Run 11299135

Paper: https://arxiv.org/abs/1011.2390

Formulas:

1-

u v b y - β

2-

d i s t a n c e (d)

3-

d (p c) = 10^{(V - M_{V} + 5 - A_{V}) / 5} = 10^{(K - M_{K} + 5 - A_{K}) / 5}

4-

{(J - H)}_{i n}

5-

{(H - K_{s})}_{i n}

6-

{(J - H)}_{i n}

7-

{(H - K_{s})}_{i n}

8-

σ_{{(J H)}_{o}}

9-

σ_{{(H K)}_{o}}

10-

{(J - H)}_{o}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0501665

Formulas:

1-

0 \overset{\circ}{.} 5

2-

1 \overset{\circ}{.} 6 \pm 1 \overset{\circ}{.} 3, 167 ° \pm 10 °

3-

14 ° \pm 2 °, 90 ° \pm 10 °

4-

- 0 \overset{\circ}{.} 2 \pm 0 \overset{\circ}{.} 3

5-

238 \overset{\circ}{.} 45 \pm 0 \overset{\circ}{.} 12

6-

α \to 180 ° - α

7-

90 ° < δ < 180 °

8-

d W / d t \sim 0

9-

\cos ρ \sin δ \cos Φ = \cos α

10-

d W / d t = 0

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/0802.1449

Formulas:

1-

E (t) = E_{0} f (t)

2-

ω_{B} = E_{0} e a / ℏ

3-

\vec{E} (t) = (E (t), 0, 0)

4-

\vec{B} (t) = (0, 0, B (t))

5-

B (t) = B_{0} g (t)

6-

ℋ = ε_{0} \sum_{m} ∣ m > < m ∣ - e a E_{0} f (t) \sum_{m} m ∣ m > < m ∣ +

7-

{V \sum_{m} \exp (- i γ / 2) | m + 1 > < m | + V \sum_{m} \exp (i γ / 2) | m > < m + 1 |}

8-

γ = γ (t) = 2 π \frac{Φ}{Φ_{0}} = 2 π β_{0} g (t)

9-

Φ = B_{0} a^{2} g (t)

10-

Φ_{0} = h c / e

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/astro-ph/9701141

Formulas:

1-

m - M = 14.13 \pm 0.11

2-

m - M = 14.49 \pm 0.06

3-

[F e / H] = - 1.17 \pm 0.01

4-

[F e / H] = - 1.4

5-

[F e / H] = - 1.3

6-

[F e / H] = - 1.9

7-

[α / F e] = 0.4

8-

[F e / H] = - 1.5

9-

R (t, m - M)

10-

(t, m - M)

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1102.1580

Formulas:

1-

{1, 2, \dots, k}

2-

(r_{1}^{t}, \dots, r_{k}^{t})

3-

I_{t} \in {1, \dots, k}

4-

γ \in [0; 1]

5-

η \in (O; \frac{1}{k}]

6-

{1, \dots, k}

7-

t = 1, 2, \dots

8-

G_{I_{t}} = G_{I_{t}} + \frac{r_{I_{t}}^{t}}{p_{I_{t}}^{t}}

9-

i \in {1, \dots, k}

10-

p_{i}^{t + 1} = (1 - γ) \frac{\exp (η G_{i})}{\sum_{j = 1}^{k} \exp (η G_{j})} + γ

Formulas (html):

Correct Categorie: cs

Guessed Categorie: cs

Result: correct

Paper: https://arxiv.org/abs/1706.07472

Formulas:

1-

E (t) \propto t^{- 2}

2-

λ \approx \sqrt{2} d^{2} / [ϕ (ℓ + 7.55 d + 2.02 d^{2} / ℓ)] \approx 1.65 cm

3-

⟨ E_{x} (0) ⟩ \approx 135 nJ

4-

⟨ E_{y} + E_{z} ⟩ / 2 \approx 90 nJ

5-

⟨ E_{rot} / 2 ⟩ \approx 64 nJ

6-

\approx 2 \dots 2.5 s

7-

J_{⟂} / J_{∥} \approx 70

8-

ξ (1 - ε^{2}) / λ

9-

E (t) = \frac{E_{0}}{{(1 + t / τ_{H})}^{2}},

10-

E (0) = E_{0}

Formulas (html):

Correct Categorie: physics

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/0805.1794

Formulas:

1-

5 \times 10^{6} L_{⊙}

2-

M > 100 M_{⊙}

3-

25 \times 10^{6} L_{⊙}

4-

\sim 3000 km s^{- 1}

5-

\sim 500 - 800 km s^{- 1}

6-

M_{⊙} {yr}^{- 1}

7-

d = D / (1 + \sqrt{η}) \approx 0.33 D

8-

ω = 270^{\circ} - ϕ

9-

20 km s^{- 1}

10-

\sim 360 km s^{- 1}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1101.1241

Formulas:

1-

H_{int} = \frac{e^{2}}{s^{3}} y_{1} y_{2},

2-

𝐬 = 𝐬 (t)

3-

y_{\pm} = \frac{y_{1} \pm y_{2}}{\sqrt{2}},

4-

H_{int \pm} = H_{int +} + H_{int -},

5-

H_{int \pm} = \pm \frac{1}{2} q y_{\pm}^{2}, q = \frac{e^{2}}{s^{3}} .

6-

Δ E = 2 \times 2 ℏ ω {| c (\infty) |}^{2},

7-

c (t) = - \frac{i}{2 ℏ} \int_{- \infty}^{t} 𝑑 t^{'} q ⟨ 2_{+} | y_{+}^{2} | 0_{+} ⟩ e^{2 i ω t^{'}},

8-

y_{\pm} = \sqrt{b} (a_{\pm} + a_{\pm}^{†}), b = \frac{ℏ}{2 m ω} .

9-

⟨ 2_{+} | y_{+}^{2} | 0_{+} ⟩ = b ⟨ 2_{+} | a_{+}^{†}^{2} | 0_{+} ⟩ = \sqrt{2} b .

10-

Δ E = 8 ℏ ω b^{2} {| I (\infty) |}^{2},

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: quant-ph

Result: correct

Paper: https://arxiv.org/abs/1903.09887

Formulas:

1-

H (X, Y)

2-

R_{X} \geq H (X | Y), R_{Y} \geq H (Y | X),

3-

R_{X} + R_{Y} \geq H (X, Y)

4-

R_{\cdot}, H (\cdot)

5-

R (X, Y) = R (Y) + R (X | Y)

6-

R (X, Y) = R (X) + R (Y | X)

7-

x \in {y - 4, y - 3, y - 2, y - 1, y, y + 1, y + 2, y + 3}

8-

R = H (Y) + H (X | Y)

9-

\tilde{x} \in {4, 5, 6, 7, 0, 1, 2, 3}

10-

\tilde{x} = (x - y) mod 8

Formulas (html):

Correct Categorie: cs

Guessed Categorie: cs

Result: correct

Paper: https://arxiv.org/abs/1910.03646

Formulas:

1-

δ t = (t_{1} - t_{2}) / 2

2-

τ = 3 π / 4

3-

δ Δ = Δ_{2} - Δ_{1}

4-

- \sum_{i} (t - {(- 1)}^{i} δ t \cos (2 τ)) a_{i}^{†} a_{i + 1} + H . c . +

5-

+ \frac{δ Δ}{2} \sin (2 τ) \sum_{i} {(- 1)}^{i} n_{i} + H_{i n t} .

6-

n_{i} = a_{i}^{†} a_{i}

7-

H_{int} = \frac{U}{2} \sum_{i} n_{i} (n_{i} - 1)

8-

H_{SSH} = - t \sum_{i} (1 + δ t {(- 1)}^{i}) a_{i}^{†} a_{i + 1} + H.c. + H_{int}

9-

t = \frac{t_{1} + t_{2}}{2}

10-

δ t = \frac{t_{1} - t_{2}}{2}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1305.0269

Formulas:

1-

{\dot{M}}_{e - \lim} \approx \frac{ϵ π F_{XUV} R_{XUV}^{3}}{G M_{p} K_{tide}}

2-

K_{tide} = (1 - \frac{3}{2 ξ} + \frac{1}{2 ξ^{3}})

3-

ξ = \frac{R_{Hill}}{R_{XUV}}

4-

J K^{- 1} g^{- 1}

5-

F_{th} \propto M_{core}^{2.4}

6-

t_{loss} = \frac{G M_{p}^{2}}{π ϵ R_{p}^{3} F_{XUV, E100}} \frac{F_{\oplus}}{F_{p}} \approx 12 G y r

7-

F_{XUV, E100} = 504

8-

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

9-

F_{th} \propto M_{core}^{2.4}

10-

F_{th} \sim \exp (- (t - 140 Myr) / 80 Myr) F_{\oplus} + 3.4 F_{\oplus}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1002.0135

Formulas:

1-

{(a; q)}_{\infty} = \prod_{k = 0}^{\infty} (1 - a q^{k}) and {(a; q)}_{n} = \frac{{(a; q)}_{\infty}}{{(a q^{n}; q)}_{\infty}}, n \in ℤ,

2-

\sum_{k = 0}^{\infty} \frac{{(- a q; q)}_{k}}{{(q; q)}_{k}} q^{(\binom{k + 1}{2})} = {(- a q^{2}; q^{2})}_{\infty} {(- q; q)}_{\infty},

3-

\sum_{m = 0}^{\infty} q^{m (m + 1) / 2} \frac{{(z; q)}_{m}}{{(q; q)}_{m}} α^{m} = {(z; q)}_{\infty} {(- α q; q)}_{\infty} \sum_{n = 0}^{\infty} \frac{z^{n}}{{(q; q)}_{n} {(- α q; q)}_{n}} .

4-

\sum_{n = 0}^{\infty} \frac{{(- a q; q)}_{n}}{{(q; q)}_{n}} b^{n} q^{(\binom{n + 1}{2})} = {(- b q; q)}_{\infty} \sum_{k = 0}^{\infty} \frac{{(a b)}^{k} q^{k (k + 1)}}{{(q; q)}_{k} {(- b q; q)}_{k}} .

5-

\sum_{n = 0}^{L} {[\binom{L}{n}]}_{q} {(- a q; q)}_{n} q^{n (n + 1) / 2} = \sum_{k = 0}^{L} {[\binom{L}{k}]}_{q^{2}} {(- q; q)}_{L - k} a^{k} q^{k (k + 1)} .

6-

λ = (λ_{1}, \dots, λ_{ℓ})

7-

| λ | = λ_{1} + \dots + λ_{ℓ}

8-

f (a, q)

9-

f (a, q) = \sum_{(α, β) \in P} a^{ℓ (β)} q^{| α | + | β |},

10-

(α, β) \in P

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/1107.1421

Formulas:

1-

d s^{2} = d t^{2} - {(R (t))}^{2} (d r^{2} + f_{k}^{2} (r) (d θ^{2} + \sin^{2} θ d ϕ^{2})),

2-

f_{k} = \sin r, r, \sinh r

3-

k = 1, 0, - 1

4-

d t = R d τ

5-

d s^{2} = {(R (t))}^{2} (d τ^{2} - d r^{2} - f_{k}^{2} (r) (d θ^{2} + \sin^{2} θ d ϕ^{2})) = {(R (t))}^{2} d {\tilde{s}}^{2},

6-

{\dot{R}}^{2} = - k + κ (ρ_{M} + ρ_{γ}) R^{2} + \frac{1}{3} Λ R^{2},

7-

κ = 8 π G / 3

8-

3 \dot{R} / R = - \dot{ρ} / (ρ + p) .

9-

ρ_{M} = A R^{- 3}, ρ_{γ} = B R^{- 4},

10-

{\dot{R}}^{2} = κ (A R^{- 1} + B R^{- 2}) + \frac{1}{3} Λ R^{2} .

Formulas (html):

Correct Categorie: gr-qc

Guessed Categorie: gr-qc

Result: correct

Paper: https://arxiv.org/abs/quant-ph/0602171

Formulas:

1-

A (z) .

2-

A B (z) = A (B (z)) .

3-

A B = B A

4-

A B \neq B A

5-

s p e c A

6-

s p e c A

7-

s p e c A

8-

P P = P,

9-

s p e c P

10-

P_{1} \land P_{2} = P_{1} P_{2}

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/gr-qc/0202043

Formulas:

1-

\partial_{t}, \partial_{z},

2-

d s^{2} = e^{- 2 U} (e^{2 K} (d r^{2} + d z^{2}) + r^{2} d ϕ^{2}) - e^{2 U} {(d t + A d ϕ)}^{2}

3-

S = \int d^{4} x \sqrt{- G} R

4-

e^{2 U} = r (a_{1} r^{n} + a_{2} r^{- n})

5-

e^{2 K - 2 U} = r^{\frac{n^{2} - 1}{2}}

6-

A = \frac{c}{n a_{2}} \frac{r^{n}}{(a_{1} r^{n} + a_{2} r^{- n})} + b

7-

c^{2} = - n^{2} a_{1} a_{2}

8-

n, c, a_{1}, a_{2}, b

9-

d s_{3 + 1}^{2} = G_{μ ν} d x^{μ} d x^{ν} = g_{a b} d x^{a} d x^{b} + e^{- 4 ϕ} d z^{2}

10-

e^{- 4 ϕ} = G_{z z} = r^{\frac{(n^{2} - 1)}{2}}

Formulas (html):

Correct Categorie: gr-qc

Guessed Categorie: gr-qc

Result: correct

Paper: https://arxiv.org/abs/1806.10101

Formulas:

1-

δ = R_{s} / R_{L} = 0.1

2-

x_{s} = ϕ_{s} / ϕ

3-

f (q, Δ t)

4-

f (q, Δ t)

5-

σ_{l^{(1)}} = 3.10

6-

σ_{l^{(2)}} = 1.98

7-

3 k_{B} T / 4 π R^{3}

8-

t_{0} = 6 π η R^{3} / k_{B} T

9-

i (x, y, t)

10-

Δ i (x, y, t + Δ t) = i (x, y, t + Δ t) - i (x, y, t)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/gr-qc/0701084

Formulas:

1-

d τ / d t ≲ 10^{- 20}

2-

d s^{2} = a^{- 2} d t^{2} - a^{2} (d x^{2} + d y^{2} + d z^{2})

3-

a (x^{i})

4-

T^{\hat{a} \hat{b}} = | \begin{matrix} A + B & 0 & 0 & 0 \\ 0 & - A & 0 & 0 \\ 0 & 0 & A & 0 \\ 0 & 0 & 0 & A \end{matrix} |

5-

a^{- 4} {| \nabla a |}^{2}

6-

- 2 a^{- 3} \nabla^{2} a

7-

\nabla^{2} a = 0

8-

\nabla^{2} a \neq 0

9-

- {(4 π a^{3})}^{- 1} \nabla^{2} a

10-

\nabla^{2} a \leq 0

Formulas (html):

Correct Categorie: gr-qc

Guessed Categorie: gr-qc

Result: correct

Paper: https://arxiv.org/abs/physics/9712044

Formulas:

1-

{(2^{4} 5! / π^{5})}^{1 / 4} (8 π^{4} / 9)

2-

108 π {(8 / 1843)}^{1 / 6}

3-

4 π^{5} / 9 + 37 / 36

4-

{(137^{2} + π^{2})}^{1 / 2}

5-

𝟕, 297 353 08 (33) \times 10^{- 3},

6-

𝟏𝟑𝟕, 035 989 5 (61) .

7-

1 / \sqrt{\frac{1}{2} (\frac{1}{2} + 1)} {(4 π)}^{2},

8-

α_{0} / 2 π (π^{2} - 2 π),

9-

2 π ρ,

10-

\frac{4}{3} π ρ^{3} .

Formulas (html):

Correct Categorie: physics

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1901.07683

Formulas:

1-

C = C N N_{c} (c_{i} | c_{r})

2-

C N N_{c}

3-

{c_{1}, \dots, c_{n}}

4-

s = {s_{1}, \dots, s_{N}}

5-

(c_{i}, s_{k})

6-

I_{i} = {I_{i 1}, \dots, I_{i n_{i}}}

7-

{\bar{c}}_{i} = {c_{1}, \dots, c_{i - 1}, c_{i + 1}, \dots, c_{n}}

8-

s = {s_{1}, \dots, s_{N}}

9-

s = S (c_{i}, {\bar{c}}_{i})

10-

s_{k} \in s, k = 1, \dots, N

Formulas (html):

Correct Categorie: cs

Guessed Categorie: cs

Result: correct

Paper: https://arxiv.org/abs/1206.4353

Formulas:

1-

[[x_{1}, x_{2}], [x_{3}, x_{4}, x_{5}], x_{6}]

2-

[x_{1}, x_{2}, x_{2}, x_{2}]

3-

γ_{1} = x_{1}, γ_{k} = [γ_{k - 1}, x_{k}] = [x_{1}, \dots, x_{k}] .

4-

γ_{k} (G)

5-

δ_{0} = x_{1}, δ_{k} = [δ_{k - 1} (x_{1}, \dots, x_{2^{k - 1}}), δ_{k - 1} (x_{2^{k - 1} + 1}, \dots, x_{2^{k}})] .

6-

δ_{k} (G) = G^{(k)}

7-

w = [x, y]

8-

{a, b, c, \dots}

9-

a, b, c, \dots

10-

x^{- 1} x^{a}

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/1609.07752

Formulas:

1-

γ = B e^{- A T}

2-

γ = B e^{- A T}

3-

D = T / γ \propto k_{B} T e^{A T}

4-

T_{N} = T_{s} / N

5-

U (x) = {\begin{matrix} U_{0} (\frac{x}{L_{0}} + 1), & if - L_{0} \leq x \leq 0; \\ U_{0} (- \frac{x}{L_{0}} + 1), & if 0 \leq x \leq L_{0} . \end{matrix}

6-

γ \frac{d x}{d t} = - \partial_{x} U - (1 - ϵ) γ^{- 1} \partial_{x} (γ T) + \sqrt{2 k_{B} γ T} ξ (t)

7-

γ = γ (x)

8-

\frac{(1 - ϵ)}{γ (x)} \frac{\partial}{\partial x} (γ (x) T (x))

9-

γ \frac{d x}{d t}

10-

- \partial_{x} U (x) + \sqrt{2 k_{B} γ (x) T} ξ (t) .

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/0902.0246

Formulas:

1-

5.9 \leq \lg N_{e} \leq 7.1

2-

\lg N_{e} \approx 6.3

3-

5.9 \leq \lg N_{e} < 6.3

4-

6.3 \leq \lg N_{e} < 6.5

5-

6.5 \leq \lg N_{e} \leq 7.1

6-

\lg N_{e} \approx 6.3

7-

5.9 \leq \lg N_{e} \leq 7.1

8-

Δ (R) = \frac{\bar{n} (R)}{{\bar{N}}_{μ} (N_{e})},

9-

\bar{n} (R)

10-

{\bar{N}}_{μ} (N_{e})

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1705.07698

Formulas:

1-

0 \overset{''}{.} 20

2-

12 + \log_{10} ([O / H]) = 8.0 \pm 0.1

3-

5 ″ \times 5 ″

4-

0 \overset{''}{.} 1

5-

2 ″ \times 2 ″

6-

r^{'} i^{'} z^{'}

7-

0 \overset{''}{.} 6

8-

0 \overset{''}{.} 8

9-

0 \overset{''}{.} 146

10-

m_{F110W} = 23.675 (12)

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/quant-ph/9810042

Formulas:

1-

| ψ ⟩ \to | ψ ⟩ | ψ ⟩

2-

c_{0} | 0 ⟩ + c_{1} | 1 ⟩

3-

| ψ ⟩ \to {| ψ ⟩}_{a} + {| ψ ⟩}_{b}

4-

m = - 1 / 2

5-

[\begin{matrix} | a_{0} ⟩ | d_{0} ⟩ \\ | a_{0} ⟩ | d_{1} ⟩ \\ | a_{1} ⟩ | d_{0} ⟩ \\ | a_{1} ⟩ | d_{1} ⟩ \end{matrix}] \begin{matrix} \to \\ \to \\ ↘ ↗ \end{matrix} [\begin{matrix} | a_{0} ⟩ | d_{0} ⟩ \\ | a_{0} ⟩ | d_{1} ⟩ \\ | a_{1} ⟩ | d_{1} ⟩ \\ | a_{1} ⟩ | d_{0} ⟩ \end{matrix}] .

6-

c_{00} | a_{0} ⟩ | d_{0} ⟩ + c_{01} | a_{0} ⟩ | d_{1} ⟩ + c_{10} | a_{1} ⟩ | d_{0} ⟩ + c_{11} | a_{1} ⟩ | d_{1} ⟩

7-

(c_{0} | a_{0} ⟩ + c_{1} | a_{1} ⟩) + (c_{0} | b_{0} ⟩ + c_{1} | b_{1} ⟩)

8-

c_{0} | a_{0} ⟩ + c_{1} | a_{1} ⟩

9-

| a_{i} ⟩ + | b_{i} ⟩

10-

ℏ g^{2} / Δ

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: quant-ph

Result: correct

Paper: https://arxiv.org/abs/physics/0209092

Formulas:

1-

{| V_{p} |}^{8 / 3}

2-

K + K + K \to K_{2} + K

3-

K_{3} \propto a_{s}^{4}

4-

V_{p} = - lim_{k \to 0} \frac{\tan δ_{p} (k)}{k^{3}},

5-

δ_{p} (k)

6-

V_{p} = a_{p}^{3}

7-

{| V_{p} |}^{8 / 3}

8-

V = v (r_{12}) + v (r_{23}) + v (r_{31})

9-

v (r_{i j}) = D {sech}^{2} (\frac{r_{i j}}{r_{0}})

10-

v (r_{i j}) = \frac{D}{1 + {(\frac{r_{i j}}{r_{0}})}^{6}} .

Formulas (html):

Correct Categorie: physics

Guessed Categorie: physics

Result: correct

Paper: https://arxiv.org/abs/0806.3124

Formulas:

1-

S U (2)

2-

N = V^{1 / 2} / a

3-

\partial_{μ} A_{μ}^{a} (x) = Λ^{a} (x),

4-

Λ^{a} (x)

5-

A_{μ}^{a} (x)

6-

1, 2, \dots, N_{c}^{2} - 1

7-

𝒵 = \int 𝒟 Λ \exp {- \frac{1}{2 ξ} \int d^{d} x \sum_{a} {[Λ^{a} (x)]}^{2}} 𝒵 (Λ),

8-

\partial_{μ} A_{μ}^{a} (x) = 0 .

9-

Λ^{a} (x)

10-

Λ^{a} (x)

Formulas (html):

Correct Categorie: hep-lat

Guessed Categorie: hep-lat

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0406415

Formulas:

1-

3 \times 10^{7} M_{⊙}

2-

5 \times 10^{9} M_{⊙}

3-

10^{43} e r g / s

4-

10^{46} e r g / s

5-

L_{b o l} < 10^{43} e r g / s

6-

G M_{B H} / c^{2}

7-

\sim 10^{44} e r g / s

8-

< 10^{43} e r g / s

9-

α_{O X} = 0.9 - 1.1

10-

L_{b o l} > 10^{43} e r g / s

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/hep-ph/0003046

Formulas:

1-

H \to Z Z^{(*)}

2-

W W^{(*)}

3-

t \bar{t} H

4-

H \to c \bar{c}

5-

H \to τ^{+} τ^{-}

6-

Z H \to ℓ^{+} ℓ^{-} X

7-

H \to b \bar{b}, c \bar{c}, τ^{+} τ^{-}, g g, and W W^{*}

8-

e^{+} e^{-} \to t \bar{t} ν \bar{ν}

9-

δ M_{W}, δ m_{t}

10-

δ m_{H} / m_{H}

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: hep-ex

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/0612497

Formulas:

1-

H = - \sum_{i, j; i \neq j} J_{i j} {\vec{e}}_{i} \cdot {\vec{e}}_{j} .

2-

J (\vec{q})

3-

J (\vec{q})

4-

\sqrt{2} a_{MgO} = 5.63

5-

M^{bcc} = 1.75 μ_{B}

6-

M_{Fe} \approx 2.2 μ_{B}

7-

J_{0} = \sum_{i \neq 0} J_{0 i}

8-

k_{B} T_{C}^{MF} = 2 J_{0} / 3

9-

T_{C}^{MF} (E)

10-

T_{C}^{MF} (E)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/0805.1189

Formulas:

1-

0.05 < M < 0.075 M_{⊙}

2-

μ_{α} = Δ α \cos δ / Δ t

3-

μ_{δ} = Δ δ / Δ t

4-

50 < μ_{α} < 180

5-

- 160 < μ_{δ} < 80

6-

δ_{cp} = 6^{\circ} {53.4}^{'}

7-

\cos D = \sin δ \sin δ_{cp} + \cos δ \cos δ_{cp} \cos DA

8-

\cos θ = \frac{\sin δ_{cp} - \sin δ \cos D}{\cos δ \sin D}

9-

θ_{o b s}

10-

{}^{- 1}{\frac{7}{100}} \sim 4^{\circ}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/2004.14966

Formulas:

1-

10 - 100 µ s

2-

E_{F} = E_{V} + 4.0 eV

3-

Φ_{B} = E_{F} - E_{V}

4-

χ = E_{C} - E_{vac} \approx - 1.3 eV

5-

Φ_{B} = E_{F} - E_{V} = - 0.15 eV

6-

2 mm \times 2 mm \times 0.5 mm

7-

[N] < 5 ppb \hat{=} 9 × 10^{14} {cm}^{- 3}

8-

R a < 5 nm

9-

5 × 10^{9} ions / cm^{2}

10-

p < 10^{- 6} mbar

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0312386

Formulas:

1-

Y_{a t m o s}

2-

T_{e f f}

3-

T_{e f f}

4-

T_{e f f}

5-

Y_{a t m o s}

6-

T_{e f f}

7-

Y_{a t m o s}

8-

T_{e f f}

9-

T_{e f f}

10-

T_{e f f}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/hep-ph/9911251

Formulas:

1-

U {(1)}_{R}

2-

U {(1)}_{R}

3-

S U (2) \times U {(1)}_{R}

4-

U {(1)}_{R}

5-

S U (2)

6-

S U (2)

7-

U {(1)}_{R}

8-

S U (2) \times U {(1)}_{R}

9-

U {(1)}_{R}

10-

S U (2)

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: hep-ph

Result: correct

Paper: https://arxiv.org/abs/1810.00181

Formulas:

1-

f (x) = (d_{0} + d_{1} x + d_{2} x^{2} + \dots + d_{k - 1} x^{k - 1}) mod p

2-

d_{1}, d_{2}, \dots, d_{k - 1}

3-

y_{i} = f (x_{i}), 1 \leq i \leq n

4-

0 < x_{1} < x_{2} \dots < x_{n} < p

5-

f (x) \approx (d_{0} (1 + x + x^{2} + \dots + x^{k - 1})) mod p .

6-

d_{1}, d_{2}, â € ¦, d_{k - 1}

7-

y \in Y \cap S^{c}

8-

X^{'} ⟵ X + y

9-

r ⟵ r + | X^{'} \cap S | + | X^{'} \cap S^{c} \cap {(X \cup Y)}^{c} |

10-

S ⟵ X^{'} \cup S

Formulas (html):

Correct Categorie: cs

Guessed Categorie: cs

Result: correct

Paper: https://arxiv.org/abs/1502.05523

Formulas:

1-

V_{\bar{p}} ≃ - 650

2-

- (100 - 300)

3-

[- i \vec{α} \vec{\nabla} + β (m_{j} + S_{j}) + V_{j}] ψ_{j}^{α} = ϵ_{j}^{α} ψ_{j}^{α}, j = N, \bar{p},

4-

S_{j} = g_{σ j} σ, V_{j} = g_{ω j} ω_{0} + g_{ρ j} ρ_{0} τ_{3} + e_{j} \frac{1 + τ_{3}}{2} A_{0}

5-

g_{σ j}, g_{ω j}, g_{ρ j}

6-

\begin{matrix} (- △ + m_{σ}^{2} + g_{2} σ + g_{3} σ^{2}) σ & = - g_{σ N} ρ_{S N} - g_{σ \bar{p}} ρ_{S \bar{p}}, \\ (- △ + m_{ω}^{2} + d ω_{0}^{2}) ω_{0} & = g_{ω N} ρ_{V N} + g_{ω \bar{p}} ρ_{V \bar{p}}, \\ (- △ + m_{ρ}^{2}) ρ_{0} & = g_{ρ N} ρ_{I N} + g_{ρ \bar{p}} ρ_{I \bar{p}}, \\ - △ A_{0} & = e_{N} ρ_{Q N} + e_{\bar{p}} ρ_{Q \bar{p}}, \end{matrix}

7-

ρ_{S j}, ρ_{V j}, ρ_{I j}

8-

m_{σ}, m_{ω}, m_{ρ}

9-

ξ \in ⟨ 0, 1 ⟩

10-

g_{σ \bar{p}} = ξ g_{σ N}, g_{ω \bar{p}} = - ξ g_{ω N}, g_{ρ \bar{p}} = ξ g_{ρ N} .

Formulas (html):

Correct Categorie: nucl-th

Guessed Categorie: nucl-th

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0607186

Formulas:

1-

\frac{d ω}{d t}

2-

\frac{d ω}{d t}

3-

13.3 m a g

4-

\frac{d ω}{d t}

5-

ω = 25.4857 d^{- 1}

6-

ω = 25.4867 d^{- 1}

7-

\frac{d ω}{d t} = - 9.90 \cdot 10^{- 7} d^{- 2}

8-

ω = 17.22004 d^{- 1}

9-

ω = 17.21960 d^{- 1}

10-

\frac{d ω}{d t} = - 5.47 \cdot 10^{- 7} d^{- 2}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1403.7078

Formulas:

1-

𝐁 = B \hat{z}

2-

Φ = [3 \sqrt{3} b^{2} B / 2] / ϕ_{0}

3-

(B x) \hat{y}

4-

R_{B} = 1 / Φ

5-

| k_{x} | < π / 3 b R_{B}

6-

| k_{y} | < π / \sqrt{3} b

7-

[\begin{matrix} ϵ_{11} (𝐪, ω) & ϵ_{12} (𝐪, ω) \\ ϵ_{21} (𝐪, ω) & ϵ_{22} (𝐪, ω) \end{matrix}] = [\begin{matrix} ϵ_{0} - \sum_{l} V_{1 l} (q) P_{l 1}^{(1)} (𝐪, ω) & - \sum_{l} V_{1 l} (q) P_{l 2}^{(1)} (𝐪, ω) \\ - \sum_{l} V_{2 l} (q) P_{l 1}^{(1)} (𝐪, ω) & ϵ_{0} - \sum_{l} V_{2 l} (q) P_{l 2}^{(1)} (𝐪, ω) \end{matrix}],

8-

V_{l l^{'}} (q) = v_{q} e^{- q | l - l^{'} | c}

9-

v_{q} = 2 π

10-

P_{l l^{'}}^{(1)} (𝐪, ω)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1302.0659

Formulas:

1-

A = 1.0 \times 10^{- 6}

2-

m_{⟂} (r)

3-

m_{1}^{x} (t)

4-

m_{2}^{x} (t)

5-

m_{tot}^{x} (t) = m_{1}^{x} (t) + m_{2}^{x} (t)

6-

m_{diff}^{x} (t) = m_{1}^{x} (t) - m_{2}^{x} (t)

7-

0.5 < I_{1} < 10

8-

m_{tot}^{x} (t) = m_{1}^{x} (t) + m_{2}^{x} (t)

9-

1.5 < I_{1} < 7

10-

P (I_{1})

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1309.1660

Formulas:

1-

SO (n + 1)

2-

SO (n + 1)

3-

SO (n + 1)

4-

SO (n + 1)

5-

SO (n + 1)

6-

SO (n, 1)

7-

SO (n - 1, 2)

8-

SO (n + 1)

9-

I S O (n)

10-

SO (n + 1)

Formulas (html):

Correct Categorie: gr-qc

Guessed Categorie: math

Result: incorrect

Paper: https://arxiv.org/abs/1005.2284

Formulas:

1-

ω_{p} = 1.367 \times 10^{17}

2-

ω_{c} = 1.22 \times 10^{14}

3-

n_{g} = ω (d n / d ω) + n

4-

v_{1} \approx v_{2} = V e^{j w t}

5-

E_{y, m a x}

6-

S_{2} = i_{2}^{*} v_{2} \sim i_{2}^{*} v = - j w q_{02} V e^{- j φ_{2}}

7-

P = P_{1} + P_{2}

8-

C_{1} \approx 4 C_{2}

9-

f_{1, 2} = \sqrt{1 - R_{1, 2}^{2} C_{1, 2} / (4 L_{1, 2})} / \sqrt{L_{1, 2} C_{1, 2}} \approx 10^{2}

10-

Q_{1} = R_{1}^{- 1} / \sqrt{L_{1} C_{1}} = 1.6

Formulas (html):

Correct Categorie: physics

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/1005.3996

Formulas:

1-

S_{a b} (k) = δ_{a b} + \frac{\sqrt{n_{a} n_{b}}}{n} \frac{Z_{a} Z_{b}}{{\bar{Z}}^{2}} [S_{i i}^{1 C} (k) - 1] .

2-

S_{i i}^{1 C}

3-

\bar{Z} = \sum_{a} n_{a} Z_{a} / \sum_{a} n_{a}

4-

S_{e e}^{t o t} (𝐤, ω)

5-

F_{e e}^{tot} (𝐤, t) = ⟨ ϱ_{e}^{tot} (𝐤, t) ϱ_{e}^{tot} (- 𝐤, 0) ⟩ .

6-

ϱ_{e}^{tot} (𝐤, t) = \sum_{a}^{N} ϱ_{a}^{c} (𝐤, t) + ϱ^{f} (𝐤, t)

7-

\sum_{a \neq b} ⟨ ϱ_{a}^{c} (𝐤, t) ϱ_{b}^{c} (- 𝐤, 0) ⟩

8-

S_{e e}^{t o t} (ω)

9-

\bar{Z} S_{e e} (ω) + 2 \sum_{a} \sqrt{\bar{Z} x_{a}} f_{a} S_{e a} (ω)

10-

+ \sum_{a} Z_{a}^{c} x_{a} \int 𝑑 ω^{'} {\tilde{S}}_{a}^{c e} (ω - ω^{'}) S_{a}^{S} (ω^{'})

Formulas (html):

Correct Categorie: physics

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/1304.7768

Formulas:

1-

T \approx 100 M \approx 35

2-

M_{BH} = 4.3 \times 10^{6} M_{⊙}

3-

T = 17 m i n = 48 M

4-

T = 28 m i n = 79 M

5-

T = 23 m i n = 65 M,

6-

T = 45 m i n = 127 M

7-

T = 2.5 - 3 h r s \approx 470 M

8-

T = 6 - 9 m i n = 17 - 25 M

9-

T \approx 170 M = 1

10-

(r, θ, ϕ)

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1101.0119

Formulas:

1-

0 ν β β

2-

0 ν β β

3-

0 ν β β

4-

0 ν β β

5-

0 ν β β

6-

0 ν β β

7-

(n, n^{'} γ)

8-

0 ν β β

9-

(n, n^{'} γ)

10-

0 ν β β

Formulas (html):

Correct Categorie: nucl-ex

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/quant-ph/0103105

Formulas:

1-

α P_{s} + (1 - α) I / 4

2-

⟨ χ | M | χ ⟩

3-

\Pr (a_{i}, b_{j} | A, B, ρ) = \int 𝑑 λ ω^{ρ} (λ) \Pr (a_{i}, b_{j} | A, B, λ),

4-

ω^{ρ} (λ)

5-

\Pr (a_{i}, b_{j} | A, B, λ) = \Pr (a_{i} | A, λ) \Pr (b_{j} | B, λ) .

6-

{| ψ ⟩}_{A B}

7-

{| ψ ⟩}_{A D}

8-

(x_{1}, x_{2})

9-

x_{1}, x_{2} \in {0, 1, 2, 3}

10-

\begin{matrix} B_{0} = (\begin{matrix} 0 & 0 \\ 1 & 1 \\ 2 & 2 \\ 3 & 3 \end{matrix}) & B_{1} = (\begin{matrix} 0 & 3 \\ 1 & 0 \\ 2 & 1 \\ 3 & 2 \end{matrix}) \\ B_{2} = (\begin{matrix} 0 & 2 \\ 1 & 3 \\ 2 & 0 \\ 3 & 1 \end{matrix}) & B_{3} = (\begin{matrix} 0 & 1 \\ 1 & 2 \\ 2 & 3 \\ 3 & 0 \end{matrix}) . \end{matrix}

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: quant-ph

Result: correct

Paper: https://arxiv.org/abs/gr-qc/0703071

Formulas:

1-

\frac{d}{d t} (\frac{m}{M_{P}}) = - \frac{a_{n}}{t_{P}} {(\frac{m}{M_{P}})}^{- \frac{2}{n - 3}},

2-

a_{n} \approx 10^{- 3}

3-

m (t) = m_{0} {(1 - \frac{t}{t_{0}})}^{\frac{n - 3}{n - 1}},

4-

0 \leq t \leq t_{0}

5-

t_{0} = \frac{n - 3}{n - 1} {(\frac{m_{0}}{M_{P}})}^{\frac{n - 1}{n - 3}} \frac{t_{P}}{a_{n}} .

6-

0 \leq t \leq t_{0}

7-

(u, v, θ_{1}, \dots, θ_{n - 2})

8-

d s^{2} = - 2 g (u, v) d u d v + r^{2} (u, v) d Ω_{n - 2}^{2},

9-

d Ω_{n - 2}^{2}

10-

g (u, v)

Formulas (html):

Correct Categorie: gr-qc

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/nlin/0006016

Formulas:

1-

S U (2)

2-

A f (1)

3-

g = (\begin{matrix} a & b \\ 0 & 1 \end{matrix}), a > 0, b \in 𝐑 .

4-

A f (1)

5-

a = \exp (θ_{1}), b = θ_{2}

6-

c_{12}^{2} = - c_{21}^{2} = 1

7-

J_{μ} := g^{- 1} \partial_{μ} g

8-

(\partial_{μ} θ_{1}, e^{- θ_{1}} \partial_{μ} θ_{2})

9-

I [g] = \int d^{2} x η^{μ ν} L (J_{μ}, J_{ν}),

10-

J_{μ} := (g^{- 1} \partial_{μ} g) \in ℒ (G),

Formulas (html):

Correct Categorie: nlin

Guessed Categorie: hep-th

Result: incorrect

Paper: https://arxiv.org/abs/1804.03754

Formulas:

1-

h_{gap} \sim 1 - 3

2-

h_{gap} \sim 1 - 3

3-

F (h, r) = 2 π r h γ - α h^{3} ε E^{2} .

4-

α = {12 \ln [(2 h / r) - 1]}^{- 1}

5-

α = {\ln [(2 h / r) - 7]}^{- 1}

6-

F (h, r)

7-

h_{c} = \sqrt{\frac{2 π r_{\min} γ}{3 ε α}} \frac{1}{E}

8-

W (E) = F [h_{c} (E), r_{\min}] = \frac{2^{5 / 2} {(π r_{\min} γ)}^{3 / 2}}{3^{3 / 2} {(α ε)}^{1 / 2} E}

9-

W (U) = W_{0} \frac{U_{0}}{U}

10-

W_{0} = 2 π γ r_{\min} H, and U_{0} = \sqrt{\frac{8 π r_{\min} γ}{27 α ε}} .

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/2008.10548

Formulas:

1-

{\begin{matrix} x_{1}, \dots, x_{K} \end{matrix}}

2-

Y \in {\begin{matrix} 0, 1 \end{matrix}}

3-

Y = {\begin{matrix} 0, & iff y_{k} = 0, f o r k \in {\begin{matrix} 1 \dots K \end{matrix}} \\ 1, & o t h e r w i s e \end{matrix}}

4-

Z_{m} = \max_{k \in {0 \dots K}} (h_{k m}),

5-

Z_{m} = \frac{1}{K} \sum_{k = 1}^{K} h_{k m},

6-

k \in {0 \dots K}

7-

Z_{m} = g (\sum_{k = 1}^{K} a_{k m} e_{k m}),

8-

k \in {0 \dots K}

9-

C_{k} = C (X_{k}) = \frac{1}{σ (X_{k}) + ϵ},

10-

Z_{m} = h_{k^{*} m} w h e r e k^{*} = a r g m a x (C_{k} \cdot h_{k m}),

Formulas (html):

Correct Categorie: cs

Guessed Categorie: cs

Result: correct

Paper: https://arxiv.org/abs/1607.04006

Formulas:

1-

D / 2 π \approx 2.87

2-

B_{z} = D / γ_{e} \approx 1024

3-

ℋ (^{14} NV)

4-

= D S_{z}^{2} + γ_{e} B_{z} S_{z} - γ_{n} B_{z} I_{z} + Q I_{z}^{2}

5-

+ A_{∥} S_{z} I_{z} + A_{⟂} (S_{x} I_{x} + S_{y} I_{y}),

6-

ℋ (^{15} NV)

7-

= D S_{z}^{2} + γ_{e} B_{z} S_{z} - γ_{n}^{'} B_{z} I_{z}^{'}

8-

+ A_{∥}^{'} S_{z} I_{z}^{'} + A_{⟂}^{'} (S_{x} I_{x}^{'} + S_{y} I_{y}^{'}),

9-

𝐒 = (S_{x}, S_{y}, S_{z})

10-

A_{∥} / 2 π = - 2.14

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0412312

Formulas:

1-

1.4 \times 10^{8} M_{⊙}

2-

P = ρ v^{2}

3-

\sim 2 \times 10^{8} M_{⊙}

4-

10^{- 4} {cm}^{- 3}

5-

Σ (R) = \frac{M_{d}}{2 π R_{d}^{2}} exp (- R / R_{d}),

6-

z_{d} \sim \frac{1}{5} R_{d}

7-

ρ_{d} (R, z) = \frac{Σ (R)}{2 z_{d}} {sech}^{2} (z / z_{d}) .

8-

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

9-

\sim 10^{- 4} - 10^{- 5} {cm}^{- 3}

10-

n_{h} \sim < 3 \times 10^{- 4} {cm}^{- 3}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Run 11299135 (Agent441)