.4.cmml">km</mi></mpadded><mo id="p3.12.m12.1.1.1b" xref="p3.12.m12.1.1.1.cmml">⁢</mo><mpadded width="+1.7pt" id="p3.12.m12.1.1.5" xref="p3.12.m12.1.1.5.cmml"><msup id="p3.12.m12.1.1.5a" xref="p3.12.m12.1.1.5.cmml"><mi id="p3.12.m12.1.1.5.2" xref="p3.12.m12.1.1.5.2.cmml">sec</mi><mrow id="p3.12.m12.1.1.5.3" xref="p3.12.m12.1.1.5.3.cmml"><mo id="p3.12.m12.1.1.5.3.1" xref="p3.12.m12.1.1.5.3.1.cmml">-</mo><mn id="p3.12.m12.1.1.5.3.2" xref="p3.12.m12.1.1.5.3.2.cmml">1</mn></mrow></msup></mpadded><mo id="p3.12.m12.1.1.1c" xref="p3.12.m12.1.1.1.cmml">⁢</mo><msup id="p3.12.m12.1.1.6" xref="p3.12.m12.1.1.6.cmml"><mi id="p3.12.m12.1.1.6.2" xref="p3.12.m12.1.1.6.2.cmml">Mpc</mi><mrow id="p3.12.m12.1.1.6.3" xref="p3.12.m12.1.1.6.3.cmml"><mo id="p3.12.m12.1.1.6.3.1" xref="p3.12.m12.1.1.6.3.1.cmml">-</mo><mn id="p3.12.m12.1.1.6.3.2" xref="p3.12.m12.1.1.6.3.2.cmml">1</mn></mrow></msup></mrow></math>, <math><mrow id="p4.1.m1.1.1" xref="p4.1.m1.1.1.cmml"><msub id="p4.1.m1.1.1.2" xref="p4.1.m1.1.1.2.cmml"><mi mathvariant="normal" id="p4.1.m1.1.1.2.2" xref="p4.1.m1.1.1.2.2.cmml">Ω</mi><mi mathvariant="normal" id="p4.1.m1.1.1.2.3" xref="p4.1.m1.1.1.2.3.cmml">m</mi></msub><mo id="p4.1.m1.1.1.1" xref="p4.1.m1.1.1.1.cmml">=</mo><mrow id="p4.1.m1.1.1.3" xref="p4.1.m1.1.1.3.cmml"><msub id="p4.1.m1.1.1.3.2" xref="p4.1.m1.1.1.3.2.cmml"><mi mathvariant="normal" id="p4.1.m1.1.1.3.2.2" xref="p4.1.m1.1.1.3.2.2.cmml">Ω</mi><mi mathvariant="normal" id="p4.1.m1.1.1.3.2.3" xref="p4.1.m1.1.1.3.2.3.cmml">b</mi></msub><mo id="p4.1.m1.1.1.3.1" xref="p4.1.m1.1.1.3.1.cmml">+</mo><msub id="p4.1.m1.1.1.3.3" xref="p4.1.m1.1.1.3.3.cmml"><mi mathvariant="normal" id="p4.1.m1.1.1.3.3.2" xref="p4.1.m1.1.1.3.3.2.cmml">Ω</mi><mi mathvariant="normal" id="p4.1.m1.1.1.3.3.3" xref="p4.1.m1.1.1.3.3.3.cmml">c</mi></msub></mrow></mrow></math>

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/0807.2186

Formulas:

1-

S = \int 𝑑 τ [{\dot{X}}_{A} P_{A} - (λ_{1} ϕ_{1} + λ_{2} ϕ_{2} + λ_{3} ϕ_{3})],

2-

(+, -, \dots, -)

3-

ϕ_{1} = \frac{1}{2} (X_{A}^{2} + α^{2}), ϕ_{2} = \frac{1}{2} (P_{A}^{2} + κ^{2}), ϕ_{3} = X_{A} P_{A} .

4-

{\dot{X}}_{A} = λ_{2} P_{A} + λ_{3} X_{A}, {\dot{P}}_{A} = - λ_{1} X_{A} - λ_{3} P_{A} .

5-

ϕ_{1} \approx ϕ_{2} \approx 0

6-

{ϕ_{1}, ϕ_{2}} \approx 0, {ϕ_{1}, ϕ_{3}} \approx - α^{2}, {ϕ_{2}, ϕ_{3}} \approx κ^{2} .

7-

ψ = \frac{1}{2} (κ^{2} X_{A}^{2} + α^{2} P_{A}^{2} + 2 α^{2} κ^{2}),

8-

χ_{1} = X_{A} P_{A}, χ_{2} = \frac{1}{2} (κ^{2} X_{A}^{2} - α^{2} P_{A}^{2}),

9-

C_{12} \equiv {χ_{1}, χ_{2}} \approx - 2 α^{2} κ^{2} .

10-

S = \int 𝑑 τ [{\dot{X}}_{A} P_{A} - \frac{1}{2} (\frac{λ_{1}}{κ^{2}} + \frac{λ_{2}}{α^{2}}) ψ - \frac{1}{2} (\frac{λ_{1}}{κ^{2}} - \frac{λ_{2}}{α^{2}}) χ_{1} - λ_{3} χ_{3}] .

Formulas (html):

Correct Categorie: gr-qc

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1106.6209

Formulas:

1-

\sqrt{s_{N N}} = 2.76

2-

v_{2} (p_{t})

3-

\sqrt{s_{N N}} = 2.76

4-

0.2 < p_{t} < 5.0

5-

Q C {2} = v^{2},

6-

Q C {4} = - v^{4},

7-

Q C {6} = 4 v^{6},

8-

Q C {8} = - 33 v^{8} .

9-

(+, -, +, -)

10-

v_{2} {2}, v_{2} {4}, v_{2} {6}

Formulas (html):

Correct Categorie: nucl-ex

Guessed Categorie: hep-ph

Result: incorrect

Paper: https://arxiv.org/abs/physics/0509032

Formulas:

1-

m_{X} = m_{X^{q +}} + q m_{e} - \frac{E_{B}}{c^{2}}

2-

E < - m c^{2}

3-

E > m c^{2}

4-

ℋ^{no pair} = \sum_{i = 1}^{N} ℋ_{D} (r_{i}) + \sum_{i < j} 𝒱 (| 𝒓_{i} - 𝒓_{j} |),

5-

𝒱_{i j} = Λ_{i j}^{+ +} V_{i j} Λ_{i j}^{+ +}

6-

Λ_{i j}^{+ +} = Λ_{i}^{+} Λ_{j}^{+}

7-

E < - m c^{2}

8-

\frac{1}{r_{i j}}

9-

- \frac{𝜶_{i} \cdot 𝜶_{j}}{r_{i j}}

10-

- \frac{𝜶_{i} \cdot 𝜶_{j}}{r_{i j}} [\cos (\frac{ω_{i j} r_{i j}}{c}) - 1]

Formulas (html):

Correct Categorie: physics

Guessed Categorie: physics

Result: correct

Paper: https://arxiv.org/abs/0803.3889

Formulas:

1-

x \notin ω (x)

2-

ω (x) = ⋂_{N \geq 0} \bar{{f^{n} (x) : n \geq 0}} .

3-

δ (z) \geq ε δ (z, z_{1}),

4-

δ (z, \partial Ω)

5-

δ (a, b) < θ

6-

a, b \in B, diam B < τ .

7-

(E x p S h r i n k)

8-

E x p S h r i n k

9-

(T C E)

10-

λ > 1, r > 0

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/1706.00974

Formulas:

1-

P_{V} = 24.24 \pm 1.09

2-

P_{R} = 24.12 \pm 0.76

3-

P_{I} = 24.82 \pm 0.73

4-

E W < 5 Å

5-

τ_{B I} = 11

6-

m_{i} = m_{i | o} + m_{i | c} - m_{i | o c}

7-

m_{i | o c}

8-

m = \frac{\sum_{i = 1}^{K} m_{i}}{K}

9-

σ = \sqrt{\frac{Σ {(m_{i} - m)}^{2}}{K - 1}}

10-

\bar{m_{V}} = 13.51 \pm 0.42

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0008497

Formulas:

1-

M_{*} (r_{b})

2-

M_{*} (r_{b})

3-

M_{*} (r_{b})

4-

\sim > 10^{7} M_{⊙}

5-

| M_{v} | \sim > 20

6-

a < a_{h} = \frac{G m_{2}}{4 σ^{2}} = 2.7 pc (\frac{m_{2}}{10^{8} M_{⊙}}) {(\frac{200 k m s^{- 1}}{σ})}^{2}

7-

M_{12} = m_{1} + m_{2}

8-

γ = (1, 1.5, 2)

9-

t = t_{h} \approx 11.1

10-

N \approx 3 \times 10^{5}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0308477

Formulas:

1-

6 m s^{- 1}

2-

20.6 m s^{- 1}

3-

m \sin i \approx 2 M_{Jup}

4-

m \sin i = 0.56 M_{Jup}

5-

10 m s^{- 1}

6-

70 m s^{- 1}

7-

3 - 4 m s^{- 1}

8-

m \sin i = 0.0126 - 0.019 M_{Jup}

9-

m \sin i = 4 - 6 M_{\oplus}

10-

5.7 m s^{- 1}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/0707.4428

Formulas:

1-

α | 00 \dots 0 ⟩ + β | 11 \dots 1 ⟩, α, β \neq 0

2-

j \in {1, \dots, n}

3-

ρ_{(j)} = {tr}_{j} ρ

4-

PTr : D_{n} \to D_{n - 1}^{n}

5-

ρ \mapsto (ρ_{(1)}, \dots, ρ_{(n)})

6-

PTr (ρ_{1}) = PTr (ρ_{2})

7-

P_{n} = {ρ \in D_{n} | ρ^{2} = ρ}

8-

ptr = {PTr |}_{P_{n}} : P_{n} \to D_{n - 1}^{n}

9-

| ψ ⟩ ⟨ ψ | \in P_{n}

10-

{ptr}^{- 1} (ptr (ψ))

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: quant-ph

Result: correct

Paper: https://arxiv.org/abs/1007.1008

Formulas:

1-

N (R) \propto R^{- Q}

2-

Δ r \sim 4 r_{H}

3-

Δ r \sim 4 r_{H}

4-

\bar{R} \sim 0.18 Δ r

5-

Δ r \sim (9 \pm 1) r_{H}

6-

\bar{R} ≲ 0.18 Δ r

7-

Δ r \sim 4 r_{H}

8-

Δ r \sim 4 r_{H}

9-

Δ r \sim 8 r_{H}

10-

Δ r \sim 4 r_{H}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0410003

Formulas:

1-

\sim 6.7 \times 10^{4} erg {cm}^{- 3}

2-

\cos ∠ (LHC, RHC)

3-

\sin ∠ (LHC, RHC)

4-

56.8 pc {cm}^{- 3}

5-

t_{s a m p l e} = 890 μ s

6-

\sim 640 μ s

7-

Δ S_{m i n} = 0.117 Jy

8-

τ_{g r p} = 3 μ s

9-

Δ S_{m i n} t_{s a m p l e} / τ_{g r p} = 25 Jy

10-

S_{ν g r p}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/physics/0511107

Formulas:

1-

𝒓^{'} (t^{'})

2-

\frac{e (𝒏 - 𝜷) (1 - β^{2})}{R^{2} {(1 - 𝜷 \cdot 𝒏)}^{3}} + \frac{e}{R c^{2}} \frac{𝒏 \times [(𝒏 - 𝜷) \times 𝒂]}{{(1 - 𝜷 \cdot 𝒏)}^{3}},

3-

𝒏 \times 𝑬 (t),

4-

𝑹 = 𝑹 (t^{'}) = 𝒓 - 𝒓^{'} (t^{'})

5-

t = t^{'} + \frac{| 𝑹 (t^{'}) |}{c},

6-

𝜷 = d 𝒓^{'} / c d t^{'}

7-

𝒂 = d^{2} 𝒓^{'} / d t^{'}^{2}

8-

𝒓^{'} (t^{'})

9-

𝑹 (t^{'})

10-

\dot{𝑹} (t^{'})

Formulas (html):

Correct Categorie: physics

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/9802226

Formulas:

1-

s_{i} \equiv (E_{i + 1} - E_{i}) / ⟨ E_{i + 1} - E_{i} ⟩

2-

P_{P} (s) = \exp (- s)

3-

P_{W D} (s) = \frac{π}{2} s \exp (- π s^{2} / 4)

4-

ρ_{B W} (E) = Γ / (2 π (E^{2} + Γ^{2} / 4))

5-

Γ \sim Q^{2} / Δ_{c}

6-

ξ \sim Γ / Δ_{n}

7-

ξ_{c} \sim Δ_{c} / Δ_{n} ≫ 1

8-

P_{b} [\sum_{i} W_{i} a_{i}^{†} a_{i} + \sum_{⟨ i; j ⟩} (U a_{i}^{†} a_{j}^{†} a_{j} a_{i} - t a_{i}^{†} a_{j})] P_{b}

9-

E_{b} \approx - 3.3 t

10-

ϵ_{g} \approx n E_{b} + n (n + 1) Δ_{1} / 2 + 3 U n (n - 1) Δ_{1} / B_{1}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/hep-lat/0110108

Formulas:

1-

S_{F} = \sum_{x} \bar{ψ} (x) (D + m_{q} + i μ_{q} γ_{5} τ_{3}) ψ (x)

2-

i μ_{q} γ_{5} τ_{3} = i μ_{q} γ_{5} (\begin{matrix} 1 & 0 \\ 0 & - 1 \end{matrix})

3-

ψ^{'} \to e^{i α γ_{5} τ_{3} / 2} ψ \bar{ψ^{'}} \to \bar{ψ} e^{i α γ_{5} τ_{3} / 2}

4-

S_{F} = \sum_{x} \bar{ψ^{'}} (x) (D + M_{Q}) ψ^{'} (x)

5-

\sqrt{m_{q}^{2} + μ_{q}^{2}}

6-

\bar{ψ} Γ \frac{τ_{i}}{2} ψ

7-

\bar{u^{'}} Γ d^{'}

8-

\bar{u} (\cos (α / 2) + i γ_{5} \sin (α / 2))

9-

(\cos (\frac{α}{2}) - i γ_{5} \sin (\frac{α}{2})) d

10-

\bar{u^{'}} Γ d^{'} = \bar{u} Γ d

Formulas (html):

Correct Categorie: hep-lat

Guessed Categorie: hep-lat

Result: correct

Paper: https://arxiv.org/abs/astro-ph/9910096

Formulas:

1-

0.5 < (n / \bar{n}) \leq 1

2-

1 < (n / \bar{n}) \leq 2

3-

(n / \bar{n}) \leq 0.5

4-

0.16 < n / \bar{n} \leq 2

5-

Δ c z ≳ 200

6-

0.5 < n / \bar{n} \leq 2

7-

Δ c z = 103 \pm 20

8-

n \leq 0.5 \bar{n}

9-

0.5 < n / \bar{n} \leq 2

10-

\approx 150 h^{- 1}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1408.1280

Formulas:

1-

c^{2} d τ^{2} = c^{2} d t^{2} - {| d 𝐫 |}^{2}

2-

{| d 𝐫 |}^{2} = d x^{2} + d y^{2} + d z^{2}

3-

d τ, d t, | d 𝐫 |

4-

c^{2} d t^{2} = c^{2} d τ^{2} + {| d 𝐫 |}^{2}

5-

\cos θ = | d 𝐫 | / c d t = v / c

6-

= \int_{P}^{Q} 𝑑 t = \int_{P}^{Q} 𝑑 τ \sqrt{1 + \cot^{2} θ}

7-

= t \sin θ = t \sqrt{1 - u^{2} / c^{2}} < t

8-

\sqrt{1 - u^{2} / c^{2}}

9-

O P O_{2}

10-

\cos θ = 2 x_{0} / c t = u / c

Formulas (html):

Correct Categorie: physics

Guessed Categorie: physics

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0604301

Formulas:

1-

\int | V (λ) | 𝑑 λ

2-

L_{t} = \int L (λ) 𝑑 λ

3-

\sqrt{Q {(λ)}^{2} + U {(λ)}^{2}}

4-

V (λ) / I_{c}

5-

δ a = \frac{a_{b} - a_{r}}{a_{b} + a_{r}},

6-

| δ a | \leq 0.05

7-

| δ a | \leq 0.05

8-

| δ a | \leq

9-

Δ λ = 2.12 \times 10^{- 6} λ

10-

Δ λ = 4.67 \times 10^{- 18} λ^{2} g_{𝐞𝐟𝐟} B

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1104.3987

Formulas:

1-

R_{p} < 100 km

2-

R_{p} \leq 100 km

3-

R_{p} ≃ 500 km

4-

\sim 10 m s^{- 1}

5-

10 m s^{- 1} \leq v_{crit} \leq 60 m s^{- 1}

6-

\sim 10^{- 8} M_{⊙} {yr}^{- 1}

7-

R_{p} \leq 10 km

8-

\hat{𝐱}, \hat{𝐲}, \hat{𝐳}

9-

\partial_{t} ρ + \nabla \cdot (ρ 𝐯)

10-

\partial_{t} (ρ 𝐯) + \nabla \cdot [ρ 𝐯𝐯 + p^{⋆} - 𝐁𝐁]

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/cond-mat/0609175

Formulas:

1-

I_{S} (ω)

2-

I_{D} (ω)

3-

R_{D}^{S} (ω) = I_{S} (ω) / I_{D} (ω)

4-

I_{A u} (ω)

5-

I_{D} (ω)

6-

R_{D}^{Au} (ω) = I_{A u} (ω) / I_{D} (ω)

7-

R (ω) = R_{D}^{S} (ω) / R_{D}^{Au} (ω)

8-

σ_{1} (ω)

9-

σ_{1} (ω)

10-

σ_{1} (ω)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/0811.2342

Formulas:

1-

^{1, 2, 3, 4}

2-

_{c o r e}

3-

_{c o r e}

4-

_{d i s s}

5-

_{d i s s}

6-

_{d i s s}

7-

{}^{F S - I S}_{d i s s}

8-

_{d i f f}

9-

{}^{F S - I S}_{d i f f}

10-

{\bar{d}}_{H - s u r f}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/nlin/0407045

Formulas:

1-

\frac{\partial ϕ}{\partial t} = ω - \int_{- π}^{π} G (x - x^{'}) \sin [ϕ (x, t) - ϕ (x^{'}, t) + α] 𝑑 x^{'} .

2-

ϕ (x, t)

3-

ϕ \to ϕ + ω t

4-

0 \leq α \leq \frac{π}{2}

5-

G (x - x^{'})

6-

| x - x^{'} |

7-

G (x) \propto \exp (- κ | x |)

8-

G (x) = \frac{1}{2 π} (1 + A \cos x)

9-

ϕ (x) = a \exp [- b x^{2}] r

10-

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

Formulas (html):

Correct Categorie: nlin

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/gr-qc/0701078

Formulas:

1-

ℏ = c = G = k_{B} = 1

2-

d s^{2} = - x^{2} d t^{2} + d x^{2} + d y^{2} + d z^{2} .

3-

d s^{2} = - g^{2} x^{2} d t^{2} + d x^{2} + d y^{2} + d z^{2},

4-

U^{μ} = {1 / (g x), 0, 0, 0}

5-

a^{μ} = U^{ν} \nabla_{ν} U^{μ} = {0, 1 / x, 0, 0}

6-

a \equiv {(a^{μ} a_{μ})}^{1 / 2} = 1 / x

7-

{x, y, z}

8-

t \to \tilde{t} and x \to (1 + g \tilde{x}) / g .

9-

d s^{2} = - {(1 + g \tilde{x})}^{2} d {\tilde{t}}^{2} + d {\tilde{x}}^{2} + d y^{2} + d z^{2} .

10-

U^{μ} = {1 / (1 + g \tilde{x}), 0, 0, 0}

Formulas (html):

Correct Categorie: gr-qc

Guessed Categorie: gr-qc

Result: correct

Paper: https://arxiv.org/abs/1409.8329

Formulas:

1-

ℒ = D^{- 1 / 2} (D - A) D^{- 1 / 2}

2-

w (u, v)

3-

w (u, v) = w (v, u)

4-

A_{u, v} = w (u, v)

5-

d (u) = w (u) + \sum_{v \sim u} w (u, v)

6-

w_{α G} (u, v) = α w_{G} (u, v)

7-

ℒ_{G} = ℒ_{α G}

8-

ℒ = D^{- 1 / 2} (D - A) D^{- 1 / 2}

9-

\begin{matrix} ℒ_{α G} = D_{α G}^{- 1 / 2} (D_{α G} - A_{α G}) D_{α G}^{- 1 / 2} = (\frac{1}{\sqrt{α}} D_{G}^{- 1 / 2}) (α (D_{G} - A_{G})) (\frac{1}{\sqrt{α}} D_{G}^{- 1 / 2}) \\ = D_{G}^{- 1 / 2} (D_{G} - A_{G}) D_{G}^{- 1 / 2} = ℒ_{G}, \end{matrix}

10-

w (u, t) = α w (v, t)

Formulas (html):

Correct Categorie: math

Guessed Categorie: cs

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0401518

Formulas:

1-

| b^{I I} | \leq 5 °

2-

≲ 1.1 \times 10^{- 12}

3-

≲ 5.6 \times 10^{- 11}

4-

| b^{I I} | \leq 5 °

5-

E (B - V) = 0.93

6-

N_{H} = 1.79 \times 10^{21} {cm}^{- 2} A_{V} = 3.40 \times 10^{21} D {cm}^{- 2}

7-

N_{H} = 5.1 \times 10^{22}

8-

4 π D^{2}

9-

V = \frac{4 π}{3} η D^{3} \sin {| b^{I I} |}_{\max},

10-

{| b^{I I} |}_{\max} = 5 °

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/0812.2008

Formulas:

1-

d I_{qpcR} / d V_{2degL}

2-

Δ E_{L} \approx 1.4

3-

Δ E_{R} \approx 1.2

4-

C_{Σ L} = 25.6

5-

C_{Σ R} = 40.9

6-

E_{C L} = 6.3

7-

E_{C R} = 4.0

8-

E_{C m} = 0.54

9-

d I_{qpcR} / d V_{2degL}

10-

(N, M + 1)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1810.01854

Formulas:

1-

B V R I

2-

R_{bar} = 90.0 \pm 4.0

3-

ℛ = R_{CR} / R_{bar}

4-

B V R I

5-

B V R I

6-

F_{2} (r) = \int_{- π}^{π} I_{r} (θ) e^{- 2 i θ} d θ

7-

θ (r) = \tan^{- 1} \frac{Re [F_{2} (r)]}{Im [F_{2} (r)]}

8-

Re [F_{2} (r)]

9-

Im [F_{2} (r)]

10-

F_{2} (r)

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1710.09054

Formulas:

1-

S = \frac{1}{16 π} \int d^{D} x \sqrt{- g} (R - 2 Λ - \frac{1}{4} F_{μ ν} F^{μ ν} - \frac{1}{2} \sum_{I = 1}^{D - 2} {(\partial ψ_{I})}^{2}),

2-

Λ = - \frac{(D - 1) (D - 2)}{2 L^{2}} .

3-

ψ_{I} = β δ_{I a} x^{a}

4-

ψ_{I} = β_{I a} x^{a}

5-

β^{2} \equiv \frac{1}{D - 2} (\sum_{a = 1}^{D - 2} \sum_{I = 1}^{D - 2} β_{I a} β_{I a})

6-

\sum_{I = 1}^{D - 2} β_{I a} β_{I b} = β^{2} δ_{a b}

7-

β_{I a} = β δ_{I a}

8-

d s^{2} = - f (r) d t^{2} + \frac{1}{f (r)} d r^{2} + r^{2} d x^{a} d x^{a}, A = A_{t} (r) d t, with

9-

f (r) = \frac{r^{2}}{L^{2}} - \frac{β^{2}}{2 (D - 3)} - \frac{m}{r^{D - 3}} + \frac{q^{2}}{r^{2 (D - 3)}}, A_{t} = \sqrt{\frac{2 (D - 2)}{D - 3}} (1 - \frac{r_{h}^{D - 3}}{r^{D - 3}}) \frac{q}{r_{h}^{D - 3}}

10-

a = 1, 2 \dots D - 2

Formulas (html):

Correct Categorie: hep-th

Guessed Categorie: hep-th

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0306238

Formulas:

1-

≲ 10^{9} M_{⊙}

2-

f_{bar} = 0.3 - 0.6

3-

≳ 10^{8} M_{⊙}

4-

1.5 \times 10^{12} M_{⊙}

5-

0.5 \times 10^{12} M_{⊙}

6-

\sim 200^{3} {kpc}^{3}

7-

Ω_{b} = 0.019 / h^{2}

8-

1.26 \times 10^{7} M_{⊙}

9-

5 \times 10^{8} M_{⊙}

10-

= Ω_{0} / Ω_{b}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/0804.3322

Formulas:

1-

\dot{γ} / 2 π

2-

\dot{α} / 2 π

3-

(n, l, k)

4-

f = n ν + l \dot{γ} / 2 π + k \dot{α} / 2 π

5-

| l |, | k | \leq 2

6-

J_{n} (n e)

7-

M \sim 10^{7} M_{⊙}

8-

\ln (m / M_{⊙})

9-

\ln (M / M_{⊙})

10-

\ln (ν_{0} / Hz)

Formulas (html):

Correct Categorie: gr-qc

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/0808.2179

Formulas:

1-

B_{y} = B_{0} \tanh ((x - L_{x} / 2) / D)

2-

N_{c s} = N_{0} / \cosh^{2} ((x - L_{x} / 2) / D)

3-

N_{B} = N_{B 0} (1 - 1 / \cosh^{2} ((x - L_{x} / 2) / D))

4-

ω_{p e} / Ω_{c e}

5-

\partial B_{n} / \partial n

6-

\partial 𝐄_{𝐭} / \partial n

7-

A_{z} = - A_{0} \exp [- {{(x - L_{x} / 2)}^{2} + {(y - H)}^{2}} / (2 λ_{i}^{2})]

8-

A_{0} = 0.1 B_{0} λ_{i}

9-

μ \equiv m_{i} / m_{e}

10-

Ω_{c i}^{- 1}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/0810.4102

Formulas:

1-

u v b y

2-

Δ [F e / H] <

3-

u v b y

4-

u z, v z, b z, y z

5-

λ_{e f f}

6-

λ_{e f f} = 4100

7-

λ_{e f f} = 3500

8-

v z - y z

9-

b z - y z

10-

v z - y z

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0610106

Formulas:

1-

0.5 - 2.3 {x10}^{14} kg

2-

\log (L_{X} / L_{b o l}) ≃ - 3

3-

λ / Δ λ \approx 40 000

4-

σ_{ν} = \frac{g_{u}}{g_{l}} \frac{c^{2}}{8 π ν^{2}} Φ (ν) A_{u l}

5-

1.06 \pm 0.04 R_{⊙}

6-

τ_{ν} = σ_{ν} N_{2}

7-

E W = \int (1 - \exp^{- τ_{ν}}) 𝑑 ν

8-

N_{C a I I}

9-

N_{C a I I}

10-

\log N_{2} = 18.61 \pm 0.05 m^{- 2}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Run 16403398 (Agent489)