Run 11163385

Paper: https://arxiv.org/abs/quant-ph/0006133

Formulas:

1-

O^{(k)} ({\vec{r}}_{1}, t_{1}, \dots, {\vec{r}}_{k}, t_{k})

2-

({\vec{r}}_{1}, t_{1})

3-

({\vec{r}}_{2}, t_{2})

4-

({\vec{r}}_{k}, t_{k})

5-

O_{12 \dots k}^{(k)}

6-

O^{(k)} ({\vec{r}}_{1}, t_{1}, \dots, {\vec{r}}_{k}, t_{k})

7-

({\vec{r}}_{i}, t_{i})

8-

G_{1, 2}^{(2)}

9-

{| 1 ⟩, | 2 ⟩}

10-

{\hat{ρ}}_{s} = (\begin{matrix} ρ_{1} & 0 \\ 0 & ρ_{2} \end{matrix}) = ρ_{1} | 1 ⟩ ⟨ 1 | + ρ_{2} | 2 ⟩ ⟨ 2 |

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: quant-ph

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0602322

Formulas:

1-

[α / Fe] \leq 0.1

2-

[α / Fe] = + 0.15

3-

01^{h} 20^{m} {06.70}^{s}

4-

+ 03^{\circ} 24^{'} {55.0}^{''}

5-

02^{h} 41^{m} {04.80}^{s}

6-

- 08^{\circ} 15^{'} {20.8}^{''}

7-

08^{h} 12^{m} {54.1}^{s}

8-

+ 55^{\circ} 40^{'} 19^{''}

9-

11^{h} 19^{m} {21.6}^{s}

10-

+ 57^{\circ} 45^{'} 29^{''}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1704.02871

Formulas:

1-

W_{n} (b)

2-

W_{n} (b)

3-

b^{n - 1} ≢ 1 (mod n)

4-

2^{i} | (n - 1)

5-

\gcd (b^{(n - 1) / 2^{i}} - 1, n)

6-

W_{n} (b)

7-

W_{n} (b)

8-

W_{n} (b)

9-

W_{n} (b)

10-

W_{n} (b)

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/1008.4576

Formulas:

1-

L < 0.1 L_{⊙}

2-

f_{λ}^{q u o t e d} = \frac{\int_{λ_{1}}^{λ_{2}} R_{i} (λ) λ f_{λ} 𝑑 λ}{\int_{λ_{1}}^{λ_{2}} λ^{- 1} R_{i} (λ) λ 𝑑 λ}

3-

λ_{e f f} = \frac{\int_{λ_{1}}^{λ_{2}} λ R_{i} (λ) λ f_{λ} 𝑑 λ}{\int_{λ_{1}}^{λ_{2}} R_{i} (λ) λ f_{λ} 𝑑 λ}

4-

R_{i} (λ) λ

5-

W = R_{i} (λ) λ f_{λ}

6-

λ_{e f f} = 18.0

7-

m_{i} = - 2.5 \log (F_{i} / Z P_{i})

8-

m_{S 9 W} < 6

9-

K_{s} - m_{S 9 W}

10-

m_{S 9 W} = 7.63

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1809.08231

Formulas:

1-

P_{R G} = P_{G R} = \frac{1}{2} {cos}^{2} (\frac{α - β}{2})

2-

α - β = \frac{2 π}{3}

3-

P_{G R} + P_{R G} = \frac{1}{8}

4-

⟨ α, β ⟩ = \sum (i \cdot j) \cdot p (i, j ∣ α, β)

5-

p (i, j ∣ α, β)

6-

⟨ α, β ⟩ = \frac{{(+ 1)}_{A} {(- 1)}_{B} + {(+ 1)}_{A} {(+ 1)}_{B} + {(- 1)}_{A} {(- 1)}_{B} + \dots}{N}

7-

⟨ α, β ⟩ = \frac{{(+ 1)}_{A} (\sum BA+) + {(- 1)}_{A} (\sum BA-)}{N}

8-

⟨ α, β ⟩ = \frac{{(+ 1)}_{A} (\sum BA+)}{N} + \frac{{(- 1)}_{A} (\sum BA-)}{N} = \frac{{(+ 1)}_{A} (\sum BA+)}{2 \frac{N}{2}} + \frac{{(- 1)}_{A} (\sum BA-)}{2 \frac{N}{2}}

9-

⟨ α, β ⟩ = \frac{1}{2} {(+ 1)}_{A} \bar{B A +} + \frac{1}{2} {(- 1)}_{A} \bar{B A -}

10-

⟨ α, β ⟩ = 0

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/0807.2538

Formulas:

1-

1, 1, 2, 3, \dots ?

2-

1, 1, 2, 3, 7, 23, 59, 314, \dots,

3-

τ_{n + 2} = \frac{τ_{n + 1} τ_{n - 1} + {(τ_{n})}^{2}}{τ_{n - 2}}, τ_{0} = τ_{1} = τ_{2} = τ_{3} = 1,

4-

y^{2} = 4 x^{3} - 4 x + 1 .

5-

τ_{n + 2} τ_{n - 2} = α τ_{n + 1} τ_{n - 1} + β {(τ_{n})}^{2}

6-

τ_{n} = A B^{n} \frac{σ (z_{0} + n κ)}{σ {(κ)}^{n^{2}}},

7-

A = \frac{τ_{0}}{σ (z_{0})}, B = \frac{σ (κ) σ (z_{0}) τ_{1}}{σ (z_{0} + κ) τ_{0}},

8-

y^{2} = 4 x^{3} - g_{2} x - g_{3}

9-

τ_{0} \neq 0, τ_{1}, τ_{2}, τ_{3}

10-

τ_{2 k} = τ_{0} {(τ_{2} / τ_{0})}^{k} β^{k (k - 1) / 2},

Formulas (html):

Correct Categorie: nlin

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/nlin/0605022

Formulas:

1-

\bar{X 1} = \bar{F} (\bar{X 1}, μ) and \bar{X 2} = \bar{F} (\bar{X 2}, μ) .

2-

\bar{X 1} = (X 1, Y 1)

3-

\bar{X 2} = (X 2, Y 2)

4-

\bar{F} (\bar{X 1}, μ) + I_{1} (ϵ, \bar{X 1}, \bar{X 2})

5-

\bar{F} (\bar{X 2}, μ) + I_{2} (ϵ, \bar{X 1}, \bar{X 2})

6-

I_{i} = ϵ X_{j}

7-

I_{i} = ϵ (X_{j} - X_{i})

8-

I_{i} = μ (1 - ϵ X_{j})

9-

i, j = 1, 2

10-

(δ \bar{X}, δ \bar{Y})

Formulas (html):

Correct Categorie: nlin

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/0812.0365

Formulas:

1-

κ_{\max} > | ω | > κ

2-

Φ = - \frac{G M}{R - 2 r_{g}}, r_{g} \equiv \frac{G M}{c^{2}},

3-

R = \sqrt{r^{2} + z^{2}}

4-

r = 6 r_{g}

5-

r = 4 r_{g}

6-

ν = α c_{s} H

7-

H \sim c_{s} r / v_{ϕ}

8-

\frac{\partial (ρ \vec{v})}{\partial t} = \nabla \cdot σ,

9-

Δ t_{visc} = C_{visc} \min (\frac{Δ x_{i}^{2}}{ν}),

10-

Δ t_{sub} = \frac{Δ t_{Cour}}{N} \leq Δ t_{visc},

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0104143

Formulas:

1-

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

2-

20 g c m^{- 2}

3-

N (E_{γ}, x)

4-

N (E_{γ}, x) = \frac{0.31}{\sqrt{\ln (\frac{E_{γ}}{E_{t}})}} \exp (t (1 - 1.5 \ln s))

5-

g c m^{- 2}

6-

s = \frac{3 t}{(t + 2 \ln \frac{E_{γ}}{E_{t}})}

7-

g c m^{- 2}

8-

h = (6740 + 2.5 x) \ln (\frac{1030}{x}) m

9-

n = 1 + n_{0}

10-

n_{0} = 2.9 \times 10^{- 4} e^{- \frac{h}{7100}}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1201.4650

Formulas:

1-

E [D] = E [T_{A}] + E [T_{C O O P}]

2-

E [T_{A}]

3-

E [T_{C O O P}]

4-

E [T_{A}]

5-

E [T_{C O O P}]

6-

E [T_{C O O P}]

7-

E [T_{C O O P}] = T_{S I F S} + T_{C F C} + T_{B} + T_{D I F S} + T_{O N C} +

8-

+ E [r] \cdot T_{A \oplus B} + T_{S I F S} + T_{A C K} + T_{S I F S} + T_{A C K}

9-

T_{S I F S}

10-

T_{D I F S}

Formulas (html):

Correct Categorie: cs

Guessed Categorie: cs

Result: correct

Paper: https://arxiv.org/abs/0810.2667

Formulas:

1-

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

2-

S U (15)

3-

S U {(3)}_{L}

4-

SU {(3)}_{L} \times U {(1)}_{Y}

5-

SU {(2)}_{L} \times U {(1)}_{Y}

6-

SU {(3)}_{L}

7-

SU {(2)}_{L} \times U {(1)}_{Y} \to U {(1)}_{e}

8-

SU {(3)}_{L}

9-

\frac{M_{Y}}{M_{Z^{'}}} = \frac{\sqrt{3 (1 - 4 \sin^{2} θ_{W})}}{2 \cos θ_{W}}

10-

S U (15)

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: hep-ph

Result: correct

Paper: https://arxiv.org/abs/2011.09715

Formulas:

1-

2 p - 1 s

2-

Δ E / E \sim 10^{- 4}

3-

50 keV to 100 keV

4-

Δ E / E \sim 8 \times 10^{- 4}

5-

α {(Z α)}^{3}

6-

α {(Z α)}^{5}

7-

α {(Z α)}^{7}

8-

α^{2} (Z α)

9-

n_{e x o t i c} \sim n_{e^{-}} \sqrt{m_{e x o t i c} / m_{e^{-}}}

10-

(2 ℓ + 1)

Formulas (html):

Correct Categorie: physics

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1907.02105

Formulas:

1-

Δ {\vec{V}}_{\vec{E} \times \vec{B}} (t) = \frac{ω_{c s}^{2}}{ω_{c s}^{2} - ω_{l}^{2}} \frac{\vec{E} (t) \times \vec{B}}{B^{2}}

2-

ω_{c e} > ω_{l} > ω_{c i}

3-

\frac{\partial ρ}{\partial t} + \vec{\nabla} . \vec{J} = 0

4-

L_{x} = 3000 c / ω_{p e}

5-

L_{y} = 100 c / ω_{p e}

6-

x = 500 c / ω_{p e}

7-

x = 500 c / ω_{p e}

8-

Δ x = 0.1 c / ω_{p e}

9-

Δ t = 0.02 ω_{p e}^{- 1}

10-

λ_{l} = 9.42 μ m

Formulas (html):

Correct Categorie: physics

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1501.05792

Formulas:

1-

\frac{\partial}{\partial t} ρ_{s} + \frac{\partial}{\partial 𝒓} \cdot ρ_{s} 𝒖_{s}

2-

m_{s} Q_{n}^{(s)},

3-

\frac{\partial}{\partial t} ρ 𝒖 + \frac{\partial}{\partial 𝒓} \cdot ({\underline{\underline{P}}}^{*} + ρ 𝒖 𝒖)

4-

- Q_{m}^{(e)},

5-

\frac{\partial}{\partial t} ℰ_{tot}^{*} + \frac{\partial}{\partial 𝒓} \cdot (ℰ_{tot}^{*} 𝒖 + 𝒒^{*} + {\underline{\underline{P}}}^{*} \cdot 𝒖)

6-

- Q_{ℰ}^{(e)} .

7-

ρ = \sum_{i = 1}^{N} ρ_{i}

8-

m_{s} Q_{n}^{(s)} = - \nabla \cdot (ρ_{i} \sum_{j = 0} 𝐕_{i}^{j}),

9-

Q_{m}^{(e)} = - \sum_{i = 1}^{n_{s}} ρ_{i} F_{i}

10-

Q_{ℰ}^{(e)} = - \sum_{i = 1}^{n_{s}} ρ_{i} ρ F_{i} (𝐮 + \sum_{j = 0} V_{i}^{(j)}),

Formulas (html):

Correct Categorie: math

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1609.08358

Formulas:

1-

A (T) = 194 (1 - 0.7 {(T / T_{C})}^{4.2})

2-

k_{s} = D / J

3-

g μ_{B} H_{c 2} \approx A k_{s}^{2}

4-

A = J \cdot S \cdot a^{2}

5-

T < T_{2, ↓, ↑}

6-

T_{2, ↓, ↑}

7-

ϵ_{𝒒} = A {(𝒒 - 𝒌_{s})}^{2} + H - H_{c 2}

8-

θ_{0} = {(2 A m_{n})}^{- 1}

9-

θ_{C}^{2} (H) = θ_{0}^{2} - \frac{θ_{0}}{E_{i}} H + θ_{B}^{2},

10-

2 π / k_{s}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1603.04771

Formulas:

1-

y [n] = (x * k) [n] + ϵ [n], k [n] \geq 0, \sum_{n} k [n] = 1,

2-

x_{p} = {x [n] : n \in p}

3-

y_{p^{+}} = {x [n] : n \in p^{+}}

4-

x_{p} [n]

5-

y_{p} [n]

6-

G_{p^{+}} [z] \in ℂ

7-

Y_{p^{+}} [z]

8-

y_{p^{+}} [n]

9-

{\hat{X}}_{p^{+}} [z] = G_{p^{+}} [z] \times Y_{p^{+}} [z] .

10-

{\hat{x}}_{p} [n]

Formulas (html):

Correct Categorie: cs

Guessed Categorie: cs

Result: correct

Paper: https://arxiv.org/abs/1401.0819

Formulas:

1-

d s^{2} = e^{ν} d t^{2} - e^{λ} d r^{2} - r^{2} d θ^{2} - r^{2} \sin^{2} θ d ϕ^{2}

2-

T_{α β} = (ρ c^{2} + p) u_{α} u_{β} - p g_{α β}

3-

T_{00} = ρ c^{2} e^{ν}, T_{11} = p e^{λ}, T_{22} = p r^{2}, T_{33} = p r^{2} \sin^{2} θ

4-

e^{- λ} (\frac{λ^{'}}{r} - \frac{1}{r^{2}}) + \frac{1}{r^{2}} = \frac{8 π k}{c^{2}} ρ

5-

e^{- λ} (\frac{λ^{'}}{r} + \frac{1}{r^{2}}) - \frac{1}{r^{2}} = \frac{8 π k}{c^{4}} p

6-

\frac{d p}{d r} = - \frac{ν^{'}}{2} (ϵ + p)

7-

ρ = ρ (p)

8-

\frac{d p (r)}{d r} = - \frac{G ρ (r) m (r)}{r^{2}} [1 + \frac{p (r)}{ρ c^{2}}] [1 + \frac{4 π p (r) r^{3}}{m (r) c^{2}}] {[1 - \frac{2 G m (r)}{c^{2} r}]}^{- 1}

9-

m (r) = \int_{0}^{r} 4 π ρ (r^{'}) r^{', 2} 𝑑 r^{'}

10-

ρ (r) = ρ_{0} (r) (1 + \frac{ϵ (r)}{ρ_{0} (r) c^{2}})

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: gr-qc

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0506282

Formulas:

1-

H J D = 2452527.89275 (\pm 0.00395) + 0.0743055 (\pm 0.0017361) E

2-

⟨ H P S ⟩ = 650 \pm 46

3-

r_{d} \sim 1.8 \times 10^{10}

4-

r_{d} \sim 1.98 \times 10^{10}

5-

ϕ_{R / B} = 0.44

6-

M_{2} = 0.17 M_{⊙}

7-

R_{2} = 0.19 R_{⊙}

8-

M_{2} = 0.03 M_{⊙}

9-

R_{2} = 0.11 R_{⊙}

10-

M_{2} = M_{1} = 0.03 M_{⊙}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0701550

Formulas:

1-

M_{NFW} (R)

2-

ρ_{NFW} (R) = \frac{ρ_{s}}{(R / r_{s}) {(1 + R / r_{s})}^{2}}

3-

ρ_{s} = \frac{Δ}{3} \frac{c^{3}}{\ln (1 + c) - \frac{c}{1 + c}} ρ_{c},

4-

c ≃ 13.6 {(\frac{M_{vir}}{10^{11} M_{⊙}})}^{- 0.13}, r_{s} ≃ 8.8 {(\frac{M_{vir}}{10^{11} M_{⊙}})}^{0.46} kpc

5-

r_{vir} = c r_{s}

6-

ρ_{PI} (R) = \frac{ρ_{0}}{1 + R^{2} / R_{C}^{2}}

7-

M_{NFW} (R_{f}) = M_{PI} (R_{f})

8-

≳ 3 - 5 R_{D}

9-

M_{h} (R) ≃ G^{- 1} V^{2} (R) R

10-

ρ_{h} (R) ≃ 1 / (4 π R^{2}) d M_{h} (R) / d R

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1806.04430

Formulas:

1-

2.19 (4) μ_{B}

2-

3.10 (6) μ_{B}

3-

I 4 / m m m

4-

𝒂_{m a g} = 𝒂 + 𝒃

5-

𝒃_{m a g} = 𝒂 - 𝒃

6-

I 4 / m m m

7-

(\frac{1}{2}, \frac{1}{2}, 0)

8-

(1, 0, 0)

9-

(μ_{B} / Cr(II))

10-

(μ_{B} / Cr(I))

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/physics/0406118

Formulas:

1-

\begin{matrix} \begin{matrix} x & \to & - x \\ y & \to & - y \\ z & \to & - z \end{matrix}} & 𝐫 & \to & - 𝐫 \\ \begin{matrix} t & \to & t \end{matrix} \end{matrix}

2-

\ddot{𝐫} = q (𝐄 + \dot{𝐫} \times 𝐁) / m

3-

q \dot{𝐫} \times 𝐁 / m

4-

𝐅 = (\begin{matrix} 0 & - E_{x} & - E_{y} & - E_{z} \\ E_{x} & 0 & B_{z} & - B_{y} \\ E_{y} & - B_{z} & 0 & B_{x} \\ E_{Z} & B_{y} & - B_{x} & 0 \end{matrix})

5-

- \nabla A_{t} - \partial_{t} (A_{x}, A_{y}, A_{z})

6-

\nabla \times (A_{x}, A_{y}, A_{z})

7-

\begin{matrix} P : & q & = & \oint 𝐄 . \hat{𝐧} dS & \to & \oint (-E) . (- \hat{𝐧}) dS & = & q \end{matrix}

8-

\begin{matrix} P : & Q_{m} & = & \oint 𝐁 . \hat{𝐧} dS & \to & \oint 𝐁 . (- \hat{𝐧}) dS & = & - Q_{m} \end{matrix}

9-

\begin{matrix} P : & \ddot{𝐫} & = & q (𝐄 + \dot{𝐫} \times 𝐁) / m & \to & (- q) (𝐄 + \dot{-r} \times -B) / m & = & \ddot{-r} \end{matrix}

10-

L_{i}, B, s, c, t, b

Formulas (html):

Correct Categorie: physics

Guessed Categorie: physics

Result: correct

Paper: https://arxiv.org/abs/1705.07664

Formulas:

1-

^{1, 2, 4, 5}

2-

diag (a_{1}, \dots, a_{n})

3-

a_{1}, \dots, a_{n}

4-

Diag (𝐀) = diag (a_{11}, \dots, a_{n n})

5-

Off (𝐀) = 𝐀 - Diag (𝐀)

6-

𝒢 = ({1, \dots, n}, ℰ, 𝐖)

7-

𝐖 = (w_{i j})

8-

w_{i j} = 0

9-

(i, j) \notin ℰ

10-

w_{i j} > 0

Formulas (html):

Correct Categorie: cs

Guessed Categorie: math

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/0309630

Formulas:

1-

n_{2 D} \sim 1 - 6 \times 10^{12}

2-

(0.208 \pm 0.002) m_{e}

3-

(n_{2 D})

4-

m_{e} < m_{0}^{*} <

5-

m_{e} < m_{0}^{*} <

6-

m_{e} < m_{0}^{*} <

7-

1 - 6 \times 10^{12}

8-

m_{0}^{*} = (0.208 \pm 0.002) m_{e}

9-

n_{2 D} = 2.3 \times 10^{12}

10-

n_{2 D} = 2.3 \times 10^{12}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1702.05524

Formulas:

1-

Γ_{k} (x) := lim_{n \to \infty} \frac{n! k^{n} {(n^{k})}^{\frac{x}{k} - 1}}{{(x)}_{n, k}}, k > 0,

2-

{(x)}_{n, k} := x (x + k) (x + 2 k) \dots (x + (n - 1) k)

3-

Γ_{k} (x) = \int_{0}^{\infty} t^{x - 1} e^{- \frac{t^{k}}{k}} 𝑑 t, Re (x) > 0 .

4-

Γ_{k} (x + k) = x Γ_{k} (x)

5-

Γ_{k} (x) = k^{\frac{x}{k} - 1} Γ (\frac{x}{k})

6-

Γ_{k} (k) = 1

7-

Γ_{k} (x + n k) = Γ_{k} (x) {(x)}_{n, k}

8-

J_{k, ν}^{γ, λ} (x) := \sum_{n = 0}^{\infty} \frac{{(γ)}_{n, k}}{Γ_{k} (λ n + υ + 1)} \frac{{(- 1)}^{n} {(x / 2)}^{n}}{{(n!)}^{2}},

9-

α, λ, γ, υ \in C

10-

Re (λ) > 0

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/physics/0603225

Formulas:

1-

σ (𝐫, t)

2-

σ_{l} (𝐫, t) = \int G_{l} (𝐫 - 𝐫^{'}) σ (𝐫^{'}, t) 𝑑 𝐫^{'}

3-

ρ_{l} (σ, t)

4-

𝐯 (𝐱 + 𝐫, t) - 𝐯 (𝐱, t)

5-

𝚺_{i j} = \frac{1}{2} (\partial_{j} u_{i} + \partial_{i} u_{j})

6-

\pm s (t)

7-

Δ t_{1 / 2}

8-

ρ_{l} (σ, t + Δ t_{1 / 2}) = 2 \int ρ_{l} (σ^{'}, t) ρ_{l} (σ - σ^{'}, t) 𝑑 σ^{'}

9-

σ - m i n (σ)

10-

\hat{ρ_{l}} (κ) = \int ρ_{l} (σ) e^{- κ σ} 𝑑 σ

Formulas (html):

Correct Categorie: physics

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/0004121

Formulas:

1-

𝐑_{0} (s)

2-

𝐭_{0} = d 𝐑_{0} / d s

3-

𝐮_{0} (s)

4-

𝐯_{0} (s)

5-

\frac{d 𝐭_{0}}{d s} = ω_{10} 𝐮_{0} + ω_{20} 𝐯_{0}, \frac{d 𝐮_{0}}{d s} = - ω_{10} 𝐭_{0} + ω_{30} 𝐯_{0}, \frac{d 𝐯_{0}}{d s} = - ω_{20} 𝐭_{0} - ω_{30} 𝐮_{0},

6-

ω_{k 0} (s)

7-

𝐫_{0} (ξ_{1}, ξ_{2}, s) = 𝐑_{0} (s) + ξ_{1} 𝐮_{0} (s) + ξ_{2} 𝐯_{0} (s) .

8-

𝐫 (ξ_{1}, ξ_{2}, s) = 𝐑 (s) + ξ_{1} 𝐮 (s) + ξ_{2} 𝐯 (s),

9-

𝐭 = d 𝐑 / d s

10-

\frac{d 𝐭}{d s} = ω_{1} 𝐮 + ω_{2} 𝐯, \frac{d 𝐮}{d s} = - ω_{1} 𝐭 + ω_{3} 𝐯, \frac{d 𝐯}{d s} = - ω_{2} 𝐭 - ω_{3} 𝐮,

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/0707.0589

Formulas:

1-

Ξ_{b}^{-} \to J / ψ Ξ^{-}

2-

J / ψ \to μ^{+} μ^{-}

3-

Ξ^{-} \to Λ π^{-}

4-

Λ \to p π^{-}

5-

u u b, d d b

6-

J / ψ Ξ^{-}

7-

J / ψ \to μ^{+} μ^{-}

8-

Ξ^{-} \to Λ π^{-}

9-

Λ \to p π^{-}

10-

J / ψ \to μ^{+} μ^{-}

Formulas (html):

Correct Categorie: hep-ex

Guessed Categorie: hep-ex

Result: correct

Paper: https://arxiv.org/abs/cond-mat/0604186

Formulas:

1-

S O (4)

2-

S O (5)

3-

Ω_{R} = 2 π \times 1.43

4-

\int 𝑑 𝐱 ψ_{m}^{†} (𝐱) (- \frac{ℏ^{2} \nabla^{2}}{4 m} + δ - 2 μ + 2 V (𝐱)) ψ_{m} (𝐱)

5-

+ \sum_{σ = ↑, ↓} \int 𝑑 𝐱 ψ_{σ}^{†} (𝐱) (- \frac{ℏ^{2} \nabla^{2}}{2 m} - μ + V (𝐱)) ψ_{σ} (𝐱)

6-

+ g \int 𝑑 𝐱 (ψ_{m}^{†} (𝐱) ψ_{↑} (𝐱) ψ_{↓} (𝐱) + ψ_{↓}^{†} (𝐱) ψ_{↑}^{†} (𝐱) ψ_{m} (𝐱)),

7-

ψ_{σ} (𝐱)

8-

ψ_{m} (𝐱)

9-

g = ℏ \sqrt{4 π a_{bg} Δ B Δ μ_{mag} / m}

10-

δ = Δ μ_{mag} (B - B_{0})

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1204.3480

Formulas:

1-

S_{d} = 5 / 2, g \approx 2

2-

T_{N} = T_{MI} = 8

3-

[0 \bar{1} 1]

4-

χ_{CW} (T)

5-

a^{*} \times b \times c \sim 0.05 \times 3 \times 3

6-

μ_{0} H = 7

7-

μ_{0} H = 7

8-

μ_{0} H = 7

9-

H ⊥ [0 \bar{1} 1]

10-

∠ (H, a^{*}) = 45^{\circ}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1412.5312

Formulas:

1-

ϕ_{t t} + α ϕ_{t} - ϕ_{x x} = β ϕ_{x x t} + η - \sin (ϕ),

2-

ϕ_{x} (0, t) = Γ + A \sin Ω t, ϕ_{x} (L, t) = Γ,

3-

α = ω_{p} / ω_{c}

4-

ω_{p} = \sqrt{2 e I_{c} / ℏ C}

5-

ω_{c} = 2 e I_{c} R_{N} / ℏ

6-

Ω = 2 π f_{FF} / ω_{p}

7-

N = Γ L / 2 π

8-

ϕ_{0} = ω t + Γ x

9-

ϕ (x, t) = ϕ_{0} + f_{+} (x) \cos Ω t + f_{-} (x) \sin Ω t + ψ (x, t) + θ

10-

ψ (x, t)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/physics/0105049

Formulas:

1-

D_{q}^{A} = {\bar{α}}_{0} ϕ^{q}

2-

D_{q}^{B} = \frac{{\bar{α}}_{0}}{2} ϕ^{q},

3-

{\bar{α}}_{0} = 136 + 6 ϕ^{3} (1 - ϕ^{3})

4-

ϕ = 1 - ϕ^{2} = (\sqrt{5} - 1) / 2 ≃ 0.618033989

5-

(136 + 6 k)

6-

(68 + 3 k)

7-

k = ϕ^{3} (1 - ϕ^{3}) ≃ 0.18033989 .

8-

q = 2, 3, \dots, 6

9-

P_{2} \to P_{2}^{'}

10-

P_{2}^{'} \to P_{2}

Formulas (html):

Correct Categorie: physics

Guessed Categorie: hep-ph

Result: incorrect

Paper: https://arxiv.org/abs/1206.4101

Formulas:

1-

ℱ = U - T S

2-

Δ U = U_{12} - (U_{11} + U_{22}) / 2

3-

Δ ℱ = - A σ \propto R^{2}

4-

Δ ℱ = V Δ U \propto R^{3}

5-

𝒫 (ε) = \frac{1}{\bar{ε} - ε_{0}} \exp [- \frac{ε - ε_{0}}{\bar{ε} - ε_{0}}]

6-

\vec{v} = (u, v)

7-

ξ (x, y, t)

8-

ξ = 1 (0)

9-

\frac{\partial}{\partial t} [ξ] + \frac{\partial}{\partial x} [ξ u] + \frac{\partial}{\partial y} [ξ v] - \frac{\partial}{\partial y} [ξ v_{s} (ξ)] = 0,

10-

\vec{v} = (u, v)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/0903.1799

Formulas:

1-

[\hat{x}, \hat{p}] = i ℏ

2-

[\hat{X}, \hat{P}] = 0

3-

10^{- 8} m / s

4-

10^{- 6} k g

5-

\frac{Δ p Δ x}{ℏ} \sim 10^{12}

6-

ρ = \int 𝑑 p 𝑑 q f (p, q) | ψ_{p q} ⟩ ⟨ ψ_{p q} |

7-

f (p, q)

8-

| ψ_{p q} ⟩

9-

| ψ_{n m} ⟩

10-

ρ^{'} = \sum_{n m} f_{n m} | ψ_{n m} ⟩ ⟨ ψ_{n m} |

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/1904.11443

Formulas:

1-

V_{P1}, V_{P2} \approx - 2

2-

Δ I_{S D} \approx 0.3

3-

Δ I = 2 e / t_{cycle} = 0.4

4-

f_{m e a s} = 89.75

5-

Δ I_{S D}

6-

F_{C} = 99.3 \pm 0.05

7-

Δ I_{S D} = a \cos (2 π f τ + ϕ) \exp (- {(τ / T_{2}^{*})}^{α^{*}})

8-

T_{2, Q 1}^{*} = 817

9-

T_{2, Q 2}^{*} = 348

10-

α_{Q 1}^{*} = 1.2 \pm 0.2

Formulas (html):

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xref="p10.4.m4.2.3.2.cmml"><msubsup id="p10.4.m4.2.3.2a" xref="p10.4.m4.2.3.2.cmml"><mi id="p10.4.m4.2.3.2.2.2" xref="p10.4.m4.2.3.2.2.2.cmml">T</mi><mrow id="p10.4.m4.2.2.2.2" xref="p10.4.m4.2.2.2.3.cmml"><mn id="p10.4.m4.1.1.1.1" xref="p10.4.m4.1.1.1.1.cmml">2</mn><mo id="p10.4.m4.2.2.2.2.2" xref="p10.4.m4.2.2.2.3.cmml">,</mo><mrow id="p10.4.m4.2.2.2.2.1" xref="p10.4.m4.2.2.2.2.1.cmml"><mi id="p10.4.m4.2.2.2.2.1.2" xref="p10.4.m4.2.2.2.2.1.2.cmml">Q</mi><mo id="p10.4.m4.2.2.2.2.1.1" xref="p10.4.m4.2.2.2.2.1.1.cmml">⁢</mo><mn id="p10.4.m4.2.2.2.2.1.3" xref="p10.4.m4.2.2.2.2.1.3.cmml">1</mn></mrow></mrow><mo id="p10.4.m4.2.3.2.3" xref="p10.4.m4.2.3.2.3.cmml">*</mo></msubsup></mpadded><mo rspace="5.8pt" id="p10.4.m4.2.3.1" xref="p10.4.m4.2.3.1.cmml">=</mo><mn id="p10.4.m4.2.3.3" xref="p10.4.m4.2.3.3.cmml">817</mn></mrow></math>, <math><mrow id="p10.5.m5.2.3" xref="p10.5.m5.2.3.cmml"><mpadded width="+3.3pt" id="p10.5.m5.2.3.2" xref="p10.5.m5.2.3.2.cmml"><msubsup id="p10.5.m5.2.3.2a" xref="p10.5.m5.2.3.2.cmml"><mi id="p10.5.m5.2.3.2.2.2" xref="p10.5.m5.2.3.2.2.2.cmml">T</mi><mrow id="p10.5.m5.2.2.2.2" xref="p10.5.m5.2.2.2.3.cmml"><mn id="p10.5.m5.1.1.1.1" xref="p10.5.m5.1.1.1.1.cmml">2</mn><mo id="p10.5.m5.2.2.2.2.2" xref="p10.5.m5.2.2.2.3.cmml">,</mo><mrow id="p10.5.m5.2.2.2.2.1" xref="p10.5.m5.2.2.2.2.1.cmml"><mi id="p10.5.m5.2.2.2.2.1.2" xref="p10.5.m5.2.2.2.2.1.2.cmml">Q</mi><mo id="p10.5.m5.2.2.2.2.1.1" xref="p10.5.m5.2.2.2.2.1.1.cmml">⁢</mo><mn id="p10.5.m5.2.2.2.2.1.3" xref="p10.5.m5.2.2.2.2.1.3.cmml">2</mn></mrow></mrow><mo id="p10.5.m5.2.3.2.3" xref="p10.5.m5.2.3.2.3.cmml">*</mo></msubsup></mpadded><mo rspace="5.8pt" id="p10.5.m5.2.3.1" xref="p10.5.m5.2.3.1.cmml">=</mo><mn id="p10.5.m5.2.3.3" xref="p10.5.m5.2.3.3.cmml">348</mn></mrow></math>, <math><mrow id="p10.6.m6.1.1" xref="p10.6.m6.1.1.cmml"><msubsup id="p10.6.m6.1.1.2" xref="p10.6.m6.1.1.2.cmml"><mi id="p10.6.m6.1.1.2.2.2" xref="p10.6.m6.1.1.2.2.2.cmml">α</mi><mrow id="p10.6.m6.1.1.2.3" xref="p10.6.m6.1.1.2.3.cmml"><mi id="p10.6.m6.1.1.2.3.2" xref="p10.6.m6.1.1.2.3.2.cmml">Q</mi><mo id="p10.6.m6.1.1.2.3.1" xref="p10.6.m6.1.1.2.3.1.cmml">⁢</mo><mn id="p10.6.m6.1.1.2.3.3" xref="p10.6.m6.1.1.2.3.3.cmml">1</mn></mrow><mo id="p10.6.m6.1.1.2.2.3" xref="p10.6.m6.1.1.2.2.3.cmml">*</mo></msubsup><mo id="p10.6.m6.1.1.1" xref="p10.6.m6.1.1.1.cmml">=</mo><mrow id="p10.6.m6.1.1.3" xref="p10.6.m6.1.1.3.cmml"><mn id="p10.6.m6.1.1.3.2" xref="p10.6.m6.1.1.3.2.cmml">1.2</mn><mo id="p10.6.m6.1.1.3.1" xref="p10.6.m6.1.1.3.1.cmml">±</mo><mn id="p10.6.m6.1.1.3.3" xref="p10.6.m6.1.1.3.3.cmml">0.2</mn></mrow></mrow></math>

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1912.03638

Formulas:

1-

10^{29} e r g s^{- 1}

2-

10^{4} e r g c m^{- 2} s^{- 1}

3-

l_{c} = α H_{P}

4-

Δ Y / Δ Z

5-

l_{o v} = 0.24 H_{P}

6-

Ω / Ω_{c} = 0.6

7-

S = α \frac{N_{H} + N_{K}}{N_{R} + N_{V}},

8-

F_{x, m i n} = o (10^{4} erg {cm}^{- 2} \sec^{- 1})

9-

M < 1.5 M_{⊙}

10-

k_{i j} = \frac{a}{2 + b} e^{- c τ_{i j}} (c o s (\frac{2 π τ_{i j}}{P}) + 1 + b) + δ_{i j} σ^{2},

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1712.04850

Formulas:

1-

I (x, y)

2-

z (x, y)

3-

{(X, Y, Z)}^{T}

4-

{(U, V, W)}^{T}

5-

u = u_{t} + u_{r}, v = v_{t} + v_{r},

6-

u_{t} = \frac{- U + x W}{Z}, v_{t} = \frac{- V + y W}{Z},

7-

Z = \sqrt{\frac{{(- U + x W)}^{2} + {(- V + y W)}^{2}}{u_{t}^{2} + v_{t}^{2}}} .

8-

{(U, V, W)}^{T}

9-

z \in [0, 1]

10-

(u_{t}, v_{t})

Formulas (html):

Correct Categorie: cs

Guessed Categorie: cs

Result: correct

Paper: https://arxiv.org/abs/1603.04559

Formulas:

1-

\frac{2 m - n + 2}{7}

2-

S \subseteq V (G)

3-

ϕ (G) \leq k

4-

ϕ (G) \leq \frac{3 n}{10}

5-

ϕ (G) \leq \frac{5 m}{23}

6-

\frac{5}{3} (n - 2)

7-

\frac{25 n - 50}{69}

8-

ϕ (G) \leq \frac{m}{g}

9-

ϕ (G) \leq \frac{2 m - n + 2}{7}

10-

\frac{5}{3} (n - 2)

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/1610.02204

Formulas:

1-

S (𝐪, 𝐪^{'}; E) = \sum_{i, j} ⟨ ϕ_{i} | e^{i 𝐪 \cdot 𝐫} | ϕ_{j} ⟩ ⟨ ϕ_{j} | e^{- i 𝐪^{'} \cdot 𝐫} | ϕ_{i} ⟩ δ (E_{j} - E_{i} - E)

2-

S (𝐪, 𝐪^{'}; E) \propto \sum_{μ L M, μ^{'} L^{'} M^{'}} {⟨ j_{λ = 1} (q) ⟩}_{L E} {⟨ j_{λ = 1} (q^{'}) ⟩}_{L^{'} E} Y_{λ = 1}^{μ} {(𝐪)}^{*} Y_{λ = 1}^{μ^{'}} (𝐪^{'}) Ξ_{λ = 1 μ L M, λ = 1 μ^{'} L^{'} M^{'}} (E)

3-

Y_{λ = 1}^{μ} (𝐪)

4-

{⟨ j_{λ = 1} (q) ⟩}_{L E}

5-

j_{λ = 1} (q)

6-

Ξ_{λ μ L M, λ^{'} μ^{'} L M} (E)

7-

\sum_{n 𝐤} D_{L M}^{n 𝐤} {(D_{L^{'} M^{'}}^{n 𝐤})}^{*} δ (E_{n} (𝐤) - E)

8-

D_{L M}^{n 𝐤}

9-

Ξ_{λ = 1 μ L M, λ = 1 μ^{'} L M} (E)

10-

T_{p_{x, y, z}}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1107.4668

Formulas:

1-

r = d U / d I

2-

A l_{x} G a_{1 - x} A s

3-

1 k A / c m^{2}

4-

N d : Y A G

5-

η = L / (U \cdot I)

6-

r = d U / d I

7-

S = d L / d I

8-

d U / d I

9-

\begin{matrix} I (U) = I_{t h} \cdot e x p (A \cdot (U - U_{0}) + B \cdot {(U - U_{0})}^{2}), f o r U < U_{0} \\ I (U) = I_{t h} \cdot e x p (C \cdot (U - U_{0}) + D \cdot {(U - U_{0})}^{2}), f o r U > U_{0} \end{matrix}

10-

I (U_{0}) = I_{t h}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/astro-ph/9612103

Formulas:

1-

L \begin{matrix} < \\ \sim \end{matrix} 4 \times 10^{33}

2-

e \begin{matrix} < \\ \sim \end{matrix} 10^{- 7}

3-

\log (r / r_{g})

4-

≃ 10^{- 2} c

5-

\tilde{R} = r / r_{a}^{0}

6-

ρ_{0} ≃ 10^{- 3}

7-

r_{a}^{0} = 1.6 \times 10^{11}

8-

\dot{m} ≃ 2 \times 10^{10}

9-

M_{a c c} ≃ 0.05 M_{⊙}

10-

M_{a c c}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1306.4817

Formulas:

1-

⟨ T (σ, N) ⟩

2-

σ_{c} (N)

3-

σ_{c} (\infty)

4-

σ_{c} (N) = σ_{c} (\infty) + A N^{- 1 / ν}

5-

⟨ T (σ_{c} (N), N) ⟩

6-

⟨ T (σ_{c} (N), N) ⟩ \sim N^{η}

7-

| Δ σ | \sim N^{- ζ}

8-

1 / N < | Δ σ | < 100 N^{- ζ}

9-

⟨ T (σ, N) ⟩ / N^{η} \sim 𝒢 [{σ_{c} (N) - σ} N^{ζ}]

10-

⟨ T (σ) ⟩ \sim {(σ - σ_{c})}^{- τ}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1611.05408

Formulas:

1-

δ = (ℓ - s) / a \sqrt{2}

2-

𝐱 = (𝐚 + 𝐛) / 2

3-

𝐲 = (- 𝐚 + 𝐛) / 2

4-

Δ = (ℓ - s) / 2 = a δ / \sqrt{2}

5-

E_{JT} (Δ) = - g Δ + C Δ^{2} / 2

6-

Δ_{JT} = g / C

7-

s = a / 2 \sqrt{2}

8-

E_{BM} = A \exp (- r_{Cu - F} / ρ)

9-

E_{CF} = Γ - \sqrt{Γ^{2} + {(g Δ)}^{2}}

10-

- C_{Ewald} Δ^{2} / 2

Formulas (html):

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xref="p2.14.m14.1.1.1.1.3.cmml">a</mi></mrow><mo id="p2.14.m14.1.1.1.2" xref="p2.14.m14.1.1.1.2.cmml">⁢</mo><msqrt id="p2.14.m14.1.1.1.3" xref="p2.14.m14.1.1.1.3.cmml"><mn id="p2.14.m14.1.1.1.3.2" xref="p2.14.m14.1.1.1.3.2.cmml">2</mn></msqrt></mrow></mrow></math>, <math><mrow id="S0.F1.6.m2.1.1" xref="S0.F1.6.m2.1.1.cmml"><mi id="S0.F1.6.m2.1.1.3" xref="S0.F1.6.m2.1.1.3.cmml">𝐱</mi><mo id="S0.F1.6.m2.1.1.2" xref="S0.F1.6.m2.1.1.2.cmml">=</mo><mrow id="S0.F1.6.m2.1.1.1" xref="S0.F1.6.m2.1.1.1.cmml"><mrow id="S0.F1.6.m2.1.1.1.1.1" xref="S0.F1.6.m2.1.1.1.1.1.1.cmml"><mo stretchy="false" id="S0.F1.6.m2.1.1.1.1.1.2" xref="S0.F1.6.m2.1.1.1.1.1.1.cmml">(</mo><mrow id="S0.F1.6.m2.1.1.1.1.1.1" xref="S0.F1.6.m2.1.1.1.1.1.1.cmml"><mi id="S0.F1.6.m2.1.1.1.1.1.1.2" xref="S0.F1.6.m2.1.1.1.1.1.1.2.cmml">𝐚</mi><mo id="S0.F1.6.m2.1.1.1.1.1.1.1" xref="S0.F1.6.m2.1.1.1.1.1.1.1.cmml">+</mo><mi id="S0.F1.6.m2.1.1.1.1.1.1.3" xref="S0.F1.6.m2.1.1.1.1.1.1.3.cmml">𝐛</mi></mrow><mo stretchy="false" id="S0.F1.6.m2.1.1.1.1.1.3" xref="S0.F1.6.m2.1.1.1.1.1.1.cmml">)</mo></mrow><mo id="S0.F1.6.m2.1.1.1.2" xref="S0.F1.6.m2.1.1.1.2.cmml">/</mo><mn id="S0.F1.6.m2.1.1.1.3" xref="S0.F1.6.m2.1.1.1.3.cmml">2</mn></mrow></mrow></math>, <math><mrow id="S0.F1.7.m3.1.1" xref="S0.F1.7.m3.1.1.cmml"><mi id="S0.F1.7.m3.1.1.3" xref="S0.F1.7.m3.1.1.3.cmml">𝐲</mi><mo id="S0.F1.7.m3.1.1.2" xref="S0.F1.7.m3.1.1.2.cmml">=</mo><mrow id="S0.F1.7.m3.1.1.1" xref="S0.F1.7.m3.1.1.1.cmml"><mrow id="S0.F1.7.m3.1.1.1.1.1" xref="S0.F1.7.m3.1.1.1.1.1.1.cmml"><mo stretchy="false" id="S0.F1.7.m3.1.1.1.1.1.2" xref="S0.F1.7.m3.1.1.1.1.1.1.cmml">(</mo><mrow id="S0.F1.7.m3.1.1.1.1.1.1" xref="S0.F1.7.m3.1.1.1.1.1.1.cmml"><mrow id="S0.F1.7.m3.1.1.1.1.1.1.2" xref="S0.F1.7.m3.1.1.1.1.1.1.2.cmml"><mo id="S0.F1.7.m3.1.1.1.1.1.1.2.1" xref="S0.F1.7.m3.1.1.1.1.1.1.2.1.cmml">-</mo><mi id="S0.F1.7.m3.1.1.1.1.1.1.2.2" xref="S0.F1.7.m3.1.1.1.1.1.1.2.2.cmml">𝐚</mi></mrow><mo id="S0.F1.7.m3.1.1.1.1.1.1.1" xref="S0.F1.7.m3.1.1.1.1.1.1.1.cmml">+</mo><mi id="S0.F1.7.m3.1.1.1.1.1.1.3" xref="S0.F1.7.m3.1.1.1.1.1.1.3.cmml">𝐛</mi></mrow><mo stretchy="false" id="S0.F1.7.m3.1.1.1.1.1.3" xref="S0.F1.7.m3.1.1.1.1.1.1.cmml">)</mo></mrow><mo id="S0.F1.7.m3.1.1.1.2" xref="S0.F1.7.m3.1.1.1.2.cmml">/</mo><mn id="S0.F1.7.m3.1.1.1.3" xref="S0.F1.7.m3.1.1.1.3.cmml">2</mn></mrow></mrow></math>, <math><mrow id="p6.1.m1.1.1" xref="p6.1.m1.1.1.cmml"><mi mathvariant="normal" id="p6.1.m1.1.1.3" xref="p6.1.m1.1.1.3.cmml">Δ</mi><mo id="p6.1.m1.1.1.4" xref="p6.1.m1.1.1.4.cmml">=</mo><mrow id="p6.1.m1.1.1.1" xref="p6.1.m1.1.1.1.cmml"><mrow id="p6.1.m1.1.1.1.1.1" xref="p6.1.m1.1.1.1.1.1.1.cmml"><mo stretchy="false" id="p6.1.m1.1.1.1.1.1.2" xref="p6.1.m1.1.1.1.1.1.1.cmml">(</mo><mrow id="p6.1.m1.1.1.1.1.1.1" xref="p6.1.m1.1.1.1.1.1.1.cmml"><mi mathvariant="normal" id="p6.1.m1.1.1.1.1.1.1.2" xref="p6.1.m1.1.1.1.1.1.1.2.cmml">ℓ</mi><mo id="p6.1.m1.1.1.1.1.1.1.1" xref="p6.1.m1.1.1.1.1.1.1.1.cmml">-</mo><mi id="p6.1.m1.1.1.1.1.1.1.3" xref="p6.1.m1.1.1.1.1.1.1.3.cmml">s</mi></mrow><mo stretchy="false" id="p6.1.m1.1.1.1.1.1.3" xref="p6.1.m1.1.1.1.1.1.1.cmml">)</mo></mrow><mo id="p6.1.m1.1.1.1.2" xref="p6.1.m1.1.1.1.2.cmml">/</mo><mn id="p6.1.m1.1.1.1.3" xref="p6.1.m1.1.1.1.3.cmml">2</mn></mrow><mo id="p6.1.m1.1.1.5" xref="p6.1.m1.1.1.5.cmml">=</mo><mrow id="p6.1.m1.1.1.6" xref="p6.1.m1.1.1.6.cmml"><mrow id="p6.1.m1.1.1.6.2" xref="p6.1.m1.1.1.6.2.cmml"><mpadded width="+1.7pt" id="p6.1.m1.1.1.6.2.2" xref="p6.1.m1.1.1.6.2.2.cmml"><mi id="p6.1.m1.1.1.6.2.2a" xref="p6.1.m1.1.1.6.2.2.cmml">a</mi></mpadded><mo id="p6.1.m1.1.1.6.2.1" xref="p6.1.m1.1.1.6.2.1.cmml">⁢</mo><mi id="p6.1.m1.1.1.6.2.3" xref="p6.1.m1.1.1.6.2.3.cmml">δ</mi></mrow><mo id="p6.1.m1.1.1.6.1" xref="p6.1.m1.1.1.6.1.cmml">/</mo><msqrt id="p6.1.m1.1.1.6.3" xref="p6.1.m1.1.1.6.3.cmml"><mn id="p6.1.m1.1.1.6.3.2" xref="p6.1.m1.1.1.6.3.2.cmml">2</mn></msqrt></mrow></mrow></math>, <math><mrow id="p6.2.m2.1.2" xref="p6.2.m2.1.2.cmml"><mrow id="p6.2.m2.1.2.2" xref="p6.2.m2.1.2.2.cmml"><msub id="p6.2.m2.1.2.2.2" xref="p6.2.m2.1.2.2.2.cmml"><mi id="p6.2.m2.1.2.2.2.2" xref="p6.2.m2.1.2.2.2.2.cmml">E</mi><mi id="p6.2.m2.1.2.2.2.3" xref="p6.2.m2.1.2.2.2.3.cmml">JT</mi></msub><mo id="p6.2.m2.1.2.2.1" xref="p6.2.m2.1.2.2.1.cmml">⁢</mo><mrow id="p6.2.m2.1.2.2.3.2" xref="p6.2.m2.1.2.2.cmml"><mo stretchy="false" id="p6.2.m2.1.2.2.3.2.1" xref="p6.2.m2.1.2.2.cmml">(</mo><mi mathvariant="normal" id="p6.2.m2.1.1" xref="p6.2.m2.1.1.cmml">Δ</mi><mo stretchy="false" id="p6.2.m2.1.2.2.3.2.2" xref="p6.2.m2.1.2.2.cmml">)</mo></mrow></mrow><mo id="p6.2.m2.1.2.1" xref="p6.2.m2.1.2.1.cmml">=</mo><mrow id="p6.2.m2.1.2.3" xref="p6.2.m2.1.2.3.cmml"><mrow id="p6.2.m2.1.2.3.2" xref="p6.2.m2.1.2.3.2.cmml"><mo id="p6.2.m2.1.2.3.2.1" xref="p6.2.m2.1.2.3.2.1.cmml">-</mo><mrow id="p6.2.m2.1.2.3.2.2" xref="p6.2.m2.1.2.3.2.2.cmml"><mi id="p6.2.m2.1.2.3.2.2.2" xref="p6.2.m2.1.2.3.2.2.2.cmml">g</mi><mo id="p6.2.m2.1.2.3.2.2.1" xref="p6.2.m2.1.2.3.2.2.1.cmml">⁢</mo><mi mathvariant="normal" id="p6.2.m2.1.2.3.2.2.3" xref="p6.2.m2.1.2.3.2.2.3.cmml">Δ</mi></mrow></mrow><mo id="p6.2.m2.1.2.3.1" xref="p6.2.m2.1.2.3.1.cmml">+</mo><mrow id="p6.2.m2.1.2.3.3" xref="p6.2.m2.1.2.3.3.cmml"><mrow id="p6.2.m2.1.2.3.3.2" xref="p6.2.m2.1.2.3.3.2.cmml"><mi id="p6.2.m2.1.2.3.3.2.2" xref="p6.2.m2.1.2.3.3.2.2.cmml">C</mi><mo id="p6.2.m2.1.2.3.3.2.1" xref="p6.2.m2.1.2.3.3.2.1.cmml">⁢</mo><msup id="p6.2.m2.1.2.3.3.2.3" xref="p6.2.m2.1.2.3.3.2.3.cmml"><mi mathvariant="normal" id="p6.2.m2.1.2.3.3.2.3.2" xref="p6.2.m2.1.2.3.3.2.3.2.cmml">Δ</mi><mn id="p6.2.m2.1.2.3.3.2.3.3" xref="p6.2.m2.1.2.3.3.2.3.3.cmml">2</mn></msup></mrow><mo id="p6.2.m2.1.2.3.3.1" xref="p6.2.m2.1.2.3.3.1.cmml">/</mo><mn id="p6.2.m2.1.2.3.3.3" xref="p6.2.m2.1.2.3.3.3.cmml">2</mn></mrow></mrow></mrow></math>, <math><mrow id="p6.6.m6.1.1" xref="p6.6.m6.1.1.cmml"><msub id="p6.6.m6.1.1.2" xref="p6.6.m6.1.1.2.cmml"><mi mathvariant="normal" id="p6.6.m6.1.1.2.2" xref="p6.6.m6.1.1.2.2.cmml">Δ</mi><mi id="p6.6.m6.1.1.2.3" xref="p6.6.m6.1.1.2.3.cmml">JT</mi></msub><mo id="p6.6.m6.1.1.1" xref="p6.6.m6.1.1.1.cmml">=</mo><mrow id="p6.6.m6.1.1.3" xref="p6.6.m6.1.1.3.cmml"><mi id="p6.6.m6.1.1.3.2" xref="p6.6.m6.1.1.3.2.cmml">g</mi><mo id="p6.6.m6.1.1.3.1" xref="p6.6.m6.1.1.3.1.cmml">/</mo><mi id="p6.6.m6.1.1.3.3" xref="p6.6.m6.1.1.3.3.cmml">C</mi></mrow></mrow></math>, <math><mrow id="S0.F4.14.m7.1.1" xref="S0.F4.14.m7.1.1.cmml"><mi id="S0.F4.14.m7.1.1.2" xref="S0.F4.14.m7.1.1.2.cmml">s</mi><mo id="S0.F4.14.m7.1.1.1" xref="S0.F4.14.m7.1.1.1.cmml">=</mo><mrow id="S0.F4.14.m7.1.1.3" xref="S0.F4.14.m7.1.1.3.cmml"><mrow id="S0.F4.14.m7.1.1.3.2" xref="S0.F4.14.m7.1.1.3.2.cmml"><mi id="S0.F4.14.m7.1.1.3.2.2" xref="S0.F4.14.m7.1.1.3.2.2.cmml">a</mi><mo id="S0.F4.14.m7.1.1.3.2.1" xref="S0.F4.14.m7.1.1.3.2.1.cmml">/</mo><mn id="S0.F4.14.m7.1.1.3.2.3" xref="S0.F4.14.m7.1.1.3.2.3.cmml">2</mn></mrow><mo id="S0.F4.14.m7.1.1.3.1" xref="S0.F4.14.m7.1.1.3.1.cmml">⁢</mo><msqrt id="S0.F4.14.m7.1.1.3.3" xref="S0.F4.14.m7.1.1.3.3.cmml"><mn id="S0.F4.14.m7.1.1.3.3.2" xref="S0.F4.14.m7.1.1.3.3.2.cmml">2</mn></msqrt></mrow></mrow></math>, <math><mrow id="p8.2.m2.2.2" xref="p8.2.m2.2.2.cmml"><msub id="p8.2.m2.2.2.3" xref="p8.2.m2.2.2.3.cmml"><mi id="p8.2.m2.2.2.3.2" xref="p8.2.m2.2.2.3.2.cmml">E</mi><mi id="p8.2.m2.2.2.3.3" xref="p8.2.m2.2.2.3.3.cmml">BM</mi></msub><mo id="p8.2.m2.2.2.2" xref="p8.2.m2.2.2.2.cmml">=</mo><mrow id="p8.2.m2.2.2.1" xref="p8.2.m2.2.2.1.cmml"><mi id="p8.2.m2.2.2.1.3" xref="p8.2.m2.2.2.1.3.cmml">A</mi><mo id="p8.2.m2.2.2.1.2" xref="p8.2.m2.2.2.1.2.cmml">⁢</mo><mrow id="p8.2.m2.2.2.1.1.1" xref="p8.2.m2.2.2.1.1.2.cmml"><mi id="p8.2.m2.1.1" xref="p8.2.m2.1.1.cmml">exp</mi><mo id="p8.2.m2.2.2.1.1.1a" xref="p8.2.m2.2.2.1.1.2.cmml">⁡</mo><mrow id="p8.2.m2.2.2.1.1.1.1" xref="p8.2.m2.2.2.1.1.2.cmml"><mo stretchy="false" id="p8.2.m2.2.2.1.1.1.1.2" xref="p8.2.m2.2.2.1.1.2.cmml">(</mo><mrow id="p8.2.m2.2.2.1.1.1.1.1" xref="p8.2.m2.2.2.1.1.1.1.1.cmml"><mo id="p8.2.m2.2.2.1.1.1.1.1.1" xref="p8.2.m2.2.2.1.1.1.1.1.1.cmml">-</mo><mrow id="p8.2.m2.2.2.1.1.1.1.1.2" xref="p8.2.m2.2.2.1.1.1.1.1.2.cmml"><msub id="p8.2.m2.2.2.1.1.1.1.1.2.2" xref="p8.2.m2.2.2.1.1.1.1.1.2.2.cmml"><mi id="p8.2.m2.2.2.1.1.1.1.1.2.2.2" xref="p8.2.m2.2.2.1.1.1.1.1.2.2.2.cmml">r</mi><mrow id="p8.2.m2.2.2.1.1.1.1.1.2.2.3" xref="p8.2.m2.2.2.1.1.1.1.1.2.2.3.cmml"><mi id="p8.2.m2.2.2.1.1.1.1.1.2.2.3.2" xref="p8.2.m2.2.2.1.1.1.1.1.2.2.3.2.cmml">Cu</mi><mo id="p8.2.m2.2.2.1.1.1.1.1.2.2.3.1" xref="p8.2.m2.2.2.1.1.1.1.1.2.2.3.1.cmml">-</mo><mi mathvariant="normal" id="p8.2.m2.2.2.1.1.1.1.1.2.2.3.3" xref="p8.2.m2.2.2.1.1.1.1.1.2.2.3.3.cmml">F</mi></mrow></msub><mo id="p8.2.m2.2.2.1.1.1.1.1.2.1" xref="p8.2.m2.2.2.1.1.1.1.1.2.1.cmml">/</mo><mi id="p8.2.m2.2.2.1.1.1.1.1.2.3" xref="p8.2.m2.2.2.1.1.1.1.1.2.3.cmml">ρ</mi></mrow></mrow><mo stretchy="false" id="p8.2.m2.2.2.1.1.1.1.3" xref="p8.2.m2.2.2.1.1.2.cmml">)</mo></mrow></mrow></mrow></mrow></math>, <math><mrow id="p8.4.m4.1.2" xref="p8.4.m4.1.2.cmml"><msub id="p8.4.m4.1.2.2" xref="p8.4.m4.1.2.2.cmml"><mi id="p8.4.m4.1.2.2.2" xref="p8.4.m4.1.2.2.2.cmml">E</mi><mi id="p8.4.m4.1.2.2.3" xref="p8.4.m4.1.2.2.3.cmml">CF</mi></msub><mo id="p8.4.m4.1.2.1" xref="p8.4.m4.1.2.1.cmml">=</mo><mrow id="p8.4.m4.1.2.3" xref="p8.4.m4.1.2.3.cmml"><mi mathvariant="normal" id="p8.4.m4.1.2.3.2" xref="p8.4.m4.1.2.3.2.cmml">Γ</mi><mo id="p8.4.m4.1.2.3.1" xref="p8.4.m4.1.2.3.1.cmml">-</mo><msqrt id="p8.4.m4.1.1" xref="p8.4.m4.1.1.cmml"><mrow id="p8.4.m4.1.1.1" xref="p8.4.m4.1.1.1.cmml"><msup id="p8.4.m4.1.1.1.3" xref="p8.4.m4.1.1.1.3.cmml"><mi mathvariant="normal" id="p8.4.m4.1.1.1.3.2" xref="p8.4.m4.1.1.1.3.2.cmml">Γ</mi><mn id="p8.4.m4.1.1.1.3.3" xref="p8.4.m4.1.1.1.3.3.cmml">2</mn></msup><mo id="p8.4.m4.1.1.1.2" xref="p8.4.m4.1.1.1.2.cmml">+</mo><msup id="p8.4.m4.1.1.1.1" xref="p8.4.m4.1.1.1.1.cmml"><mrow id="p8.4.m4.1.1.1.1.1.1" xref="p8.4.m4.1.1.1.1.1.1.1.cmml"><mo stretchy="false" id="p8.4.m4.1.1.1.1.1.1.2" xref="p8.4.m4.1.1.1.1.1.1.1.cmml">(</mo><mrow id="p8.4.m4.1.1.1.1.1.1.1" xref="p8.4.m4.1.1.1.1.1.1.1.cmml"><mi id="p8.4.m4.1.1.1.1.1.1.1.2" xref="p8.4.m4.1.1.1.1.1.1.1.2.cmml">g</mi><mo id="p8.4.m4.1.1.1.1.1.1.1.1" xref="p8.4.m4.1.1.1.1.1.1.1.1.cmml">⁢</mo><mi mathvariant="normal" id="p8.4.m4.1.1.1.1.1.1.1.3" xref="p8.4.m4.1.1.1.1.1.1.1.3.cmml">Δ</mi></mrow><mo stretchy="false" id="p8.4.m4.1.1.1.1.1.1.3" xref="p8.4.m4.1.1.1.1.1.1.1.cmml">)</mo></mrow><mn id="p8.4.m4.1.1.1.1.3" xref="p8.4.m4.1.1.1.1.3.cmml">2</mn></msup></mrow></msqrt></mrow></mrow></math>, <math><mrow id="p8.12.m12.1.1" xref="p8.12.m12.1.1.cmml"><mo id="p8.12.m12.1.1.1" xref="p8.12.m12.1.1.1.cmml">-</mo><mrow id="p8.12.m12.1.1.2" xref="p8.12.m12.1.1.2.cmml"><mrow id="p8.12.m12.1.1.2.2" xref="p8.12.m12.1.1.2.2.cmml"><mpadded width="+1.7pt" id="p8.12.m12.1.1.2.2.2" xref="p8.12.m12.1.1.2.2.2.cmml"><msub id="p8.12.m12.1.1.2.2.2a" xref="p8.12.m12.1.1.2.2.2.cmml"><mi id="p8.12.m12.1.1.2.2.2.2" xref="p8.12.m12.1.1.2.2.2.2.cmml">C</mi><mi id="p8.12.m12.1.1.2.2.2.3" xref="p8.12.m12.1.1.2.2.2.3.cmml">Ewald</mi></msub></mpadded><mo id="p8.12.m12.1.1.2.2.1" xref="p8.12.m12.1.1.2.2.1.cmml">⁢</mo><msup id="p8.12.m12.1.1.2.2.3" xref="p8.12.m12.1.1.2.2.3.cmml"><mi mathvariant="normal" id="p8.12.m12.1.1.2.2.3.2" xref="p8.12.m12.1.1.2.2.3.2.cmml">Δ</mi><mn id="p8.12.m12.1.1.2.2.3.3" xref="p8.12.m12.1.1.2.2.3.3.cmml">2</mn></msup></mrow><mo id="p8.12.m12.1.1.2.1" xref="p8.12.m12.1.1.2.1.cmml">/</mo><mn id="p8.12.m12.1.1.2.3" xref="p8.12.m12.1.1.2.3.cmml">2</mn></mrow></mrow></math>

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1909.08264

Formulas:

1-

\frac{d M_{g}}{d t} = - (1 - ℛ) ψ,

2-

ψ = M_{gas} / τ_{SF} .

3-

\frac{d Z}{d t} = \frac{y}{τ_{SF}},

4-

M_{⋆} = M_{g, 0} - M_{g} .

5-

M_{g} = M_{g, 0}

6-

m = (4 π / 3) a^{3} s

7-

n (a, t)

8-

n (a, t) d a

9-

ρ_{d, tot} (t)

10-

ρ_{d, tot} (t) = \int_{0}^{\infty} \frac{4}{3} π a^{3} s n (a, t) d a .

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1806.06967

Formulas:

1-

x_{t = d a y, h}^{i}

2-

x_{d a y, h}^{i}

3-

z_{d a y, h}^{i} = (x_{d a y, h}^{i} - μ_{h}^{i}) / σ_{h}^{i}

4-

z_{d a y, h}^{i}

5-

z_{d a y, h}^{j}

6-

\frac{1}{N} \sum_{d a y = 1}^{N} I (z_{d a y, h}^{i}; z_{d a y, h}^{j})

7-

I (z_{d a y, h}^{i}; z_{d a y, h}^{j}) = \int_{z_{d a y, h}^{i}} \int_{z_{d a y, h}^{j}} p (z_{d a y, h}^{i}, z_{d a y, h}^{j}) l o g (\frac{p (z_{d a y, h}^{i}, z_{d a y, h}^{j})}{p (z_{d a y, h}^{i}) p (z_{d a y, h}^{j})})

8-

T o t_{C A}

9-

R_{a d j}^{2}

10-

R_{a d j}^{2}

Formulas (html):

Correct Categorie: cs

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1112.3147

Formulas:

1-

v_{e} \sin i

2-

\log N_{el} / N_{Tot}

3-

χ^{2} = \frac{1}{N} \sum {(\frac{I_{obs} - I_{th}}{δ I_{obs}})}^{2}

4-

b - y = 0.164 \pm 0.004

5-

m_{1} = 0.249 \pm 0.015

6-

c_{1} = 0.847 \pm 0.007

7-

{(b - y)}_{0} = 0.140

8-

v_{e} \sin i

9-

v_{e} \sin i

10-

v_{e} \sin i

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/0903.0315

Formulas:

1-

D (ω_{l}) = \int 𝑑 Ω 2 Ω B (Ω) / (Ω^{2} + ω_{l}^{2})

2-

Σ_{α} (i ω_{n})

3-

- T \sum_{m, β} V_{α, β} D (ω_{n} - ω_{m}) G_{β} (i ω_{m}),

4-

V_{α, β} = V_{β, α}

5-

V_{α, β} > 0

6-

G_{α} (z)

7-

G_{α} (z)

8-

\int_{E_{\min, α}}^{E_{\max, α}} 𝑑 ϵ N_{α} (ϵ) \frac{1}{z - ϵ - Σ_{α} (z) + μ} .

9-

N_{α} (ϵ)

10-

N_{α} (ϵ) \approx N_{α} (μ)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/0710.0471

Formulas:

1-

{Proj}_{U (3)} [(1 - α_{1}) U_{n, μ} + \frac{α_{1}}{6} \sum_{\pm ν \neq μ} {\tilde{V}}_{n, ν; μ} {\tilde{V}}_{n + \hat{ν}, μ; ν} {\tilde{V}}_{n + \hat{μ}, ν; μ}^{†}],

2-

{\tilde{V}}_{n, μ; ν}

3-

{Proj}_{U (3)} [(1 - α_{2}) U_{n, μ} + \frac{α_{2}}{4} \sum_{\pm ρ \neq ν, μ} {\bar{V}}_{n, ρ; ν μ} {\bar{V}}_{n + \hat{ρ}, μ; ρ ν} {\bar{V}}_{n + \hat{μ}, ρ; ν μ}^{†}],

4-

{\bar{V}}_{n, μ; ν ρ}

5-

{Proj}_{U (3)} [(1 - α_{3}) U_{n, μ} + \frac{α_{3}}{2} \sum_{\pm η \neq ρ, ν, μ} U_{n, η} U_{n + \hat{η}, μ} U_{n + \hat{μ}, η}^{†}] .

6-

(x_{0}, 𝐱)

7-

V_{i} (0, 𝐱) = {\tilde{V}}_{i} (0, 𝐱) = {\bar{V}}_{i} (0, 𝐱)

8-

U_{i} (0, 𝐱)

9-

V_{i} (T, 𝐱) = {\tilde{V}}_{i} (T, 𝐱) = {\bar{V}}_{i} (T, 𝐱)

10-

U_{i} (T, 𝐱)

Formulas (html):

Correct Categorie: hep-lat

Guessed Categorie: hep-lat

Result: correct

Paper: https://arxiv.org/abs/0908.4270

Formulas:

1-

V \sim - {(Z α)}^{2} M

2-

E_{m a x} \approx

3-

\propto {(E_{m a x} - E)}^{5}

4-

ℳ_{m i g}

5-

\vec{y} = ℳ_{m i g} \cdot \vec{x} .

6-

ℳ^{u f o}

7-

ℳ_{m i g}^{- 1}

8-

ℳ^{u f o}

9-

ℳ_{m i g}

10-

τ_{μ^{-}}^{Al} = (864.6 \pm 0.8 (stat.) \pm 0.9 (syst.)) ns

Formulas (html):

Correct Categorie: hep-ex

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/1806.03400

Formulas:

1-

x i e h o n g b @ m a i l . u s t c . e d u . c n

2-

l i y a n g 9 @ u s t c . e d u . c n

3-

s h e n q i @ u s t c . e d u . c n

4-

s k l i a o @ u s t c . e d u . c n

5-

2.5 G b p s

6-

c a r r y 8

7-

< 100 M H z

8-

> 1 G b p s

9-

< 40 p s

10-

c a r r y 8

Formulas (html):

Correct Categorie: eess

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/0807.0561

Formulas:

1-

n_{s} / m^{*} \propto T_{c}

2-

n_{s} / m^{*} \propto T_{c}

3-

B_{c 1} < B < B_{c 2}

4-

ω_{μ} = γ_{μ} B

5-

= 2 π \times 135.5

6-

P_{x} (t)

7-

P_{x} (t) = \int_{0}^{\infty} p (B) \cos (γ_{μ} B t + ϕ) d B,

8-

B_{VL} (0)

9-

B_{rms}^{2} (T) = B_{VL}^{2} (0) {[1 - {(T / T_{c})}^{r}]}^{2} + B_{bg}^{2}

10-

B_{VL} (0)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Run 11163385 (Agent890)