Run 11329971

Paper: https://arxiv.org/abs/1411.0821

Formulas:

1-

x_{1}, \dots, x_{k}

2-

{0, 1}^{d}

3-

{0, 1}^{d}

4-

\sum_{i = 1}^{k} \max [a g r e e (c_{1}, x_{i}), a g r e e (c_{2}, x_{i})]

5-

a g r e e (x, y)

6-

x_{1}, \dots, x_{k}

7-

{1, - 1}^{d}

8-

{1, - 1}^{d}

9-

2 \sqrt{2} - 2 ≃ 0.828

10-

{1, - 1}^{M}

Formulas (html):

Correct Categorie: cs

Guessed Categorie: cs

Result: correct

Paper: https://arxiv.org/abs/0803.1759

Formulas:

1-

\sim 6 h^{- 1}

2-

\approx 6 h^{- 1}

3-

- 5 \log_{10} h

4-

100 km s^{- 1} {Mpc}^{- 1}

5-

- 23 < M_{{}^{0.1}r} < - 17

6-

{(g - r)}_{0.1}

7-

{(g - r)}_{0.1}

8-

μ_{*} = M_{*} / 2 π r_{50, z}^{2}

9-

h^{2} M_{⊙} {kpc}^{- 2}

10-

\approx 6 h^{- 1}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0209247

Formulas:

1-

M_{⋆} < 8 M_{⊙}

2-

\dot{M} \sim 10^{- 4} M_{⊙}

3-

(Q_{ext} / a)

4-

Q (λ) \sim λ^{- β}

5-

M_{⋆} = 1.0 M_{⊙}

6-

α_{C_{2} H} = 0.34

7-

α_{C_{2} H_{2}} = 0.34

8-

Δ u_{p} = 4

9-

α_{C_{2} H_{2}}

10-

α_{C_{2} H_{2}}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1009.4355

Formulas:

1-

O (\log^{2} k)

2-

O (\log k)

3-

O (\log k)

4-

O (\log k / \log \log k)

5-

O (n^{k + 1})

6-

O (n^{C + 1})

7-

Ω (k^{1 / 3})

8-

O (n \log C)

9-

O (n^{k + 1})

10-

O (1 / ϵ)

Formulas (html):

Correct Categorie: cs

Guessed Categorie: cs

Result: correct

Paper: https://arxiv.org/abs/1803.09722

Formulas:

1-

d (\cdot, \cdot)

2-

d (𝐳_{i}, 𝐳_{j}) = {[Δ x, Δ y, Δ z, Δ x^{2}, Δ y^{2}, Δ z^{2}]}^{T},

3-

𝐳_{i} = (x_{i}, y_{i}, z_{i})

4-

𝐳_{j} = (x_{j}, y_{j}, z_{j})

5-

Δ x = x_{i} - x_{j}, Δ y = y_{i} - y_{j}

6-

Δ z = z_{i} - z_{j}

7-

Δ x^{2} = {(x_{i} - x_{j})}^{2}, Δ y^{2} = {(y_{i} - y_{j})}^{2}

8-

Δ z^{2} = {(z_{i} - z_{j})}^{2}

9-

𝐈 = {(I_{n}, 𝐳_{n})}_{n = 1}^{N}

10-

N = {N_{2 D}, N_{3 D}}

Formulas (html):

Correct Categorie: cs

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/1809.03883

Formulas:

1-

E = p^{2} / 2 m

2-

E = m / ϵ - p^{2} / 2 m

3-

(i γ^{μ} \partial_{μ} - m) ψ = 0

4-

(γ_{0} E - γ_{i} p_{i} - m) ψ = 0

5-

(η_{1} E^{'} - γ_{i} p_{i} + η_{2} m) u = 0

6-

η_{1} = (γ_{0} + I) / 2

7-

η_{2} = (γ_{0} - I)

8-

E^{'} = p_{i}^{2} / 2 m

9-

η_{1} η_{2} = 0

10-

H_{L} = η^{', - 1} (- i γ_{i} \partial_{i} - m η^{†})

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/math/0611826

Formulas:

1-

F (x) = u (x) f (x) + v (x) f^{'} (x)

2-

{1, 2, \dots, n}

3-

π = a_{1} a_{2} \dots a_{n} \in S_{n}

4-

A_{n} (x)

5-

A_{0} (x) = 1, A_{n} (x) = \sum_{π \in S_{n}} x^{exc (π) + 1} for n \geq 1,

6-

A_{n + 1} (x) = (n + 1) x A_{n} (x) + x (1 - x) A_{n}^{'} (x)

7-

A_{0} (x; q) = 1, A_{n} (x; q) = \sum_{π \in 𝒮_{n}} x^{exc (π)} q^{c (π)} for n \geq 1,

8-

A_{0} (x; q) = 1, A_{1} (x; q) = q, A_{2} (x; q) = q (x + q), A_{3} (x; q) = q [x^{2} + (3 q + 1) x + q^{2}] .

9-

A_{n} (x) = x A_{n} (x; 1)

10-

A_{n + 1} (x; q) = (n x + q) A_{n} (x; q) + x (1 - x) \frac{d}{d x} A_{n} (x; q)

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0201113

Formulas:

1-

A_{L R} = \frac{G_{F} Q^{2}}{4 π α \sqrt{2}} [4 \sin^{2} θ_{W} - 1 + \frac{F_{n} (Q^{2})}{F_{p} (Q^{2})}],

2-

F_{p} (Q^{2})

3-

F_{n} (Q^{2})

4-

G_{F} Q^{2} / α

5-

F_{p} (Q^{2})

6-

F_{n} (Q^{2})

7-

4 π R_{\infty}^{2}

8-

R_{\infty} = R_{*} / {(1 - 2 G M / R_{*})}^{1 / 2},

9-

R_{\infty} = 15 \pm 6

10-

R_{\infty} = 15.5 \pm 1.5

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: hep-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0606180

Formulas:

1-

N_{HI} \geq 2 \times 10^{20}

2-

N_{HI} = 1.823 \times 10^{18} T_{spin} \int τ 𝑑 v .

3-

τ \equiv - \ln (1 - \frac{σ}{f S})

4-

σ / f . S \overset{<}{_{\sim}} 0.3

5-

N_{HI} = 1.823 \times 10^{18} \frac{T_{spin}}{f} \int \frac{σ}{S} 𝑑 v,

6-

T_{spin} / f \propto N_{HI} / \int \frac{σ}{S} 𝑑 v

7-

0.2 \leq z_{abs} \leq 2.2

8-

1.781 \overset{<}{_{\sim}} z_{abs} \overset{<}{_{\sim}} 1.808

9-

\int τ 𝑑 v / N_{HI} \propto f / T_{spin}

10-

N_{HI} \approx 5 \times 10^{21}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/cond-mat/9409106

Formulas:

1-

h_{j} ⟶ h_{j} - Δ_{i j} whenever h_{i} > 0 .

2-

Δ_{i i} > 0 \forall i \in I,

3-

Δ_{i j} \leq 0 \forall i \neq j,

4-

\sum_{j \in I} Δ_{i j} \geq 0 \forall i \in I .

5-

𝐚_{i} \circ 𝐚_{j} (α) = 𝐚_{j} \circ 𝐚_{i} (α)

6-

𝐚_{i} (β) = α

7-

𝐚_{i}^{- 1} = 𝐚_{i}^{det Δ - 1}

8-

\vec{0} \equiv (0, 0, \dots, 0)

9-

γ \equiv {(γ_{j})}_{j \in I} \equiv 𝐚 (\vec{0}) = {(a_{j} - \sum_{k} n_{k} Δ_{k j})}_{j \in I} \in Ω

10-

a_{j} = δ_{i j}

Formulas (html):

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xref="S0.E2.2.m1.2.2.2.2.3.cmml"><mi id="S0.E2.2.m1.2.2.2.2.3.2" xref="S0.E2.2.m1.2.2.2.2.3.2.cmml">j</mi><mo id="S0.E2.2.m1.2.2.2.2.3.1" xref="S0.E2.2.m1.2.2.2.2.3.1.cmml">⁢</mo><mtext id="S0.E2.2.m1.2.2.2.2.3.3" xref="S0.E2.2.m1.2.2.2.2.3.3a.cmml">,</mtext></mrow></mrow></mrow></math>, <math><mrow id="S0.E2.3.m1.2.2.2" xref="S0.E2.3.m1.2.2.3.cmml"><mrow id="S0.E2.3.m1.1.1.1.1" xref="S0.E2.3.m1.1.1.1.1.cmml"><mrow id="S0.E2.3.m1.1.1.1.1.2" xref="S0.E2.3.m1.1.1.1.1.2.cmml"><munder id="S0.E2.3.m1.1.1.1.1.2.1" xref="S0.E2.3.m1.1.1.1.1.2.1.cmml"><mo largeop="true" movablelimits="false" symmetric="true" id="S0.E2.3.m1.1.1.1.1.2.1.2" xref="S0.E2.3.m1.1.1.1.1.2.1.2.cmml">∑</mo><mrow id="S0.E2.3.m1.1.1.1.1.2.1.3" xref="S0.E2.3.m1.1.1.1.1.2.1.3.cmml"><mi id="S0.E2.3.m1.1.1.1.1.2.1.3.2" xref="S0.E2.3.m1.1.1.1.1.2.1.3.2.cmml">j</mi><mo id="S0.E2.3.m1.1.1.1.1.2.1.3.1" xref="S0.E2.3.m1.1.1.1.1.2.1.3.1.cmml">∈</mo><mi id="S0.E2.3.m1.1.1.1.1.2.1.3.3" xref="S0.E2.3.m1.1.1.1.1.2.1.3.3.cmml">I</mi></mrow></munder><msub id="S0.E2.3.m1.1.1.1.1.2.2" xref="S0.E2.3.m1.1.1.1.1.2.2.cmml"><mi mathvariant="normal" id="S0.E2.3.m1.1.1.1.1.2.2.2" xref="S0.E2.3.m1.1.1.1.1.2.2.2.cmml">Δ</mi><mrow id="S0.E2.3.m1.1.1.1.1.2.2.3" xref="S0.E2.3.m1.1.1.1.1.2.2.3.cmml"><mi id="S0.E2.3.m1.1.1.1.1.2.2.3.2" xref="S0.E2.3.m1.1.1.1.1.2.2.3.2.cmml">i</mi><mo id="S0.E2.3.m1.1.1.1.1.2.2.3.1" xref="S0.E2.3.m1.1.1.1.1.2.2.3.1.cmml">⁢</mo><mi id="S0.E2.3.m1.1.1.1.1.2.2.3.3" xref="S0.E2.3.m1.1.1.1.1.2.2.3.3.cmml">j</mi></mrow></msub></mrow><mo id="S0.E2.3.m1.1.1.1.1.1" xref="S0.E2.3.m1.1.1.1.1.1.cmml">≥</mo><mn id="S0.E2.3.m1.1.1.1.1.3" xref="S0.E2.3.m1.1.1.1.1.3.cmml">0</mn></mrow><mo mathvariant="italic" separator="true" id="S0.E2.3.m1.2.2.2.3" xref="S0.E2.3.m1.2.2.3a.cmml">   </mo><mrow id="S0.E2.3.m1.2.2.2.2" xref="S0.E2.3.m1.2.2.2.2.cmml"><mrow id="S0.E2.3.m1.2.2.2.2.2" xref="S0.E2.3.m1.2.2.2.2.2.cmml"><mo rspace="7.5pt" id="S0.E2.3.m1.2.2.2.2.2.1" xref="S0.E2.3.m1.2.2.2.2.2.1.cmml">∀</mo><mi id="S0.E2.3.m1.2.2.2.2.2.2" xref="S0.E2.3.m1.2.2.2.2.2.2.cmml">i</mi></mrow><mo id="S0.E2.3.m1.2.2.2.2.1" xref="S0.E2.3.m1.2.2.2.2.1.cmml">∈</mo><mrow id="S0.E2.3.m1.2.2.2.2.3" xref="S0.E2.3.m1.2.2.2.2.3.cmml"><mi id="S0.E2.3.m1.2.2.2.2.3.2" xref="S0.E2.3.m1.2.2.2.2.3.2.cmml">I</mi><mo id="S0.E2.3.m1.2.2.2.2.3.1" xref="S0.E2.3.m1.2.2.2.2.3.1.cmml">⁢</mo><mtext id="S0.E2.3.m1.2.2.2.2.3.3" xref="S0.E2.3.m1.2.2.2.2.3.3a.cmml">.</mtext></mrow></mrow></mrow></math>, <math><mrow id="p4.1.m1.2.3" xref="p4.1.m1.2.3.cmml"><mrow id="p4.1.m1.2.3.2" xref="p4.1.m1.2.3.2.cmml"><mrow id="p4.1.m1.2.3.2.2" xref="p4.1.m1.2.3.2.2.cmml"><msub id="p4.1.m1.2.3.2.2.2" xref="p4.1.m1.2.3.2.2.2.cmml"><mi id="p4.1.m1.2.3.2.2.2.2" xref="p4.1.m1.2.3.2.2.2.2.cmml">𝐚</mi><mi id="p4.1.m1.2.3.2.2.2.3" xref="p4.1.m1.2.3.2.2.2.3.cmml">i</mi></msub><mo id="p4.1.m1.2.3.2.2.1" xref="p4.1.m1.2.3.2.2.1.cmml">∘</mo><msub id="p4.1.m1.2.3.2.2.3" xref="p4.1.m1.2.3.2.2.3.cmml"><mi id="p4.1.m1.2.3.2.2.3.2" xref="p4.1.m1.2.3.2.2.3.2.cmml">𝐚</mi><mi id="p4.1.m1.2.3.2.2.3.3" xref="p4.1.m1.2.3.2.2.3.3.cmml">j</mi></msub></mrow><mo id="p4.1.m1.2.3.2.1" xref="p4.1.m1.2.3.2.1.cmml">⁢</mo><mrow id="p4.1.m1.2.3.2.3.2" xref="p4.1.m1.2.3.2.cmml"><mo stretchy="false" id="p4.1.m1.2.3.2.3.2.1" xref="p4.1.m1.2.3.2.cmml">(</mo><mi id="p4.1.m1.1.1" xref="p4.1.m1.1.1.cmml">α</mi><mo stretchy="false" id="p4.1.m1.2.3.2.3.2.2" xref="p4.1.m1.2.3.2.cmml">)</mo></mrow></mrow><mo id="p4.1.m1.2.3.1" xref="p4.1.m1.2.3.1.cmml">=</mo><mrow id="p4.1.m1.2.3.3" xref="p4.1.m1.2.3.3.cmml"><mrow id="p4.1.m1.2.3.3.2" xref="p4.1.m1.2.3.3.2.cmml"><msub id="p4.1.m1.2.3.3.2.2" xref="p4.1.m1.2.3.3.2.2.cmml"><mi id="p4.1.m1.2.3.3.2.2.2" xref="p4.1.m1.2.3.3.2.2.2.cmml">𝐚</mi><mi id="p4.1.m1.2.3.3.2.2.3" xref="p4.1.m1.2.3.3.2.2.3.cmml">j</mi></msub><mo id="p4.1.m1.2.3.3.2.1" xref="p4.1.m1.2.3.3.2.1.cmml">∘</mo><msub id="p4.1.m1.2.3.3.2.3" xref="p4.1.m1.2.3.3.2.3.cmml"><mi id="p4.1.m1.2.3.3.2.3.2" xref="p4.1.m1.2.3.3.2.3.2.cmml">𝐚</mi><mi id="p4.1.m1.2.3.3.2.3.3" xref="p4.1.m1.2.3.3.2.3.3.cmml">i</mi></msub></mrow><mo id="p4.1.m1.2.3.3.1" xref="p4.1.m1.2.3.3.1.cmml">⁢</mo><mrow id="p4.1.m1.2.3.3.3.2" xref="p4.1.m1.2.3.3.cmml"><mo stretchy="false" id="p4.1.m1.2.3.3.3.2.1" xref="p4.1.m1.2.3.3.cmml">(</mo><mi id="p4.1.m1.2.2" xref="p4.1.m1.2.2.cmml">α</mi><mo stretchy="false" id="p4.1.m1.2.3.3.3.2.2" xref="p4.1.m1.2.3.3.cmml">)</mo></mrow></mrow></mrow></math>, <math><mrow id="p6.4.m4.1.2" xref="p6.4.m4.1.2.cmml"><mrow id="p6.4.m4.1.2.2" xref="p6.4.m4.1.2.2.cmml"><msub id="p6.4.m4.1.2.2.2" xref="p6.4.m4.1.2.2.2.cmml"><mi id="p6.4.m4.1.2.2.2.2" xref="p6.4.m4.1.2.2.2.2.cmml">𝐚</mi><mi id="p6.4.m4.1.2.2.2.3" xref="p6.4.m4.1.2.2.2.3.cmml">i</mi></msub><mo id="p6.4.m4.1.2.2.1" xref="p6.4.m4.1.2.2.1.cmml">⁢</mo><mrow id="p6.4.m4.1.2.2.3.2" xref="p6.4.m4.1.2.2.cmml"><mo stretchy="false" id="p6.4.m4.1.2.2.3.2.1" xref="p6.4.m4.1.2.2.cmml">(</mo><mi id="p6.4.m4.1.1" xref="p6.4.m4.1.1.cmml">β</mi><mo stretchy="false" id="p6.4.m4.1.2.2.3.2.2" xref="p6.4.m4.1.2.2.cmml">)</mo></mrow></mrow><mo id="p6.4.m4.1.2.1" xref="p6.4.m4.1.2.1.cmml">=</mo><mi id="p6.4.m4.1.2.3" xref="p6.4.m4.1.2.3.cmml">α</mi></mrow></math>, <math><mrow id="p6.13.m13.1.1" xref="p6.13.m13.1.1.cmml"><msubsup id="p6.13.m13.1.1.2" xref="p6.13.m13.1.1.2.cmml"><mi id="p6.13.m13.1.1.2.2.2" xref="p6.13.m13.1.1.2.2.2.cmml">𝐚</mi><mi id="p6.13.m13.1.1.2.2.3" xref="p6.13.m13.1.1.2.2.3.cmml">i</mi><mrow id="p6.13.m13.1.1.2.3" xref="p6.13.m13.1.1.2.3.cmml"><mo id="p6.13.m13.1.1.2.3.1" xref="p6.13.m13.1.1.2.3.1.cmml">-</mo><mn id="p6.13.m13.1.1.2.3.2" xref="p6.13.m13.1.1.2.3.2.cmml">1</mn></mrow></msubsup><mo id="p6.13.m13.1.1.1" xref="p6.13.m13.1.1.1.cmml">=</mo><msubsup id="p6.13.m13.1.1.3" xref="p6.13.m13.1.1.3.cmml"><mi id="p6.13.m13.1.1.3.2.2" xref="p6.13.m13.1.1.3.2.2.cmml">𝐚</mi><mi id="p6.13.m13.1.1.3.2.3" xref="p6.13.m13.1.1.3.2.3.cmml">i</mi><mrow id="p6.13.m13.1.1.3.3" xref="p6.13.m13.1.1.3.3.cmml"><mrow id="p6.13.m13.1.1.3.3.2" xref="p6.13.m13.1.1.3.3.2.cmml"><mo id="p6.13.m13.1.1.3.3.2.1" xref="p6.13.m13.1.1.3.3.2.1.cmml">det</mo><mo id="p6.13.m13.1.1.3.3.2a" xref="p6.13.m13.1.1.3.3.2.cmml">⁡</mo><mi mathvariant="normal" id="p6.13.m13.1.1.3.3.2.2" xref="p6.13.m13.1.1.3.3.2.2.cmml">Δ</mi></mrow><mo id="p6.13.m13.1.1.3.3.1" xref="p6.13.m13.1.1.3.3.1.cmml">-</mo><mn id="p6.13.m13.1.1.3.3.3" xref="p6.13.m13.1.1.3.3.3.cmml">1</mn></mrow></msubsup></mrow></math>, <math><mrow id="p8.3.m3.4.5" xref="p8.3.m3.4.5.cmml"><mover accent="true" id="p8.3.m3.4.5.2" xref="p8.3.m3.4.5.2.cmml"><mn id="p8.3.m3.4.5.2.2" xref="p8.3.m3.4.5.2.2.cmml">0</mn><mo stretchy="false" id="p8.3.m3.4.5.2.1" xref="p8.3.m3.4.5.2.1.cmml">→</mo></mover><mo id="p8.3.m3.4.5.1" xref="p8.3.m3.4.5.1.cmml">≡</mo><mrow id="p8.3.m3.4.5.3.2" xref="p8.3.m3.4.5.3.1.cmml"><mo stretchy="false" id="p8.3.m3.4.5.3.2.1" xref="p8.3.m3.4.5.3.1.cmml">(</mo><mn id="p8.3.m3.1.1" xref="p8.3.m3.1.1.cmml">0</mn><mo id="p8.3.m3.4.5.3.2.2" xref="p8.3.m3.4.5.3.1.cmml">,</mo><mn id="p8.3.m3.2.2" xref="p8.3.m3.2.2.cmml">0</mn><mo id="p8.3.m3.4.5.3.2.3" xref="p8.3.m3.4.5.3.1.cmml">,</mo><mi mathvariant="normal" id="p8.3.m3.3.3" xref="p8.3.m3.3.3.cmml">…</mi><mo id="p8.3.m3.4.5.3.2.4" xref="p8.3.m3.4.5.3.1.cmml">,</mo><mn id="p8.3.m3.4.4" xref="p8.3.m3.4.4.cmml">0</mn><mo stretchy="false" id="p8.3.m3.4.5.3.2.5" xref="p8.3.m3.4.5.3.1.cmml">)</mo></mrow></mrow></math>, <math><mrow id="S0.E3.m1.4.4" xref="S0.E3.m1.4.4.cmml"><mi id="S0.E3.m1.4.4.4" xref="S0.E3.m1.4.4.4.cmml">γ</mi><mo id="S0.E3.m1.4.4.5" xref="S0.E3.m1.4.4.5.cmml">≡</mo><msub id="S0.E3.m1.3.3.1" xref="S0.E3.m1.3.3.1.cmml"><mrow id="S0.E3.m1.3.3.1.1.1" xref="S0.E3.m1.3.3.1.1.1.1.cmml"><mo id="S0.E3.m1.3.3.1.1.1.2" xref="S0.E3.m1.3.3.1.1.1.1.cmml">(</mo><msub id="S0.E3.m1.3.3.1.1.1.1" xref="S0.E3.m1.3.3.1.1.1.1.cmml"><mi id="S0.E3.m1.3.3.1.1.1.1.2" xref="S0.E3.m1.3.3.1.1.1.1.2.cmml">γ</mi><mi id="S0.E3.m1.3.3.1.1.1.1.3" xref="S0.E3.m1.3.3.1.1.1.1.3.cmml">j</mi></msub><mo id="S0.E3.m1.3.3.1.1.1.3" xref="S0.E3.m1.3.3.1.1.1.1.cmml">)</mo></mrow><mrow id="S0.E3.m1.3.3.1.3" xref="S0.E3.m1.3.3.1.3.cmml"><mi id="S0.E3.m1.3.3.1.3.2" xref="S0.E3.m1.3.3.1.3.2.cmml">j</mi><mo id="S0.E3.m1.3.3.1.3.1" xref="S0.E3.m1.3.3.1.3.1.cmml">∈</mo><mi id="S0.E3.m1.3.3.1.3.3" xref="S0.E3.m1.3.3.1.3.3.cmml">I</mi></mrow></msub><mo id="S0.E3.m1.4.4.6" xref="S0.E3.m1.4.4.6.cmml">≡</mo><mrow id="S0.E3.m1.4.4.7" xref="S0.E3.m1.4.4.7.cmml"><mi id="S0.E3.m1.4.4.7.2" xref="S0.E3.m1.4.4.7.2.cmml">𝐚</mi><mo id="S0.E3.m1.4.4.7.1" xref="S0.E3.m1.4.4.7.1.cmml">⁢</mo><mrow id="S0.E3.m1.4.4.7.3.2" xref="S0.E3.m1.2.2.cmml"><mo stretchy="false" id="S0.E3.m1.4.4.7.3.2.1" xref="S0.E3.m1.2.2.cmml">(</mo><mover accent="true" id="S0.E3.m1.2.2" xref="S0.E3.m1.2.2.cmml"><mn id="S0.E3.m1.2.2.2" xref="S0.E3.m1.2.2.2.cmml">0</mn><mo stretchy="false" id="S0.E3.m1.2.2.1" xref="S0.E3.m1.2.2.1.cmml">→</mo></mover><mo stretchy="false" id="S0.E3.m1.4.4.7.3.2.2" xref="S0.E3.m1.2.2.cmml">)</mo></mrow></mrow><mo id="S0.E3.m1.4.4.8" xref="S0.E3.m1.4.4.8.cmml">=</mo><msub id="S0.E3.m1.4.4.2" xref="S0.E3.m1.4.4.2.cmml"><mrow id="S0.E3.m1.4.4.2.1.1" xref="S0.E3.m1.4.4.2.1.1.1.cmml"><mo id="S0.E3.m1.4.4.2.1.1.2" xref="S0.E3.m1.4.4.2.1.1.1.cmml">(</mo><mrow id="S0.E3.m1.4.4.2.1.1.1" xref="S0.E3.m1.4.4.2.1.1.1.cmml"><msub id="S0.E3.m1.4.4.2.1.1.1.2" xref="S0.E3.m1.4.4.2.1.1.1.2.cmml"><mi id="S0.E3.m1.4.4.2.1.1.1.2.2" xref="S0.E3.m1.4.4.2.1.1.1.2.2.cmml">a</mi><mi id="S0.E3.m1.4.4.2.1.1.1.2.3" xref="S0.E3.m1.4.4.2.1.1.1.2.3.cmml">j</mi></msub><mo id="S0.E3.m1.4.4.2.1.1.1.1" xref="S0.E3.m1.4.4.2.1.1.1.1.cmml">-</mo><mrow id="S0.E3.m1.4.4.2.1.1.1.3" xref="S0.E3.m1.4.4.2.1.1.1.3.cmml"><mstyle displaystyle="false" id="S0.E3.m1.1.1.1" xref="S0.E3.m1.1.1.1.cmml"><msub id="S0.E3.m1.1.1.1a" xref="S0.E3.m1.1.1.1.cmml"><mo largeop="true" symmetric="true" id="S0.E3.m1.1.1.1.3" xref="S0.E3.m1.1.1.1.3.cmml">∑</mo><mi id="S0.E3.m1.1.1.1.4" xref="S0.E3.m1.1.1.1.4.cmml">k</mi></msub></mstyle><mo id="S0.E3.m1.4.4.2.1.1.1.3.1" xref="S0.E3.m1.4.4.2.1.1.1.3.1.cmml">⁢</mo><msub id="S0.E3.m1.4.4.2.1.1.1.3.2" xref="S0.E3.m1.4.4.2.1.1.1.3.2.cmml"><mi id="S0.E3.m1.4.4.2.1.1.1.3.2.2" xref="S0.E3.m1.4.4.2.1.1.1.3.2.2.cmml">n</mi><mi id="S0.E3.m1.4.4.2.1.1.1.3.2.3" xref="S0.E3.m1.4.4.2.1.1.1.3.2.3.cmml">k</mi></msub><mo id="S0.E3.m1.4.4.2.1.1.1.3.1a" xref="S0.E3.m1.4.4.2.1.1.1.3.1.cmml">⁢</mo><msub id="S0.E3.m1.4.4.2.1.1.1.3.3" xref="S0.E3.m1.4.4.2.1.1.1.3.3.cmml"><mi mathvariant="normal" id="S0.E3.m1.4.4.2.1.1.1.3.3.2" xref="S0.E3.m1.4.4.2.1.1.1.3.3.2.cmml">Δ</mi><mrow id="S0.E3.m1.4.4.2.1.1.1.3.3.3" xref="S0.E3.m1.4.4.2.1.1.1.3.3.3.cmml"><mi id="S0.E3.m1.4.4.2.1.1.1.3.3.3.2" xref="S0.E3.m1.4.4.2.1.1.1.3.3.3.2.cmml">k</mi><mo id="S0.E3.m1.4.4.2.1.1.1.3.3.3.1" xref="S0.E3.m1.4.4.2.1.1.1.3.3.3.1.cmml">⁢</mo><mi id="S0.E3.m1.4.4.2.1.1.1.3.3.3.3" xref="S0.E3.m1.4.4.2.1.1.1.3.3.3.3.cmml">j</mi></mrow></msub></mrow></mrow><mo id="S0.E3.m1.4.4.2.1.1.3" xref="S0.E3.m1.4.4.2.1.1.1.cmml">)</mo></mrow><mrow id="S0.E3.m1.4.4.2.3" xref="S0.E3.m1.4.4.2.3.cmml"><mi id="S0.E3.m1.4.4.2.3.2" xref="S0.E3.m1.4.4.2.3.2.cmml">j</mi><mo id="S0.E3.m1.4.4.2.3.1" xref="S0.E3.m1.4.4.2.3.1.cmml">∈</mo><mi id="S0.E3.m1.4.4.2.3.3" xref="S0.E3.m1.4.4.2.3.3.cmml">I</mi></mrow></msub><mo id="S0.E3.m1.4.4.9" xref="S0.E3.m1.4.4.9.cmml">∈</mo><mi mathvariant="normal" id="S0.E3.m1.4.4.10" xref="S0.E3.m1.4.4.10.cmml">Ω</mi></mrow></math>, <math><mrow id="p9.7.m6.1.1" xref="p9.7.m6.1.1.cmml"><msub id="p9.7.m6.1.1.2" xref="p9.7.m6.1.1.2.cmml"><mi id="p9.7.m6.1.1.2.2" xref="p9.7.m6.1.1.2.2.cmml">a</mi><mi id="p9.7.m6.1.1.2.3" xref="p9.7.m6.1.1.2.3.cmml">j</mi></msub><mo id="p9.7.m6.1.1.1" xref="p9.7.m6.1.1.1.cmml">=</mo><msub id="p9.7.m6.1.1.3" xref="p9.7.m6.1.1.3.cmml"><mi id="p9.7.m6.1.1.3.2" xref="p9.7.m6.1.1.3.2.cmml">δ</mi><mrow id="p9.7.m6.1.1.3.3" xref="p9.7.m6.1.1.3.3.cmml"><mi id="p9.7.m6.1.1.3.3.2" xref="p9.7.m6.1.1.3.3.2.cmml">i</mi><mo id="p9.7.m6.1.1.3.3.1" xref="p9.7.m6.1.1.3.3.1.cmml">⁢</mo><mi id="p9.7.m6.1.1.3.3.3" xref="p9.7.m6.1.1.3.3.3.cmml">j</mi></mrow></msub></mrow></math>

Correct Categorie: cond-mat

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/1401.3612

Formulas:

1-

∥ x - y ∥ \geq (1 - ε) (∥ x ∥ + ∥ y ∥) for all x \in E .

2-

B (x, r)

3-

x_{1}, \dots, x_{n} \in S_{X}

4-

∥ x_{i} - y ∥ \geq 2 - ε for all i \in {1, \dots, n} .

5-

μ_{2} (X) = 2

6-

μ_{2} (X) = inf_{\begin{matrix} x_{1}, \dots, x_{n} \in S_{X} \\ n \in ℕ \end{matrix}} sup_{x \in S_{X}} \frac{1}{n} \sum_{i = 1}^{n} ∥ x_{i} - x ∥ .

7-

{sup}_{x \in S_{X}} \sum_{i = 1}^{n} ∥ x_{i} - x ∥ = 2 n

8-

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

9-

μ_{2} (X) = 2

10-

μ_{2} (X) = 2

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/astro-ph/9903436

Formulas:

1-

ρ_{b} (r) = \frac{M_{b}}{2 π r_{b}^{2}} \frac{1}{r {(1 + r / r_{b})}^{3}},

2-

ρ_{h} (r) = \frac{M_{h}}{2 π^{3 / 2}} \frac{α}{r_{t} r_{h}^{2}} \frac{e x p (- r^{2} / r_{t}^{2})}{(1 + r^{2} / r_{h}^{2})}

3-

α = 1 / {1 - π^{1 / 2} q e x p (q^{2}) [1 - e r f (q)]}

4-

e r f (q)

5-

q = r_{h} / r_{t}

6-

ρ_{d} (R, z) = \frac{M_{d}}{4 π R_{d}^{2} z_{d}} e x p (- R / R_{d}) s e c h^{2} (z / z_{d})

7-

220 km s^{- 1}

8-

R_{s t r}

9-

P = ρ_{i c m} v^{2}

10-

ρ_{i c m}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/quant-ph/0612013

Formulas:

1-

{| ψ_{i} ⟩}

2-

ℋ_{Q} = \otimes_{j = 1}^{n} ℋ_{j}

3-

𝒮 = {| ψ_{i} ⟩}

4-

| ψ_{i} ⟩ \in 𝒮

5-

𝒮 = {| ψ_{i} ⟩}

6-

| ψ_{x} ⟩ \in 𝒮

7-

\forall i \neq x ⟨ ψ_{i} | ϕ ⟩ = 0

8-

⟨ ψ_{x} | ϕ ⟩ \neq 0

9-

{| ⟨ ψ_{x} | ϕ ⟩ |}^{2}

10-

M^{†} M = A^{†} A \otimes B^{†} B \otimes \dots

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/0412126

Formulas:

1-

τ = \frac{ℏ}{m α^{2} c^{2}}

2-

\frac{1}{v^{2}} \frac{\partial^{2} T}{\partial t^{2}} + \frac{m_{e} γ}{ℏ} \frac{\partial T}{\partial t} + \frac{2 V m_{e} γ}{ℏ^{2}} T - \frac{\partial^{2} T}{\partial x^{2}} = F (x, t) .

3-

γ = {(1 - α^{2})}^{- \frac{1}{2}}

4-

F (x, t)

5-

T (x, t) = e^{- \frac{t}{2 τ}} u (x, t),

6-

\frac{1}{v^{2}} \frac{\partial^{2} u}{\partial t^{2}} - \frac{\partial^{2} u}{\partial x^{2}} + q u (x, t) = e^{\frac{t}{2 τ}} F (x, t)

7-

q = \frac{2 V m}{ℏ^{2}} - {(\frac{m v}{2 ℏ})}^{2}

8-

m = m_{e} γ .

9-

F (x, t) \to 0

10-

\frac{1}{v^{2}} \frac{\partial^{2} u}{\partial t^{2}} - \frac{\partial^{2} u}{\partial x^{2}} - {(\frac{m v}{2 ℏ})}^{2} u (x, t) = 0 .

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/gr-qc/0701076

Formulas:

1-

1.4 M_{⊙}, 1.4 M_{⊙}

2-

Φ_{0} (f)

3-

Φ (f) = {\begin{matrix} Φ_{0} (f) + (1 - f / f_{0}) Δ Φ & f_{0} - f ≫ Δ f_{res} \\ Φ_{0} (f) & f - f_{0} ≫ Δ f_{res} . \end{matrix}

4-

Δ f_{res} \sim 0.1 Hz {(\frac{ℳ}{1.2 M_{⊙}})}^{5 / 6} {(\frac{f_{0}}{10 Hz})}^{11 / 6},

5-

ω \sim \sqrt{M / R^{3}}

6-

10 Hz ≲ ω_{m} / (2 π) ≲ 100 Hz

7-

(2 M_{⊙}, 1 M_{⊙})

8-

(1.4 M_{⊙}, 1.4 M_{⊙})

9-

(10 M_{⊙}, 1.4 M_{⊙})

10-

(15 M_{⊙}, 5 M_{⊙})

Formulas (html):

Correct Categorie: gr-qc

Guessed Categorie: gr-qc

Result: correct

Paper: https://arxiv.org/abs/math/0502473

Formulas:

1-

\int_{ℝ^{N}} {∥ x ∥}^{k} μ (d x) < \infty

2-

x_{1}, \dots, x_{k} \in supp μ

3-

λ_{1}, \dots, λ_{k} > 0

4-

\int_{ℝ^{N}} P (x) μ (d x) = \sum_{i = 1}^{k} λ_{i} P (x_{i})

5-

μ (O) = 0

6-

\bar{conv} (S)

7-

y \in \partial C := \bar{C} ∖ int (C)

8-

\bar{cone} (A)

9-

x - ϵ (y - x) \in C

10-

ϕ : Ω \to ℝ^{N}

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/0705.4100

Formulas:

1-

Ω_{Λ 0} = 0.7

2-

α = 00^{h} 57^{m} 48^{s} .883

3-

δ = + 30^{\circ} 21^{'} 08^{''} .81

4-

α = 00^{h} 57^{m} 48^{s} .68

5-

δ = + 30^{\circ} 21^{'} 11^{''} .3

6-

α = 00^{h} 57^{m} 48^{s} .1

7-

α = 00^{h} 57^{m} 47^{s} .1

8-

α = 00^{h} 57^{m} 46^{s} .5

9-

α = 00^{h} 57^{m} 47^{s} .1

10-

α = 00^{h} 57^{m} 38^{s} .720

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/0711.4589

Formulas:

1-

M \leq 5 \times 10^{9} M_{⊙}

2-

Δ σ_{z}^{2} = 2 Δ E / M_{s}

3-

Δ E ≃ 4 π G^{2} M_{s}^{2} Σ / v_{s}^{2}

4-

\partial_{z} (ρ_{d} σ_{z}^{2}) + ρ_{d} \partial_{z} Φ = 0

5-

\partial_{z}^{2} Φ = 4 π G ρ_{d}

6-

ρ_{d} \propto \exp (- z / z_{d})

7-

σ_{z}^{2} = 2 π G Σ z_{d}

8-

Δ σ_{z}^{2} = 2 π G Σ Δ z_{d}

9-

M_{s} = {[M_{d} v_{s}^{2} Δ z_{d} / (4 G)]}^{1 / 2}

10-

5.2 \times 10^{9} M_{⊙}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/2010.10925

Formulas:

1-

(M^{n}, ω)

2-

Ric (ω) \geq ω,

3-

Vol (M, ω) := \int_{M} ω^{n} \leq Vol (ℂ ℙ^{n}, ω_{ℂ ℙ^{n}}) .

4-

Ric (ω_{ℂ ℙ^{n}}) = ω_{ℂ ℙ^{n}}

5-

(ℂ ℙ^{n}, ω_{ℂ ℙ^{n}})

6-

δ = δ (ε, n) > 0

7-

(M^{n}, ω)

8-

Vol (M, ω) > (1 - δ) Vol (ℂ ℙ^{n}, ω_{ℂ ℙ^{n}}),

9-

d_{G H} ((M, ω), (ℂ ℙ^{n}, ω_{ℂ ℙ^{n}})) < ε,

10-

(M^{n}, ω)

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/2009.00889

Formulas:

1-

H_{MQ} = - \frac{D}{4} [{(I^{+})}^{2} + {(I^{-})}^{2}],

2-

I^{\pm} = \sum_{j = 1}^{N} I_{j}^{\pm},

3-

i \frac{d ρ (τ)}{d τ} = [H_{MQ}, ρ (τ)]

4-

ρ (0) = ρ_{eq} = \frac{1}{Z} e^{\frac{ℏ ω_{0}}{k} α_{z} I_{z} + \frac{ℏ}{k} β_{d} H_{dz}},

5-

Z = Tr {e^{\frac{ℏ ω_{0}}{k} α_{z} I_{z} + \frac{ℏ}{k} β_{d} H_{dz}}}

6-

(\frac{ℏ ω_{0}}{k} α_{z} ≫ 1)

7-

(\frac{ℏ D}{k} β_{d} ≪ 1)

8-

ω_{0} = 2 π \cdot 500 \cdot 10^{6}

9-

D = 2 π \cdot 10^{4}

10-

ρ_{i} = \frac{1}{Z_{i}} e^{\frac{ℏ β_{d} H_{dz}}{k}} \approx \frac{1}{Z_{i}} (1 + \frac{ℏ β_{d}}{k} H_{dz}),

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/0912.4898

Formulas:

1-

m_{i} \to m_{i}^{'} = m_{i} - Δ m,

2-

m_{j} \to m_{j}^{'} = m_{j} + Δ m .

3-

m_{i} + m_{j} = m_{i}^{'} + m_{j}^{'},

4-

M = \sum_{i} m_{i}

5-

P (m_{k}) = N_{k} / N

6-

Ω = \frac{N!}{N_{1}! N_{2}! N_{3}! \dots} .

7-

S = N \ln N - \sum_{k} N_{k} \ln N_{k} = - \sum_{k} N_{k} \ln (\frac{N_{k}}{N}) .

8-

N = \sum_{k} N_{k}

9-

M = \sum_{k} m_{k} N_{k}

10-

\tilde{S} = S + α \sum_{k} N_{k} - β \sum_{k} m_{k} N_{k} .

Formulas (html):

Correct Categorie: q-fin

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/hep-ph/0105185

Formulas:

1-

k (i_{1}) = 2 \sin^{2} φ

2-

k (i_{2}) = 2 \cos^{2} φ

3-

k (η^{'})

4-

k (f_{2}^{'})

5-

k (f_{2})

6-

k (f_{0})

7-

f_{0}^{b a r e}

8-

| φ_{S}^{b a r e} |

9-

η_{1} = (u \bar{u} + d \bar{d} + s \bar{s}) / \sqrt{3}, η_{8} = (u \bar{u} + d \bar{d} - 2 s \bar{s}) / \sqrt{6}

10-

η = η_{8} \cdot \cos θ_{P} - η_{1} \cdot \sin θ_{P},

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0311303

Formulas:

1-

S_{ν} \propto ν^{+ α}

2-

\sim 3.3 \times 10^{6} M_{☉}

3-

α_{1.4}^{5} > - 0.35

4-

μ Jy {beam}^{- 1}

5-

μ Jy {beam}^{- 1}

6-

α_{1.7}^{8.4} = 0.16 \pm 0.08

7-

α_{8.4}^{22} = - 0.11 \pm 0.13

8-

\bar{α} = 0.084 \pm 0.029

9-

\dot{m} = 10^{- 2.5}

10-

P_{ν} \propto ν^{1 / 3}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1612.08637

Formulas:

1-

C = C_{n} (U, V)

2-

\frac{1}{| V |} \int_{V} f (x) 𝑑 x \leq C \frac{1}{| U |} \int_{U} f (x) 𝑑 x,

3-

U, V \subset ℝ^{n}

4-

f : ℤ_{q} \to ℝ_{+}

5-

\sum_{0 \leq k \leq 2 n} f (k) \leq C \sum_{0 \leq k \leq n} f (k),

6-

\int_{| x | \leq 2 R} f (x) 𝑑 x \leq C \int_{| x | \leq R} f (x) 𝑑 x, R > 0,

7-

f : ℝ^{n} \to ℝ_{+}

8-

f \in C (ℝ^{n})

9-

{c_{a} : a \in X}

10-

\sum_{a, b \in X} c_{a} \bar{c_{b}} f (a - b) \geq 0 .

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/1312.3551

Formulas:

1-

(f, m_{f}) = (3, + 3)

2-

(1, + 1)

3-

(1, + 1) + (3, + 3)

4-

(f = 3, m_{f} = + 3)

5-

+ 651 (\pm 10) a_{0}

6-

| n (f_{Rb}, f_{Cs}) L (m_{f_{Rb}}, m_{f_{Cs}}) ⟩

7-

(f_{Rb}, f_{Cs})

8-

(f = 1, m_{f} = - 1)

9-

(3, - 3)

10-

(1, + 1)

Formulas (html):

Correct Categorie: physics

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0407307

Formulas:

1-

H_{0} = 75 {kms}^{- 1} {Mpc}^{- 1}

2-

\log L_{[OIII]}

3-

erg s^{- 1} {Hz}^{- 1}

4-

erg s^{- 1} {Hz}^{- 1}

5-

L_{5500 Å} > 10^{23}

6-

4 \times 4 {arcsec}^{2}

7-

\sim 1.5 \times 10^{- 29}

8-

erg s^{- 1} {Hz}^{- 1}

9-

erg s^{- 1} {Hz}^{- 1}

10-

{EW}_{[OIII]} \sim 100

Formulas (html):

<math><mrow id="S1.p7.1.m1.1.1" xref="S1.p7.1.m1.1.1.cmml"><msub id="S1.p7.1.m1.1.1.2" xref="S1.p7.1.m1.1.1.2.cmml"><mi mathvariant="normal" id="S1.p7.1.m1.1.1.2.2" xref="S1.p7.1.m1.1.1.2.2.cmml">H</mi><mn id="S1.p7.1.m1.1.1.2.3" xref="S1.p7.1.m1.1.1.2.3.cmml">0</mn></msub><mo id="S1.p7.1.m1.1.1.1" xref="S1.p7.1.m1.1.1.1.cmml">=</mo><mrow id="S1.p7.1.m1.1.1.3" xref="S1.p7.1.m1.1.1.3.cmml"><mpadded width="+1.7pt" id="S1.p7.1.m1.1.1.3.2" xref="S1.p7.1.m1.1.1.3.2.cmml"><mn id="S1.p7.1.m1.1.1.3.2a" xref="S1.p7.1.m1.1.1.3.2.cmml">75</mn></mpadded><mo id="S1.p7.1.m1.1.1.3.1" xref="S1.p7.1.m1.1.1.3.1.cmml">⁢</mo><msup id="S1.p7.1.m1.1.1.3.3" xref="S1.p7.1.m1.1.1.3.3.cmml"><mi id="S1.p7.1.m1.1.1.3.3.2" xref="S1.p7.1.m1.1.1.3.3.2.cmml">kms</mi><mrow id="S1.p7.1.m1.1.1.3.3.3" xref="S1.p7.1.m1.1.1.3.3.3.cmml"><mo id="S1.p7.1.m1.1.1.3.3.3.1" xref="S1.p7.1.m1.1.1.3.3.3.1.cmml">-</mo><mn id="S1.p7.1.m1.1.1.3.3.3.2" xref="S1.p7.1.m1.1.1.3.3.3.2.cmml">1</mn></mrow></msup><mo id="S1.p7.1.m1.1.1.3.1a" xref="S1.p7.1.m1.1.1.3.1.cmml">⁢</mo><msup id="S1.p7.1.m1.1.1.3.4" xref="S1.p7.1.m1.1.1.3.4.cmml"><mi id="S1.p7.1.m1.1.1.3.4.2" xref="S1.p7.1.m1.1.1.3.4.2.cmml">Mpc</mi><mrow id="S1.p7.1.m1.1.1.3.4.3" xref="S1.p7.1.m1.1.1.3.4.3.cmml"><mo id="S1.p7.1.m1.1.1.3.4.3.1" xref="S1.p7.1.m1.1.1.3.4.3.1.cmml">-</mo><mn id="S1.p7.1.m1.1.1.3.4.3.2" xref="S1.p7.1.m1.1.1.3.4.3.2.cmml">1</mn></mrow></msup></mrow></mrow></math>, <math><mrow id="S2.T1.3.3.3.m1.1.2" xref="S2.T1.3.3.3.m1.1.2.cmml"><mi id="S2.T1.3.3.3.m1.1.2.1" xref="S2.T1.3.3.3.m1.1.2.1.cmml">log</mi><mo id="S2.T1.3.3.3.m1.1.2a" xref="S2.T1.3.3.3.m1.1.2.cmml">⁡</mo><msub id="S2.T1.3.3.3.m1.1.2.2" xref="S2.T1.3.3.3.m1.1.2.2.cmml"><mi mathvariant="normal" id="S2.T1.3.3.3.m1.1.2.2.2" xref="S2.T1.3.3.3.m1.1.2.2.2.cmml">L</mi><mrow id="S2.T1.3.3.3.m1.1.1.1.3" xref="S2.T1.3.3.3.m1.1.1.1.2.cmml"><mo stretchy="false" id="S2.T1.3.3.3.m1.1.1.1.3.1" xref="S2.T1.3.3.3.m1.1.1.1.2.1.cmml">[</mo><mi id="S2.T1.3.3.3.m1.1.1.1.1" xref="S2.T1.3.3.3.m1.1.1.1.1.cmml">OIII</mi><mo stretchy="false" id="S2.T1.3.3.3.m1.1.1.1.3.2" xref="S2.T1.3.3.3.m1.1.1.1.2.1.cmml">]</mo></mrow></msub></mrow></math>, <math><mrow id="S2.T1.5.5.2.m1.1.1" xref="S2.T1.5.5.2.m1.1.1.cmml"><mpadded width="+1.7pt" id="S2.T1.5.5.2.m1.1.1.2" xref="S2.T1.5.5.2.m1.1.1.2.cmml"><mi id="S2.T1.5.5.2.m1.1.1.2a" xref="S2.T1.5.5.2.m1.1.1.2.cmml">erg</mi></mpadded><mo id="S2.T1.5.5.2.m1.1.1.1" xref="S2.T1.5.5.2.m1.1.1.1.cmml">⁢</mo><mpadded width="+1.7pt" id="S2.T1.5.5.2.m1.1.1.3" xref="S2.T1.5.5.2.m1.1.1.3.cmml"><msup id="S2.T1.5.5.2.m1.1.1.3a" xref="S2.T1.5.5.2.m1.1.1.3.cmml"><mi mathvariant="normal" id="S2.T1.5.5.2.m1.1.1.3.2" xref="S2.T1.5.5.2.m1.1.1.3.2.cmml">s</mi><mrow id="S2.T1.5.5.2.m1.1.1.3.3" xref="S2.T1.5.5.2.m1.1.1.3.3.cmml"><mo id="S2.T1.5.5.2.m1.1.1.3.3.1" xref="S2.T1.5.5.2.m1.1.1.3.3.1.cmml">-</mo><mn id="S2.T1.5.5.2.m1.1.1.3.3.2" xref="S2.T1.5.5.2.m1.1.1.3.3.2.cmml">1</mn></mrow></msup></mpadded><mo id="S2.T1.5.5.2.m1.1.1.1a" xref="S2.T1.5.5.2.m1.1.1.1.cmml">⁢</mo><msup id="S2.T1.5.5.2.m1.1.1.4" xref="S2.T1.5.5.2.m1.1.1.4.cmml"><mi id="S2.T1.5.5.2.m1.1.1.4.2" xref="S2.T1.5.5.2.m1.1.1.4.2.cmml">Hz</mi><mrow id="S2.T1.5.5.2.m1.1.1.4.3" xref="S2.T1.5.5.2.m1.1.1.4.3.cmml"><mo id="S2.T1.5.5.2.m1.1.1.4.3.1" xref="S2.T1.5.5.2.m1.1.1.4.3.1.cmml">-</mo><mn id="S2.T1.5.5.2.m1.1.1.4.3.2" xref="S2.T1.5.5.2.m1.1.1.4.3.2.cmml">1</mn></mrow></msup></mrow></math>, <math><mrow id="S2.T1.6.6.3.m1.1.1" xref="S2.T1.6.6.3.m1.1.1.cmml"><mpadded width="+1.7pt" id="S2.T1.6.6.3.m1.1.1.2" xref="S2.T1.6.6.3.m1.1.1.2.cmml"><mi id="S2.T1.6.6.3.m1.1.1.2a" xref="S2.T1.6.6.3.m1.1.1.2.cmml">erg</mi></mpadded><mo id="S2.T1.6.6.3.m1.1.1.1" xref="S2.T1.6.6.3.m1.1.1.1.cmml">⁢</mo><mpadded width="+1.7pt" id="S2.T1.6.6.3.m1.1.1.3" xref="S2.T1.6.6.3.m1.1.1.3.cmml"><msup id="S2.T1.6.6.3.m1.1.1.3a" xref="S2.T1.6.6.3.m1.1.1.3.cmml"><mi mathvariant="normal" id="S2.T1.6.6.3.m1.1.1.3.2" xref="S2.T1.6.6.3.m1.1.1.3.2.cmml">s</mi><mrow id="S2.T1.6.6.3.m1.1.1.3.3" xref="S2.T1.6.6.3.m1.1.1.3.3.cmml"><mo id="S2.T1.6.6.3.m1.1.1.3.3.1" xref="S2.T1.6.6.3.m1.1.1.3.3.1.cmml">-</mo><mn id="S2.T1.6.6.3.m1.1.1.3.3.2" xref="S2.T1.6.6.3.m1.1.1.3.3.2.cmml">1</mn></mrow></msup></mpadded><mo id="S2.T1.6.6.3.m1.1.1.1a" xref="S2.T1.6.6.3.m1.1.1.1.cmml">⁢</mo><msup id="S2.T1.6.6.3.m1.1.1.4" xref="S2.T1.6.6.3.m1.1.1.4.cmml"><mi id="S2.T1.6.6.3.m1.1.1.4.2" xref="S2.T1.6.6.3.m1.1.1.4.2.cmml">Hz</mi><mrow id="S2.T1.6.6.3.m1.1.1.4.3" xref="S2.T1.6.6.3.m1.1.1.4.3.cmml"><mo id="S2.T1.6.6.3.m1.1.1.4.3.1" xref="S2.T1.6.6.3.m1.1.1.4.3.1.cmml">-</mo><mn id="S2.T1.6.6.3.m1.1.1.4.3.2" xref="S2.T1.6.6.3.m1.1.1.4.3.2.cmml">1</mn></mrow></msup></mrow></math>, <math><mrow id="S2.p3.1.m1.1.1" xref="S2.p3.1.m1.1.1.cmml"><msub id="S2.p3.1.m1.1.1.2" xref="S2.p3.1.m1.1.1.2.cmml"><mi mathvariant="normal" id="S2.p3.1.m1.1.1.2.2" xref="S2.p3.1.m1.1.1.2.2.cmml">L</mi><mrow id="S2.p3.1.m1.1.1.2.3" xref="S2.p3.1.m1.1.1.2.3.cmml"><mn id="S2.p3.1.m1.1.1.2.3.2" xref="S2.p3.1.m1.1.1.2.3.2.cmml">5500</mn><mo id="S2.p3.1.m1.1.1.2.3.1" xref="S2.p3.1.m1.1.1.2.3.1.cmml">⁢</mo><mi mathvariant="normal" id="S2.p3.1.m1.1.1.2.3.3" xref="S2.p3.1.m1.1.1.2.3.3.cmml">Å</mi></mrow></msub><mo id="S2.p3.1.m1.1.1.1" xref="S2.p3.1.m1.1.1.1.cmml">></mo><msup id="S2.p3.1.m1.1.1.3" xref="S2.p3.1.m1.1.1.3.cmml"><mn id="S2.p3.1.m1.1.1.3.2" xref="S2.p3.1.m1.1.1.3.2.cmml">10</mn><mn id="S2.p3.1.m1.1.1.3.3" xref="S2.p3.1.m1.1.1.3.3.cmml">23</mn></msup></mrow></math>, <math><mrow id="S3.F1.2.m1.1.1" xref="S3.F1.2.m1.1.1.cmml"><mrow id="S3.F1.2.m1.1.1.2" xref="S3.F1.2.m1.1.1.2.cmml"><mn mathvariant="normal" id="S3.F1.2.m1.1.1.2.2" xref="S3.F1.2.m1.1.1.2.2.cmml">4</mn><mo mathvariant="normal" id="S3.F1.2.m1.1.1.2.1" xref="S3.F1.2.m1.1.1.2.1.cmml">×</mo><mpadded width="+1.7pt" id="S3.F1.2.m1.1.1.2.3" xref="S3.F1.2.m1.1.1.2.3.cmml"><mn mathvariant="normal" id="S3.F1.2.m1.1.1.2.3b" xref="S3.F1.2.m1.1.1.2.3.cmml">4</mn></mpadded></mrow><mo mathvariant="bold-sans-serif" id="S3.F1.2.m1.1.1.1" xref="S3.F1.2.m1.1.1.1.cmml">⁢</mo><msup id="S3.F1.2.m1.1.1.3" xref="S3.F1.2.m1.1.1.3.cmml"><mi mathvariant="normal" id="S3.F1.2.m1.1.1.3.2" xref="S3.F1.2.m1.1.1.3.2.cmml">arcsec</mi><mn mathvariant="normal" id="S3.F1.2.m1.1.1.3.3" xref="S3.F1.2.m1.1.1.3.3.cmml">2</mn></msup></mrow></math>, <math><mrow id="S4.p6.6.m6.1.1" xref="S4.p6.6.m6.1.1.cmml"><mi id="S4.p6.6.m6.1.1.2" xref="S4.p6.6.m6.1.1.2.cmml"/><mo id="S4.p6.6.m6.1.1.1" xref="S4.p6.6.m6.1.1.1.cmml">∼</mo><mrow id="S4.p6.6.m6.1.1.3" xref="S4.p6.6.m6.1.1.3.cmml"><mn id="S4.p6.6.m6.1.1.3.2" xref="S4.p6.6.m6.1.1.3.2.cmml">1.5</mn><mo id="S4.p6.6.m6.1.1.3.1" xref="S4.p6.6.m6.1.1.3.1.cmml">×</mo><msup id="S4.p6.6.m6.1.1.3.3" xref="S4.p6.6.m6.1.1.3.3.cmml"><mn id="S4.p6.6.m6.1.1.3.3.2" xref="S4.p6.6.m6.1.1.3.3.2.cmml">10</mn><mrow id="S4.p6.6.m6.1.1.3.3.3" xref="S4.p6.6.m6.1.1.3.3.3.cmml"><mo id="S4.p6.6.m6.1.1.3.3.3.1" xref="S4.p6.6.m6.1.1.3.3.3.1.cmml">-</mo><mn id="S4.p6.6.m6.1.1.3.3.3.2" xref="S4.p6.6.m6.1.1.3.3.3.2.cmml">29</mn></mrow></msup></mrow></mrow></math>, <math><mrow id="S4.T3.5.5.1.m1.1.1" xref="S4.T3.5.5.1.m1.1.1.cmml"><mpadded width="+1.7pt" id="S4.T3.5.5.1.m1.1.1.2" xref="S4.T3.5.5.1.m1.1.1.2.cmml"><mi id="S4.T3.5.5.1.m1.1.1.2a" xref="S4.T3.5.5.1.m1.1.1.2.cmml">erg</mi></mpadded><mo id="S4.T3.5.5.1.m1.1.1.1" xref="S4.T3.5.5.1.m1.1.1.1.cmml">⁢</mo><msup id="S4.T3.5.5.1.m1.1.1.3" xref="S4.T3.5.5.1.m1.1.1.3.cmml"><mi mathvariant="normal" id="S4.T3.5.5.1.m1.1.1.3.2" xref="S4.T3.5.5.1.m1.1.1.3.2.cmml">s</mi><mrow id="S4.T3.5.5.1.m1.1.1.3.3" xref="S4.T3.5.5.1.m1.1.1.3.3.cmml"><mo id="S4.T3.5.5.1.m1.1.1.3.3.1" xref="S4.T3.5.5.1.m1.1.1.3.3.1.cmml">-</mo><mn id="S4.T3.5.5.1.m1.1.1.3.3.2" xref="S4.T3.5.5.1.m1.1.1.3.3.2.cmml">1</mn></mrow></msup><mo id="S4.T3.5.5.1.m1.1.1.1a" xref="S4.T3.5.5.1.m1.1.1.1.cmml">⁢</mo><msup id="S4.T3.5.5.1.m1.1.1.4" xref="S4.T3.5.5.1.m1.1.1.4.cmml"><mi id="S4.T3.5.5.1.m1.1.1.4.2" xref="S4.T3.5.5.1.m1.1.1.4.2.cmml">Hz</mi><mrow id="S4.T3.5.5.1.m1.1.1.4.3" xref="S4.T3.5.5.1.m1.1.1.4.3.cmml"><mo id="S4.T3.5.5.1.m1.1.1.4.3.1" xref="S4.T3.5.5.1.m1.1.1.4.3.1.cmml">-</mo><mn id="S4.T3.5.5.1.m1.1.1.4.3.2" xref="S4.T3.5.5.1.m1.1.1.4.3.2.cmml">1</mn></mrow></msup></mrow></math>, <math><mrow id="S4.T3.6.6.2.m1.1.1" xref="S4.T3.6.6.2.m1.1.1.cmml"><mpadded width="+1.7pt" id="S4.T3.6.6.2.m1.1.1.2" xref="S4.T3.6.6.2.m1.1.1.2.cmml"><mi id="S4.T3.6.6.2.m1.1.1.2a" xref="S4.T3.6.6.2.m1.1.1.2.cmml">erg</mi></mpadded><mo id="S4.T3.6.6.2.m1.1.1.1" xref="S4.T3.6.6.2.m1.1.1.1.cmml">⁢</mo><msup id="S4.T3.6.6.2.m1.1.1.3" xref="S4.T3.6.6.2.m1.1.1.3.cmml"><mi mathvariant="normal" id="S4.T3.6.6.2.m1.1.1.3.2" xref="S4.T3.6.6.2.m1.1.1.3.2.cmml">s</mi><mrow id="S4.T3.6.6.2.m1.1.1.3.3" xref="S4.T3.6.6.2.m1.1.1.3.3.cmml"><mo id="S4.T3.6.6.2.m1.1.1.3.3.1" xref="S4.T3.6.6.2.m1.1.1.3.3.1.cmml">-</mo><mn id="S4.T3.6.6.2.m1.1.1.3.3.2" xref="S4.T3.6.6.2.m1.1.1.3.3.2.cmml">1</mn></mrow></msup><mo id="S4.T3.6.6.2.m1.1.1.1a" xref="S4.T3.6.6.2.m1.1.1.1.cmml">⁢</mo><msup id="S4.T3.6.6.2.m1.1.1.4" xref="S4.T3.6.6.2.m1.1.1.4.cmml"><mi id="S4.T3.6.6.2.m1.1.1.4.2" xref="S4.T3.6.6.2.m1.1.1.4.2.cmml">Hz</mi><mrow id="S4.T3.6.6.2.m1.1.1.4.3" xref="S4.T3.6.6.2.m1.1.1.4.3.cmml"><mo id="S4.T3.6.6.2.m1.1.1.4.3.1" xref="S4.T3.6.6.2.m1.1.1.4.3.1.cmml">-</mo><mn id="S4.T3.6.6.2.m1.1.1.4.3.2" xref="S4.T3.6.6.2.m1.1.1.4.3.2.cmml">1</mn></mrow></msup></mrow></math>, <math><mrow id="S5.SS1.p4.1.m1.1.2" xref="S5.SS1.p4.1.m1.1.2.cmml"><msub id="S5.SS1.p4.1.m1.1.2.2" xref="S5.SS1.p4.1.m1.1.2.2.cmml"><mi id="S5.SS1.p4.1.m1.1.2.2.2" xref="S5.SS1.p4.1.m1.1.2.2.2.cmml">EW</mi><mrow id="S5.SS1.p4.1.m1.1.1.1.3" xref="S5.SS1.p4.1.m1.1.1.1.2.cmml"><mo stretchy="false" id="S5.SS1.p4.1.m1.1.1.1.3.1" xref="S5.SS1.p4.1.m1.1.1.1.2.1.cmml">[</mo><mi id="S5.SS1.p4.1.m1.1.1.1.1" xref="S5.SS1.p4.1.m1.1.1.1.1.cmml">OIII</mi><mo stretchy="false" id="S5.SS1.p4.1.m1.1.1.1.3.2" xref="S5.SS1.p4.1.m1.1.1.1.2.1.cmml">]</mo></mrow></msub><mo id="S5.SS1.p4.1.m1.1.2.1" xref="S5.SS1.p4.1.m1.1.2.1.cmml">∼</mo><mn id="S5.SS1.p4.1.m1.1.2.3" xref="S5.SS1.p4.1.m1.1.2.3.cmml">100</mn></mrow></math>

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1306.3259

Formulas:

1-

11' \times 9'

2-

55 ″ \times 55 ″

3-

18^{h} 20^{m} {25.1}^{s}

4-

- 16^{\circ} 13^{'} {02.1}^{''}

5-

4^{'} 25^{''} \times 2^{'} 45^{''}

6-

p \geq 3 σ_{p}

7-

2 σ_{p} \leq p \leq 3 σ_{p}

8-

18^{h} 20^{m} 25^{s}

9-

- 16 ° 13' 02 ″

10-

p \geq 3 σ_{p}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1812.01892

Formulas:

1-

u^{'} = f (u, p, t),

2-

\frac{\partial u (p, t)}{\partial p_{i}}

3-

\frac{d C}{d p}

4-

\frac{d u (t_{i})}{d p}

5-

\frac{\partial u (t)}{\partial p_{i}} = \frac{u (p + Δ p_{i}, t) - u (p, t)}{Δ p_{i}} + 𝒪 (Δ p_{i}),

6-

p + Δ p_{i}

7-

\frac{d}{d t} (\frac{\partial u}{\partial p_{i}}) = \frac{\partial f}{\partial u} \frac{\partial u}{\partial p_{i}} + \frac{\partial f}{\partial p_{i}}

8-

\frac{\partial f}{\partial u}

9-

\frac{\partial f}{\partial p_{i}}

10-

C (u (p)) = \sum_{i} c (u (p, t_{i}))

Formulas (html):

Correct Categorie: cs

Guessed Categorie: cs

Result: correct

Paper: https://arxiv.org/abs/1507.04576

Formulas:

1-

T^{i} = {t_{b}^{i}, \dots, t_{s}^{i}, \dots, t_{e}^{i}}

2-

P_{s} = {p_{s, i}}_{i = 0}^{R - 1}

3-

P_{t} = {p_{t, i}}_{i = 0}^{R - 1}

4-

{0 \dots R - 1} \to {0 \dots R - 1}

5-

Λ (w^{*}) = \max_{w \in W} S (w) = \max_{w \in W} M_{i} {s i m (P_{s} (i), P_{t} (w (i)))}_{i = 0, \dots, R - 1}

6-

𝕋 = {T^{i}}

7-

𝒮 (T^{j}, T^{i}) = \frac{1}{| T^{i} |} \sum_{k} \frac{| t_{k}^{j} ⋂ t_{k}^{i} |}{| t_{k}^{j} ⋃ t_{k}^{i} |},

8-

k \in [1, | T^{i} |]

9-

\tilde{𝒮} (T^{j}, 𝕋) = \frac{1}{| 𝕋 |} \sum_{T^{i} \in 𝕋} 𝒮 (T^{j}, T^{i})

10-

d (𝕋) = \frac{| 𝕋 |}{| \tilde{T} |}

Formulas (html):

Correct Categorie: cs

Guessed Categorie: cs

Result: correct

Paper: https://arxiv.org/abs/1108.1389

Formulas:

1-

H = \sum_{⟨ i, j ⟩} \sum_{m, s} - t_{i j}^{m m^{'}} (c_{i m s}^{†} c_{j m^{'} s} + H.c.) + H_{int} .

2-

c_{i m s}^{(†)}

3-

t_{i j}^{m m^{'}}

4-

H_{i n t}

5-

n = 2 (k_{A} + k_{B}) / π

6-

k_{A} \neq k_{B} \neq π / 2

7-

k_{A} = \frac{π}{2} \neq k_{B}

8-

k_{A} + k_{B} = π

9-

k_{A} = k_{B} = \frac{π}{2}

10-

O (3) ≃ S U (2)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0510500

Formulas:

1-

1.0 h^{- 1} Mpc

2-

1.0 h^{- 1} Mpc

3-

1.0 h^{- 1} Mpc

4-

\sim 1.0 h^{- 1} Mpc

5-

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

6-

Ω_{m} = 0.3, Ω_{Λ} = 0.7

7-

\sim 8 \times 10^{- 5} h^{3} {Mpc}^{- 3}

8-

\sim 8 \times 10^{- 5} h^{3} {Mpc}^{- 3}

9-

5 \times 10^{13} h^{- 1} M_{☉}

10-

\int_{- \infty}^{m} ϕ (m^{'}) d m^{'},

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/hep-ph/9908216

Formulas:

1-

F_{2}^{D (3)}

2-

F_{2}^{D (3)} (x_{I P}, β, Q^{2})

3-

e p \to e X Y

4-

0.4 \leq Q^{2} \leq 5

5-

200 \leq β \leq 800 {GeV}^{2}

6-

x_{I P} < 0.05

7-

M_{_{Y}} < 1.6 GeV

8-

| t | < 1.0 {GeV}^{2}

9-

F_{2}^{D (3)}

10-

F_{2}^{D (3)}

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: hep-ph

Result: correct

Paper: https://arxiv.org/abs/1812.09610

Formulas:

1-

β_{2} = - 0.047 {ps}^{2} / m

2-

D_{2} / (2 π)

3-

\sim 8 μ s

4-

Ω = \frac{8 c τ_{R} Q β_{2}}{15 n_{0} ω_{0}} \frac{1}{τ_{s}^{4}}

5-

ω_{μ} = ω_{0} + μ D_{1} + \frac{1}{2} μ^{2} D_{2} + \frac{1}{6} μ^{3} D_{3} + \dots

6-

D_{1} / (2 π)

7-

D_{2} = - \frac{c}{n} D_{1}^{2} β_{2}

8-

D_{int} \equiv ω_{μ} - ω_{0} - μ D_{1}

9-

D_{1} / (2 π)

10-

D_{2} / (2 π)

Formulas (html):

Correct Categorie: physics

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/1906.08995

Formulas:

1-

{| α ⟩}_{A} {| 0 ⟩}_{B}

2-

{| α / \sqrt{2} ⟩}_{A} {| i α / \sqrt{2} ⟩}_{B}

3-

{\hat{U}}_{k} (φ) = \exp [i φ {({\hat{a}}^{†} \hat{a})}^{k}]

4-

| ψ ⟩ = \exp [i φ {({\hat{a}}^{†} \hat{a})}^{2}] \exp (i θ {\hat{b}}^{†} \hat{b}) {| \frac{α}{\sqrt{2}} ⟩}_{A} {| \frac{i α}{\sqrt{2}} ⟩}_{B},

5-

{\hat{X}}_{B} = \hat{b} + {\hat{b}}^{†}

6-

⟨ {\hat{X}}_{B} ⟩ = \frac{1}{\sqrt{2}} ⟨ ψ | [(\hat{b} + {\hat{b}}^{†}) + i (\hat{a} - {\hat{a}}^{†})] | ψ ⟩ .

7-

{\hat{U}}_{BS}^{†} \hat{b} {\hat{U}}_{BS} = (\hat{b} + i \hat{a}) / \sqrt{2}

8-

{\hat{U}}_{BS} = \exp [i π ({\hat{a}}^{†} \hat{b} + {\hat{b}}^{†} \hat{a}) / 4]

9-

\frac{1}{\sqrt{2}} ⟨ \hat{b} + {\hat{b}}^{†} ⟩ = - | α | \sin θ,

10-

\hat{a} g ({\hat{a}}^{†} \hat{a}) = g ({\hat{a}}^{†} \hat{a} + 1) \hat{a}

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: quant-ph

Result: correct

Paper: https://arxiv.org/abs/0711.1144

Formulas:

1-

\sqrt{{(Δ v_{r})}^{2} + {(Δ v_{l})}^{2} + {(Δ v_{b})}^{2}}

2-

V_{iss, α} = V_{E, α} - V_{ism, α}; V_{iss, δ} = V_{E, δ} - V_{ism, δ} .

3-

t_{iss} = s_{iss} / {(a V_{iss, α}^{2} + b V_{iss, δ}^{2} + c V_{iss, α} V_{iss, δ})}^{0.5},

4-

a = \cos^{2} θ_{A} / A + A \sin^{2} θ_{A}

5-

b = \sin^{2} θ_{A} / A + A \cos^{2} θ_{A}

6-

c = 2 \sin θ_{A} \cos θ_{A} (1 / A - A)

7-

V_{ism, α}, V_{ism, δ}

8-

V_{ism, α}, V_{ism, δ}

9-

V_{i s s, α} = - 49.2

10-

V_{i s s, δ} = 11.5

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1607.06403

Formulas:

1-

| ψ_{out} ⟩ = \tilde{t} | ψ_{in} ⟩

2-

T = ⟨ ψ_{out} | ψ_{out} ⟩ = ⟨ ψ_{in} | {\tilde{t}}^{†} \tilde{t} | ψ_{in} ⟩

3-

{\tilde{t}}^{†} \tilde{t}

4-

Var (\tilde{τ})

5-

{\tilde{t}}^{†} \tilde{t}

6-

Var ({\tilde{τ}}^{(MP)}) = {⟨ \tilde{τ} ⟩}^{2} M_{1} / M_{2}

7-

Var (\tilde{τ})

8-

Var ({\tilde{τ}}^{(MP)})

9-

D_{in} \approx 4, 8, 16

10-

M_{1} = 128, 512, 2048

Formulas (html):

Correct Categorie: physics

Guessed Categorie: hep-ph

Result: incorrect

Paper: https://arxiv.org/abs/1603.01385

Formulas:

1-

\frac{d Σ}{d N_{Sou}} \propto μ^{2}

2-

\frac{d Σ}{d N_{Sou}}

3-

N_{Sou} = N_{Sou, \lim}

4-

\frac{d N_{Sou}}{d μ}

5-

= \frac{L}{4 π d_{L}^{2} (z) \cdot {(1 + z)}^{γ - 2}} \cdot b (γ)

6-

d_{L} (z)

7-

= \frac{\sum_{IC} T^{IC} \int_{100 GeV}^{100 TeV} d E A_{eff}^{IC} (E) E^{- γ}}{f (γ) \cdot \int_{100 GeV}^{100 TeV} d E E^{1 - γ}},

8-

A_{eff}^{IC} (E)

9-

L = 7 \cdot 10^{44} \frac{erg}{s}

10-

d_{L} (z)

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: nucl-ex

Result: incorrect

Paper: https://arxiv.org/abs/0712.1567

Formulas:

1-

D^{0} - {\bar{D}}^{0}

2-

D^{0} \to K^{+} π^{-}

3-

D^{0} \to K^{-} π^{+}

4-

D^{0} \to K^{+} π^{-}

5-

D^{0} - {\bar{D}}^{0}

6-

R_{D} = (3.04 \pm 0.55) \times 10^{- 3}

7-

y^{'} = (8.5 \pm 7.6) \times 10^{- 3}

8-

x^{', 2} = (- 0.12 \pm 0.35) \times 10^{- 3}

9-

x^{', 2} - y^{'}

10-

D^{0} \to K^{+} π^{-}

Formulas (html):

Correct Categorie: hep-ex

Guessed Categorie: hep-ph

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/0402054

Formulas:

1-

τ_{s o}^{e y}

2-

τ_{s o}^{e y} = τ / α

3-

R_{Q} = h / e^{2} = 25.8 k Ω

4-

t_{D} = t_{H} R_{g} / R_{Q}

5-

t_{H} = h / δ

6-

τ_{s o}^{e y} = D / (α v_{F})

7-

τ_{s o}^{e y}

8-

t_{H} / τ_{s o}^{e y}

9-

t_{H} < τ_{s o}^{e y}

10-

τ_{s o}^{e y}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0507181

Formulas:

1-

R_{s} \sim 20 r_{*}

2-

\partial_{t} ρ + \nabla \cdot ρ 𝐮 = 0

3-

\partial_{t} ρ 𝐮 + \nabla \cdot ρ 𝐮𝐮 + \nabla p = - ρ G M / r^{2}

4-

\partial_{t} ρ ℰ + \nabla \cdot (ρ ℰ 𝐮 + p 𝐮) = - ℒ

5-

ℰ = \frac{1}{2} 𝐮^{2} + e - G M / r

6-

ρ e = p / (γ - 1)

7-

ℒ = A ρ^{β - α} p^{α} .

8-

\dot{E} \propto ρ T^{6}

9-

\dot{M} = 4 π

10-

u_{s} = \frac{γ - 1}{γ + 1}, ρ_{s} = \frac{γ + 1}{γ - 1}, p_{s} = \frac{2}{γ + 1} .

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/1909.02288

Formulas:

1-

𝝍 = {[ξ_{1}, ξ_{2}, \dots, ξ_{m}]}^{⊤}

2-

𝚿 = {[𝝍_{1}, 𝝍_{2}, \dots, 𝝍_{n}]}^{⊤}

3-

𝐲 = {[y_{1}, y_{2}, \dots, y_{n}]}^{⊤}

4-

𝐖 \in ℛ^{m \times j}

5-

𝐖 = \underset{|| 𝐫 || = 1}{\arg \max} {[c o v (𝚿 𝐫, 𝐲)]}^{2} .

6-

𝝁 = 𝐖^{⊤} 𝝍

7-

w_{i} = \frac{1}{1 + \exp (- a \hat{y} - b)}

8-

π^{*^{'}} = M (x, ψ),

9-

π^{*^{'}} = α_{1} (x, t) π_{1}^{*} (x, t) + \dots + α_{n} (x, t) π_{n}^{*} (x, t),

10-

α (x, t)

Formulas (html):

Correct Categorie: cs

Guessed Categorie: cs

Result: correct

Paper: https://arxiv.org/abs/0801.2691

Formulas:

1-

a / a_{p} = {(m / n)}^{2 / 3}

2-

\dot{v_{p}} = 0.5 \dot{a_{p}} \sqrt{G M_{*} / a_{p}^{3}}

3-

m > 0.45 μ^{- 2 / 7} + 1

4-

μ = m_{p} / M_{*}

5-

e_{m a x} = {(2 / 5 m_{p})}^{1 / 2}

6-

ℋ_{0} = - \frac{𝒢 M_{*}}{2 a} - 𝒢 m_{p} (\frac{1}{| r - r_{p} |} - \frac{r \cdot r_{p}}{r_{p}^{3}}),

7-

a = 1.3 a_{p}

8-

a = 1.3 a_{p}

9-

a = 1.3 a_{p}

10-

a = 1.3 a_{p}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/quant-ph/0304103

Formulas:

1-

H = ℏ ω a^{†} a + ℏ ϵ J_{z} + \frac{ℏ G}{\sqrt{2 J}} (a J_{+} + a^{†} J_{-})

2-

a \to - a, J_{\pm} \to - J_{\pm}, J_{z} \to J_{z},

3-

ℋ = ℋ_{1} \otimes ℋ_{2},

4-

ρ_{1} = {tr}_{2} | ψ ⟩ ⟨ ψ | .

5-

I [ρ_{1}] = {tr}_{1} ρ_{1}^{2}

6-

{| ⟨ ϕ | ψ ⟩ |}^{4} \leq I [ρ_{1}] .

7-

| ϕ ⟩ = | ϕ_{1} ⟩ \otimes | ϕ_{2} ⟩

8-

ρ = | ψ ⟩ ⟨ ψ |

9-

σ = | ϕ ⟩ ⟨ ϕ |

10-

{| ⟨ ϕ | ψ ⟩ |}^{2} = tr ρ σ \leq {tr}_{1} [{tr}_{2} ρ {tr}_{2} σ] = ⟨ ϕ_{1} | ρ_{1} | ϕ_{1} ⟩ .

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: quant-ph

Result: correct

Paper: https://arxiv.org/abs/1909.05958

Formulas:

1-

n S_{1 / 2}

2-

n S_{1 / 2}

3-

n S_{1 / 2}

4-

n S_{1 / 2}

5-

δ_{s} (n)

6-

ν_{HFS} = \frac{A_{H F S}}{{[n - δ_{s} (n)]}^{3}},

7-

n P_{3 / 2} \to n S_{1 / 2}

8-

| 5 S_{1 / 2}, F = 3 ⟩

9-

| 5 P_{3 / 2}, F^{'} = 4 ⟩

10-

| 5 P_{3 / 2}, F^{'} = 4 ⟩

Formulas (html):

Correct Categorie: physics

Guessed Categorie: physics

Result: correct

Paper: https://arxiv.org/abs/1809.02979

Formulas:

1-

n (ν) \propto \frac{1}{e^{\frac{h ν}{k_{b} T}} - 1},

2-

n (500 THz) \approx 2 \times 10^{- 35}

3-

n (5 GHz) \approx 1250

4-

n (5 GHz) \approx 3 \times 10^{- 4}

5-

| Ψ_{S I} ⟩

6-

L = L_{A} G_{t} G_{r} L_{P} = L_{A} G_{t} G_{r} {(\frac{λ}{4 π d})}^{2} .

7-

G_{t, r} = 4 π / Ω_{r, t}

8-

θ_{t, r} = λ / D_{t, r}

9-

D_{t, r} ≃ 1 m

10-

≃ 65 - 82 dB

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/1906.07978

Formulas:

1-

[s_{i}, s_{i}, 0]

2-

[s_{i}, 0, s_{i}]

3-

W_{d} \in ℝ^{| s_{i} | \times | s_{i} | / 3}

4-

b i a s_{1}, b i a s_{2}

5-

b i a s_{1}

6-

b i a s_{2}

7-

P (y_{i} | X, y_{< i}) = s o f t m a x (W_{t} s_{i} + b i a s)

8-

W_{t} \in ℝ^{| s_{i} | \times | V |}

9-

b i a s

10-

[s_{i}, s_{i}, 0]

Formulas (html):

Correct Categorie: cs

Guessed Categorie: cs

Result: correct

Paper: https://arxiv.org/abs/cond-mat/0310591

Formulas:

1-

{𝐙𝐧}_{𝟏 - 𝐱} {𝐌𝐧}_{𝐱} 𝐎

2-

{Zn}_{1 - x} {Mn}_{x} O

3-

J_{1} / k_{B} = - 18.2 \pm 0.5 K

4-

J_{1}^{'} / k_{B} = - 24.3 \pm 0.6 K

5-

d M / d H

6-

{Cd}_{1 - x} {Mn}_{x} S

7-

{Cd}_{1 - x} {Mn}_{x} Se

8-

𝐇 ∥ [10 \bar{1} 0]

9-

[10 \bar{1} 0]

10-

J / k_{B} = - 0.543 \pm 0.005 K

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/quant-ph/0203100

Formulas:

1-

H = h_{0} I + \vec{h} ∙ \vec{σ}

2-

\vec{s} (t) = \frac{1}{2} Tr (ρ \vec{σ})

3-

\dot{\vec{s}} (t) = \vec{b} \times \vec{s}

4-

\vec{b} = 2 \vec{h} / ℏ

5-

\dot{\vec{s}} = (b_{x} 𝒥_{x} + b_{y} 𝒥_{y} + b_{z} 𝒥_{z}) \vec{s}

6-

T = t_{f} - t_{i}

7-

t_{i} = 0, t_{f} = 1

8-

\vec{b} = \vec{s} \times \dot{\vec{s}} s^{- 2} - f (t) \vec{s}

9-

S = \int_{t_{0}}^{t_{f}} 𝑑 t {\frac{1}{2} \vec{b} ∙ \vec{b} + \vec{λ} ∙ (\dot{\vec{s}} - \vec{b} \times \vec{s})},

10-

\vec{b} = 2 \vec{h} / ℏ

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/1803.02389

Formulas:

1-

n = n_{c 1}

2-

n > n_{c 2}

3-

τ^{- 1} \geq 10 T_{c}

4-

ξ_{1, 𝐤} = \frac{k^{2}}{2 m_{1}} - μ

5-

ξ_{2, 𝐤} = ε_{0} + \frac{k^{2}}{2 m_{2}} - μ

6-

V_{i j} < 0

7-

V_{i j} > 0

8-

| λ_{i j} | ≪ 1

9-

λ_{i j} \equiv - ρ_{j, 0} V_{i j}

10-

λ_{i j} > 0

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/cond-mat/0510503

Formulas:

1-

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

2-

{Al}_{0.34} {Ga}_{0.66} As

3-

H ψ = E ψ

4-

[\frac{1}{2 m} {(𝐩 + e 𝐀)}^{2} + V (x)] ψ (x, y) = E ψ (x, y),

5-

m = 0.067 m_{e}

6-

𝐀 = (0, x B, 0)

7-

H = \frac{ℏ^{2}}{2 m} [{(\frac{1}{i} \frac{d}{d y} + \frac{x}{ℓ^{2}})}^{2} - \frac{d^{2}}{d x^{2}}] + V (x),

8-

ℓ = \sqrt{ℏ / e B}

9-

ψ (x, y) \propto e^{i k y} φ (x)

10-

k \in ℤ \times 2 π / L_{y}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Run 11329971 (Agent787)