Run 10953591

Paper: https://arxiv.org/abs/2002.08698

Formulas:

1-

y = η (x, t)

2-

ω^{2} = g k + \frac{γ (μ)}{ρ} B^{2} k^{2} + \frac{σ}{ρ} k^{3},

3-

γ (μ) = {(μ - 1)}^{2} {(μ_{0} (μ + 1))}^{- 1}

4-

v_{m i n} = {(4 σ g / ρ)}^{1 / 4}

5-

v_{m i n}^{2}

6-

B_{c}^{2} = \frac{2 {(ρ g σ)}^{1 / 2}}{γ (μ)} .

7-

λ_{0} = 2 π {(\frac{σ}{g ρ})}^{1 / 2}, t_{0} = 2 π {(\frac{σ}{g^{3} ρ})}^{1 / 4} .

8-

ρ = 1324 {kg/m}^{3}, σ = 0.059 N/m, μ = 1.69 .

9-

2 \leq B / B_{c} \leq 6

10-

B_{m a x}

Formulas (html):

Correct Categorie: physics

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/0911.3054

Formulas:

1-

L = 10, 12, 15, 24 σ

2-

ρ \equiv N / L^{3}

3-

- 2 ⟨ E ⟩ / N u_{0}

4-

k_{B} T / u_{0} = 0.3

5-

ρ σ^{3} = 0.001

6-

ρ σ^{3} = 0.01

7-

ρ σ^{3} = 0.1

8-

ρ σ^{3} = 0.4

9-

ρ σ^{3} = 0.55

10-

ρ σ^{3} = 0.001

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1507.00762

Formulas:

1-

a_{0} \sqrt{3} τ

2-

T_{C} (x)

3-

E_{A} (θ) = a_{2 c} (\cos 2 θ - 1) .

4-

- 5 / 2 \leq M, M^{'} \leq 5 / 2

5-

H = \frac{a}{6} (S_{x}^{4} + S_{y}^{4} + S_{z}^{4}) .

6-

10^{- 4} - 10^{- 1}

7-

E_{A} (θ, φ)

8-

D (θ, φ)

9-

D (θ, φ) = D_{z} (φ) D_{y} (θ),

10-

S_{z} = 5 / 2

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1204.5500

Formulas:

1-

O (\frac{n R}{ϵ^{2}} \ln (m))

2-

Ω (R n^{1 + l g \frac{3}{2} (1 - ϵ)})

3-

\frac{1}{d (u)}

4-

\frac{1}{d (u)}

5-

\frac{n R}{ϵ^{2}} \ln (m)

6-

\frac{n R}{ϵ^{2}} \ln (m)

7-

Ω (R n^{1 + l g \frac{3}{2} (1 - ϵ)}) .

8-

Ω (R n^{1.26})

9-

O (R n \log (m))

10-

{(1 - ϵ)}^{i}

Formulas (html):

Correct Categorie: cs

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1308.4858

Formulas:

1-

J_{M G} = \frac{9}{8} μ ε_{0} ε_{r} \frac{V^{2}}{L^{3}}

2-

h (E) = \frac{N_{t}}{k_{B} T_{c}} e^{- E / k_{B} T_{c}}

3-

J_{T} = \frac{μ N_{c}}{q^{m - 2}} {(\frac{2 m - 1}{m})}^{m} {(\frac{ε_{0} ε_{r} (m - 1)}{N_{t} m})}^{l} \frac{V^{m}}{L^{2 m - 1}}

4-

m = \frac{T_{c}}{T} + 1

5-

I_{D S} \propto V_{D S}^{m}

6-

I - V_{B G}

7-

V_{B G} = 0 V

8-

V_{B G} = - 40 V

9-

I - V_{B G}

10-

V_{D S} \leq 100

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1204.6223

Formulas:

1-

0 \leq z_{i} \leq 127

2-

z_{i_{1}} \equiv (z_{i - 1} + z_{i}) / 2

3-

z_{i_{2}} \equiv (z_{i + 1} + z_{i}) / 2

4-

𝜷_{N} = 𝜷_{1} - \sum_{i = 1}^{N - 1} \frac{d_{i N}}{d_{N}} 𝜶_{i} (𝜷_{i})

5-

𝜶_{i} (𝜷_{i})

6-

D_{i} \equiv D (z_{i})

7-

d_{i N} / d_{N} = (D_{N} - D_{i}) / D_{N}

8-

D_{i_{2}} - D_{i_{1}}

9-

𝜶_{i}^{bcg} (𝜷_{i}) = \frac{2}{(1 + z_{i}) c^{2}} \int_{D_{i_{1}}}^{D_{i_{2}}} 𝒈_{⟂} (D, 𝜷_{i}) 𝑑 D

10-

(D β_{x}, D β_{y})

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1107.3322

Formulas:

1-

m_{gas} \sim ρ_{\infty} m^{3}

2-

ρ_{\infty} m^{3} / m = ρ_{\infty} m^{2} ≪ 1

3-

r ≪ R_{\max} = m {(ρ_{\infty} m^{2})}^{- 1 / 3}

4-

\dot{m} / m ≪ c_{s} / m

5-

\dot{m} = 4 π A (ρ_{\infty} + p_{\infty}) m^{2},

6-

p = p (ρ)

7-

c_{s} = O (1)

8-

\dot{m} \sim ρ_{\infty} m^{2} ≪ 1

9-

\dot{m} = c o n s t ≪ 1

10-

d s^{2} = e^{ν (t, r)} d t^{2} - e^{λ (t, r)} d r^{2} - r^{2} (d θ^{2} + \sin^{2} θ d ϕ^{2}) .

Formulas (html):

Correct Categorie: gr-qc

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/quant-ph/0404104

Formulas:

1-

\frac{1}{\sqrt{2}} (| | | 00 ⟩ ⟩ ⟩ + | | | 11 ⟩ ⟩ ⟩)

2-

Y = σ_{x} σ_{z}

3-

| | | 0 ⟩ ⟩ ⟩

4-

| | | + ⟩ ⟩ ⟩

5-

| | | i π / 4 ⟩ ⟩ ⟩

6-

| | | π / 8 ⟩ ⟩ ⟩

7-

| L | + 1 = | K |

8-

q_{π (l)} = p_{l}

9-

Prob (Π_{k \in K} q_{k}) / Prob (Π_{l \in L} p_{l})

10-

Π_{k \in K} q_{k}

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/0003058

Formulas:

1-

λ_{J} = \sqrt{\frac{Φ_{0}}{2 π μ_{0} J_{c} (2 λ_{L} + d)}},

2-

2.07 \times 10^{- 15} W b

3-

H_{c J} = 2 μ_{0} J_{c} λ_{J} \propto \sqrt{J_{c} / λ_{L}} .

4-

λ_{J}^{2} \frac{\partial^{2} ϕ (x, t)}{\partial x^{2}} = \sin ϕ (x, t) + τ_{J} \frac{\partial ϕ}{\partial t},

5-

ϕ (x, t)

6-

τ_{J} = Φ_{0} / 2 π d J_{c} ρ_{n}

7-

{\frac{\partial ϕ}{\partial x} |}_{x = 0, L} = \frac{2 π (2 λ_{L} + d) [H_{d c} \pm H_{0} \sin (ω t)]}{Φ_{0}},

8-

E_{y} (x, t) = \frac{Φ_{0}}{2 π d} \frac{\partial ϕ (x, t)}{\partial t} .

9-

R_{n} = \frac{2}{H_{0}} \int_{0}^{T_{rf}} 𝑑 t E_{y} (0, t) \sin (n ω t),

10-

X_{n} = \frac{2}{H_{0}} \int_{0}^{T_{rf}} 𝑑 t E_{y} (0, t) \cos (n ω t),

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/quant-ph/9803074

Formulas:

1-

\hat{H} = \sum_{i = 1}^{N} (- \frac{ℏ^{2}}{2 m} \nabla_{i}^{2} + V_{0} (𝐫_{i})) + \frac{1}{2} \sum_{i j = 1}^{N} V (𝐫_{i}, 𝐫_{j}),

2-

V_{0} (𝐫)

3-

V (𝐫, 𝐫^{'})

4-

Ψ_{α} (𝐫)

5-

α_{1}, \dots, α_{N}

6-

Φ_{α_{1} \dots α_{N}} (𝐫_{1}, \dots, 𝐫_{N}) = \sqrt{\frac{N_{α_{1}}! \dots N_{α_{N}}!}{N!}} \sum_{\hat{P}} Ψ_{\hat{P} α_{1}} (𝐫_{1}) \dots Ψ_{\hat{P} α_{N}} (𝐫_{N}),

7-

N_{α_{2}} = \dots = N_{α_{N}} = 0

8-

Φ_{α} (𝐫_{1}, \dots, 𝐫_{N}) = Ψ_{α} (𝐫_{1}) \dots Ψ_{α} (𝐫_{N}) .

9-

ϵ = < Φ_{α} | \frac{\hat{H}}{N} | Φ_{α} > = \frac{1}{N} \int d^{3} 𝐫_{1} \dots d^{3} 𝐫_{N} Φ_{α}^{*} (𝐫_{1}, \dots, 𝐫_{N}) \hat{H} Φ_{α} (𝐫_{1}, \dots, 𝐫_{N}),

10-

ϵ [Ψ_{α}] = \int d^{3} 𝐫 \frac{ℏ^{2}}{2 m} {| \nabla Ψ_{α} (𝐫) |}^{2} + V_{0} (𝐫) {| Ψ_{α} (𝐫) |}^{2} + \frac{(N - 1)}{2} \int d^{3} 𝐫 d^{3} 𝐫^{'} {| Ψ_{α} (𝐫) |}^{2} V (𝐫, 𝐫^{'}) {| Ψ_{α} (𝐫^{'}) |}^{2},

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/2002.06477

Formulas:

1-

R e^{t} = 0.17

2-

Γ_{i} = 5.2 \times 10^{- 4}

3-

6 π η Ω_{0} r_{s}^{2}

4-

𝐅 = \sum_{i} A R e \hat{𝐔} \times \hat{𝛀} / r_{i}^{3} S (R e) + B \hat{𝛀} \times {\hat{𝐫}}_{i} / r_{i}^{3} - Γ {\hat{𝐫}}_{i} / r_{i}^{2},

5-

R e = ρ r_{s}^{2} Ω_{0} / η

6-

R e < R e^{t}

7-

S (R e) = 1 / (1 + e^{- G (R e - R e^{t})})

8-

\dot{𝐫} = 𝐅 + \sqrt{\frac{2}{P e}} 𝝃 (t)

9-

⟨ ξ (t) ⟩ = 0

10-

⟨ ξ (t) ξ (t^{'}) ⟩ = δ (t - t^{'})

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1508.01291

Formulas:

1-

x \mapsto a x + b

2-

x \mapsto \frac{a x + b}{c x + d}

3-

⟨ a, t ⟩ ≅ S_{3}

4-

(x_{0}, x_{0} a, x_{0} a^{2}) = (x_{0}, x_{0} a, x_{0} a t)

5-

B = (x, y, z)

6-

A = (x_{0}, x_{0} a, x_{0} a^{2}) = (x_{0}, x_{0} a, x_{0} a t)

7-

G = ((⟨ a ⟩ \times F (U)) *_{⟨ a ⟩} G_{0} *_{⟨ t ⟩} ((⟨ t ⟩ \times F (S)))) * F (R)

8-

F (R), F (S), F (U)

9-

| R |, | S |, | U | = \max {| G_{0} |, ℵ_{0}}

10-

P G L (2, 2) ≅ S_{3}

Formulas (html):

Correct Categorie: math

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1004.0308

Formulas:

1-

σ_{x y} (ω)

2-

ω \sim 10^{12} Hz \sim 10^{- 2} eV / ℏ

3-

ℏ ω_{c} \sim 10^{- 2} eV

4-

e t a l .

5-

σ_{x y} (ω)

6-

1 \times 1 {cm}^{2}

7-

n = 2.7 \times 10^{11} {cm}^{- 2}

8-

E_{y} (t) \propto \exp (- t / τ) \sin (ω_{c} t)

9-

μ = 1.4 \times 10^{5} {cm}^{2} / Vs

10-

m^{*} = 0.070 m_{0}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1302.3425

Formulas:

1-

10^{- 4} - 10^{- 5}

2-

\sim 10^{4} γ / (keV \cdot s)

3-

\sim 10^{6} γ / (eV \cdot s)

4-

Δ E \approx 1 keV

5-

Γ σ \approx 0.1 eV \cdot b

6-

Γ σ \approx 10 eV \cdot b

7-

E^{*} = 5.6 - 5.8

8-

ℏ ω_{I I}

9-

E_{I I I}

10-

ℏ ω_{I I}

Formulas (html):

Correct Categorie: nucl-ex

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1504.06854

Formulas:

1-

d \vec{S} / d θ = \vec{Ω} (\vec{z}, θ) \times \vec{S}

2-

\vec{Ω} (\vec{z}, θ) = {\vec{Ω}}_{0} (θ) + \vec{ω} (\vec{z}, θ)

3-

{\vec{Ω}}_{0} (θ)

4-

\vec{ω} (\vec{z}, θ)

5-

\hat{n} (z, θ)

6-

\vec{n} (\vec{z}, θ + 2 π) = \vec{n} (\vec{z}, θ)

7-

J_{s} = \vec{S} \cdot \vec{n}

8-

P_{lim} = | ⟨ \vec{n} (\vec{z}, θ) ⟩ |

9-

ν_{0} = G γ_{0}

10-

ν_{s} = k + k_{x} ν_{x} + k_{y} ν_{y} + k_{z} ν_{z}, k, k_{x}, k_{y}, k_{z} \in ℤ .

Formulas (html):

Correct Categorie: physics

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/1410.7327

Formulas:

1-

κ_{S Z T O}

2-

κ_{S Z T O}

3-

_{S r 3 d 5 / 2}

4-

_{S Z T O}

5-

_{G e 3 d 5 / 2}

6-

_{S r 3 d 5 / 2}

7-

_{G e 3 d 5 / 2}

8-

_{S r 3 d 5 / 2}

9-

_{G e 3 d 5 / 2}

10-

_{G e 3 d 5 / 2}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1303.3426

Formulas:

1-

φ (T) = n_{e}^{2} \frac{d h}{d T} .

2-

T_{D E M}

3-

T_{D E M} = \frac{Σ {DEM (T_{i}) T_{i} Δ T_{i}}}{Σ {DEM (T_{i}) Δ T_{i}}},

4-

Δ T_{i} = 0.1

5-

T_{D E M}

6-

2^{''} .4 \times 15^{''}

7-

2^{''} .4 \times 15^{''}

8-

log (T) \approx 6.0

9-

T_{D E M}

10-

6.0 < \log_{10} T_{\max} < 6.4

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/hep-th/0410162

Formulas:

1-

X^{μ} (x^{a})

2-

1 \leq μ, ν, \dots \leq d

3-

1 \leq a, b, \dots \leq 2

4-

S = \frac{1}{4 π l_{s}^{2}} \int d^{2} x \sum_{a, b = 1, 2} g_{μ ν} (X) \partial_{a} X^{μ} \partial_{b} X^{ν} γ^{a b}

5-

g_{μ ν} (X)

6-

X^{μ} (x^{a})

7-

i ϵ^{a b} b_{μ ν} (X) \partial_{a} X^{μ} \partial_{b} X^{ν} + l_{s}^{2} R Φ (X)

8-

b_{μ ν} (X)

9-

α^{'} = l_{s}^{2}

10-

{(l_{s} / l)}^{2}

Formulas (html):

Correct Categorie: hep-th

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/0911.1721

Formulas:

1-

S U (2)

2-

S U (2)

3-

S U (2)

4-

S U (2)

5-

S U (2)

6-

S = β \sum_{x, μ < ν} {1 - \frac{1}{2} ReTr P_{μ ν} (x)} - \frac{κ}{2} \sum_{x, μ > 0} Tr [ϕ^{†} (x) U_{μ} (x + \hat{μ}) ϕ (x + \hat{μ})]

7-

S U (2)

8-

λ {\frac{1}{2} Tr [ϕ^{†} (x) ϕ (x)] - 1}^{2}

9-

S U (2)

10-

S U (2)

Formulas (html):

Correct Categorie: hep-lat

Guessed Categorie: hep-lat

Result: correct

Paper: https://arxiv.org/abs/2003.02771

Formulas:

1-

𝐒 = 1 / 2 (𝚿^{†} σ 𝚿)

2-

σ_{x, y, z}

3-

𝚿 = (Ψ_{+}, Ψ_{-})

4-

\begin{matrix} i ℏ \partial_{t} Ψ_{\pm} = (α_{1} {| Ψ_{\pm} |}^{2} + α_{2} {| Ψ_{\mp} |}^{2} + α_{r} n) Ψ_{\pm} + \\ + \frac{i ℏ}{2} (R n - γ_{c}) Ψ_{\pm} + \frac{δ_{l}}{2} Ψ_{\mp} + \sqrt{D} η_{\pm} (t), \end{matrix}

5-

𝚿 = (Ψ_{+}, Ψ_{-})

6-

η_{\pm} (t)

7-

D = ⟨ η_{i} (t) η_{j}^{*} (t^{'}) ⟩ = 1 / 2 R n δ (t - t^{'}) δ_{i j}

8-

i, j = +, -

9-

\partial_{t} n = P - γ_{r} n - R n ({| Ψ_{+} |}^{2} + {| Ψ_{-} |}^{2}),

10-

Q_{x} (0)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/cond-mat/0501494

Formulas:

1-

Δ T_{0} = - m_{e} c_{0} (1 - k_{e}) / k_{e}

2-

ϕ (x, t)

3-

S = \int_{Ω} [s (e, c, ϕ) - (ε a (ϕ, \nabla ϕ) + \frac{1}{ε} w (ϕ))] 𝑑 x .

4-

c = (c_{1}, \dots, c_{N})

5-

ϕ = (ϕ_{1}, \dots, ϕ_{M})

6-

i = 1, \dots, N

7-

α = 1, \dots, M

8-

a (ϕ, \nabla ϕ)

9-

\partial_{t} ϕ_{α} \sim \frac{δ S}{δ ϕ_{α}} - λ

10-

ω ε \frac{\partial ϕ_{α}}{\partial t} = ε (\nabla \frac{\partial a}{\partial \nabla ϕ_{α}} - \frac{\partial a}{\partial ϕ_{α}}) - \frac{1}{ε} \frac{\partial w}{\partial ϕ_{α}} - \frac{1}{T} \frac{\partial f}{\partial ϕ_{α}} - λ,

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/9902109

Formulas:

1-

A_{V_{S F D}}

2-

A_{V_{I S S A}}

3-

A_{V_{I S S A}}

4-

E {(B V)}_{S F D}

5-

E {(B V)}_{S F D}

6-

A_{V} = R_{V} E (B V)

7-

A_{V_{S F D}}

8-

A_{V_{I S S A}}

9-

A_{V_{I S S A}}

10-

A_{V_{S F D}}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1611.05014

Formulas:

1-

0 \leq a \leq 𝜷 \leq b < \infty .

2-

(a, b) .

3-

p (β) : [a, b] \to [0, 1]

4-

X (β) = \int_{0}^{β} \frac{2 ρ W_{0} y}{{(1 - ρ + ρ F (y))}^{3}} 𝑑 F (y)

5-

W_{0} = \frac{λ}{2} \int_{0}^{\infty} τ^{2} 𝑑 G (μ τ)

6-

W (β) = \frac{μ^{2} W_{0}}{{(μ - λ (1 - F (β)))}^{2}} .

7-

p (β),

8-

λ_{2} := λ \int_{0}^{\infty} p (β) 𝑑 F (β)

9-

λ_{1} := λ - λ_{2}

10-

ρ_{i} := λ_{i} / μ_{i} .

Formulas (html):

Correct Categorie: cs

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/2005.13868

Formulas:

1-

a b i n i t i o

2-

I P R = 1 / (N \sum_{i = 1}^{N} {| a_{i}^{α} |}^{4}),

3-

σ = 1 - (d^{'} / d)

4-

h_{m a x}

5-

h_{m a x} / R = 0.04

6-

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

7-

d_{1} = d_{x z}, d_{y z}

8-

d_{0} = d_{3 z^{2} - r^{2}}

9-

p_{x y} = p_{x}, p_{y}

10-

\sum_{α} λ_{α} 𝐋 \cdot 𝐒

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1605.00351

Formulas:

1-

h (x) \in 𝔽_{q} [x]

2-

W \subseteq [0, n] := {0, 1, \dots, n}

3-

S_{W} (h) = \sum_{w \in W} [x^{w}] h (x)

4-

W \subseteq [0, n]

5-

S_{W} (P) = c

6-

W \subseteq [0, n]

7-

S_{W} (P) \neq c

8-

r \leq [(1 / 4 - ϵ) n]

9-

n / 4 + o (n)

10-

𝔽_{q} [x]

Formulas (html):

Correct Categorie: math

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0508336

Formulas:

1-

10^{7.5} M_{⊙} - 10^{8.0} M_{⊙}

2-

140 M_{⊙} \overset{<}{\sim} M_{⋆} \overset{<}{\sim} 260 M_{⊙},

3-

\sim 10^{3} M_{⊙}

4-

\sim 10^{3} M_{⊙}

5-

\frac{1}{\sqrt{2 π} σ_{C}} e^{- {(M - M_{C})}^{2} / 2 σ_{C}^{2}},

6-

100 M_{⊙} \leq M_{C} \leq 1000 M_{⊙}

7-

σ_{C}^{\min} \leq σ_{C} \leq σ_{C}^{\max}

8-

E_{g}^{I I I}

9-

N_{S N}^{I I I}

10-

E_{SN}^{I I I}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/0908.4102

Formulas:

1-

d s^{2} = - d t^{2} + \frac{{(r^{'})}^{2}}{1 + f} d {\tilde{r}}^{2} + r^{2} (d θ^{2} + \sin^{2} θ d ϕ^{2})

2-

u^{a} = {(\partial / \partial t)}^{a}

3-

u^{a} = γ (t^{a} + v r^{a})

4-

γ = 1 / \sqrt{1 - v^{2}}

5-

n_{-}^{a} = ω (t^{a} - r^{a})

6-

n_{+}^{a} = ω (t^{a} + r^{a})

7-

α = \frac{u_{a} n_{+}^{a}}{u_{a} n_{-}^{a}}

8-

v = \frac{1 - α}{1 + α}

9-

{\dot{r}}^{2} = f + \frac{F}{r}

10-

ρ = \frac{F^{'}}{8 π r^{2} r^{'}}

Formulas (html):

Correct Categorie: gr-qc

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1609.07001

Formulas:

1-

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

2-

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

3-

e^{+} e^{-} \to V π X

4-

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

5-

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

6-

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

7-

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

8-

ρ = (1 + \vec{S} \cdot \vec{σ}) / 2

9-

S^{μ} = λ \frac{p^{+}}{M} {\bar{n}}^{μ} + S_{T}^{μ} - λ \frac{M}{2 p^{+}} n^{μ},

10-

ρ = \frac{1}{3} (𝟏 + \frac{3}{2} S^{i} Σ^{i} + 3 T^{i j} Σ^{i j}),

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1206.2823

Formulas:

1-

4 \times 10^{12} a t / c m^{2} / s

2-

G a_{M n}

3-

M n O_{x}

4-

R_{M n M n} = 2.69

5-

R_{M n O} = 2.22

6-

R_{M n A s} = 2.59

7-

R_{M n A s} = 2.50

8-

R_{G a A s} = 2.399

9-

R_{M n A s} / R_{G a A s}

10-

R_{M n A s} = 2.45

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1112.2366

Formulas:

1-

α = a / R_{E}

2-

0.5 < α < 2,

3-

α = a / R_{E} .

4-

R_{E} = 1.01 AU {[(\frac{M_{*}}{1 M_{⊙}}) (\frac{D_{L}}{125 pc}) (1 - \frac{D_{L}}{D_{S}})]}^{\frac{1}{2}},

5-

D_{L} / D_{S} << 1

6-

(D_{S} - D_{L}) / D_{S} << 1,

7-

α = a / R_{E},

8-

a, M_{*}, M_{p l}, D_{L},

9-

q = M_{p l} / M_{*} .

10-

P = 71.3 days {(\frac{α}{\frac{1}{3}})}^{\frac{3}{2}} {(\frac{M_{*}}{M_{⊙}})}^{\frac{1}{4}} {(\frac{D_{L}}{125 pc} (1 - \frac{D_{L}}{D_{S}}))}^{\frac{3}{4}}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1312.1833

Formulas:

1-

H = \sum_{i \neq j}^{N} \frac{J r_{0}^{3}}{{| {\vec{r}}_{i} - {\vec{r}}_{j} |}^{3}} σ_{i}^{-} σ_{j}^{+},

2-

σ_{i}^{-, / +}

3-

ϵ = \max_{t \in [0, 𝒯]} {| ⟨ i n | e^{i H t} | o u t ⟩ |}^{2} .

4-

| o u t ⟩

5-

𝒯 = \frac{1}{10} \frac{2 π ℏ}{J} \frac{r_{i n - o u t}^{3}}{r_{0}^{3}}

6-

IPR (t) = \frac{1}{\sum_{i = 1}^{N} q_{i}^{2} (t)},

7-

(N - 2)!

8-

S^{2} = \min \sum_{i = 1}^{n} \frac{d_{i}^{2}}{n},

9-

A_{M C L}

10-

𝒫_{ℐ} / \sum_{ℐ} 𝒫_{ℐ}

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/0203277

Formulas:

1-

(2 \sqrt{2} \times \sqrt{2}) R 45^{\circ}

2-

c (2 \times 2)

3-

(2 \sqrt{2} \times \sqrt{2}) R 45^{\circ}

4-

c (2 \times 2)

5-

(2 \sqrt{2} \times \sqrt{2}) R 45^{\circ}

6-

c (2 \times 2)

7-

c (2 \times 2)

8-

(2 \sqrt{2} \times \sqrt{2}) R 45^{\circ}

9-

(2 \sqrt{2} \times \sqrt{2}) R 45^{\circ}

10-

z_{C u 1}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/physics/0510092

Formulas:

1-

U = - \frac{1}{2} α_{g} {| E |}^{2}

2-

σ_{p}^{2} (t)

3-

\frac{1}{2} σ_{p}^{2} (0) [1 + {(\frac{ω_{1}}{ω_{0}})}^{2} + (1 - {(\frac{ω_{1}}{ω_{0}})}^{2}) \cos (2 ω_{1} t)]

4-

σ_{z}^{2} (t)

5-

\frac{1}{2} σ_{z}^{2} (0) [1 + {(\frac{ω_{0}}{ω_{1}})}^{2} + (1 - {(\frac{ω_{0}}{ω_{1}})}^{2}) \cos (2 ω_{1} t)]

6-

t = \frac{π}{2 ω_{1}}

7-

σ_{p}^{2} (\frac{π}{2 ω_{1}})

8-

{(\frac{ω_{1}}{ω_{0}})}^{2} σ_{p}^{2} (0)

9-

σ_{z}^{2} (\frac{π}{2 ω_{1}})

10-

{(\frac{ω_{0}}{ω_{1}})}^{2} σ_{z}^{2} (0) .

Formulas (html):

Correct Categorie: physics

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1808.01424

Formulas:

1-

𝐱 \in ℝ^{n \times n \times c}

2-

𝒇 (𝐱; θ) \in ℝ^{d}

3-

𝒇 (𝐱; θ)

4-

{𝐱, 𝐱^{'}}

5-

{∥ 𝒇 (𝐱) - 𝒇 (𝐱^{'}) ∥}_{2}

6-

{𝐱, 𝐱^{'}} \in 𝒫

7-

{𝐱, 𝐱^{'}} \in 𝒩

8-

\begin{matrix} 𝑳_{0} (𝐱, 𝐱^{'}; θ) & = {∥ 𝒇 (𝐱; θ) - 𝒇 (𝐱^{'}; θ) ∥}_{2} \\ 𝑳_{1} (𝐱, 𝐱^{'}; θ) & = \max (0, μ - {∥ 𝒇 (𝐱; θ) - 𝒇 (𝐱^{'}; θ) ∥}_{2}) \end{matrix}

9-

\underset{θ}{\arg \min} (\sum_{i = 1}^{| 𝒫 |} 𝑳_{0} (𝐱_{i}, 𝐱_{i}^{'}; θ) + \sum_{j = 1}^{| 𝒩 |} 𝑳_{1} (𝐱_{j}, 𝐱_{j}^{'}; θ))

10-

{I, I^{'}}

Formulas (html):

Correct Categorie: cs

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/1502.02740

Formulas:

1-

| l | < 10^{\circ}

2-

| b | < 2^{\circ}

3-

| v | ≃ 270 km s^{- 1}

4-

| l | ≃ 2^{\circ}

5-

\frac{\partial ρ}{\partial t} = α (ρ_{0}^{2} - ρ^{2}),

6-

α = 0.3 M_{⊙} {pc}^{- 2} {Gyr}^{- 1}

7-

ρ_{0} = 1 M_{⊙} {pc}^{- 2}

8-

d x = 5 pc

9-

ρ_{b} (a) = ρ_{b0} {\begin{matrix} {(a / a_{0})}^{- α} if a \leq a_{0} \\ {(a / a_{0})}^{- β} if a > a_{0} \end{matrix}

10-

a = \sqrt{x^{2} + (y^{2} + z^{2}) / q^{2}}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/hep-th/0508196

Formulas:

1-

K_{2 m} = L_{2 m} - L_{- 2 m}

2-

g (\pm i) = 1

3-

g (w) = g_{+} (w) + g_{-} (w),

4-

g_{\pm} (w)

5-

g_{\pm} (- w) = \pm g_{\pm} (w)

6-

Ψ = Ψ_{+} + Ψ_{-},

7-

g (w) = 1 + \frac{a}{2} {(w + \frac{1}{w})}^{2} - i b (w - \frac{1}{w} + w^{3} - \frac{1}{w^{3}}) .

8-

S [Ψ] = - \frac{1}{g_{o}^{2}} (\frac{1}{2} ⟨ Ψ, Q_{B} Ψ ⟩ + \frac{1}{3} ⟨ Ψ, Ψ, Ψ ⟩),

9-

[L_{0}, ϕ_{n}] = n ϕ_{n}

10-

Ω (ϕ_{n}) = {(- 1)}^{n} ϕ_{n} .

Formulas (html):

Correct Categorie: hep-th

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1012.0430

Formulas:

1-

3 d^{10} 4 s^{2}

2-

2 p^{4} 2 s^{2}

3-

3 d^{n} 4 s^{2}

4-

E [{Zn}_{m} O_{n} (α, q)] - E [{Zn}_{p} O_{p} (pure)]

5-

\sum_{α} n_{α} μ_{α} + q (E_{v} + ϵ_{F}),

6-

n_{α} = - 1 (+ 1)

7-

E [{Zn}_{m} O_{n} (α, q)]

8-

E [{Zn}_{p} O_{p} (pure)]

9-

p (μ_{Zn} + μ_{O}) = E [{Zn}_{p} O_{p} (pure)],

10-

μ_{Zn} \leq μ_{Zn}^{s} and μ_{O} \leq μ_{O}^{s},

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1607.02350

Formulas:

1-

P {(T)}^{3} = \frac{1}{x_{MgO}^{2} x_{{SiO}_{2}} e^{- Δ G_{s, l} / R T}}

2-

Δ G_{s, l}

3-

x_{MgO, {SiO}_{2}} = f ϵ_{Mg, Si}

4-

[10^{- 6} - 10^{- 3}] bar

5-

\frac{d T}{d t} = - \frac{2 π R_{disk}^{2} σ_{S B} T_{p h}^{4}}{M_{disk} C_{p}} \sim - 2 K {hr}^{- 1}

6-

R_{disk} = 4 R_{Mars}

7-

σ_{S B} = 5.67 \times 10^{- 8} J m^{- 2} K^{- 1}

8-

T_{p h} = 2000

9-

M_{disk} = 5 \times 10^{20} kg

10-

C_{p} = 4 \times 10^{3} J {kg}^{- 1} K^{- 1}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1309.0682

Formulas:

1-

G (𝐫, 𝐫^{'}; E) = \sum_{b = h, A, \bar{α}} \frac{f_{b} (𝐫) {\bar{f}}_{b} (𝐫^{'})}{E_{b} - E \mp i η},

2-

g_{i j} (r, r^{'})

3-

(\begin{matrix} - M^{*} - V + E & d / d r - κ / r \\ d / d r + κ / r & - M^{*} + V - E \end{matrix}) (\begin{matrix} g_{11}^{κ} (r, r^{'}) & g_{12}^{κ} (r, r^{'}) \\ g_{21}^{κ} (r, r^{'}) & g_{22}^{κ} (r, r^{'}) \end{matrix}) = δ (r - r^{'}) (\begin{matrix} - 1 & 0 \\ 0 & 1 \end{matrix}) .

4-

u^{κ} (r) = (\begin{matrix} u_{1}^{κ} (r) \\ u_{2}^{κ} (r) \end{matrix}), v^{κ} (r) = (\begin{matrix} v_{1}^{κ} (r) \\ v_{2}^{κ} (r) \end{matrix}) .

5-

g_{i j}^{κ} (r, r^{'}) = \frac{1}{Δ^{κ}} {\begin{matrix} u_{i}^{κ} (r) v_{j}^{κ} (r^{'}) \begin{matrix} , & r \leq r^{'} \end{matrix} \\ v_{i}^{κ} (r) u_{j}^{κ} (r^{'}) \begin{matrix} , & r > r^{'} \end{matrix} \end{matrix} \begin{matrix} i, j = 1, 2 \end{matrix} .

6-

Δ^{κ} = v_{1}^{κ} u_{2}^{κ} - u_{1}^{κ} v_{2}^{κ}

7-

R (P, P; E) = {\frac{1}{π} I m Π^{R} (P, P; 𝐤, 𝐤^{'}; E) |}_{𝐤 = 𝐤^{'} = 0},

8-

P = γ_{0} r^{J} Y_{J M} (\hat{r})

9-

Π (P, P; 𝐤, 𝐤^{'}, E) =

10-

Π_{0} (P, P; 𝐤, 𝐤^{'}, E) - \sum_{i} g_{i}^{2} \int d^{3} k_{1} d^{3} k_{2} Π_{0} (P, Γ^{i}; 𝐤, 𝐤_{1}, E) D_{i} (𝐤_{1}, 𝐤_{2}, E) Π (Γ_{i}, P; 𝐤_{2}, 𝐤^{'}, E) .

Formulas (html):

Correct Categorie: nucl-th

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1905.02271

Formulas:

1-

w_{i} = H x_{i} + e_{i} = [\begin{matrix} I^{'} \\ Y \end{matrix}] x_{i} + e_{i},

2-

R = diag [σ_{1}^{2}, σ_{2}^{2}, \dots, σ_{n}^{2}]

3-

{\hat{x}}_{i} = {(H^{T} R^{- 1} H)}^{- 1} H^{T} R^{- 1} w_{i} .

4-

r_{i, S} = w_{i} - H {\hat{x}}_{i}

5-

{\bar{w}}_{i} = w_{i} + d_{i},

6-

d_{i} = H c_{i},

7-

{\bar{x}}_{i} = {\hat{x}}_{i} + c_{i} .

8-

= {\bar{w}}_{i} - H {\bar{x}}_{i}

9-

= w_{i} + d_{i} - H {\hat{x}}_{i} - H c_{i} = w_{i} - H {\hat{x}}_{i}

10-

x_{(i | i - 1)} = 3 x_{i - 1} - 3 x_{i - 2} + x_{i - 3},

Formulas (html):

Correct Categorie: cs

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/0808.4075

Formulas:

1-

⟨ 𝒪_{d} (x) 𝒪_{d} (0) ⟩ = C_{d} \frac{1}{{(x^{2})}^{d}} .

2-

{⟨ 𝒪_{d} (p) 𝒪_{d} (- p) ⟩}_{ren} = A_{d} \frac{π (ν + 1)}{\sin (π ν)} {(- t)}^{ν} + P_{ν} (t) \equiv Δ_{d} (t),

3-

t = p^{2} / μ^{2}

4-

Δ_{d} (t)

5-

Δ_{d} (t)

6-

{\tilde{Δ}}_{d} = Δ_{d} - P_{ν}

7-

Δ_{d} (t) = \int_{0}^{\infty} \frac{σ_{d} (w)}{t - w} d w,

8-

σ_{d} (w)

9-

= - \frac{1}{π} Im Δ (w + i ϵ)

10-

= (ν + 1) w^{ν} .

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: hep-ph

Result: correct

Paper: https://arxiv.org/abs/1306.1628

Formulas:

1-

r e g u l a r

2-

i r r e g u l a r

3-

T_{r e c}

4-

i r r e g u l a r

5-

r e g u l a r

6-

r e g u l a r

7-

i r r e g u l a r

8-

⟨ E ⟩ = 0.0232 + 0.0464 ⟨ C ⟩ keV .

9-

r e g u l a r

10-

i r r e g u l a r

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0507136

Formulas:

1-

μ = \cos (θ)

2-

I_{i n c, λ} (μ, ϕ) = I_{\circ, λ} δ (μ - μ^{'}) δ (ϕ - ϕ^{'}),

3-

F_{i n c, λ} (μ) = μ I_{\circ, λ} = μ {(\frac{R_{⋆}}{d})}^{2} F_{⋆, λ},

4-

4 π R_{p}^{2} σ T_{int}^{4}

5-

F_{l o s, λ} = \int_{l o s} I_{λ} (θ, ϕ) 𝑑 Ω .

6-

F_{l o s, λ} = \sum_{i (v i s i b l e)} w_{i} μ_{i} I_{λ} (μ_{i}) .

7-

μ = c o s (β)

8-

F_{inc, λ} = α {(\frac{R_{⋆}}{d})}^{2} F_{⋆, λ} .

9-

\nabla T_{P} = {(\partial T / \partial μ)}_{P}

10-

{(R_{p} / R_{⋆})}^{2}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/2012.01169

Formulas:

1-

P (V, T) - P_{0} (V) = \frac{Γ (V)}{V} [E (V, T) - E_{0} (V)],

2-

P (V, T) - P_{0} (V) = \frac{Γ}{V} [E (V, T) - E_{0} (V)],

3-

Γ = V {(\frac{\partial P}{\partial E})}_{V} = - \frac{V}{T} {(\frac{\partial T}{\partial V})}_{S} .

4-

Γ = Γ (V) .

5-

S = f (x),

6-

x = T / Θ (V)

7-

C_{V} = {(\frac{\partial E}{\partial T})}_{V} = T {(\frac{\partial S}{\partial T})}_{V},

8-

C_{V} = C_{V} (S) .

9-

A (V, T) = ϕ (V) + Θ (V) f (x),

10-

x = T / Θ (V)

Formulas (html):

Correct Categorie: physics

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1606.03429

Formulas:

1-

x = \sum_{n \in 𝐙} x_{n}

2-

n = \deg (x)

3-

{x_{i}}_{i \in I}

4-

in (x_{i})

5-

{x_{i}}_{i \in I}

6-

y = \sum_{i \in I} a_{i} x_{i}

7-

\deg (a_{i}) + \deg (x_{i}) \leq \deg (y)

8-

{x_{i}}_{i \in I}

9-

\sum_{i \in I} c_{i, j} in (x_{i}) = 0

10-

in (x_{i})

Formulas (html):

Correct Categorie: math

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1409.5637

Formulas:

1-

E = E_{c} {(n - n_{g})}^{2}

2-

E_{c} = e^{2} / 2 C_{Σ}

3-

n_{g} \equiv - C_{g} V_{g} / e

4-

Δ E_{2} = e V / 2 + E_{c} (1 - 2 n_{g})

5-

Δ E_{1} = e V / 2 - E_{c} (1 - 2 n_{g})

6-

Δ E_{1} = 2 k_{B} T_{1}

7-

{\dot{Q}}_{o p t} ≃ 0.31 \frac{{(k_{B} T_{1})}^{2}}{e^{2} R_{T, 1}} .

8-

{\dot{Q}}_{e - p h}^{k} = Σ Ω_{k} (T_{k}^{5} - T_{p}^{5})

9-

{\dot{Q}}_{e - p h}^{k}

10-

A l_{2} O_{3}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/quant-ph/0601064

Formulas:

1-

(κ >> γ, g)

2-

γ \to γ (1 + 2 C_{1})

3-

C_{1} = g^{2} / (κ γ)

4-

(1 + 2 C_{1}^{'})

5-

C_{1}^{'} = C_{1} 2 κ / (γ + 2 κ)

6-

2 κ / (γ + 2 κ)

7-

C = C_{1} N

8-

n_{0} = γ^{2} / 8 g^{2}

9-

y = ε / (κ \sqrt{n_{0}})

10-

Ω = ω_{l} - ω_{c}

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1503.04656

Formulas:

1-

F = I l B

2-

l B = V / v

3-

V (t, z) = v (t) l B (z)

4-

V_{nom} \approx v_{nom} l B

5-

ε (t) = V (t) - v (t) l B (z_{o}) .

6-

⟨ ε (t) ⟩ = 0

7-

l B (z_{o})

8-

l B = \frac{V}{v} .

9-

\frac{σ_{l B}^{2}}{{(l B)}^{2}} = \frac{σ_{V}^{2}}{V_{nom}^{2}} + \frac{σ_{v}^{2}}{v_{nom}^{2}} - 2 r_{v V} \frac{σ_{V}}{V_{nom}} \frac{σ_{v}}{v_{nom}}

10-

σ_{ε}^{2} = σ_{V}^{2} + {(l B)}^{2} \frac{σ_{v}^{2}}{v^{2}} - 2 l B r_{v V} σ_{V} σ_{v} .

Formulas (html):

Correct Categorie: physics

Guessed Categorie: astro-ph

Result: incorrect

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

Formulas:

1-

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

2-

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

3-

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

4-

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

5-

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

6-

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

7-

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

8-

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

9-

S_{eff} (ψ, \bar{ψ}, ϕ)

10-

{⟨ 𝐣 ⟩}_{ψ \bar{ψ} ϕ}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1803.08639

Formulas:

1-

α_{i j} = - \frac{\log (S_{i} / S_{j})}{\log (ν_{i} / ν_{j})}

2-

L_{1 k e V}

3-

L_{5 G H z}

4-

L_{1 k e V}

5-

L_{5 G H z}

6-

L_{1 k e V}

7-

L_{5 G H z}

8-

δ = 1 / Γ (1 - β \cos θ)

9-

γ_{e} \in [γ_{\min}, γ_{\max}]

10-

ν_{CMB} = 1.6 \times 10^{11}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

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