Run 10953582

Paper: https://arxiv.org/abs/astro-ph/0506031

Formulas:

1-

\dot{P} = d P / d t \sim 10^{- 19 - 21}

2-

B \propto {(P \dot{P})}^{1 / 2} \sim 10^{8 - 9}

3-

τ \equiv P / 2 \dot{P} ≳ 10^{9}

4-

N_{H} = (1.3 \pm 0.3) \times 10^{20}

5-

0 \overset{''}{.} 049

6-

0 \overset{''}{.} 027

7-

5 \overset{''}{.} 5

8-

T_{eff} = (1.56 \pm 0.28) \times 10^{6}

9-

R_{eff} = 0.45 \pm 0.43

10-

F_{X} = (1.4 \pm 0.3) \times 10^{- 14}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1103.2520

Formulas:

1-

P_{1}, \dots, P_{n}

2-

r_{1}, \dots, r_{n}

3-

f_{i} (j)

4-

2^{(O \sqrt{\log n})}

5-

2^{(O \sqrt{\log n})}

6-

f (t) / t

7-

\max_{t} [(f_{i} (t) / t) \cdot (D / n)]

8-

D / n \leq t \leq D

9-

O (1 / \log n)

10-

Ω (1 / \log n)

Formulas (html):

Correct Categorie: cs

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/2007.12218

Formulas:

1-

E_{T B S M A}^{i} = \sum_{j \neq i}^{n_{v}} A e^{- p (\frac{r_{i j}}{r_{0}} - 1)} - \sqrt{\sum_{j \neq i}^{n_{v}} ξ^{2} e^{- 2 q (\frac{r_{i j}}{r_{0}} - 1)}},

2-

Δ = (E_{tot} - N E_{coh}) / N^{2 / 3},

3-

C N_{o p e n} = C N_{b u l k} - C N_{i}

4-

E_{i}^{M - E} = - ϵ C N_{o p e n}^{ρ},

5-

C N_{b u l k}

6-

C N_{i} = \sum_{j \neq i} f (r_{i j}),

7-

f (r_{i j}) = {\begin{matrix} 1 & if r_{i j} \leq d_{0}, \\ \frac{1 - {(\frac{r_{i j} - d_{0}}{r_{0}})}^{n}}{1 - {(\frac{r_{i j} - d_{0}}{r_{0}})}^{m}} & if r_{i j} > d_{0}, \end{matrix}

8-

g (d) = \frac{1}{(N) (N - 1)} \sum_{i}^{N} \sum_{j \neq i}^{N} δ (r_{i j} - d)

9-

_{m e l t}

10-

_{m e l t}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/cond-mat/0608120

Formulas:

1-

E_{a} = ρ_{a b} j_{b}

2-

ρ_{a b} = (ρ_{0} + α^{'} {| 𝐁 |}^{2}) δ_{a b} + α B_{a} B_{b} - ρ_{H} ϵ_{a b c} B_{c},

3-

ρ = ρ^{s} + ρ^{a}

4-

E_{a}^{H} = 1 / 2 (ρ_{a b} - ρ_{b a}) j_{b}

5-

𝐄^{H} = ρ_{H} 𝐁 \times 𝐣 .

6-

S = ⟨ M_{x} M_{y} M_{z} ⟩ \neq 0

7-

a = x, y, z

8-

⟨ M_{a} M_{b} ⟩

9-

⟨ M_{a} M_{b} M_{c} ⟩

10-

S | ϵ_{a b c} | .

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1909.04287

Formulas:

1-

F (x) = x^{n} + ϵ f (x)

2-

f : ℤ_{p} \to ℤ_{p}

3-

F (x) = 0

4-

x = p^{r} \frac{n}{m}

5-

(p, n) = 1

6-

(p, m) = 1

7-

{| x |}_{p} = {\begin{matrix} p^{- r} for x \neq 0 \\ 0 for x = 0 . \end{matrix}

8-

{| x + y |}_{p} \leq \max {{| x |}_{p}, {| y |}_{p}} .

9-

x = p^{γ (x)} (x_{0} + x_{1} p + x_{2} p^{2} + \dots),

10-

γ (x) \in ℤ

Formulas (html):

Correct Categorie: math

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/physics/0509139

Formulas:

1-

μ_{eff} ≫ ϵ_{eff}, μ_{eff} ≫ 1

2-

μ_{eff} ≫ ϵ_{eff}, μ_{eff} ≫ 1

3-

ϵ_{eff} = 3.84 (1 - j 0.001)

4-

μ_{eff} = 8.61 (1 - j 0.018)

5-

μ_{eff} ≃ 3.1, ϵ_{eff} ≃ 9.6

6-

{B W |}_{- 10 d B}

7-

ϵ_{eff} = 1, μ_{eff} ≫ 1

8-

ϵ_{eff} = μ_{eff} = - 1

9-

{μ_{eff}} > 1

10-

{μ_{eff}} = 1.5 - 4

Formulas (html):

Correct Categorie: physics

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/quant-ph/9802043

Formulas:

1-

V_{1}, \dots, V_{n}

2-

{V_{1} = false, V_{2} = false, V_{3} = true}

3-

d (r, s)

4-

d (r, s) = | r | + | s | - 2 | r \land s |

5-

V_{1} = 0, V_{2} = 0

6-

N = 2^{n} = 4

7-

m 2^{n - k}

8-

c_{avg} = m / 2^{k}

9-

(\binom{n}{k}) 2^{k}

10-

m_{\max} = (\binom{n}{k}) (2^{k} - 1)

Formulas (html):

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xref="S2.p5.4.m4.1.1.1.1.cmml"><msub id="S2.p5.4.m4.1.1.1.1.2" xref="S2.p5.4.m4.1.1.1.1.2.cmml"><mi id="S2.p5.4.m4.1.1.1.1.2.2" xref="S2.p5.4.m4.1.1.1.1.2.2.cmml">V</mi><mn id="S2.p5.4.m4.1.1.1.1.2.3" xref="S2.p5.4.m4.1.1.1.1.2.3.cmml">1</mn></msub><mo id="S2.p5.4.m4.1.1.1.1.1" xref="S2.p5.4.m4.1.1.1.1.1.cmml">=</mo><mn id="S2.p5.4.m4.1.1.1.1.3" xref="S2.p5.4.m4.1.1.1.1.3.cmml">0</mn></mrow><mo id="S2.p5.4.m4.2.2.2.3" xref="S2.p5.4.m4.2.2.3a.cmml">,</mo><mrow id="S2.p5.4.m4.2.2.2.2" xref="S2.p5.4.m4.2.2.2.2.cmml"><msub id="S2.p5.4.m4.2.2.2.2.2" xref="S2.p5.4.m4.2.2.2.2.2.cmml"><mi id="S2.p5.4.m4.2.2.2.2.2.2" xref="S2.p5.4.m4.2.2.2.2.2.2.cmml">V</mi><mn id="S2.p5.4.m4.2.2.2.2.2.3" xref="S2.p5.4.m4.2.2.2.2.2.3.cmml">2</mn></msub><mo id="S2.p5.4.m4.2.2.2.2.1" xref="S2.p5.4.m4.2.2.2.2.1.cmml">=</mo><mn id="S2.p5.4.m4.2.2.2.2.3" xref="S2.p5.4.m4.2.2.2.2.3.cmml">0</mn></mrow></mrow></math>, <math><mrow id="S2.p5.7.m7.1.1" xref="S2.p5.7.m7.1.1.cmml"><mi id="S2.p5.7.m7.1.1.2" xref="S2.p5.7.m7.1.1.2.cmml">N</mi><mo id="S2.p5.7.m7.1.1.3" xref="S2.p5.7.m7.1.1.3.cmml">=</mo><msup id="S2.p5.7.m7.1.1.4" xref="S2.p5.7.m7.1.1.4.cmml"><mn id="S2.p5.7.m7.1.1.4.2" xref="S2.p5.7.m7.1.1.4.2.cmml">2</mn><mi id="S2.p5.7.m7.1.1.4.3" xref="S2.p5.7.m7.1.1.4.3.cmml">n</mi></msup><mo id="S2.p5.7.m7.1.1.5" xref="S2.p5.7.m7.1.1.5.cmml">=</mo><mn id="S2.p5.7.m7.1.1.6" xref="S2.p5.7.m7.1.1.6.cmml">4</mn></mrow></math>, <math><mrow id="S2.p6.5.m5.1.1" xref="S2.p6.5.m5.1.1.cmml"><mi id="S2.p6.5.m5.1.1.2" xref="S2.p6.5.m5.1.1.2.cmml">m</mi><mo id="S2.p6.5.m5.1.1.1" xref="S2.p6.5.m5.1.1.1.cmml">⁢</mo><msup id="S2.p6.5.m5.1.1.3" xref="S2.p6.5.m5.1.1.3.cmml"><mn id="S2.p6.5.m5.1.1.3.2" xref="S2.p6.5.m5.1.1.3.2.cmml">2</mn><mrow id="S2.p6.5.m5.1.1.3.3" xref="S2.p6.5.m5.1.1.3.3.cmml"><mi id="S2.p6.5.m5.1.1.3.3.2" xref="S2.p6.5.m5.1.1.3.3.2.cmml">n</mi><mo id="S2.p6.5.m5.1.1.3.3.1" xref="S2.p6.5.m5.1.1.3.3.1.cmml">-</mo><mi id="S2.p6.5.m5.1.1.3.3.3" xref="S2.p6.5.m5.1.1.3.3.3.cmml">k</mi></mrow></msup></mrow></math>, <math><mrow id="S2.E2.m1.1.1" xref="S2.E2.m1.1.1.cmml"><msub id="S2.E2.m1.1.1.2" xref="S2.E2.m1.1.1.2.cmml"><mi id="S2.E2.m1.1.1.2.2" xref="S2.E2.m1.1.1.2.2.cmml">c</mi><mi id="S2.E2.m1.1.1.2.3" xref="S2.E2.m1.1.1.2.3.cmml">avg</mi></msub><mo id="S2.E2.m1.1.1.1" xref="S2.E2.m1.1.1.1.cmml">=</mo><mrow id="S2.E2.m1.1.1.3" xref="S2.E2.m1.1.1.3.cmml"><mi id="S2.E2.m1.1.1.3.2" xref="S2.E2.m1.1.1.3.2.cmml">m</mi><mo id="S2.E2.m1.1.1.3.1" xref="S2.E2.m1.1.1.3.1.cmml">/</mo><msup id="S2.E2.m1.1.1.3.3" xref="S2.E2.m1.1.1.3.3.cmml"><mn id="S2.E2.m1.1.1.3.3.2" xref="S2.E2.m1.1.1.3.3.2.cmml">2</mn><mi id="S2.E2.m1.1.1.3.3.3" xref="S2.E2.m1.1.1.3.3.3.cmml">k</mi></msup></mrow></mrow></math>, <math><mrow id="S2.p8.3.m3.3.4" xref="S2.p8.3.m3.3.4.cmml"><mrow id="S2.p8.3.m3.3.3.5" xref="S2.p8.3.m3.3.3.4.cmml"><mo id="S2.p8.3.m3.3.3.5.1" xref="S2.p8.3.m3.1.1.1.1.1.cmml">(</mo><mfrac linethickness="0pt" id="S2.p8.3.m3.3.3.3.3" xref="S2.p8.3.m3.3.3.4.cmml"><mi id="S2.p8.3.m3.2.2.2.2.2" xref="S2.p8.3.m3.2.2.2.2.2.cmml">n</mi><mi id="S2.p8.3.m3.3.3.3.3.3" xref="S2.p8.3.m3.3.3.3.3.3.cmml">k</mi></mfrac><mo id="S2.p8.3.m3.3.3.5.2" xref="S2.p8.3.m3.1.1.1.1.1.cmml">)</mo></mrow><mo id="S2.p8.3.m3.3.4.1" xref="S2.p8.3.m3.3.4.1.cmml">⁢</mo><msup id="S2.p8.3.m3.3.4.2" xref="S2.p8.3.m3.3.4.2.cmml"><mn id="S2.p8.3.m3.3.4.2.2" xref="S2.p8.3.m3.3.4.2.2.cmml">2</mn><mi id="S2.p8.3.m3.3.4.2.3" xref="S2.p8.3.m3.3.4.2.3.cmml">k</mi></msup></mrow></math>, <math><mrow id="S2.E3.m1.4.4" xref="S2.E3.m1.4.4.cmml"><msub id="S2.E3.m1.4.4.3" xref="S2.E3.m1.4.4.3.cmml"><mi id="S2.E3.m1.4.4.3.2" xref="S2.E3.m1.4.4.3.2.cmml">m</mi><mi id="S2.E3.m1.4.4.3.3" xref="S2.E3.m1.4.4.3.3.cmml">max</mi></msub><mo id="S2.E3.m1.4.4.2" xref="S2.E3.m1.4.4.2.cmml">=</mo><mrow id="S2.E3.m1.4.4.1" xref="S2.E3.m1.4.4.1.cmml"><mrow id="S2.E3.m1.3.3.5" xref="S2.E3.m1.3.3.4.cmml"><mo id="S2.E3.m1.3.3.5.1" xref="S2.E3.m1.1.1.1.1.1.cmml">(</mo><mfrac linethickness="0pt" id="S2.E3.m1.3.3.3.3" xref="S2.E3.m1.3.3.4.cmml"><mi id="S2.E3.m1.2.2.2.2.2" xref="S2.E3.m1.2.2.2.2.2.cmml">n</mi><mi id="S2.E3.m1.3.3.3.3.3" xref="S2.E3.m1.3.3.3.3.3.cmml">k</mi></mfrac><mo id="S2.E3.m1.3.3.5.2" xref="S2.E3.m1.1.1.1.1.1.cmml">)</mo></mrow><mo id="S2.E3.m1.4.4.1.2" xref="S2.E3.m1.4.4.1.2.cmml">⁢</mo><mrow id="S2.E3.m1.4.4.1.1.1" xref="S2.E3.m1.4.4.1.1.1.1.cmml"><mo stretchy="false" id="S2.E3.m1.4.4.1.1.1.2" xref="S2.E3.m1.4.4.1.1.1.1.cmml">(</mo><mrow id="S2.E3.m1.4.4.1.1.1.1" xref="S2.E3.m1.4.4.1.1.1.1.cmml"><msup id="S2.E3.m1.4.4.1.1.1.1.2" xref="S2.E3.m1.4.4.1.1.1.1.2.cmml"><mn id="S2.E3.m1.4.4.1.1.1.1.2.2" xref="S2.E3.m1.4.4.1.1.1.1.2.2.cmml">2</mn><mi id="S2.E3.m1.4.4.1.1.1.1.2.3" xref="S2.E3.m1.4.4.1.1.1.1.2.3.cmml">k</mi></msup><mo id="S2.E3.m1.4.4.1.1.1.1.1" xref="S2.E3.m1.4.4.1.1.1.1.1.cmml">-</mo><mn id="S2.E3.m1.4.4.1.1.1.1.3" xref="S2.E3.m1.4.4.1.1.1.1.3.cmml">1</mn></mrow><mo stretchy="false" id="S2.E3.m1.4.4.1.1.1.3" xref="S2.E3.m1.4.4.1.1.1.1.cmml">)</mo></mrow></mrow></mrow></math>

Correct Categorie: quant-ph

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/0201317

Formulas:

1-

{| F - F_{c} |}^{\frac{1}{2}}

2-

\frac{d u_{n}}{d t} = u_{n + 1} - 2 u_{n} + u_{n - 1} + F - A g (u_{n}) .

3-

g (u) = V^{'} (u)

4-

A g (u) - F

5-

U_{1} < U_{2} < U_{3}

6-

g^{'} (U_{i} (F / A)) > 0

7-

g^{'} (U_{2} (F / A)) < 0

8-

U_{2} (0)

9-

| F | \leq F_{c}

10-

U_{1} (F / A)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1807.09255

Formulas:

1-

ϵ = 1 - \frac{ω_{p}^{2}}{ω^{2}}

2-

ω_{n}^{T O} = ω_{p} \sqrt{e^{- n s} \sinh (n s)}, n = 1, 2, 3, \dots,

3-

\sinh^{2} s = (δ / R) (1 + δ / 4 R)

4-

| ω_{n}^{T O} ⟩

5-

(B_{1}, B_{2})

6-

(B_{2}, B_{3})

7-

(B_{1}, B_{2})

8-

(B_{2}, B_{3})

9-

(a_{n}, b_{n})

10-

a_{n} | ω_{n}^{T O} (B_{1}, B_{2}) ⟩ + b_{n} | ω_{n}^{T O} (B_{2}, B_{3}) ⟩

Formulas (html):

Correct Categorie: physics

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/9709120

Formulas:

1-

d_{x^{2} - y^{2}}

2-

j_{s} (χ)

3-

χ_{m i n}

4-

χ_{m i n}

5-

d_{x^{2} - y^{2}}

6-

\exp (\pm i χ / 2)

7-

\hat{g} (\hat{𝐩}, 𝐑; ϵ_{n})

8-

({\hat{𝐩}}_{i n}, {\hat{𝐩}}_{o u t})

9-

{\hat{𝐩}}_{o u t} = {\hat{𝐩}}_{i n} - 2 \hat{𝐧} (\hat{𝐧} \cdot {\hat{𝐩}}_{i n}),

10-

[i ϵ_{n} {\hat{τ}}_{3} - \hat{Δ} (\hat{𝐩}, 𝐑), \hat{g} (\hat{𝐩}, 𝐑; ϵ_{n})] + i 𝐯_{f} \cdot \nabla_{𝐑} \hat{g} (\hat{𝐩}, 𝐑; ϵ_{n}) = 0

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1205.3066

Formulas:

1-

S w i f t

2-

σ_{P S F} < 5^{'}

3-

F e r m i

4-

_S w i f t

5-

S w i f t_

6-

S w i f t_

7-

S w i f t_

8-

μ e r g / c m^{2}

9-

S w i f t_

10-

S w i f t_

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/q-bio/0503002

Formulas:

1-

S_{1} = ρ N

2-

S_{2} = (1 - ρ) N

3-

\begin{matrix} \dot{S_{1}} & = & - β S_{1} \frac{(I + q E + l J)}{N}, \\ \dot{S_{2}} & = & - β p S_{2} \frac{(I + q E + l J)}{N}, \\ \dot{E} & = & β (S_{1} + p S_{2}) \frac{(I + q E + l J)}{N} - k E, \\ \dot{I} & = & k E - (α + γ_{1} + δ) I, \\ \dot{J} & = & α I - (γ_{2} + δ) J, \\ \dot{R} & = & γ_{1} I + γ_{2} J, \end{matrix}

4-

1 / γ_{2} = 1 / γ_{1} - 1 / α

5-

\begin{matrix} ℛ_{0} & = & {β [ρ + p (1 - ρ)]} {\frac{q}{k} + \frac{1}{α + γ_{1} + δ} + \frac{α l}{(α + γ_{1} + δ) (γ_{2} + δ)}} \end{matrix}

6-

I (0) = 1

7-

t_{0} = t - (\frac{1}{r} \log (x (t)))

8-

\sim \exp (0.081 t)

9-

1 / α \approx 1 / γ_{1} - 2 \approx 6

10-

1 / α_{1} \leq 3

Formulas (html):

Correct Categorie: q-bio

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0602366

Formulas:

1-

R \overset{>}{\sim} 0.01 - 0.1

2-

2.5 \times 10^{- 4} M_{⊙}

3-

H (R) = 0.1 R

4-

M_{BH} = 3.5 \times 10^{6} M_{⊙}

5-

Σ_{*} (R) \propto R^{- 1}

6-

t_{var} \sim 0.04 - 0.4 year {(R / 0.1 pc)}^{3 / 2} M_{8}^{- 1 / 2}

7-

\dot{M} \equiv \frac{\int 𝑑 Σ 4 π R^{2} ρ v_{R}}{\int 𝑑 Σ},

8-

\dot{M} \sim 4 π R^{2} ρ v_{R}

9-

\sim 1 - 10 M_{⊙}

10-

M_{c} = Σ_{c} π R_{c}^{2}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0310855

Formulas:

1-

J H K_{S}

2-

[M_{V}, {(V - K)}_{0}]

3-

[V, V - K]

4-

A_{K} = 0.116 A_{V}

5-

J H K_{S}

6-

σ_{J H K}

7-

σ_{J H K}^{t o t}

8-

(J - K_{B B}) = [(J - K_{S}) - (- 0.011 \pm 0.005)] / (0.972 \pm 0.006)

9-

K_{B B} = [K_{S} - (- 0.044 \pm 0.003)] - (0.000 \pm 0.005) (J - K_{B B}) .

10-

Δ M_{L K} = - 7.60 {(σ_{π} / π)}^{2} - 47.20 {(σ_{π} / π)}^{4} .

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/0712.1287

Formulas:

1-

R_{1}^{2} \geq R_{2}^{2} \dots \geq R_{D}^{2}

2-

𝐆 = \sum_{i = 1}^{N} ({\vec{x}}_{i}^{2} 𝟏 - {\vec{x}}_{i} {\vec{x}}_{i})

3-

⟨ R_{i}^{2} ⟩ = r_{i} N^{2 ν} (1 + a_{i} N^{- θ} + b_{i} N^{- 1} + \dots)

4-

A_{N} = R_{D}^{2} / R_{1}^{2}

5-

⟨ A_{N} ⟩ = 1

6-

⟨ A_{\infty} ⟩ ≅ 0.4

7-

Δ_{D} = \frac{D}{D - 1} \frac{T r 𝐐^{2}}{{(T r 𝐆)}^{2}}

8-

𝐐 = 𝐆 - \bar{R^{2}} 𝐈

9-

\bar{R^{2}} = D^{- 1} T r 𝐆

10-

Δ_{2} = \frac{{(R_{1}^{2} - R_{2}^{2})}^{2}}{{(R_{1}^{2} + R_{2}^{2})}^{2}}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/cond-mat/0109232

Formulas:

1-

N (x) d x \propto x^{- α} d x,

2-

r (x) = \int_{x}^{\infty} N (y) 𝑑 y \propto x^{1 - α} .

3-

x (n) \propto n^{1 / (1 - α)} .

4-

1 / (1 - α)

5-

N (x) = N_{0} x^{c - 1} \exp (- λ x^{c})

6-

N (x) = b / {(c + x)}^{α}

7-

N (x) = N_{0} \exp_{q^{'}} (- a x) \equiv N_{0} {[1 - (1 - q^{'}) a x]}^{1 / (1 - q^{'})},

8-

N_{0} = b c^{- α}

9-

q^{'} = 1 + 1 / α

10-

1 - (1 - q^{'}) a x < 0

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1509.03370

Formulas:

1-

\begin{matrix} \partial_{t} x_{1} (t) = F (x_{1} (t)) + U_{1} (x_{1}, x_{2}) \\ \partial_{t} x_{2} (t) = F (x_{2} (t)) + U_{2} (x_{1}, x_{2}) \end{matrix}

2-

x_{1} (t)

3-

x_{2} (t)

4-

x_{-} (t) \equiv | x_{1} (t) - x_{2} (t) | \to 0

5-

ϕ_{1} (t)

6-

ϕ_{2} (t)

7-

x_{1} (t)

8-

x_{2} (t)

9-

ϕ_{-} (t) \equiv | ϕ_{1} (t) - ϕ_{2} (t) | \to 0

10-

x_{-} (t)

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/2009.06682

Formulas:

1-

𝑱 = σ 𝑬 - \frac{c}{4 π λ^{2}} (𝑨 + \frac{ϕ_{0}}{2 π} \nabla θ),

2-

ω τ_{n} ≪ 1

3-

curl curl 𝑯 + \frac{1}{λ^{2}} 𝑯 = - \frac{4 π σ}{c^{2}} \frac{\partial 𝑯}{\partial t} .

4-

𝑯 = H_{0} \hat{𝒙} e^{- i ω t}

5-

- \frac{\partial^{2} H_{x}}{\partial z^{2}} + \frac{1}{λ^{2}} H_{x} = - \frac{4 π σ}{c^{2}} \frac{\partial H_{x}}{\partial t} .

6-

H_{x} (z) e^{- i ω t}

7-

H_{x} = H_{0} e^{- k z - i ω t}, k^{2} = \frac{1}{λ^{2}} - \frac{2 i}{δ^{2}},

8-

δ = c / \sqrt{2 π σ ω}

9-

𝑬 = - \partial_{t} 𝑯 / c

10-

E_{y} = (i ω / c k) H_{0} e^{- k z - i ω t}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/0811.2749

Formulas:

1-

Φ - \int_{0}^{ϖ} Ω^{2} (ϖ^{'}) ϖ^{'} 𝑑 ϖ^{'}

2-

Φ - \frac{Ω^{2} ϖ^{2}}{2} + \int_{0}^{ϖ} ϖ^{', 2} Ω (ϖ^{'}) \frac{d Ω (ϖ^{'})}{d ϖ^{'}} 𝑑 ϖ^{'}

3-

x s i n θ

4-

Ω (ϖ) = \frac{Ω_{o}}{1 + {(a ϖ)}^{β}}

5-

e^{i [ω t + m ϕ]}

6-

δ (\frac{d \vec{v}}{d t}) = δ (\frac{\partial \vec{v}}{\partial t} + [\vec{v} \cdot ▽] \vec{v}) = ▽ (δ ϕ) + (\frac{δ ρ}{ρ^{2}}) ▽ P - \frac{1}{ρ} ▽ δ P

7-

\vec{v} = v \hat{ϕ} = Ω r s i n (θ) \hat{ϕ} .

8-

ϖ = r s i n (θ)

9-

δ \vec{v} = \frac{\partial \vec{ξ}}{\partial t} + (\vec{v} \cdot ▽) \vec{ξ} - (\vec{ξ} \cdot ▽) \vec{v} .

10-

σ^{2} ξ_{r} + 2 i σ Ω ξ_{ϕ} s i n θ - ϖ s i n θ [ξ_{r} \frac{\partial Ω^{2}}{\partial r} + \frac{ξ_{θ}}{r} \frac{\partial Ω^{2}}{\partial θ}] - \frac{\partial δ p}{\partial r} = - A g_{r} (▽ \cdot \vec{ξ})

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/2003.02302

Formulas:

1-

G := (V, E)

2-

(L_{e}, Q_{e}), e \in E

3-

P := {e_{0}, e_{1}, \dots, e_{n - 1}}

4-

λ_{e}^{i} \in Q_{e}, i \in {1, 2}

5-

(0, 0, 0)

6-

(0, 0, 0)

7-

(0, 1, 0)

8-

(1, 0, 0)

9-

(0, 0, 1)

10-

λ_{p_{i - 1}}^{0}

Formulas (html):

Correct Categorie: cs

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/1305.5212

Formulas:

1-

{(x, y)}_{1}

2-

{(x, y)}_{1}

3-

{(x, y)}_{2}

4-

{(x_{i}, y_{i})}_{i = 0}^{N}

5-

{(x_{i}, y_{i})}_{j}

6-

{[\begin{matrix} x_{i} \\ c t_{i} \end{matrix}]}_{k} = T (v_{k j}) {[\begin{matrix} x_{i} \\ c t_{i} \end{matrix}]}_{j}

7-

T (v_{k j}) = [\begin{matrix} T_{11} (v_{k j}) & T_{12} (v_{k j}) \\ T_{21} (v_{k j}) & T_{22} (v_{k j}) \end{matrix}]

8-

v_{j k} = - v_{k j}

9-

l i m_{v \to 0} T (v) = 1

10-

T (v) T (- v) = T (- v) T (v) = 1

Formulas (html):

Correct Categorie: physics

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/9909203

Formulas:

1-

Q ({He}^{+})

2-

Q (H^{0})

3-

Q ({He}^{+})

4-

Q (H^{0})

5-

Q ({He}^{+})

6-

Q (H^{0})

7-

Q ({He}^{+})

8-

Q (H^{0})

9-

Q ({He}^{0})

10-

Q (H^{0})

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1107.4163

Formulas:

1-

N (t) = λ

2-

c a n d i d a t e_{1}

3-

c a n d i d a t e_{2}

4-

c a n d i d a t e_{1}

5-

c a n d i d a t e_{2}

6-

p_{n} = p_{s} = p_{e} = p_{w} = \frac{1}{4} (1 - β)

7-

p a r e n t_{1}

8-

p a r e n t_{2}

9-

c h i l d_{1}

10-

c h i l d_{2}

Formulas (html):

Correct Categorie: cs

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/2002.05583

Formulas:

1-

e ≐ (u, v, p, t),

2-

ℱ_{i} \in ℕ^{h \times w \times 2}

3-

t_{k - 1} / t_{k}

4-

e_{k} = {u_{k}, v_{k}, p_{k}, t_{k}}

5-

ℱ_{i} = r o u n d (ℱ_{i} * t_{k - 1} / t_{k}), ℱ_{i} (u_{k}, v_{k}) = 255,

6-

t_{k - 1} / t_{k}

7-

N Z G E_{i} = \frac{1}{n_{i}^{g r i d}} \sum_{x = 1}^{p} \sum_{y = 1}^{q} e n t r o p y_{x, y}^{i},

8-

n_{i}^{g r i d}

9-

e n t r o p y_{x, y}^{i}

10-

e n t r o p y_{x, y} = - \sum_{z = 0}^{255} p r o b_{_{z}}^{x, y} \log p r o b_{_{z}}^{x, y},

Formulas (html):

Correct Categorie: cs

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/9605064

Formulas:

1-

Δ V_{T O}^{H B}

2-

Δ V_{T O}^{H B}

3-

d M_{V} / d [Fe/H] = + 0.16

4-

d M_{V} / d [Fe/H] = + 0.315

5-

d M_{V} / d [Fe/H] \equiv 0

6-

d M_{V} / d [Fe/H] = + 0.17

7-

d M_{V} / d [Fe/H] = + 0.35

8-

d M_{V} / d [Fe/H]

9-

d M_{V} / d [Fe/H] = + 0.20

10-

Δ V_{T O}^{H B}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1101.2892

Formulas:

1-

(J = 1 - 0)

2-

L_{CO} (M_{halo})

3-

L_{CO} (M)

4-

L_{CO} (M) = L_{0} {(M / M_{c})}^{b} {(1 + M / M_{c})}^{- d}

5-

z = 6, 7,

6-

L_{0} = 4.3 \times 10^{6}, 6.2 \times 10^{6}, 4.0 \times 10^{6}

7-

b = 2.4, 2.6, 2.8

8-

M_{c} = 3.5 \times 10^{11}, 3.0 \times 10^{11}, 2.0 \times 10^{11}

9-

d = 2.8, 3.4, 3.3

10-

L_{CO} (M)

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1801.10476

Formulas:

1-

O^{*} ({1.274}^{P})

2-

O^{*} ({1.325}^{P})

3-

O^{*} ({1.619}^{k})

4-

O^{*} (k^{k})

5-

n^{o (t)}

6-

G = (V, E)

7-

G = (V, E)

8-

O^{*} ({1.274}^{P})

9-

O^{*} ({1.325}^{P})

10-

O^{*} ({1.619}^{k})

Formulas (html):

Correct Categorie: cs

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/physics/0601135

Formulas:

1-

f^{e} (δ) = \frac{μ}{e^{- μ δ_{m}} - e^{- μ δ_{M}}} e^{- μ δ}

2-

[δ_{m}, δ_{M}]

3-

f^{p} (δ) = \frac{n + 1}{{(δ_{M} - δ_{m})}^{n + 1}} {(δ - δ_{m})}^{n}

4-

[δ_{m}, δ_{M}]

5-

f^{u} (δ) = 1 / (δ_{M} - δ_{m})

6-

f^{u} (δ)

7-

[δ_{m}, δ_{M}]

8-

(x_{o}, y_{o})

9-

(x_{d}, y_{d})

10-

{\begin{matrix} δ_{x} = x_{d} - x_{0} 𝚒𝚏 (x_{d} - x_{0}) \geq 0; \\ δ_{x} = L + (x_{d} - x_{0}) 𝚒𝚏 (x_{d} - x_{0}) < 0 . \end{matrix}

Formulas (html):

Correct Categorie: physics

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0001373

Formulas:

1-

μ_{b} (0)

2-

μ_{b} (0)

3-

μ_{b} (0)

4-

H_{0} = 50 km \sec^{- 1} {Mpc}^{- 1}

5-

I_{b u l g e} (r) = I_{b} (0) e^{- 2.303 b_{n} {(r / r_{e})}^{1 / n}},

6-

b_{n} = 0.8682 n - 0.1405

7-

I_{d} (r) = I_{d} (0) e^{- (r / r_{d})}

8-

I_{d} (0)

9-

⟨ μ_{b} (r_{e}) ⟩ = 2.57 \log r_{e} + 14.07

10-

μ_{b} (0)

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: hep-ph

Result: incorrect

Paper: https://arxiv.org/abs/hep-ph/0211047

Formulas:

1-

V (Φ) = - μ^{2} Φ^{†} Φ + λ {(Φ^{†} Φ)}^{2}

2-

m_{h}^{2} = 2 λ v^{2}

3-

e^{+} e^{-} \to h h Z

4-

e^{+} e^{-} \to (W W) ν \bar{ν} \to h h ν \bar{ν}

5-

\sqrt{s} < \sim 1

6-

h h ν \bar{ν}

7-

V (h^{3}) = (λ_{3} + δ λ_{3}) h h h

8-

λ_{3} (\equiv λ v)

9-

e^{+} e^{-} \to h h Z

10-

e^{+} e^{-} \to h h ν \bar{ν}

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/0204484

Formulas:

1-

ℱ = \int 𝑑 𝐱 [a {| ψ |}^{2} + \frac{b}{2} {| ψ |}^{4} + \frac{ℏ^{2}}{2 m^{*}} {| (\nabla - i \frac{e^{*}}{ℏ c} 𝐀) ψ |}^{2}],

2-

a = a_{0} (T - T_{c})

3-

(τ + i τ^{'}) (\frac{\partial}{\partial t} + i \frac{e^{*}}{ℏ} ϕ) ψ = - \frac{δ ℱ}{δ ψ^{*}} + ζ .

4-

⟨ ζ^{*} (𝐫, t) ζ (𝐫^{'}, t^{'}) ⟩ = 2 T τ δ (𝐫 - 𝐫^{'}) δ (t - t^{'}) .

5-

ψ (𝐫, t) = \int 𝑑 𝐫^{'} 𝑑 t^{'} G (𝐫, t; 𝐫^{'}, t^{'}) ζ (𝐫^{'}, t^{'})

6-

𝐣^{e} = - i \frac{e^{*} ℏ}{2 m^{*}} ⟨ ψ^{*} (\nabla - i \frac{e^{*}}{ℏ c} 𝐀) ψ ⟩ + c.c.,

7-

𝐣^{Q} = - \frac{ℏ^{2}}{2 m^{*}} ⟨ (\frac{\partial}{\partial t} - i \frac{e^{*}}{ℏ} ϕ) ψ^{*} (\nabla - \frac{i e^{*}}{ℏ c} 𝐀) ψ ⟩ + c.c.

8-

⟨ 𝐣 ⟩ = \frac{\int D ψ D \bar{ψ} {⟨ 𝐣 ⟩}_{ψ \bar{ψ} ϕ} e^{- S_{eff} (ψ, \bar{ψ}, ϕ)}}{\int D ψ D \bar{ψ} e^{- S_{eff} (ψ, \bar{ψ}, ϕ)}},

9-

S_{eff} (ψ, \bar{ψ}, ϕ)

10-

{⟨ 𝐣 ⟩}_{ψ \bar{ψ} ϕ}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/0802.0563

Formulas:

1-

q \in {(\sqrt{3} - 1) / 2, (3 - \sqrt{5}) / 2, \sqrt{2} - 1, (\sqrt{5} - 1) / 2}

2-

f : I R \to I R

3-

(- q / (1 - q), - q / (1 - q) + δ)

4-

(q / (1 - q) - δ, q / (1 - q))

5-

f (q x) = \frac{1}{4 q} [f (x - 1) + f (x + 1) + 2 f (x)],

6-

f : I R \to I R

7-

f (x) = 0 for ∣ x ∣ > \frac{q}{1 - q} .

8-

f : I R \to I R

9-

q \in {2^{- \frac{1}{n}} : n \in I N}

10-

q = 2^{- \frac{1}{n}}

Formulas (html):

Correct Categorie: math

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1104.5089

Formulas:

1-

1 \leq i \leq L - 1

2-

P_{t} (𝒞)

3-

\frac{d P_{t} (𝒞)}{d t} = \sum_{𝒞^{'}} M (𝒞, 𝒞^{'}) P_{t} (𝒞^{'}) .

4-

M (𝒞, 𝒞^{'})

5-

M (𝒞, 𝒞) = - \sum_{𝒞^{'} \neq 𝒞} M (𝒞^{'}, 𝒞)

6-

(τ_{1}, \dots, τ_{L})

7-

P (𝒞) = \frac{1}{Z_{L}} ⟨ α | \prod_{i = 1}^{L} (τ_{i} 𝐃 + (1 - τ_{i}) 𝐄) | β ⟩ .

8-

\frac{1}{β} | β ⟩

9-

\frac{1}{α} ⟨ α | .

10-

Z_{L} = ⟨ α | {(𝐃 + 𝐄)}^{L} | β ⟩ .

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1309.5699

Formulas:

1-

p = f (k)

2-

[x_{i}, p_{j}] = i \frac{\partial p_{i}}{\partial k_{j}}

3-

d^{3} p det | \frac{\partial k_{i}}{\partial p_{j}} | = d^{3} p \prod_{i} | \frac{\partial k_{i}}{\partial p_{j}} |,

4-

\frac{\partial k_{i}}{\partial p_{j}} = δ_{i j} e^{λ p_{i}^{2}}

5-

d g_{+} (ω) = \frac{d^{3} x d^{3} p}{{(2 π ℏ)}^{3}} e^{- λ p^{2}},

6-

p^{2} = p_{i} p^{i}

7-

G = ℏ = c = k_{B} \equiv 1

8-

S_{a c t} = \frac{1}{16 π} \int d^{4} x \sqrt{- g} (R - £),

9-

£ = (6 m / (2 | α | α^{2})) {(\sqrt{2 α^{2} F} / (1 + \sqrt{2 α^{2} F}))}^{5 / 2}

10-

d s^{2} = - f (r) d t^{2} + \frac{1}{f (r)} d r^{2} + r^{2} (d θ^{2} + s i n^{2} θ d φ^{2}),

Formulas (html):

Correct Categorie: gr-qc

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/1907.05512

Formulas:

1-

[3.6] - [4.5] > 0.5

2-

[4.5] - [3.6] > 0.5

3-

M_{U V} < - 21

4-

S / N_{350} < 1.5

5-

S / N_{140} \geq 6

6-

S / N_{160} \geq 4

7-

Y_{105} - J H_{140} > 1.5

8-

Y_{105} - J H_{140} > 5.33 \times (J H_{140} - H_{160}) + 0.7

9-

J H_{140} - H_{160} < 0.3

10-

S / N_{350} < 1.5

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0110186

Formulas:

1-

1.5 \sim < P \sim < 12

2-

P = P_{0} ≃ 76

3-

M_{2} \sim < 0.1 M_{⊙}

4-

t_{M} = - M_{2} / {\dot{M}}_{2}

5-

p (P) \propto \frac{{(- {\dot{M}}_{2})}^{α}}{| \dot{P} |} .

6-

t_{c o n t a c t}

7-

t_{c o n t a c t} \sim > t_{Gal} - t_{evol}

8-

- \dot{P} = G (P)

9-

d G / d P > 0

10-

M_{2} \sim > 0.3 M_{⊙}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/astro-ph/9910375

Formulas:

1-

< 0 \overset{''}{.} 1

2-

k T \approx 0.6 - 0.8

3-

H_{0} = 75 km s^{- 1} {Mpc}^{- 1}

4-

0 \overset{''}{.} 0455 {pixel}^{- 1}

5-

0 \overset{''}{.} 10 {pixel}^{- 1}

6-

10 ″ \times 10 ″

7-

H_{0} = 75 km s^{- 1} {Mpc}^{- 1}

8-

σ \approx 500 km s^{- 1}

9-

500 - 600 k m s^{- 1}

10-

\sim 0 \overset{''}{.} 2

Formulas (html):

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xref="S1.p4.1.m1.1.1.cmml"><mrow id="S1.p4.1.m1.1.1.2" xref="S1.p4.1.m1.1.1.2.cmml"><mi id="S1.p4.1.m1.1.1.2.2" xref="S1.p4.1.m1.1.1.2.2.cmml">k</mi><mo id="S1.p4.1.m1.1.1.2.1" xref="S1.p4.1.m1.1.1.2.1.cmml">⁢</mo><mi id="S1.p4.1.m1.1.1.2.3" xref="S1.p4.1.m1.1.1.2.3.cmml">T</mi></mrow><mo id="S1.p4.1.m1.1.1.1" xref="S1.p4.1.m1.1.1.1.cmml">≈</mo><mrow id="S1.p4.1.m1.1.1.3" xref="S1.p4.1.m1.1.1.3.cmml"><mn id="S1.p4.1.m1.1.1.3.2" xref="S1.p4.1.m1.1.1.3.2.cmml">0.6</mn><mo id="S1.p4.1.m1.1.1.3.1" xref="S1.p4.1.m1.1.1.3.1.cmml">-</mo><mn id="S1.p4.1.m1.1.1.3.3" xref="S1.p4.1.m1.1.1.3.3.cmml">0.8</mn></mrow></mrow></math>, <math><mrow id="S1.p5.4.m4.1.1" xref="S1.p5.4.m4.1.1.cmml"><msub id="S1.p5.4.m4.1.1.2" xref="S1.p5.4.m4.1.1.2.cmml"><mi id="S1.p5.4.m4.1.1.2.2" xref="S1.p5.4.m4.1.1.2.2.cmml">H</mi><mn id="S1.p5.4.m4.1.1.2.3" xref="S1.p5.4.m4.1.1.2.3.cmml">0</mn></msub><mo id="S1.p5.4.m4.1.1.1" xref="S1.p5.4.m4.1.1.1.cmml">=</mo><mrow id="S1.p5.4.m4.1.1.3" xref="S1.p5.4.m4.1.1.3.cmml"><mpadded width="+3.3pt" id="S1.p5.4.m4.1.1.3.2" xref="S1.p5.4.m4.1.1.3.2.cmml"><mn id="S1.p5.4.m4.1.1.3.2a" xref="S1.p5.4.m4.1.1.3.2.cmml">75</mn></mpadded><mo id="S1.p5.4.m4.1.1.3.1" xref="S1.p5.4.m4.1.1.3.1.cmml">⁢</mo><mpadded width="+3.3pt" id="S1.p5.4.m4.1.1.3.3" xref="S1.p5.4.m4.1.1.3.3.cmml"><mi id="S1.p5.4.m4.1.1.3.3a" xref="S1.p5.4.m4.1.1.3.3.cmml">km</mi></mpadded><mo id="S1.p5.4.m4.1.1.3.1a" xref="S1.p5.4.m4.1.1.3.1.cmml">⁢</mo><mpadded width="+3.3pt" id="S1.p5.4.m4.1.1.3.4" xref="S1.p5.4.m4.1.1.3.4.cmml"><msup id="S1.p5.4.m4.1.1.3.4a" xref="S1.p5.4.m4.1.1.3.4.cmml"><mi mathvariant="normal" id="S1.p5.4.m4.1.1.3.4.2" xref="S1.p5.4.m4.1.1.3.4.2.cmml">s</mi><mrow id="S1.p5.4.m4.1.1.3.4.3" xref="S1.p5.4.m4.1.1.3.4.3.cmml"><mo id="S1.p5.4.m4.1.1.3.4.3.1" xref="S1.p5.4.m4.1.1.3.4.3.1.cmml">-</mo><mn id="S1.p5.4.m4.1.1.3.4.3.2" xref="S1.p5.4.m4.1.1.3.4.3.2.cmml">1</mn></mrow></msup></mpadded><mo id="S1.p5.4.m4.1.1.3.1b" xref="S1.p5.4.m4.1.1.3.1.cmml">⁢</mo><msup id="S1.p5.4.m4.1.1.3.5" xref="S1.p5.4.m4.1.1.3.5.cmml"><mi id="S1.p5.4.m4.1.1.3.5.2" xref="S1.p5.4.m4.1.1.3.5.2.cmml">Mpc</mi><mrow id="S1.p5.4.m4.1.1.3.5.3" xref="S1.p5.4.m4.1.1.3.5.3.cmml"><mo id="S1.p5.4.m4.1.1.3.5.3.1" xref="S1.p5.4.m4.1.1.3.5.3.1.cmml">-</mo><mn id="S1.p5.4.m4.1.1.3.5.3.2" xref="S1.p5.4.m4.1.1.3.5.3.2.cmml">1</mn></mrow></msup></mrow></mrow></math>, <math><mrow id="S2.p2.1.m1.1.1" xref="S2.p2.1.m1.1.1.cmml"><mn id="S2.p2.1.m1.1.1.2" xref="S2.p2.1.m1.1.1.2.cmml">0</mn><mo id="S2.p2.1.m1.1.1.1" xref="S2.p2.1.m1.1.1.1.cmml">⁢</mo><mover id="S2.p2.1.m1.1.1.3.2" xref="S2.p2.1.m1.1.1.cmml"><mi mathvariant="normal" id="S2.p2.1.m1.1.1.3.2.2" xref="S2.p2.1.m1.1.1.3.1.cmml">.</mi><mrow id="S2.p2.1.m1.1.1.3.2.3" xref="S2.p2.1.m1.1.1.cmml"><mo mathsize="142%" stretchy="false" id="S2.p2.1.m1.1.1.3.2.3.1" xref="S2.p2.1.m1.1.1.3.1.cmml">′</mo><mo mathsize="142%" stretchy="false" id="S2.p2.1.m1.1.1.3.2.3.2" xref="S2.p2.1.m1.1.1.3.1.cmml">′</mo></mrow></mover><mo id="S2.p2.1.m1.1.1.1a" xref="S2.p2.1.m1.1.1.1.cmml">⁢</mo><mpadded width="+3.3pt" id="S2.p2.1.m1.1.1.4" xref="S2.p2.1.m1.1.1.4.cmml"><mn id="S2.p2.1.m1.1.1.4a" xref="S2.p2.1.m1.1.1.4.cmml">0455</mn></mpadded><mo id="S2.p2.1.m1.1.1.1b" xref="S2.p2.1.m1.1.1.1.cmml">⁢</mo><msup id="S2.p2.1.m1.1.1.5" xref="S2.p2.1.m1.1.1.5.cmml"><mi id="S2.p2.1.m1.1.1.5.2" xref="S2.p2.1.m1.1.1.5.2.cmml">pixel</mi><mrow id="S2.p2.1.m1.1.1.5.3" xref="S2.p2.1.m1.1.1.5.3.cmml"><mo id="S2.p2.1.m1.1.1.5.3.1" xref="S2.p2.1.m1.1.1.5.3.1.cmml">-</mo><mn id="S2.p2.1.m1.1.1.5.3.2" xref="S2.p2.1.m1.1.1.5.3.2.cmml">1</mn></mrow></msup></mrow></math>, <math><mrow id="S2.p2.2.m2.1.1" xref="S2.p2.2.m2.1.1.cmml"><mn id="S2.p2.2.m2.1.1.2" xref="S2.p2.2.m2.1.1.2.cmml">0</mn><mo id="S2.p2.2.m2.1.1.1" xref="S2.p2.2.m2.1.1.1.cmml">⁢</mo><mover id="S2.p2.2.m2.1.1.3.2" xref="S2.p2.2.m2.1.1.cmml"><mi mathvariant="normal" id="S2.p2.2.m2.1.1.3.2.2" xref="S2.p2.2.m2.1.1.3.1.cmml">.</mi><mrow id="S2.p2.2.m2.1.1.3.2.3" xref="S2.p2.2.m2.1.1.cmml"><mo mathsize="142%" stretchy="false" id="S2.p2.2.m2.1.1.3.2.3.1" xref="S2.p2.2.m2.1.1.3.1.cmml">′</mo><mo mathsize="142%" stretchy="false" id="S2.p2.2.m2.1.1.3.2.3.2" xref="S2.p2.2.m2.1.1.3.1.cmml">′</mo></mrow></mover><mo id="S2.p2.2.m2.1.1.1a" xref="S2.p2.2.m2.1.1.1.cmml">⁢</mo><mpadded width="+3.3pt" id="S2.p2.2.m2.1.1.4" xref="S2.p2.2.m2.1.1.4.cmml"><mn id="S2.p2.2.m2.1.1.4a" xref="S2.p2.2.m2.1.1.4.cmml">10</mn></mpadded><mo id="S2.p2.2.m2.1.1.1b" xref="S2.p2.2.m2.1.1.1.cmml">⁢</mo><msup id="S2.p2.2.m2.1.1.5" xref="S2.p2.2.m2.1.1.5.cmml"><mi id="S2.p2.2.m2.1.1.5.2" xref="S2.p2.2.m2.1.1.5.2.cmml">pixel</mi><mrow id="S2.p2.2.m2.1.1.5.3" xref="S2.p2.2.m2.1.1.5.3.cmml"><mo id="S2.p2.2.m2.1.1.5.3.1" xref="S2.p2.2.m2.1.1.5.3.1.cmml">-</mo><mn id="S2.p2.2.m2.1.1.5.3.2" xref="S2.p2.2.m2.1.1.5.3.2.cmml">1</mn></mrow></msup></mrow></math>, <math><mrow id="S3.SS1.p1.4.m4.1.1" xref="S3.SS1.p1.4.m4.1.1.cmml"><mrow id="S3.SS1.p1.4.m4.1.1.2" xref="S3.SS1.p1.4.m4.1.1.2.cmml"><mrow id="S3.SS1.p1.4.m4.1.1.2.2" xref="S3.SS1.p1.4.m4.1.1.2.2.cmml"><mn id="S3.SS1.p1.4.m4.1.1.2.2.2" xref="S3.SS1.p1.4.m4.1.1.2.2.2.cmml">10</mn><mo id="S3.SS1.p1.4.m4.1.1.2.2.1" xref="S3.SS1.p1.4.m4.1.1.2.2.1.cmml">⁢</mo><mi mathvariant="normal" id="S3.SS1.p1.4.m4.1.1.2.2.3" xref="S3.SS1.p1.4.m4.1.1.2.2.3.cmml">″</mi></mrow><mo id="S3.SS1.p1.4.m4.1.1.2.1" xref="S3.SS1.p1.4.m4.1.1.2.1.cmml">×</mo><mn id="S3.SS1.p1.4.m4.1.1.2.3" xref="S3.SS1.p1.4.m4.1.1.2.3.cmml">10</mn></mrow><mo id="S3.SS1.p1.4.m4.1.1.1" xref="S3.SS1.p1.4.m4.1.1.1.cmml">⁢</mo><mi mathvariant="normal" id="S3.SS1.p1.4.m4.1.1.3" xref="S3.SS1.p1.4.m4.1.1.3.cmml">″</mi></mrow></math>, <math><mrow id="S3.SSx1.p2.1.m1.1.1" xref="S3.SSx1.p2.1.m1.1.1.cmml"><msub id="S3.SSx1.p2.1.m1.1.1.2" xref="S3.SSx1.p2.1.m1.1.1.2.cmml"><mi id="S3.SSx1.p2.1.m1.1.1.2.2" xref="S3.SSx1.p2.1.m1.1.1.2.2.cmml">H</mi><mn id="S3.SSx1.p2.1.m1.1.1.2.3" xref="S3.SSx1.p2.1.m1.1.1.2.3.cmml">0</mn></msub><mo id="S3.SSx1.p2.1.m1.1.1.1" xref="S3.SSx1.p2.1.m1.1.1.1.cmml">=</mo><mrow id="S3.SSx1.p2.1.m1.1.1.3" xref="S3.SSx1.p2.1.m1.1.1.3.cmml"><mpadded width="+3.3pt" id="S3.SSx1.p2.1.m1.1.1.3.2" xref="S3.SSx1.p2.1.m1.1.1.3.2.cmml"><mn id="S3.SSx1.p2.1.m1.1.1.3.2a" xref="S3.SSx1.p2.1.m1.1.1.3.2.cmml">75</mn></mpadded><mo id="S3.SSx1.p2.1.m1.1.1.3.1" xref="S3.SSx1.p2.1.m1.1.1.3.1.cmml">⁢</mo><mpadded width="+3.3pt" id="S3.SSx1.p2.1.m1.1.1.3.3" xref="S3.SSx1.p2.1.m1.1.1.3.3.cmml"><mi id="S3.SSx1.p2.1.m1.1.1.3.3a" xref="S3.SSx1.p2.1.m1.1.1.3.3.cmml">km</mi></mpadded><mo id="S3.SSx1.p2.1.m1.1.1.3.1a" xref="S3.SSx1.p2.1.m1.1.1.3.1.cmml">⁢</mo><mpadded width="+3.3pt" id="S3.SSx1.p2.1.m1.1.1.3.4" xref="S3.SSx1.p2.1.m1.1.1.3.4.cmml"><msup id="S3.SSx1.p2.1.m1.1.1.3.4a" xref="S3.SSx1.p2.1.m1.1.1.3.4.cmml"><mi mathvariant="normal" id="S3.SSx1.p2.1.m1.1.1.3.4.2" xref="S3.SSx1.p2.1.m1.1.1.3.4.2.cmml">s</mi><mrow id="S3.SSx1.p2.1.m1.1.1.3.4.3" xref="S3.SSx1.p2.1.m1.1.1.3.4.3.cmml"><mo id="S3.SSx1.p2.1.m1.1.1.3.4.3.1" xref="S3.SSx1.p2.1.m1.1.1.3.4.3.1.cmml">-</mo><mn id="S3.SSx1.p2.1.m1.1.1.3.4.3.2" xref="S3.SSx1.p2.1.m1.1.1.3.4.3.2.cmml">1</mn></mrow></msup></mpadded><mo id="S3.SSx1.p2.1.m1.1.1.3.1b" xref="S3.SSx1.p2.1.m1.1.1.3.1.cmml">⁢</mo><msup id="S3.SSx1.p2.1.m1.1.1.3.5" xref="S3.SSx1.p2.1.m1.1.1.3.5.cmml"><mi id="S3.SSx1.p2.1.m1.1.1.3.5.2" xref="S3.SSx1.p2.1.m1.1.1.3.5.2.cmml">Mpc</mi><mrow id="S3.SSx1.p2.1.m1.1.1.3.5.3" xref="S3.SSx1.p2.1.m1.1.1.3.5.3.cmml"><mo id="S3.SSx1.p2.1.m1.1.1.3.5.3.1" xref="S3.SSx1.p2.1.m1.1.1.3.5.3.1.cmml">-</mo><mn id="S3.SSx1.p2.1.m1.1.1.3.5.3.2" xref="S3.SSx1.p2.1.m1.1.1.3.5.3.2.cmml">1</mn></mrow></msup></mrow></mrow></math>, <math><mrow id="S4.p9.1.m1.1.1" xref="S4.p9.1.m1.1.1.cmml"><mi id="S4.p9.1.m1.1.1.2" xref="S4.p9.1.m1.1.1.2.cmml">σ</mi><mo id="S4.p9.1.m1.1.1.1" xref="S4.p9.1.m1.1.1.1.cmml">≈</mo><mrow id="S4.p9.1.m1.1.1.3" xref="S4.p9.1.m1.1.1.3.cmml"><mpadded width="+3.3pt" id="S4.p9.1.m1.1.1.3.2" xref="S4.p9.1.m1.1.1.3.2.cmml"><mn id="S4.p9.1.m1.1.1.3.2a" xref="S4.p9.1.m1.1.1.3.2.cmml">500</mn></mpadded><mo id="S4.p9.1.m1.1.1.3.1" xref="S4.p9.1.m1.1.1.3.1.cmml">⁢</mo><mpadded width="+3.3pt" id="S4.p9.1.m1.1.1.3.3" xref="S4.p9.1.m1.1.1.3.3.cmml"><mi id="S4.p9.1.m1.1.1.3.3a" xref="S4.p9.1.m1.1.1.3.3.cmml">km</mi></mpadded><mo id="S4.p9.1.m1.1.1.3.1a" xref="S4.p9.1.m1.1.1.3.1.cmml">⁢</mo><msup id="S4.p9.1.m1.1.1.3.4" xref="S4.p9.1.m1.1.1.3.4.cmml"><mi mathvariant="normal" id="S4.p9.1.m1.1.1.3.4.2" xref="S4.p9.1.m1.1.1.3.4.2.cmml">s</mi><mrow id="S4.p9.1.m1.1.1.3.4.3" xref="S4.p9.1.m1.1.1.3.4.3.cmml"><mo id="S4.p9.1.m1.1.1.3.4.3.1" xref="S4.p9.1.m1.1.1.3.4.3.1.cmml">-</mo><mn id="S4.p9.1.m1.1.1.3.4.3.2" xref="S4.p9.1.m1.1.1.3.4.3.2.cmml">1</mn></mrow></msup></mrow></mrow></math>, <math><mrow id="S4.p9.4.m4.1.1" xref="S4.p9.4.m4.1.1.cmml"><mn id="S4.p9.4.m4.1.1.2" xref="S4.p9.4.m4.1.1.2.cmml">500</mn><mo id="S4.p9.4.m4.1.1.1" xref="S4.p9.4.m4.1.1.1.cmml">-</mo><mrow id="S4.p9.4.m4.1.1.3" xref="S4.p9.4.m4.1.1.3.cmml"><mn id="S4.p9.4.m4.1.1.3.2" xref="S4.p9.4.m4.1.1.3.2.cmml">600</mn><mo id="S4.p9.4.m4.1.1.3.1" xref="S4.p9.4.m4.1.1.3.1.cmml">⁢</mo><mi mathvariant="normal" id="S4.p9.4.m4.1.1.3.3" xref="S4.p9.4.m4.1.1.3.3.cmml">k</mi><mo id="S4.p9.4.m4.1.1.3.1a" xref="S4.p9.4.m4.1.1.3.1.cmml">⁢</mo><mpadded width="+3.3pt" id="S4.p9.4.m4.1.1.3.4" xref="S4.p9.4.m4.1.1.3.4.cmml"><mi mathvariant="normal" id="S4.p9.4.m4.1.1.3.4a" xref="S4.p9.4.m4.1.1.3.4.cmml">m</mi></mpadded><mo id="S4.p9.4.m4.1.1.3.1b" xref="S4.p9.4.m4.1.1.3.1.cmml">⁢</mo><msup id="S4.p9.4.m4.1.1.3.5" xref="S4.p9.4.m4.1.1.3.5.cmml"><mi mathvariant="normal" id="S4.p9.4.m4.1.1.3.5.2" xref="S4.p9.4.m4.1.1.3.5.2.cmml">s</mi><mrow id="S4.p9.4.m4.1.1.3.5.3" xref="S4.p9.4.m4.1.1.3.5.3.cmml"><mo id="S4.p9.4.m4.1.1.3.5.3.1" xref="S4.p9.4.m4.1.1.3.5.3.1.cmml">-</mo><mn id="S4.p9.4.m4.1.1.3.5.3.2" xref="S4.p9.4.m4.1.1.3.5.3.2.cmml">1</mn></mrow></msup></mrow></mrow></math>, <math><mrow id="S4.p9.5.m5.1.1" xref="S4.p9.5.m5.1.1.cmml"><mi id="S4.p9.5.m5.1.1.2" xref="S4.p9.5.m5.1.1.2.cmml"/><mo id="S4.p9.5.m5.1.1.1" xref="S4.p9.5.m5.1.1.1.cmml">∼</mo><mrow id="S4.p9.5.m5.1.1.3" xref="S4.p9.5.m5.1.1.3.cmml"><mn id="S4.p9.5.m5.1.1.3.2" xref="S4.p9.5.m5.1.1.3.2.cmml">0</mn><mo id="S4.p9.5.m5.1.1.3.1" xref="S4.p9.5.m5.1.1.3.1.cmml">⁢</mo><mover id="S4.p9.5.m5.1.1.3.3.2" xref="S4.p9.5.m5.1.1.3.cmml"><mi mathvariant="normal" id="S4.p9.5.m5.1.1.3.3.2.2" xref="S4.p9.5.m5.1.1.3.3.1.cmml">.</mi><mrow id="S4.p9.5.m5.1.1.3.3.2.3" xref="S4.p9.5.m5.1.1.3.cmml"><mo mathsize="142%" stretchy="false" id="S4.p9.5.m5.1.1.3.3.2.3.1" xref="S4.p9.5.m5.1.1.3.3.1.cmml">′</mo><mo mathsize="142%" stretchy="false" id="S4.p9.5.m5.1.1.3.3.2.3.2" xref="S4.p9.5.m5.1.1.3.3.1.cmml">′</mo></mrow></mover><mo id="S4.p9.5.m5.1.1.3.1a" xref="S4.p9.5.m5.1.1.3.1.cmml">⁢</mo><mn id="S4.p9.5.m5.1.1.3.4" xref="S4.p9.5.m5.1.1.3.4.cmml">2</mn></mrow></mrow></math>

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0603337

Formulas:

1-

(h, Ω_{0}, λ_{0}) = (0.7, 0.3, 0.7)

2-

h \equiv H_{0} / 100 [{km s}^{- 1} {Mpc}^{- 1}]

3-

ϕ (m) \propto m^{- 2.35}

4-

(m_{l}, m_{u}) = (0.1 M_{⊙}, 100 M_{⊙})

5-

Q (a, λ)

6-

SFR = 1 M_{⊙} {yr}^{- 1}

7-

10^{6.5} – 10^{8}

8-

λ ≃ 20 – 30 μ

9-

z = 1 – 3

10-

SFR = 1.7 M_{⊙} {yr}^{- 1}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/2005.02417

Formulas:

1-

T_{90} = 2100 \pm 100

2-

E_{γ} = (6.2 \pm 0.3) \times 10^{49}

3-

L_{γ} \sim 3 \times 10^{46}

4-

E (B - V) \sim 0.13

5-

E (B - V) \sim 0.04

6-

F_{ν_{opt}}^{obs} = 5.5 \times 10^{- 27}

7-

F_{ν_{X}}^{obs} = 10^{- 27}

8-

h ν_{opt} = 3 eV

9-

h ν_{X} = 5 keV

10-

r \sim 3 \times 10^{16}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0009068

Formulas:

1-

ρ (r) \propto {(r / r_{s})}^{- 1} {(1 + r / r_{s})}^{- 2}

2-

ρ (r) \propto {(r / r_{s})}^{- 1} {(1 + r / r_{s})}^{- 3} .

3-

3 \times 10^{11} M_{⊙}

4-

3 \times 10^{15} M_{⊙}

5-

\sim 1000 km \sec^{- 1}

6-

\sim 3 \times 10^{12} h^{- 1} M_{⊙}

7-

ρ (r) \propto r^{- 0.2}

8-

ρ (r) \propto r^{- 1.5}

9-

M \geq 7.5 \times 10^{14} M_{⊙}

10-

Ω_{0} \equiv ρ_{0} / ρ_{c}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/2004.12432

Formulas:

1-

(n, c, h, w)

2-

(n, c, h, w)

3-

(k n, c, h / \sqrt{k}, w / \sqrt{k})

4-

k = 1, 2^{2}, 3^{2}, . .

5-

(h / \sqrt{k}, w / \sqrt{k})

6-

k = 1^{2}, 2^{2}, 3^{2}, \dots

7-

(k n, c, h / \sqrt{k}, w / \sqrt{k})

8-

\approx h_{o} \times w_{o}

9-

L_{s}^{r e g}

10-

= L_{a_{o} < A_{s}}^{t}

Formulas (html):

Correct Categorie: cs

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1307.0301

Formulas:

1-

400 - 5, 000 H z

2-

700 - 2, 200 H z

3-

150 m m \times 150 m m \times 40 m m .

4-

Δ P = - E Δ V / V

5-

E_{e f f}^{- 1} = E^{- 1} [1 - \frac{F ω_{o}^{2}}{ω^{2} - ω_{o}^{2} + i Γ ω}],

6-

f_{o} < f < \sqrt{1 + F} f_{o},

7-

f_{o} = ω_{o} / 2 π

8-

e^{i k x} = e^{- 2 π | n | x / λ},

9-

x = λ / 2 π

10-

40 m m \times 3 = 120 m m

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1210.7205

Formulas:

1-

θ = \cos^{- 1} ({\hat{z}}_{i} \cdot {\hat{z}}_{i + n})

2-

L = | r_{i + n} - r_{i} |

3-

L_{0} = \sum_{i}^{n - 1} | r_{i + 1} - r_{i} |

4-

F = k_{B} T N b V^{- 1},

5-

⟨ \cos θ_{i, j} ⟩ = e^{- L_{i, j} / A}

6-

⟨ \cos θ_{i, j} ⟩ ≅ 1 - \frac{1}{2} ⟨ θ_{i, j}^{2} ⟩ \equiv 1 - \frac{L_{i, j}}{A},

7-

⟨ θ_{i, j}^{2} ⟩

8-

A_{a p p}

9-

⟨ θ^{2} ⟩ = ⟨ θ_{s}^{2} ⟩ + ⟨ θ_{d}^{2} ⟩ .

10-

1 / A = 1 / A_{s} + 1 / A_{d}

Formulas (html):

Correct Categorie: q-bio

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1210.3029

Formulas:

1-

v \sim 0.05 - 0.1 c

2-

r ≲ 100 r_{g}

3-

r_{g} = G M / c^{2}

4-

r ≲ 10 r_{g}

5-

r \sim 100 r_{g}

6-

v_{esc} \sim 0.1 - 0.2 c

7-

v_{\infty} = f_{v} v_{esc} (r_{0})

8-

v_{esc} (r_{0}) = \sqrt{2 G M / r_{0}}

9-

n (r) = n_{0} {(r_{0} / r)}^{2}

10-

τ_{e} = σ_{T} \int_{r_{0}}^{\infty} n (r) 𝑑 r = σ_{T} n_{0} r_{0}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/cond-mat/9905233

Formulas:

1-

e V < 2 Δ / n

2-

T^{⋆} = Δ / 3

3-

(e / 3) (1 + 2 Δ / e V)

4-

S = 2 e I

5-

e V < 2 E_{g}

6-

e V = 2 E_{g} / n

7-

E_{g} \sim E_{T h} ≪ Δ

8-

e V < 2 Δ

9-

e V = 2 Δ / n

10-

e V ≪ 2 Δ

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/hep-ph/0007036

Formulas:

1-

f_{ζ} (x, t) \equiv \int \frac{d x^{-}}{4 π} ⟨ p^{'} | \bar{ψ} (0) γ^{+} ψ (x^{-}) | p ⟩ e^{i x p^{+} x^{-}},

2-

x^{\pm} = x^{0} \pm x^{3}

3-

p^{+} = p^{0} + p^{3}

4-

t \equiv q^{2} = {(p - p^{'})}^{2}

5-

ζ \equiv \frac{q^{+}}{p^{+}}

6-

f_{ζ} (x, t)

7-

f_{ζ} (x, t)

8-

f (x, t) \equiv f_{ζ = 0} (x, t)

9-

| Ψ ⟩ = \int \frac{d^{2} p_{⟂}}{\sqrt{2 E_{\vec{p}} {(2 π)}^{2}}} Ψ ({\vec{p}}_{⟂}) | \vec{p} ⟩ .

10-

F_{Ψ} (x, {\vec{b}}_{⟂}) \equiv \int \frac{d x^{-}}{4 π} ⟨ Ψ | \bar{ψ} (0^{-}, {\vec{b}}_{⟂}) γ^{+} ψ (x^{-}, {\vec{b}}_{⟂}) | Ψ ⟩ e^{i x p^{+} x^{-}},

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/0808.1791

Formulas:

1-

O (N_{f} α_{s} a^{2})

2-

O ({(m a)}^{4})

3-

U^{H I S Q} = (F_{{asq}^{'}} \circ P_{U (3)} \circ F_{Fat7}) [U]

4-

U = \exp (g A)

5-

P_{U (3)}

6-

S U (3)

7-

U_{μ}^{Fat7R} (x) = (P_{U (3)} \circ F_{Fat7}) [U_{μ}] = e^{B_{μ} (x + \binom{1}{2} \hat{μ})}

8-

V_{r} = \frac{g^{r}}{r!} \sum_{i} f_{r; i}^{asq’} \bar{ψ} (x_{r; i}) B_{μ_{1}} (v_{r; i, 1}) \dots B_{μ_{r}} (v_{r; i, r}) Γ_{r; i} ψ (y_{r; i})

9-

F_{Fat7} [U] = M = H V

10-

V \in U (3)

Formulas (html):

Correct Categorie: hep-lat

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/1601.07905

Formulas:

1-

M_{vir} \sim 10^{12.1} M_{⊙}

2-

M_{star} \sim 10^{8} - 10^{10} M_{⊙}

3-

10^{8} - 10^{9} M_{⊙}

4-

M_{star} < 10^{5} M_{⊙}

5-

10^{5} < M_{star} / M_{⊙} < 10^{8}

6-

M_{star} > 10^{8} M_{⊙}

7-

M_{star} ≲ 10^{5} M_{⊙}

8-

M_{vir} \sim 10^{12.1 \pm 0.03} M_{⊙}

9-

M_{vir} = 10^{12.1 \pm 0.03} M_{⊙}

10-

3.0 \times 10^{5} M_{⊙} h^{- 1}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1309.2180

Formulas:

1-

τ \sim {(g / J)}^{N - 1} / κ

2-

x_{l, r} > 0

3-

x_{l, r} < 0

4-

x_{l, r} = 0

5-

κ = {| V_{l, r} |}^{2} / v_{g}

6-

H = H_{MM} + H_{w} + H_{MM w}

7-

j = 1, \dots, N

8-

i = 1, \dots, K

9-

H_{MM} = H_{CCA} + ω_{q} σ^{+} σ^{-} + g (σ^{+} a_{s} + a_{s}^{†} σ^{-})

10-

H_{CCA} = ω_{c} \sum_{j = 1}^{N} a_{j}^{†} a_{j} - J \sum_{j = 1}^{N - 1} (a_{j}^{†} a_{j + 1} + hc) .

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: quant-ph

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0103513

Formulas:

1-

c o s (θ_{c}) = \frac{1}{β \cdot n}

2-

T_{l i v e}

3-

N_{\bar{p}}^{T O A}

4-

Flux(E) = \frac{1}{T_{l i v e} \times G \times Δ E \times T F} \times N_{\bar{p}}^{T O A} (E),

5-

({12.6}_{- 4.8}^{+ 6.3}) \times 10^{- 3}

6-

({3.4}_{- 1.3}^{+ 1.8}) \times 10^{- 3}

7-

({1.1}_{- 0.8}^{+ 1.4}) \times 10^{- 3}

8-

({0.77}_{- 0.60}^{+ 1.23}) \times 10^{- 3}

9-

({1.3}_{- 0.5}^{+ 0.6}) \times 10^{- 4}

10-

({2.3}_{- 0.9}^{+ 1.2}) \times 10^{- 4}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Run 10953582 (Agent054)