Run 11274853

Paper: https://arxiv.org/abs/1712.02276

Formulas:

1-

\nabla_{μ} (ρ u^{μ}) = 0 \nabla_{μ} T^{μ ν} = 0

2-

T^{μ ν} = T_{gas}^{μ ν} + T_{E M}^{μ ν}

3-

T_{g a s}^{μ ν} = ρ h u^{μ} u^{ν} + p g^{μ ν} = (ρ + u + p) u^{μ} u^{ν} + p g^{μ ν}

4-

T_{E M}^{μ ν} = b^{2} u^{μ} u^{ν} + \frac{1}{2} b^{2} g^{μ ν} - b^{μ} b^{ν}; b^{μ} = u_{ν} {}^{^{*}}F^{μ ν}

5-

b^{μ} = \frac{1}{2} ϵ^{μ ν ρ σ} u_{ν} F_{ρ σ}

6-

E_{ν} = u_{μ} F^{μ ν} = 0

7-

A_{ϕ} = (ρ / ρ_{m a x})

8-

β = P_{g a s} / P_{m a g} = 50

9-

\dot{E} \equiv 2 π \int_{0}^{π} 𝑑 θ \sqrt{- g} F_{E}

10-

F_{E} \equiv - T_{t}^{r}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/0808.4132

Formulas:

1-

\sim 2300 km s^{- 1}

2-

| v_{peaks} | < 300 km s^{- 1}

3-

v_{o b s - m} = - 570 km s^{- 1}

4-

\sim - 1000 km s^{- 1}

5-

\sim - 1800 km s^{- 1}

6-

- 640 km s^{- 1}

7-

- 450 km s^{- 1}

8-

- 1000 km s^{- 1}

9-

M_{1} = 120 M_{⊙}

10-

M_{2} = 30 M_{⊙}

Formulas (html):

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id="S1.p2.3.m3.1.1.3.2.3a" xref="S1.p2.3.m3.1.1.3.2.3.cmml">km</mi></mpadded><mo id="S1.p2.3.m3.1.1.3.2.1a" xref="S1.p2.3.m3.1.1.3.2.1.cmml">⁢</mo><msup id="S1.p2.3.m3.1.1.3.2.4" xref="S1.p2.3.m3.1.1.3.2.4.cmml"><mi mathvariant="normal" id="S1.p2.3.m3.1.1.3.2.4.2" xref="S1.p2.3.m3.1.1.3.2.4.2.cmml">s</mi><mrow id="S1.p2.3.m3.1.1.3.2.4.3" xref="S1.p2.3.m3.1.1.3.2.4.3.cmml"><mo id="S1.p2.3.m3.1.1.3.2.4.3.1" xref="S1.p2.3.m3.1.1.3.2.4.3.1.cmml">-</mo><mn id="S1.p2.3.m3.1.1.3.2.4.3.2" xref="S1.p2.3.m3.1.1.3.2.4.3.2.cmml">1</mn></mrow></msup></mrow></mrow></mrow></math>, <math><mrow id="S1.p2.4.m4.1.1" xref="S1.p2.4.m4.1.1.cmml"><mi id="S1.p2.4.m4.1.1.2" xref="S1.p2.4.m4.1.1.2.cmml"/><mo id="S1.p2.4.m4.1.1.1" xref="S1.p2.4.m4.1.1.1.cmml">∼</mo><mrow id="S1.p2.4.m4.1.1.3" xref="S1.p2.4.m4.1.1.3.cmml"><mo id="S1.p2.4.m4.1.1.3.1" xref="S1.p2.4.m4.1.1.3.1.cmml">-</mo><mrow id="S1.p2.4.m4.1.1.3.2" xref="S1.p2.4.m4.1.1.3.2.cmml"><mpadded width="+3.3pt" id="S1.p2.4.m4.1.1.3.2.2" 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xref="S1.p2.7.m7.1.1.2.4.3.1.cmml">-</mo><mn id="S1.p2.7.m7.1.1.2.4.3.2" xref="S1.p2.7.m7.1.1.2.4.3.2.cmml">1</mn></mrow></msup></mrow></mrow></math>, <math><mrow id="S1.p2.8.m8.1.1" xref="S1.p2.8.m8.1.1.cmml"><mo id="S1.p2.8.m8.1.1.1" xref="S1.p2.8.m8.1.1.1.cmml">-</mo><mrow id="S1.p2.8.m8.1.1.2" xref="S1.p2.8.m8.1.1.2.cmml"><mpadded width="+3.3pt" id="S1.p2.8.m8.1.1.2.2" xref="S1.p2.8.m8.1.1.2.2.cmml"><mn id="S1.p2.8.m8.1.1.2.2a" xref="S1.p2.8.m8.1.1.2.2.cmml">450</mn></mpadded><mo id="S1.p2.8.m8.1.1.2.1" xref="S1.p2.8.m8.1.1.2.1.cmml">⁢</mo><mpadded width="+3.3pt" id="S1.p2.8.m8.1.1.2.3" xref="S1.p2.8.m8.1.1.2.3.cmml"><mi id="S1.p2.8.m8.1.1.2.3a" xref="S1.p2.8.m8.1.1.2.3.cmml">km</mi></mpadded><mo id="S1.p2.8.m8.1.1.2.1a" xref="S1.p2.8.m8.1.1.2.1.cmml">⁢</mo><msup id="S1.p2.8.m8.1.1.2.4" xref="S1.p2.8.m8.1.1.2.4.cmml"><mi mathvariant="normal" id="S1.p2.8.m8.1.1.2.4.2" xref="S1.p2.8.m8.1.1.2.4.2.cmml">s</mi><mrow id="S1.p2.8.m8.1.1.2.4.3" xref="S1.p2.8.m8.1.1.2.4.3.cmml"><mo id="S1.p2.8.m8.1.1.2.4.3.1" xref="S1.p2.8.m8.1.1.2.4.3.1.cmml">-</mo><mn id="S1.p2.8.m8.1.1.2.4.3.2" xref="S1.p2.8.m8.1.1.2.4.3.2.cmml">1</mn></mrow></msup></mrow></mrow></math>, <math><mrow id="S1.p3.2.m2.1.1" xref="S1.p3.2.m2.1.1.cmml"><mo id="S1.p3.2.m2.1.1.1" xref="S1.p3.2.m2.1.1.1.cmml">-</mo><mrow id="S1.p3.2.m2.1.1.2" xref="S1.p3.2.m2.1.1.2.cmml"><mpadded width="+3.3pt" id="S1.p3.2.m2.1.1.2.2" xref="S1.p3.2.m2.1.1.2.2.cmml"><mn id="S1.p3.2.m2.1.1.2.2a" xref="S1.p3.2.m2.1.1.2.2.cmml">1000</mn></mpadded><mo id="S1.p3.2.m2.1.1.2.1" xref="S1.p3.2.m2.1.1.2.1.cmml">⁢</mo><mpadded width="+3.3pt" id="S1.p3.2.m2.1.1.2.3" xref="S1.p3.2.m2.1.1.2.3.cmml"><mi id="S1.p3.2.m2.1.1.2.3a" xref="S1.p3.2.m2.1.1.2.3.cmml">km</mi></mpadded><mo id="S1.p3.2.m2.1.1.2.1a" xref="S1.p3.2.m2.1.1.2.1.cmml">⁢</mo><msup id="S1.p3.2.m2.1.1.2.4" xref="S1.p3.2.m2.1.1.2.4.cmml"><mi mathvariant="normal" id="S1.p3.2.m2.1.1.2.4.2" xref="S1.p3.2.m2.1.1.2.4.2.cmml">s</mi><mrow id="S1.p3.2.m2.1.1.2.4.3" xref="S1.p3.2.m2.1.1.2.4.3.cmml"><mo id="S1.p3.2.m2.1.1.2.4.3.1" xref="S1.p3.2.m2.1.1.2.4.3.1.cmml">-</mo><mn id="S1.p3.2.m2.1.1.2.4.3.2" xref="S1.p3.2.m2.1.1.2.4.3.2.cmml">1</mn></mrow></msup></mrow></mrow></math>, <math><mrow id="S2.p1.2.m2.1.1" xref="S2.p1.2.m2.1.1.cmml"><msub id="S2.p1.2.m2.1.1.2" xref="S2.p1.2.m2.1.1.2.cmml"><mi id="S2.p1.2.m2.1.1.2.2" xref="S2.p1.2.m2.1.1.2.2.cmml">M</mi><mn id="S2.p1.2.m2.1.1.2.3" xref="S2.p1.2.m2.1.1.2.3.cmml">1</mn></msub><mo id="S2.p1.2.m2.1.1.1" xref="S2.p1.2.m2.1.1.1.cmml">=</mo><mrow id="S2.p1.2.m2.1.1.3" xref="S2.p1.2.m2.1.1.3.cmml"><mn id="S2.p1.2.m2.1.1.3.2" xref="S2.p1.2.m2.1.1.3.2.cmml">120</mn><mo id="S2.p1.2.m2.1.1.3.1" xref="S2.p1.2.m2.1.1.3.1.cmml">⁢</mo><msub id="S2.p1.2.m2.1.1.3.3" xref="S2.p1.2.m2.1.1.3.3.cmml"><mi id="S2.p1.2.m2.1.1.3.3.2" xref="S2.p1.2.m2.1.1.3.3.2.cmml">M</mi><mo id="S2.p1.2.m2.1.1.3.3.3" xref="S2.p1.2.m2.1.1.3.3.3.cmml">⊙</mo></msub></mrow></mrow></math>, <math><mrow id="S2.p1.3.m3.1.1" xref="S2.p1.3.m3.1.1.cmml"><msub id="S2.p1.3.m3.1.1.2" xref="S2.p1.3.m3.1.1.2.cmml"><mi id="S2.p1.3.m3.1.1.2.2" xref="S2.p1.3.m3.1.1.2.2.cmml">M</mi><mn id="S2.p1.3.m3.1.1.2.3" xref="S2.p1.3.m3.1.1.2.3.cmml">2</mn></msub><mo id="S2.p1.3.m3.1.1.1" xref="S2.p1.3.m3.1.1.1.cmml">=</mo><mrow id="S2.p1.3.m3.1.1.3" xref="S2.p1.3.m3.1.1.3.cmml"><mn id="S2.p1.3.m3.1.1.3.2" xref="S2.p1.3.m3.1.1.3.2.cmml">30</mn><mo id="S2.p1.3.m3.1.1.3.1" xref="S2.p1.3.m3.1.1.3.1.cmml">⁢</mo><msub id="S2.p1.3.m3.1.1.3.3" xref="S2.p1.3.m3.1.1.3.3.cmml"><mi id="S2.p1.3.m3.1.1.3.3.2" xref="S2.p1.3.m3.1.1.3.3.2.cmml">M</mi><mo id="S2.p1.3.m3.1.1.3.3.3" xref="S2.p1.3.m3.1.1.3.3.3.cmml">⊙</mo></msub></mrow></mrow></math>

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/2007.05743

Formulas:

1-

N_{T o t a l} = 56416

2-

N_{T r a i n} = 36517

3-

N_{T e s t} = 19899

4-

N_{G r a y - S c a l e} = 338496

5-

N_{C l a s s} = 1108

6-

n_{S a m p l e s / C l a s s} = N_{T r a i n} / N_{C l a s s}

7-

N_{T o t a l}

8-

n_{S a m p l e s / C l a s s}

9-

n_{S a m p l e s / C l a s s}

10-

x_{l} = H_{l} (x_{l - 1}) + x_{l - 1}

Formulas (html):

Correct Categorie: cs

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1809.09039

Formulas:

1-

1 / μ = B / c

2-

T SP = \frac{1}{μ_{SP} - λ}

3-

μ_{SP} = c / B

4-

1 / μ MPD = B / c

5-

T MPD = E [S] + \frac{λ E [S 2]}{2 (1 - λ E [S])}

6-

E [S] = \frac{1}{μ MPD} (H_{n} - H_{n - 1})

7-

V [S] = \frac{(H_{n 2} - H_{(n - 1) 2})}{μ^{2} MPD}

8-

H_{n} = \sum_{j = 1}^{n} \frac{1}{j} and H_{n^{2}} = \sum_{j = 1}^{n} \frac{1}{j 2}

9-

1 / μ MPC = B / (k c)

10-

E [S] = \frac{1}{μ MPC} \sum_{i = 1}^{k} \frac{1}{n - k + i} = \frac{1}{μ MPC} (H_{n} - H_{n - k})

Formulas (html):

Correct Categorie: cs

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/cs/0309040

Formulas:

1-

G (n, m)

2-

⌊ n / (k + 1) ⌋

3-

O (k \log^{*} n)

4-

O (m \log k + n \log k \log^{*} n)

5-

G (n, m)

6-

⌊ n / (k + 1) ⌋

7-

⌊ n / (k + 1) ⌋

8-

⌊ n / (k + 1) ⌋

9-

D_{1}, \dots, D_{k + 1}

10-

x_{ℓ} mod (k + 1) = ℓ

Formulas (html):

Correct Categorie: cs

Guessed Categorie: cs

Result: correct

Paper: https://arxiv.org/abs/2011.10974

Formulas:

1-

x_{t} \in ℝ^{C \times H \times W}

2-

𝐰 \in ℝ^{C \times 3 \times 3 \times 3}

3-

p^{n} \in {(- 1, - 1), (- 1, 0), \dots, (1, 1)}

4-

τ \in {- 1, 0, 1}

5-

Δ 𝐩_{t + τ}^{n}

6-

𝐩 + 𝐩^{n} + Δ 𝐩_{t + τ}^{n}

7-

𝐩 + 𝐩^{n} + Δ 𝐩_{t + τ}^{n}

8-

Δ 𝐩_{t + τ}^{n}

9-

Δ 𝐩_{t + τ}^{n}

10-

𝐱_{t + τ} (\tilde{𝐩})

Formulas (html):

Correct Categorie: cs

Guessed Categorie: cs

Result: correct

Paper: https://arxiv.org/abs/1810.10193

Formulas:

1-

T_{v e h}^{L}

2-

{\tilde{X}}_{L, i} = T_{E g o}^{- Δ_{i} / Δ_{0}} \cdot T_{v e h}^{L} \cdot {\bar{X}}_{L, i}

3-

T_{E g o}

4-

R = \frac{H}{t a n (α)} - \frac{W}{2}

5-

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

6-

r_{n} = r_{n}^{s} + c

7-

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

8-

D = \sqrt{R^{2} + d^{2}}

9-

\partial = \frac{1}{4} \sqrt{(q + r_{n}) (D - R + r_{n}) (q - r_{n}) (- D + R + r_{n})}

10-

y_{n} = - \frac{d}{2} - \frac{d (R^{2} - r_{c}^{2})}{2 D^{2}} + \frac{R}{D^{2}} \partial

Formulas (html):

Correct Categorie: cs

Guessed Categorie: gr-qc

Result: incorrect

Paper: https://arxiv.org/abs/1110.0406

Formulas:

1-

H_{a, b} = - \frac{1}{2 m} {(\nabla - i e 𝑨)}^{2} - μ \mp h

2-

μ = (μ_{a} + μ_{b}) / 2

3-

h = (μ_{a} - μ_{b}) / 2

4-

u_{i} (𝒓)

5-

v_{i} (𝒓)

6-

u_{i} = u_{i}^{(0)} + u_{i}^{(1)}, v_{i} = v_{i}^{(0)} + v_{i}^{(1)}, Δ = Δ^{(0)} + Δ^{(1)}

7-

u_{i}^{(0)} (𝒓)

8-

v_{i}^{(0)} (𝒓)

9-

Δ^{(1)} \approx 0

10-

(\frac{1}{2 m} \nabla^{2} + E + μ + h) u_{a}^{(1)} - Δ v_{b}^{(1)} = \frac{i e}{m} 𝑨 \cdot \nabla u_{a}^{(0)}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: hep-ph

Result: incorrect

Paper: https://arxiv.org/abs/quant-ph/0207125

Formulas:

1-

ℱ \equiv var (m) / ⟨ m ⟩

2-

1 / p_{d} \to 0

3-

σ_{j} \equiv ξ J

4-

j = 0, 1, 2

5-

1 / p_{d} = 0

6-

N = n_{0} + n_{2} .

7-

= (m + 1) n_{2},

8-

= γ n_{2},

9-

= \sqrt{{(\hat{J} + γ + 1)}^{2} - 4 \hat{J} γ} - γ - 1,

10-

= \frac{α m}{m + 1},

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/1905.04757

Formulas:

1-

- 45^{\circ}, 0^{\circ}, + 45^{\circ}

2-

𝐅 = {F_{p, t} | p \in {1, \dots, P}, t \in {1, \dots, T}}

3-

s_{c, p} = r_{c, p} / \sum_{u = 1}^{P} r_{c, u}

4-

𝐒_{c} = {s_{c, p} | p \in {1, \dots, P}}

5-

L = \sum_{p = 1}^{P} \sum_{t = 1}^{T} s_{c, p} l (c, {\hat{c}}_{p, t})

6-

l (c, {\hat{c}}_{p, t})

7-

f (a, 𝐛)

8-

f (Ω, 𝐒_{c_{Ω}}) = \sum_{p = 1}^{P} \sum_{t = 1}^{T} s_{c_{Ω}, p} F_{p, t}

9-

D (i, Ω) = D_{\cos} (f (i, 𝐒_{c_{Ω}}), f (Ω, 𝐒_{c_{Ω}}))

10-

f (i, 𝐒_{c_{Ω}})

Formulas (html):

Correct Categorie: cs

Guessed Categorie: cs

Result: correct

Paper: https://arxiv.org/abs/1505.06704

Formulas:

1-

U_{t o t a l} = U_{C} (S_{C}, ρ) + U_{R} (S_{R}) .

2-

U_{C} (S_{C}, ρ)

3-

S_{C} (U_{C}, ρ)

4-

U_{R} (S_{R})

5-

k_{B} T = θ = \partial U_{R} / \partial S_{R}

6-

χ = {(\frac{\partial U_{C}}{\partial S_{C}})}_{ρ},

7-

U_{C} (S_{C}, ρ) = U_{0} (ρ) + U_{1} (S_{1}),

8-

S_{C} (U_{C}, ρ) = S_{0} (ρ) + S_{1} (U_{1}),

9-

U_{0} (ρ)

10-

U_{0} (ρ) = A ρ e_{D}; e_{D} = L γ_{D},

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1703.06360

Formulas:

1-

β = p_{kin} / p_{B}

2-

H_{β - p h} \approx 1

3-

H_{c h r} \approx 2.5

4-

n = 2, 3, 4, 6, 7, 9

5-

{\bar{B}}_{α} = \frac{1}{n^{3}} \sum_{i = 1}^{n^{3}} B_{α} [i], α = x, y, or z,

6-

δ B_{α}^{2} = \frac{1}{n^{3} - 1} \sum_{i = 1}^{n^{3}} {(B_{α} [i] - {\bar{B}}_{α})}^{2}, α = x, y, or z .

7-

θ = a r c s i n (\frac{\sum_{i}^{N} σ_{i}}{N}), θ_{j} = a r c s i n (\frac{\sum_{i}^{N} {| 𝒋 |}_{i} σ_{i}}{\sum_{i}^{N} {| 𝒋 |}_{i}}),

8-

σ_{i} = \frac{{| 𝒋 \times 𝑩 |}_{i}}{{| 𝒋 |}_{i} {| 𝑩 |}_{i}},

9-

f = \frac{1}{N} \sum_{i}^{N} \frac{{| \nabla 𝑩 |}_{i}}{6 {| 𝑩 |}_{i}} d x,

10-

E_{pix} = \frac{N_{err}}{N},

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1612.00231

Formulas:

1-

\sim 20 % to 75 %

2-

F_{v a r} = 0.35 \pm 0.01

3-

F_{v a r} = \sqrt{\frac{S^{2} - σ_{e r r}^{2}}{{\bar{x}}^{2}}}

4-

σ_{e r r}^{2}

5-

F_{v a r}

6-

σ_{F_{v a r}} = \sqrt{{(\sqrt{\frac{1}{2 N}} \cdot \frac{σ_{e r r}^{2}}{{\bar{x}}^{2} F_{v a r}})}^{2} + {(\sqrt{\frac{σ_{e r r}^{2}}{N}} \cdot \frac{1}{\bar{x}})}^{2}} .

7-

r s = - 0.25

8-

P S F (r) = {[1 + {(r / r_{c})}^{2}]}^{- β}

9-

d N / d E = K {(E / E_{b})}^{- α - β l o g (E / E_{b})},

10-

1 k e V

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: hep-ex

Result: incorrect

Paper: https://arxiv.org/abs/1609.07334

Formulas:

1-

\sqrt{s_{NN}} = 5.02 𝐓𝐞𝐕

2-

\sqrt{s_{NN}} = 5.02 TeV

3-

\sqrt{s_{NN}} = 200 GeV

4-

\sqrt{s_{NN}} = 2.76 TeV

5-

R_{AA} (𝑝_{T}) = \frac{1}{⟨ T_{AA} ⟩} \frac{d N_{AA} / d 𝑝_{T}}{d σ_{p p} / d 𝑝_{T}} .

6-

d N_{AA} / d 𝑝_{T}

7-

d σ_{p p} / d 𝑝_{T}

8-

⟨ T_{AA} ⟩ = ⟨ N_{coll} ⟩ / σ_{i n e l}^{N N}

9-

\sqrt{s_{NN}} = 2.76 TeV

10-

𝑝_{T} \approx 7 GeV / 𝑐

Formulas (html):

Correct Categorie: nucl-ex

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/1312.7834

Formulas:

1-

\frac{S_{450} (J y / 450 b e a m)}{S_{850} (J y / 850 b e a m)} = {(\frac{850}{450})}^{3 + β} \frac{\exp (17 K / T_{d}) - 1}{\exp (32 K / T_{d}) - 1}

2-

β = 1.5, 2, 2.5

3-

{⟨ T_{d} ⟩}_{l o s}

4-

{⟨ T_{d} ⟩}_{l o s}

5-

{⟨ T_{d} ⟩}_{l o s}

6-

{⟨ T_{d} ⟩}_{l o s}

7-

{⟨ T_{d} ⟩}_{l o s}

8-

τ_{850} = \frac{F_{850}}{Ω_{b} B_{850} (T_{d})} .

9-

N_{H}_{850} = \frac{τ_{850}}{κ_{850} μ m_{H}},

10-

κ_{850, d} = 1

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1502.01759

Formulas:

1-

\hat{I} (t)

2-

{\hat{I}}_{Ω} (t) = \frac{1}{\sqrt{2}} \int_{t}^{t + T} e^{i Ω t^{'}} \hat{I} (t^{'}) 𝑑 t^{'} .

3-

{\hat{I}}_{Ω} (t)

4-

Δ Ω = 2 π / T

5-

{\hat{I}}_{Ω} (t)

6-

{\hat{I}}_{Ω} = \frac{1}{\sqrt{2}} ({\hat{I}}_{\cos} + i {\hat{I}}_{\sin}) .

7-

{\hat{I}}_{\cos} (t)

8-

{\hat{I}}_{\sin} (t)

9-

{\hat{a}}_{\pm Ω} = ({\hat{p}}_{\pm Ω} + i {\hat{q}}_{\pm Ω}) / 2

10-

[{\hat{p}}_{Ω}, {\hat{q}}_{Ω^{'}}] = 2 i δ (Ω - Ω^{'})

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/1406.1103

Formulas:

1-

A \sin Ω t

2-

{𝑅𝑒}_{s} = ρ_{f} Ω R^{2} / μ

3-

ϵ = A / R ≪ 1

4-

δ_{A C} \sim R e^{- 1 / 2} R

5-

δ_{D C} \sim O (R)

6-

R^{2} / ν = R e T / 2 π

7-

T = 2 π / Ω

8-

V_{s} = ϵ A Ω

9-

R / ϵ A Ω = ϵ^{- 2} T / 2 π

10-

{𝑅𝑒}_{s} = ρ_{f} V_{s} R / μ = ϵ^{2} 𝑅𝑒

Formulas (html):

Correct Categorie: physics

Guessed Categorie: physics

Result: correct

Paper: https://arxiv.org/abs/1707.06830

Formulas:

1-

video popularity y = \frac{number of l i k e s}{number of v i e w s}

2-

𝐕 = [𝐯_{1}, 𝐯_{2}, \dots, 𝐯_{T}]

3-

ϕ (𝐯_{i})

4-

θ (𝐯_{i})

5-

ψ (𝐯_{i})

6-

𝐟 = ϕ (𝐯)

7-

𝐩 = θ (𝐯)

8-

𝐜 = ψ (𝐯)

9-

= \tanh (𝐖_{f} 𝐟 + 𝐛_{f})

10-

= \tanh (𝐖_{p} 𝐩 + 𝐛_{p})

Formulas (html):

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xref="S4.SS2.p3.2.m2.1.2.2.cmml">𝐟</mi><mo id="S4.SS2.p3.2.m2.1.2.1" xref="S4.SS2.p3.2.m2.1.2.1.cmml">=</mo><mrow id="S4.SS2.p3.2.m2.1.2.3" xref="S4.SS2.p3.2.m2.1.2.3.cmml"><mi id="S4.SS2.p3.2.m2.1.2.3.2" xref="S4.SS2.p3.2.m2.1.2.3.2.cmml">ϕ</mi><mo id="S4.SS2.p3.2.m2.1.2.3.1" xref="S4.SS2.p3.2.m2.1.2.3.1.cmml">⁢</mo><mrow id="S4.SS2.p3.2.m2.1.2.3.3.2" xref="S4.SS2.p3.2.m2.1.2.3.cmml"><mo stretchy="false" id="S4.SS2.p3.2.m2.1.2.3.3.2.1" xref="S4.SS2.p3.2.m2.1.2.3.cmml">(</mo><mi id="S4.SS2.p3.2.m2.1.1" xref="S4.SS2.p3.2.m2.1.1.cmml">𝐯</mi><mo stretchy="false" id="S4.SS2.p3.2.m2.1.2.3.3.2.2" xref="S4.SS2.p3.2.m2.1.2.3.cmml">)</mo></mrow></mrow></mrow></math>, <math><mrow id="S4.SS2.p3.3.m3.1.2" xref="S4.SS2.p3.3.m3.1.2.cmml"><mi id="S4.SS2.p3.3.m3.1.2.2" xref="S4.SS2.p3.3.m3.1.2.2.cmml">𝐩</mi><mo id="S4.SS2.p3.3.m3.1.2.1" xref="S4.SS2.p3.3.m3.1.2.1.cmml">=</mo><mrow id="S4.SS2.p3.3.m3.1.2.3" xref="S4.SS2.p3.3.m3.1.2.3.cmml"><mi id="S4.SS2.p3.3.m3.1.2.3.2" xref="S4.SS2.p3.3.m3.1.2.3.2.cmml">θ</mi><mo id="S4.SS2.p3.3.m3.1.2.3.1" xref="S4.SS2.p3.3.m3.1.2.3.1.cmml">⁢</mo><mrow id="S4.SS2.p3.3.m3.1.2.3.3.2" xref="S4.SS2.p3.3.m3.1.2.3.cmml"><mo stretchy="false" id="S4.SS2.p3.3.m3.1.2.3.3.2.1" xref="S4.SS2.p3.3.m3.1.2.3.cmml">(</mo><mi id="S4.SS2.p3.3.m3.1.1" xref="S4.SS2.p3.3.m3.1.1.cmml">𝐯</mi><mo stretchy="false" id="S4.SS2.p3.3.m3.1.2.3.3.2.2" xref="S4.SS2.p3.3.m3.1.2.3.cmml">)</mo></mrow></mrow></mrow></math>, <math><mrow id="S4.SS2.p3.4.m4.1.2" xref="S4.SS2.p3.4.m4.1.2.cmml"><mi id="S4.SS2.p3.4.m4.1.2.2" xref="S4.SS2.p3.4.m4.1.2.2.cmml">𝐜</mi><mo id="S4.SS2.p3.4.m4.1.2.1" xref="S4.SS2.p3.4.m4.1.2.1.cmml">=</mo><mrow id="S4.SS2.p3.4.m4.1.2.3" xref="S4.SS2.p3.4.m4.1.2.3.cmml"><mi id="S4.SS2.p3.4.m4.1.2.3.2" xref="S4.SS2.p3.4.m4.1.2.3.2.cmml">ψ</mi><mo id="S4.SS2.p3.4.m4.1.2.3.1" xref="S4.SS2.p3.4.m4.1.2.3.1.cmml">⁢</mo><mrow id="S4.SS2.p3.4.m4.1.2.3.3.2" xref="S4.SS2.p3.4.m4.1.2.3.cmml"><mo stretchy="false" id="S4.SS2.p3.4.m4.1.2.3.3.2.1" 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id="S4.E1X.3.2.2.m1.2.2.1.1.1.1.2.2" xref="S4.E1X.3.2.2.m1.2.2.1.1.1.1.2.2.cmml"><mi id="S4.E1X.3.2.2.m1.2.2.1.1.1.1.2.2.2" xref="S4.E1X.3.2.2.m1.2.2.1.1.1.1.2.2.2.cmml">𝐖</mi><mi mathvariant="normal" id="S4.E1X.3.2.2.m1.2.2.1.1.1.1.2.2.3" xref="S4.E1X.3.2.2.m1.2.2.1.1.1.1.2.2.3.cmml">f</mi></msub><mo id="S4.E1X.3.2.2.m1.2.2.1.1.1.1.2.1" xref="S4.E1X.3.2.2.m1.2.2.1.1.1.1.2.1.cmml">⁢</mo><mi id="S4.E1X.3.2.2.m1.2.2.1.1.1.1.2.3" xref="S4.E1X.3.2.2.m1.2.2.1.1.1.1.2.3.cmml">𝐟</mi></mrow><mo id="S4.E1X.3.2.2.m1.2.2.1.1.1.1.1" xref="S4.E1X.3.2.2.m1.2.2.1.1.1.1.1.cmml">+</mo><msub id="S4.E1X.3.2.2.m1.2.2.1.1.1.1.3" xref="S4.E1X.3.2.2.m1.2.2.1.1.1.1.3.cmml"><mi id="S4.E1X.3.2.2.m1.2.2.1.1.1.1.3.2" xref="S4.E1X.3.2.2.m1.2.2.1.1.1.1.3.2.cmml">𝐛</mi><mi mathvariant="normal" id="S4.E1X.3.2.2.m1.2.2.1.1.1.1.3.3" xref="S4.E1X.3.2.2.m1.2.2.1.1.1.1.3.3.cmml">f</mi></msub></mrow><mo stretchy="false" id="S4.E1X.3.2.2.m1.2.2.1.1.1.3" xref="S4.E1X.3.2.2.m1.2.2.1.2.cmml">)</mo></mrow></mrow></mrow></math>, <math><mrow id="S4.E1Xa.3.2.2.m1.2.2" xref="S4.E1Xa.3.2.2.m1.2.2.cmml"><mi id="S4.E1Xa.3.2.2.m1.2.2.3" xref="S4.E1Xa.3.2.2.m1.2.2.3.cmml"/><mo id="S4.E1Xa.3.2.2.m1.2.2.2" xref="S4.E1Xa.3.2.2.m1.2.2.2.cmml">=</mo><mrow id="S4.E1Xa.3.2.2.m1.2.2.1.1" xref="S4.E1Xa.3.2.2.m1.2.2.1.2.cmml"><mi id="S4.E1Xa.3.2.2.m1.1.1" xref="S4.E1Xa.3.2.2.m1.1.1.cmml">tanh</mi><mo id="S4.E1Xa.3.2.2.m1.2.2.1.1a" xref="S4.E1Xa.3.2.2.m1.2.2.1.2.cmml">⁡</mo><mrow id="S4.E1Xa.3.2.2.m1.2.2.1.1.1" xref="S4.E1Xa.3.2.2.m1.2.2.1.2.cmml"><mo stretchy="false" id="S4.E1Xa.3.2.2.m1.2.2.1.1.1.2" xref="S4.E1Xa.3.2.2.m1.2.2.1.2.cmml">(</mo><mrow id="S4.E1Xa.3.2.2.m1.2.2.1.1.1.1" xref="S4.E1Xa.3.2.2.m1.2.2.1.1.1.1.cmml"><mrow id="S4.E1Xa.3.2.2.m1.2.2.1.1.1.1.2" xref="S4.E1Xa.3.2.2.m1.2.2.1.1.1.1.2.cmml"><msub id="S4.E1Xa.3.2.2.m1.2.2.1.1.1.1.2.2" xref="S4.E1Xa.3.2.2.m1.2.2.1.1.1.1.2.2.cmml"><mi id="S4.E1Xa.3.2.2.m1.2.2.1.1.1.1.2.2.2" xref="S4.E1Xa.3.2.2.m1.2.2.1.1.1.1.2.2.2.cmml">𝐖</mi><mi mathvariant="normal" id="S4.E1Xa.3.2.2.m1.2.2.1.1.1.1.2.2.3" xref="S4.E1Xa.3.2.2.m1.2.2.1.1.1.1.2.2.3.cmml">p</mi></msub><mo id="S4.E1Xa.3.2.2.m1.2.2.1.1.1.1.2.1" xref="S4.E1Xa.3.2.2.m1.2.2.1.1.1.1.2.1.cmml">⁢</mo><mi id="S4.E1Xa.3.2.2.m1.2.2.1.1.1.1.2.3" xref="S4.E1Xa.3.2.2.m1.2.2.1.1.1.1.2.3.cmml">𝐩</mi></mrow><mo id="S4.E1Xa.3.2.2.m1.2.2.1.1.1.1.1" xref="S4.E1Xa.3.2.2.m1.2.2.1.1.1.1.1.cmml">+</mo><msub id="S4.E1Xa.3.2.2.m1.2.2.1.1.1.1.3" xref="S4.E1Xa.3.2.2.m1.2.2.1.1.1.1.3.cmml"><mi id="S4.E1Xa.3.2.2.m1.2.2.1.1.1.1.3.2" xref="S4.E1Xa.3.2.2.m1.2.2.1.1.1.1.3.2.cmml">𝐛</mi><mi mathvariant="normal" id="S4.E1Xa.3.2.2.m1.2.2.1.1.1.1.3.3" xref="S4.E1Xa.3.2.2.m1.2.2.1.1.1.1.3.3.cmml">p</mi></msub></mrow><mo stretchy="false" id="S4.E1Xa.3.2.2.m1.2.2.1.1.1.3" xref="S4.E1Xa.3.2.2.m1.2.2.1.2.cmml">)</mo></mrow></mrow></mrow></math>

Correct Categorie: cs

Guessed Categorie: cs

Result: correct

Paper: https://arxiv.org/abs/1108.4301

Formulas:

1-

η = L_{rot} / (\dot{M} V_{w} c)

2-

V_{w} = 10^{8} V_{8}

3-

L_{rot} \approx 6 \times 10^{35} B_{12}^{2} P_{m s}^{- 4} erg s^{- 1},

4-

P = 100 P_{100}

5-

B = 10^{12} B_{12}

6-

R_{pul}^{sh} = D \sqrt{η} / (1 + \sqrt{η})

7-

R_{⋆}^{sh} = D / (1 + \sqrt{η})

8-

D = (1 \pm e) a

9-

ξ \sim {(v_{w} / c)}^{2}

10-

{\dot{P}}_{acc} = ξ c E / R_{L} \approx 10^{4} ξ B GeV s^{- 1}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1809.09867

Formulas:

1-

H = H_{d} + H_{f} + H_{d f} + H_{U},

2-

H_{d} = \sum_{𝐤, α} (ϵ_{𝐤}^{d} - μ) d_{𝐤 α}^{†} d_{𝐤 α}

3-

H_{f} = \sum_{𝐤, α} (ϵ_{f} + ϵ_{𝐤}^{f} - μ) f_{𝐤 α}^{†} f_{𝐤 α}

4-

H_{d f} = V \sum_{𝐤, α, β} 𝐒_{𝐤} \cdot {\vec{σ}}_{α β} d_{𝐤 α}^{†} f_{𝐤 β} + h . c .

5-

𝐒_{𝐤} = (\sin 𝐤 \cdot 𝐚_{1}, \sin 𝐤 \cdot 𝐚_{2}, \sin 𝐤 \cdot 𝐚_{3})

6-

H_{U} = U \sum_{i} n_{i ↑}^{f} n_{i ↓}^{f}

7-

t_{d (f)}

8-

t_{d (f)}^{'}

9-

t_{d (f)}^{''}

10-

ϵ_{𝐤}^{d (f)}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/0705.3187

Formulas:

1-

ℋ = \sum_{i_{1} < \dots < i_{s}}^{1, N} J_{i_{1} \dots i_{s}}^{(s)} σ_{i_{1}} \dots σ_{i_{s}} + \sum_{i_{1} < \dots < i_{p}}^{1, N} J_{i_{1} \dots i_{p}}^{(p)} σ_{i_{1}} \dots σ_{i_{p}},

2-

\sum_{i = 1}^{N} σ_{i}^{2} = N

3-

J_{i_{1} \dots i_{s}}^{(s)}

4-

J_{i_{1} \dots i_{p}}^{(p)}

5-

s! J_{s}^{2} / 2 N^{s - 1}

6-

p! J_{p}^{2} / 2 N^{p - 1}

7-

μ_{s} = {(β J_{s})}^{2} s / 2

8-

μ_{p} = {(β J_{p})}^{2} p / 2

9-

m (t) = v_{p} ϕ {(t)}^{p} + v_{q} ϕ {(t)}^{q}

10-

f = {lim}_{t \to + \infty} ϕ (t)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: math

Result: incorrect

Paper: https://arxiv.org/abs/nucl-ex/0611016

Formulas:

1-

x_{T} = 2 p_{T} / \sqrt{s}

2-

E \frac{d^{3} σ}{d p^{3}} = \frac{1}{{\sqrt{s}}^{n (\sqrt{s}, x_{T})}} G (x_{T})

3-

Δ ϕ = π / 2

4-

Δ ϕ = π / 4

5-

Λ \to p π^{-}

6-

\bar{Λ} \to \bar{p} π^{+}

7-

1 + 2 v_{2}^{t r i g} v_{2}^{p a r t} \cos (Δ ϕ)

8-

v_{2}^{t r i g}

9-

v_{2}^{p a r t}

10-

⟨ \cos [2 (ϕ - Ψ)] ⟩

Formulas (html):

Correct Categorie: nucl-ex

Guessed Categorie: hep-ph

Result: incorrect

Paper: https://arxiv.org/abs/1301.4998

Formulas:

1-

M_{⊙} {yr}^{- 1}

2-

2 \times 10^{5} K

3-

\sim 2 M_{⊙} {yr}^{- 1}

4-

4.3 < \log (T / K) < 5.3

5-

\log (T / K) < 4.3

6-

10 - 20 km s^{- 1}

7-

\sim 30 km s^{- 1}

8-

| v_{LOS} | < 90 km s^{- 1}

9-

| b | < 15^{\circ}

10-

σ = 30 km s^{- 1}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/0706.2780

Formulas:

1-

{(m - M)}_{0} = 11.0

2-

{(m - M)}_{0}

3-

{(m - M)}_{V}

4-

l o w e r e d

5-

= + 0.46 \pm 0.02 \pm 0.08

6-

T_{e f f}

7-

[Na / Fe] = + 0.13

8-

[Ca / Fe] = - 0.15

9-

[Mg / Fe] = + 0.20

10-

[Ti / Fe] = + 0.03

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/astro-ph/9907326

Formulas:

1-

M \propto σ^{α} r_{e}^{γ}

2-

L = 2 π I_{e} r_{e}^{2}

3-

L \propto σ^{a} r_{e}^{b}

4-

M - σ_{o} - r_{e}

5-

\frac{d}{d r} (ρ σ_{r}^{2}) + \frac{2 ρ σ_{r}^{2} β}{r} = - ρ g

6-

β = 1 - σ_{t}^{2} / σ_{r}^{2}

7-

g μ (g / a_{o}) = \frac{G M_{r}}{r^{2}} = \frac{4 π G}{r^{2}} \int_{0}^{r} r^{'}^{2} ρ (r^{'}) 𝑑 r^{'} .

8-

μ (x) = x / \sqrt{(1 + x^{2})}

9-

σ_{r}^{2} = A_{n σ} ρ^{\frac{1}{n}}

10-

β (r) = \frac{{(r / r_{a})}^{2}}{[1 + {(r / r_{a})}^{2}]}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1904.10389

Formulas:

1-

10 mm \times 5 mm

2-

(1 - 2^{- 6}) \approx 0.984

3-

g_{syn} = C_{syn} \cdot f

4-

P h i_{1}

5-

P h i_{2}

6-

C_{s y n, 1 - 5}

7-

C_{s y n, 1}

8-

P h i_{1}

9-

P h i_{2}

10-

P h i_{1}

Formulas (html):

Correct Categorie: cs

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0512215

Formulas:

1-

L_{8 - 1000 µm} \approx 10^{13} L_{⊙}

2-

L_{8 - 1000 µm} = 10^{12} L_{⊙}

3-

B_{W} R I K

4-

\sim 4 \times 10^{- 15}

5-

B_{W} R I

6-

f_{ν} (24 µm) > 0.75

7-

14^{h} 28^{m} 24 \overset{s}{.} 07

8-

f_{ν} (160 µm) = 430 \pm 90

9-

L_{8 - 1000 µm} ≃ 10^{13} L_{⊙}

10-

L_{8 - 1000 µm} = (3.2 \pm 0.7) \times 10^{13} L_{⊙}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/0805.0820

Formulas:

1-

| v_{LSR} | < 500 km s^{- 1}

2-

N_{HI} ≃ 10^{18} {cm}^{- 2}

3-

Δ v = 25 km s^{- 1}

4-

+ 495 km s^{- 1}

5-

10^{20} {cm}^{- 2}

6-

v_{LSR} = - 500 \dots - 140

7-

+ 60 \dots + 500 km s^{- 1}

8-

- 3.07 \pm 0.25 km s^{- 1}

9-

- 0.08 \pm 0.25 km s^{- 1}

10-

⟨ v_{GSR} ⟩ = - 203.0 km s^{- 1}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/0711.2538

Formulas:

1-

1 μ m^{3}

2-

4 π a c_{r} D

3-

c_{r} \propto R^{- 3}

4-

D \sim D_{0} p

5-

p = (1 - c)

6-

a (1 - N b^{3} R^{- 3}) / R^{3}

7-

\bar{τ} = \frac{1}{V} \int_{V} τ (\vec{x}) d^{d} \vec{x}

8-

τ (\vec{x})

9-

D \nabla^{2} τ (\vec{x}) = - 1 .

10-

\frac{1}{2 D (c) (R^{2} - a^{2})} (R^{4} \ln (\frac{R}{a}) - \frac{3 R^{4}}{4} + R^{2} a^{2} - \frac{a^{4}}{4})

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/hep-ph/0008017

Formulas:

1-

M^{2} = M_{0}^{2} + U

2-

M_{0} = w_{1} + w_{2} = \sqrt{m_{1}^{2} + 𝐤^{2}} + \sqrt{m_{2}^{2} + 𝐤^{2}}

3-

⟨ 𝐤 | U | 𝐤^{'} ⟩ = \frac{1}{{(2 π)}^{3}} \sqrt{\frac{w_{1} + w_{2}}{2 w_{1} w_{2}}} {\hat{I}}_{inst} (𝐤, 𝐤^{'}) \sqrt{\frac{w_{1}^{'} + w_{2}^{'}}{2 w_{1}^{'} w_{2}^{'}}},

4-

W = \frac{1}{3} ⟨ Tr P \exp (\oint 𝑑 x^{μ} A_{μ}) ⟩

5-

i \ln W = i {(\ln W)}_{pert} + σ S_{\min},

6-

α_{s} (𝐐) = \frac{4 π}{(11 - \frac{2}{3} N_{f}) \ln \frac{𝐐^{2}}{Λ^{2}}}

7-

α_{s} (0)

8-

m_{u} = m_{d} = 10 MeV

9-

m_{s} = 200 MeV

10-

m_{c} = 1.394 GeV

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: hep-ph

Result: correct

Paper: https://arxiv.org/abs/0911.2461

Formulas:

1-

{(d / ℓ)}_{c}

2-

e B_{⟂} / h

3-

ν_{T} \equiv n_{T} / (e B_{⟂} / h) = 1

4-

ℓ = {(ℏ / e B_{⟂})}^{1 / 2}

5-

{(d / ℓ)}_{c}

6-

{(d / ℓ)}_{c}

7-

n \approx 5.5 \times 10^{10}

8-

μ \approx 1 \times 10^{6}

9-

E_{Z} = g μ_{B} B_{T}

10-

= d \sqrt{2 π n_{T}}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/0908.0463

Formulas:

1-

2 \times 10^{6} \to 1.4 \times 10^{6}

2-

E_{y, TE} E_{x, TM}

3-

λ_{TE} = 1.5 μ m

4-

χ_{i j k}^{(2)}

5-

ω_{T} = ω_{1} - ω_{2}

6-

k = 1, 2, T

7-

Γ_{k} \equiv γ_{k, s} / γ_{k}

8-

β \approx \frac{κ_{T} d_{eff}}{2 \sqrt{ϵ_{0} λ_{T}^{3}}} \frac{\int_{d} d^{3} 𝐫 E_{TE, y}^{*} E_{TM, x}}{\sqrt{\int d^{3} 𝐫 ϵ_{r} {| 𝐄_{TE} |}^{2}} \sqrt{\int d^{3} 𝐫 ϵ_{r} {| 𝐄_{TM} |}^{2}}},

9-

κ_{T} \equiv λ_{T}^{3 / 2} E_{z, T, NIR} / [\sqrt{\int d^{3} 𝐫 ϵ_{r} {| 𝐄_{T} |}^{2}}]

10-

E_{z, T, NIR}

Formulas (html):

Correct Categorie: physics

Guessed Categorie: physics

Result: correct

Paper: https://arxiv.org/abs/gr-qc/9903067

Formulas:

1-

2 m / R \leq 8 / 9

2-

ρ + S_{ℒ} \geq 0

3-

ρ + S_{ℒ} \geq 0

4-

ρ + S_{ℒ} \geq 0

5-

2 m / R < 8 / 9

6-

γ_{m a x}

7-

2 m / R < 0.974

8-

γ_{m a x}

9-

d s^{2} = - N^{2} d t^{2} + g_{a b} d x^{a} d x^{b},

10-

ℛ = 16 π ρ,

Formulas (html):

Correct Categorie: gr-qc

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1510.02643

Formulas:

1-

X \subseteq E (G)

2-

K_{3}^{k, l, m}

3-

(X_{1}, X_{2})

4-

V (G | X_{1}) \cap V (G | X_{2}) = {u_{1}, u_{2}}

5-

{u_{1}, u_{2}}

6-

M (G_{1}) ≅ M (G_{2})

7-

L (G_{1}) = L (G_{2})

8-

L (G_{1}) = L (G_{2})

9-

L (G_{1})

10-

L (G_{1})

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/0911.3417

Formulas:

1-

L \approx L_{0} \approx 10^{- 24} (T / 100)

2-

Λ = L n (H_{2}) n (m)

3-

n (H_{2})

4-

n (H_{2} O) / n (H_{2}) \approx 8.8 \times 10^{- 4}

5-

n (m) / n (H_{2}) \approx 10^{- 3}

6-

Λ \approx 9 \times 10^{19} (T / 100) ρ^{2}

7-

ρ_{m a x}

8-

10^{- 4} M_{⊙}

9-

D = 1.3 \times 10^{- 4}

10-

D = 1.9 \times 10^{- 3}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/cond-mat/0204604

Formulas:

1-

\frac{d \vec{μ}}{d t} = - \frac{μ_{0} γ}{ℏ} \vec{B} \times \vec{μ} .

2-

μ_{0} = \frac{e ℏ}{2 m}

3-

\vec{B} = B_{0} \hat{z} + B_{1} (e^{i ω t} + e^{- i ω t}) \hat{x}; B_{1} ≪ B_{0} .

4-

{\vec{B}}_{c} = B_{0} \hat{z} + \sqrt{2} B_{1} [\hat{x} \cos (ω t) - \hat{y} \sin (ω t)]

5-

P = {[- ⟨ \vec{μ} ⟩ \cdot \frac{d \vec{B}}{d t}]}_{t} = {[\vec{B} \cdot \frac{d ⟨ \vec{μ} ⟩}{d t}]}_{t},

6-

\frac{d \vec{B}}{d t}

7-

\vec{B} \cdot (\vec{B} \times \vec{μ}) = 0

8-

\frac{d \vec{B}}{d t}

9-

\hat{V} (r)

10-

\vec{B} (t)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/1005.3037

Formulas:

1-

𝐦 = m (𝐒 / S)

2-

- 𝐝 \cdot 𝐄 = - d (𝐒 / S) \cdot 𝐄

3-

- d (𝐒 / S) \cdot 𝐄

4-

M = χ k d_{e} E / μ_{a},

5-

D^{a b} = g_{S} S^{a b}

6-

m^{a} = c g_{S} S^{a}, d^{a} = g_{S} Z^{a},

7-

𝐝 = d 𝐒 / S

8-

d^{a} u_{a} = S^{a} u_{a} = 0

9-

- d (𝐒 / S) \cdot 𝐄

10-

L_{i n t}

Formulas (html):

Correct Categorie: physics

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0511203

Formulas:

1-

λ / Δ λ \sim 2000

2-

H_{0} = 70 km s^{- 1} {Mpc}^{- 1}

3-

y_{j} = {\vec{𝐛}}_{j} \cdot {\vec{𝐅}}_{λ}

4-

\vec{𝐲} - {\vec{𝐲}}_{\mod}

5-

λ / Δ λ \approx 2000

6-

- 2.0 < [Fe / H] < + 0.50

7-

F_{λ}^{LP} = \int_{λ - l_{s} / 2}^{λ + l_{s} / 2} 𝑑 λ^{'} W (λ - λ^{'}) F_{λ^{'}} .

8-

F_{λ}^{HP} = \frac{F_{λ}}{F_{λ}^{LP}}

9-

F_{λ}^{HP} = F_{λ} - F_{λ}^{LP} .

10-

Z = 0.4 Z_{⊙}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/physics/0503224

Formulas:

1-

R_{M T} K_{m a x}

2-

d E_{k} / d k

3-

\frac{Δ c / c_{0}}{Δ a / a_{0}} = - \frac{2 ν}{1 - ν},

4-

H = - \sum_{n} J_{n} \sum_{i > j} {\vec{S}}_{i} \cdot {\vec{S}}_{j},

5-

E_{F M} = E_{0} + 6 J_{1} + 3 J_{2} + 12 J_{3},

6-

E_{A F M_{I}} = E_{0} - 2 J_{1} + 3 J_{2} - 4 J_{3},

7-

E_{A F M_{I I}} = E_{0} - 3 J_{2},

8-

E_{A F M_{I I I}} = E_{0} - 2 J_{1} + J_{2} + 4 J_{3},

9-

12 J_{1} + 6 J_{2} + 24 J_{3}

10-

10 a \times 10 a \times 10 a

Formulas (html):

Correct Categorie: physics

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/0105121

Formulas:

1-

n (s) ≃ s^{- τ} 𝒞 (s / s_{\max}),

2-

ρ_{patch} (t)

3-

{\dot{ρ}}_{patch} (t) = p (1 - ρ_{patch} (t))

4-

\bar{s} = \frac{p (1 - ρ)}{f ρ} .

5-

s_{\max} \sim {(f / p)}^{- λ},

6-

ξ \sim {(f / p)}^{- λ / 2}

7-

\int n (s) 𝑑 s = ρ

8-

n (s) / s

9-

n (s) = n_{1} (s) + n_{2} (s),

10-

n_{1} (s)

Formulas (html):

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xref="S1.E1.m1.2.2.1.1.1.1.1.1.3.3.cmml">max</mi></msub></mrow><mo rspace="4.2pt" stretchy="false" id="S1.E1.m1.2.2.1.1.1.1.1.3" xref="S1.E1.m1.2.2.1.1.1.1.1.1.cmml">)</mo></mrow></mrow></mrow><mo id="S1.E1.m1.2.2.1.2" xref="S1.E1.m1.2.2.1.1.cmml">,</mo></mrow></math>, <math><mrow id="S2.SS2.p1.7.m7.1.2" xref="S2.SS2.p1.7.m7.1.2.cmml"><msub id="S2.SS2.p1.7.m7.1.2.2" xref="S2.SS2.p1.7.m7.1.2.2.cmml"><mi id="S2.SS2.p1.7.m7.1.2.2.2" xref="S2.SS2.p1.7.m7.1.2.2.2.cmml">ρ</mi><mi mathsize="128%" id="S2.SS2.p1.7.m7.1.2.2.3" xref="S2.SS2.p1.7.m7.1.2.2.3.cmml">patch</mi></msub><mo id="S2.SS2.p1.7.m7.1.2.1" xref="S2.SS2.p1.7.m7.1.2.1.cmml">⁢</mo><mrow id="S2.SS2.p1.7.m7.1.2.3.2" xref="S2.SS2.p1.7.m7.1.2.cmml"><mo stretchy="false" id="S2.SS2.p1.7.m7.1.2.3.2.1" xref="S2.SS2.p1.7.m7.1.2.cmml">(</mo><mi id="S2.SS2.p1.7.m7.1.1" xref="S2.SS2.p1.7.m7.1.1.cmml">t</mi><mo stretchy="false" id="S2.SS2.p1.7.m7.1.2.3.2.2" xref="S2.SS2.p1.7.m7.1.2.cmml">)</mo></mrow></mrow></math>, <math><mrow 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stretchy="false" id="S2.E3.m1.1.1.1.1.1.2" xref="S2.E3.m1.1.1.1.1.1.1.cmml">(</mo><mrow id="S2.E3.m1.1.1.1.1.1.1" xref="S2.E3.m1.1.1.1.1.1.1.cmml"><mn id="S2.E3.m1.1.1.1.1.1.1.2" xref="S2.E3.m1.1.1.1.1.1.1.2.cmml">1</mn><mo id="S2.E3.m1.1.1.1.1.1.1.1" xref="S2.E3.m1.1.1.1.1.1.1.1.cmml">-</mo><mi id="S2.E3.m1.1.1.1.1.1.1.3" xref="S2.E3.m1.1.1.1.1.1.1.3.cmml">ρ</mi></mrow><mo stretchy="false" id="S2.E3.m1.1.1.1.1.1.3" xref="S2.E3.m1.1.1.1.1.1.1.cmml">)</mo></mrow></mrow><mrow id="S2.E3.m1.1.1.3" xref="S2.E3.m1.1.1.3.cmml"><mi id="S2.E3.m1.1.1.3.2" xref="S2.E3.m1.1.1.3.2.cmml">f</mi><mo id="S2.E3.m1.1.1.3.1" xref="S2.E3.m1.1.1.3.1.cmml">⁢</mo><mi id="S2.E3.m1.1.1.3.3" xref="S2.E3.m1.1.1.3.3.cmml">ρ</mi></mrow></mfrac></mrow><mo id="S2.E3.m1.2.2.1.2" xref="S2.E3.m1.2.2.1.1.cmml">.</mo></mrow></math>, <math><mrow id="S2.E4.m1.1.1.1" xref="S2.E4.m1.1.1.1.1.cmml"><mrow id="S2.E4.m1.1.1.1.1" xref="S2.E4.m1.1.1.1.1.cmml"><msub id="S2.E4.m1.1.1.1.1.3" xref="S2.E4.m1.1.1.1.1.3.cmml"><mi id="S2.E4.m1.1.1.1.1.3.2" xref="S2.E4.m1.1.1.1.1.3.2.cmml">s</mi><mi mathsize="128%" id="S2.E4.m1.1.1.1.1.3.3" xref="S2.E4.m1.1.1.1.1.3.3.cmml">max</mi></msub><mo id="S2.E4.m1.1.1.1.1.2" xref="S2.E4.m1.1.1.1.1.2.cmml">∼</mo><msup id="S2.E4.m1.1.1.1.1.1" xref="S2.E4.m1.1.1.1.1.1.cmml"><mrow id="S2.E4.m1.1.1.1.1.1.1.1" xref="S2.E4.m1.1.1.1.1.1.1.1.1.cmml"><mo stretchy="false" id="S2.E4.m1.1.1.1.1.1.1.1.2" xref="S2.E4.m1.1.1.1.1.1.1.1.1.cmml">(</mo><mrow id="S2.E4.m1.1.1.1.1.1.1.1.1" xref="S2.E4.m1.1.1.1.1.1.1.1.1.cmml"><mi id="S2.E4.m1.1.1.1.1.1.1.1.1.2" xref="S2.E4.m1.1.1.1.1.1.1.1.1.2.cmml">f</mi><mo id="S2.E4.m1.1.1.1.1.1.1.1.1.1" xref="S2.E4.m1.1.1.1.1.1.1.1.1.1.cmml">/</mo><mi id="S2.E4.m1.1.1.1.1.1.1.1.1.3" xref="S2.E4.m1.1.1.1.1.1.1.1.1.3.cmml">p</mi></mrow><mo stretchy="false" id="S2.E4.m1.1.1.1.1.1.1.1.3" xref="S2.E4.m1.1.1.1.1.1.1.1.1.cmml">)</mo></mrow><mrow id="S2.E4.m1.1.1.1.1.1.3" xref="S2.E4.m1.1.1.1.1.1.3.cmml"><mo id="S2.E4.m1.1.1.1.1.1.3.1" xref="S2.E4.m1.1.1.1.1.1.3.1.cmml">-</mo><mi id="S2.E4.m1.1.1.1.1.1.3.2" xref="S2.E4.m1.1.1.1.1.1.3.2.cmml">λ</mi></mrow></msup></mrow><mo id="S2.E4.m1.1.1.1.2" xref="S2.E4.m1.1.1.1.1.cmml">,</mo></mrow></math>, <math><mrow id="S2.SS3.p1.7.m2.1.1" xref="S2.SS3.p1.7.m2.1.1.cmml"><mi id="S2.SS3.p1.7.m2.1.1.3" xref="S2.SS3.p1.7.m2.1.1.3.cmml">ξ</mi><mo id="S2.SS3.p1.7.m2.1.1.2" xref="S2.SS3.p1.7.m2.1.1.2.cmml">∼</mo><msup id="S2.SS3.p1.7.m2.1.1.1" xref="S2.SS3.p1.7.m2.1.1.1.cmml"><mrow id="S2.SS3.p1.7.m2.1.1.1.1.1" xref="S2.SS3.p1.7.m2.1.1.1.1.1.1.cmml"><mo stretchy="false" id="S2.SS3.p1.7.m2.1.1.1.1.1.2" xref="S2.SS3.p1.7.m2.1.1.1.1.1.1.cmml">(</mo><mrow id="S2.SS3.p1.7.m2.1.1.1.1.1.1" xref="S2.SS3.p1.7.m2.1.1.1.1.1.1.cmml"><mi id="S2.SS3.p1.7.m2.1.1.1.1.1.1.2" xref="S2.SS3.p1.7.m2.1.1.1.1.1.1.2.cmml">f</mi><mo id="S2.SS3.p1.7.m2.1.1.1.1.1.1.1" xref="S2.SS3.p1.7.m2.1.1.1.1.1.1.1.cmml">/</mo><mi id="S2.SS3.p1.7.m2.1.1.1.1.1.1.3" xref="S2.SS3.p1.7.m2.1.1.1.1.1.1.3.cmml">p</mi></mrow><mo stretchy="false" id="S2.SS3.p1.7.m2.1.1.1.1.1.3" xref="S2.SS3.p1.7.m2.1.1.1.1.1.1.cmml">)</mo></mrow><mrow id="S2.SS3.p1.7.m2.1.1.1.3" xref="S2.SS3.p1.7.m2.1.1.1.3.cmml"><mo id="S2.SS3.p1.7.m2.1.1.1.3.1" xref="S2.SS3.p1.7.m2.1.1.1.3.1.cmml">-</mo><mrow id="S2.SS3.p1.7.m2.1.1.1.3.2" xref="S2.SS3.p1.7.m2.1.1.1.3.2.cmml"><mi id="S2.SS3.p1.7.m2.1.1.1.3.2.2" xref="S2.SS3.p1.7.m2.1.1.1.3.2.2.cmml">λ</mi><mo id="S2.SS3.p1.7.m2.1.1.1.3.2.1" xref="S2.SS3.p1.7.m2.1.1.1.3.2.1.cmml">/</mo><mn id="S2.SS3.p1.7.m2.1.1.1.3.2.3" xref="S2.SS3.p1.7.m2.1.1.1.3.2.3.cmml">2</mn></mrow></mrow></msup></mrow></math>, <math><mrow id="S2.SS3.p2.3.m3.1.2" xref="S2.SS3.p2.3.m3.1.2.cmml"><mrow id="S2.SS3.p2.3.m3.1.2.2" xref="S2.SS3.p2.3.m3.1.2.2.cmml"><mo largeop="true" symmetric="true" id="S2.SS3.p2.3.m3.1.2.2.1" xref="S2.SS3.p2.3.m3.1.2.2.1.cmml">∫</mo><mrow id="S2.SS3.p2.3.m3.1.2.2.2" xref="S2.SS3.p2.3.m3.1.2.2.2.cmml"><mi id="S2.SS3.p2.3.m3.1.2.2.2.2" xref="S2.SS3.p2.3.m3.1.2.2.2.2.cmml">n</mi><mo id="S2.SS3.p2.3.m3.1.2.2.2.1" xref="S2.SS3.p2.3.m3.1.2.2.2.1.cmml">⁢</mo><mrow id="S2.SS3.p2.3.m3.1.2.2.2.3.2" xref="S2.SS3.p2.3.m3.1.2.2.2.cmml"><mo stretchy="false" id="S2.SS3.p2.3.m3.1.2.2.2.3.2.1" xref="S2.SS3.p2.3.m3.1.2.2.2.cmml">(</mo><mi id="S2.SS3.p2.3.m3.1.1" xref="S2.SS3.p2.3.m3.1.1.cmml">s</mi><mo stretchy="false" id="S2.SS3.p2.3.m3.1.2.2.2.3.2.2" xref="S2.SS3.p2.3.m3.1.2.2.2.cmml">)</mo></mrow><mo id="S2.SS3.p2.3.m3.1.2.2.2.1a" xref="S2.SS3.p2.3.m3.1.2.2.2.1.cmml">⁢</mo><mrow id="S2.SS3.p2.3.m3.1.2.2.2.4" xref="S2.SS3.p2.3.m3.1.2.2.2.4.cmml"><mo rspace="0pt" id="S2.SS3.p2.3.m3.1.2.2.2.4.1" xref="S2.SS3.p2.3.m3.1.2.2.2.4.1.cmml">𝑑</mo><mi id="S2.SS3.p2.3.m3.1.2.2.2.4.2" xref="S2.SS3.p2.3.m3.1.2.2.2.4.2.cmml">s</mi></mrow></mrow></mrow><mo id="S2.SS3.p2.3.m3.1.2.1" xref="S2.SS3.p2.3.m3.1.2.1.cmml">=</mo><mi id="S2.SS3.p2.3.m3.1.2.3" xref="S2.SS3.p2.3.m3.1.2.3.cmml">ρ</mi></mrow></math>, <math><mrow id="S2.SS3.p2.4.m4.1.2" xref="S2.SS3.p2.4.m4.1.2.cmml"><mrow id="S2.SS3.p2.4.m4.1.2.2" xref="S2.SS3.p2.4.m4.1.2.2.cmml"><mi id="S2.SS3.p2.4.m4.1.2.2.2" xref="S2.SS3.p2.4.m4.1.2.2.2.cmml">n</mi><mo id="S2.SS3.p2.4.m4.1.2.2.1" xref="S2.SS3.p2.4.m4.1.2.2.1.cmml">⁢</mo><mrow id="S2.SS3.p2.4.m4.1.2.2.3.2" xref="S2.SS3.p2.4.m4.1.2.2.cmml"><mo stretchy="false" id="S2.SS3.p2.4.m4.1.2.2.3.2.1" xref="S2.SS3.p2.4.m4.1.2.2.cmml">(</mo><mi id="S2.SS3.p2.4.m4.1.1" xref="S2.SS3.p2.4.m4.1.1.cmml">s</mi><mo stretchy="false" id="S2.SS3.p2.4.m4.1.2.2.3.2.2" xref="S2.SS3.p2.4.m4.1.2.2.cmml">)</mo></mrow></mrow><mo id="S2.SS3.p2.4.m4.1.2.1" xref="S2.SS3.p2.4.m4.1.2.1.cmml">/</mo><mi id="S2.SS3.p2.4.m4.1.2.3" xref="S2.SS3.p2.4.m4.1.2.3.cmml">s</mi></mrow></math>, <math><mrow id="S2.E5.m1.4.4.1" xref="S2.E5.m1.4.4.1.1.cmml"><mrow id="S2.E5.m1.4.4.1.1" xref="S2.E5.m1.4.4.1.1.cmml"><mrow id="S2.E5.m1.4.4.1.1.2" xref="S2.E5.m1.4.4.1.1.2.cmml"><mi id="S2.E5.m1.4.4.1.1.2.2" xref="S2.E5.m1.4.4.1.1.2.2.cmml">n</mi><mo id="S2.E5.m1.4.4.1.1.2.1" xref="S2.E5.m1.4.4.1.1.2.1.cmml">⁢</mo><mrow id="S2.E5.m1.4.4.1.1.2.3.2" xref="S2.E5.m1.4.4.1.1.2.cmml"><mo stretchy="false" id="S2.E5.m1.4.4.1.1.2.3.2.1" xref="S2.E5.m1.4.4.1.1.2.cmml">(</mo><mi id="S2.E5.m1.1.1" xref="S2.E5.m1.1.1.cmml">s</mi><mo stretchy="false" id="S2.E5.m1.4.4.1.1.2.3.2.2" xref="S2.E5.m1.4.4.1.1.2.cmml">)</mo></mrow></mrow><mo id="S2.E5.m1.4.4.1.1.1" xref="S2.E5.m1.4.4.1.1.1.cmml">=</mo><mrow id="S2.E5.m1.4.4.1.1.3" xref="S2.E5.m1.4.4.1.1.3.cmml"><mrow id="S2.E5.m1.4.4.1.1.3.2" xref="S2.E5.m1.4.4.1.1.3.2.cmml"><msub id="S2.E5.m1.4.4.1.1.3.2.2" xref="S2.E5.m1.4.4.1.1.3.2.2.cmml"><mi id="S2.E5.m1.4.4.1.1.3.2.2.2" xref="S2.E5.m1.4.4.1.1.3.2.2.2.cmml">n</mi><mn id="S2.E5.m1.4.4.1.1.3.2.2.3" xref="S2.E5.m1.4.4.1.1.3.2.2.3.cmml">1</mn></msub><mo id="S2.E5.m1.4.4.1.1.3.2.1" xref="S2.E5.m1.4.4.1.1.3.2.1.cmml">⁢</mo><mrow id="S2.E5.m1.4.4.1.1.3.2.3.2" xref="S2.E5.m1.4.4.1.1.3.2.cmml"><mo stretchy="false" id="S2.E5.m1.4.4.1.1.3.2.3.2.1" xref="S2.E5.m1.4.4.1.1.3.2.cmml">(</mo><mi id="S2.E5.m1.2.2" xref="S2.E5.m1.2.2.cmml">s</mi><mo stretchy="false" id="S2.E5.m1.4.4.1.1.3.2.3.2.2" xref="S2.E5.m1.4.4.1.1.3.2.cmml">)</mo></mrow></mrow><mo id="S2.E5.m1.4.4.1.1.3.1" xref="S2.E5.m1.4.4.1.1.3.1.cmml">+</mo><mrow id="S2.E5.m1.4.4.1.1.3.3" xref="S2.E5.m1.4.4.1.1.3.3.cmml"><msub id="S2.E5.m1.4.4.1.1.3.3.2" xref="S2.E5.m1.4.4.1.1.3.3.2.cmml"><mi id="S2.E5.m1.4.4.1.1.3.3.2.2" xref="S2.E5.m1.4.4.1.1.3.3.2.2.cmml">n</mi><mn id="S2.E5.m1.4.4.1.1.3.3.2.3" xref="S2.E5.m1.4.4.1.1.3.3.2.3.cmml">2</mn></msub><mo id="S2.E5.m1.4.4.1.1.3.3.1" xref="S2.E5.m1.4.4.1.1.3.3.1.cmml">⁢</mo><mrow id="S2.E5.m1.4.4.1.1.3.3.3.2" xref="S2.E5.m1.4.4.1.1.3.3.cmml"><mo stretchy="false" id="S2.E5.m1.4.4.1.1.3.3.3.2.1" xref="S2.E5.m1.4.4.1.1.3.3.cmml">(</mo><mi id="S2.E5.m1.3.3" xref="S2.E5.m1.3.3.cmml">s</mi><mo stretchy="false" id="S2.E5.m1.4.4.1.1.3.3.3.2.2" xref="S2.E5.m1.4.4.1.1.3.3.cmml">)</mo></mrow></mrow></mrow></mrow><mo id="S2.E5.m1.4.4.1.2" xref="S2.E5.m1.4.4.1.1.cmml">,</mo></mrow></math>, <math><mrow id="S2.SS3.p2.5.m1.1.2" xref="S2.SS3.p2.5.m1.1.2.cmml"><msub id="S2.SS3.p2.5.m1.1.2.2" xref="S2.SS3.p2.5.m1.1.2.2.cmml"><mi id="S2.SS3.p2.5.m1.1.2.2.2" xref="S2.SS3.p2.5.m1.1.2.2.2.cmml">n</mi><mn id="S2.SS3.p2.5.m1.1.2.2.3" xref="S2.SS3.p2.5.m1.1.2.2.3.cmml">1</mn></msub><mo id="S2.SS3.p2.5.m1.1.2.1" xref="S2.SS3.p2.5.m1.1.2.1.cmml">⁢</mo><mrow id="S2.SS3.p2.5.m1.1.2.3.2" xref="S2.SS3.p2.5.m1.1.2.cmml"><mo stretchy="false" id="S2.SS3.p2.5.m1.1.2.3.2.1" xref="S2.SS3.p2.5.m1.1.2.cmml">(</mo><mi id="S2.SS3.p2.5.m1.1.1" xref="S2.SS3.p2.5.m1.1.1.cmml">s</mi><mo stretchy="false" id="S2.SS3.p2.5.m1.1.2.3.2.2" xref="S2.SS3.p2.5.m1.1.2.cmml">)</mo></mrow></mrow></math>

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/0907.5131

Formulas:

1-

(2, 0, 0)

2-

(3 / 2, \sqrt{3} / 2, 0)

3-

(- 1, 0, 0)

4-

(3 / 2, 1 / 2, - 1 / 2)

5-

(1 / 2, 1 / 2, 0)

6-

(- 2.01059, 5.93236, 0)

7-

(1, \sqrt{3}, 0)

8-

(3 / 2, 3 \sqrt{3} / 2, 0)

9-

(1 / 2, \sqrt{3} / 2, \sqrt{8 / 3})

10-

(1 / 2, 3 / 2, 1 / 2)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1012.2255

Formulas:

1-

H_{KLM} = \sum_{\vec{k}, σ} ϵ_{\vec{k}} {\hat{c}}_{\vec{k}, σ}^{†} {\hat{c}}_{\vec{k}, σ} - J \sum_{i} {\vec{s}}_{i} \cdot {\vec{S}}_{i} .

2-

{\hat{c}}_{\vec{k}, σ}^{(†)}

3-

H = H_{KLM} + ω_{0} \sum_{i} b_{i}^{†} b_{i} + g \sum_{i σ} (c_{i σ}^{†} c_{i σ} - 1) (b_{i}^{†} + b_{i})

4-

U_{eff} = - 2 g^{2} / ω_{0}

5-

| J | = 0.25 W

6-

| J | / W = 0.25

7-

| J | = 0.25 W

8-

n (\vec{k})

9-

n (\vec{k})

10-

n (\vec{k})

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1904.08020

Formulas:

1-

\underline{k} = {\underline{k}}_{r} + i {\underline{k}}_{i},

2-

{\underline{k}}_{r}, {\underline{k}}_{i} \in ℝ^{3}

3-

{\underline{k}}_{r} \times {\underline{k}}_{i} \neq \underline{0}

4-

\begin{matrix} \underline{E} (\underline{r}) = {\underline{E}}_{o} \exp (i {\underline{k}}_{r}^{∙} \underline{r}) \exp (- {\underline{k}}_{i}^{∙} \underline{r}) \\ \underline{H} (\underline{r}) = {\underline{H}}_{o} \exp (i {\underline{k}}_{r}^{∙} \underline{r}) \exp (- {\underline{k}}_{i}^{∙} \underline{r}) \end{matrix}}

5-

{\underline{E}}_{o}, {\underline{H}}_{o} \in ℂ^{3}

6-

\underline{k} = k_{x} {u_{¯}^{^}}_{x} + k_{y} {u_{¯}^{^}}_{y} + k_{z} {u_{¯}^{^}}_{z}

7-

k_{x}, k_{y} \in ℝ

8-

\begin{matrix} \underline{k} \times {\underline{E}}_{o} = ω μ_{0} {\underline{H}}_{o} \\ \underline{k} \times {\underline{H}}_{o} = - ω ε_{0} {\underline{\underline{ε}}}_{𝒜}^{∙} {\underline{E}}_{o} \end{matrix}},

9-

{\underline{\underline{ε}}}_{𝒜} = ε_{𝒜} \underline{\underline{I}}

10-

k_{z} = \sqrt{k_{0}^{2} ε_{𝒜} - k_{x}^{2} - k_{y}^{2}},

Formulas (html):

Correct Categorie: physics

Guessed Categorie: cs

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/9606034

Formulas:

1-

τ_{1 / 2} = 17.5

2-

τ_{1 / 2} = 5.7

3-

τ_{1 / 2} = 53.3

4-

τ_{1 / 2} = 78.8

5-

τ_{1 / 2} = 312

6-

τ_{1 / 2} = 2.6

7-

τ_{1 / 2} = 0.72

8-

m_{i} V^{2} / 2

9-

\frac{d N_{i}}{d t} (E) = K_{i} {(\frac{E}{E_{0}})}^{- 1.5} e^{- E / E_{0}},

10-

\frac{d N_{i}}{d t} (E) = K_{i} {(\frac{E}{E_{c}})}^{- s} for E > E_{c}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/hep-ph/9602407

Formulas:

1-

y_{c u t}

2-

P_{n} (α; {\bar{n}}_{1}, k_{1}; {\bar{n}}_{2}, k_{2}) = α P_{n}^{N B} ({\bar{n}}_{1}, k_{1}) + (1 - α) P_{n}^{N B} ({\bar{n}}_{2}, k_{2})

3-

P_{n}^{N B} (\bar{n}, k)

4-

D^{2} / {\bar{n}}^{2} = 1 / \bar{n} + 1 / k

5-

P_{n}^{N B} (\bar{n}, k) = \frac{k (k + 1) \dots (k + n - 1)}{n!} {(\frac{k}{\bar{n} + k})}^{k} {(\frac{\bar{n}}{\bar{n} + k})}^{n}

6-

y_{c u t}

7-

y_{c u t}

8-

P_{n} = {\begin{matrix} A P_{n} (α; {\bar{n}}_{1}, k_{1}; {\bar{n}}_{2}, k_{2}) & if n even \\ 0 & otherwise \end{matrix}

9-

\sum_{n = 0}^{\infty} P_{n} = 1

10-

y_{c u t}

Formulas (html):

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stretchy="false" id="S2.E2.m1.3.3.1" xref="S2.E2.m1.3.3.1.cmml">¯</mo></mover><mo id="S2.E2.m1.6.7.2.3.2.2" xref="S2.E2.m1.6.7.2.3.1.cmml">,</mo><mi id="S2.E2.m1.4.4" xref="S2.E2.m1.4.4.cmml">k</mi><mo stretchy="false" id="S2.E2.m1.6.7.2.3.2.3" xref="S2.E2.m1.6.7.2.3.1.cmml">)</mo></mrow></mrow><mo id="S2.E2.m1.6.7.1" xref="S2.E2.m1.6.7.1.cmml">=</mo><mrow id="S2.E2.m1.6.7.3" xref="S2.E2.m1.6.7.3.cmml"><mfrac id="S2.E2.m1.2.2" xref="S2.E2.m1.2.2.cmml"><mrow id="S2.E2.m1.2.2.2" xref="S2.E2.m1.2.2.2.cmml"><mi id="S2.E2.m1.2.2.2.4" xref="S2.E2.m1.2.2.2.4.cmml">k</mi><mo id="S2.E2.m1.2.2.2.3" xref="S2.E2.m1.2.2.2.3.cmml">⁢</mo><mrow id="S2.E2.m1.1.1.1.1.1" xref="S2.E2.m1.1.1.1.1.1.1.cmml"><mo stretchy="false" id="S2.E2.m1.1.1.1.1.1.2" xref="S2.E2.m1.1.1.1.1.1.1.cmml">(</mo><mrow id="S2.E2.m1.1.1.1.1.1.1" xref="S2.E2.m1.1.1.1.1.1.1.cmml"><mi id="S2.E2.m1.1.1.1.1.1.1.2" xref="S2.E2.m1.1.1.1.1.1.1.2.cmml">k</mi><mo id="S2.E2.m1.1.1.1.1.1.1.1" xref="S2.E2.m1.1.1.1.1.1.1.1.cmml">+</mo><mn 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xref="S2.E3.m1.1.1.1.1.1.1c.cmml">if </mtext><mi id="S2.E3.m1.1.1.1.1.1.1.1.m1.1.1" xref="S2.E3.m1.1.1.1.1.1.1.1.m1.1.1.cmml">n</mi><mtext id="S2.E3.m1.1.1.1.1.1.1b" xref="S2.E3.m1.1.1.1.1.1.1c.cmml"> even</mtext></mrow></mtd></mtr><mtr id="S2.E3.m1.4.4.4d" xref="S2.E3.m1.4.5.3.1.cmml"><mtd columnalign="left" id="S2.E3.m1.4.4.4e" xref="S2.E3.m1.4.5.3.1.cmml"><mn id="S2.E3.m1.3.3.3.3.1.1" xref="S2.E3.m1.3.3.3.3.1.1.cmml">0</mn></mtd><mtd columnalign="left" id="S2.E3.m1.4.4.4f" xref="S2.E3.m1.4.5.3.1.cmml"><mtext id="S2.E3.m1.4.4.4.4.2.1" xref="S2.E3.m1.4.4.4.4.2.1a.cmml">otherwise</mtext></mtd></mtr></mtable></mrow></mrow></math>, <math><mrow id="S2.p4.2.m2.1.1" xref="S2.p4.2.m2.1.1.cmml"><mrow id="S2.p4.2.m2.1.1.2" xref="S2.p4.2.m2.1.1.2.cmml"><msubsup id="S2.p4.2.m2.1.1.2.1" xref="S2.p4.2.m2.1.1.2.1.cmml"><mo largeop="true" symmetric="true" id="S2.p4.2.m2.1.1.2.1.2.2" xref="S2.p4.2.m2.1.1.2.1.2.2.cmml">∑</mo><mrow id="S2.p4.2.m2.1.1.2.1.2.3" xref="S2.p4.2.m2.1.1.2.1.2.3.cmml"><mi id="S2.p4.2.m2.1.1.2.1.2.3.2" xref="S2.p4.2.m2.1.1.2.1.2.3.2.cmml">n</mi><mo id="S2.p4.2.m2.1.1.2.1.2.3.1" xref="S2.p4.2.m2.1.1.2.1.2.3.1.cmml">=</mo><mn id="S2.p4.2.m2.1.1.2.1.2.3.3" xref="S2.p4.2.m2.1.1.2.1.2.3.3.cmml">0</mn></mrow><mi mathvariant="normal" id="S2.p4.2.m2.1.1.2.1.3" xref="S2.p4.2.m2.1.1.2.1.3.cmml">∞</mi></msubsup><msub id="S2.p4.2.m2.1.1.2.2" xref="S2.p4.2.m2.1.1.2.2.cmml"><mi id="S2.p4.2.m2.1.1.2.2.2" xref="S2.p4.2.m2.1.1.2.2.2.cmml">P</mi><mi id="S2.p4.2.m2.1.1.2.2.3" xref="S2.p4.2.m2.1.1.2.2.3.cmml">n</mi></msub></mrow><mo id="S2.p4.2.m2.1.1.1" xref="S2.p4.2.m2.1.1.1.cmml">=</mo><mn id="S2.p4.2.m2.1.1.3" xref="S2.p4.2.m2.1.1.3.cmml">1</mn></mrow></math>, <math><msub id="S2.p5.6.m6.1.1" xref="S2.p5.6.m6.1.1.cmml"><mi id="S2.p5.6.m6.1.1.2" xref="S2.p5.6.m6.1.1.2.cmml">y</mi><mrow id="S2.p5.6.m6.1.1.3" xref="S2.p5.6.m6.1.1.3.cmml"><mi id="S2.p5.6.m6.1.1.3.2" xref="S2.p5.6.m6.1.1.3.2.cmml">c</mi><mo id="S2.p5.6.m6.1.1.3.1" xref="S2.p5.6.m6.1.1.3.1.cmml">⁢</mo><mi id="S2.p5.6.m6.1.1.3.3" xref="S2.p5.6.m6.1.1.3.3.cmml">u</mi><mo id="S2.p5.6.m6.1.1.3.1a" xref="S2.p5.6.m6.1.1.3.1.cmml">⁢</mo><mi id="S2.p5.6.m6.1.1.3.4" xref="S2.p5.6.m6.1.1.3.4.cmml">t</mi></mrow></msub></math>

Correct Categorie: hep-ph

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/0801.3161

Formulas:

1-

\exp (- i ω t)

2-

u^{i} (x, y) = \int_{- k_{0}}^{k_{0}} A (k_{x}) e^{i (k_{x} x + k_{y 0} y)} 𝑑 k_{x}

3-

k_{y 0} = \sqrt{k_{0}^{2} - k_{x}^{2}}

4-

A (k_{x})

5-

A (k_{x}) = e^{- \frac{w^{2}}{4} {(k_{x} - k_{m})}^{2}}

6-

k_{m} = k_{0} \sin θ

7-

X_{i} = \frac{\int x {| u^{i} (x, 0) |}^{2} 𝑑 x}{\int {| u^{i} (x, 0) |}^{2} 𝑑 x}

8-

k_{0} < π / d

9-

u_{r} (x, y) = \int A (k_{x}) r_{N} (k_{x}) e^{i (k_{x} x - k_{y 0} y)} 𝑑 k_{x}

10-

u_{t} (x, y) = \int A (k_{x}) t_{N} (k_{x}) e^{i (k_{x} x + k_{y 0} y)} 𝑑 k_{x}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1107.4383

Formulas:

1-

k [x_{1}, \dots, x_{n}]

2-

S = k [x_{1}, \dots, x_{n}]

3-

ℂ [x_{1}, \dots, x_{n}]

4-

ϕ : R^{n} \to R^{m}

5-

ψ : R^{m} \to R^{n}

6-

ϕ ψ = {id}_{R^{m}}

7-

S = R [x_{1}, \dots, x_{n}]

8-

U \in {𝑀𝑎𝑡}_{m \times n} (R)

9-

V \in {𝑀𝑎𝑡}_{n \times n} (S)

10-

U V = [\begin{matrix} 1 & 0 & \dots & 0 & 0 & \dots & 0 \\ 0 & 1 & \dots & 0 & 0 & \dots & 0 \\ ⋮ & ⋮ & ⋱ & ⋮ & ⋮ & ⋱ & ⋮ \\ 0 & 0 & \dots & 1 & 0 & \dots & 0 \end{matrix}] .

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/quant-ph/0109092

Formulas:

1-

K (b, a)

2-

K (b, a) = \sum_{R} N (R) {(i ϵ m)}^{R}

3-

K (b, a)

4-

(\sum_{R = 0, 4, \dots} N (R) {(ϵ m)}^{R} - \sum_{R = 2, 6, \dots} N (R) {(ϵ m)}^{R})

5-

i (\sum_{R = 1, 5 \dots} N (R) {(ϵ m)}^{R} - \sum_{R = 3, 7, \dots} N (R) {(ϵ m)}^{R})

6-

Φ_{R} + i Φ_{I} .

7-

{(ϵ m)}^{R}

8-

P_{R} = (σ_{1}, σ_{2}, \dots, σ_{n})

9-

P_{R} = (l_{1}, l_{2}, \dots, l_{R + 1})

10-

P_{R} = (l_{1}, l_{2}, \dots, l_{R + 1}, - l_{R + 1})

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/1807.11891

Formulas:

1-

{\hat{a}}^{†} {\hat{b}}^{†}

2-

ω_{c} / ω_{s} = 0.57

3-

χ / ω_{s} = 2.5 \times 10^{- 4}

4-

ω_{c} / ω_{s} = 1

5-

χ / ω_{s} = 2.5 \times 10^{- 4}

6-

H = ω_{c} {\hat{a}}^{†} \hat{a} + ω_{s} \hat{S_{z}} + g ({\hat{a}}^{†} + \hat{a}) ({\hat{S}}^{+} + {\hat{S}}^{-})

7-

{\hat{S}}_{z} = 1 / 2 \sum_{j = 1}^{N} σ_{z}^{(j)}

8-

{\hat{S}}^{+} ({\hat{S}}^{-})

9-

{\hat{b}}^{†} = {\hat{S}}^{-} / \sqrt{N}

10-

{\hat{S}}_{z} \approx N / 2 - {\hat{b}}^{†} \hat{b}

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: quant-ph

Result: correct

Paper: https://arxiv.org/abs/1003.0144

Formulas:

1-

Ig {(p^{n})}^{ord}

2-

1 \leq σ_{0} \leq 10

3-

σ_{0} \leq σ_{0} (p^{n})

4-

\begin{matrix} p^{n} & 8 & 7 & 5 & 4 & 3 \\ σ_{0} (p^{n}) & 1 & 1 & 2 & 3 & 6 \end{matrix}

5-

σ_{0} \leq σ_{0} (p^{n})

6-

σ_{0} \leq σ_{0} (p^{n})

7-

[Ig {(p^{n})}^{ord}]

8-

ℰ^{(p^{n})} = {(F^{n})}^{*} (ℰ)

9-

Ig {(p^{n})}^{ord}

10-

ℰ \to Ig {(p^{n})}^{ord}

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Run 11274853 (Agent925)