Run 6831305

Paper: https://arxiv.org/abs/astro-ph/9710041

Formulas:

1-

⟨ B ⟩ = 24.95 \pm 0.30

2-

σ_{B} = 1.55 \pm 0.21

3-

S_{N} = 3.5 \pm 0.4

4-

(B - I) \sim 1

5-

(B - I) > 2.5

6-

(B - I) < 2.5

7-

(B - I) \sim 1.0

8-

N_{t o t}

9-

S_{N} = N_{t o t} 10^{0.4 (M_{V} + 15)}

10-

B_{t o t} = 12.07

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1708.01153

Formulas:

1-

G a m m a

2-

ν f (ν)

3-

E^{2} d N / d E_{peak}

4-

Φ (E_{i}) = f (N, Γ, E_{cut})

5-

Θ = {N, Γ, E_{cut}}

6-

P (Θ | Y)

7-

P (Y | Θ)

8-

P (Θ | Y) \propto P (Θ) P (Y | Θ) .

9-

P (Y | Θ)

10-

\prod_{i} P (ϕ_{i} | Θ) = \prod_{i} 𝒩 (ϕ_{i} | Φ (E_{i}), σ_{i}) .

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1801.07913

Formulas:

1-

Γ_{0} = {(m_{p} / M_{⋆})}^{2} h^{- 2} Σ_{g}_{0} r_{p}^{4} Ω_{p}^{2}

2-

α = 3 \times 10^{- 3}

3-

ψ (r) = 1 / r + γ / [{(r - r_{p})}^{2} + γ^{2}]

4-

r \in [0.48, 2.08] r_{p}

5-

5 \times 10^{- 4} r_{p}

6-

m_{p} = 10^{- 6} M_{⋆}

7-

\sim 2.7 \times 10^{- 4} r_{p} / cell

8-

m_{p} \in [10^{- 6}, 3 \times 10^{- 5}] M_{⋆}

9-

[10^{- 2}, 10]

10-

\sim r_{p} \sqrt{m_{p} / (h M_{⋆})}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1105.5522

Formulas:

1-

G = (V, E)

2-

m (G, k)

3-

Z (G) = \sum_{k = 0}^{⌊ n / 2 ⌋} m (G, k) .

4-

v \in V (G)

5-

e \in E (G)

6-

d e g (v)

7-

P_{n - k + 1}

8-

P_{n - k + 1}

9-

F_{n} = F_{n - 1} + F_{n - 2}, F_{1} = 1, F_{0} = 0, n \geq 2

10-

F_{n} = F_{k} F_{n - k + 1} + F_{k - 1} F_{n - k}, 1 \leq k \leq n

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/cond-mat/0402209

Formulas:

1-

{𝐗_{1}, 𝐗_{2} \dots 𝐗_{N}}

2-

\tilde{V} = \frac{1}{2} k_{s p r} \sum_{i = 1}^{N + 1} {| 𝐗_{i} - 𝐗_{i - 1} |}^{2} .

3-

𝐠_{i}^{∥} = (▽_{i} V_{i} \cdot {\hat{𝝉}}_{i}) {\hat{𝝉}}_{i}, 𝐠_{i}^{⟂} = ▽_{i} V_{i} - 𝐠_{i}^{∥},

4-

V_{i} = V (𝐗_{i})

5-

k_{s p r}

6-

k_{s p r}

7-

{\hat{𝝉}}_{i} = \frac{𝐗_{i + 1} - 𝐗_{i - 1}}{| 𝐗_{i + 1} - 𝐗_{i - 1} |} .

8-

g_{i}^{∥} / g_{j}^{⟂}

9-

{\hat{𝝉}}_{i} = \frac{(j - i) (𝐗_{j} - 𝐗_{i})}{| 𝐗_{j} - 𝐗_{i} |},

10-

(\tilde{𝐠} \cdot \hat{𝝉}) \hat{𝝉}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/hep-ex/0005011

Formulas:

1-

M (Σ_{c}^{0} - Λ_{c}^{+}) = 167.38 \pm 0.21 \pm 0.13 MeV / c^{2}

2-

M (Σ_{c}^{+ +} - Λ_{c}^{+}) = 167.35 \pm 0.19 \pm 0.12 MeV / c^{2}

3-

M (Σ_{c}^{+ +} - Σ_{c}^{0})

4-

- 0.03 \pm 0.28 \pm 0.11 MeV / c^{2}

5-

0.5 MeV / c^{2}

6-

⟨ E ⟩ \approx 180 GeV

7-

Σ_{c} \to Λ_{c}^{+} π^{\pm}

8-

Λ_{c}^{+} \to {𝑝 𝐾}^{-} π^{+}

9-

Λ_{c}^{+} \to {𝑝 𝐾}^{-} π^{+}

10-

Λ_{c}^{+} \to {𝑝 𝐾}^{-} π^{+}

Formulas (html):

Correct Categorie: hep-ex

Guessed Categorie: hep-ph

Result: incorrect

Paper: https://arxiv.org/abs/hep-th/0108047

Formulas:

1-

S U (2)

2-

π_{3} (S^{2}) = 𝖹 𝖹

3-

S U (2)

4-

L = 4 \int d^{3} x [L_{μ}^{a} L_{μ}^{a} - {(ϵ^{3 a b} L_{μ}^{a} L_{ν}^{b})}^{2}] .

5-

S U (2)

6-

𝐋_{μ} \equiv i τ_{i} L_{μ}^{i} = U^{- 1} \partial_{μ} U,

7-

i = 1, 2, 3

8-

U (\vec{r}, t)

9-

S U (2)

10-

S U (2)

Formulas (html):

Correct Categorie: hep-th

Guessed Categorie: hep-lat

Result: incorrect

Paper: https://arxiv.org/abs/1008.3963

Formulas:

1-

e^{+} / (e^{+} + e^{-})

2-

R = {(- 1)}^{2 S + 3 B + L}

3-

W = W_{M S S M} + λ_{i j k} L_{i} L_{j} {\bar{E}}_{k} + λ_{i j k}^{^{'}} L_{i} Q_{j} {\bar{D}}_{k} + λ_{i j k}^{^{''}} {\bar{U}}_{i} {\bar{D}}_{j} {\bar{D}}_{k} + μ_{i}^{^{'}} L_{i} H_{u}

4-

L L \bar{E}

5-

τ (10^{26} s)

6-

λ^{^{'}} (10^{- 25})

7-

τ (10^{26} s)

8-

λ^{^{'}} (10^{- 25})

9-

e^{+} e^{-} \to U γ

10-

U \to e^{+} e^{-}

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: hep-ph

Result: correct

Paper: https://arxiv.org/abs/1311.5169

Formulas:

1-

(P W, l^{1})

2-

(P W, l^{1}) = {f \in L^{2} (ℝ) : \sum {∥ \hat{f} (ξ + 2 π m) ∥}_{L^{2} ([- π, π])} < \infty}

3-

{ϕ_{α} (x) : α \in A}

4-

{x_{n} : n \in ℤ}

5-

L^{2} ([- π, π])

6-

{e^{2 π i m x} ϕ_{α} (x - x_{n}) : m, n \in ℤ, α \in A}

7-

f \in (P W, l^{1})

8-

(P W, l^{1}) := {f \in L^{2} (ℝ) : \sum_{m \in ℤ} {∥ \hat{f} (ξ + 2 π m) ∥}_{L^{2} ([- π, π])} < \infty} .

9-

g \in L^{1} (ℝ)

10-

\hat{g} (ξ) = {(2 π)}^{- 1 / 2} \int_{ℝ} g (x) e^{- i x ξ} 𝑑 x

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/quant-ph/0203031

Formulas:

1-

| r, ϕ > = e^{r e^{i ϕ} (a_{1} a_{2} - a_{1}^{†} a_{2}^{†})} | 00 > = \sum_{k = 0}^{\infty} λ^{k} e^{i k ϕ} | 00 ⟩,

2-

\frac{1}{2 π} \int_{0}^{2 π} | r, ϕ > < r, ϕ | d ϕ = \sum_{0}^{\infty} λ^{2 n} | n n > < n n | .

3-

| r, ϕ > {< r, ϕ |}^{\otimes N}

4-

s e n s i t i v e

5-

| ψ_{1} (ϕ) > = \sum_{l = 0}^{\infty} λ^{l} e^{i l ϕ} {| l >}_{a h} {| l >}_{b v},

6-

| ψ_{2} (ϕ) > = \sum_{m = 0}^{\infty} λ^{m} e^{i m ϕ} {| m >}_{a v} {| m >}_{b h}

7-

| Ψ > = | ψ_{1} > | ψ_{2} > = \sum_{l = 0}^{\infty} \sum_{m = 0}^{\infty} λ^{l + m} e^{i (l + m) ϕ} {| l >}_{a h} {| m >}_{a v} {| l >}_{b v} {| m >}_{b h} .

8-

\sum_{m = 0}^{n} e^{i [(n - m) ϕ + m ϕ]} {| n - m >}_{a h} {| m >}_{a v} {| n - m >}_{b v} {| m >}_{b h}

9-

n = l + m = 1

10-

| Ψ_{1} > = e^{2 i ϕ} ({| 1 >}_{a h} {| 0 >}_{a v} {| 1 >}_{b v} {| 0 >}_{b h}) + {| 0 >}_{a h} {| 1 >}_{a v} {| 0 >}_{b v} {| 1 >}_{b h} .

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0607282

Formulas:

1-

ν = α c_{s} H,

2-

\frac{d}{d r} {(r^{2} Ω)}^{2} > 0 .

3-

\partial_{t} 𝐯 + 𝐯 \cdot \nabla 𝐯 + ρ^{- 1} \nabla p + 2 Ω \hat{𝐳} \times 𝐯 - 4 A Ω x \hat{𝐱} = ν \nabla^{2} 𝐯,

4-

A \equiv - {\frac{1}{2} r \partial_{r} Ω |}_{r_{0}} = \frac{3}{4} Ω_{0} .

5-

- 2 A x \hat{𝐲}

6-

𝐯 = - 2 A x \hat{𝐲} + 𝐮

7-

(u_{x}, u_{y}) = (\partial_{y} ψ, - \partial_{x} ψ)

8-

ψ (x, y, t) = ϕ (x, t) e^{i β y},

9-

\partial_{t} ϕ = {[\partial_{x}^{2} - β^{2}]}^{- 1} i β [{(i β R)}^{- 1} {(\partial_{x}^{2} - β^{2})}^{2} - 2 A x (\partial_{x}^{2} - β^{2})] ϕ,

10-

ψ (0, y, t) = ψ (L, y - 2 A L t, t) .

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0010143

Formulas:

1-

𝐧 \cdot 𝝎 = 0,

2-

ℓ ω_{x} + m ω_{y} = 0,

3-

0 < ω_{x} \leq ω_{y}

4-

x (t) = \cos (ω_{x} t), y (t) = \cos (ω_{y} t + ϕ) .

5-

ϕ \equiv k π / 2 ω_{x}

6-

θ \in [0, 2 π)

7-

t \in [0, π)

8-

(ℓ, m) = (1, - 1)

9-

ω_{x} = ω_{y} = 1

10-

t \in [0, π)

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: math

Result: incorrect

Paper: https://arxiv.org/abs/1205.2147

Formulas:

1-

F e r m i

2-

L_{sd} ≃ 8 \times 10^{35}

3-

F e r m i

4-

F e r m i

5-

110 º - 130 º

6-

F e r m i

7-

r_{s} = d \frac{η^{1 / 2}}{1 + η^{1 / 2}},

8-

L_{sd} / c \dot{M} v_{w}

9-

θ = 2.1 (1 - \frac{{\bar{η}}^{2 / 5}}{4}) {\bar{η}}^{1 / 3},

10-

\bar{η} = \min (η, η^{- 1})

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1305.1119

Formulas:

1-

\sim 10^{''} - 40^{''}

2-

145 / 63 = 0.12 \pm 0.05

3-

n_{cr} (H_{2}) > 10^{7}

4-

d T_{k} = a T_{k}^{- b}

5-

ζ_{CR} ≳ 10^{- 15}

6-

ζ_{X, CR} > 10^{- 13}

7-

{}^{3}P_{2} - {}^{3}P_{1}

8-

{}^{2}P_{3 / 2} - {}^{2}P_{1 / 2}

9-

{}^{3}P_{1} - {}^{3}P_{2}

10-

{}^{3}P_{1} - {}^{3}P_{0}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1810.09095

Formulas:

1-

\hat{D} (α)

2-

n_{S} = N_{S} / M ≫ 1

3-

δ α_{η = 1}^{E} ≃ 1 / (4 M \sqrt{n_{S}})

4-

δ α_{η = 1}^{P} ≃ 1 / (4 \sqrt{M n_{S}})

5-

\hat{D} (α)

6-

{\hat{ρ}}_{in}^{(i)}

7-

{\hat{ρ}}_{in}^{(i)}

8-

{\hat{ρ}}_{in}^{(i)} = | α_{i} ⟩ ⟨ α_{i} |

9-

| α_{i} ⟩ = | α / \sqrt{N} ⟩ ≃ | 0 ⟩ + α_{i} | 1 ⟩

10-

{| α_{i} |}^{2} ≪ 1

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: quant-ph

Result: correct

Paper: https://arxiv.org/abs/1704.08026

Formulas:

1-

L_{m} \equiv \frac{1}{L_{C}} \oint_{L_{C}} \frac{U (Ω)}{U_{max}} 𝑑 Ω,

2-

k = (2 π / λ) \sin θ

3-

k = a / 2 b^{2}

4-

α \partial_{t} Ψ + θ Ψ - (α + i) [- (1 + η) + \frac{2 C (I - 1)}{1 + {| Ψ |}^{2}}] Ψ

5-

+ (α - i d) \nabla_{⟂}^{2} Ψ = 0 .

6-

\partial_{t} Ψ = - \nabla_{⟂}^{2} Ψ + \frac{2 C (I - 1)}{1 + {| Ψ |}^{2}} Ψ .

7-

\partial_{t} Ψ = 0

8-

- \frac{d^{2} Ψ}{d η^{2}} + V_{G} (η) Ψ = γ \frac{Ψ}{1 + {| Ψ |}^{2}},

9-

γ = - 2 C (I - 1) R^{2}

10-

V_{G} (η)

Formulas (html):

Correct Categorie: physics

Guessed Categorie: physics

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0309607

Formulas:

1-

r_{E} = \sqrt{2 R_{S} D}

2-

R_{S} = (2 G M) / c^{2}

3-

D = D_{L} (D_{S} - D_{L}) / D_{S}

4-

D \sim 2.5 kpc {[r_{E} / (2.5 AU)]}^{2}

5-

M \sim 0.3 M_{⊙}

6-

D_{S} \sim 8.5 kpc

7-

D_{L} \sim 6 kpc

8-

D_{S} ≫ D_{S} - D_{L}

9-

q_{\min} = 2 \times 10^{- 3} {[R_{⋆} / (100 R_{⊙})]}^{2}

10-

r_{E} \sim 2.5 AU

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/0810.4687

Formulas:

1-

M_{C r / F e}

2-

_{C r / F e}

3-

_{C r / F e}

4-

M_{C r / F e}

5-

M_{C r / F e}

6-

M_{C r / F e}

7-

M_{C r / F e}

8-

M_{C r / F e}

9-

M_{C r / F e}

10-

M_{C r / F e}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1305.7108

Formulas:

1-

Q = (1 / τ) \int_{0}^{τ} m (t) 𝑑 t

2-

h_{0}^{c} (τ)

3-

h_{0}^{c} (τ)

4-

\int_{n τ}^{(n + 1) τ} h (t) 𝑑 t = 0

5-

Q = (1 / τ) \int_{0}^{τ} m (t) 𝑑 t

6-

= 1 - \frac{{< Q^{4} >}_{L}}{3 {< Q^{2} >}_{L}^{2}}

7-

(L^{2} / k_{B} T) [{< Q^{2} >}_{L} - {< Q >}_{L}^{2}]

8-

h_{0}^{c} (τ)

9-

h_{0}^{c} (τ)

10-

h_{0}^{c} (τ)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/hep-ex/0002040

Formulas:

1-

b \to u ℓ \bar{ν}

2-

b \to u ℓ \bar{ν}

3-

| V_{u b} |

4-

b \to u ℓ \bar{ν}

5-

| V_{u b} |

6-

| V_{u b} |

7-

b \to c ℓ \bar{ν}

8-

| V_{u b} |

9-

b \to c ℓ \bar{ν}

10-

B \to π ℓ \bar{ν}

Formulas (html):

Correct Categorie: hep-ex

Guessed Categorie: hep-ph

Result: incorrect

Paper: https://arxiv.org/abs/0809.0747

Formulas:

1-

T_{B K T}

2-

T_{B K T}

3-

\int d^{3} 𝐱 {\hat{Ψ}}^{†} (- \frac{ℏ^{2}}{2 m} \nabla^{2} + \frac{1}{2} m \sum_{j} ω_{j}^{2} x_{j}^{2}) \hat{Ψ}

4-

+ \frac{2 π a ℏ^{2}}{m} \int d^{3} 𝐱 {\hat{Ψ}}^{†} {\hat{Ψ}}^{†} \hat{Ψ} \hat{Ψ},

5-

\hat{Ψ} (𝐱)

6-

ℏ ω_{x, y} ≪ k_{B} T \sim ℏ ω_{z}

7-

ψ_{k σ} (x, y, z) = f_{k σ} (x, y) ξ_{k} (z)

8-

ξ_{k} (z)

9-

𝐫 = (x, y)

10-

f_{k σ} (x, y)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/0711.4589

Formulas:

1-

M \leq 5 \times 10^{9} M_{⊙}

2-

Δ σ_{z}^{2} = 2 Δ E / M_{s}

3-

Δ E ≃ 4 π G^{2} M_{s}^{2} Σ / v_{s}^{2}

4-

\partial_{z} (ρ_{d} σ_{z}^{2}) + ρ_{d} \partial_{z} Φ = 0

5-

\partial_{z}^{2} Φ = 4 π G ρ_{d}

6-

ρ_{d} \propto \exp (- z / z_{d})

7-

σ_{z}^{2} = 2 π G Σ z_{d}

8-

Δ σ_{z}^{2} = 2 π G Σ Δ z_{d}

9-

M_{s} = {[M_{d} v_{s}^{2} Δ z_{d} / (4 G)]}^{1 / 2}

10-

5.2 \times 10^{9} M_{⊙}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/2003.02523

Formulas:

1-

- 8 < α \leq 1

2-

- 8 < α < 0

3-

(-, +, +, +)

4-

I = \frac{1}{16 π G} \int \sqrt{- g} d^{4} x [R + α (R_{μ ν λ δ} R^{μ ν λ δ} - 4 R_{μ ν} R^{μ ν} + R^{2})],

5-

α \to \frac{α}{D - 4},

6-

d s^{2} = - f (r) d t^{2} + \frac{d r^{2}}{f (r)} + r^{2} d Ω^{2},

7-

f (r) = 1 + \frac{r^{2}}{2 α} (1 - \sqrt{1 + \frac{8 α M}{r^{3}}}),

8-

r^{3} < - 8 α M

9-

- 8 < α \leq 1

10-

r = - 2 {(α M)}^{1 / 3}

Formulas (html):

Correct Categorie: gr-qc

Guessed Categorie: gr-qc

Result: correct

Paper: https://arxiv.org/abs/hep-th/0211237

Formulas:

1-

E^{2} = m^{2} + p^{2} .

2-

\hat{H} = \frac{1}{2} ω ({\hat{a}}^{†} \hat{a} - \hat{a} {\hat{a}}^{†}) .

3-

{\hat{a}}^{†} \hat{a} = \hat{N}, \hat{a} {\hat{a}}^{†} = \hat{1 - N} .

4-

\hat{H} = \frac{1}{2} ω (\hat{N} - (\hat{1 - N})) .

5-

E = \frac{1}{2} ω (n - (1 - n)) = \frac{1}{2} ω (2 n - 1) .

6-

n = \frac{\sqrt{m^{2} + p^{2}}}{ω} + \frac{1}{2} .

7-

{\hat{a}}_{q}^{†} {\hat{a}}_{q} = {[\hat{N}]}_{q}, {\hat{a}}_{q} {\hat{a}}_{q}^{†} = {[\hat{1 - N}]}_{q}, {[x]}_{q} \equiv \frac{q^{x} - q^{- x}}{q - q^{- 1}},

8-

{\hat{H}}_{q} = \frac{ω}{2} ({[\hat{N}]}_{q} - {[\hat{1 - N}]}_{q}) .

9-

E = \frac{ω}{2} ({[\frac{\sqrt{m^{2} + p^{2}}}{ω} + \frac{1}{2}]}_{q} - {[\frac{1}{2} - \frac{\sqrt{m^{2} + p^{2}}}{ω}]}_{q}) .

10-

\hat{H} = \frac{1}{2} ω ({\hat{b}}^{†} \hat{b} + \hat{b} {\hat{b}}^{†}),

Formulas (html):

Correct Categorie: hep-th

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/math/0411265

Formulas:

1-

X = X (Δ)

2-

# Δ (1) - 2

3-

X = X (Δ)

4-

ϵ : M \to {\pm 1}

5-

T_{ϵ} := {t \in T (ℝ) \subset X (ℝ) : sgn (χ^{u} (t)) = ϵ (u) for all u \in M} .

6-

X_{ϵ} \subset X (ℝ)

7-

μ : X (ℝ) \to P

8-

ϵ_{0} (M) = + 1

9-

t_{ϵ} \in T (ℝ)

10-

X (ℝ) = ⋃_{ϵ} X_{ϵ}

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/astro-ph/9601063

Formulas:

1-

Q_{r m s - P S} \sim {15.3}_{- 2.8}^{+ 3.7} μ

2-

Q_{r m s - P S} \sim 18 μ

3-

δ Q / Q \overset{<}{\sim} 0.07

4-

Q_{r m s - P S}

5-

Q_{r m s - P S}

6-

| b | > 20^{\circ}

7-

| b | > 20^{\circ}

8-

| b | > 30^{\circ}

9-

| b | > 20^{\circ}

10-

\begin{matrix} Δ_{31} = 0.611 Δ_{31 A} + 0.389 Δ_{31 B}, \\ Δ_{53} = 0.579 Δ_{53 A} + 0.421 Δ_{53 B}, \\ Δ_{90} = 0.382 Δ_{90 A} + 0.618 Δ_{90 B}, \end{matrix}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/cond-mat/0301449

Formulas:

1-

δ G = \frac{2 e^{2} (β - 2)}{3 β h},

2-

l ≪ L, l_{so}, l_{H} ≪ ξ

3-

H = - i σ_{0} \otimes τ_{3} \otimes 𝟙_{ℕ} \frac{\partial}{\partial 𝕩} + \sum_{𝕛} 𝕍_{𝕛} δ (𝕩 - 𝕛 𝕒),

4-

2 N \times 2 N

5-

X^{R} = σ_{2} X^{T} σ_{2}

6-

X^{*} = {(X^{†})}^{R}

7-

⟨ G ⟩ = \frac{e^{2}}{h} g, g = ⟨ tr (1 - r^{†} r) ⟩,

8-

S_{j} = (\begin{matrix} t_{j} & r_{j}^{'} \\ r_{j} & t_{j}^{'} \end{matrix}) = \frac{2 i - V_{j}}{2 i + V_{j}} .

9-

r \to r_{j} + t_{j}^{'} r {(1 - r_{j}^{'} r)}^{- 1} t_{j} .

10-

V = (\begin{matrix} v_{L L} & v_{L R} \\ v_{R L} & v_{R R} \end{matrix}),

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1608.08739

Formulas:

1-

p p \underline{} c n o \underline{} e x t r a s \underline{} o 18 \underline{} n e 22 . n e t

2-

10^{- 3} M_{⊙} {yr}^{- 1}

3-

M_{i} = 0.8 M_{⊙}

4-

T_{eff} - \log g

5-

T_{eff} - \log g

6-

T_{eff} - \log g

7-

T_{eff} - \log g

8-

M_{i} = 0.8 M_{⊙}

9-

M_{c} = 0.448 M_{⊙}

10-

M_{i} = 0.8 M_{⊙}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/0812.2172

Formulas:

1-

S U (3)

2-

S U (3)

3-

S U (3)

4-

h^{2, 1} = 0

5-

C^{i}, i = 1 \dots h

6-

h^{2, 1} = 0

7-

h^{1, 1} > h^{2, 1} \neq 0

8-

K = - 3 \log (T + \bar{T}) + α^{'} \frac{6}{(T + \bar{T})} C^{A} {\bar{C}}_{A} + 𝒪 (α^{'}^{2}),

9-

W = i e T - \frac{α^{'}}{3} j_{A B C} C^{A} C^{B} C^{C} + 𝒪 (α^{'}^{2}) .

10-

i e - \frac{3}{T + \bar{T}} W - \frac{6 α^{'} C^{A} {\bar{C}}_{A}}{{(T + \bar{T})}^{2}} W + 𝒪 (α^{'}^{2}),

Formulas (html):

Correct Categorie: hep-th

Guessed Categorie: hep-ph

Result: incorrect

Paper: https://arxiv.org/abs/2005.04131

Formulas:

1-

D_{L} {(1 + z)}^{- 2} / D_{A} = η = 1

2-

η = η (z)

3-

\frac{D_{L} (z)}{D_{A} (z) {(1 + z)}^{2}} = 1

4-

\frac{D_{L} (z)}{D_{A} (z) {(1 + z)}^{2}} = η (z)

5-

η (z) = 1 + η_{0} z

6-

η (z) = 1 + η_{0} z / (1 + z)

7-

η (z) = η_{0} + η_{1} z

8-

η (z) = η_{0} + η_{1} z / (1 + z)

9-

η (z) = η_{0} + η_{1} \ln (1 + z)

10-

η (z) = {(1 + z)}^{ϵ}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/1003.3162

Formulas:

1-

\sum_{i, σ} ε_{i} c_{i σ}^{†} c_{i σ} + \sum_{i \neq j} \sum_{σ} t_{i j} c_{i σ}^{†} c_{j σ} + \sum_{i} U {\hat{n}}_{i ↑} {\hat{n}}_{i ↓} + \frac{1}{2} \sum_{i \neq j} V_{i j} {\hat{n}}_{i} {\hat{n}}_{j}

2-

{\hat{H}}_{0} + {\hat{H}}_{T} + {\hat{H}}_{U} + {\hat{H}}_{V},

3-

{\hat{n}}_{i σ} = c_{i σ}^{†} c_{i σ}

4-

{\hat{n}}_{i} = {\hat{n}}_{i ↑} + {\hat{n}}_{i ↓}

5-

t_{i j} = t

6-

V_{i j} = V

7-

t_{i j} = t^{'}

8-

V_{i j} = V^{'}

9-

ε_{i} = ε_{0} + V^{'}

10-

R y = m_{e}^{*} e^{4} / 2 ϵ^{2} ℏ^{2}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1111.4557

Formulas:

1-

{\hat{H}}_{int} = κ {\hat{P}}_{S} {\hat{P}}_{A}

2-

| Ψ ⟩ = \sqrt{1 - λ^{2}} \sum_{n = 0}^{\infty} λ^{n} | n n ⟩

3-

𝐑 = {(x_{1}, p_{1}, \dots, x_{N}, p_{N})}^{T}

4-

𝒲 (x_{1}, p_{1}, \dots, x_{N}, p_{N}) = \frac{\exp [- (𝐑^{T} - 𝐝^{T}) γ^{- 1} (𝐑 - 𝐝)]}{π^{N} \sqrt{det γ}}

5-

𝐝 = {(⟨ x_{1} ⟩, ⟨ p_{1} ⟩, \dots, ⟨ x_{N} ⟩, ⟨ p_{N} ⟩)}^{T}

6-

γ_{l m} = ⟨ {\hat{R}}_{l} {\hat{R}}_{m} + {\hat{R}}_{m} {\hat{R}}_{l} ⟩ - 2 d_{l} d_{m} .

7-

γ_{A B}^{T M S S} = (\begin{matrix} \cosh (2 r) & 0 & \sinh (2 r) & 0 \\ 0 & \cosh (2 r) & 0 & - \sinh (2 r) \\ \sinh (2 r) & 0 & \cosh (2 r) & 0 \\ 0 & - \sinh (2 r) & 0 & \cosh (2 r) \end{matrix}) .

8-

Ω = \oplus_{j = 1}^{N} i σ_{y}

9-

S_{Q N D}^{(κ \hat{P} \hat{P})} = (\begin{matrix} 1 & 0 & 0 & κ \\ 0 & 1 & 0 & 0 \\ 0 & κ & 1 & 0 \\ 0 & 0 & 0 & 1 \end{matrix})

10-

S_{Q N D}^{(κ \hat{X} \hat{X})}

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: quant-ph

Result: correct

Paper: https://arxiv.org/abs/hep-ph/9904340

Formulas:

1-

ν_{L α} = \sum_{j} U_{α j} ν_{L j}

2-

α = e, μ, τ, \dots

3-

j = 1, 2, 3, \dots

4-

P_{ν_{α} \to ν_{β}} (L / E_{ν}) = {| \sum_{j} U_{β j} U_{α j}^{*} \exp (- i \frac{m_{j}^{2} L}{2 E_{ν}}) |}^{2},

5-

L = | {\vec{x}}_{D} - {\vec{x}}_{S} |

6-

ϕ (\vec{x}, t) = ψ_{D} (\vec{x} - {\vec{x}}_{D}) e^{- i E_{D P} t},

7-

ψ_{D} (\vec{y})

8-

{⟨ P_{{\overset{(-)}{ν}}_{α}, \to {\overset{(-)}{ν}}_{β}} ⟩}_{𝒫} \propto \int 𝑑 P_{S} \int_{𝒫} \frac{d^{3} p_{D 1}^{'}}{2 E_{D 1}^{'}} \dots \frac{d^{3} p_{D n_{D}}^{'}}{2 E_{D n_{D}}^{'}} {| 𝒜_{{\overset{(-)}{ν}}_{α}, \to {\overset{(-)}{ν}}_{β}} |}^{2} .

9-

\int d^{4} x_{1}

10-

\int d^{4} x_{2}

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/0707.2577

Formulas:

1-

R o = P_{rot} / τ_{c}

2-

ω_{crit} (τ_{c})

3-

8 < \bar{V} < 12.5

4-

Θ_{AoV} = s_{1}^{2} / s_{2}^{2}

5-

(r - 1) s_{1}^{2} = \sum_{i = 1}^{r} n_{i} {(\bar{x_{i}} - \bar{x})}^{2}

6-

(n - r) s_{2}^{2} = \sum_{i = 1}^{r} \sum_{j = 1}^{n_{i}} {(x_{i j} - \bar{x_{i}})}^{2}

7-

Θ_{AoV} (P) \geq 8.0

8-

B C = - 0.083 - 0.501 (R - I) - 0.646 (R - I)

9-

\log R_{x} = \log (L_{x} / L_{bol})

10-

B C = - 0.397 M_{V} + 2.386

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/cond-mat/0111544

Formulas:

1-

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

2-

d + i d_{x y}

3-

G / G_{N} - V

4-

G \equiv d I / d V

5-

G_{0} / G_{N} \approx 3

6-

- Δ_{S C} < V < Δ_{S C}

7-

- π / 2 < θ < π / 2

8-

H_{c} = ϕ_{0} / π^{2} ξ λ

9-

i d_{x y}

10-

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

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1502.02655

Formulas:

1-

Flesch Reading Ease = 206.835 - 1.015 (N_{Words} / N_{Sentences}) - 84.6 (N_{Syllables} / N_{Words})

2-

Flesch-Kincaid = 0.39 (N_{Words} / N_{Sentences}) + 11.8 (N_{Syllables} / N_{Words}) - 15.59

3-

S D_{W o W} = .087

4-

S D_{u k W a C} = .059

5-

g r o w t h . r a t e_{W o W} = .033, g r o w t h . r a t e_{u k W a C} = .059

6-

S D_{W o W} = 7.6

7-

S D_{u k W a C} = 13

8-

M_{W o W} = 70

9-

M_{u k W a C} = 57

10-

M_{W o W} = 7.8

Formulas (html):

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xref="S3.SS1.SSS0.Px3.p1.1.m1.1.1.1.1.1.1.1.cmml">(</mo><mrow id="S3.SS1.SSS0.Px3.p1.1.m1.1.1.1.1.1.1.1" xref="S3.SS1.SSS0.Px3.p1.1.m1.1.1.1.1.1.1.1.cmml"><msub id="S3.SS1.SSS0.Px3.p1.1.m1.1.1.1.1.1.1.1.2" xref="S3.SS1.SSS0.Px3.p1.1.m1.1.1.1.1.1.1.1.2.cmml"><mi id="S3.SS1.SSS0.Px3.p1.1.m1.1.1.1.1.1.1.1.2.2" xref="S3.SS1.SSS0.Px3.p1.1.m1.1.1.1.1.1.1.1.2.2.cmml">N</mi><mtext id="S3.SS1.SSS0.Px3.p1.1.m1.1.1.1.1.1.1.1.2.3" xref="S3.SS1.SSS0.Px3.p1.1.m1.1.1.1.1.1.1.1.2.3a.cmml">Words</mtext></msub><mo id="S3.SS1.SSS0.Px3.p1.1.m1.1.1.1.1.1.1.1.1" xref="S3.SS1.SSS0.Px3.p1.1.m1.1.1.1.1.1.1.1.1.cmml">/</mo><msub id="S3.SS1.SSS0.Px3.p1.1.m1.1.1.1.1.1.1.1.3" xref="S3.SS1.SSS0.Px3.p1.1.m1.1.1.1.1.1.1.1.3.cmml"><mi id="S3.SS1.SSS0.Px3.p1.1.m1.1.1.1.1.1.1.1.3.2" xref="S3.SS1.SSS0.Px3.p1.1.m1.1.1.1.1.1.1.1.3.2.cmml">N</mi><mtext id="S3.SS1.SSS0.Px3.p1.1.m1.1.1.1.1.1.1.1.3.3" xref="S3.SS1.SSS0.Px3.p1.1.m1.1.1.1.1.1.1.1.3.3a.cmml">Sentences</mtext></msub></mrow><mo stretchy="false" id="S3.SS1.SSS0.Px3.p1.1.m1.1.1.1.1.1.1.3" xref="S3.SS1.SSS0.Px3.p1.1.m1.1.1.1.1.1.1.1.cmml">)</mo></mrow></mrow><mo id="S3.SS1.SSS0.Px3.p1.1.m1.2.2.2.3a" xref="S3.SS1.SSS0.Px3.p1.1.m1.2.2.2.3.cmml">-</mo><mrow id="S3.SS1.SSS0.Px3.p1.1.m1.2.2.2.2" xref="S3.SS1.SSS0.Px3.p1.1.m1.2.2.2.2.cmml"><mn id="S3.SS1.SSS0.Px3.p1.1.m1.2.2.2.2.3" xref="S3.SS1.SSS0.Px3.p1.1.m1.2.2.2.2.3.cmml">84.6</mn><mo id="S3.SS1.SSS0.Px3.p1.1.m1.2.2.2.2.2" xref="S3.SS1.SSS0.Px3.p1.1.m1.2.2.2.2.2.cmml">⁢</mo><mrow id="S3.SS1.SSS0.Px3.p1.1.m1.2.2.2.2.1.1" xref="S3.SS1.SSS0.Px3.p1.1.m1.2.2.2.2.1.1.1.cmml"><mo stretchy="false" id="S3.SS1.SSS0.Px3.p1.1.m1.2.2.2.2.1.1.2" xref="S3.SS1.SSS0.Px3.p1.1.m1.2.2.2.2.1.1.1.cmml">(</mo><mrow id="S3.SS1.SSS0.Px3.p1.1.m1.2.2.2.2.1.1.1" xref="S3.SS1.SSS0.Px3.p1.1.m1.2.2.2.2.1.1.1.cmml"><msub id="S3.SS1.SSS0.Px3.p1.1.m1.2.2.2.2.1.1.1.2" xref="S3.SS1.SSS0.Px3.p1.1.m1.2.2.2.2.1.1.1.2.cmml"><mi id="S3.SS1.SSS0.Px3.p1.1.m1.2.2.2.2.1.1.1.2.2" xref="S3.SS1.SSS0.Px3.p1.1.m1.2.2.2.2.1.1.1.2.2.cmml">N</mi><mtext id="S3.SS1.SSS0.Px3.p1.1.m1.2.2.2.2.1.1.1.2.3" xref="S3.SS1.SSS0.Px3.p1.1.m1.2.2.2.2.1.1.1.2.3a.cmml">Syllables</mtext></msub><mo id="S3.SS1.SSS0.Px3.p1.1.m1.2.2.2.2.1.1.1.1" xref="S3.SS1.SSS0.Px3.p1.1.m1.2.2.2.2.1.1.1.1.cmml">/</mo><msub id="S3.SS1.SSS0.Px3.p1.1.m1.2.2.2.2.1.1.1.3" xref="S3.SS1.SSS0.Px3.p1.1.m1.2.2.2.2.1.1.1.3.cmml"><mi id="S3.SS1.SSS0.Px3.p1.1.m1.2.2.2.2.1.1.1.3.2" xref="S3.SS1.SSS0.Px3.p1.1.m1.2.2.2.2.1.1.1.3.2.cmml">N</mi><mtext id="S3.SS1.SSS0.Px3.p1.1.m1.2.2.2.2.1.1.1.3.3" xref="S3.SS1.SSS0.Px3.p1.1.m1.2.2.2.2.1.1.1.3.3a.cmml">Words</mtext></msub></mrow><mo stretchy="false" id="S3.SS1.SSS0.Px3.p1.1.m1.2.2.2.2.1.1.3" xref="S3.SS1.SSS0.Px3.p1.1.m1.2.2.2.2.1.1.1.cmml">)</mo></mrow></mrow></mrow></mrow></math>, <math><mrow id="S3.SS1.SSS0.Px3.p1.2.m2.2.2" xref="S3.SS1.SSS0.Px3.p1.2.m2.2.2.cmml"><mtext id="S3.SS1.SSS0.Px3.p1.2.m2.2.2.4" xref="S3.SS1.SSS0.Px3.p1.2.m2.2.2.4a.cmml">Flesch-Kincaid</mtext><mo id="S3.SS1.SSS0.Px3.p1.2.m2.2.2.3" xref="S3.SS1.SSS0.Px3.p1.2.m2.2.2.3.cmml">=</mo><mrow id="S3.SS1.SSS0.Px3.p1.2.m2.2.2.2" xref="S3.SS1.SSS0.Px3.p1.2.m2.2.2.2.cmml"><mrow id="S3.SS1.SSS0.Px3.p1.2.m2.2.2.2.2" xref="S3.SS1.SSS0.Px3.p1.2.m2.2.2.2.2.cmml"><mrow id="S3.SS1.SSS0.Px3.p1.2.m2.1.1.1.1.1" xref="S3.SS1.SSS0.Px3.p1.2.m2.1.1.1.1.1.cmml"><mn id="S3.SS1.SSS0.Px3.p1.2.m2.1.1.1.1.1.3" xref="S3.SS1.SSS0.Px3.p1.2.m2.1.1.1.1.1.3.cmml">0.39</mn><mo id="S3.SS1.SSS0.Px3.p1.2.m2.1.1.1.1.1.2" xref="S3.SS1.SSS0.Px3.p1.2.m2.1.1.1.1.1.2.cmml">⁢</mo><mrow id="S3.SS1.SSS0.Px3.p1.2.m2.1.1.1.1.1.1.1" xref="S3.SS1.SSS0.Px3.p1.2.m2.1.1.1.1.1.1.1.1.cmml"><mo stretchy="false" id="S3.SS1.SSS0.Px3.p1.2.m2.1.1.1.1.1.1.1.2" xref="S3.SS1.SSS0.Px3.p1.2.m2.1.1.1.1.1.1.1.1.cmml">(</mo><mrow id="S3.SS1.SSS0.Px3.p1.2.m2.1.1.1.1.1.1.1.1" xref="S3.SS1.SSS0.Px3.p1.2.m2.1.1.1.1.1.1.1.1.cmml"><msub id="S3.SS1.SSS0.Px3.p1.2.m2.1.1.1.1.1.1.1.1.2" 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id="S5.SS2.p2.1.m1.3.3.2.2.1.1" xref="S5.SS2.p2.1.m1.3.3.2.2.1.2.cmml"><mn id="S5.SS2.p2.1.m1.1.1" xref="S5.SS2.p2.1.m1.1.1.cmml">.033</mn><mo id="S5.SS2.p2.1.m1.3.3.2.2.1.1.2" xref="S5.SS2.p2.1.m1.3.3.2.2.1.2.cmml">,</mo><mrow id="S5.SS2.p2.1.m1.3.3.2.2.1.1.1" xref="S5.SS2.p2.1.m1.3.3.2.2.1.1.1.cmml"><mi id="S5.SS2.p2.1.m1.3.3.2.2.1.1.1.2" xref="S5.SS2.p2.1.m1.3.3.2.2.1.1.1.2.cmml">g</mi><mo id="S5.SS2.p2.1.m1.3.3.2.2.1.1.1.1" xref="S5.SS2.p2.1.m1.3.3.2.2.1.1.1.1.cmml">⁢</mo><mi id="S5.SS2.p2.1.m1.3.3.2.2.1.1.1.3" xref="S5.SS2.p2.1.m1.3.3.2.2.1.1.1.3.cmml">r</mi><mo id="S5.SS2.p2.1.m1.3.3.2.2.1.1.1.1a" xref="S5.SS2.p2.1.m1.3.3.2.2.1.1.1.1.cmml">⁢</mo><mi id="S5.SS2.p2.1.m1.3.3.2.2.1.1.1.4" xref="S5.SS2.p2.1.m1.3.3.2.2.1.1.1.4.cmml">o</mi><mo id="S5.SS2.p2.1.m1.3.3.2.2.1.1.1.1b" xref="S5.SS2.p2.1.m1.3.3.2.2.1.1.1.1.cmml">⁢</mo><mi id="S5.SS2.p2.1.m1.3.3.2.2.1.1.1.5" xref="S5.SS2.p2.1.m1.3.3.2.2.1.1.1.5.cmml">w</mi><mo id="S5.SS2.p2.1.m1.3.3.2.2.1.1.1.1c" xref="S5.SS2.p2.1.m1.3.3.2.2.1.1.1.1.cmml">⁢</mo><mi id="S5.SS2.p2.1.m1.3.3.2.2.1.1.1.6" xref="S5.SS2.p2.1.m1.3.3.2.2.1.1.1.6.cmml">t</mi><mo id="S5.SS2.p2.1.m1.3.3.2.2.1.1.1.1d" xref="S5.SS2.p2.1.m1.3.3.2.2.1.1.1.1.cmml">⁢</mo><mi id="S5.SS2.p2.1.m1.3.3.2.2.1.1.1.7" xref="S5.SS2.p2.1.m1.3.3.2.2.1.1.1.7.cmml">h</mi></mrow></mrow></mrow><mo id="S5.SS2.p2.1.m1.4.4.3.5" xref="S5.SS2.p2.1.m1.4.4.4a.cmml">.</mo><mrow id="S5.SS2.p2.1.m1.4.4.3.3" xref="S5.SS2.p2.1.m1.4.4.3.3.cmml"><mrow id="S5.SS2.p2.1.m1.4.4.3.3.2" xref="S5.SS2.p2.1.m1.4.4.3.3.2.cmml"><mi id="S5.SS2.p2.1.m1.4.4.3.3.2.2" xref="S5.SS2.p2.1.m1.4.4.3.3.2.2.cmml">r</mi><mo id="S5.SS2.p2.1.m1.4.4.3.3.2.1" xref="S5.SS2.p2.1.m1.4.4.3.3.2.1.cmml">⁢</mo><mi id="S5.SS2.p2.1.m1.4.4.3.3.2.3" xref="S5.SS2.p2.1.m1.4.4.3.3.2.3.cmml">a</mi><mo id="S5.SS2.p2.1.m1.4.4.3.3.2.1a" xref="S5.SS2.p2.1.m1.4.4.3.3.2.1.cmml">⁢</mo><mi id="S5.SS2.p2.1.m1.4.4.3.3.2.4" xref="S5.SS2.p2.1.m1.4.4.3.3.2.4.cmml">t</mi><mo id="S5.SS2.p2.1.m1.4.4.3.3.2.1b" xref="S5.SS2.p2.1.m1.4.4.3.3.2.1.cmml">⁢</mo><msub id="S5.SS2.p2.1.m1.4.4.3.3.2.5" xref="S5.SS2.p2.1.m1.4.4.3.3.2.5.cmml"><mi id="S5.SS2.p2.1.m1.4.4.3.3.2.5.2" xref="S5.SS2.p2.1.m1.4.4.3.3.2.5.2.cmml">e</mi><mrow id="S5.SS2.p2.1.m1.4.4.3.3.2.5.3" xref="S5.SS2.p2.1.m1.4.4.3.3.2.5.3.cmml"><mi id="S5.SS2.p2.1.m1.4.4.3.3.2.5.3.2" xref="S5.SS2.p2.1.m1.4.4.3.3.2.5.3.2.cmml">u</mi><mo id="S5.SS2.p2.1.m1.4.4.3.3.2.5.3.1" xref="S5.SS2.p2.1.m1.4.4.3.3.2.5.3.1.cmml">⁢</mo><mi id="S5.SS2.p2.1.m1.4.4.3.3.2.5.3.3" xref="S5.SS2.p2.1.m1.4.4.3.3.2.5.3.3.cmml">k</mi><mo id="S5.SS2.p2.1.m1.4.4.3.3.2.5.3.1a" xref="S5.SS2.p2.1.m1.4.4.3.3.2.5.3.1.cmml">⁢</mo><mi id="S5.SS2.p2.1.m1.4.4.3.3.2.5.3.4" xref="S5.SS2.p2.1.m1.4.4.3.3.2.5.3.4.cmml">W</mi><mo id="S5.SS2.p2.1.m1.4.4.3.3.2.5.3.1b" xref="S5.SS2.p2.1.m1.4.4.3.3.2.5.3.1.cmml">⁢</mo><mi id="S5.SS2.p2.1.m1.4.4.3.3.2.5.3.5" xref="S5.SS2.p2.1.m1.4.4.3.3.2.5.3.5.cmml">a</mi><mo id="S5.SS2.p2.1.m1.4.4.3.3.2.5.3.1c" xref="S5.SS2.p2.1.m1.4.4.3.3.2.5.3.1.cmml">⁢</mo><mi id="S5.SS2.p2.1.m1.4.4.3.3.2.5.3.6" xref="S5.SS2.p2.1.m1.4.4.3.3.2.5.3.6.cmml">C</mi></mrow></msub></mrow><mo id="S5.SS2.p2.1.m1.4.4.3.3.1" xref="S5.SS2.p2.1.m1.4.4.3.3.1.cmml">=</mo><mn id="S5.SS2.p2.1.m1.4.4.3.3.3" xref="S5.SS2.p2.1.m1.4.4.3.3.3.cmml">.059</mn></mrow></mrow></math>, <math><mrow id="S5.SS4.p1.1.m1.1.1" xref="S5.SS4.p1.1.m1.1.1.cmml"><mrow id="S5.SS4.p1.1.m1.1.1.2" xref="S5.SS4.p1.1.m1.1.1.2.cmml"><mi id="S5.SS4.p1.1.m1.1.1.2.2" xref="S5.SS4.p1.1.m1.1.1.2.2.cmml">S</mi><mo id="S5.SS4.p1.1.m1.1.1.2.1" xref="S5.SS4.p1.1.m1.1.1.2.1.cmml">⁢</mo><msub id="S5.SS4.p1.1.m1.1.1.2.3" xref="S5.SS4.p1.1.m1.1.1.2.3.cmml"><mi id="S5.SS4.p1.1.m1.1.1.2.3.2" xref="S5.SS4.p1.1.m1.1.1.2.3.2.cmml">D</mi><mrow id="S5.SS4.p1.1.m1.1.1.2.3.3" xref="S5.SS4.p1.1.m1.1.1.2.3.3.cmml"><mi id="S5.SS4.p1.1.m1.1.1.2.3.3.2" xref="S5.SS4.p1.1.m1.1.1.2.3.3.2.cmml">W</mi><mo id="S5.SS4.p1.1.m1.1.1.2.3.3.1" xref="S5.SS4.p1.1.m1.1.1.2.3.3.1.cmml">⁢</mo><mi id="S5.SS4.p1.1.m1.1.1.2.3.3.3" xref="S5.SS4.p1.1.m1.1.1.2.3.3.3.cmml">o</mi><mo id="S5.SS4.p1.1.m1.1.1.2.3.3.1a" xref="S5.SS4.p1.1.m1.1.1.2.3.3.1.cmml">⁢</mo><mi id="S5.SS4.p1.1.m1.1.1.2.3.3.4" xref="S5.SS4.p1.1.m1.1.1.2.3.3.4.cmml">W</mi></mrow></msub></mrow><mo id="S5.SS4.p1.1.m1.1.1.1" xref="S5.SS4.p1.1.m1.1.1.1.cmml">=</mo><mn id="S5.SS4.p1.1.m1.1.1.3" xref="S5.SS4.p1.1.m1.1.1.3.cmml">7.6</mn></mrow></math>, <math><mrow id="S5.SS4.p1.2.m2.1.1" xref="S5.SS4.p1.2.m2.1.1.cmml"><mrow id="S5.SS4.p1.2.m2.1.1.2" xref="S5.SS4.p1.2.m2.1.1.2.cmml"><mi id="S5.SS4.p1.2.m2.1.1.2.2" xref="S5.SS4.p1.2.m2.1.1.2.2.cmml">S</mi><mo id="S5.SS4.p1.2.m2.1.1.2.1" xref="S5.SS4.p1.2.m2.1.1.2.1.cmml">⁢</mo><msub id="S5.SS4.p1.2.m2.1.1.2.3" xref="S5.SS4.p1.2.m2.1.1.2.3.cmml"><mi id="S5.SS4.p1.2.m2.1.1.2.3.2" xref="S5.SS4.p1.2.m2.1.1.2.3.2.cmml">D</mi><mrow id="S5.SS4.p1.2.m2.1.1.2.3.3" xref="S5.SS4.p1.2.m2.1.1.2.3.3.cmml"><mi id="S5.SS4.p1.2.m2.1.1.2.3.3.2" xref="S5.SS4.p1.2.m2.1.1.2.3.3.2.cmml">u</mi><mo id="S5.SS4.p1.2.m2.1.1.2.3.3.1" xref="S5.SS4.p1.2.m2.1.1.2.3.3.1.cmml">⁢</mo><mi id="S5.SS4.p1.2.m2.1.1.2.3.3.3" xref="S5.SS4.p1.2.m2.1.1.2.3.3.3.cmml">k</mi><mo id="S5.SS4.p1.2.m2.1.1.2.3.3.1a" xref="S5.SS4.p1.2.m2.1.1.2.3.3.1.cmml">⁢</mo><mi id="S5.SS4.p1.2.m2.1.1.2.3.3.4" xref="S5.SS4.p1.2.m2.1.1.2.3.3.4.cmml">W</mi><mo id="S5.SS4.p1.2.m2.1.1.2.3.3.1b" xref="S5.SS4.p1.2.m2.1.1.2.3.3.1.cmml">⁢</mo><mi id="S5.SS4.p1.2.m2.1.1.2.3.3.5" xref="S5.SS4.p1.2.m2.1.1.2.3.3.5.cmml">a</mi><mo id="S5.SS4.p1.2.m2.1.1.2.3.3.1c" xref="S5.SS4.p1.2.m2.1.1.2.3.3.1.cmml">⁢</mo><mi id="S5.SS4.p1.2.m2.1.1.2.3.3.6" xref="S5.SS4.p1.2.m2.1.1.2.3.3.6.cmml">C</mi></mrow></msub></mrow><mo id="S5.SS4.p1.2.m2.1.1.1" xref="S5.SS4.p1.2.m2.1.1.1.cmml">=</mo><mn id="S5.SS4.p1.2.m2.1.1.3" xref="S5.SS4.p1.2.m2.1.1.3.cmml">13</mn></mrow></math>, <math><mrow id="S5.SS4.p1.3.m3.1.1" xref="S5.SS4.p1.3.m3.1.1.cmml"><msub id="S5.SS4.p1.3.m3.1.1.2" xref="S5.SS4.p1.3.m3.1.1.2.cmml"><mi id="S5.SS4.p1.3.m3.1.1.2.2" xref="S5.SS4.p1.3.m3.1.1.2.2.cmml">M</mi><mrow id="S5.SS4.p1.3.m3.1.1.2.3" xref="S5.SS4.p1.3.m3.1.1.2.3.cmml"><mi id="S5.SS4.p1.3.m3.1.1.2.3.2" xref="S5.SS4.p1.3.m3.1.1.2.3.2.cmml">W</mi><mo id="S5.SS4.p1.3.m3.1.1.2.3.1" xref="S5.SS4.p1.3.m3.1.1.2.3.1.cmml">⁢</mo><mi id="S5.SS4.p1.3.m3.1.1.2.3.3" xref="S5.SS4.p1.3.m3.1.1.2.3.3.cmml">o</mi><mo id="S5.SS4.p1.3.m3.1.1.2.3.1a" xref="S5.SS4.p1.3.m3.1.1.2.3.1.cmml">⁢</mo><mi id="S5.SS4.p1.3.m3.1.1.2.3.4" xref="S5.SS4.p1.3.m3.1.1.2.3.4.cmml">W</mi></mrow></msub><mo id="S5.SS4.p1.3.m3.1.1.1" xref="S5.SS4.p1.3.m3.1.1.1.cmml">=</mo><mn id="S5.SS4.p1.3.m3.1.1.3" xref="S5.SS4.p1.3.m3.1.1.3.cmml">70</mn></mrow></math>, <math><mrow id="S5.SS4.p1.4.m4.1.1" xref="S5.SS4.p1.4.m4.1.1.cmml"><msub id="S5.SS4.p1.4.m4.1.1.2" xref="S5.SS4.p1.4.m4.1.1.2.cmml"><mi id="S5.SS4.p1.4.m4.1.1.2.2" xref="S5.SS4.p1.4.m4.1.1.2.2.cmml">M</mi><mrow id="S5.SS4.p1.4.m4.1.1.2.3" xref="S5.SS4.p1.4.m4.1.1.2.3.cmml"><mi id="S5.SS4.p1.4.m4.1.1.2.3.2" xref="S5.SS4.p1.4.m4.1.1.2.3.2.cmml">u</mi><mo id="S5.SS4.p1.4.m4.1.1.2.3.1" xref="S5.SS4.p1.4.m4.1.1.2.3.1.cmml">⁢</mo><mi id="S5.SS4.p1.4.m4.1.1.2.3.3" xref="S5.SS4.p1.4.m4.1.1.2.3.3.cmml">k</mi><mo id="S5.SS4.p1.4.m4.1.1.2.3.1a" xref="S5.SS4.p1.4.m4.1.1.2.3.1.cmml">⁢</mo><mi id="S5.SS4.p1.4.m4.1.1.2.3.4" xref="S5.SS4.p1.4.m4.1.1.2.3.4.cmml">W</mi><mo id="S5.SS4.p1.4.m4.1.1.2.3.1b" xref="S5.SS4.p1.4.m4.1.1.2.3.1.cmml">⁢</mo><mi id="S5.SS4.p1.4.m4.1.1.2.3.5" xref="S5.SS4.p1.4.m4.1.1.2.3.5.cmml">a</mi><mo id="S5.SS4.p1.4.m4.1.1.2.3.1c" xref="S5.SS4.p1.4.m4.1.1.2.3.1.cmml">⁢</mo><mi id="S5.SS4.p1.4.m4.1.1.2.3.6" xref="S5.SS4.p1.4.m4.1.1.2.3.6.cmml">C</mi></mrow></msub><mo id="S5.SS4.p1.4.m4.1.1.1" xref="S5.SS4.p1.4.m4.1.1.1.cmml">=</mo><mn id="S5.SS4.p1.4.m4.1.1.3" xref="S5.SS4.p1.4.m4.1.1.3.cmml">57</mn></mrow></math>, <math><mrow id="S5.SS4.p1.7.m7.1.1" xref="S5.SS4.p1.7.m7.1.1.cmml"><msub id="S5.SS4.p1.7.m7.1.1.2" xref="S5.SS4.p1.7.m7.1.1.2.cmml"><mi id="S5.SS4.p1.7.m7.1.1.2.2" xref="S5.SS4.p1.7.m7.1.1.2.2.cmml">M</mi><mrow id="S5.SS4.p1.7.m7.1.1.2.3" xref="S5.SS4.p1.7.m7.1.1.2.3.cmml"><mi id="S5.SS4.p1.7.m7.1.1.2.3.2" xref="S5.SS4.p1.7.m7.1.1.2.3.2.cmml">W</mi><mo id="S5.SS4.p1.7.m7.1.1.2.3.1" xref="S5.SS4.p1.7.m7.1.1.2.3.1.cmml">⁢</mo><mi id="S5.SS4.p1.7.m7.1.1.2.3.3" xref="S5.SS4.p1.7.m7.1.1.2.3.3.cmml">o</mi><mo id="S5.SS4.p1.7.m7.1.1.2.3.1a" xref="S5.SS4.p1.7.m7.1.1.2.3.1.cmml">⁢</mo><mi id="S5.SS4.p1.7.m7.1.1.2.3.4" xref="S5.SS4.p1.7.m7.1.1.2.3.4.cmml">W</mi></mrow></msub><mo id="S5.SS4.p1.7.m7.1.1.1" xref="S5.SS4.p1.7.m7.1.1.1.cmml">=</mo><mn id="S5.SS4.p1.7.m7.1.1.3" xref="S5.SS4.p1.7.m7.1.1.3.cmml">7.8</mn></mrow></math>

Correct Categorie: cs

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/1411.1326

Formulas:

1-

(E_{c r}, T_{c r})

2-

E_{t h} < E_{0} < E_{t r}

3-

(Δ^{2} / v_{0}) / (k_{B} T_{c}^{0}) = 2.0 \times 10^{- 2}

4-

Δ S (T, E_{0})

5-

Δ E_{0} = 0 \to E_{0}

6-

\frac{| Δ S (T, E_{0}) |}{N k_{B}} = (2 π ζ a^{2} / 3) [ξ^{- 2} (T, E_{0}) - ξ^{- 2} (T, 0)] .

7-

ξ (T, E_{0})

8-

ξ (0, T) \propto {(| T - T_{c} |)}^{- 1 / 2}

9-

Δ T (T_{1}, E_{0}) = T_{2} - T_{1}

10-

\frac{Δ T (T_{1}, E_{0})}{T_{1}} = (π ζ a^{2} / 3) [ξ^{- 2} (E_{0}, T_{2}) - ξ^{- 2} (0, T_{1})] .

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/nucl-th/0606061

Formulas:

1-

ν = η / T s,

2-

η / s = 1 / 4 π

3-

T_{z x} = - η \partial v_{x} / \partial z;

4-

T_{z r} = - η \partial u / \partial z .

5-

T_{0 r} = γ^{2} (ϵ + p) v_{r}

6-

γ = {(1 - v^{2})}^{- 1 / 2}

7-

g_{t} (𝐱) = δ T_{0 r} \approx (ϵ + p) u

8-

\partial_{μ} T^{μ ν} = 0

9-

\partial g_{t} / \partial t = - \partial T_{z r} / \partial z

10-

(\frac{\partial}{\partial t} - ν \nabla^{2}) g_{t} = 0

Formulas (html):

Correct Categorie: nucl-th

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/hep-ph/9812225

Formulas:

1-

i = 1, 2, 3

2-

{(τ_{2})}^{T} = - (τ_{2})

3-

S U {(3)}_{H}

4-

U_{(L, R)}

5-

D_{(L, R)}

6-

S U (2)

7-

S U (3)

8-

S U {(3)}_{H}

9-

L_{e f f} = \frac{\bar{d_{R}} (g_{d} ϕ^{a} λ^{a} + g_{d}^{^{'}} ϕ_{0}) q_{L} H h_{d}}{M_{D}},

10-

S U {(3)}_{H}

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: hep-ph

Result: correct

Paper: https://arxiv.org/abs/1904.11976

Formulas:

1-

B_{a v g}

2-

{(B_{a v g} / L)}^{0.52 \pm 0.13}

3-

ϵ_{H} \sim B_{a v g}^{0.3 \pm 0.2} / L^{0.2 \pm_{0.1}^{0.2}}

4-

ϵ_{H} \propto B_{a v g}^{α} / L^{β}

5-

B_{a v g}^{0.3} / L

6-

B_{a v g} \sim B_{0} / L

7-

\nabla \times 𝐁 = \frac{4 π}{c} 𝐉 = α 𝐁

8-

𝐁 \cdot \nabla α = 0

9-

B_{a v g}

10-

s^{- 1} {pixel}^{- 1}

Formulas (html):

<math><msub id="id5.1.m1.1.1" xref="id5.1.m1.1.1.cmml"><mi id="id5.1.m1.1.1.2" xref="id5.1.m1.1.1.2.cmml">B</mi><mrow id="id5.1.m1.1.1.3" xref="id5.1.m1.1.1.3.cmml"><mi id="id5.1.m1.1.1.3.2" xref="id5.1.m1.1.1.3.2.cmml">a</mi><mo id="id5.1.m1.1.1.3.1" xref="id5.1.m1.1.1.3.1.cmml">⁢</mo><mi id="id5.1.m1.1.1.3.3" xref="id5.1.m1.1.1.3.3.cmml">v</mi><mo id="id5.1.m1.1.1.3.1a" xref="id5.1.m1.1.1.3.1.cmml">⁢</mo><mi id="id5.1.m1.1.1.3.4" xref="id5.1.m1.1.1.3.4.cmml">g</mi></mrow></msub></math>, <math><msup id="id7.3.m3.1.1" xref="id7.3.m3.1.1.cmml"><mrow id="id7.3.m3.1.1.1.1" xref="id7.3.m3.1.1.1.1.1.cmml"><mo stretchy="false" id="id7.3.m3.1.1.1.1.2" xref="id7.3.m3.1.1.1.1.1.cmml">(</mo><mrow id="id7.3.m3.1.1.1.1.1" xref="id7.3.m3.1.1.1.1.1.cmml"><msub id="id7.3.m3.1.1.1.1.1.2" xref="id7.3.m3.1.1.1.1.1.2.cmml"><mi id="id7.3.m3.1.1.1.1.1.2.2" xref="id7.3.m3.1.1.1.1.1.2.2.cmml">B</mi><mrow id="id7.3.m3.1.1.1.1.1.2.3" xref="id7.3.m3.1.1.1.1.1.2.3.cmml"><mi id="id7.3.m3.1.1.1.1.1.2.3.2" xref="id7.3.m3.1.1.1.1.1.2.3.2.cmml">a</mi><mo id="id7.3.m3.1.1.1.1.1.2.3.1" xref="id7.3.m3.1.1.1.1.1.2.3.1.cmml">⁢</mo><mi id="id7.3.m3.1.1.1.1.1.2.3.3" xref="id7.3.m3.1.1.1.1.1.2.3.3.cmml">v</mi><mo id="id7.3.m3.1.1.1.1.1.2.3.1a" xref="id7.3.m3.1.1.1.1.1.2.3.1.cmml">⁢</mo><mi id="id7.3.m3.1.1.1.1.1.2.3.4" xref="id7.3.m3.1.1.1.1.1.2.3.4.cmml">g</mi></mrow></msub><mo id="id7.3.m3.1.1.1.1.1.1" xref="id7.3.m3.1.1.1.1.1.1.cmml">/</mo><mi id="id7.3.m3.1.1.1.1.1.3" xref="id7.3.m3.1.1.1.1.1.3.cmml">L</mi></mrow><mo stretchy="false" id="id7.3.m3.1.1.1.1.3" xref="id7.3.m3.1.1.1.1.1.cmml">)</mo></mrow><mrow id="id7.3.m3.1.1.3" xref="id7.3.m3.1.1.3.cmml"><mn id="id7.3.m3.1.1.3.2" xref="id7.3.m3.1.1.3.2.cmml">0.52</mn><mo id="id7.3.m3.1.1.3.1" xref="id7.3.m3.1.1.3.1.cmml">±</mo><mn id="id7.3.m3.1.1.3.3" xref="id7.3.m3.1.1.3.3.cmml">0.13</mn></mrow></msup></math>, <math><mrow id="id8.4.m4.1.1" xref="id8.4.m4.1.1.cmml"><msub id="id8.4.m4.1.1.2" xref="id8.4.m4.1.1.2.cmml"><mi id="id8.4.m4.1.1.2.2" xref="id8.4.m4.1.1.2.2.cmml">ϵ</mi><mi id="id8.4.m4.1.1.2.3" xref="id8.4.m4.1.1.2.3.cmml">H</mi></msub><mo id="id8.4.m4.1.1.1" xref="id8.4.m4.1.1.1.cmml">∼</mo><mrow id="id8.4.m4.1.1.3" xref="id8.4.m4.1.1.3.cmml"><msubsup id="id8.4.m4.1.1.3.2" xref="id8.4.m4.1.1.3.2.cmml"><mi id="id8.4.m4.1.1.3.2.2.2" xref="id8.4.m4.1.1.3.2.2.2.cmml">B</mi><mrow id="id8.4.m4.1.1.3.2.2.3" xref="id8.4.m4.1.1.3.2.2.3.cmml"><mi id="id8.4.m4.1.1.3.2.2.3.2" xref="id8.4.m4.1.1.3.2.2.3.2.cmml">a</mi><mo id="id8.4.m4.1.1.3.2.2.3.1" xref="id8.4.m4.1.1.3.2.2.3.1.cmml">⁢</mo><mi id="id8.4.m4.1.1.3.2.2.3.3" xref="id8.4.m4.1.1.3.2.2.3.3.cmml">v</mi><mo id="id8.4.m4.1.1.3.2.2.3.1a" xref="id8.4.m4.1.1.3.2.2.3.1.cmml">⁢</mo><mi id="id8.4.m4.1.1.3.2.2.3.4" xref="id8.4.m4.1.1.3.2.2.3.4.cmml">g</mi></mrow><mrow id="id8.4.m4.1.1.3.2.3" xref="id8.4.m4.1.1.3.2.3.cmml"><mn id="id8.4.m4.1.1.3.2.3.2" xref="id8.4.m4.1.1.3.2.3.2.cmml">0.3</mn><mo id="id8.4.m4.1.1.3.2.3.1" xref="id8.4.m4.1.1.3.2.3.1.cmml">±</mo><mn id="id8.4.m4.1.1.3.2.3.3" xref="id8.4.m4.1.1.3.2.3.3.cmml">0.2</mn></mrow></msubsup><mo id="id8.4.m4.1.1.3.1" xref="id8.4.m4.1.1.3.1.cmml">/</mo><msup id="id8.4.m4.1.1.3.3" xref="id8.4.m4.1.1.3.3.cmml"><mi id="id8.4.m4.1.1.3.3.2" xref="id8.4.m4.1.1.3.3.2.cmml">L</mi><mrow id="id8.4.m4.1.1.3.3.3" xref="id8.4.m4.1.1.3.3.3.cmml"><mn id="id8.4.m4.1.1.3.3.3.2" xref="id8.4.m4.1.1.3.3.3.2.cmml">0.2</mn><msubsup id="id8.4.m4.1.1.3.3.3.3" xref="id8.4.m4.1.1.3.3.3.3.cmml"><mo id="id8.4.m4.1.1.3.3.3.3.2.2" xref="id8.4.m4.1.1.3.3.3.3.2.2.cmml">±</mo><mn id="id8.4.m4.1.1.3.3.3.3.3" xref="id8.4.m4.1.1.3.3.3.3.3.cmml">0.1</mn><mn id="id8.4.m4.1.1.3.3.3.3.2.3" xref="id8.4.m4.1.1.3.3.3.3.2.3.cmml">0.2</mn></msubsup></mrow></msup></mrow></mrow></math>, <math><mrow id="S1.p6.1.m1.1.1" xref="S1.p6.1.m1.1.1.cmml"><msub id="S1.p6.1.m1.1.1.2" xref="S1.p6.1.m1.1.1.2.cmml"><mi id="S1.p6.1.m1.1.1.2.2" xref="S1.p6.1.m1.1.1.2.2.cmml">ϵ</mi><mi id="S1.p6.1.m1.1.1.2.3" xref="S1.p6.1.m1.1.1.2.3.cmml">H</mi></msub><mo id="S1.p6.1.m1.1.1.1" xref="S1.p6.1.m1.1.1.1.cmml">∝</mo><mrow id="S1.p6.1.m1.1.1.3" xref="S1.p6.1.m1.1.1.3.cmml"><msubsup id="S1.p6.1.m1.1.1.3.2" xref="S1.p6.1.m1.1.1.3.2.cmml"><mi id="S1.p6.1.m1.1.1.3.2.2.2" xref="S1.p6.1.m1.1.1.3.2.2.2.cmml">B</mi><mrow id="S1.p6.1.m1.1.1.3.2.2.3" xref="S1.p6.1.m1.1.1.3.2.2.3.cmml"><mi id="S1.p6.1.m1.1.1.3.2.2.3.2" xref="S1.p6.1.m1.1.1.3.2.2.3.2.cmml">a</mi><mo id="S1.p6.1.m1.1.1.3.2.2.3.1" xref="S1.p6.1.m1.1.1.3.2.2.3.1.cmml">⁢</mo><mi id="S1.p6.1.m1.1.1.3.2.2.3.3" xref="S1.p6.1.m1.1.1.3.2.2.3.3.cmml">v</mi><mo id="S1.p6.1.m1.1.1.3.2.2.3.1a" xref="S1.p6.1.m1.1.1.3.2.2.3.1.cmml">⁢</mo><mi id="S1.p6.1.m1.1.1.3.2.2.3.4" xref="S1.p6.1.m1.1.1.3.2.2.3.4.cmml">g</mi></mrow><mi id="S1.p6.1.m1.1.1.3.2.3" xref="S1.p6.1.m1.1.1.3.2.3.cmml">α</mi></msubsup><mo id="S1.p6.1.m1.1.1.3.1" xref="S1.p6.1.m1.1.1.3.1.cmml">/</mo><msup id="S1.p6.1.m1.1.1.3.3" xref="S1.p6.1.m1.1.1.3.3.cmml"><mi id="S1.p6.1.m1.1.1.3.3.2" xref="S1.p6.1.m1.1.1.3.3.2.cmml">L</mi><mi id="S1.p6.1.m1.1.1.3.3.3" xref="S1.p6.1.m1.1.1.3.3.3.cmml">β</mi></msup></mrow></mrow></math>, <math><mrow id="S1.p6.5.m5.1.1" xref="S1.p6.5.m5.1.1.cmml"><msubsup id="S1.p6.5.m5.1.1.2" xref="S1.p6.5.m5.1.1.2.cmml"><mi id="S1.p6.5.m5.1.1.2.2.2" xref="S1.p6.5.m5.1.1.2.2.2.cmml">B</mi><mrow id="S1.p6.5.m5.1.1.2.2.3" xref="S1.p6.5.m5.1.1.2.2.3.cmml"><mi id="S1.p6.5.m5.1.1.2.2.3.2" xref="S1.p6.5.m5.1.1.2.2.3.2.cmml">a</mi><mo id="S1.p6.5.m5.1.1.2.2.3.1" xref="S1.p6.5.m5.1.1.2.2.3.1.cmml">⁢</mo><mi id="S1.p6.5.m5.1.1.2.2.3.3" xref="S1.p6.5.m5.1.1.2.2.3.3.cmml">v</mi><mo id="S1.p6.5.m5.1.1.2.2.3.1a" xref="S1.p6.5.m5.1.1.2.2.3.1.cmml">⁢</mo><mi id="S1.p6.5.m5.1.1.2.2.3.4" xref="S1.p6.5.m5.1.1.2.2.3.4.cmml">g</mi></mrow><mn id="S1.p6.5.m5.1.1.2.3" xref="S1.p6.5.m5.1.1.2.3.cmml">0.3</mn></msubsup><mo id="S1.p6.5.m5.1.1.1" xref="S1.p6.5.m5.1.1.1.cmml">/</mo><mi id="S1.p6.5.m5.1.1.3" xref="S1.p6.5.m5.1.1.3.cmml">L</mi></mrow></math>, <math><mrow id="S1.p6.8.m8.1.1" xref="S1.p6.8.m8.1.1.cmml"><msub id="S1.p6.8.m8.1.1.2" xref="S1.p6.8.m8.1.1.2.cmml"><mi id="S1.p6.8.m8.1.1.2.2" xref="S1.p6.8.m8.1.1.2.2.cmml">B</mi><mrow id="S1.p6.8.m8.1.1.2.3" xref="S1.p6.8.m8.1.1.2.3.cmml"><mi id="S1.p6.8.m8.1.1.2.3.2" xref="S1.p6.8.m8.1.1.2.3.2.cmml">a</mi><mo id="S1.p6.8.m8.1.1.2.3.1" xref="S1.p6.8.m8.1.1.2.3.1.cmml">⁢</mo><mi id="S1.p6.8.m8.1.1.2.3.3" xref="S1.p6.8.m8.1.1.2.3.3.cmml">v</mi><mo id="S1.p6.8.m8.1.1.2.3.1a" xref="S1.p6.8.m8.1.1.2.3.1.cmml">⁢</mo><mi id="S1.p6.8.m8.1.1.2.3.4" xref="S1.p6.8.m8.1.1.2.3.4.cmml">g</mi></mrow></msub><mo id="S1.p6.8.m8.1.1.1" xref="S1.p6.8.m8.1.1.1.cmml">∼</mo><mrow id="S1.p6.8.m8.1.1.3" xref="S1.p6.8.m8.1.1.3.cmml"><msub id="S1.p6.8.m8.1.1.3.2" xref="S1.p6.8.m8.1.1.3.2.cmml"><mi id="S1.p6.8.m8.1.1.3.2.2" xref="S1.p6.8.m8.1.1.3.2.2.cmml">B</mi><mn id="S1.p6.8.m8.1.1.3.2.3" xref="S1.p6.8.m8.1.1.3.2.3.cmml">0</mn></msub><mo id="S1.p6.8.m8.1.1.3.1" xref="S1.p6.8.m8.1.1.3.1.cmml">/</mo><mi id="S1.p6.8.m8.1.1.3.3" xref="S1.p6.8.m8.1.1.3.3.cmml">L</mi></mrow></mrow></math>, <math><mrow id="S2.SS3.p3.2.m2.1.1" xref="S2.SS3.p3.2.m2.1.1.cmml"><mrow id="S2.SS3.p3.2.m2.1.1.2" xref="S2.SS3.p3.2.m2.1.1.2.cmml"><mo id="S2.SS3.p3.2.m2.1.1.2.2" xref="S2.SS3.p3.2.m2.1.1.2.2.cmml">∇</mo><mo id="S2.SS3.p3.2.m2.1.1.2.1" xref="S2.SS3.p3.2.m2.1.1.2.1.cmml">×</mo><mi id="S2.SS3.p3.2.m2.1.1.2.3" xref="S2.SS3.p3.2.m2.1.1.2.3.cmml">𝐁</mi></mrow><mo id="S2.SS3.p3.2.m2.1.1.3" xref="S2.SS3.p3.2.m2.1.1.3.cmml">=</mo><mrow id="S2.SS3.p3.2.m2.1.1.4" xref="S2.SS3.p3.2.m2.1.1.4.cmml"><mfrac id="S2.SS3.p3.2.m2.1.1.4.2" xref="S2.SS3.p3.2.m2.1.1.4.2.cmml"><mrow id="S2.SS3.p3.2.m2.1.1.4.2.2" xref="S2.SS3.p3.2.m2.1.1.4.2.2.cmml"><mn id="S2.SS3.p3.2.m2.1.1.4.2.2.2" xref="S2.SS3.p3.2.m2.1.1.4.2.2.2.cmml">4</mn><mo id="S2.SS3.p3.2.m2.1.1.4.2.2.1" xref="S2.SS3.p3.2.m2.1.1.4.2.2.1.cmml">⁢</mo><mi id="S2.SS3.p3.2.m2.1.1.4.2.2.3" xref="S2.SS3.p3.2.m2.1.1.4.2.2.3.cmml">π</mi></mrow><mi id="S2.SS3.p3.2.m2.1.1.4.2.3" xref="S2.SS3.p3.2.m2.1.1.4.2.3.cmml">c</mi></mfrac><mo id="S2.SS3.p3.2.m2.1.1.4.1" xref="S2.SS3.p3.2.m2.1.1.4.1.cmml">⁢</mo><mi id="S2.SS3.p3.2.m2.1.1.4.3" xref="S2.SS3.p3.2.m2.1.1.4.3.cmml">𝐉</mi></mrow><mo id="S2.SS3.p3.2.m2.1.1.5" xref="S2.SS3.p3.2.m2.1.1.5.cmml">=</mo><mrow id="S2.SS3.p3.2.m2.1.1.6" xref="S2.SS3.p3.2.m2.1.1.6.cmml"><mi id="S2.SS3.p3.2.m2.1.1.6.2" xref="S2.SS3.p3.2.m2.1.1.6.2.cmml">α</mi><mo id="S2.SS3.p3.2.m2.1.1.6.1" xref="S2.SS3.p3.2.m2.1.1.6.1.cmml">⁢</mo><mi id="S2.SS3.p3.2.m2.1.1.6.3" xref="S2.SS3.p3.2.m2.1.1.6.3.cmml">𝐁</mi></mrow></mrow></math>, <math><mrow id="S2.SS3.p3.5.m5.1.1" xref="S2.SS3.p3.5.m5.1.1.cmml"><mrow id="S2.SS3.p3.5.m5.1.1.2" xref="S2.SS3.p3.5.m5.1.1.2.cmml"><mi id="S2.SS3.p3.5.m5.1.1.2.2" xref="S2.SS3.p3.5.m5.1.1.2.2.cmml">𝐁</mi><mo id="S2.SS3.p3.5.m5.1.1.2.1" xref="S2.SS3.p3.5.m5.1.1.2.1.cmml">⋅</mo><mrow id="S2.SS3.p3.5.m5.1.1.2.3" xref="S2.SS3.p3.5.m5.1.1.2.3.cmml"><mo id="S2.SS3.p3.5.m5.1.1.2.3.1" xref="S2.SS3.p3.5.m5.1.1.2.3.1.cmml">∇</mo><mo id="S2.SS3.p3.5.m5.1.1.2.3a" xref="S2.SS3.p3.5.m5.1.1.2.3.cmml">⁡</mo><mi id="S2.SS3.p3.5.m5.1.1.2.3.2" xref="S2.SS3.p3.5.m5.1.1.2.3.2.cmml">α</mi></mrow></mrow><mo id="S2.SS3.p3.5.m5.1.1.1" xref="S2.SS3.p3.5.m5.1.1.1.cmml">=</mo><mn id="S2.SS3.p3.5.m5.1.1.3" xref="S2.SS3.p3.5.m5.1.1.3.cmml">0</mn></mrow></math>, <math><msub id="S2.T1.1.1.1.m1.1.1" xref="S2.T1.1.1.1.m1.1.1.cmml"><mi id="S2.T1.1.1.1.m1.1.1.2" xref="S2.T1.1.1.1.m1.1.1.2.cmml">B</mi><mrow id="S2.T1.1.1.1.m1.1.1.3" xref="S2.T1.1.1.1.m1.1.1.3.cmml"><mi id="S2.T1.1.1.1.m1.1.1.3.2" xref="S2.T1.1.1.1.m1.1.1.3.2.cmml">a</mi><mo id="S2.T1.1.1.1.m1.1.1.3.1" xref="S2.T1.1.1.1.m1.1.1.3.1.cmml">⁢</mo><mi id="S2.T1.1.1.1.m1.1.1.3.3" xref="S2.T1.1.1.1.m1.1.1.3.3.cmml">v</mi><mo id="S2.T1.1.1.1.m1.1.1.3.1a" xref="S2.T1.1.1.1.m1.1.1.3.1.cmml">⁢</mo><mi id="S2.T1.1.1.1.m1.1.1.3.4" xref="S2.T1.1.1.1.m1.1.1.3.4.cmml">g</mi></mrow></msub></math>, <math><mrow id="S2.T1.2.m1a.1.1" xref="S2.T1.2.m1a.1.1.cmml"><msup id="S2.T1.2.m1a.1.1.2" xref="S2.T1.2.m1a.1.1.2.cmml"><mi mathvariant="normal" id="S2.T1.2.m1a.1.1.2.2" xref="S2.T1.2.m1a.1.1.2.2.cmml">s</mi><mrow id="S2.T1.2.m1a.1.1.2.3" xref="S2.T1.2.m1a.1.1.2.3.cmml"><mo id="S2.T1.2.m1a.1.1.2.3.1" xref="S2.T1.2.m1a.1.1.2.3.1.cmml">-</mo><mn id="S2.T1.2.m1a.1.1.2.3.2" xref="S2.T1.2.m1a.1.1.2.3.2.cmml">1</mn></mrow></msup><mo id="S2.T1.2.m1a.1.1.1" xref="S2.T1.2.m1a.1.1.1.cmml">⁢</mo><msup id="S2.T1.2.m1a.1.1.3" xref="S2.T1.2.m1a.1.1.3.cmml"><mi id="S2.T1.2.m1a.1.1.3.2" xref="S2.T1.2.m1a.1.1.3.2.cmml">pixel</mi><mrow id="S2.T1.2.m1a.1.1.3.3" xref="S2.T1.2.m1a.1.1.3.3.cmml"><mo id="S2.T1.2.m1a.1.1.3.3.1" xref="S2.T1.2.m1a.1.1.3.3.1.cmml">-</mo><mn id="S2.T1.2.m1a.1.1.3.3.2" xref="S2.T1.2.m1a.1.1.3.3.2.cmml">1</mn></mrow></msup></mrow></math>

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1407.7387

Formulas:

1-

u (x, n)

2-

G^{h} (z)

3-

\frac{d n}{d y} = \frac{x_{E}}{σ_{i n e l}} \cdot \frac{d σ}{d x_{F}} = \sum_{n = 1}^{\infty} w_{n} \cdot ϕ_{n}^{h} (x) + w_{D} \cdot ϕ_{D}^{h} (x),

4-

ϕ_{n}^{h} (x)

5-

w_{D} \cdot ϕ_{D}^{h} (x)

6-

ϕ_{n}^{h} (x)

7-

f_{q q}^{h} (x_{+}, n) \cdot f_{q}^{h} (x_{-}, n) + f_{q}^{h} (x_{+}, n) \cdot f_{q q}^{h} (x_{-}, n)

8-

2 (n - 1) \cdot f_{s}^{h} (x_{+}, n) \cdot f_{s}^{h} (x_{-}, n),

9-

\frac{1}{2} [\sqrt{4 m_{T}^{2} / s + x^{2}} \pm x],

10-

f_{q q}^{h} (x_{+}, n)

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: hep-ph

Result: correct

Paper: https://arxiv.org/abs/1504.06060

Formulas:

1-

A_{x} G_{y} C_{z}

2-

T_{S R}^{Fe / Mn}

3-

G_{x} A_{y} F_{z}

4-

T_{S R}^{Fe / Mn}

5-

G_{x} A_{y} F_{z}

6-

G_{z} C_{y} F_{x}

7-

G_{x} A_{y} F_{z}

8-

P b n m

9-

P b n m

10-

P b n m

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/0806.0319

Formulas:

1-

𝐰 \equiv (𝐱, 𝐯)

2-

𝜽 (t) = 𝜽 (0) + 𝛀 (𝐉) t,

3-

𝐰 \leftrightarrow (𝜽, 𝐉)

4-

Φ_{eff} (R, z) \equiv Φ (R, z) + J_{ϕ}^{2} / 2 R^{2}

5-

(R, z, p_{R}, p_{z}) \leftrightarrow (θ_{R}^{T}, θ_{z}^{T}, J_{R}^{T}, J_{z}^{T})

6-

Φ_{eff}^{T} (r, ϑ) = \frac{- G M}{b + \sqrt{b^{2} + {(r - r_{0})}^{2}}} + \frac{L_{z}^{2}}{2 {[(r - r_{0}) \sin ϑ]}^{2}},

7-

S (𝜽^{T}, 𝐉) = 𝜽^{T} \cdot 𝐉 + 2 \sum_{𝐧 > 0} S_{𝐧} (𝐉) \sin (𝐧 \cdot 𝜽^{T}),

8-

𝐉^{T} = \frac{\partial S (𝜽^{T}, 𝐉)}{\partial 𝜽^{T}}; 𝜽 = \frac{\partial S (𝜽^{T}, 𝐉)}{\partial 𝐉} .

9-

𝐉^{T} = 𝐉 + 2 \sum_{𝐧 > 0} 𝐧 S_{𝐧} (𝐉) \cos (𝐧 \cdot 𝜽^{T})

10-

𝜽 = 𝜽^{T} + 2 \sum_{𝐧 > 0} \frac{\partial S_{𝐧} (𝐉)}{\partial 𝐉} \sin (𝐧 \cdot 𝜽^{T}) .

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: cs

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/0009040

Formulas:

1-

C / (T - θ)

2-

A T^{- 1 / 2} e^{- Δ / T}

3-

T (χ_{m a x})

4-

Δ / T (χ_{m a x})

5-

Δ / T (χ_{m a x})

6-

{(2.37 / 1.91)}^{- 11}

7-

Δ / T (χ_{m a x})

8-

T (χ_{m a x}) / J

9-

T (χ_{m a x}) / J

10-

χ_{o} + C / (T - θ)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1107.3889

Formulas:

1-

\sim 2 M_{⊙} {yr}^{- 1}

2-

Δ x \approx 1.86 \times 10^{10}

3-

ρ 𝕧_{rel} 𝕧_{rel} \cdot 𝕟

4-

N = 32 {(R_{acc} / Δ x)}^{2}

5-

\dot{M} = \int ρ 𝐯_{rel} \cdot 𝐧 𝑑 A \approx \frac{2 π^{2} R_{acc}^{2}}{N} \sum_{i = 1}^{N} ρ_{i} 𝐯_{rel, i} \cdot 𝐧_{i} \sin θ_{i},

6-

\sim 10^{- 2} M_{⊙}

7-

\sim 6 \times 10^{- 2} M_{⊙}

8-

(1.5 \times 10^{12} cm, 0, 0)

9-

(1.5 \times 10^{12} cm, 0, 0)

10-

\sim 2 M_{⊙} {yr}^{- 1}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/0905.1496

Formulas:

1-

E_{n} = (n + \frac{1}{2}) ℏ ω_{c}

2-

n = 0, 1, 2, \dots

3-

ℏ ω_{c} = e B / m^{*}

4-

- \frac{ℏ^{2}}{2 m^{*}} \frac{d^{2} ψ_{σ_{z}} (z)}{d z^{2}} + U_{σ_{z}} (z) ψ_{σ_{z}} (z) = E_{z} ψ_{σ_{z}} (z),

5-

U_{σ_{z}} (z)

6-

U_{σ_{z}} (z) = V_{s} + U_{0} - e V_{a} z / L

7-

0 < z < L_{1}

8-

L_{1} + L_{2} < z < L

9-

U_{σ_{z}} (z) = V_{s} + V_{x} (z) + V_{σ_{z}} (z) - e V_{a} z / L

10-

L_{1} < z < L_{1} + L_{2}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/0803.3577

Formulas:

1-

𝝅 = 𝒑 - e 𝑨

2-

𝒑 \equiv - i \nabla

3-

μ = μ_{0} + μ^{'}, μ_{0} = \frac{e S}{m}, μ^{'} = μ - μ_{0} .

4-

g = \frac{2 m μ}{e S} .

5-

\int Ψ^{†} ρ_{3} Ψ 𝑑 V = \int (ϕ^{†} ϕ - χ^{†} χ) 𝑑 V = 1,

6-

Ψ = (\begin{matrix} ϕ \\ χ \end{matrix})

7-

S_{x}, S_{y}, S_{z}

8-

ρ_{1} = (\begin{matrix} 0 & 1 \\ 1 & 0 \end{matrix}), ρ_{2} = (\begin{matrix} 0 & - i \\ i & 0 \end{matrix}), ρ_{3} = (\begin{matrix} 1 & 0 \\ 0 & - 1 \end{matrix}) .

9-

ℋ = ρ_{3} ℋ^{†} ρ_{3}, ℋ^{†} = ρ_{3} ℋ ρ_{3} .

10-

U^{- 1} = ρ_{3} U^{†} ρ_{3}, U^{†} = ρ_{3} U^{- 1} ρ_{3} .

Formulas (html):

Correct Categorie: hep-th

Guessed Categorie: hep-th

Result: correct

Paper: https://arxiv.org/abs/1908.07396

Formulas:

1-

I m m m

2-

H = \sum_{⟨ l m ⟩} J_{l m} 𝐒_{l} \cdot 𝐒_{m}

3-

k_{x} = k_{y} = 0

4-

k_{x} = k_{z} = 0

5-

k_{y} = k_{z} = 0

6-

𝐝 (𝐤) = φ (𝐤) (1, i, 0)

7-

𝐝 (𝐤) = φ (𝐤) 𝐝_{𝟎}

8-

𝐝_{0} \times 𝐝_{0} = 0

9-

k_{x} k_{y} k_{z} 𝐝_{0}

10-

η_{1} k_{x} \hat{𝐱} + η_{2} k_{y} \hat{𝐲} + η_{3} k_{z} \hat{𝐳}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/physics/0411051

Formulas:

1-

n_{e} (r) = n_{i} (r) = n_{0} θ (1 - r / R),

2-

θ (x) = 1

3-

θ (x) = 0

4-

N_{0} = n_{0} (4 π R^{3} / 3)

5-

λ_{d} = {(T_{0} / 4 π n_{0} e^{2})}^{1 / 2}

6-

ω_{p e}^{- 1} = {(4 π e^{2} n_{0} / m_{e})}^{- 1 / 2}

7-

v_{t h, 0} = \sqrt{T_{0} / m_{e}}

8-

U_{k} = 3 N_{e} T / 2

9-

ϕ_{T} = e Φ_{R} / T = (1 - N_{e}) R^{2} / 3 T

10-

v^{2} / 2 T \geq ϕ_{T}

Formulas (html):

Correct Categorie: physics

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/quant-ph/9511006

Formulas:

1-

[\frac{\partial^{2}}{\partial t^{2}} - \sum_{i = 1}^{3} \frac{\partial^{2}}{\partial x^{i 2}} + m^{2}] Φ (t, 𝐱) = 0,

2-

x = (t, 𝐱), 𝐱 = (x^{1}, x^{2}, x^{3})

3-

Φ (x^{'}) = \int \frac{d^{4} x}{\sqrt{8 π}} Δ (x - x^{'}; m^{2}) (δ^{'} (t - t_{0}) Φ (t_{0}, x) + δ (t - t_{0}) \partial_{t} Φ (t_{0}, 𝐱))

4-

Δ (x; m^{2}) = Δ_{+} (x; m^{2}) - Δ_{+} (- x; m^{2})

5-

Δ_{+} (x; m^{2}) = \frac{i}{2 {(2 π)}^{3}} \int e^{- i t p^{0} + i 𝐱 \cdot 𝐩} \frac{d^{3} p}{p^{0}}, p^{0} = \sqrt{𝐩^{2} + m^{2}}

6-

Φ (t_{0}, 𝐱)

7-

\partial_{t} Φ (t_{0}, 𝐱)

8-

i \partial_{t} Ψ = H Ψ

9-

s u p p (H Ψ) \subset s u p p Ψ

10-

Φ (t_{0}, 𝐱)

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: physics

Result: incorrect

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