Run 11277761

Paper: https://arxiv.org/abs/1903.01694

Formulas:

1-

\frac{1}{c} \frac{\partial 𝐁}{\partial t}

2-

\frac{1}{c} \frac{\partial 𝐄}{\partial t}

3-

\nabla \times 𝐁 - \frac{4 π}{c} 𝐉,

4-

4 π ρ_{e},

5-

𝐉 = c ρ_{e} \frac{𝐄 \times 𝐁}{B^{2}} + \frac{c}{4 π} \frac{(𝐁 \cdot \nabla \times 𝐁 - 𝐄 \cdot \nabla \times 𝐄) 𝐁}{B^{2}} .

6-

𝐉 = c ρ_{e} \frac{𝐄 \times 𝐁}{B^{2} + E_{0}^{2}} + σ 𝐄_{∥},

7-

B_{0}^{2} - E_{0}^{2}

8-

𝐁^{2} - 𝐄^{2},

9-

𝐄 \cdot 𝐁, E_{0} \geq 0 .

10-

r_{\min} = 0.2 r_{L}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1808.05718

Formulas:

1-

2 \overset{\circ}{.} 5

2-

E (B - V) = 0.044

3-

α_{2000} = 1^{h} 56^{m} 32 \overset{s}{.} 11

4-

δ_{2000} = + 38 ° 19' 02 \overset{''}{.} 2

5-

G_{B P} - G_{R P} = 0.860

6-

μ_{α} = 10.43 \pm 0.69

7-

μ_{δ} = - 11.15 \pm 0.50

8-

0 \overset{\circ}{.} 56

9-

g r i z y

10-

J H K_{s}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1412.8193

Formulas:

1-

x_{1}, x_{2}, x_{3}, x_{4} \in Fix (f)

2-

A = {x_{1}, x_{2}}

3-

B = {x_{3}, x_{4}} .

4-

{x_{1}, x_{2}, x_{3}, x_{4}} .

5-

α : [0, 1] \to S^{2} ∖ B

6-

β : [0, 1] \to S^{2} ∖ A

7-

[δ * β] \in H_{1} (S^{2} ∖ A) ≅ ℤ

8-

[δ * β] = (α \cdot β) [u],

9-

H_{1} (S^{2} ∖ A)

10-

[α] \in H_{1} (S^{2} ∖ B, A)

Formulas (html):

Correct Categorie: math

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1912.01015

Formulas:

1-

P_{ph} = 1.12 \times 10^{5}

2-

ρ_{ph} = 3.20 \times 10^{- 7}

3-

T = 3 \times 10^{4}

4-

𝐄 = - 𝐮 \times 𝐁 + η 𝐉 - η_{_{amb}} \frac{(𝐉 \times 𝐁) \times 𝐁}{{| 𝐁 |}^{2}} + η_{_{Hall}} \frac{(𝐉 \times 𝐁)}{| 𝐁 |},

5-

η = \frac{m_{e} ν_{e, n i}}{n_{e} q_{e}^{2}};

6-

η_{_{amb}} = \frac{{(ρ_{N} / ρ)}^{2} {| 𝐁 |}^{𝟐}}{Σ_{n} Σ_{i} ρ_{n} ν_{n i}^{*}};

7-

η_{_{Hall}} = \frac{| 𝐁 |}{q_{e} n_{e}},

8-

ρ_{N} = Σ_{n} ρ_{n}

9-

ν_{e, n i}

10-

ν_{n i}^{*} = \frac{m_{n i}}{m_{n}} n_{_{i}} σ_{n i} {(\frac{8 K_{B} T}{π m_{n i}})}^{1 / 2},

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1809.04239

Formulas:

1-

0 = F_{H} + F_{C} + F_{R}

2-

F_{R} = F_{0} \exp (- κ h) .

3-

κ^{- 1} = 0.02 a

4-

F_{C, t a n} \leq μ F_{C, n o r},

5-

η_{0} \dot{γ_{0}}

6-

\dot{γ_{0}} = F_{0} / (6 π η_{0} a^{2})

7-

η_{r} = η / η_{0}

8-

𝐀_{a b} = {\begin{matrix} 0 \\ 1, if α_{a b} is satisfied \end{matrix}}

9-

r_{s m a l l} / r_{l a r g e}

10-

r_{s m a l l} / r_{l a r g e} > \sqrt{2} - 1

Formulas (html):

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id="S2.SS2.p1.3.m3.1.1.3" xref="S2.SS2.p1.3.m3.1.1.3.cmml"><msub id="S2.SS2.p1.3.m3.1.1.3.2" xref="S2.SS2.p1.3.m3.1.1.3.2.cmml"><mi id="S2.SS2.p1.3.m3.1.1.3.2.2" xref="S2.SS2.p1.3.m3.1.1.3.2.2.cmml">γ</mi><mn id="S2.SS2.p1.3.m3.1.1.3.2.3" xref="S2.SS2.p1.3.m3.1.1.3.2.3.cmml">0</mn></msub><mo id="S2.SS2.p1.3.m3.1.1.3.1" xref="S2.SS2.p1.3.m3.1.1.3.1.cmml">˙</mo></mover></mrow></math>, <math><mrow id="S2.SS2.p1.5.m5.1.1" xref="S2.SS2.p1.5.m5.1.1.cmml"><mover accent="true" id="S2.SS2.p1.5.m5.1.1.3" xref="S2.SS2.p1.5.m5.1.1.3.cmml"><msub id="S2.SS2.p1.5.m5.1.1.3.2" xref="S2.SS2.p1.5.m5.1.1.3.2.cmml"><mi id="S2.SS2.p1.5.m5.1.1.3.2.2" xref="S2.SS2.p1.5.m5.1.1.3.2.2.cmml">γ</mi><mn id="S2.SS2.p1.5.m5.1.1.3.2.3" xref="S2.SS2.p1.5.m5.1.1.3.2.3.cmml">0</mn></msub><mo id="S2.SS2.p1.5.m5.1.1.3.1" xref="S2.SS2.p1.5.m5.1.1.3.1.cmml">˙</mo></mover><mo id="S2.SS2.p1.5.m5.1.1.2" xref="S2.SS2.p1.5.m5.1.1.2.cmml">=</mo><mrow id="S2.SS2.p1.5.m5.1.1.1" xref="S2.SS2.p1.5.m5.1.1.1.cmml"><msub id="S2.SS2.p1.5.m5.1.1.1.3" xref="S2.SS2.p1.5.m5.1.1.1.3.cmml"><mi id="S2.SS2.p1.5.m5.1.1.1.3.2" xref="S2.SS2.p1.5.m5.1.1.1.3.2.cmml">F</mi><mn id="S2.SS2.p1.5.m5.1.1.1.3.3" xref="S2.SS2.p1.5.m5.1.1.1.3.3.cmml">0</mn></msub><mo id="S2.SS2.p1.5.m5.1.1.1.2" xref="S2.SS2.p1.5.m5.1.1.1.2.cmml">/</mo><mrow id="S2.SS2.p1.5.m5.1.1.1.1.1" xref="S2.SS2.p1.5.m5.1.1.1.1.1.1.cmml"><mo stretchy="false" id="S2.SS2.p1.5.m5.1.1.1.1.1.2" xref="S2.SS2.p1.5.m5.1.1.1.1.1.1.cmml">(</mo><mrow id="S2.SS2.p1.5.m5.1.1.1.1.1.1" xref="S2.SS2.p1.5.m5.1.1.1.1.1.1.cmml"><mn id="S2.SS2.p1.5.m5.1.1.1.1.1.1.2" xref="S2.SS2.p1.5.m5.1.1.1.1.1.1.2.cmml">6</mn><mo id="S2.SS2.p1.5.m5.1.1.1.1.1.1.1" xref="S2.SS2.p1.5.m5.1.1.1.1.1.1.1.cmml">⁢</mo><mi id="S2.SS2.p1.5.m5.1.1.1.1.1.1.3" xref="S2.SS2.p1.5.m5.1.1.1.1.1.1.3.cmml">π</mi><mo id="S2.SS2.p1.5.m5.1.1.1.1.1.1.1a" xref="S2.SS2.p1.5.m5.1.1.1.1.1.1.1.cmml">⁢</mo><msub id="S2.SS2.p1.5.m5.1.1.1.1.1.1.4" xref="S2.SS2.p1.5.m5.1.1.1.1.1.1.4.cmml"><mi id="S2.SS2.p1.5.m5.1.1.1.1.1.1.4.2" xref="S2.SS2.p1.5.m5.1.1.1.1.1.1.4.2.cmml">η</mi><mn id="S2.SS2.p1.5.m5.1.1.1.1.1.1.4.3" xref="S2.SS2.p1.5.m5.1.1.1.1.1.1.4.3.cmml">0</mn></msub><mo id="S2.SS2.p1.5.m5.1.1.1.1.1.1.1b" xref="S2.SS2.p1.5.m5.1.1.1.1.1.1.1.cmml">⁢</mo><msup id="S2.SS2.p1.5.m5.1.1.1.1.1.1.5" xref="S2.SS2.p1.5.m5.1.1.1.1.1.1.5.cmml"><mi id="S2.SS2.p1.5.m5.1.1.1.1.1.1.5.2" xref="S2.SS2.p1.5.m5.1.1.1.1.1.1.5.2.cmml">a</mi><mn id="S2.SS2.p1.5.m5.1.1.1.1.1.1.5.3" xref="S2.SS2.p1.5.m5.1.1.1.1.1.1.5.3.cmml">2</mn></msup></mrow><mo stretchy="false" id="S2.SS2.p1.5.m5.1.1.1.1.1.3" xref="S2.SS2.p1.5.m5.1.1.1.1.1.1.cmml">)</mo></mrow></mrow></mrow></math>, <math><mrow id="S2.SS2.p1.6.m6.1.1" xref="S2.SS2.p1.6.m6.1.1.cmml"><msub id="S2.SS2.p1.6.m6.1.1.2" xref="S2.SS2.p1.6.m6.1.1.2.cmml"><mi id="S2.SS2.p1.6.m6.1.1.2.2" xref="S2.SS2.p1.6.m6.1.1.2.2.cmml">η</mi><mi id="S2.SS2.p1.6.m6.1.1.2.3" xref="S2.SS2.p1.6.m6.1.1.2.3.cmml">r</mi></msub><mo id="S2.SS2.p1.6.m6.1.1.1" xref="S2.SS2.p1.6.m6.1.1.1.cmml">=</mo><mrow id="S2.SS2.p1.6.m6.1.1.3" xref="S2.SS2.p1.6.m6.1.1.3.cmml"><mi id="S2.SS2.p1.6.m6.1.1.3.2" xref="S2.SS2.p1.6.m6.1.1.3.2.cmml">η</mi><mo id="S2.SS2.p1.6.m6.1.1.3.1" xref="S2.SS2.p1.6.m6.1.1.3.1.cmml">/</mo><msub id="S2.SS2.p1.6.m6.1.1.3.3" xref="S2.SS2.p1.6.m6.1.1.3.3.cmml"><mi id="S2.SS2.p1.6.m6.1.1.3.3.2" xref="S2.SS2.p1.6.m6.1.1.3.3.2.cmml">η</mi><mn id="S2.SS2.p1.6.m6.1.1.3.3.3" xref="S2.SS2.p1.6.m6.1.1.3.3.3.cmml">0</mn></msub></mrow></mrow></math>, <math><mrow id="S2.E4.m1.2.3" xref="S2.E4.m1.2.3.cmml"><msub id="S2.E4.m1.2.3.2" xref="S2.E4.m1.2.3.2.cmml"><mi id="S2.E4.m1.2.3.2.2" xref="S2.E4.m1.2.3.2.2.cmml">𝐀</mi><mrow id="S2.E4.m1.2.3.2.3" xref="S2.E4.m1.2.3.2.3.cmml"><mi id="S2.E4.m1.2.3.2.3.2" xref="S2.E4.m1.2.3.2.3.2.cmml">a</mi><mo id="S2.E4.m1.2.3.2.3.1" xref="S2.E4.m1.2.3.2.3.1.cmml">⁢</mo><mi id="S2.E4.m1.2.3.2.3.3" xref="S2.E4.m1.2.3.2.3.3.cmml">b</mi></mrow></msub><mo id="S2.E4.m1.2.3.1" xref="S2.E4.m1.2.3.1.cmml">=</mo><mrow id="S2.E4.m1.2.3.3.2" xref="S2.E4.m1.2.3.3.1.cmml"><mo id="S2.E4.m1.2.3.3.2.1" xref="S2.E4.m1.2.3.3.1.cmml">{</mo><mtable displaystyle="true" rowspacing="0pt" id="S2.E4.m1.2.2" xref="S2.E4.m1.2.2.cmml"><mtr id="S2.E4.m1.2.2a" xref="S2.E4.m1.2.2.cmml"><mtd columnalign="center" id="S2.E4.m1.2.2b" xref="S2.E4.m1.2.2.cmml"><mn id="S2.E4.m1.2.2.3.1.1" xref="S2.E4.m1.2.2.3.1.1.cmml">0</mn></mtd></mtr><mtr id="S2.E4.m1.2.2c" xref="S2.E4.m1.2.2.cmml"><mtd columnalign="center" id="S2.E4.m1.2.2d" xref="S2.E4.m1.2.2.cmml"><mrow id="S2.E4.m1.2.2.2.2.2.2" xref="S2.E4.m1.2.2.2.2.2.3.cmml"><mn id="S2.E4.m1.1.1.1.1.1.1" xref="S2.E4.m1.1.1.1.1.1.1.cmml">1</mn><mo id="S2.E4.m1.2.2.2.2.2.2.2" xref="S2.E4.m1.2.2.2.2.2.3.cmml">,</mo><mrow id="S2.E4.m1.2.2.2.2.2.2.1" xref="S2.E4.m1.2.2.2.2.2.2.1.cmml"><mtext id="S2.E4.m1.2.2.2.2.2.2.1.2" xref="S2.E4.m1.2.2.2.2.2.2.1.2a.cmml">if </mtext><mo id="S2.E4.m1.2.2.2.2.2.2.1.1" xref="S2.E4.m1.2.2.2.2.2.2.1.1.cmml">⁢</mo><msub id="S2.E4.m1.2.2.2.2.2.2.1.3" xref="S2.E4.m1.2.2.2.2.2.2.1.3.cmml"><mi id="S2.E4.m1.2.2.2.2.2.2.1.3.2" xref="S2.E4.m1.2.2.2.2.2.2.1.3.2.cmml">α</mi><mrow id="S2.E4.m1.2.2.2.2.2.2.1.3.3" xref="S2.E4.m1.2.2.2.2.2.2.1.3.3.cmml"><mi id="S2.E4.m1.2.2.2.2.2.2.1.3.3.2" xref="S2.E4.m1.2.2.2.2.2.2.1.3.3.2.cmml">a</mi><mo id="S2.E4.m1.2.2.2.2.2.2.1.3.3.1" xref="S2.E4.m1.2.2.2.2.2.2.1.3.3.1.cmml">⁢</mo><mi id="S2.E4.m1.2.2.2.2.2.2.1.3.3.3" xref="S2.E4.m1.2.2.2.2.2.2.1.3.3.3.cmml">b</mi></mrow></msub><mo id="S2.E4.m1.2.2.2.2.2.2.1.1a" xref="S2.E4.m1.2.2.2.2.2.2.1.1.cmml">⁢</mo><mtext id="S2.E4.m1.2.2.2.2.2.2.1.4" xref="S2.E4.m1.2.2.2.2.2.2.1.4a.cmml"> is satisfied</mtext></mrow></mrow></mtd></mtr></mtable><mo id="S2.E4.m1.2.3.3.2.2" xref="S2.E4.m1.2.3.3.1.cmml">}</mo></mrow></mrow></math>, <math><mrow id="S2.SS3.p3.1.m1.1.1" xref="S2.SS3.p3.1.m1.1.1.cmml"><msub id="S2.SS3.p3.1.m1.1.1.2" xref="S2.SS3.p3.1.m1.1.1.2.cmml"><mi id="S2.SS3.p3.1.m1.1.1.2.2" xref="S2.SS3.p3.1.m1.1.1.2.2.cmml">r</mi><mrow id="S2.SS3.p3.1.m1.1.1.2.3" xref="S2.SS3.p3.1.m1.1.1.2.3.cmml"><mi id="S2.SS3.p3.1.m1.1.1.2.3.2" xref="S2.SS3.p3.1.m1.1.1.2.3.2.cmml">s</mi><mo id="S2.SS3.p3.1.m1.1.1.2.3.1" xref="S2.SS3.p3.1.m1.1.1.2.3.1.cmml">⁢</mo><mi id="S2.SS3.p3.1.m1.1.1.2.3.3" xref="S2.SS3.p3.1.m1.1.1.2.3.3.cmml">m</mi><mo id="S2.SS3.p3.1.m1.1.1.2.3.1a" xref="S2.SS3.p3.1.m1.1.1.2.3.1.cmml">⁢</mo><mi id="S2.SS3.p3.1.m1.1.1.2.3.4" xref="S2.SS3.p3.1.m1.1.1.2.3.4.cmml">a</mi><mo id="S2.SS3.p3.1.m1.1.1.2.3.1b" xref="S2.SS3.p3.1.m1.1.1.2.3.1.cmml">⁢</mo><mi id="S2.SS3.p3.1.m1.1.1.2.3.5" xref="S2.SS3.p3.1.m1.1.1.2.3.5.cmml">l</mi><mo id="S2.SS3.p3.1.m1.1.1.2.3.1c" xref="S2.SS3.p3.1.m1.1.1.2.3.1.cmml">⁢</mo><mi id="S2.SS3.p3.1.m1.1.1.2.3.6" xref="S2.SS3.p3.1.m1.1.1.2.3.6.cmml">l</mi></mrow></msub><mo id="S2.SS3.p3.1.m1.1.1.1" xref="S2.SS3.p3.1.m1.1.1.1.cmml">/</mo><msub id="S2.SS3.p3.1.m1.1.1.3" xref="S2.SS3.p3.1.m1.1.1.3.cmml"><mi id="S2.SS3.p3.1.m1.1.1.3.2" xref="S2.SS3.p3.1.m1.1.1.3.2.cmml">r</mi><mrow id="S2.SS3.p3.1.m1.1.1.3.3" xref="S2.SS3.p3.1.m1.1.1.3.3.cmml"><mi id="S2.SS3.p3.1.m1.1.1.3.3.2" xref="S2.SS3.p3.1.m1.1.1.3.3.2.cmml">l</mi><mo id="S2.SS3.p3.1.m1.1.1.3.3.1" xref="S2.SS3.p3.1.m1.1.1.3.3.1.cmml">⁢</mo><mi id="S2.SS3.p3.1.m1.1.1.3.3.3" xref="S2.SS3.p3.1.m1.1.1.3.3.3.cmml">a</mi><mo id="S2.SS3.p3.1.m1.1.1.3.3.1a" xref="S2.SS3.p3.1.m1.1.1.3.3.1.cmml">⁢</mo><mi id="S2.SS3.p3.1.m1.1.1.3.3.4" xref="S2.SS3.p3.1.m1.1.1.3.3.4.cmml">r</mi><mo id="S2.SS3.p3.1.m1.1.1.3.3.1b" xref="S2.SS3.p3.1.m1.1.1.3.3.1.cmml">⁢</mo><mi id="S2.SS3.p3.1.m1.1.1.3.3.5" xref="S2.SS3.p3.1.m1.1.1.3.3.5.cmml">g</mi><mo id="S2.SS3.p3.1.m1.1.1.3.3.1c" xref="S2.SS3.p3.1.m1.1.1.3.3.1.cmml">⁢</mo><mi id="S2.SS3.p3.1.m1.1.1.3.3.6" xref="S2.SS3.p3.1.m1.1.1.3.3.6.cmml">e</mi></mrow></msub></mrow></math>, <math><mrow id="S2.SS3.p3.2.m2.1.1" xref="S2.SS3.p3.2.m2.1.1.cmml"><mrow id="S2.SS3.p3.2.m2.1.1.2" xref="S2.SS3.p3.2.m2.1.1.2.cmml"><msub id="S2.SS3.p3.2.m2.1.1.2.2" xref="S2.SS3.p3.2.m2.1.1.2.2.cmml"><mi id="S2.SS3.p3.2.m2.1.1.2.2.2" xref="S2.SS3.p3.2.m2.1.1.2.2.2.cmml">r</mi><mrow id="S2.SS3.p3.2.m2.1.1.2.2.3" xref="S2.SS3.p3.2.m2.1.1.2.2.3.cmml"><mi id="S2.SS3.p3.2.m2.1.1.2.2.3.2" xref="S2.SS3.p3.2.m2.1.1.2.2.3.2.cmml">s</mi><mo id="S2.SS3.p3.2.m2.1.1.2.2.3.1" xref="S2.SS3.p3.2.m2.1.1.2.2.3.1.cmml">⁢</mo><mi id="S2.SS3.p3.2.m2.1.1.2.2.3.3" xref="S2.SS3.p3.2.m2.1.1.2.2.3.3.cmml">m</mi><mo id="S2.SS3.p3.2.m2.1.1.2.2.3.1a" xref="S2.SS3.p3.2.m2.1.1.2.2.3.1.cmml">⁢</mo><mi id="S2.SS3.p3.2.m2.1.1.2.2.3.4" xref="S2.SS3.p3.2.m2.1.1.2.2.3.4.cmml">a</mi><mo id="S2.SS3.p3.2.m2.1.1.2.2.3.1b" xref="S2.SS3.p3.2.m2.1.1.2.2.3.1.cmml">⁢</mo><mi id="S2.SS3.p3.2.m2.1.1.2.2.3.5" xref="S2.SS3.p3.2.m2.1.1.2.2.3.5.cmml">l</mi><mo id="S2.SS3.p3.2.m2.1.1.2.2.3.1c" xref="S2.SS3.p3.2.m2.1.1.2.2.3.1.cmml">⁢</mo><mi id="S2.SS3.p3.2.m2.1.1.2.2.3.6" xref="S2.SS3.p3.2.m2.1.1.2.2.3.6.cmml">l</mi></mrow></msub><mo id="S2.SS3.p3.2.m2.1.1.2.1" xref="S2.SS3.p3.2.m2.1.1.2.1.cmml">/</mo><msub id="S2.SS3.p3.2.m2.1.1.2.3" xref="S2.SS3.p3.2.m2.1.1.2.3.cmml"><mi id="S2.SS3.p3.2.m2.1.1.2.3.2" xref="S2.SS3.p3.2.m2.1.1.2.3.2.cmml">r</mi><mrow id="S2.SS3.p3.2.m2.1.1.2.3.3" xref="S2.SS3.p3.2.m2.1.1.2.3.3.cmml"><mi id="S2.SS3.p3.2.m2.1.1.2.3.3.2" xref="S2.SS3.p3.2.m2.1.1.2.3.3.2.cmml">l</mi><mo id="S2.SS3.p3.2.m2.1.1.2.3.3.1" xref="S2.SS3.p3.2.m2.1.1.2.3.3.1.cmml">⁢</mo><mi id="S2.SS3.p3.2.m2.1.1.2.3.3.3" xref="S2.SS3.p3.2.m2.1.1.2.3.3.3.cmml">a</mi><mo id="S2.SS3.p3.2.m2.1.1.2.3.3.1a" xref="S2.SS3.p3.2.m2.1.1.2.3.3.1.cmml">⁢</mo><mi id="S2.SS3.p3.2.m2.1.1.2.3.3.4" xref="S2.SS3.p3.2.m2.1.1.2.3.3.4.cmml">r</mi><mo id="S2.SS3.p3.2.m2.1.1.2.3.3.1b" xref="S2.SS3.p3.2.m2.1.1.2.3.3.1.cmml">⁢</mo><mi id="S2.SS3.p3.2.m2.1.1.2.3.3.5" xref="S2.SS3.p3.2.m2.1.1.2.3.3.5.cmml">g</mi><mo id="S2.SS3.p3.2.m2.1.1.2.3.3.1c" xref="S2.SS3.p3.2.m2.1.1.2.3.3.1.cmml">⁢</mo><mi id="S2.SS3.p3.2.m2.1.1.2.3.3.6" xref="S2.SS3.p3.2.m2.1.1.2.3.3.6.cmml">e</mi></mrow></msub></mrow><mo id="S2.SS3.p3.2.m2.1.1.1" xref="S2.SS3.p3.2.m2.1.1.1.cmml">></mo><mrow id="S2.SS3.p3.2.m2.1.1.3" xref="S2.SS3.p3.2.m2.1.1.3.cmml"><msqrt id="S2.SS3.p3.2.m2.1.1.3.2" xref="S2.SS3.p3.2.m2.1.1.3.2.cmml"><mn id="S2.SS3.p3.2.m2.1.1.3.2.2" xref="S2.SS3.p3.2.m2.1.1.3.2.2.cmml">2</mn></msqrt><mo id="S2.SS3.p3.2.m2.1.1.3.1" xref="S2.SS3.p3.2.m2.1.1.3.1.cmml">-</mo><mn id="S2.SS3.p3.2.m2.1.1.3.3" xref="S2.SS3.p3.2.m2.1.1.3.3.cmml">1</mn></mrow></mrow></math>

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1805.01031

Formulas:

1-

A \in ℝ^{n \times n}

2-

{\dot{𝒙}}_{i} = 𝒇 (𝒙_{i}) + \sum_{j = 1}^{n} A_{i j} 𝒈 (𝒙_{i}, 𝒙_{j}), i = 1, 2, \dots, n

3-

𝒇 (𝒙_{i})

4-

𝒈 (𝒙_{i}, 𝒙_{j})

5-

Q = \frac{1}{2 n_{e}} \sum_{i j} [A_{i j} - \frac{s_{i}^{in} s_{j}^{out}}{2 n_{e}}] δ (c_{i}, c_{j}),

6-

s_{i}^{in} = \sum_{j = 1}^{n} A_{i j}

7-

s_{j}^{out} = \sum_{i = 1}^{n} A_{i j}

8-

δ (i, j)

9-

l = 1, 2, \dots, m

10-

{𝒙_{i}}_{i = 1}^{n}

Formulas (html):

Correct Categorie: physics

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0404294

Formulas:

1-

n_{H_{2}} > 5 \times 10^{5}

2-

\sim 0.5 - 1.5 M_{⊙}

3-

5.8 ″ \times 4.0 ″

4-

Δ F_{1} = \pm 1

5-

n_{𝗛_{2}} > 10^{5}

6-

L_{b o l} \sim 0.15 L_{⊙}

7-

r_{θ} < 20 ″

8-

τ_{101 - 012} < 1.7

9-

r_{θ} < 20 ″

10-

r_{θ} \sim 20 ″

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/0810.5307

Formulas:

1-

W_{micro}^{tree} = m_{a b} {\tilde{Q}}_{a}^{i} Q_{i}^{b} .

2-

S U (N_{f})

3-

m_{a b} = m 𝟏_{a b} .

4-

b_{0}^{micro} = 3 N_{c} - N_{f} > 0

5-

N_{c} + 1 \leq N_{f} < \frac{3}{2} N_{c}

6-

S U (N_{c})

7-

S U (N)

8-

c = 1, \dots, N

9-

i = 1, \dots, N_{f} .

10-

N = N_{f} - N_{c} .

Formulas (html):

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id="S2.p2.9.m9.3.3.1.1.3" xref="S2.p2.9.m9.3.3.1.1.3.cmml">i</mi><mo id="S2.p2.9.m9.3.3.1.1.2" xref="S2.p2.9.m9.3.3.1.1.2.cmml">=</mo><mrow id="S2.p2.9.m9.3.3.1.1.1.1" xref="S2.p2.9.m9.3.3.1.1.1.2.cmml"><mn id="S2.p2.9.m9.1.1" xref="S2.p2.9.m9.1.1.cmml">1</mn><mo id="S2.p2.9.m9.3.3.1.1.1.1.2" xref="S2.p2.9.m9.3.3.1.1.1.2.cmml">,</mo><mi mathvariant="normal" id="S2.p2.9.m9.2.2" xref="S2.p2.9.m9.2.2.cmml">…</mi><mo id="S2.p2.9.m9.3.3.1.1.1.1.3" xref="S2.p2.9.m9.3.3.1.1.1.2.cmml">,</mo><msub id="S2.p2.9.m9.3.3.1.1.1.1.1" xref="S2.p2.9.m9.3.3.1.1.1.1.1.cmml"><mi id="S2.p2.9.m9.3.3.1.1.1.1.1.2" xref="S2.p2.9.m9.3.3.1.1.1.1.1.2.cmml">N</mi><mtext id="S2.p2.9.m9.3.3.1.1.1.1.1.3" xref="S2.p2.9.m9.3.3.1.1.1.1.1.3a.cmml">f</mtext></msub></mrow></mrow><mo id="S2.p2.9.m9.3.3.1.2" xref="S2.p2.9.m9.3.3.1.1.cmml">.</mo></mrow></math>, <math><mrow id="S2.E4.m1.1.1.1" xref="S2.E4.m1.1.1.1.1.cmml"><mrow id="S2.E4.m1.1.1.1.1" xref="S2.E4.m1.1.1.1.1.cmml"><mi id="S2.E4.m1.1.1.1.1.2" xref="S2.E4.m1.1.1.1.1.2.cmml">N</mi><mo id="S2.E4.m1.1.1.1.1.1" xref="S2.E4.m1.1.1.1.1.1.cmml">=</mo><mrow id="S2.E4.m1.1.1.1.1.3" xref="S2.E4.m1.1.1.1.1.3.cmml"><msub id="S2.E4.m1.1.1.1.1.3.2" xref="S2.E4.m1.1.1.1.1.3.2.cmml"><mi id="S2.E4.m1.1.1.1.1.3.2.2" xref="S2.E4.m1.1.1.1.1.3.2.2.cmml">N</mi><mtext id="S2.E4.m1.1.1.1.1.3.2.3" xref="S2.E4.m1.1.1.1.1.3.2.3a.cmml">f</mtext></msub><mo id="S2.E4.m1.1.1.1.1.3.1" xref="S2.E4.m1.1.1.1.1.3.1.cmml">-</mo><msub id="S2.E4.m1.1.1.1.1.3.3" xref="S2.E4.m1.1.1.1.1.3.3.cmml"><mi id="S2.E4.m1.1.1.1.1.3.3.2" xref="S2.E4.m1.1.1.1.1.3.3.2.cmml">N</mi><mtext id="S2.E4.m1.1.1.1.1.3.3.3" xref="S2.E4.m1.1.1.1.1.3.3.3a.cmml">c</mtext></msub></mrow></mrow><mo id="S2.E4.m1.1.1.1.2" xref="S2.E4.m1.1.1.1.1.cmml">.</mo></mrow></math>

Correct Categorie: hep-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1001.5324

Formulas:

1-

F △ x = T △ S,

2-

△ S = 2 π k_{B} \frac{m c}{ℏ} △ x,

3-

F = 2 π k_{B} T \frac{m c}{ℏ},

4-

N = \frac{A c^{3}}{G ℏ}, M c^{2} = \frac{1}{2} N k_{B} T,

5-

F = G \frac{M m}{R^{2}} .

6-

N = \frac{A c^{3}}{G ℏ} .

7-

a_{r} = - \ddot{a} r

8-

𝒯 = \frac{1}{2 π k_{B} c} ℏ a_{r} .

9-

E = \frac{1}{2} N k_{B} 𝒯 .

10-

E = ℳ c^{2} .

Formulas (html):

Correct Categorie: hep-th

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/0901.2536

Formulas:

1-

10^{7} - 10^{9} M_{⊙}

2-

M_{cl} \sim 10^{7} - 10^{9} M_{⊙}

3-

100 - 200 M_{⊙} {yr}^{- 1}

4-

M ≲ 10^{11.6} M_{⊙}

5-

T \sim 10^{4} K

6-

Z = 10^{- 3} Z_{⊙}

7-

m_{p} = 2.2 \times 10^{5} M_{⊙}

8-

Δ x \sim 40 pc

9-

M_{vir} = 2 \times 10^{12} M_{⊙}

10-

n_{H} = 4 {cm}^{- 3}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1601.07330

Formulas:

1-

m_{γ γ} \sim 750 GeV

2-

\begin{matrix} ℒ (𝜽) & = \prod_{i = 1}^{n_{bins}} \frac{{(N_{e}^{i})}^{N_{o}^{i}}}{N_{o}^{i}!} \exp (- N_{e}^{i}), \end{matrix}

3-

N_{e}^{i} = N_{e}^{i} (𝜽)

4-

m_{γ γ} \in [150, 1750] GeV

5-

f_{k} (x)

6-

= 𝒩 {(1 - x^{1 / 3})}^{b} x^{\sum_{j = 0}^{k} a_{j} {(\log x)}^{j}}

7-

x = m_{γ γ} / \sqrt{s}

8-

k = 0, 1, 2

9-

m_{γ γ} \sim 750 GeV

10-

m_{γ γ} = m_{B}

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/9906367

Formulas:

1-

f (t^{'})

2-

J (t) = \int_{0}^{t} M (t - t^{'}) f (t^{'}) d t^{'} .

3-

M (t - t^{'})

4-

M (t - t^{'}) = γ δ (t - t^{'}),

5-

δ (t - t^{'})

6-

J (t) = γ f (t),

7-

f (t^{'})

8-

M (t - t^{'}) = γ / t .

9-

\int_{0}^{t} M (t - t^{'}) d t^{'} = γ .

10-

f (t) = \int_{- i \infty}^{+ i \infty} f (λ) e^{- λ t} \frac{d λ}{2 π i}, f (λ) = \int_{0}^{\infty} f (t) e^{λ t} d t,

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1912.05706

Formulas:

1-

ρ_{s} = 2.8 \times 10^{14}

2-

1 \overset{'}{.} 5

3-

\dot{P} \equiv d P / d t = 1.37 \times 10^{- 20}

4-

B \approx 3 \times 10^{8}

5-

\dot{E} \approx 3.8 \times 10^{33}

6-

k T_{BB} \sim 30

7-

\dot{P} = 1.02 \times 10^{- 20}

8-

B \approx 2.7 \times 10^{8}

9-

\dot{E} \approx 3 \times 10^{33}

10-

D = 410 {}^{+ 90}_{- 70}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/0910.3090

Formulas:

1-

2 ν β β

2-

2 ν β β

3-

2 ν β β

4-

0 ν β β

5-

2 ν β β

6-

0 ν β β

7-

M_{e x p}^{2 ν}

8-

2 ν β β

9-

M_{G T}^{2 ν}

10-

2 ν β β

Formulas (html):

Correct Categorie: nucl-th

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/2008.10397

Formulas:

1-

0 \leq s \leq 2 .

2-

ρ (t, r) = t^{- 3} {(r / t g)}^{- n}

3-

ρ (r) = q r^{- s}

4-

R_{c} = {(\frac{A g^{n}}{q})}^{\frac{1}{n - s}} t^{\frac{n - 3}{n - s}}

5-

λ = (n - s) / (n - 3)

6-

\begin{matrix} \frac{\partial u}{\partial t} + u \frac{\partial u}{\partial r} & = - \frac{1}{ρ} \frac{\partial p}{\partial r} \\ \frac{\partial ρ}{\partial t} + \frac{1}{r^{2}} \frac{\partial (r^{2} ρ u)}{\partial r} & = 0 \\ \frac{\partial p}{\partial t} + u \frac{\partial p}{\partial r} & = γ \frac{p}{ρ} \frac{d ρ}{d t} \end{matrix}

7-

\begin{matrix} η & = t^{- 1} r^{λ} \\ p & = t^{n - 5} r^{2 - n} P (η) \\ u & = \frac{r}{t} U (η) \\ ρ & = t^{n - 3} r^{- n} Ω (η) \\ C^{2} (η) & = \frac{γ P (η)}{Ω (η)} \end{matrix}

8-

\begin{matrix} U^{2} - U + (λ U - 1) η \frac{d U}{d η} & = - \frac{(2 - n)}{γ} C^{2} - \frac{λ η}{γ} \frac{C^{2}}{P} \frac{d P}{d η} \\ (n - 3) (1 - U) + η (λ U - 1) (\frac{1}{P} \frac{d P}{d η} - \frac{2}{C} \frac{d C}{d η}) + λ η \frac{d U}{d η} & = 0 \\ P [(n - 5) - γ (n - 3) - U (n - 2 - n γ)] + \frac{d P}{d η} η (λ U - 1) (1 - γ) & = - \frac{2 η γ (λ U - 1)}{C} P \frac{d C}{d η} \end{matrix}

9-

\begin{matrix} U_{2} & = \frac{1}{4} (\frac{3}{λ} + 1) \\ P_{2} & = \frac{3}{4} g^{n} {(1 - \frac{1}{λ})}^{2} \\ C_{2} & = \frac{\sqrt{3 γ}}{4} (1 - \frac{1}{λ}) . \end{matrix}

10-

U_{c} = λ^{- 1}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/0809.0310

Formulas:

1-

𝑩 = \bar{𝑩} + 𝒃

2-

𝑼 = \bar{𝑼} + 𝒖

3-

\bar{𝒃} = \bar{𝒖} = 0

4-

\frac{\partial \bar{𝑩}}{\partial t} = \nabla \times (\bar{𝑼} \times \bar{𝑩} + \bar{𝓔} - η \nabla \times \bar{𝑩}), \nabla \cdot \bar{𝑩} = 0 .

5-

\bar{𝓔} = \bar{𝒖 \times 𝒃}

6-

\bar{𝓔} \equiv \bar{𝒖 \times 𝒃} = α \bar{𝑩} - η_{t} \bar{𝑱}

7-

\bar{𝑱} = \nabla \times \bar{𝑩} / μ_{0}

8-

α = α_{k} = - \frac{1}{3} τ \bar{𝒖 \cdot \nabla \times 𝒖}

9-

η_{t} = \frac{1}{3} τ \bar{𝒖^{2}}

10-

α = α_{k} = \bar{α} (z) + α_{1} (z, t)

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

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

Formulas:

1-

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

2-

V_{d r i f t} ≃

3-

μ m / n s

4-

x = c o n s t

5-

V_{d r i f t}

6-

m m / μ s

7-

∣ \cos θ ∣ <

8-

σ_{v t x} =

9-

\pm V_{d r i f t} \times Δ t

10-

\pm V_{d r i f t} \times Δ t

Formulas (html):

Correct Categorie: hep-ex

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1309.5924

Formulas:

1-

σ_{\max} = σ (X_{\max})

2-

X_{\max} = X_{\max} (A)

3-

⟨ X_{\max} ∣ A ⟩ = C + D Log (\frac{E}{E_{0} A}) .

4-

D = \frac{d ⟨ x_{\max} ⟩}{dLog E}

5-

⟨ x_{\max} ⟩ = ⟨ X_{\max} ∣ A = 1 ⟩

6-

C = ⟨ x_{\max} ⟩ (E_{0})

7-

σ^{2} (X_{\max} ∣ A) = σ_{fr}^{2} + σ_{sh}^{2},

8-

σ_{fr}^{2} = σ_{fr}^{2} (A, E)

9-

σ_{sh}^{2} = σ_{sh}^{2} (A, E)

10-

⟨ X_{\max} ⟩ = ⟨ ⟨ X_{\max} ∣ A ⟩ ⟩ = ⟨ x_{\max} ⟩ - d ⟨ \ln A ⟩,

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/0710.0944

Formulas:

1-

N_{c} < N_{f} < \frac{2}{3} N_{c}

2-

N_{c} + 1 \leq N_{f} < \frac{3}{2} N_{c}

3-

W = {(m_{Q})}_{i j} Q_{i} {\bar{Q}}_{j}

4-

{(m_{Q})}_{i j}

5-

N_{f} = N_{c} + 1

6-

N_{f} = N_{c} + 1

7-

g_{M^{†} M}^{- 1} \sim α \frac{Tr (M^{†} M)}{Λ^{2}} + β \frac{Tr M Tr M^{†}}{Λ^{2}} + γ \frac{{(B_{+} + B_{+}^{†})}^{2}}{Λ^{2}} + \dots

8-

Im (B_{+})

9-

Re (B_{+})

10-

U {(1)}_{A}

Formulas (html):

Correct Categorie: hep-th

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/9810024

Formulas:

1-

{< Q >}_{T} = \frac{\sum_{E} {< Q >}_{E} g (E) \exp (- E / k_{B} T)}{\sum_{E} g (E) \exp (- E / k_{B} T)},

2-

\exp (- E / k_{B} T)

3-

X_{o l d}

4-

X_{n e w}

5-

X_{o l d} \to X_{n e w} ⟺ X_{n e w} \to X_{o l d}

6-

Δ E_{f i x}

7-

N_{u p} (X)

8-

N_{d n} (X)

9-

Δ E_{f i x}

10-

< N_{u p} (E) >

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/0704.1322

Formulas:

1-

d a v i d_p a l a t n i k @ y a h o o . c o m

2-

m = \int 𝑑 V \sqrt{γ} μ,

3-

d m = d V \frac{μ_{*}}{\sqrt{1 - \frac{v^{2}}{c^{2}}}};

4-

d V μ_{*} \frac{c d t}{d s}

5-

d Ω \frac{μ_{*}}{d s}

6-

d Ω \sqrt{- g} \frac{μ_{*}}{d s},

7-

d Ω = c d t d V

8-

d s^{2} = g_{a b} d x^{a} d x^{b}

9-

g_{00} = 1 + \frac{2 ϕ (x)}{c^{2}}

10-

d Ω \sqrt{- g} \frac{μ_{*}}{\sqrt{g_{00}} c d t}

Formulas (html):

Correct Categorie: physics

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1804.10294

Formulas:

1-

2.7 \pm 0.5 (s t a t) \pm 0.5 (s y s t) \times 10^{- 37} {cm}^{2} / Ar

2-

8.4 \pm 0.9 {(s t a t)}_{- 0.8}^{+ 1.0} (s y s t) \times 10^{- 38} {cm}^{2} / Ar

3-

d E / d x

4-

d E / d x

5-

\frac{d σ}{d X} = \frac{N - N_{b}}{Δ X N_{A r} Φ ϵ_{UF}},

6-

d σ / d p_{μ}

7-

d σ / d θ_{μ}

8-

d σ / d θ_{π}

9-

d σ / d θ_{μ π}

10-

d σ / d p_{μ}

Formulas (html):

Correct Categorie: hep-ex

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1109.2625

Formulas:

1-

R_{d p} \sim 60

2-

R_{d p} ≳ 12

3-

R_{d p} \sim 18

4-

μ_{V} \sim 29 mag {arcsec}^{- 2}

5-

R_{d p} \sim 40

6-

μ_{V} \sim 32 mag {arcsec}^{- 2}

7-

R_{d p} \sim 20 - 30

8-

R_{d p} = 44

9-

\sim 10^{11} M_{☉}

10-

\sim 135 km s^{- 1}

Formulas (html):

<math><mrow id="id12.1.m1.1.1" xref="id12.1.m1.1.1.cmml"><msub id="id12.1.m1.1.1.2" xref="id12.1.m1.1.1.2.cmml"><mi id="id12.1.m1.1.1.2.2" xref="id12.1.m1.1.1.2.2.cmml">R</mi><mrow id="id12.1.m1.1.1.2.3" xref="id12.1.m1.1.1.2.3.cmml"><mi id="id12.1.m1.1.1.2.3.2" xref="id12.1.m1.1.1.2.3.2.cmml">d</mi><mo id="id12.1.m1.1.1.2.3.1" xref="id12.1.m1.1.1.2.3.1.cmml">⁢</mo><mi id="id12.1.m1.1.1.2.3.3" xref="id12.1.m1.1.1.2.3.3.cmml">p</mi></mrow></msub><mo id="id12.1.m1.1.1.1" xref="id12.1.m1.1.1.1.cmml">∼</mo><mn id="id12.1.m1.1.1.3" xref="id12.1.m1.1.1.3.cmml">60</mn></mrow></math>, <math><mrow id="id14.3.m3.1.1" xref="id14.3.m3.1.1.cmml"><msub id="id14.3.m3.1.1.2" xref="id14.3.m3.1.1.2.cmml"><mi id="id14.3.m3.1.1.2.2" xref="id14.3.m3.1.1.2.2.cmml">R</mi><mrow id="id14.3.m3.1.1.2.3" xref="id14.3.m3.1.1.2.3.cmml"><mi id="id14.3.m3.1.1.2.3.2" xref="id14.3.m3.1.1.2.3.2.cmml">d</mi><mo id="id14.3.m3.1.1.2.3.1" xref="id14.3.m3.1.1.2.3.1.cmml">⁢</mo><mi id="id14.3.m3.1.1.2.3.3" xref="id14.3.m3.1.1.2.3.3.cmml">p</mi></mrow></msub><mo id="id14.3.m3.1.1.1" xref="id14.3.m3.1.1.1.cmml">≳</mo><mn id="id14.3.m3.1.1.3" xref="id14.3.m3.1.1.3.cmml">12</mn></mrow></math>, <math><mrow id="id16.5.m5.1.1" xref="id16.5.m5.1.1.cmml"><msub id="id16.5.m5.1.1.2" xref="id16.5.m5.1.1.2.cmml"><mi id="id16.5.m5.1.1.2.2" xref="id16.5.m5.1.1.2.2.cmml">R</mi><mrow id="id16.5.m5.1.1.2.3" xref="id16.5.m5.1.1.2.3.cmml"><mi id="id16.5.m5.1.1.2.3.2" xref="id16.5.m5.1.1.2.3.2.cmml">d</mi><mo id="id16.5.m5.1.1.2.3.1" xref="id16.5.m5.1.1.2.3.1.cmml">⁢</mo><mi id="id16.5.m5.1.1.2.3.3" xref="id16.5.m5.1.1.2.3.3.cmml">p</mi></mrow></msub><mo id="id16.5.m5.1.1.1" xref="id16.5.m5.1.1.1.cmml">∼</mo><mn id="id16.5.m5.1.1.3" xref="id16.5.m5.1.1.3.cmml">18</mn></mrow></math>, <math><mrow id="id18.7.m7.1.1" xref="id18.7.m7.1.1.cmml"><msub id="id18.7.m7.1.1.2" xref="id18.7.m7.1.1.2.cmml"><mi id="id18.7.m7.1.1.2.2" xref="id18.7.m7.1.1.2.2.cmml">μ</mi><mi id="id18.7.m7.1.1.2.3" xref="id18.7.m7.1.1.2.3.cmml">V</mi></msub><mo id="id18.7.m7.1.1.1" xref="id18.7.m7.1.1.1.cmml">∼</mo><mrow id="id18.7.m7.1.1.3" xref="id18.7.m7.1.1.3.cmml"><mpadded width="+5pt" id="id18.7.m7.1.1.3.2" xref="id18.7.m7.1.1.3.2.cmml"><mn id="id18.7.m7.1.1.3.2a" xref="id18.7.m7.1.1.3.2.cmml">29</mn></mpadded><mo id="id18.7.m7.1.1.3.1" xref="id18.7.m7.1.1.3.1.cmml">⁢</mo><mpadded width="+5pt" id="id18.7.m7.1.1.3.3" xref="id18.7.m7.1.1.3.3.cmml"><mi id="id18.7.m7.1.1.3.3a" xref="id18.7.m7.1.1.3.3.cmml">mag</mi></mpadded><mo id="id18.7.m7.1.1.3.1a" xref="id18.7.m7.1.1.3.1.cmml">⁢</mo><msup id="id18.7.m7.1.1.3.4" xref="id18.7.m7.1.1.3.4.cmml"><mi id="id18.7.m7.1.1.3.4.2" xref="id18.7.m7.1.1.3.4.2.cmml">arcsec</mi><mrow id="id18.7.m7.1.1.3.4.3" xref="id18.7.m7.1.1.3.4.3.cmml"><mo id="id18.7.m7.1.1.3.4.3.1" xref="id18.7.m7.1.1.3.4.3.1.cmml">-</mo><mn id="id18.7.m7.1.1.3.4.3.2" xref="id18.7.m7.1.1.3.4.3.2.cmml">2</mn></mrow></msup></mrow></mrow></math>, <math><mrow id="id19.8.m8.1.1" xref="id19.8.m8.1.1.cmml"><msub id="id19.8.m8.1.1.2" xref="id19.8.m8.1.1.2.cmml"><mi id="id19.8.m8.1.1.2.2" xref="id19.8.m8.1.1.2.2.cmml">R</mi><mrow id="id19.8.m8.1.1.2.3" xref="id19.8.m8.1.1.2.3.cmml"><mi id="id19.8.m8.1.1.2.3.2" xref="id19.8.m8.1.1.2.3.2.cmml">d</mi><mo id="id19.8.m8.1.1.2.3.1" xref="id19.8.m8.1.1.2.3.1.cmml">⁢</mo><mi id="id19.8.m8.1.1.2.3.3" xref="id19.8.m8.1.1.2.3.3.cmml">p</mi></mrow></msub><mo id="id19.8.m8.1.1.1" xref="id19.8.m8.1.1.1.cmml">∼</mo><mn id="id19.8.m8.1.1.3" xref="id19.8.m8.1.1.3.cmml">40</mn></mrow></math>, <math><mrow id="id20.9.m9.1.1" xref="id20.9.m9.1.1.cmml"><msub id="id20.9.m9.1.1.2" xref="id20.9.m9.1.1.2.cmml"><mi id="id20.9.m9.1.1.2.2" xref="id20.9.m9.1.1.2.2.cmml">μ</mi><mi id="id20.9.m9.1.1.2.3" xref="id20.9.m9.1.1.2.3.cmml">V</mi></msub><mo id="id20.9.m9.1.1.1" xref="id20.9.m9.1.1.1.cmml">∼</mo><mrow id="id20.9.m9.1.1.3" xref="id20.9.m9.1.1.3.cmml"><mpadded width="+5pt" id="id20.9.m9.1.1.3.2" xref="id20.9.m9.1.1.3.2.cmml"><mn id="id20.9.m9.1.1.3.2a" xref="id20.9.m9.1.1.3.2.cmml">32</mn></mpadded><mo id="id20.9.m9.1.1.3.1" xref="id20.9.m9.1.1.3.1.cmml">⁢</mo><mpadded width="+5pt" id="id20.9.m9.1.1.3.3" xref="id20.9.m9.1.1.3.3.cmml"><mi id="id20.9.m9.1.1.3.3a" xref="id20.9.m9.1.1.3.3.cmml">mag</mi></mpadded><mo id="id20.9.m9.1.1.3.1a" xref="id20.9.m9.1.1.3.1.cmml">⁢</mo><msup id="id20.9.m9.1.1.3.4" xref="id20.9.m9.1.1.3.4.cmml"><mi id="id20.9.m9.1.1.3.4.2" xref="id20.9.m9.1.1.3.4.2.cmml">arcsec</mi><mrow id="id20.9.m9.1.1.3.4.3" xref="id20.9.m9.1.1.3.4.3.cmml"><mo id="id20.9.m9.1.1.3.4.3.1" xref="id20.9.m9.1.1.3.4.3.1.cmml">-</mo><mn id="id20.9.m9.1.1.3.4.3.2" xref="id20.9.m9.1.1.3.4.3.2.cmml">2</mn></mrow></msup></mrow></mrow></math>, <math><mrow id="id22.11.m11.1.1" xref="id22.11.m11.1.1.cmml"><msub id="id22.11.m11.1.1.2" xref="id22.11.m11.1.1.2.cmml"><mi id="id22.11.m11.1.1.2.2" xref="id22.11.m11.1.1.2.2.cmml">R</mi><mrow id="id22.11.m11.1.1.2.3" xref="id22.11.m11.1.1.2.3.cmml"><mi id="id22.11.m11.1.1.2.3.2" xref="id22.11.m11.1.1.2.3.2.cmml">d</mi><mo id="id22.11.m11.1.1.2.3.1" xref="id22.11.m11.1.1.2.3.1.cmml">⁢</mo><mi id="id22.11.m11.1.1.2.3.3" xref="id22.11.m11.1.1.2.3.3.cmml">p</mi></mrow></msub><mo id="id22.11.m11.1.1.1" xref="id22.11.m11.1.1.1.cmml">∼</mo><mrow id="id22.11.m11.1.1.3" xref="id22.11.m11.1.1.3.cmml"><mn id="id22.11.m11.1.1.3.2" xref="id22.11.m11.1.1.3.2.cmml">20</mn><mo id="id22.11.m11.1.1.3.1" xref="id22.11.m11.1.1.3.1.cmml">-</mo><mn id="id22.11.m11.1.1.3.3" xref="id22.11.m11.1.1.3.3.cmml">30</mn></mrow></mrow></math>, <math><mrow id="S1.p4.1.m1.1.1" xref="S1.p4.1.m1.1.1.cmml"><msub id="S1.p4.1.m1.1.1.2" xref="S1.p4.1.m1.1.1.2.cmml"><mi id="S1.p4.1.m1.1.1.2.2" xref="S1.p4.1.m1.1.1.2.2.cmml">R</mi><mrow id="S1.p4.1.m1.1.1.2.3" xref="S1.p4.1.m1.1.1.2.3.cmml"><mi id="S1.p4.1.m1.1.1.2.3.2" xref="S1.p4.1.m1.1.1.2.3.2.cmml">d</mi><mo id="S1.p4.1.m1.1.1.2.3.1" xref="S1.p4.1.m1.1.1.2.3.1.cmml">⁢</mo><mi id="S1.p4.1.m1.1.1.2.3.3" xref="S1.p4.1.m1.1.1.2.3.3.cmml">p</mi></mrow></msub><mo id="S1.p4.1.m1.1.1.1" xref="S1.p4.1.m1.1.1.1.cmml">=</mo><mn id="S1.p4.1.m1.1.1.3" xref="S1.p4.1.m1.1.1.3.cmml">44</mn></mrow></math>, <math><mrow id="S1.p6.1.m1.1.1" xref="S1.p6.1.m1.1.1.cmml"><mi id="S1.p6.1.m1.1.1.2" xref="S1.p6.1.m1.1.1.2.cmml"/><mo id="S1.p6.1.m1.1.1.1" xref="S1.p6.1.m1.1.1.1.cmml">∼</mo><mrow id="S1.p6.1.m1.1.1.3" xref="S1.p6.1.m1.1.1.3.cmml"><msup id="S1.p6.1.m1.1.1.3.2" xref="S1.p6.1.m1.1.1.3.2.cmml"><mn id="S1.p6.1.m1.1.1.3.2.2" xref="S1.p6.1.m1.1.1.3.2.2.cmml">10</mn><mn id="S1.p6.1.m1.1.1.3.2.3" xref="S1.p6.1.m1.1.1.3.2.3.cmml">11</mn></msup><mo id="S1.p6.1.m1.1.1.3.1" xref="S1.p6.1.m1.1.1.3.1.cmml">⁢</mo><msub id="S1.p6.1.m1.1.1.3.3" xref="S1.p6.1.m1.1.1.3.3.cmml"><mi id="S1.p6.1.m1.1.1.3.3.2" xref="S1.p6.1.m1.1.1.3.3.2.cmml">M</mi><mi mathvariant="normal" id="S1.p6.1.m1.1.1.3.3.3" xref="S1.p6.1.m1.1.1.3.3.3.cmml">☉</mi></msub></mrow></mrow></math>, <math><mrow id="S1.p6.2.m2.1.1" xref="S1.p6.2.m2.1.1.cmml"><mi id="S1.p6.2.m2.1.1.2" xref="S1.p6.2.m2.1.1.2.cmml"/><mo id="S1.p6.2.m2.1.1.1" xref="S1.p6.2.m2.1.1.1.cmml">∼</mo><mrow id="S1.p6.2.m2.1.1.3" xref="S1.p6.2.m2.1.1.3.cmml"><mpadded width="+5pt" id="S1.p6.2.m2.1.1.3.2" xref="S1.p6.2.m2.1.1.3.2.cmml"><mn id="S1.p6.2.m2.1.1.3.2a" xref="S1.p6.2.m2.1.1.3.2.cmml">135</mn></mpadded><mo id="S1.p6.2.m2.1.1.3.1" xref="S1.p6.2.m2.1.1.3.1.cmml">⁢</mo><mpadded width="+5pt" id="S1.p6.2.m2.1.1.3.3" xref="S1.p6.2.m2.1.1.3.3.cmml"><mi id="S1.p6.2.m2.1.1.3.3a" xref="S1.p6.2.m2.1.1.3.3.cmml">km</mi></mpadded><mo id="S1.p6.2.m2.1.1.3.1a" xref="S1.p6.2.m2.1.1.3.1.cmml">⁢</mo><msup id="S1.p6.2.m2.1.1.3.4" xref="S1.p6.2.m2.1.1.3.4.cmml"><mi mathvariant="normal" id="S1.p6.2.m2.1.1.3.4.2" xref="S1.p6.2.m2.1.1.3.4.2.cmml">s</mi><mrow id="S1.p6.2.m2.1.1.3.4.3" xref="S1.p6.2.m2.1.1.3.4.3.cmml"><mo id="S1.p6.2.m2.1.1.3.4.3.1" xref="S1.p6.2.m2.1.1.3.4.3.1.cmml">-</mo><mn id="S1.p6.2.m2.1.1.3.4.3.2" xref="S1.p6.2.m2.1.1.3.4.3.2.cmml">1</mn></mrow></msup></mrow></mrow></math>

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/0910.2789

Formulas:

1-

G_{i j} (t)

2-

= (\sum_{\vec{x}} {Tr}_{sp} {Γ_{\pm} ⟨ Ω | χ_{i} (x) {\bar{χ}}_{j} (0) | Ω ⟩}),

3-

= \sum_{α} λ_{i}^{α} {\bar{λ}}_{j}^{α} e^{- m_{α} t},

4-

{\bar{χ}}_{j} u_{j}^{α}

5-

G_{i j} (t + △ t) u_{j}^{α}

6-

= e^{- m_{α} △ t} G_{i j} (t) u_{j}^{α},

7-

{[G_{i j} (t)]}^{- 1}

8-

{[{(G (t))}^{- 1} G (t + △ t)]}_{i j} u_{j}^{α}

9-

= c^{α} u_{i}^{α},

10-

c^{α} = e^{- m_{α} △ t}

Formulas (html):

Correct Categorie: hep-lat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1206.0403

Formulas:

1-

({CF}^{+}) = (1.5 - 2.0) \times 10^{12} {cm}^{- 2}

2-

F/H = (0.6 - 1.5) \times 10^{- 8}

3-

{}^{2}P_{1 / 2} 157.8 μ

4-

α_{2000} = 05^{h} 40^{m} {54.27}^{s}

5-

δ_{2000} = - 02^{\circ} 28^{'} 00^{''}

6-

1_{0, 1} 3 / 2, 2 - 0_{0, 0} 1 / 2, 1

7-

(- 5^{''}, 0^{''})

8-

(20^{''}, 22^{''})

9-

(- 100^{''}, 0^{''})

10-

10.7 km s^{- 1}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0203387

Formulas:

1-

μ \sim 10^{26} - 10^{27}

2-

P_{MAG} \propto μ^{2} r^{- 6}

3-

R_{BC} = 4.18 \times 10^{7} L_{37}^{2 / 3} R_{6}^{2 / 3} m^{- 1 / 3} cm

4-

P_{DISC} \propto {\dot{M}}^{17 / 20} r^{- 21 / 8}

5-

P_{RAD} \propto μ^{2} P_{spin}^{- 4} r^{- 2}

6-

P_{spin} ≃ 3.65 \times 10^{- 3}

7-

{\dot{P}}_{spin} = 1.59 \times 10^{- 19}

8-

Δ t \propto ν^{- 2.02 \pm 0.30}

9-

Δ n_{e} \sim 8 \times 10^{17} Δ t_{- 3}

10-

Δ t_{- 3} \sim 8

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1710.09493

Formulas:

1-

a (S) = k / n

2-

a (S) = 1

3-

a (S) \geq \frac{k - 1}{m - 1}

4-

m - 1 = (k - 1) q + r

5-

a (S) \geq ⌈ \frac{n - r}{q} ⌉ / n

6-

\frac{k - 1}{m - 1 - r}

7-

S = (X, E)

8-

S = (X, E)

9-

a (S) := \frac{Δ (S)}{| E |} .

10-

H = (V, E)

Formulas (html):

Correct Categorie: math

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1310.7211

Formulas:

1-

Y_{i} = θ_{i} + ϵ_{i},

2-

θ_{i} = 𝐱_{i}^{'} 𝜷 + u_{i},

3-

i = 1, \dots, n

4-

u_{i} | u_{j} \sim G a u (\sum_{i \sim j} ρ w_{i j} u_{j}, τ_{i}^{2}),

5-

G a u (a, b)

6-

w_{i j} = 1 / w_{i +}

7-

τ^{2} / w_{i +}

8-

𝐮 \equiv {(u_{1}, \dots, u_{n})}^{'}

9-

𝐮 \sim G a u (𝟎, τ^{2} {(𝐃 - ρ 𝐖)}^{- 1}),

10-

j = 1, \dots, m

Formulas (html):

Correct Categorie: stat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/0712.2930

Formulas:

1-

f (c o n t)

2-

f (N_{t})

3-

f (c o n t)

4-

f (N_{t})

5-

T^{4} / (m^{2} Δ χ)

6-

(T_{c}^{3} V)

7-

χ = (T / V) \cdot (\partial^{2} \log Z / \partial m_{u d}^{2})

8-

\cdot [\log Z (N_{s}, N_{t}) / (N_{t} N_{s}^{3}) - \log Z (N_{s 0}, N_{t 0}) / (N_{t 0} N_{s 0}^{3})]

9-

m_{u d}^{2} [χ (N_{s}, N_{t}) - χ (N_{s 0}, N_{t 0})]

10-

m^{2} Δ χ_{\bar{ψ} ψ} / T^{4}

Formulas (html):

Correct Categorie: hep-lat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/2011.12670

Formulas:

1-

- \frac{ℏ}{2} [Ω_{v} | 1 ⟩ ⟨ 2 | + Ω_{p} | 2 ⟩ ⟨ 3 | + Ω_{l} | 3 ⟩ ⟨ 4 |] + h . c .

2-

- ℏ [0 | 1 ⟩ ⟨ 1 | - δ_{v} | 2 ⟩ ⟨ 2 | + (- δ_{v} + δ_{p}) | 3 ⟩ ⟨ 3 | + (- δ_{v} + δ_{p} + δ_{l}) | 4 ⟩ ⟨ 4 |]

3-

| 1 ⟩, | 2 ⟩

4-

| D_{g}^{1} ⟩, | D_{g}^{2} ⟩

5-

| 3 ⟩, | 4 ⟩

6-

| D_{e}^{1} ⟩, | D_{e}^{2} ⟩

7-

1 / 2 (- δ_{l} + δ_{v} + \sqrt{δ_{l}^{2} + Ω_{l}^{2}} - \sqrt{δ_{v}^{2} + Ω_{v}^{2}}),

8-

1 / 2 (- δ_{l} + δ_{v} - \sqrt{δ_{l}^{2} + Ω_{l}^{2}} + \sqrt{δ_{v}^{2} + Ω_{v}^{2}}),

9-

1 / 2 (- δ_{l} + δ_{v} - \sqrt{δ_{l}^{2} + Ω_{l}^{2}} - \sqrt{δ_{v}^{2} + Ω_{v}^{2}}),

10-

1 / 2 (- δ_{l} + δ_{v} + \sqrt{δ_{l}^{2} + Ω_{l}^{2}} + \sqrt{δ_{v}^{2} + Ω_{v}^{2}})

Formulas (html):

Correct Categorie: physics

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1710.08417

Formulas:

1-

α_{ov} / f_{ov} = 11.36 \pm 0.22

2-

d_{ov} = α_{ov} H_{p}

3-

D_{ov} = D_{0} \exp (\frac{- 2 z}{H_{ν}}),

4-

H_{ν} = f_{ov} H_{p}

5-

Δ Y / Δ Z = 2.0

6-

Δ Y / Δ Z = 1.67

7-

Δ Y / Δ Z = 2.0

8-

Δ Y / Δ Z = 1.67

9-

α_{ov} / f_{ov} \approx 10

10-

f_{ov} = 0.0181 \pm 0.0003

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0103231

Formulas:

1-

N_{Ly}^{'} = f N_{Ly}

2-

N_{Ly} = \frac{4 π}{3} r_{S}^{3} n_{e} n_{p} α^{(2)},

3-

N_{Ly}^{'} = f N_{Ly} = \frac{4 π}{3} r_{i}^{3} n_{e} n_{p} α^{(2)} .

4-

f = y_{i}^{3} .

5-

τ_{S, d} ≃ 13 E_{B - V} / 2.5 \log e ≃ 12 E_{B - V}

6-

E_{B - V} / N_{H}

7-

E_{B - V} = (\frac{𝒟}{6 \times 10^{- 3}}) (\frac{N_{H}}{5.9 \times 10^{21} {cm}^{- 2}}) [mag],

8-

τ_{S, d} = 12 (\frac{𝒟}{6 \times 10^{- 3}}) (\frac{N_{H}}{5.9 \times 10^{21} {cm}^{- 2}}) .

9-

N_{H} \equiv n_{H} r_{S}

10-

τ_{S, d} = 0.92 (\frac{𝒟}{6 \times 10^{- 3}}) {(\frac{n_{H}}{10^{2} {cm}^{- 3}})}^{1 / 3} {(\frac{N_{Ly}}{10^{48} s^{- 1}})}^{1 / 3},

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/2004.11553

Formulas:

1-

1.5 \times 10^{6} {cm}^{2} / Vs

2-

1.46 \times 10^{11} {cm}^{- 2}

3-

H = \frac{ϵ}{2} | l ⟩ ⟨ l | - τ | u ⟩ ⟨ l | - τ | l ⟩ ⟨ u | - \frac{ϵ}{2} | u ⟩ ⟨ u |,

4-

| ϕ (t) ⟩ = e^{\frac{- i H t}{ℏ}} | ϕ (0) ⟩

5-

| ϕ (0) ⟩ = | l ⟩

6-

V_{gdr} = V_{gr1} - V_{gr2}

7-

V_{gdl} = V_{gl1} - V_{gl2}

8-

V_{gsr} = \frac{V_{gr1} + V_{gr2}}{2}

9-

V_{gsl} = \frac{V_{gl1} + V_{gl2}}{2}

10-

I_{tot} = I_{1} + I_{2}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1111.5127

Formulas:

1-

τ_{cap}^{- 1} \sim 3 \times 10^{- 5}

2-

W \sim 3 \times 10^{52}

3-

D_{B} \sim 3 \times 10^{30}

4-

ν_{s} \sim 10^{- 4}

5-

W \sim 4 \times 10^{52} M_{*}^{2} R_{*}^{- 1} M_{bh}^{1 / 3} {(b / 0.1)}^{- 2}

6-

\dot{W} \sim 3 \times 10^{40}

7-

10^{15} (u / 10^{8} cm s^{- 1}) (l_{sh} / 30 pc) (B / 5 μ G)

8-

\frac{\partial f}{\partial t} + \frac{\partial}{\partial z} (u (z) f - D \frac{\partial f}{\partial z}) - \frac{1}{3 p^{2}} \frac{d u (z)}{d z} \frac{\partial}{\partial p} (p^{3} f) = 0,

9-

f (p) \propto p^{- γ}

10-

N (E) \propto E^{- ν}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/hep-ph/0701110

Formulas:

1-

i f_{a b c} ⟨ 0 | j_{c}^{0} (x) | 0 ⟩ = ⟨ 0 | [j_{a}^{0} (x), Q_{b}] | 0 ⟩ = 2 i Im \sum_{n} ⟨ 0 | j_{a}^{0} (0) | n ⟩ ⟨ n | j_{b}^{0} (0) | 0 ⟩,

2-

f_{a b c}

3-

⟨ 0 | j_{c}^{0} | 0 ⟩

4-

| π (𝐤) ⟩

5-

j_{a}^{μ} (0)

6-

⟨ 0 | j_{a}^{μ} | π (𝐤) ⟩ = i k^{μ} F_{a} (| 𝐤 |) + i δ^{μ 0} G_{a} (| 𝐤 |) .

7-

(ω^{2} - 𝐤^{2}) F_{a} + ω G_{a} = 0 .

8-

𝒪 (| 𝐤 |)

9-

{lim}_{| 𝐤 | \to 0} G_{a} \neq 0

10-

ω (𝐤) = 𝐤^{2} \frac{F_{a}}{G_{a}} .

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/0903.5351

Formulas:

1-

f_{l} (n)

2-

= \max {μ (G) : | G | = n, C_{l} ⊈ G},

3-

g_{l} (n)

4-

= \max {μ (G) : | G | = n, C_{l} ⊈ G and C_{l + 1} ⊈ G}

5-

h_{l} (n)

6-

= \max {μ (G) : | G | = n, P_{l} ⊈ G} .

7-

g_{l} (n)

8-

\max {μ (G) : | G | = n, and C_{p} ⊈ G for p \geq l} .

9-

g_{l} (n),

10-

f_{l} (n)

Formulas (html):

Correct Categorie: math

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0005380

Formulas:

1-

L \approx 50 h^{- 1} {(1 + z)}^{- 1}

2-

v_{L} \approx L H {(δ ρ / ρ)}_{L}

3-

{(δ ρ / ρ)}_{L}

4-

v_{L} \propto k^{3 / 2} v_{k} \propto k^{1 / 2} P {(k)}^{1 / 2}

5-

c t_{e q} (1 + z_{e q}) = 50 h^{- 1} Mpc {(Ω_{M} h / 0.2)}^{- 1}

6-

1 + z_{e q} = 4780 [Ω_{M} h / 0.2]

7-

v_{L} \propto L^{- 1}

8-

\approx {(1 + z)}^{- 1 / 2}

9-

v / c ≃ δ T / T ≃ 10^{- 5}

10-

v ≃ 3 k m s^{- 1}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/0903.1133

Formulas:

1-

ℒ 𝒪 𝒞 𝒜 ℒ

2-

ℒ 𝒪 𝒞 𝒜 ℒ

3-

φ - ℒ 𝒪 𝒞 𝒜 ℒ

4-

ℒ 𝒪 𝒞 𝒜 ℒ

5-

𝒞 𝒪 𝒩 𝒢 ℰ 𝒮 𝒯

6-

𝒞 𝒪 𝒩 𝒢 ℰ 𝒮 𝒯

7-

𝒞 𝒪 𝒩 𝒢 ℰ 𝒮 𝒯

8-

ℒ 𝒪 𝒞 𝒞

9-

ℒ 𝒪 𝒞 𝒞

10-

ℒ 𝒪 𝒞 𝒜 ℒ

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: quant-ph

Result: correct

Paper: https://arxiv.org/abs/0907.0220

Formulas:

1-

\vec{u} = ⟨ 271, 0, 0 ⟩

2-

\vec{v} = ⟨ \frac{9826}{271}, \frac{60 \sqrt{202398}}{271}, 0 ⟩

3-

\vec{w} = ⟨ \frac{6647}{271}, \frac{143754}{271} \sqrt{\frac{42}{4819}}, 66 \sqrt{\frac{8358}{4819}} ⟩

4-

∥ \vec{u} ∥ = 271

5-

∥ \vec{v} ∥ = 106

6-

∥ \vec{w} ∥ = 103

7-

∥ \vec{u} - \vec{v} ∥ = 255

8-

∥ \vec{u} - \vec{w} ∥ = 266

9-

∥ \vec{v} - \vec{w} ∥ = 101

10-

∥ \vec{u} + \vec{v} ∥ = 323

Formulas (html):

Correct Categorie: math

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1410.8112

Formulas:

1-

a_{n, n - 1}

2-

a_{i, k} = - a_{i, i + 1 - k}

3-

0 < a_{1} < a_{2} < \dots < a_{⌊ \frac{n}{2} ⌋}

4-

A_{n}^{q} (a_{1}, a_{2}, \dots, a_{⌊ \frac{n}{2} ⌋})

5-

a_{1}, a_{2}, \dots, a_{⌊ \frac{n}{2} ⌋}

6-

A_{1}^{q} (\emptyset) := 1

7-

A_{2 k}^{2} (a_{1}, a_{2}, \dots, a_{k}) = \frac{2^{k^{2}}}{0! 2! 4! \dots (2 k - 2)!} \prod_{1 ⩽ i < j ⩽ k} (a_{j} - a_{i}) \prod_{1 ⩽ i < j ⩽ k} (a_{i} + a_{j} - 1)

8-

A_{2 k + 1}^{2} (a_{1}, a_{2}, \dots, a_{k}) = \frac{2^{k^{2}}}{1! 3! 5! \dots (2 k - 1)!} \prod_{1 ⩽ i < j ⩽ k} (a_{j} - a_{i}) \prod_{1 ⩽ i ⩽ j ⩽ k} (a_{i} + a_{j} - 1),

9-

\prod_{1 ⩽ i < j ⩽ k} (a_{j} - a_{i})

10-

E (a_{1}, a_{2}, \dots, a_{k})

Formulas (html):

Correct Categorie: math

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/0201491

Formulas:

1-

2.5 \times 10^{10} \leq p \leq 4.0 \times 10^{11}

2-

p ≳ 1 \times 10^{11}

3-

p = 2.5 \times 10^{10}

4-

p = 3.3 \times 10^{11}

5-

[01 \bar{1}]

6-

2.5 \times 10^{10} \leq p \leq 4.0 \times 10^{11}

7-

[01 \bar{1}]

8-

[\bar{2} 33]

9-

[01 \bar{1}]

10-

[\bar{2} 33]

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1412.8498

Formulas:

1-

d e t A = d e t_{1} A λ^{d}

2-

d e t_{1} A \in 𝒦

3-

d e t A \cdot d e t B = d e t A B

4-

d e t A

5-

d e t A

6-

h \in 𝒦 [\partial]

7-

d e t_{1} A

8-

d e t_{1} A = 0

9-

t o r d (A) = \max_{σ \in S_{n}} \sum_{i = 1}^{n} o r d (A_{i, σ (i)})

10-

{1, 2, \dots n}

Formulas (html):

Correct Categorie: math

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1703.10769

Formulas:

1-

t_{E} = 10 \pm 1

2-

q = 2.1 \times 10^{- 4}

3-

{6.7}_{- 3.6}^{+ 10.7} M_{\oplus}

4-

{0.10}_{- 0.05}^{+ 0.16} M_{⊙}

5-

θ_{E} = 0.12 \pm 0.02

6-

10 k \times 8 k

7-

(α, δ) (2000) = (17^{h} 52^{m} 34^{s} .34, - 32^{\circ} 02^{'} 24^{''} .33)

8-

(l, b) = (- {1.892}^{\circ}, - {2.881}^{\circ})

9-

σ_{i}^{'} = k \sqrt{σ_{i}^{2} + e_{m i n}^{2}}

10-

e_{m i n}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1512.07148

Formulas:

1-

g^{(2)} (0) = 2

2-

Δ n = \bar{n}

3-

g^{(2)} (0) > 1

4-

ℏ ω_{c} = 2.13 eV

5-

560 - 610 nm

6-

3 k_{B} T

7-

N_{c} ≃ 80, 000

8-

Δ n / \bar{n} = \sqrt{g^{(2)} (0) - 1}

9-

I (t) = I_{c} + I_{ℓ} + 2 \sqrt{I_{c} I_{ℓ}} \cos [(ω_{c} - ω_{ℓ}) t + Δ ϕ (t)],

10-

Δ ϕ (t)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/0801.4435

Formulas:

1-

μ_{i} (ω)

2-

μ_{i}^{(0)} (ω) + \sum_{j} \sum_{ω_{1}} α_{i j} (ω; \pm ω_{1}) \cdot E_{j} (ω_{1})

3-

+ \frac{1}{2} \sum_{j k} \sum_{ω_{1}, ω_{2}} β_{i j k} (ω; \pm ω_{1}, \pm ω_{2}) \cdot E_{j} (ω_{1}) E_{k} (ω_{2})

4-

+ \frac{1}{6} \sum_{j k l} \sum_{ω_{1}, ω_{2}, ω_{3}} γ_{i j k l} (ω; \pm ω_{1}, \pm ω_{2}, \pm ω_{3}) \cdot E_{j} (ω_{1}) E_{k} (ω_{2}) E_{l} (ω_{3}) + \dots .

5-

E_{m} (ω_{s})

6-

μ_{i}^{(0)} (ω)

7-

α_{i j} (ω; \pm ω_{1})

8-

β_{i j k} (ω; \pm ω_{1}, \pm ω_{2})

9-

γ_{i j k l} (ω; \pm ω_{1}, \pm ω_{2}, \pm ω_{3})

10-

γ_{i j k l} (ω; \pm ω_{1}, \pm ω_{2}, \pm ω_{3})

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1808.03658

Formulas:

1-

\max ({j : j < i, A [j] < A [i]} \cup {0})

2-

\max ({j : j < i, A [j] > A [i]} \cup {0})

3-

\min ({j : j > i, A [j] < A [i]} \cup {n + 1})

4-

\min ({j : j > i, A [j] > A [i]} \cup {n + 1})

5-

2 n - Θ (\log n)

6-

\log (3 + 2 \sqrt{2}) \cdot n - Θ (\log n) < 2.544 n

7-

3 n - Θ (\log n)

8-

4 n + o (n)

9-

\log_{2} 17 \cdot n + o (n) < 4.088 n

10-

4 n + o (n)

Formulas (html):

Correct Categorie: cs

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1705.10754

Formulas:

1-

Δ = [\begin{matrix} w_{11} & w_{12} & \dots & w_{1 m} & δ (d_{1}) \\ w_{21} & w_{22} & \dots & w_{2 m} & δ (d_{2}) \\ \dots & \dots & \dots & \dots \\ w_{n 1} & w_{n 2} & \dots & w_{n m} & δ (d_{n}) \end{matrix}],

2-

δ (d_{i})

3-

W (t, c) = \frac{\sum_{d \in D / c = δ (d)} w_{d t}}{\sum_{d \in D} w_{d t}}, \forall d \in D, c \in C

4-

W (t, c)

5-

d = {F (c_{1}), F (c_{2}), \dots, F (c_{n})} \sim \forall c \in C,

6-

F (c_{i}) = {a v g, s t d, m i n, m a x, p r o b, p r o p}

7-

F (c_{i})

8-

w (t - c), w (t - c + 1), \dots, w (t + c)

9-

\frac{1}{T} \sum_{t = 1}^{T} \sum_{- c \leq j \leq c, j \neq 0} \log p (w_{t + j} | w_{t})

10-

p (w_{t + j} | w_{t})

Formulas (html):

Correct Categorie: cs

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0110608

Formulas:

1-

\sim 1 \div 2 \times 10^{4}

2-

\approx 1.5 \times 10^{- 12}

3-

\approx 10^{'} \times 6^{'}

4-

\approx 9^{'} \times 4^{'}

5-

7 \div 9 \times 10^{21}

6-

N_{H} \approx 6 \times 10^{21}

7-

N_{H} = (8.0 \pm 1.5) \times 10^{21}

8-

0.77 ≲ f_{ic} ≲ 0.95

9-

N_{H} = 9.1 \times 10^{21}

10-

N_{H} = 9.1 \times 10^{21}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/hep-ex/0011030

Formulas:

1-

{}^{3}S_{1}^{(8)}

2-

1 + α \cos^{2} (θ)

3-

p + C u \to μ^{+} μ^{-} + X .

4-

8.1 < m_{μ^{+} μ^{-}} < 15.0

5-

0.0 < x_{F} < 0.6

6-

s x_{1} x_{2} = m^{2}

7-

x_{1} - x_{2} = x_{F}

8-

1 + \cos^{2} (θ)

9-

8.8 < m_{μ^{+} μ^{-}} < 10.0

10-

1 + α c o s^{2} (θ)

Formulas (html):

Correct Categorie: hep-ex

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/0203277

Formulas:

1-

(2 \sqrt{2} \times \sqrt{2}) R 45^{\circ}

2-

c (2 \times 2)

3-

(2 \sqrt{2} \times \sqrt{2}) R 45^{\circ}

4-

c (2 \times 2)

5-

(2 \sqrt{2} \times \sqrt{2}) R 45^{\circ}

6-

c (2 \times 2)

7-

c (2 \times 2)

8-

(2 \sqrt{2} \times \sqrt{2}) R 45^{\circ}

9-

(2 \sqrt{2} \times \sqrt{2}) R 45^{\circ}

10-

z_{C u 1}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Run 11277761 (Agent389)