Run 11369308

Paper: https://arxiv.org/abs/1412.3176

Formulas:

1-

\sim 10 μ m

2-

R / r = 3 .

3-

v = 53.76 μ m / s

4-

R / r = 3 .

5-

ℓ_{m}^{L, R} (t) = ℓ_{m 0}^{L, R} + A_{m}^{L, R} c o s (ω t + φ_{m}^{L, R})

6-

ℓ_{s a}^{L, R} (t) = ℓ_{s a 0}^{L, R} + A_{s a}^{L, R} c o s (ω t + φ_{s a}^{L, R})

7-

ℓ_{s b}^{L, R} (t) = ℓ_{s b 0}^{L, R} + A_{s b}^{L, R} c o s (ω t + φ_{s b}^{L, R})

8-

ℓ_{m 0}^{L, R}

9-

ℓ_{s a 0}^{L, R}

10-

ℓ_{s b 0}^{L, R}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/nucl-th/0304060

Formulas:

1-

T (T + 1.025)

2-

T (T + x)

3-

T (T + 1)

4-

H = H_{0} - G 𝐏^{†} \cdot 𝐏 + \frac{κ 𝐓^{2}}{2}, H_{0} = \sum_{k σ τ} ϵ_{k} a_{k σ τ}^{†} a_{k σ τ} .

5-

a_{k σ τ}

6-

R = H - λ A_{v} - μ T_{z},

7-

⟨ A_{v} ⟩ = 2 Ω

8-

A_{v} / 2 \pm T_{z}

9-

𝚫 = - G ⟨ 𝐏 ⟩

10-

A_{v} = ⟨ A_{v} ⟩

Formulas (html):

Correct Categorie: nucl-th

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0011511

Formulas:

1-

M_{b h} = σ_{s p h}^{5} f_{c o l d} α,

2-

f_{c o l d}

3-

M_{b h} \propto σ_{s p h}^{2}

4-

r_{c r} = G M_{b h} / σ_{s p h}^{2} .

5-

σ_{s p h}

6-

v_{r o t}^{2} = G M_{b h} r_{d}^{- 1} .

7-

t_{v i s} = r_{d}^{2} / ν .

8-

ν = R_{c r}^{- 1} v_{r o t} r_{d},

9-

R_{c r} \approx 100 - 1000

10-

t_{v i s} = G M_{b h} R_{c r} σ_{s p h}^{- 3},

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/astro-ph/9705144

Formulas:

1-

M \sim 10^{5} M_{⊙}

2-

T \sim > 10^{4}

3-

10^{2 - 3} M_{⊙}

4-

3 - 8 M_{⊙}

5-

M > 10^{20} M_{⊙}

6-

M_{tot} \sim > 10^{8} {[(1 + z) / 10]}^{- 3 / 2} M_{⊙}

7-

σ_{8 h^{- 1}}

8-

M = 4 M_{⊙}

9-

σ_{8 h^{- 1}}

10-

f_{esc} (z)

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1310.6579

Formulas:

1-

{(m - M)}_{V} = 5 \log (d / 10) + A_{V}

2-

{(m - M)}_{V} = 12.3

3-

E (B - V) = 0.45

4-

{(m - M)}_{V} = 12.2

5-

E (B - V) = 0.30

6-

{(m - M)}_{V} = 14.25

7-

E (B - V) = 0.35

8-

{(m - M)}_{V} = 13.0

9-

E (B - V) = 0.55

10-

{(m - M)}_{V} = 14.0

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-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/math/9909095

Formulas:

1-

S O (4)

2-

G_{K} \subset S O (4)

3-

S O (4) / G_{K}

4-

ℳ_{K} = S O (4) / G_{K}

5-

G_{K} \subset S O (4)

6-

O (2) \times O (2)

7-

ℳ_{K} = S O (4) / G_{K}

8-

K = K_{p, q}

9-

(z^{p}, z^{q}) / \sqrt{2}

10-

S^{1} \subset S O (4)

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/cond-mat/9601149

Formulas:

1-

l \equiv \sqrt{ℏ / e B}

2-

𝒪 (l^{2} e^{2} / ϵ a^{3})

3-

𝒪 (d^{2} e^{2} / ϵ a^{3})

4-

ℏ^{2} / M a^{2}

5-

⟨ 𝒓_{e}, 𝒓_{h} | 𝑷 ⟩ = \frac{1}{\sqrt{2 π A}} e^{i P . (r_{e} + r_{h}) / 2} e^{i r_{e} \times r_{h} . \hat{z} / 2} e^{- {(r_{e} - r_{h} - r_{P})}^{2} / 4},

6-

𝒓_{P} \equiv \hat{𝒛} \times 𝑷 l^{2} / ℏ

7-

𝑨 (𝒓) = 𝑩 \times 𝒓 / 2

8-

e^{2} / 4 π ϵ ϵ_{0} l

9-

V_{d}^{e h} (𝒓) = - \frac{e^{2}}{4 π ϵ ϵ_{0}} \frac{1}{\sqrt{{| 𝒓 |}^{2} + d^{2}}} .

10-

E_{d} (𝑷)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/nucl-ex/0206005

Formulas:

1-

\bar{p} p \to \bar{Λ} Λ

2-

\bar{p} p \to \bar{Λ} Λ

3-

\bar{p} p \to \bar{Y} Y

4-

\bar{p} p \to \bar{Λ} Λ

5-

K^{*} (892)

6-

\bar{p} p \to \bar{Λ} Λ

7-

⟨ {\vec{𝝈}}_{Λ} \cdot \hat{𝒏} ⟩ = \begin{matrix} P_{n} + D_{n n} \cdot \hat{𝐧} \\ 1 + A_{n} \cdot \hat{𝐧} \end{matrix} .

8-

⟨ {\vec{𝝈}}_{\bar{Λ}} \cdot \hat{𝒏} ⟩ = \begin{matrix} P_{n} + K_{n n} \cdot \hat{𝐧} \\ 1 + A_{n} \cdot \hat{𝐧} \end{matrix} .

9-

⟨ \vec{𝝈} \cdot \hat{𝒏} ⟩

10-

{\vec{𝒑}}_{\bar{p}} \times {\vec{𝒑}}_{\bar{Λ}}

Formulas (html):

Correct Categorie: nucl-ex

Guessed Categorie: hep-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0103355

Formulas:

1-

μ = {0.34}^{''} y r^{- 1}, θ = 264^{\circ}

2-

q (= M_{2} / M_{1})

3-

V_{d} s i n i

4-

V_{r, b} = γ \pm V_{d} s i n i + K_{1} s i n ϕ,

5-

V_{r, b} = \frac{\int_{r_{1}, b_{1}}^{r_{2}, b_{2}} I (v) v 𝑑 v}{\int_{r_{1}, b_{1}}^{r_{2}, b_{2}} I (v) 𝑑 v},

6-

γ - V_{d} s i n i = - 490

7-

K_{1} = 8 \pm 1

8-

q = \frac{m_{2}}{m_{1}}

9-

\frac{q}{{(1 + q)}^{1 / 2}} = (\frac{K_{1}}{V_{d} s i n i}) {(\frac{a}{r_{d}})}^{1 / 2},

10-

V_{d} s i n i

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/cond-mat/0409516

Formulas:

1-

[1 \bar{1} 0]

2-

[1 \bar{1} 0]

3-

[1 \bar{1} 0]

4-

[1 \bar{1} 0]

5-

(a_{0} / 4) ⟨ 1 \bar{1} 0 ⟩

6-

[1 \bar{1} 0]

7-

(a_{0} / 4) [1 \bar{1} 0]

8-

(a_{0} / 4) [1 \bar{1} 0]

9-

(a_{0} / 4) [1 \bar{1} 0]

10-

(a_{0} / 4) [1 \bar{1} 0]

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/cond-mat/9608040

Formulas:

1-

2 nm \times 2 nm

2-

2 \times 10^{18} {cm}^{- 3}

3-

1 \bar{1} 0

4-

2 \cdot 10^{10} {cm}^{- 2}

5-

3 nm \times 1 nm

6-

\frac{V_{g}}{V} = L \equiv \frac{t}{d} .

7-

f < 2 π R C

8-

C_{\exp} = C_{b} + C_{dot} .

9-

C_{b}^{'} = \frac{S V_{d}}{(V - V_{0}) d} [\sqrt{1 + \frac{V - V_{0}}{2 π V_{d}}} - 1],

10-

V_{d} = e^{2} N_{d} / κ

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/0912.3623

Formulas:

1-

v_{4} / {(v_{2})}^{2}

2-

v_{4} / {(v_{2})}^{2}

3-

\frac{d N}{d ϕ} \propto 1 + 2 v_{2} \cos (2 ϕ) + 2 v_{4} \cos (4 ϕ) + \dots

4-

v_{4} ≃ {(v_{2})}^{2}

5-

v_{4} = \frac{1}{2} {(v_{2})}^{2}

6-

ϵ_{P P} = \frac{\sqrt{{(σ_{y}^{2} - σ_{x}^{2})}^{2} + 4 σ_{x y}^{2}}}{σ_{x}^{2} + σ_{y}^{2}}

7-

σ_{x}^{2} = ⟨ x^{2} ⟩ - {⟨ x ⟩}^{2}

8-

σ_{x y} = ⟨ x y ⟩ - ⟨ x ⟩ ⟨ y ⟩

9-

w = (1 - x) + x N_{c o l l - n u c l e o n}

10-

N_{c o l l - n u c l e o n}

Formulas (html):

Correct Categorie: nucl-th

Guessed Categorie: nucl-th

Result: correct

Paper: https://arxiv.org/abs/nucl-th/0411078

Formulas:

1-

ρ^{2} \equiv \frac{1}{m M} \sum_{i < k} m_{i} m_{k} 𝐫_{𝐢𝐤}^{2} = (𝐱_{𝐣}^{2} + 𝐲_{𝐣}^{2}), 𝐫_{𝐢𝐤}^{2} = {(𝐫_{𝐢} - 𝐫_{𝐤})}^{2},

2-

(i, j, k)

3-

(1, 2, 3)

4-

E_{12, 3} = E - E_{12}

5-

v_{12, 3} = {(2 E_{12, 3} / μ_{12, 3})}^{1 / 2}

6-

t_{12} = ℏ / Γ_{12}

7-

\frac{d_{12, 3}}{R_{0}} = \frac{v_{12, 3} t_{12}}{R_{0}} = \frac{1}{Γ_{12}} \sqrt{\frac{2 ℏ^{2} (E - E_{12})}{μ_{12, 3} R_{0}^{2}}},

8-

T = \frac{1}{1 + \exp (2 S)} \approx \exp (- 2 S), S = \frac{1}{ℏ} \int_{ρ_{0}}^{ρ_{t}} d ρ \sqrt{2 m (V (ρ) - E)},

9-

V (ρ_{0}) = V (ρ_{t}) = E

10-

ρ_{0} = ρ_{t}, S = 0

Formulas (html):

Correct Categorie: nucl-th

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/9903174

Formulas:

1-

ρ = μ / ξ^{2}

2-

\bar{ξ} (\neq ξ)

3-

v_{r m s}

4-

d ξ / d a

5-

d \bar{ξ} / d a

6-

d ζ / d a

7-

γ = 1 / H ξ

8-

\bar{γ} = 1 / H \bar{ξ}

9-

ϵ = 1 / H ζ

10-

{d ζ / d t |}_{G B R} = \hat{C} Γ G μ

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/1204.1155

Formulas:

1-

M_{1, i} \sim 4.0

2-

M_{2, i} \sim 1.0

3-

M_{1, i} \sim 2.5 - 6.5 M_{⊙}

4-

M_{2, i} \sim 1.5 - 3.0 M_{⊙}

5-

P^{i} \sim 200 - 900

6-

M_{1, i} \sim 4.5

7-

M_{2, i} \sim 1.5

8-

0.6 - 1.1 \times 10^{- 3} {yr}^{- 1}

9-

1.8 \times 10^{- 3} {yr}^{- 1}

10-

M_{1, i} \sim 5.0

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/cond-mat/0703477

Formulas:

1-

e t a l .

2-

e t a l .

3-

M = χ_{H > 2 T} H + M_{0}

4-

χ_{H > 2 T}

5-

χ_{H > 2 T}

6-

χ_{H > 2 T} = \partial M / \partial H_{H > 2 T} = N C / (T - Θ) + χ_{0}

7-

C = {(g μ_{B})}^{2} S (S + 1) / 3 k_{B}

8-

Θ = - 16.3 \pm 3.0

9-

\times 10^{15} μ_{B} / T

10-

(p d σ) = - 1.3 \pm 0.2

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1702.06118

Formulas:

1-

{\tilde{R}}_{n} (i, j)

2-

{\tilde{R}}_{n} (i, j) = ϕ_{n} (i, j) \cdot g_{n} (i, j) + {\tilde{o}}_{n} (i, j) + η,

3-

ϕ_{n} (i, j)

4-

g (i, j)

5-

{\tilde{o}}_{n} (i, j)

6-

{\tilde{o}}_{n} (i, j) \equiv \tilde{o} (i, j)

7-

g {(i, j)}^{- 1}

8-

R_{n} (i, j) = ϕ_{n} (i, j) + o (i, j),

9-

{\begin{matrix} R_{n} (i, j) \equiv {\tilde{R}}_{n} (i, j) \cdot g {(i, j)}^{- 1} \\ o (i, j) \equiv \tilde{o} (i, j) \cdot g {(i, j)}^{- 1} \end{matrix} .

10-

R_{n + 1} (i, j) = ϕ_{n + 1} (i, j + 1) + o (i, j) .

Formulas (html):

Correct Categorie: cs

Guessed Categorie: cs

Result: correct

Paper: https://arxiv.org/abs/cond-mat/9604100

Formulas:

1-

Δ_{3} (L)

2-

Δ_{3} (L)

3-

H = \sum_{\underline{i}} ε_{\underline{i}} | \underline{i} ⟩ ⟨ \underline{i} | + \sum_{\underline{i}, {\underline{i}}^{'}} V_{\underline{i}, {\underline{i}}^{'}} | \underline{i} ⟩ ⟨ {\underline{i}}^{'} |,

4-

ε_{l m n}

5-

σ^{2} = W^{2} / 12

6-

𝐁 = B (1, 1, 1)

7-

𝐀 = B (z, x, y)

8-

| V_{l m n, l^{'} m^{'} n^{'}} | = 1

9-

V_{l m n, l^{'} m^{'} n^{'}}

10-

{\begin{matrix} \exp (\pm i \frac{2 π a^{2} B m}{h}) & if l^{'} = l \pm 1, m^{'} = m, n^{'} = n \\ \exp (\pm i \frac{2 π a^{2} B n}{h}) & if l^{'} = l, m^{'} = m \pm 1, n^{'} = n \\ \exp (\pm i \frac{2 π a^{2} B l}{h}) & if l^{'} = l, m^{'} = m, n^{'} = n \pm 1, \end{matrix}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/nucl-th/0001029

Formulas:

1-

T = V + V G_{0} (E) T

2-

T = U + U G_{0} (E) P T,

3-

U = V + V G_{0} (E) Q U .

4-

V = \sum_{i = 1}^{A} v_{0 i}

5-

ρ (𝐫^{'}, 𝐫) = Φ_{A}^{†} (𝐫^{'}) Φ_{A} (𝐫) .

6-

Φ_{A} (𝐫)

7-

ρ^{'} (𝐩^{'}, 𝐩) = \frac{1}{8 π^{3}} \int d^{3} 𝐫^{'} e^{- i 𝐫^{'} \cdot 𝐩^{'}} \int d^{3} 𝐫 e^{- i 𝐫 \cdot 𝐩} ρ (𝐫^{'}, 𝐫),

8-

r_{r m s}

9-

r_{r m s}

10-

r_{r m s}

Formulas (html):

Correct Categorie: nucl-th

Guessed Categorie: nucl-th

Result: correct

Paper: https://arxiv.org/abs/1708.02558

Formulas:

1-

J : B^{0} \to ℂ

2-

j (ℰ_{P})

3-

ℰ_{P} = f^{- 1} (P)

4-

f^{'} : ℰ^{'} \to B

5-

P i c_{ℰ^{0} / B^{0}}^{0} \to B^{0}

6-

ℰ^{0} := f^{- 1} (B^{0})

7-

J : B \to ℙ^{1} = ℂ \cup {\infty}

8-

𝒪_{L} [1 / M]

9-

k_{p} = R_{p} / p R_{p}

10-

𝔽_{p} = ℤ / p ℤ

Formulas (html):

Correct Categorie: math

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1707.02139

Formulas:

1-

\int 𝑑 t ⟨ ψ (t) | \hat{H} - i ℏ d / d t | ψ (t) ⟩

2-

| ψ (t) ⟩

3-

⟨ ψ | ψ ⟩ = 1

4-

| ψ (t) ⟩

5-

ϕ_{i} (t)

6-

\frac{d}{d t} ϕ_{i} (t) = - \frac{i}{ℏ} \hat{H_{0}} [{ϕ_{\cdot}}] ϕ_{i} (t),

7-

\frac{\partial}{\partial t} \underline{\underline{ρ}} = - \frac{i}{ℏ} [\underline{\underline{F}} [\underline{\underline{ρ}}] + \underline{\underline{L}}, \underline{\underline{ρ}}] .

8-

[A, B] \equiv A B - B A

9-

{\tilde{F}}_{m n} \equiv ⟨ {\tilde{χ}}_{m} | \hat{F} | {\tilde{χ}}_{n} ⟩ = {[\underline{F_{¯}^{~}}]}_{m n} = {[{\underline{\underline{S}}}^{- 1 / 2} \underline{\underline{F}} {\underline{\underline{S}}}^{- 1 / 2}]}_{m n},

10-

| {\tilde{χ}}_{n} ⟩ = \sum_{j}^{AO} | χ_{j} ⟩ {({\underline{\underline{S}}}^{- 1 / 2})}_{j n}

Formulas (html):

Correct Categorie: physics

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1811.09945

Formulas:

1-

q_{02} = Δ q

2-

\begin{matrix} H_{1} (q) & = H_{01} + \frac{k}{2} q^{2}, \\ H_{2} (q) & = H_{02} + \frac{k}{2} {(q - Δ q)}^{2} . \end{matrix}

3-

k = m ω_{v}^{2}

4-

Δ H = Δ H_{0} + λ_{v} - \sqrt{S} ℏ ω_{v} (a^{†} + a),

5-

λ_{v} = \frac{1}{2} k Δ q^{2}

6-

S = λ_{v} / ℏ ω_{v}

7-

Δ H_{0} = H_{02} - H_{01}

8-

w (ω) = \frac{2 V^{2}}{ℏ^{2}} Re \int_{0}^{\infty} 𝑑 t e^{i ω t - \frac{i t}{ℏ} (Δ H_{0} + λ_{v}) + F (t)}

9-

e^{F (t)} = ⟨ \exp [i ω_{v} \sqrt{S} \int_{0}^{t} (a^{†} (τ) + a (τ)) 𝑑 τ] ⟩ .

10-

⟨ e^{c} ⟩ = e^{⟨ c^{2} ⟩ / 2}

Formulas (html):

Correct Categorie: physics

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/1001.1263

Formulas:

1-

\hat{H} = \sum_{i, j} t {\hat{c}}_{i}^{†} {\hat{c}}_{j} + U \sum_{i} ({\hat{n}}_{i ↑} ⟨ {\hat{n}}_{i ↓} ⟩ + {\hat{n}}_{i ↓} ⟨ {\hat{n}}_{i ↑} ⟩) - U \sum_{i} ⟨ {\hat{n}}_{i ↓} ⟩ ⟨ {\hat{n}}_{i ↑} ⟩ .

2-

{\hat{n}}_{i η} = {\hat{c}}_{i η}^{+} {\hat{c}}_{i η}

3-

H = H_{C} + H_{R} + H_{L} + V_{L C} + V_{R C}

4-

G_{C} (E) = {[E S_{C} - H_{C} - Σ_{L} (E) - Σ_{R} (E)]}^{- 1} .

5-

G (E) = \frac{e^{2}}{h} T (E)

6-

T (E) = \sum_{η} Tr {[G_{C}^{†} (E) Γ_{R} (E) G_{C} (E) Γ_{L} (E)]}_{η},

7-

Γ_{R (L)} = i (Σ_{R (L)} - Σ_{R (L)}^{†})

8-

Σ = \sqrt{\sum_{i} {⟨ m_{i} ⟩}^{2}}

9-

M R = G_{F} - G_{A F} / G_{F} + G_{A F}

10-

N = 3 m - 1

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/quant-ph/0603104

Formulas:

1-

i = 1, \dots, N

2-

r a n k (ρ) = n \leq N^{2}

3-

ρ = \sum_{i = 1}^{n} λ_{i} | v_{i} > < v_{i} |,

4-

| v_{i} > = \sum_{k, l = 1}^{N} a_{k l}^{i} | k l >, a_{k l}^{i} \in 𝒞, \sum_{k, l = 1}^{N} a_{k l}^{i} a_{k l}^{i, *} = 1, i = 1, \dots, n .

5-

{(A_{i})}_{k l} = a_{k l}^{i}

6-

{ρ_{i}}, {θ_{i}}

7-

ρ_{i} = T r_{2} | v_{i} > < v_{i} | = A_{i} A_{i}^{†}, θ_{i} = T r_{1} | v_{i} > < v_{i} | = A_{i}^{t} A_{i}^{*}, i = 1, 2, \dots, n,

8-

ρ^{'} = (U_{1} \otimes U_{2}) ρ {(U_{1} \otimes U_{2})}^{†} .

9-

Ω {(ρ)}_{i j} = T r (ρ_{i} ρ_{j}), Θ {(ρ)}_{i j} = T r (θ_{i} θ_{j}), for i, j = 1, \dots, n .

10-

det (Ω (ρ)) \neq 0 and det (Θ (ρ)) \neq 0 .

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: quant-ph

Result: correct

Paper: https://arxiv.org/abs/hep-th/0308160

Formulas:

1-

U {(1)}_{Q}

2-

S U {(3)}_{c} \otimes S U {(2)}_{L} \otimes U {(1)}_{Y}

3-

S U {(3)}_{c}

4-

S U {(2)}_{L} \otimes U {(1)}_{Y}

5-

S U {(3)}_{c}

6-

U (y) = - C y^{2} + B y^{4}

7-

f_{0} \cos γ t

8-

l_{0} = l + d

9-

F = - 2 k (s - l_{0}) \sin θ = - 2 k (s - l - d) \sin θ .

10-

s = {(l^{2} + y^{2})}^{1 / 2}

Formulas (html):

Correct Categorie: hep-th

Guessed Categorie: hep-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0301124

Formulas:

1-

M {(H_{2})}_{_{v = 1 \to 0 S (1)}} = 1.76 \times 10^{- 20} \frac{4 π F_{i f} D^{2}}{E_{i f} A_{i f}},

2-

χ_{v, J} (T)

3-

\frac{M {(H_{2})}_{_{v = 1 \to 0 S (1)}}}{χ_{v, J} (T)} .

4-

χ_{v, J} (T)

5-

M_{d i s k} = f M {(H_{2})}_{_{v = 1 \to 0 S (1)}} .

6-

_{d i s k}

7-

F_{UV} = \frac{4 π F_{v = 1 \to 0 S (1)}}{Ω_{Disk} ε f_{1 \to 0}},

8-

_{v = 1 \to 0 S (1)}

9-

_{e x c e s s}

10-

_{e x c e s s}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/astro-ph/9706193

Formulas:

1-

(B - V) = 0.95,

2-

(U - V) = 1.5

3-

(U - V),

4-

λ_{peak} = 2091 Å,

5-

Δ λ = 356 Å;

6-

λ_{peak} = 2483 Å,

7-

Δ λ = 408 Å;

8-

λ_{peak} = 2760 Å,

9-

Δ λ = 728 Å .

10-

(U - V) .

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/cond-mat/9910019

Formulas:

1-

ν = n_{e} / n_{s}

2-

n_{s} = A e B / ℏ c = A / 2 π ℓ_{0}^{2}

3-

S = n_{e} / 2

4-

⟨ S_{z} (T) ⟩ \equiv \frac{1}{Z} \sum e^{- ε_{j} / k T} ⟨ j | S_{z} | j ⟩

5-

Z = \sum_{j} e^{- ε_{j} / k T}

6-

ℋ = \sum_{j_{1}, j_{2}, j_{3}, j_{4}} 𝒜_{n j_{1}, n j_{2}, n j_{3}, n j_{4}} a_{n j_{1}}^{†} a_{n j_{2}}^{†} a_{n j_{3}} a_{n j_{4}},

7-

𝒜_{n j_{1}, n j_{2}, n j_{3}, n j_{4}} = δ_{j_{1} + j_{2}, j_{3} + j_{4}}^{'} ℱ_{n} (j_{1} - j_{4}, j_{2} - j_{3}),

8-

ℱ_{n} (j_{a}, j_{b}) = \frac{1}{2 a b} \sum_{𝐪}^{^{'}} \sum_{k_{1}} \sum_{k_{2}} δ_{q_{x}, 2 π k_{1} / a} δ_{q_{y}, 2 π k_{2} / b} δ_{j_{a} k_{2}}^{'}

9-

\times \frac{2 π e^{2}}{ϵ q} [\frac{8 + 9 (q / b^{'}) + 3 {(q / b^{'})}^{2}}{8 {(1 + q / b^{'})}^{3}}]

10-

\times ℬ_{n} (q) \exp (\frac{1}{2} q^{2} ℓ_{0}^{2} - 2 π i k_{1} j_{b} / n_{s}),

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1303.3254

Formulas:

1-

a (x, y) u_{x x} + b (x, y) u_{x y} + c (x, y) u_{y y} = 0 in Ω,

2-

u \in W^{2, 2} (Ω)

3-

u \in C^{1, α} (Ω)

4-

α \in (0, 1)

5-

u \in C^{1, α} (Ω)

6-

α \in (0, 1)

7-

u \in C^{2} (Ω)

8-

𝟎 = (0, 0)

9-

a (𝟎) = 1 = c (𝟎)

10-

b (𝟎) = 0

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0407562

Formulas:

1-

(i^{'} - z^{'})

2-

{(i^{'} - z^{'})}_{A B} > 1.3

3-

z_{A B}^{'} < 28.5

4-

1 M_{⊙} {yr}^{- 1}

5-

0.1 L_{U V}^{*}

6-

i_{A B}^{'} = 29.35

7-

z_{A B}^{'} = 28.21

8-

{(i^{'} - z^{'})}_{A B} = 1.16

9-

{(i^{'} - z^{'})}_{A B} > 1.3

10-

z_{A B}^{'} \approx 25.3

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/0808.0010

Formulas:

1-

m_{U V} - B

2-

- 5.5 \leq T < - 3.5

3-

- 3.5 \leq T < - 1.5

4-

F U V - V

5-

+ 34^{\circ} 17^{'}

6-

λ_{e f f} = 1528

7-

λ_{e f f} = 2271

8-

3.6 - 4.5 μ m

9-

0.5 \leq \log (\frac{L_{bol}}{10^{10} L_{⊙}}) \leq 1.5

10-

- 24 \leq M_{R} \leq - 21.5

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1311.5597

Formulas:

1-

M_{PS} L < 10

2-

a m_{0} = - 1.05, - 1.15

3-

f_{Γ Γ^{'}} (t) = \sum_{\vec{x}} ⟨ Φ_{Γ} {(\vec{x}, t)}^{†} Φ_{Γ^{'}} (\vec{0}, 0) ⟩,

4-

Φ_{Γ} (\vec{x}, t) = {\bar{ψ}}_{1} (\vec{x}, t) Γ ψ_{2} (\vec{x}, t) .

5-

T / a = 16, 24

6-

a m_{0} = - 1.15

7-

a m_{0} = - 1.05

8-

a m = 0.2688 (15)

9-

a m_{0} = - 1.05

10-

t Δ M_{PS} ≫ 1

Formulas (html):

Correct Categorie: hep-lat

Guessed Categorie: hep-lat

Result: correct

Paper: https://arxiv.org/abs/1301.4921

Formulas:

1-

S U (2) \times U (1)

2-

j_{μ}^{E M} = Q \bar{ψ} γ_{μ} ψ

3-

L_{μ}^{E M} = e j_{μ}^{E M} A^{μ}

4-

G e V^{2}

5-

j^{E M} = \sum γ_{V} Ψ^{V} = \sum_{V} \frac{m_{V}^{2}}{f_{V}} Ψ^{V}

6-

ρ^{0} \to e^{+} + e^{-}

7-

| M (V e^{+} e^{-}) |

8-

\begin{matrix} {| M (V e^{+} e^{-}) |}^{2} = {| M (V γ^{*}) |}^{2} \frac{1}{q^{2}} {| M (γ^{*} e^{+} e^{-}) |}^{2} \\ = \frac{e^{2} m_{V}^{4}}{f_{V}^{2}} \frac{1}{m_{V}^{4}} {| M (γ^{*} e^{+} e^{-}) |}^{2} \end{matrix}

9-

q^{2} = m_{V}^{2}

10-

{| M (γ^{*} e^{+} e^{-}) |}^{2} = \frac{4 π α}{3} q^{2}

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: hep-ph

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0611447

Formulas:

1-

0 .^{''} 78

2-

V_{ring}^{2} = {(\frac{2 λ}{π θ_{in} r_{uv} (2 f + f^{2})} {(1 + f) J_{1} (\frac{[1 + f] π θ_{in} r_{uv}}{λ}) - J_{1} (\frac{π θ_{in} r_{uv}}{λ})})}^{2},

3-

r_{uv} = {(u^{2} + v^{2})}^{1 / 2}

4-

F_{ν} (R) = \frac{2 π \cos i}{d^{2}} B_{ν} (T_{ring}) R_{in}^{2} (f + f^{2} / 2) \approx \frac{2 π \cos i}{d^{2}} B_{ν} (T_{ring}) R_{in}^{2} f .

5-

T = T_{in} {(\frac{R}{R_{in}})}^{- α} .

6-

d F_{ν} (R) = \frac{2 π \cos i}{d^{2}} B_{ν} (T) R d R,

7-

R_{2} = R_{1} + d R

8-

V (R) = \frac{λ d}{π r_{uv} (R_{2}^{2} - R_{1}^{2})} [R_{2} J_{1} (\frac{2 π r_{uv} R_{2}}{λ d}) - R_{1} J_{1} (\frac{2 π r_{uv} R_{1}}{λ d})] .

9-

T = T_{in} {(R / R_{in})}^{- α}

10-

τ_{ν} \propto R^{- 1}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1307.5653

Formulas:

1-

𝔑 (o_{t}^{i})

2-

d (o_{t}^{i}) = \frac{u n i o n (o_{t}^{i}, 𝔑 (o_{t}^{i}))}{c o v e r (o_{t}^{i}, 𝔑 (o_{t}^{i}))}

3-

u n i o n (o_{t}^{i}, 𝔑 (o_{t}^{i}))

4-

𝔑 (o_{t}^{i})

5-

c o v e r (o_{t}^{i}, 𝔑 (o_{t}^{i}))

6-

𝔑 (o_{t}^{i})

7-

𝒪 (o_{t}^{i}, o_{t}^{j}) = \frac{a_{t}^{i j}}{m i n (a_{t}^{i}, a_{t}^{j})}

8-

𝒪_{t} (o_{t}^{i})

9-

m a x {𝒪 (o_{t}^{i}, o_{t}^{j}) | j \in 𝔑 (o_{t}^{i})}

10-

𝒪_{t - 1} (o_{t}^{i})

Formulas (html):

Correct Categorie: cs

Guessed Categorie: cs

Result: correct

Paper: https://arxiv.org/abs/0706.3772

Formulas:

1-

{[0, 1]}^{κ}

2-

K \cap Σ (κ)

3-

f j = {id}_{Y}

4-

𝕊 = ⟨ K_{α}, r_{α}^{β}, δ ⟩

5-

{r_{α}^{ϱ}}_{α < ϱ}

6-

𝕊 ↾ ϱ = ⟨ K_{ξ}, r_{ξ}^{η}, ϱ ⟩

7-

{[0, 1]}^{κ}

8-

K \cap Σ (κ)

9-

Σ (κ) = {x \in {[0, 1]}^{κ} : | suppt (x) | ⩽ ℵ_{0}}

10-

suppt (x) = {α : x (α) \neq 0}

Formulas (html):

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xref="S2.p2.4.m4.3.3.2.3.cmml">⟩</mo></mrow></mrow></math>, <math><msub id="S2.p2.9.m9.1.1" xref="S2.p2.9.m9.1.1.cmml"><mrow id="S2.p2.9.m9.1.1.1.1" xref="S2.p2.9.m9.1.1.1.2.cmml"><mo stretchy="false" id="S2.p2.9.m9.1.1.1.1.2" xref="S2.p2.9.m9.1.1.1.2.cmml">{</mo><msubsup id="S2.p2.9.m9.1.1.1.1.1" xref="S2.p2.9.m9.1.1.1.1.1.cmml"><mi id="S2.p2.9.m9.1.1.1.1.1.2.2" xref="S2.p2.9.m9.1.1.1.1.1.2.2.cmml">r</mi><mi id="S2.p2.9.m9.1.1.1.1.1.3" xref="S2.p2.9.m9.1.1.1.1.1.3.cmml">α</mi><mi id="S2.p2.9.m9.1.1.1.1.1.2.3" xref="S2.p2.9.m9.1.1.1.1.1.2.3.cmml">ϱ</mi></msubsup><mo stretchy="false" id="S2.p2.9.m9.1.1.1.1.3" xref="S2.p2.9.m9.1.1.1.2.cmml">}</mo></mrow><mrow id="S2.p2.9.m9.1.1.3" xref="S2.p2.9.m9.1.1.3.cmml"><mi id="S2.p2.9.m9.1.1.3.2" xref="S2.p2.9.m9.1.1.3.2.cmml">α</mi><mo id="S2.p2.9.m9.1.1.3.1" xref="S2.p2.9.m9.1.1.3.1.cmml"><</mo><mi id="S2.p2.9.m9.1.1.3.3" xref="S2.p2.9.m9.1.1.3.3.cmml">ϱ</mi></mrow></msub></math>, <math><mrow id="S2.p2.10.m10.3.3" xref="S2.p2.10.m10.3.3.cmml"><mi id="S2.p2.10.m10.3.3.4" xref="S2.p2.10.m10.3.3.4.cmml">𝕊</mi><mo id="S2.p2.10.m10.3.3.5" xref="S2.p2.10.m10.3.3.5.cmml">↾</mo><mi id="S2.p2.10.m10.3.3.6" xref="S2.p2.10.m10.3.3.6.cmml">ϱ</mi><mo id="S2.p2.10.m10.3.3.7" xref="S2.p2.10.m10.3.3.7.cmml">=</mo><mrow id="S2.p2.10.m10.3.3.2.2" xref="S2.p2.10.m10.3.3.2.3.cmml"><mo stretchy="false" id="S2.p2.10.m10.3.3.2.2.3" xref="S2.p2.10.m10.3.3.2.3.cmml">⟨</mo><msub id="S2.p2.10.m10.2.2.1.1.1" xref="S2.p2.10.m10.2.2.1.1.1.cmml"><mi id="S2.p2.10.m10.2.2.1.1.1.2" xref="S2.p2.10.m10.2.2.1.1.1.2.cmml">K</mi><mi id="S2.p2.10.m10.2.2.1.1.1.3" xref="S2.p2.10.m10.2.2.1.1.1.3.cmml">ξ</mi></msub><mo id="S2.p2.10.m10.3.3.2.2.4" xref="S2.p2.10.m10.3.3.2.3.cmml">,</mo><msubsup id="S2.p2.10.m10.3.3.2.2.2" xref="S2.p2.10.m10.3.3.2.2.2.cmml"><mi id="S2.p2.10.m10.3.3.2.2.2.2.2" xref="S2.p2.10.m10.3.3.2.2.2.2.2.cmml">r</mi><mi id="S2.p2.10.m10.3.3.2.2.2.2.3" xref="S2.p2.10.m10.3.3.2.2.2.2.3.cmml">ξ</mi><mi id="S2.p2.10.m10.3.3.2.2.2.3" xref="S2.p2.10.m10.3.3.2.2.2.3.cmml">η</mi></msubsup><mo id="S2.p2.10.m10.3.3.2.2.5" xref="S2.p2.10.m10.3.3.2.3.cmml">,</mo><mi id="S2.p2.10.m10.1.1" xref="S2.p2.10.m10.1.1.cmml">ϱ</mi><mo stretchy="false" id="S2.p2.10.m10.3.3.2.2.6" xref="S2.p2.10.m10.3.3.2.3.cmml">⟩</mo></mrow></mrow></math>, <math><msup id="S2.p3.3.m3.2.3" xref="S2.p3.3.m3.2.3.cmml"><mrow id="S2.p3.3.m3.2.3.2.2" xref="S2.p3.3.m3.2.3.2.1.cmml"><mo stretchy="false" id="S2.p3.3.m3.2.3.2.2.1" xref="S2.p3.3.m3.2.3.2.1.cmml">[</mo><mn id="S2.p3.3.m3.1.1" xref="S2.p3.3.m3.1.1.cmml">0</mn><mo id="S2.p3.3.m3.2.3.2.2.2" xref="S2.p3.3.m3.2.3.2.1.cmml">,</mo><mn id="S2.p3.3.m3.2.2" xref="S2.p3.3.m3.2.2.cmml">1</mn><mo stretchy="false" id="S2.p3.3.m3.2.3.2.2.3" xref="S2.p3.3.m3.2.3.2.1.cmml">]</mo></mrow><mi id="S2.p3.3.m3.2.3.3" xref="S2.p3.3.m3.2.3.3.cmml">κ</mi></msup></math>, <math><mrow id="S2.p3.4.m4.1.2" xref="S2.p3.4.m4.1.2.cmml"><mi id="S2.p3.4.m4.1.2.2" xref="S2.p3.4.m4.1.2.2.cmml">K</mi><mo id="S2.p3.4.m4.1.2.1" xref="S2.p3.4.m4.1.2.1.cmml">∩</mo><mrow id="S2.p3.4.m4.1.2.3" xref="S2.p3.4.m4.1.2.3.cmml"><mi mathvariant="normal" id="S2.p3.4.m4.1.2.3.2" xref="S2.p3.4.m4.1.2.3.2.cmml">Σ</mi><mo id="S2.p3.4.m4.1.2.3.1" xref="S2.p3.4.m4.1.2.3.1.cmml">⁢</mo><mrow id="S2.p3.4.m4.1.2.3.3.2" xref="S2.p3.4.m4.1.2.3.cmml"><mo stretchy="false" id="S2.p3.4.m4.1.2.3.3.2.1" xref="S2.p3.4.m4.1.2.3.cmml">(</mo><mi id="S2.p3.4.m4.1.1" xref="S2.p3.4.m4.1.1.cmml">κ</mi><mo stretchy="false" id="S2.p3.4.m4.1.2.3.3.2.2" xref="S2.p3.4.m4.1.2.3.cmml">)</mo></mrow></mrow></mrow></math>, <math><mrow id="S2.p3.6.m6.7.7" xref="S2.p3.6.m6.7.7.cmml"><mrow id="S2.p3.6.m6.7.7.4" xref="S2.p3.6.m6.7.7.4.cmml"><mi mathvariant="normal" id="S2.p3.6.m6.7.7.4.2" xref="S2.p3.6.m6.7.7.4.2.cmml">Σ</mi><mo id="S2.p3.6.m6.7.7.4.1" xref="S2.p3.6.m6.7.7.4.1.cmml">⁢</mo><mrow id="S2.p3.6.m6.7.7.4.3.2" xref="S2.p3.6.m6.7.7.4.cmml"><mo stretchy="false" id="S2.p3.6.m6.7.7.4.3.2.1" xref="S2.p3.6.m6.7.7.4.cmml">(</mo><mi id="S2.p3.6.m6.1.1" xref="S2.p3.6.m6.1.1.cmml">κ</mi><mo stretchy="false" id="S2.p3.6.m6.7.7.4.3.2.2" xref="S2.p3.6.m6.7.7.4.cmml">)</mo></mrow></mrow><mo id="S2.p3.6.m6.7.7.3" xref="S2.p3.6.m6.7.7.3.cmml">=</mo><mrow id="S2.p3.6.m6.7.7.2.2" xref="S2.p3.6.m6.7.7.2.3.cmml"><mo stretchy="false" id="S2.p3.6.m6.7.7.2.2.3" xref="S2.p3.6.m6.7.7.2.3.1.cmml">{</mo><mrow id="S2.p3.6.m6.6.6.1.1.1" xref="S2.p3.6.m6.6.6.1.1.1.cmml"><mi id="S2.p3.6.m6.6.6.1.1.1.2" xref="S2.p3.6.m6.6.6.1.1.1.2.cmml">x</mi><mo id="S2.p3.6.m6.6.6.1.1.1.1" xref="S2.p3.6.m6.6.6.1.1.1.1.cmml">∈</mo><msup id="S2.p3.6.m6.6.6.1.1.1.3" xref="S2.p3.6.m6.6.6.1.1.1.3.cmml"><mrow id="S2.p3.6.m6.6.6.1.1.1.3.2.2" xref="S2.p3.6.m6.6.6.1.1.1.3.2.1.cmml"><mo stretchy="false" id="S2.p3.6.m6.6.6.1.1.1.3.2.2.1" xref="S2.p3.6.m6.6.6.1.1.1.3.2.1.cmml">[</mo><mn id="S2.p3.6.m6.2.2" xref="S2.p3.6.m6.2.2.cmml">0</mn><mo id="S2.p3.6.m6.6.6.1.1.1.3.2.2.2" xref="S2.p3.6.m6.6.6.1.1.1.3.2.1.cmml">,</mo><mn id="S2.p3.6.m6.3.3" xref="S2.p3.6.m6.3.3.cmml">1</mn><mo stretchy="false" id="S2.p3.6.m6.6.6.1.1.1.3.2.2.3" xref="S2.p3.6.m6.6.6.1.1.1.3.2.1.cmml">]</mo></mrow><mi id="S2.p3.6.m6.6.6.1.1.1.3.3" xref="S2.p3.6.m6.6.6.1.1.1.3.3.cmml">κ</mi></msup></mrow><mo id="S2.p3.6.m6.7.7.2.2.4" xref="S2.p3.6.m6.7.7.2.3.1.cmml">:</mo><mrow id="S2.p3.6.m6.7.7.2.2.2" xref="S2.p3.6.m6.7.7.2.2.2.cmml"><mrow id="S2.p3.6.m6.7.7.2.2.2.1.1" xref="S2.p3.6.m6.7.7.2.2.2.1.2.cmml"><mo stretchy="false" id="S2.p3.6.m6.7.7.2.2.2.1.1.2" xref="S2.p3.6.m6.7.7.2.2.2.1.2.1.cmml">|</mo><mrow id="S2.p3.6.m6.7.7.2.2.2.1.1.1.2" xref="S2.p3.6.m6.7.7.2.2.2.1.1.1.1.cmml"><mi id="S2.p3.6.m6.4.4" xref="S2.p3.6.m6.4.4.cmml">suppt</mi><mo id="S2.p3.6.m6.7.7.2.2.2.1.1.1.2a" xref="S2.p3.6.m6.7.7.2.2.2.1.1.1.1.cmml">⁡</mo><mrow id="S2.p3.6.m6.7.7.2.2.2.1.1.1.2.1" xref="S2.p3.6.m6.7.7.2.2.2.1.1.1.1.cmml"><mo stretchy="false" id="S2.p3.6.m6.7.7.2.2.2.1.1.1.2.1.1" xref="S2.p3.6.m6.7.7.2.2.2.1.1.1.1.cmml">(</mo><mi id="S2.p3.6.m6.5.5" xref="S2.p3.6.m6.5.5.cmml">x</mi><mo stretchy="false" id="S2.p3.6.m6.7.7.2.2.2.1.1.1.2.1.2" xref="S2.p3.6.m6.7.7.2.2.2.1.1.1.1.cmml">)</mo></mrow></mrow><mo stretchy="false" id="S2.p3.6.m6.7.7.2.2.2.1.1.3" xref="S2.p3.6.m6.7.7.2.2.2.1.2.1.cmml">|</mo></mrow><mo id="S2.p3.6.m6.7.7.2.2.2.2" xref="S2.p3.6.m6.7.7.2.2.2.2.cmml">⩽</mo><msub id="S2.p3.6.m6.7.7.2.2.2.3" xref="S2.p3.6.m6.7.7.2.2.2.3.cmml"><mi mathvariant="normal" id="S2.p3.6.m6.7.7.2.2.2.3.2" xref="S2.p3.6.m6.7.7.2.2.2.3.2.cmml">ℵ</mi><mn id="S2.p3.6.m6.7.7.2.2.2.3.3" xref="S2.p3.6.m6.7.7.2.2.2.3.3.cmml">0</mn></msub></mrow><mo stretchy="false" id="S2.p3.6.m6.7.7.2.2.5" xref="S2.p3.6.m6.7.7.2.3.1.cmml">}</mo></mrow></mrow></math>, <math><mrow id="S2.p3.7.m7.5.5" xref="S2.p3.7.m7.5.5.cmml"><mrow id="S2.p3.7.m7.5.5.3.2" xref="S2.p3.7.m7.5.5.3.1.cmml"><mi id="S2.p3.7.m7.1.1" xref="S2.p3.7.m7.1.1.cmml">suppt</mi><mo id="S2.p3.7.m7.5.5.3.2a" xref="S2.p3.7.m7.5.5.3.1.cmml">⁡</mo><mrow id="S2.p3.7.m7.5.5.3.2.1" xref="S2.p3.7.m7.5.5.3.1.cmml"><mo stretchy="false" id="S2.p3.7.m7.5.5.3.2.1.1" xref="S2.p3.7.m7.5.5.3.1.cmml">(</mo><mi id="S2.p3.7.m7.2.2" xref="S2.p3.7.m7.2.2.cmml">x</mi><mo stretchy="false" id="S2.p3.7.m7.5.5.3.2.1.2" xref="S2.p3.7.m7.5.5.3.1.cmml">)</mo></mrow></mrow><mo id="S2.p3.7.m7.5.5.2" xref="S2.p3.7.m7.5.5.2.cmml">=</mo><mrow id="S2.p3.7.m7.5.5.1.1" xref="S2.p3.7.m7.5.5.1.2.cmml"><mo stretchy="false" id="S2.p3.7.m7.5.5.1.1.2" xref="S2.p3.7.m7.5.5.1.2.1.cmml">{</mo><mi id="S2.p3.7.m7.4.4" xref="S2.p3.7.m7.4.4.cmml">α</mi><mo id="S2.p3.7.m7.5.5.1.1.3" xref="S2.p3.7.m7.5.5.1.2.1.cmml">:</mo><mrow id="S2.p3.7.m7.5.5.1.1.1" xref="S2.p3.7.m7.5.5.1.1.1.cmml"><mrow id="S2.p3.7.m7.5.5.1.1.1.2" xref="S2.p3.7.m7.5.5.1.1.1.2.cmml"><mi id="S2.p3.7.m7.5.5.1.1.1.2.2" xref="S2.p3.7.m7.5.5.1.1.1.2.2.cmml">x</mi><mo id="S2.p3.7.m7.5.5.1.1.1.2.1" xref="S2.p3.7.m7.5.5.1.1.1.2.1.cmml">⁢</mo><mrow id="S2.p3.7.m7.5.5.1.1.1.2.3.2" xref="S2.p3.7.m7.5.5.1.1.1.2.cmml"><mo stretchy="false" id="S2.p3.7.m7.5.5.1.1.1.2.3.2.1" xref="S2.p3.7.m7.5.5.1.1.1.2.cmml">(</mo><mi id="S2.p3.7.m7.3.3" xref="S2.p3.7.m7.3.3.cmml">α</mi><mo stretchy="false" id="S2.p3.7.m7.5.5.1.1.1.2.3.2.2" xref="S2.p3.7.m7.5.5.1.1.1.2.cmml">)</mo></mrow></mrow><mo id="S2.p3.7.m7.5.5.1.1.1.1" xref="S2.p3.7.m7.5.5.1.1.1.1.cmml">≠</mo><mn id="S2.p3.7.m7.5.5.1.1.1.3" xref="S2.p3.7.m7.5.5.1.1.1.3.cmml">0</mn></mrow><mo stretchy="false" id="S2.p3.7.m7.5.5.1.1.4" xref="S2.p3.7.m7.5.5.1.2.1.cmml">}</mo></mrow></mrow></math>

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/gr-qc/0505154

Formulas:

1-

G_{μ ν} = - 8 π G T_{μ ν} - Λ g_{μ ν}

2-

d s^{2} = - d t^{2} + U (t, r) d r^{2} + V (t, r) (d θ^{2} + {sin}^{2} θ d ϕ^{2})

3-

U (t, r)

4-

V (t, r)

5-

a^{2} (t) \cdot f (r)

6-

a^{2} (t) \cdot r^{2}

7-

U (t, r_{1}) = a_{1} (t) \cdot f (r_{1})

8-

U (t, r_{2}) = a_{2} (t) \cdot f (r_{2})

9-

a_{1} (t) = a_{2} (t)

10-

G^{- 1} H_{0}^{2}

Formulas (html):

Correct Categorie: gr-qc

Guessed Categorie: gr-qc

Result: correct

Paper: https://arxiv.org/abs/gr-qc/0101100

Formulas:

1-

d s^{2} = (1 - 2 m (r) / r) σ^{2} (r) d t^{2} - d r^{2} / (1 - 2 m (r) / r) - r^{2} d Ω,

2-

g_{r r}^{- 1}

3-

m \approx M_{k} \equiv m (R_{k})

4-

σ \approx σ_{k} \equiv σ (R_{k})

5-

x_{k} = {(r_{k} / R_{k})}^{2} ≫ 1

6-

x_{k + 1} = e^{x_{k}} / x_{k}^{3}

7-

r_{k + 1} / r_{k} = x_{k} e^{- x_{k} / 2},

8-

r_{k} ≫ r_{k + 1}

9-

\frac{M_{k}}{M_{k - 1}} = \frac{e^{x_{k} / 2}}{x_{k}},

10-

\frac{σ_{k + 1}}{σ_{k}} = e^{- x_{k} / 2}

Formulas (html):

Correct Categorie: gr-qc

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1802.07884

Formulas:

1-

\dot{P} = 6.5 \times 10^{- 12}

2-

B = 1.6 \times 10^{14} G

3-

2 \overset{''}{.} 4

4-

1778 \pm 3 {cm}^{- 3} pc

5-

- 66960 \pm 50 rad m^{- 2}

6-

1778 {cm}^{- 3} pc

7-

P (E / ⟨ E ⟩) = \frac{⟨ E ⟩}{\sqrt{2 π} σ E} \exp [- {(\ln \frac{E}{⟨ E ⟩} - μ)}^{2} / (2 σ^{2})],

8-

0 \overset{\circ}{.} 08 \pm 0 \overset{\circ}{.} 04 {day}^{- 1}

9-

0 \overset{\circ}{.} 07 \pm 0 \overset{\circ}{.} 03 {day}^{- 1}

10-

0 \overset{\circ}{.} 2 - 0 \overset{\circ}{.} 9

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1409.8662

Formulas:

1-

10 \bar{1} 0

2-

E^{SE} = Φ - h ν_{probe}

3-

h ν_{pump} = 3.76 – 4.2 eV

4-

10 \bar{1} 0

5-

T_{max} = 850 K

6-

p_{base} = 1 \times 10^{- 10} mbar

7-

E - E_{F} = - 3.18 (6) eV

8-

10 and 35 μ {J/cm}^{2}

9-

1.45 - 5.22 \times 10^{18} {cm}^{- 3}

10-

1.5 and 6 \times 10^{18} {cm}^{- 3}

Formulas (html):

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xref="S0.F1.8.m3.1.1.3.1.cmml">-</mo><mrow id="S0.F1.8.m3.1.1.3.3" xref="S0.F1.8.m3.1.1.3.3.cmml"><mi id="S0.F1.8.m3.1.1.3.3.2" xref="S0.F1.8.m3.1.1.3.3.2.cmml">h</mi><mo id="S0.F1.8.m3.1.1.3.3.1" xref="S0.F1.8.m3.1.1.3.3.1.cmml">⁢</mo><msub id="S0.F1.8.m3.1.1.3.3.3" xref="S0.F1.8.m3.1.1.3.3.3.cmml"><mi id="S0.F1.8.m3.1.1.3.3.3.2" xref="S0.F1.8.m3.1.1.3.3.3.2.cmml">ν</mi><mtext id="S0.F1.8.m3.1.1.3.3.3.3" xref="S0.F1.8.m3.1.1.3.3.3.3a.cmml">probe</mtext></msub></mrow></mrow></mrow></math>, <math><mrow id="footnote1.m1.1.1" xref="footnote1.m1.1.1.cmml"><mrow id="footnote1.m1.1.1.2" xref="footnote1.m1.1.1.2.cmml"><mi id="footnote1.m1.1.1.2.2" xref="footnote1.m1.1.1.2.2.cmml">h</mi><mo id="footnote1.m1.1.1.2.1" xref="footnote1.m1.1.1.2.1.cmml">⁢</mo><msub id="footnote1.m1.1.1.2.3" xref="footnote1.m1.1.1.2.3.cmml"><mi id="footnote1.m1.1.1.2.3.2" xref="footnote1.m1.1.1.2.3.2.cmml">ν</mi><mtext id="footnote1.m1.1.1.2.3.3" xref="footnote1.m1.1.1.2.3.3a.cmml">pump</mtext></msub></mrow><mo id="footnote1.m1.1.1.1" xref="footnote1.m1.1.1.1.cmml">=</mo><mrow id="footnote1.m1.1.1.3" xref="footnote1.m1.1.1.3.cmml"><mn id="footnote1.m1.1.1.3.2" xref="footnote1.m1.1.1.3.2.cmml">3.76</mn><mo id="footnote1.m1.1.1.3.1" xref="footnote1.m1.1.1.3.1.cmml">⁢</mo><mtext id="footnote1.m1.1.1.3.3" xref="footnote1.m1.1.1.3.3a.cmml">–</mtext><mo id="footnote1.m1.1.1.3.1b" xref="footnote1.m1.1.1.3.1.cmml">⁢</mo><mpadded width="+3.3pt" id="footnote1.m1.1.1.3.4" xref="footnote1.m1.1.1.3.4.cmml"><mn id="footnote1.m1.1.1.3.4b" xref="footnote1.m1.1.1.3.4.cmml">4.2</mn></mpadded><mo id="footnote1.m1.1.1.3.1c" xref="footnote1.m1.1.1.3.1.cmml">⁢</mo><mtext id="footnote1.m1.1.1.3.5" xref="footnote1.m1.1.1.3.5a.cmml">eV</mtext></mrow></mrow></math>, <math><mrow id="p5.1.m1.1.1" xref="p5.1.m1.1.1.cmml"><mn id="p5.1.m1.1.1.2" xref="p5.1.m1.1.1.2.cmml">10</mn><mo id="p5.1.m1.1.1.1" xref="p5.1.m1.1.1.1.cmml">⁢</mo><mover accent="true" id="p5.1.m1.1.1.3" xref="p5.1.m1.1.1.3.cmml"><mn id="p5.1.m1.1.1.3.2" xref="p5.1.m1.1.1.3.2.cmml">1</mn><mo id="p5.1.m1.1.1.3.1" xref="p5.1.m1.1.1.3.1.cmml">¯</mo></mover><mo id="p5.1.m1.1.1.1a" xref="p5.1.m1.1.1.1.cmml">⁢</mo><mn id="p5.1.m1.1.1.4" xref="p5.1.m1.1.1.4.cmml">0</mn></mrow></math>, <math><mrow id="p5.3.m3.1.1" xref="p5.3.m3.1.1.cmml"><msub id="p5.3.m3.1.1.2" xref="p5.3.m3.1.1.2.cmml"><mi id="p5.3.m3.1.1.2.2" xref="p5.3.m3.1.1.2.2.cmml">T</mi><mtext id="p5.3.m3.1.1.2.3" xref="p5.3.m3.1.1.2.3a.cmml">max</mtext></msub><mo id="p5.3.m3.1.1.1" xref="p5.3.m3.1.1.1.cmml">=</mo><mrow id="p5.3.m3.1.1.3" xref="p5.3.m3.1.1.3.cmml"><mpadded width="+3.3pt" id="p5.3.m3.1.1.3.2" xref="p5.3.m3.1.1.3.2.cmml"><mn id="p5.3.m3.1.1.3.2a" xref="p5.3.m3.1.1.3.2.cmml">850</mn></mpadded><mo id="p5.3.m3.1.1.3.1" xref="p5.3.m3.1.1.3.1.cmml">⁢</mo><mtext id="p5.3.m3.1.1.3.3" xref="p5.3.m3.1.1.3.3a.cmml">K</mtext></mrow></mrow></math>, <math><mrow id="p5.4.m4.1.1" xref="p5.4.m4.1.1.cmml"><msub id="p5.4.m4.1.1.2" xref="p5.4.m4.1.1.2.cmml"><mi id="p5.4.m4.1.1.2.2" xref="p5.4.m4.1.1.2.2.cmml">p</mi><mtext id="p5.4.m4.1.1.2.3" xref="p5.4.m4.1.1.2.3a.cmml">base</mtext></msub><mo id="p5.4.m4.1.1.1" xref="p5.4.m4.1.1.1.cmml">=</mo><mrow id="p5.4.m4.1.1.3" xref="p5.4.m4.1.1.3.cmml"><mrow id="p5.4.m4.1.1.3.2" xref="p5.4.m4.1.1.3.2.cmml"><mn id="p5.4.m4.1.1.3.2.2" xref="p5.4.m4.1.1.3.2.2.cmml">1</mn><mo id="p5.4.m4.1.1.3.2.1" xref="p5.4.m4.1.1.3.2.1.cmml">×</mo><mpadded width="+3.3pt" id="p5.4.m4.1.1.3.2.3" xref="p5.4.m4.1.1.3.2.3.cmml"><msup id="p5.4.m4.1.1.3.2.3a" xref="p5.4.m4.1.1.3.2.3.cmml"><mn id="p5.4.m4.1.1.3.2.3.2" xref="p5.4.m4.1.1.3.2.3.2.cmml">10</mn><mrow id="p5.4.m4.1.1.3.2.3.3" xref="p5.4.m4.1.1.3.2.3.3.cmml"><mo id="p5.4.m4.1.1.3.2.3.3.1" xref="p5.4.m4.1.1.3.2.3.3.1.cmml">-</mo><mn id="p5.4.m4.1.1.3.2.3.3.2" xref="p5.4.m4.1.1.3.2.3.3.2.cmml">10</mn></mrow></msup></mpadded></mrow><mo id="p5.4.m4.1.1.3.1" xref="p5.4.m4.1.1.3.1.cmml">⁢</mo><mtext id="p5.4.m4.1.1.3.3" xref="p5.4.m4.1.1.3.3a.cmml">mbar</mtext></mrow></mrow></math>, <math><mrow id="p5.5.m5.1.2" xref="p5.5.m5.1.2.cmml"><mrow id="p5.5.m5.1.2.2" xref="p5.5.m5.1.2.2.cmml"><mi id="p5.5.m5.1.2.2.2" xref="p5.5.m5.1.2.2.2.cmml">E</mi><mo id="p5.5.m5.1.2.2.1" xref="p5.5.m5.1.2.2.1.cmml">-</mo><msub id="p5.5.m5.1.2.2.3" xref="p5.5.m5.1.2.2.3.cmml"><mi id="p5.5.m5.1.2.2.3.2" xref="p5.5.m5.1.2.2.3.2.cmml">E</mi><mtext id="p5.5.m5.1.2.2.3.3" xref="p5.5.m5.1.2.2.3.3a.cmml">F</mtext></msub></mrow><mo id="p5.5.m5.1.2.1" xref="p5.5.m5.1.2.1.cmml">=</mo><mrow id="p5.5.m5.1.2.3" xref="p5.5.m5.1.2.3.cmml"><mo id="p5.5.m5.1.2.3.1" xref="p5.5.m5.1.2.3.1.cmml">-</mo><mrow id="p5.5.m5.1.2.3.2" xref="p5.5.m5.1.2.3.2.cmml"><mn id="p5.5.m5.1.2.3.2.2" xref="p5.5.m5.1.2.3.2.2.cmml">3.18</mn><mo id="p5.5.m5.1.2.3.2.1" xref="p5.5.m5.1.2.3.2.1.cmml">⁢</mo><mrow id="p5.5.m5.1.2.3.2.3.2" xref="p5.5.m5.1.2.3.2.cmml"><mo stretchy="false" id="p5.5.m5.1.2.3.2.3.2.1" xref="p5.5.m5.1.2.3.2.cmml">(</mo><mn id="p5.5.m5.1.1" xref="p5.5.m5.1.1.cmml">6</mn><mo rspace="5.8pt" stretchy="false" id="p5.5.m5.1.2.3.2.3.2.2" xref="p5.5.m5.1.2.3.2.cmml">)</mo></mrow><mo id="p5.5.m5.1.2.3.2.1a" xref="p5.5.m5.1.2.3.2.1.cmml">⁢</mo><mtext id="p5.5.m5.1.2.3.2.4" xref="p5.5.m5.1.2.3.2.4a.cmml">eV</mtext></mrow></mrow></mrow></math>, <math><mrow id="p5.8.m8.1.1" xref="p5.8.m8.1.1.cmml"><mn id="p5.8.m8.1.1.2" xref="p5.8.m8.1.1.2.cmml">10</mn><mo id="p5.8.m8.1.1.1" xref="p5.8.m8.1.1.1.cmml">⁢</mo><mpadded width="+3.3pt" id="p5.8.m8.1.1.3" xref="p5.8.m8.1.1.3b.cmml"><mtext id="p5.8.m8.1.1.3a" xref="p5.8.m8.1.1.3b.cmml"> and </mtext></mpadded><mo id="p5.8.m8.1.1.1a" xref="p5.8.m8.1.1.1.cmml">⁢</mo><mn id="p5.8.m8.1.1.4" xref="p5.8.m8.1.1.4.cmml">35</mn><mo id="p5.8.m8.1.1.1b" xref="p5.8.m8.1.1.1.cmml">⁢</mo><mi id="p5.8.m8.1.1.5" xref="p5.8.m8.1.1.5.cmml">μ</mi><mo id="p5.8.m8.1.1.1c" xref="p5.8.m8.1.1.1.cmml">⁢</mo><msup id="p5.8.m8.1.1.6" xref="p5.8.m8.1.1.6.cmml"><mtext id="p5.8.m8.1.1.6.2" xref="p5.8.m8.1.1.6.2a.cmml">J/cm</mtext><mn id="p5.8.m8.1.1.6.3" xref="p5.8.m8.1.1.6.3.cmml">2</mn></msup></mrow></math>, <math><mrow id="p5.9.m9.1.1" xref="p5.9.m9.1.1.cmml"><mn id="p5.9.m9.1.1.2" xref="p5.9.m9.1.1.2.cmml">1.45</mn><mo id="p5.9.m9.1.1.1" xref="p5.9.m9.1.1.1.cmml">-</mo><mrow id="p5.9.m9.1.1.3" xref="p5.9.m9.1.1.3.cmml"><mrow id="p5.9.m9.1.1.3.2" xref="p5.9.m9.1.1.3.2.cmml"><mn id="p5.9.m9.1.1.3.2.2" xref="p5.9.m9.1.1.3.2.2.cmml">5.22</mn><mo id="p5.9.m9.1.1.3.2.1" xref="p5.9.m9.1.1.3.2.1.cmml">×</mo><mpadded width="+3.3pt" id="p5.9.m9.1.1.3.2.3" xref="p5.9.m9.1.1.3.2.3.cmml"><msup id="p5.9.m9.1.1.3.2.3a" xref="p5.9.m9.1.1.3.2.3.cmml"><mn id="p5.9.m9.1.1.3.2.3.2" xref="p5.9.m9.1.1.3.2.3.2.cmml">10</mn><mn id="p5.9.m9.1.1.3.2.3.3" xref="p5.9.m9.1.1.3.2.3.3.cmml">18</mn></msup></mpadded></mrow><mo id="p5.9.m9.1.1.3.1" xref="p5.9.m9.1.1.3.1.cmml">⁢</mo><msup id="p5.9.m9.1.1.3.3" xref="p5.9.m9.1.1.3.3.cmml"><mtext id="p5.9.m9.1.1.3.3.2" xref="p5.9.m9.1.1.3.3.2a.cmml">cm</mtext><mrow id="p5.9.m9.1.1.3.3.3" xref="p5.9.m9.1.1.3.3.3.cmml"><mo id="p5.9.m9.1.1.3.3.3.1" xref="p5.9.m9.1.1.3.3.3.1.cmml">-</mo><mn id="p5.9.m9.1.1.3.3.3.2" xref="p5.9.m9.1.1.3.3.3.2.cmml">3</mn></mrow></msup></mrow></mrow></math>, <math><mrow id="footnote3.m1.1.1" xref="footnote3.m1.1.1.cmml"><mrow id="footnote3.m1.1.1.2" xref="footnote3.m1.1.1.2.cmml"><mrow id="footnote3.m1.1.1.2.2" xref="footnote3.m1.1.1.2.2.cmml"><mpadded width="+3.3pt" id="footnote3.m1.1.1.2.2.2" xref="footnote3.m1.1.1.2.2.2.cmml"><mn id="footnote3.m1.1.1.2.2.2b" xref="footnote3.m1.1.1.2.2.2.cmml">1.5</mn></mpadded><mo id="footnote3.m1.1.1.2.2.1" xref="footnote3.m1.1.1.2.2.1.cmml">⁢</mo><mpadded width="+3.3pt" id="footnote3.m1.1.1.2.2.3" xref="footnote3.m1.1.1.2.2.3b.cmml"><mtext id="footnote3.m1.1.1.2.2.3b" xref="footnote3.m1.1.1.2.2.3b.cmml">and</mtext></mpadded><mo id="footnote3.m1.1.1.2.2.1b" xref="footnote3.m1.1.1.2.2.1.cmml">⁢</mo><mn id="footnote3.m1.1.1.2.2.4" xref="footnote3.m1.1.1.2.2.4.cmml">6</mn></mrow><mo id="footnote3.m1.1.1.2.1" xref="footnote3.m1.1.1.2.1.cmml">×</mo><mpadded width="+3.3pt" id="footnote3.m1.1.1.2.3" xref="footnote3.m1.1.1.2.3.cmml"><msup id="footnote3.m1.1.1.2.3b" xref="footnote3.m1.1.1.2.3.cmml"><mn id="footnote3.m1.1.1.2.3.2" xref="footnote3.m1.1.1.2.3.2.cmml">10</mn><mn id="footnote3.m1.1.1.2.3.3" xref="footnote3.m1.1.1.2.3.3.cmml">18</mn></msup></mpadded></mrow><mo id="footnote3.m1.1.1.1" xref="footnote3.m1.1.1.1.cmml">⁢</mo><msup id="footnote3.m1.1.1.3" xref="footnote3.m1.1.1.3.cmml"><mtext id="footnote3.m1.1.1.3.2" xref="footnote3.m1.1.1.3.2a.cmml">cm</mtext><mrow id="footnote3.m1.1.1.3.3" xref="footnote3.m1.1.1.3.3.cmml"><mo id="footnote3.m1.1.1.3.3.1" xref="footnote3.m1.1.1.3.3.1.cmml">-</mo><mn id="footnote3.m1.1.1.3.3.2" xref="footnote3.m1.1.1.3.3.2.cmml">3</mn></mrow></msup></mrow></math>

Correct Categorie: cond-mat

Guessed Categorie: astro-ph

Result: incorrect

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/0806.1821

Formulas:

1-

R_{H} = \frac{h}{e^{2}} \frac{1}{N},

2-

R = \frac{h}{2 e^{2}} \frac{1}{N} .

3-

R_{q} = \frac{h}{2 e^{2}} .

4-

\exp (i k x) χ_{k} (y)

5-

μ, μ + d E

6-

d I = e v d ρ

7-

v = ℏ^{- 1} d E / d k

8-

d ρ = (d ρ / d k) (d k / d E) d E

9-

(d ρ / d k) = 1 / 2 π

10-

(d k / d E) = (1 / ℏ v)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1011.1208

Formulas:

1-

B \to π l ν

2-

G (t) = a^{6} \sum_{\vec{x}} {(a m_{q})}^{2} ⟨ 0 | j_{5} (\vec{x}, t) j_{5} (0, 0) | 0 ⟩ .

3-

G_{n} = \sum_{t} {(\frac{t}{a})}^{n} G (t)

4-

R_{4}^{latt} = \frac{G_{4}}{G_{4}^{(0)}}, and R_{n}^{latt} = {(\frac{G_{n}}{G_{n}^{(0)}})}^{\frac{1}{n - 4}} for n \geq 6 .

5-

R_{4}^{cont} = \frac{g_{4}}{g_{4}^{(0)}}, and R_{n}^{cont} = \frac{m_{η_{h}}}{2 m_{h} (μ)} \frac{g_{n}}{g_{n}^{(0)}} for n \geq 6 .

6-

α_{s} (μ)

7-

α_{s}^{3} (μ)

8-

α_{s}^{2} (μ)

9-

m_{η_{h}} / (2 m_{h} (μ))

10-

α_{s}^{2} (μ)

Formulas (html):

Correct Categorie: hep-lat

Guessed Categorie: hep-ph

Result: incorrect

Paper: https://arxiv.org/abs/1103.3097

Formulas:

1-

[D_{μ}, F_{α β}] = 0

2-

[D_{μ}, 𝑬] = [D_{μ}, 𝑩] = 𝟎

3-

D_{μ} \equiv \partial_{μ} - i g A_{μ}

4-

𝑬^{i} = F^{i 0}

5-

𝑩^{i} = - ϵ^{i j k} F_{j k} / 2

6-

F_{μ ν} \equiv i [D_{μ}, D_{ν}] / g

7-

\partial_{μ} 𝑬 = \partial_{μ} 𝑩 = 𝟎

8-

𝑬 = (0, 0, E)

9-

𝑩 = (0, 0, B)

10-

B, E \equiv {[{(ℱ^{2} + 𝒢^{2})}^{1 / 2} \pm ℱ]}^{1 / 2}

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: nlin

Result: incorrect

Paper: https://arxiv.org/abs/nucl-th/0103034

Formulas:

1-

{\bar{Ψ}}_{i} (i γ^{μ} \partial_{μ} - M) Ψ_{i} + \frac{1}{2} \partial^{μ} σ \partial_{μ} σ - U (σ) - g_{σ} {\bar{Ψ}}_{i} σ Ψ_{i}

2-

- \frac{1}{4} Ω^{μ ν} Ω_{μ ν} + \frac{1}{2} m_{ω}^{2} ω^{μ} ω_{μ} - g_{ω} {\bar{Ψ}}_{i} γ^{μ} ω_{μ} Ψ_{i} - \frac{1}{4} {\vec{R}}^{μ ν} {\vec{R}}_{μ ν} + \frac{1}{2} m_{ρ}^{2} {\vec{ρ}}^{μ} {\vec{ρ}}_{μ}

3-

- g_{ρ} {\bar{Ψ}}_{i} γ^{μ} {\vec{ρ}}_{μ} \vec{τ} Ψ_{i} - \frac{1}{4} F^{μ ν} F_{μ ν} - e {\bar{Ψ}}_{i} γ^{μ} \frac{(1 - τ_{3})}{2} A_{μ} Ψ_{i} .

4-

U (σ) = \frac{1}{2} m_{σ}^{2} σ^{2} + \frac{1}{3} g_{2} σ^{3} + \frac{1}{4} g_{3} σ^{4} .

5-

e^{2} / 4 π = 1 / 137

6-

2 ℏ ω_{0}

7-

3 ℏ ω_{0}

8-

{}^{1 / 2}f_{7 / 2}

9-

{}^{1 / 2}h_{9 / 2}

10-

{}^{3 / 2}h_{9 / 2}

Formulas (html):

Correct Categorie: nucl-th

Guessed Categorie: hep-th

Result: incorrect

Paper: https://arxiv.org/abs/0804.0532

Formulas:

1-

| 3 / 2, 3 / 2 ⟩

2-

(ω_{x}, ω_{y}, ω_{z}) / 2 π = (762, 762, 190) Hz

3-

(ω_{x}, ω_{y}, ω_{z}) / 2 π

4-

T_{z} ≃ 0.9 μ

5-

δ = ω_{2} - ω_{1} = 2 ℏ q^{2} / m = 2 π \cdot 295

6-

q = 2 π / λ

7-

I_{1} = I_{2} = 13.7

8-

Ω_{i} = \sqrt{6 π c^{2} Γ I_{i} / ℏ ν^{3}}

9-

Ω_{R} = Ω_{1} Ω_{2} / 2 Δ_{L}

10-

2 π (47..450)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1409.7576

Formulas:

1-

ω_{2} = ω_{23} + Δ

2-

ω_{1} = ω_{13} + Δ

3-

ω_{2} = ω_{23} + Δ

4-

γ_{3} = 10, Γ_{s} = 10^{- 4}, γ_{s} = 10^{- 3}, Ω_{1} = Ω_{2} = 0.5

5-

- (+) ℏ δ

6-

k_{B} T >> ℏ ω_{z}

7-

ω_{1} = ω_{2} + ω_{z}

8-

| Ψ ⟩ \propto Ω_{2} | 1 ⟩ - Ω_{1} | 2 ⟩

9-

(ρ_{22} - ρ_{11}) / 2

10-

{\bar{Γ}}_{h} / Γ_{d} = 0.01

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/cond-mat/0406192

Formulas:

1-

T \geq 0.85 T_{m}

2-

(V_{R}, T_{R})

3-

(V_{o}, T_{o})

4-

E (V, T)

5-

(V_{o}, T_{o})

6-

(V_{o}, T_{o})

7-

(V_{o}, T_{o})

8-

E (V, T)

9-

P (V, T)

10-

S (V_{o}, T_{o}) = S_{R} + \int_{T_{R}}^{T_{o}} \frac{1}{T} {(\frac{\partial E}{\partial T})}_{V_{R}} 𝑑 T + \frac{1}{T_{o}} \int_{V_{R}}^{V_{o}} P (V, T_{o}) 𝑑 V

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/cond-mat/0410363

Formulas:

1-

𝐂 = n 𝐚_{1} + m 𝐚_{2}

2-

R = {(n^{2} + m^{2} - n m)}^{1 / 2} | 𝐚_{𝟏} | / 𝟐 π

3-

n = 5, 4, 3

4-

n \geq m > n / 2

5-

(n, n - m)

6-

E_{b} (n, m) = E_{T} (A) - E_{T} (n, m) / N

7-

E_{T} (A)

8-

E_{T} (n, m) / N

9-

E_{c} (n, m) = E_{b} (2D) - E_{b} (n, m)

10-

E_{b} (2D) = 2.84

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Run 11369308 (Agent384)