Run 10695631

Paper: https://arxiv.org/abs/1711.02154

Formulas:

1-

𝒪 (N^{3}) \sim 𝒪 (N^{4})

2-

| Φ ⟩ = \sum_{i = 1}^{n_{d}} c_{i} | φ_{i} ⟩,

3-

⟨ φ_{i} | φ_{j} ⟩ \neq 0

4-

| φ_{i} ⟩ = e^{\sum_{p q} Z_{p q}^{i} {\hat{c}}_{p}^{†} {\hat{c}}_{q}} | φ_{ref} ⟩,

5-

E = ⟨ Φ | \hat{H} | Φ ⟩ / ⟨ Φ | Φ ⟩

6-

i = 1, 2, \dots, n_{d} - 1

7-

| Ψ_{0} ⟩ = lim_{τ \to \infty} e^{- τ \hat{H}} | Ψ_{T} ⟩,

8-

| Ψ^{(ℓ + 1)} ⟩ = e^{- Δ τ \hat{H}} | Ψ^{(ℓ)} ⟩,

9-

e^{- Δ τ \hat{H}} \approx e^{- Δ τ \hat{K} / 2} e^{- Δ τ \hat{V}} e^{- Δ τ \hat{K} / 2},

10-

𝒪 (Δ τ^{2})

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/2005.07251

Formulas:

1-

\frac{d S}{d t}, \frac{d E}{d t}, \frac{d I}{d t}

2-

\frac{d R}{d t}

3-

\frac{d S}{d t} = - β_{t} \frac{S}{N} I

4-

\frac{d E}{d t} = β_{t} \frac{S}{N} I - σ E

5-

\frac{d I}{d t} = σ E - γ I

6-

\frac{d R}{d t} = γ I

7-

β_{t} = R_{t} γ

8-

R_{t} = {\begin{matrix} R_{0} & 0 < t < t_{1} \\ R_{1} & t > t_{1} \end{matrix}

9-

R_{t} = {\begin{matrix} R_{0} & 0 < t < t_{1} \\ R_{1} & t_{1} < t < t_{2} \\ R_{2} & t > t_{2} \end{matrix}

10-

R_{1} < R_{2} < R_{0} .

Formulas (html):

Correct Categorie: physics

Guessed Categorie: q-bio

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/9908058

Formulas:

1-

P_{s} = Π \exp (2 i χ)

2-

σ_{P}^{2} = 1 / π \int_{0}^{π} 𝑑 χ {(P_{s} - ⟨ P_{s} ⟩)}^{2} = 1 / π \int_{0}^{π} 𝑑 χ Π^{2} [\cos^{2} (2 χ) + \sin^{2} (2 χ)] = Π^{2} .

3-

N = n (S) d S d Ω

4-

σ_{P, d Ω}^{2} = \frac{Π^{2}}{N} .

5-

S_{P} = N S P_{s}

6-

σ_{S_{P}, d Ω}^{2} = ⟨ {(S_{P} - ⟨ S_{P} ⟩)}^{2} ⟩ = ⟨ S_{P}^{2} ⟩ = \int_{0}^{\infty} 𝑑 N ρ (N) N S^{2} Π^{2} = Π^{2} S^{2} ⟨ N (S) ⟩ .

7-

σ_{I_{P}} = Π σ_{I}

8-

S_{ν} \propto ν^{- α}

9-

R A > 9^{h}

10-

Δ P_{m} = t_{ν} (0.32) σ_{P} {(N - 1)}^{- 1 / 2}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: hep-ph

Result: incorrect

Paper: https://arxiv.org/abs/hep-ph/0701066

Formulas:

1-

L_{e} - L_{μ} - L_{τ}

2-

L = L_{e} - L_{μ} - L_{τ}

3-

Δ m_{12}^{2} / Δ m_{23}^{2} ≃ 0.033

4-

\sin^{2} θ_{23} ≃ 0.5

5-

\sin^{2} θ_{12} = 0.31

6-

S U {(3)}_{c} \otimes S U {(3)}_{L} \otimes U {(1)}_{X}

7-

L = L_{e} - L_{μ} - L_{τ}

8-

γ / β = m (μ) / (τ)

9-

L = L_{e} - L_{μ} - L_{τ}

10-

\begin{matrix} f_{α L} = {(\begin{matrix} e_{α} \\ ν_{α} \\ ν_{α}^{c} \end{matrix})}_{L} \sim (𝟏, 𝟑^{*}, - 1 / 3) & e_{α L}^{c} \sim (𝟏, 𝟏, 1) \end{matrix}

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: hep-ph

Result: correct

Paper: https://arxiv.org/abs/math/0504280

Formulas:

1-

1 \leq N, K < p .

2-

J = \frac{K N}{p} + O (p^{1 / 2} \log^{2} p),

3-

x \in [H + 1, H + K]

4-

g^{x} \in [M + 1, M + N] .

5-

J = \frac{K N}{p} + O (\frac{K^{1 / 2} N^{1 / 2}}{p^{1 / 4}} + p^{1 / 2}) .

6-

J \sim K N / p

7-

\frac{K N}{p^{3 / 2}} \to \infty as p \to \infty,

8-

\frac{K N}{p^{3 / 2} \log^{2} p} \to \infty as p \to \infty .

9-

K N / p^{3 / 2} = O (1),

10-

J ≪ p^{1 / 2},

Formulas (html):

Correct Categorie: math

Guessed Categorie: nucl-th

Result: incorrect

Paper: https://arxiv.org/abs/1610.00698

Formulas:

1-

f : V (G) \to 𝒫 (X)

2-

f^{\oplus} : E (G) \to 𝒫 (X)

3-

f^{\oplus} (u v) = f (u) \oplus f (v)

4-

f (u) \oplus f (v)

5-

f : V (G) \to 𝒫 (X)

6-

f^{\oplus} : E (G) \to 𝒫 (X)

7-

f^{\oplus} (u v) = f (u) \oplus f (v) \forall u v \in E (G)

8-

f : V (G) \to 𝒫 (X)

9-

f^{\oplus} : E (G) \to 𝒫 (X)

10-

Σ (G, σ)

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

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/astro-ph/0310032

Formulas:

1-

\log L_{X} \sim 32

2-

v \sin i \sim 50

3-

L_{X} = 2.2 \times 10^{32}

4-

N_{H} = 7.5 \times 10^{20}

5-

[N / H] = + 0.3

6-

[C / N] = - 0.8

7-

v \sin i ≫ 50

8-

σ_{D} = (λ / c) \times \sqrt{k T / m}

9-

L_{X} = 4.4 \times 10^{30}

10-

[Fe / H] = - 0.5

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1904.10533

Formulas:

1-

D^{'} := ℝ^{3} ∖ D

2-

k = c o n s t > 0

3-

α, β \in S^{2}

4-

g = g (x, y) := \frac{e^{i k | x - y |}}{4 π | x - y |}

5-

{e_{j}}_{j = 1}^{3}

6-

\nabla^{2} u + k^{2} u = 0 i n D^{'}, {u |}_{S} = 0, u = u_{0} + v,

7-

u_{0} := e^{i k α \cdot x}

8-

v_{r} - i k v = O (r^{- 2}), r = | x | \to \infty, x / r = β,

9-

u = u (x) := u (x, α)

10-

u = u_{0} (x, α) - \int_{S} g (x, s) h (s) 𝑑 s, h := u_{N} (s, α) .

Formulas (html):

Correct Categorie: math

Guessed Categorie: nlin

Result: incorrect

Paper: https://arxiv.org/abs/2011.05764

Formulas:

1-

(ω = - \frac{3}{2} & n = - 1)

2-

S_{δ} = γ A^{δ}

3-

S = \int d^{4} x \sqrt{g} (- φ R + \frac{ω}{φ} g^{i j} \partial_{i φ} \partial_{j φ} + ℒ_{m})

4-

φ = \frac{ϕ^{2}}{8 ω}

5-

S = \int d^{4} x \sqrt{g} (- \frac{ϕ^{2}}{8 ω} R + \frac{1}{2} g^{i j} \partial_{i ϕ} \partial_{j ϕ} + ℒ_{m})

6-

d s^{2} = - d t^{2} + a {(t)}^{2} (\frac{d r^{2}}{1 - k r^{2}} + r^{2} d Ω^{2})

7-

\frac{3}{4 ω} ϕ^{2} (H^{2} + \frac{k}{a^{2}}) - \frac{{\dot{ϕ}}^{2}}{2} + \frac{3}{2 ω} H ϕ \dot{ϕ} = ρ_{m} + ρ_{D}

8-

- \frac{ϕ^{2}}{4 ω} (2 \frac{\ddot{a}}{a} + H^{2} + \frac{k}{a^{2}}) - \frac{1}{ω} H ϕ \dot{ϕ} - \frac{1}{2 ω} \ddot{ϕ} ϕ - \frac{{\dot{ϕ}}^{2}}{2} (1 + \frac{1}{ω}) = p_{D}

9-

\frac{\ddot{ϕ}}{ϕ} + 3 H \frac{\dot{ϕ}}{ϕ} - \frac{3}{2 ω} (\frac{\ddot{a}}{a} + H^{2} + \frac{k}{a^{2}}) = 0

10-

\frac{\dot{ϕ}}{ϕ} = n H

Formulas (html):

Correct Categorie: physics

Guessed Categorie: gr-qc

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/9805029

Formulas:

1-

14^{h} 09^{m} 17^{s} .5

2-

- 65^{o} 06^{^{'}} 19^{"}

3-

erg {cm}^{- 2} s^{- 1}

4-

\sim 10^{- 11} erg {cm}^{- 2} s^{- 1}

5-

\sim 2 \times 10^{- 9}

6-

erg {cm}^{- 2} s^{- 1}

7-

{cm}^{- 2} s^{- 1} {eV}^{- 1}

8-

{cm}^{- 2} s^{- 1} {eV}^{- 1}

9-

\sim 10^{53.5} s^{- 1}

10-

10^{- 2} T^{- 1.35} ν^{- 2.1}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/0712.1764

Formulas:

1-

(μ_{α}, μ_{δ}) = (195.6 \pm 3.6, 43.5 \pm 3.6)

2-

(μ_{α}, μ_{δ}) = (75.4 \pm 6.1, - 125.2 \pm 5.8)

3-

(μ_{α}, μ_{δ}) = (203 \pm 8, 44 \pm 5)

4-

(μ_{α}, μ_{δ}) = (116 \pm 18, - 117 \pm 18)

5-

{(S / N)}^{- 0.42}

6-

- 1.2 \times 10^{- 4} \pm 6.6 \times 10^{- 4}

7-

3.4 \times 10^{- 4} \pm 6.2 \times 10^{- 4}

8-

(α, δ) = (5^{h} 18 \overset{m}{.} 8, - 68 ° 34')

9-

- 1 < m_{606 W} - m_{814 W} < 2

10-

26 > m_{606 W} > 14

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/cond-mat/9510149

Formulas:

1-

ℋ = \sum_{j = 1}^{L} (S_{j}^{x} S_{j + 1}^{x} + S_{j}^{y} S_{j + 1}^{y} + λ S_{j}^{z} S_{j + 1}^{z})

2-

S_{j}^{x}, S_{j}^{y}

3-

λ < λ_{c} = 0

4-

(- 1 \leq λ \leq 0)

5-

x_{n, m}^{(b)}, x_{n}^{(s)}

6-

x_{n, m}^{(b)} = n^{2} x_{p} + \frac{m^{2}}{4 x_{p}}, x_{n}^{(s)} = 2 x_{p} n^{2}

7-

x_{p} = \frac{π - \cos^{- 1} (λ)}{4 π}, n, m = 0, \pm 1, \pm 2, \dots .

8-

x_{0, 1}^{(b)} = \frac{1}{4 x_{p}} = \frac{π}{π - \cos^{- 1} (λ)}

9-

λ = λ_{c} = 0

10-

λ = λ_{c} = 0.068 \pm 0.003

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: nlin

Result: incorrect

Paper: https://arxiv.org/abs/physics/0607018

Formulas:

1-

(\begin{matrix} x_{F} \\ y_{F} \\ z_{F} \end{matrix}) = (\begin{matrix} \cos (α) & - \sin (α) & 0 \\ \sin (α) & \cos (α) & 0 \\ 0 & 0 & 1 \end{matrix}) (\begin{matrix} x_{T} \\ y_{T} \\ z_{T} \end{matrix}) .

2-

(\begin{matrix} x_{I} \\ y_{I} \\ z_{I} \end{matrix}) = (\begin{matrix} x_{F} \\ y_{F} \\ z_{F} \end{matrix}) - (\begin{matrix} x_{0} \\ y_{0} \\ z_{0} \end{matrix}) .

3-

(\begin{matrix} x_{M} \\ y_{M} \\ z_{M} \end{matrix}) = (\begin{matrix} \cos (β) & 0 & - \sin (β) \\ 0 & 1 & 0 \\ \sin (β) & 0 & \cos (β) \end{matrix}) (\begin{matrix} x_{I} \\ y_{I} \\ z_{I} \end{matrix}) .

4-

∣ M^{'} Q ∣

5-

∣ M^{'} Q ∣ = (R + \frac{D}{\cos (γ)}) \frac{r \cos (θ + γ + ϕ)}{R \cos (γ) - r \sin (θ + ϕ)} .

6-

∣ M Q ∣ = ∣ M^{'} Q ∣ - ∣ M^{'} M ∣ = ∣ M^{'} Q ∣ - s_{x}

7-

∣ Q P^{'} ∣

8-

∣ Q P^{'} ∣ = \frac{R \cos (γ) + D}{R \cos (γ) - r \sin (θ + ϕ)} y_{M} .

9-

∣ Q P^{'} ∣ - s_{y}

10-

(\begin{matrix} x_{d}^{'} \\ y_{d}^{'} \end{matrix}) = (\begin{matrix} \cos (η) & \sin (η) \\ - \sin (η) & \cos (η) \end{matrix}) (\begin{matrix} x_{d} \\ y_{d} \end{matrix}) .

Formulas (html):

Correct Categorie: physics

Guessed Categorie: hep-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/9807146

Formulas:

1-

R \sim n σ < v > / m_{n}

2-

n = \frac{ρ_{o}}{m_{χ}}

3-

M_{d e t}

4-

f (\vec{v})

5-

f (\vec{v})

6-

\frac{d σ}{d {| q |}^{2}} \propto F^{2} (Q)

7-

f (\vec{v})

8-

\vec{v} = c o s α \hat{x} + s i n α s i n β \hat{y} + s i n α c o s β \hat{z}

9-

E_{n} = \frac{m_{n} m_{χ}^{2}}{{(m_{n} + m_{χ})}^{2}} v^{2} (1 - μ)

10-

μ = c o s θ^{*}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: nucl-th

Result: incorrect

Paper: https://arxiv.org/abs/1308.2090

Formulas:

1-

C \propto \int P^{2} ϵ (T) / T^{2} 𝑑 l

2-

ϵ (T) / T^{2}

3-

\int P^{2} 𝑑 l

4-

10^{- 14} {(4 π)}^{- 1} D_{A}^{- 2} {(1 + z)}^{- 2} \int n_{e} n_{H} 𝑑 V

5-

K = k T / n_{e}^{2 / 3}

6-

P = n_{e} k T

7-

n_{e} = 2.18 \times 10^{- 5} h_{70}^{- 1 / 2} {cm}^{- 3} \sqrt{\frac{{norm}_{apec}}{V ({Mpc}^{3})}} D_{A} (Mpc) (1 + z)

8-

V \approx (4 / 3) D_{A}^{3} Ω {(θ_{o u t}^{2} - θ_{i n}^{2})}^{1 / 2}

9-

θ_{o u t}

10-

= \frac{[(γ - 1) M_{1}^{2} + 2] [2 γ M_{1}^{2} - (γ - 1)]}{{(γ + 1)}^{2} M_{1}^{2}}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1409.4951

Formulas:

1-

(ω^{2} - k_{∥}^{2}) D_{z z} = k_{⟂}^{2},

2-

D_{z z} = 1 - \sum_{i} \frac{ω_{p i}^{2}}{γ_{i}^{3} {(ω - k_{∥} v_{i})}^{2}},

3-

ω_{p i}^{2} = 4 π n_{i} q_{i}^{2} / m_{i}

4-

D_{z z} = 1 - \frac{ω_{1}^{2}}{γ_{1}^{3} {(ω - k_{∥} v_{1})}^{2}} - \frac{ω_{2}^{2}}{γ_{2}^{3} {(ω - k_{∥} v_{2})}^{2}} +

5-

\frac{m_{e} ω_{e}^{2}}{k_{∥}} \int_{- \infty}^{\infty} 𝑑 p \frac{\partial f}{\partial p} \frac{1}{ω - k_{∥} v (p) + i ϵ},

6-

D_{z z} > 0

7-

\partial f / \partial p < 0

8-

\partial f / \partial p

9-

ω = (1 + s) ω_{1}^{*}

10-

ω_{1}^{*} = ω_{1} γ_{1}^{- 3 / 2}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1204.5321

Formulas:

1-

3 s 3 p^{6} n ℓ

2-

3 s 3 p^{6} n ℓ

3-

3 s 3 p^{6} n ℓ

4-

3 s^{2} 3 p^{5} ε ℓ^{'}

5-

3 s 3 p^{6}

6-

i \frac{\partial}{\partial t} Ψ (𝐗_{N + 1}, t) = H (t) Ψ (𝐗_{N + 1}, t) .

7-

t_{q} = q Δ t, q = 0, 1, 2, \dots .

8-

\exp [- i t H (t)]

9-

[H (t_{q + 1 / 2}) - E] Ψ (𝐗_{N + 1}, t_{q + 1}) = 𝚯 (𝐗_{N + 1}, t_{q}),

10-

𝚯 (𝐗_{N + 1}, t_{q}) = - [H (t_{q + 1 / 2}) + E] Ψ (𝐗_{N + 1}, t_{q}),

Formulas (html):

Correct Categorie: physics

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/2002.03874

Formulas:

1-

- V (x)

2-

δ ρ (E) = - \frac{1}{π} lim_{ϵ \to 0} ImTr [\hat{G} (E + i ϵ) - {\hat{G}}^{(0)} (E + i ϵ)],

3-

\hat{G} (E) = 1 / (E - \hat{H})

4-

{\hat{G}}^{(0)} = 1 / (E - {\hat{H}}^{(0)})

5-

Δ ρ (ℰ)

6-

ℰ = E - \frac{i}{2} Γ

7-

{\hat{H}}_{NH} = \hat{S} \hat{H} {\hat{S}}^{- 1}

8-

{\hat{H}}_{NH}^{(0)} = \hat{S} {\hat{H}}^{(0)} {\hat{S}}^{- 1}

9-

ℰ_{k} = E_{k} - \frac{i}{2} Γ_{k}

10-

ℰ_{k}^{(0)} = E_{k}^{(0)} - \frac{i}{2} Γ_{k}^{(0)}

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: quant-ph

Result: correct

Paper: https://arxiv.org/abs/1306.1088

Formulas:

1-

I_{C} = k_{C} I_{0} \frac{1 + r_{C}}{1 + r_{S}} {1 - \exp [- d / Λ_{C, E_{A}}]},

2-

I_{E P} = k_{E P} I_{0} {R_{C} - (R_{C} - R_{S}) \exp [- 2 d / Λ_{C, E_{E P}}]} .

3-

Λ_{C, E_{E P}}

4-

λ_{C, E_{E_{A}}}

5-

λ_{C, E_{E P}}

6-

\frac{I_{C}}{I_{E P}} = α \frac{1 - \exp (- d / Λ_{C, E_{A}})}{R_{C} - (R_{C} - R_{S}) \exp (- 2 d / Λ_{C, E_{E P}})},

7-

α = [k_{C} (1 + r_{C})] / [k_{E P} (1 + r_{S})]

8-

I_{C} \propto Δ C

9-

I_{E P} \propto Δ E P

10-

C_{K L L}

Formulas (html):

Correct Categorie: physics

Guessed Categorie: physics

Result: correct

Paper: https://arxiv.org/abs/1604.04030

Formulas:

1-

ℋ = v_{0} 𝒌 \cdot 𝝈 + 𝒘 \cdot 𝒌,

2-

\hat{𝒘} = 𝒘 / w

3-

(w / v_{0}) < 1

4-

(w / v_{0}) > 1

5-

𝒌 \to 𝒌 + e 𝑨

6-

𝑨 = (- B y, 0, 0)

7-

- e w_{⊥} B y

8-

E_{eff} = w_{⊥} B

9-

w_{⊥} = | 𝒘 \times 𝑩 / B |

10-

v_{d} = E_{eff} / B

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/astro-ph/9807195

Formulas:

1-

V = {26.20}_{- 0.13}^{+ 0.14}

2-

I_{c} = {23.94}_{- 0.09}^{+ 0.10}

3-

V = {26.52}_{- 0.18}^{+ 0.16}

4-

I_{c} = {24.31}_{- 0.11}^{+ 0.15}

5-

R_{c} = {27.09}_{- 0.14}^{+ 0.14}

6-

R_{c} = {25.48}_{- 0.20}^{+ 0.22}

7-

R_{c} = {25.54}_{- 0.22}^{+ 0.33}

8-

V_{606} - I_{814} = - {0.18}_{- 0.61}^{+ 0.51}

9-

α = - 1.10 \pm 0.04

10-

V_{606} - I_{814} = 0.70

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1103.0432

Formulas:

1-

α, β = A, B

2-

v_{α β} (r)

3-

4 ϵ_{α β} [{(\frac{σ_{α β}}{r})}^{12} - {(\frac{σ_{α β}}{r})}^{6} + C_{α β}], for r \leq r_{α β}^{c}

4-

0, for r \geq r_{α β}^{c},

5-

v_{α β} (r)

6-

2.5 σ_{α β}

7-

v_{α β} (r_{α β}^{c}) = 0

8-

ϵ_{A A} / k_{B}

9-

{(m σ_{A A}^{2} / 48 ϵ_{A A})}^{1 / 2}

10-

T_{c} (ρ)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0006133

Formulas:

1-

\geq 40 T e V

2-

\geq a f e w T e V

3-

q = \frac{N_{a}^{γ}}{N_{T}^{γ}} {(\frac{N_{a}^{c r}}{N_{T}^{c r}})}^{- \frac{1}{2}}

4-

v i z .

5-

v i z .

6-

v i z .

7-

e t a l .

8-

v i z .

9-

\geq 10^{15} e V

10-

\geq 100 T e V

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0305504

Formulas:

1-

Δ ν_{1 / 2}

2-

Δ ν_{1 / 2}

3-

Δ ν_{1 / 2}

4-

Δ ν_{1 / 2}

5-

E_{u} / k = 103

6-

N = \frac{3 k}{8 π^{3}} \frac{\int T_{R} d v}{ν S μ^{2} g_{I} g_{K}} Q (T_{rot}) \exp (\frac{E_{u}}{k T_{rot}}),

7-

\int T_{R} d v

8-

Q (T_{rot})

9-

\log (\frac{3 k}{8 π^{3}} \frac{\int T_{R} d v}{ν S μ^{2} g_{I} g_{K}}) = \log (\frac{N}{Q (T_{rot})}) - \frac{E_{u}}{k} \frac{\log e}{T_{rot}}

10-

- l o g e / T_{rot}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1604.00134

Formulas:

1-

Γ_{1 i} = 0

2-

Γ_{1 i} = 0

3-

\bar{𝐙} = (\bar{𝐗}, \bar{𝐔}, \bar{μ}, \bar{θ})

4-

𝐙 = (𝐗, U, μ, θ)

5-

\bar{𝐙} = e^{G^{i} \partial_{Z^{i}}} 𝐙

6-

G^{i} = ε g^{i}

7-

(\bar{𝐗}, \bar{U}, \bar{μ}, \bar{θ})

8-

G^{i} \partial_{Z^{i}}

9-

𝐀_{1} (𝐗, t) = \sum_{𝐤^{'}} (A_{c 𝐤^{'}} \cos (𝐗 \cdot 𝐤^{'} - ω_{k^{'}} t) + A_{s 𝐤^{'}} \sin (𝐗 \cdot 𝐤^{'} - ω_{k^{'}} t))

10-

(ω_{k}, 𝐤)

Formulas (html):

Correct Categorie: physics

Guessed Categorie: physics

Result: correct

Paper: https://arxiv.org/abs/1906.01976

Formulas:

1-

{F_{K}^{n} (t, ℓ)}_{n = 1}^{\infty}

2-

\nabla J_{n} (D)

3-

\nabla J_{n} (D_{c})

4-

c \in C (D)

5-

sgn (c) = + 1

6-

sgn (c) = - 1

7-

λ (α) = \sum_{c \in O (α)} sgn (c)

8-

Ind (c) = sgn (c) (a - b - 1)

9-

P_{D} (t) = \sum_{c \in C (D)} sgn (c) (t^{Ind (c)} - 1),

10-

n \in ℤ ∖ {0}

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/1012.2078

Formulas:

1-

_{t r i g}

2-

I_{I V N}

3-

\geq 0 \overset{''}{.} 18

4-

I_{I V N}

5-

J H K_{s}

6-

J H K_{s}

7-

J H K_{s}

8-

V R I J H K

9-

_{p l a t e}

10-

_{p l a t e}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1711.04260

Formulas:

1-

C_{F O V}

2-

T P E^{t}

3-

B O R^{t}

4-

T P E = | C_{G T} - C_{P T} |

5-

B O R^{t} = \frac{A_{G T} \cap A_{P T}}{A_{G T} \cup A_{P T}}

6-

T P O^{t}

7-

T P O^{t} = | C_{F O V} - C_{G T} |

8-

T F^{t} = {\begin{matrix} 1, & if T P E^{t} is invalid \\ 0, & otherwise \end{matrix}

9-

T P E^{t}

10-

T P O^{t}

Formulas (html):

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xref="S2.SS2.p1.6.m6.1.1.4.cmml"><mi id="S2.SS2.p1.6.m6.1.1.4.2" xref="S2.SS2.p1.6.m6.1.1.4.2.cmml">E</mi><mi id="S2.SS2.p1.6.m6.1.1.4.3" xref="S2.SS2.p1.6.m6.1.1.4.3.cmml">t</mi></msup></mrow></math>, <math><mrow id="S2.SS2.p1.7.m7.1.1" xref="S2.SS2.p1.7.m7.1.1.cmml"><mi id="S2.SS2.p1.7.m7.1.1.2" xref="S2.SS2.p1.7.m7.1.1.2.cmml">B</mi><mo id="S2.SS2.p1.7.m7.1.1.1" xref="S2.SS2.p1.7.m7.1.1.1.cmml">⁢</mo><mi id="S2.SS2.p1.7.m7.1.1.3" xref="S2.SS2.p1.7.m7.1.1.3.cmml">O</mi><mo id="S2.SS2.p1.7.m7.1.1.1a" xref="S2.SS2.p1.7.m7.1.1.1.cmml">⁢</mo><msup id="S2.SS2.p1.7.m7.1.1.4" xref="S2.SS2.p1.7.m7.1.1.4.cmml"><mi id="S2.SS2.p1.7.m7.1.1.4.2" xref="S2.SS2.p1.7.m7.1.1.4.2.cmml">R</mi><mi id="S2.SS2.p1.7.m7.1.1.4.3" xref="S2.SS2.p1.7.m7.1.1.4.3.cmml">t</mi></msup></mrow></math>, <math><mrow id="S2.E1.m1.1.1" xref="S2.E1.m1.1.1.cmml"><mi id="S2.E1.m1.1.1.3" xref="S2.E1.m1.1.1.3.cmml">T</mi><mo id="S2.E1.m1.1.1.2" xref="S2.E1.m1.1.1.2.cmml">⁢</mo><mi id="S2.E1.m1.1.1.4" xref="S2.E1.m1.1.1.4.cmml">P</mi><mo id="S2.E1.m1.1.1.2a" xref="S2.E1.m1.1.1.2.cmml">⁢</mo><mi id="S2.E1.m1.1.1.5" xref="S2.E1.m1.1.1.5.cmml">E</mi><mo id="S2.E1.m1.1.1.2b" xref="S2.E1.m1.1.1.2.cmml">⁢</mo><mtext id="S2.E1.m1.1.1.6" xref="S2.E1.m1.1.1.6a.cmml"> = </mtext><mo id="S2.E1.m1.1.1.2c" xref="S2.E1.m1.1.1.2.cmml">⁢</mo><mrow id="S2.E1.m1.1.1.1.1" xref="S2.E1.m1.1.1.1.2.cmml"><mo stretchy="false" id="S2.E1.m1.1.1.1.1.2" xref="S2.E1.m1.1.1.1.2.1.cmml">|</mo><mrow id="S2.E1.m1.1.1.1.1.1" xref="S2.E1.m1.1.1.1.1.1.cmml"><msub id="S2.E1.m1.1.1.1.1.1.2" xref="S2.E1.m1.1.1.1.1.1.2.cmml"><mi id="S2.E1.m1.1.1.1.1.1.2.2" xref="S2.E1.m1.1.1.1.1.1.2.2.cmml">C</mi><mrow id="S2.E1.m1.1.1.1.1.1.2.3" xref="S2.E1.m1.1.1.1.1.1.2.3.cmml"><mi id="S2.E1.m1.1.1.1.1.1.2.3.2" xref="S2.E1.m1.1.1.1.1.1.2.3.2.cmml">G</mi><mo id="S2.E1.m1.1.1.1.1.1.2.3.1" xref="S2.E1.m1.1.1.1.1.1.2.3.1.cmml">⁢</mo><mi id="S2.E1.m1.1.1.1.1.1.2.3.3" xref="S2.E1.m1.1.1.1.1.1.2.3.3.cmml">T</mi></mrow></msub><mo id="S2.E1.m1.1.1.1.1.1.1" xref="S2.E1.m1.1.1.1.1.1.1.cmml">-</mo><msub id="S2.E1.m1.1.1.1.1.1.3" xref="S2.E1.m1.1.1.1.1.1.3.cmml"><mi id="S2.E1.m1.1.1.1.1.1.3.2" xref="S2.E1.m1.1.1.1.1.1.3.2.cmml">C</mi><mrow id="S2.E1.m1.1.1.1.1.1.3.3" xref="S2.E1.m1.1.1.1.1.1.3.3.cmml"><mi id="S2.E1.m1.1.1.1.1.1.3.3.2" xref="S2.E1.m1.1.1.1.1.1.3.3.2.cmml">P</mi><mo id="S2.E1.m1.1.1.1.1.1.3.3.1" xref="S2.E1.m1.1.1.1.1.1.3.3.1.cmml">⁢</mo><mi id="S2.E1.m1.1.1.1.1.1.3.3.3" xref="S2.E1.m1.1.1.1.1.1.3.3.3.cmml">T</mi></mrow></msub></mrow><mo stretchy="false" id="S2.E1.m1.1.1.1.1.3" xref="S2.E1.m1.1.1.1.2.1.cmml">|</mo></mrow></mrow></math>, <math><mrow id="S2.E2.m1.1.1" xref="S2.E2.m1.1.1.cmml"><mi id="S2.E2.m1.1.1.2" xref="S2.E2.m1.1.1.2.cmml">B</mi><mo id="S2.E2.m1.1.1.1" xref="S2.E2.m1.1.1.1.cmml">⁢</mo><mi id="S2.E2.m1.1.1.3" xref="S2.E2.m1.1.1.3.cmml">O</mi><mo id="S2.E2.m1.1.1.1a" xref="S2.E2.m1.1.1.1.cmml">⁢</mo><msup id="S2.E2.m1.1.1.4" xref="S2.E2.m1.1.1.4.cmml"><mi id="S2.E2.m1.1.1.4.2" xref="S2.E2.m1.1.1.4.2.cmml">R</mi><mi id="S2.E2.m1.1.1.4.3" xref="S2.E2.m1.1.1.4.3.cmml">t</mi></msup><mo id="S2.E2.m1.1.1.1b" xref="S2.E2.m1.1.1.1.cmml">⁢</mo><mtext id="S2.E2.m1.1.1.5" xref="S2.E2.m1.1.1.5a.cmml"> = </mtext><mo id="S2.E2.m1.1.1.1c" xref="S2.E2.m1.1.1.1.cmml">⁢</mo><mfrac id="S2.E2.m1.1.1.6" xref="S2.E2.m1.1.1.6.cmml"><mrow id="S2.E2.m1.1.1.6.2" xref="S2.E2.m1.1.1.6.2.cmml"><msub id="S2.E2.m1.1.1.6.2.2" xref="S2.E2.m1.1.1.6.2.2.cmml"><mi id="S2.E2.m1.1.1.6.2.2.2" xref="S2.E2.m1.1.1.6.2.2.2.cmml">A</mi><mrow id="S2.E2.m1.1.1.6.2.2.3" xref="S2.E2.m1.1.1.6.2.2.3.cmml"><mi id="S2.E2.m1.1.1.6.2.2.3.2" xref="S2.E2.m1.1.1.6.2.2.3.2.cmml">G</mi><mo id="S2.E2.m1.1.1.6.2.2.3.1" xref="S2.E2.m1.1.1.6.2.2.3.1.cmml">⁢</mo><mi id="S2.E2.m1.1.1.6.2.2.3.3" xref="S2.E2.m1.1.1.6.2.2.3.3.cmml">T</mi></mrow></msub><mo id="S2.E2.m1.1.1.6.2.1" xref="S2.E2.m1.1.1.6.2.1.cmml">∩</mo><msub id="S2.E2.m1.1.1.6.2.3" xref="S2.E2.m1.1.1.6.2.3.cmml"><mi id="S2.E2.m1.1.1.6.2.3.2" xref="S2.E2.m1.1.1.6.2.3.2.cmml">A</mi><mrow id="S2.E2.m1.1.1.6.2.3.3" xref="S2.E2.m1.1.1.6.2.3.3.cmml"><mi id="S2.E2.m1.1.1.6.2.3.3.2" xref="S2.E2.m1.1.1.6.2.3.3.2.cmml">P</mi><mo id="S2.E2.m1.1.1.6.2.3.3.1" xref="S2.E2.m1.1.1.6.2.3.3.1.cmml">⁢</mo><mi id="S2.E2.m1.1.1.6.2.3.3.3" xref="S2.E2.m1.1.1.6.2.3.3.3.cmml">T</mi></mrow></msub></mrow><mrow id="S2.E2.m1.1.1.6.3" xref="S2.E2.m1.1.1.6.3.cmml"><msub id="S2.E2.m1.1.1.6.3.2" xref="S2.E2.m1.1.1.6.3.2.cmml"><mi id="S2.E2.m1.1.1.6.3.2.2" xref="S2.E2.m1.1.1.6.3.2.2.cmml">A</mi><mrow id="S2.E2.m1.1.1.6.3.2.3" xref="S2.E2.m1.1.1.6.3.2.3.cmml"><mi id="S2.E2.m1.1.1.6.3.2.3.2" xref="S2.E2.m1.1.1.6.3.2.3.2.cmml">G</mi><mo id="S2.E2.m1.1.1.6.3.2.3.1" xref="S2.E2.m1.1.1.6.3.2.3.1.cmml">⁢</mo><mi id="S2.E2.m1.1.1.6.3.2.3.3" xref="S2.E2.m1.1.1.6.3.2.3.3.cmml">T</mi></mrow></msub><mo id="S2.E2.m1.1.1.6.3.1" xref="S2.E2.m1.1.1.6.3.1.cmml">∪</mo><msub id="S2.E2.m1.1.1.6.3.3" xref="S2.E2.m1.1.1.6.3.3.cmml"><mi id="S2.E2.m1.1.1.6.3.3.2" xref="S2.E2.m1.1.1.6.3.3.2.cmml">A</mi><mrow id="S2.E2.m1.1.1.6.3.3.3" xref="S2.E2.m1.1.1.6.3.3.3.cmml"><mi id="S2.E2.m1.1.1.6.3.3.3.2" xref="S2.E2.m1.1.1.6.3.3.3.2.cmml">P</mi><mo id="S2.E2.m1.1.1.6.3.3.3.1" xref="S2.E2.m1.1.1.6.3.3.3.1.cmml">⁢</mo><mi id="S2.E2.m1.1.1.6.3.3.3.3" xref="S2.E2.m1.1.1.6.3.3.3.3.cmml">T</mi></mrow></msub></mrow></mfrac></mrow></math>, <math><mrow id="S2.SS2.p2.1.m1.1.1" xref="S2.SS2.p2.1.m1.1.1.cmml"><mi id="S2.SS2.p2.1.m1.1.1.2" xref="S2.SS2.p2.1.m1.1.1.2.cmml">T</mi><mo id="S2.SS2.p2.1.m1.1.1.1" xref="S2.SS2.p2.1.m1.1.1.1.cmml">⁢</mo><mi id="S2.SS2.p2.1.m1.1.1.3" xref="S2.SS2.p2.1.m1.1.1.3.cmml">P</mi><mo id="S2.SS2.p2.1.m1.1.1.1a" xref="S2.SS2.p2.1.m1.1.1.1.cmml">⁢</mo><msup id="S2.SS2.p2.1.m1.1.1.4" xref="S2.SS2.p2.1.m1.1.1.4.cmml"><mi id="S2.SS2.p2.1.m1.1.1.4.2" xref="S2.SS2.p2.1.m1.1.1.4.2.cmml">O</mi><mi id="S2.SS2.p2.1.m1.1.1.4.3" xref="S2.SS2.p2.1.m1.1.1.4.3.cmml">t</mi></msup></mrow></math>, <math><mrow id="S2.E3.m1.1.1" xref="S2.E3.m1.1.1.cmml"><mi id="S2.E3.m1.1.1.3" xref="S2.E3.m1.1.1.3.cmml">T</mi><mo id="S2.E3.m1.1.1.2" xref="S2.E3.m1.1.1.2.cmml">⁢</mo><mi id="S2.E3.m1.1.1.4" xref="S2.E3.m1.1.1.4.cmml">P</mi><mo id="S2.E3.m1.1.1.2a" xref="S2.E3.m1.1.1.2.cmml">⁢</mo><msup id="S2.E3.m1.1.1.5" xref="S2.E3.m1.1.1.5.cmml"><mi id="S2.E3.m1.1.1.5.2" xref="S2.E3.m1.1.1.5.2.cmml">O</mi><mi id="S2.E3.m1.1.1.5.3" xref="S2.E3.m1.1.1.5.3.cmml">t</mi></msup><mo id="S2.E3.m1.1.1.2b" xref="S2.E3.m1.1.1.2.cmml">⁢</mo><mtext id="S2.E3.m1.1.1.6" xref="S2.E3.m1.1.1.6a.cmml"> = </mtext><mo id="S2.E3.m1.1.1.2c" xref="S2.E3.m1.1.1.2.cmml">⁢</mo><mrow id="S2.E3.m1.1.1.1.1" xref="S2.E3.m1.1.1.1.2.cmml"><mo stretchy="false" id="S2.E3.m1.1.1.1.1.2" xref="S2.E3.m1.1.1.1.2.1.cmml">|</mo><mrow id="S2.E3.m1.1.1.1.1.1" xref="S2.E3.m1.1.1.1.1.1.cmml"><msub id="S2.E3.m1.1.1.1.1.1.2" xref="S2.E3.m1.1.1.1.1.1.2.cmml"><mi id="S2.E3.m1.1.1.1.1.1.2.2" xref="S2.E3.m1.1.1.1.1.1.2.2.cmml">C</mi><mrow id="S2.E3.m1.1.1.1.1.1.2.3" xref="S2.E3.m1.1.1.1.1.1.2.3.cmml"><mi id="S2.E3.m1.1.1.1.1.1.2.3.2" xref="S2.E3.m1.1.1.1.1.1.2.3.2.cmml">F</mi><mo id="S2.E3.m1.1.1.1.1.1.2.3.1" xref="S2.E3.m1.1.1.1.1.1.2.3.1.cmml">⁢</mo><mi id="S2.E3.m1.1.1.1.1.1.2.3.3" xref="S2.E3.m1.1.1.1.1.1.2.3.3.cmml">O</mi><mo id="S2.E3.m1.1.1.1.1.1.2.3.1a" xref="S2.E3.m1.1.1.1.1.1.2.3.1.cmml">⁢</mo><mi id="S2.E3.m1.1.1.1.1.1.2.3.4" xref="S2.E3.m1.1.1.1.1.1.2.3.4.cmml">V</mi></mrow></msub><mo id="S2.E3.m1.1.1.1.1.1.1" xref="S2.E3.m1.1.1.1.1.1.1.cmml">-</mo><msub id="S2.E3.m1.1.1.1.1.1.3" xref="S2.E3.m1.1.1.1.1.1.3.cmml"><mi id="S2.E3.m1.1.1.1.1.1.3.2" xref="S2.E3.m1.1.1.1.1.1.3.2.cmml">C</mi><mrow id="S2.E3.m1.1.1.1.1.1.3.3" xref="S2.E3.m1.1.1.1.1.1.3.3.cmml"><mi id="S2.E3.m1.1.1.1.1.1.3.3.2" xref="S2.E3.m1.1.1.1.1.1.3.3.2.cmml">G</mi><mo id="S2.E3.m1.1.1.1.1.1.3.3.1" xref="S2.E3.m1.1.1.1.1.1.3.3.1.cmml">⁢</mo><mi id="S2.E3.m1.1.1.1.1.1.3.3.3" xref="S2.E3.m1.1.1.1.1.1.3.3.3.cmml">T</mi></mrow></msub></mrow><mo stretchy="false" id="S2.E3.m1.1.1.1.1.3" xref="S2.E3.m1.1.1.1.2.1.cmml">|</mo></mrow></mrow></math>, <math><mrow id="S2.E4.m1.4.5" xref="S2.E4.m1.4.5.cmml"><mrow id="S2.E4.m1.1.1.1" xref="S2.E4.m1.1.1.1b.cmml"><mrow id="S2.E4.m1.1.1.1.m1.1.1" xref="S2.E4.m1.1.1.1.m1.1.1.cmml"><mi id="S2.E4.m1.1.1.1.m1.1.1.2" xref="S2.E4.m1.1.1.1.m1.1.1.2.cmml">T</mi><mo id="S2.E4.m1.1.1.1.m1.1.1.1" xref="S2.E4.m1.1.1.1.m1.1.1.1.cmml">⁢</mo><msup id="S2.E4.m1.1.1.1.m1.1.1.3" xref="S2.E4.m1.1.1.1.m1.1.1.3.cmml"><mi id="S2.E4.m1.1.1.1.m1.1.1.3.2" xref="S2.E4.m1.1.1.1.m1.1.1.3.2.cmml">F</mi><mi id="S2.E4.m1.1.1.1.m1.1.1.3.3" xref="S2.E4.m1.1.1.1.m1.1.1.3.3.cmml">t</mi></msup></mrow><mtext id="S2.E4.m1.1.1.1a" xref="S2.E4.m1.1.1.1b.cmml"> =</mtext></mrow><mo id="S2.E4.m1.4.5.1" xref="S2.E4.m1.4.5.1.cmml">⁢</mo><mrow id="S2.E4.m1.4.5.2.2" xref="S2.E4.m1.4.5.2.1.cmml"><mo id="S2.E4.m1.4.5.2.2.1" xref="S2.E4.m1.4.5.2.1.1.cmml">{</mo><mtable columnspacing="5pt" displaystyle="true" rowspacing="0pt" id="S2.E4.m1.4.4" xref="S2.E4.m1.4.4.cmml"><mtr id="S2.E4.m1.4.4a" xref="S2.E4.m1.4.4.cmml"><mtd columnalign="left" id="S2.E4.m1.4.4b" xref="S2.E4.m1.4.4.cmml"><mrow id="S2.E4.m1.3.3.2.2.1.3" xref="S2.E4.m1.4.4.cmml"><mn id="S2.E4.m1.3.3.2.2.1.1" xref="S2.E4.m1.3.3.2.2.1.1.cmml">1</mn><mo id="S2.E4.m1.3.3.2.2.1.3.1" xref="S2.E4.m1.4.4.cmml">,</mo></mrow></mtd><mtd columnalign="right" id="S2.E4.m1.4.4c" xref="S2.E4.m1.4.4.cmml"><mrow id="S2.E4.m1.2.2.1.1.1" xref="S2.E4.m1.2.2.1.1.1c.cmml"><mtext id="S2.E4.m1.2.2.1.1.1a" xref="S2.E4.m1.2.2.1.1.1c.cmml">if </mtext><mrow id="S2.E4.m1.2.2.1.1.1.1.1.m1.1.1" xref="S2.E4.m1.2.2.1.1.1.1.1.m1.1.1.cmml"><mi id="S2.E4.m1.2.2.1.1.1.1.1.m1.1.1.2" xref="S2.E4.m1.2.2.1.1.1.1.1.m1.1.1.2.cmml">T</mi><mo id="S2.E4.m1.2.2.1.1.1.1.1.m1.1.1.1" xref="S2.E4.m1.2.2.1.1.1.1.1.m1.1.1.1.cmml">⁢</mo><mi id="S2.E4.m1.2.2.1.1.1.1.1.m1.1.1.3" xref="S2.E4.m1.2.2.1.1.1.1.1.m1.1.1.3.cmml">P</mi><mo id="S2.E4.m1.2.2.1.1.1.1.1.m1.1.1.1a" xref="S2.E4.m1.2.2.1.1.1.1.1.m1.1.1.1.cmml">⁢</mo><msup id="S2.E4.m1.2.2.1.1.1.1.1.m1.1.1.4" xref="S2.E4.m1.2.2.1.1.1.1.1.m1.1.1.4.cmml"><mi id="S2.E4.m1.2.2.1.1.1.1.1.m1.1.1.4.2" xref="S2.E4.m1.2.2.1.1.1.1.1.m1.1.1.4.2.cmml">E</mi><mi id="S2.E4.m1.2.2.1.1.1.1.1.m1.1.1.4.3" xref="S2.E4.m1.2.2.1.1.1.1.1.m1.1.1.4.3.cmml">t</mi></msup></mrow><mtext id="S2.E4.m1.2.2.1.1.1b" xref="S2.E4.m1.2.2.1.1.1c.cmml"> is invalid</mtext></mrow></mtd></mtr><mtr id="S2.E4.m1.4.4d" xref="S2.E4.m1.4.4.cmml"><mtd columnalign="left" id="S2.E4.m1.4.4e" xref="S2.E4.m1.4.4.cmml"><mrow id="S2.E4.m1.4.4.3.1.1.3" xref="S2.E4.m1.4.4.cmml"><mn id="S2.E4.m1.4.4.3.1.1.1" xref="S2.E4.m1.4.4.3.1.1.1.cmml">0</mn><mo id="S2.E4.m1.4.4.3.1.1.3.1" xref="S2.E4.m1.4.4.cmml">,</mo></mrow></mtd><mtd columnalign="right" id="S2.E4.m1.4.4f" xref="S2.E4.m1.4.4.cmml"><mtext id="S2.E4.m1.4.4.3.2.1" xref="S2.E4.m1.4.4.3.2.1a.cmml">otherwise </mtext></mtd></mtr></mtable><mi id="S2.E4.m1.4.5.2.2.2" xref="S2.E4.m1.4.5.2.1.1.cmml"/></mrow></mrow></math>, <math><mrow id="S2.SS2.p2.4.m2.1.1" xref="S2.SS2.p2.4.m2.1.1.cmml"><mi id="S2.SS2.p2.4.m2.1.1.2" xref="S2.SS2.p2.4.m2.1.1.2.cmml">T</mi><mo id="S2.SS2.p2.4.m2.1.1.1" xref="S2.SS2.p2.4.m2.1.1.1.cmml">⁢</mo><mi id="S2.SS2.p2.4.m2.1.1.3" xref="S2.SS2.p2.4.m2.1.1.3.cmml">P</mi><mo id="S2.SS2.p2.4.m2.1.1.1a" xref="S2.SS2.p2.4.m2.1.1.1.cmml">⁢</mo><msup id="S2.SS2.p2.4.m2.1.1.4" xref="S2.SS2.p2.4.m2.1.1.4.cmml"><mi id="S2.SS2.p2.4.m2.1.1.4.2" xref="S2.SS2.p2.4.m2.1.1.4.2.cmml">E</mi><mi id="S2.SS2.p2.4.m2.1.1.4.3" xref="S2.SS2.p2.4.m2.1.1.4.3.cmml">t</mi></msup></mrow></math>, <math><mrow id="S2.SS2.p2.5.m3.1.1" xref="S2.SS2.p2.5.m3.1.1.cmml"><mi id="S2.SS2.p2.5.m3.1.1.2" xref="S2.SS2.p2.5.m3.1.1.2.cmml">T</mi><mo id="S2.SS2.p2.5.m3.1.1.1" xref="S2.SS2.p2.5.m3.1.1.1.cmml">⁢</mo><mi id="S2.SS2.p2.5.m3.1.1.3" xref="S2.SS2.p2.5.m3.1.1.3.cmml">P</mi><mo id="S2.SS2.p2.5.m3.1.1.1a" xref="S2.SS2.p2.5.m3.1.1.1.cmml">⁢</mo><msup id="S2.SS2.p2.5.m3.1.1.4" xref="S2.SS2.p2.5.m3.1.1.4.cmml"><mi id="S2.SS2.p2.5.m3.1.1.4.2" xref="S2.SS2.p2.5.m3.1.1.4.2.cmml">O</mi><mi id="S2.SS2.p2.5.m3.1.1.4.3" xref="S2.SS2.p2.5.m3.1.1.4.3.cmml">t</mi></msup></mrow></math>

Correct Categorie: cs

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/physics/0212054

Formulas:

1-

G \propto - \frac{G_{0}}{T},

2-

\frac{G M m}{L}

3-

\frac{G M}{T L}

4-

\frac{1}{\sqrt{N} τ} = \frac{1}{T}

5-

\frac{G M}{T L}

6-

\frac{G M m}{L} = c o n s t .

7-

\frac{μ}{L} \equiv \frac{G M}{L} = c o n s t .

8-

μ = μ_{0} - t K

9-

L = L_{0} (1 - α K)

10-

δ L = - \frac{L t K}{μ_{0}}

Formulas (html):

Correct Categorie: physics

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/nucl-th/0407035

Formulas:

1-

p p \to Λ K^{+} p

2-

p p \to p p K^{-} K^{+}

3-

π Σ \to K^{-} p

4-

K^{-} N \to Y π

5-

\frac{K^{-}}{K^{+}} = \frac{Z_{K^{-}}^{1}}{Z_{K^{+}}^{1}} \frac{Z_{K^{+}}^{1} + Z_{M, S = + 1}^{1}}{Z_{K^{-}}^{1} + Z_{B, S = - 1}^{1} + Z_{M, S = - 1}}

6-

(Z_{K^{-}}^{1})

7-

K^{+} (K^{-})

8-

Z_{B, S = \pm 1}^{1}

9-

(Z_{M, S = \pm 1}^{1})

10-

\frac{K^{+}}{K^{-}} = \frac{Z_{K^{+}}^{1} (Z_{K^{-}}^{1} + Z_{Λ}^{1} + Z_{Σ}^{1} + Z_{Σ^{*}}^{1})}{Z_{K^{-}}^{1} Z_{K^{+}}^{1}} = 1 + \frac{Z_{Λ}^{1} + Z_{Σ}^{1} + Z_{Σ^{*}}^{1}}{Z_{K^{-}}^{1}}

Formulas (html):

Correct Categorie: nucl-th

Guessed Categorie: nucl-th

Result: correct

Paper: https://arxiv.org/abs/1108.2068

Formulas:

1-

M_{⊙} {yr}^{- 1}

2-

1 M_{⊙} {yr}^{- 1}

3-

10 M_{⊙} {yr}^{- 1}

4-

100 M_{⊙} {yr}^{- 1}

5-

H_{0} = 70 km s^{- 1} Mpc

6-

f_{g} = C_{0} \ln (t λ^{- 1} + 1)

7-

{\dot{f}}_{g} = C_{0} / (t + λ) \approx 4 \times 10^{- 12} {yr}^{- 1}

8-

M_{I} (< 10 kpc) = - 23.11

9-

M_{I} (< 50 kpc) = - 24.26

10-

M_{I} (< 300 kpc) = - 24.96

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/nucl-ex/9910001

Formulas:

1-

\sqrt{x} d^{2} χ / d x^{2} = χ^{3 / 2}

2-

χ (0) = 1

3-

χ (\infty) = 0

4-

χ^{'} (0)

5-

r = x b Z^{- 1 / 3}; b = \frac{1}{2} {(\frac{3}{4} π)}^{2 / 3} = 0.885

6-

m_{e} e^{2} / ℏ^{2} = 1

7-

ϕ (r) = \frac{Z e}{r} χ (\frac{r Z^{1 / 3}}{b}) = \frac{Z^{4 / 3}}{b} \frac{χ (x)}{x} .

8-

V (r) = - d e \vec{σ} \cdot \vec{E} (r)

9-

\vec{E} (r)

10-

a = - \frac{m_{n}}{2 π ℏ^{2}} \int V (r) e^{i \vec{q} \cdot \vec{r}} d^{3} r

Formulas (html):

Correct Categorie: nucl-ex

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/1607.04006

Formulas:

1-

D / 2 π \approx 2.87

2-

B_{z} = D / γ_{e} \approx 1024

3-

ℋ (^{14} NV)

4-

= D S_{z}^{2} + γ_{e} B_{z} S_{z} - γ_{n} B_{z} I_{z} + Q I_{z}^{2}

5-

+ A_{∥} S_{z} I_{z} + A_{⟂} (S_{x} I_{x} + S_{y} I_{y}),

6-

ℋ (^{15} NV)

7-

= D S_{z}^{2} + γ_{e} B_{z} S_{z} - γ_{n}^{'} B_{z} I_{z}^{'}

8-

+ A_{∥}^{'} S_{z} I_{z}^{'} + A_{⟂}^{'} (S_{x} I_{x}^{'} + S_{y} I_{y}^{'}),

9-

𝐒 = (S_{x}, S_{y}, S_{z})

10-

A_{∥} / 2 π = - 2.14

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1801.01044

Formulas:

1-

\frac{1}{2} [110]

2-

\frac{1}{2} [110]

3-

- \frac{1}{2} [201]

4-

E_{t o t} = J_{0} N + \sum_{n = 1}^{M} \sum_{i = 1}^{N} J_{n} σ_{i} σ_{i + n},

5-

E_{t o t}

6-

σ_{1} = σ_{N + 1}

7-

E_{f} (SF)

8-

E_{f} (SF) = \frac{E_{t o t} (SF)}{A} - \frac{N E_{t o t} (0)}{A},

9-

E_{t o t} (0)

10-

\bar{V (z_{0})} = \frac{\int_{z_{0} - τ / 2}^{z_{0} + τ / 2} \int \int V (x, y, z) 𝑑 x 𝑑 y 𝑑 z}{τ \int \int 𝑑 x 𝑑 y},

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1801.02377

Formulas:

1-

1 - e x p (- \frac{Δ t}{τ})

2-

\min_{x \in 𝒳} 𝐟 (x) = (f_{1} (x), f_{2} (x), \dots, f_{K} (x))

3-

f_{i} (u) \leq f_{i} (v)

4-

i = 1, \dots, n

5-

j = 1, \dots, m

6-

P_{N D} = \sum_{i = 1}^{n} π_{i} \cdot \exp (- \frac{1}{τ} \sum_{j = 1}^{m} \frac{l_{i, j}}{v_{j}} δ_{j})

7-

T = \sum_{j = 1}^{m} \frac{l_{j}}{v_{j}} δ_{j}

8-

v_{\min} \leq v_{j} \leq v_{\max}

9-

j = 1, \dots, m

10-

\sum_{j = 1}^{m} \frac{l_{j}}{v_{j}} δ_{j} \leq T_{\max} .

Formulas (html):

Correct Categorie: cs

Guessed Categorie: stat

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0306376

Formulas:

1-

\sim 3 \times 10^{- 5} M_{⊙} {yr}^{- 1}

2-

10 km s^{- 1}

3-

ρ_{w} \propto r^{- 2}

4-

r_{f} / r_{r} = 1.5

5-

m_{f} = d \ln r_{f} / d \ln t

6-

ρ_{w} = A r^{- 2}

7-

A = \dot{M} / 4 π v_{w}

8-

ρ_{s n} \propto r^{- 10.12}

9-

r_{f} / r_{r} = 1.26

10-

r^{'} = r / R^{'}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1401.0929

Formulas:

1-

d (u, v)

2-

B = {b_{1}, b_{2}, b_{3}, \dots b_{k}}

3-

r (v | B)

4-

(d (v, b_{1}), d (v, b_{2}), \dots, d (v, b_{k}))

5-

r (u | B) \neq r (v | B)

6-

D = (V, A)

7-

u, v \in V (D)

8-

d (u, v)

9-

B = {b_{1}, b_{2}, b_{3}, \dots b_{k}}

10-

r (v | B)

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/1107.0774

Formulas:

1-

R_{n} \equiv N_{n}^{ref} / n

2-

T_{n} \equiv 1 - R_{n}

3-

u = 9.05 [ℏ η T^{- 1}]

4-

u = 144.8 [ℏ η T^{- 1}]

5-

N_{site} \equiv 4 D + 1

6-

0, 1, \dots, 2 D, \dots, 4 D

7-

x = - 2 a

8-

Δ x \equiv a / D

9-

V_{-}^{ext} (x) \equiv \frac{1}{2} m ω^{2} {(x + a)}^{2}

10-

V_{+}^{ext} (x) \equiv \frac{1}{2} m ω^{2} {(x - a)}^{2}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/0906.1102

Formulas:

1-

T_{e f f}

2-

ϕ \to K \bar{K}

3-

ϕ \to K^{+} K^{-}

4-

N_{p a r t}

5-

⟨ ϕ ⟩ / N_{p a r t}

6-

p_{T} > 1.1 GeV

7-

ϕ \to K^{+} K^{-}

8-

p_{T} < 1.6 GeV

9-

T_{e f f}

10-

T_{e f f}

Formulas (html):

Correct Categorie: hep-ex

Guessed Categorie: nucl-ex

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/0207228

Formulas:

1-

p (k, t) = \frac{k + α}{D (t) + α N (t)} .

2-

P (k) \sim k^{- τ}

3-

1 / N (t)

4-

P (k) \sim 2^{- k}

5-

l_{a} (t) = \sum_{a c t i v e} q (t)

6-

S_{X} (f) = {| \sum_{t = 1}^{\infty} X (t) e^{i f t} |}^{2} .

7-

S_{X} (f)

8-

r_{X} (k) \sim k^{- ϕ}

9-

S_{X} (f) \sim f^{- ϕ}

10-

μ = R - \frac{n (t)}{t} .

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1304.4405

Formulas:

1-

- 42^{d} 08^{m} {37.5}^{s}

2-

k T = {0.092}_{- 0.041}^{+ 0.038}

3-

Γ = {0.77}_{- 0.11}^{+ 0.10}

4-

N_{H (Gal)} = 1.65 \times 10^{21}

5-

- 42^{d} 08^{m} {44.6}^{s}

6-

N_{H (Gal)} Â = 1.66 \times 10^{21}

7-

Γ = {1.51}_{- 0.25}^{+ 0.26}

8-

- 49^{d} 53^{m} {02.9}^{s}

9-

N_{H (Gal)} = 2.04 \times 10^{21}

10-

L o g R = L o g (L_5 G H z / L_B) = 3.50

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/nucl-th/0608038

Formulas:

1-

p (\bar{p}) + p

2-

p (\bar{p}) + p

3-

p (\bar{p}) + p

4-

p (\bar{p}) + p

5-

p (\bar{p}) + p

6-

p (\bar{p}) + p

7-

p (\bar{p}) + p

8-

p (\bar{p}) + p

9-

p (\bar{p}) + p

10-

n_{A} (r) = \frac{n_{0}}{1 + \exp [(r - R_{n}) / d]},

Formulas (html):

Correct Categorie: nucl-th

Guessed Categorie: hep-ph

Result: incorrect

Paper: https://arxiv.org/abs/1307.6347

Formulas:

1-

θ = R_{S N R} + θ_{P S F}

2-

R_{S N R}

3-

R_{S N R} = \sqrt{R_{m i n} \cdot R_{m a j}}

4-

θ_{P S F}

5-

\frac{d N}{d E} \propto {(\frac{E}{1 T e V})}^{- Γ}

6-

N = \int_{1 T e V}^{100 T e V} T \cdot A (E) \cdot {(\frac{E}{1 T e V})}^{- Γ} d E

7-

n_{99 %}^{U L}

8-

Φ_{99 %}^{U L} (> 1 T e V) = \frac{n_{99 %}^{UL}}{N} \int_{1 T e V}^{100 T e V} {(\frac{E}{1 T e V})}^{- Γ} dE

9-

D_{I S M} (E) \propto E^{δ}

10-

F_{γ} (> E) \approx \frac{1}{4 π d^{2}} θ E_{S N} n q_{γ} E^{1 - α}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: hep-ex

Result: incorrect

Paper: https://arxiv.org/abs/physics/0009065

Formulas:

1-

n_{2} [e s u] = \frac{K \sqrt{E_{p}} G_{2} (\frac{ℏ ω}{E_{g}})}{n_{0} E_{g}^{4}} .

2-

E_{p} = 21 e V

3-

K = 1.5 \cdot 10^{- 8}

4-

E_{g} = 2.58 e V

5-

G_{2} (x) = 0.01373 + \frac{0.656 \cdot 10^{- 14}}{x^{2}} + \frac{0.1889 \cdot 10^{- 37}}{x^{6}},

6-

n_{0} = 2.4215 + \frac{0.4995 \cdot 10^{- 7}}{λ} - \frac{0.1747 \cdot 10^{- 13}}{λ^{2}} + \frac{0.3429 \cdot 10^{- 19}}{λ^{3}}

7-

d = 80 p m / V^{6}

8-

n = n_{0} + n_{2} I

9-

\frac{{(\frac{Δ k}{2 χ})}^{2}}{I} << 1

10-

χ = \frac{2 ω d}{\sqrt{2 ϵ_{0} n_{0}^{2} n_{2 ω} c^{3}}}

Formulas (html):

Correct Categorie: physics

Guessed Categorie: physics

Result: correct

Paper: https://arxiv.org/abs/1210.1774

Formulas:

1-

(M, F, p)

2-

d : M \times M ⟶ [0, \infty)

3-

F (- v) = F (v)

4-

d (x, y) \neq d (y, x)

5-

{(x^{i})}_{i = 1}^{n}

6-

{(x^{i}, v^{j})}_{i, j = 1}^{n}

7-

v := {\sum_{j = 1}^{n} v^{j} \frac{\partial}{\partial x^{j}} |}_{x}, x \in 𝒪 .

8-

v \in T_{x} M ∖ {0}

9-

{(g_{i j} (v))}_{i, j = 1}^{n} := {(\frac{1}{2} \frac{\partial^{2} (F^{2})}{\partial v^{i} \partial v^{j}} (v))}_{i, j = 1}^{n}

10-

g_{v} ({\sum_{i = 1}^{n} a^{i} \frac{\partial}{\partial x^{i}} |}_{x}, {\sum_{j = 1}^{n} b^{j} \frac{\partial}{\partial x^{j}} |}_{x}) := \sum_{i, j = 1}^{n} g_{i j} (v) a^{i} b^{j} .

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/1406.1357

Formulas:

1-

{(M_{2} / M_{1})}^{1 / 3}

2-

{(m_{p l} / m_{J u p})}^{1 / 3}

3-

b e f o r e

4-

(10 A U / a_{bin}) M_{Jup}

5-

M_{2} / M_{1} = 0.35

6-

Δ v_{s_{1}, s_{2}} \geq v_{e r o - M}

7-

v_{e r o - M}

8-

v_{e s c - m} \leq Δ v_{s_{1}, s_{2}} \leq v_{e r o - M}

9-

v_{e s c - m}

10-

Δ v_{s_{1}, s_{2}} \leq v_{e s c}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1811.02905

Formulas:

1-

τ_{f} = ρ_{p} / ρ_{g} \cdot d / c

2-

ρ_{p} = 10^{3} kg / m^{3}

3-

ρ_{g} = 10^{- 6} kg / m^{3}

4-

c = 1000 m / s

5-

k = a - b \exp (T - c)

6-

Δ t_{h e a t}

7-

\propto Δ t_{h e a t}^{1 / 4}

8-

T_{s} = 1200 K

9-

T_{C} = 1400 K

10-

T_{m} = 1500 K

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/0903.0717

Formulas:

1-

\frac{1}{\sqrt{2}} ({| 0 ⟩}^{\otimes N} + {| 1 ⟩}^{\otimes N})

2-

(N - n) | n

3-

1 | (N - 1)

4-

N / 2 | N / 2

5-

| Ψ_{2} ⟩ = α {| 0 ⟩}^{\otimes N} + β {| 1 ⟩}^{\otimes N}

6-

(N - n) | n

7-

X | i ⟩ = | i + 1 ⟩

8-

Z | i ⟩ = ω^{i} | i ⟩

9-

i = 0, \dots, d - 1

10-

ω = \exp (2 π i / d)

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: quant-ph

Result: correct

Paper: https://arxiv.org/abs/cond-mat/0404627

Formulas:

1-

𝒪 (N^{3})

2-

δ 𝐱 = - 𝐠 \cdot 𝐡^{- 1}

3-

w_{k}^{(i)} = {(1 / g_{k}^{(i)})}^{2}

4-

w_{k}^{(i)} = {[\sum_{l} g_{l}^{(i)} \frac{1}{| H_{l l} |} g_{l}^{(i)}]}^{- 1},

5-

G_{i} = B B^{t}

6-

φ_{k}^{(i + 1)} = φ_{k}^{(i)} - g_{k}^{(i)} / | H_{k k}^{(i)} |,

7-

H_{k k}^{(i)}

8-

𝒪 (N_{int})

9-

H_{k k}^{(i)}

10-

\log_{10} Δ E_{i + 1}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: astro-ph

Result: incorrect

Run 10695631 (Agent093)