Run 6938508

Paper: https://arxiv.org/abs/0707.4650

Formulas:

1-

μ = m^{'} / (m_{0} + m^{'})

2-

Δ μ = 5 \times 10^{- 4}

3-

Δ e^{'} = 0.025

4-

a, λ - λ^{'}

5-

a, λ - λ^{'}

6-

1, 2, \dots, 7 m_{J}

7-

e^{'} = 0 - 0.30

8-

m = 100 m_{E}

9-

m = 1 m_{J}

10-

m^{'} = 1 m_{J}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/1503.05603

Formulas:

1-

[a, a^{†}] = [b, b^{†}] = 𝟙

2-

x_{c} = (a + a^{†}) / \sqrt{2}

3-

p_{c} = - i (a - a^{†}) / \sqrt{2}

4-

x_{m} = (b + b^{†}) / \sqrt{2}

5-

p_{m} = - i (b - b^{†}) / \sqrt{2}

6-

𝐫 = {(x_{c}, p_{c}, x_{m}, p_{m})}^{𝖳} .

7-

H = ω_{m} b^{†} b - Δ a^{†} a + g (a + a^{†}) (b + b^{†}),

8-

Δ = ω_{L} - ω_{c}

9-

\frac{d ϱ}{d t}

10-

= - i [H, ϱ] + κ 𝒟 [a] ϱ + Γ 𝒟 [b + b^{†}] ϱ,

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: quant-ph

Result: correct

Paper: https://arxiv.org/abs/1609.04123

Formulas:

1-

ℋ_{H} = \sum_{i j σ} t_{i j} d_{i σ}^{†} d_{j σ} + U \sum_{i} n_{i ↑}^{d} n_{i ↓}^{d},

2-

t_{i j} = - t

3-

d_{i σ}^{†}, d_{i σ}

4-

n_{i σ}^{d} = d_{i σ}^{†} d_{i σ}

5-

\begin{matrix} ℋ_{A} = \sum_{i j σ} t_{i j} c_{i σ}^{†} c_{j σ} + ϵ_{d} \sum_{i σ} d_{i σ}^{†} d_{i σ} \\ + V \sum_{i σ} (c_{i σ}^{†} d_{i σ} + d_{i σ}^{†} c_{i σ}) + U \sum_{i} n_{i ↑}^{d} n_{i ↓}^{d}, \end{matrix}

6-

c_{i σ}^{†}, c_{i σ}

7-

n = n_{s} + n_{d}

8-

n_{s} = \sum_{σ} ⟨ c_{i σ}^{†} c_{i σ} ⟩

9-

n_{d} = \sum_{σ} ⟨ d_{i σ}^{†} d_{i σ} ⟩

10-

| V | ≪ ϵ_{F} - ϵ_{d}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1204.5264

Formulas:

1-

ν_{H B O}

2-

ν_{H B O}

3-

ν_{H B O}

4-

ν_{H B O}

5-

ν_{H B O}

6-

ν_{H B O}

7-

ν_{H B O}

8-

k T_{i n}

9-

N_{d i s k}

10-

k T_{b b}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1310.8395

Formulas:

1-

n_{0} = N_{0} / (π h^{*})

2-

h^{*} = H_{0} / R_{0}

3-

U_{η} = F / (6 π η a)

4-

𝐝 = (d_{x}, d_{y}, d_{z})

5-

u_{k}^{*} = \frac{3}{4} a^{*} (\frac{d_{k}}{d^{2}} [\frac{2 l^{*}}{d} (1 - E) - E] + \frac{E}{d} δ_{k z}); k = x, y, z

6-

E = \exp (- (1 + \frac{d_{z}}{d}) \frac{d}{2 l^{*}}); a^{*} = a / R_{0}; l^{*} = η / (U_{η} ρ_{f} R_{0})

7-

τ_{η} = R_{0} / U_{η}

8-

ρ_{f} (𝐔_{η} \cdot 𝐠𝐫𝐚𝐝) 𝐮 = - 𝐠𝐫𝐚𝐝 p + η △ 𝐮

9-

\frac{d M_{k i}}{d t} = \sum_{j \neq i} u_{k}^{*} k = x, y, z i = 1, N_{0} j = 1, N_{0}

10-

M = (x, y, z)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1703.03601

Formulas:

1-

ℋ = - K V M_{z}^{2} - V M_{x} h \cos Φ (t) - V M_{y} h \sin Φ (t),

2-

ω (t) \equiv \dot{Φ} (t)

3-

| M | = μ_{s}

4-

\dot{𝐬} = γ 𝐬 \times 𝐇 - α γ 𝐬 \times (𝐬 \times 𝐇),

5-

𝐇 = - (1 / V) \partial ℋ / \partial 𝐌

6-

𝐇 = 2 d s_{z} 𝐞_{z} + h 𝐞_{x} + ω (t) 𝐞_{z},

7-

d = K M_{s}

8-

γ = 1.76 \times 10^{11} T S^{- 1}

9-

K = 2.2 \times 10^{5} J / m^{3}

10-

V = 14.1 \times 10^{- 27} m^{3}

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/quant-ph/0007056

Formulas:

1-

H_{1} = 2 κ J_{z}^{2},

2-

H_{2} = i κ (J_{+}^{2} - J_{-}^{2}) .

3-

H_{3} = 2 κ J_{z}^{2} + Ω J_{x} .

4-

ξ_{s} = \frac{\sqrt{2} ⟨ {(Δ J_{⊥})}_{m i n} ⟩}{J^{1 / 2}},

5-

⟨ {(Δ J_{⊥})}_{m i n} ⟩

6-

| J, m_{x} = - J ⟩

7-

2 κ J_{z}^{2}

8-

| J, m_{x} = - J ⟩

9-

| J, m_{x} = - J ⟩

10-

⟨ J_{y} ⟩ = ⟨ J_{y} ⟩ = 0

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/1408.4909

Formulas:

1-

^{2 +, / 3 +}

2-

P R := \frac{R_{d a r k} - R_{i l l u m}}{R_{i l l u m}} = \frac{R_{d a r k}}{R_{i l l u m}} - 1,

3-

R_{d a r k}

4-

R_{i l l u m}

5-

M R = \frac{R (B) - R (0)}{R (0)} = \frac{R (B)}{R (0)} - 1 .

6-

M R (B) \propto ℬ_{J}^{2} [g μ_{B} J B / (k_{B} T)] for T > T_{C},

7-

M R (B) \propto ℬ_{J} [g μ_{B} J B / (k_{B} T)] for T < T_{C},

8-

r_{M C} = {(\frac{3}{4 π} \frac{J}{J (M n^{3 +})})}^{1 / 3} \cdot c,

9-

J (M n^{3 +}) = 2

10-

J / J (M n^{3 +})

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/quant-ph/0509180

Formulas:

1-

q_{a} = \frac{1}{\sqrt{2}} (a^{†} + a), p_{a} = \frac{i}{\sqrt{2}} (a^{†} - a),

2-

𝝈 = (\begin{matrix} Δ q_{a}^{2} & Δ q_{a} p_{a} & Δ q_{a} q_{b} & Δ q_{a} p_{b} \\ Δ p_{a} q_{a} & Δ p_{a}^{2} & Δ p_{a} q_{b} & Δ p_{a} p_{b} \\ Δ q_{b} q_{a} & Δ q_{b} p_{a} & Δ q_{b}^{2} & Δ q_{b} p_{b} \\ Δ p_{b} q_{a} & Δ p_{b} p_{a} & Δ p_{b} q_{b} & Δ p_{b}^{2} \end{matrix}),

3-

Δ X^{2} = ⟨ X^{2} ⟩ - {⟨ X ⟩}^{2}

4-

Δ X Y = \frac{1}{2} ⟨ {[X, Y]}_{+} ⟩ - ⟨ X ⟩ ⟨ Y ⟩

5-

{[X, Y]}_{+} = X Y + Y X

6-

⟨ X ⟩ = Tr [R X]

7-

χ (λ_{1}, λ_{2}) = ⟨ D (λ_{1}) \otimes D (λ_{2}) ⟩

8-

D (λ) = \exp {λ a^{†} - λ^{*} a}

9-

χ (𝝀) = \exp {- \frac{1}{2} 𝝀^{T} 𝝈 𝝀 - i 𝝀^{T} 𝑿},

10-

𝝀 = {(Re [λ_{1}], Im [λ_{1}], Re [λ_{2}], Im [λ_{2}])}^{T}

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: quant-ph

Result: correct

Paper: https://arxiv.org/abs/1411.1494

Formulas:

1-

[\begin{matrix} E_{x}^{o}^{*} & E_{y}^{o}^{*} \\ E_{x}^{i} & E_{y}^{i} \end{matrix}] [\begin{matrix} T_{x x} \\ T_{y x} \end{matrix}] = [\begin{matrix} E_{x}^{i}^{*} \\ E_{x}^{o} \end{matrix}]

2-

i, j = x, y

3-

T_{x y} = T_{y x}

4-

T_{y y} = - \exp (2 i ∠ T_{y x}) T_{x x}^{*}

5-

𝐓 = 𝐕 [\begin{matrix} e^{i ϕ_{1}} & 0 \\ 0 & e^{i ϕ_{2}} \end{matrix}] 𝐕^{T} = 𝐑 (θ) 𝚫 𝐑 (- θ),

6-

𝐕^{T} = 𝐕^{- 1}

7-

\exp (i ϕ)

8-

T = 1 - \sqrt{{| t_{x} - e^{i ϕ_{x}} |}^{2} + {| t_{y} - e^{i ϕ_{y}} |}^{2}} .

9-

T_{x x} E_{x}^{i} + T_{y x} E_{y}^{i} = E_{x}^{o},

10-

T_{y x} E_{x}^{i} - \frac{T_{y x}}{T_{y x}^{*}} T_{x x}^{*} E_{y}^{i} = E_{y}^{o},

Formulas (html):

Correct Categorie: physics

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/1005.2548

Formulas:

1-

E_{u} / k = 4080

2-

J_{K_{- 1} K_{+ 1}} = 7_{07}

3-

E_{u} / k = 843

4-

E_{u} / k = 290

5-

λ / Δ λ = 200

6-

9 \overset{''}{.} 4 \times 9 \overset{''}{.} 4

7-

n = 4 \times 10^{6}

8-

n = 5 \times 10^{5}

9-

T_{R o t}

10-

T_{R o t} \sim 380

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1012.4646

Formulas:

1-

E = E_{kin} + E_{Coul} + E_{Sky},

2-

E_{Sky} = \int d^{3} 𝒓 ℰ_{Sky} (𝒓)

3-

ρ_{q} (𝒓, σ; 𝒓^{'}, σ^{'})

4-

σ, σ^{'} = 1, - 1

5-

ℰ_{Sky} (𝒓)

6-

ρ_{q} (𝒓) = \sum_{σ = \pm 1} ρ_{q} (𝒓, σ; 𝒓, σ),

7-

τ_{q} (𝒓) = \sum_{σ = \pm 1} \int d^{3} 𝒓^{'} δ (𝒓 - 𝒓^{'}) \nabla \cdot \nabla^{'} ρ_{q} (𝒓, σ; 𝒓^{'}, σ),

8-

𝒋_{𝒒} (𝒓) = - \frac{i}{2} \sum_{σ = \pm 1} \int d^{3} 𝒓^{'} δ (𝒓 - 𝒓^{'}) (\nabla - \nabla^{'}) ρ_{q} (𝒓, σ; 𝒓^{'}, σ),

9-

𝒔_{𝒒} (𝒓) = \sum_{σ, σ^{'} = \pm 1} ρ_{q} (𝒓, σ; 𝒓, σ^{'}) ⟨ σ^{'} | \hat{𝝈} | σ ⟩,

10-

T_{q μ} (𝒓) = \sum_{σ, σ^{'} = \pm 1} \int d^{3} 𝒓^{'} δ (𝒓 - 𝒓^{'}) \nabla \cdot \nabla^{'} ρ_{q} (𝒓, σ; 𝒓^{'}, σ^{'}) ⟨ σ^{'} | {\hat{σ}}_{μ} | σ ⟩,

Formulas (html):

Correct Categorie: nucl-th

Guessed Categorie: nucl-th

Result: correct

Paper: https://arxiv.org/abs/1808.07727

Formulas:

1-

Δ m_{a t m}

2-

Δ m_{s o l}

3-

S U {(2)}_{L}

4-

S U {(2)}_{L}

5-

SU {(2)}_{L}

6-

U {(1)}_{Y}

7-

U {(1)}_{L}

8-

ℒ = ℒ_{SM} + ℒ_{k i n} (N, N^{'}, η, ϕ) + ℒ_{ATM} + ℒ_{DM, SOL} - V (H, η, ϕ)

9-

ℒ_{k i n} (N, N^{'}, η, ϕ)

10-

- Y_{i}^{(0)} {\bar{L}}_{i} \tilde{H} N + Y^{N} ϕ \bar{N^{c}} N + h . c .

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: hep-ph

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0612556

Formulas:

1-

g (z) := {(z + 1)}^{2} ℓ (z)

2-

(z_{i}, Y_{i}, σ_{i})

3-

i = 1, \dots, n

4-

Y_{i} = \log_{10} g (z_{i})

5-

R (r, s) = [z_{r + 1}, z_{s}]

6-

T (r, s)

7-

z_{i} \in R (r, s)

8-

T = {sup}_{r, s} T (r, s)

9-

[z_{r + 1}, z_{s}], 0 \leq r \leq s - m \leq n - m

10-

[z_{r + 1}, z_{n}]

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: cs

Result: incorrect

Paper: https://arxiv.org/abs/1506.03789

Formulas:

1-

Q \equiv ρ / σ^{3}

2-

\frac{\partial f}{\partial t} + 𝐯 \cdot \frac{\partial f}{\partial 𝐱} + 𝐠 \cdot \frac{\partial f}{\partial 𝐯} = 0,

3-

ρ (𝐱, t) = \int d^{3} v f (𝐱, 𝐯, t) .

4-

G \int d^{3} x^{'} [ρ (𝐱^{'}, t) - {\bar{ρ}}_{0} (t)] \frac{𝐱 - 𝐱^{'}}{{| 𝐱 - 𝐱^{'} |}^{3}}

5-

G \int d^{3} x^{'} d^{3} v [f (𝐱^{'}, 𝐯, t) - {\bar{f}}_{0} (𝐯, t)] \frac{𝐱 - 𝐱^{'}}{{| 𝐱 - 𝐱^{'} |}^{3}} .

6-

δ (𝐯 - 𝐯_{0} (𝐱)) ρ (𝐱)

7-

f = f_{0} + f_{1}

8-

𝐠 = 𝐠_{0} + 𝐠_{1}

9-

\frac{\partial f_{1}}{\partial t} + 𝐯 \cdot \frac{\partial f_{1}}{\partial 𝐱} + 𝐠_{0} \cdot \frac{\partial f_{1}}{\partial 𝐯} = - 𝐠_{1} \cdot \frac{\partial f_{0}}{\partial 𝐯} - 𝐠_{1} \cdot \frac{\partial f_{1}}{\partial 𝐯}

10-

𝐠_{1} = G \int d^{3} x^{'} d^{3} v f_{1} (𝐱^{'}, 𝐯, t) \frac{(𝐱 - 𝐱^{'})}{{| 𝐱 - 𝐱^{'} |}^{3}}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1611.01316

Formulas:

1-

\frac{d σ_{DPS}}{d x_{1} d {\bar{x}}_{1} d x_{2} d {\bar{x}}_{2}}

2-

= \frac{1}{C} {\hat{σ}}_{i k \to A} {\hat{σ}}_{j l \to B} \int d^{2} 𝐲 F^{i j} (x_{1}, x_{2}, 𝐲) F^{k l} ({\bar{x}}_{1}, {\bar{x}}_{2}, 𝐲),

3-

{\hat{σ}}_{i j \to X}

4-

F^{i j} (x_{1}, x_{2}, 𝐲)

5-

F^{i j} (x_{1}, x_{2}, 𝐲)

6-

= \frac{1}{y^{2}} \frac{α_{s}}{2 π^{2}} \sum_{k} \frac{f_{k} (x_{1} + x_{2})}{x_{1} + x_{2}} T_{k \to i j} (\frac{x_{1}}{x_{1} + x_{2}})

7-

1 / (2 Q)

8-

\int d^{2} 𝐲 [Φ (ν y)] {}^{2}F^{i j} (x_{1}, x_{2}, 𝐲) F^{k l} ({\bar{x}}_{1}, {\bar{x}}_{2}, 𝐲),

9-

Φ (u) \to 0

10-

Φ (u) \to 1

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: hep-ph

Result: correct

Paper: https://arxiv.org/abs/1402.4152

Formulas:

1-

\frac{\partial ρ}{\partial t} + \nabla \cdot (ρ 𝐯) = 0

2-

ρ \frac{\partial 𝐯}{\partial t} + ρ (𝐯 \cdot \nabla) 𝐯 = - \nabla p + μ \nabla^{2} 𝐯 + (μ_{b} + \frac{1}{3} μ) \nabla (\nabla \cdot 𝐯),

3-

p = c_{0}^{2} ρ,

4-

= 𝐯_{0} + ε {\tilde{𝐯}}_{1} + ε^{2} {\tilde{𝐯}}_{2} + O (ε^{3}) + \dots,

5-

= p_{0} + ε {\tilde{p}}_{1} + ε^{2} {\tilde{p}}_{2} + O (ε^{3}) + \dots,

6-

= ρ_{0} + ε {\tilde{ρ}}_{1} + ε^{2} {\tilde{ρ}}_{2} + O (ε^{3}) + \dots,

7-

= ϵ {\tilde{𝐯}}_{1},

8-

= ϵ {\tilde{p}}_{1},

9-

= ϵ {\tilde{ρ}}_{1},

10-

= ϵ^{2} {\tilde{𝐯}}_{2},

Formulas (html):

Correct Categorie: physics

Guessed Categorie: physics

Result: correct

Paper: https://arxiv.org/abs/1308.2965

Formulas:

1-

\frac{d 𝐲}{d x} = 𝗔 (x) 𝐲

2-

x^{a} \leq x \leq x^{b}

3-

𝗕^{a} 𝐲 (x^{a}) = 𝟎, 𝗕^{b} 𝐲 (x^{b}) = 𝟎 .

4-

𝗔 \in ℂ^{n \times n}

5-

n_{b} \equiv n - n_{a}

6-

𝗕^{a} \in ℂ^{n_{a} \times n}

7-

𝗕^{b} \in ℂ^{n_{b} \times n}

8-

x^{a} \equiv x^{1} < x^{2} < \dots < x^{N - 1}, x^{N} \equiv x^{b} .

9-

x^{k} \leq x \leq x^{k + 1}

10-

k = 1, 2, \dots, N - 1

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: cs

Result: incorrect

Paper: https://arxiv.org/abs/0809.0383

Formulas:

1-

A N N s

2-

S V M s

3-

p n - Q R P A

4-

p n - Q R P A

5-

Q R P A

6-

C Q R P A

7-

p n - Q R P A

8-

R Q R P A

9-

A N N s

10-

S V M s

Formulas (html):

Correct Categorie: nucl-th

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/9907153

Formulas:

1-

k T = 7.4 \pm 0.3

2-

k T = 0.38 \pm 0.03

3-

k T = 5 - 10

4-

k T = 6 - 13

5-

k T = {0.36}_{- 0.06}^{+ 0.09}

6-

k T = 7.4 \pm 0.3

7-

k T \propto σ^{1.45}

8-

k T = 0.78 \pm 0.07

9-

k T = 0.27 - 0.41

10-

k T = 4.3 - 12.8

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1008.3752

Formulas:

1-

10^{- 4} - 10^{- 2}

2-

(p_{loss}, p_{u}) = (10^{- 3}, 10^{- 4})

3-

p_{s} = 1 / 2

4-

(p_{s}, p_{u}) = (0.9, 0.03 %)

5-

(0.95, 0.3 %)

6-

p_{s} < 1 / 2

7-

p_{s} < 1 / 2

8-

(p_{s}, p_{u}) = (0.9, 6.0 \times 10^{- 4})

9-

(0.5, 4.0 \times 10^{- 4})

10-

(0.1, 1.6 \times 10^{- 4})

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: hep-ph

Result: incorrect

Paper: https://arxiv.org/abs/1312.6796

Formulas:

1-

𝐫_{i} (t)

2-

i = 1, 2, 3

3-

𝐫_{i} (t) = 𝐫_{i} (t + n T)

4-

M = 2 N_{s}

5-

{\dot{x}}_{1} (0)

6-

{\dot{y}}_{1} (0)

7-

(x_{1}, y_{1})

8-

x_{1} (200)

9-

y_{1} (200)

10-

Δ t = 10^{- 5}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/0806.3070

Formulas:

1-

S O (2, 2)

2-

L_{0}, {\bar{L}}_{0}

3-

L_{0} = \frac{M l + J}{2},

4-

{\bar{L}}_{0} = \frac{M l - J}{2}

5-

I S O (d - 1, 1)

6-

I S O (2, 1)

7-

S O (2, 2)

8-

S O (2, 2) \equiv S L (2, ℝ) \times S L (2, ℝ) / ℤ_{2}

9-

S L (2, ℝ)

10-

S L (2, ℝ)

Formulas (html):

Correct Categorie: hep-th

Guessed Categorie: hep-th

Result: correct

Paper: https://arxiv.org/abs/hep-lat/9307004

Formulas:

1-

𝒪 (g^{7})

2-

\sqrt{σ} / Λ_{\bar{M S}}^{n_{f} = 0}

3-

2.2 (\pm 0.1)

4-

s = e x p [\int_{g (β)}^{g (β - Δ β)} \frac{d g}{β_{f} (g)}] = \frac{f (\frac{1}{g {(β - Δ β)}^{2}})}{f (\frac{1}{g {(β)}^{2}})}

5-

f (1 / g^{2}) = a Λ

6-

β_{f} (g)

7-

1 / g^{2} = β / 6

8-

q = 0.0, 0.02, 0.04

9-

1 / g_{\bar{M S}} {(π / a)}^{2} = < U_{p l a q} > / g^{2} + 0.025

10-

< U_{p l a q} >

Formulas (html):

Correct Categorie: hep-lat

Guessed Categorie: hep-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0611260

Formulas:

1-

Γ m_{p} c^{2}

2-

ω_{B} = e B / m_{e} c

3-

\frac{\partial N}{\partial t} + div (\dot{γ} N) = f (γ),

4-

N (γ) = - \frac{1}{\dot{γ}} \int_{γ}^{\infty} f (γ^{'}) 𝑑 γ^{'} .

5-

ν F_{ν} \propto \frac{d F}{d \ln γ} \propto η γ \int_{γ}^{\infty} f (γ^{'}) 𝑑 γ^{'},

6-

f (γ) \propto γ^{- 2.2}

7-

f (γ) \propto γ^{- 2.2}

8-

ν F_{ν} \propto ν^{- 0.1}

9-

γ \sim m_{p} / m_{e}

10-

ε_{peak} \sim Γ_{b} {(\frac{m_{p}}{m_{e}})}^{2} \frac{ℏ e B}{m_{e} c},

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1204.1202

Formulas:

1-

(k - 1) d + 1

2-

(r + 1) (k - 1) d + 1

3-

(k - 1) (d + 1) + 1

4-

A_{1}, A_{2}, \dots, A_{k}

5-

(k - 1) (d + 1) + 1

6-

F_{1}, F_{2}, \dots, F_{d + 1}

7-

A_{1}, A_{2}, \dots, A_{k}

8-

t = t (k, d)

9-

F_{1}, F_{2}, \dots, F_{d + 1}

10-

t (k, d) \leq 2 k - 2

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/hep-ph/9405287

Formulas:

1-

Π_{N} (q)

2-

Π_{N} (q) \equiv i \int d^{4} x e^{i q \cdot x} ⟨ vac | T η_{N} (x) {\bar{η}}_{N} (0) | vac ⟩,

3-

η_{p} = ϵ_{a b c} (u_{a}^{T} C γ_{μ} u_{b}) γ_{5} γ^{μ} d_{c},

4-

Π_{N} (q)

5-

Π_{N} (q) \equiv Π_{1} (q^{2}) 𝟙 + Π_{𝕢} (𝕢^{𝟚}) / 𝕢,

6-

Π_{i} (s)

7-

i = {1, q}

8-

\int_{0}^{R} 𝑑 s W_{i} (s) Δ Π_{i} (s) \overset{R \to \infty}{=} - \int_{| s | = R} 𝑑 s W_{i} (s) Π_{i}^{OPE} (s),

9-

W_{i} (s)

10-

Δ Π_{i} (s) \equiv lim_{ϵ \to 0^{+}} Π_{i} (s + i ϵ) - Π_{i} (s - i ϵ) .

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: hep-lat

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/0403174

Formulas:

1-

1 \cdot 10^{- 10} mbar

2-

1 - 1.5 {mV}_{RMS}

3-

\frac{d I}{d V} \sim \frac{{(q + \tilde{ϵ})}^{2}}{1 + {\tilde{ϵ}}^{2}},

4-

\tilde{ϵ} = \frac{ω - ϵ_{K}}{Γ}

5-

k_{B} T_{K} \sim \sqrt{\frac{Δ \cdot U}{2}} e^{- \frac{π}{2 Δ \cdot U} | ϵ_{d} + U | \cdot | ϵ_{d} |} .

6-

ϵ_{d} = - \frac{U}{2}

7-

ϵ_{d} > - \frac{U}{2}

8-

ϵ_{d} < - \frac{U}{2}

9-

ϵ_{d} < - \frac{U}{2}

10-

n_{d} = - \frac{ϵ_{d}}{U} + \frac{1}{2}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/cond-mat/9811012

Formulas:

1-

T \leq 0.65 T_{0}

2-

v (𝒓 - 𝒓^{'}) = g δ (𝒓 - 𝒓^{'})

3-

g = 4 π ℏ^{2} a / m

4-

\hat{ψ} (𝒓, t)

5-

\hat{ψ} (𝒓, t) = Φ (𝒓) + \tilde{ψ} (𝒓, t)

6-

\tilde{ψ} (𝒓, t)

7-

i \frac{\partial \hat{ψ} (𝒓, t)}{\partial t} = (- \frac{\nabla^{2}}{2 m} + U_{trap} (𝒓) - μ) \hat{ψ} (𝒓, t) + g {\hat{ψ}}^{†} (𝒓, t) \hat{ψ} (𝒓, t) \hat{ψ} (𝒓, t)

8-

U_{trap} (𝒓) = m (ω_{ρ}^{2} ρ^{2} + ω_{z}^{2} z^{2}) / 2

9-

{\tilde{ψ}}^{†} (𝒓, t) \tilde{ψ} (𝒓, t) \tilde{ψ} (𝒓, t)

10-

2 ⟨ {\tilde{ψ}}^{†} (𝒓, t) \tilde{ψ} (𝒓, t) ⟩ \tilde{ψ} (𝒓, t)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/2009.04162

Formulas:

1-

H_{int} = G ({\hat{a}}_{i}^{†} {\hat{a}}_{o} \hat{m} + {\hat{a}}_{i} {\hat{a}}_{o}^{†} \hat{m})

2-

G = - i θ_{f} \frac{c}{n} \sqrt{\frac{4 g μ_{B}}{M_{s}}} \sqrt{\frac{η_{mag} η_{opt}}{V_{opt}}} .

3-

V_{i} \approx V_{o} = V_{opt} = \int {| 𝐮_{i, o} (𝐫) |}^{2}

4-

𝐮_{i, o} (𝐫)

5-

\max ({| 𝐮_{i, o} (𝐫) |}^{2}) = 1

6-

η_{mag} = V_{int} / V_{mag}

7-

η_{opt} = V_{int} / V_{opt}

8-

V_{int} = \int 𝑑 𝐫 𝐮_{m} (𝐫) \cdot [𝐮_{i}^{*} (𝐫) \times 𝐮_{o} (𝐫)] .

9-

\max ({| 𝐮_{m} (𝐫) |}^{2}) = 1

10-

Δ ω_{fsr} / 2 π \approx 6.7

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1111.1621

Formulas:

1-

T_{2} = 2 T_{1}

2-

2 ℏ / T_{2} = ℏ / T_{1}

3-

g^{(1)} (τ)

4-

g^{(2)} (τ)

5-

δ = E_{L} - E_{X}

6-

[1 \bar{1} 0]

7-

δ = E_{L} - E_{X} = - 74 μ e V

8-

2 ℏ / T_{2}

9-

g^{(1)} (τ)

10-

g^{(1)} (τ)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1910.09299

Formulas:

1-

T_{c d} = 15

2-

Ω_{c d} = 10^{- 14}

3-

M_{0, ⋆} = 0.02 M_{⊙}

4-

R_{⋆} = 3 R_{⊙}

5-

M_{t o t} = 1 M_{⊙}

6-

α_{a c t i v e} = 10^{- 2}

7-

α_{d e a d} = 10^{- 5}

8-

M_{t o t} = M_{⊙}

9-

{\dot{M}}_{in} = 5 \times 10^{- 6} M_{⊙} \cdot a^{- 1}

10-

\frac{\partial Σ_{p}}{\partial t} + \frac{1}{R} \frac{\partial}{\partial R} [R (Σ_{p} v_{R} - D_{R} Σ \frac{\partial}{\partial R} (\frac{Σ_{p}}{Σ}))] = {\dot{Σ}}_{p}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/0907.1507

Formulas:

1-

(M, J, g)

2-

J^{2} x = - x, g (J x, J y) = - g (x, y),

3-

\tilde{g} (x, y) = g (x, J y)

4-

F (x, y, z) = g ((\nabla_{x} J) y, z) .

5-

F (x, y, z) = F (x, z, y) = F (x, J y, J z), F (x, J y, z) = - F (x, y, J z) .

6-

𝒲_{1} \oplus 𝒲_{2} \oplus 𝒲_{3}

7-

F (x, y, z) = 0

8-

𝒲_{1} \oplus 𝒲_{2} \oplus 𝒲_{3}

9-

\underset{x, y, z}{𝔖} F (x, y, z) = 0,

10-

\underset{x, y, z}{𝔖}

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/quant-ph/9506015

Formulas:

1-

y^{^{'}} = a (z) y^{- 1} + b (z) y

2-

y^{^{'}} = \frac{d y}{d z}

3-

a (z) = z (1 + 2 π f z)

4-

b (z) = 1 / F =

5-

f \approx 2 π F

6-

d i v 𝐀 (𝐱, t) = 0 .

7-

𝐀 (𝐱, t) = \int [𝐚 (𝐤, t) \cos (𝐤, 𝐱) + 𝐛 (𝐤, t) \sin (𝐤, 𝐱)] 𝑑 𝐤 .

8-

𝐤 \cdot 𝐚 = 𝐤 \cdot 𝐛 = 0 .

9-

𝐥_{1} (𝐤)

10-

𝐥_{2} (𝐤)

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/1906.03449

Formulas:

1-

[- L, 0]

2-

Δ t = L / N

3-

= \frac{1}{\sqrt{N}} \sum_{n = 0}^{N - 1} B_{n} e^{- i ω_{k} n Δ t},

4-

= \frac{1}{\sqrt{N}} \sum_{k = 0}^{N - 1} b_{k} e^{i ω_{k} n Δ t},

5-

ω_{k} = 2 π k / L

6-

- n Δ t

7-

- (n + 1) Δ t

8-

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

9-

H_{E} = \sum_{k = 0}^{N - 1} ω_{k} b_{k}^{†} b_{k}

10-

H_{I} = \sum_{k = 0}^{N - 1} (κ_{k} a^{†} b_{k} + κ_{k}^{*} b_{k}^{†} a),

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: quant-ph

Result: correct

Paper: https://arxiv.org/abs/1409.7497

Formulas:

1-

k_{1}, k_{2} \in

2-

U = k_{1} A k_{2}

3-

\frac{d ρ_{Q P}}{d t} = - i [H_{Q P}, ρ_{Q P}] + ℒ_{S} (ρ_{Q P}),

4-

H_{Q P} = H_{Q} + \sum_{i = 1}^{n_{P}} H_{P}^{(i)} + \sum_{i = 1}^{n_{P}} H_{i n t}^{(i)},

5-

E_{n} = n ω_{Q} + β n (n + 1) / 2

6-

H_{P}^{(i)} = ω_{i} σ_{i}^{z}

7-

H_{i n t}^{(i)} = \frac{S^{(i)}}{2} (a σ_{i}^{+} + a^{†} σ_{i}^{-}),

8-

ℒ_{S} (ρ) = \sum_{k} (A_{k} ρ A_{k}^{†} - \frac{1}{2} {[A_{k}^{†} A_{k}, ρ]}_{+}),

9-

A_{n} = \sqrt{n / T_{1}} | n - 1 ⟩ ⟨ n |

10-

A_{i} = \sqrt{1 / T_{1}^{(i)}} σ_{i}^{-}

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: quant-ph

Result: correct

Paper: https://arxiv.org/abs/1708.01471

Formulas:

1-

z = MLB (x, y) = (U^{T} x) \circ (V^{T} y)

2-

U \in ℝ^{m \times o}

3-

V \in ℝ^{n \times o}

4-

t a n h

5-

z_{i} = x^{T} W_{i} y

6-

W_{i} \in ℝ^{m \times n}

7-

W = [W_{i}, \dots, W_{o}] \in ℝ^{m \times n \times o}

8-

\begin{matrix} z_{i} & = & x^{T} U_{i} V_{i}^{T} y = \sum_{d = 1}^{k} x^{T} u_{d} v_{d}^{T} y \\ = & 𝟙^{T} (U_{i}^{T} x \circ V_{i}^{T} y) \end{matrix}

9-

U_{i} = [u_{1}, \dots, u_{k}] \in ℝ^{m \times k}

10-

V_{i} = [v_{1}, \dots, v_{k}] \in ℝ^{n \times k}

Formulas (html):

Correct Categorie: cs

Guessed Categorie: cs

Result: correct

Paper: https://arxiv.org/abs/1002.2188

Formulas:

1-

{(\vec{𝒆}, 𝒆^{'} \vec{𝒑})}^{𝟑}

2-

{(\vec{e}, e^{'} \vec{p})}^{3}

3-

(\vec{e}, e^{'} \vec{p})

4-

P_{x}^{'} / P_{z}^{'}

5-

P_{x}^{'} / P_{z}^{'}

6-

P_{x}^{'} / P_{z}^{'}

7-

{(\vec{e}, e^{'} \vec{p})}^{3}

8-

(\vec{e}, e^{'} \vec{p})

9-

P_{x}^{'} / P_{z}^{'}

10-

{(\vec{e}, e^{'} \vec{p})}^{3}

Formulas (html):

Correct Categorie: nucl-ex

Guessed Categorie: nucl-th

Result: incorrect

Paper: https://arxiv.org/abs/1902.07059

Formulas:

1-

ℰ_{p} ℓ_{p} = 1 / 2

2-

2 ℓ_{p} m_{p} = 1

3-

Δ x Δ p \geq \frac{1}{2},

4-

Δ x Δ p

5-

\frac{1}{2} (1 + 4 β ℓ_{p}^{2} Δ p^{2})

6-

[1 + β {(\frac{Δ p}{m_{p}})}^{2}],

7-

⟨ \hat{p} ⟩ = 0

8-

[\hat{x}, \hat{p}] = i [1 + β {(\frac{\hat{p}}{m_{p}})}^{2}],

9-

Δ x Δ p \geq (1 / 2) | ⟨ [\hat{x}, \hat{p}] ⟩ |

10-

T_{U} = \frac{a}{2 π k_{B}},

Formulas (html):

Correct Categorie: hep-th

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/0707.0943

Formulas:

1-

{}^{1}S_{0} \to^{3} S_{1}

2-

{}^{1}D_{2} \to^{3} S_{1}

3-

{}^{1}D_{2} \to^{3} S_{1}

4-

p p \to d π^{+}

5-

π^{+} d \to p p

6-

π^{+} d \to p p

7-

π^{+} d \to p p

8-

(σ (π^{-} d) - σ (π - p)) / σ (π^{-} p) \approx 3

9-

π^{-} {}^{12}C \to π^{-} n^{11} C

10-

{}^{12}C π^{-} \to π^{-} n^{11} C

Formulas (html):

Correct Categorie: nucl-th

Guessed Categorie: nucl-th

Result: correct

Paper: https://arxiv.org/abs/0707.0176

Formulas:

1-

{⟨ n_{B} ⟩}_{F} = a + b n_{F}, b \equiv D_{F B}^{2} / D_{F F}^{2},

2-

D_{F B}^{2} \equiv ⟨ n_{F} n_{B} ⟩ - ⟨ n_{F} ⟩ ⟨ n_{B} ⟩ = \frac{⟨ n_{F} ⟩ ⟨ n_{B} ⟩}{K},

3-

D_{F F}^{2} \equiv ⟨ n_{F}^{2} ⟩ - {⟨ n_{F} ⟩}^{2} = \frac{{⟨ n_{F} ⟩}^{2}}{K} + ⟨ n_{F} ⟩,

4-

b = \frac{⟨ n_{B} ⟩ / ⟨ n_{F} ⟩}{1 + K / ⟨ n_{F} ⟩} .

5-

b = A {[1 + B]}^{- 1}

6-

b = \frac{x}{1 + K^{'} x},

7-

K^{'} \equiv K / ⟨ n_{B} ⟩

8-

x \equiv ⟨ n_{B} ⟩ / ⟨ n_{F} ⟩

9-

x \to 1, b \to \frac{1}{1 + K^{'}}; x \to \infty, b \to \frac{1}{K^{'}} .

10-

K^{'} \sim a^{1 / 2} A^{- 1 / 6} e^{λ Y},

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: hep-ph

Result: correct

Paper: https://arxiv.org/abs/1409.5447

Formulas:

1-

ϕ = 90^{\circ} - ξ

2-

θ_{BH} = 68_{- 20}^{+ 5}

3-

θ_{BH} = 60 \pm 15

4-

ϕ_{BH} = 142_{- 17}^{+ 15}

5-

ϕ_{BH} = 160_{- 86}^{+ 15}

6-

θ_{CW} = 54 \pm 3.2

7-

ϕ_{CW} = 256 \pm 3.2

8-

θ_{G2} = 59 \pm 3

9-

ϕ_{G2} = 304 \pm 11

10-

\sim 10^{4} M_{⊙}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1602.01316

Formulas:

1-

{(\frac{σ_{A}}{A})}^{2} = (f^{2} + (F a n o)) / n_{p r i m a r y} + σ_{i n s t r u m e n t a l}^{2}

2-

n_{p r i m a r y}

3-

σ_{N}^{2} = \bar{N^{2}} - {\bar{N}}^{2}

4-

f = σ_{N} / \bar{N}

5-

E_{d r i f t}

6-

f_{a l l}

7-

f_{α} = \sqrt{\bar{α^{2}} - {\bar{α}}^{2}} / \bar{α} = σ_{α} / \bar{α}

8-

(α * α) (k) = \sum_{m = 0}^{k} α (m) α (k - m)

9-

{(α)}^{l, *} (k)

10-

{(α)}^{(l + 1), *} (k) = \sum_{m = 0}^{k} (α^{l, *}) (m) α (k - m)

Formulas (html):

Correct Categorie: physics

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1603.04638

Formulas:

1-

𝐤 \cdot 𝐕_{A} ≲ Ω

2-

k_{y}^{2} / k_{z}^{2} < 0.015

3-

k_{z}^{2} > k_{y}^{2}

4-

\frac{\partial ρ}{\partial t} + 𝐯 \cdot \nabla ρ

5-

- ρ \nabla \cdot 𝐯,

6-

ρ (\frac{\partial 𝐯}{\partial t} + 𝐯 \cdot \nabla 𝐯)

7-

- \nabla (p + \frac{B^{2}}{2}) + 𝐁 \cdot \nabla 𝐁 - 2 ρ 𝛀 \times 𝐯 - 2 ρ Ω x v_{y 0}^{'} {\hat{𝐞}}_{x},

8-

\frac{\partial 𝐁}{\partial t}

9-

\nabla \times (𝐯 \times 𝐁),

10-

\frac{\partial p}{\partial t} + 𝐯 \cdot \nabla p

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0607434

Formulas:

1-

- 22.3 < M_{B} < - 17.3

2-

15 \times 15 μ m^{2}

3-

χ_{p}^{2} = χ^{2} (1 + λ^{2} \cdot D^{2}) .

4-

h_{3 i n}

5-

h_{4 i n}

6-

0 < σ_{in} < 250

7-

h_{3 o u t}

8-

h_{4 o u t}

9-

h_{3 i n} = - 0.07

10-

h_{4 i n} = 0.09

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1710.00038

Formulas:

1-

= i ω 𝐁,

2-

= - i ω 𝐃 + 𝐉_{free} .

3-

\exp (- i ω t)

4-

μ_{0}^{- 1} \nabla \times 𝐁

5-

= - i ω ϵ 𝐄 .

6-

\nabla \cdot ϵ_{0} 𝐄

7-

μ_{0}^{- 1} \nabla \times 𝐁

8-

= - i ω ϵ_{0} 𝐄 + 𝐉,

9-

ϵ 𝐄 = ϵ_{0} 𝐄 + 𝐏

10-

= - i ω 𝐏,

Formulas (html):

Correct Categorie: physics

Guessed Categorie: physics

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0308177

Formulas:

1-

M_{B, gal} = - 21.5

2-

M_{B, gal} = - 23.0

3-

M_{B, gal} = - 21.2

4-

1 \overset{''}{.} 1

5-

1 \overset{''}{.} 7

6-

I (r) = I_{0} \exp [- 1.68 \frac{r}{r_{0}}]

7-

I (r) = I_{0} \exp [- 7.67 {(\frac{r}{r_{0}})}^{\frac{1}{4}}]

8-

1 \overset{''}{.} 4 \pm 0 \overset{''}{.} 3

9-

Δ B_{err, gal}

10-

Δ B_{err, gal}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0410679

Formulas:

1-

h ν + H_{2} O \to H + O H

2-

h ν + O H \to H + O

3-

{\dot{N}}_{H_{2} O}

4-

{\dot{N}}_{H_{2} O} = \frac{L_{*} a}{4 π R^{2} Δ E}

5-

R_{o u t}

6-

R_{o u t}

7-

n_{H_{2} O} (r)

8-

\frac{1}{r^{2}} \frac{\partial (n_{H_{2} O} r^{2} v_{O})}{\partial r} = - J_{H_{2} O} n_{H_{2} O}

9-

J_{H_{2} O} (R)

10-

n_{H_{2} O} (r) = \frac{{\dot{N}}_{H_{2} O}}{4 π r^{2} v_{O}} e^{- r / r_{H_{2} O}}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/gr-qc/0311037

Formulas:

1-

({35.68}^{\circ} N, {139.54}^{\circ} E)

2-

5 \times 10^{- 21} / \sqrt{Hz}

3-

3 \times 10^{- 21} / \sqrt{Hz}

4-

S_{n} (f)

5-

h (t) = 𝒜 [h_{c} (t - t_{c}) \cos ϕ_{0} + h_{s} (t - t_{c}) \sin ϕ_{0}],

6-

h_{c} (t)

7-

h_{s} (t)

8-

ℳ (\equiv M η^{3 / 5})

9-

(M = m_{1} + m_{2})

10-

η (\equiv m_{1} m_{2} / M^{2})

Formulas (html):

Correct Categorie: gr-qc

Guessed Categorie: hep-ph

Result: incorrect

Paper: https://arxiv.org/abs/1604.04651

Formulas:

1-

L e f t

2-

R i g h t

3-

B o t t o m

4-

L e f t

5-

R i g h t

6-

L e f t

7-

R i g h t

8-

L e f t

9-

R i g h t

10-

H e r s c h e l

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Run 6938508 (Agent767)