Run 6938497

Paper: https://arxiv.org/abs/1111.3278

Formulas:

1-

10^{\circ} \leq 2 θ \leq 110^{\circ}

2-

κ = D_{t} C_{p} D

3-

5 s^{2} 5 p^{6} 6 s^{2}

4-

3 p^{6} 3 d^{10} 3 s^{1}

5-

3 s^{2} 3 p^{2}

6-

ρ = σ^{- 1} σ (T, E_{F}) = e^{2} K_{0}

7-

S (T, E_{F}) = \frac{K_{1}}{e T K_{0}}

8-

\frac{1}{4 π^{3}} \frac{τ}{ℏ} \sum_{i, 𝐤} 𝐯 (𝐢, 𝐤) 𝐯 (𝐢, 𝐤) {(E (i, 𝐤) - E_{F})}^{n}

9-

(- \frac{\partial f_{E_{F}} (T, E (i, 𝐤))}{\partial E}) .

10-

𝐯 = \partial E (i, 𝐤) / \partial 𝐤

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/cond-mat/9701026

Formulas:

1-

I_{0} = e v_{F} / L

2-

I_{0} ℓ / L

3-

S U (M)

4-

V (x) = g / x^{2}

5-

V (x) = U δ (x)

6-

k_{F} L > 2 π M

7-

S U (M)

8-

U > 16 M^{4} ℏ v_{F} / 3 π

9-

(ℏ c / e) ϕ

10-

S U (M)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1601.05465

Formulas:

1-

T_{o b s} >

2-

T_{o b s} >

3-

\bar{K} / R M S

4-

\bar{K} / R M S

5-

\bar{K} / R M S

6-

\frac{\bar{K}}{R M S} = 2.28 \pm 0.42 - (0.093 \pm 0.036) \sqrt{N},

7-

P_{S a t u r n} =

8-

K_{S a t u r n} = 3

9-

8 / 202 = 4.0 %

10-

(N_{d e t e c t e d} + N_{m i s s e d}) / N_{d e t e c t e d}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1906.10137

Formulas:

1-

{p_{1} \dots p_{n}}

2-

{k_{1}^{(t)} \dots k_{t}^{(t)}}

3-

k_{1}^{(1)} = p_{1} + \dots + p_{n}

4-

{k_{1}^{(n)} \dots k_{n}^{(n)}} = {p_{1} \dots p_{n}}

5-

{k_{1}^{(t)} \dots k_{t}^{(t)}} \to {k_{1}^{(t + 1)} \dots k_{t + 1}^{(t + 1)}}

6-

{p_{1} \dots p_{n}}

7-

P_{𝒥} (jet)

8-

= [\prod_{t = 1}^{n - 1} P^{(t)} (k_{1}^{(t + 1)} \dots k_{t + 1}^{(t + 1)} | k_{1}^{(t)} \dots k_{t}^{(t)})]

9-

\times P^{(n)} (end | k_{1}^{(n)} \dots k_{n}^{(n)})

10-

{k_{1}^{(t)} \dots k_{t}^{(t)}}

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: math

Result: incorrect

Paper: https://arxiv.org/abs/1206.3811

Formulas:

1-

H = - \sum_{⟨ i j ⟩} s \cos [θ_{i} - θ_{j}] + (1 - s) \cos [2 (θ_{i} - θ_{j})]

2-

\arg [\sum_{k \sim j} g_{s} (θ_{j}^{t}, θ_{k}^{t})] + η ξ_{j}^{t}

3-

𝐫_{j}^{t} + v_{0} 𝐯_{j}^{t + 1},

4-

𝐯_{j}^{t} = {(\cos θ_{j}^{t}, \sin θ_{j}^{t})}^{T}

5-

[- \frac{π}{2}, \frac{π}{2}]

6-

g_{s} (θ, θ^{'})

7-

g_{s} (θ, θ^{'}) = {\begin{matrix} e^{i θ^{'}} & with prob . s \\ sign [\cos (θ - θ^{'})] e^{i θ^{'}} & otherwise \end{matrix}

8-

g_{s} (θ, θ^{'})

9-

θ^{'} \to θ^{'} + π

10-

ρ = N / L^{2}

Formulas (html):

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xref="S0.E1.m3.2.2.1.1.1.1.3.cmml"><mo largeop="true" movablelimits="false" symmetric="true" id="S0.E1.m3.2.2.1.1.1.1.3.2" xref="S0.E1.m3.2.2.1.1.1.1.3.2.cmml">∑</mo><mrow id="S0.E1.m3.2.2.1.1.1.1.3.3" xref="S0.E1.m3.2.2.1.1.1.1.3.3.cmml"><mi id="S0.E1.m3.2.2.1.1.1.1.3.3.2" xref="S0.E1.m3.2.2.1.1.1.1.3.3.2.cmml">k</mi><mo id="S0.E1.m3.2.2.1.1.1.1.3.3.1" xref="S0.E1.m3.2.2.1.1.1.1.3.3.1.cmml">∼</mo><mi id="S0.E1.m3.2.2.1.1.1.1.3.3.3" xref="S0.E1.m3.2.2.1.1.1.1.3.3.3.cmml">j</mi></mrow></munder></mstyle><mrow id="S0.E1.m3.2.2.1.1.1.1.2" xref="S0.E1.m3.2.2.1.1.1.1.2.cmml"><msub id="S0.E1.m3.2.2.1.1.1.1.2.4" xref="S0.E1.m3.2.2.1.1.1.1.2.4.cmml"><mi id="S0.E1.m3.2.2.1.1.1.1.2.4.2" xref="S0.E1.m3.2.2.1.1.1.1.2.4.2.cmml">g</mi><mi id="S0.E1.m3.2.2.1.1.1.1.2.4.3" xref="S0.E1.m3.2.2.1.1.1.1.2.4.3.cmml">s</mi></msub><mo id="S0.E1.m3.2.2.1.1.1.1.2.3" xref="S0.E1.m3.2.2.1.1.1.1.2.3.cmml">⁢</mo><mrow id="S0.E1.m3.2.2.1.1.1.1.2.2.2" xref="S0.E1.m3.2.2.1.1.1.1.2.2.3.cmml"><mo stretchy="false" id="S0.E1.m3.2.2.1.1.1.1.2.2.2.3" xref="S0.E1.m3.2.2.1.1.1.1.2.2.3.cmml">(</mo><msubsup id="S0.E1.m3.2.2.1.1.1.1.1.1.1.1" xref="S0.E1.m3.2.2.1.1.1.1.1.1.1.1.cmml"><mi id="S0.E1.m3.2.2.1.1.1.1.1.1.1.1.2.2" xref="S0.E1.m3.2.2.1.1.1.1.1.1.1.1.2.2.cmml">θ</mi><mi id="S0.E1.m3.2.2.1.1.1.1.1.1.1.1.2.3" xref="S0.E1.m3.2.2.1.1.1.1.1.1.1.1.2.3.cmml">j</mi><mi id="S0.E1.m3.2.2.1.1.1.1.1.1.1.1.3" xref="S0.E1.m3.2.2.1.1.1.1.1.1.1.1.3.cmml">t</mi></msubsup><mo id="S0.E1.m3.2.2.1.1.1.1.2.2.2.4" xref="S0.E1.m3.2.2.1.1.1.1.2.2.3.cmml">,</mo><msubsup id="S0.E1.m3.2.2.1.1.1.1.2.2.2.2" xref="S0.E1.m3.2.2.1.1.1.1.2.2.2.2.cmml"><mi id="S0.E1.m3.2.2.1.1.1.1.2.2.2.2.2.2" xref="S0.E1.m3.2.2.1.1.1.1.2.2.2.2.2.2.cmml">θ</mi><mi id="S0.E1.m3.2.2.1.1.1.1.2.2.2.2.2.3" xref="S0.E1.m3.2.2.1.1.1.1.2.2.2.2.2.3.cmml">k</mi><mi id="S0.E1.m3.2.2.1.1.1.1.2.2.2.2.3" xref="S0.E1.m3.2.2.1.1.1.1.2.2.2.2.3.cmml">t</mi></msubsup><mo stretchy="false" id="S0.E1.m3.2.2.1.1.1.1.2.2.2.5" xref="S0.E1.m3.2.2.1.1.1.1.2.2.3.cmml">)</mo></mrow></mrow></mrow><mo id="S0.E1.m3.2.2.1.1.1.3" xref="S0.E1.m3.2.2.1.2.cmml">]</mo></mrow></mrow><mo id="S0.E1.m3.2.2.2" xref="S0.E1.m3.2.2.2.cmml">+</mo><mrow id="S0.E1.m3.2.2.3" xref="S0.E1.m3.2.2.3.cmml"><mpadded width="+1.7pt" id="S0.E1.m3.2.2.3.2" xref="S0.E1.m3.2.2.3.2.cmml"><mi id="S0.E1.m3.2.2.3.2a" xref="S0.E1.m3.2.2.3.2.cmml">η</mi></mpadded><mo id="S0.E1.m3.2.2.3.1" xref="S0.E1.m3.2.2.3.1.cmml">⁢</mo><msubsup id="S0.E1.m3.2.2.3.3" xref="S0.E1.m3.2.2.3.3.cmml"><mi id="S0.E1.m3.2.2.3.3.2.2" xref="S0.E1.m3.2.2.3.3.2.2.cmml">ξ</mi><mi id="S0.E1.m3.2.2.3.3.2.3" xref="S0.E1.m3.2.2.3.3.2.3.cmml">j</mi><mi id="S0.E1.m3.2.2.3.3.3" xref="S0.E1.m3.2.2.3.3.3.cmml">t</mi></msubsup></mrow></mrow></math>, <math><mrow id="S0.E2.m3.1.1.1" xref="S0.E2.m3.1.1.1.1.cmml"><mrow id="S0.E2.m3.1.1.1.1" xref="S0.E2.m3.1.1.1.1.cmml"><msubsup id="S0.E2.m3.1.1.1.1.2" xref="S0.E2.m3.1.1.1.1.2.cmml"><mi id="S0.E2.m3.1.1.1.1.2.2.2" xref="S0.E2.m3.1.1.1.1.2.2.2.cmml">𝐫</mi><mi id="S0.E2.m3.1.1.1.1.2.2.3" xref="S0.E2.m3.1.1.1.1.2.2.3.cmml">j</mi><mi id="S0.E2.m3.1.1.1.1.2.3" xref="S0.E2.m3.1.1.1.1.2.3.cmml">t</mi></msubsup><mo id="S0.E2.m3.1.1.1.1.1" xref="S0.E2.m3.1.1.1.1.1.cmml">+</mo><mrow id="S0.E2.m3.1.1.1.1.3" xref="S0.E2.m3.1.1.1.1.3.cmml"><mpadded width="+1.7pt" id="S0.E2.m3.1.1.1.1.3.2" xref="S0.E2.m3.1.1.1.1.3.2.cmml"><msub id="S0.E2.m3.1.1.1.1.3.2a" xref="S0.E2.m3.1.1.1.1.3.2.cmml"><mi id="S0.E2.m3.1.1.1.1.3.2.2" xref="S0.E2.m3.1.1.1.1.3.2.2.cmml">v</mi><mn id="S0.E2.m3.1.1.1.1.3.2.3" xref="S0.E2.m3.1.1.1.1.3.2.3.cmml">0</mn></msub></mpadded><mo id="S0.E2.m3.1.1.1.1.3.1" xref="S0.E2.m3.1.1.1.1.3.1.cmml">⁢</mo><mpadded width="+1.7pt" id="S0.E2.m3.1.1.1.1.3.3" xref="S0.E2.m3.1.1.1.1.3.3.cmml"><msubsup id="S0.E2.m3.1.1.1.1.3.3a" xref="S0.E2.m3.1.1.1.1.3.3.cmml"><mi id="S0.E2.m3.1.1.1.1.3.3.2.2" xref="S0.E2.m3.1.1.1.1.3.3.2.2.cmml">𝐯</mi><mi id="S0.E2.m3.1.1.1.1.3.3.2.3" xref="S0.E2.m3.1.1.1.1.3.3.2.3.cmml">j</mi><mrow id="S0.E2.m3.1.1.1.1.3.3.3" xref="S0.E2.m3.1.1.1.1.3.3.3.cmml"><mi id="S0.E2.m3.1.1.1.1.3.3.3.2" xref="S0.E2.m3.1.1.1.1.3.3.3.2.cmml">t</mi><mo id="S0.E2.m3.1.1.1.1.3.3.3.1" xref="S0.E2.m3.1.1.1.1.3.3.3.1.cmml">+</mo><mn id="S0.E2.m3.1.1.1.1.3.3.3.3" xref="S0.E2.m3.1.1.1.1.3.3.3.3.cmml">1</mn></mrow></msubsup></mpadded></mrow></mrow><mo id="S0.E2.m3.1.1.1.2" xref="S0.E2.m3.1.1.1.1.cmml">,</mo></mrow></math>, <math><mrow id="p5.7.m1.2.2" xref="p5.7.m1.2.2.cmml"><msubsup id="p5.7.m1.2.2.4" xref="p5.7.m1.2.2.4.cmml"><mi id="p5.7.m1.2.2.4.2.2" xref="p5.7.m1.2.2.4.2.2.cmml">𝐯</mi><mi id="p5.7.m1.2.2.4.2.3" xref="p5.7.m1.2.2.4.2.3.cmml">j</mi><mi id="p5.7.m1.2.2.4.3" xref="p5.7.m1.2.2.4.3.cmml">t</mi></msubsup><mo id="p5.7.m1.2.2.3" xref="p5.7.m1.2.2.3.cmml">=</mo><msup id="p5.7.m1.2.2.2" xref="p5.7.m1.2.2.2.cmml"><mrow id="p5.7.m1.2.2.2.2.2" xref="p5.7.m1.2.2.2.2.3.cmml"><mo id="p5.7.m1.2.2.2.2.2.3" xref="p5.7.m1.2.2.2.2.3.cmml">(</mo><mrow id="p5.7.m1.1.1.1.1.1.1" xref="p5.7.m1.1.1.1.1.1.1.cmml"><mi id="p5.7.m1.1.1.1.1.1.1.1" xref="p5.7.m1.1.1.1.1.1.1.1.cmml">cos</mi><mo id="p5.7.m1.1.1.1.1.1.1a" xref="p5.7.m1.1.1.1.1.1.1.cmml">⁡</mo><msubsup id="p5.7.m1.1.1.1.1.1.1.2" xref="p5.7.m1.1.1.1.1.1.1.2.cmml"><mi id="p5.7.m1.1.1.1.1.1.1.2.2.2" xref="p5.7.m1.1.1.1.1.1.1.2.2.2.cmml">θ</mi><mi id="p5.7.m1.1.1.1.1.1.1.2.2.3" xref="p5.7.m1.1.1.1.1.1.1.2.2.3.cmml">j</mi><mi id="p5.7.m1.1.1.1.1.1.1.2.3" xref="p5.7.m1.1.1.1.1.1.1.2.3.cmml">t</mi></msubsup></mrow><mo id="p5.7.m1.2.2.2.2.2.4" xref="p5.7.m1.2.2.2.2.3.cmml">,</mo><mrow id="p5.7.m1.2.2.2.2.2.2" xref="p5.7.m1.2.2.2.2.2.2.cmml"><mi id="p5.7.m1.2.2.2.2.2.2.1" xref="p5.7.m1.2.2.2.2.2.2.1.cmml">sin</mi><mo id="p5.7.m1.2.2.2.2.2.2a" xref="p5.7.m1.2.2.2.2.2.2.cmml">⁡</mo><msubsup id="p5.7.m1.2.2.2.2.2.2.2" xref="p5.7.m1.2.2.2.2.2.2.2.cmml"><mi id="p5.7.m1.2.2.2.2.2.2.2.2.2" xref="p5.7.m1.2.2.2.2.2.2.2.2.2.cmml">θ</mi><mi id="p5.7.m1.2.2.2.2.2.2.2.2.3" xref="p5.7.m1.2.2.2.2.2.2.2.2.3.cmml">j</mi><mi id="p5.7.m1.2.2.2.2.2.2.2.3" xref="p5.7.m1.2.2.2.2.2.2.2.3.cmml">t</mi></msubsup></mrow><mo id="p5.7.m1.2.2.2.2.2.5" xref="p5.7.m1.2.2.2.2.3.cmml">)</mo></mrow><mi id="p5.7.m1.2.2.2.4" xref="p5.7.m1.2.2.2.4.cmml">T</mi></msup></mrow></math>, <math><mrow id="p5.12.m6.2.2.1" xref="p5.12.m6.2.2.2.cmml"><mo id="p5.12.m6.2.2.1.2" xref="p5.12.m6.2.2.2.cmml">[</mo><mrow id="p5.12.m6.2.2.1.1" xref="p5.12.m6.2.2.1.1.cmml"><mo id="p5.12.m6.2.2.1.1.1" xref="p5.12.m6.2.2.1.1.1.cmml">-</mo><mfrac id="p5.12.m6.2.2.1.1.2" xref="p5.12.m6.2.2.1.1.2.cmml"><mi id="p5.12.m6.2.2.1.1.2.2" xref="p5.12.m6.2.2.1.1.2.2.cmml">π</mi><mn id="p5.12.m6.2.2.1.1.2.3" xref="p5.12.m6.2.2.1.1.2.3.cmml">2</mn></mfrac></mrow><mo id="p5.12.m6.2.2.1.3" xref="p5.12.m6.2.2.2.cmml">,</mo><mfrac id="p5.12.m6.1.1" xref="p5.12.m6.1.1.cmml"><mi id="p5.12.m6.1.1.2" xref="p5.12.m6.1.1.2.cmml">π</mi><mn id="p5.12.m6.1.1.3" xref="p5.12.m6.1.1.3.cmml">2</mn></mfrac><mo id="p5.12.m6.2.2.1.4" xref="p5.12.m6.2.2.2.cmml">]</mo></mrow></math>, <math><mrow id="p5.13.m7.2.2" xref="p5.13.m7.2.2.cmml"><msub id="p5.13.m7.2.2.3" xref="p5.13.m7.2.2.3.cmml"><mi id="p5.13.m7.2.2.3.2" xref="p5.13.m7.2.2.3.2.cmml">g</mi><mi id="p5.13.m7.2.2.3.3" xref="p5.13.m7.2.2.3.3.cmml">s</mi></msub><mo id="p5.13.m7.2.2.2" xref="p5.13.m7.2.2.2.cmml">⁢</mo><mrow id="p5.13.m7.2.2.1.1" xref="p5.13.m7.2.2.1.2.cmml"><mo stretchy="false" id="p5.13.m7.2.2.1.1.2" xref="p5.13.m7.2.2.1.2.cmml">(</mo><mi id="p5.13.m7.1.1" xref="p5.13.m7.1.1.cmml">θ</mi><mo id="p5.13.m7.2.2.1.1.3" xref="p5.13.m7.2.2.1.2.cmml">,</mo><msup id="p5.13.m7.2.2.1.1.1" xref="p5.13.m7.2.2.1.1.1.cmml"><mi id="p5.13.m7.2.2.1.1.1.2" xref="p5.13.m7.2.2.1.1.1.2.cmml">θ</mi><mo id="p5.13.m7.2.2.1.1.1.3" xref="p5.13.m7.2.2.1.1.1.3.cmml">′</mo></msup><mo stretchy="false" id="p5.13.m7.2.2.1.1.4" xref="p5.13.m7.2.2.1.2.cmml">)</mo></mrow></mrow></math>, <math><mrow id="S0.E3.m1.6.6" xref="S0.E3.m1.6.6.cmml"><mrow id="S0.E3.m1.6.6.1" xref="S0.E3.m1.6.6.1.cmml"><msub id="S0.E3.m1.6.6.1.3" xref="S0.E3.m1.6.6.1.3.cmml"><mi id="S0.E3.m1.6.6.1.3.2" xref="S0.E3.m1.6.6.1.3.2.cmml">g</mi><mi id="S0.E3.m1.6.6.1.3.3" xref="S0.E3.m1.6.6.1.3.3.cmml">s</mi></msub><mo id="S0.E3.m1.6.6.1.2" xref="S0.E3.m1.6.6.1.2.cmml">⁢</mo><mrow id="S0.E3.m1.6.6.1.1.1" xref="S0.E3.m1.6.6.1.1.2.cmml"><mo stretchy="false" id="S0.E3.m1.6.6.1.1.1.2" xref="S0.E3.m1.6.6.1.1.2.cmml">(</mo><mi id="S0.E3.m1.5.5" xref="S0.E3.m1.5.5.cmml">θ</mi><mo id="S0.E3.m1.6.6.1.1.1.3" xref="S0.E3.m1.6.6.1.1.2.cmml">,</mo><msup id="S0.E3.m1.6.6.1.1.1.1" xref="S0.E3.m1.6.6.1.1.1.1.cmml"><mi id="S0.E3.m1.6.6.1.1.1.1.2" xref="S0.E3.m1.6.6.1.1.1.1.2.cmml">θ</mi><mo id="S0.E3.m1.6.6.1.1.1.1.3" xref="S0.E3.m1.6.6.1.1.1.1.3.cmml">′</mo></msup><mo stretchy="false" id="S0.E3.m1.6.6.1.1.1.4" xref="S0.E3.m1.6.6.1.1.2.cmml">)</mo></mrow></mrow><mo id="S0.E3.m1.6.6.2" xref="S0.E3.m1.6.6.2.cmml">=</mo><mrow id="S0.E3.m1.6.6.3.2" xref="S0.E3.m1.6.6.3.1.cmml"><mo id="S0.E3.m1.6.6.3.2.1" xref="S0.E3.m1.6.6.3.1.1.cmml">{</mo><mtable columnspacing="5pt" displaystyle="true" rowspacing="0pt" id="S0.E3.m1.4.4" xref="S0.E3.m1.4.4.cmml"><mtr id="S0.E3.m1.4.4a" xref="S0.E3.m1.4.4.cmml"><mtd columnalign="left" id="S0.E3.m1.4.4b" xref="S0.E3.m1.4.4.cmml"><msup id="S0.E3.m1.2.2.2.3.1" xref="S0.E3.m1.2.2.2.3.1.cmml"><mi id="S0.E3.m1.2.2.2.3.1.2" xref="S0.E3.m1.2.2.2.3.1.2.cmml">e</mi><mrow id="S0.E3.m1.2.2.2.3.1.3" xref="S0.E3.m1.2.2.2.3.1.3.cmml"><mi id="S0.E3.m1.2.2.2.3.1.3.2" xref="S0.E3.m1.2.2.2.3.1.3.2.cmml">i</mi><mo id="S0.E3.m1.2.2.2.3.1.3.1" xref="S0.E3.m1.2.2.2.3.1.3.1.cmml">⁢</mo><msup id="S0.E3.m1.2.2.2.3.1.3.3" xref="S0.E3.m1.2.2.2.3.1.3.3.cmml"><mi id="S0.E3.m1.2.2.2.3.1.3.3.2" xref="S0.E3.m1.2.2.2.3.1.3.3.2.cmml">θ</mi><mo id="S0.E3.m1.2.2.2.3.1.3.3.3" xref="S0.E3.m1.2.2.2.3.1.3.3.3.cmml">′</mo></msup></mrow></msup></mtd><mtd columnalign="left" id="S0.E3.m1.4.4c" xref="S0.E3.m1.4.4.cmml"><mrow id="S0.E3.m1.2.2.2.2.2.2" xref="S0.E3.m1.2.2.2.2.2.3.cmml"><mrow id="S0.E3.m1.2.2.2.2.2.2.1" xref="S0.E3.m1.2.2.2.2.2.2.1.cmml"><mpadded width="+5.6pt" id="S0.E3.m1.2.2.2.2.2.2.1.2" xref="S0.E3.m1.2.2.2.2.2.2.1.2.cmml"><mi id="S0.E3.m1.2.2.2.2.2.2.1.2a" xref="S0.E3.m1.2.2.2.2.2.2.1.2.cmml">with</mi></mpadded><mo id="S0.E3.m1.2.2.2.2.2.2.1.1" xref="S0.E3.m1.2.2.2.2.2.2.1.1.cmml">⁢</mo><mi id="S0.E3.m1.2.2.2.2.2.2.1.3" xref="S0.E3.m1.2.2.2.2.2.2.1.3.cmml">prob</mi></mrow><mo rspace="5.3pt" id="S0.E3.m1.2.2.2.2.2.2.2" xref="S0.E3.m1.2.2.2.2.2.3a.cmml">.</mo><mi id="S0.E3.m1.1.1.1.1.1.1" xref="S0.E3.m1.1.1.1.1.1.1.cmml">s</mi></mrow></mtd></mtr><mtr id="S0.E3.m1.4.4d" xref="S0.E3.m1.4.4.cmml"><mtd columnalign="left" id="S0.E3.m1.4.4e" xref="S0.E3.m1.4.4.cmml"><mrow id="S0.E3.m1.4.4.4.2.2" xref="S0.E3.m1.4.4.4.2.2.cmml"><mi id="S0.E3.m1.4.4.4.2.2.4" xref="S0.E3.m1.4.4.4.2.2.4.cmml">sign</mi><mo id="S0.E3.m1.4.4.4.2.2.3" xref="S0.E3.m1.4.4.4.2.2.3.cmml">⁢</mo><mrow id="S0.E3.m1.4.4.4.2.2.2.1" xref="S0.E3.m1.4.4.4.2.2.2.2.cmml"><mo id="S0.E3.m1.4.4.4.2.2.2.1.2" xref="S0.E3.m1.4.4.4.2.2.2.2.1.cmml">[</mo><mrow id="S0.E3.m1.4.4.4.2.2.2.1.1.1" xref="S0.E3.m1.4.4.4.2.2.2.1.1.2.cmml"><mi id="S0.E3.m1.3.3.3.1.1.1" xref="S0.E3.m1.3.3.3.1.1.1.cmml">cos</mi><mo id="S0.E3.m1.4.4.4.2.2.2.1.1.1a" xref="S0.E3.m1.4.4.4.2.2.2.1.1.2.cmml">⁡</mo><mrow id="S0.E3.m1.4.4.4.2.2.2.1.1.1.1" xref="S0.E3.m1.4.4.4.2.2.2.1.1.2.cmml"><mo stretchy="false" id="S0.E3.m1.4.4.4.2.2.2.1.1.1.1.2" xref="S0.E3.m1.4.4.4.2.2.2.1.1.2.cmml">(</mo><mrow id="S0.E3.m1.4.4.4.2.2.2.1.1.1.1.1" xref="S0.E3.m1.4.4.4.2.2.2.1.1.1.1.1.cmml"><mi id="S0.E3.m1.4.4.4.2.2.2.1.1.1.1.1.2" xref="S0.E3.m1.4.4.4.2.2.2.1.1.1.1.1.2.cmml">θ</mi><mo id="S0.E3.m1.4.4.4.2.2.2.1.1.1.1.1.1" xref="S0.E3.m1.4.4.4.2.2.2.1.1.1.1.1.1.cmml">-</mo><msup id="S0.E3.m1.4.4.4.2.2.2.1.1.1.1.1.3" xref="S0.E3.m1.4.4.4.2.2.2.1.1.1.1.1.3.cmml"><mi id="S0.E3.m1.4.4.4.2.2.2.1.1.1.1.1.3.2" xref="S0.E3.m1.4.4.4.2.2.2.1.1.1.1.1.3.2.cmml">θ</mi><mo id="S0.E3.m1.4.4.4.2.2.2.1.1.1.1.1.3.3" xref="S0.E3.m1.4.4.4.2.2.2.1.1.1.1.1.3.3.cmml">′</mo></msup></mrow><mo stretchy="false" id="S0.E3.m1.4.4.4.2.2.2.1.1.1.1.3" xref="S0.E3.m1.4.4.4.2.2.2.1.1.2.cmml">)</mo></mrow></mrow><mo id="S0.E3.m1.4.4.4.2.2.2.1.3" xref="S0.E3.m1.4.4.4.2.2.2.2.1.cmml">]</mo></mrow><mo id="S0.E3.m1.4.4.4.2.2.3a" xref="S0.E3.m1.4.4.4.2.2.3.cmml">⁢</mo><msup id="S0.E3.m1.4.4.4.2.2.5" xref="S0.E3.m1.4.4.4.2.2.5.cmml"><mi id="S0.E3.m1.4.4.4.2.2.5.2" xref="S0.E3.m1.4.4.4.2.2.5.2.cmml">e</mi><mrow id="S0.E3.m1.4.4.4.2.2.5.3" xref="S0.E3.m1.4.4.4.2.2.5.3.cmml"><mi id="S0.E3.m1.4.4.4.2.2.5.3.2" xref="S0.E3.m1.4.4.4.2.2.5.3.2.cmml">i</mi><mo id="S0.E3.m1.4.4.4.2.2.5.3.1" xref="S0.E3.m1.4.4.4.2.2.5.3.1.cmml">⁢</mo><msup id="S0.E3.m1.4.4.4.2.2.5.3.3" xref="S0.E3.m1.4.4.4.2.2.5.3.3.cmml"><mi id="S0.E3.m1.4.4.4.2.2.5.3.3.2" xref="S0.E3.m1.4.4.4.2.2.5.3.3.2.cmml">θ</mi><mo id="S0.E3.m1.4.4.4.2.2.5.3.3.3" xref="S0.E3.m1.4.4.4.2.2.5.3.3.3.cmml">′</mo></msup></mrow></msup></mrow></mtd><mtd columnalign="left" id="S0.E3.m1.4.4f" xref="S0.E3.m1.4.4.cmml"><mi id="S0.E3.m1.4.4.4.3.1" xref="S0.E3.m1.4.4.4.3.1.cmml">otherwise</mi></mtd></mtr></mtable><mi id="S0.E3.m1.6.6.3.2.2" xref="S0.E3.m1.6.6.3.1.1.cmml"/></mrow></mrow></math>, <math><mrow id="p5.14.m1.2.2" xref="p5.14.m1.2.2.cmml"><msub id="p5.14.m1.2.2.3" xref="p5.14.m1.2.2.3.cmml"><mi id="p5.14.m1.2.2.3.2" xref="p5.14.m1.2.2.3.2.cmml">g</mi><mi id="p5.14.m1.2.2.3.3" xref="p5.14.m1.2.2.3.3.cmml">s</mi></msub><mo id="p5.14.m1.2.2.2" xref="p5.14.m1.2.2.2.cmml">⁢</mo><mrow id="p5.14.m1.2.2.1.1" xref="p5.14.m1.2.2.1.2.cmml"><mo stretchy="false" id="p5.14.m1.2.2.1.1.2" xref="p5.14.m1.2.2.1.2.cmml">(</mo><mi id="p5.14.m1.1.1" xref="p5.14.m1.1.1.cmml">θ</mi><mo id="p5.14.m1.2.2.1.1.3" xref="p5.14.m1.2.2.1.2.cmml">,</mo><msup id="p5.14.m1.2.2.1.1.1" xref="p5.14.m1.2.2.1.1.1.cmml"><mi id="p5.14.m1.2.2.1.1.1.2" xref="p5.14.m1.2.2.1.1.1.2.cmml">θ</mi><mo id="p5.14.m1.2.2.1.1.1.3" xref="p5.14.m1.2.2.1.1.1.3.cmml">′</mo></msup><mo stretchy="false" id="p5.14.m1.2.2.1.1.4" xref="p5.14.m1.2.2.1.2.cmml">)</mo></mrow></mrow></math>, <math><mrow id="p5.15.m2.1.1" xref="p5.15.m2.1.1.cmml"><msup id="p5.15.m2.1.1.2" xref="p5.15.m2.1.1.2.cmml"><mi id="p5.15.m2.1.1.2.2" xref="p5.15.m2.1.1.2.2.cmml">θ</mi><mo id="p5.15.m2.1.1.2.3" xref="p5.15.m2.1.1.2.3.cmml">′</mo></msup><mo id="p5.15.m2.1.1.1" xref="p5.15.m2.1.1.1.cmml">→</mo><mrow id="p5.15.m2.1.1.3" xref="p5.15.m2.1.1.3.cmml"><msup id="p5.15.m2.1.1.3.2" xref="p5.15.m2.1.1.3.2.cmml"><mi id="p5.15.m2.1.1.3.2.2" xref="p5.15.m2.1.1.3.2.2.cmml">θ</mi><mo id="p5.15.m2.1.1.3.2.3" xref="p5.15.m2.1.1.3.2.3.cmml">′</mo></msup><mo id="p5.15.m2.1.1.3.1" xref="p5.15.m2.1.1.3.1.cmml">+</mo><mi id="p5.15.m2.1.1.3.3" xref="p5.15.m2.1.1.3.3.cmml">π</mi></mrow></mrow></math>, <math><mrow id="p5.19.m6.1.1" xref="p5.19.m6.1.1.cmml"><mi id="p5.19.m6.1.1.2" xref="p5.19.m6.1.1.2.cmml">ρ</mi><mo id="p5.19.m6.1.1.1" xref="p5.19.m6.1.1.1.cmml">=</mo><mrow id="p5.19.m6.1.1.3" xref="p5.19.m6.1.1.3.cmml"><mi id="p5.19.m6.1.1.3.2" xref="p5.19.m6.1.1.3.2.cmml">N</mi><mo id="p5.19.m6.1.1.3.1" xref="p5.19.m6.1.1.3.1.cmml">/</mo><msup id="p5.19.m6.1.1.3.3" xref="p5.19.m6.1.1.3.3.cmml"><mi id="p5.19.m6.1.1.3.3.2" xref="p5.19.m6.1.1.3.3.2.cmml">L</mi><mn id="p5.19.m6.1.1.3.3.3" xref="p5.19.m6.1.1.3.3.3.cmml">2</mn></msup></mrow></mrow></math>

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1510.01863

Formulas:

1-

\vec{n} (\vec{r}) \equiv \exp [i θ (\vec{r})]

2-

θ (\vec{r})

3-

{⟨ \vec{n} (\vec{r}) \cdot \vec{n} ({\vec{r}}^{'}) ⟩}_{n} = {⟨ e^{i θ (\vec{r})} e^{- i θ ({\vec{r}}^{'})} ⟩}_{n} ∽ {| \vec{r} - {\vec{r}}^{'} |}^{- η}

4-

z (s) = x (s) + i y (s)

5-

\frac{d z}{d s} = e^{i θ (s)}

6-

{⟨ {| z (s) - z (s^{'}) |}^{2} ⟩}_{n c} = \int_{0}^{N} 𝑑 s \int_{0}^{N} 𝑑 s^{'} {⟨ | e^{i θ [z (s)]} e^{- i θ [z (s^{'})]} | ⟩}_{n c}

7-

z (N) ∽ N^{ν}

8-

ν = \frac{2}{2 + η}

9-

R_{1} = m_{c} / N^{2} ρ_{f}

10-

B N / R_{c}^{2}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/cond-mat/0111402

Formulas:

1-

Q_{t} \equiv Q_{0} + C_{p} V_{p} (t)

2-

Q_{0} \equiv C_{g} V_{g} + C_{b} V_{b}

3-

i = p, g, b

4-

| ↑ ⟩ \equiv | 0 ⟩

5-

| ↓ ⟩ \equiv | 1 ⟩

6-

H = \frac{1}{2} δ E (Q_{t}) σ_{z} - \frac{1}{2} E_{J} σ_{x}

7-

δ E (Q_{t}) \equiv 4 E_{C} (Q_{t} / e - 1)

8-

E_{C} \equiv e^{2} / (2 C_{Σ})

9-

\vec{B} = (B_{x}, 0, B_{z}) = (E_{J}, 0, - δ E (Q_{t}))

10-

E_{C} = 122 \pm 3

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/9808052

Formulas:

1-

𝒪 (ρ_{c})

2-

{(σ v)}_{S} \propto m_{f}^{2} / {\tilde{m}}^{4}

3-

χ χ \to t \bar{t}

4-

t \to b W^{+}

5-

W^{+} \to e^{+} ν

6-

W^{+} \to e^{+} ν

7-

b \to e^{+} ν c

8-

W = λ S H_{u} \cdot H_{d} + λ^{'} S^{3} / 3

9-

χ_{S} χ_{S} \to γ γ

10-

g_{1}^{- 2} \sim 10

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: hep-ph

Result: incorrect

Paper: https://arxiv.org/abs/0908.1927

Formulas:

1-

(x \cdot y) \times (x \cdot y) \dots \times (x \cdot y) = (x \times x \times \dots \times x) \cdot (y \times y \times \dots \times y)

2-

(x * y) \times (x * y) \times \dots \times (x * y) = (x \times x \times \dots \times x) * (y \times y \times \dots \times y)

3-

C H_{𝐐}^{n} (X) = C H^{n} (X) \otimes 𝐐

4-

C H^{n} (X)

5-

1_{A} \in End (h (A)) = C H_{𝐐}^{g} (A \times A)

6-

1_{A} = \sum_{i = 0}^{2 g} π_{i}

7-

π_{i} {⟨ m ⟩}^{*} = m^{i} π_{i}

8-

h (A) = \oplus_{i = 0}^{2 g} h^{i} (A), h^{i} (A) = (A, π_{i})

9-

C H_{𝐐}^{n} (A) = Hom (𝕃^{n}, h (A))

10-

C H^{n} {(A)}_{[r]} := {x \in C H_{𝐐}^{n} (A) ∣ {⟨ m ⟩}^{*} x = m^{r} x \forall m \in 𝐙} = Hom (𝕃^{n}, h^{r} (A)) .

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/gr-qc/0701167

Formulas:

1-

10^{- 5} \leq f / Hz \leq 1

2-

h (t, \vec{x})

3-

H = \frac{π (\vec{y}) p (s | \vec{y}) q (\vec{x} | \vec{y})}{π (\vec{x}) p (s | \vec{x}) q (\vec{y} | \vec{x})} .

4-

π (\vec{x})

5-

p (s | \vec{x})

6-

q (\vec{x} | \vec{y})

7-

α = m i n (1, H)

8-

f_{cut} = {\begin{matrix} 10^{- B (1 - i)} f_{\max} & f < f_{\max} \\ f_{\max} & f \geq f_{\max} \end{matrix},

9-

β = {\begin{matrix} 1.0 & 0 \leq SNR \leq 20 \\ {(\frac{SNR}{20})}^{2} & SNR > 20 \end{matrix},

10-

β = {\begin{matrix} 10^{- ξ (1 - \frac{j}{N_{c}})} & 0 \leq j \leq N_{c} \\ 1 & j > N_{c} \end{matrix},

Formulas (html):

Correct Categorie: gr-qc

Guessed Categorie: math

Result: incorrect

Paper: https://arxiv.org/abs/0811.2938

Formulas:

1-

⟨ W_{i r r} ⟩ = ⟨ W ⟩ - Δ F

2-

⟨ W ⟩ = ⟨ H (τ) ⟩ - ⟨ H (0) ⟩

3-

Δ F = F (τ) - F (0) = - k T \ln Z (τ) / Z (0)

4-

⟨ W_{i r r} ⟩

5-

H (t) = \frac{1}{2} (p^{2} + ω^{2} (t) q^{2}) .

6-

ω (0) = ω_{0}

7-

ω (τ) = ω_{1}

8-

q (0) Y (t) + p (0) X (t),

9-

\dot{q} (t),

10-

\ddot{X} + ω^{2} (t) X = 0

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: quant-ph

Result: correct

Paper: https://arxiv.org/abs/1004.2759

Formulas:

1-

(\binom{n}{k}) \leq (\binom{n}{k + 1})

2-

sl (2, ℂ)

3-

[n] = {1, 2, \dots, n}

4-

B {(n)}_{k}

5-

V (B (n)) = V (B {(n)}_{0}) \oplus V (B {(n)}_{1}) \oplus \dots \oplus V (B {(n)}_{n})

6-

v \in V (B (n))

7-

v \in V (B {(n)}_{k})

8-

r (v) = k

9-

v \in V (B {(n)}_{k})

10-

U : V (B (n)) \to V (B (n))

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/1711.08965

Formulas:

1-

\forall s \in S : R_{s} = \prod_{v \in V_{s}} R_{v}

2-

R_{s} = 0.96 \cdot 0.92 \cdot 0.89 \cdot 0.95 = 0.747

3-

V N F_{2}

4-

V N F_{3}

5-

R_{s} = 0.96 \cdot 0.97 \cdot 0.96 \cdot 0.95 = 0.849

6-

\forall s \in S : R_{s} = \prod_{v \in V_{s}} [1 - \prod_{w \in V_{v}^{s}} (1 - R_{w})]

7-

V N F_{2}

8-

V N F_{3}

9-

R_{s} = 0.96 \cdot [1 - (1 - 0.92) (1 - 0.97)] \cdot [1 - (1 - 0.89) (1 - 0.96)] \cdot 0.95 = 0.906

10-

V N F_{2}

Formulas (html):

Correct Categorie: cs

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/1302.5086

Formulas:

1-

\sum m_{ν} = 0.39 \pm 0.10

2-

σ_{8} Ω_{m}^{γ}

3-

w_{i, c l} = w_{i} \exp [- \frac{1}{2} \frac{{(s_{8, i} - s_{8, p r i o r})}^{2}}{σ_{s}^{2}}]

4-

s_{8} = σ_{8} Ω_{m}^{γ}

5-

\sum m_{ν} = X_{- b}^{+ a}

6-

s_{8} \equiv σ_{8} {(Ω_{m} / 0.25)}^{0.47} = 0.813 \pm 0.013

7-

s_{8} = 0.866 \pm 0.058

8-

s_{8} = 0.898 \pm 0.029

9-

s_{8} = 0.828 \pm 0.053

10-

\sum m_{ν} = {0.31}_{- 0.11}^{+ 0.10} eV WMAP9+BAO+Cl (V09)

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0012080

Formulas:

1-

q (p) = - \partial \ln f / \partial \ln p

2-

Δ \ln (p) = 12

3-

q_{s} = 3 r / (r - 1)

4-

ρ_{j} / ρ_{a} = 10^{- 2}

5-

B_{t} / B_{p 0} = 2

6-

β_{0} = 8 π P_{g} / B_{p 0}^{2} = 10^{2}

7-

M_{A} = (4 π u \sqrt{ρ}) / | B | < 1

8-

f (p) \propto p^{- q_{s}}

9-

q_{s} = 3 r / (r - 1)

10-

f (p) \propto p^{- q_{j}}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1402.2225

Formulas:

1-

H = - t \sum_{i, j, σ} c_{i, σ}^{†} c_{j, σ},

2-

{| Φ (\vec{R}) |}^{2}

3-

= c t e + \cos (\vec{K} - \vec{K^{'}}) \cdot \vec{R}

4-

\to (\vec{K} - \vec{K^{'}}) \cdot \vec{R} = 2 n π

5-

3 n \times 3 n

6-

H = H_{C} + H_{R} + H_{L} + h_{L C} + h_{L R},

7-

𝒢_{C} (E) = {(E - H_{C} - Σ_{L} - Σ_{R})}^{- 1},

8-

Σ_{ℓ} = h_{ℓ C} g_{ℓ} h_{ℓ C}^{†}

9-

g_{ℓ} = {(E - H_{ℓ})}^{- 1}

10-

G_{0} = 2 e^{2} / h

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1304.7086

Formulas:

1-

0 \leq k \leq n / 2

2-

H_{c}^{2 k} (M / F)

3-

{ch}_{a}^{k} ({Ind}_{a} (D^{+})) = {ch}_{a}^{k} ([P_{0}]) .

4-

{ch}_{a} ({Ind}_{a} (D^{+})) = {ch}_{a} ([P_{0}]) .

5-

𝕋^{n} \times 𝕋^{n} \times ℝ^{n}

6-

{\hat{E}}_{n} \to 𝕋^{n} \times 𝕋^{n}

7-

ξ \in ℤ^{n} = π_{1} (𝕋^{n})

8-

(x, w, z) \in ℝ^{n} \times 𝕋^{n} \times ℂ

9-

ξ \cdot (x, w, z) = (x + ξ, w, (ξ w) \cdot z),

10-

(ξ w) \cdot z = (\exp (2 π i ξ_{1} w_{1}) z_{1}, \dots, \exp (2 π i ξ_{n} w_{n}) z_{n}) .

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/1702.01325

Formulas:

1-

(x_{i}, y_{i}, z_{i})

2-

(R_{i}, G_{i}, B_{i})

3-

S^{^{'}} = (\begin{matrix} x_{1}, \dots, x_{N} \\ y_{1}, \dots, y_{N} \\ z_{1}, \dots, z_{N} \end{matrix})

4-

T^{^{'}} = (\begin{matrix} R_{1}, \dots, R_{N} \\ G_{1}, \dots, G_{N} \\ B_{1}, \dots, B_{N} \end{matrix}) .

5-

S^{^{'}} = {(\begin{matrix} x_{1}, \dots, x_{N}, y_{1}, \dots, y_{N}, z_{1}, \dots, z_{N} \end{matrix})}^{T},

6-

T^{^{'}} = {(\begin{matrix} R_{1}, \dots, R_{N}, G_{1}, \dots, G_{N}, B_{1}, \dots, B_{N} \end{matrix})}^{T}

7-

S = \sum_{i = 1}^{200} α_{i} . S_{i} T = \sum_{i = 1}^{200} β_{i} . T_{i} .

8-

\sum α_{i} = 1, \sum β_{i} = 1, α_{i}, β_{i} \in [0, 1]

9-

\bar{S} = \frac{1}{200} \sum_{i = 1}^{200} S_{i} .

10-

a_{i} = v e c (S_{i} - \bar{S}) .

Formulas (html):

Correct Categorie: cs

Guessed Categorie: cs

Result: correct

Paper: https://arxiv.org/abs/1201.0544

Formulas:

1-

G (n, k)

2-

ξ \in S^{n - 1}

3-

{vol}_{i} (Q)

4-

T (C) = D

5-

h_{K} (x) = \max {⟨ x, y ⟩ : y \in K}, x \in ℝ^{n} .

6-

ρ_{K} (x) = \max {λ > 0 : λ x \in K}, x \in S^{n - 1} .

7-

V_{i} (K)

8-

{vol}_{n} (K + ϵ B_{2}^{n}) = \sum_{i = 0}^{n} κ_{n - i} V_{i} (K) ϵ^{n - i},

9-

V_{n} (K)

10-

V_{n - 1} (K)

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/0809.3209

Formulas:

1-

r = \frac{1}{2} \cdot \frac{1.22 λ}{N A}

2-

| g_{1}^{*} | = 0.34

3-

| g_{2}^{*} | = 0.44

4-

g^{*} = h ν / μ_{B} \vec{B}

5-

| g_{1}^{*} | = 0.34

6-

| g_{2}^{*} | = 0.44

7-

1 / τ_{K} = 1 / T_{2}^{*} + 1 / τ_{e}

8-

| g_{2}^{*} | = 0.44

9-

| g^{*} | = 0.44

10-

τ_{K} \propto N_{e x}^{- 0.4}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/2009.03519

Formulas:

1-

P = - \frac{Λ}{8 π}

2-

V = {(\frac{\partial M}{\partial P})}_{S, Q, J}

3-

I = \frac{1}{16 π} \int d^{4} x \sqrt{- g} (R + \frac{6}{l^{2}} - L (ℱ)),

4-

Λ = - \frac{3}{l^{2}}

5-

ℱ \equiv \frac{1}{4} F^{μ ν} F_{μ ν}

6-

\nabla (ℓ_{ℱ} F^{μ ν}) = 0,

7-

G_{μ ν} = T_{μ ν},

8-

G_{μ ν} = R_{μ ν} - \frac{1}{2} R g_{μ ν}

9-

L_{ℱ} = \frac{\partial L}{\partial ℱ}

10-

T_{μ ν} = 2 (L_{ℱ} ℱ_{μ ν}^{2} - \frac{1}{4} g_{μ ν} L)

Formulas (html):

Correct Categorie: hep-th

Guessed Categorie: gr-qc

Result: incorrect

Paper: https://arxiv.org/abs/gr-qc/0008023

Formulas:

1-

G_{a b} + Λ g_{a b} = κ T_{a b}

2-

T_{a b} = \nabla_{a} ϕ \nabla_{b} ϕ - \frac{1}{2} \nabla^{c} ϕ \nabla_{c} ϕ g_{a b}

3-

2 π \bar{r}

4-

d s^{2} = - e^{2 ν} d u^{2} - 2 e^{ν + λ} d u d \bar{r} + {\bar{r}}^{2} d θ^{2}

5-

l^{a} = e^{- λ} {(\frac{\partial}{\partial \bar{r}})}^{a}

6-

n^{a} = e^{- ν} {(\frac{\partial}{\partial u})}^{a} - \frac{1}{2} e^{- λ} {(\frac{\partial}{\partial \bar{r}})}^{a}

7-

G_{a b} l^{a} l^{b} = 4 π {(l^{a} \nabla_{a} ϕ)}^{2}

8-

G_{a b} l^{a} n^{b} = Λ

9-

\frac{1}{\bar{r}} e^{- 2 λ} \frac{\partial}{\partial \bar{r}} (λ + ν) = 4 π e^{- 2 λ} {(\frac{\partial ϕ}{\partial \bar{r}})}^{2}

10-

\frac{- 1}{2 \bar{r}} e^{- 2 λ} \frac{\partial}{\partial \bar{r}} (ν - λ) = Λ

Formulas (html):

Correct Categorie: gr-qc

Guessed Categorie: gr-qc

Result: correct

Paper: https://arxiv.org/abs/1609.09201

Formulas:

1-

η_{c} \to η π^{+} π^{-}

2-

f_{0} (500)

3-

f_{0} (980)

4-

a_{0} (980)

5-

η_{c} \to η π^{+} π^{-}

6-

η π^{+} π^{-}

7-

M_{π^{+} π^{-}}

8-

f_{0} (500)

9-

f_{0} (980)

10-

a_{0} (980)

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: hep-ex

Result: incorrect

Paper: https://arxiv.org/abs/0709.2974

Formulas:

1-

\sim 10^{6} M_{⊙}

2-

v_{rot, H i}

3-

{< σ >}_{H i}

4-

σ_{Peak, H i}

5-

M_{H i} [10^{9} M_{⊙}]

6-

δ r = 5 pc

7-

E (H^{+}) = 4.6 \cdot 10^{50} ergs

8-

v_{rot} = \sqrt{\frac{G M_{s}}{3} {\frac{r}{r + r_{s}}}^{2}}

9-

v_{esc} = \sqrt{2 | - \frac{G M_{s}}{r} \log (1 + \frac{r}{r_{s}}) |}

10-

\sim 10^{9} M_{⊙}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/cond-mat/0409609

Formulas:

1-

P (N) \sim 10^{- 0.38 N}

2-

P_{c} (M)

3-

P_{c} (M)

4-

P_{c} (M) = 0.150 + {0.857 10}^{- 0.042 M}

5-

P_{c} (M) = {0.410 10}^{- 0.010 M}

6-

P_{c} (G)

7-

P_{c} (G)

8-

P_{c} (G)

9-

P_{c} (G) = - 0.259 + 1.256 G^{- 0.500}

10-

P_{c} (G) = - 0.004 + 4.454 G^{- 1.440}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1608.08837

Formulas:

1-

0.6 - 1.6 \times 10^{8} L_{⊙}

2-

\sim 10 - 15 M_{⊙}

3-

M_{⊙} y r^{- 1}

4-

S F R > 15 - 30 M_{⊙} y r^{- 1}

5-

M_{S E D}

6-

M_{⊙} y r^{- 1}

7-

r m s_{c o n t}

8-

t_{i n t}

9-

Δ p o s

10-

M_{d y n} * s i n {(i)}^{2}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1205.2425

Formulas:

1-

O (n^{2})

2-

O (n \log n)

3-

Ω (n \log n)

4-

{(n - 1)}^{2}

5-

A_{1} B_{1}, \dots, A_{1} B_{7}

6-

A_{2} B_{7}, \dots, A_{6} B_{7}

7-

v_{1}, v_{2}, v_{3}

8-

(v_{1}, v_{2})

9-

(v_{2}, v_{3})

10-

{v_{1}, v_{3}}

Formulas (html):

Correct Categorie: cs

Guessed Categorie: cs

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0507120

Formulas:

1-

Q_{i} (𝐱, 𝐬)

2-

P_{i} (𝐱) = \frac{n_{s}}{N} Q_{i} (𝐱, 𝐬) + \frac{N - n_{s}}{N} R (𝐱) .

3-

R (𝐬_{j})

4-

Q_{i}^{t o t}

5-

Q_{i}^{t o t} (𝐱) = \sum_{j = 1}^{M} R (𝐬_{j}) Q_{i} (𝐱, 𝐬_{j}) / \sum_{k = 1}^{M} R (𝐬_{k}) .

6-

Q_{i}^{t o t}

7-

P_{i} (𝐱_{i}) = \frac{n_{s}}{N} Q_{i}^{t o t} (𝐱_{i}) + \frac{N - n_{s}}{N} R (𝐱_{i}) .

8-

ℒ (n_{s}) = \prod_{i = 1}^{N} P_{i} (𝐱_{i}) .

9-

ℛ (n_{s}) = \frac{ℒ (n_{s})}{ℒ (0)} = \prod_{i = 1}^{N} {\frac{n_{s}}{N} (\frac{Q_{i}^{t o t} (𝐱_{i})}{R (𝐱_{i})} - 1) + 1}

10-

χ^{2} = 2 \ln ℛ

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/2011.09905

Formulas:

1-

Δ 𝐲 = \sum_{k} | Δ y_{k} | \approx Δ w_{i} \sum_{k} | \frac{\partial y_{k}}{\partial w_{i}} | .

2-

P (\frac{\partial L}{\partial w_{i}})

3-

sign (\frac{\partial L}{\partial w_{i}})

4-

Δ L \approx Δ w_{i} | \frac{\partial L}{\partial 𝐲} \cdot \frac{\partial 𝐲}{\partial w_{i}} | = Δ w_{i} | \frac{\partial L}{\partial w_{i}} | .

5-

S (L, w_{i}) = | \frac{\partial L}{\partial w_{i}} | .

6-

w_{i}^{t + 1} := w_{i}^{t}

7-

- η \frac{\partial L}{\partial w_{i}^{t}} +

8-

- λ w_{i}^{t} [1 - S (L, w_{i}^{t})] P [S (L, w_{i}^{t})],

9-

P (x) = Θ [1 - | x |],

10-

w_{i}^{t + 1} = w_{i}^{t} - η \frac{\partial L}{\partial w_{i}^{t}} - λ Γ (L, w_{i}^{t}) [1 - | \frac{\partial L}{\partial w_{i}^{t}} |],

Formulas (html):

Correct Categorie: cs

Guessed Categorie: cs

Result: correct

Paper: https://arxiv.org/abs/2001.02624

Formulas:

1-

Δ σ_{1 a}

2-

Δ σ_{1 c}

3-

Δ σ_{1 a}

4-

Δ σ_{1 a}

5-

Δ σ_{1 c}

6-

Δ σ_{1 c}

7-

Δ σ_{1 a}

8-

Δ σ_{1 c}

9-

Δ σ_{1 c}

10-

Δ σ_{1 a}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1101.4938

Formulas:

1-

α / F e - σ

2-

α / F e - σ

3-

α / F e - σ

4-

ψ \propto M_{g} / t_{d}

5-

t_{d} \approx 2 - 10

6-

10^{43} \leq L / e r g s^{- 1} \leq 10^{46}

7-

{< α / F e >}_{*} ≃ \frac{\int (α / F e) (t) ψ (t) L_{V}^{S S P} (t_{0} - t) 𝑑 t}{\int ψ (t) L_{V} (t_{0} - t) 𝑑 t}

8-

(α / F e)

9-

L_{V}^{S S P} (t_{0} - t)

10-

(t_{0} - t)

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/cond-mat/9812121

Formulas:

1-

G_{t i p, s u r f} = (e^{2} / h) 4 π^{2} ν_{t i p} {| t |}^{2} ν (x)

2-

ν_{t i p}

3-

V_{t i p}

4-

ν (x, 1)

5-

⟨ {(Δ I_{t i p})}^{2} ⟩

6-

G_{α β} = (e^{2} / h) T_{α β}

7-

G_{t i p, α}

8-

G_{α, t i p}

9-

T_{t i p, α}

10-

T_{t i p, α}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1512.07203

Formulas:

1-

10^{50} - 10^{51} erg s^{- 1}

2-

erg {cm}^{- 2} s^{- 1}

3-

\log Q_{ν_{e}} = 39.78 + 0.15 a_{*} + 1.19 \log \dot{m} - 3.46 \log r,

4-

\log Q_{{\bar{ν}}_{e}} = 40.02 + 0.29 a_{*} + 1.35 \log \dot{m} - 3.59 \log r,

5-

\log T = 11.09 + 0.10 a_{*} + 0.20 \log \dot{m} - 0.59 \log r,

6-

0 \leq a_{*} \leq 1

7-

\dot{m} = \dot{M} / M_{⊙} s^{- 1}

8-

r = R / R_{g}

9-

R_{g} = 2 G M_{BH} / c^{2}

10-

M_{BH} = 3 M_{⊙}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/2001.08554

Formulas:

1-

< T < T_{c} = 89

2-

t_{C} / L_{G} ≳ 2

3-

β_{L} = I_{c} L_{SQ} / Φ_{0}

4-

j_{c} ≃ 3 \cdot 10^{6}

5-

L_{k} = L μ_{0} λ^{2} / w t

6-

2 I_{c} L_{k} / Φ_{0} = 4 j_{c} L μ_{0} λ^{2} / Φ_{0}

7-

I_{c}^{G} / w t

8-

S_{V, a}^{1 / 2}

9-

S_{Φ, a}^{1 / 2} = S_{V, a}^{1 / 2} / V_{Φ}

10-

V_{Φ} = \max (δ V / δ Φ) ≃ π Δ V_{\max} / Φ_{0}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/2007.12959

Formulas:

1-

F = 0.0042 T_{0.01} / (0.4665 + 0.003595 δ - 4.98 \times 10^{- 5} δ^{2}) Jy,

2-

T_{0.01} = 0.01 K

3-

G = 8.5 K {Jy}^{- 1}

4-

G = 0.74 K {Jy}^{- 1}

5-

\begin{matrix} F_{b} (V) & = \int_{V_{c} - V}^{V_{c}} F_{V} 𝑑 V, \\ F_{r} (V) & = \int_{V_{c}}^{V_{c} + V} F_{V} 𝑑 V, \\ F_{t} (V) & = F_{b} (V) + F_{r} (V), \end{matrix}

6-

f = F_{t} (V) / F

7-

f = F_{b} (V) / F

8-

f = F_{r} (V) / F

9-

F_{t} (V)

10-

f = F_{t} (V) / F = 0.85

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1602.06625

Formulas:

1-

E_{γ} Q_{γ} (E_{γ}) \approx {(2 / 3) E_{ν} Q_{ν} (E_{ν}) |}_{E_{ν} = E_{γ} / 2}

2-

p (n, r) = \frac{4 π N^{n - 1}}{(n - 1)!} e^{- N} r^{2} ρ

3-

N = \int ρ 4 π r^{2} 𝑑 r

4-

ρ = ρ (0) f (z)

5-

\bar{r} (n) = \int_{0}^{\infty} p (n, r) r 𝑑 r

6-

Φ_{γ, un} (E_{γ}) = \sum_{F_{n} < F_{sens}}^{n} F_{n} (E_{γ}) \leq Φ_{IGRB} (E_{γ}) .

7-

Φ_{γ, un} (E_{γ})

8-

F_{n} (E_{γ})

9-

Φ_{γ, tot} (E_{γ}) = \sum^{n} F_{n} (E_{γ}) \leq Φ_{EGB} (E_{γ}) .

10-

Φ_{γ, tot} (E_{γ})

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/cond-mat/0110302

Formulas:

1-

H = ℏ (ω_{0} + δ ω n_{1}) c^{†} c

2-

| 𝟢 ⟩ = | ↑ ⟩ \otimes | ϕ ⟩

3-

| 𝟣 ⟩ = | ↓ ⟩ \otimes | ψ ⟩

4-

n_{1} = | 𝟣 ⟩ ⟨ 𝟣 |

5-

| Ψ ⟩ = a | 𝟢 ⟩ + b | 𝟣 ⟩

6-

ℏ ℰ (\hat{c} + {\hat{c}}^{†})

7-

Δ = δ ω / γ

8-

{\hat{H}}_{D} = ℏ E (\hat{c} + {\hat{c}}^{†}) + ℏ Δ n_{1} {\hat{c}}^{†} \hat{c}

9-

Q = ω_{0} / γ_{M}

10-

γ_{M} ≪ ω_{0}, k T / ℏ

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/0703100

Formulas:

1-

I > I_{t h}

2-

ω = n \times ω_{c}

3-

n \times ℏ ω_{c} = 2 R_{c} E_{H}

4-

I_{d c} > I_{t h}

5-

I_{d c} > I_{t h}

6-

I_{d c} > I_{t h}

7-

V_{x x} - I_{d c}

8-

r_{x x} = d V_{x x} / d I

9-

V_{x x} - I_{d c}

10-

r_{m i n} > 0

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/0710.1539

Formulas:

1-

λ = ν_{0} P

2-

ν_{0} = 10^{19} s^{- 1}

3-

T_{1 / 2} (Q_{e x})

4-

T_{1 / 2} (Q_{e x})

5-

T_{1 / 2} (Q_{A u d i})

6-

T_{1 / 2} (Q_{e x})

7-

T_{1 / 2} (Q_{A u d i})

8-

T_{1 / 2}^{G L D M}

9-

T_{1 / 2}^{V S S}

10-

T_{1 / 2}^{G L D M}

Formulas (html):

Correct Categorie: nucl-ex

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1110.0587

Formulas:

1-

P n m a

2-

M i - M i

3-

f_{μ} = γ_{μ} / (2 π) B

4-

γ_{μ} / 2 π = 135.5

5-

P n m a

6-

a = 5.0639 (5)

7-

b = 10.397 (1)

8-

c = 17.467 (2)

9-

P n m a

10-

x, y, z [u, v, w]

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1108.5660

Formulas:

1-

n! n^{- n}

2-

μ (X) = 1

3-

ξ_{j} = {B_{j}, S B_{j}, S^{2} B_{j}, \dots, S^{h_{j} - 1} B_{j}, C_{j}^{1}, \dots, C_{j}^{m_{j}} \dots}

4-

μ (U_{j}) \to β

5-

U_{j} = ⊔_{0 \leq k < h_{j}} S^{k} B_{j}

6-

β (T^{\otimes n}) \leq n^{- n}

7-

β (T^{⊙ n}) \leq n! n^{- n}

8-

R a n k (T^{⊙ n}) = \infty

9-

β (T^{\times n}) \geq n^{- n}

10-

β (T^{⊙ n}) \geq n! n^{- n}

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/hep-ph/0010213

Formulas:

1-

\sin^{2} 2 θ_{V} = 1

2-

Δ m^{2} / 2 E

3-

ν_{2} = \sin θ_{V} ν_{e} + \cos θ_{V} ν_{x} .

4-

\sin^{2} θ_{V} F_{0}

5-

ν_{1} = \cos θ_{V} ν_{e} - \sin θ_{V} ν_{x} .

6-

a ν_{2} + b ν_{1}

7-

ν_{1} - ν_{2}

8-

i \frac{\partial}{\partial t} (\begin{matrix} ν_{1} \\ ν_{2} \end{matrix}) = ℋ (\begin{matrix} ν_{1} \\ ν_{2} \end{matrix}),

9-

ℋ = \frac{1}{2} (\begin{matrix} B & A \\ A & - B \end{matrix}),

10-

\sqrt{2} G_{F} N_{e} \sin 2 θ_{V},

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: hep-ph

Result: correct

Paper: https://arxiv.org/abs/1302.2670

Formulas:

1-

ϕ_{σ} (x, t)

2-

ρ_{σ} = (e / 2 π) \partial_{x} ϕ_{σ}

3-

j_{σ} = - (e / 2 π) \partial_{t} ϕ_{σ}

4-

[\partial_{x} ϕ_{σ} (x, t), ϕ_{σ^{'}} (y, t)] = 2 π i σ δ_{σ σ^{'}} δ (x - y) .

5-

\frac{ℏ v_{F}}{4 π} \sum_{σ} \int_{- \infty}^{\infty} 𝑑 x {(\partial_{x} ϕ_{σ})}^{2} + \frac{Q^{2}}{2 C},

6-

\int_{- \infty}^{0} 𝑑 x e^{ϵ x / v_{F}} [ρ_{+} (x) + ρ_{-} (x)] .

7-

σ \partial_{t} ϕ_{σ} (x, t) + v_{F} \partial_{x} ϕ_{σ} (x, t) = - \frac{e}{ℏ C} Q (t) e^{ϵ x / v_{F}} θ (- x) .

8-

\partial_{t} ϕ_{+} (- \infty, t)

9-

- (2 π / e) j_{c} (t),

10-

\partial_{t} ϕ_{-} (0, t)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: nucl-th

Result: incorrect

Paper: https://arxiv.org/abs/cs/9809113

Formulas:

1-

t r a i n (A_{i}, 𝒞^{j})

2-

t e s t (𝒯, A_{1}, M_{1}^{i}, A_{2}, M_{2}^{i})

3-

t a g (𝒩, A_{i}, M_{i}^{j})

4-

c o m b i n e (𝒞^{0}, 𝒩_{1}^{i} \cap 𝒩_{2}^{i})

5-

𝒩_{1}^{i} \cap 𝒩_{2}^{i}

6-

t r a i n (A_{1}, 𝒞^{0})

7-

t r a i n (A_{2}, 𝒞^{0})

8-

t e s t (𝒯, A_{1}, M_{1}^{0}, A_{2}, M_{2}^{0})

9-

t a g (𝒩, A_{1}, M_{1}^{i})

10-

t a g (𝒩, A_{2}, M_{2}^{i})

Formulas (html):

Correct Categorie: cs

Guessed Categorie: cs

Result: correct

Paper: https://arxiv.org/abs/1812.01855

Formulas:

1-

𝒱 = {𝐯_{1}, \dots, 𝐯_{N}}

2-

ℰ = {𝐞_{i j} | i, j = 1, \dots, N}

3-

𝐃 \in ℝ^{C \times d}

4-

𝐞_{i j} = [𝐯_{i}; 𝐯_{j}]

5-

𝐚 \in {[0, 1]}^{N}

6-

𝐖 \in {[0, 1]}^{N \times N}

7-

𝐚 = f (𝒱, 𝐪) .

8-

range (f) = [0, 1]

9-

𝐖 = g (ℰ, 𝐪),

10-

range (g) = [0, 1]

Formulas (html):

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stretchy="false" id="S3.SS2.p2.4.m3.3.4.2.3.2.1" xref="S3.SS2.p2.4.m3.3.4.2.cmml">(</mo><mi id="S3.SS2.p2.4.m3.1.1" xref="S3.SS2.p2.4.m3.1.1.cmml">f</mi><mo stretchy="false" id="S3.SS2.p2.4.m3.3.4.2.3.2.2" xref="S3.SS2.p2.4.m3.3.4.2.cmml">)</mo></mrow></mrow><mo id="S3.SS2.p2.4.m3.3.4.1" xref="S3.SS2.p2.4.m3.3.4.1.cmml">=</mo><mrow id="S3.SS2.p2.4.m3.3.4.3.2" xref="S3.SS2.p2.4.m3.3.4.3.1.cmml"><mo stretchy="false" id="S3.SS2.p2.4.m3.3.4.3.2.1" xref="S3.SS2.p2.4.m3.3.4.3.1.cmml">[</mo><mn id="S3.SS2.p2.4.m3.2.2" xref="S3.SS2.p2.4.m3.2.2.cmml">0</mn><mo id="S3.SS2.p2.4.m3.3.4.3.2.2" xref="S3.SS2.p2.4.m3.3.4.3.1.cmml">,</mo><mn id="S3.SS2.p2.4.m3.3.3" xref="S3.SS2.p2.4.m3.3.3.cmml">1</mn><mo stretchy="false" id="S3.SS2.p2.4.m3.3.4.3.2.3" xref="S3.SS2.p2.4.m3.3.4.3.1.cmml">]</mo></mrow></mrow></math>, <math><mrow id="S3.E2.m1.3.3.1" xref="S3.E2.m1.3.3.1.1.cmml"><mrow id="S3.E2.m1.3.3.1.1" xref="S3.E2.m1.3.3.1.1.cmml"><mi id="S3.E2.m1.3.3.1.1.2" xref="S3.E2.m1.3.3.1.1.2.cmml">𝐖</mi><mo id="S3.E2.m1.3.3.1.1.1" xref="S3.E2.m1.3.3.1.1.1.cmml">=</mo><mrow id="S3.E2.m1.3.3.1.1.3" xref="S3.E2.m1.3.3.1.1.3.cmml"><mi id="S3.E2.m1.3.3.1.1.3.2" xref="S3.E2.m1.3.3.1.1.3.2.cmml">g</mi><mo id="S3.E2.m1.3.3.1.1.3.1" xref="S3.E2.m1.3.3.1.1.3.1.cmml">⁢</mo><mrow id="S3.E2.m1.3.3.1.1.3.3.2" xref="S3.E2.m1.3.3.1.1.3.3.1.cmml"><mo stretchy="false" id="S3.E2.m1.3.3.1.1.3.3.2.1" xref="S3.E2.m1.3.3.1.1.3.3.1.cmml">(</mo><mi class="ltx_font_mathcaligraphic" id="S3.E2.m1.1.1" xref="S3.E2.m1.1.1.cmml">ℰ</mi><mo id="S3.E2.m1.3.3.1.1.3.3.2.2" xref="S3.E2.m1.3.3.1.1.3.3.1.cmml">,</mo><mi id="S3.E2.m1.2.2" xref="S3.E2.m1.2.2.cmml">𝐪</mi><mo stretchy="false" id="S3.E2.m1.3.3.1.1.3.3.2.3" xref="S3.E2.m1.3.3.1.1.3.3.1.cmml">)</mo></mrow></mrow></mrow><mo id="S3.E2.m1.3.3.1.2" xref="S3.E2.m1.3.3.1.1.cmml">,</mo></mrow></math>, <math><mrow id="S3.SS2.p3.4.m3.3.4" xref="S3.SS2.p3.4.m3.3.4.cmml"><mrow id="S3.SS2.p3.4.m3.3.4.2" xref="S3.SS2.p3.4.m3.3.4.2.cmml"><mi id="S3.SS2.p3.4.m3.3.4.2.2" xref="S3.SS2.p3.4.m3.3.4.2.2.cmml">range</mi><mo id="S3.SS2.p3.4.m3.3.4.2.1" xref="S3.SS2.p3.4.m3.3.4.2.1.cmml">⁢</mo><mrow id="S3.SS2.p3.4.m3.3.4.2.3.2" xref="S3.SS2.p3.4.m3.3.4.2.cmml"><mo stretchy="false" id="S3.SS2.p3.4.m3.3.4.2.3.2.1" xref="S3.SS2.p3.4.m3.3.4.2.cmml">(</mo><mi id="S3.SS2.p3.4.m3.1.1" xref="S3.SS2.p3.4.m3.1.1.cmml">g</mi><mo stretchy="false" id="S3.SS2.p3.4.m3.3.4.2.3.2.2" xref="S3.SS2.p3.4.m3.3.4.2.cmml">)</mo></mrow></mrow><mo id="S3.SS2.p3.4.m3.3.4.1" xref="S3.SS2.p3.4.m3.3.4.1.cmml">=</mo><mrow id="S3.SS2.p3.4.m3.3.4.3.2" xref="S3.SS2.p3.4.m3.3.4.3.1.cmml"><mo stretchy="false" id="S3.SS2.p3.4.m3.3.4.3.2.1" xref="S3.SS2.p3.4.m3.3.4.3.1.cmml">[</mo><mn id="S3.SS2.p3.4.m3.2.2" xref="S3.SS2.p3.4.m3.2.2.cmml">0</mn><mo id="S3.SS2.p3.4.m3.3.4.3.2.2" xref="S3.SS2.p3.4.m3.3.4.3.1.cmml">,</mo><mn id="S3.SS2.p3.4.m3.3.3" xref="S3.SS2.p3.4.m3.3.3.cmml">1</mn><mo stretchy="false" id="S3.SS2.p3.4.m3.3.4.3.2.3" xref="S3.SS2.p3.4.m3.3.4.3.1.cmml">]</mo></mrow></mrow></math>

Correct Categorie: cs

Guessed Categorie: cs

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0112440

Formulas:

1-

0.3 - 0.4 R_{SS L 1}

2-

0.2 R_{SS L 1}

3-

q = ℳ_{r d} / ℳ_{w d} = 0.15

4-

ℳ_{w d} = 0.61 ℳ_{⊙}

5-

R_{w d} = 0.0118 ℛ_{⊙} = 0.0263 R_{SS L 1}

6-

E (B - V)

7-

λ λ 7165, 7665

8-

λ λ 7165, 7665

9-

λ 7165 / λ 7665

10-

M_{r d} = 0.09 M_{⊙}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1904.08768

Formulas:

1-

100 - 550 M P a

2-

850 - 1050^{\circ} C

3-

f_{i j}^{p a r t i c l e} = {\begin{matrix} \frac{1}{2} \frac{χ_{A P B}}{∥ 𝐛 ∥} ∥ 𝐥_{i j} ∥ \tanh (\frac{3 (L - d_{m i n})}{L}) 𝐧^{𝐬} & d_{m i n} \leq L \\ 0 & d_{m i n} > L \end{matrix}

4-

f_{i j}^{p a r t i c l e}

5-

χ_{A P B}

6-

d_{m i n}

7-

B_{i j} (ξ) = {\begin{matrix} B^{g} m_{i} m_{j} + B^{c} n_{i} n_{j} + B^{l} t_{i} t_{j}, & \forall 𝐧 \in {111} \\ B^{c} δ_{i j} + (B^{g} - B^{l}) t_{i} t_{j}, & \forall 𝐧 \notin {111} \end{matrix}

8-

B_{i j} (ξ)

9-

m_{i} = ϵ_{i j k} n_{j} t_{k}

10-

ϵ_{i j k}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/1804.08412

Formulas:

1-

I_{ω} (t)

2-

I_{ω} (t) \propto ω \sum_{l_{h} l_{e}} {| M_{𝟎}^{l_{h} l_{e}} |}^{2} ({| P_{𝟎}^{l_{h} l_{e}} (t) |}^{2} + N_{𝟎}^{l_{h} l_{e}} (t)) ℒ_{γ} (Δ E_{ω}^{l_{h} l_{e}})

3-

M_{𝟎}^{l_{h} l_{e}}

4-

P_{𝑸}^{l_{h} l_{e}} (t)

5-

N_{𝑸}^{l_{h} l_{e}}

6-

P_{𝑸}^{l_{h} l_{e}} (t)

7-

P_{𝑸}^{l_{h} l_{e}} (t) = \sum_{𝒒} φ_{𝒒}^{* h e} ⟨ v_{𝒒 + β^{l_{h} l_{e}} 𝑸}^{† h} c_{𝒒 - α^{l_{h} l_{e}} 𝑸}^{e} ⟩

8-

v^{(†)}, c^{(†)}

9-

N_{𝑸}^{l_{h} l_{e}} (t) = \sum_{𝒒, 𝒒^{'}} φ_{𝒒^{'}}^{* h e} φ_{𝒒}^{l_{h} l_{e}} δ ⟨ c_{𝒒 - α^{l_{h} l_{e}} 𝑸}^{† e} v_{𝒒 + β^{l_{h} l_{e}} 𝑸}^{h} v_{𝒒^{'} + β^{l_{h} l_{e}} 𝑸}^{† h} c_{𝒒^{'} - α^{l_{h} l_{e}} 𝑸}^{e} ⟩ (t)

10-

α = m_{e} / (m_{h} + m_{e})

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1605.08150

Formulas:

1-

N o n l i n e a r F u n c t i o n * G a u s s i a n

2-

\begin{matrix} E [{| {\hat{x}}_{T} (ω) |}^{2}] = E [\frac{1}{T} \int_{T}^{0} x^{*} (t) e^{i ω t} 𝑑 t \int_{T}^{0} x (t^{'}) e^{- i ω t^{'}} 𝑑 t^{'}] \\ = \frac{1}{T} \int_{T}^{0} \int_{T}^{0} E [x^{*} (t) x (t^{'}) e^{i ω (t - t^{'})} d t d t^{'}] \end{matrix}

3-

x_{i} = A s_{i} + μ + η_{i}

4-

η_i \sim N (0, σ^{2} \sum i)

5-

\hat{x} = W x

6-

μ_{M L} = < x_{i} >

7-

x_{i} = A (s_{i} + W_{μ M L}) + \tilde{η_{i}}

8-

\tilde{η_{i}} = η_{i} + {(I - A W)}_{μ M L}

9-

{\hat{A}}_{M L} = U_{q} {(△_{q} - σ^{2} I_{q})}^{1 / 2}

10-

{\hat{S}}_{M L} = {({\hat{A}}^{t} \hat{A})}^{- 1} {\hat{A}}^{t} x

Formulas (html):

Correct Categorie: cs

Guessed Categorie: cs

Result: correct

Paper: https://arxiv.org/abs/1409.1585

Formulas:

1-

λ / Δ λ \approx 1300

2-

L_{c} = (8.1 \pm 1.3) \times 10^{5}

3-

L^{'} = (2.1 \pm 0.3) \times 10^{9}

4-

L^{'} = 1.2 \times 10^{9}

5-

M_{H2} \sim < 10^{9}

6-

L_{c} \approx 2.6 \times 10^{6}

7-

L^{'} \approx 6.6 \times 10^{9}

8-

M_{H2} \approx 5 \times 10^{9}

9-

L_{c} = (4.8 \pm 1.4) \times 10^{5}

10-

L^{'} = (1.2 \pm 0.4) \times 10^{9}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Run 6938497 (Agent767)