Run 11299131

Paper: https://arxiv.org/abs/astro-ph/0006210

Formulas:

1-

N_{obs} = ZHR \times r^{- (6.5 - lm)} \times Δ t_{h},

2-

N_{obs} = 2 \times ZHR \times r^{- x} .

3-

Z H R \approx 4000

4-

N_{\exp} = 10 \times {3.4}^{- x} \times Δ t_{h} .

5-

N_{\exp} \approx 1 / 900

6-

N_{e c l} = 1 / 90 – 1 / 30

7-

M v^{2} / 2

8-

Δ T \approx C_{M} / M

9-

Δ T \approx 2 \times 10^{5}

10-

W_{M} = \frac{σ T^{4} \times A_{M}}{4 π d_{Moon}^{2}} \approx 3 \times 10^{- 8} W/m^{2},

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/cond-mat/0609181

Formulas:

1-

r_{s} \equiv E_{C} / E_{F} > 10

2-

k_{B} T < ℏ / τ < E_{F}

3-

C_{e e} (T)

4-

C_{e e} (T)

5-

Δ σ (B, T) \equiv σ (B, T) - σ (0, T)

6-

b \equiv g μ_{B} B / k_{B} T ≪ 1

7-

ℏ / τ < k_{B} T < E_{F}

8-

Δ σ (B, T)

9-

Δ σ (B, T)

10-

n_{s} = 9.14 \times 10^{10}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/quant-ph/0607107

Formulas:

1-

ρ^{(0)} = | j, j ⟩ ⟨ j, j |

2-

{Π_{+} \equiv Π_{j + 1 / 2}, Π_{-} \equiv Π_{j - 1 / 2}}

3-

ℍ_{j} \otimes ℍ_{1 / 2}

4-

ρ^{(n + 1)} = ℰ (ρ^{(n)})

5-

ℰ (ρ) = {Tr}_{S} (\sum_{c \in {+, -}} Π_{c} (ρ \otimes I / 2) Π_{c}),

6-

ℰ (ρ) = \frac{1}{2} \sum_{\overset{c \in {+, -}}{a, b \in {0, 1}}} E_{a b}^{c} ρ E_{a b}^{c, †},

7-

E_{a b}^{c} \equiv ⟨ a | Π_{c} | b ⟩

8-

{| 0 ⟩, | 1 ⟩}

9-

F_{Q} = \frac{1}{2} {Tr}_{R} (ρ (E_{00}^{+} + E_{11}^{-})),

10-

ρ^{(0)} = | j, j ⟩ ⟨ j, j |

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: quant-ph

Result: correct

Paper: https://arxiv.org/abs/1410.8839

Formulas:

1-

I = 1, S = 0, T_{1 u}^{+}

2-

𝒞_{i j} (t) = ⟨ 0 | O_{i} (t + t_{0}) {\bar{O}}_{j} (t_{0}) | 0 ⟩,

3-

𝒞_{i j} (t)

4-

\pm \hat{𝒙}, \pm \hat{𝒚}, \pm \hat{𝒛}

5-

\pm \hat{𝒙} \pm \hat{𝒚}, \pm \hat{𝒙} \pm \hat{𝒛}, \pm \hat{𝒚} \pm \hat{𝒛}

6-

\pm \hat{𝒙} \pm \hat{𝒚} \pm \hat{𝒛}

7-

\pm 2 \hat{𝒙} \pm \hat{𝒚}

8-

𝒞_{i j} (t) = \sum_{n} Z_{i}^{(n)} Z_{j}^{(n), *} e^{- E_{n} t}, Z_{j}^{(n)} = ⟨ 0 | O_{j} | n ⟩,

9-

C_{i j} (t) = 𝒞_{i j} (t) {(𝒞_{i i} (τ_{N}) 𝒞_{j j} (τ_{N}))}^{- 1 / 2}

10-

A x = λ B x

Formulas (html):

Correct Categorie: hep-lat

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/0106333

Formulas:

1-

{Co}_{1 - x} {Mg}_{x} O

2-

- J_{FM} \sum_{⟨ i, j ⟩} \vec{S_{i}} \cdot \vec{S_{j}} - \sum_{i} (d_{z} S_{i z}^{2} + d_{x} S_{i x}^{2} + \vec{S_{i}} \cdot \vec{B})

3-

- J_{AFM} \sum_{⟨ i, j ⟩} ϵ_{i} ϵ_{j} \vec{σ_{i}} \cdot \vec{σ_{j}} - \sum_{i} ϵ_{i} (k_{z} σ_{i z}^{2} + \vec{σ_{i}} \cdot \vec{B})

4-

- J_{INT} \sum_{⟨ i, j ⟩} ϵ_{j} \vec{S_{i}} \cdot \vec{σ_{j}}

5-

(d_{z} > 0)

6-

(d_{x} < 0)

7-

(ϵ_{i} = 0, 1)

8-

(k_{z} > 0)

9-

\vec{B} = B \hat{z}

10-

J_{FM} = - 2 J_{AFM} = 2 J_{INT}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1306.4209

Formulas:

1-

g_{0} / 2 π

2-

+ ℏ δ ω

3-

- ℏ δ ω

4-

H = ℏ Ω_{0} (a^{†} a + 1 / 2) + ℏ ω_{0} σ_{z} / 2 + ℏ g_{0} σ_{z} (a^{†} + a),

5-

Ω_{0} / 2 π

6-

σ_{z} = | e ⟩ ⟨ e | - | g ⟩ ⟨ g |

7-

g_{0} = {\frac{\partial ω}{\partial x} |}_{x = 0} δ x_{Z P F},

8-

δ x_{Z P F}

9-

Ω_{0} / 2 π = 530

10-

Ω_{0} / 2 π = 522.4

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1009.3816

Formulas:

1-

E_{G M R}

2-

K (Z, A) = \frac{M}{ℏ^{2}} R^{2} E_{G M R}^{2},

3-

K (Z, A)

4-

I = (N - Z) / A

5-

K (Z, A) = K^{(1)} (Z, A) \equiv K_{v} + K_{s f} A^{- 1 / 3} + K_{τ} I^{2} + K_{c o u l} \frac{Z^{2}}{A^{4 / 3}} .

6-

K (Z, A)

7-

K_{c o u l}

8-

K_{s a t, 2}

9-

K_{c o u l}

10-

K (Z, A) = K^{(1)} (Z, A) + K_{s s} I^{2} A^{- 1 / 3} + K_{c v} A^{- 2 / 3} + K_{τ 4} I^{4} .

Formulas (html):

Correct Categorie: nucl-th

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/1012.1905

Formulas:

1-

H_{m i x} = H_{U_{x} C e_{1 - x} O_{2}} - (x H_{U O_{2}} + (1 - x) H_{C e O_{2}}),

2-

H_{U_{x} C e_{1 - x} O_{2}}

3-

H_{C e O_{2}}

4-

< \frac{1}{2} \frac{1}{2} \frac{1}{2} >

5-

Δ G_{m i x} =

6-

H_{m i x} (x_{C e (I I I)}, x_{C e (I V)}, x_{U (I V)}, x_{U (V)})

7-

R T [\sum_{i} x_{i} l n (x_{i})]

8-

\sum_{i} x_{i} = x_{C e (I I I)} + x_{C e (I V)} + x_{U (I V)} + x_{U (V)} = 1

9-

3 x_{C e (I I I)} + 4 x_{C e (I V)} + 4 x_{U (I V)} + 5 x_{U (V)} = 4

10-

C = x_{C e (I I I)} / (x_{C e (I I I)} + x_{C e (I V)})

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/math/0702166

Formulas:

1-

(K_{5} - H)

2-

π = (d_{1}, d_{2}, \dots, d_{n})

3-

e x (n, H)

4-

2 e x (n, H) + 2

5-

σ (π) \geq l

6-

σ (K_{k}, n) \geq (k - 2) (2 n - k + 1) + 2

7-

n \geq (\binom{k}{2}) + 3

8-

σ (F_{k}, n)

9-

σ (H, n)

10-

π = (d_{1}, d_{2}, \dots, d_{n})

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/1806.04430

Formulas:

1-

2.19 (4) μ_{B}

2-

3.10 (6) μ_{B}

3-

I 4 / m m m

4-

𝒂_{m a g} = 𝒂 + 𝒃

5-

𝒃_{m a g} = 𝒂 - 𝒃

6-

I 4 / m m m

7-

(\frac{1}{2}, \frac{1}{2}, 0)

8-

(1, 0, 0)

9-

(μ_{B} / Cr(II))

10-

(μ_{B} / Cr(I))

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/math/0003136

Formulas:

1-

G L_{2} (𝐅_{p})

2-

𝐙_{p} [[T_{1}, T_{2}, T_{3}]]

3-

27 + 4 a^{3}

4-

x^{3} + a x + 1

5-

27 + 4 a^{3}

6-

27 + 4 a^{3} < 10^{15} / 2

7-

x^{3} + 7 x - 12

8-

{(𝔭_{1} 𝔭_{2} 𝔭_{3})}^{2}

9-

𝔭_{1}, 𝔭_{2}, 𝔭_{3}

10-

x^{3} + a x + 1 = 0

Formulas (html):

Correct Categorie: math

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/0310767

Formulas:

1-

V_{N N} = 0

2-

ρ_{P} (𝐑)

3-

ρ_{N} (𝐫, 𝝎)

4-

Ω [ρ_{P} (𝐑), ρ_{N} (𝐫, 𝝎)] = F_{i d} [ρ_{P} (𝐑), ρ_{N} (𝐫, 𝝎)] +

5-

F_{e x} [ρ_{P} (𝐑), ρ_{N} (𝐫, 𝝎)] + \int 𝑑 𝐑 ρ_{P} (𝐑) (V_{e x t}^{(P)} (𝐑) - μ_{P})

6-

\int 𝑑 𝐫 \int \frac{d 𝝎}{4 π} ρ_{N} (𝐫, 𝝎) (V_{e x t}^{(N)} (𝐫, 𝝎) - μ_{N}),

7-

𝐑 \equiv (𝐫_{1}, 𝐫_{2}, \dots, 𝐫_{M})

8-

V_{e x t}^{(P)} (𝐑)

9-

V_{e x t}^{(N)} (𝐫, 𝝎)

10-

β F_{i d} [ρ_{P} (𝐑), ρ_{N} (𝐫, 𝝎)] = β \int 𝑑 𝐑 ρ_{P} (𝐑) V_{b} (𝐑) +

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1609.00741

Formulas:

1-

\cos ϕ^{'''} = - \frac{(1 + {(\frac{v}{V})}^{2}) \cos ϕ - 2 \frac{v}{V}}{1 - 2 \frac{v}{V} \cos ϕ + {(\frac{v}{V})}^{2}},

2-

F = (0, 0)

3-

x (t) = v t + x_{0}

4-

c > | v | > 0

5-

x_{τ} = v τ + x_{0}

6-

H = (x, y)

7-

| F H | = ℓ

8-

ℓ = c (T - τ)

9-

x - x_{τ} = v (T - τ)

10-

(x - x_{τ}) / ℓ = v / c

Formulas (html):

Correct Categorie: physics

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/0302176

Formulas:

1-

W (x_{A}, x_{D})

2-

W (x_{A}, x_{D})

3-

E^{A} (x_{A}, x_{D}) = N \cdot (W (x_{A} + 1 / N, x_{D}) - W (x_{A}, x_{D})) + E_{a t o m} (X) - E_{a t o m} (A) .

4-

E_{a t o m} (X) - E_{a t o m} (A)

5-

W (x_{A}, x_{D})

6-

E^{A} (x_{A}, x_{D}) = \frac{\partial W (x_{A}, x_{D})}{\partial x_{A}} + E_{a t o m} (X) - E_{a t o m} (A),

7-

E^{D} (x_{A}, x_{D}) = \frac{\partial W (x_{A}, x_{D})}{\partial x_{D}} + E_{a t o m} (Y) - E_{a t o m} (D),

8-

K (x_{A}, x_{D}) = \frac{\partial E^{A}}{\partial x_{D}} = \frac{\partial E^{D}}{d x_{A}} = \frac{\partial^{2} W (x_{A}, x_{D})}{\partial x_{A} \partial x_{D}} .

9-

K = W {L U C^{(A D)}} - W {L U C^{(A Y)}} - W {L U C^{(X D)}} + W {L U C^{(X Y)}}

10-

K (x_{A}, x_{D})

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1402.1791

Formulas:

1-

\sqrt{s_{_{N N}}} = 200

2-

\sqrt{s_{_{N N}}} = 200

3-

M_{e e} < 1.1

4-

1.1 < M_{e e} < 2.9

5-

M_{l l} < 1.1

6-

ρ (770), ω (782)

7-

0.15 < M_{e e} < 0.75

8-

\sqrt{s_{_{N N}}} = 200

9-

1.5 \pm {0.3}^{stat} \pm {0.5}^{syst} \pm {0.3}^{model}

10-

7.6 \pm {0.5}^{stat} \pm {1.3}^{syst} \pm {1.5}^{model}

Formulas (html):

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id="id5.4.m4.1.1.2.3.3" xref="id5.4.m4.1.1.2.3.3.cmml">e</mi></mrow></msub></mpadded><mo id="id5.4.m4.1.1.1" xref="id5.4.m4.1.1.1.cmml"><</mo><mn id="id5.4.m4.1.1.3" xref="id5.4.m4.1.1.3.cmml">1.1</mn></mrow></math>, <math><mrow id="id12.11.m11.1.1" xref="id12.11.m11.1.1.cmml"><mpadded width="-1.7pt" id="id12.11.m11.1.1.2" xref="id12.11.m11.1.1.2.cmml"><mn id="id12.11.m11.1.1.2a" xref="id12.11.m11.1.1.2.cmml">1.1</mn></mpadded><mo id="id12.11.m11.1.1.3" xref="id12.11.m11.1.1.3.cmml"><</mo><mpadded width="-1.7pt" id="id12.11.m11.1.1.4" xref="id12.11.m11.1.1.4.cmml"><msub id="id12.11.m11.1.1.4a" xref="id12.11.m11.1.1.4.cmml"><mi id="id12.11.m11.1.1.4.2" xref="id12.11.m11.1.1.4.2.cmml">M</mi><mrow id="id12.11.m11.1.1.4.3" xref="id12.11.m11.1.1.4.3.cmml"><mi id="id12.11.m11.1.1.4.3.2" xref="id12.11.m11.1.1.4.3.2.cmml">e</mi><mo id="id12.11.m11.1.1.4.3.1" xref="id12.11.m11.1.1.4.3.1.cmml">⁢</mo><mi id="id12.11.m11.1.1.4.3.3" xref="id12.11.m11.1.1.4.3.3.cmml">e</mi></mrow></msub></mpadded><mo id="id12.11.m11.1.1.5" xref="id12.11.m11.1.1.5.cmml"><</mo><mn id="id12.11.m11.1.1.6" xref="id12.11.m11.1.1.6.cmml">2.9</mn></mrow></math>, <math><mrow id="S1.p2.1.m1.1.1" xref="S1.p2.1.m1.1.1.cmml"><mpadded width="-1.7pt" id="S1.p2.1.m1.1.1.2" xref="S1.p2.1.m1.1.1.2.cmml"><msub id="S1.p2.1.m1.1.1.2a" xref="S1.p2.1.m1.1.1.2.cmml"><mi id="S1.p2.1.m1.1.1.2.2" xref="S1.p2.1.m1.1.1.2.2.cmml">M</mi><mrow id="S1.p2.1.m1.1.1.2.3" xref="S1.p2.1.m1.1.1.2.3.cmml"><mi id="S1.p2.1.m1.1.1.2.3.2" xref="S1.p2.1.m1.1.1.2.3.2.cmml">l</mi><mo id="S1.p2.1.m1.1.1.2.3.1" xref="S1.p2.1.m1.1.1.2.3.1.cmml">⁢</mo><mi id="S1.p2.1.m1.1.1.2.3.3" xref="S1.p2.1.m1.1.1.2.3.3.cmml">l</mi></mrow></msub></mpadded><mo rspace="0.8pt" id="S1.p2.1.m1.1.1.1" xref="S1.p2.1.m1.1.1.1.cmml"><</mo><mn id="S1.p2.1.m1.1.1.3" xref="S1.p2.1.m1.1.1.3.cmml">1.1</mn></mrow></math>, <math><mrow id="S1.p2.3.m3.4.4.2" xref="S1.p2.3.m3.4.4.3.cmml"><mrow id="S1.p2.3.m3.3.3.1.1" xref="S1.p2.3.m3.3.3.1.1.cmml"><mi id="S1.p2.3.m3.3.3.1.1.2" xref="S1.p2.3.m3.3.3.1.1.2.cmml">ρ</mi><mo id="S1.p2.3.m3.3.3.1.1.1" xref="S1.p2.3.m3.3.3.1.1.1.cmml">⁢</mo><mrow id="S1.p2.3.m3.3.3.1.1.3.2" xref="S1.p2.3.m3.3.3.1.1.cmml"><mo stretchy="false" id="S1.p2.3.m3.3.3.1.1.3.2.1" xref="S1.p2.3.m3.3.3.1.1.cmml">(</mo><mn id="S1.p2.3.m3.1.1" xref="S1.p2.3.m3.1.1.cmml">770</mn><mo stretchy="false" id="S1.p2.3.m3.3.3.1.1.3.2.2" xref="S1.p2.3.m3.3.3.1.1.cmml">)</mo></mrow></mrow><mo id="S1.p2.3.m3.4.4.2.3" xref="S1.p2.3.m3.4.4.3.cmml">,</mo><mrow id="S1.p2.3.m3.4.4.2.2" xref="S1.p2.3.m3.4.4.2.2.cmml"><mi id="S1.p2.3.m3.4.4.2.2.2" xref="S1.p2.3.m3.4.4.2.2.2.cmml">ω</mi><mo id="S1.p2.3.m3.4.4.2.2.1" xref="S1.p2.3.m3.4.4.2.2.1.cmml">⁢</mo><mrow id="S1.p2.3.m3.4.4.2.2.3.2" xref="S1.p2.3.m3.4.4.2.2.cmml"><mo stretchy="false" id="S1.p2.3.m3.4.4.2.2.3.2.1" xref="S1.p2.3.m3.4.4.2.2.cmml">(</mo><mn id="S1.p2.3.m3.2.2" xref="S1.p2.3.m3.2.2.cmml">782</mn><mo stretchy="false" id="S1.p2.3.m3.4.4.2.2.3.2.2" xref="S1.p2.3.m3.4.4.2.2.cmml">)</mo></mrow></mrow></mrow></math>, <math><mrow id="S1.p3.1.m1.1.1" xref="S1.p3.1.m1.1.1.cmml"><mpadded width="-1.7pt" id="S1.p3.1.m1.1.1.2" xref="S1.p3.1.m1.1.1.2.cmml"><mn id="S1.p3.1.m1.1.1.2a" xref="S1.p3.1.m1.1.1.2.cmml">0.15</mn></mpadded><mo id="S1.p3.1.m1.1.1.3" xref="S1.p3.1.m1.1.1.3.cmml"><</mo><mpadded width="-1.7pt" id="S1.p3.1.m1.1.1.4" xref="S1.p3.1.m1.1.1.4.cmml"><msub id="S1.p3.1.m1.1.1.4a" xref="S1.p3.1.m1.1.1.4.cmml"><mi id="S1.p3.1.m1.1.1.4.2" xref="S1.p3.1.m1.1.1.4.2.cmml">M</mi><mrow id="S1.p3.1.m1.1.1.4.3" xref="S1.p3.1.m1.1.1.4.3.cmml"><mi id="S1.p3.1.m1.1.1.4.3.2" xref="S1.p3.1.m1.1.1.4.3.2.cmml">e</mi><mo id="S1.p3.1.m1.1.1.4.3.1" xref="S1.p3.1.m1.1.1.4.3.1.cmml">⁢</mo><mi id="S1.p3.1.m1.1.1.4.3.3" xref="S1.p3.1.m1.1.1.4.3.3.cmml">e</mi></mrow></msub></mpadded><mo rspace="0.8pt" id="S1.p3.1.m1.1.1.5" xref="S1.p3.1.m1.1.1.5.cmml"><</mo><mn id="S1.p3.1.m1.1.1.6" xref="S1.p3.1.m1.1.1.6.cmml">0.75</mn></mrow></math>, <math><mrow id="S1.p3.3.m3.1.1" xref="S1.p3.3.m3.1.1.cmml"><msqrt id="S1.p3.3.m3.1.1.2" xref="S1.p3.3.m3.1.1.2.cmml"><msub id="S1.p3.3.m3.1.1.2.2" xref="S1.p3.3.m3.1.1.2.2.cmml"><mi id="S1.p3.3.m3.1.1.2.2.2" xref="S1.p3.3.m3.1.1.2.2.2.cmml">s</mi><msub id="S1.p3.3.m3.1.1.2.2.3" xref="S1.p3.3.m3.1.1.2.2.3.cmml"><mi id="S1.p3.3.m3.1.1.2.2.3a" xref="S1.p3.3.m3.1.1.2.2.3.cmml"/><mrow id="S1.p3.3.m3.1.1.2.2.3.1" xref="S1.p3.3.m3.1.1.2.2.3.1.cmml"><mi id="S1.p3.3.m3.1.1.2.2.3.1.2" xref="S1.p3.3.m3.1.1.2.2.3.1.2.cmml">N</mi><mo id="S1.p3.3.m3.1.1.2.2.3.1.1" xref="S1.p3.3.m3.1.1.2.2.3.1.1.cmml">⁢</mo><mi id="S1.p3.3.m3.1.1.2.2.3.1.3" xref="S1.p3.3.m3.1.1.2.2.3.1.3.cmml">N</mi></mrow></msub></msub></msqrt><mo id="S1.p3.3.m3.1.1.1" xref="S1.p3.3.m3.1.1.1.cmml">=</mo><mn id="S1.p3.3.m3.1.1.3" xref="S1.p3.3.m3.1.1.3.cmml">200</mn></mrow></math>, <math><mrow id="S1.p3.7.m7.1.1" xref="S1.p3.7.m7.1.1.cmml"><mn id="S1.p3.7.m7.1.1.2" xref="S1.p3.7.m7.1.1.2.cmml">1.5</mn><mo id="S1.p3.7.m7.1.1.1" xref="S1.p3.7.m7.1.1.1.cmml">±</mo><msup id="S1.p3.7.m7.1.1.3" xref="S1.p3.7.m7.1.1.3.cmml"><mn id="S1.p3.7.m7.1.1.3.2" xref="S1.p3.7.m7.1.1.3.2.cmml">0.3</mn><mtext id="S1.p3.7.m7.1.1.3.3" xref="S1.p3.7.m7.1.1.3.3a.cmml">stat</mtext></msup><mo id="S1.p3.7.m7.1.1.1a" xref="S1.p3.7.m7.1.1.1.cmml">±</mo><msup id="S1.p3.7.m7.1.1.4" xref="S1.p3.7.m7.1.1.4.cmml"><mn id="S1.p3.7.m7.1.1.4.2" xref="S1.p3.7.m7.1.1.4.2.cmml">0.5</mn><mtext id="S1.p3.7.m7.1.1.4.3" xref="S1.p3.7.m7.1.1.4.3a.cmml">syst</mtext></msup><mo id="S1.p3.7.m7.1.1.1b" xref="S1.p3.7.m7.1.1.1.cmml">±</mo><msup id="S1.p3.7.m7.1.1.5" xref="S1.p3.7.m7.1.1.5.cmml"><mn id="S1.p3.7.m7.1.1.5.2" xref="S1.p3.7.m7.1.1.5.2.cmml">0.3</mn><mtext id="S1.p3.7.m7.1.1.5.3" xref="S1.p3.7.m7.1.1.5.3a.cmml">model</mtext></msup></mrow></math>, <math><mrow id="S1.p3.8.m8.1.1" xref="S1.p3.8.m8.1.1.cmml"><mn id="S1.p3.8.m8.1.1.2" xref="S1.p3.8.m8.1.1.2.cmml">7.6</mn><mo id="S1.p3.8.m8.1.1.1" xref="S1.p3.8.m8.1.1.1.cmml">±</mo><msup id="S1.p3.8.m8.1.1.3" xref="S1.p3.8.m8.1.1.3.cmml"><mn id="S1.p3.8.m8.1.1.3.2" xref="S1.p3.8.m8.1.1.3.2.cmml">0.5</mn><mtext id="S1.p3.8.m8.1.1.3.3" xref="S1.p3.8.m8.1.1.3.3a.cmml">stat</mtext></msup><mo id="S1.p3.8.m8.1.1.1a" xref="S1.p3.8.m8.1.1.1.cmml">±</mo><msup id="S1.p3.8.m8.1.1.4" xref="S1.p3.8.m8.1.1.4.cmml"><mn id="S1.p3.8.m8.1.1.4.2" xref="S1.p3.8.m8.1.1.4.2.cmml">1.3</mn><mtext id="S1.p3.8.m8.1.1.4.3" xref="S1.p3.8.m8.1.1.4.3a.cmml">syst</mtext></msup><mo id="S1.p3.8.m8.1.1.1b" xref="S1.p3.8.m8.1.1.1.cmml">±</mo><msup id="S1.p3.8.m8.1.1.5" xref="S1.p3.8.m8.1.1.5.cmml"><mn id="S1.p3.8.m8.1.1.5.2" xref="S1.p3.8.m8.1.1.5.2.cmml">1.5</mn><mtext id="S1.p3.8.m8.1.1.5.3" xref="S1.p3.8.m8.1.1.5.3a.cmml">model</mtext></msup></mrow></math>

Correct Categorie: nucl-ex

Guessed Categorie: hep-ph

Result: incorrect

Paper: https://arxiv.org/abs/1901.04608

Formulas:

1-

Δ p_{z} = \frac{e V_{0}}{β c} (\sin ϕ_{0} + ω \frac{ζ}{β c} \cos (ϕ_{0}))

2-

ϕ_{0} = π / 2

3-

⟨ ζ, Δ_{γ β} ⟩

4-

Δ_{γ β} = (p_{z} - p_{z c}) / m c

5-

R_{R F} = (\begin{matrix} 1 & 0 \\ \frac{e V_{0} ω / c}{m β^{2} c^{2}} \cos ϕ_{0} & 1 \end{matrix})

6-

\frac{1}{f} = \frac{e V_{0} ω}{m c^{3} γ^{3} β^{4}} \cos ϕ_{0}

7-

R_{t o t} = (\begin{matrix} 1 & \frac{L_{2}}{β_{2}^{2} γ_{2}^{3}} \\ 0 & 1 \end{matrix}) R_{R F} (\begin{matrix} 1 & \frac{L_{1}}{β_{1}^{2} γ_{1}^{3}} \\ 0 & 1 \end{matrix})

8-

M = (L_{2} / L_{1}) (β_{1}^{2} γ_{1}^{3} / β_{2}^{2} γ_{2}^{3})

9-

(β_{1}^{2} γ_{1}^{3} / β_{2}^{2} γ_{2}^{3})

10-

f_{s} (ζ, Δ_{γ β})

Formulas (html):

Correct Categorie: physics

Guessed Categorie: physics

Result: correct

Paper: https://arxiv.org/abs/cond-mat/9706305

Formulas:

1-

z_{c} (M)

2-

z_{d} (M)

3-

z > z_{d} (M)

4-

z_{d} (M)

5-

z_{d} (M) \sim M - 2 + 2 / (3 M^{2}) + \dots

6-

z_{c} (M)

7-

z_{c} < z < z_{d}

8-

I = 1, \dots, M

9-

ρ_{e} (I) = M^{- 1} ρ_{e}

10-

ρ_{o} (I) = M^{- 1} ρ_{o}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/0901.0894

Formulas:

1-

0 < J^{'} \leq 1

2-

0 \leq J_{2} < 0.3

3-

𝐒_{i} \cdot 𝐒_{j} = S_{i}^{z} S_{j}^{z} + λ (S_{i}^{x} S_{j}^{x} + S_{i}^{y} S_{j}^{y}) .

4-

⟨ 𝐒_{i} \cdot 𝐒_{j} ⟩

5-

α = \frac{1}{\sqrt{1 + N}}

6-

Δ C_{i j} / C_{i j}^{0} = - \frac{{⟨ \vec{S_{i}} \cdot \vec{S_{j}} ⟩}_{S I} - {⟨ \vec{S_{i}} \cdot \vec{S_{j}} ⟩}_{\infty}}{{⟨ \vec{S_{i}} \cdot \vec{S_{j}} ⟩}_{\infty}}

7-

Δ M = (M_{S I} - M_{\infty})

8-

Δ C_{i j} / C_{i j}^{0}

9-

Δ C_{i j} / C_{i j}^{0}

10-

J_{2} / J_{1} \approx 0.35 - 0.4

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/0705.3444

Formulas:

1-

μ \equiv M_{C} / (M_{⋆} + M_{C})

2-

Q_{B} \equiv a_{B} (1 + e_{B})

3-

m_{p} < 1 M_{\oplus}

4-

i 0_3

5-

i 0_1

6-

i 0_2

7-

i 0_4

8-

i 0_1

9-

i 0_2

10-

i 15_2

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1012.4564

Formulas:

1-

P 2_{1} / n

2-

a_{p} = {(\frac{V}{Z})}^{\frac{1}{3}}

3-

T_{A F E}

4-

t = \frac{r_{A} + r_{O}}{\sqrt{2} (\frac{r_{B}}{2} + \frac{r_{B^{'}}}{2} + r_{O})}

5-

P 2_{1} / n

6-

P \bar{3} m

7-

F m \bar{3} m

8-

P 2_{1} / n

9-

P 2_{1} / n

10-

F m \bar{3} m

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/0901.0167

Formulas:

1-

Γ_{s o f t} = 2.0 \pm 0.2

2-

Γ_{h a r d} = 1.49 \pm 0.03

3-

E_{b r e a k} = 0.66 \pm 0.08

4-

R M S = 16 \pm 4

5-

R M S < 8

6-

Γ_{s o f t} = {2.8}_{- 0.4}^{+ 0.7}

7-

Γ_{h a r d} = {1.5}_{- 0.6}^{+ 0.5}

8-

E_{b r e a k} = 1.0 \pm 0.4

9-

γ_{m i n}

10-

γ_{b r e a k}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1504.04609

Formulas:

1-

σ_{0} = 89.80 \pm 0.05

2-

ζ_{an} = \frac{1}{2} R_{e} {\bar{ϵ}}_{ρ} E_{2, 0} \cos σ_{0} \cos (2 φ - 2 ℓ - σ_{0})

3-

E_{2, 0} = 1 - \frac{5}{2} e^{2} + \dots

4-

\tan σ_{0} \equiv \frac{ν}{γ}

5-

ν = 2 Ω - 2 n

6-

2 φ - 2 ℓ - σ_{0} = 0

7-

10 - 100 s^{- 1}

8-

10^{- 6} s^{- 1}

9-

10^{- 8} - 10^{- 7} s^{- 1}

10-

(0, π / 2)

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/0811.3077

Formulas:

1-

H = - \sum_{i, j} t_{i j} \sum_{σ = ↑, ↓} b_{i, σ}^{†} b_{j, σ} + α \sum_{k} n_{k, ↑} n_{k, ↓}

2-

t_{i j} = δ_{i, j + 1} + δ_{i, j - 1}

3-

M_{0} = \sum_{k} n_{k, ↑} n_{k, ↓} .

4-

[[[H, M_{i}], M_{i}], M_{i}] = [H, M_{i}]

5-

i = 0, 1, 2

6-

H = H_{ref, i} + R_{i} + R_{i}^{†}

7-

[H_{ref, i}, M_{i}]

8-

[R_{i}, M_{i}]

9-

H_{ref} \equiv H_{ref, 1} = H_{ref, 2}

10-

μ_{m} = ν_{n} + m

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/0711.0947

Formulas:

1-

{a_{i}}_{i \in ℕ}

2-

a_{1} a_{2} \dots a_{n} = 0

3-

{A_{λ} ∣ λ \in Λ}

4-

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

5-

a_{i} \in A_{λ_{i}}

6-

a_{1} a_{2} a_{3} \dots a_{n} = 0

7-

f \in End (F)

8-

Jac (End (F))

9-

{π_{λ} (Im (f))}_{Λ}

10-

Rad (R^{(ℕ)})

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/cond-mat/9602106

Formulas:

1-

\tilde{α} = | \begin{matrix} α_{⊥} + α_{⊥}^{'} \cdot d ℓ \\ α_{⊥} + α_{⊥}^{'} \cdot d ℓ \\ α_{∥} + α_{∥}^{'} \cdot d ℓ \end{matrix} |

2-

2 α_{⊥} + α_{∥} \equiv 𝒫

3-

α_{∥} - α_{⊥} \equiv 𝒬

4-

𝒬^{'} / 𝒬 = 0.43 Å = 0.3 r_{0}

5-

r_{0} = 1.4 Å

6-

𝒫_{s}^{'} / 𝒬_{s}^{'}

7-

𝒬_{s} / 𝒬_{s}^{'} r_{0}

8-

𝒬_{d}^{'} / 𝒬_{s}^{'}

9-

𝒫_{d}^{'} / 𝒬_{s}^{'}

10-

𝒬_{d} / 𝒬_{s}^{'} r_{0}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/0803.1790

Formulas:

1-

ℋ = \frac{1}{2 E} U (\begin{matrix} 0 & 0 & 0 \\ 0 & Δ m_{21}^{2} & 0 \\ 0 & 0 & Δ m_{31}^{2} \end{matrix}) U^{†} + \frac{1}{2 E} (\begin{matrix} V & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{matrix}) + \frac{V}{2 E} (\begin{matrix} 0 & 0 & ε_{e τ} \\ 0 & 0 & 0 \\ ε_{e τ} & 0 & ε_{τ τ} \end{matrix}),

2-

ε_{e e} = 0

3-

⟨ E ⟩ ≃ 3 GeV

4-

⟨ E ⟩ ≃ 17 GeV

5-

t_{r u n}

6-

ν_{e, μ, τ}

7-

⟨ E ⟩ ≃ 3 GeV

8-

4.5 \times 10^{19} pot

9-

⟨ E ⟩ ≃ 17 GeV

10-

⟨ E ⟩ ≃ 4 MeV

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: hep-ph

Result: correct

Paper: https://arxiv.org/abs/gr-qc/9812029

Formulas:

1-

6 L + 2 N - 6

2-

C_{μ ν ρ}

3-

g_{s} = ⟨ e^{ϕ} ⟩

4-

m_{s}^{2} = 2 π R m_{p}^{3}

5-

g_{s} = 2 π R m_{s} .

6-

T_{F 1} = 2 π R T_{M 2} .

7-

T_{F 1} = 2 π m_{s}^{2}

8-

T_{M 2} = 2 π m_{p}^{3}

9-

T_{D p} = 2 π m_{s}^{p + 1} / g_{s} .

10-

T_{D 2} = 2 π m_{s}^{3} / g_{s} = 2 π m_{p}^{3} = T_{M 2}

Formulas (html):

Correct Categorie: gr-qc

Guessed Categorie: hep-ph

Result: incorrect

Paper: https://arxiv.org/abs/0802.1273

Formulas:

1-

M_{i j} = {[R \otimes K]}_{i j} + B_{i j}

2-

χ^{2} = \sum_{i, j} {(\frac{I_{i j} - M_{i j}}{σ_{i j}})}^{2}

3-

M_{i j} = \sum_{l, m} K_{l m} R_{(i + l) (j + m)} + B_{0}

4-

\begin{matrix} U_{p q} = {\begin{matrix} \sum_{i, j} \frac{R_{(i + l) (j + m)} R_{(i + l^{'}) (j + m^{'})}}{σ_{i j}^{2}} & for 1 \leq p \leq N_{K} and 1 \leq q \leq N_{K} \\ \sum_{i, j} \frac{R_{(i + l^{'}) (j + m^{'})}}{σ_{i j}^{2}} & for p = N_{K} + 1 and 1 \leq q \leq N_{K} \\ \sum_{i, j} \frac{R_{(i + l) (j + m)}}{σ_{i j}^{2}} & for 1 \leq p \leq N_{K} and q = N_{K} + 1 \\ \sum_{i, j} \frac{1}{σ_{i j}^{2}} & for p = q = N_{K} + 1 \end{matrix} \\ a_{p} = {\begin{matrix} K_{l m} & for 1 \leq p \leq N_{K} \\ B_{0} & for p = N_{K} + 1 \end{matrix} \\ b_{p} = {\begin{matrix} \sum_{i, j} \frac{I_{i j} R_{(i + l) (j + m)}}{σ_{i j}^{2}} & for 1 \leq p \leq N_{K} \\ \sum_{i, j} \frac{I_{i j}}{σ_{i j}^{2}} & for p = N_{K} + 1 \end{matrix} \end{matrix}

5-

(l^{'}, m^{'})

6-

𝐚 = 𝐔^{- 𝟏} 𝐛

7-

P = \sum_{l, m} K_{l m}

8-

D_{i j} = I_{i j} - M_{i j}

9-

σ_{i j}^{2} = \frac{σ_{0}^{2}}{F_{i j}^{2}} + \frac{M_{i j}}{G F_{i j}}

10-

r_{i j} = | D_{i j} / σ_{i j} |

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1309.2284

Formulas:

1-

{2.9}_{- 1.9}^{+ 3.6} %

2-

18_{- 5}^{+ 5} %

3-

9_{- 2}^{+ 3} %

4-

29_{- 19}^{+ 26} %

5-

0 \sim < z \sim < 1

6-

1 \overset{''}{.} 5

7-

λ λ 4959, 5007

8-

λ λ 6548, 6584

9-

λ λ 6716, 6731

10-

\frac{χ_{single}^{2} - χ_{double}^{2}}{χ_{double}^{2}} > 0.2,

Formulas (html):

<math><mrow id="id9.5.m5.1.1" xref="id9.5.m5.1.1.cmml"><msubsup id="id9.5.m5.1.1.2" xref="id9.5.m5.1.1.2.cmml"><mn id="id9.5.m5.1.1.2.2.2" xref="id9.5.m5.1.1.2.2.2.cmml">2.9</mn><mrow id="id9.5.m5.1.1.2.3" xref="id9.5.m5.1.1.2.3.cmml"><mo id="id9.5.m5.1.1.2.3.1" xref="id9.5.m5.1.1.2.3.1.cmml">-</mo><mn id="id9.5.m5.1.1.2.3.2" xref="id9.5.m5.1.1.2.3.2.cmml">1.9</mn></mrow><mrow id="id9.5.m5.1.1.2.2.3" xref="id9.5.m5.1.1.2.2.3.cmml"><mo id="id9.5.m5.1.1.2.2.3.1" xref="id9.5.m5.1.1.2.2.3.1.cmml">+</mo><mn id="id9.5.m5.1.1.2.2.3.2" xref="id9.5.m5.1.1.2.2.3.2.cmml">3.6</mn></mrow></msubsup><mo id="id9.5.m5.1.1.1" xref="id9.5.m5.1.1.1.cmml">%</mo></mrow></math>, <math><mrow id="id10.6.m6.1.1" xref="id10.6.m6.1.1.cmml"><msubsup id="id10.6.m6.1.1.2" xref="id10.6.m6.1.1.2.cmml"><mn id="id10.6.m6.1.1.2.2.2" xref="id10.6.m6.1.1.2.2.2.cmml">18</mn><mrow id="id10.6.m6.1.1.2.3" xref="id10.6.m6.1.1.2.3.cmml"><mo id="id10.6.m6.1.1.2.3.1" xref="id10.6.m6.1.1.2.3.1.cmml">-</mo><mn id="id10.6.m6.1.1.2.3.2" xref="id10.6.m6.1.1.2.3.2.cmml">5</mn></mrow><mrow id="id10.6.m6.1.1.2.2.3" xref="id10.6.m6.1.1.2.2.3.cmml"><mo id="id10.6.m6.1.1.2.2.3.1" xref="id10.6.m6.1.1.2.2.3.1.cmml">+</mo><mn id="id10.6.m6.1.1.2.2.3.2" xref="id10.6.m6.1.1.2.2.3.2.cmml">5</mn></mrow></msubsup><mo id="id10.6.m6.1.1.1" xref="id10.6.m6.1.1.1.cmml">%</mo></mrow></math>, <math><mrow id="id12.8.m8.1.1" xref="id12.8.m8.1.1.cmml"><msubsup id="id12.8.m8.1.1.2" xref="id12.8.m8.1.1.2.cmml"><mn id="id12.8.m8.1.1.2.2.2" xref="id12.8.m8.1.1.2.2.2.cmml">9</mn><mrow id="id12.8.m8.1.1.2.3" xref="id12.8.m8.1.1.2.3.cmml"><mo id="id12.8.m8.1.1.2.3.1" xref="id12.8.m8.1.1.2.3.1.cmml">-</mo><mn id="id12.8.m8.1.1.2.3.2" xref="id12.8.m8.1.1.2.3.2.cmml">2</mn></mrow><mrow id="id12.8.m8.1.1.2.2.3" xref="id12.8.m8.1.1.2.2.3.cmml"><mo id="id12.8.m8.1.1.2.2.3.1" xref="id12.8.m8.1.1.2.2.3.1.cmml">+</mo><mn id="id12.8.m8.1.1.2.2.3.2" xref="id12.8.m8.1.1.2.2.3.2.cmml">3</mn></mrow></msubsup><mo id="id12.8.m8.1.1.1" xref="id12.8.m8.1.1.1.cmml">%</mo></mrow></math>, <math><mrow id="id13.9.m9.1.1" xref="id13.9.m9.1.1.cmml"><msubsup id="id13.9.m9.1.1.2" xref="id13.9.m9.1.1.2.cmml"><mn id="id13.9.m9.1.1.2.2.2" xref="id13.9.m9.1.1.2.2.2.cmml">29</mn><mrow id="id13.9.m9.1.1.2.3" xref="id13.9.m9.1.1.2.3.cmml"><mo id="id13.9.m9.1.1.2.3.1" xref="id13.9.m9.1.1.2.3.1.cmml">-</mo><mn id="id13.9.m9.1.1.2.3.2" xref="id13.9.m9.1.1.2.3.2.cmml">19</mn></mrow><mrow id="id13.9.m9.1.1.2.2.3" xref="id13.9.m9.1.1.2.2.3.cmml"><mo id="id13.9.m9.1.1.2.2.3.1" xref="id13.9.m9.1.1.2.2.3.1.cmml">+</mo><mn id="id13.9.m9.1.1.2.2.3.2" xref="id13.9.m9.1.1.2.2.3.2.cmml">26</mn></mrow></msubsup><mo id="id13.9.m9.1.1.1" xref="id13.9.m9.1.1.1.cmml">%</mo></mrow></math>, <math><mrow id="S1.p4.4.m4.4.5" xref="S1.p4.4.m4.4.5.cmml"><mn id="S1.p4.4.m4.4.5.2" xref="S1.p4.4.m4.4.5.2.cmml">0</mn><mrow id="S1.p4.4.m4.2.2.2" xref="S1.p4.4.m4.2.2.2c.cmml"><mpadded depth="+3.0pt" height="-3.0pt" voffset="-3.0pt" width="0.0pt" id="S1.p4.4.m4.2.2.2a" xref="S1.p4.4.m4.2.2.2c.cmml"><mi mathvariant="normal" id="S1.p4.4.m4.1.1.1.1.1.1.m1.1.1" xref="S1.p4.4.m4.1.1.1.1.1.1.m1.1.1.cmml">∼</mi></mpadded><mpadded depth="-2.0pt" height="+2.0pt" voffset="2.0pt" id="S1.p4.4.m4.2.2.2b" xref="S1.p4.4.m4.2.2.2c.cmml"><mo id="S1.p4.4.m4.2.2.2.2.1.m1.1.1" xref="S1.p4.4.m4.2.2.2.2.1.m1.1.1.cmml"><</mo></mpadded></mrow><mi id="S1.p4.4.m4.4.5.3" xref="S1.p4.4.m4.4.5.3.cmml">z</mi><mrow id="S1.p4.4.m4.4.4.2" xref="S1.p4.4.m4.4.4.2c.cmml"><mpadded depth="+3.0pt" height="-3.0pt" voffset="-3.0pt" width="0.0pt" id="S1.p4.4.m4.4.4.2a" xref="S1.p4.4.m4.4.4.2c.cmml"><mi mathvariant="normal" id="S1.p4.4.m4.3.3.1.1.1.1.m1.1.1" xref="S1.p4.4.m4.3.3.1.1.1.1.m1.1.1.cmml">∼</mi></mpadded><mpadded depth="-2.0pt" height="+2.0pt" voffset="2.0pt" id="S1.p4.4.m4.4.4.2b" xref="S1.p4.4.m4.4.4.2c.cmml"><mo id="S1.p4.4.m4.4.4.2.2.1.m1.1.1" xref="S1.p4.4.m4.4.4.2.2.1.m1.1.1.cmml"><</mo></mpadded></mrow><mn id="S1.p4.4.m4.4.5.4" xref="S1.p4.4.m4.4.5.4.cmml">1</mn></mrow></math>, <math><mrow id="S2.SS1.p1.1.m1.1.1" xref="S2.SS1.p1.1.m1.1.1.cmml"><mn id="S2.SS1.p1.1.m1.1.1.2" xref="S2.SS1.p1.1.m1.1.1.2.cmml">1</mn><mo id="S2.SS1.p1.1.m1.1.1.1" xref="S2.SS1.p1.1.m1.1.1.1.cmml">⁢</mo><mover id="S2.SS1.p1.1.m1.1.1.3.2" xref="S2.SS1.p1.1.m1.1.1.cmml"><mi mathvariant="normal" id="S2.SS1.p1.1.m1.1.1.3.2.2" xref="S2.SS1.p1.1.m1.1.1.3.1.cmml">.</mi><mrow id="S2.SS1.p1.1.m1.1.1.3.2.3" xref="S2.SS1.p1.1.m1.1.1.cmml"><mo mathsize="142%" stretchy="false" id="S2.SS1.p1.1.m1.1.1.3.2.3.1" xref="S2.SS1.p1.1.m1.1.1.3.1.cmml">′</mo><mo mathsize="142%" stretchy="false" id="S2.SS1.p1.1.m1.1.1.3.2.3.2" xref="S2.SS1.p1.1.m1.1.1.3.1.cmml">′</mo></mrow></mover><mo id="S2.SS1.p1.1.m1.1.1.1a" xref="S2.SS1.p1.1.m1.1.1.1.cmml">⁢</mo><mn id="S2.SS1.p1.1.m1.1.1.4" xref="S2.SS1.p1.1.m1.1.1.4.cmml">5</mn></mrow></math>, <math><mrow id="S2.SS3.p1.3.m2.2.2.1" xref="S2.SS3.p1.3.m2.2.2.2.cmml"><mrow id="S2.SS3.p1.3.m2.2.2.1.1" xref="S2.SS3.p1.3.m2.2.2.1.1.cmml"><mi id="S2.SS3.p1.3.m2.2.2.1.1.2" xref="S2.SS3.p1.3.m2.2.2.1.1.2.cmml">λ</mi><mo id="S2.SS3.p1.3.m2.2.2.1.1.1" xref="S2.SS3.p1.3.m2.2.2.1.1.1.cmml">⁢</mo><mi id="S2.SS3.p1.3.m2.2.2.1.1.3" xref="S2.SS3.p1.3.m2.2.2.1.1.3.cmml">λ</mi><mo id="S2.SS3.p1.3.m2.2.2.1.1.1a" xref="S2.SS3.p1.3.m2.2.2.1.1.1.cmml">⁢</mo><mn id="S2.SS3.p1.3.m2.2.2.1.1.4" xref="S2.SS3.p1.3.m2.2.2.1.1.4.cmml">4959</mn></mrow><mo id="S2.SS3.p1.3.m2.2.2.1.2" xref="S2.SS3.p1.3.m2.2.2.2.cmml">,</mo><mn id="S2.SS3.p1.3.m2.1.1" xref="S2.SS3.p1.3.m2.1.1.cmml">5007</mn></mrow></math>, <math><mrow id="S2.SS3.p1.8.m6.2.2.1" xref="S2.SS3.p1.8.m6.2.2.2.cmml"><mrow id="S2.SS3.p1.8.m6.2.2.1.1" xref="S2.SS3.p1.8.m6.2.2.1.1.cmml"><mi id="S2.SS3.p1.8.m6.2.2.1.1.2" xref="S2.SS3.p1.8.m6.2.2.1.1.2.cmml">λ</mi><mo id="S2.SS3.p1.8.m6.2.2.1.1.1" xref="S2.SS3.p1.8.m6.2.2.1.1.1.cmml">⁢</mo><mi id="S2.SS3.p1.8.m6.2.2.1.1.3" xref="S2.SS3.p1.8.m6.2.2.1.1.3.cmml">λ</mi><mo id="S2.SS3.p1.8.m6.2.2.1.1.1a" xref="S2.SS3.p1.8.m6.2.2.1.1.1.cmml">⁢</mo><mn id="S2.SS3.p1.8.m6.2.2.1.1.4" xref="S2.SS3.p1.8.m6.2.2.1.1.4.cmml">6548</mn></mrow><mo id="S2.SS3.p1.8.m6.2.2.1.2" xref="S2.SS3.p1.8.m6.2.2.2.cmml">,</mo><mn id="S2.SS3.p1.8.m6.1.1" xref="S2.SS3.p1.8.m6.1.1.cmml">6584</mn></mrow></math>, <math><mrow id="S2.SS3.p1.10.m8.2.2.1" xref="S2.SS3.p1.10.m8.2.2.2.cmml"><mrow id="S2.SS3.p1.10.m8.2.2.1.1" xref="S2.SS3.p1.10.m8.2.2.1.1.cmml"><mi id="S2.SS3.p1.10.m8.2.2.1.1.2" xref="S2.SS3.p1.10.m8.2.2.1.1.2.cmml">λ</mi><mo id="S2.SS3.p1.10.m8.2.2.1.1.1" xref="S2.SS3.p1.10.m8.2.2.1.1.1.cmml">⁢</mo><mi id="S2.SS3.p1.10.m8.2.2.1.1.3" xref="S2.SS3.p1.10.m8.2.2.1.1.3.cmml">λ</mi><mo id="S2.SS3.p1.10.m8.2.2.1.1.1a" xref="S2.SS3.p1.10.m8.2.2.1.1.1.cmml">⁢</mo><mn id="S2.SS3.p1.10.m8.2.2.1.1.4" xref="S2.SS3.p1.10.m8.2.2.1.1.4.cmml">6716</mn></mrow><mo id="S2.SS3.p1.10.m8.2.2.1.2" xref="S2.SS3.p1.10.m8.2.2.2.cmml">,</mo><mn id="S2.SS3.p1.10.m8.1.1" xref="S2.SS3.p1.10.m8.1.1.cmml">6731</mn></mrow></math>, <math><mrow id="S2.E1.m1.1.1.1" xref="S2.E1.m1.1.1.1.1.cmml"><mrow id="S2.E1.m1.1.1.1.1" xref="S2.E1.m1.1.1.1.1.cmml"><mfrac id="S2.E1.m1.1.1.1.1.2" xref="S2.E1.m1.1.1.1.1.2.cmml"><mrow id="S2.E1.m1.1.1.1.1.2.2" xref="S2.E1.m1.1.1.1.1.2.2.cmml"><msubsup id="S2.E1.m1.1.1.1.1.2.2.2" xref="S2.E1.m1.1.1.1.1.2.2.2.cmml"><mi id="S2.E1.m1.1.1.1.1.2.2.2.2.2" xref="S2.E1.m1.1.1.1.1.2.2.2.2.2.cmml">χ</mi><mi id="S2.E1.m1.1.1.1.1.2.2.2.3" xref="S2.E1.m1.1.1.1.1.2.2.2.3.cmml">single</mi><mn id="S2.E1.m1.1.1.1.1.2.2.2.2.3" xref="S2.E1.m1.1.1.1.1.2.2.2.2.3.cmml">2</mn></msubsup><mo id="S2.E1.m1.1.1.1.1.2.2.1" xref="S2.E1.m1.1.1.1.1.2.2.1.cmml">-</mo><msubsup id="S2.E1.m1.1.1.1.1.2.2.3" xref="S2.E1.m1.1.1.1.1.2.2.3.cmml"><mi id="S2.E1.m1.1.1.1.1.2.2.3.2.2" xref="S2.E1.m1.1.1.1.1.2.2.3.2.2.cmml">χ</mi><mi id="S2.E1.m1.1.1.1.1.2.2.3.3" xref="S2.E1.m1.1.1.1.1.2.2.3.3.cmml">double</mi><mn id="S2.E1.m1.1.1.1.1.2.2.3.2.3" xref="S2.E1.m1.1.1.1.1.2.2.3.2.3.cmml">2</mn></msubsup></mrow><msubsup id="S2.E1.m1.1.1.1.1.2.3" xref="S2.E1.m1.1.1.1.1.2.3.cmml"><mi id="S2.E1.m1.1.1.1.1.2.3.2.2" xref="S2.E1.m1.1.1.1.1.2.3.2.2.cmml">χ</mi><mi id="S2.E1.m1.1.1.1.1.2.3.3" xref="S2.E1.m1.1.1.1.1.2.3.3.cmml">double</mi><mn id="S2.E1.m1.1.1.1.1.2.3.2.3" xref="S2.E1.m1.1.1.1.1.2.3.2.3.cmml">2</mn></msubsup></mfrac><mo id="S2.E1.m1.1.1.1.1.1" xref="S2.E1.m1.1.1.1.1.1.cmml">></mo><mpadded width="+2.8pt" id="S2.E1.m1.1.1.1.1.3" xref="S2.E1.m1.1.1.1.1.3.cmml"><mn id="S2.E1.m1.1.1.1.1.3a" xref="S2.E1.m1.1.1.1.1.3.cmml">0.2</mn></mpadded></mrow><mo id="S2.E1.m1.1.1.1.2" xref="S2.E1.m1.1.1.1.1.cmml">,</mo></mrow></math>

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1805.02863

Formulas:

1-

𝜶 = (α_{1}, \dots, α_{d})

2-

𝜷 = (β_{1}, \dots, β_{d})

3-

ψ_{q} (x) = ζ_{p}^{Tr (x)}

4-

χ : 𝔽_{q}^{\times} \to ℂ^{\times}

5-

g (χ) = \sum_{x \in 𝔽_{q}^{\times}} χ (x) ψ_{q} (x) .

6-

g (m) = g (ω^{m})

7-

(q - 1) α_{i}, (q - 1) β_{j} \in ℤ

8-

H_{q} (𝜶, 𝜷 | t) = \frac{1}{1 - q} \sum_{m = 0}^{q - 2} \prod_{i = 1}^{d} (\frac{g (m + α_{i} 𝕢) g (- m - β_{i} 𝕢)}{g (α_{i} 𝕢) g (- β_{i} 𝕢)}) ω {({(- 1)}^{d} t)}^{m} .

9-

H_{q} (𝜶, 𝜷 | t)

10-

{(\prod_{i = 1}^{d} g (α_{i} 𝕢) g (- β_{i} 𝕢))}^{- 1}

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/0910.3748

Formulas:

1-

{\hat{H}}_{t} + {\hat{H}}_{u}

2-

\sum_{12} Ê c_{1}^{+} t_{12} c_{2} + \frac{1}{2} \sum_{1234} c_{1}^{+} c_{2}^{+} U_{1234} c_{3} c_{4},

3-

1 = (i_{1}, m_{1}, σ_{1})

4-

W_{n} (𝐫) = \sum_{𝐓 μ} ω_{n μ 𝐓} ψ_{μ} (𝐫 - 𝐓),

5-

ψ_{μ} (𝐫 - 𝐓)

6-

ω_{n μ 𝐓}

7-

i_{1} = i_{2} = i_{3} = i_{4}

8-

H_{D M} = \sum_{i j} {\vec{D}}_{i j} [{\vec{e}}_{i} \times {\vec{e}}_{j}],

9-

{\vec{e}}_{i} = η_{i} {\vec{e}}_{0} + Ê [δ {\vec{φ}}_{i} \times η_{i} {\vec{e}}_{0}],

10-

δ E = \sum_{i j} {\vec{D}}_{i j} (δ {\vec{φ}}_{i} - δ {\vec{φ}}_{j}) .

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/q-bio/0601036

Formulas:

1-

V = N (t) / K

2-

V = 1 - N (t) / K

3-

X = 1 / 3^{1 / L}

4-

M_{R} = 1 / 2

5-

L = 64, B = 1, x = 0.8, M_{R} = 0

6-

M = 0.27, M_{R} = 1 / 2

7-

L = 8, 16, 32, 64

8-

L = 64, M = 0.1

9-

L = 64, B = 4, R = 1, M = 0.1, M_{R} = 0

10-

M_{R} = 1 / 2

Formulas (html):

Correct Categorie: q-bio

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/1405.1954

Formulas:

1-

Q = (- 1.3 \pm 1.1 \pm 0.4) \times 10^{- 8}

2-

μ_{\bar{H}} ({| 𝐁 |}_{Wall} - {| 𝐁 |}_{Center})

3-

r = 0.6 R_{Wall} = 13.6

4-

r = 0.6 R_{Wall}

5-

r = 0.6 R_{Wall}

6-

U (z) = μ_{\bar{H}} B (z) - \frac{Q e E}{k_{b}} z,

7-

{⟨ z ⟩}_{Δ} \propto Q E / β,

8-

B (z) = B_{0} + β z^{2}

9-

| Q | ≳ 2 \times 10^{- 6}

10-

0 < | Q | < 2 \times 10^{- 6}

Formulas (html):

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id="S3.E1.m1.3.3.1.1.3.3.2.2.3" xref="S3.E1.m1.3.3.1.1.3.3.2.2.3.cmml">e</mi><mo id="S3.E1.m1.3.3.1.1.3.3.2.2.1a" xref="S3.E1.m1.3.3.1.1.3.3.2.2.1.cmml">⁢</mo><mi id="S3.E1.m1.3.3.1.1.3.3.2.2.4" xref="S3.E1.m1.3.3.1.1.3.3.2.2.4.cmml">E</mi></mrow><msub id="S3.E1.m1.3.3.1.1.3.3.2.3" xref="S3.E1.m1.3.3.1.1.3.3.2.3.cmml"><mi id="S3.E1.m1.3.3.1.1.3.3.2.3.2" xref="S3.E1.m1.3.3.1.1.3.3.2.3.2.cmml">k</mi><mi id="S3.E1.m1.3.3.1.1.3.3.2.3.3" xref="S3.E1.m1.3.3.1.1.3.3.2.3.3.cmml">b</mi></msub></mfrac><mo id="S3.E1.m1.3.3.1.1.3.3.1" xref="S3.E1.m1.3.3.1.1.3.3.1.cmml">⁢</mo><mi id="S3.E1.m1.3.3.1.1.3.3.3" xref="S3.E1.m1.3.3.1.1.3.3.3.cmml">z</mi></mrow></mrow></mrow><mo id="S3.E1.m1.3.3.1.2" xref="S3.E1.m1.3.3.1.1.cmml">,</mo></mrow></math>, <math><mrow id="S3.E2.m1.2.2.1" xref="S3.E2.m1.2.2.1.1.cmml"><mrow id="S3.E2.m1.2.2.1.1" xref="S3.E2.m1.2.2.1.1.cmml"><msub id="S3.E2.m1.2.2.1.1.2" xref="S3.E2.m1.2.2.1.1.2.cmml"><mrow id="S3.E2.m1.2.2.1.1.2.2.2" xref="S3.E2.m1.2.2.1.1.2.2.1.cmml"><mo stretchy="false" id="S3.E2.m1.2.2.1.1.2.2.2.1" xref="S3.E2.m1.2.2.1.1.2.2.1.1.cmml">⟨</mo><mi id="S3.E2.m1.1.1" xref="S3.E2.m1.1.1.cmml">z</mi><mo stretchy="false" id="S3.E2.m1.2.2.1.1.2.2.2.2" xref="S3.E2.m1.2.2.1.1.2.2.1.1.cmml">⟩</mo></mrow><mi mathvariant="normal" id="S3.E2.m1.2.2.1.1.2.3" xref="S3.E2.m1.2.2.1.1.2.3.cmml">Δ</mi></msub><mo id="S3.E2.m1.2.2.1.1.1" xref="S3.E2.m1.2.2.1.1.1.cmml">∝</mo><mrow id="S3.E2.m1.2.2.1.1.3" xref="S3.E2.m1.2.2.1.1.3.cmml"><mrow id="S3.E2.m1.2.2.1.1.3.2" xref="S3.E2.m1.2.2.1.1.3.2.cmml"><mi id="S3.E2.m1.2.2.1.1.3.2.2" xref="S3.E2.m1.2.2.1.1.3.2.2.cmml">Q</mi><mo id="S3.E2.m1.2.2.1.1.3.2.1" xref="S3.E2.m1.2.2.1.1.3.2.1.cmml">⁢</mo><mi id="S3.E2.m1.2.2.1.1.3.2.3" xref="S3.E2.m1.2.2.1.1.3.2.3.cmml">E</mi></mrow><mo id="S3.E2.m1.2.2.1.1.3.1" xref="S3.E2.m1.2.2.1.1.3.1.cmml">/</mo><mi id="S3.E2.m1.2.2.1.1.3.3" xref="S3.E2.m1.2.2.1.1.3.3.cmml">β</mi></mrow></mrow><mo id="S3.E2.m1.2.2.1.2" xref="S3.E2.m1.2.2.1.1.cmml">,</mo></mrow></math>, <math><mrow id="S3.p1.11.m1.1.2" xref="S3.p1.11.m1.1.2.cmml"><mrow id="S3.p1.11.m1.1.2.2" xref="S3.p1.11.m1.1.2.2.cmml"><mi id="S3.p1.11.m1.1.2.2.2" xref="S3.p1.11.m1.1.2.2.2.cmml">B</mi><mo id="S3.p1.11.m1.1.2.2.1" xref="S3.p1.11.m1.1.2.2.1.cmml">⁢</mo><mrow id="S3.p1.11.m1.1.2.2.3.2" xref="S3.p1.11.m1.1.2.2.cmml"><mo stretchy="false" id="S3.p1.11.m1.1.2.2.3.2.1" xref="S3.p1.11.m1.1.2.2.cmml">(</mo><mi id="S3.p1.11.m1.1.1" xref="S3.p1.11.m1.1.1.cmml">z</mi><mo stretchy="false" id="S3.p1.11.m1.1.2.2.3.2.2" xref="S3.p1.11.m1.1.2.2.cmml">)</mo></mrow></mrow><mo id="S3.p1.11.m1.1.2.1" xref="S3.p1.11.m1.1.2.1.cmml">=</mo><mrow id="S3.p1.11.m1.1.2.3" xref="S3.p1.11.m1.1.2.3.cmml"><msub id="S3.p1.11.m1.1.2.3.2" xref="S3.p1.11.m1.1.2.3.2.cmml"><mi id="S3.p1.11.m1.1.2.3.2.2" xref="S3.p1.11.m1.1.2.3.2.2.cmml">B</mi><mn id="S3.p1.11.m1.1.2.3.2.3" xref="S3.p1.11.m1.1.2.3.2.3.cmml">0</mn></msub><mo id="S3.p1.11.m1.1.2.3.1" xref="S3.p1.11.m1.1.2.3.1.cmml">+</mo><mrow id="S3.p1.11.m1.1.2.3.3" xref="S3.p1.11.m1.1.2.3.3.cmml"><mi id="S3.p1.11.m1.1.2.3.3.2" xref="S3.p1.11.m1.1.2.3.3.2.cmml">β</mi><mo id="S3.p1.11.m1.1.2.3.3.1" xref="S3.p1.11.m1.1.2.3.3.1.cmml">⁢</mo><msup id="S3.p1.11.m1.1.2.3.3.3" xref="S3.p1.11.m1.1.2.3.3.3.cmml"><mi id="S3.p1.11.m1.1.2.3.3.3.2" xref="S3.p1.11.m1.1.2.3.3.3.2.cmml">z</mi><mn id="S3.p1.11.m1.1.2.3.3.3.3" xref="S3.p1.11.m1.1.2.3.3.3.3.cmml">2</mn></msup></mrow></mrow></mrow></math>, <math><mrow id="S4.SS1.p1.2.m2.1.2" xref="S4.SS1.p1.2.m2.1.2.cmml"><mrow id="S4.SS1.p1.2.m2.1.2.2.2" xref="S4.SS1.p1.2.m2.1.2.2.1.cmml"><mo stretchy="false" id="S4.SS1.p1.2.m2.1.2.2.2.1" xref="S4.SS1.p1.2.m2.1.2.2.1.1.cmml">|</mo><mi id="S4.SS1.p1.2.m2.1.1" xref="S4.SS1.p1.2.m2.1.1.cmml">Q</mi><mo stretchy="false" id="S4.SS1.p1.2.m2.1.2.2.2.2" xref="S4.SS1.p1.2.m2.1.2.2.1.1.cmml">|</mo></mrow><mo id="S4.SS1.p1.2.m2.1.2.1" xref="S4.SS1.p1.2.m2.1.2.1.cmml">≳</mo><mrow id="S4.SS1.p1.2.m2.1.2.3" xref="S4.SS1.p1.2.m2.1.2.3.cmml"><mn id="S4.SS1.p1.2.m2.1.2.3.2" xref="S4.SS1.p1.2.m2.1.2.3.2.cmml">2</mn><mo id="S4.SS1.p1.2.m2.1.2.3.1" xref="S4.SS1.p1.2.m2.1.2.3.1.cmml">×</mo><msup id="S4.SS1.p1.2.m2.1.2.3.3" xref="S4.SS1.p1.2.m2.1.2.3.3.cmml"><mn id="S4.SS1.p1.2.m2.1.2.3.3.2" xref="S4.SS1.p1.2.m2.1.2.3.3.2.cmml">10</mn><mrow id="S4.SS1.p1.2.m2.1.2.3.3.3" xref="S4.SS1.p1.2.m2.1.2.3.3.3.cmml"><mo id="S4.SS1.p1.2.m2.1.2.3.3.3.1" xref="S4.SS1.p1.2.m2.1.2.3.3.3.1.cmml">-</mo><mn id="S4.SS1.p1.2.m2.1.2.3.3.3.2" xref="S4.SS1.p1.2.m2.1.2.3.3.3.2.cmml">6</mn></mrow></msup></mrow></mrow></math>, <math><mrow id="S4.SS1.p1.3.m3.1.2" xref="S4.SS1.p1.3.m3.1.2.cmml"><mn id="S4.SS1.p1.3.m3.1.2.2" xref="S4.SS1.p1.3.m3.1.2.2.cmml">0</mn><mo id="S4.SS1.p1.3.m3.1.2.3" xref="S4.SS1.p1.3.m3.1.2.3.cmml"><</mo><mrow id="S4.SS1.p1.3.m3.1.2.4.2" xref="S4.SS1.p1.3.m3.1.2.4.1.cmml"><mo stretchy="false" id="S4.SS1.p1.3.m3.1.2.4.2.1" xref="S4.SS1.p1.3.m3.1.2.4.1.1.cmml">|</mo><mi id="S4.SS1.p1.3.m3.1.1" xref="S4.SS1.p1.3.m3.1.1.cmml">Q</mi><mo stretchy="false" id="S4.SS1.p1.3.m3.1.2.4.2.2" xref="S4.SS1.p1.3.m3.1.2.4.1.1.cmml">|</mo></mrow><mo id="S4.SS1.p1.3.m3.1.2.5" xref="S4.SS1.p1.3.m3.1.2.5.cmml"><</mo><mrow id="S4.SS1.p1.3.m3.1.2.6" xref="S4.SS1.p1.3.m3.1.2.6.cmml"><mn id="S4.SS1.p1.3.m3.1.2.6.2" xref="S4.SS1.p1.3.m3.1.2.6.2.cmml">2</mn><mo id="S4.SS1.p1.3.m3.1.2.6.1" xref="S4.SS1.p1.3.m3.1.2.6.1.cmml">×</mo><msup id="S4.SS1.p1.3.m3.1.2.6.3" xref="S4.SS1.p1.3.m3.1.2.6.3.cmml"><mn id="S4.SS1.p1.3.m3.1.2.6.3.2" xref="S4.SS1.p1.3.m3.1.2.6.3.2.cmml">10</mn><mrow id="S4.SS1.p1.3.m3.1.2.6.3.3" xref="S4.SS1.p1.3.m3.1.2.6.3.3.cmml"><mo id="S4.SS1.p1.3.m3.1.2.6.3.3.1" xref="S4.SS1.p1.3.m3.1.2.6.3.3.1.cmml">-</mo><mn id="S4.SS1.p1.3.m3.1.2.6.3.3.2" xref="S4.SS1.p1.3.m3.1.2.6.3.3.2.cmml">6</mn></mrow></msup></mrow></mrow></math>

Correct Categorie: physics

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1905.05826

Formulas:

1-

\log (M_{⋆} / M_{⊙}) ≲ 10.5

2-

Δ \log Z_{g} = m Δ \log Σ_{SFR},

3-

Δ \log Z_{g} = \log Z_{g} - \log Z_{g 0},

4-

Δ \log Σ_{SFR} = \log Σ_{SFR} - \log Σ_{SFR0},

5-

Δ Z_{g} = Z_{g} - Z_{g 0}

6-

Δ Σ_{SFR} = Σ_{SFR} - Σ_{SFR0}

7-

| Δ Z_{g} | ≪ Z_{g}

8-

| Δ Σ_{SFR} | ≪ Σ_{SFR}

9-

Δ Z_{g} / Z_{g 0} ≃ m Δ Σ_{SFR} / Σ_{SFR0} .

10-

⟨ Z_{g} ⟩ = {⟨ M_{g} ⟩}^{- 1} \int W Z_{g} Σ_{g} 𝑑 x 𝑑 y,

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/quant-ph/0404122

Formulas:

1-

ℋ_{d_{1}} \otimes ℋ_{d_{2}}

2-

d (d + 1)

3-

𝒫 = {Π_{i}, π_{i}}

4-

Π_{i} = | ψ_{i} ⟩ ⟨ ψ_{i} |

5-

ℰ = {E_{b}}

6-

ℳ : b \to σ_{b}

7-

F_{𝒫} (ℰ, ℳ) = \sum_{b, i} π_{i} tr (Π_{i} E_{b}) tr (Π_{i} σ_{b}),

8-

F_{𝒫} (ℰ) = sup_{ℳ} F_{𝒫} (ℰ, ℳ) .

9-

Ψ : ℒ (ℋ_{d}) \to ℒ (ℋ_{d})

10-

Ψ (X) = \sum_{i} π_{i} Π_{i} X Π_{i} .

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: quant-ph

Result: correct

Paper: https://arxiv.org/abs/1011.0175

Formulas:

1-

{X_{i}}_{i = 1}^{n}

2-

E X_{i} = μ

3-

var X_{i} = σ^{2}

4-

(X_{1}, \dots, X_{n})

5-

\sqrt{\frac{n}{τ}} \cdot \frac{{\bar{X}}_{n} - μ}{σ} ⟹ N (0, 1)

6-

σ^{2} \cdot τ / m

7-

{\hat{τ}}_{n, m} = m \frac{s_{m}^{2}}{s^{2}}

8-

\hat{τ} = \frac{{\hat{I}}_{0}}{s^{2}}

9-

τ = 1 + 2 \sum_{k = 1}^{\infty} ρ_{k}

10-

{\hat{ρ}}_{k} = \frac{1}{n s^{2}} \sum_{i = 1}^{n - k} (X_{i} - {\bar{X}}_{n}) (X_{i + k} - {\bar{X}}_{n})

Formulas (html):

Correct Categorie: stat

Guessed Categorie: math

Result: incorrect

Paper: https://arxiv.org/abs/1402.2313

Formulas:

1-

λ = 355 nm, τ = 5 ns, E = 7 - 10 mJ

2-

\begin{matrix} S (I) \propto 1 + \frac{e^{- (s_{1} + s_{2}) I τ / (2 h ν)} (s_{1} - s_{2})}{2 s_{2}} - \\ \frac{e^{- (s_{1} - s_{2}) I τ / (2 h ν)} (s_{1} + s_{2})}{2 s_{2}}, \end{matrix}

3-

s_{1} = 2 σ_{1} + σ_{2}

4-

s_{2} = \sqrt{4 σ_{1}^{2} + σ_{2}^{2}}

5-

σ_{1} = 1.0 (4) \times 10^{- 16} {cm}^{2}

6-

σ_{2} = 6 (4) \times 10^{- 16} {cm}^{2}

7-

Δ t = 12 μ

8-

Δ v / v < 2 %

9-

σ_{1} = 6 (2) \times 10^{- 16} {cm}^{2}

10-

σ_{2} = 3 (1) \times 10^{- 16} {cm}^{2}

Formulas (html):

Correct Categorie: physics

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0211088

Formulas:

1-

t_{cool} \leq 3 Ω^{- 1}

2-

t_{cool} > 3 Ω^{- 1}

3-

t_{cool} = 3 Ω^{- 1}

4-

m \sim 10 m_{earth}

5-

Q = \frac{c_{s} κ}{π G Σ}

6-

t_{c o o l} > 3 Ω^{- 1}

7-

t_{c o o l} \leq 3 Ω^{- 1}

8-

t_{c o o l} > 3 Ω^{- 1}

9-

M_{disc} = 0.1 M_{*}

10-

M_{disc} = 0.25 M_{*}

Formulas (html):

<math><mrow id="id9.1.m1.1.1" xref="id9.1.m1.1.1.cmml"><msub id="id9.1.m1.1.1.2" xref="id9.1.m1.1.1.2.cmml"><mi id="id9.1.m1.1.1.2.2" xref="id9.1.m1.1.1.2.2.cmml">t</mi><mi id="id9.1.m1.1.1.2.3" xref="id9.1.m1.1.1.2.3.cmml">cool</mi></msub><mo id="id9.1.m1.1.1.1" xref="id9.1.m1.1.1.1.cmml">≤</mo><mrow id="id9.1.m1.1.1.3" xref="id9.1.m1.1.1.3.cmml"><mn id="id9.1.m1.1.1.3.2" xref="id9.1.m1.1.1.3.2.cmml">3</mn><mo id="id9.1.m1.1.1.3.1" xref="id9.1.m1.1.1.3.1.cmml">⁢</mo><msup id="id9.1.m1.1.1.3.3" xref="id9.1.m1.1.1.3.3.cmml"><mi mathvariant="normal" id="id9.1.m1.1.1.3.3.2" xref="id9.1.m1.1.1.3.3.2.cmml">Ω</mi><mrow id="id9.1.m1.1.1.3.3.3" xref="id9.1.m1.1.1.3.3.3.cmml"><mo id="id9.1.m1.1.1.3.3.3.1" xref="id9.1.m1.1.1.3.3.3.1.cmml">-</mo><mn id="id9.1.m1.1.1.3.3.3.2" xref="id9.1.m1.1.1.3.3.3.2.cmml">1</mn></mrow></msup></mrow></mrow></math>, <math><mrow id="id10.2.m2.1.1" xref="id10.2.m2.1.1.cmml"><msub id="id10.2.m2.1.1.2" xref="id10.2.m2.1.1.2.cmml"><mi id="id10.2.m2.1.1.2.2" xref="id10.2.m2.1.1.2.2.cmml">t</mi><mi id="id10.2.m2.1.1.2.3" xref="id10.2.m2.1.1.2.3.cmml">cool</mi></msub><mo id="id10.2.m2.1.1.1" xref="id10.2.m2.1.1.1.cmml">></mo><mrow id="id10.2.m2.1.1.3" xref="id10.2.m2.1.1.3.cmml"><mn id="id10.2.m2.1.1.3.2" xref="id10.2.m2.1.1.3.2.cmml">3</mn><mo id="id10.2.m2.1.1.3.1" xref="id10.2.m2.1.1.3.1.cmml">⁢</mo><msup id="id10.2.m2.1.1.3.3" xref="id10.2.m2.1.1.3.3.cmml"><mi mathvariant="normal" id="id10.2.m2.1.1.3.3.2" xref="id10.2.m2.1.1.3.3.2.cmml">Ω</mi><mrow id="id10.2.m2.1.1.3.3.3" xref="id10.2.m2.1.1.3.3.3.cmml"><mo id="id10.2.m2.1.1.3.3.3.1" xref="id10.2.m2.1.1.3.3.3.1.cmml">-</mo><mn id="id10.2.m2.1.1.3.3.3.2" xref="id10.2.m2.1.1.3.3.3.2.cmml">1</mn></mrow></msup></mrow></mrow></math>, <math><mrow id="id11.3.m3.1.1" xref="id11.3.m3.1.1.cmml"><msub id="id11.3.m3.1.1.2" xref="id11.3.m3.1.1.2.cmml"><mi id="id11.3.m3.1.1.2.2" xref="id11.3.m3.1.1.2.2.cmml">t</mi><mi id="id11.3.m3.1.1.2.3" xref="id11.3.m3.1.1.2.3.cmml">cool</mi></msub><mo id="id11.3.m3.1.1.1" xref="id11.3.m3.1.1.1.cmml">=</mo><mrow id="id11.3.m3.1.1.3" xref="id11.3.m3.1.1.3.cmml"><mn id="id11.3.m3.1.1.3.2" xref="id11.3.m3.1.1.3.2.cmml">3</mn><mo id="id11.3.m3.1.1.3.1" xref="id11.3.m3.1.1.3.1.cmml">⁢</mo><msup id="id11.3.m3.1.1.3.3" xref="id11.3.m3.1.1.3.3.cmml"><mi mathvariant="normal" id="id11.3.m3.1.1.3.3.2" xref="id11.3.m3.1.1.3.3.2.cmml">Ω</mi><mrow id="id11.3.m3.1.1.3.3.3" xref="id11.3.m3.1.1.3.3.3.cmml"><mo id="id11.3.m3.1.1.3.3.3.1" xref="id11.3.m3.1.1.3.3.3.1.cmml">-</mo><mn id="id11.3.m3.1.1.3.3.3.2" xref="id11.3.m3.1.1.3.3.3.2.cmml">1</mn></mrow></msup></mrow></mrow></math>, <math><mrow id="S1.p1.1.m1.1.1" xref="S1.p1.1.m1.1.1.cmml"><mi id="S1.p1.1.m1.1.1.2" xref="S1.p1.1.m1.1.1.2.cmml">m</mi><mo id="S1.p1.1.m1.1.1.1" xref="S1.p1.1.m1.1.1.1.cmml">∼</mo><mrow id="S1.p1.1.m1.1.1.3" xref="S1.p1.1.m1.1.1.3.cmml"><mn id="S1.p1.1.m1.1.1.3.2" xref="S1.p1.1.m1.1.1.3.2.cmml">10</mn><mo id="S1.p1.1.m1.1.1.3.1" xref="S1.p1.1.m1.1.1.3.1.cmml">⁢</mo><msub id="S1.p1.1.m1.1.1.3.3" xref="S1.p1.1.m1.1.1.3.3.cmml"><mi id="S1.p1.1.m1.1.1.3.3.2" xref="S1.p1.1.m1.1.1.3.3.2.cmml">m</mi><mi id="S1.p1.1.m1.1.1.3.3.3" xref="S1.p1.1.m1.1.1.3.3.3.cmml">earth</mi></msub></mrow></mrow></math>, <math><mrow id="S1.E1.m1.1.1" xref="S1.E1.m1.1.1.cmml"><mi id="S1.E1.m1.1.1.2" xref="S1.E1.m1.1.1.2.cmml">Q</mi><mo id="S1.E1.m1.1.1.1" xref="S1.E1.m1.1.1.1.cmml">=</mo><mfrac id="S1.E1.m1.1.1.3" xref="S1.E1.m1.1.1.3.cmml"><mrow id="S1.E1.m1.1.1.3.2" xref="S1.E1.m1.1.1.3.2.cmml"><msub id="S1.E1.m1.1.1.3.2.2" xref="S1.E1.m1.1.1.3.2.2.cmml"><mi id="S1.E1.m1.1.1.3.2.2.2" xref="S1.E1.m1.1.1.3.2.2.2.cmml">c</mi><mi id="S1.E1.m1.1.1.3.2.2.3" xref="S1.E1.m1.1.1.3.2.2.3.cmml">s</mi></msub><mo id="S1.E1.m1.1.1.3.2.1" xref="S1.E1.m1.1.1.3.2.1.cmml">⁢</mo><mi id="S1.E1.m1.1.1.3.2.3" xref="S1.E1.m1.1.1.3.2.3.cmml">κ</mi></mrow><mrow id="S1.E1.m1.1.1.3.3" xref="S1.E1.m1.1.1.3.3.cmml"><mi id="S1.E1.m1.1.1.3.3.2" xref="S1.E1.m1.1.1.3.3.2.cmml">π</mi><mo id="S1.E1.m1.1.1.3.3.1" xref="S1.E1.m1.1.1.3.3.1.cmml">⁢</mo><mi id="S1.E1.m1.1.1.3.3.3" xref="S1.E1.m1.1.1.3.3.3.cmml">G</mi><mo id="S1.E1.m1.1.1.3.3.1a" xref="S1.E1.m1.1.1.3.3.1.cmml">⁢</mo><mi mathvariant="normal" id="S1.E1.m1.1.1.3.3.4" xref="S1.E1.m1.1.1.3.3.4.cmml">Σ</mi></mrow></mfrac></mrow></math>, <math><mrow id="S1.p3.1.m1.1.1" xref="S1.p3.1.m1.1.1.cmml"><msub id="S1.p3.1.m1.1.1.2" xref="S1.p3.1.m1.1.1.2.cmml"><mi id="S1.p3.1.m1.1.1.2.2" xref="S1.p3.1.m1.1.1.2.2.cmml">t</mi><mrow id="S1.p3.1.m1.1.1.2.3" xref="S1.p3.1.m1.1.1.2.3.cmml"><mi id="S1.p3.1.m1.1.1.2.3.2" xref="S1.p3.1.m1.1.1.2.3.2.cmml">c</mi><mo id="S1.p3.1.m1.1.1.2.3.1" xref="S1.p3.1.m1.1.1.2.3.1.cmml">⁢</mo><mi id="S1.p3.1.m1.1.1.2.3.3" xref="S1.p3.1.m1.1.1.2.3.3.cmml">o</mi><mo id="S1.p3.1.m1.1.1.2.3.1a" xref="S1.p3.1.m1.1.1.2.3.1.cmml">⁢</mo><mi id="S1.p3.1.m1.1.1.2.3.4" xref="S1.p3.1.m1.1.1.2.3.4.cmml">o</mi><mo id="S1.p3.1.m1.1.1.2.3.1b" xref="S1.p3.1.m1.1.1.2.3.1.cmml">⁢</mo><mi id="S1.p3.1.m1.1.1.2.3.5" xref="S1.p3.1.m1.1.1.2.3.5.cmml">l</mi></mrow></msub><mo id="S1.p3.1.m1.1.1.1" xref="S1.p3.1.m1.1.1.1.cmml">></mo><mrow id="S1.p3.1.m1.1.1.3" xref="S1.p3.1.m1.1.1.3.cmml"><mn id="S1.p3.1.m1.1.1.3.2" xref="S1.p3.1.m1.1.1.3.2.cmml">3</mn><mo id="S1.p3.1.m1.1.1.3.1" xref="S1.p3.1.m1.1.1.3.1.cmml">⁢</mo><msup id="S1.p3.1.m1.1.1.3.3" xref="S1.p3.1.m1.1.1.3.3.cmml"><mi mathvariant="normal" id="S1.p3.1.m1.1.1.3.3.2" xref="S1.p3.1.m1.1.1.3.3.2.cmml">Ω</mi><mrow id="S1.p3.1.m1.1.1.3.3.3" xref="S1.p3.1.m1.1.1.3.3.3.cmml"><mo id="S1.p3.1.m1.1.1.3.3.3.1" xref="S1.p3.1.m1.1.1.3.3.3.1.cmml">-</mo><mn id="S1.p3.1.m1.1.1.3.3.3.2" xref="S1.p3.1.m1.1.1.3.3.3.2.cmml">1</mn></mrow></msup></mrow></mrow></math>, <math><mrow id="S1.p3.3.m3.1.1" xref="S1.p3.3.m3.1.1.cmml"><msub id="S1.p3.3.m3.1.1.2" xref="S1.p3.3.m3.1.1.2.cmml"><mi id="S1.p3.3.m3.1.1.2.2" xref="S1.p3.3.m3.1.1.2.2.cmml">t</mi><mrow id="S1.p3.3.m3.1.1.2.3" xref="S1.p3.3.m3.1.1.2.3.cmml"><mi id="S1.p3.3.m3.1.1.2.3.2" xref="S1.p3.3.m3.1.1.2.3.2.cmml">c</mi><mo id="S1.p3.3.m3.1.1.2.3.1" xref="S1.p3.3.m3.1.1.2.3.1.cmml">⁢</mo><mi id="S1.p3.3.m3.1.1.2.3.3" xref="S1.p3.3.m3.1.1.2.3.3.cmml">o</mi><mo id="S1.p3.3.m3.1.1.2.3.1a" xref="S1.p3.3.m3.1.1.2.3.1.cmml">⁢</mo><mi id="S1.p3.3.m3.1.1.2.3.4" xref="S1.p3.3.m3.1.1.2.3.4.cmml">o</mi><mo id="S1.p3.3.m3.1.1.2.3.1b" xref="S1.p3.3.m3.1.1.2.3.1.cmml">⁢</mo><mi id="S1.p3.3.m3.1.1.2.3.5" xref="S1.p3.3.m3.1.1.2.3.5.cmml">l</mi></mrow></msub><mo id="S1.p3.3.m3.1.1.1" xref="S1.p3.3.m3.1.1.1.cmml">≤</mo><mrow id="S1.p3.3.m3.1.1.3" xref="S1.p3.3.m3.1.1.3.cmml"><mn id="S1.p3.3.m3.1.1.3.2" xref="S1.p3.3.m3.1.1.3.2.cmml">3</mn><mo id="S1.p3.3.m3.1.1.3.1" xref="S1.p3.3.m3.1.1.3.1.cmml">⁢</mo><msup id="S1.p3.3.m3.1.1.3.3" xref="S1.p3.3.m3.1.1.3.3.cmml"><mi mathvariant="normal" id="S1.p3.3.m3.1.1.3.3.2" xref="S1.p3.3.m3.1.1.3.3.2.cmml">Ω</mi><mrow id="S1.p3.3.m3.1.1.3.3.3" xref="S1.p3.3.m3.1.1.3.3.3.cmml"><mo id="S1.p3.3.m3.1.1.3.3.3.1" xref="S1.p3.3.m3.1.1.3.3.3.1.cmml">-</mo><mn id="S1.p3.3.m3.1.1.3.3.3.2" xref="S1.p3.3.m3.1.1.3.3.3.2.cmml">1</mn></mrow></msup></mrow></mrow></math>, <math><mrow id="S1.p3.4.m4.1.1" xref="S1.p3.4.m4.1.1.cmml"><msub id="S1.p3.4.m4.1.1.2" xref="S1.p3.4.m4.1.1.2.cmml"><mi id="S1.p3.4.m4.1.1.2.2" xref="S1.p3.4.m4.1.1.2.2.cmml">t</mi><mrow id="S1.p3.4.m4.1.1.2.3" xref="S1.p3.4.m4.1.1.2.3.cmml"><mi id="S1.p3.4.m4.1.1.2.3.2" xref="S1.p3.4.m4.1.1.2.3.2.cmml">c</mi><mo id="S1.p3.4.m4.1.1.2.3.1" xref="S1.p3.4.m4.1.1.2.3.1.cmml">⁢</mo><mi id="S1.p3.4.m4.1.1.2.3.3" xref="S1.p3.4.m4.1.1.2.3.3.cmml">o</mi><mo id="S1.p3.4.m4.1.1.2.3.1a" xref="S1.p3.4.m4.1.1.2.3.1.cmml">⁢</mo><mi id="S1.p3.4.m4.1.1.2.3.4" xref="S1.p3.4.m4.1.1.2.3.4.cmml">o</mi><mo id="S1.p3.4.m4.1.1.2.3.1b" xref="S1.p3.4.m4.1.1.2.3.1.cmml">⁢</mo><mi id="S1.p3.4.m4.1.1.2.3.5" xref="S1.p3.4.m4.1.1.2.3.5.cmml">l</mi></mrow></msub><mo id="S1.p3.4.m4.1.1.1" xref="S1.p3.4.m4.1.1.1.cmml">></mo><mrow id="S1.p3.4.m4.1.1.3" xref="S1.p3.4.m4.1.1.3.cmml"><mn id="S1.p3.4.m4.1.1.3.2" xref="S1.p3.4.m4.1.1.3.2.cmml">3</mn><mo id="S1.p3.4.m4.1.1.3.1" xref="S1.p3.4.m4.1.1.3.1.cmml">⁢</mo><msup id="S1.p3.4.m4.1.1.3.3" xref="S1.p3.4.m4.1.1.3.3.cmml"><mi mathvariant="normal" id="S1.p3.4.m4.1.1.3.3.2" xref="S1.p3.4.m4.1.1.3.3.2.cmml">Ω</mi><mrow id="S1.p3.4.m4.1.1.3.3.3" xref="S1.p3.4.m4.1.1.3.3.3.cmml"><mo id="S1.p3.4.m4.1.1.3.3.3.1" xref="S1.p3.4.m4.1.1.3.3.3.1.cmml">-</mo><mn id="S1.p3.4.m4.1.1.3.3.3.2" xref="S1.p3.4.m4.1.1.3.3.3.2.cmml">1</mn></mrow></msup></mrow></mrow></math>, <math><mrow id="S2.SS2.p1.3.m3.1.1" xref="S2.SS2.p1.3.m3.1.1.cmml"><msub id="S2.SS2.p1.3.m3.1.1.2" xref="S2.SS2.p1.3.m3.1.1.2.cmml"><mi id="S2.SS2.p1.3.m3.1.1.2.2" xref="S2.SS2.p1.3.m3.1.1.2.2.cmml">M</mi><mi id="S2.SS2.p1.3.m3.1.1.2.3" xref="S2.SS2.p1.3.m3.1.1.2.3.cmml">disc</mi></msub><mo id="S2.SS2.p1.3.m3.1.1.1" xref="S2.SS2.p1.3.m3.1.1.1.cmml">=</mo><mrow id="S2.SS2.p1.3.m3.1.1.3" xref="S2.SS2.p1.3.m3.1.1.3.cmml"><mn id="S2.SS2.p1.3.m3.1.1.3.2" xref="S2.SS2.p1.3.m3.1.1.3.2.cmml">0.1</mn><mo id="S2.SS2.p1.3.m3.1.1.3.1" xref="S2.SS2.p1.3.m3.1.1.3.1.cmml">⁢</mo><msub id="S2.SS2.p1.3.m3.1.1.3.3" xref="S2.SS2.p1.3.m3.1.1.3.3.cmml"><mi id="S2.SS2.p1.3.m3.1.1.3.3.2" xref="S2.SS2.p1.3.m3.1.1.3.3.2.cmml">M</mi><mo id="S2.SS2.p1.3.m3.1.1.3.3.3" xref="S2.SS2.p1.3.m3.1.1.3.3.3.cmml">*</mo></msub></mrow></mrow></math>, <math><mrow id="S2.SS2.p1.4.m4.1.1" xref="S2.SS2.p1.4.m4.1.1.cmml"><msub id="S2.SS2.p1.4.m4.1.1.2" xref="S2.SS2.p1.4.m4.1.1.2.cmml"><mi id="S2.SS2.p1.4.m4.1.1.2.2" xref="S2.SS2.p1.4.m4.1.1.2.2.cmml">M</mi><mi id="S2.SS2.p1.4.m4.1.1.2.3" xref="S2.SS2.p1.4.m4.1.1.2.3.cmml">disc</mi></msub><mo id="S2.SS2.p1.4.m4.1.1.1" xref="S2.SS2.p1.4.m4.1.1.1.cmml">=</mo><mrow id="S2.SS2.p1.4.m4.1.1.3" xref="S2.SS2.p1.4.m4.1.1.3.cmml"><mn id="S2.SS2.p1.4.m4.1.1.3.2" xref="S2.SS2.p1.4.m4.1.1.3.2.cmml">0.25</mn><mo id="S2.SS2.p1.4.m4.1.1.3.1" xref="S2.SS2.p1.4.m4.1.1.3.1.cmml">⁢</mo><msub id="S2.SS2.p1.4.m4.1.1.3.3" xref="S2.SS2.p1.4.m4.1.1.3.3.cmml"><mi id="S2.SS2.p1.4.m4.1.1.3.3.2" xref="S2.SS2.p1.4.m4.1.1.3.3.2.cmml">M</mi><mo id="S2.SS2.p1.4.m4.1.1.3.3.3" xref="S2.SS2.p1.4.m4.1.1.3.3.3.cmml">*</mo></msub></mrow></mrow></math>

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0112472

Formulas:

1-

𝒟 = {(Γ (1 - β \cos θ))}^{- 1}

2-

e^{-}, e^{+}, p

3-

U_{e} / U_{B} \propto T_{b}^{7 + 2 α},

4-

N (γ) \propto γ^{- p}

5-

π_{L} \propto {(k_{0} R)}^{- 3 / 2}

6-

π_{L} \propto τ / τ_{F}

7-

{(k_{0} R)}^{- 1}

8-

π_{L} \approx \frac{α + 1}{α + 5 / 3} {(k_{0} R)}^{- 1 / 2} {(γ_{rad} / γ_{\min})}^{- p} \frac{γ_{\min}}{\ln γ_{\min}} .

9-

Δ z = (1 - \sqrt{\frac{Γ_{S}^{2} - 4}{Γ_{S}^{2} - 1}}) z,

10-

\tilde{τ} \approx Δ z / (\sqrt{π} z \sin ψ) = (1 - \sqrt{\frac{Γ_{S}^{2} - 4}{Γ_{S}^{2} - 1}}) / (\sqrt{π} \sin ψ),

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/nlin/0703058

Formulas:

1-

\dot{θ} = f (θ),

2-

\dot{θ} = a_{0} + a_{1} \cos θ,

3-

a_{0} > | a_{1} |

4-

\ddot{Ψ} + γ \dot{Ψ} + κ^{2} \sin Ψ = \frac{K}{I},

5-

I_{c} \sin Ψ

6-

\dot{Ψ} = \frac{2 e}{ℏ} V,

7-

I = I_{c} \sin Ψ + \frac{ℏ}{2 e R} \frac{d Ψ}{d t} + \frac{C ℏ}{2 e} \frac{d^{2} Ψ}{d t^{2}} .

8-

ν_{0} = \frac{1}{2 π} \sqrt{a_{0}^{2} - a_{1}^{2}} .

9-

\dot{θ} = a_{0} + a_{1} \cos θ + B \sin (ω t),

10-

θ_{i} \equiv θ (t_{i})

Formulas (html):

Correct Categorie: nlin

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/1502.00666

Formulas:

1-

f (x, p)

2-

σ_{x} σ_{p} \geq ℏ / 2

3-

a x + b p

4-

a x + b p

5-

f (x, p)

6-

(x, p) \in R

7-

c x p \exp (- a x^{2} - b p^{2})

8-

g (x, p)

9-

\hat{f} (ξ) = \frac{1}{\sqrt{2 π}} \int f (x) e^{- i ξ x} 𝑑 x .

10-

\overset{ˇ}{g} (x) = \frac{1}{\sqrt{2 π}} \int g (ξ) e^{i ξ x} 𝑑 ξ,

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: quant-ph

Result: correct

Paper: https://arxiv.org/abs/1307.3209

Formulas:

1-

U_{3 d} (Ga) = 10.9

2-

U_{3 d} (Zn) = 7.6

3-

Δ ε_{4 f}

4-

Δ ε_{4 f}

5-

U_{4 f} (Gd) = 6.8 eV

6-

Δ ε_{4 f} (Gd) = 11.7 eV

7-

Δ ε_{4 f}

8-

Δ ε_{4 f}

9-

Δ ε_{4 f} (Gd)

10-

Δ ε_{4 f}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/cond-mat/0010260

Formulas:

1-

𝐁 = - [2 m_{e} (1 + ζ) c / e] 𝛀,

2-

ζ \approx {(v_{F} / c)}^{2} \approx 2 \times 10^{- 4} .

3-

ζ = \tilde{μ} / c^{2} \approx - 10^{- 10},

4-

= \int 𝐁 \cdot d 𝐚

5-

Δ 𝐀 = - (𝛀 \times 𝒓) Δ Φ / c .

6-

m_{i} N_{+} + m_{e} N_{-},

7-

| e | (N_{+} - N_{-}) .

8-

N_{a} \equiv M / (m_{i} + m_{e})

9-

μ_{+} d N_{+} + μ_{-} d N_{-}

10-

μ d M + Δ Φ d Q

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1806.09381

Formulas:

1-

Γ_{i} = γ_{i} \min (\frac{E_{i} - β E}{E - β E}, 0)

2-

𝒟 = {d_{1}, d_{2}, \dots, d_{N}}

3-

𝒮 = {s_{1}, s_{2}, \dots, s_{M}}

4-

G = (V, W)

5-

P_{l, m i}

6-

P_{s, i j}

7-

S N R_{L R}

8-

S N R_{S R}

9-

P_{l, m i}

10-

P_{s, i j}

Formulas (html):

Correct Categorie: cs

Guessed Categorie: cs

Result: correct

Paper: https://arxiv.org/abs/quant-ph/9710011

Formulas:

1-

i \frac{\partial Ψ}{\partial t} = - \frac{1}{2 m} Δ Ψ + V Ψ

2-

Ψ = R \exp (i S)

3-

\frac{\partial R^{2}}{\partial t} + \frac{1}{m} \vec{\nabla} \cdot (R^{2} \vec{\nabla} S) = 0,

4-

\frac{1}{m} Δ R - 2 R \frac{\partial S}{\partial t} - 2 R V - \frac{1}{m} R {(\vec{\nabla} S)}^{2} = 0 .

5-

L^{S E} (\vec{r}, t) = \frac{i}{2} (Ψ^{*} \frac{\partial Ψ}{\partial t} - \frac{\partial Ψ^{*}}{\partial t} Ψ) - \frac{1}{2 m} \vec{\nabla} Ψ^{*} \vec{\nabla} Ψ + Ψ^{*} V Ψ .

6-

L^{S E} (R, S) = R^{2} \frac{\partial S}{\partial t} + \frac{1}{2 m} [{(\vec{\nabla} R)}^{2} + R^{2} {(\vec{\nabla} S)}^{2}] + R^{2} V .

7-

j = \frac{1}{m} R^{2} \vec{\nabla} S

8-

{| Ψ |}^{2} Ψ

9-

L_{m o d}^{S E} = R^{2} \frac{\partial S}{\partial t} + \frac{1}{2 m} [{(\vec{\nabla} R)}^{2} + R^{2} {(\vec{\nabla} S)}^{2}] + R^{2} V + 2 γ {(Δ S)}^{2} .

10-

{(Δ S)}^{2}

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/nucl-ex/0702012

Formulas:

1-

V (t) = A e^{B \ln (t) - C t} (1 + D t + E t^{2}),

2-

D = - 3.839 \cdot 10^{- 2}

3-

E = 1.148 \cdot 10^{- 3}

4-

α (z_{t r u e}) = \frac{Q_{r} (z_{t r u e}) - Q_{l} (z_{t r u e})}{Q_{r} (z_{t r u e}) + Q_{l} (z_{t r u e})},

5-

z_{t r u e}

6-

- l / 2 ⩽ z_{t r u e} ⩽ l / 2

7-

Q_{l} (z_{t r u e})

8-

Q_{r} (z_{t r u e})

9-

l_{e f f}

10-

l_{e f f} = \frac{l}{α (l / 2)} .

Formulas (html):

Correct Categorie: nucl-ex

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1810.09161

Formulas:

1-

\frac{d m_{i}}{d t} =

2-

\frac{α_{m 1} (θ_{f} f_{i}) + α_{m 2} (θ_{w} w_{i} + ψ_{f} f_{i}^{2})}{1 + θ_{f} f_{i} + θ_{w} w_{i} + θ_{g} g_{i} + ψ_{g} f_{i} p_{i} + ψ_{f} f_{i}^{2}} - μ_{m} m_{i},

3-

\frac{d s_{i}}{d t} =

4-

- β_{a} a_{i} s_{i} + γ_{a} c_{i},

5-

\frac{d c_{i}}{d t} =

6-

β_{a} a_{i} s_{i} - γ_{a} c_{i} + (γ_{p} + μ_{p}) e_{i} - β_{p} p_{i} c_{i},

7-

\frac{d e_{i}}{d t} =

8-

β_{p} p_{i} c_{i} - (γ_{p} + μ_{p}) e_{i},

9-

\frac{d f_{i}}{d t} =

10-

- 2 β_{f} f_{i}^{2} + 2 γ_{f} w_{i} - β_{g} p_{i} f_{i} + γ_{g} g_{i},

Formulas (html):

Correct Categorie: q-bio

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/math/0606293

Formulas:

1-

D \cap π (K)

2-

N (c_{i}; K)

3-

P = S_{+}^{2} \cap S_{-}^{2}

4-

S_{+}^{2} \cup S_{-}^{2} = P \cup ⋃ \partial B_{i}

5-

P - π (K)

6-

\partial B \cap R_{j}

7-

l \cap \partial B_{i}

8-

K \cap \partial_{+} B_{i}

9-

K \cap \partial_{+} B_{j}

10-

K \cap \partial_{-} B_{i}

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/2003.12959

Formulas:

1-

gp (P_{\infty}^{n}) = 2^{2^{n - 1}}

2-

n \in {1, 2}

3-

S \subseteq V (G)

4-

d_{G} (u, v) \neq d_{G} (u, w) + d_{G} (w, v)

5-

{u, v, w} \in (\binom{S}{3})

6-

d_{G} (x, y)

7-

V (G) \times V (H)

8-

(g^{'}, h^{'})

9-

h h^{'} \in E (H)

10-

g g^{'} \in E (G)

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/cond-mat/0202103

Formulas:

1-

T < T_{c 2}

2-

Ψ = | Ψ | e x p (i ϕ)

3-

j = \frac{h e n_{s}}{4 π m} (\frac{d ϕ}{d r} - \frac{4 π e}{h c} A) = \frac{1}{λ_{L}^{2}} (\frac{Φ_{0}}{2 π} \frac{d ϕ}{d r} - A)

4-

Φ = Φ_{0} n

5-

d ϕ / d r

6-

λ_{L} = {(m c / e^{2} n_{s})}^{0.5}

7-

Φ_{0} = h c / 2 e

8-

V = \frac{h}{4 π e} \frac{d ϕ}{d t}

9-

Y B a_{2} C u_{3} O_{7 - x}

10-

N b_{1 - x} O_{x}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

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