Run 11314760

Paper: https://arxiv.org/abs/1303.3688

Formulas:

1-

J_{eff} = 1 / 2

2-

J_{eff} = 1 / 2

3-

J_{eff} = 3 / 2

4-

J_{eff} = 1 / 2

5-

J_{eff} = 1 / 2

6-

\Pr_{x} {Ca}_{1 - x} {Fe}_{2} {As}_{2}

7-

J_{eff} = 3 / 2

8-

J_{eff} = 1 / 2

9-

J_{eff} = 1 / 2

10-

{Sr}_{3} {Ir}_{2} O_{7}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/0912.4046

Formulas:

1-

q / p \geq 2 g (K) - 1

2-

\hat{H F} (Y) and \hat{H F K} (Y, K)

3-

\hat{H F K} (K)

4-

rk \hat{H F} (Y) \geq | H_{1} (Y, ℤ) | .

5-

S_{n}^{3} (K)

6-

Δ_{K} (t)

7-

K_{- p, - q} = - K_{p, q}

8-

K_{1, q} = K

9-

q / p \geq 2 g (K) - 1

10-

q / p \geq 2 g (K) - 1

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/cond-mat/0503405

Formulas:

1-

\exp (ⅈ k r)

2-

⟨ ψ_{f i n a l} | 𝐩 | ψ_{i n i t i a l} ⟩ .

3-

⟨ even | odd | even ⟩ = 0 .

4-

d_{y^{2} - z^{2}}

5-

d_{y^{2} - z^{2}}

6-

⟨ α^{'} d_{y z} + β^{'} p_{y} | y | α d_{y^{2} - z^{2}} + β p_{z} ⟩ \neq 0,

7-

⟨ α^{'} d_{y z} + β^{'} p_{y} | x | α d_{y^{2} - z^{2}} + β p_{z} ⟩ = 0 .

8-

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

9-

⟨ d_{x z} | z | p_{x} ⟩ ⟨ p_{x} | y | d_{x y} ⟩ \neq 0 .

10-

k_{1} = - k_{2}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1901.10369

Formulas:

1-

SWAP = (\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 \end{matrix})

2-

ψ_{1} \otimes ψ_{2} \overset{SWAP}{\to} ψ_{2} \otimes ψ_{1}

3-

U_{RBS} (θ, ϕ) = (\begin{matrix} s i n (θ / 2) & c o s (θ / 2) \\ e^{i ϕ} c o s (θ / 2) & - e^{i ϕ} s i n (θ / 2) \end{matrix})

4-

α | 00 ⟩ + β | 01 ⟩ + γ | 10 ⟩ + δ | 11 ⟩

5-

{| α |}^{2} + {| β |}^{2} + {| γ |}^{2} + {| δ |}^{2} = 1

6-

(α a_{1}^{†} a_{3}^{†} + β a_{1}^{†} a_{4}^{†} + γ a_{2}^{†} a_{3}^{†} + δ a_{2}^{†} a_{4}^{†}) | 0 ⟩

7-

(α a_{1}^{†} a_{2}^{†} + β a_{1}^{†} a_{4}^{†} + γ a_{2}^{†} a_{3}^{†} + δ a_{3}^{†} a_{4}^{†}) | 0 ⟩

8-

(α a_{1}^{†} a_{2}^{†} + β a_{2}^{†} a_{3}^{†} + γ a_{1}^{†} a_{4}^{†} + δ a_{3}^{†} a_{4}^{†}) | 0 ⟩

9-

(α a_{1}^{†} a_{3}^{†} + β a_{2}^{†} a_{3}^{†} + γ a_{1}^{†} a_{4}^{†} + δ a_{2}^{†} a_{4}^{†}) | 0 ⟩

10-

α | 00 ⟩ + β | 10 ⟩ + γ | 01 ⟩ + δ | 11 ⟩

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: quant-ph

Result: correct

Paper: https://arxiv.org/abs/1804.11110

Formulas:

1-

[X_{i}, X_{j}] = i ℏ θ_{i j},

2-

[X_{i}, P_{j}] = i ℏ (δ_{i j} + γ_{i j}),

3-

[P_{i}, P_{j}] = i ℏ η_{i j} .

4-

γ_{i j} = \sum_{k} θ_{i k} η_{j k} / 4

5-

θ_{i j} = \frac{c_{θ} l_{P}^{2}}{ℏ} \sum_{k} ε_{i j k} {\tilde{a}}_{k},

6-

η_{i j} = \frac{c_{η} ℏ}{l_{P}^{2}} \sum_{k} ε_{i j k} {\tilde{p}}_{k}^{b} .

7-

[X_{i}, X_{j}] = i c_{θ} l_{P}^{2} \sum_{k} ε_{i j k} {\tilde{a}}_{k},

8-

[X_{i}, P_{j}] = i ℏ (δ_{i j} + \frac{c_{θ} c_{η}}{4} (\tilde{𝐚} \cdot {\tilde{𝐩}}^{𝐛}) δ_{i j} - \frac{c_{θ} c_{η}}{4} {\tilde{a}}_{j} {\tilde{p}}_{i}^{b}),

9-

[P_{i}, P_{j}] = \frac{c_{η} ℏ^{2}}{l_{P}^{2}} \sum_{k} ε_{i j k} {\tilde{p}}_{k}^{b} .

10-

H_{o s c}^{a} = ℏ ω_{o s c} (\frac{{({\tilde{p}}^{a})}^{2}}{2} + \frac{{\tilde{a}}^{2}}{2}),

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: quant-ph

Result: correct

Paper: https://arxiv.org/abs/1006.2872

Formulas:

1-

H = \frac{p^{2}}{2 m^{*}} - μ + α ({\hat{σ}}_{x} p_{y} - {\hat{σ}}_{y} p_{x}) + β ({\hat{σ}}_{x} p_{x} - {\hat{σ}}_{y} p_{y}),

2-

E_{p}^{\pm} = p^{2} / 2 m - μ \pm Δ_{p}

3-

Δ_{p} = \sqrt{(α^{2} + β^{2}) p^{2} + 4 α β p_{x} p_{y}}

4-

ϕ_{+} = \tan^{- 1} (- \frac{α p_{x} + β p_{y}}{β p_{x} + α p_{y}})

5-

ϕ_{-} = ϕ_{+} + π

6-

(x^{'}, y^{'})

7-

⟨ x, y, t | x^{'}, y^{'}, 0 ⟩

8-

ψ (L, y, t) = \int_{- \frac{d}{2}}^{\frac{d}{2}} 𝑑 y^{'} ⟨ L, y, t | 0, y^{'}, 0 ⟩ ϕ (0, y^{'}, 0),

9-

ϕ (x^{'}, y^{'}, 0)

10-

ϕ (x^{'}, y^{'}, 0)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/0901.4415

Formulas:

1-

\begin{matrix} H = & \sum_{𝐤, τ, σ} ϵ_{𝐤} c_{𝐤 τ σ}^{†} c_{𝐤 τ σ} + U \sum_{i, τ} n_{i τ ↑} n_{i τ ↓} \\ + U^{'} \sum_{i} n_{i 1} n_{i 2} + J \sum_{i, σ, σ^{'}} c_{i 1 σ}^{†} c_{i 2 σ^{'}}^{†} c_{i 1 σ^{'}} c_{i 2 σ} \\ + J^{'} \sum_{i, τ \neq τ^{'}} c_{i τ ↑}^{†} c_{i τ ↓}^{†} c_{i τ^{'} ↓} c_{i τ^{'} ↑}, \end{matrix}

2-

c_{i τ σ}

3-

c_{𝐤 τ σ}

4-

n_{i τ σ} = c_{i τ σ}^{†} c_{i τ σ}

5-

n_{i τ} = \sum_{σ} n_{i τ σ}

6-

U = U^{'} + J + J^{'}

7-

ϵ_{𝐤} = 2 t (\cos k_{x} + \cos k_{y})

8-

| Ψ ⟩ = P_{G} | Φ ⟩ = \prod_{i γ} [1 - (1 - g_{γ}) | i γ ⟩ ⟨ i γ |] | Φ ⟩,

9-

| i γ ⟩ ⟨ i γ |

10-

| Φ ⟩ = \prod_{𝐤 a τ σ} b_{𝐤 τ σ}^{(a), †} | 0 ⟩,

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1607.00875

Formulas:

1-

(n + 1) -

2-

L^{(1)} (p_{1}, p_{2}, \dots, p_{N}) = \int_{ℓ} \prod_{i = 1}^{N} G_{F} (q_{i}),

3-

G_{F} (q_{i}) = 1 / (q_{i}^{2} - m_{i}^{2} + i 0)

4-

\int_{ℓ} = - i \int d^{d} ℓ / {(2 π)}^{d}

5-

L^{(1)} (p_{1}, p_{2}, \dots, p_{N}) =

6-

\tilde{δ} (q_{i}) = 2 π i δ_{+} (q_{i}^{2} - m_{i}^{2})

7-

1.01359 (23) \times 10^{- 15}

8-

+ i 2.68657 (26) \times 10^{- 15}

9-

1.01345 (130) \times 10^{- 15}

10-

+ i 2.68633 (130) \times 10^{- 15}

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: hep-ph

Result: correct

Paper: https://arxiv.org/abs/gr-qc/0701148

Formulas:

1-

z (t) = x (t) + i y (t)

2-

y (t) = \frac{1}{π} P \int_{- \infty}^{\infty} \frac{x (t^{'})}{t - t^{'}} 𝑑 t^{'}

3-

a (t) = | z (t) |

4-

θ (t) = \arg z (t)

5-

ω (t) = d θ (t) / d t

6-

f = \frac{1}{8 π} {(\frac{G M_{t}}{c^{3}})}^{- \frac{5}{8}} {(\frac{μ}{M_{t}} (t_{0} - t))}^{- \frac{3}{8}}

7-

μ = m_{1} m_{2} / (m_{1} + m_{2})

8-

Δ t Δ f \sim 1

9-

Δ f / f \sim 2 \sqrt{δ t / 5 m s e c} / SN

10-

δ t < 20 m s e c

Formulas (html):

Correct Categorie: gr-qc

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1909.07566

Formulas:

1-

S S I M (l, r) = \frac{(2 μ_{l} μ_{r} + C_{1}) (2 σ_{l r} + C_{2})}{(μ_{l}^{2} + μ_{r}^{2} + C_{1}) (σ_{l}^{2} + σ_{r}^{2} + C_{2})},

2-

i_{l} = [\begin{matrix} 0 & \dots & w \\ ⋮ & ⋱ \\ 0 & \dots & w \end{matrix}] .

3-

x_{l} = i_{l} + e_{l},

4-

x_{r} = x_{l} - d_{g} .

5-

i_{r} = \frac{(x_{r} - e_{r})}{w_{b}} w,

6-

d_{l} = i_{l} - i_{r} .

7-

D = \frac{f_{u} b}{d_{g}^{*}} .

8-

x = \frac{(u - c_{u}) z}{f_{u}}, y = \frac{(v - c_{v}) z}{f_{v}}, z = D (u, v),

9-

(c_{u}, c_{v})

10-

A P_{B E V}

Formulas (html):

Correct Categorie: cs

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/hep-ph/0607074

Formulas:

1-

M_{ν} = - M_{ν D}^{T} {(M_{R})}^{- 1} M_{ν D},

2-

⟨ m_{e e} ⟩

3-

{(β β)}_{0 ν}

4-

Δ m_{12}^{2} = (7.1 - 8.9) \times 10^{- 5} {eV}^{2}, Δ m_{23}^{2} = (2.0 - 3.2) \times 10^{- 3} {eV}^{2},

5-

\sin^{2} θ_{12} = 0.24 - 0.40, \sin^{2} θ_{23} = 0.34 - 0.68, \sin^{2} θ_{13} \leq 0.040 .

6-

M_{l} = (\begin{matrix} 0 & A_{l} & 0 \\ A_{l}^{*} & D_{l} & B_{l} \\ 0 & B_{l}^{*} & C_{l} \end{matrix}), M_{ν D} = (\begin{matrix} 0 & A_{ν} & 0 \\ A_{ν}^{*} & D_{ν} & B_{ν} \\ 0 & B_{ν}^{*} & C_{ν} \end{matrix}),

7-

A_{l (ν)} = | A_{l (ν)} | e^{i α_{l (ν)}}

8-

B_{l (ν)} = | B_{l (ν)} | e^{i β_{l (ν)}}

9-

A_{l (ν)}^{*}

10-

B_{l (ν)}^{*}

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: hep-ex

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/0502674

Formulas:

1-

R u S r_{2} G d_{1.5} C e_{0.5} C u_{2} O_{10 - δ}

2-

R u S r_{2} G d_{1.5} C e_{0.5} C u_{2} O_{10 - δ}

3-

R u S r_{2} G d_{1.5} C e_{0.5} C u_{2} O_{10 - δ}

4-

R u S r_{2} G d C u_{2} O_{8 - δ}

5-

C u O_{2}

6-

R u S r_{2} G d_{1.5} C e_{0.5} C u_{2} O_{10 - δ}

7-

R u O_{2}

8-

S r C O_{3}

9-

G d_{2} O_{3}

10-

C e O_{2}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1805.06065

Formulas:

1-

k T_{bb} = 1

2-

k T_{e} = 50

3-

k T_{bb} = 1

4-

k T_{e} = 400

5-

k T_{bb} = 1

6-

k T_{bb} = 1

7-

k T_{bb} = 50

8-

k T_{e} = 100

9-

k T_{bb} = 1

10-

θ_{o} = 9 °

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/hep-ph/0512037

Formulas:

1-

U {(1)}_{e m}

2-

U {(1)}_{e m}

3-

U {(1)}_{e m}

4-

Φ_{1} = (\begin{matrix} φ_{1} + i φ_{2} \\ φ_{5} + i φ_{7} \end{matrix}), Φ_{2} = (\begin{matrix} φ_{3} + i φ_{4} \\ φ_{6} + i φ_{8} \end{matrix}),

5-

S U {(2)}_{W} \times U {(1)}_{Y}

6-

x_{1} \equiv {| Φ_{1} |}^{2}

7-

= φ_{1}^{2} + φ_{2}^{2} + φ_{5}^{2} + φ_{7}^{2}

8-

x_{2} \equiv {| Φ_{2} |}^{2}

9-

= φ_{3}^{2} + φ_{4}^{2} + φ_{6}^{2} + φ_{8}^{2}

10-

x_{3} \equiv R e (Φ_{1}^{†} Φ_{2})

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: hep-ph

Result: correct

Paper: https://arxiv.org/abs/1807.10531

Formulas:

1-

O (m^{3 / 2} \log n)

2-

O (m^{3 / 2} n)

3-

2 k^{2} + k

4-

ψ (e) \in {1, \dots, t}

5-

f (v) \in {1, \dots, t}

6-

ψ (u v) = f (u) = f (v)

7-

O (m^{3 / 2} n)

8-

O (m^{3 / 2} \log n)

9-

O (m n)

10-

G = (V, E)

Formulas (html):

Correct Categorie: cs

Guessed Categorie: math

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/0110646

Formulas:

1-

< R > / {< R >}_{0}

2-

N_{t o t}

3-

r_{n} (T_{n}) = r_{0} [1 + α (T_{n} - T_{0})]

4-

T_{n} = T_{0} + A [r_{n} i_{n}^{2} + \frac{B}{N_{n e i g}} \sum_{l = 1}^{N_{n e i g}} (r_{l} i_{l}^{2} - r_{n} i_{n}^{2})] .

5-

N_{n e i g}

6-

W_{D} = \exp [- E_{D} / K_{B} T_{n}]

7-

E_{R} < E_{D} + k_{B} T \ln [1 + \exp (- E_{D} / K_{B} T_{0})]

8-

A = 5 \times 10^{5}

9-

0.026 \leq E_{R} \leq 0.16

10-

1 \leq r_{0} \leq 10

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1811.11870

Formulas:

1-

q_{z} = 0.16 - 0.5

2-

Δ q / q_{0}

3-

Δ I / I_{0}

4-

0.16 - 0.5 Å^{- 1}

5-

Δ I (t) \sim A [1 - \exp (- t / τ)]

6-

Δ ⟨ u_{x y}^{2} ⟩ = [\ln (I_{0} / I)] / q_{x y}^{2} = 0.0018 Å^{2}

7-

⟨ u_{x y} ⟩

8-

⟨ u_{x y}^{2} ⟩

9-

Δ q (t) \sim A [1 - \exp (- t_{q} / τ_{1})]

10-

τ_{1} = 2.9 \pm 1.2

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

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/2001.05151

Formulas:

1-

ν / Δ ν \sim 1000

2-

ν / Δ ν \sim 380

3-

δ x (T) \equiv (f (T) - f_{load}) / f_{load}

4-

δ x (T) = p_{0} (\sqrt{T + T_{0}} - \sqrt{T_{load} + T_{0}}),

5-

T_{0} = - \frac{h ν}{2 k_{b}}

6-

T = η_{fwd} T_{sky} + (1 - η_{fwd}) T_{amb}

7-

T_{sky}^{resp} (δ x) = \frac{1}{p_{0}^{2} η_{fwd}} {(δ x + p_{0} \sqrt{T_{load} + T_{0}})}^{2} - \frac{1}{η_{fwd}} (T_{0} + (1 - η_{fwd}) T_{amb}) .

8-

T_{load} = κ_{eff} T_{room}

9-

η_{atm} (E l, P W V) = \frac{\int g (ν) e^{- τ_{0} (ν, P W V) \csc (E l)} d ν}{\int g (ν) d ν},

10-

\csc (E l)

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1003.0350

Formulas:

1-

x_{1}, \dots, x_{m}

2-

L_{m, c} = L_{m} / (L_{m}^{''} + L_{m}^{c + 1})

3-

Inn (L_{m, c})

4-

Out (L_{m, c})

5-

Aut (L_{m, c})

6-

IA (L_{m, c})

7-

{GL}_{m} (K)

8-

Inn (L_{m, c}) \subset IA (L_{m, c})

9-

Out (L_{m, c}) = Aut (L_{m, c}) / Inn (L_{m, c})

10-

IA (L_{m, c}) / Inn (L_{m, c})

Formulas (html):

Correct Categorie: math

Guessed Categorie: cs

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/0609290

Formulas:

1-

ℏ ω_{o s c}

2-

a_{o s c} = \sqrt{ℏ / m ω_{o s c}}

3-

ℏ ω_{o s c}

4-

a_{o s c}

5-

A X_{n} + B Y_{n}

6-

E_{n} X_{n},

7-

- B^{*} X_{n} - A^{*} Y_{n}

8-

E_{n} Y_{n} .

9-

A (p h, p^{'} h^{'}) = (ϵ_{p} + S (p) - ϵ_{h} - S (h)) δ_{p h, p^{'} h^{'}} + Σ (p h, p^{'} h^{'}),

10-

X_{n} (p h) = ⟨ Ψ_{n} | a_{p}^{†} a_{h} | Ψ_{0} ⟩

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1011.5465

Formulas:

1-

θ \in [0, 1]

2-

ℝ^{d} ∖ {0}

3-

\begin{matrix} ϑ (p, d) := \frac{d (p - 2)}{2 p}, a_{c} := \frac{d - 2}{2}, Λ (a) := {(a - a_{c})}^{2} \\ and p (a, b) := \frac{2 d}{d - 2 + 2 (b - a)} . \end{matrix}

4-

2^{*} := \frac{2 d}{d - 2}

5-

b \in (a + 1 / 2, a + 1]

6-

θ \in (1 / 2, 1]

7-

b \in (a, a + 1]

8-

b \in [a, a + 1]

9-

p = p (a, b)

10-

θ \in [ϑ (p, d), 1]

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/1304.7088

Formulas:

1-

τ_{R o s s} = 1

2-

| B c o s (γ) |

3-

v_{L N M}

4-

v_{L N M}

5-

v_{L N M}

6-

ν_{m i n} = 2 / T_{l e n g t h}

7-

x - a x i s

8-

(- 70^{\circ}, - 110^{\circ})

9-

ϕ (v_{z} - v_{h})

10-

v_{z, p r o j e c t e d} = v_{h} s i n (γ)

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/math/0005136

Formulas:

1-

ν_{3} = 1.5 \pm 0.1

2-

ν_{4} = 1.25 \pm 0.05

3-

ν_{5} = 1.1 \pm 0.05

4-

ν_{6} = 1.05 \pm 0.05

5-

m / n < α_{3} - ε

6-

m / n > α_{3} + ε

7-

(\log 2) 2^{k - 1} - (\log 2 + 1) / 2 - o_{k} (1)

8-

(\log 2) 2^{k}

9-

Δ = Θ (n^{1 - 1 / ν})

10-

Θ (n^{1 / 2})

Formulas (html):

Correct Categorie: math

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0607059

Formulas:

1-

- 2.70 \log (P) - 1.49,

2-

- 2.96 \log (P) - 1.34 for \log (P) < 1.0,

3-

- 2.57 \log (P) - 1.63 for \log (P) > 1.0 .

4-

V = - 1.80 \log (P) - 2.50

5-

\log (P) > 1.5

6-

E (B - V)

7-

\log (P) < 0.4

8-

\log (P) < 0.4

9-

\log [P] < 0.4

10-

X = {5.0, 4.5, 4.0, 3.5, 3.0, 2.5, 2.0, 1.5, 1.0, 0.5}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/astro-ph/9811311

Formulas:

1-

T_{A} = S \frac{λ^{2}}{2 k Ω},

2-

T_{A} = \frac{x}{e^{x} - 1} T,

3-

x \equiv h ν / k T

4-

\frac{d T}{d T_{A}} = \frac{{(e^{x} - 1)}^{2}}{x^{2} e^{x}} .

5-

| b | > 30^{\circ}

6-

0 \overset{\circ}{.} 3

7-

0 \overset{\circ}{.} 2

8-

∣ (S_{P} - S_{O}) / S_{P} ∣

9-

\log_{10} \frac{Δ T}{T}

10-

1 / F W H M

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1404.2394

Formulas:

1-

(X, d, T)

2-

d_{T, n} (x, y) = \max_{0 \leq j < n} d (T^{j} (x), T^{j} (y)) .

3-

(n, ϵ, K, T)

4-

d_{T, n} (x, y) > ϵ

5-

r (n, ϵ, K, T)

6-

(n, ϵ, K, T)

7-

(n, ϵ, K, T)

8-

d_{T, n} (x, y) \leq ϵ

9-

s (n, ϵ, K, T)

10-

(n, ϵ, K, T)

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/astro-ph/9512115

Formulas:

1-

B \sim 10^{14} - 10^{15}

2-

B ¿ \sim B_{c}

3-

B_{c} = 4.414 \times 10^{13}

4-

ω_{B} \equiv e B / m_{e} c

5-

σ_{T} = 6.65 \times 10^{- 25} {cm}^{2}

6-

σ_{⟂} \sim {(ω / ω_{B})}^{2} σ_{T} ≪ σ_{T}

7-

ω_{c 2} \sim n^{1 / 2} B^{- 1}

8-

ω_{c 2} \sim n^{1 / 2} B^{- 1 / 2}

9-

ω \approx ω_{c 2}

10-

σ_{∥} \approx σ_{⟂} \approx σ_{T}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/astro-ph/9811014

Formulas:

1-

γ_{m a x}

2-

γ_{m a x}

3-

γ_{m a x}

4-

t_{v a r}

5-

t_{v a r}

6-

t_{v a r}

7-

α = (p - 1) / 2

8-

N (γ) \propto γ^{- s}

9-

\propto γ^{- s - 1}

10-

\propto γ^{- s - 2}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0112440

Formulas:

1-

0.3 - 0.4 R_{SS L 1}

2-

0.2 R_{SS L 1}

3-

q = ℳ_{r d} / ℳ_{w d} = 0.15

4-

ℳ_{w d} = 0.61 ℳ_{⊙}

5-

R_{w d} = 0.0118 ℛ_{⊙} = 0.0263 R_{SS L 1}

6-

E (B - V)

7-

λ λ 7165, 7665

8-

λ λ 7165, 7665

9-

λ 7165 / λ 7665

10-

M_{r d} = 0.09 M_{⊙}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1503.01857

Formulas:

1-

U = (\begin{matrix} c_{u} & s_{u} & 0 \\ - s_{u} & c_{u} & 0 \\ 0 & 0 & 1 \end{matrix}) \times (\begin{matrix} e^{- i δ} & 0 & 0 \\ 0 & c & s \\ 0 & - s & c \end{matrix}) \times (\begin{matrix} c_{d} & - s_{d} & 0 \\ s_{d} & c_{d} & 0 \\ 0 & 0 & 1 \end{matrix}),

2-

c_{u, d} \sim \cos θ_{u, d}

3-

s_{u, d} \sim \sin θ_{u, d}

4-

\tan θ_{C} ≃ \sqrt{m_{d} / m_{s}} .

5-

\tan θ_{C} ≃ 0.23,

6-

\sqrt{m_{d} / m_{s}} ≃ 0.23 .

7-

M = (\begin{matrix} 0 & A \\ A^{*} & B \end{matrix}) .

8-

θ_{u} ≃ \sqrt{m_{u} / m_{c}} ≃ 0.09, θ_{d} ≃ \sqrt{m_{d} / m_{s}} ≃ 0.23 .

9-

θ_{C} ≃ | \sqrt{m_{d} / m_{s}} - e^{i ϕ} \sqrt{m_{u} / m_{c}} | .

10-

θ_{C} ≃ \sqrt{m_{d} / m_{s}} .

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: hep-ph

Result: correct

Paper: https://arxiv.org/abs/1606.00077

Formulas:

1-

e \oint 𝐀 \cdot 𝑑 𝐫

2-

C P_{j k}

3-

Φ_{B} \equiv φ_{12} + φ_{23} + φ_{31}

4-

ψ_{0} = | 100 ⟩

5-

Φ_{B} = π / 2, 0, - π / 2

6-

Φ_{B} = - π / 2

7-

ψ_{0} = | 110 ⟩

8-

H (t) = ℏ \sum_{j = 1}^{3} ω_{j} (\hat{n} + 1 / 2) + ℏ \sum_{j, k} g_{j k} (t) (a_{j}^{†} a_{k} + a_{j} a_{k}^{†}) + H_{int},

9-

a^{†} (a)

10-

\hat{n} = a_{j}^{†} a_{j}

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/0912.4898

Formulas:

1-

m_{i} \to m_{i}^{'} = m_{i} - Δ m,

2-

m_{j} \to m_{j}^{'} = m_{j} + Δ m .

3-

m_{i} + m_{j} = m_{i}^{'} + m_{j}^{'},

4-

M = \sum_{i} m_{i}

5-

P (m_{k}) = N_{k} / N

6-

Ω = \frac{N!}{N_{1}! N_{2}! N_{3}! \dots} .

7-

S = N \ln N - \sum_{k} N_{k} \ln N_{k} = - \sum_{k} N_{k} \ln (\frac{N_{k}}{N}) .

8-

N = \sum_{k} N_{k}

9-

M = \sum_{k} m_{k} N_{k}

10-

\tilde{S} = S + α \sum_{k} N_{k} - β \sum_{k} m_{k} N_{k} .

Formulas (html):

Correct Categorie: q-fin

Guessed Categorie: hep-ph

Result: incorrect

Paper: https://arxiv.org/abs/nucl-ex/0211008

Formulas:

1-

\sqrt{s_{N N}} = 200

2-

S p \bar{p} S

3-

\sqrt{s_{N N}} = 200

4-

\frac{1}{N_{t r i g}} \frac{d N_{c h}}{d Δ ϕ} = A c c (Δ ϕ) ⟨ ϵ ⟩ (a_{b k g} + a_{p y t h i a} \frac{1}{N_{p y t h i a}} \frac{d N_{c h}^{p y t h i a}}{d Δ ϕ})

5-

\sqrt{s_{N N}} = 200

6-

c o s (2 Δ ϕ)

7-

\frac{1}{N_{t r i g}} \frac{d N_{c h}}{d Δ ϕ} = A c c (Δ ϕ) ⟨ ϵ ⟩ (a_{b k g} + a_{f l o w} c o s (2 Δ ϕ) + a_{p y t h i a} \frac{1}{N_{p y t h i a}} \frac{d N_{c h}}{d Δ ϕ})

8-

a_{f l o w} = a_{b k g} * 2 v_{2}^{t r i g} v_{2}^{c h}

9-

| Δ η | > 0.35

10-

| Δ η | < 0.35

Formulas (html):

Correct Categorie: nucl-ex

Guessed Categorie: hep-ph

Result: incorrect

Paper: https://arxiv.org/abs/1110.3864

Formulas:

1-

p (k) \sim k^{- (1 + β)}

2-

p (w) \sim w^{- (1 + α)}

3-

ρ = 2 L / (N^{2} - N)

4-

f (w) = ⟨ w ⟩ p (w / ⟨ w ⟩)

5-

w_{i j} \geq 0

6-

d_{i j} = 1 / w_{i j}

7-

w_{n_{i} n_{i + 1}} > 0

8-

l = \sum_{i = 1}^{K - 1} d_{n_{i} n_{i + 1}}

9-

t_{i j} (r) = 1

10-

t_{i j} (r) = 0

Formulas (html):

Correct Categorie: physics

Guessed Categorie: physics

Result: correct

Paper: https://arxiv.org/abs/0712.2161

Formulas:

1-

u = u^{#} \circ s

2-

u^{#} = \nabla ψ

3-

u (x) \in \partial ψ (y)

4-

u : X \to ℝ^{n}

5-

u = u^{#} \circ s

6-

u^{#} = \nabla ψ

7-

u (x) \in \partial ψ (y)

8-

\partial ψ (y)

9-

{(i d \times s)}_{#} μ

10-

c (x, y) = {| u (x) - y |}^{2} / 2

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/1102.1580

Formulas:

1-

{1, 2, \dots, k}

2-

(r_{1}^{t}, \dots, r_{k}^{t})

3-

I_{t} \in {1, \dots, k}

4-

γ \in [0; 1]

5-

η \in (O; \frac{1}{k}]

6-

{1, \dots, k}

7-

t = 1, 2, \dots

8-

G_{I_{t}} = G_{I_{t}} + \frac{r_{I_{t}}^{t}}{p_{I_{t}}^{t}}

9-

i \in {1, \dots, k}

10-

p_{i}^{t + 1} = (1 - γ) \frac{\exp (η G_{i})}{\sum_{j = 1}^{k} \exp (η G_{j})} + γ

Formulas (html):

Correct Categorie: cs

Guessed Categorie: cs

Result: correct

Paper: https://arxiv.org/abs/1407.8221

Formulas:

1-

B E = < H_{m} > - E_{C} - E_{s y m} + E_{P},

2-

E_{s y m} = a_{s y m} \frac{T (T + 1)}{A ρ} - a_{s s y m} \frac{T (T + 1)}{A^{4 / 3} ρ^{2}},

3-

ρ = A^{1 / 3} {[1 - {(\frac{T}{A})}^{2}]}^{2}

4-

H_{m} = H_{M} + H_{s} + H_{d},

5-

(M + T) / ρ

6-

T (T - 1 / 2) / A ρ^{4}

7-

2 T / A ρ

8-

N (Z) = 28, 50, 82, 126

9-

< H_{s} > = \frac{1}{ρ} [a_{s} S_{3} + b_{s} \frac{S_{3}}{ρ} + c_{s} S_{4}],

10-

E_{P} = a_{p} \frac{2 - v}{ρ},

Formulas (html):

Correct Categorie: nucl-th

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/nucl-th/0109067

Formulas:

1-

j = l - 1 / 2

2-

j = (l - 2) + 1 / 2

3-

\tilde{η} = η - 1

4-

\tilde{l} = l - 1

5-

{1^{n_{α}^{N}}} {{\tilde{f}}_{α}} {f_{α}} γ_{α} (λ_{α}, μ_{α}) {\tilde{S}}_{α} K_{α}

6-

U (Ω_{α}^{N}) \supset U (Ω_{α}^{N} / 2) \times U (2) \supset S U (3) \times S U (2) \supset

7-

{\tilde{L}}_{α} J_{α}^{N}

8-

S O (3) \times S U (2) \supset S U_{J} (2),

9-

{\tilde{S}}_{π, ν} = 0

10-

H_{s p, π [ν]}

Formulas (html):

Correct Categorie: nucl-th

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/1003.5351

Formulas:

1-

g (a, q_{1}, \dots, q_{n})

2-

\int_{a}^{b} L (t, q_{1}, \dots, q_{n}, {\dot{q}}_{1}, \dots, {\dot{q}}_{n}) 𝑑 t + g (a, q_{1}, \dots, q_{n}) .

3-

q = (q_{1}, \dots, q_{n})

4-

\frac{\partial L}{\partial q_{i}} - \frac{d}{d t} (\frac{\partial L}{\partial \dot{q_{i}}}) = 0

5-

{\frac{\partial L}{\partial \dot{q_{i}}} |}_{t = a} - \frac{\partial g}{\partial q_{i}} = 0 .

6-

g (a, q)

7-

p_{i} (a, q, \dot{q}) = \frac{\partial g (a, q)}{\partial q_{i}}

8-

p_{i} (t, q, \dot{q}) = \frac{\partial L (t, q, \dot{q})}{\partial \dot{q_{i}}} .

9-

g (a, q)

10-

g (t, q)

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: math

Result: incorrect

Paper: https://arxiv.org/abs/hep-ph/0004171

Formulas:

1-

S U {(2)}_{L}

2-

U {(1)}_{Y}

3-

{Sin}^{2} 2 θ \geq 0.82

4-

m_{a t m}^{2}

5-

(5 \times 10^{- 4} - 6 \times 10^{- 3})

6-

(0.8 - 2) \times 10^{- 5} {eV}^{2}

7-

{Sin}^{2} 2 θ

8-

(0.5 - 6) \times 10^{- 10} {eV}^{2}

9-

{Sin}^{2} 2 θ

10-

Δ m_{e X}^{2} < 10^{- 3}

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: hep-ph

Result: correct

Paper: https://arxiv.org/abs/quant-ph/9906097

Formulas:

1-

M d ξ = 0, M {(d ξ)}^{2} = 0, M {| d ξ |}^{2} = d t .

2-

\frac{d | ψ (t) ⟩}{d t} = - (i / ℏ) 𝐇 | ψ (t) ⟩ - \frac{1}{2} c^{2} 𝐆_{Δ}^{2} | ψ (t) ⟩ + c 𝐆_{Δ} | ψ (t) ⟩ \frac{d ξ}{d t},

3-

𝐆_{Δ} = 𝐆 - ⟨ ψ (t) | 𝐆 | ψ (t) ⟩

4-

| ψ (t) ⟩

5-

d ξ / d t

6-

E_{j} = ℏ ω_{j}

7-

ψ_{j} = \frac{1}{\sqrt{2}} (q_{j} + i p_{j})

8-

i {\dot{ψ}}_{j} = ω_{j} ψ_{j}, so that

9-

{\dot{q}}_{j} = {q_{j}, H} = ω_{j} p_{j}, {\dot{p}}_{j} = {p_{j}, H} = - ω_{j} q_{j}, with H = \sum_{j} \frac{ω_{j}}{2} (p_{j}^{2} + q_{j}^{2}),

10-

ψ_{j} = \frac{1}{\sqrt{2}} (q_{j} + i p_{j}) and i ψ_{j}^{*} = \frac{1}{\sqrt{2}} (i q_{j} + p_{j}) .

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: quant-ph

Result: correct

Paper: https://arxiv.org/abs/1407.3382

Formulas:

1-

a b i n t i o

2-

E_{g r a p h - A A} = E_{ϕ}^{A A}

3-

ϕ^{AA} (d)

4-

d \geq 2 d_{1} = 5.2

5-

ϕ^{AA} (d)

6-

ϕ^{AA} (d)

7-

d < 2 d_{1}

8-

ϕ^{AA} (d)

9-

a b i n i t i o

10-

E_{AB}^{a b i n i t i o} (d)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: math

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/0412347

Formulas:

1-

(0, 0, 0)

2-

(0.5, 0.5, 0.5)

3-

2 θ ∽ {9.5}^{\circ}

4-

(0, 0, 0)

5-

(0.75, 0.25, 0.5)

6-

a = 3.7974 (3)

7-

b = 4.238 (4)

8-

c = 5.6358 (1)

9-

a = 3.4500 (3)

10-

B_{0} = 45 (2)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1808.00701

Formulas:

1-

E (K_{C M}) = E_{g} - E_{B} + \frac{ℏ^{2}}{2 M} K_{C M}^{2}

2-

K_{C M} \approx 0

3-

E = E_{g} - E_{B}

4-

K_{C M} \approx 0

5-

K_{C M} \neq 0

6-

E C (τ, ℏ ω)

7-

E C (τ, ℏ ω) \equiv {P L (τ, ℏ ω) - P L (0, ℏ ω)} / P L (0, ℏ ω),

8-

P L (τ, ℏ ω)

9-

P L (0, ℏ ω)

10-

τ_{a} = ν^{- 1} \exp (Δ E / k_{B} T)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/0912.1462

Formulas:

1-

θ = 1 \overset{''}{.} 13

2-

θ = 1 \overset{''}{.} 27

3-

θ = 1 \overset{''}{.} 15

4-

θ = 1 \overset{''}{.} 46

5-

θ = 1 \overset{''}{.} 87

6-

θ = 3 \overset{''}{.} 00

7-

θ = 1 \overset{''}{.} 73

8-

θ = 2 \overset{''}{.} 77

9-

H_{0} = 72 k m s^{- 1} {Mpc}^{- 1}

10-

≲ 2 \overset{''}{.} 5

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/0802.2765

Formulas:

1-

i n i t i o

2-

P \bar{6} m 2

3-

P \bar{6} m 2

4-

P \bar{6} m 2

5-

k_{4} ⟨ u^{2} ⟩

6-

i n i t i o

7-

i n i t i o

8-

λ_{𝐪 λ} = \frac{2}{π N (0)} \frac{γ_{𝐪 λ}}{ω_{𝐪 λ}^{2}}

9-

i n i t i o

10-

P h o n o n s

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0009481

Formulas:

1-

(2.50 \pm 0.15) \times 10^{- 13}

2-

δ t = \frac{δ P}{P} (t - t_{0}) + \frac{1}{2} \frac{\dot{P}}{P} {(t - t_{0})}^{2} + x \sin (l) - \frac{3}{2} x e \sin (w) + \frac{1}{2} x e \cos (w) \sin (2 l) - \frac{1}{2} x e \sin (w) \cos (2 l) .

3-

x = a_{x} \sin (i) / c

4-

l = 2 π (t - T_{π / 2}) / P_{o r b i t} + π / 2

5-

P_{o r b i t}

6-

\dot{ν} = (2.5 \pm 0.15) \times 10^{- 13}

7-

f (M) = \frac{4 π^{2} {(a_{x} \sin i)}^{3}}{G P_{o r b}^{2}} = \frac{{(M_{c} s i n i)}^{3}}{{(M_{x} + M_{c})}^{2}} \sim 2.5 M_{⊙} .

8-

- \dot{P} = 2.2 \times 10^{- 12} μ_{30}^{2 / 7} m_{x}^{- 3 / 7} R_{6}^{6 / 7} I_{45}^{- 1} P^{2} L_{37}^{6 / 7} s s^{- 1}

9-

m_{x} = M_{x} / M_{⊙}

10-

- 3.2 \times 10^{- 8}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1010.1624

Formulas:

1-

O (2^{n / 2})

2-

O (2^{n / 2})

3-

O (2^{n})

4-

O (2^{n / 2})

5-

O (2^{n / 3})

6-

{0, 1}^{N}

7-

{0, 1}^{N}

8-

{0, 1}^{n}

9-

{0, 1}^{n}

10-

[I^{1}, I^{2}, \dots I^{k}]

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: math

Result: incorrect

Paper: https://arxiv.org/abs/1412.7761

Formulas:

1-

[Fe / H] = 0.08 \pm 0.10

2-

M_{⋆} = 1.04 \pm 0.07

3-

R_{⋆} = 0.96 \pm 0.13

4-

M_{p} = 1.09 \pm 0.03

5-

R_{p} = 1.44 \pm 0.02

6-

21 : 43 - 01 : 42

7-

02 : 39 - 06 : 41

8-

01 : 18 - 05 : 15

9-

04 : 23 - 07 : 55

10-

03 : 39 - 08 : 07

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Run 11314760 (Agent202)