Run 11277772

Paper: https://arxiv.org/abs/0902.1675

Formulas:

1-

c / (B ν)

2-

c / (B ν) / 8

3-

c / (ν D)

4-

11 B ν / c

5-

40 ° < l < 100 °, - 0 \overset{\circ}{.} 25 < b < 7 \overset{\circ}{.} 25

6-

b = 0, 3, 6

7-

b = 0, 3, 6

8-

- 3.3 (2)

9-

19^{h} 37^{m} 47 \overset{s}{.} 603 (14)

10-

20^{h} 27^{m} 16 \overset{s}{.} 233 (3)

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0108350

Formulas:

1-

1 \leq a / AU \leq 50

2-

2 km s^{- 1}

3-

0.5 - 1.0 M_{⊙}

4-

10 km s^{- 1}

5-

70 km s^{- 1}

6-

0.1 - 0.2 M_{⊙}

7-

0.2 - 0.5 M_{⊙}

8-

0.5 - 1.0 M_{⊙}

9-

1.0 - 1.6 M_{⊙}

10-

1.6 - 3.0 M_{⊙}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/nucl-th/0103049

Formulas:

1-

(n, γ) \leftrightarrow (γ, n)

2-

S_{n} \approx - k T \ln {\frac{n_{n}}{2} {(\frac{2 π ℏ^{2}}{m_{n} k T})}^{3 / 2}},

3-

(n, γ) \leftrightarrow (γ, n)

4-

(n, γ) \leftrightarrow (γ, n)

5-

(n, γ) \leftrightarrow (γ, n)

6-

(n, γ) \leftrightarrow (γ, n)

7-

ρ < 100 g / {cm}^{3}

8-

(n, γ) \leftrightarrow (γ, n)

9-

(n, γ) \leftrightarrow (γ, n)

10-

(n, γ) \leftrightarrow (γ, n)

Formulas (html):

Correct Categorie: nucl-th

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1602.00218

Formulas:

1-

H = (V, E)

2-

m (n) = O (n^{2} 2^{n})

3-

m (n) = O ({(\sqrt{7} + o (1))}^{n})

4-

m (n) \leq m (a) m {(b)}^{a}

5-

a \geq 1, b \geq 1

6-

m (n) = O (2^{(1 + o (1)) n})

7-

m (1) \leq 1

8-

m (2) \leq 3

9-

m (3) \leq 7

10-

m (6) \leq 147

Formulas (html):

Correct Categorie: math

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/9504099

Formulas:

1-

E_{C} = e^{2} / 2 C

2-

U (N_{1}, N_{2})

3-

E_{C} {(N_{1} + N_{2} - 2 X)}^{2}

4-

+ {\tilde{E}}_{C} {[N_{1} - N_{2} + λ (N_{1} + N_{2}) - α X]}^{2} .

5-

G_{0} ≪ e^{2} / h

6-

U (n + 1, n)

7-

U (n, n)

8-

U (n + 1, n + 1)

9-

X^{*} = n + \frac{1}{2} \pm \frac{1}{4} (1 - \frac{{\tilde{E}}_{C}}{E_{C}}) .

10-

E_{C} - {\tilde{E}}_{C} ≪ E_{C}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/0803.0665

Formulas:

1-

n \in {2, 4, 8}

2-

φ (M^{m}, N^{n})

3-

0 \leq m - n - 1 \leq 3

4-

φ (M^{m}, N^{n + 1})

5-

φ (M^{m}, N^{n + 1}) \in {0, 1}

6-

(m, n + 1) \in {(2, 2), (4, 3), (4, 2), (5, 2), (6, 3), (8, 5)}

7-

φ (M, N) = 1

8-

m - n - 1 \geq 4

9-

n \in {2, 4, 8}

10-

Σ^{4} ∖ int (D^{4})

Formulas (html):

Correct Categorie: math

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/9701015

Formulas:

1-

\log L_{H α} = 41.5

2-

\log L_{I R} = 10.0

3-

L_{I R} / L_{B} = 0.56

4-

b \equiv S F R / {< S F R >}_{p a s t} = 0.72

5-

L_{H α} = 1 \times 10^{39}

6-

b / a = 0.45 \pm 0.06

7-

v_{c i r c} = 490

8-

v_{c i r c} = 225

9-

v_{s y s} = 1475 \pm 10

10-

v \sin i = 220 \pm 10

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/2008.05461

Formulas:

1-

T \approx 5 \times 10^{4}

2-

u g r i

3-

- 21 < M_{R} < - 19

4-

g - R < - 0.1

5-

L \propto t^{- 5 / 3}

6-

â ˆ ’ 3000

7-

^{â ˆ ’ 1}

8-

λ λ 2796, 2803

9-

λ λ 2796, 2803

10-

\sim 10^{3} - 10^{4}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1405.5723

Formulas:

1-

E_{i s o}

2-

E_{p, i} < 100

3-

E_{i s o}

4-

E_{i s o} ≃ 10^{54}

5-

q \bar{q} \to W Z H^{0}

6-

e^{+} e^{-} \to μ^{+} μ^{-}

7-

E_{i s o} = 2.7 \times 10^{53}

8-

Γ ≃ 10^{2} \sim 10^{3}

9-

E_{i s o} = 2.49 \times 10^{53}

10-

B = 1.98 \times 10^{- 3}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1605.03318

Formulas:

1-

J = n q v

2-

G_{p h} α (λ) \exp (- α (λ) x)

3-

J_{T U}^{i} = q (\frac{A τ}{L_{i}}) \int_{0}^{L_{i}} G_{p} α (x) \exp [- α (λ) x] 𝑑 x \int_{E_{i}}^{E_{f}} g (E) v (E) P (E) \frac{1}{1 + e^{\frac{E - E_{F}}{k T}}} 𝑑 E,

4-

1 / [1 + \exp (\frac{E - E_{F}}{k_{b} T})]

5-

τ = t_{c} / g

6-

g (E) = \frac{g_{s} g_{v} m_{i}}{2 π ℏ^{2}}

7-

v (E) = \sqrt{2 (Δ_{c} - E) / m}

8-

P (E) = {(1 + \frac{Δ_{c}^{2} \sinh^{2} (k_{b} L_{b})}{4 E (Δ_{c} - E)})}^{- 1}

9-

k_{b} = (\sqrt{2 m_{e} (Δ_{c} - E)} / ℏ)

10-

P_{2} (E) = \frac{16 E (Δ_{c} - E)}{Δ_{c}^{2}} \exp (- k_{b} \sqrt{1 - E / Δ_{c}})

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1501.06067

Formulas:

1-

I d A \cap I d \bar{A}

2-

S e p A

3-

S e p A

4-

x \bar{A} \subseteq \bar{A}

5-

\bar{A} x \subseteq \bar{A}

6-

S e p A

7-

S e p A = S e p \bar{A}

8-

S e p \emptyset = S e p S = S

9-

S e p A

10-

R \cap S e p R = \emptyset

Formulas (html):

Correct Categorie: math

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0411159

Formulas:

1-

\frac{3}{5} \frac{G M_{N S}^{2}}{R_{N S}} \approx 3 \times 10^{53} ergs \frac{{(M_{N S} / 1.4 M_{⊙})}^{2}}{R_{N S} / 10 k m}

2-

\frac{d P}{d r} = - \frac{G M_{NS} ρ}{r^{2}},

3-

S_{total} = {(\frac{δ P}{δ T})}_{μ},

4-

T S = \frac{G M_{NS} m_{B}}{r},

5-

\frac{S}{k} = \frac{2 π^{2}}{45} \frac{g_{s}}{ρ_{B}} {(\frac{k T}{ℏ c})}^{3},

6-

g_{s} = \sum_{bosons} g_{b} + \frac{7}{8} \sum_{fermions} g_{f} .

7-

ρ_{3} \sim 38 (\frac{g_{s}}{11 / 2}) \frac{1}{S_{100}^{4} r_{7}^{3}},

8-

M_{NS} = 1.4 M_{⊙}

9-

T_{9} S_{100} \sim \frac{2.25}{r_{7}} .

10-

t_{P B} \approx 4

Formulas (html):

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xref="S1.E1.m1.1.1.1.1.1.1.2.2.cmml"><mi id="S1.E1.m1.1.1.1.1.1.1.2.2.2" xref="S1.E1.m1.1.1.1.1.1.1.2.2.2.cmml">M</mi><mrow id="S1.E1.m1.1.1.1.1.1.1.2.2.3" xref="S1.E1.m1.1.1.1.1.1.1.2.2.3.cmml"><mi id="S1.E1.m1.1.1.1.1.1.1.2.2.3.2" xref="S1.E1.m1.1.1.1.1.1.1.2.2.3.2.cmml">N</mi><mo id="S1.E1.m1.1.1.1.1.1.1.2.2.3.1" xref="S1.E1.m1.1.1.1.1.1.1.2.2.3.1.cmml">⁢</mo><mi id="S1.E1.m1.1.1.1.1.1.1.2.2.3.3" xref="S1.E1.m1.1.1.1.1.1.1.2.2.3.3.cmml">S</mi></mrow></msub><mo id="S1.E1.m1.1.1.1.1.1.1.2.1" xref="S1.E1.m1.1.1.1.1.1.1.2.1.cmml">/</mo><mn id="S1.E1.m1.1.1.1.1.1.1.2.3" xref="S1.E1.m1.1.1.1.1.1.1.2.3.cmml">1.4</mn></mrow><mo id="S1.E1.m1.1.1.1.1.1.1.1" xref="S1.E1.m1.1.1.1.1.1.1.1.cmml">⁢</mo><msub id="S1.E1.m1.1.1.1.1.1.1.3" xref="S1.E1.m1.1.1.1.1.1.1.3.cmml"><mi id="S1.E1.m1.1.1.1.1.1.1.3.2" xref="S1.E1.m1.1.1.1.1.1.1.3.2.cmml">M</mi><mo id="S1.E1.m1.1.1.1.1.1.1.3.3" xref="S1.E1.m1.1.1.1.1.1.1.3.3.cmml">⊙</mo></msub></mrow><mo stretchy="false" id="S1.E1.m1.1.1.1.1.1.3" xref="S1.E1.m1.1.1.1.1.1.1.cmml">)</mo></mrow><mn id="S1.E1.m1.1.1.1.3" xref="S1.E1.m1.1.1.1.3.cmml">2</mn></msup><mrow 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">R</mi><mrow id="S1.E1.m1.1.1.3.2.2.3" xref="S1.E1.m1.1.1.3.2.2.3.cmml"><mi id="S1.E1.m1.1.1.3.2.2.3.2" xref="S1.E1.m1.1.1.3.2.2.3.2.cmml">N</mi><mo id="S1.E1.m1.1.1.3.2.2.3.1" xref="S1.E1.m1.1.1.3.2.2.3.1.cmml">⁢</mo><mi id="S1.E1.m1.1.1.3.2.2.3.3" xref="S1.E1.m1.1.1.3.2.2.3.3.cmml">S</mi></mrow></msub><mo id="S1.E1.m1.1.1.3.2.1" xref="S1.E1.m1.1.1.3.2.1.cmml">/</mo><mn id="S1.E1.m1.1.1.3.2.3" xref="S1.E1.m1.1.1.3.2.3.cmml">10</mn></mrow><mo id="S1.E1.m1.1.1.3.1" xref="S1.E1.m1.1.1.3.1.cmml">⁢</mo><mi mathvariant="normal" id="S1.E1.m1.1.1.3.3" xref="S1.E1.m1.1.1.3.3.cmml">k</mi><mo id="S1.E1.m1.1.1.3.1a" xref="S1.E1.m1.1.1.3.1.cmml">⁢</mo><mi mathvariant="normal" id="S1.E1.m1.1.1.3.4" xref="S1.E1.m1.1.1.3.4.cmml">m</mi></mrow></mfrac></mrow></mrow></math>, <math><mrow id="S2.E2.m1.1.1.1" xref="S2.E2.m1.1.1.1.1.cmml"><mrow id="S2.E2.m1.1.1.1.1" xref="S2.E2.m1.1.1.1.1.cmml"><mfrac id="S2.E2.m1.1.1.1.1.2" xref="S2.E2.m1.1.1.1.1.2.cmml"><mrow id="S2.E2.m1.1.1.1.1.2.2" xref="S2.E2.m1.1.1.1.1.2.2.cmml"><mi id="S2.E2.m1.1.1.1.1.2.2.2" xref="S2.E2.m1.1.1.1.1.2.2.2.cmml">d</mi><mo id="S2.E2.m1.1.1.1.1.2.2.1" xref="S2.E2.m1.1.1.1.1.2.2.1.cmml">⁢</mo><mi id="S2.E2.m1.1.1.1.1.2.2.3" xref="S2.E2.m1.1.1.1.1.2.2.3.cmml">P</mi></mrow><mrow id="S2.E2.m1.1.1.1.1.2.3" xref="S2.E2.m1.1.1.1.1.2.3.cmml"><mi id="S2.E2.m1.1.1.1.1.2.3.2" xref="S2.E2.m1.1.1.1.1.2.3.2.cmml">d</mi><mo id="S2.E2.m1.1.1.1.1.2.3.1" xref="S2.E2.m1.1.1.1.1.2.3.1.cmml">⁢</mo><mi id="S2.E2.m1.1.1.1.1.2.3.3" xref="S2.E2.m1.1.1.1.1.2.3.3.cmml">r</mi></mrow></mfrac><mo id="S2.E2.m1.1.1.1.1.1" xref="S2.E2.m1.1.1.1.1.1.cmml">=</mo><mrow id="S2.E2.m1.1.1.1.1.3" xref="S2.E2.m1.1.1.1.1.3.cmml"><mo id="S2.E2.m1.1.1.1.1.3.1" xref="S2.E2.m1.1.1.1.1.3.1.cmml">-</mo><mfrac id="S2.E2.m1.1.1.1.1.3.2" xref="S2.E2.m1.1.1.1.1.3.2.cmml"><mrow id="S2.E2.m1.1.1.1.1.3.2.2" xref="S2.E2.m1.1.1.1.1.3.2.2.cmml"><mi id="S2.E2.m1.1.1.1.1.3.2.2.2" xref="S2.E2.m1.1.1.1.1.3.2.2.2.cmml">G</mi><mo id="S2.E2.m1.1.1.1.1.3.2.2.1" xref="S2.E2.m1.1.1.1.1.3.2.2.1.cmml">⁢</mo><msub id="S2.E2.m1.1.1.1.1.3.2.2.3" xref="S2.E2.m1.1.1.1.1.3.2.2.3.cmml"><mi id="S2.E2.m1.1.1.1.1.3.2.2.3.2" xref="S2.E2.m1.1.1.1.1.3.2.2.3.2.cmml">M</mi><mi id="S2.E2.m1.1.1.1.1.3.2.2.3.3" xref="S2.E2.m1.1.1.1.1.3.2.2.3.3.cmml">NS</mi></msub><mo id="S2.E2.m1.1.1.1.1.3.2.2.1a" xref="S2.E2.m1.1.1.1.1.3.2.2.1.cmml">⁢</mo><mi id="S2.E2.m1.1.1.1.1.3.2.2.4" xref="S2.E2.m1.1.1.1.1.3.2.2.4.cmml">ρ</mi></mrow><msup id="S2.E2.m1.1.1.1.1.3.2.3" xref="S2.E2.m1.1.1.1.1.3.2.3.cmml"><mi id="S2.E2.m1.1.1.1.1.3.2.3.2" xref="S2.E2.m1.1.1.1.1.3.2.3.2.cmml">r</mi><mn id="S2.E2.m1.1.1.1.1.3.2.3.3" xref="S2.E2.m1.1.1.1.1.3.2.3.3.cmml">2</mn></msup></mfrac></mrow></mrow><mo id="S2.E2.m1.1.1.1.2" xref="S2.E2.m1.1.1.1.1.cmml">,</mo></mrow></math>, <math><mrow id="S2.E3.m1.2.2.1" xref="S2.E3.m1.2.2.1.1.cmml"><mrow id="S2.E3.m1.2.2.1.1" xref="S2.E3.m1.2.2.1.1.cmml"><msub id="S2.E3.m1.2.2.1.1.2" xref="S2.E3.m1.2.2.1.1.2.cmml"><mi id="S2.E3.m1.2.2.1.1.2.2" xref="S2.E3.m1.2.2.1.1.2.2.cmml">S</mi><mi id="S2.E3.m1.2.2.1.1.2.3" xref="S2.E3.m1.2.2.1.1.2.3.cmml">total</mi></msub><mo id="S2.E3.m1.2.2.1.1.1" xref="S2.E3.m1.2.2.1.1.1.cmml">=</mo><msub id="S2.E3.m1.2.2.1.1.3" xref="S2.E3.m1.2.2.1.1.3.cmml"><mrow id="S2.E3.m1.2.2.1.1.3.2.2" xref="S2.E3.m1.1.1.cmml"><mo id="S2.E3.m1.2.2.1.1.3.2.2.1" xref="S2.E3.m1.1.1.cmml">(</mo><mfrac id="S2.E3.m1.1.1" xref="S2.E3.m1.1.1.cmml"><mrow id="S2.E3.m1.1.1.2" xref="S2.E3.m1.1.1.2.cmml"><mi id="S2.E3.m1.1.1.2.2" xref="S2.E3.m1.1.1.2.2.cmml">δ</mi><mo id="S2.E3.m1.1.1.2.1" xref="S2.E3.m1.1.1.2.1.cmml">⁢</mo><mi id="S2.E3.m1.1.1.2.3" xref="S2.E3.m1.1.1.2.3.cmml">P</mi></mrow><mrow id="S2.E3.m1.1.1.3" xref="S2.E3.m1.1.1.3.cmml"><mi id="S2.E3.m1.1.1.3.2" xref="S2.E3.m1.1.1.3.2.cmml">δ</mi><mo id="S2.E3.m1.1.1.3.1" xref="S2.E3.m1.1.1.3.1.cmml">⁢</mo><mi id="S2.E3.m1.1.1.3.3" xref="S2.E3.m1.1.1.3.3.cmml">T</mi></mrow></mfrac><mo id="S2.E3.m1.2.2.1.1.3.2.2.2" xref="S2.E3.m1.1.1.cmml">)</mo></mrow><mi id="S2.E3.m1.2.2.1.1.3.3" xref="S2.E3.m1.2.2.1.1.3.3.cmml">μ</mi></msub></mrow><mo id="S2.E3.m1.2.2.1.2" xref="S2.E3.m1.2.2.1.1.cmml">,</mo></mrow></math>, <math><mrow id="S2.E4.m1.1.1.1" xref="S2.E4.m1.1.1.1.1.cmml"><mrow id="S2.E4.m1.1.1.1.1" xref="S2.E4.m1.1.1.1.1.cmml"><mrow id="S2.E4.m1.1.1.1.1.2" xref="S2.E4.m1.1.1.1.1.2.cmml"><mi id="S2.E4.m1.1.1.1.1.2.2" xref="S2.E4.m1.1.1.1.1.2.2.cmml">T</mi><mo id="S2.E4.m1.1.1.1.1.2.1" xref="S2.E4.m1.1.1.1.1.2.1.cmml">⁢</mo><mi id="S2.E4.m1.1.1.1.1.2.3" xref="S2.E4.m1.1.1.1.1.2.3.cmml">S</mi></mrow><mo id="S2.E4.m1.1.1.1.1.1" xref="S2.E4.m1.1.1.1.1.1.cmml">=</mo><mfrac id="S2.E4.m1.1.1.1.1.3" xref="S2.E4.m1.1.1.1.1.3.cmml"><mrow id="S2.E4.m1.1.1.1.1.3.2" xref="S2.E4.m1.1.1.1.1.3.2.cmml"><mi id="S2.E4.m1.1.1.1.1.3.2.2" xref="S2.E4.m1.1.1.1.1.3.2.2.cmml">G</mi><mo id="S2.E4.m1.1.1.1.1.3.2.1" xref="S2.E4.m1.1.1.1.1.3.2.1.cmml">⁢</mo><msub id="S2.E4.m1.1.1.1.1.3.2.3" xref="S2.E4.m1.1.1.1.1.3.2.3.cmml"><mi id="S2.E4.m1.1.1.1.1.3.2.3.2" xref="S2.E4.m1.1.1.1.1.3.2.3.2.cmml">M</mi><mi id="S2.E4.m1.1.1.1.1.3.2.3.3" xref="S2.E4.m1.1.1.1.1.3.2.3.3.cmml">NS</mi></msub><mo id="S2.E4.m1.1.1.1.1.3.2.1a" xref="S2.E4.m1.1.1.1.1.3.2.1.cmml">⁢</mo><msub id="S2.E4.m1.1.1.1.1.3.2.4" xref="S2.E4.m1.1.1.1.1.3.2.4.cmml"><mi id="S2.E4.m1.1.1.1.1.3.2.4.2" xref="S2.E4.m1.1.1.1.1.3.2.4.2.cmml">m</mi><mi id="S2.E4.m1.1.1.1.1.3.2.4.3" xref="S2.E4.m1.1.1.1.1.3.2.4.3.cmml">B</mi></msub></mrow><mi id="S2.E4.m1.1.1.1.1.3.3" xref="S2.E4.m1.1.1.1.1.3.3.cmml">r</mi></mfrac></mrow><mo id="S2.E4.m1.1.1.1.2" xref="S2.E4.m1.1.1.1.1.cmml">,</mo></mrow></math>, <math><mrow id="S2.E5.m1.2.2.1" xref="S2.E5.m1.2.2.1.1.cmml"><mrow id="S2.E5.m1.2.2.1.1" xref="S2.E5.m1.2.2.1.1.cmml"><mfrac id="S2.E5.m1.2.2.1.1.2" xref="S2.E5.m1.2.2.1.1.2.cmml"><mi id="S2.E5.m1.2.2.1.1.2.2" xref="S2.E5.m1.2.2.1.1.2.2.cmml">S</mi><mi id="S2.E5.m1.2.2.1.1.2.3" xref="S2.E5.m1.2.2.1.1.2.3.cmml">k</mi></mfrac><mo id="S2.E5.m1.2.2.1.1.1" xref="S2.E5.m1.2.2.1.1.1.cmml">=</mo><mrow id="S2.E5.m1.2.2.1.1.3" xref="S2.E5.m1.2.2.1.1.3.cmml"><mfrac id="S2.E5.m1.2.2.1.1.3.2" xref="S2.E5.m1.2.2.1.1.3.2.cmml"><mrow id="S2.E5.m1.2.2.1.1.3.2.2" xref="S2.E5.m1.2.2.1.1.3.2.2.cmml"><mn id="S2.E5.m1.2.2.1.1.3.2.2.2" xref="S2.E5.m1.2.2.1.1.3.2.2.2.cmml">2</mn><mo id="S2.E5.m1.2.2.1.1.3.2.2.1" xref="S2.E5.m1.2.2.1.1.3.2.2.1.cmml">⁢</mo><msup id="S2.E5.m1.2.2.1.1.3.2.2.3" xref="S2.E5.m1.2.2.1.1.3.2.2.3.cmml"><mi id="S2.E5.m1.2.2.1.1.3.2.2.3.2" xref="S2.E5.m1.2.2.1.1.3.2.2.3.2.cmml">π</mi><mn id="S2.E5.m1.2.2.1.1.3.2.2.3.3" xref="S2.E5.m1.2.2.1.1.3.2.2.3.3.cmml">2</mn></msup></mrow><mn id="S2.E5.m1.2.2.1.1.3.2.3" xref="S2.E5.m1.2.2.1.1.3.2.3.cmml">45</mn></mfrac><mo id="S2.E5.m1.2.2.1.1.3.1" xref="S2.E5.m1.2.2.1.1.3.1.cmml">⁢</mo><mfrac id="S2.E5.m1.2.2.1.1.3.3" xref="S2.E5.m1.2.2.1.1.3.3.cmml"><msub id="S2.E5.m1.2.2.1.1.3.3.2" xref="S2.E5.m1.2.2.1.1.3.3.2.cmml"><mi id="S2.E5.m1.2.2.1.1.3.3.2.2" xref="S2.E5.m1.2.2.1.1.3.3.2.2.cmml">g</mi><mi id="S2.E5.m1.2.2.1.1.3.3.2.3" xref="S2.E5.m1.2.2.1.1.3.3.2.3.cmml">s</mi></msub><msub id="S2.E5.m1.2.2.1.1.3.3.3" xref="S2.E5.m1.2.2.1.1.3.3.3.cmml"><mi id="S2.E5.m1.2.2.1.1.3.3.3.2" xref="S2.E5.m1.2.2.1.1.3.3.3.2.cmml">ρ</mi><mi id="S2.E5.m1.2.2.1.1.3.3.3.3" xref="S2.E5.m1.2.2.1.1.3.3.3.3.cmml">B</mi></msub></mfrac><mo id="S2.E5.m1.2.2.1.1.3.1a" xref="S2.E5.m1.2.2.1.1.3.1.cmml">⁢</mo><msup id="S2.E5.m1.2.2.1.1.3.4" xref="S2.E5.m1.2.2.1.1.3.4.cmml"><mrow id="S2.E5.m1.2.2.1.1.3.4.2.2" xref="S2.E5.m1.1.1.cmml"><mo id="S2.E5.m1.2.2.1.1.3.4.2.2.1" xref="S2.E5.m1.1.1.cmml">(</mo><mfrac id="S2.E5.m1.1.1" xref="S2.E5.m1.1.1.cmml"><mrow id="S2.E5.m1.1.1.2" xref="S2.E5.m1.1.1.2.cmml"><mi id="S2.E5.m1.1.1.2.2" xref="S2.E5.m1.1.1.2.2.cmml">k</mi><mo id="S2.E5.m1.1.1.2.1" xref="S2.E5.m1.1.1.2.1.cmml">⁢</mo><mi id="S2.E5.m1.1.1.2.3" xref="S2.E5.m1.1.1.2.3.cmml">T</mi></mrow><mrow id="S2.E5.m1.1.1.3" xref="S2.E5.m1.1.1.3.cmml"><mi mathvariant="normal" id="S2.E5.m1.1.1.3.2" xref="S2.E5.m1.1.1.3.2.cmml">ℏ</mi><mo id="S2.E5.m1.1.1.3.1" xref="S2.E5.m1.1.1.3.1.cmml">⁢</mo><mi id="S2.E5.m1.1.1.3.3" xref="S2.E5.m1.1.1.3.3.cmml">c</mi></mrow></mfrac><mo id="S2.E5.m1.2.2.1.1.3.4.2.2.2" xref="S2.E5.m1.1.1.cmml">)</mo></mrow><mn id="S2.E5.m1.2.2.1.1.3.4.3" xref="S2.E5.m1.2.2.1.1.3.4.3.cmml">3</mn></msup></mrow></mrow><mo id="S2.E5.m1.2.2.1.2" xref="S2.E5.m1.2.2.1.1.cmml">,</mo></mrow></math>, <math><mrow id="S2.E6.m1.1.1.1" xref="S2.E6.m1.1.1.1.1.cmml"><mrow id="S2.E6.m1.1.1.1.1" xref="S2.E6.m1.1.1.1.1.cmml"><msub id="S2.E6.m1.1.1.1.1.2" xref="S2.E6.m1.1.1.1.1.2.cmml"><mi id="S2.E6.m1.1.1.1.1.2.2" xref="S2.E6.m1.1.1.1.1.2.2.cmml">g</mi><mi id="S2.E6.m1.1.1.1.1.2.3" xref="S2.E6.m1.1.1.1.1.2.3.cmml">s</mi></msub><mo id="S2.E6.m1.1.1.1.1.1" xref="S2.E6.m1.1.1.1.1.1.cmml">=</mo><mrow id="S2.E6.m1.1.1.1.1.3" xref="S2.E6.m1.1.1.1.1.3.cmml"><mrow id="S2.E6.m1.1.1.1.1.3.2" xref="S2.E6.m1.1.1.1.1.3.2.cmml"><munder id="S2.E6.m1.1.1.1.1.3.2.1" xref="S2.E6.m1.1.1.1.1.3.2.1.cmml"><mo largeop="true" movablelimits="false" symmetric="true" id="S2.E6.m1.1.1.1.1.3.2.1.2" xref="S2.E6.m1.1.1.1.1.3.2.1.2.cmml">∑</mo><mi id="S2.E6.m1.1.1.1.1.3.2.1.3" xref="S2.E6.m1.1.1.1.1.3.2.1.3.cmml">bosons</mi></munder><msub id="S2.E6.m1.1.1.1.1.3.2.2" xref="S2.E6.m1.1.1.1.1.3.2.2.cmml"><mi id="S2.E6.m1.1.1.1.1.3.2.2.2" xref="S2.E6.m1.1.1.1.1.3.2.2.2.cmml">g</mi><mi id="S2.E6.m1.1.1.1.1.3.2.2.3" xref="S2.E6.m1.1.1.1.1.3.2.2.3.cmml">b</mi></msub></mrow><mo id="S2.E6.m1.1.1.1.1.3.1" xref="S2.E6.m1.1.1.1.1.3.1.cmml">+</mo><mrow id="S2.E6.m1.1.1.1.1.3.3" xref="S2.E6.m1.1.1.1.1.3.3.cmml"><mfrac id="S2.E6.m1.1.1.1.1.3.3.2" xref="S2.E6.m1.1.1.1.1.3.3.2.cmml"><mn id="S2.E6.m1.1.1.1.1.3.3.2.2" xref="S2.E6.m1.1.1.1.1.3.3.2.2.cmml">7</mn><mn id="S2.E6.m1.1.1.1.1.3.3.2.3" xref="S2.E6.m1.1.1.1.1.3.3.2.3.cmml">8</mn></mfrac><mo id="S2.E6.m1.1.1.1.1.3.3.1" xref="S2.E6.m1.1.1.1.1.3.3.1.cmml">⁢</mo><mrow id="S2.E6.m1.1.1.1.1.3.3.3" xref="S2.E6.m1.1.1.1.1.3.3.3.cmml"><munder id="S2.E6.m1.1.1.1.1.3.3.3.1" xref="S2.E6.m1.1.1.1.1.3.3.3.1.cmml"><mo largeop="true" movablelimits="false" symmetric="true" id="S2.E6.m1.1.1.1.1.3.3.3.1.2" xref="S2.E6.m1.1.1.1.1.3.3.3.1.2.cmml">∑</mo><mi id="S2.E6.m1.1.1.1.1.3.3.3.1.3" xref="S2.E6.m1.1.1.1.1.3.3.3.1.3.cmml">fermions</mi></munder><msub id="S2.E6.m1.1.1.1.1.3.3.3.2" xref="S2.E6.m1.1.1.1.1.3.3.3.2.cmml"><mi id="S2.E6.m1.1.1.1.1.3.3.3.2.2" xref="S2.E6.m1.1.1.1.1.3.3.3.2.2.cmml">g</mi><mi id="S2.E6.m1.1.1.1.1.3.3.3.2.3" xref="S2.E6.m1.1.1.1.1.3.3.3.2.3.cmml">f</mi></msub></mrow></mrow></mrow></mrow><mo id="S2.E6.m1.1.1.1.2" xref="S2.E6.m1.1.1.1.1.cmml">.</mo></mrow></math>, <math><mrow id="S2.E7.m1.2.2.1" xref="S2.E7.m1.2.2.1.1.cmml"><mrow id="S2.E7.m1.2.2.1.1" xref="S2.E7.m1.2.2.1.1.cmml"><msub id="S2.E7.m1.2.2.1.1.2" xref="S2.E7.m1.2.2.1.1.2.cmml"><mi id="S2.E7.m1.2.2.1.1.2.2" xref="S2.E7.m1.2.2.1.1.2.2.cmml">ρ</mi><mn id="S2.E7.m1.2.2.1.1.2.3" xref="S2.E7.m1.2.2.1.1.2.3.cmml">3</mn></msub><mo id="S2.E7.m1.2.2.1.1.1" xref="S2.E7.m1.2.2.1.1.1.cmml">∼</mo><mrow id="S2.E7.m1.2.2.1.1.3" xref="S2.E7.m1.2.2.1.1.3.cmml"><mn id="S2.E7.m1.2.2.1.1.3.2" xref="S2.E7.m1.2.2.1.1.3.2.cmml">38</mn><mo id="S2.E7.m1.2.2.1.1.3.1" xref="S2.E7.m1.2.2.1.1.3.1.cmml">⁢</mo><mrow id="S2.E7.m1.2.2.1.1.3.3.2" xref="S2.E7.m1.1.1.cmml"><mo id="S2.E7.m1.2.2.1.1.3.3.2.1" xref="S2.E7.m1.1.1.cmml">(</mo><mfrac id="S2.E7.m1.1.1" xref="S2.E7.m1.1.1.cmml"><msub id="S2.E7.m1.1.1.2" xref="S2.E7.m1.1.1.2.cmml"><mi id="S2.E7.m1.1.1.2.2" xref="S2.E7.m1.1.1.2.2.cmml">g</mi><mi id="S2.E7.m1.1.1.2.3" xref="S2.E7.m1.1.1.2.3.cmml">s</mi></msub><mrow id="S2.E7.m1.1.1.3" xref="S2.E7.m1.1.1.3.cmml"><mn id="S2.E7.m1.1.1.3.2" xref="S2.E7.m1.1.1.3.2.cmml">11</mn><mo id="S2.E7.m1.1.1.3.1" xref="S2.E7.m1.1.1.3.1.cmml">/</mo><mn id="S2.E7.m1.1.1.3.3" xref="S2.E7.m1.1.1.3.3.cmml">2</mn></mrow></mfrac><mo id="S2.E7.m1.2.2.1.1.3.3.2.2" xref="S2.E7.m1.1.1.cmml">)</mo></mrow><mo id="S2.E7.m1.2.2.1.1.3.1a" xref="S2.E7.m1.2.2.1.1.3.1.cmml">⁢</mo><mfrac id="S2.E7.m1.2.2.1.1.3.4" xref="S2.E7.m1.2.2.1.1.3.4.cmml"><mn id="S2.E7.m1.2.2.1.1.3.4.2" xref="S2.E7.m1.2.2.1.1.3.4.2.cmml">1</mn><mrow id="S2.E7.m1.2.2.1.1.3.4.3" xref="S2.E7.m1.2.2.1.1.3.4.3.cmml"><msubsup id="S2.E7.m1.2.2.1.1.3.4.3.2" xref="S2.E7.m1.2.2.1.1.3.4.3.2.cmml"><mi id="S2.E7.m1.2.2.1.1.3.4.3.2.2.2" xref="S2.E7.m1.2.2.1.1.3.4.3.2.2.2.cmml">S</mi><mn id="S2.E7.m1.2.2.1.1.3.4.3.2.2.3" xref="S2.E7.m1.2.2.1.1.3.4.3.2.2.3.cmml">100</mn><mn id="S2.E7.m1.2.2.1.1.3.4.3.2.3" xref="S2.E7.m1.2.2.1.1.3.4.3.2.3.cmml">4</mn></msubsup><mo id="S2.E7.m1.2.2.1.1.3.4.3.1" xref="S2.E7.m1.2.2.1.1.3.4.3.1.cmml">⁢</mo><msubsup id="S2.E7.m1.2.2.1.1.3.4.3.3" xref="S2.E7.m1.2.2.1.1.3.4.3.3.cmml"><mi id="S2.E7.m1.2.2.1.1.3.4.3.3.2.2" xref="S2.E7.m1.2.2.1.1.3.4.3.3.2.2.cmml">r</mi><mn id="S2.E7.m1.2.2.1.1.3.4.3.3.3" xref="S2.E7.m1.2.2.1.1.3.4.3.3.3.cmml">7</mn><mn id="S2.E7.m1.2.2.1.1.3.4.3.3.2.3" xref="S2.E7.m1.2.2.1.1.3.4.3.3.2.3.cmml">3</mn></msubsup></mrow></mfrac></mrow></mrow><mo id="S2.E7.m1.2.2.1.2" xref="S2.E7.m1.2.2.1.1.cmml">,</mo></mrow></math>, <math><mrow id="S2.SS1.p1.14.m4.1.1" xref="S2.SS1.p1.14.m4.1.1.cmml"><msub id="S2.SS1.p1.14.m4.1.1.2" xref="S2.SS1.p1.14.m4.1.1.2.cmml"><mi id="S2.SS1.p1.14.m4.1.1.2.2" xref="S2.SS1.p1.14.m4.1.1.2.2.cmml">M</mi><mi id="S2.SS1.p1.14.m4.1.1.2.3" xref="S2.SS1.p1.14.m4.1.1.2.3.cmml">NS</mi></msub><mo id="S2.SS1.p1.14.m4.1.1.1" xref="S2.SS1.p1.14.m4.1.1.1.cmml">=</mo><mrow id="S2.SS1.p1.14.m4.1.1.3" xref="S2.SS1.p1.14.m4.1.1.3.cmml"><mn id="S2.SS1.p1.14.m4.1.1.3.2" xref="S2.SS1.p1.14.m4.1.1.3.2.cmml">1.4</mn><mo id="S2.SS1.p1.14.m4.1.1.3.1" xref="S2.SS1.p1.14.m4.1.1.3.1.cmml">⁢</mo><msub id="S2.SS1.p1.14.m4.1.1.3.3" xref="S2.SS1.p1.14.m4.1.1.3.3.cmml"><mi id="S2.SS1.p1.14.m4.1.1.3.3.2" xref="S2.SS1.p1.14.m4.1.1.3.3.2.cmml">M</mi><mo id="S2.SS1.p1.14.m4.1.1.3.3.3" xref="S2.SS1.p1.14.m4.1.1.3.3.3.cmml">⊙</mo></msub></mrow></mrow></math>, <math><mrow id="S2.E8.m1.1.1.1" xref="S2.E8.m1.1.1.1.1.cmml"><mrow id="S2.E8.m1.1.1.1.1" xref="S2.E8.m1.1.1.1.1.cmml"><mrow id="S2.E8.m1.1.1.1.1.2" xref="S2.E8.m1.1.1.1.1.2.cmml"><msub id="S2.E8.m1.1.1.1.1.2.2" xref="S2.E8.m1.1.1.1.1.2.2.cmml"><mi id="S2.E8.m1.1.1.1.1.2.2.2" xref="S2.E8.m1.1.1.1.1.2.2.2.cmml">T</mi><mn id="S2.E8.m1.1.1.1.1.2.2.3" xref="S2.E8.m1.1.1.1.1.2.2.3.cmml">9</mn></msub><mo id="S2.E8.m1.1.1.1.1.2.1" xref="S2.E8.m1.1.1.1.1.2.1.cmml">⁢</mo><msub id="S2.E8.m1.1.1.1.1.2.3" xref="S2.E8.m1.1.1.1.1.2.3.cmml"><mi id="S2.E8.m1.1.1.1.1.2.3.2" xref="S2.E8.m1.1.1.1.1.2.3.2.cmml">S</mi><mn id="S2.E8.m1.1.1.1.1.2.3.3" xref="S2.E8.m1.1.1.1.1.2.3.3.cmml">100</mn></msub></mrow><mo id="S2.E8.m1.1.1.1.1.1" xref="S2.E8.m1.1.1.1.1.1.cmml">∼</mo><mfrac id="S2.E8.m1.1.1.1.1.3" xref="S2.E8.m1.1.1.1.1.3.cmml"><mn id="S2.E8.m1.1.1.1.1.3.2" xref="S2.E8.m1.1.1.1.1.3.2.cmml">2.25</mn><msub id="S2.E8.m1.1.1.1.1.3.3" xref="S2.E8.m1.1.1.1.1.3.3.cmml"><mi id="S2.E8.m1.1.1.1.1.3.3.2" xref="S2.E8.m1.1.1.1.1.3.3.2.cmml">r</mi><mn id="S2.E8.m1.1.1.1.1.3.3.3" xref="S2.E8.m1.1.1.1.1.3.3.3.cmml">7</mn></msub></mfrac></mrow><mo id="S2.E8.m1.1.1.1.2" xref="S2.E8.m1.1.1.1.1.cmml">.</mo></mrow></math>, <math><mrow id="S2.F1.8.m4.1.1" xref="S2.F1.8.m4.1.1.cmml"><msub id="S2.F1.8.m4.1.1.2" xref="S2.F1.8.m4.1.1.2.cmml"><mi id="S2.F1.8.m4.1.1.2.2" xref="S2.F1.8.m4.1.1.2.2.cmml">t</mi><mrow id="S2.F1.8.m4.1.1.2.3" xref="S2.F1.8.m4.1.1.2.3.cmml"><mi id="S2.F1.8.m4.1.1.2.3.2" xref="S2.F1.8.m4.1.1.2.3.2.cmml">P</mi><mo id="S2.F1.8.m4.1.1.2.3.1" xref="S2.F1.8.m4.1.1.2.3.1.cmml">⁢</mo><mi id="S2.F1.8.m4.1.1.2.3.3" xref="S2.F1.8.m4.1.1.2.3.3.cmml">B</mi></mrow></msub><mo id="S2.F1.8.m4.1.1.1" xref="S2.F1.8.m4.1.1.1.cmml">≈</mo><mn id="S2.F1.8.m4.1.1.3" xref="S2.F1.8.m4.1.1.3.cmml">4</mn></mrow></math>

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/9910462

Formulas:

1-

\partial_{t} 𝐔 + \partial_{i} 𝐅^{(i)} = 0

2-

𝐅^{(i)} (𝐔)

3-

i = 1, 2, 3

4-

𝐔 = {(D, S^{1}, S^{2}, S^{3}, τ)}^{T}

5-

𝐅^{(i)} = {(D v^{i}, S^{1} v^{i} + p δ^{1 i}, S^{2} v^{i} + p δ^{2 i}, S^{3} v^{i} + p δ^{3 i}, S^{i} - D v^{i})}^{T} .

6-

(ρ, v^{i}, ε)

7-

D = ρ W, S^{i} = ρ h W^{2} v^{i}, τ = ρ h W^{2} - p - D

8-

W = {(1 - v^{2})}^{- 1 / 2}

9-

h = 1 + ε + p / ρ

10-

ε = \frac{p}{(γ - 1) ρ} .

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/nucl-th/9308020

Formulas:

1-

V (𝐪^{'}, 𝐪)

2-

[𝜶 \cdot 𝐤 + β (m + U_{S}) + U_{V}^{0}] \tilde{u} (𝐤, s) = E \tilde{u} (𝐤, s)

3-

\tilde{G} (𝐪^{'}, 𝐪 | 𝐏, \tilde{z}) = \tilde{V} (𝐪^{'}, 𝐪) + \int \frac{d^{3} k}{{(2 π)}^{3}} \tilde{V} (𝐪^{'}, 𝐤) \frac{{\tilde{m}}^{2}}{{\tilde{E}}_{(1 / 2) 𝐏 + 𝐤}^{2}} \frac{Q (𝐤, 𝐏)}{2 {\tilde{E}}_{(1 / 2) 𝐏 + 𝐪} - 2 {\tilde{E}}_{(1 / 2) 𝐏 + 𝐤}} \tilde{G} (𝐤, 𝐪 | 𝐏, \tilde{z})

4-

\tilde{m} = m + U_{S} and {\tilde{E}}_{𝐤} = {(𝐤^{2} + {\tilde{m}}^{2})}^{(1 / 2)}

5-

ℒ = \bar{ψ} [i γ_{μ} \partial^{μ} - m - g_{σ} (ρ) ϕ_{σ} - g_{ω} (ρ) γ_{μ} ϕ_{ω}^{μ}] ψ

6-

+ \frac{1}{2} {(\partial^{μ} ϕ_{σ})}^{2} - \frac{1}{2} m_{σ}^{2} ϕ_{σ}^{2} - \frac{1}{4} {(\partial_{μ} ϕ_{ω}^{ν} - \partial_{ν} ϕ_{ω}^{μ})}^{2} + \frac{1}{2} m_{ω}^{2} ϕ_{ω}^{μ 2}

7-

Σ (k_{μ}) = Σ_{S} (k_{μ}) + γ^{0} Σ_{0} (k_{μ}) + 𝜸 \cdot 𝐤 Σ_{V} (k_{μ})

8-

Σ_{S} (ρ, k) = - \frac{2}{π^{2}} \frac{g_{σ}^{2} (ρ)}{m_{σ}^{2}} \int_{0}^{k_{F}} 𝑑 q q^{2} \frac{m_{q}^{*}}{E_{q}^{*}}

9-

+ \frac{1}{16 π^{2} k} \int_{0}^{k_{F}} 𝑑 q q \frac{m_{q}^{*}}{E_{q}^{*}} [g_{σ}^{2} (ρ) Θ_{σ} (k, q) - 4 g_{ω}^{2} (ρ) Θ_{ω} (k, q)]

10-

Σ_{0} (ρ, k) = \frac{2}{π^{2}} \frac{g_{ω}^{2} (ρ)}{m_{ω}^{2}} \int_{0}^{k_{F}} 𝑑 q q^{2}

Formulas (html):

Correct Categorie: nucl-th

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0410239

Formulas:

1-

r i u z g

2-

r_{P e t r o s i a n} = 17.77

3-

r_{P e t r o s i a n} = 19.5

4-

u g r i z

5-

s = - 0.249 u + 0.794 g - 0.555 r + 0.234

6-

u - g, g - r

7-

w = - 0.227 g + 0.792 r - 0.567 i + 0.050

8-

r - i, g - r

9-

x = 0.707 g - 0.707 r - 0.983

10-

r - i, g - r

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1310.6130

Formulas:

1-

F m \bar{3} m

2-

F \bar{4} 3 m

3-

F m m m

4-

I 4 / m m m

5-

l_{m a x}

6-

H_{e x} = - \sum_{i j α β} J_{i j}^{α β} e_{i}^{α} . e_{j}^{β}

7-

{}^{α β}_{i j}

8-

{}^{α β}_{i j}

9-

{}^{α β}_{i j}

10-

J_{i j}^{α β} = \frac{1}{4 π} \int^{E_{F}} 𝑑 E I m T r_{L} {Δ_{i}^{α} τ_{i j ↑}^{α β} Δ_{j}^{β} τ_{i j ↓}^{α β}}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/hep-ph/0509053

Formulas:

1-

d N / d η

2-

m_{T} = \sqrt{m^{2} + p_{T}^{2}}

3-

η = \frac{1}{2} \frac{p_{0} + p_{z}}{p_{0} - p_{z}}

4-

η_{s} = \frac{1}{2} \frac{t + z}{t - z}

5-

d N / d η

6-

d N / d η

7-

d N / d η

8-

d N d η

9-

d N / d η

10-

d N / d η

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/0801.0860

Formulas:

1-

E (k) \propto ϵ^{2 / 3} k^{- 5 / 3}

2-

F_{A} (t)

3-

F_{A} (t)

4-

F_{A} (t)

5-

σ_{F_{A}} \propto ρ S_{P} σ_{V}

6-

S_{P} = L h

7-

I (t) / ⟨ I ⟩

8-

F_{A} (t) V (t)

9-

I (t) < 0

10-

σ_{I} \propto ⟨ I ⟩ = c ρ S_{P} σ_{V}^{2}

Formulas (html):

Correct Categorie: physics

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/9812342

Formulas:

1-

< T_{e f f} >

2-

U_{S} = Q_{H^{o}} / (4 π R_{S}^{2} n c)

3-

\bar{U} = 3 U_{S}

4-

\bar{U} \propto Q_{H^{o}} (t)

5-

\bar{U} \propto {(Q_{H^{o}} (t))}^{\frac{1}{3}}

6-

\bar{U} \propto t^{- \frac{6}{5}} Q_{H^{o}} (t)

7-

\bar{U} \propto t^{- 1} {(Q_{H^{o}} (t))}^{\frac{1}{3}}

8-

M_{i o n}

9-

< T_{e f f} >

10-

< T_{e f f} >

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1811.12055

Formulas:

1-

N = (n - 1) \times 10^{6}

2-

Z_{D}^{H} = \frac{0.62291}{T^{2}} + 0.0023081 P

3-

Z_{W}^{H} = 0.07402 \cdot \frac{e}{T^{2}} \cdot H_{T}

4-

Z_{D}^{S} = \frac{0.0022767 P}{1 - 0.00266 \cos 2 ϕ - 0.00028 h}

5-

Z_{W}^{S} = 0.002277 (\frac{1255}{T} + 0.05) e

6-

e = \frac{5854}{T^{5}} 10^{20 - \frac{2950}{T}}

7-

N = 77.6 \frac{P}{T} + 6.48 \frac{e}{T} + 3.75 \times 10^{5} \frac{e}{T}

8-

\frac{0.62291}{T^{2}} + 3.14 \times 10^{- 5} P

9-

Z_{D}^{H} - Z_{D}^{S} \approx \frac{0.62291}{T^{2}} + 3.14 \times 10^{- 5} P

10-

h < 1 k m

Formulas (html):

Correct Categorie: physics

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1808.10361

Formulas:

1-

i = 1, \dots, N

2-

f = \frac{α}{4} \sum_{i}^{N} ϕ_{i}^{2} {(ϕ_{i} - ϕ_{0})}^{2} + \frac{K}{2} \sum_{i}^{N} {(\nabla ϕ_{i})}^{2} + ϵ \sum_{i, j, i < j} ϕ_{i} ϕ_{j} .

3-

γ = \sqrt{8 K α / 9}

4-

\frac{\partial ϕ_{i}}{\partial t} + \nabla \cdot (𝐯 ϕ_{i}) = M \nabla^{2} μ_{i},

5-

μ_{i} = \partial f / \partial ϕ_{i} - \partial_{α} f / \partial (\partial_{α} ϕ)

6-

ρ (\frac{\partial}{\partial t} + 𝐯 \cdot \nabla) 𝐯 = - \nabla p - \sum_{i} ϕ_{i} \nabla μ_{i} + η_{0} \nabla^{2} 𝐯,

7-

\sum_{i} ϕ_{i} \nabla μ_{i}

8-

\sum_{i} ϕ_{i} \nabla μ_{i}

9-

i = 1, \dots, N

10-

\frac{\partial μ_{i}}{\partial z} = 0, \frac{\partial \nabla^{2} ϕ_{i}}{\partial z} = 0 .

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1103.3403

Formulas:

1-

ρ (T) = ρ_{0} + A T^{n}

2-

α_{i} = \frac{1}{L_{i}} \frac{d L_{i}}{d T}

3-

β = Σ (α_{i})

4-

ρ_{c, P, /, / a}

5-

T_{a c} = | V_{a c} | / S_{t h}

6-

\frac{d T_{C}}{d P_{i}} = \frac{V_{m} Δ α_{i} T_{C}}{Δ C_{p}}

7-

\frac{d T_{C}}{d P} = \frac{V_{m} Δ β T_{C}}{Δ C_{p}}

8-

d ρ (T) / d T

9-

d ρ (T) / d T

10-

d ρ / d T

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/0911.3678

Formulas:

1-

< T / T_{c} <

2-

H_{m a x}

3-

J_{c} (T)

4-

J_{c} (H)

5-

U_{b u l k}

6-

U_{s u r f a c e}

7-

U_{b u l k} < U_{s u r f a c e}

8-

T_{s i n t}

9-

d J_{c} / d H

10-

d H / d t \approx 0.1

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0312386

Formulas:

1-

Y_{a t m o s}

2-

T_{e f f}

3-

T_{e f f}

4-

T_{e f f}

5-

Y_{a t m o s}

6-

T_{e f f}

7-

Y_{a t m o s}

8-

T_{e f f}

9-

T_{e f f}

10-

T_{e f f}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1206.4892

Formulas:

1-

a_{p} = 7.5 μ

2-

n_{d} = 3 \times 10^{5} {cm}^{- 3}

3-

{\bar{r}}_{d} = {(3 / 4 π n_{d})}^{1 / 3} = 9.3 \times 10^{- 3}

4-

β_{d p} = 2 Z_{p} Z_{d} e^{2} / λ M_{d} u^{2}

5-

Z_{p} Z_{d} e^{2} / λ

6-

M_{d} u^{2} / 2

7-

M_{d} = 1.31 \times 10^{- 11}

8-

λ ≃ 6 \times 10^{- 3}

9-

β_{d p} ≃ 100

10-

≃ λ \ln β_{d p} ≃ 2.7 \times 10^{- 2}

Formulas (html):

Correct Categorie: physics

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/0609510

Formulas:

1-

𝐰_{𝐫}^{𝗇𝖾𝗐} = 𝐰_{𝐫}^{𝗈𝗅𝖽} + ε \cdot g_{𝐫𝐬} \cdot {(𝐯 - 𝐰_{𝐫}^{𝗈𝗅𝖽})}^{K}

2-

| 𝐰_{𝐬} - 𝐯 | = \min_{𝐫 \in R} | 𝐰_{𝐫} - 𝐯 |

3-

{\vec{w}}_{\vec{r} + {\vec{e}}_{i}} - {\vec{w}}_{\vec{r}}

4-

sgn (w_{r + 1} - w_{r})

5-

χ ({{\vec{w}}_{\vec{r}}}) :=

6-

1 - \frac{1}{N} | \sum_{\vec{r}} sgn (det (({\vec{w}}_{\vec{r} + {\vec{e}}_{1}} - {\vec{w}}_{\vec{r}}), \dots ({\vec{w}}_{\vec{r} + {\vec{e}}_{i}} - {\vec{w}}_{\vec{r}}), \dots ({\vec{w}}_{\vec{r} + {\vec{e}}_{d}} - {\vec{w}}_{\vec{r}}))) | .

7-

(1 - | N_{+} - N_{-} | / N)

8-

\sim \sin (π x_{i})

9-

ε_{\max} (σ)

10-

\exp (- t / k)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/2009.00135

Formulas:

1-

{ex}^{*} (n, F)

2-

{ex}^{*} (n, H, F)

3-

{ex}^{*} (n, C_{ℓ}, P_{ℓ})

4-

ℓ = 3, 4, 5

5-

{ex}^{*} (n, P_{5})

6-

{ex}^{*} (n, P_{ℓ})

7-

{ex}^{*} (n, F)

8-

ex (n, F) \leq {ex}^{*} (n, F)

9-

ex (n, F) \leq {ex}^{*} (n, F) \leq ex (n, F) + o (n^{2}) .

10-

ex (n, F)

Formulas (html):

Correct Categorie: math

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0510760

Formulas:

1-

F \equiv g_{p} {[α^{2} / μ]}^{1.57}

2-

[Δ F / F] = (0.44 \pm {0.36}^{stat} \pm {1.0}^{syst}) \times 10^{- 5}

3-

[Δ α / α] < 6.7 \times 10^{- 6}

4-

[Δ μ / μ] < 1.4 \times 10^{- 5}

5-

μ \equiv m_{e} / m_{p}

6-

(1 / α) [Δ α / Δ t] < 4 \times 10^{- 15}

7-

Δ α / α < 1.2 \times 10^{- 7}

8-

Δ α / α = (- 5.4 \pm 1.2) \times 10^{- 6}

9-

Δ α / α = (- 0.6 \pm 0.6) \times 10^{- 6}

10-

(- 10^{3} \times τ)

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/0803.1683

Formulas:

1-

M_{t} = 172.6 \pm 0.8 (stat) \pm 1.1 (syst) GeV / c^{2}

2-

1.4 GeV / c^{2}

3-

t \bar{t} \to q q^{'} b q q^{'} \bar{b}

4-

t \bar{t} \to ℓ ν q q^{'} b \bar{b}

5-

t \bar{t} \to ℓ^{+} ν b ℓ^{-} \bar{ν} \bar{b}

6-

1.9 - 2.1 {fb}^{- 1}

7-

W \to q q^{'}

8-

W \to q q^{'}

9-

W \to q q^{'}

10-

W \to q q^{'}

Formulas (html):

Correct Categorie: hep-ex

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1803.05577

Formulas:

1-

N_{z} (t) \in ℕ

2-

𝒩_{z} (t) = {1, \dots, N_{z} (t)}

3-

i = N_{z} (t) + 1

4-

N_{z} (t) + 1

5-

{\dot{p}}_{i} (t) = v_{i} (t), p_{i} (t_{i}^{0}) = 0; {\dot{v}}_{i} (t) = u_{i} (t), v_{i} (t_{i}^{0}) given

6-

p_{i} (t)

7-

v_{i} (t)

8-

u_{i} (t)

9-

[t_{i}^{0}, t_{i}^{f}]

10-

\begin{matrix} u_{i, m i n} & \leq u_{i} (t) \leq u_{i, m a x}, and \\ 0 & \leq v_{m i n} \leq v_{i} (t) \leq v_{m a x}, \forall t \in [t_{i}^{0}, t_{i}^{m}], \end{matrix}

Formulas (html):

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xref="S2.p2.4.m4.5.5.3.2.cmml"><mi class="ltx_font_mathcaligraphic" id="S2.p2.4.m4.5.5.3.2.2" xref="S2.p2.4.m4.5.5.3.2.2.cmml">𝒩</mi><mi id="S2.p2.4.m4.5.5.3.2.3" xref="S2.p2.4.m4.5.5.3.2.3.cmml">z</mi></msub><mo id="S2.p2.4.m4.5.5.3.1" xref="S2.p2.4.m4.5.5.3.1.cmml">⁢</mo><mrow id="S2.p2.4.m4.5.5.3.3.2" xref="S2.p2.4.m4.5.5.3.cmml"><mo stretchy="false" id="S2.p2.4.m4.5.5.3.3.2.1" xref="S2.p2.4.m4.5.5.3.cmml">(</mo><mi id="S2.p2.4.m4.1.1" xref="S2.p2.4.m4.1.1.cmml">t</mi><mo stretchy="false" id="S2.p2.4.m4.5.5.3.3.2.2" xref="S2.p2.4.m4.5.5.3.cmml">)</mo></mrow></mrow><mo id="S2.p2.4.m4.5.5.2" xref="S2.p2.4.m4.5.5.2.cmml">=</mo><mrow id="S2.p2.4.m4.5.5.1.1" xref="S2.p2.4.m4.5.5.1.2.cmml"><mo stretchy="false" id="S2.p2.4.m4.5.5.1.1.2" xref="S2.p2.4.m4.5.5.1.2.cmml">{</mo><mn id="S2.p2.4.m4.3.3" xref="S2.p2.4.m4.3.3.cmml">1</mn><mo id="S2.p2.4.m4.5.5.1.1.3" xref="S2.p2.4.m4.5.5.1.2.cmml">,</mo><mi mathvariant="normal" id="S2.p2.4.m4.4.4" xref="S2.p2.4.m4.4.4.cmml">…</mi><mo id="S2.p2.4.m4.5.5.1.1.4" xref="S2.p2.4.m4.5.5.1.2.cmml">,</mo><mrow id="S2.p2.4.m4.5.5.1.1.1" xref="S2.p2.4.m4.5.5.1.1.1.cmml"><msub id="S2.p2.4.m4.5.5.1.1.1.2" xref="S2.p2.4.m4.5.5.1.1.1.2.cmml"><mi id="S2.p2.4.m4.5.5.1.1.1.2.2" xref="S2.p2.4.m4.5.5.1.1.1.2.2.cmml">N</mi><mi id="S2.p2.4.m4.5.5.1.1.1.2.3" xref="S2.p2.4.m4.5.5.1.1.1.2.3.cmml">z</mi></msub><mo id="S2.p2.4.m4.5.5.1.1.1.1" xref="S2.p2.4.m4.5.5.1.1.1.1.cmml">⁢</mo><mrow id="S2.p2.4.m4.5.5.1.1.1.3.2" xref="S2.p2.4.m4.5.5.1.1.1.cmml"><mo stretchy="false" id="S2.p2.4.m4.5.5.1.1.1.3.2.1" xref="S2.p2.4.m4.5.5.1.1.1.cmml">(</mo><mi id="S2.p2.4.m4.2.2" xref="S2.p2.4.m4.2.2.cmml">t</mi><mo stretchy="false" id="S2.p2.4.m4.5.5.1.1.1.3.2.2" xref="S2.p2.4.m4.5.5.1.1.1.cmml">)</mo></mrow></mrow><mo stretchy="false" id="S2.p2.4.m4.5.5.1.1.5" xref="S2.p2.4.m4.5.5.1.2.cmml">}</mo></mrow></mrow></math>, <math><mrow id="S2.p2.6.m6.1.2" xref="S2.p2.6.m6.1.2.cmml"><mi id="S2.p2.6.m6.1.2.2" xref="S2.p2.6.m6.1.2.2.cmml">i</mi><mo id="S2.p2.6.m6.1.2.1" xref="S2.p2.6.m6.1.2.1.cmml">=</mo><mrow id="S2.p2.6.m6.1.2.3" xref="S2.p2.6.m6.1.2.3.cmml"><mrow id="S2.p2.6.m6.1.2.3.2" xref="S2.p2.6.m6.1.2.3.2.cmml"><msub id="S2.p2.6.m6.1.2.3.2.2" xref="S2.p2.6.m6.1.2.3.2.2.cmml"><mi id="S2.p2.6.m6.1.2.3.2.2.2" xref="S2.p2.6.m6.1.2.3.2.2.2.cmml">N</mi><mi id="S2.p2.6.m6.1.2.3.2.2.3" xref="S2.p2.6.m6.1.2.3.2.2.3.cmml">z</mi></msub><mo id="S2.p2.6.m6.1.2.3.2.1" xref="S2.p2.6.m6.1.2.3.2.1.cmml">⁢</mo><mrow id="S2.p2.6.m6.1.2.3.2.3.2" xref="S2.p2.6.m6.1.2.3.2.cmml"><mo stretchy="false" id="S2.p2.6.m6.1.2.3.2.3.2.1" xref="S2.p2.6.m6.1.2.3.2.cmml">(</mo><mi id="S2.p2.6.m6.1.1" xref="S2.p2.6.m6.1.1.cmml">t</mi><mo stretchy="false" id="S2.p2.6.m6.1.2.3.2.3.2.2" xref="S2.p2.6.m6.1.2.3.2.cmml">)</mo></mrow></mrow><mo id="S2.p2.6.m6.1.2.3.1" xref="S2.p2.6.m6.1.2.3.1.cmml">+</mo><mn id="S2.p2.6.m6.1.2.3.3" xref="S2.p2.6.m6.1.2.3.3.cmml">1</mn></mrow></mrow></math>, <math><mrow id="S2.p2.7.m7.1.2" xref="S2.p2.7.m7.1.2.cmml"><mrow id="S2.p2.7.m7.1.2.2" xref="S2.p2.7.m7.1.2.2.cmml"><msub id="S2.p2.7.m7.1.2.2.2" xref="S2.p2.7.m7.1.2.2.2.cmml"><mi id="S2.p2.7.m7.1.2.2.2.2" xref="S2.p2.7.m7.1.2.2.2.2.cmml">N</mi><mi id="S2.p2.7.m7.1.2.2.2.3" xref="S2.p2.7.m7.1.2.2.2.3.cmml">z</mi></msub><mo id="S2.p2.7.m7.1.2.2.1" xref="S2.p2.7.m7.1.2.2.1.cmml">⁢</mo><mrow id="S2.p2.7.m7.1.2.2.3.2" xref="S2.p2.7.m7.1.2.2.cmml"><mo stretchy="false" id="S2.p2.7.m7.1.2.2.3.2.1" xref="S2.p2.7.m7.1.2.2.cmml">(</mo><mi id="S2.p2.7.m7.1.1" xref="S2.p2.7.m7.1.1.cmml">t</mi><mo stretchy="false" id="S2.p2.7.m7.1.2.2.3.2.2" xref="S2.p2.7.m7.1.2.2.cmml">)</mo></mrow></mrow><mo id="S2.p2.7.m7.1.2.1" xref="S2.p2.7.m7.1.2.1.cmml">+</mo><mn id="S2.p2.7.m7.1.2.3" xref="S2.p2.7.m7.1.2.3.cmml">1</mn></mrow></math>, <math><mrow id="S2.E1.m1.6.6" xref="S2.E1.m1.6.6.cmml"><mrow id="S2.E1.m1.6.6.4" xref="S2.E1.m1.6.6.4.cmml"><msub id="S2.E1.m1.6.6.4.2" xref="S2.E1.m1.6.6.4.2.cmml"><mover accent="true" id="S2.E1.m1.6.6.4.2.2" xref="S2.E1.m1.6.6.4.2.2.cmml"><mi id="S2.E1.m1.6.6.4.2.2.2" xref="S2.E1.m1.6.6.4.2.2.2.cmml">p</mi><mo id="S2.E1.m1.6.6.4.2.2.1" xref="S2.E1.m1.6.6.4.2.2.1.cmml">˙</mo></mover><mi id="S2.E1.m1.6.6.4.2.3" xref="S2.E1.m1.6.6.4.2.3.cmml">i</mi></msub><mo id="S2.E1.m1.6.6.4.1" xref="S2.E1.m1.6.6.4.1.cmml">⁢</mo><mrow id="S2.E1.m1.6.6.4.3.2" xref="S2.E1.m1.6.6.4.cmml"><mo stretchy="false" id="S2.E1.m1.6.6.4.3.2.1" xref="S2.E1.m1.6.6.4.cmml">(</mo><mi id="S2.E1.m1.1.1" xref="S2.E1.m1.1.1.cmml">t</mi><mo stretchy="false" id="S2.E1.m1.6.6.4.3.2.2" xref="S2.E1.m1.6.6.4.cmml">)</mo></mrow></mrow><mo id="S2.E1.m1.6.6.5" xref="S2.E1.m1.6.6.5.cmml">=</mo><mrow id="S2.E1.m1.5.5.1" xref="S2.E1.m1.5.5.1.cmml"><msub id="S2.E1.m1.5.5.1.3" xref="S2.E1.m1.5.5.1.3.cmml"><mi id="S2.E1.m1.5.5.1.3.2" xref="S2.E1.m1.5.5.1.3.2.cmml">v</mi><mi id="S2.E1.m1.5.5.1.3.3" xref="S2.E1.m1.5.5.1.3.3.cmml">i</mi></msub><mo id="S2.E1.m1.5.5.1.2" xref="S2.E1.m1.5.5.1.2.cmml">⁢</mo><mrow id="S2.E1.m1.5.5.1.4.2" xref="S2.E1.m1.5.5.1.cmml"><mo stretchy="false" id="S2.E1.m1.5.5.1.4.2.1" xref="S2.E1.m1.5.5.1.cmml">(</mo><mi id="S2.E1.m1.2.2" xref="S2.E1.m1.2.2.cmml">t</mi><mo stretchy="false" id="S2.E1.m1.5.5.1.4.2.2" xref="S2.E1.m1.5.5.1.cmml">)</mo></mrow><mo id="S2.E1.m1.5.5.1.2a" xref="S2.E1.m1.5.5.1.2.cmml">⁢</mo><mpadded width="+3.3pt" id="S2.E1.m1.5.5.1.5" xref="S2.E1.m1.5.5.1.5b.cmml"><mtext id="S2.E1.m1.5.5.1.5a" xref="S2.E1.m1.5.5.1.5b.cmml">, </mtext></mpadded><mo id="S2.E1.m1.5.5.1.2b" xref="S2.E1.m1.5.5.1.2.cmml">⁢</mo><msub id="S2.E1.m1.5.5.1.6" xref="S2.E1.m1.5.5.1.6.cmml"><mi id="S2.E1.m1.5.5.1.6.2" xref="S2.E1.m1.5.5.1.6.2.cmml">p</mi><mi id="S2.E1.m1.5.5.1.6.3" xref="S2.E1.m1.5.5.1.6.3.cmml">i</mi></msub><mo id="S2.E1.m1.5.5.1.2c" xref="S2.E1.m1.5.5.1.2.cmml">⁢</mo><mrow id="S2.E1.m1.5.5.1.1.1" xref="S2.E1.m1.5.5.1.1.1.1.cmml"><mo stretchy="false" id="S2.E1.m1.5.5.1.1.1.2" xref="S2.E1.m1.5.5.1.1.1.1.cmml">(</mo><msubsup id="S2.E1.m1.5.5.1.1.1.1" xref="S2.E1.m1.5.5.1.1.1.1.cmml"><mi id="S2.E1.m1.5.5.1.1.1.1.2.2" xref="S2.E1.m1.5.5.1.1.1.1.2.2.cmml">t</mi><mi id="S2.E1.m1.5.5.1.1.1.1.2.3" xref="S2.E1.m1.5.5.1.1.1.1.2.3.cmml">i</mi><mn id="S2.E1.m1.5.5.1.1.1.1.3" xref="S2.E1.m1.5.5.1.1.1.1.3.cmml">0</mn></msubsup><mo stretchy="false" id="S2.E1.m1.5.5.1.1.1.3" xref="S2.E1.m1.5.5.1.1.1.1.cmml">)</mo></mrow></mrow><mo id="S2.E1.m1.6.6.6" xref="S2.E1.m1.6.6.6.cmml">=</mo><mrow id="S2.E1.m1.6.6.7" xref="S2.E1.m1.6.6.7.cmml"><mn id="S2.E1.m1.6.6.7.2" xref="S2.E1.m1.6.6.7.2.cmml">0</mn><mo id="S2.E1.m1.6.6.7.1" xref="S2.E1.m1.6.6.7.1.cmml">⁢</mo><mpadded width="+3.3pt" id="S2.E1.m1.6.6.7.3" xref="S2.E1.m1.6.6.7.3b.cmml"><mtext id="S2.E1.m1.6.6.7.3a" xref="S2.E1.m1.6.6.7.3b.cmml">; </mtext></mpadded><mo id="S2.E1.m1.6.6.7.1a" xref="S2.E1.m1.6.6.7.1.cmml">⁢</mo><msub id="S2.E1.m1.6.6.7.4" xref="S2.E1.m1.6.6.7.4.cmml"><mover accent="true" id="S2.E1.m1.6.6.7.4.2" xref="S2.E1.m1.6.6.7.4.2.cmml"><mi id="S2.E1.m1.6.6.7.4.2.2" xref="S2.E1.m1.6.6.7.4.2.2.cmml">v</mi><mo id="S2.E1.m1.6.6.7.4.2.1" xref="S2.E1.m1.6.6.7.4.2.1.cmml">˙</mo></mover><mi id="S2.E1.m1.6.6.7.4.3" xref="S2.E1.m1.6.6.7.4.3.cmml">i</mi></msub><mo id="S2.E1.m1.6.6.7.1b" xref="S2.E1.m1.6.6.7.1.cmml">⁢</mo><mrow id="S2.E1.m1.6.6.7.5.2" xref="S2.E1.m1.6.6.7.cmml"><mo stretchy="false" id="S2.E1.m1.6.6.7.5.2.1" xref="S2.E1.m1.6.6.7.cmml">(</mo><mi id="S2.E1.m1.3.3" xref="S2.E1.m1.3.3.cmml">t</mi><mo stretchy="false" id="S2.E1.m1.6.6.7.5.2.2" xref="S2.E1.m1.6.6.7.cmml">)</mo></mrow></mrow><mo id="S2.E1.m1.6.6.8" xref="S2.E1.m1.6.6.8.cmml">=</mo><mrow id="S2.E1.m1.6.6.2" xref="S2.E1.m1.6.6.2.cmml"><msub id="S2.E1.m1.6.6.2.3" xref="S2.E1.m1.6.6.2.3.cmml"><mi id="S2.E1.m1.6.6.2.3.2" xref="S2.E1.m1.6.6.2.3.2.cmml">u</mi><mi id="S2.E1.m1.6.6.2.3.3" xref="S2.E1.m1.6.6.2.3.3.cmml">i</mi></msub><mo id="S2.E1.m1.6.6.2.2" xref="S2.E1.m1.6.6.2.2.cmml">⁢</mo><mrow id="S2.E1.m1.6.6.2.4.2" xref="S2.E1.m1.6.6.2.cmml"><mo stretchy="false" id="S2.E1.m1.6.6.2.4.2.1" xref="S2.E1.m1.6.6.2.cmml">(</mo><mi id="S2.E1.m1.4.4" xref="S2.E1.m1.4.4.cmml">t</mi><mo stretchy="false" id="S2.E1.m1.6.6.2.4.2.2" xref="S2.E1.m1.6.6.2.cmml">)</mo></mrow><mo id="S2.E1.m1.6.6.2.2a" xref="S2.E1.m1.6.6.2.2.cmml">⁢</mo><mtext id="S2.E1.m1.6.6.2.5" xref="S2.E1.m1.6.6.2.5a.cmml">, </mtext><mo id="S2.E1.m1.6.6.2.2b" xref="S2.E1.m1.6.6.2.2.cmml">⁢</mo><msub id="S2.E1.m1.6.6.2.6" xref="S2.E1.m1.6.6.2.6.cmml"><mi id="S2.E1.m1.6.6.2.6.2" xref="S2.E1.m1.6.6.2.6.2.cmml">v</mi><mi id="S2.E1.m1.6.6.2.6.3" xref="S2.E1.m1.6.6.2.6.3.cmml">i</mi></msub><mo id="S2.E1.m1.6.6.2.2c" xref="S2.E1.m1.6.6.2.2.cmml">⁢</mo><mrow id="S2.E1.m1.6.6.2.1.1" xref="S2.E1.m1.6.6.2.1.1.1.cmml"><mo stretchy="false" id="S2.E1.m1.6.6.2.1.1.2" xref="S2.E1.m1.6.6.2.1.1.1.cmml">(</mo><msubsup id="S2.E1.m1.6.6.2.1.1.1" xref="S2.E1.m1.6.6.2.1.1.1.cmml"><mi id="S2.E1.m1.6.6.2.1.1.1.2.2" xref="S2.E1.m1.6.6.2.1.1.1.2.2.cmml">t</mi><mi id="S2.E1.m1.6.6.2.1.1.1.2.3" xref="S2.E1.m1.6.6.2.1.1.1.2.3.cmml">i</mi><mn id="S2.E1.m1.6.6.2.1.1.1.3" xref="S2.E1.m1.6.6.2.1.1.1.3.cmml">0</mn></msubsup><mo stretchy="false" id="S2.E1.m1.6.6.2.1.1.3" xref="S2.E1.m1.6.6.2.1.1.1.cmml">)</mo></mrow><mo id="S2.E1.m1.6.6.2.2d" xref="S2.E1.m1.6.6.2.2.cmml">⁢</mo><mtext id="S2.E1.m1.6.6.2.7" xref="S2.E1.m1.6.6.2.7a.cmml"> given</mtext></mrow></mrow></math>, <math><mrow id="S2.p3.1.m1.1.2" xref="S2.p3.1.m1.1.2.cmml"><msub id="S2.p3.1.m1.1.2.2" xref="S2.p3.1.m1.1.2.2.cmml"><mi id="S2.p3.1.m1.1.2.2.2" xref="S2.p3.1.m1.1.2.2.2.cmml">p</mi><mi id="S2.p3.1.m1.1.2.2.3" xref="S2.p3.1.m1.1.2.2.3.cmml">i</mi></msub><mo id="S2.p3.1.m1.1.2.1" xref="S2.p3.1.m1.1.2.1.cmml">⁢</mo><mrow id="S2.p3.1.m1.1.2.3.2" xref="S2.p3.1.m1.1.2.cmml"><mo stretchy="false" id="S2.p3.1.m1.1.2.3.2.1" xref="S2.p3.1.m1.1.2.cmml">(</mo><mi id="S2.p3.1.m1.1.1" xref="S2.p3.1.m1.1.1.cmml">t</mi><mo stretchy="false" id="S2.p3.1.m1.1.2.3.2.2" xref="S2.p3.1.m1.1.2.cmml">)</mo></mrow></mrow></math>, <math><mrow id="S2.p3.2.m2.1.2" xref="S2.p3.2.m2.1.2.cmml"><msub id="S2.p3.2.m2.1.2.2" xref="S2.p3.2.m2.1.2.2.cmml"><mi id="S2.p3.2.m2.1.2.2.2" xref="S2.p3.2.m2.1.2.2.2.cmml">v</mi><mi id="S2.p3.2.m2.1.2.2.3" xref="S2.p3.2.m2.1.2.2.3.cmml">i</mi></msub><mo id="S2.p3.2.m2.1.2.1" xref="S2.p3.2.m2.1.2.1.cmml">⁢</mo><mrow id="S2.p3.2.m2.1.2.3.2" xref="S2.p3.2.m2.1.2.cmml"><mo stretchy="false" id="S2.p3.2.m2.1.2.3.2.1" xref="S2.p3.2.m2.1.2.cmml">(</mo><mi id="S2.p3.2.m2.1.1" xref="S2.p3.2.m2.1.1.cmml">t</mi><mo stretchy="false" id="S2.p3.2.m2.1.2.3.2.2" xref="S2.p3.2.m2.1.2.cmml">)</mo></mrow></mrow></math>, <math><mrow id="S2.p3.3.m3.1.2" xref="S2.p3.3.m3.1.2.cmml"><msub id="S2.p3.3.m3.1.2.2" xref="S2.p3.3.m3.1.2.2.cmml"><mi id="S2.p3.3.m3.1.2.2.2" xref="S2.p3.3.m3.1.2.2.2.cmml">u</mi><mi id="S2.p3.3.m3.1.2.2.3" xref="S2.p3.3.m3.1.2.2.3.cmml">i</mi></msub><mo id="S2.p3.3.m3.1.2.1" xref="S2.p3.3.m3.1.2.1.cmml">⁢</mo><mrow id="S2.p3.3.m3.1.2.3.2" xref="S2.p3.3.m3.1.2.cmml"><mo stretchy="false" id="S2.p3.3.m3.1.2.3.2.1" xref="S2.p3.3.m3.1.2.cmml">(</mo><mi id="S2.p3.3.m3.1.1" xref="S2.p3.3.m3.1.1.cmml">t</mi><mo stretchy="false" id="S2.p3.3.m3.1.2.3.2.2" xref="S2.p3.3.m3.1.2.cmml">)</mo></mrow></mrow></math>, <math><mrow id="S2.p3.5.m5.2.2.2" xref="S2.p3.5.m5.2.2.3.cmml"><mo stretchy="false" id="S2.p3.5.m5.2.2.2.3" xref="S2.p3.5.m5.2.2.3.cmml">[</mo><msubsup id="S2.p3.5.m5.1.1.1.1" xref="S2.p3.5.m5.1.1.1.1.cmml"><mi id="S2.p3.5.m5.1.1.1.1.2.2" xref="S2.p3.5.m5.1.1.1.1.2.2.cmml">t</mi><mi id="S2.p3.5.m5.1.1.1.1.2.3" xref="S2.p3.5.m5.1.1.1.1.2.3.cmml">i</mi><mn id="S2.p3.5.m5.1.1.1.1.3" xref="S2.p3.5.m5.1.1.1.1.3.cmml">0</mn></msubsup><mo id="S2.p3.5.m5.2.2.2.4" xref="S2.p3.5.m5.2.2.3.cmml">,</mo><msubsup id="S2.p3.5.m5.2.2.2.2" xref="S2.p3.5.m5.2.2.2.2.cmml"><mi id="S2.p3.5.m5.2.2.2.2.2.2" xref="S2.p3.5.m5.2.2.2.2.2.2.cmml">t</mi><mi id="S2.p3.5.m5.2.2.2.2.2.3" xref="S2.p3.5.m5.2.2.2.2.2.3.cmml">i</mi><mi id="S2.p3.5.m5.2.2.2.2.3" xref="S2.p3.5.m5.2.2.2.2.3.cmml">f</mi></msubsup><mo stretchy="false" id="S2.p3.5.m5.2.2.2.5" xref="S2.p3.5.m5.2.2.3.cmml">]</mo></mrow></math>, <math><mtable columnspacing="0pt" displaystyle="true" rowspacing="0pt" id="S2.E2.m1.42.42.2" xref="S2.E2.m1.42.42.3.cmml"><mtr id="S2.E2.m1.42.42.2a" xref="S2.E2.m1.42.42.3.cmml"><mtd columnalign="right" id="S2.E2.m1.42.42.2b" xref="S2.E2.m1.42.42.3.cmml"><msub id="S2.E2.m1.2.2.2.2.2" xref="S2.E2.m1.42.42.3.cmml"><mi id="S2.E2.m1.1.1.1.1.1.1" xref="S2.E2.m1.1.1.1.1.1.1.cmml">u</mi><mrow id="S2.E2.m1.2.2.2.2.2.2.1.2" xref="S2.E2.m1.2.2.2.2.2.2.1.3.cmml"><mi id="S2.E2.m1.2.2.2.2.2.2.1.1" xref="S2.E2.m1.2.2.2.2.2.2.1.1.cmml">i</mi><mo id="S2.E2.m1.2.2.2.2.2.2.1.2.2" xref="S2.E2.m1.2.2.2.2.2.2.1.3.cmml">,</mo><mrow id="S2.E2.m1.2.2.2.2.2.2.1.2.1" xref="S2.E2.m1.2.2.2.2.2.2.1.2.1.cmml"><mi id="S2.E2.m1.2.2.2.2.2.2.1.2.1.2" xref="S2.E2.m1.2.2.2.2.2.2.1.2.1.2.cmml">m</mi><mo id="S2.E2.m1.2.2.2.2.2.2.1.2.1.1" xref="S2.E2.m1.2.2.2.2.2.2.1.2.1.1.cmml">⁢</mo><mi id="S2.E2.m1.2.2.2.2.2.2.1.2.1.3" xref="S2.E2.m1.2.2.2.2.2.2.1.2.1.3.cmml">i</mi><mo id="S2.E2.m1.2.2.2.2.2.2.1.2.1.1a" xref="S2.E2.m1.2.2.2.2.2.2.1.2.1.1.cmml">⁢</mo><mi id="S2.E2.m1.2.2.2.2.2.2.1.2.1.4" xref="S2.E2.m1.2.2.2.2.2.2.1.2.1.4.cmml">n</mi></mrow></mrow></msub></mtd><mtd columnalign="left" id="S2.E2.m1.42.42.2c" xref="S2.E2.m1.42.42.3.cmml"><mrow id="S2.E2.m1.41.41.1.41.14.12.12" xref="S2.E2.m1.42.42.3.cmml"><mrow id="S2.E2.m1.41.41.1.41.14.12.12.1" xref="S2.E2.m1.42.42.3.cmml"><mi id="S2.E2.m1.41.41.1.41.14.12.12.1.2" xref="S2.E2.m1.42.42.3a.cmml"/><mo id="S2.E2.m1.3.3.3.3.1.1" xref="S2.E2.m1.3.3.3.3.1.1.cmml">≤</mo><mrow id="S2.E2.m1.41.41.1.41.14.12.12.1.3" xref="S2.E2.m1.42.42.3.cmml"><msub id="S2.E2.m1.41.41.1.41.14.12.12.1.3.2" xref="S2.E2.m1.42.42.3.cmml"><mi id="S2.E2.m1.4.4.4.4.2.2" xref="S2.E2.m1.4.4.4.4.2.2.cmml">u</mi><mi id="S2.E2.m1.5.5.5.5.3.3.1" xref="S2.E2.m1.5.5.5.5.3.3.1.cmml">i</mi></msub><mo id="S2.E2.m1.41.41.1.41.14.12.12.1.3.1" xref="S2.E2.m1.42.42.3a.cmml">⁢</mo><mrow id="S2.E2.m1.41.41.1.41.14.12.12.1.3.3" xref="S2.E2.m1.42.42.3.cmml"><mo stretchy="false" id="S2.E2.m1.6.6.6.6.4.4" xref="S2.E2.m1.6.6.6.6.4.4.cmml">(</mo><mi id="S2.E2.m1.7.7.7.7.5.5" xref="S2.E2.m1.7.7.7.7.5.5.cmml">t</mi><mo stretchy="false" id="S2.E2.m1.8.8.8.8.6.6" xref="S2.E2.m1.8.8.8.8.6.6.cmml">)</mo></mrow></mrow><mo id="S2.E2.m1.9.9.9.9.7.7" xref="S2.E2.m1.9.9.9.9.7.7.cmml">≤</mo><msub id="S2.E2.m1.41.41.1.41.14.12.12.1.4" xref="S2.E2.m1.42.42.3.cmml"><mi id="S2.E2.m1.10.10.10.10.8.8" xref="S2.E2.m1.10.10.10.10.8.8.cmml">u</mi><mrow id="S2.E2.m1.11.11.11.11.9.9.1.2" xref="S2.E2.m1.11.11.11.11.9.9.1.3.cmml"><mi id="S2.E2.m1.11.11.11.11.9.9.1.1" xref="S2.E2.m1.11.11.11.11.9.9.1.1.cmml">i</mi><mo id="S2.E2.m1.11.11.11.11.9.9.1.2.2" xref="S2.E2.m1.11.11.11.11.9.9.1.3.cmml">,</mo><mrow id="S2.E2.m1.11.11.11.11.9.9.1.2.1" xref="S2.E2.m1.11.11.11.11.9.9.1.2.1.cmml"><mi id="S2.E2.m1.11.11.11.11.9.9.1.2.1.2" xref="S2.E2.m1.11.11.11.11.9.9.1.2.1.2.cmml">m</mi><mo id="S2.E2.m1.11.11.11.11.9.9.1.2.1.1" xref="S2.E2.m1.11.11.11.11.9.9.1.2.1.1.cmml">⁢</mo><mi id="S2.E2.m1.11.11.11.11.9.9.1.2.1.3" xref="S2.E2.m1.11.11.11.11.9.9.1.2.1.3.cmml">a</mi><mo id="S2.E2.m1.11.11.11.11.9.9.1.2.1.1a" xref="S2.E2.m1.11.11.11.11.9.9.1.2.1.1.cmml">⁢</mo><mi id="S2.E2.m1.11.11.11.11.9.9.1.2.1.4" xref="S2.E2.m1.11.11.11.11.9.9.1.2.1.4.cmml">x</mi></mrow></mrow></msub></mrow><mo rspace="12.5pt" id="S2.E2.m1.12.12.12.12.10.10" xref="S2.E2.m1.12.12.12.12.10.10.cmml">,</mo><mtext id="S2.E2.m1.13.13.13.13.11.11" xref="S2.E2.m1.13.13.13.13.11.11a.cmml">and</mtext></mrow></mtd></mtr><mtr id="S2.E2.m1.42.42.2d" xref="S2.E2.m1.42.42.3.cmml"><mtd columnalign="right" id="S2.E2.m1.42.42.2e" xref="S2.E2.m1.42.42.3.cmml"><mn id="S2.E2.m1.14.14.14.1.1.1" xref="S2.E2.m1.14.14.14.1.1.1.cmml">0</mn></mtd><mtd columnalign="left" id="S2.E2.m1.42.42.2f" xref="S2.E2.m1.42.42.3.cmml"><mrow id="S2.E2.m1.42.42.2.42.28.27.27" xref="S2.E2.m1.42.42.3.cmml"><mrow id="S2.E2.m1.42.42.2.42.28.27.27.1" xref="S2.E2.m1.42.42.3.cmml"><mrow id="S2.E2.m1.42.42.2.42.28.27.27.1.1.1" xref="S2.E2.m1.42.42.3.cmml"><mi id="S2.E2.m1.42.42.2.42.28.27.27.1.1.1.2" xref="S2.E2.m1.42.42.3a.cmml"/><mo id="S2.E2.m1.15.15.15.2.1.1" xref="S2.E2.m1.15.15.15.2.1.1.cmml">≤</mo><msub id="S2.E2.m1.42.42.2.42.28.27.27.1.1.1.3" xref="S2.E2.m1.42.42.3.cmml"><mi id="S2.E2.m1.16.16.16.3.2.2" xref="S2.E2.m1.16.16.16.3.2.2.cmml">v</mi><mrow id="S2.E2.m1.17.17.17.4.3.3.1" xref="S2.E2.m1.17.17.17.4.3.3.1.cmml"><mi id="S2.E2.m1.17.17.17.4.3.3.1.2" xref="S2.E2.m1.17.17.17.4.3.3.1.2.cmml">m</mi><mo id="S2.E2.m1.17.17.17.4.3.3.1.1" xref="S2.E2.m1.17.17.17.4.3.3.1.1.cmml">⁢</mo><mi id="S2.E2.m1.17.17.17.4.3.3.1.3" xref="S2.E2.m1.17.17.17.4.3.3.1.3.cmml">i</mi><mo id="S2.E2.m1.17.17.17.4.3.3.1.1a" xref="S2.E2.m1.17.17.17.4.3.3.1.1.cmml">⁢</mo><mi id="S2.E2.m1.17.17.17.4.3.3.1.4" 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id="S2.E2.m1.42.42.2.42.28.27.27.1.1.1.5" xref="S2.E2.m1.42.42.3.cmml"><mi id="S2.E2.m1.25.25.25.12.11.11" xref="S2.E2.m1.25.25.25.12.11.11.cmml">v</mi><mrow id="S2.E2.m1.26.26.26.13.12.12.1" xref="S2.E2.m1.26.26.26.13.12.12.1.cmml"><mi id="S2.E2.m1.26.26.26.13.12.12.1.2" xref="S2.E2.m1.26.26.26.13.12.12.1.2.cmml">m</mi><mo id="S2.E2.m1.26.26.26.13.12.12.1.1" xref="S2.E2.m1.26.26.26.13.12.12.1.1.cmml">⁢</mo><mi id="S2.E2.m1.26.26.26.13.12.12.1.3" xref="S2.E2.m1.26.26.26.13.12.12.1.3.cmml">a</mi><mo id="S2.E2.m1.26.26.26.13.12.12.1.1a" xref="S2.E2.m1.26.26.26.13.12.12.1.1.cmml">⁢</mo><mi id="S2.E2.m1.26.26.26.13.12.12.1.4" xref="S2.E2.m1.26.26.26.13.12.12.1.4.cmml">x</mi></mrow></msub></mrow><mo rspace="12.5pt" id="S2.E2.m1.27.27.27.14.13.13" xref="S2.E2.m1.27.27.27.14.13.13.cmml">,</mo><mrow id="S2.E2.m1.42.42.2.42.28.27.27.1.2.2" xref="S2.E2.m1.42.42.3.cmml"><mrow id="S2.E2.m1.42.42.2.42.28.27.27.1.2.2.3" xref="S2.E2.m1.42.42.3.cmml"><mo id="S2.E2.m1.28.28.28.15.14.14" xref="S2.E2.m1.28.28.28.15.14.14.cmml">∀</mo><mi id="S2.E2.m1.29.29.29.16.15.15" xref="S2.E2.m1.29.29.29.16.15.15.cmml">t</mi></mrow><mo id="S2.E2.m1.30.30.30.17.16.16" xref="S2.E2.m1.30.30.30.17.16.16.cmml">∈</mo><mrow id="S2.E2.m1.42.42.2.42.28.27.27.1.2.2.2.2" xref="S2.E2.m1.42.42.3.cmml"><mo stretchy="false" id="S2.E2.m1.31.31.31.18.17.17" xref="S2.E2.m1.31.31.31.18.17.17.cmml">[</mo><msubsup id="S2.E2.m1.42.42.2.42.28.27.27.1.2.2.1.1.1" xref="S2.E2.m1.42.42.3.cmml"><mi id="S2.E2.m1.32.32.32.19.18.18" xref="S2.E2.m1.32.32.32.19.18.18.cmml">t</mi><mi id="S2.E2.m1.33.33.33.20.19.19.1" xref="S2.E2.m1.33.33.33.20.19.19.1.cmml">i</mi><mn id="S2.E2.m1.34.34.34.21.20.20.1" xref="S2.E2.m1.34.34.34.21.20.20.1.cmml">0</mn></msubsup><mo id="S2.E2.m1.35.35.35.22.21.21" xref="S2.E2.m1.35.35.35.22.21.21.cmml">,</mo><msubsup id="S2.E2.m1.42.42.2.42.28.27.27.1.2.2.2.2.2" xref="S2.E2.m1.42.42.3.cmml"><mi id="S2.E2.m1.36.36.36.23.22.22" xref="S2.E2.m1.36.36.36.23.22.22.cmml">t</mi><mi id="S2.E2.m1.37.37.37.24.23.23.1" xref="S2.E2.m1.37.37.37.24.23.23.1.cmml">i</mi><mi id="S2.E2.m1.38.38.38.25.24.24.1" xref="S2.E2.m1.38.38.38.25.24.24.1.cmml">m</mi></msubsup><mo stretchy="false" id="S2.E2.m1.39.39.39.26.25.25" xref="S2.E2.m1.39.39.39.26.25.25.cmml">]</mo></mrow></mrow></mrow><mo id="S2.E2.m1.40.40.40.27.26.26" xref="S2.E2.m1.42.42.3a.cmml">,</mo></mrow></mtd></mtr></mtable></math>

Correct Categorie: math

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1411.4629

Formulas:

1-

= - γ \dot{𝒓} + F_{a} 𝒏 (θ) - \partial_{𝒓} V + \sqrt{2 γ^{2} D} 𝝃 (t)

2-

= \sqrt{2 D_{r}} ξ_{r} (t)

3-

D_{r} = 3 D / σ^{2}

4-

⟨ ξ_{i} (t) ⟩ = 0

5-

⟨ ξ_{i} (t) \cdot ξ_{j} (t^{'}) ⟩ = δ_{i j} δ (t - t^{'})

6-

⟨ ξ_{r} (t) ⟩ = 0

7-

⟨ ξ_{r} (t) \cdot ξ_{r} (t^{'}) ⟩ = δ (t - t^{'})

8-

U_{b} = ε_{b} {(r - r_{0})}^{2}

9-

ε_{b} = 10^{3} k_{B} T / σ^{2}

10-

r_{0} = 2^{1 / 6} σ

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/0107540

Formulas:

1-

B i_{2} S r_{2} C a C u_{2} O_{8 + δ}

2-

B i_{2} S r_{2} C a C u_{2} O_{8 + δ}

3-

B i_{2} S r_{2} C a C u_{2} O_{8 + δ}

4-

d I / d V - V

5-

E_{d i p}

6-

Δ_{p - p} (T)

7-

Δ_{p - p} (T)

8-

2 / 3 T_{c} < T < T_{c}

9-

Δ_{p - p} (T)

10-

Δ_{p - p} (T)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/9608021

Formulas:

1-

Y_{1 - x} C a_{x} T i O_{3}

2-

H = - \sum_{(i j)} t_{i j σ} C_{i σ}^{+} C_{j σ} + \sum_{i} (ϵ_{i} - μ) C_{i σ}^{+} C_{i σ} + \sum_{i} n_{i ↑} n_{i ↓} U

3-

2 D = 4 t

4-

(1 - 2 δ)

5-

(ϵ_{B} - ϵ_{A})

6-

(ϵ_{B} - ϵ_{A})

7-

U_{A} = U_{B} =

8-

\sum_{k} ϵ_{k} a_{k σ}^{+} a_{k σ} + U f_{↑}^{+} f_{↑} f_{↓}^{+} f_{↓}

9-

+ \sum_{k} V_{k} (a_{k σ}^{+} f_{σ} + f_{σ}^{+} a_{k o}) + ϵ_{f} f_{σ}^{+} f_{σ}

10-

Δ (i ω_{n})

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/2003.05231

Formulas:

1-

r \approx 0.45 (3)

2-

- \frac{ℏ^{2}}{2 m_{1}} \sum_{i = 1}^{N_{1}} \frac{\partial^{2}}{\partial x_{i}^{2}} - \frac{ℏ^{2}}{2 m_{2}} \sum_{α = 1}^{N_{2}} \frac{\partial^{2}}{\partial x_{α}^{2}} + g_{11} \sum_{i < j} δ (x_{i} - x_{j})

3-

g_{22} \sum_{α < β} δ (x_{α} - x_{β}) + g_{12} \sum_{i, α} δ (x_{i} - x_{α}),

4-

m_{1} = m_{2} = m

5-

g_{11} = g_{22} = g

6-

N_{1} = N_{2} = N / 2

7-

\frac{(g - | g_{12} |)}{4} n^{2}

8-

\frac{\sqrt{m} n^{3 / 2}}{3 \sqrt{2} π ℏ} [{(g + | g_{12} |)}^{3 / 2} + {(g - | g_{12} |)}^{3 / 2}] .

9-

n = n_{1} + n_{2}

10-

n | a | ≫ 1

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1309.4847

Formulas:

1-

[\hat{c}, {\hat{c}}^{†}] = 1

2-

Ψ (x_{A}, x_{B}) = \sum_{p = 0}^{\infty} \sqrt{λ_{p}} ϕ_{p}^{(A)} (x_{A}) ϕ_{p}^{(B)} (x_{B}) .

3-

{\hat{c}}^{†} = \sum_{p = 0}^{\infty} \sqrt{λ_{p}} {\hat{a}}_{p}^{†} {\hat{b}}_{p}^{†}

4-

[\hat{c}, {\hat{c}}^{†}] = 1 + s Δ

5-

Δ = \sum λ_{p} ({\hat{a}}_{p}^{†} {\hat{a}}_{p} + {\hat{b}}_{p}^{†} {\hat{b}}_{p})

6-

⟨ [\hat{c}, {\hat{c}}^{†}] ⟩

7-

\hat{c} \equiv \sum_{n = 0}^{\infty} | n ⟩ ⟨ n + 1 | f_{n + 1}, {\hat{c}}^{†} = \sum_{n = 0}^{\infty} f_{n + 1}^{*} | n + 1 ⟩ ⟨ n |,

8-

{| n ⟩ : n \in ℕ}

9-

| ψ ⟩ = \frac{1}{\sqrt{\sum_{n = 0}^{\infty} {| ψ_{n} |}^{2}}} \sum_{n = 0}^{\infty} ψ_{n} | n ⟩,

10-

\hat{c} | ψ ⟩

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: quant-ph

Result: correct

Paper: https://arxiv.org/abs/2008.04621

Formulas:

1-

M_{r} = 1 - M

2-

ℐ_{M} = ℐ ⊙ M

3-

ℐ_{p} r e d = G_{θ} (ℐ_{M})

4-

ℐ_{p r e d}

5-

ℐ_{M p r e d} = ℐ_{p r e d} ⊙ M_{r}

6-

ℒ_{p} = \frac{1}{κ} \sum_{i \in ϕ} {(ϕ_{i} [ℐ] - ϕ_{i} [ℐ_{p r e d}])}^{2}

7-

ϕ_{i} [I]

8-

ϕ_{i} [ℐ_{p r e d}]

9-

G_{θ} [I_{M}]

10-

X_{i n p u t}

Formulas (html):

Correct Categorie: cs

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/quant-ph/0304060

Formulas:

1-

| ψ ⟩ = \frac{1}{\sqrt{2}} (| 00 ⟩ + | 11 ⟩)

2-

H = \frac{1}{\sqrt{2}} [\begin{matrix} 1 & 1 \\ 1 & - 1 \end{matrix}]

3-

\frac{1}{\sqrt{2}} (| 0 ⟩ + | 1 ⟩)

4-

\frac{1}{\sqrt{2}} (| 00 ⟩ + | 01 ⟩) = | 0 ⟩ (\frac{1}{\sqrt{2}} (| 0 ⟩ + | 1 ⟩))

5-

\frac{1}{2} (| 00 ⟩ + | 01 ⟩ + | 10 ⟩ - | 11 ⟩)

6-

H (A) = \frac{1}{\sqrt{2}} [\begin{matrix} 1 & 0 & 1 & 0 \\ 0 & 1 & 0 & 1 \\ 1 & 0 & - 1 & 0 \\ 0 & 1 & 0 & - 1 \end{matrix}]

7-

H (B) = \frac{1}{\sqrt{2}} [\begin{matrix} 1 & 1 & 0 & 0 \\ 1 & - 1 & 0 & 0 \\ 0 & 0 & 1 & 1 \\ 0 & 0 & 1 & - 1 \end{matrix}]

8-

\frac{1}{2} (| 00 ⟩ + | 01 ⟩ + | 10 ⟩ - | 11 ⟩)

9-

\frac{1}{\sqrt{2}} (| 00 ⟩ + | 11 ⟩)

10-

H (A) | ψ ⟩ = H (B) | ψ ⟩

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: quant-ph

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0511593

Formulas:

1-

0.24 \leq z_{lens} \leq 0.5

2-

\sim 500 h^{- 1}

3-

σ ≳ 300 km s^{- 1}

4-

E (B V) \leq 0.2

5-

\sim 36' \times 36'

6-

r_{vir} \approx 500 h^{- 1} kpc \sim 3'

7-

0.35 \leq z_{lens} \leq 0.5

8-

= 1 \overset{''}{.} 3

9-

V + a_{0} + a_{1} (V - I) + a_{2} (X - 1.25)

10-

R + b_{0} + b_{1} (R - I) + b_{2} (X - 1.25)

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1312.2971

Formulas:

1-

(X, d, μ)

2-

(X, δ, μ)

3-

d (x, y) = 0

4-

d (x, y) = d (y, x)

5-

d (x, y) \leq K (d (x, z) + d (z, y))

6-

x, y, z \in X

7-

B (x, r) = {y \in X : d (x, y) < r}

8-

diam (E) = sup {d (x, y) : x, y \in E} .

9-

B (x, 2 r)

10-

d (x, y) \geq r

Formulas (html):

Correct Categorie: math

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/hep-ph/9705218

Formulas:

1-

e^{+} e^{-} \to

2-

𝒪 (α_{s}^{3})

3-

e^{+} e^{-} \to q \bar{q} q^{'} {\bar{q}}^{'}

4-

e^{+} e^{-} \to q \bar{q} g g

5-

q \bar{q} g g

6-

σ_{4 - jet}^{1 - loop} = N_{c}^{2} (N_{c}^{2} - 1) [σ_{4}^{(a)} + \frac{N_{f}}{N_{c}} σ_{4}^{(b)} + \frac{N_{f}^{2}}{N_{c}^{2}} σ_{4}^{(c)} + \frac{N_{f}}{N_{c}^{3}} σ_{4}^{(d)} + 𝒪 (\frac{1}{N_{c}^{2}})]

7-

σ_{4}^{(a, b, c, d)}

8-

e^{+} e^{-} \to q \bar{q} q^{'} {\bar{q}}^{'} g

9-

e^{+} e^{-} \to q \bar{q} g g g

10-

𝒪 (α_{s}^{3})

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/nucl-th/0008058

Formulas:

1-

T > 2.5 T_{c}

2-

2 ω_{q} (m_{q 0} + ω_{q}), ω_{q}^{2} = \frac{1}{6} [T^{2} + \frac{μ_{q}^{2}}{π^{2}}] g_{eff}^{2},

3-

\frac{1}{6} [(3 + \frac{1}{2} N_{f}) T^{2} + \frac{3}{2 π^{2}} \sum_{q} μ_{q}^{2}] g_{eff}^{2},

4-

m_{i}^{2} = m_{i 0}^{2} + Π_{i}^{*}

5-

i = (q, g)

6-

\sum_{q} {n_{q}^{id} (T, μ; m_{q} [T, μ]) - n_{\bar{q}}^{id} (T, μ; m_{q} [T, μ])},

7-

s_{g}^{id} (T, μ; m_{g} [T, μ]) + \sum_{q} s_{q}^{id} (T, μ; m_{q} [T, μ]) .

8-

g_{eff} (T, μ) \to g_{1 - loop}

9-

p = \sum_{i} p_{i}^{id} (T, μ; m_{i} [T, μ]) - B (T, μ)

10-

e = \sum_{i} e_{i}^{id} (T, μ; m_{i} [T, μ]) + B (T, μ)

Formulas (html):

Correct Categorie: nucl-th

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1402.4256

Formulas:

1-

Z T = σ S^{2} T / κ

2-

△ T = T_{h o t} - T_{c o l d}

3-

△ T / T_{h o t}

4-

η = \frac{△ T}{T_{h o t}} (\frac{\sqrt{1 + Z T_{a v g}} - 1}{\sqrt{1 + Z T_{a v g}} + \frac{T_{c o l d}}{T_{h o t}}})

5-

T_{h o t}

6-

T_{c o l d}

7-

T_{a v g} = (T_{h o t} - T_{c o l d}) / 2

8-

Z T_{a v g} = {(\frac{S_{h} - S_{e}}{\sqrt{\frac{κ_{h}}{σ_{h}}} + \sqrt{\frac{κ_{e}}{σ_{e}}}})}^{2} T_{a v g}

9-

\sqrt{1 + Z T_{a v g}}

10-

Z T_{a v g}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1710.07472

Formulas:

1-

D_{n} (k)

2-

W_{S} = (1 + \frac{D}{R}) V_{S},

3-

u (t) = U_{S} + (u_{S} - U_{S}) (1 - \exp (\frac{- t}{τ})),

4-

τ = \frac{4 Δ D}{3 U_{S}},

5-

Δ x = 500 µ m

6-

Δ x = 500 µ m

7-

Δ x = 50 µ m

8-

\frac{\partial z ρ_{1}}{\partial t} + \nabla \cdot z ρ_{1} 𝐮

9-

\frac{\partial (1 - z) ρ_{2}}{\partial t} + \nabla \cdot (1 - z) ρ_{2} 𝐮

10-

\frac{\partial ρ 𝐮}{\partial t} + \nabla \cdot (ρ 𝐮 \otimes 𝐮 + p I)

Formulas (html):

Correct Categorie: physics

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/cs/0303012

Formulas:

1-

θ_{i} = \frac{A}{i^{α}},

2-

S_{e f f}

3-

S_{e f f} / ν_{i n t}

4-

T_{s t} \geq m o n t h

5-

T_{s t} ≲ t_{u}

6-

ϑ_{i} = θ_{i} k

7-

ν_{i n t}

8-

ν_{o u t}

9-

ν_{o u t} = λ N

10-

K b p s

Formulas (html):

Correct Categorie: cs

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0405134

Formulas:

1-

f_{X} (0.5 - 8 keV) \approx 10^{- 14} erg s^{- 1} {cm}^{- 2}

2-

L_{X} (0.5 - 8 keV) \approx 10^{41} erg s^{- 1}

3-

L_{1.4 GHz} \approx 5 \times 10^{22} W {Hz}^{- 1}

4-

\log f_{X} / f_{o p t} \approx - 2

5-

\approx 10^{- 13} erg s^{- 1} {cm}^{- 2}

6-

\approx 10^{- 16} erg s^{- 1} {cm}^{- 2}

7-

> 10^{- 13} erg s^{- 1} {cm}^{- 2}

8-

< 10^{- 15} erg s^{- 1} {cm}^{- 2}

9-

\approx 10^{- 14} erg s^{- 1} {cm}^{- 2}

10-

f_{X} (0.5 - 8 keV) \approx 10^{- 14} erg s^{- 1} {cm}^{- 2}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1506.03821

Formulas:

1-

u, g, r, i, z

2-

R_{V} \equiv A_{V} / E (B - V)

3-

E (B - V) = A_{B} - A_{V}

4-

ψ (t) \propto δ (t - t_{0})

5-

[- 2, + 0.9]

6-

\log Z / Z_{⊙}

7-

[- 1.5, + 0.3]

8-

F U V - U V W 2

9-

F U V, U V W 2, U V M 2, U V W 1, u, g, r, i, z

10-

E (B - V) = 0.140

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1602.02594

Formulas:

1-

Γ_{n e w} (u)

2-

k_{u}^{'} = | Γ_{n e w} (u) |

3-

Γ_{n e w} (u) = z; z \in Γ (r) \land r \in Γ (u) \land z \neq u

4-

E_{p o s} \subset E

5-

E_{n e g}

6-

E_{p o s}

7-

E_{n e g}

8-

E_{n e g}

9-

A U C = \frac{m_{1} + \frac{m_{2}}{2}}{\frac{| E |}{10}}

10-

- s (x, y)

Formulas (html):

Correct Categorie: cs

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1705.08917

Formulas:

1-

J_{𝐪}^{eff} \sim χ_{𝐪}^{- 1}

2-

{| 𝐒_{j} |}^{2} = 1

3-

𝐐_{0} = (0, 0)

4-

𝐐_{0} = (π, π)

5-

T_{c} \propto {| 𝐐 - 𝐐_{0} |}^{2}

6-

| 𝐐 - 𝐐_{0} | \to 0

7-

q_{x} = - q_{y}

8-

H = \sum_{𝐪} J_{𝐪} {| 𝐒_{𝐪} |}^{2} .

9-

{| 𝐒_{i} |}^{2} = 1

10-

𝐒_{α i} = 𝐮 \cos 𝐐_{α} \cdot 𝐑_{i} + 𝐯 \sin 𝐐_{α} \cdot 𝐑_{i}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/quant-ph/9908077

Formulas:

1-

| Ψ ⟩ = Σ_{i} C_{i} | a_{i} ⟩ | Φ_{i} ⟩ | Θ_{i} ⟩ .

2-

| Φ_{k} ⟩ ⟨ Φ_{k} | | Ψ ⟩ = C_{k} | a_{k} ⟩ | Φ_{k} ⟩ | Θ_{k} ⟩

3-

δ_{k m} C_{k}

4-

p e r c e p t i o n

5-

{(e N)}_{1} [x_{1}]

6-

{(e N)}_{2} [x_{2}]

7-

(e^{i ϕ} e_{1} + e_{2})

8-

p_{0} = N_{L} / N

9-

q_{0} = 1 - p_{0}

10-

p_{0} = 1261 / 2500 = 0.5044

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: quant-ph

Result: correct

Paper: https://arxiv.org/abs/1803.04883

Formulas:

1-

p_{a t m}

2-

{\dot{Q}}_{m i n}

3-

α = k / (ρ c_{p})

4-

\dot{Q} = η P

5-

\dot{q} = \dot{Q} / A

6-

{\dot{Q}}_{m i n}

7-

{\dot{Q}}_{m i n} = W A ρ_{S} [h_{m} + c_{p, S} (T_{m} - T_{S})] .

8-

{\dot{Q}}_{m i n}

9-

{\dot{Q}}_{L} = \frac{8 k_{S} T_{S}}{π} \int_{0}^{L} \int_{0}^{\infty} \frac{\exp (- \frac{α_{S} b^{2} z}{W})}{b (J_{0}^{2} (R b) Y_{0}^{2} (R b))} 𝑑 b 𝑑 z,

10-

α_{S} = k_{S} / (ρ_{S} c_{p, S})

Formulas (html):

Correct Categorie: physics

Guessed Categorie: quant-ph

Result: incorrect

Run 11277772 (Agent389)