Run 11329983

Paper: https://arxiv.org/abs/cond-mat/0207733

Formulas:

1-

σ (ω) = 4 π^{2} α_{0} ℏ ω \sum_{f} {| M_{i \to f} |}^{2} δ (E_{f} - E_{i} - ℏ ω),

2-

M_{i \to f} = ⟨ ψ_{f} | 𝔒 | ψ_{i} ⟩ .

3-

\hat{𝜺} \cdot 𝒓 (1 + \frac{i}{2} 𝒌 \cdot 𝒓)

4-

| ψ_{f} ⟩ = 𝒯 | {\tilde{ψ}}_{f} ⟩ .

5-

𝒯 = 𝟏 + \sum_{𝑹, n} [| ϕ_{𝑹, n} ⟩ - | {\tilde{ϕ}}_{𝑹, n} ⟩] ⟨ {\tilde{p}}_{𝑹, n} | .

6-

| ϕ_{𝑹, n} ⟩

7-

| {\tilde{ϕ}}_{𝑹, n} ⟩

8-

⟨ {\tilde{p}}_{𝑹, n} |

9-

⟨ {\tilde{p}}_{𝑹, n} | {\tilde{ϕ}}_{𝑹^{'}, n^{'}} ⟩ = δ_{𝑹 𝑹^{'}} δ_{n n^{'}}

10-

| ϕ_{𝑹, n} ⟩

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/1203.2841

Formulas:

1-

Δ = μ_{f} / r_{g}

2-

P (Δ, p)

3-

P (Δ, p)

4-

P (Δ, p)

5-

P (Δ, p)

6-

P (Δ, p) = \min {1, Δ p} = \min {1, \frac{μ_{f}}{r_{g}} \cdot p} .

7-

P (Δ, p)

8-

n P (Δ, p)

9-

n_{b s} = n P (Δ, p) \cdot \max {\frac{r_{t}}{R_{\max}}, \frac{1}{N_{\max}}} .

10-

\max {\frac{r_{t}}{R_{\max}}, \frac{1}{N_{\max}}}

Formulas (html):

Correct Categorie: cs

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0007041

Formulas:

1-

\frac{EW (H α)}{EW (H β)}

2-

\frac{E_{H α}}{E_{H β}}

3-

\frac{EW (λ 8542)}{EW (λ 8498)}

4-

\frac{EW (H α)}{EW (H β)}

5-

\frac{E_{H α}}{E_{H β}}

6-

\frac{E_{H α}}{E_{H β}} = \frac{EW (H α)}{EW (H β)} * 0.2444 * {2.512}^{(B - R)}

7-

\frac{E_{H α}}{E_{H β}}

8-

\frac{E_{H α}}{E_{H β}}

9-

_{c o n j}

10-

\frac{E_{H α}}{E_{H β}}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/1809.09882

Formulas:

1-

V_{g} = \dot{T} / G \sim

2-

φ = 5^{\circ}, θ = 5^{\circ}, ψ = 5^{\circ}

3-

t = 0.05, 0.075, 0.1, 0.15

4-

V_{x}^{0} = V_{g} \sin φ \sin θ

5-

V_{y}^{0} = - V_{g} \cos φ \sin θ

6-

V_{x} \approx 0.88 V_{x}^{0}

7-

V_{y} \approx 0.90 V_{y}^{0}

8-

t = 0.05, 0.075, 0.1, 0.15

9-

λ = 1 / \sqrt{2.6} μ

10-

D = 2 \times 10^{- 9}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0510362

Formulas:

1-

\sim (2 - 10) \times 10^{- 3} M_{⊙}

2-

\sim (1 - 2) \times 10^{3}

3-

F_{ν} \propto ν^{- 0.37}

4-

1800 km s^{- 1}

5-

13 - 16 M_{⊙}

6-

M \approx 2.5 M_{⊙}

7-

E \approx 1.6 \times 10^{51}

8-

v_{sn} = {(2 E / M)}^{1 / 2} \approx 8 \times 10^{8}

9-

R_{cs} \sim v_{sn} t \sim 6 \times 10^{16}

10-

u_{c s} \sim 20 km s^{- 1}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1308.3207

Formulas:

1-

n (a) = n_{0} a^{- 3.5}

2-

a_{m a x}

3-

a_{m a x}

4-

a_{m a x}

5-

ξ_{s t a n d a r d}

6-

ξ_{s t a n d a r d}

7-

ξ_{I S M}

8-

M g_{2 (x)} F e_{2 (1 - x)} S i O_{4}

9-

M g_{x} F e_{1 - x} S i O_{3}

10-

x = M g / (M g + F e)

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1911.09389

Formulas:

1-

I (x) = J (x) \cdot t (x) + A \cdot (1 - t (x)),

2-

t (x) = e^{- β d (x)},

3-

\underset{G}{m i n} \underset{D}{m a x} = E_{I \sim p_{d a t a (I)}, z \sim p_{(z)}} [l o g (1 - D (I, G (I, z)))]

4-

+ E_{I \sim p_{d a t a (I, J)}} [l o g (D (I, J^{*}))]

5-

L_{M S E}

6-

L_{M S E} = \frac{1}{S} \sum_{x = 1}^{N} {(J (x) - J^{*} (x))}^{2}

7-

J^{*} (x)

8-

L_{G A N} = \frac{1}{S} \sum_{x = 1}^{N} l o g (1 - D (I (x), J^{*} (x)))

9-

L_{C E} = - \sum_{i = 1}^{C} y_{i} l o g (P_{i})

10-

P_{i} = \frac{e x p (a_{i})}{\sum_{r = 1}^{C} e x p (a_{r})}

Formulas (html):

Correct Categorie: cs

Guessed Categorie: hep-lat

Result: incorrect

Paper: https://arxiv.org/abs/1811.02214

Formulas:

1-

P W V = \frac{d}{P T T}

2-

c = \sqrt{\frac{E h}{ρ d}}

3-

E = E_{0} e^{γ P}

4-

Q_{m a x}

5-

Q_{m a x}

6-

{[\begin{matrix} 𝐱_{1}^{T} 𝐱_{2}^{T} \dots 𝐱_{M}^{T} \end{matrix}]}^{T}

7-

{[\begin{matrix} 𝐲_{1}^{T} 𝐲_{2}^{T} \dots 𝐲_{M}^{T} \end{matrix}]}^{T}

8-

{[\begin{matrix} 𝐱_{1}^{T} 𝐱_{2}^{T} \dots 𝐱_{i}^{T} \dots 𝐱_{M}^{T} \end{matrix}]}^{T}

9-

{[\begin{matrix} 𝐲_{1}^{T} 𝐲_{2}^{T} \dots 𝐲_{i}^{T} \dots 𝐲_{M}^{T} \end{matrix}]}^{T}

10-

M A E = \frac{1}{N} \sum_{i = 1}^{N} ∣ z_{i_{M}} - y_{i_{M}} ∣

Formulas (html):

Correct Categorie: eess

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/1810.04478

Formulas:

1-

10^{- 15} - 10^{- 14}

2-

\sim 10^{- 13} - 10^{- 12}

3-

\sim 10^{- 12} - 10^{- 11}

4-

C_{e} (T_{e}) \frac{\partial T_{e}}{\partial t} = \nabla . (K_{e} (T_{e}) \nabla T_{e}) - (T_{e} - T_{l}) G (T_{e}) + A_{e} (r, t)

5-

C_{l} (T_{l}) \frac{\partial T_{l}}{\partial t} = \nabla . (K_{l} (T_{l}) \nabla T_{l}) + (T_{e} - T_{l}) G (T_{e}) .

6-

G (T_{e})

7-

A_{e} (r, t)

8-

\int \int 2 π r A_{e} (r, t) 𝑑 r 𝑑 t

9-

G (T_{e})

10-

C_{e} (T_{e}) = \frac{π^{2} g (ϵ_{F}) k_{B}^{2}}{2 ϵ_{F}} T_{e},

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/hep-ph/9910454

Formulas:

1-

| 𝚫 𝐈 | = 𝟏 / 𝟐

2-

| Δ I | = 1 / 2

3-

K^{+} \to π^{+} π^{0}

4-

K_{1} \to π^{+} π^{-}

5-

K_{1} \to π^{0} π^{0}

6-

| A_{+ 0} | = (1.831 \pm 0.006) \times 10^{- 8} Gev,

7-

| A_{+ -} | = (3.911 \pm 0.007) \times 10^{- 7} Gev,

8-

| A_{00} | = (3.714 \pm 0.015) \times 10^{- 7} Gev .

9-

| A_{+ -} | \approx | A_{00} | ≫ | A_{+ 0} |

10-

| A_{+ -} | = | A_{00} |

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: nucl-th

Result: incorrect

Paper: https://arxiv.org/abs/1403.0757

Formulas:

1-

\bar{K} N N

2-

K^{-} p p

3-

K^{-} p p

4-

\bar{K} N N

5-

K^{-} p p

6-

\bar{K} N N

7-

K^{-} p p

8-

K^{-} p p

9-

K^{-} p p

10-

K^{-} p p

Formulas (html):

Correct Categorie: nucl-th

Guessed Categorie: nucl-ex

Result: incorrect

Paper: https://arxiv.org/abs/1808.04892

Formulas:

1-

2 L = 10 c m

2-

W = 3 c m

3-

h = 130 μ m

4-

Ψ = π + θ (0^{+}) - θ (0^{-}),

5-

\begin{matrix} ℒ = & \frac{B W}{2 L} \int_{- 1}^{1} θ^{'} {(s)}^{2} d s - F_{x} L \int_{- 1}^{1} \cos θ (s) d s \\ - F_{y} L \int_{- 1}^{1} \sin θ (s) d s + W U (Ψ), \end{matrix}

6-

θ^{'} (s) = d θ / d s

7-

θ^{''} (s) - α \sin θ (s) + β \cos θ (s) = 0,

8-

α = \frac{F_{x} L^{2}}{B W}

9-

β = \frac{F_{y} L^{2}}{B W}

10-

\frac{B}{L} ({[θ^{'} (s) δ θ]}_{- 1}^{0^{-}} + {[θ^{'} (s) δ θ]}_{0^{+}}^{1}) + \frac{d U}{d Ψ} (δ θ (0^{+}) - δ θ (0^{-})) = 0 .

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/1910.02634

Formulas:

1-

M \equiv (\begin{matrix} 0 & 1 & 2 \\ C & ρ & \frac{2}{3} ρ & \frac{1}{3} ρ \\ D & 1 + \frac{2}{3} ρ & 1 + \frac{1}{3} ρ & 1 \end{matrix}),

2-

M_{D, 2} = 1

3-

2^{3 \times 3} = 512

4-

{c c, d c}

5-

{c d, d d}

6-

c d c c

7-

d d c c

8-

A_{t - 2} A_{t - 1} B_{t - 2} B_{t - 1}

9-

c c c c

10-

c d c c

Formulas (html):

Correct Categorie: q-bio

Guessed Categorie: math

Result: incorrect

Paper: https://arxiv.org/abs/math/0511403

Formulas:

1-

π = π^{(1)} ℏ + π^{(2)} ℏ^{2} + π^{(3)} ℏ^{3} + \dots

2-

T N \to T^{*} N

3-

T^{*} N \to T N

4-

(T \oplus T^{*}) N

5-

⟨ (u, α), (v, β) ⟩ = α (v) + β (u) .

6-

(T \oplus T^{*}) N

7-

(T \oplus T^{*}) N

8-

[[(u, α), (v, β)]] = [u, v] + ℒ_{u} β - i_{v} d α,

9-

(T \oplus T^{*}) N

10-

(T \oplus T^{*}) N

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/1503.04635

Formulas:

1-

m i c r o s c o p i c

2-

m o d e l . -

3-

H_{S} = (p_{S}^{2} + ω_{S}^{2} q_{S}^{2}) / 2

4-

H_{E} = \sum_{i = 1}^{N} (P_{i}^{2} + Ω_{i}^{2} Q_{i}^{2}) / 2

5-

H_{I} = q_{S} \sum_{i = 1}^{N} g_{i} Q_{i}

6-

H = H_{S} + H_{E} + k H_{I}

7-

γ (t) = \sum_{i = 1}^{N} (k^{2} g_{i}^{2} / Ω_{i}^{2}) \cos (Ω_{i} t)

8-

J (ω) = \frac{π}{2} \sum_{i} \frac{k^{2} g_{i}^{2}}{Ω_{i}} δ (ω - Ω_{i})

9-

J (ω) = ω \int_{0}^{\infty} γ (t) \cos (ω t) 𝑑 t .

10-

E n g i n e e r i n g

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: quant-ph

Result: correct

Paper: https://arxiv.org/abs/1511.08942

Formulas:

1-

>> q^{\frac{d + 2}{3}}

2-

>> q^{\frac{d + 2}{2}}

3-

(a, b, c)

4-

(x, y, z) \in 𝔽_{q}^{d} \times 𝔽_{q}^{d} \times 𝔽_{q}^{d}

5-

A, B \subset 𝔽_{q}^{d}

6-

{| A |}^{2} | B | >> q^{d + 2}

7-

(x, y, z)

8-

| A | >> q^{\frac{d + 2}{3}}

9-

| A | ≫ q^{\frac{d + 2}{2}}

10-

| B | ≫ \frac{1}{\log q} q^{\frac{d + 2}{2}}

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/1304.4427

Formulas:

1-

| P_{Λ, \bar{Λ}} | \leq 0.02

2-

μ_{N} g_{Λ} B / T \approx 10^{- 6}

3-

Π_{μ} (p) = ℏ ϵ_{μ ρ σ τ} \frac{p^{τ}}{8 m} \frac{\int d Σ_{λ} p^{λ} n_{F} (1 - n_{F}) \partial^{ρ} β^{σ}}{\int d Σ_{λ} p^{λ} n_{F}},

4-

β^{μ} (x) = (1 / T (x)) u^{μ} (x)

5-

1 / (e^{β (x) \cdot p - ξ (x)} + 1)

6-

ξ (x) = μ (x) / T (x)

7-

(1 - n_{F})

8-

ϖ^{μ ν} = \frac{1}{2} (\partial^{ν} β^{μ} - \partial^{μ} β^{ν})

9-

𝚷 (p) = \frac{ℏ ε}{8 m} \frac{\int d Σ_{λ} p^{λ} n_{F} (\nabla \times 𝜷)}{\int d Σ_{λ} p^{λ} n_{F}}

10-

+ \frac{ℏ 𝐩}{8 m} \times \frac{\int d Σ_{λ} p^{λ} n_{F} (\partial_{t} 𝜷 + \nabla β^{0})}{\int d Σ_{λ} p^{λ} n_{F}} .

Formulas (html):

Correct Categorie: nucl-th

Guessed Categorie: nucl-th

Result: correct

Paper: https://arxiv.org/abs/astro-ph/9809266

Formulas:

1-

{\bar{I}}_{F 814 W} = 31.31 \pm 0.05

2-

{(m - M)}_{0} = 32.99 \pm 0.11

3-

I_{F 814 W}

4-

(V - I_{C}) = 1.23

5-

I_{F 814 W} = 21.546 - 2.5 \log DN + 2.5 \log (\frac{t}{s}),

6-

1 < (V - I_{C}) < 1.4

7-

A_{B} (mag) = \frac{F_{100}}{14 \pm 2 MJy / ster}

8-

A_{F 814 W} = 0.479 A_{B}

9-

E_{V - I} = 0.301 A_{B}

10-

I_{c u t} = 25.0

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1512.05790

Formulas:

1-

A d N D P

2-

A d N D P

3-

A d N D P

4-

[11 \bar{2}]

5-

E_{t o t}

6-

E_{t o t}

7-

2 c - 2 e

8-

3 c - 2 e

9-

7 c - 2 e

10-

2 c - 2 e

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0309031

Formulas:

1-

2 - 20 M_{⊙}

2-

Ω ≪ \frac{1}{τ_{dyn}} \equiv {(\frac{G M_{1}}{R_{1}^{3}})}^{1 / 2},

3-

\vec{r} = (r, θ, ϕ)

4-

ε_{T} W (\vec{r}, t)

5-

ε_{T} = {(\frac{R_{1}}{a})}^{3} \frac{M_{2}}{M_{1}}

6-

Y_{ℓ}^{m} (θ, ϕ)

7-

n = 2 π / P_{orb}

8-

ε_{T} W (\vec{r}, t) = - ε_{T} \frac{G M_{1}}{R_{1}} \sum_{ℓ = 2}^{4} \sum_{m = - ℓ}^{ℓ} \sum_{k = - \infty}^{\infty}

9-

c_{ℓ, m, k} {(\frac{r}{R_{1}})}^{ℓ} Y_{ℓ}^{m} (θ, ϕ) \exp [i (σ_{T} t - k n τ)],

10-

σ_{T} = k n + m Ω

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/0801.4071

Formulas:

1-

𝐚_{1} = a \hat{x}

2-

𝐚_{2} = a \hat{y}

3-

P 4 m m m

4-

P 4 m m

5-

A m m 2

6-

P (\hat{x} + \hat{y})

7-

P m m 2

8-

c_{α} \hat{x} + c \hat{z}

9-

P \hat{x} + P_{z} \hat{z}

10-

c_{α} (\hat{x} + \hat{y}) + c \hat{z}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/cond-mat/0202474

Formulas:

1-

3 p, 3 s

2-

M (μ_{B} / F e)

3-

N (ε) = {(2 W)}^{- 1}

4-

H = \sum_{λ, 𝐤, σ} (ε_{λ 𝐤} - σ μ_{B} B) n_{λ 𝐤 σ} - \frac{1}{2} \sum_{𝐑} (I {\hat{m}}_{𝐑}^{2} + V {\hat{ρ}}_{𝐑}^{2}),

5-

λ = - 1, + 1

6-

n_{λ 𝐤 σ}

7-

{\hat{ρ}}_{𝐑} = 2 + \sum_{λ σ} λ n_{λ 𝐑 σ}

8-

{\hat{m}}_{𝐑} = \sum_{λ σ} σ n_{λ 𝐑 σ}

9-

ω_{λ, σ} = ε - λ V ρ - σ (μ_{B} B + I m)

10-

⟨ n_{-, σ} ⟩

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1806.03852

Formulas:

1-

[\begin{matrix} x^{'} \\ y^{'} \\ 1 \end{matrix}] = [\begin{matrix} f_{h} z_{x} \cos (θ) & - z_{y} \sin (θ + ϕ) & t_{x} \\ z_{x} \sin (θ) & z_{y} \cos (θ + ϕ) & t_{y} \\ 0 & 0 & 1 \end{matrix}] [\begin{matrix} x \\ y \\ 1 \end{matrix}]

2-

x^{'} = γ (x - \bar{x}) + \bar{x}

3-

x^{'} = x + δ

4-

𝒰 (a, b)

5-

1 - 2 B (0.5)

6-

𝒰 (- 0.1, 0.1)

7-

𝒰 (- 0.1, 0.1)

8-

𝒰 (0.85, 1.15)

9-

𝒰 (0.85, 1.15)

10-

𝒰 (- \frac{π}{180} 22.5, \frac{π}{180} 22.5)

Formulas (html):

Correct Categorie: cs

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/1605.05203

Formulas:

1-

E = \sqrt{η^{2} + Δ^{2}},

2-

γ_{E}^{+} = γ_{- E}

3-

γ_{0}^{+} = γ_{0}

4-

C_{b u l k} \sim V P_{F}^{2} {(\frac{Δ}{k T})}^{3 / 2} \exp (- \frac{Δ}{k T})

5-

≃ 2 k T_{c}

6-

C_{m a j} \sim S ξ P_{F}^{2} {(\frac{Δ}{k T})}^{- 2},

7-

\frac{C_{m a j}}{C_{b u l k}} = \frac{π^{3}}{8 \sqrt{2}} \frac{ξ S}{V} {(\frac{Δ}{k T})}^{- 7 / 2} \exp (\frac{Δ}{k T}) .

8-

W (T) \sim α \exp (- Δ / k T),

9-

E_{e l e c t r i c} = \int U I 𝑑 t

10-

σ = \frac{Δ W}{U} = \frac{1}{C (T)} \frac{d W (T)}{d T},

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: nucl-th

Result: incorrect

Paper: https://arxiv.org/abs/hep-ph/9603295

Formulas:

1-

S U (4)

2-

S U (3)

3-

Λ_{c} (2.2851 \pm 0.0006)

4-

Ξ_{c} (2.4677 \pm 0.0017)

5-

Σ_{c} (2.4531 \pm 0.0007)

6-

Λ_{b} (5.641 \pm 0.050)

7-

Ω_{c} (2.7068 \pm 0.001)

8-

Σ_{c}^{*} (2.530 \pm 0.007)

9-

Ξ_{c}^{*} (2.643 \pm 0.002)

10-

Λ_{b} (5.638 \pm 0.016)

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: hep-lat

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/0508314

Formulas:

1-

V (r) = V_{o} [\frac{ν}{μ - ν} e^{- μ (r - b)} - \frac{μ}{μ - ν} e^{- ν (r - b)}],

2-

ε = (b - a) / a

3-

γ = μ ν V_{0}

4-

γ = μ ν V_{0}

5-

μ = 2 ν = 12

6-

N_{13}, N_{14}, N_{23} \dots

7-

μ = 2 ν = 12

8-

N_{0} = 841 = 29 \times 29

9-

μ = 2 ν = 36

10-

Δ G_{m a x}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1504.04527

Formulas:

1-

M \in ℝ^{m \times n}

2-

M \in ℝ^{m \times n}

3-

X \in ℝ^{n \times m}

4-

M = M X M, X = X M X, {(M X)}^{T} = M X

5-

{(X M)}^{T} = X M

6-

M^{- 1} = M^{†}

7-

M \in ℝ^{n \times n}

8-

R (M^{T}) = R (M)

9-

M \in ℝ^{m \times n}

10-

(\begin{matrix} A & B \\ C & D \end{matrix})

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/1104.4064

Formulas:

1-

\frac{Γ ⊢ Θ, A A, Δ ⊢ Λ}{Γ, Δ ⊢ Θ, Λ}

2-

\frac{Γ ⊢ A, Θ Δ, A ⊢ Λ}{Δ, Γ ⊢ Λ, Θ}

3-

\frac{Γ ⊢ A Δ_{1}, A, Δ_{2} ⊢ Λ}{Δ_{1}, Γ, Δ_{2} ⊢ Λ} \frac{Γ ⊢ Θ_{1}, A, Θ_{2} A ⊢ Λ}{Γ ⊢ Θ_{1}, Λ, Θ_{2}}

4-

(PC) \frac{Γ ⊢ Θ_{1}, A, Θ_{2} Δ_{1}, A, Δ_{2} ⊢ Λ}{Δ_{1}, Γ, Δ_{2} ⊢ Θ_{1}, Λ, Θ_{2}}

5-

(a, c) \in D

6-

(c, a) \in D

7-

k_{W}, k_{E} \geq 1

8-

N W (B)

9-

S W (B)

10-

N E (B)

Formulas (html):

Correct Categorie: math

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1110.6779

Formulas:

1-

R (n, k)

2-

{1, 2, \dots, n}

3-

R (n, k)

4-

[n] = {1, 2, \dots, n}

5-

π = π (1) π (2) \dots π (n) \in 𝒮_{n}

6-

π (i - 1) < π (i) > π (i + 1)

7-

π (i - 1) > π (i) < π (i + 1)

8-

i \in {2, 3, \dots, n - 1}

9-

R (n, k)

10-

R (n, k) = k R (n - 1, k) + 2 R (n - 1, k - 1) + (n - k) R (n - 1, k - 2)

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/1710.00236

Formulas:

1-

{}^{b c}_{a c}

2-

{}^{a c}_{b c}

3-

{}_{a c}^{a c}

4-

{}_{b c}^{b c}

5-

{}^{a c}_{a c}

6-

{}^{a c}_{b c}

7-

{}^{b c}_{b c}

8-

\vec{p} = \sum_{i} \vec{x_{i}} q_{i},

9-

\vec{Q} = \frac{e}{V} (\begin{matrix} a \\ b \\ c \end{matrix}),

10-

{}^{a c}_{a c}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1409.4074

Formulas:

1-

σ_{1}, \dots, σ_{n - 1}

2-

σ_{i} σ_{j} = σ_{j} σ_{i}

3-

| i - j | > 1

4-

σ_{i} σ_{j} σ_{i} = σ_{j} σ_{i} σ_{j}

5-

| i - j | = 1

6-

𝐮 = (u_{1}, \dots, u_{n})

7-

0 \leq u_{i} \leq N

8-

β = σ_{1} σ_{2} σ_{1} = σ_{2} σ_{1} σ_{2} .

9-

(0, 1, 2), (0, 2, 1), (1, 2, 0), (2, 1, 0), (2, 0, 1), (1, 0, 2) .

10-

(0, 1, 2)

Formulas (html):

Correct Categorie: math

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/9602116

Formulas:

1-

H = \sum_{i = 1}^{N} H_{0, i} + \int d^{2} x m \sum_{i = 1}^{N} ε_{i} (x) - g \int d^{2} x \sum_{i \neq j}^{N} ε_{i} ε_{j} (x) .

2-

β (g) \equiv \frac{d g}{d l n (r)} = ϵ g (r) + 4 π (N - 2) g^{2} (r) - 16 π^{2} (N - 2) g^{3} (r) + O (g^{4} (r))

3-

γ_{ε} \equiv \frac{d l n (Z_{ε} (r))}{d l n (r)} = 4 π (N - 1) g - 8 π^{2} (N - 1) g^{2} + O (g^{3})

4-

γ_{σ} \equiv \frac{d l n (Z_{σ} (r))}{d l n (r)} = (N - 1) g^{2} (r) π^{2} ϵ [1 + 2 \frac{Γ^{2} (- \frac{2}{3}) Γ^{2} (\frac{1}{6})}{Γ^{2} (- \frac{1}{3}) Γ^{2} (- \frac{1}{6})}]

5-

+ 4 (N - 1) (N - 2) π^{3} g^{3} (r) + O (g^{4})

6-

ϵ = 2 - 2 Δ_{ε}

7-

g_{c} = - \frac{ϵ}{4 π (N - 2)} + \frac{ϵ^{2}}{4 π {(N - 2)}^{2}} + O (ϵ^{3})

8-

Δ_{ε}^{'} = Δ_{ε} - γ_{ε} (g_{c})

9-

= Δ_{ε} + \frac{(N - 1)}{(N - 2)} ϵ - \frac{(N - 1)}{2 {(N - 2)}^{2}} ϵ^{2} + O (ϵ^{3})

10-

Δ_{σ}^{'} = Δ_{σ} - γ_{σ} (g_{c})

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/astro-ph/9605005

Formulas:

1-

t_{c o o l}

2-

t_{h y d}

3-

t_{h y d} > t_{c o o l}

4-

t_{h y d}

5-

t_{c o o l}

6-

D = t_{c o o l} / t_{h y d}

7-

t_{h y d} < t_{c o o l}

8-

t_{h y d}

9-

t_{h y d}

10-

t_{h y d} > t_{c o o l}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1801.02516

Formulas:

1-

m = 1, 2, \dots, M

2-

Σ_{m} = 𝐱_{m} + r_{m} 𝐁_{m},

3-

μ (𝐱) = {\begin{matrix} μ_{0}, & 𝐱 \in ℝ^{2} \ \bar{Σ} \\ μ_{m}, & 𝐱 \in Σ_{m} . \end{matrix}

4-

k = ω \sqrt{ε_{0} μ_{0}} = 2 π / λ

5-

m = 1, 2, \dots, M

6-

k | 𝐱_{m} - 𝐱_{m^{'}} | ≫ 0.75,

7-

m, m^{'} = 1, 2, \dots, M

8-

ψ_{inc} := \exp (i k 𝐝 \cdot 𝐱)

9-

\nabla \cdot (\frac{1}{μ (𝐱)} \nabla ψ (𝐱)) + ω^{2} ψ (𝐱) = 0

10-

ψ_{scat} (𝐱)

Formulas (html):

Correct Categorie: math

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0610675

Formulas:

1-

(r, ϕ) = (1, π)

2-

q = M_{p} / M_{*}

3-

p = c_{s}^{2} Σ_{g}

4-

c_{s} = H Ω_{K} = h v_{K}

5-

v_{K} = r Ω_{K}

6-

\frac{d v}{d t} = \frac{L^{2}}{r^{3}} - \frac{\partial Φ}{\partial r} + f_{r}

7-

\frac{d L}{d t} = - \frac{\partial Φ}{\partial ϕ} + f_{ϕ}

8-

K n = \frac{λ}{2 s}

9-

F_{eps} = - π s^{2} ρ_{g} | Δ v | Δ v

10-

[(1 + \frac{1}{m^{2}} - \frac{1}{4 m^{4}}) \erf (m) + (\frac{1}{m} + \frac{1}{2 m^{3}}) \frac{e^{- m^{2}}}{\sqrt{π}}]

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

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

Formulas:

1-

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

2-

(i, j, k)

3-

(1, 2, 3)

4-

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

5-

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

6-

t_{12} = ℏ / Γ_{12}

7-

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

8-

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

9-

V (ρ_{0}) = V (ρ_{t}) = E

10-

ρ_{0} = ρ_{t}, S = 0

Formulas (html):

Correct Categorie: nucl-th

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/1812.02428

Formulas:

1-

(| r | \leq p / 2)

2-

c = p q + 2 r + m

3-

m = (c mod p) mod 2

4-

c_{1} = q_{1} * p + 2 * r_{1} + m_{1}

5-

c_{2} = q_{2} * p + 2 * r_{2} + m_{2}

6-

c_{1} + c_{2} = (q_{1} + q_{2}) * p + 2 * (r_{1} + r_{2}) + (m_{1} + m_{2})

7-

c_{1} = q_{1} * p + 2 * r_{1} + m_{1}

8-

c_{2} = q_{2} * p + 2 * r_{2} + m_{2}

9-

c_{1} * c_{2} = ((c_{1} * q_{2}) + q_{1} * c_{2} * q_{1} * q_{2}) * p + 2 (2 * r_{1} * r_{2} + r_{1} * m_{2} + m_{1} * r_{2}) + m_{1} * m_{2}

10-

B (A^{B})

Formulas (html):

Correct Categorie: cs

Guessed Categorie: cs

Result: correct

Paper: https://arxiv.org/abs/quant-ph/0210096

Formulas:

1-

α | 0 ⟩ + β | 1 ⟩ + γ | 2 ⟩

2-

α | 0 ⟩ + β | 1 ⟩ + γ | 2 ⟩

3-

P_{e} = | H, H ⟩ ⟨ H, H | + | V, V ⟩ ⟨ V, V | .

4-

| H, H ⟩ = {| H ⟩}_{1} {| H ⟩}_{2} = {| H ⟩}_{1} \otimes {| H ⟩}_{2}

5-

| V, V ⟩ = {| V ⟩}_{1} {| V ⟩}_{2} = {| V ⟩}_{1} \otimes {| V ⟩}_{2}

6-

α | 0 ⟩ + β | 1 ⟩ + γ | 2 ⟩

7-

Ψ_{i n} = α {| 0 ⟩}_{1} + β {| 1 ⟩}_{1} + γ {| 2 ⟩}_{1} .

8-

| Ψ_{23} ⟩ = {| 1 ⟩}_{2} {| 1 ⟩}_{3}

9-

Ψ_{23}^{'} = \frac{1}{\sqrt{2}} ({| 2 ⟩}_{2^{'}} {| 0 ⟩}_{3^{'}} - {| 0 ⟩}_{2^{'}} {| 2 ⟩}_{3^{'}}) .

10-

| Ψ_{i n} ⟩ | Ψ_{23}^{'} ⟩

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: quant-ph

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0702417

Formulas:

1-

O F F^{+}

2-

O F F^{-}

3-

O F F^{+}

4-

O F F^{-}

5-

< O F F^{-} - O F F^{+} > = (2.44 \pm 0.33) \times 10^{- 2}

6-

σ = 4.33 \times 10^{- 2}

7-

O F F^{-}

8-

excess = \frac{observed - predicted}{error} .

9-

O F F^{-}

10-

O F F^{-}

Formulas (html):

<math><mrow id="S2.p1.1.m1.1.1" xref="S2.p1.1.m1.1.1.cmml"><mi id="S2.p1.1.m1.1.1.2" xref="S2.p1.1.m1.1.1.2.cmml">O</mi><mo id="S2.p1.1.m1.1.1.1" xref="S2.p1.1.m1.1.1.1.cmml">⁢</mo><mi id="S2.p1.1.m1.1.1.3" xref="S2.p1.1.m1.1.1.3.cmml">F</mi><mo id="S2.p1.1.m1.1.1.1a" xref="S2.p1.1.m1.1.1.1.cmml">⁢</mo><msup id="S2.p1.1.m1.1.1.4" xref="S2.p1.1.m1.1.1.4.cmml"><mi id="S2.p1.1.m1.1.1.4.2" xref="S2.p1.1.m1.1.1.4.2.cmml">F</mi><mo id="S2.p1.1.m1.1.1.4.3" xref="S2.p1.1.m1.1.1.4.3.cmml">+</mo></msup></mrow></math>, <math><mrow id="S2.p1.2.m2.1.1" xref="S2.p1.2.m2.1.1.cmml"><mi id="S2.p1.2.m2.1.1.2" xref="S2.p1.2.m2.1.1.2.cmml">O</mi><mo id="S2.p1.2.m2.1.1.1" xref="S2.p1.2.m2.1.1.1.cmml">⁢</mo><mi id="S2.p1.2.m2.1.1.3" xref="S2.p1.2.m2.1.1.3.cmml">F</mi><mo id="S2.p1.2.m2.1.1.1a" xref="S2.p1.2.m2.1.1.1.cmml">⁢</mo><msup id="S2.p1.2.m2.1.1.4" xref="S2.p1.2.m2.1.1.4.cmml"><mi id="S2.p1.2.m2.1.1.4.2" xref="S2.p1.2.m2.1.1.4.2.cmml">F</mi><mo id="S2.p1.2.m2.1.1.4.3" xref="S2.p1.2.m2.1.1.4.3.cmml">-</mo></msup></mrow></math>, <math><mrow id="S2.p1.3.m3.1.1" xref="S2.p1.3.m3.1.1.cmml"><mi id="S2.p1.3.m3.1.1.2" xref="S2.p1.3.m3.1.1.2.cmml">O</mi><mo id="S2.p1.3.m3.1.1.1" xref="S2.p1.3.m3.1.1.1.cmml">⁢</mo><mi id="S2.p1.3.m3.1.1.3" xref="S2.p1.3.m3.1.1.3.cmml">F</mi><mo id="S2.p1.3.m3.1.1.1a" xref="S2.p1.3.m3.1.1.1.cmml">⁢</mo><msup id="S2.p1.3.m3.1.1.4" xref="S2.p1.3.m3.1.1.4.cmml"><mi id="S2.p1.3.m3.1.1.4.2" xref="S2.p1.3.m3.1.1.4.2.cmml">F</mi><mo id="S2.p1.3.m3.1.1.4.3" xref="S2.p1.3.m3.1.1.4.3.cmml">+</mo></msup></mrow></math>, <math><mrow id="S2.p1.4.m4.1.1" xref="S2.p1.4.m4.1.1.cmml"><mi id="S2.p1.4.m4.1.1.2" xref="S2.p1.4.m4.1.1.2.cmml">O</mi><mo id="S2.p1.4.m4.1.1.1" xref="S2.p1.4.m4.1.1.1.cmml">⁢</mo><mi id="S2.p1.4.m4.1.1.3" xref="S2.p1.4.m4.1.1.3.cmml">F</mi><mo id="S2.p1.4.m4.1.1.1a" xref="S2.p1.4.m4.1.1.1.cmml">⁢</mo><msup id="S2.p1.4.m4.1.1.4" xref="S2.p1.4.m4.1.1.4.cmml"><mi id="S2.p1.4.m4.1.1.4.2" xref="S2.p1.4.m4.1.1.4.2.cmml">F</mi><mo id="S2.p1.4.m4.1.1.4.3" xref="S2.p1.4.m4.1.1.4.3.cmml">-</mo></msup></mrow></math>, <math><mrow id="S2.p1.6.m6.2.2" xref="S2.p1.6.m6.2.2.cmml"><mrow id="S2.p1.6.m6.1.1.1.1" xref="S2.p1.6.m6.1.1.1.2.cmml"><mo id="S2.p1.6.m6.1.1.1.1.2" xref="S2.p1.6.m6.1.1.1.2.1.cmml"><</mo><mrow id="S2.p1.6.m6.1.1.1.1.1" xref="S2.p1.6.m6.1.1.1.1.1.cmml"><mrow id="S2.p1.6.m6.1.1.1.1.1.2" xref="S2.p1.6.m6.1.1.1.1.1.2.cmml"><mi id="S2.p1.6.m6.1.1.1.1.1.2.2" xref="S2.p1.6.m6.1.1.1.1.1.2.2.cmml">O</mi><mo id="S2.p1.6.m6.1.1.1.1.1.2.1" xref="S2.p1.6.m6.1.1.1.1.1.2.1.cmml">⁢</mo><mi id="S2.p1.6.m6.1.1.1.1.1.2.3" xref="S2.p1.6.m6.1.1.1.1.1.2.3.cmml">F</mi><mo id="S2.p1.6.m6.1.1.1.1.1.2.1a" xref="S2.p1.6.m6.1.1.1.1.1.2.1.cmml">⁢</mo><msup id="S2.p1.6.m6.1.1.1.1.1.2.4" xref="S2.p1.6.m6.1.1.1.1.1.2.4.cmml"><mi id="S2.p1.6.m6.1.1.1.1.1.2.4.2" xref="S2.p1.6.m6.1.1.1.1.1.2.4.2.cmml">F</mi><mo id="S2.p1.6.m6.1.1.1.1.1.2.4.3" xref="S2.p1.6.m6.1.1.1.1.1.2.4.3.cmml">-</mo></msup></mrow><mo id="S2.p1.6.m6.1.1.1.1.1.1" xref="S2.p1.6.m6.1.1.1.1.1.1.cmml">-</mo><mrow id="S2.p1.6.m6.1.1.1.1.1.3" xref="S2.p1.6.m6.1.1.1.1.1.3.cmml"><mi id="S2.p1.6.m6.1.1.1.1.1.3.2" xref="S2.p1.6.m6.1.1.1.1.1.3.2.cmml">O</mi><mo id="S2.p1.6.m6.1.1.1.1.1.3.1" xref="S2.p1.6.m6.1.1.1.1.1.3.1.cmml">⁢</mo><mi id="S2.p1.6.m6.1.1.1.1.1.3.3" xref="S2.p1.6.m6.1.1.1.1.1.3.3.cmml">F</mi><mo id="S2.p1.6.m6.1.1.1.1.1.3.1a" xref="S2.p1.6.m6.1.1.1.1.1.3.1.cmml">⁢</mo><msup id="S2.p1.6.m6.1.1.1.1.1.3.4" xref="S2.p1.6.m6.1.1.1.1.1.3.4.cmml"><mi id="S2.p1.6.m6.1.1.1.1.1.3.4.2" xref="S2.p1.6.m6.1.1.1.1.1.3.4.2.cmml">F</mi><mo id="S2.p1.6.m6.1.1.1.1.1.3.4.3" xref="S2.p1.6.m6.1.1.1.1.1.3.4.3.cmml">+</mo></msup></mrow></mrow><mo id="S2.p1.6.m6.1.1.1.1.3" xref="S2.p1.6.m6.1.1.1.2.1.cmml">></mo></mrow><mo id="S2.p1.6.m6.2.2.3" xref="S2.p1.6.m6.2.2.3.cmml">=</mo><mrow id="S2.p1.6.m6.2.2.2" xref="S2.p1.6.m6.2.2.2.cmml"><mrow id="S2.p1.6.m6.2.2.2.1.1" xref="S2.p1.6.m6.2.2.2.1.1.1.cmml"><mo stretchy="false" id="S2.p1.6.m6.2.2.2.1.1.2" xref="S2.p1.6.m6.2.2.2.1.1.1.cmml">(</mo><mrow id="S2.p1.6.m6.2.2.2.1.1.1" xref="S2.p1.6.m6.2.2.2.1.1.1.cmml"><mn id="S2.p1.6.m6.2.2.2.1.1.1.2" xref="S2.p1.6.m6.2.2.2.1.1.1.2.cmml">2.44</mn><mo id="S2.p1.6.m6.2.2.2.1.1.1.1" xref="S2.p1.6.m6.2.2.2.1.1.1.1.cmml">±</mo><mn id="S2.p1.6.m6.2.2.2.1.1.1.3" xref="S2.p1.6.m6.2.2.2.1.1.1.3.cmml">0.33</mn></mrow><mo stretchy="false" id="S2.p1.6.m6.2.2.2.1.1.3" xref="S2.p1.6.m6.2.2.2.1.1.1.cmml">)</mo></mrow><mo id="S2.p1.6.m6.2.2.2.2" xref="S2.p1.6.m6.2.2.2.2.cmml">×</mo><msup id="S2.p1.6.m6.2.2.2.3" xref="S2.p1.6.m6.2.2.2.3.cmml"><mn id="S2.p1.6.m6.2.2.2.3.2" xref="S2.p1.6.m6.2.2.2.3.2.cmml">10</mn><mrow id="S2.p1.6.m6.2.2.2.3.3" xref="S2.p1.6.m6.2.2.2.3.3.cmml"><mo id="S2.p1.6.m6.2.2.2.3.3.1" xref="S2.p1.6.m6.2.2.2.3.3.1.cmml">-</mo><mn id="S2.p1.6.m6.2.2.2.3.3.2" xref="S2.p1.6.m6.2.2.2.3.3.2.cmml">2</mn></mrow></msup></mrow></mrow></math>, <math><mrow id="S2.p1.7.m7.1.1" xref="S2.p1.7.m7.1.1.cmml"><mi id="S2.p1.7.m7.1.1.2" xref="S2.p1.7.m7.1.1.2.cmml">σ</mi><mo id="S2.p1.7.m7.1.1.1" xref="S2.p1.7.m7.1.1.1.cmml">=</mo><mrow id="S2.p1.7.m7.1.1.3" xref="S2.p1.7.m7.1.1.3.cmml"><mn id="S2.p1.7.m7.1.1.3.2" xref="S2.p1.7.m7.1.1.3.2.cmml">4.33</mn><mo id="S2.p1.7.m7.1.1.3.1" xref="S2.p1.7.m7.1.1.3.1.cmml">×</mo><msup id="S2.p1.7.m7.1.1.3.3" xref="S2.p1.7.m7.1.1.3.3.cmml"><mn id="S2.p1.7.m7.1.1.3.3.2" xref="S2.p1.7.m7.1.1.3.3.2.cmml">10</mn><mrow id="S2.p1.7.m7.1.1.3.3.3" xref="S2.p1.7.m7.1.1.3.3.3.cmml"><mo id="S2.p1.7.m7.1.1.3.3.3.1" xref="S2.p1.7.m7.1.1.3.3.3.1.cmml">-</mo><mn id="S2.p1.7.m7.1.1.3.3.3.2" xref="S2.p1.7.m7.1.1.3.3.3.2.cmml">2</mn></mrow></msup></mrow></mrow></math>, <math><mrow id="S2.p1.10.m10.1.1" xref="S2.p1.10.m10.1.1.cmml"><mi id="S2.p1.10.m10.1.1.2" xref="S2.p1.10.m10.1.1.2.cmml">O</mi><mo id="S2.p1.10.m10.1.1.1" xref="S2.p1.10.m10.1.1.1.cmml">⁢</mo><mi id="S2.p1.10.m10.1.1.3" xref="S2.p1.10.m10.1.1.3.cmml">F</mi><mo id="S2.p1.10.m10.1.1.1a" xref="S2.p1.10.m10.1.1.1.cmml">⁢</mo><msup id="S2.p1.10.m10.1.1.4" xref="S2.p1.10.m10.1.1.4.cmml"><mi id="S2.p1.10.m10.1.1.4.2" xref="S2.p1.10.m10.1.1.4.2.cmml">F</mi><mo id="S2.p1.10.m10.1.1.4.3" xref="S2.p1.10.m10.1.1.4.3.cmml">-</mo></msup></mrow></math>, <math><mrow id="S3.E1.m1.1.1.1" xref="S3.E1.m1.1.1.1.1.cmml"><mrow id="S3.E1.m1.1.1.1.1" xref="S3.E1.m1.1.1.1.1.cmml"><mi id="S3.E1.m1.1.1.1.1.2" xref="S3.E1.m1.1.1.1.1.2.cmml">excess</mi><mo id="S3.E1.m1.1.1.1.1.1" xref="S3.E1.m1.1.1.1.1.1.cmml">=</mo><mfrac id="S3.E1.m1.1.1.1.1.3" xref="S3.E1.m1.1.1.1.1.3.cmml"><mrow id="S3.E1.m1.1.1.1.1.3.2" xref="S3.E1.m1.1.1.1.1.3.2.cmml"><mi id="S3.E1.m1.1.1.1.1.3.2.2" xref="S3.E1.m1.1.1.1.1.3.2.2.cmml">observed</mi><mo id="S3.E1.m1.1.1.1.1.3.2.1" xref="S3.E1.m1.1.1.1.1.3.2.1.cmml">-</mo><mi id="S3.E1.m1.1.1.1.1.3.2.3" xref="S3.E1.m1.1.1.1.1.3.2.3.cmml">predicted</mi></mrow><mi id="S3.E1.m1.1.1.1.1.3.3" xref="S3.E1.m1.1.1.1.1.3.3.cmml">error</mi></mfrac></mrow><mo id="S3.E1.m1.1.1.1.2" xref="S3.E1.m1.1.1.1.1.cmml">.</mo></mrow></math>, <math><mrow id="S3.F1.6.m2.1.1" xref="S3.F1.6.m2.1.1.cmml"><mi id="S3.F1.6.m2.1.1.2" xref="S3.F1.6.m2.1.1.2.cmml">O</mi><mo id="S3.F1.6.m2.1.1.1" xref="S3.F1.6.m2.1.1.1.cmml">⁢</mo><mi id="S3.F1.6.m2.1.1.3" xref="S3.F1.6.m2.1.1.3.cmml">F</mi><mo id="S3.F1.6.m2.1.1.1b" xref="S3.F1.6.m2.1.1.1.cmml">⁢</mo><msup id="S3.F1.6.m2.1.1.4" xref="S3.F1.6.m2.1.1.4.cmml"><mi id="S3.F1.6.m2.1.1.4.2" xref="S3.F1.6.m2.1.1.4.2.cmml">F</mi><mo id="S3.F1.6.m2.1.1.4.3" xref="S3.F1.6.m2.1.1.4.3.cmml">-</mo></msup></mrow></math>, <math><mrow id="S3.p2.4.m4.1.1" xref="S3.p2.4.m4.1.1.cmml"><mi id="S3.p2.4.m4.1.1.2" xref="S3.p2.4.m4.1.1.2.cmml">O</mi><mo id="S3.p2.4.m4.1.1.1" xref="S3.p2.4.m4.1.1.1.cmml">⁢</mo><mi id="S3.p2.4.m4.1.1.3" xref="S3.p2.4.m4.1.1.3.cmml">F</mi><mo id="S3.p2.4.m4.1.1.1a" xref="S3.p2.4.m4.1.1.1.cmml">⁢</mo><msup id="S3.p2.4.m4.1.1.4" xref="S3.p2.4.m4.1.1.4.cmml"><mi id="S3.p2.4.m4.1.1.4.2" xref="S3.p2.4.m4.1.1.4.2.cmml">F</mi><mo id="S3.p2.4.m4.1.1.4.3" xref="S3.p2.4.m4.1.1.4.3.cmml">-</mo></msup></mrow></math>

Correct Categorie: astro-ph

Guessed Categorie: hep-ph

Result: incorrect

Paper: https://arxiv.org/abs/1405.0731

Formulas:

1-

\log τ \propto {(1 - I)}^{β (I)}

2-

M_{S} = | 𝐌 |

3-

K = (1 / 2) μ_{0} M_{S} H_{K} V

4-

K_{M} = μ_{0} M_{S}^{2} V

5-

U (𝐦) = K [D {({\hat{𝐧}}_{D} \cdot 𝐦)}^{2} - {({\hat{𝐧}}_{K} \cdot 𝐦)}^{2}],

6-

𝐦 = 𝐌 / | 𝐌 |

7-

D \equiv K_{M} / K = M_{S} / H_{K}

8-

{\dot{m}}_{i} = A_{i} (𝐦) + B_{i k} (𝐦) \circ H_{t h, k}

9-

⟨ H_{t h, i} (t) H_{t h, k} (t^{'}) ⟩ = 2 C δ_{i, k} δ (t - t^{'})

10-

C = \frac{α}{2 (1 + α^{2}) ξ}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0005029

Formulas:

1-

\log g - \log T_{eff}

2-

α_{ov} \approx 0.6 \pm 0.1

3-

V_{m a x}

4-

0 \overset{p}{.} 5

5-

T_{MinI} = HJD 2441256.544 + 12.425719 E

6-

0 \overset{p}{.} 403

7-

0 \overset{p}{.} 15

8-

0 \overset{p}{.} 15

9-

f_{λ \oplus} = {(\frac{R_{P}}{d})}^{2} [F_{λ}^{P} + {(\frac{R_{S}}{R_{P}})}^{2} F_{λ}^{S}] \times 10^{- 0.4 E (B - V) [k (λ - V) + R (V)]}

10-

E (B - V)

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/cond-mat/0602006

Formulas:

1-

C = \frac{2 e γ}{ℏ} \int T (E) [- \frac{\partial f (E)}{\partial E}] 𝑑 E

2-

G^{R} = {[(E - e U) I - H_{0} - Σ^{R}]}^{- 1},

3-

H_{0}^{2 l, 2 l - 1} = H_{0}^{2 l - 1, 2 l} = 2 γ \cos (\frac{π J}{M})

4-

H_{0}^{2 l, 2 l + 1} = H_{0}^{2 l + 1, 2 l} = γ

5-

J = 1, \dots, M

6-

σ (r, z, ϕ) = - \sum_{l} g (z - z_{l}, r - R) \frac{e}{π} \int 𝑑 E Im G_{l l}^{R}

7-

g (z - z_{l}, r - R) = {(4 π^{2} R σ_{z} σ_{r})}^{- 1} \exp [- {(z - z_{l})}^{2} / 2 σ_{z}^{2}] \exp [- {(r - R)}^{2} / 2 σ_{r}^{2}]

8-

V_{g s} = 0

9-

A (1 - e^{- d / λ})

10-

V_{g s} = 0

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1505.05818

Formulas:

1-

6 d^{2} 7 s

2-

0_{3 / 2} \to 25027_{1 / 2}

3-

5 f 6 d^{2}

4-

0_{3 / 2} \to 24874_{5 / 2}

5-

Δ F = - 1, 0, + 1

6-

Th {({NO}_{3})}_{4}

7-

F = 1 \to F^{'} = 2

8-

Th {({NO}_{3})}_{4}

9-

18.86 (7) GHz

10-

6 d^{2} 7 s

Formulas (html):

Correct Categorie: physics

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/1612.03543

Formulas:

1-

ζ_{e} (q) := \prod_{d | n} {(q^{d} - 1)}^{e (d)}

2-

{\hat{ζ}}_{e} (q) := \prod_{d | n} {(q^{d} - 1)}^{- e (\frac{n}{d})} .

3-

ζ_{e}^{*} (q) := {\hat{ζ}}_{e}^{- 1} (q) = \prod_{d | n} {(q^{d} - 1)}^{e (\frac{n}{d})},

4-

ζ_{e} (q)

5-

ζ_{e} (q)

6-

Φ_{n} (q)

7-

q^{n} - 1 = \prod_{d | n} Φ_{d} (q),

8-

Φ_{n} (q) = \prod_{d | n} {(q^{d} - 1)}^{μ (\frac{n}{d})},

9-

Φ_{d} (q)

10-

\prod_{d | n} {(q^{d} - 1)}^{e (d)} = \prod_{d | n} Φ_{d}^{m (\frac{n}{d})} (q) .

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/1903.01047

Formulas:

1-

{dist}_{H} (u, v) \leq t \cdot {dist}_{G} (u, v)

2-

{dist}_{G} (u, v)

3-

{dist}_{H} (u, v)

4-

(2 t - 1)

5-

O (n^{1 + 1 / t})

6-

{dist}_{H} (u, v) \leq {dist}_{G} (u, v) + t

7-

O (n^{3 / 2})

8-

O (n^{7 / 5} poly (\log n))

9-

O (n^{4 / 3})

10-

O (n^{4 / 3 - ϵ})

Formulas (html):

Correct Categorie: cs

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/hep-ph/0603144

Formulas:

1-

π N \to η N

2-

π N \to η N

3-

π N \to η N

4-

N_{P} (N_{R})

5-

(\binom{Re W}{- 2 Im W})

6-

(\binom{Re W}{- 2 Im W})

7-

(\binom{Re W}{- 2 Im W})

8-

N_{P} + (N_{P} \times N_{C})

9-

Σ = γ^{T} Φ γ

10-

T = \sqrt{Im Φ} γ G γ^{T} \sqrt{Im Φ}

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: hep-lat

Result: incorrect

Paper: https://arxiv.org/abs/0811.2704

Formulas:

1-

⌊ 3 Δ^{*} / 2 ⌋

2-

⌈ 5 Δ^{*} / 3 ⌉

3-

(\frac{3}{2} + ε) Δ^{*}

4-

Δ^{*} \in {3, 4}

5-

d \in {2, 3}

6-

ℓ - 1 \leq D - 1

7-

d \in {4, 5}

8-

d \in {4, 5}

9-

v_{1}, \dots, v_{ℓ}

10-

v_{3}, \dots, v_{ℓ}

Formulas (html):

Correct Categorie: math

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1812.05240

Formulas:

1-

S U (3) \times S U (2) \times U (1)

2-

M_{G}, M, \tan β,

3-

M \equiv M_{V} = M_{S U S Y}

4-

\tan β = v_{u} / v_{d}

5-

α_{1} (M_{G})

6-

α_{2} (M_{G})

7-

α_{3} (M_{G}) \in [0.1, 0.3]

8-

y_{t} (M_{G})

9-

y_{b} (M_{G})

10-

y_{τ} (M_{G})

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: math

Result: incorrect

Paper: https://arxiv.org/abs/0806.3836

Formulas:

1-

E (B) = E_{0} + Γ B^{2}

2-

E (B) = E_{0} + Γ B^{2}

3-

E (B) - E_{0} = \frac{q^{2} ⟨ ρ^{2} ⟩}{8 μ} B^{2} \equiv Γ B^{2}

4-

Γ = 0.5 μ e V T^{- 2}

5-

1.3 μ e V T^{- 2}

6-

a_{B} = 4 π ϵ ϵ_{0} ℏ^{2} / (μ e^{2})

7-

E_{loc} = ℏ^{2} / [2 μ l_{c}^{2}]

8-

μ = 0.1 m_{0}

9-

σ / E_{loc} ≫ 1

10-

σ^{2} / [k_{B} T]

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1003.1402

Formulas:

1-

{\hat{E} (i)}

2-

\hat{1} = \sum_{i} \hat{E} (i)

3-

{\hat{C}}_{A B} = \frac{1}{2} \sum_{i} {({\hat{E}}_{A} (i) \otimes {\hat{1}}_{B} - {\hat{1}}_{A} \otimes {\hat{E}}_{B} (i))}^{2} .

4-

C_{A B} = Tr [{\hat{ρ}}_{A B} {\hat{C}}_{A B}]

5-

{\hat{E}}_{A} (i) \otimes {\hat{1}}_{B}

6-

{\hat{1}}_{A} \otimes {\hat{E}}_{B} (i)

7-

{\hat{E} (i)}

8-

{\hat{E} (i)}

9-

\hat{1} = \oint \hat{E} (ϕ) 𝑑 ν

10-

\hat{E} (ϕ) = | ϕ ⟩ ⟨ ϕ |

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: quant-ph

Result: correct

Run 11329983 (Agent787)