Run 11332337

Paper: https://arxiv.org/abs/1309.2272

Formulas:

1-

F (α, s) = \frac{2}{π (1 - s)} \sum_{k = 0}^{\infty} {(\frac{s + 1}{s - 1})}^{k} ⟨ α, k | ρ | α, k ⟩

2-

ρ = \frac{1}{π} \int d^{2} α P (α) | α ⟩ ⟨ α | = \frac{1}{π} \int d^{2} α F (α, 1) | α ⟩ ⟨ α |,

3-

Q (α) = F (α, - 1) = \frac{1}{π} ⟨ α | ρ | α ⟩ .

4-

F (α, s) = \frac{2}{π (1 - s)} \sum_{k = 0}^{\infty} {(\frac{s + 1}{s - 1})}^{k} ⟨ k | D^{†} (α) ρ D (α) | k ⟩

5-

D (α) = \exp (α a^{†} - α^{*} a)

6-

F (α, s) = \frac{2}{π (1 - s)} T r {{(\frac{s + 1}{s - 1})}^{a^{†} a} D^{†} (α) ρ D (α)} .

7-

F (α, s) = \frac{2}{π (1 - s)} T r {D (α) {(\frac{s + 1}{s - 1})}^{a^{†} a} D^{†} (α) ρ} = \frac{2}{π (1 - s)} ⟨ ψ | D (α) {(\frac{s + 1}{s - 1})}^{a^{†} a} D^{†} (α) | ψ ⟩

8-

H = ω a^{†} a + β a^{†} + β^{*} a

9-

| ψ (t) ⟩ = e^{- i H t} | ψ (0) ⟩ = D^{†} (β / ω) e^{- i ω t a^{†} a} D (β / ω) | ψ (0) ⟩

10-

A (t) = ⟨ ψ (0) | ψ (t) ⟩ = ⟨ ψ (0) | D^{†} (β / ω) e^{- i ω t a^{†} a} D (β / ω) | ψ (0) ⟩

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: quant-ph

Result: correct

Paper: https://arxiv.org/abs/1301.6212

Formulas:

1-

(1, 2, 3, 4) = (q q \bar{q} \bar{q})

2-

Ψ = ψ_{T} | T ⟩ + ψ_{M} | M ⟩

3-

= | {(12)}_{\bar{3}} {(34)}_{3} ⟩,

4-

= | {(12)}_{6} {(34)}_{\bar{6}} ⟩,

5-

= | {(13)}_{1} {(24)}_{1} ⟩,

6-

= | {(13)}_{8} {(24)}_{8} ⟩,

7-

= | {(14)}_{1} {(23)}_{1} ⟩,

8-

= | {(14)}_{8} {(23)}_{8} ⟩ .

9-

= \sqrt{\frac{1}{3}} | T ⟩ + \sqrt{\frac{2}{3}} | M ⟩,

10-

= - \sqrt{\frac{2}{3}} | T ⟩ + \sqrt{\frac{1}{3}} | M ⟩,

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: hep-ph

Result: correct

Paper: https://arxiv.org/abs/physics/0201037

Formulas:

1-

κ_{u s a t}

2-

S_{u} \propto Q^{0.30 \pm 0.05}

3-

Δ S = 0.04 \exp^{- Q / 0.032}

4-

1 / κ_{u} = 0.02 + 0.32 \exp^{- Q / 0.032}

5-

κ_{u s a t}

6-

S_{u} \propto Q^{0.3 \pm 0.05}

7-

Δ S = 0.04 \exp^{- Q / 0.032}

8-

1 / κ_{u} = 0.02 + 0.32 \exp^{- Q / 0.032}

9-

S_{u} \propto Q^{0.3 \pm 0.05}

10-

1 / κ_{u} = 0.02 + 0.32 \exp^{- Q / 0.032}

Formulas (html):

Correct Categorie: physics

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1011.0257

Formulas:

1-

⟨ \bar{q} q ⟩ \neq 0

2-

U {(1)}_{V}

3-

S U {(N_{f})}_{V}

4-

S U {(N_{f})}_{V} \times S U {(N_{f})}_{A} \times U {(1)}_{V} \times U {(1)}_{A} \to S U {(N_{f})}_{V} \times U {(1)}_{V}

5-

U {(1)}_{A}

6-

U {(1)}_{A}

7-

U {(1)}_{A}

8-

U {(1)}_{A}

9-

U {(1)}_{A}

10-

U {(1)}_{A}

Formulas (html):

Correct Categorie: hep-lat

Guessed Categorie: hep-ph

Result: incorrect

Paper: https://arxiv.org/abs/1908.01202

Formulas:

1-

\sqrt[4]{9^{2} + 19^{2} / 22}

2-

6 / 5 \cdot (1 + ϕ) \approx 3.1416

3-

ϕ = \frac{1 + \sqrt{5}}{2}

4-

6 / 5 \cdot (1 + ϕ)

5-

\sqrt{\frac{63}{25} (1 + \frac{5}{2} \frac{15 \sqrt{5} - 7}{269})}

6-

\sqrt[8]{9^{2} + 19^{2} / 22}

7-

6 / 5 \cdot (1 + ϕ)

8-

\sqrt{6 / 5 (1 + ϕ)}

9-

A D ⟂ A B

10-

G F = 3 A F / 10

Formulas (html):

Correct Categorie: math

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/0104020

Formulas:

1-

L a_{2 - x} S r_{x} C u O_{4}

2-

T l_{2} B a_{2} C u O_{6}

3-

B i_{2} S r_{2} C u O_{6}

4-

B i_{2} S r_{2} C a C u_{2} O_{8}

5-

M = - H / 4 π

6-

Y B a_{2} C u_{3} O_{7 - δ}

7-

Y B a_{2} C u_{3} O_{7 - δ}

8-

Y B a_{2} C u_{3} O_{7 - δ}

9-

Y B a_{2} C u_{3} O_{7 - δ}

10-

t_{c} = T_{c} / T_{c}^{o p t}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/hep-lat/0409134

Formulas:

1-

κ (ℳ) \propto m^{- α}

2-

κ (\sqrt{M}) = \sqrt{κ (ℳ)}

3-

2 m^{- α / 2}

4-

\sqrt[n]{ℳ} ψ_{j} = ψ_{j + 1}

5-

κ (ℳ^{1 / n}) = κ {(ℳ)}^{1 / n}

6-

n κ {(ℳ)}^{1 / n}

7-

ℳ^{1 / n} x = b

8-

n κ (ℳ)

9-

n κ {(ℳ)}^{1 / n}

10-

n κ {(ℳ)}^{1 / n} δ τ

Formulas (html):

Correct Categorie: hep-lat

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/0808.0465

Formulas:

1-

V_{S D} = 0.8

2-

S_{I} (f)

3-

S_{I; B G} (f)

4-

Δ V_{E G}

5-

G_{Q P C} \approx e^{2} / h

6-

d I_{Q P C} / d V_{G}

7-

G_{QPC} \approx e^{2} / h

8-

S_{I} (f)

9-

S_{I} (f)

10-

τ_{eff}^{- 1} = τ_{u}^{- 1} + τ_{d}^{- 1}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1911.10557

Formulas:

1-

ψ^{''} : 𝒢 ⟶ (0, 1]

2-

ψ^{''} (G) = \frac{ψ (G)}{{| G |}^{2}}

3-

ψ (G) = \sum_{x \in G} o (x),

4-

ψ (G) \leq ψ (C_{n})

5-

ψ^{'} (G) = \frac{ψ (G)}{ψ (C_{| G |})}

6-

ψ^{'} (G) > \frac{7}{11}

7-

ψ^{'} (G) > \frac{13}{21}

8-

ψ^{'} (G) > \frac{31}{77}

9-

ψ^{'} (G) > \frac{1}{6.68}

10-

ψ^{'} (G) > \frac{211}{1617}

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/1512.06350

Formulas:

1-

\sim 150 h^{- 1} Mpc

2-

150 h^{- 1} Mpc

3-

70 - 150 h^{- 1} Mpc

4-

100 h^{- 1} Mpc

5-

≳ 300 h^{- 1} Mpc

6-

120 h^{- 1} Mpc

7-

120 - 130 h^{- 1} Mpc

8-

120 h^{- 1} Mpc

9-

240 h^{- 1} Mpc

10-

120 h^{- 1} Mpc

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1502.03288

Formulas:

1-

U = {0, \dots, u - 1}

2-

H_{0}^{g a p}

3-

n H_{0}^{g a p} \in o (g a p)

4-

n H_{0}^{g a p} \leq n \log (u / n) + n

5-

n H_{0}^{g a p}

6-

𝒪 (\log \log u)

7-

n H_{0}^{g a p} + 𝒪 (n) + 𝒪 (u / p o l y l o g (u))

8-

n \in Θ (u / p o l y l o g (u))

9-

H_{0}^{g a p} \in 𝒪 (1)

10-

𝒪 (\log \log n)

Formulas (html):

Correct Categorie: cs

Guessed Categorie: cs

Result: correct

Paper: https://arxiv.org/abs/1710.01053

Formulas:

1-

\dot{M} > 1000 M_{⊙}

2-

{\dot{E}}_{kin} \sim - 0.05 L_{AGN}

3-

t_{dyn, out} \sim R_{out} / v_{out} \sim 1 R_{kpc} v_{3}^{- 1}

4-

R_{out} \equiv 1 R_{kpc}

5-

v_{out} \equiv 10^{3} v_{3}

6-

v_{w} \sim 0.1 c

7-

L_{w} = \frac{{\dot{M}}_{w} v_{w}^{2}}{2} = \frac{η}{2} L_{AGN} \sim - 0.05 L_{AGN},

8-

L_{crit} \sim - L_{Edd} (M_{σ})

9-

M_{σ} \sim - 3.68 \times 10^{8} σ_{200}^{4} M_{⊙}

10-

t_{q} \sim 5 \times 10^{4} - 2 \times 10^{5}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1710.07467

Formulas:

1-

n_{f} = 2 + 1 + 1

2-

| q^{2} | = 0.1

3-

q^{2} \approx - {(\vec{q})}^{2}

4-

f_{+} (q^{2})

5-

⟨ r^{2} ⟩ = {6 \frac{d f_{+} (q^{2})}{d q^{2}} |}_{q^{2} = 0} .

6-

a m_{ℓ, s e a}

7-

a m_{s, s e a}

8-

a m_{c, s e a}

9-

m_{u} = m_{d} = m_{ℓ}

10-

f_{+} (q^{2}) {(p_{1} + p_{2})}_{i} = ⟨ π (p_{1}) | V_{i} | π (p_{2}) ⟩ = Z \sqrt{4 E_{0} (p_{1}) E_{0} (p_{2})} J_{0, 0} (p_{1}, p_{2}),

Formulas (html):

Correct Categorie: hep-lat

Guessed Categorie: hep-ph

Result: incorrect

Paper: https://arxiv.org/abs/1301.1684

Formulas:

1-

M ≳ 10^{15} M_{⊙}

2-

ρ (r) / σ^{3} (r)

3-

Σ (R) = \int 𝑑 x_{∥} ρ (x_{∥}, R),

4-

𝐫 = (x_{∥}, R)

5-

M ≳ 10^{15} M_{⊙}

6-

r_{v i r}

7-

M_{v i r}

8-

(M p c h^{- 1})

9-

(10^{15} M_{⊙} h^{- 1})

10-

ρ (r) = \frac{ρ_{s}}{(r / r_{s}) {(1 + r / r_{s})}^{2}},

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/cond-mat/0211072

Formulas:

1-

\exp [- E_{a} / k_{B} T]

2-

γ \in (0, 1]

3-

- \ln (γ) / \sum_{i} r_{i}

4-

E (n, b, x)

5-

E (n, b, x)

6-

E_{V_{f}}^{S i}

7-

E (n, b, x) = E_{V f}^{S i} - F (b) - (n - b) S - M x

8-

\tilde{p} (n, b, x)

9-

(\binom{4}{b}) x^{b} {(1 - x)}^{4 - b}

10-

(\binom{12}{n - b}) x^{n - b} {(1 - x)}^{12 - (n - b)}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/astro-ph/9808278

Formulas:

1-

V ≲ v_{A} ≪ v_{i}

2-

\sim ϵ^{2 / 3} k_{⟂}^{- 2 / 3}

3-

ϵ \sim V^{3} / L

4-

k_{∥} ≲ k_{⟂}^{2 / 3} L^{- 1 / 3}

5-

| v_{∥} | ≲ v_{A}

6-

v_{∥} = ω / k_{∥}

7-

| v_{∥} | = v_{A}

8-

ω = | k_{∥} | v_{A}

9-

k_{⟂} \sim ρ^{- 1}

10-

ω ≲ ω_{n l}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/0206573

Formulas:

1-

[1 - {(B / B_{0})}^{2}]

2-

C = γ_{r} T + β_{r} T^{3}

3-

C_{mag} (T)

4-

C = γ T + β T^{3}

5-

C_{mag} = γ T + A \exp (- Δ / T)

6-

C_{mag} = γ T + β T^{3}

7-

ω = \sqrt{Δ^{2} + D k^{2}}

8-

C_{mag} = γ_{0} T + α Δ^{7 / 2} T^{1 / 2} ⅇ^{- Δ / T} [1 + (39 / 20) (T / Δ) + (51 / 32) {(T / Δ)}^{2}]

9-

α \propto D^{- 3 / 2}

10-

[1 - {(B / B_{0})}^{2}]

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/astro-ph/9408062

Formulas:

1-

σ = .05 - .2

2-

η \overset{>}{\sim} 4 \times 10^{- 10}

3-

(2.6 \pm 1.0) \times 10^{- 5}

4-

(.5 - 2.0) \times 10^{- 5}

5-

\sim 7.5 \times 10^{- 5}

6-

{}^{232}T h /^{238} U

7-

\frac{d M_{G}}{d t} = e (t) - ψ (t) + f (t),

8-

e (t) = \int_{m (t)}^{m_{u p p}} (m - m_{R}) ψ (t - τ_{m}) ϕ (m) 𝑑 m .

9-

m_{u p p}

10-

m_{R} = .11 m + .45 M_{⊙} m \leq 6.8 M_{⊙}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/physics/0507210

Formulas:

1-

χ^{(3)} (ω; ω, ω, - ω)

2-

{(| 𝐄 | / | 𝐄_{0} |)}^{4}

3-

λ = 497 n m

4-

χ^{(3)} (ω; ω, ω, - ω)

5-

χ^{(3)} (ω; ω, ω, - ω)

6-

a = 50 n m

7-

2 h = 1 n m

8-

λ = 2 π c / ω

9-

ε = ε_{0} - ω_{p}^{2} / ω (ω + i γ) .

10-

γ / ω_{p} = 0.002

Formulas (html):

Correct Categorie: physics

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/physics/0611244

Formulas:

1-

τ_{s t a r t}

2-

𝒢 = (𝒩, 𝒮)

3-

i \in 𝒩 = {1, \dots, n}

4-

(i, j) \in 𝒮

5-

x_{i} (t) \in ℝ

6-

Θ (y) = \frac{1 - \exp (- α y)}{1 + \exp [- α (y - θ_{i})]},

7-

t_{i j} > 0

8-

\frac{d x_{i}}{d_{t}} = - \frac{x_{i}}{τ_{i}} + Θ (\sum_{i \neq j} \frac{M_{j i} x_{j} (t - t_{j i})}{f (O_{j})} e^{- β t_{j i}}),

9-

f (O_{j}) = (a O_{j}) / (1 + b O_{j})

10-

α_{1} + β_{1} + γ_{1} = 1

Formulas (html):

Correct Categorie: physics

Guessed Categorie: q-bio

Result: incorrect

Paper: https://arxiv.org/abs/gr-qc/9309026

Formulas:

1-

ℜ^{2} \times 𝒮^{d - 2}

2-

\frac{1}{2} \int_{M} \sqrt{g} g^{μ ν} R_{μ α ν}^{α} d^{2} x - \int_{\partial M} \sqrt{g} K d^{1} x = 2 π χ (M) .

3-

\sqrt{g} g^{μ ν}

4-

I_{H} = \frac{1}{2} \int_{M} \sqrt{g} g^{μ ν} R_{μ α ν}^{α} d^{d} x - \int_{\partial M} \sqrt{g} K d^{d - 1} x .

5-

\exp (+ I)

6-

\sqrt{g} g^{μ ν}

7-

I_{C} = \int (π^{i j} {\dot{g}}_{i j} - N ℋ - N^{i} ℋ_{i}) .

8-

ℋ = 0 = ℋ_{i}

9-

ℜ^{2} \times 𝒮^{d - 2}

10-

△_{ϵ} \times 𝒮^{d - 2}

Formulas (html):

Correct Categorie: gr-qc

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/1703.03218

Formulas:

1-

µ V K^{- 1}

2-

a_{GdIG} = 12.471 Å

3-

a_{DyIG} = 12.405 Å

4-

2 d_{h k l} \sin (Θ)

5-

with d_{h k l}

6-

= \frac{a}{\sqrt{h^{2} + k^{2} + l^{2}}},

7-

a_{YAG} = 12.008 Å

8-

41 nm and 100 nm

9-

a_{GGG} = 12.375 Å

10-

41 nm, 100 nm and 155 nm

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: math

Result: incorrect

Paper: https://arxiv.org/abs/1409.7517

Formulas:

1-

P 3_{1} 21

2-

P 3_{1} 21

3-

P 3_{2} 21

4-

H_{m n}^{G W +SO} (𝑹)

5-

⟨ ϕ_{m 𝟎} | ℋ^{LDA+SO} | ϕ_{n 𝑹} ⟩

6-

⟨ ϕ_{m 𝟎} | - V_{xc}^{LDA} + Σ^{G W} | ϕ_{n 𝑹} ⟩,

7-

(| p_{y^{'} i} ⟩ + | p_{z^{'} (i + 1)} ⟩) / \sqrt{2}

8-

(| p_{y^{'} i} ⟩ - | p_{z^{'} (i + 1)} ⟩) / \sqrt{2}

9-

| p_{y^{'} i} ⟩

10-

| p_{z^{'} i} ⟩

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0306264

Formulas:

1-

\frac{1}{ρ_{g} (r)} \frac{d P (r)}{d r} = - \frac{G M (r)}{r^{2}} ≃ - \frac{G M_{dm} (r)}{r^{2}}

2-

P = (ρ_{g} k T) / (μ m_{p})

3-

P (r) \propto ρ_{g}^{γ} (r)

4-

ρ_{g} (r) = ρ_{0} {[1 + {(r / r_{c})}^{2}]}^{- 3 β / 2}

5-

S_{X} (θ) = S_{0} {[1 + {(θ / r_{c})}^{2}]}^{- 3 β + 1 / 2}

6-

Ω_{b} = 0.02 h^{- 2}

7-

2.96 \times 10^{8} h^{- 1}

8-

ϵ = 2 - 5 h^{- 1}

9-

10^{13} h^{- 1}

10-

[0.1 - 0.5 M_{200}]

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/0908.3367

Formulas:

1-

- \frac{m_{g}^{2}}{4} (h_{μ ν} h^{μ ν} - ξ h^{2})

2-

(a = 0, 1, 2, 3)

3-

g_{μ ν} £

4-

g_{μ ν}^{ϕ} = η_{a b} \partial_{μ} ϕ^{a} \partial_{ν} ϕ^{b}

5-

η_{a b} = d i a g (- 1, 1, 1, 1)

6-

η_{a b} \neq δ_{a b}

7-

\sqrt{-det (g_{μ ν}^{ϕ})} = ε^{α β γ ρ} \partial_{α} ϕ^{0} \partial_{β} ϕ^{1} \partial_{γ} ϕ^{2} \partial_{ρ} ϕ^{3}

8-

ε^{α β γ ρ}

9-

det (g_{μ ν}^{ϕ}) / det (g_{μ ν})

10-

g_{μ ν} = η_{μ ν} + h_{μ ν}

Formulas (html):

Correct Categorie: gr-qc

Guessed Categorie: gr-qc

Result: correct

Paper: https://arxiv.org/abs/1312.5677

Formulas:

1-

T_{N} (x)

2-

T_{N} (x)

3-

(T_{n} (x))

4-

T_{n} (x) = 2 x T_{n - 1} (x) - T_{n - 2} (x), n = 2, 3, \dots,

5-

T_{0} (x) = 1, T_{1} (x) = x

6-

T_{N} (x)

7-

T_{N} (x)

8-

T_{N} (x)

9-

T_{N} (x) = a_{0} + a_{1} x + \dots + a_{N} x^{N}

10-

T_{N} (x)

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/1603.01678

Formulas:

1-

\frac{1}{2 m_{s}} {(ℏ 𝐤 - e 𝐀)}^{2} + α {[𝝈 \times (ℏ 𝐤 - e 𝐀)]}_{z}

2-

β [𝝈 \cdot (ℏ 𝐤 - e 𝐀)],

3-

𝝈 = (σ_{x}, σ_{y}, σ_{z})

4-

𝐤 = (k_{x}, k_{y})

5-

𝐀 = (0, [E / ω] \cos ω t)

6-

{\hat{ℋ}}_{e} = {\hat{ℋ}}_{0} + {\hat{ℋ}}_{k}

7-

{\hat{ℋ}}_{0} = \frac{e^{2} E^{2}}{2 m_{s} ω^{2}} \cos^{2} ω t - (α σ_{x} + β σ_{y}) \frac{e E}{ω} \cos ω t

8-

{\hat{ℋ}}_{k} = \frac{ℏ^{2} k_{x}^{2}}{2 m_{s}} + (β σ_{x} - α σ_{y}) ℏ k_{x}

9-

i ℏ \partial Ψ_{0} / \partial t = {\hat{ℋ}}_{0} Ψ_{0}

10-

Ψ_{0}^{\pm} = \frac{1}{\sqrt{2}} (\begin{matrix} 1 \\ \pm \frac{α + i β}{γ} \end{matrix}) e^{- i \frac{e^{2} E^{2}}{4 m_{s} ℏ ω^{2}} (t + \frac{\sin 2 ω t}{2 ω})} e^{\pm i \frac{e E γ}{ℏ ω^{2}} \sin ω t},

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/0802.0956

Formulas:

1-

\bar{n} (s)

2-

\bar{n} (s)

3-

\begin{matrix} σ_{γ N} (s) = \bar{n} (s) \cdot σ_{γ N}^{(0)} (s / \bar{n} (s)), \\ σ_{γ γ} (s) = {\bar{n}}^{2} (s) \cdot σ_{γ γ}^{(0)} (s / {\bar{n}}^{2} (s)), \end{matrix}

4-

σ_{γ N} (s)

5-

σ_{γ γ} (s)

6-

σ_{γ N}^{(0)}

7-

σ_{γ γ}^{(0)}

8-

\bar{n} (s)

9-

\sqrt{s_{γ N}}, \sqrt{s_{γ γ}} \sim

10-

σ_{γ N}^{(0)}

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: hep-ph

Result: correct

Paper: https://arxiv.org/abs/1502.05604

Formulas:

1-

μ_{S} = - 2 ⟨ S_{z} ⟩

2-

𝐓 = \sum_{𝐢} [𝐬_{𝐢} - 𝟑 𝐫_{𝐢} (𝐫_{𝐢} \cdot 𝐬_{𝐢}) / 𝐫_{𝐢}^{𝟐}]

3-

⟨ S_{eff} ⟩ \equiv ⟨ S_{z} ⟩ + 3 ⟨ T_{z} ⟩

4-

⟨ T_{z} ⟩ = 0

5-

⟨ L_{z} ⟩ = - ⟨ S_{z} ⟩

6-

2.8 (1) μ_{B}

7-

T_{C} \sim 700 K

8-

\sim 40 \times 200 \times 150 μ m

9-

T_{C} \sim 700 K

10-

B = I_{M_{5}} / (I_{M_{5}} + I_{M_{4}})

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/2003.06883

Formulas:

1-

I \in R^{H \times W \times 3}

2-

\in R^{H \times W \times C}

3-

\in R^{H \times W \times C}

4-

I \in R^{H \times W \times 3}

5-

M_{S} \in R^{H \times W \times C}

6-

M_{E} \in {[0, 1]}^{H \times W}

7-

L = α L_{c} + β L_{e}

8-

\hat{f_{S}} = w_{1} f_{S} + w_{2} f_{S} \otimes W_{r},

9-

δ (W * f_{E} + b)

10-

E F 1_{g} = (1 + β^{2}) * \frac{(p r e c i s i o n_{g} * r e c a l l_{g})}{β^{2} * p r e c i s i o n_{g} + r e c a l l_{g}},

Formulas (html):

Correct Categorie: cs

Guessed Categorie: cs

Result: correct

Paper: https://arxiv.org/abs/nucl-th/0304060

Formulas:

1-

T (T + 1.025)

2-

T (T + x)

3-

T (T + 1)

4-

H = H_{0} - G 𝐏^{†} \cdot 𝐏 + \frac{κ 𝐓^{2}}{2}, H_{0} = \sum_{k σ τ} ϵ_{k} a_{k σ τ}^{†} a_{k σ τ} .

5-

a_{k σ τ}

6-

R = H - λ A_{v} - μ T_{z},

7-

⟨ A_{v} ⟩ = 2 Ω

8-

A_{v} / 2 \pm T_{z}

9-

𝚫 = - G ⟨ 𝐏 ⟩

10-

A_{v} = ⟨ A_{v} ⟩

Formulas (html):

Correct Categorie: nucl-th

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/1410.7569

Formulas:

1-

{g_{1}, \dots, g_{u}}

2-

| g_{1} |, \dots, | g_{u} |

3-

x_{1}, \dots, x_{u} \in G

4-

{g_{1}^{x_{1}}, \dots, g_{u}^{x_{u}}}

5-

π_{1}, \dots, π_{u}

6-

k_{π_{i}} (S)

7-

\prod_{i = 1}^{u} k_{π_{i}} (S) \leq \frac{| S |}{2 | Out S |} .

8-

{g_{1}, \dots, g_{u}}

9-

{g_{1}^{x_{1}}, \dots, g_{u}^{x_{u}}}

10-

{g_{1}, \dots, g_{u}}

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/hep-ph/0306118

Formulas:

1-

S (X, K)

2-

< {\hat{a}}_{p}^{†} {\hat{a}}_{p^{'}} > = ρ (𝐩^{'}, 𝐩)

3-

ρ (𝐩, 𝐩^{'}) = \int d^{4} X e^{i q X} S (X, K),

4-

q = p - p^{'}

5-

K = (p + p^{'}) / 2

6-

S (X, K)

7-

S (X, K)

8-

| 𝐩, t ⟩ = e^{i E (p) t} | 𝐩 ⟩

9-

W (𝐗, 𝐊)

10-

ρ (𝐩, 𝐩^{'}, t) = \int d^{3} X e^{- i 𝐪 \cdot 𝐗} W (𝐗, 𝐊, t) .

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: nucl-th

Result: incorrect

Paper: https://arxiv.org/abs/1908.02635

Formulas:

1-

𝐬 = {s_{i} ∣ 1 \leq i \leq N \leq h}

2-

s_{i} = (v_{i}^{b}, v_{i}^{t}, m_{i}, p_{i}, 𝐭_{i}, c_{i})

3-

v_{i}^{b}, v_{i}^{t}

4-

Φ (𝐬, 𝐟, 𝐥)

5-

\min_{𝐬} E (𝐬, 𝐟, 𝐥)

6-

\min_{𝐬} (Ψ (𝐬) + Φ (𝐬, 𝐟, 𝐥))

7-

Ψ_{s t r} (s_{i}, s_{i - 1})

8-

Ψ (𝐬) = \sum_{i = 1}^{N} (Ψ_{s t r} (s_{i}, s_{i - 1}) + β_{m c})

9-

s_{i} \in {𝕊 𝕆, 𝔻 𝕆}

10-

s_{i - 1} \in {𝔾, 𝕊}

Formulas (html):

Correct Categorie: cs

Guessed Categorie: cs

Result: correct

Paper: https://arxiv.org/abs/1102.2231

Formulas:

1-

{(m - M)}_{0} = 13.11 \pm 0.06

2-

{(m - M)}_{0} = 11.85 \pm 0.05

3-

1.20 \pm 0.01 M_{⊙}

4-

1.68 \pm 0.03 M_{⊙}

5-

\frac{Δ ν}{Δ ν_{⊙}} = \sqrt{\frac{M / M_{⊙}}{{(R / R_{⊙})}^{3}}} .

6-

\frac{ν_{\max}}{ν_{\max, ⊙}} = \frac{M / M_{⊙}}{{(R / R_{⊙})}^{2} \sqrt{(T_{eff} / T_{eff, ⊙})}} .

7-

(B - V) = 0.16 \pm 0.02

8-

(B - V) = 0.15

9-

(B - V) = 0.16

10-

1.20 \pm 0.01 M_{⊙}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1310.8282

Formulas:

1-

[\frac{\partial^{2}}{\partial x^{2}} + k^{2} ϵ ({| Ψ |}^{2})] Ψ = 0,

2-

ϵ ({| Ψ |}^{2}) = 1 + χ_{0} η ({| Ψ |}^{2}),

3-

η ({| Ψ |}^{2}) = {\begin{matrix} \frac{δ + i}{1 + δ^{2} + α {| Ψ |}^{2}} & 0 < x < L \\ \frac{δ - i}{1 + δ^{2} + α {| Ψ |}^{2}} & - L < x < 0 \end{matrix},

4-

δ = (ω - ω_{0}) / \tilde{Γ}

5-

\tilde{Γ} = γ + Γ

6-

ω = (1 + 10^{- 4} δ) ω_{0}

7-

[\begin{matrix} c \\ d \end{matrix}] = ℳ [\begin{matrix} a \\ b \end{matrix}] .

8-

Ψ^{l} (x) = {\begin{matrix} c_{l} (e^{i k x} + r_{l} e^{- i k x}) & x < - L \\ c_{l} t_{l} e^{i k x} & x > L \end{matrix},

9-

Ψ^{r} (x) = {\begin{matrix} c_{r} t_{r} e^{- i k x} & x < - L \\ c_{r} (e^{- i k x} + r_{r} e^{i k x}) & x > L \end{matrix},

10-

I_{l} = {| c_{l} |}^{2}

Formulas (html):

Correct Categorie: physics

Guessed Categorie: physics

Result: correct

Paper: https://arxiv.org/abs/0710.2768

Formulas:

1-

cf (λ) > ℵ_{0}

2-

{(λ^{+})}^{ℵ_{0}} = \max {λ^{+}, λ^{ℵ_{0}}} = λ^{+},

3-

λ = {(κ^{ℵ_{0}})}^{+}

4-

{[η]}_{ϵ} = {η} \cup {ρ \in λ^{*} : η \subset ρ and ρ (| η |) \geq ϵ},

5-

| λ^{*} | = λ

6-

| Y | < cf (λ)

7-

{η ⌢ ϵ : ϵ < λ}

8-

ν, η \in λ^{*}

9-

ϵ_{ν, η} < λ

10-

{[η]}_{ϵ_{ν, η}} \cap {[ν]}_{ϵ_{ν, η}} = \emptyset

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/0911.2838

Formulas:

1-

H = \dot{a} / a

2-

q = - \ddot{a} / a H^{2}

3-

{r (z), s (z)}

4-

r \equiv \frac{\overset{˙˙˙}{a}}{a H^{3}},

5-

s \equiv \frac{r - 1}{3 (q - \frac{1}{2})} .

6-

{r, s} = {1, 0}

7-

δ t = λ t_{p}^{2 / 3} t^{1 / 3},

8-

ℏ = c = k_{B} = 1

9-

l_{p} = t_{p} = 1 / m_{p}

10-

δ t^{3} \sim t_{p}^{2} t

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: gr-qc

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/0608506

Formulas:

1-

τ_{e} \sim N^{1 + 2 ν}

2-

τ \sim N^{2 ν}

3-

τ \sim N^{1 + ν}

4-

τ \sim N^{1 + ν}

5-

τ_{e q u i l} \sim N^{1 + 2 ν}

6-

τ_{e} \sim N^{1 + 2 ν}

7-

τ_{e} \sim N^{1 + 2 ν}

8-

τ \sim N^{2 ν}

9-

τ \sim N^{1 + ν}

10-

U_{L J} (r) = {\begin{matrix} 4 ε [{(\frac{σ}{r})}^{12} - {(\frac{σ}{r})}^{6}] + ε, & r \leq 2^{1 / 6} σ; \\ 0, & r > 2^{1 / 6} σ, \end{matrix}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1503.04408

Formulas:

1-

A = (a_{i j})

2-

2 k \times 2 k

3-

a_{i j} + a_{k l} = a_{i l} + a_{k j}

4-

ℂ [x_{1}, \dots x_{n}]

5-

2 \deg (F) = trace (A)

6-

F = pfaff (M_{1}) + \dots + pfaff (M_{s (A)})

7-

M_{i} = (F_{l m}^{i})

8-

2 k \times 2 k

9-

s (A) \leq k

10-

F \in ℂ [x_{1}, \dots, x_{n}]

Formulas (html):

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xref="id4.4.m4.1.1.3.2.3.3.cmml">l</mi></mrow></msub><mo id="id4.4.m4.1.1.3.1" xref="id4.4.m4.1.1.3.1.cmml">+</mo><msub id="id4.4.m4.1.1.3.3" xref="id4.4.m4.1.1.3.3.cmml"><mi id="id4.4.m4.1.1.3.3.2" xref="id4.4.m4.1.1.3.3.2.cmml">a</mi><mrow id="id4.4.m4.1.1.3.3.3" xref="id4.4.m4.1.1.3.3.3.cmml"><mi id="id4.4.m4.1.1.3.3.3.2" xref="id4.4.m4.1.1.3.3.3.2.cmml">k</mi><mo id="id4.4.m4.1.1.3.3.3.1" xref="id4.4.m4.1.1.3.3.3.1.cmml">⁢</mo><mi id="id4.4.m4.1.1.3.3.3.3" xref="id4.4.m4.1.1.3.3.3.3.cmml">j</mi></mrow></msub></mrow></mrow></math>, <math><mrow id="id7.7.m7.2.2" xref="id7.7.m7.2.2.cmml"><mi id="id7.7.m7.2.2.4" xref="id7.7.m7.2.2.4.cmml">ℂ</mi><mo id="id7.7.m7.2.2.3" xref="id7.7.m7.2.2.3.cmml">⁢</mo><mrow id="id7.7.m7.2.2.2.2" xref="id7.7.m7.2.2.2.3.cmml"><mo stretchy="false" id="id7.7.m7.2.2.2.2.3" xref="id7.7.m7.2.2.2.3.cmml">[</mo><msub id="id7.7.m7.1.1.1.1.1" xref="id7.7.m7.1.1.1.1.1.cmml"><mi id="id7.7.m7.1.1.1.1.1.2" xref="id7.7.m7.1.1.1.1.1.2.cmml">x</mi><mn id="id7.7.m7.1.1.1.1.1.3" xref="id7.7.m7.1.1.1.1.1.3.cmml">1</mn></msub><mo id="id7.7.m7.2.2.2.2.4" xref="id7.7.m7.2.2.2.3.cmml">,</mo><mrow id="id7.7.m7.2.2.2.2.2" xref="id7.7.m7.2.2.2.2.2.cmml"><mi mathvariant="normal" id="id7.7.m7.2.2.2.2.2.2" xref="id7.7.m7.2.2.2.2.2.2.cmml">…</mi><mo id="id7.7.m7.2.2.2.2.2.1" xref="id7.7.m7.2.2.2.2.2.1.cmml">⁢</mo><msub id="id7.7.m7.2.2.2.2.2.3" xref="id7.7.m7.2.2.2.2.2.3.cmml"><mi id="id7.7.m7.2.2.2.2.2.3.2" xref="id7.7.m7.2.2.2.2.2.3.2.cmml">x</mi><mi id="id7.7.m7.2.2.2.2.2.3.3" xref="id7.7.m7.2.2.2.2.2.3.3.cmml">n</mi></msub></mrow><mo stretchy="false" id="id7.7.m7.2.2.2.2.5" xref="id7.7.m7.2.2.2.3.cmml">]</mo></mrow></mrow></math>, <math><mrow id="id8.8.m8.3.4" xref="id8.8.m8.3.4.cmml"><mrow id="id8.8.m8.3.4.2" xref="id8.8.m8.3.4.2.cmml"><mn id="id8.8.m8.3.4.2.2" xref="id8.8.m8.3.4.2.2.cmml">2</mn><mo id="id8.8.m8.3.4.2.1" xref="id8.8.m8.3.4.2.1.cmml">⁢</mo><mrow id="id8.8.m8.3.4.2.3.2" xref="id8.8.m8.3.4.2.3.1.cmml"><mi id="id8.8.m8.1.1" xref="id8.8.m8.1.1.cmml">deg</mi><mo id="id8.8.m8.3.4.2.3.2a" xref="id8.8.m8.3.4.2.3.1.cmml">⁡</mo><mrow id="id8.8.m8.3.4.2.3.2.1" xref="id8.8.m8.3.4.2.3.1.cmml"><mo stretchy="false" id="id8.8.m8.3.4.2.3.2.1.1" xref="id8.8.m8.3.4.2.3.1.cmml">(</mo><mi id="id8.8.m8.2.2" xref="id8.8.m8.2.2.cmml">F</mi><mo stretchy="false" id="id8.8.m8.3.4.2.3.2.1.2" xref="id8.8.m8.3.4.2.3.1.cmml">)</mo></mrow></mrow></mrow><mo id="id8.8.m8.3.4.1" xref="id8.8.m8.3.4.1.cmml">=</mo><mrow id="id8.8.m8.3.4.3" xref="id8.8.m8.3.4.3.cmml"><mi id="id8.8.m8.3.4.3.2" xref="id8.8.m8.3.4.3.2.cmml">trace</mi><mo id="id8.8.m8.3.4.3.1" xref="id8.8.m8.3.4.3.1.cmml">⁢</mo><mrow id="id8.8.m8.3.4.3.3.2" xref="id8.8.m8.3.4.3.cmml"><mo stretchy="false" id="id8.8.m8.3.4.3.3.2.1" xref="id8.8.m8.3.4.3.cmml">(</mo><mi id="id8.8.m8.3.3" xref="id8.8.m8.3.3.cmml">A</mi><mo stretchy="false" id="id8.8.m8.3.4.3.3.2.2" xref="id8.8.m8.3.4.3.cmml">)</mo></mrow></mrow></mrow></math>, <math><mrow id="id10.10.m10.5.5" xref="id10.10.m10.5.5.cmml"><mi id="id10.10.m10.5.5.4" xref="id10.10.m10.5.5.4.cmml">F</mi><mo id="id10.10.m10.5.5.3" xref="id10.10.m10.5.5.3.cmml">=</mo><mrow id="id10.10.m10.5.5.2" xref="id10.10.m10.5.5.2.cmml"><mrow id="id10.10.m10.4.4.1.1.1" xref="id10.10.m10.4.4.1.1.2.cmml"><mi id="id10.10.m10.2.2" xref="id10.10.m10.2.2.cmml">pfaff</mi><mo id="id10.10.m10.4.4.1.1.1a" xref="id10.10.m10.4.4.1.1.2.cmml">⁡</mo><mrow id="id10.10.m10.4.4.1.1.1.1" xref="id10.10.m10.4.4.1.1.2.cmml"><mo stretchy="false" id="id10.10.m10.4.4.1.1.1.1.2" xref="id10.10.m10.4.4.1.1.2.cmml">(</mo><msub id="id10.10.m10.4.4.1.1.1.1.1" xref="id10.10.m10.4.4.1.1.1.1.1.cmml"><mi id="id10.10.m10.4.4.1.1.1.1.1.2" xref="id10.10.m10.4.4.1.1.1.1.1.2.cmml">M</mi><mn id="id10.10.m10.4.4.1.1.1.1.1.3" xref="id10.10.m10.4.4.1.1.1.1.1.3.cmml">1</mn></msub><mo stretchy="false" id="id10.10.m10.4.4.1.1.1.1.3" xref="id10.10.m10.4.4.1.1.2.cmml">)</mo></mrow></mrow><mo id="id10.10.m10.5.5.2.3" xref="id10.10.m10.5.5.2.3.cmml">+</mo><mi mathvariant="normal" id="id10.10.m10.5.5.2.4" xref="id10.10.m10.5.5.2.4.cmml">⋯</mi><mo id="id10.10.m10.5.5.2.3a" xref="id10.10.m10.5.5.2.3.cmml">+</mo><mrow id="id10.10.m10.5.5.2.2.1" xref="id10.10.m10.5.5.2.2.2.cmml"><mi id="id10.10.m10.3.3" xref="id10.10.m10.3.3.cmml">pfaff</mi><mo id="id10.10.m10.5.5.2.2.1a" xref="id10.10.m10.5.5.2.2.2.cmml">⁡</mo><mrow id="id10.10.m10.5.5.2.2.1.1" xref="id10.10.m10.5.5.2.2.2.cmml"><mo stretchy="false" id="id10.10.m10.5.5.2.2.1.1.2" xref="id10.10.m10.5.5.2.2.2.cmml">(</mo><msub id="id10.10.m10.5.5.2.2.1.1.1" xref="id10.10.m10.5.5.2.2.1.1.1.cmml"><mi id="id10.10.m10.5.5.2.2.1.1.1.2" xref="id10.10.m10.5.5.2.2.1.1.1.2.cmml">M</mi><mrow id="id10.10.m10.1.1.1" xref="id10.10.m10.1.1.1.cmml"><mi id="id10.10.m10.1.1.1.3" xref="id10.10.m10.1.1.1.3.cmml">s</mi><mo id="id10.10.m10.1.1.1.2" xref="id10.10.m10.1.1.1.2.cmml">⁢</mo><mrow id="id10.10.m10.1.1.1.4.2" xref="id10.10.m10.1.1.1.cmml"><mo stretchy="false" id="id10.10.m10.1.1.1.4.2.1" xref="id10.10.m10.1.1.1.cmml">(</mo><mi id="id10.10.m10.1.1.1.1" xref="id10.10.m10.1.1.1.1.cmml">A</mi><mo stretchy="false" id="id10.10.m10.1.1.1.4.2.2" xref="id10.10.m10.1.1.1.cmml">)</mo></mrow></mrow></msub><mo stretchy="false" id="id10.10.m10.5.5.2.2.1.1.3" xref="id10.10.m10.5.5.2.2.2.cmml">)</mo></mrow></mrow></mrow></mrow></math>, <math><mrow id="id11.11.m11.1.1" xref="id11.11.m11.1.1.cmml"><msub id="id11.11.m11.1.1.3" xref="id11.11.m11.1.1.3.cmml"><mi id="id11.11.m11.1.1.3.2" xref="id11.11.m11.1.1.3.2.cmml">M</mi><mi id="id11.11.m11.1.1.3.3" xref="id11.11.m11.1.1.3.3.cmml">i</mi></msub><mo id="id11.11.m11.1.1.2" xref="id11.11.m11.1.1.2.cmml">=</mo><mrow id="id11.11.m11.1.1.1.1" xref="id11.11.m11.1.1.1.1.1.cmml"><mo stretchy="false" id="id11.11.m11.1.1.1.1.2" xref="id11.11.m11.1.1.1.1.1.cmml">(</mo><msubsup id="id11.11.m11.1.1.1.1.1" xref="id11.11.m11.1.1.1.1.1.cmml"><mi id="id11.11.m11.1.1.1.1.1.2.2" xref="id11.11.m11.1.1.1.1.1.2.2.cmml">F</mi><mrow id="id11.11.m11.1.1.1.1.1.3" xref="id11.11.m11.1.1.1.1.1.3.cmml"><mi id="id11.11.m11.1.1.1.1.1.3.2" xref="id11.11.m11.1.1.1.1.1.3.2.cmml">l</mi><mo id="id11.11.m11.1.1.1.1.1.3.1" xref="id11.11.m11.1.1.1.1.1.3.1.cmml">⁢</mo><mi id="id11.11.m11.1.1.1.1.1.3.3" xref="id11.11.m11.1.1.1.1.1.3.3.cmml">m</mi></mrow><mi id="id11.11.m11.1.1.1.1.1.2.3" xref="id11.11.m11.1.1.1.1.1.2.3.cmml">i</mi></msubsup><mo stretchy="false" id="id11.11.m11.1.1.1.1.3" xref="id11.11.m11.1.1.1.1.1.cmml">)</mo></mrow></mrow></math>, <math><mrow id="id12.12.m12.1.1" xref="id12.12.m12.1.1.cmml"><mrow id="id12.12.m12.1.1.2" xref="id12.12.m12.1.1.2.cmml"><mrow id="id12.12.m12.1.1.2.2" xref="id12.12.m12.1.1.2.2.cmml"><mn id="id12.12.m12.1.1.2.2.2" xref="id12.12.m12.1.1.2.2.2.cmml">2</mn><mo id="id12.12.m12.1.1.2.2.1" xref="id12.12.m12.1.1.2.2.1.cmml">⁢</mo><mi id="id12.12.m12.1.1.2.2.3" xref="id12.12.m12.1.1.2.2.3.cmml">k</mi></mrow><mo id="id12.12.m12.1.1.2.1" xref="id12.12.m12.1.1.2.1.cmml">×</mo><mn id="id12.12.m12.1.1.2.3" xref="id12.12.m12.1.1.2.3.cmml">2</mn></mrow><mo id="id12.12.m12.1.1.1" xref="id12.12.m12.1.1.1.cmml">⁢</mo><mi id="id12.12.m12.1.1.3" xref="id12.12.m12.1.1.3.cmml">k</mi></mrow></math>, <math><mrow id="id15.15.m15.1.2" xref="id15.15.m15.1.2.cmml"><mrow id="id15.15.m15.1.2.2" xref="id15.15.m15.1.2.2.cmml"><mi id="id15.15.m15.1.2.2.2" xref="id15.15.m15.1.2.2.2.cmml">s</mi><mo id="id15.15.m15.1.2.2.1" xref="id15.15.m15.1.2.2.1.cmml">⁢</mo><mrow id="id15.15.m15.1.2.2.3.2" xref="id15.15.m15.1.2.2.cmml"><mo stretchy="false" id="id15.15.m15.1.2.2.3.2.1" xref="id15.15.m15.1.2.2.cmml">(</mo><mi id="id15.15.m15.1.1" xref="id15.15.m15.1.1.cmml">A</mi><mo stretchy="false" id="id15.15.m15.1.2.2.3.2.2" xref="id15.15.m15.1.2.2.cmml">)</mo></mrow></mrow><mo id="id15.15.m15.1.2.1" xref="id15.15.m15.1.2.1.cmml">≤</mo><mi id="id15.15.m15.1.2.3" xref="id15.15.m15.1.2.3.cmml">k</mi></mrow></math>, <math><mrow id="Sx1.p1.1.m1.3.3" xref="Sx1.p1.1.m1.3.3.cmml"><mi id="Sx1.p1.1.m1.3.3.4" xref="Sx1.p1.1.m1.3.3.4.cmml">F</mi><mo id="Sx1.p1.1.m1.3.3.3" xref="Sx1.p1.1.m1.3.3.3.cmml">∈</mo><mrow id="Sx1.p1.1.m1.3.3.2" xref="Sx1.p1.1.m1.3.3.2.cmml"><mi id="Sx1.p1.1.m1.3.3.2.4" xref="Sx1.p1.1.m1.3.3.2.4.cmml">ℂ</mi><mo id="Sx1.p1.1.m1.3.3.2.3" xref="Sx1.p1.1.m1.3.3.2.3.cmml">⁢</mo><mrow id="Sx1.p1.1.m1.3.3.2.2.2" xref="Sx1.p1.1.m1.3.3.2.2.3.cmml"><mo stretchy="false" id="Sx1.p1.1.m1.3.3.2.2.2.3" xref="Sx1.p1.1.m1.3.3.2.2.3.cmml">[</mo><msub id="Sx1.p1.1.m1.2.2.1.1.1.1" xref="Sx1.p1.1.m1.2.2.1.1.1.1.cmml"><mi id="Sx1.p1.1.m1.2.2.1.1.1.1.2" xref="Sx1.p1.1.m1.2.2.1.1.1.1.2.cmml">x</mi><mn id="Sx1.p1.1.m1.2.2.1.1.1.1.3" xref="Sx1.p1.1.m1.2.2.1.1.1.1.3.cmml">1</mn></msub><mo id="Sx1.p1.1.m1.3.3.2.2.2.4" xref="Sx1.p1.1.m1.3.3.2.2.3.cmml">,</mo><mi mathvariant="normal" id="Sx1.p1.1.m1.1.1" xref="Sx1.p1.1.m1.1.1.cmml">…</mi><mo id="Sx1.p1.1.m1.3.3.2.2.2.5" xref="Sx1.p1.1.m1.3.3.2.2.3.cmml">,</mo><msub id="Sx1.p1.1.m1.3.3.2.2.2.2" xref="Sx1.p1.1.m1.3.3.2.2.2.2.cmml"><mi id="Sx1.p1.1.m1.3.3.2.2.2.2.2" xref="Sx1.p1.1.m1.3.3.2.2.2.2.2.cmml">x</mi><mi id="Sx1.p1.1.m1.3.3.2.2.2.2.3" xref="Sx1.p1.1.m1.3.3.2.2.2.2.3.cmml">n</mi></msub><mo stretchy="false" id="Sx1.p1.1.m1.3.3.2.2.2.6" xref="Sx1.p1.1.m1.3.3.2.2.3.cmml">]</mo></mrow></mrow></mrow></math>

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/0803.3106

Formulas:

1-

\frac{d_{2}}{v_{w}} + \underset{1}{\underset{⏟}{\int_{0}^{t_{w}} (\frac{1}{t_{b}} (\frac{d - d_{2}}{v_{b}})) 𝑑 t}} + \underset{2}{\underset{⏟}{(1 - \int_{0}^{t_{w}} p (t) 𝑑 t) (\frac{d}{v_{w}} + t_{w})}}

2-

\underset{1}{\underset{⏟}{\int_{0}^{t_{w}} (\frac{1}{t_{b}} (\frac{d - d_{2}}{v_{b}} + t)) 𝑑 t}} + \underset{2}{\underset{⏟}{(1 - \int_{0}^{t_{w}} p (t) 𝑑 t) (\frac{d}{v_{w}} + t_{w})}} = \frac{d - d_{2}}{v_{w}}

3-

(1 - \int_{0}^{t_{w}} p (t) 𝑑 t) (\frac{d - d_{2}}{v_{w}} + t_{w})

4-

p (t_{\circ} - \frac{d_{2}}{v_{b}} + \frac{d_{2}}{v_{w}})

5-

t_{\circ}^{'} - \frac{d_{2}}{v_{b}}

6-

p (t_{c o r r e c t e d})

7-

\int_{0}^{t_{w}} p (t_{c o r r e c t e d}) (\frac{d - d_{2}}{v_{b}} + t) 𝑑 t

8-

t_{c o r r e c t e d}

9-

t - \frac{d_{2}}{v_{b}} + \frac{d_{2}}{v_{w}}

10-

\int_{0}^{\frac{d_{2}}{v_{w}}} \frac{1}{t_{b}} [\underset{1}{\underset{⏟}{(t_{b} - t)}} - \underset{2}{\underset{⏟}{(\frac{d_{2} - v_{w} t}{v_{w}})}}] 𝑑 t

Formulas (html):

Correct Categorie: math

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1902.11244

Formulas:

1-

diag (a_{1}, a_{2}, \dots, a_{n})

2-

a_{1}, a_{2}, \dots, a_{n}

3-

\ker (A) := {x \in 𝒳 ∣ A x = 0}

4-

im (A) := {A x ∣ x \in 𝒳}

5-

𝒢 = (𝒱, ℰ)

6-

𝒱 = {1, 2, \dots, N}

7-

(i, j) \in ℰ

8-

𝒩_{i} := {j \in 𝒱 ∣ (i, j) \in ℰ}

9-

A = [a_{i j}] \in ℝ^{N \times N}

10-

a_{i j} = 1

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/math/0204331

Formulas:

1-

\dot{γ} (t_{0})

2-

G γ (t_{0})

3-

T^{k} \times N = \hat{M}

4-

(h, k) \cdot g = h g k^{- 1}

5-

π : G \to G / K

6-

J (0) = 0

7-

[𝔥, 𝔥^{⟂}] \subset 𝔥^{⟂}

8-

𝔥 \cdot a + a \cdot 𝔨

9-

𝔩^{a} := 𝔨 + {Ad}_{a^{- 1}} 𝔥

10-

𝔪^{a} := 𝔭 \cap {{Ad}_{a^{- 1}} 𝔥}^{⟂}

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/0802.3787

Formulas:

1-

26 km s^{- 1}

2-

3 \cdot 10^{- 16} kg

3-

1.5 \times 10^{- 4} m^{- 2} s^{- 1}

4-

0.5 \times 10^{- 4} m^{- 2} s^{- 1}

5-

10^{- 4} m^{- 2} s^{- 1}

6-

q / m = 0.59 C {kg}^{- 1}

7-

n (H^{o}) \sim 0.2 {cm}^{- 3}

8-

n (e^{-}) \sim 0.10 {cm}^{- 3}

9-

\sim 26 km s^{- 1}

10-

> 0.04 {cm}^{- 3}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1511.05049

Formulas:

1-

A U C_{α}

2-

S = (x_{1}, \dots, x_{k}, \dots, x_{K}) \in 𝐑^{2 K}

3-

R^{1 \dots T}

4-

f^{t} = h^{t} (I, S^{t - 1})

5-

Δ S = R^{t} (f^{t})

6-

S^{t} = S^{t - 1} + Δ S

7-

e_{x} = \frac{|| \hat{x} - x^{G T} ||}{D_{I O D}}

8-

|| \hat{x} - x^{G T} ||

9-

D_{I O D}

10-

A U C_{α} = \int_{0}^{α} f (e) 𝑑 e

Formulas (html):

Correct Categorie: cs

Guessed Categorie: cs

Result: correct

Paper: https://arxiv.org/abs/nucl-th/0305031

Formulas:

1-

(E - T - V_{i}) ψ_{i} = V_{i} (ψ_{j} + ψ_{k}),

2-

V_{i} \equiv V (𝐱_{i})

3-

Ψ = ψ_{1} (𝐱_{1}, 𝐲_{1}) + ψ_{2} (𝐱_{2}, 𝐲_{2}) + ψ_{3} (𝐱_{3}, 𝐲_{3}),

4-

𝐱_{i} \equiv 𝐫_{j} - 𝐫_{k},

5-

𝐲_{i} \equiv \frac{1}{2} (𝐫_{j} + 𝐫_{k}) - 𝐫_{i} .

6-

(E - T - V_{1} - V_{2} - V_{3}) Ψ = 0 .

7-

ϕ_{d} (𝐱_{i})

8-

χ (𝐲_{i})

9-

χ (𝐲_{i})

10-

ϕ_{i} (𝐱_{i}, 𝐲_{i}) = ϕ_{d} (𝐱_{i}) χ (𝐲_{i}),

Formulas (html):

Correct Categorie: nucl-th

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1104.0394

Formulas:

1-

0 < ε_{B} < 2

2-

ε_{B} > 10^{- 3}

3-

k T_{e} ≫ m_{e} c^{2}

4-

r \sim 0.1 R_{⋆}

5-

0 < ε_{B} < 2

6-

τ_{n} = \frac{n_{n} σ_{n} r}{Γ_{n}} = \frac{L_{n} σ_{n}}{4 π m_{n} c^{3} r Γ_{n}^{3}} = \frac{R_{n}}{r},

7-

L_{n} = 4 π m_{n} c^{3} r^{2} Γ_{n}^{2} n_{n}

8-

σ_{n} \sim 3 \times 10^{- 26} {cm}^{2}

9-

τ_{n} (R_{n}) = 1

10-

R_{n} = \frac{L_{n} σ_{n}}{4 π m_{n} c^{3} Γ_{n}^{3}} .

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/0809.2042

Formulas:

1-

M_{*} > 10^{10} M_{⊙}

2-

\sim 0.2 M_{⊙} {yr}^{- 1}

3-

H_{0} = 70 k m s^{- 1} {Mpc}^{- 1}

4-

δ z / (1 + z) \sim 0.02

5-

1 \deg \times 0.5 \deg

6-

5 \times 5 {Mpc}^{2} h_{70}^{- 2}

7-

> 1.8 \times 10^{- 15} erg {cm}^{- 2} s^{- 1}

8-

18 ≲ m_{R} ≲ 23

9-

L_{U V} = 1.5 ν l_{ν, 2800}

10-

S F R [M_{⊙} y r^{- 1}] = 9.8 \times 10^{- 11} (L_{I R} + 2.2 L_{U V})

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1207.2458

Formulas:

1-

P (k) = \frac{Γ (k + M)}{Γ (M) Γ (k + 1)} {(1 + \frac{M}{\bar{k}})}^{- k} {(1 + \frac{\bar{k}}{M})}^{- M},

2-

P (k) = {\bar{k}}^{k} \exp (- \bar{k}) / k!

3-

⟨ β ⟩ = 0.276 \pm 0.004

4-

β_{c a l c}

5-

n_{p a t t}

6-

n_{p i x} = 3.6, 7.2, or 13.2 \times 10^{5}

7-

L = 18, 35 to 37, or 142

8-

n_{p a t t}

9-

β_{c a l c}

10-

β_{c a l c}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0407039

Formulas:

1-

= \sqrt{Ω_{o}^{2} R^{3} / G M}

2-

S_{o} \approx 0.5 - 0.6

3-

F_{m o} (g) \propto g,

4-

v_{\infty} (g) \propto g^{1 / 2},

5-

g (θ) = \frac{G M}{R^{2}} - \frac{{(Ω_{o} R \sin θ)}^{2}}{R \sin θ} \sin θ

6-

= \frac{G M}{R^{2}} - Ω_{o}^{2} R \sin^{2} θ

7-

= g_{o} (1 - \frac{{(Ω_{o} R)}^{2}}{G M / R} \sin^{2} θ)

8-

= g_{o} (1 - S_{o}^{2} \sin^{2} θ),

9-

S_{o} = \sqrt{Ω_{o}^{2} R^{3} / G M}

10-

g_{o} = \frac{G M}{R^{2}} (1 - Γ_{r a d})

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Run 11332337 (Agent397)