Run 16330496

Paper: https://arxiv.org/abs/astro-ph/0304231

Formulas:

1-

\log L_{X} / L_{b o l} = - 3.4

2-

\log L_{X} / L_{b o l}

3-

R O S A T

4-

\log L_{X} / L_{b o l} ≃ - 3

5-

C h a n d r a

6-

L_{X} = 1 \times 10^{26}

7-

\log L_{X} / L_{b o l} ≃ - 4.1

8-

X M M - N e w t o n

9-

\log L_{X} / L_{b o l} ≃ - 2.6

10-

C h a n d r a

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: math

Result: incorrect

Paper: https://arxiv.org/abs/1506.07178

Formulas:

1-

\sim 4 - 20 μ

2-

\sim 8^{\circ} - 37^{\circ}

3-

Σ \sim 10 - 100 M_{⊙} {pc}^{- 2}

4-

| x |, | y | ≪ R

5-

𝐯_{c} \equiv u_{c} \hat{𝐱} + v_{c} \hat{𝐲} = R (Ω - Ω_{p}) \sin i \hat{𝐱} + [R (Ω - Ω_{p}) - q_{c} Ω x] \hat{𝐲},

6-

q_{c} \equiv - d \ln Ω / d \ln R

7-

κ = {(R^{- 3} d [Ω^{2} R^{4}] / d R)}^{1 / 2} = {(4 - 2 q_{c})}^{1 / 2} Ω

8-

\frac{\partial Σ}{\partial t} + \nabla \cdot (Σ 𝐯_{T}) = 0,

9-

\frac{\partial 𝐯}{\partial t} + 𝐯_{T} \cdot \nabla 𝐯 = - c_{s}^{2} \nabla \ln Σ + q_{c} Ω v_{x} \hat{𝐲} - 2 𝛀 \times 𝐯 - \nabla Φ_{s} + \frac{1}{4 π Σ} (\nabla \times 𝐁) \times 𝐁,

10-

\frac{\partial 𝐁}{\partial t} = \nabla \times (𝐯_{T} \times 𝐁),

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/1410.7741

Formulas:

1-

λ^{c y c}

2-

T_{c} \approx 4 K

3-

ρ (300 K)

4-

ρ (5 K)

5-

A / A_{0} = X / \sinh (X)

6-

X = 2 π^{2} k_{B} T / ℏ ω_{c}

7-

F = 2 π e S_{k} / ℏ

8-

m^{*} / m_{e} = 1.5

9-

γ^{c a l c}

10-

γ^{e x p}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/hep-th/0702156

Formulas:

1-

J^{P C} = 0^{+ +}

2-

J^{P C} = 0^{- -}

3-

S U (N)

4-

A_{i} = - i A_{i}^{a} t^{a}

5-

i = 1 \dots 2

6-

𝔰 𝔲 (N)

7-

[t^{a}, t^{b}] = i f^{a b c} t^{c}

8-

tr (t^{a} t^{b}) = \frac{1}{2} δ^{a b}

9-

D_{i} = \partial_{i} + A_{i}

10-

A_{i} = - (\partial_{i} M_{i}) M_{i}^{- 1}, (no summation),

Formulas (html):

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id="S2.SS1.p1.8.m8.2.2.4.3.3.3" xref="S2.SS1.p1.8.m8.2.2.4.3.3.3.cmml">b</mi><mo id="S2.SS1.p1.8.m8.2.2.4.3.3.1a" xref="S2.SS1.p1.8.m8.2.2.4.3.3.1.cmml">⁢</mo><mi id="S2.SS1.p1.8.m8.2.2.4.3.3.4" xref="S2.SS1.p1.8.m8.2.2.4.3.3.4.cmml">c</mi></mrow></msup><mo id="S2.SS1.p1.8.m8.2.2.4.1a" xref="S2.SS1.p1.8.m8.2.2.4.1.cmml">⁢</mo><msup id="S2.SS1.p1.8.m8.2.2.4.4" xref="S2.SS1.p1.8.m8.2.2.4.4.cmml"><mi id="S2.SS1.p1.8.m8.2.2.4.4.2" xref="S2.SS1.p1.8.m8.2.2.4.4.2.cmml">t</mi><mi id="S2.SS1.p1.8.m8.2.2.4.4.3" xref="S2.SS1.p1.8.m8.2.2.4.4.3.cmml">c</mi></msup></mrow></mrow></math>, <math><mrow id="S2.SS1.p1.9.m9.2.2" xref="S2.SS1.p1.9.m9.2.2.cmml"><mrow id="S2.SS1.p1.9.m9.2.2.1.1" xref="S2.SS1.p1.9.m9.2.2.1.2.cmml"><mi id="S2.SS1.p1.9.m9.1.1" xref="S2.SS1.p1.9.m9.1.1.cmml">tr</mi><mo id="S2.SS1.p1.9.m9.2.2.1.1a" xref="S2.SS1.p1.9.m9.2.2.1.2.cmml">⁡</mo><mrow id="S2.SS1.p1.9.m9.2.2.1.1.1" xref="S2.SS1.p1.9.m9.2.2.1.2.cmml"><mo stretchy="false" id="S2.SS1.p1.9.m9.2.2.1.1.1.2" 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id="S2.SS1.p1.9.m9.2.2.3.2" xref="S2.SS1.p1.9.m9.2.2.3.2.cmml"><mn id="S2.SS1.p1.9.m9.2.2.3.2.2" xref="S2.SS1.p1.9.m9.2.2.3.2.2.cmml">1</mn><mn id="S2.SS1.p1.9.m9.2.2.3.2.3" xref="S2.SS1.p1.9.m9.2.2.3.2.3.cmml">2</mn></mfrac><mo id="S2.SS1.p1.9.m9.2.2.3.1" xref="S2.SS1.p1.9.m9.2.2.3.1.cmml">⁢</mo><msup id="S2.SS1.p1.9.m9.2.2.3.3" xref="S2.SS1.p1.9.m9.2.2.3.3.cmml"><mi id="S2.SS1.p1.9.m9.2.2.3.3.2" xref="S2.SS1.p1.9.m9.2.2.3.3.2.cmml">δ</mi><mrow id="S2.SS1.p1.9.m9.2.2.3.3.3" xref="S2.SS1.p1.9.m9.2.2.3.3.3.cmml"><mi id="S2.SS1.p1.9.m9.2.2.3.3.3.2" xref="S2.SS1.p1.9.m9.2.2.3.3.3.2.cmml">a</mi><mo id="S2.SS1.p1.9.m9.2.2.3.3.3.1" xref="S2.SS1.p1.9.m9.2.2.3.3.3.1.cmml">⁢</mo><mi id="S2.SS1.p1.9.m9.2.2.3.3.3.3" xref="S2.SS1.p1.9.m9.2.2.3.3.3.3.cmml">b</mi></mrow></msup></mrow></mrow></math>, <math><mrow id="S2.SS1.p1.10.m10.1.1" xref="S2.SS1.p1.10.m10.1.1.cmml"><msub id="S2.SS1.p1.10.m10.1.1.2" xref="S2.SS1.p1.10.m10.1.1.2.cmml"><mi id="S2.SS1.p1.10.m10.1.1.2.2" xref="S2.SS1.p1.10.m10.1.1.2.2.cmml">D</mi><mi id="S2.SS1.p1.10.m10.1.1.2.3" xref="S2.SS1.p1.10.m10.1.1.2.3.cmml">i</mi></msub><mo id="S2.SS1.p1.10.m10.1.1.1" xref="S2.SS1.p1.10.m10.1.1.1.cmml">=</mo><mrow id="S2.SS1.p1.10.m10.1.1.3" xref="S2.SS1.p1.10.m10.1.1.3.cmml"><msub id="S2.SS1.p1.10.m10.1.1.3.2" xref="S2.SS1.p1.10.m10.1.1.3.2.cmml"><mo id="S2.SS1.p1.10.m10.1.1.3.2.2" xref="S2.SS1.p1.10.m10.1.1.3.2.2.cmml">∂</mo><mi id="S2.SS1.p1.10.m10.1.1.3.2.3" xref="S2.SS1.p1.10.m10.1.1.3.2.3.cmml">i</mi></msub><mo id="S2.SS1.p1.10.m10.1.1.3.1" xref="S2.SS1.p1.10.m10.1.1.3.1.cmml">+</mo><msub id="S2.SS1.p1.10.m10.1.1.3.3" xref="S2.SS1.p1.10.m10.1.1.3.3.cmml"><mi id="S2.SS1.p1.10.m10.1.1.3.3.2" xref="S2.SS1.p1.10.m10.1.1.3.3.2.cmml">A</mi><mi id="S2.SS1.p1.10.m10.1.1.3.3.3" xref="S2.SS1.p1.10.m10.1.1.3.3.3.cmml">i</mi></msub></mrow></mrow></math>, <math><mrow id="S2.E1.m1.2.2.1" xref="S2.E1.m1.2.2.1.1.cmml"><mrow id="S2.E1.m1.2.2.1.1" xref="S2.E1.m1.2.2.1.1.cmml"><msub id="S2.E1.m1.2.2.1.1.3" xref="S2.E1.m1.2.2.1.1.3.cmml"><mi id="S2.E1.m1.2.2.1.1.3.2" xref="S2.E1.m1.2.2.1.1.3.2.cmml">A</mi><mi id="S2.E1.m1.2.2.1.1.3.3" xref="S2.E1.m1.2.2.1.1.3.3.cmml">i</mi></msub><mo id="S2.E1.m1.2.2.1.1.2" xref="S2.E1.m1.2.2.1.1.2.cmml">=</mo><mrow id="S2.E1.m1.2.2.1.1.1.1" xref="S2.E1.m1.2.2.1.1.1.2.cmml"><mrow id="S2.E1.m1.2.2.1.1.1.1.1" xref="S2.E1.m1.2.2.1.1.1.1.1.cmml"><mo id="S2.E1.m1.2.2.1.1.1.1.1.2" xref="S2.E1.m1.2.2.1.1.1.1.1.2.cmml">-</mo><mrow id="S2.E1.m1.2.2.1.1.1.1.1.1" xref="S2.E1.m1.2.2.1.1.1.1.1.1.cmml"><mrow id="S2.E1.m1.2.2.1.1.1.1.1.1.1.1" xref="S2.E1.m1.2.2.1.1.1.1.1.1.1.1.1.cmml"><mo stretchy="false" id="S2.E1.m1.2.2.1.1.1.1.1.1.1.1.2" xref="S2.E1.m1.2.2.1.1.1.1.1.1.1.1.1.cmml">(</mo><mrow id="S2.E1.m1.2.2.1.1.1.1.1.1.1.1.1" xref="S2.E1.m1.2.2.1.1.1.1.1.1.1.1.1.cmml"><msub id="S2.E1.m1.2.2.1.1.1.1.1.1.1.1.1.1" xref="S2.E1.m1.2.2.1.1.1.1.1.1.1.1.1.1.cmml"><mo id="S2.E1.m1.2.2.1.1.1.1.1.1.1.1.1.1.2" xref="S2.E1.m1.2.2.1.1.1.1.1.1.1.1.1.1.2.cmml">∂</mo><mi id="S2.E1.m1.2.2.1.1.1.1.1.1.1.1.1.1.3" xref="S2.E1.m1.2.2.1.1.1.1.1.1.1.1.1.1.3.cmml">i</mi></msub><mo id="S2.E1.m1.2.2.1.1.1.1.1.1.1.1.1a" xref="S2.E1.m1.2.2.1.1.1.1.1.1.1.1.1.cmml">⁡</mo><msub id="S2.E1.m1.2.2.1.1.1.1.1.1.1.1.1.2" xref="S2.E1.m1.2.2.1.1.1.1.1.1.1.1.1.2.cmml"><mi id="S2.E1.m1.2.2.1.1.1.1.1.1.1.1.1.2.2" xref="S2.E1.m1.2.2.1.1.1.1.1.1.1.1.1.2.2.cmml">M</mi><mi id="S2.E1.m1.2.2.1.1.1.1.1.1.1.1.1.2.3" xref="S2.E1.m1.2.2.1.1.1.1.1.1.1.1.1.2.3.cmml">i</mi></msub></mrow><mo stretchy="false" id="S2.E1.m1.2.2.1.1.1.1.1.1.1.1.3" xref="S2.E1.m1.2.2.1.1.1.1.1.1.1.1.1.cmml">)</mo></mrow><mo id="S2.E1.m1.2.2.1.1.1.1.1.1.2" xref="S2.E1.m1.2.2.1.1.1.1.1.1.2.cmml">⁢</mo><msubsup id="S2.E1.m1.2.2.1.1.1.1.1.1.3" xref="S2.E1.m1.2.2.1.1.1.1.1.1.3.cmml"><mi id="S2.E1.m1.2.2.1.1.1.1.1.1.3.2.2" xref="S2.E1.m1.2.2.1.1.1.1.1.1.3.2.2.cmml">M</mi><mi id="S2.E1.m1.2.2.1.1.1.1.1.1.3.2.3" xref="S2.E1.m1.2.2.1.1.1.1.1.1.3.2.3.cmml">i</mi><mrow id="S2.E1.m1.2.2.1.1.1.1.1.1.3.3" xref="S2.E1.m1.2.2.1.1.1.1.1.1.3.3.cmml"><mo id="S2.E1.m1.2.2.1.1.1.1.1.1.3.3.1" xref="S2.E1.m1.2.2.1.1.1.1.1.1.3.3.1.cmml">-</mo><mn id="S2.E1.m1.2.2.1.1.1.1.1.1.3.3.2" xref="S2.E1.m1.2.2.1.1.1.1.1.1.3.3.2.cmml">1</mn></mrow></msubsup></mrow></mrow><mo id="S2.E1.m1.2.2.1.1.1.1.2" xref="S2.E1.m1.2.2.1.1.1.2.cmml">,</mo><mtext id="S2.E1.m1.1.1" xref="S2.E1.m1.1.1a.cmml"> (no summation)</mtext></mrow></mrow><mo id="S2.E1.m1.2.2.1.2" xref="S2.E1.m1.2.2.1.1.cmml">,</mo></mrow></math>

Correct Categorie: hep-th

Guessed Categorie: hep-lat

Result: incorrect

Paper: https://arxiv.org/abs/1108.3091

Formulas:

1-

| 𝑽_{𝒕 𝒃} |

2-

σ (p \bar{p} \to t b + X, t q b + X) = 3.43 \pm_{0.74}^{0.73} pb

3-

0.79 < | V_{t b} | \leq 1

4-

σ (p \bar{p} \to t b + X) = 0.68 \pm_{0.35}^{0.38} pb

5-

σ (p \bar{p} \to t q b + X) = 2.86 \pm_{0.63}^{0.69} pb

6-

t b = t \bar{b} + \bar{t} b

7-

t q b = t q \bar{b} + \bar{t} q b

8-

| V_{t b} |

9-

| V_{t d} | = ({8.62}_{- 0.20}^{+ 0.26}) \times 10^{- 3}

10-

| V_{t s} | = ({4.03}_{- 0.07}^{+ 0.11}) \times 10^{- 4}

Formulas (html):

Correct Categorie: hep-ex

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/hep-lat/0309152

Formulas:

1-

N_{σ}^{3} \times N_{τ} = 16^{3} \times 32

2-

𝒪_{u d s}^{a} = ϵ^{i j k} (u^{i T} C Γ d^{j}) Γ^{'} s^{k} .

3-

(Γ Γ^{'})

4-

𝒪_{u s d}^{a}

5-

𝒪_{d u s}^{a}

6-

𝒪_{u d s}^{a}

7-

𝒪_{u d u}

8-

𝒪_{r e n}^{a} = Z^{a b} 𝒪_{l a t t}^{b} .

9-

G^{a} (x_{0}, x_{1}, x_{2}, x_{3}) = ⟨ 𝒪_{u d s}^{a} (x_{0}) \bar{u} (x_{1}) \bar{d} (x_{2}) \bar{s} (x_{3}) ⟩ .

10-

Λ^{a} (p^{2}) = {F.T. G^{a} (0, x_{1}, x_{2}, x_{3}) |}_{A m p} .

Formulas (html):

Correct Categorie: hep-lat

Guessed Categorie: gr-qc

Result: incorrect

Paper: https://arxiv.org/abs/1109.1109

Formulas:

1-

N (L_{4}) / N (L_{5}) = 1.6 \pm 0.1

2-

ϕ (t) = λ - λ^{'} - χ

3-

[0, 360^{\circ})

4-

N (L_{4}) / N (L_{5}) ≃ 1.8

5-

(d, e, \sin I)

6-

\sin I = 0.125 to 0.135

7-

(a \equiv \bar{a} + d, \sin I)

8-

(e, \sin I)

9-

(e, \sin I)

10-

N (v_{cutoff})

Formulas (html):

<math><mrow id="S1.p3.3.m3.2.2" xref="S1.p3.3.m3.2.2.cmml"><mrow id="S1.p3.3.m3.2.2.2" xref="S1.p3.3.m3.2.2.2.cmml"><mrow id="S1.p3.3.m3.1.1.1.1" xref="S1.p3.3.m3.1.1.1.1.cmml"><mrow id="S1.p3.3.m3.1.1.1.1.1" xref="S1.p3.3.m3.1.1.1.1.1.cmml"><mi id="S1.p3.3.m3.1.1.1.1.1.3" xref="S1.p3.3.m3.1.1.1.1.1.3.cmml">N</mi><mo id="S1.p3.3.m3.1.1.1.1.1.2" xref="S1.p3.3.m3.1.1.1.1.1.2.cmml">⁢</mo><mrow id="S1.p3.3.m3.1.1.1.1.1.1.1" xref="S1.p3.3.m3.1.1.1.1.1.1.1.1.cmml"><mo stretchy="false" id="S1.p3.3.m3.1.1.1.1.1.1.1.2" xref="S1.p3.3.m3.1.1.1.1.1.1.1.1.cmml">(</mo><msub id="S1.p3.3.m3.1.1.1.1.1.1.1.1" xref="S1.p3.3.m3.1.1.1.1.1.1.1.1.cmml"><mi id="S1.p3.3.m3.1.1.1.1.1.1.1.1.2" xref="S1.p3.3.m3.1.1.1.1.1.1.1.1.2.cmml">L</mi><mn id="S1.p3.3.m3.1.1.1.1.1.1.1.1.3" xref="S1.p3.3.m3.1.1.1.1.1.1.1.1.3.cmml">4</mn></msub><mo stretchy="false" id="S1.p3.3.m3.1.1.1.1.1.1.1.3" xref="S1.p3.3.m3.1.1.1.1.1.1.1.1.cmml">)</mo></mrow></mrow><mo id="S1.p3.3.m3.1.1.1.1.2" xref="S1.p3.3.m3.1.1.1.1.2.cmml">/</mo><mi id="S1.p3.3.m3.1.1.1.1.3" xref="S1.p3.3.m3.1.1.1.1.3.cmml">N</mi></mrow><mo id="S1.p3.3.m3.2.2.2.3" xref="S1.p3.3.m3.2.2.2.3.cmml">⁢</mo><mrow id="S1.p3.3.m3.2.2.2.2.1" xref="S1.p3.3.m3.2.2.2.2.1.1.cmml"><mo stretchy="false" id="S1.p3.3.m3.2.2.2.2.1.2" xref="S1.p3.3.m3.2.2.2.2.1.1.cmml">(</mo><msub id="S1.p3.3.m3.2.2.2.2.1.1" xref="S1.p3.3.m3.2.2.2.2.1.1.cmml"><mi id="S1.p3.3.m3.2.2.2.2.1.1.2" xref="S1.p3.3.m3.2.2.2.2.1.1.2.cmml">L</mi><mn id="S1.p3.3.m3.2.2.2.2.1.1.3" xref="S1.p3.3.m3.2.2.2.2.1.1.3.cmml">5</mn></msub><mo stretchy="false" id="S1.p3.3.m3.2.2.2.2.1.3" xref="S1.p3.3.m3.2.2.2.2.1.1.cmml">)</mo></mrow></mrow><mo id="S1.p3.3.m3.2.2.3" xref="S1.p3.3.m3.2.2.3.cmml">=</mo><mrow id="S1.p3.3.m3.2.2.4" xref="S1.p3.3.m3.2.2.4.cmml"><mn id="S1.p3.3.m3.2.2.4.2" xref="S1.p3.3.m3.2.2.4.2.cmml">1.6</mn><mo id="S1.p3.3.m3.2.2.4.1" xref="S1.p3.3.m3.2.2.4.1.cmml">±</mo><mn id="S1.p3.3.m3.2.2.4.3" xref="S1.p3.3.m3.2.2.4.3.cmml">0.1</mn></mrow></mrow></math>, <math><mrow id="S2.SS1.p2.2.m2.1.2" xref="S2.SS1.p2.2.m2.1.2.cmml"><mrow id="S2.SS1.p2.2.m2.1.2.2" xref="S2.SS1.p2.2.m2.1.2.2.cmml"><mi id="S2.SS1.p2.2.m2.1.2.2.2" xref="S2.SS1.p2.2.m2.1.2.2.2.cmml">ϕ</mi><mo id="S2.SS1.p2.2.m2.1.2.2.1" xref="S2.SS1.p2.2.m2.1.2.2.1.cmml">⁢</mo><mrow id="S2.SS1.p2.2.m2.1.2.2.3.2" xref="S2.SS1.p2.2.m2.1.2.2.cmml"><mo stretchy="false" id="S2.SS1.p2.2.m2.1.2.2.3.2.1" xref="S2.SS1.p2.2.m2.1.2.2.cmml">(</mo><mi id="S2.SS1.p2.2.m2.1.1" xref="S2.SS1.p2.2.m2.1.1.cmml">t</mi><mo stretchy="false" id="S2.SS1.p2.2.m2.1.2.2.3.2.2" xref="S2.SS1.p2.2.m2.1.2.2.cmml">)</mo></mrow></mrow><mo id="S2.SS1.p2.2.m2.1.2.1" xref="S2.SS1.p2.2.m2.1.2.1.cmml">=</mo><mrow id="S2.SS1.p2.2.m2.1.2.3" xref="S2.SS1.p2.2.m2.1.2.3.cmml"><mi id="S2.SS1.p2.2.m2.1.2.3.2" xref="S2.SS1.p2.2.m2.1.2.3.2.cmml">λ</mi><mo id="S2.SS1.p2.2.m2.1.2.3.1" xref="S2.SS1.p2.2.m2.1.2.3.1.cmml">-</mo><msup id="S2.SS1.p2.2.m2.1.2.3.3" xref="S2.SS1.p2.2.m2.1.2.3.3.cmml"><mi id="S2.SS1.p2.2.m2.1.2.3.3.2" xref="S2.SS1.p2.2.m2.1.2.3.3.2.cmml">λ</mi><mo id="S2.SS1.p2.2.m2.1.2.3.3.3" xref="S2.SS1.p2.2.m2.1.2.3.3.3.cmml">′</mo></msup><mo id="S2.SS1.p2.2.m2.1.2.3.1a" xref="S2.SS1.p2.2.m2.1.2.3.1.cmml">-</mo><mi id="S2.SS1.p2.2.m2.1.2.3.4" xref="S2.SS1.p2.2.m2.1.2.3.4.cmml">χ</mi></mrow></mrow></math>, <math><mrow id="S2.SS1.p2.9.m9.2.2.1" xref="S2.SS1.p2.9.m9.2.2.2.cmml"><mo stretchy="false" id="S2.SS1.p2.9.m9.2.2.1.2" xref="S2.SS1.p2.9.m9.2.2.2.cmml">[</mo><mn id="S2.SS1.p2.9.m9.1.1" xref="S2.SS1.p2.9.m9.1.1.cmml">0</mn><mo id="S2.SS1.p2.9.m9.2.2.1.3" xref="S2.SS1.p2.9.m9.2.2.2.cmml">,</mo><msup id="S2.SS1.p2.9.m9.2.2.1.1" xref="S2.SS1.p2.9.m9.2.2.1.1.cmml"><mn id="S2.SS1.p2.9.m9.2.2.1.1.2" xref="S2.SS1.p2.9.m9.2.2.1.1.2.cmml">360</mn><mo id="S2.SS1.p2.9.m9.2.2.1.1.3" xref="S2.SS1.p2.9.m9.2.2.1.1.3.cmml">∘</mo></msup><mo stretchy="false" id="S2.SS1.p2.9.m9.2.2.1.4" xref="S2.SS1.p2.9.m9.2.2.2.cmml">)</mo></mrow></math>, <math><mrow id="S2.SS1.p4.4.m4.2.2" xref="S2.SS1.p4.4.m4.2.2.cmml"><mrow id="S2.SS1.p4.4.m4.2.2.2" xref="S2.SS1.p4.4.m4.2.2.2.cmml"><mrow id="S2.SS1.p4.4.m4.1.1.1.1" xref="S2.SS1.p4.4.m4.1.1.1.1.cmml"><mrow id="S2.SS1.p4.4.m4.1.1.1.1.1" xref="S2.SS1.p4.4.m4.1.1.1.1.1.cmml"><mi id="S2.SS1.p4.4.m4.1.1.1.1.1.3" xref="S2.SS1.p4.4.m4.1.1.1.1.1.3.cmml">N</mi><mo id="S2.SS1.p4.4.m4.1.1.1.1.1.2" xref="S2.SS1.p4.4.m4.1.1.1.1.1.2.cmml">⁢</mo><mrow id="S2.SS1.p4.4.m4.1.1.1.1.1.1.1" xref="S2.SS1.p4.4.m4.1.1.1.1.1.1.1.1.cmml"><mo stretchy="false" id="S2.SS1.p4.4.m4.1.1.1.1.1.1.1.2" xref="S2.SS1.p4.4.m4.1.1.1.1.1.1.1.1.cmml">(</mo><msub id="S2.SS1.p4.4.m4.1.1.1.1.1.1.1.1" xref="S2.SS1.p4.4.m4.1.1.1.1.1.1.1.1.cmml"><mi id="S2.SS1.p4.4.m4.1.1.1.1.1.1.1.1.2" xref="S2.SS1.p4.4.m4.1.1.1.1.1.1.1.1.2.cmml">L</mi><mn id="S2.SS1.p4.4.m4.1.1.1.1.1.1.1.1.3" xref="S2.SS1.p4.4.m4.1.1.1.1.1.1.1.1.3.cmml">4</mn></msub><mo stretchy="false" id="S2.SS1.p4.4.m4.1.1.1.1.1.1.1.3" xref="S2.SS1.p4.4.m4.1.1.1.1.1.1.1.1.cmml">)</mo></mrow></mrow><mo id="S2.SS1.p4.4.m4.1.1.1.1.2" xref="S2.SS1.p4.4.m4.1.1.1.1.2.cmml">/</mo><mi id="S2.SS1.p4.4.m4.1.1.1.1.3" xref="S2.SS1.p4.4.m4.1.1.1.1.3.cmml">N</mi></mrow><mo id="S2.SS1.p4.4.m4.2.2.2.3" xref="S2.SS1.p4.4.m4.2.2.2.3.cmml">⁢</mo><mrow id="S2.SS1.p4.4.m4.2.2.2.2.1" xref="S2.SS1.p4.4.m4.2.2.2.2.1.1.cmml"><mo stretchy="false" id="S2.SS1.p4.4.m4.2.2.2.2.1.2" xref="S2.SS1.p4.4.m4.2.2.2.2.1.1.cmml">(</mo><msub id="S2.SS1.p4.4.m4.2.2.2.2.1.1" xref="S2.SS1.p4.4.m4.2.2.2.2.1.1.cmml"><mi id="S2.SS1.p4.4.m4.2.2.2.2.1.1.2" xref="S2.SS1.p4.4.m4.2.2.2.2.1.1.2.cmml">L</mi><mn id="S2.SS1.p4.4.m4.2.2.2.2.1.1.3" xref="S2.SS1.p4.4.m4.2.2.2.2.1.1.3.cmml">5</mn></msub><mo stretchy="false" id="S2.SS1.p4.4.m4.2.2.2.2.1.3" xref="S2.SS1.p4.4.m4.2.2.2.2.1.1.cmml">)</mo></mrow></mrow><mo id="S2.SS1.p4.4.m4.2.2.3" xref="S2.SS1.p4.4.m4.2.2.3.cmml">≃</mo><mn id="S2.SS1.p4.4.m4.2.2.4" xref="S2.SS1.p4.4.m4.2.2.4.cmml">1.8</mn></mrow></math>, <math><mrow id="S2.SS1.p5.1.m1.3.3.1" xref="S2.SS1.p5.1.m1.3.3.2.cmml"><mo stretchy="false" id="S2.SS1.p5.1.m1.3.3.1.2" xref="S2.SS1.p5.1.m1.3.3.2.cmml">(</mo><mi id="S2.SS1.p5.1.m1.1.1" xref="S2.SS1.p5.1.m1.1.1.cmml">d</mi><mo id="S2.SS1.p5.1.m1.3.3.1.3" xref="S2.SS1.p5.1.m1.3.3.2.cmml">,</mo><mi id="S2.SS1.p5.1.m1.2.2" xref="S2.SS1.p5.1.m1.2.2.cmml">e</mi><mo id="S2.SS1.p5.1.m1.3.3.1.4" xref="S2.SS1.p5.1.m1.3.3.2.cmml">,</mo><mrow id="S2.SS1.p5.1.m1.3.3.1.1" xref="S2.SS1.p5.1.m1.3.3.1.1.cmml"><mi id="S2.SS1.p5.1.m1.3.3.1.1.1" xref="S2.SS1.p5.1.m1.3.3.1.1.1.cmml">sin</mi><mo id="S2.SS1.p5.1.m1.3.3.1.1a" xref="S2.SS1.p5.1.m1.3.3.1.1.cmml">⁡</mo><mi id="S2.SS1.p5.1.m1.3.3.1.1.2" xref="S2.SS1.p5.1.m1.3.3.1.1.2.cmml">I</mi></mrow><mo stretchy="false" id="S2.SS1.p5.1.m1.3.3.1.5" xref="S2.SS1.p5.1.m1.3.3.2.cmml">)</mo></mrow></math>, <math><mrow id="S2.SS1.p5.2.m2.1.1" xref="S2.SS1.p5.2.m2.1.1.cmml"><mrow id="S2.SS1.p5.2.m2.1.1.2" xref="S2.SS1.p5.2.m2.1.1.2.cmml"><mi id="S2.SS1.p5.2.m2.1.1.2.1" xref="S2.SS1.p5.2.m2.1.1.2.1.cmml">sin</mi><mo id="S2.SS1.p5.2.m2.1.1.2a" xref="S2.SS1.p5.2.m2.1.1.2.cmml">⁡</mo><mi id="S2.SS1.p5.2.m2.1.1.2.2" xref="S2.SS1.p5.2.m2.1.1.2.2.cmml">I</mi></mrow><mo id="S2.SS1.p5.2.m2.1.1.1" xref="S2.SS1.p5.2.m2.1.1.1.cmml">=</mo><mrow id="S2.SS1.p5.2.m2.1.1.3" xref="S2.SS1.p5.2.m2.1.1.3.cmml"><mn id="S2.SS1.p5.2.m2.1.1.3.2" xref="S2.SS1.p5.2.m2.1.1.3.2.cmml">0.125</mn><mo id="S2.SS1.p5.2.m2.1.1.3.1" xref="S2.SS1.p5.2.m2.1.1.3.1.cmml">⁢</mo><mtext id="S2.SS1.p5.2.m2.1.1.3.3" xref="S2.SS1.p5.2.m2.1.1.3.3a.cmml"> to </mtext><mo id="S2.SS1.p5.2.m2.1.1.3.1a" xref="S2.SS1.p5.2.m2.1.1.3.1.cmml">⁢</mo><mn id="S2.SS1.p5.2.m2.1.1.3.4" xref="S2.SS1.p5.2.m2.1.1.3.4.cmml">0.135</mn></mrow></mrow></math>, <math><mrow id="S2.F2.22.m1.1.1.1" xref="S2.F2.22.m1.1.1.1.1.cmml"><mo stretchy="false" id="S2.F2.22.m1.1.1.1.2" xref="S2.F2.22.m1.1.1.1.1.cmml">(</mo><mrow id="S2.F2.22.m1.1.1.1.1" xref="S2.F2.22.m1.1.1.1.1.cmml"><mi id="S2.F2.22.m1.1.1.1.1.4" xref="S2.F2.22.m1.1.1.1.1.4.cmml">a</mi><mo id="S2.F2.22.m1.1.1.1.1.3" xref="S2.F2.22.m1.1.1.1.1.3.cmml">≡</mo><mrow id="S2.F2.22.m1.1.1.1.1.2.2" xref="S2.F2.22.m1.1.1.1.1.2.3.cmml"><mrow id="S2.F2.22.m1.1.1.1.1.1.1.1" xref="S2.F2.22.m1.1.1.1.1.1.1.1.cmml"><mover accent="true" id="S2.F2.22.m1.1.1.1.1.1.1.1.2" xref="S2.F2.22.m1.1.1.1.1.1.1.1.2.cmml"><mi id="S2.F2.22.m1.1.1.1.1.1.1.1.2.2" xref="S2.F2.22.m1.1.1.1.1.1.1.1.2.2.cmml">a</mi><mo stretchy="false" id="S2.F2.22.m1.1.1.1.1.1.1.1.2.1" xref="S2.F2.22.m1.1.1.1.1.1.1.1.2.1.cmml">¯</mo></mover><mo id="S2.F2.22.m1.1.1.1.1.1.1.1.1" xref="S2.F2.22.m1.1.1.1.1.1.1.1.1.cmml">+</mo><mi id="S2.F2.22.m1.1.1.1.1.1.1.1.3" xref="S2.F2.22.m1.1.1.1.1.1.1.1.3.cmml">d</mi></mrow><mo id="S2.F2.22.m1.1.1.1.1.2.2.3" xref="S2.F2.22.m1.1.1.1.1.2.3.cmml">,</mo><mrow id="S2.F2.22.m1.1.1.1.1.2.2.2" xref="S2.F2.22.m1.1.1.1.1.2.2.2.cmml"><mi id="S2.F2.22.m1.1.1.1.1.2.2.2.1" xref="S2.F2.22.m1.1.1.1.1.2.2.2.1.cmml">sin</mi><mo id="S2.F2.22.m1.1.1.1.1.2.2.2b" xref="S2.F2.22.m1.1.1.1.1.2.2.2.cmml">⁡</mo><mi id="S2.F2.22.m1.1.1.1.1.2.2.2.2" xref="S2.F2.22.m1.1.1.1.1.2.2.2.2.cmml">I</mi></mrow></mrow></mrow><mo stretchy="false" id="S2.F2.22.m1.1.1.1.3" xref="S2.F2.22.m1.1.1.1.1.cmml">)</mo></mrow></math>, <math><mrow id="S2.F2.23.m2.2.2.1" xref="S2.F2.23.m2.2.2.2.cmml"><mo stretchy="false" id="S2.F2.23.m2.2.2.1.2" xref="S2.F2.23.m2.2.2.2.cmml">(</mo><mi id="S2.F2.23.m2.1.1" xref="S2.F2.23.m2.1.1.cmml">e</mi><mo id="S2.F2.23.m2.2.2.1.3" xref="S2.F2.23.m2.2.2.2.cmml">,</mo><mrow id="S2.F2.23.m2.2.2.1.1" xref="S2.F2.23.m2.2.2.1.1.cmml"><mi id="S2.F2.23.m2.2.2.1.1.1" xref="S2.F2.23.m2.2.2.1.1.1.cmml">sin</mi><mo id="S2.F2.23.m2.2.2.1.1b" xref="S2.F2.23.m2.2.2.1.1.cmml">⁡</mo><mi id="S2.F2.23.m2.2.2.1.1.2" xref="S2.F2.23.m2.2.2.1.1.2.cmml">I</mi></mrow><mo stretchy="false" id="S2.F2.23.m2.2.2.1.4" xref="S2.F2.23.m2.2.2.2.cmml">)</mo></mrow></math>, <math><mrow id="S2.F2.36.m15.2.2.1" xref="S2.F2.36.m15.2.2.2.cmml"><mo stretchy="false" id="S2.F2.36.m15.2.2.1.2" xref="S2.F2.36.m15.2.2.2.cmml">(</mo><mi id="S2.F2.36.m15.1.1" xref="S2.F2.36.m15.1.1.cmml">e</mi><mo id="S2.F2.36.m15.2.2.1.3" xref="S2.F2.36.m15.2.2.2.cmml">,</mo><mrow id="S2.F2.36.m15.2.2.1.1" xref="S2.F2.36.m15.2.2.1.1.cmml"><mi id="S2.F2.36.m15.2.2.1.1.1" xref="S2.F2.36.m15.2.2.1.1.1.cmml">sin</mi><mo id="S2.F2.36.m15.2.2.1.1b" xref="S2.F2.36.m15.2.2.1.1.cmml">⁡</mo><mi id="S2.F2.36.m15.2.2.1.1.2" xref="S2.F2.36.m15.2.2.1.1.2.cmml">I</mi></mrow><mo stretchy="false" id="S2.F2.36.m15.2.2.1.4" xref="S2.F2.36.m15.2.2.2.cmml">)</mo></mrow></math>, <math><mrow id="S2.SS2.p1.6.m6.1.1" xref="S2.SS2.p1.6.m6.1.1.cmml"><mi id="S2.SS2.p1.6.m6.1.1.3" xref="S2.SS2.p1.6.m6.1.1.3.cmml">N</mi><mo id="S2.SS2.p1.6.m6.1.1.2" xref="S2.SS2.p1.6.m6.1.1.2.cmml">⁢</mo><mrow id="S2.SS2.p1.6.m6.1.1.1.1" xref="S2.SS2.p1.6.m6.1.1.1.1.1.cmml"><mo stretchy="false" id="S2.SS2.p1.6.m6.1.1.1.1.2" xref="S2.SS2.p1.6.m6.1.1.1.1.1.cmml">(</mo><msub id="S2.SS2.p1.6.m6.1.1.1.1.1" xref="S2.SS2.p1.6.m6.1.1.1.1.1.cmml"><mi id="S2.SS2.p1.6.m6.1.1.1.1.1.2" xref="S2.SS2.p1.6.m6.1.1.1.1.1.2.cmml">v</mi><mi id="S2.SS2.p1.6.m6.1.1.1.1.1.3" xref="S2.SS2.p1.6.m6.1.1.1.1.1.3.cmml">cutoff</mi></msub><mo stretchy="false" id="S2.SS2.p1.6.m6.1.1.1.1.3" xref="S2.SS2.p1.6.m6.1.1.1.1.1.cmml">)</mo></mrow></mrow></math>

Correct Categorie: astro-ph

Guessed Categorie: cs

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0606625

Formulas:

1-

d N / d M \propto M^{α}

2-

10^{4} < M / M_{⊙} < 10^{6}

3-

10^{2} < M / M_{⊙} < 10^{7}

4-

M > 10^{4} M_{⊙}

5-

M > 10^{5} M_{⊙}

6-

M > 10^{6} M_{⊙}

7-

M > 10^{5} M_{⊙}

8-

M > 10^{6} M_{⊙}

9-

10^{4} < M / M_{⊙} < 10^{5}

10-

t_{dis} = 1.3 Gyrs {(M / 10^{4} M_{⊙})}^{0.62}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: gr-qc

Result: incorrect

Paper: https://arxiv.org/abs/1701.07677

Formulas:

1-

F : X \subseteq ℝ^{n} \to ℝ^{n}

2-

⟨ y - x^{*}, F (x^{*}) ⟩ \geq 0 for all y \in X .

3-

ℝ_{+}^{n} := {x \in ℝ^{n} : x \geq 0}

4-

x \geq 0, F (x) \geq 0, x^{⊤} F (x) = 0,

5-

F : X \subseteq ℝ^{n} \to ℝ^{n}

6-

⟨ F (x) - F (y), x - y ⟩ > 0 for all x, y \in X with x \neq y;

7-

⟨ F (x) - F (y), x - y ⟩ \geq c {∥ x - y ∥}^{2} for all x, y \in X .

8-

F (x) = A x + q

9-

A \in ℝ^{n \times n}

10-

{x^{r}}_{r > 0}

Formulas (html):

Correct Categorie: math

Guessed Categorie: hep-ph

Result: incorrect

Paper: https://arxiv.org/abs/1701.05596

Formulas:

1-

S_{𝚌𝚘𝚖𝚋𝚂𝚄𝙼} (i) = \sum_{k = 1}^{N_{k}} S_{k} (i)

2-

S_{k} (i)

3-

S_{𝚌𝚘𝚖𝚋𝙼𝙽𝚉} (i) = F (i) * S_{𝚌𝚘𝚖𝚋𝚂𝚄𝙼} (i)

4-

S_{𝚌𝚘𝚖𝚋𝙼𝚊𝚡} (i) = \max_{k} S_{k} (i)

5-

S_{k} (i)

6-

S_{𝚌𝚘𝚖𝚋𝙼𝚒𝚗} (i) = \min_{k} S_{k} (i)

7-

S_{k} (i)

8-

S_{𝚕𝚒𝚗𝚎𝚊𝚛} (i) = \sum_{k = 1}^{N_{k}} w_{k} S_{k} (i)

9-

w_{k} \in [0, 1]

10-

\sum_{k = 1}^{N_{k}} w_{k} = 1

Formulas (html):

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id="S2.E1.m1.2.3.3.1.2.3" xref="S2.E1.m1.2.3.3.1.2.3.cmml"><mi id="S2.E1.m1.2.3.3.1.2.3.2" xref="S2.E1.m1.2.3.3.1.2.3.2.cmml">k</mi><mo id="S2.E1.m1.2.3.3.1.2.3.1" xref="S2.E1.m1.2.3.3.1.2.3.1.cmml">=</mo><mn id="S2.E1.m1.2.3.3.1.2.3.3" xref="S2.E1.m1.2.3.3.1.2.3.3.cmml">1</mn></mrow><msub id="S2.E1.m1.2.3.3.1.3" xref="S2.E1.m1.2.3.3.1.3.cmml"><mi id="S2.E1.m1.2.3.3.1.3.2" xref="S2.E1.m1.2.3.3.1.3.2.cmml">N</mi><mi id="S2.E1.m1.2.3.3.1.3.3" xref="S2.E1.m1.2.3.3.1.3.3.cmml">k</mi></msub></munderover><mrow id="S2.E1.m1.2.3.3.2" xref="S2.E1.m1.2.3.3.2.cmml"><msub id="S2.E1.m1.2.3.3.2.2" xref="S2.E1.m1.2.3.3.2.2.cmml"><mi id="S2.E1.m1.2.3.3.2.2.2" xref="S2.E1.m1.2.3.3.2.2.2.cmml">S</mi><mi id="S2.E1.m1.2.3.3.2.2.3" xref="S2.E1.m1.2.3.3.2.2.3.cmml">k</mi></msub><mo id="S2.E1.m1.2.3.3.2.1" xref="S2.E1.m1.2.3.3.2.1.cmml">⁢</mo><mrow id="S2.E1.m1.2.3.3.2.3.2" xref="S2.E1.m1.2.3.3.2.cmml"><mo stretchy="false" id="S2.E1.m1.2.3.3.2.3.2.1" xref="S2.E1.m1.2.3.3.2.cmml">(</mo><mi id="S2.E1.m1.2.2" xref="S2.E1.m1.2.2.cmml">i</mi><mo stretchy="false" id="S2.E1.m1.2.3.3.2.3.2.2" xref="S2.E1.m1.2.3.3.2.cmml">)</mo></mrow></mrow></mrow></mrow></math>, <math><mrow id="S2.I6.i1.p1.1.m1.1.2" xref="S2.I6.i1.p1.1.m1.1.2.cmml"><msub id="S2.I6.i1.p1.1.m1.1.2.2" xref="S2.I6.i1.p1.1.m1.1.2.2.cmml"><mi id="S2.I6.i1.p1.1.m1.1.2.2.2" xref="S2.I6.i1.p1.1.m1.1.2.2.2.cmml">S</mi><mi id="S2.I6.i1.p1.1.m1.1.2.2.3" xref="S2.I6.i1.p1.1.m1.1.2.2.3.cmml">k</mi></msub><mo id="S2.I6.i1.p1.1.m1.1.2.1" xref="S2.I6.i1.p1.1.m1.1.2.1.cmml">⁢</mo><mrow id="S2.I6.i1.p1.1.m1.1.2.3.2" xref="S2.I6.i1.p1.1.m1.1.2.cmml"><mo stretchy="false" id="S2.I6.i1.p1.1.m1.1.2.3.2.1" xref="S2.I6.i1.p1.1.m1.1.2.cmml">(</mo><mi id="S2.I6.i1.p1.1.m1.1.1" xref="S2.I6.i1.p1.1.m1.1.1.cmml">i</mi><mo stretchy="false" id="S2.I6.i1.p1.1.m1.1.2.3.2.2" xref="S2.I6.i1.p1.1.m1.1.2.cmml">)</mo></mrow></mrow></math>, <math><mrow id="S2.E2.m1.3.4" xref="S2.E2.m1.3.4.cmml"><mrow id="S2.E2.m1.3.4.2" xref="S2.E2.m1.3.4.2.cmml"><msub id="S2.E2.m1.3.4.2.2" xref="S2.E2.m1.3.4.2.2.cmml"><mi id="S2.E2.m1.3.4.2.2.2" xref="S2.E2.m1.3.4.2.2.2.cmml">S</mi><mtext mathsize="114%" id="S2.E2.m1.3.4.2.2.3" xref="S2.E2.m1.3.4.2.2.3a.cmml">𝚌𝚘𝚖𝚋𝙼𝙽𝚉</mtext></msub><mo id="S2.E2.m1.3.4.2.1" xref="S2.E2.m1.3.4.2.1.cmml">⁢</mo><mrow id="S2.E2.m1.3.4.2.3.2" xref="S2.E2.m1.3.4.2.cmml"><mo stretchy="false" id="S2.E2.m1.3.4.2.3.2.1" xref="S2.E2.m1.3.4.2.cmml">(</mo><mi id="S2.E2.m1.1.1" xref="S2.E2.m1.1.1.cmml">i</mi><mo stretchy="false" id="S2.E2.m1.3.4.2.3.2.2" xref="S2.E2.m1.3.4.2.cmml">)</mo></mrow></mrow><mo id="S2.E2.m1.3.4.1" xref="S2.E2.m1.3.4.1.cmml">=</mo><mrow id="S2.E2.m1.3.4.3" xref="S2.E2.m1.3.4.3.cmml"><mrow id="S2.E2.m1.3.4.3.2" xref="S2.E2.m1.3.4.3.2.cmml"><mrow id="S2.E2.m1.3.4.3.2.2" xref="S2.E2.m1.3.4.3.2.2.cmml"><mi id="S2.E2.m1.3.4.3.2.2.2" xref="S2.E2.m1.3.4.3.2.2.2.cmml">F</mi><mo id="S2.E2.m1.3.4.3.2.2.1" xref="S2.E2.m1.3.4.3.2.2.1.cmml">⁢</mo><mrow id="S2.E2.m1.3.4.3.2.2.3.2" xref="S2.E2.m1.3.4.3.2.2.cmml"><mo stretchy="false" id="S2.E2.m1.3.4.3.2.2.3.2.1" xref="S2.E2.m1.3.4.3.2.2.cmml">(</mo><mi id="S2.E2.m1.2.2" xref="S2.E2.m1.2.2.cmml">i</mi><mo stretchy="false" id="S2.E2.m1.3.4.3.2.2.3.2.2" xref="S2.E2.m1.3.4.3.2.2.cmml">)</mo></mrow></mrow><mo id="S2.E2.m1.3.4.3.2.1" xref="S2.E2.m1.3.4.3.2.1.cmml">*</mo><msub id="S2.E2.m1.3.4.3.2.3" xref="S2.E2.m1.3.4.3.2.3.cmml"><mi id="S2.E2.m1.3.4.3.2.3.2" xref="S2.E2.m1.3.4.3.2.3.2.cmml">S</mi><mtext mathsize="114%" id="S2.E2.m1.3.4.3.2.3.3" xref="S2.E2.m1.3.4.3.2.3.3a.cmml">𝚌𝚘𝚖𝚋𝚂𝚄𝙼</mtext></msub></mrow><mo id="S2.E2.m1.3.4.3.1" xref="S2.E2.m1.3.4.3.1.cmml">⁢</mo><mrow id="S2.E2.m1.3.4.3.3.2" xref="S2.E2.m1.3.4.3.cmml"><mo stretchy="false" id="S2.E2.m1.3.4.3.3.2.1" xref="S2.E2.m1.3.4.3.cmml">(</mo><mi id="S2.E2.m1.3.3" xref="S2.E2.m1.3.3.cmml">i</mi><mo stretchy="false" id="S2.E2.m1.3.4.3.3.2.2" xref="S2.E2.m1.3.4.3.cmml">)</mo></mrow></mrow></mrow></math>, <math><mrow id="S2.E3.m1.2.3" xref="S2.E3.m1.2.3.cmml"><mrow id="S2.E3.m1.2.3.2" xref="S2.E3.m1.2.3.2.cmml"><msub id="S2.E3.m1.2.3.2.2" xref="S2.E3.m1.2.3.2.2.cmml"><mi id="S2.E3.m1.2.3.2.2.2" xref="S2.E3.m1.2.3.2.2.2.cmml">S</mi><mtext mathsize="114%" id="S2.E3.m1.2.3.2.2.3" xref="S2.E3.m1.2.3.2.2.3a.cmml">𝚌𝚘𝚖𝚋𝙼𝚊𝚡</mtext></msub><mo id="S2.E3.m1.2.3.2.1" xref="S2.E3.m1.2.3.2.1.cmml">⁢</mo><mrow id="S2.E3.m1.2.3.2.3.2" xref="S2.E3.m1.2.3.2.cmml"><mo stretchy="false" id="S2.E3.m1.2.3.2.3.2.1" xref="S2.E3.m1.2.3.2.cmml">(</mo><mi id="S2.E3.m1.1.1" xref="S2.E3.m1.1.1.cmml">i</mi><mo stretchy="false" id="S2.E3.m1.2.3.2.3.2.2" xref="S2.E3.m1.2.3.2.cmml">)</mo></mrow></mrow><mo id="S2.E3.m1.2.3.1" xref="S2.E3.m1.2.3.1.cmml">=</mo><mrow id="S2.E3.m1.2.3.3" xref="S2.E3.m1.2.3.3.cmml"><mrow id="S2.E3.m1.2.3.3.2" xref="S2.E3.m1.2.3.3.2.cmml"><munder id="S2.E3.m1.2.3.3.2.1" xref="S2.E3.m1.2.3.3.2.1.cmml"><mi id="S2.E3.m1.2.3.3.2.1.2" xref="S2.E3.m1.2.3.3.2.1.2.cmml">max</mi><mi id="S2.E3.m1.2.3.3.2.1.3" xref="S2.E3.m1.2.3.3.2.1.3.cmml">k</mi></munder><mo id="S2.E3.m1.2.3.3.2a" xref="S2.E3.m1.2.3.3.2.cmml">⁡</mo><msub id="S2.E3.m1.2.3.3.2.2" xref="S2.E3.m1.2.3.3.2.2.cmml"><mi id="S2.E3.m1.2.3.3.2.2.2" xref="S2.E3.m1.2.3.3.2.2.2.cmml">S</mi><mi id="S2.E3.m1.2.3.3.2.2.3" xref="S2.E3.m1.2.3.3.2.2.3.cmml">k</mi></msub></mrow><mo id="S2.E3.m1.2.3.3.1" xref="S2.E3.m1.2.3.3.1.cmml">⁢</mo><mrow id="S2.E3.m1.2.3.3.3.2" xref="S2.E3.m1.2.3.3.cmml"><mo stretchy="false" id="S2.E3.m1.2.3.3.3.2.1" xref="S2.E3.m1.2.3.3.cmml">(</mo><mi id="S2.E3.m1.2.2" xref="S2.E3.m1.2.2.cmml">i</mi><mo stretchy="false" id="S2.E3.m1.2.3.3.3.2.2" xref="S2.E3.m1.2.3.3.cmml">)</mo></mrow></mrow></mrow></math>, <math><mrow id="S2.I6.i3.p1.1.m1.1.2" xref="S2.I6.i3.p1.1.m1.1.2.cmml"><msub id="S2.I6.i3.p1.1.m1.1.2.2" xref="S2.I6.i3.p1.1.m1.1.2.2.cmml"><mi id="S2.I6.i3.p1.1.m1.1.2.2.2" xref="S2.I6.i3.p1.1.m1.1.2.2.2.cmml">S</mi><mi id="S2.I6.i3.p1.1.m1.1.2.2.3" xref="S2.I6.i3.p1.1.m1.1.2.2.3.cmml">k</mi></msub><mo id="S2.I6.i3.p1.1.m1.1.2.1" xref="S2.I6.i3.p1.1.m1.1.2.1.cmml">⁢</mo><mrow id="S2.I6.i3.p1.1.m1.1.2.3.2" xref="S2.I6.i3.p1.1.m1.1.2.cmml"><mo stretchy="false" id="S2.I6.i3.p1.1.m1.1.2.3.2.1" xref="S2.I6.i3.p1.1.m1.1.2.cmml">(</mo><mi id="S2.I6.i3.p1.1.m1.1.1" xref="S2.I6.i3.p1.1.m1.1.1.cmml">i</mi><mo stretchy="false" id="S2.I6.i3.p1.1.m1.1.2.3.2.2" xref="S2.I6.i3.p1.1.m1.1.2.cmml">)</mo></mrow></mrow></math>, <math><mrow id="S2.E4.m1.2.3" xref="S2.E4.m1.2.3.cmml"><mrow id="S2.E4.m1.2.3.2" xref="S2.E4.m1.2.3.2.cmml"><msub id="S2.E4.m1.2.3.2.2" xref="S2.E4.m1.2.3.2.2.cmml"><mi id="S2.E4.m1.2.3.2.2.2" xref="S2.E4.m1.2.3.2.2.2.cmml">S</mi><mtext mathsize="114%" id="S2.E4.m1.2.3.2.2.3" xref="S2.E4.m1.2.3.2.2.3a.cmml">𝚌𝚘𝚖𝚋𝙼𝚒𝚗</mtext></msub><mo id="S2.E4.m1.2.3.2.1" xref="S2.E4.m1.2.3.2.1.cmml">⁢</mo><mrow id="S2.E4.m1.2.3.2.3.2" xref="S2.E4.m1.2.3.2.cmml"><mo stretchy="false" id="S2.E4.m1.2.3.2.3.2.1" xref="S2.E4.m1.2.3.2.cmml">(</mo><mi id="S2.E4.m1.1.1" xref="S2.E4.m1.1.1.cmml">i</mi><mo stretchy="false" id="S2.E4.m1.2.3.2.3.2.2" xref="S2.E4.m1.2.3.2.cmml">)</mo></mrow></mrow><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" xref="S2.E4.m1.2.3.3.cmml"><mrow id="S2.E4.m1.2.3.3.2" xref="S2.E4.m1.2.3.3.2.cmml"><munder id="S2.E4.m1.2.3.3.2.1" xref="S2.E4.m1.2.3.3.2.1.cmml"><mi id="S2.E4.m1.2.3.3.2.1.2" xref="S2.E4.m1.2.3.3.2.1.2.cmml">min</mi><mi id="S2.E4.m1.2.3.3.2.1.3" xref="S2.E4.m1.2.3.3.2.1.3.cmml">k</mi></munder><mo id="S2.E4.m1.2.3.3.2a" xref="S2.E4.m1.2.3.3.2.cmml">⁡</mo><msub id="S2.E4.m1.2.3.3.2.2" xref="S2.E4.m1.2.3.3.2.2.cmml"><mi id="S2.E4.m1.2.3.3.2.2.2" xref="S2.E4.m1.2.3.3.2.2.2.cmml">S</mi><mi id="S2.E4.m1.2.3.3.2.2.3" xref="S2.E4.m1.2.3.3.2.2.3.cmml">k</mi></msub></mrow><mo id="S2.E4.m1.2.3.3.1" xref="S2.E4.m1.2.3.3.1.cmml">⁢</mo><mrow id="S2.E4.m1.2.3.3.3.2" xref="S2.E4.m1.2.3.3.cmml"><mo stretchy="false" id="S2.E4.m1.2.3.3.3.2.1" xref="S2.E4.m1.2.3.3.cmml">(</mo><mi id="S2.E4.m1.2.2" xref="S2.E4.m1.2.2.cmml">i</mi><mo stretchy="false" id="S2.E4.m1.2.3.3.3.2.2" xref="S2.E4.m1.2.3.3.cmml">)</mo></mrow></mrow></mrow></math>, <math><mrow id="S2.I6.i4.p1.1.m1.1.2" xref="S2.I6.i4.p1.1.m1.1.2.cmml"><msub id="S2.I6.i4.p1.1.m1.1.2.2" xref="S2.I6.i4.p1.1.m1.1.2.2.cmml"><mi id="S2.I6.i4.p1.1.m1.1.2.2.2" xref="S2.I6.i4.p1.1.m1.1.2.2.2.cmml">S</mi><mi id="S2.I6.i4.p1.1.m1.1.2.2.3" xref="S2.I6.i4.p1.1.m1.1.2.2.3.cmml">k</mi></msub><mo id="S2.I6.i4.p1.1.m1.1.2.1" xref="S2.I6.i4.p1.1.m1.1.2.1.cmml">⁢</mo><mrow id="S2.I6.i4.p1.1.m1.1.2.3.2" xref="S2.I6.i4.p1.1.m1.1.2.cmml"><mo stretchy="false" id="S2.I6.i4.p1.1.m1.1.2.3.2.1" xref="S2.I6.i4.p1.1.m1.1.2.cmml">(</mo><mi id="S2.I6.i4.p1.1.m1.1.1" xref="S2.I6.i4.p1.1.m1.1.1.cmml">i</mi><mo stretchy="false" id="S2.I6.i4.p1.1.m1.1.2.3.2.2" xref="S2.I6.i4.p1.1.m1.1.2.cmml">)</mo></mrow></mrow></math>, <math><mrow id="S2.E5.m1.2.3" xref="S2.E5.m1.2.3.cmml"><mrow id="S2.E5.m1.2.3.2" xref="S2.E5.m1.2.3.2.cmml"><msub id="S2.E5.m1.2.3.2.2" xref="S2.E5.m1.2.3.2.2.cmml"><mi id="S2.E5.m1.2.3.2.2.2" xref="S2.E5.m1.2.3.2.2.2.cmml">S</mi><mtext mathsize="114%" id="S2.E5.m1.2.3.2.2.3" xref="S2.E5.m1.2.3.2.2.3a.cmml">𝚕𝚒𝚗𝚎𝚊𝚛</mtext></msub><mo id="S2.E5.m1.2.3.2.1" xref="S2.E5.m1.2.3.2.1.cmml">⁢</mo><mrow id="S2.E5.m1.2.3.2.3.2" xref="S2.E5.m1.2.3.2.cmml"><mo stretchy="false" id="S2.E5.m1.2.3.2.3.2.1" xref="S2.E5.m1.2.3.2.cmml">(</mo><mi id="S2.E5.m1.1.1" xref="S2.E5.m1.1.1.cmml">i</mi><mo stretchy="false" id="S2.E5.m1.2.3.2.3.2.2" xref="S2.E5.m1.2.3.2.cmml">)</mo></mrow></mrow><mo id="S2.E5.m1.2.3.1" xref="S2.E5.m1.2.3.1.cmml">=</mo><mrow id="S2.E5.m1.2.3.3" xref="S2.E5.m1.2.3.3.cmml"><munderover id="S2.E5.m1.2.3.3.1" xref="S2.E5.m1.2.3.3.1.cmml"><mo largeop="true" movablelimits="false" symmetric="true" id="S2.E5.m1.2.3.3.1.2.2" xref="S2.E5.m1.2.3.3.1.2.2.cmml">∑</mo><mrow id="S2.E5.m1.2.3.3.1.2.3" xref="S2.E5.m1.2.3.3.1.2.3.cmml"><mi id="S2.E5.m1.2.3.3.1.2.3.2" xref="S2.E5.m1.2.3.3.1.2.3.2.cmml">k</mi><mo id="S2.E5.m1.2.3.3.1.2.3.1" xref="S2.E5.m1.2.3.3.1.2.3.1.cmml">=</mo><mn id="S2.E5.m1.2.3.3.1.2.3.3" xref="S2.E5.m1.2.3.3.1.2.3.3.cmml">1</mn></mrow><msub id="S2.E5.m1.2.3.3.1.3" xref="S2.E5.m1.2.3.3.1.3.cmml"><mi id="S2.E5.m1.2.3.3.1.3.2" xref="S2.E5.m1.2.3.3.1.3.2.cmml">N</mi><mi id="S2.E5.m1.2.3.3.1.3.3" xref="S2.E5.m1.2.3.3.1.3.3.cmml">k</mi></msub></munderover><mrow id="S2.E5.m1.2.3.3.2" xref="S2.E5.m1.2.3.3.2.cmml"><msub id="S2.E5.m1.2.3.3.2.2" xref="S2.E5.m1.2.3.3.2.2.cmml"><mi id="S2.E5.m1.2.3.3.2.2.2" xref="S2.E5.m1.2.3.3.2.2.2.cmml">w</mi><mi id="S2.E5.m1.2.3.3.2.2.3" xref="S2.E5.m1.2.3.3.2.2.3.cmml">k</mi></msub><mo id="S2.E5.m1.2.3.3.2.1" xref="S2.E5.m1.2.3.3.2.1.cmml">⁢</mo><msub id="S2.E5.m1.2.3.3.2.3" xref="S2.E5.m1.2.3.3.2.3.cmml"><mi id="S2.E5.m1.2.3.3.2.3.2" xref="S2.E5.m1.2.3.3.2.3.2.cmml">S</mi><mi id="S2.E5.m1.2.3.3.2.3.3" xref="S2.E5.m1.2.3.3.2.3.3.cmml">k</mi></msub><mo id="S2.E5.m1.2.3.3.2.1a" xref="S2.E5.m1.2.3.3.2.1.cmml">⁢</mo><mrow id="S2.E5.m1.2.3.3.2.4.2" xref="S2.E5.m1.2.3.3.2.cmml"><mo stretchy="false" id="S2.E5.m1.2.3.3.2.4.2.1" xref="S2.E5.m1.2.3.3.2.cmml">(</mo><mi id="S2.E5.m1.2.2" xref="S2.E5.m1.2.2.cmml">i</mi><mo stretchy="false" id="S2.E5.m1.2.3.3.2.4.2.2" xref="S2.E5.m1.2.3.3.2.cmml">)</mo></mrow></mrow></mrow></mrow></math>, <math><mrow id="S2.I6.i5.p1.1.m1.2.3" xref="S2.I6.i5.p1.1.m1.2.3.cmml"><msub id="S2.I6.i5.p1.1.m1.2.3.2" xref="S2.I6.i5.p1.1.m1.2.3.2.cmml"><mi id="S2.I6.i5.p1.1.m1.2.3.2.2" xref="S2.I6.i5.p1.1.m1.2.3.2.2.cmml">w</mi><mi id="S2.I6.i5.p1.1.m1.2.3.2.3" xref="S2.I6.i5.p1.1.m1.2.3.2.3.cmml">k</mi></msub><mo id="S2.I6.i5.p1.1.m1.2.3.1" xref="S2.I6.i5.p1.1.m1.2.3.1.cmml">∈</mo><mrow id="S2.I6.i5.p1.1.m1.2.3.3.2" xref="S2.I6.i5.p1.1.m1.2.3.3.1.cmml"><mo stretchy="false" id="S2.I6.i5.p1.1.m1.2.3.3.2.1" xref="S2.I6.i5.p1.1.m1.2.3.3.1.cmml">[</mo><mn id="S2.I6.i5.p1.1.m1.1.1" xref="S2.I6.i5.p1.1.m1.1.1.cmml">0</mn><mo id="S2.I6.i5.p1.1.m1.2.3.3.2.2" xref="S2.I6.i5.p1.1.m1.2.3.3.1.cmml">,</mo><mn id="S2.I6.i5.p1.1.m1.2.2" xref="S2.I6.i5.p1.1.m1.2.2.cmml">1</mn><mo stretchy="false" id="S2.I6.i5.p1.1.m1.2.3.3.2.3" xref="S2.I6.i5.p1.1.m1.2.3.3.1.cmml">]</mo></mrow></mrow></math>, <math><mrow id="S2.I6.i5.p1.2.m2.1.1" xref="S2.I6.i5.p1.2.m2.1.1.cmml"><mrow id="S2.I6.i5.p1.2.m2.1.1.2" xref="S2.I6.i5.p1.2.m2.1.1.2.cmml"><msubsup id="S2.I6.i5.p1.2.m2.1.1.2.1" xref="S2.I6.i5.p1.2.m2.1.1.2.1.cmml"><mo largeop="true" symmetric="true" id="S2.I6.i5.p1.2.m2.1.1.2.1.2.2" xref="S2.I6.i5.p1.2.m2.1.1.2.1.2.2.cmml">∑</mo><mrow id="S2.I6.i5.p1.2.m2.1.1.2.1.2.3" xref="S2.I6.i5.p1.2.m2.1.1.2.1.2.3.cmml"><mi id="S2.I6.i5.p1.2.m2.1.1.2.1.2.3.2" xref="S2.I6.i5.p1.2.m2.1.1.2.1.2.3.2.cmml">k</mi><mo id="S2.I6.i5.p1.2.m2.1.1.2.1.2.3.1" xref="S2.I6.i5.p1.2.m2.1.1.2.1.2.3.1.cmml">=</mo><mn id="S2.I6.i5.p1.2.m2.1.1.2.1.2.3.3" xref="S2.I6.i5.p1.2.m2.1.1.2.1.2.3.3.cmml">1</mn></mrow><msub id="S2.I6.i5.p1.2.m2.1.1.2.1.3" xref="S2.I6.i5.p1.2.m2.1.1.2.1.3.cmml"><mi id="S2.I6.i5.p1.2.m2.1.1.2.1.3.2" xref="S2.I6.i5.p1.2.m2.1.1.2.1.3.2.cmml">N</mi><mi id="S2.I6.i5.p1.2.m2.1.1.2.1.3.3" xref="S2.I6.i5.p1.2.m2.1.1.2.1.3.3.cmml">k</mi></msub></msubsup><msub id="S2.I6.i5.p1.2.m2.1.1.2.2" xref="S2.I6.i5.p1.2.m2.1.1.2.2.cmml"><mi id="S2.I6.i5.p1.2.m2.1.1.2.2.2" xref="S2.I6.i5.p1.2.m2.1.1.2.2.2.cmml">w</mi><mi id="S2.I6.i5.p1.2.m2.1.1.2.2.3" xref="S2.I6.i5.p1.2.m2.1.1.2.2.3.cmml">k</mi></msub></mrow><mo id="S2.I6.i5.p1.2.m2.1.1.1" xref="S2.I6.i5.p1.2.m2.1.1.1.cmml">=</mo><mn id="S2.I6.i5.p1.2.m2.1.1.3" xref="S2.I6.i5.p1.2.m2.1.1.3.cmml">1</mn></mrow></math>

Correct Categorie: cs

Guessed Categorie: math

Result: incorrect

Paper: https://arxiv.org/abs/1707.04910

Formulas:

1-

χ_{ρ} (G)

2-

(a, b, c)

3-

ω (G) = a

4-

χ (G) = b

5-

χ_{ρ} (G) = c

6-

(a, b, c)

7-

(2, k, k + 1)

8-

(2, k, k + 2)

9-

χ_{ρ} (G)

10-

χ_{ρ} (G)

Formulas (html):

Correct Categorie: math

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/math/0107093

Formulas:

1-

γ (0) \in S

2-

(S, γ^{'} (0))

3-

𝐇^{n} (𝐂)

4-

𝐇^{n} (𝐂)

5-

𝐇^{n - 1} (𝐂)

6-

𝐇^{n} (𝐑)

7-

𝐇^{n} (𝐂)

8-

𝐇^{n} (𝐂)

9-

𝐇^{n} (𝐂)

10-

𝐇^{2} (𝐂)

Formulas (html):

Correct Categorie: math

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0410379

Formulas:

1-

f_{psf} (d)

2-

S (100) < 3

3-

S (100) < 1 J y

4-

T_{C} = 19 K

5-

S_{k} (θ) = {⟨ {| B (\underline{x}) - \frac{1}{k} \sum_{i = 1}^{k} B (\underline{x} + {\underline{θ}}_{i}) |}^{2} ⟩}_{x}

6-

B (\underline{x})

7-

N_{str} = \sqrt{S_{k}} \times Ω

8-

N_{str}^{2} = N_{conf}^{2} + 2 N_{inst}^{2}

9-

N_{s t r}

10-

\log_{10} (N) = (- 1.68 \pm 0.09) \times \log_{10} (S [Jy]) - (0.43 \pm 0.07)

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1701.04402

Formulas:

1-

V_{o b s} = V_{t r u e} * A

2-

I_{o b s} = I_{t r u e} \times B

3-

V_{o b s}

4-

V_{t r u e}

5-

I_{o b s}

6-

I_{t r u e}

7-

V (u, v) \overset{ℱ}{⇌} I (l, m)

8-

S (u, v)

9-

V_{o b s} (u, v) = [V_{t r u e} (u, v) * A (u, v)] \times S (u, v)

10-

S (u, v) = \sum_{k} δ (u - u_{k}) δ (v - v_{k})

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: hep-th

Result: incorrect

Paper: https://arxiv.org/abs/1504.08249

Formulas:

1-

D_{x x} = 10^{24} β D_{0} {(ρ / ρ_{0})}^{δ}

2-

D_{x x} = 10^{24} β D_{0} {(ρ / ρ_{0})}^{δ}

3-

ρ (r, z) = {(\frac{r + r_{o f f}}{R_{⊙} + r_{o f f}})}^{α} \exp {β (\frac{r - R_{⊙}}{R_{⊙} + r_{o f f}})} \exp {- \frac{| z |}{z_{0}}}

4-

r_{o f f} = 0.55

5-

ρ (r, z) = 0

6-

\max Φ / \min Φ ≃ 2

7-

\max Φ / \min Φ ≃ 1.2

8-

E_{k i n}

9-

E_{k i n}

10-

E_{k i n}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: gr-qc

Result: incorrect

Paper: https://arxiv.org/abs/1811.05773

Formulas:

1-

y \in [0, 1]

2-

f_{a s} (I_{A})

3-

f_{a s} (I_{A}) = y = σ (f_{d n n} (I_{A})) .

4-

f_{d n n} (I_{A})

5-

l \in [0, 1]

6-

ℒ_{a s s e s s o r} = \frac{1}{n} \sum_{i = 1}^{n} {(f_{a s} (I_{A}^{i}) - l^{i})}^{2} .

7-

g_{d n n} (I_{L})

8-

g_{d n n} (I_{L}) = A_{θ} = [\begin{matrix} θ_{1} & 0 & θ_{2} \\ 0 & θ_{3} & θ_{4} \end{matrix}] .

9-

x_{w_{o}}, y_{h_{o}}

10-

i \in [0, \dots, W_{o}]

Formulas (html):

Correct Categorie: cs

Guessed Categorie: gr-qc

Result: incorrect

Paper: https://arxiv.org/abs/1912.02117

Formulas:

1-

\geq 0.1 μ m

2-

< 0.01 μ m

3-

0.02 - 0.28 M_{⊙}

4-

\sim 0.1 - 1.0 M_{⊙}

5-

\sim 10^{8} M_{⊙}

6-

≲ 0.05 μ m

7-

a ≳ 0.2 μ m

8-

\geq 0.1 μ m

9-

> 0.1 μ m

10-

a_{\min} \sim 0.01 μ m

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: math

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/0702335

Formulas:

1-

Ω_{1} = 2 π / (τ + 1)

2-

[τ = (1 + \sqrt{5}) / 2]

3-

Ω_{p} = 2 π / (τ + p)

4-

2 π - Ω_{2}

5-

ϵ = p^{2} R^{- 3}

6-

v_{i, j} = 𝒑_{i} \cdot 𝒑_{j} / r_{i, j}^{3} - 3 (𝒑_{i} \cdot 𝒓_{i, j}) (𝒑_{j} \cdot 𝒓_{i, j}) / r_{i, j}^{5}

7-

z_{n} = a n

8-

V = 1 / 2 \sum_{n \neq m} v_{n, m}

9-

E = \frac{1}{2} I \sum_{i} {\dot{θ}}_{i}^{2} + V

10-

θ_{n} = Ω n

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1607.08643

Formulas:

1-

D_{n} (4000)

2-

12 + l o g (O / H)

3-

l o g (M_{*} / M_{☉}) < 10.0

4-

f_{b a r}

5-

H_{0} = 100 {kms}^{- 1} Mpc

6-

r_{l i m} < 17.77

7-

C = r 90 / r 50

8-

f r a c d e V

9-

f r a c d e V = 1

10-

f r a c d e V = 0

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: gr-qc

Result: incorrect

Paper: https://arxiv.org/abs/1707.01382

Formulas:

1-

r_{f a c}

2-

10^{11} {cm}^{- 3}

3-

5 S_{1 / 2}

4-

70 S_{1 / 2}

5-

Ω = Ω_{1013} Ω_{420} / 2 Δ_{6 P}

6-

6 P_{3 / 2}

7-

Δ_{6 P} \approx 2 π \times 40 MHz

8-

r_{b} \approx 10 μ m

9-

r_{f a c} \approx 6 μ m

10-

γ = 2 π \times 700 kHz

Formulas (html):

Correct Categorie: physics

Guessed Categorie: math

Result: incorrect

Paper: https://arxiv.org/abs/1202.6676

Formulas:

1-

M_{B} = 8 \times 10^{- 5}

2-

(λ \approx 0.0030, Ω \approx 0.098)

3-

M_{B} = 8 \times 10^{- 4}

4-

(λ \approx 0.013, Ω \approx 0.098)

5-

M_{B} = 8 \times 10^{- 3}

6-

(λ \approx 0.056, Ω \approx 0.098)

7-

𝐮 = ψ (𝝃 + ω 𝜼)

8-

u^{α} u_{α} = - 1

9-

p = μ_{0} [(ψ / ψ_{Σ}) - 1]

10-

r_{Σ} = r_{s} [1 + σ Ω^{2} P_{2} (\cos θ)] + 𝒪 (Ω^{4})

Formulas (html):

Correct Categorie: gr-qc

Guessed Categorie: hep-lat

Result: incorrect

Paper: https://arxiv.org/abs/1805.06771

Formulas:

1-

𝐗 = [𝐱^{(t - t_{h})}, \dots, 𝐱^{(t - 1)}, 𝐱^{(t)}]

2-

𝐱^{(t)} = [x_{0}^{(t)}, y_{0}^{(t)}, x_{1}^{(t)}, y_{1}^{(t)}, \dots, x_{n}^{(t)}, y_{n}^{(t)}]

3-

𝐘 = [𝐲^{(t + 1)}, \dots, 𝐲^{(t + t_{f})}]

4-

𝐲^{(t)} = [x_{0}^{(t)}, y_{0}^{(t)}]

5-

P (𝐘 | 𝐗)

6-

P (𝐘 | 𝐗) = \sum_{i} P_{Θ} (𝐘 | m_{i}, 𝐗) P (m_{i} | 𝐗)

7-

Θ = [Θ^{(t + 1)}, \dots, Θ^{(t + t_{f})}]

8-

(m + 1, n)

9-

(m, n + 1)

10-

P (m_{i} | 𝐗)

Formulas (html):

Correct Categorie: cs

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/1112.5657

Formulas:

1-

{0, 1}^{n} \subset ℓ_{1}^{(n)}

2-

S = {𝐱_{0}, 𝐱_{1}, \dots, 𝐱_{k}}

3-

{0, 1}^{n} \subset ℓ_{1}^{(n)}

4-

{𝐱_{1} - 𝐱_{0}, 𝐱_{2} - 𝐱_{0}, \dots, 𝐱_{k} - 𝐱_{0}}

5-

{𝐱_{1} - 𝐱_{0}, 𝐱_{2} - 𝐱_{0}, \dots, 𝐱_{k} - 𝐱_{0}}

6-

{0, 1}^{n} \subset ℓ_{1}^{(n)}

7-

{x_{1}, \dots, x_{n}} \subseteq X

8-

η_{1}, \dots, η_{n}

9-

η_{1} + \dots + η_{n} = 0

10-

\sum_{1 \leq i, j \leq n} d {(x_{i}, x_{j})}^{p} η_{i} η_{j}

Formulas (html):

Correct Categorie: math

Guessed Categorie: hep-lat

Result: incorrect

Paper: https://arxiv.org/abs/1912.01780

Formulas:

1-

α (G) + 1

2-

H (n, k)

3-

H (n, k)

4-

α (H (n, k))

5-

G = (V, E)

6-

α (G) + 1

7-

H (n, k)

8-

H (n, 2) = Q^{n}

9-

f (Q^{n})

10-

\frac{1}{2} (\log n - \log \log n + 1) < f (Q^{n}) \leq ⌈ \sqrt{n} ⌉

Formulas (html):

Correct Categorie: math

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/0803.2137

Formulas:

1-

M_{P l}^{2} = 8 π M_{D}^{n + 2} R^{n}

2-

q \bar{q} \to γ G_{K K}

3-

Z + γ \to ν \bar{ν} + γ

4-

1.1 < | η | < 1.4

5-

p_{T} > 20 GeV

6-

1.05 \pm 0.06 {fb}^{- 1}

7-

ℐ = [E_{tot} (0.4) - E_{em} (0.2)] / E_{em} (0.2)

8-

E_{tot} (0.4)

9-

ℛ = \sqrt{{(Δ η)}^{2} + {(Δ ϕ)}^{2}} = 0.4

10-

E_{em} (0.2)

Formulas (html):

Correct Categorie: hep-ex

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/hep-th/0411265

Formulas:

1-

p = ρ / (1 + k \sqrt{ρ})

2-

U (T, V)

3-

- P V = F (β, V)

4-

F (β) = - \frac{V}{8 {(2 α^{'})}^{5}} \int_{0}^{+ \infty} d t t^{- 6} [θ_{3} (0, \frac{i β^{2}}{4 α^{'} t}) - θ_{4} (0, \frac{i β^{2}}{4 α^{'} t})] θ_{4}^{- 8} (0, i t / π^{2}) .

5-

θ_{4}^{- 8} (0, i t / π^{2})

6-

θ_{4} (0, i / t) = t^{1 / 2} θ_{2} (0, i t)

7-

\begin{matrix} F (β) \approx & - \frac{V}{8 {(2 α^{'})}^{5}} \int_{ϵ}^{+ \infty} d t t^{- 6} [θ_{3} (0, \frac{i β^{2}}{4 α^{'} t}) - θ_{4} (0, \frac{i β^{2}}{4 α^{'} t})] θ_{4}^{- 8} (0, i t / π^{2}) \\ - \frac{V}{2^{9} π^{8} {(2 α^{'})}^{5}} \int_{0}^{ϵ} d t t^{- 2} e^{(8 α^{'} π^{3} - β^{2} π) / (4 α^{'} t)}, \end{matrix}

8-

1 / β_{H} = T_{H} = 1 / (π \sqrt{8 α^{'}})

9-

\int_{0}^{ϵ} d t t^{- 2} e^{(8 α^{'} π^{3} - β^{2} π) / (4 α^{'} t)} = \frac{β_{H}^{2}}{2 π^{3} (β^{2} - β_{H}^{2})} e^{- 2 π^{3} (β^{2} - β_{H}^{2}) / (ϵ β_{H}^{2})},

10-

(β - β_{H})

Formulas (html):

Correct Categorie: hep-th

Guessed Categorie: hep-ph

Result: incorrect

Paper: https://arxiv.org/abs/1204.4597

Formulas:

1-

(1 - {| 𝐯_{i} |}^{2}) 𝐯_{i} - \frac{a}{N} {\sum_{j = 1}^{N}}_{i \neq j} (𝐫_{i} (t) - 𝐫_{j} (t - τ)) + 𝜼_{i} (t),

2-

i = 1, 2 \dots, N

3-

(1 - {| 𝐯_{i} |}^{2}) 𝐯_{i}

4-

| 𝐯_{i} | = 1

5-

𝜼_{i} (t) = (η_{i}^{(1)}, η_{i}^{(2)})

6-

⟨ η_{i}^{(ℓ)} (t) ⟩ = 0

7-

⟨ η_{i}^{(ℓ)} (t) η_{j}^{(k)} (t^{'}) ⟩ = 2 D δ (t - t^{'}) δ_{i j} δ_{ℓ k}

8-

i, j = 1, 2, \dots N

9-

ℓ, k = 1, 2

10-

𝐑 (t) = \frac{1}{N} \sum_{i = 1}^{N} 𝐫_{i} (t) .

Formulas (html):

Correct Categorie: nlin

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/1308.3342

Formulas:

1-

D_{cir} ≃ 1 - \frac{P_{lin}}{2 P_{cir}} - F_{A},

2-

P_{lin} / (2 P_{cir})

3-

P_{lin} / (2 P_{cir})

4-

\hat{C} = (k_{w} - \frac{ω (1 + K^{2})}{2 c γ^{2}}) Γ^{- 1} .

5-

k_{w} = 2 π / λ_{w}

6-

Γ = 4 π ρ / λ_{w}

7-

\hat{z} = Γ z ≫ 1

8-

\hat{η} = P / (ρ P_{beam})

9-

| \hat{C} | < 1

10-

Re \hat{Λ} = Re Λ / Γ

Formulas (html):

Correct Categorie: physics

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0608008

Formulas:

1-

X_{i} = ρ_{i} / ρ_{n}

2-

ρ_{i, n} = m_{i, n} n_{i, n}

3-

\frac{\partial ρ_{j}}{\partial t} + \nabla \cdot (ρ_{j} 𝐯_{j}) = 0,

4-

j = n, i, e

5-

0 = - e n_{e} (𝐄 + \frac{𝐯_{e} \times 𝐁}{c}) - ρ_{e} \sum_{j = i, n} ν_{e j} (𝐯_{e} - 𝐯_{j})

6-

ρ_{i} \frac{d 𝐯_{i}}{d t}

7-

e n_{i} (𝐄 + \frac{𝐯_{i} \times 𝐁}{c}) - ρ_{i} \sum_{j = e, n} ν_{i j} (𝐯_{i} - 𝐯_{j})

8-

ρ_{n} \frac{d 𝐯_{n}}{d t}

9-

\sum_{j = e, i} ρ_{j} ν_{j n} (𝐯_{j} - 𝐯_{n})

10-

ν_{j k} \equiv ρ_{k} γ_{j k} = ρ_{k} {< σ v >}_{j} / (m_{k} + m_{j})

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/0303278

Formulas:

1-

f \propto 1 / \sqrt{L C}

2-

T_{i r r}

3-

T_{i r r}

4-

T_{1}^{- 1} \propto e x p (- Δ_{s p i n} / T) .

5-

Δ_{s p i n}

6-

T_{1}^{- 1} / γ_{N}^{2}

7-

T_{1}^{- 1} \propto b T

8-

K = K_{o r b} + K_{s p i n}

9-

K (T) = K_{0} + \frac{K_{1}}{\sqrt{T}} e x p (- Δ_{s p i n} / T) .

10-

Δ_{s p i n}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: math

Result: incorrect

Paper: https://arxiv.org/abs/1806.01002

Formulas:

1-

σ = \pm 1 / 2

2-

(S = \pm 1, 0)

3-

σ_{i} = \pm \frac{1}{2}

4-

S_{i} = \pm 1, 0

5-

J_{R} = J \exp [- λ (n + 1)] / {(n + 1)}^{δ},

6-

ℋ = - J_{A} \sum_{< i j >} σ_{i} σ_{j} - J_{B} \sum_{< k l >} S_{k} S_{l} + J_{R} \sum_{< i k >} σ_{i} S_{k} - D_{B} \sum_{k} {(S_{k})}^{2},

7-

M_{α} = ⟨ \sum_{t} m_{α} (t) ⟩, α = A, B, T

8-

m_{α} (t)

9-

χ = \frac{N_{T}}{k_{B} T} [⟨ \sum_{t} {(m_{T} (t))}^{2} ⟩ - {⟨ \sum_{t} m_{T} (t) ⟩}^{2}],

10-

M_{T} = [M_{A} + M_{B}] / 2.0,

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1512.05124

Formulas:

1-

Z T = S^{2} σ T / κ

2-

A (E, 𝐤)

3-

A (E, 𝐤)

4-

I \cdot D (E_{F}) > 1

5-

D (E_{F})

6-

D (E_{F})

7-

D (E_{F})

8-

k_{B} T_{c}^{M F A} = \frac{2}{3} Δ E

9-

m_{t o t}

10-

m_{t o t}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: gr-qc

Result: incorrect

Paper: https://arxiv.org/abs/hep-ph/9612481

Formulas:

1-

S U (2)

2-

S U {(3)}_{c o l o r}

3-

g g, γ g, q \bar{q}

4-

T_{c}^{i}, T_{c}

5-

q \bar{q}, l \bar{l}

6-

g g, q \bar{q}, l \bar{l}

7-

{(\frac{f_{S - 1}}{f_{E T C}})}^{2} \bar{ψ_{L}} γ^{μ} (\partial_{μ} Σ) Σ^{†} ψ_{L} and {(\frac{f_{S - 1}}{f_{E T C}})}^{2} \bar{d_{R}} γ^{μ} (\partial_{μ} Σ) Σ^{†} d_{R},

8-

Σ = \exp (2 i T_{a} π^{a} / f_{S - 1})

9-

f_{E T C}

10-

S U (2)

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/2012.02869

Formulas:

1-

{(x - n)}^{2} + {(y - n)}^{2} = 2 n^{2}

2-

M \frac{(a + b)}{2 a} \in ℕ

3-

M \frac{(a - b)}{2 a} \in ℕ

4-

M = \frac{M (a + b)}{2 a} + \frac{M (a - b)}{2 a}

5-

M = (K - α) + (K + α) = (10 k_{1} + 3) + (10 k_{2} + 3)

6-

k_{2} = \frac{K - 3 + α}{10}

7-

k_{1} = \frac{K - 3 - α}{10}

8-

F (x, y) = (10 k_{1} + 3) x + (10 k_{2} + 3) y .

9-

\ker F = {(- (10 k_{2} + 3), 10 k_{1} + 3)}

10-

{\ker F}^{⊥} = {(10 k_{1} + 3, 10 k_{2} + 3)}

Formulas (html):

Correct Categorie: math

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/1011.1520

Formulas:

1-

A_{d i a}

2-

A_{S D W}

3-

A_{S D W}

4-

A_{S D W}

5-

B (x, y) = A_{S D W} c o s (2 π x / λ) c o s (2 π y / λ) e^{(- (x^{2} + y^{2}) / 2 τ^{2})}

6-

A_{S D W}

7-

H = 4, 10, 15, 25

8-

A_{S D W} \leq A_{d i a}

9-

A_{S D W}

10-

A_{S D W}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: gr-qc

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0109559

Formulas:

1-

10^{- 8} - 10^{- 7} I_{N S}

2-

Q \sim 4.5 \times 10^{37}

3-

5 \times 10^{- 8} I_{N S}

4-

h \sim 10^{- 27} - 10^{- 26}

5-

h_{s} (t) = A (t) \sin (2 π (ν t + \dot{ν} t^{2}))

6-

H_{k_{0}, k_{1}} = \sum_{j_{0}} h_{j_{0}} \exp (2 π i (k_{0} (j_{0} / N_{0}) + k_{1} {(j_{0} / N_{0})}^{2}))

7-

0 < j_{0} < N_{0} - 1

8-

O (N_{0} N_{1} l o g_{2} (N_{0} N_{1}))

9-

O (N_{0}^{2})

10-

{\dot{ν}}_{m a x} = N_{1} / 2 T^{2}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/0812.2274

Formulas:

1-

𝐁_{eff, I} = B_{1 I} {\hat{x}}^{'} + \frac{2 π}{γ_{I}} Δ ν_{I} \hat{z}

2-

Δ ν_{I} = ν_{I} - \frac{γ_{I}}{2 π} B_{0}

3-

γ_{I} | 𝐁_{eff, I} | = γ_{S} | 𝐁_{eff, S} |

4-

Δ ν_{I} = Δ ν_{S} = 0

5-

γ_{H} B_{1 H} = γ_{C} B_{1 C}

6-

\frac{\partial n_{I}}{\partial t}

7-

- k_{I} n_{I} - \frac{k_{I S}}{N} (N_{S} n_{I} - N_{I} n_{S}) + r_{I} (t) + r_{I S} (t),

8-

\frac{\partial n_{S}}{\partial t}

9-

- k_{S} n_{S} + \frac{k_{I S}}{N} (N_{S} n_{I} - N_{I} n_{S}) + r_{S} (t) - r_{I S} (t),

10-

N = N_{I} + N_{S}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/1204.0362

Formulas:

1-

ℓ_{V} (Γ, x)

2-

ℓ_{V} (Γ) = (ℓ_{0}, ℓ_{1}, \dots, ℓ_{n})

3-

ℓ_{V} (Γ, x) = ℓ_{0} + ℓ_{1} x + \dots + ℓ_{n} x^{n}

4-

ℓ_{V} (Γ, x)

5-

ξ_{V} (Γ, x) = ξ_{0} + ξ_{1} x + \dots + ξ_{⌊ n / 2 ⌋} x^{⌊ n / 2 ⌋}

6-

ℓ_{V} (Γ, x) = \sum_{i = 0}^{⌊ n / 2 ⌋} ξ_{i} x^{i} {(1 + x)}^{n - 2 i} .

7-

ξ_{V} (Γ, x)

8-

ξ_{V} (Γ) = (ξ_{0}, ξ_{1}, \dots, ξ_{⌊ n / 2 ⌋})

9-

ξ_{V} (Γ, x)

10-

ξ_{V} (Γ, x)

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0301025

Formulas:

1-

{(V - I)}_{0}

2-

L_{V, b a r y}

3-

L_{V, b a r y} = L_{V} + 1.33 M_{HI} \cdot {⟨ M_{V} / L_{V} ⟩}^{- 1},

4-

⟨ M_{V} / L_{V} ⟩

5-

L_{V, b a r y}

6-

M_{HI} = 2.36 \cdot 10^{5} D^{2} \sum S_{v} d v M_{⊙}

7-

\sum S_{v} d v

8-

⟨ [F e / H] ⟩

9-

L_{b a r y}

10-

⟨ [Fe / H] ⟩

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1101.0648

Formulas:

1-

g \to b \bar{b}

2-

H \to b \bar{b}

3-

g \to b \bar{b}

4-

H \to b \bar{b}

5-

t \bar{t} \to W b W \bar{b} \to ℓ ν b j \bar{j} \bar{b}

6-

σ_{t \bar{t}} = 8.50

7-

1.1 < | η | < 1.4

8-

15 % / \sqrt{E} \oplus 0.3 %

9-

50 % / \sqrt{E} \oplus 5 %

10-

Δ R = \sqrt{{(Δ ϕ)}^{2} + {(Δ η)}^{2}} < 0.7

Formulas (html):

Correct Categorie: hep-ex

Guessed Categorie: gr-qc

Result: incorrect

Paper: https://arxiv.org/abs/hep-lat/9707033

Formulas:

1-

\int d^{3} x [\frac{1}{4} {(\partial_{i} A_{j} - \partial_{j} A_{i})}^{2} + {| (\partial_{i} + i e_{3} A_{i}) ϕ |}^{2} + m_{3}^{2} ϕ^{*} ϕ + λ_{3} {(ϕ^{*} ϕ)}^{2}] .

2-

(e_{3}, m_{3}, λ_{3})

3-

y \equiv m_{3}^{2} (e_{3}^{2}) / e_{3}^{4}, x \equiv λ_{3} / e_{3}^{2}

4-

y_{c} (x)

5-

β_{G} \sum_{𝐱, i < j} {1 - \cos [α_{i j} (𝐱)]} - β_{H} \sum_{𝐱, i} Re ϕ^{*} (𝐱) U_{i} (𝐱) ϕ (𝐱 + \hat{i})

6-

+ \sum_{𝐱} ϕ^{*} (𝐱) ϕ (𝐱) + β_{R} \sum_{𝐱} {[ϕ^{*} (𝐱) ϕ (𝐱)]}^{2},

7-

β_{G} = 1 / e_{3}^{2} a

8-

α_{i j} (𝐱) = α_{i} (𝐱) + α_{j} (𝐱 + \hat{i}) - α_{i} (𝐱 + \hat{j}) - α_{j} (𝐱)

9-

m_{γ} / e_{3}^{2} = 0.003

10-

ϕ^{*} (𝐱) ϕ (𝐱), O_{i} (𝐱) = Im ϕ^{*} (𝐱) U_{i} (𝐱) ϕ (𝐱 + \hat{i}),

Formulas (html):

Correct Categorie: hep-lat

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1709.05397

Formulas:

1-

w \in S_{i}^{{+, -}}

2-

w = ⟨ w^{a}, w^{r} ⟩ .

3-

B = \log_{2} | V |

4-

\log_{2} | A |

5-

C = \sum_{x \in X} [\sum_{r \in R_{x}} [\sum_{w \in W_{r}} \log_{2} | V | + B^{'}]],

6-

A_{i j} / \min (A_{i}, A_{j})

7-

⌊ δ | M | ⌋

8-

⌈ (1 - δ) | M | ⌉

9-

[1 - \exp (- d^{2} / σ_{d}^{2})]

10-

p = \min_{c} p_{c} .

Formulas (html):

Correct Categorie: cs

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1904.13315

Formulas:

1-

E (k) \propto \exp - {(k / k_{β})}^{2 / 3}

2-

\partial_{t} 𝐯 + (𝐯 \cdot \nabla) 𝐯 = - \nabla p + ν \nabla^{2} 𝐯 + 𝐅_{e},

3-

D = v_{c} l_{c}

4-

Φ (x, t)

5-

Φ (x, t)

6-

Φ (x, t)

7-

E (k) \propto \exp - (k / k_{c})

8-

k_{c} = 1 / l_{c}

9-

k_{c} = 1 / l_{c}

10-

E (k) \propto \int_{0}^{\infty} P (k_{c}) \exp - (k / k_{c}) d k_{c} \propto \exp - {(k / k_{β})}^{β}

Formulas (html):

Correct Categorie: physics

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1401.6291

Formulas:

1-

H^{LDA} (𝐤)

2-

U_{m m^{'}}^{σ σ^{'}}

3-

\hat{H} (𝐤) = \sum_{𝐤, i m, j m^{'}, σ} (H_{i m, j m^{'}}^{LDA} (𝐤) - H_{i m, j m^{'}}^{DC}) {\hat{a}}_{𝐤, i m σ}^{†} {\hat{a}}_{𝐤, j m^{'} σ}

4-

+ \frac{1}{2} \sum_{i, m \neq m^{'}, σ, σ^{'}} U_{m m^{'}}^{σ σ^{'}} {\hat{n}}_{i m σ}^{d} {\hat{n}}_{i m^{'} σ^{'}}^{d} .

5-

{\hat{a}}_{𝐤, i m σ}^{†}

6-

{\hat{a}}_{i m σ}^{†}

7-

{\hat{n}}_{i m σ}^{d}

8-

E^{DC} = \bar{U} (n_{d} - 0.5)

9-

A_{i} (ω)

10-

A_{i} (ω) = \sum_{𝐤} {[I (ω + μ) - (H^{LDA} (𝐤) - H^{DC}) - Σ (ω)]}_{i i}^{- 1},

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: gr-qc

Result: incorrect

Paper: https://arxiv.org/abs/2012.04107

Formulas:

1-

{s_{1}, s_{2}, \dots, s_{n}}

2-

{m_{1}, m_{2}, \dots, m_{k}}

3-

{a_{1}, a_{2}, \dots, a_{n}}

4-

i \in {1, 2, \dots, n}

5-

f : [2 n] \to [2 n]

6-

{s_{1}, s_{2}, \dots, s_{2 n}}

7-

{m_{1}, m_{2}, \dots, m_{n}} + {\neg}

8-

{a_{1}, a_{2}, \dots, a_{2 n}}

9-

f^{- 1} (a)

10-

{m_{1}, m_{2}, \dots, m_{n + 1}}

Formulas (html):

Correct Categorie: cs

Guessed Categorie: hep-th

Result: incorrect

Paper: https://arxiv.org/abs/1612.05415

Formulas:

1-

𝐅_{i j}^{n} = [k_{n} δ - 2 γ_{n} m_{eff} (𝐕_{i j} \cdot {\hat{𝐫}}_{i j})] {\hat{𝐫}}_{i j}

2-

𝐕_{i j} = 𝐕_{i} - 𝐕_{j}

3-

m_{eff} = m_{i} m_{j} / (m_{i} + m_{j})

4-

k_{n} = m_{eff} [{(\frac{π}{Δ t})}^{2} + γ_{n}^{2}]

5-

γ_{n} = \ln e / Δ t

6-

𝐅_{i j}^{t} = - \min (| μ 𝐅_{i j}^{n} |, | k_{s} ζ |) sign (𝐕_{i j}^{s})

7-

ζ (t) = \int_{t_{0}}^{t} 𝐕_{i j}^{s} (t^{'}) d t^{'}

8-

k_{n} = 7.32 \times 10^{4}

9-

Δ t / 50 = 2 \times 10^{- 6}

10-

d_{t} / d = 1.2

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: gr-qc

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0605652

Formulas:

1-

L_{8 µm - 1000 µm} \geq 10^{11} L_{⊙}

2-

L_{8 µm - 1000 µm} \geq 10^{12} L_{⊙}

3-

F (25 µm) / F (60 µm) ≳ 0.2

4-

F (25 µm) / F (60 µm)

5-

Ł_{bol} = ϵ_{r} \dot{M} c^{2}

6-

V_{vir} = 160 km s^{- 1}

7-

η = 0.005, v_{W} = 837 km / s

8-

η = 0.05, v_{W} = 837 km / s

9-

η = 0.5, v_{W} = 837 km / s

10-

η vs v_{W}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/2003.08885

Formulas:

1-

𝝉, 𝝈 \in ℝ^{2}

2-

S (𝐱 + 𝝉) = S (𝐱)

3-

S (𝐱 + 𝝈) = S (𝐱)

4-

I (𝐱 + 𝝉) = I (𝐱)

5-

I (𝐱 + 𝝈) = I (𝐱)

6-

T = R_{1} F R_{2}

7-

det (T^{⊤} T - I) = 0

8-

T = R_{1} F R_{2}

9-

T^{⊤} T = R_{2}^{⊤} F^{2} R_{2}

10-

T^{⊤} T - I = R_{2}^{⊤} F^{2} R_{2} - I = R_{2}^{⊤} (F^{2} - I) R_{2}

Formulas (html):

Correct Categorie: cs

Guessed Categorie: hep-th

Result: incorrect

Paper: https://arxiv.org/abs/1707.00576

Formulas:

1-

μ (I) = μ_{c} + a I^{α}

2-

N = 2 \cdot 10^{3}

3-

k_{t} = 0.5 k_{n}

4-

| \dot{Γ} - \dot{γ} | / \dot{γ}

5-

S = k_{n} / P

6-

I = \dot{γ} \sqrt{m / P}

7-

μ (I) = μ_{c} + a I^{α}

8-

μ (I) - μ_{c}

9-

\dot{Γ} (\vec{r}, t)

10-

{\vec{r}}_{i} = (x_{i}, z_{i})

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/nucl-ex/0703030

Formulas:

1-

2.9 < m_{μ μ} < 4.5

2-

σ_{J / ψ} / σ_{DY}

3-

d N_{J / ψ} / d E_{ZDC}

4-

d σ_{J / ψ} / d E_{ZDC}

5-

σ_{J / ψ} / σ_{DY}

6-

σ_{J / ψ} / σ_{DY}

7-

σ_{J / ψ} / σ_{DY}

8-

σ_{J / ψ} / σ_{DY}

9-

- 0.5 < y_{c m} < 0.5

10-

{(σ_{J / ψ} / σ_{DY})}_{E_{0}}^{p p}

Formulas (html):

Correct Categorie: nucl-ex

Guessed Categorie: physics

Result: incorrect

Run 16330496 (TestAgent)