Run 16330494

Paper: https://arxiv.org/abs/1709.01323

Formulas:

1-

I_{c} \sin φ

2-

d φ / d t

3-

\frac{d φ}{d t} = \frac{2 e V}{ℏ} .

4-

I_{DC} = I_{c} \sin φ + \frac{V}{R} + C \frac{d V}{d t},

5-

\frac{I_{DC}}{I_{c}} = \sin φ + \frac{1}{ω_{c}} \frac{d φ}{d t} + \frac{β_{c}}{ω_{c}^{2}} \frac{d^{2} φ}{d t^{2}} .

6-

ω_{c} = 2 e I_{c} R / ℏ

7-

β_{c} = ω_{c} R C

8-

β_{c} = | Z_{R} | / | Z_{C} |

9-

Z_{C} = - i / ω_{c} C

10-

d q / d t

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1703.01831

Formulas:

1-

H = \sum_{α} H_{α} + H_{c} + \sum_{α} H_{α T},

2-

\sum_{j = 1}^{\infty} t_{0} c_{α j}^{†} c_{α, j + 1} + h . c .

3-

\sum_{l = 1}^{3} E_{l} d_{l}^{†} d_{l} + \sum_{l^{'} = 1}^{2} t_{l^{'}} d_{l^{'} + 1}^{†} d_{l^{'}} + t_{3} d_{1}^{†} d_{3} + h . c .,

4-

\sum_{l} v_{α l} c_{α 1}^{†} d_{l} + h . c . .

5-

[𝒫 𝒯, H] = 0

6-

𝒫 d_{N + 1 - l} 𝒫 = d_{l}

7-

𝒯 i 𝒯 = - i

8-

v_{α 1} = v_{α^{'} N}

9-

E_{l} = E_{N + 1 - l}^{*}

10-

T (ω) = Tr [Γ^{L} G^{a} (ω) Γ^{R} G^{r} (ω)] .

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/1608.00023

Formulas:

1-

Γ_{S} / Γ_{L} = 16

2-

Γ_{R} / Γ_{L} = {0.5, 1, 2, 4}

3-

H = H_{Q D} + \sum_{α = L, R, S} H_{α} + H_{T},

4-

H_{Q D} = ϵ_{0} \sum_{σ} d_{σ}^{†} d_{σ} + U n_{↑} n_{↓}

5-

n_{σ} \equiv d_{σ}^{†} d_{σ}

6-

H_{α} = \sum_{k, σ} ϵ_{α k} c_{α k σ}^{†} c_{α k σ}

7-

c_{α k σ}^{†}

8-

c_{α k σ}

9-

α = {L, R}

10-

H_{S} = \sum_{k, σ} ϵ_{S k} c_{S k σ}^{†} c_{S k σ} + \sum_{k} (Δ c_{S - k ↑}^{†} c_{S k ↓}^{†} + Δ^{*} c_{S k ↓} c_{S - k ↑})

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/1809.07967

Formulas:

1-

\dot{M} (R_{ν})

2-

\dot{M} (R_{ν}) = 0.015 {(\frac{R_{in}}{R_{s}})}^{1.2} {(1 + \frac{R_{ν}}{10 R_{in}})}^{2} M_{⊙} s^{- 1},

3-

R_{in} ≃ 3 R_{s}

4-

{\dot{M}}_{w} (t)

5-

\dot{M} (R_{ν})

6-

\frac{\dot{M} (R_{ν})}{0.015 M_{⊙} s^{- 1}} (\frac{3 M_{⊙}}{M_{B H}}) = {(\frac{R_{in}}{R_{s}})}^{1.2} {(1 + \frac{R_{ν}}{10 R_{in}})}^{2} .

7-

\dot{M} (R_{ν})

8-

{(α / 0.1)}^{5 / 3}

9-

R_{in} < R_{ν} < R_{d}

10-

\dot{M} (R) = {\dot{M}}_{d} {(\frac{R}{R_{d}})}^{s},

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: math

Result: incorrect

Paper: https://arxiv.org/abs/1303.1593

Formulas:

1-

(l, b) = (242^{\circ} \pm 44^{\circ}, - 42^{\circ} \pm 23^{\circ})

2-

68 % C . L .

3-

(l, b) = (309^{\circ}_{- 3^{\circ}}^{+ 23^{\circ}}, 18^{\circ}_{- 10^{\circ}}^{+ 11^{\circ}})

4-

(l, b) = (314^{\circ}_{- 13^{\circ}}^{+ 20^{\circ}}, 28^{\circ}_{- 33^{\circ}}^{+ 11^{\circ}})

5-

(l, b) \approx (- 35^{\circ}, - 19^{\circ})

6-

95 % C . L .

7-

d τ = {(η_{μ ν} d x^{μ} d x^{ν})}^{\frac{1 - b}{2}} {(n_{σ} d x^{σ})}^{b}

8-

D I S I M_{b} (2)

9-

T E (2)

10-

T E (2)

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: math

Result: incorrect

Paper: https://arxiv.org/abs/1204.4486

Formulas:

1-

M_{*} ≳ 8 M_{⊙}

2-

3.6, 4.5, 5.8 μ

3-

7 \overset{''}{.} 5

4-

[3, 5, 8, 20, 35] \times 1.6

5-

1 \overset{''}{.} 8 \times 1 \overset{''}{.} 5

6-

1 \overset{''}{.} 8 \times 1 \overset{''}{.} 5

7-

0 \overset{''}{.} 9

8-

1 \overset{''}{.} 7

9-

M = F_{SMA} d^{2} / κ_{ν} B_{ν} (T)

10-

B_{ν} (T)

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/1505.01894

Formulas:

1-

Δ ϵ \cdot t = v + f (t)

2-

v + f (t) = 0

3-

| Ψ ⟩ = e^{T_{2}} | 0 ⟩

4-

T_{2} = \frac{1}{4} \sum_{i j a b} t_{i j}^{a b} c_{a}^{†} c_{b}^{†} c_{j} c_{i}

5-

E = \frac{1}{4} \sum_{i j a b} t_{i j}^{a b} v_{a b}^{i j}

6-

v_{a b}^{i j} = ⟨ i j ∥ a b ⟩

7-

= f_{c}^{a} t_{i j}^{c b} + f_{c}^{b} t_{i j}^{a c} - f_{i}^{k} t_{k j}^{a b} - f_{j}^{k} t_{i k}^{a b} + v_{i j}^{a b}

8-

+ \frac{1}{2} t_{k l}^{a b} v_{i j}^{k l} + \frac{1}{2} t_{i j}^{c d} v_{c d}^{a b} + \frac{1}{4} t_{i j}^{c d} t_{k l}^{a b} v_{c d}^{k l}

9-

+ t_{i k}^{a c} v_{c j}^{k b} + t_{k j}^{c b} v_{c i}^{k a} + t_{i k}^{a c} t_{j l}^{b d} v_{c d}^{k l}

10-

- t_{i k}^{b c} v_{c j}^{k a} - t_{k j}^{c a} v_{c i}^{k b} - t_{i k}^{b c} t_{j l}^{a d} v_{c d}^{k l}

Formulas (html):

Correct Categorie: physics

Guessed Categorie: hep-lat

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0703296

Formulas:

1-

\log τ_{5000} \approx - 1

2-

\log τ_{5000} = - 1.5

3-

\log τ_{5000} \approx - 1

4-

\log τ_{5000} \approx - 1

5-

v_{e} \sin i

6-

\log (C a / N_{tot}) = - 5.14

7-

- 1.3 \geq \log τ_{5000} \leq - 0.5

8-

l o g τ_{5000} = - 1.5

9-

\log g f ϵ

10-

l o g τ_{5000} = - 2.0

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/astro-ph/9808078

Formulas:

1-

e x p e r i m e n t a l

2-

a c t i v e

3-

p a s s i v e

4-

C h l o r i n e

5-

g o o d

6-

C h l o r i n e

7-

f i r s t

8-

b e s t

9-

p e r c h l o r e t y l e n e

10-

t e t r a c h l o r o e t h e n e

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: cs

Result: incorrect

Paper: https://arxiv.org/abs/2008.00495

Formulas:

1-

d s^{2} = - (1 - \frac{2 M}{r} + \frac{Q^{2}}{r^{2}} + \frac{r^{2}}{L^{2}}) d t^{2} + {(1 - \frac{2 M}{r} + \frac{Q^{2}}{r^{2}} + \frac{r^{2}}{L^{2}})}^{- 1} d r^{2} + r^{2} d Ω^{2},

2-

f (r) = 1 - \frac{2 M}{r} + \frac{Q^{2}}{r^{2}} + \frac{r^{2}}{L^{2}} = 0 .

3-

M = \frac{r_{+}}{2} (1 + \frac{r_{+}^{2}}{L^{2}} + \frac{Q^{2}}{r_{+}^{2}}) .

4-

T_{H} = {\frac{1}{4 π} f^{'} (r) |}_{r = r_{+}} = \frac{1}{4 π r_{+}} (1 + \frac{3 r_{+}^{2}}{L^{2}} - \frac{Q^{2}}{r_{+}^{2}}) .

5-

P = \frac{3}{8 π} \frac{1}{L^{2}} .

6-

T_{H} = \frac{1}{4 π r_{+}} (1 + 8 π P r_{+}^{2} - \frac{Q^{2}}{r_{+}^{2}}) .

7-

P_{c} = \frac{1}{96 π Q^{2}}

8-

\frac{\partial T_{H}}{\partial r_{+}} = 0,

9-

r_{m i n / m a x} = {[\frac{1 \pm \sqrt{1 - 96 π P Q^{2}}}{16 π P}]}^{1 / 2} .

10-

T_{m i n / m a x}

Formulas (html):

Correct Categorie: hep-th

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1204.4664

Formulas:

1-

\log C (t)

2-

S U (N)

3-

S U (3)

4-

S U (5)

5-

S U (7)

6-

S U (3)

7-

S U (3)

8-

μ_{n} = ⟨ x^{n} ⟩,

9-

κ_{n} = μ_{n} - \sum_{m = 1}^{n - 1} (\begin{matrix} n - 1 \\ m - 1 \end{matrix}) κ_{m} μ_{n - m} .

10-

C (t) = \sum_{x} O_{l} (x, t) O_{m} (0, 0)

Formulas (html):

Correct Categorie: hep-lat

Guessed Categorie: hep-ph

Result: incorrect

Paper: https://arxiv.org/abs/1306.0253

Formulas:

1-

σ^{t} (a)

2-

0 \leq σ^{t} (s) \leq 3

3-

0 \leq σ^{t} (o) \leq 6

4-

a^{t + 1} = 𝐚_{a^{t}} [σ {(a)}^{t}],

5-

(𝐬_{0}, 𝐬_{1}, 𝐨_{0}, 𝐨_{1})

6-

ℛ (d e c (𝐬_{0}), d e c (𝐬_{1}), d e c (𝐨_{0}), d e c (𝐬_{1}))

7-

ℛ_{65} = ℛ (5, 2, 16, 65)

8-

ℛ_{68} = ℛ (5, 2, 16, 68)

9-

ℛ_{72} = ℛ (5, 2, 16, 72)

10-

𝐬_{0} = (0101)

Formulas (html):

Correct Categorie: nlin

Guessed Categorie: gr-qc

Result: incorrect

Paper: https://arxiv.org/abs/hep-ph/9801451

Formulas:

1-

μ H_{1} H_{2}

2-

λ N H_{1} H_{2}

3-

W_{ϕ N M S S M} = λ N H_{1} H_{2} - k ϕ N^{2}

4-

< N > \sim ϕ_{c}

5-

< ϕ > \sim ϕ_{c}

6-

λ, k \sim 10^{- 10}

7-

U {(1)}_{P Q}

8-

Q_{N} + Q_{H_{1}} + Q_{H_{2}} = 0, Q_{ϕ} + 2 Q_{N} = 0 .

9-

ϕ H_{1} H_{2}

10-

V (0) + V (ϕ, N)

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: math

Result: incorrect

Paper: https://arxiv.org/abs/1111.3297

Formulas:

1-

(p, q) \in P

2-

i = q + m p

3-

[u, v] \subset ℕ

4-

u = f 2^{l + 1} + 1

5-

v = (f + n) 2^{l + 1}

6-

0 \leq j < n 2^{l}

7-

2 (f 2^{l} + j) + 1 \in [u, v] = [f 2^{l^{+} 1}, (f + n) 2^{l + 1}]

8-

2 (f 2^{l} + j) + 1

9-

2 (f 2^{l} + j) + 1

10-

S_{q}^{(t)} = S_{t 2^{l} + q}

Formulas (html):

Correct Categorie: cs

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/1203.2549

Formulas:

1-

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

2-

\sqrt{s_{N N}} = 2.765

3-

p + p \to p + p + η

4-

d σ / d M_{e e}

5-

θ_{e e} > 9^{\circ}

6-

d σ / d M_{e e}

7-

θ_{e e} > 9^{\circ}

8-

d σ / d M_{e e}

9-

θ_{e e} > 9^{\circ}

10-

M_{e e} > 0.15

Formulas (html):

Correct Categorie: nucl-ex

Guessed Categorie: hep-th

Result: incorrect

Paper: https://arxiv.org/abs/1101.5579

Formulas:

1-

n_{f} = 2 + 1

2-

n_{f} = 2 + 1

3-

| ϵ | = (2.228 \pm 0.011) \times 10^{- 3}

4-

Re (ϵ^{'} / ϵ) = (1.65 \pm 0.26) \times 10^{- 3}

5-

Δ I = 3 / 2

6-

Δ s = 1, Δ d = - 1

7-

S U {(3)}_{L} \times S U {(3)}_{R}

8-

Δ I = 3 / 2

9-

Δ I = 1 / 2

10-

\begin{matrix} Operator & S U {(3)}_{L} \times S U {(3)}_{R} & Δ I \\ Q_{1}^{'} & (27, 1) & 1 / 2, 3 / 2 \\ Q_{2}^{'}, Q_{3}^{'}, Q_{5}^{'}, Q_{6}^{'} & (8, 1) & 1 / 2 \\ Q_{7}^{'}, Q_{8}^{'} & (8, 8) & 1 / 2, 3 / 2 \end{matrix}

Formulas (html):

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xref="S1.p1.3.m3.2.2.1.1.1.1.3.cmml">0.011</mn></mrow><mo stretchy="false" id="S1.p1.3.m3.2.2.1.1.1.3" xref="S1.p1.3.m3.2.2.1.1.1.1.cmml">)</mo></mrow><mo id="S1.p1.3.m3.2.2.1.2" xref="S1.p1.3.m3.2.2.1.2.cmml">×</mo><msup id="S1.p1.3.m3.2.2.1.3" xref="S1.p1.3.m3.2.2.1.3.cmml"><mn id="S1.p1.3.m3.2.2.1.3.2" xref="S1.p1.3.m3.2.2.1.3.2.cmml">10</mn><mrow id="S1.p1.3.m3.2.2.1.3.3" xref="S1.p1.3.m3.2.2.1.3.3.cmml"><mo id="S1.p1.3.m3.2.2.1.3.3.1" xref="S1.p1.3.m3.2.2.1.3.3.1.cmml">-</mo><mn id="S1.p1.3.m3.2.2.1.3.3.2" xref="S1.p1.3.m3.2.2.1.3.3.2.cmml">3</mn></mrow></msup></mrow></mrow></math>, <math><mrow id="S1.p1.4.m4.2.2" xref="S1.p1.4.m4.2.2.cmml"><mrow id="S1.p1.4.m4.1.1.1" xref="S1.p1.4.m4.1.1.1.cmml"><mi id="S1.p1.4.m4.1.1.1.3" xref="S1.p1.4.m4.1.1.1.3.cmml">Re</mi><mo id="S1.p1.4.m4.1.1.1.2" xref="S1.p1.4.m4.1.1.1.2.cmml">⁢</mo><mrow id="S1.p1.4.m4.1.1.1.1.1" xref="S1.p1.4.m4.1.1.1.1.1.1.cmml"><mo stretchy="false" id="S1.p1.4.m4.1.1.1.1.1.2" xref="S1.p1.4.m4.1.1.1.1.1.1.cmml">(</mo><mrow id="S1.p1.4.m4.1.1.1.1.1.1" xref="S1.p1.4.m4.1.1.1.1.1.1.cmml"><msup id="S1.p1.4.m4.1.1.1.1.1.1.2" xref="S1.p1.4.m4.1.1.1.1.1.1.2.cmml"><mi id="S1.p1.4.m4.1.1.1.1.1.1.2.2" xref="S1.p1.4.m4.1.1.1.1.1.1.2.2.cmml">ϵ</mi><mo id="S1.p1.4.m4.1.1.1.1.1.1.2.3" xref="S1.p1.4.m4.1.1.1.1.1.1.2.3.cmml">′</mo></msup><mo id="S1.p1.4.m4.1.1.1.1.1.1.1" xref="S1.p1.4.m4.1.1.1.1.1.1.1.cmml">/</mo><mi id="S1.p1.4.m4.1.1.1.1.1.1.3" xref="S1.p1.4.m4.1.1.1.1.1.1.3.cmml">ϵ</mi></mrow><mo stretchy="false" id="S1.p1.4.m4.1.1.1.1.1.3" xref="S1.p1.4.m4.1.1.1.1.1.1.cmml">)</mo></mrow></mrow><mo id="S1.p1.4.m4.2.2.3" xref="S1.p1.4.m4.2.2.3.cmml">=</mo><mrow id="S1.p1.4.m4.2.2.2" xref="S1.p1.4.m4.2.2.2.cmml"><mrow id="S1.p1.4.m4.2.2.2.1.1" xref="S1.p1.4.m4.2.2.2.1.1.1.cmml"><mo stretchy="false" id="S1.p1.4.m4.2.2.2.1.1.2" xref="S1.p1.4.m4.2.2.2.1.1.1.cmml">(</mo><mrow id="S1.p1.4.m4.2.2.2.1.1.1" xref="S1.p1.4.m4.2.2.2.1.1.1.cmml"><mn id="S1.p1.4.m4.2.2.2.1.1.1.2" xref="S1.p1.4.m4.2.2.2.1.1.1.2.cmml">1.65</mn><mo id="S1.p1.4.m4.2.2.2.1.1.1.1" xref="S1.p1.4.m4.2.2.2.1.1.1.1.cmml">±</mo><mn id="S1.p1.4.m4.2.2.2.1.1.1.3" xref="S1.p1.4.m4.2.2.2.1.1.1.3.cmml">0.26</mn></mrow><mo stretchy="false" id="S1.p1.4.m4.2.2.2.1.1.3" xref="S1.p1.4.m4.2.2.2.1.1.1.cmml">)</mo></mrow><mo id="S1.p1.4.m4.2.2.2.2" xref="S1.p1.4.m4.2.2.2.2.cmml">×</mo><msup id="S1.p1.4.m4.2.2.2.3" xref="S1.p1.4.m4.2.2.2.3.cmml"><mn id="S1.p1.4.m4.2.2.2.3.2" xref="S1.p1.4.m4.2.2.2.3.2.cmml">10</mn><mrow id="S1.p1.4.m4.2.2.2.3.3" xref="S1.p1.4.m4.2.2.2.3.3.cmml"><mo id="S1.p1.4.m4.2.2.2.3.3.1" xref="S1.p1.4.m4.2.2.2.3.3.1.cmml">-</mo><mn id="S1.p1.4.m4.2.2.2.3.3.2" xref="S1.p1.4.m4.2.2.2.3.3.2.cmml">3</mn></mrow></msup></mrow></mrow></math>, <math><mrow id="S1.p1.5.m5.1.1" xref="S1.p1.5.m5.1.1.cmml"><mrow id="S1.p1.5.m5.1.1.2" xref="S1.p1.5.m5.1.1.2.cmml"><mi mathvariant="normal" id="S1.p1.5.m5.1.1.2.2" xref="S1.p1.5.m5.1.1.2.2.cmml">Δ</mi><mo id="S1.p1.5.m5.1.1.2.1" xref="S1.p1.5.m5.1.1.2.1.cmml">⁢</mo><mi id="S1.p1.5.m5.1.1.2.3" xref="S1.p1.5.m5.1.1.2.3.cmml">I</mi></mrow><mo id="S1.p1.5.m5.1.1.1" xref="S1.p1.5.m5.1.1.1.cmml">=</mo><mrow id="S1.p1.5.m5.1.1.3" xref="S1.p1.5.m5.1.1.3.cmml"><mn id="S1.p1.5.m5.1.1.3.2" xref="S1.p1.5.m5.1.1.3.2.cmml">3</mn><mo id="S1.p1.5.m5.1.1.3.1" xref="S1.p1.5.m5.1.1.3.1.cmml">/</mo><mn id="S1.p1.5.m5.1.1.3.3" xref="S1.p1.5.m5.1.1.3.3.cmml">2</mn></mrow></mrow></math>, <math><mrow id="S2.SS1.p1.1.m1.2.2.2" xref="S2.SS1.p1.1.m1.2.2.3.cmml"><mrow id="S2.SS1.p1.1.m1.1.1.1.1" xref="S2.SS1.p1.1.m1.1.1.1.1.cmml"><mrow id="S2.SS1.p1.1.m1.1.1.1.1.2" xref="S2.SS1.p1.1.m1.1.1.1.1.2.cmml"><mi mathvariant="normal" id="S2.SS1.p1.1.m1.1.1.1.1.2.2" xref="S2.SS1.p1.1.m1.1.1.1.1.2.2.cmml">Δ</mi><mo id="S2.SS1.p1.1.m1.1.1.1.1.2.1" xref="S2.SS1.p1.1.m1.1.1.1.1.2.1.cmml">⁢</mo><mi id="S2.SS1.p1.1.m1.1.1.1.1.2.3" xref="S2.SS1.p1.1.m1.1.1.1.1.2.3.cmml">s</mi></mrow><mo id="S2.SS1.p1.1.m1.1.1.1.1.1" xref="S2.SS1.p1.1.m1.1.1.1.1.1.cmml">=</mo><mn id="S2.SS1.p1.1.m1.1.1.1.1.3" xref="S2.SS1.p1.1.m1.1.1.1.1.3.cmml">1</mn></mrow><mo rspace="5.3pt" id="S2.SS1.p1.1.m1.2.2.2.3" xref="S2.SS1.p1.1.m1.2.2.3a.cmml">,</mo><mrow id="S2.SS1.p1.1.m1.2.2.2.2" xref="S2.SS1.p1.1.m1.2.2.2.2.cmml"><mrow id="S2.SS1.p1.1.m1.2.2.2.2.2" xref="S2.SS1.p1.1.m1.2.2.2.2.2.cmml"><mi mathvariant="normal" id="S2.SS1.p1.1.m1.2.2.2.2.2.2" xref="S2.SS1.p1.1.m1.2.2.2.2.2.2.cmml">Δ</mi><mo id="S2.SS1.p1.1.m1.2.2.2.2.2.1" xref="S2.SS1.p1.1.m1.2.2.2.2.2.1.cmml">⁢</mo><mi id="S2.SS1.p1.1.m1.2.2.2.2.2.3" xref="S2.SS1.p1.1.m1.2.2.2.2.2.3.cmml">d</mi></mrow><mo id="S2.SS1.p1.1.m1.2.2.2.2.1" xref="S2.SS1.p1.1.m1.2.2.2.2.1.cmml">=</mo><mrow id="S2.SS1.p1.1.m1.2.2.2.2.3" xref="S2.SS1.p1.1.m1.2.2.2.2.3.cmml"><mo id="S2.SS1.p1.1.m1.2.2.2.2.3.1" xref="S2.SS1.p1.1.m1.2.2.2.2.3.1.cmml">-</mo><mn id="S2.SS1.p1.1.m1.2.2.2.2.3.2" xref="S2.SS1.p1.1.m1.2.2.2.2.3.2.cmml">1</mn></mrow></mrow></mrow></math>, <math><mrow id="S2.SS1.p1.2.m2.2.3" xref="S2.SS1.p1.2.m2.2.3.cmml"><mrow id="S2.SS1.p1.2.m2.2.3.2" xref="S2.SS1.p1.2.m2.2.3.2.cmml"><mrow id="S2.SS1.p1.2.m2.2.3.2.2" xref="S2.SS1.p1.2.m2.2.3.2.2.cmml"><mi id="S2.SS1.p1.2.m2.2.3.2.2.2" xref="S2.SS1.p1.2.m2.2.3.2.2.2.cmml">S</mi><mo id="S2.SS1.p1.2.m2.2.3.2.2.1" xref="S2.SS1.p1.2.m2.2.3.2.2.1.cmml">⁢</mo><mi id="S2.SS1.p1.2.m2.2.3.2.2.3" xref="S2.SS1.p1.2.m2.2.3.2.2.3.cmml">U</mi><mo id="S2.SS1.p1.2.m2.2.3.2.2.1a" xref="S2.SS1.p1.2.m2.2.3.2.2.1.cmml">⁢</mo><msub id="S2.SS1.p1.2.m2.2.3.2.2.4" xref="S2.SS1.p1.2.m2.2.3.2.2.4.cmml"><mrow id="S2.SS1.p1.2.m2.2.3.2.2.4.2.2" xref="S2.SS1.p1.2.m2.2.3.2.2.4.cmml"><mo stretchy="false" id="S2.SS1.p1.2.m2.2.3.2.2.4.2.2.1" xref="S2.SS1.p1.2.m2.2.3.2.2.4.cmml">(</mo><mn id="S2.SS1.p1.2.m2.1.1" xref="S2.SS1.p1.2.m2.1.1.cmml">3</mn><mo stretchy="false" id="S2.SS1.p1.2.m2.2.3.2.2.4.2.2.2" xref="S2.SS1.p1.2.m2.2.3.2.2.4.cmml">)</mo></mrow><mi mathvariant="normal" id="S2.SS1.p1.2.m2.2.3.2.2.4.3" xref="S2.SS1.p1.2.m2.2.3.2.2.4.3.cmml">L</mi></msub></mrow><mo id="S2.SS1.p1.2.m2.2.3.2.1" xref="S2.SS1.p1.2.m2.2.3.2.1.cmml">×</mo><mi id="S2.SS1.p1.2.m2.2.3.2.3" xref="S2.SS1.p1.2.m2.2.3.2.3.cmml">S</mi></mrow><mo id="S2.SS1.p1.2.m2.2.3.1" xref="S2.SS1.p1.2.m2.2.3.1.cmml">⁢</mo><mi id="S2.SS1.p1.2.m2.2.3.3" xref="S2.SS1.p1.2.m2.2.3.3.cmml">U</mi><mo id="S2.SS1.p1.2.m2.2.3.1a" xref="S2.SS1.p1.2.m2.2.3.1.cmml">⁢</mo><msub id="S2.SS1.p1.2.m2.2.3.4" xref="S2.SS1.p1.2.m2.2.3.4.cmml"><mrow id="S2.SS1.p1.2.m2.2.3.4.2.2" xref="S2.SS1.p1.2.m2.2.3.4.cmml"><mo stretchy="false" id="S2.SS1.p1.2.m2.2.3.4.2.2.1" xref="S2.SS1.p1.2.m2.2.3.4.cmml">(</mo><mn id="S2.SS1.p1.2.m2.2.2" xref="S2.SS1.p1.2.m2.2.2.cmml">3</mn><mo stretchy="false" id="S2.SS1.p1.2.m2.2.3.4.2.2.2" xref="S2.SS1.p1.2.m2.2.3.4.cmml">)</mo></mrow><mi mathvariant="normal" id="S2.SS1.p1.2.m2.2.3.4.3" xref="S2.SS1.p1.2.m2.2.3.4.3.cmml">R</mi></msub></mrow></math>, <math><mrow id="S2.SS1.p1.6.m6.1.1" xref="S2.SS1.p1.6.m6.1.1.cmml"><mrow id="S2.SS1.p1.6.m6.1.1.2" xref="S2.SS1.p1.6.m6.1.1.2.cmml"><mi mathvariant="normal" id="S2.SS1.p1.6.m6.1.1.2.2" xref="S2.SS1.p1.6.m6.1.1.2.2.cmml">Δ</mi><mo id="S2.SS1.p1.6.m6.1.1.2.1" xref="S2.SS1.p1.6.m6.1.1.2.1.cmml">⁢</mo><mi id="S2.SS1.p1.6.m6.1.1.2.3" xref="S2.SS1.p1.6.m6.1.1.2.3.cmml">I</mi></mrow><mo id="S2.SS1.p1.6.m6.1.1.1" xref="S2.SS1.p1.6.m6.1.1.1.cmml">=</mo><mrow id="S2.SS1.p1.6.m6.1.1.3" xref="S2.SS1.p1.6.m6.1.1.3.cmml"><mn id="S2.SS1.p1.6.m6.1.1.3.2" xref="S2.SS1.p1.6.m6.1.1.3.2.cmml">3</mn><mo id="S2.SS1.p1.6.m6.1.1.3.1" xref="S2.SS1.p1.6.m6.1.1.3.1.cmml">/</mo><mn id="S2.SS1.p1.6.m6.1.1.3.3" xref="S2.SS1.p1.6.m6.1.1.3.3.cmml">2</mn></mrow></mrow></math>, <math><mrow id="S2.SS1.p1.7.m7.1.1" xref="S2.SS1.p1.7.m7.1.1.cmml"><mrow id="S2.SS1.p1.7.m7.1.1.2" xref="S2.SS1.p1.7.m7.1.1.2.cmml"><mi mathvariant="normal" id="S2.SS1.p1.7.m7.1.1.2.2" xref="S2.SS1.p1.7.m7.1.1.2.2.cmml">Δ</mi><mo id="S2.SS1.p1.7.m7.1.1.2.1" xref="S2.SS1.p1.7.m7.1.1.2.1.cmml">⁢</mo><mi id="S2.SS1.p1.7.m7.1.1.2.3" xref="S2.SS1.p1.7.m7.1.1.2.3.cmml">I</mi></mrow><mo id="S2.SS1.p1.7.m7.1.1.1" xref="S2.SS1.p1.7.m7.1.1.1.cmml">=</mo><mrow id="S2.SS1.p1.7.m7.1.1.3" xref="S2.SS1.p1.7.m7.1.1.3.cmml"><mn id="S2.SS1.p1.7.m7.1.1.3.2" xref="S2.SS1.p1.7.m7.1.1.3.2.cmml">1</mn><mo id="S2.SS1.p1.7.m7.1.1.3.1" xref="S2.SS1.p1.7.m7.1.1.3.1.cmml">/</mo><mn id="S2.SS1.p1.7.m7.1.1.3.3" xref="S2.SS1.p1.7.m7.1.1.3.3.cmml">2</mn></mrow></mrow></math>, <math><mtable columnspacing="5pt" displaystyle="true" rowspacing="0pt" id="S2.E1.m1.18.18" xref="S2.E1.m1.18.18.cmml"><mtr id="S2.E1.m1.18.18a" xref="S2.E1.m1.18.18.cmml"><mtd class="ltx_border_r" columnalign="center" id="S2.E1.m1.18.18b" xref="S2.E1.m1.18.18.cmml"><mtext id="S2.E1.m1.2.2.2.3.1" xref="S2.E1.m1.2.2.2.3.1a.cmml">Operator</mtext></mtd><mtd class="ltx_border_r" columnalign="center" id="S2.E1.m1.18.18c" xref="S2.E1.m1.18.18.cmml"><mrow id="S2.E1.m1.2.2.2.2.2" xref="S2.E1.m1.2.2.2.2.2.cmml"><mrow id="S2.E1.m1.2.2.2.2.2.4" xref="S2.E1.m1.2.2.2.2.2.4.cmml"><mrow id="S2.E1.m1.2.2.2.2.2.4.2" xref="S2.E1.m1.2.2.2.2.2.4.2.cmml"><mi id="S2.E1.m1.2.2.2.2.2.4.2.2" xref="S2.E1.m1.2.2.2.2.2.4.2.2.cmml">S</mi><mo id="S2.E1.m1.2.2.2.2.2.4.2.1" xref="S2.E1.m1.2.2.2.2.2.4.2.1.cmml">⁢</mo><mi id="S2.E1.m1.2.2.2.2.2.4.2.3" xref="S2.E1.m1.2.2.2.2.2.4.2.3.cmml">U</mi><mo id="S2.E1.m1.2.2.2.2.2.4.2.1a" xref="S2.E1.m1.2.2.2.2.2.4.2.1.cmml">⁢</mo><msub id="S2.E1.m1.2.2.2.2.2.4.2.4" xref="S2.E1.m1.2.2.2.2.2.4.2.4.cmml"><mrow id="S2.E1.m1.2.2.2.2.2.4.2.4.2.2" xref="S2.E1.m1.2.2.2.2.2.4.2.4.cmml"><mo stretchy="false" id="S2.E1.m1.2.2.2.2.2.4.2.4.2.2.1" xref="S2.E1.m1.2.2.2.2.2.4.2.4.cmml">(</mo><mn id="S2.E1.m1.1.1.1.1.1.1" xref="S2.E1.m1.1.1.1.1.1.1.cmml">3</mn><mo stretchy="false" id="S2.E1.m1.2.2.2.2.2.4.2.4.2.2.2" xref="S2.E1.m1.2.2.2.2.2.4.2.4.cmml">)</mo></mrow><mi mathvariant="normal" id="S2.E1.m1.2.2.2.2.2.4.2.4.3" xref="S2.E1.m1.2.2.2.2.2.4.2.4.3.cmml">L</mi></msub></mrow><mo id="S2.E1.m1.2.2.2.2.2.4.1" xref="S2.E1.m1.2.2.2.2.2.4.1.cmml">×</mo><mi id="S2.E1.m1.2.2.2.2.2.4.3" xref="S2.E1.m1.2.2.2.2.2.4.3.cmml">S</mi></mrow><mo id="S2.E1.m1.2.2.2.2.2.3" xref="S2.E1.m1.2.2.2.2.2.3.cmml">⁢</mo><mi id="S2.E1.m1.2.2.2.2.2.5" xref="S2.E1.m1.2.2.2.2.2.5.cmml">U</mi><mo id="S2.E1.m1.2.2.2.2.2.3a" xref="S2.E1.m1.2.2.2.2.2.3.cmml">⁢</mo><msub id="S2.E1.m1.2.2.2.2.2.6" xref="S2.E1.m1.2.2.2.2.2.6.cmml"><mrow id="S2.E1.m1.2.2.2.2.2.6.2.2" xref="S2.E1.m1.2.2.2.2.2.6.cmml"><mo stretchy="false" id="S2.E1.m1.2.2.2.2.2.6.2.2.1" xref="S2.E1.m1.2.2.2.2.2.6.cmml">(</mo><mn id="S2.E1.m1.2.2.2.2.2.2" xref="S2.E1.m1.2.2.2.2.2.2.cmml">3</mn><mo stretchy="false" id="S2.E1.m1.2.2.2.2.2.6.2.2.2" xref="S2.E1.m1.2.2.2.2.2.6.cmml">)</mo></mrow><mi mathvariant="normal" id="S2.E1.m1.2.2.2.2.2.6.3" xref="S2.E1.m1.2.2.2.2.2.6.3.cmml">R</mi></msub></mrow></mtd><mtd columnalign="center" id="S2.E1.m1.18.18d" xref="S2.E1.m1.18.18.cmml"><mrow id="S2.E1.m1.2.2.2.4.1" xref="S2.E1.m1.2.2.2.4.1.cmml"><mi mathvariant="normal" 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Correct Categorie: hep-lat

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1312.5328

Formulas:

1-

T^{6} / (ℤ_{2} \times ℤ_{2})

2-

(h^{(1, 1)}, h^{(2, 1)}) = (3, 3)

3-

K = - \log [- i (S - \bar{S})] - 3 \log [- i (T - \bar{T})] - 3 \log [- i (U - \bar{U})] .

4-

M_{P}^{- 2} = 8 π G = 1

5-

V = e^{K} ({| D W |}^{2} - 3 {| W |}^{2}),

6-

{| D W |}^{2} = K^{I \bar{J}} D_{I} W D_{\bar{J}} \bar{W}

7-

D_{I} W = \partial_{I} W + \partial_{I} K W

8-

W_{t r e e} = P (a_{i}, U) - S P (b_{i}, U),

9-

P (f_{i}, U)

10-

P (f_{i}, U) = f_{0} - 3 f_{1} U + 3 f_{2} U^{2} - f_{3} U^{3} .

Formulas (html):

Correct Categorie: hep-th

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/0801.3784

Formulas:

1-

P_{r e t} (h) = \frac{(\binom{N / 2}{h})}{(\binom{N}{h})},

2-

P_{r e t} (h) ≃ \frac{1}{2^{h}}

3-

N / 4 \leq h \leq 3 N / 4

4-

P_{r e t} (h)

5-

P_{r e t} (h) = P_{r e t} {(1)}^{h} .

6-

P_{r e t} = 1

7-

P_{r e t}

8-

P_{r e t} (h)

9-

P_{r e t}

10-

P_{r e t} = \frac{2 (N - 1)}{2^{N}},

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1010.1588

Formulas:

1-

F e r m i

2-

F e r m i

3-

F e r m i

4-

S w i f t

5-

F e r m i

6-

m a t c h e d f i l t e r

7-

a p r i o r i

8-

F e r m i

9-

F e r m i

10-

f e r m i g b r s t

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/hep-th/9712193

Formulas:

1-

C^{2} / {𝖹𝖹}_{3}

2-

S O (N + 4) \times S U (N)

3-

S P (2 M) \times S U (2 M + 4)

4-

S U (N) \times S O (N + 4)

5-

S U (2 M + 4) \times S P (2 M)

6-

G = {1, α, α^{2}, Ω R {(- 1)}^{F_{L}}, Ω R {(- 1)}^{F_{L}} α, Ω R {(- 1)}^{F_{L}} α^{2}} .

7-

v = X^{4} + i X^{5}

8-

w = X^{8} + i X^{9}

9-

(v, w) \to (α v, α^{- 1} w), α \equiv e^{\frac{2 π i}{3}},

10-

X^{4}, X^{5},

Formulas (html):

Correct Categorie: hep-th

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/1112.1759

Formulas:

1-

{θ^{1 / n}} \neq 0

2-

M_{θ} (n) = [1 / {θ^{1 / n}}]

3-

M_{θ} (n)

4-

{lim}_{n \to \infty} M_{θ} (n) / n = 1 / \log θ

5-

M_{θ} (n)

6-

M_{θ} (n)

7-

M_{θ} (n)

8-

θ = [θ] + {θ}

9-

0 \leq {θ} < 1

10-

∥ θ ∥ = \min ({θ}, 1 - {θ})

Formulas (html):

Correct Categorie: math

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1512.01508

Formulas:

1-

O_{x y z}

2-

(x, y, z)

3-

\exp (- i ω t)

4-

𝑬 (𝒓) = 𝑬 (x, y)

5-

𝑯 = 𝑯 (x, y)

6-

𝖨_{Ω_{j}} (𝒓) = 1 if 𝒓 \in Ω_{j} and 𝖨_{Ω_{j}} (𝒓) = 0

7-

ϵ_{j} (ω) = ϵ_{j} (ω) 𝖨_{𝖽}

8-

ϵ (ω, 𝒓) = \sum_{j} 𝖨_{Ω_{j}} (𝒓) ϵ_{j} (ω) 𝖨_{𝖽} .

9-

ϵ_{j} (ω) = ϵ_{\infty_{j}} - \sum_{k} \frac{ω_{p, j k}^{2}}{ω^{2} + i γ_{D, j k} ω - ω_{D, j k}^{2}},

10-

γ_{D, j k}

Formulas (html):

Correct Categorie: physics

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/1705.09190

Formulas:

1-

𝔻_{2, 4, 6}

2-

R : \prod_{j} | s_{j} ⟩ \to \prod_{j} U_{j} (R) | s_{j^{'} = R j} ⟩

3-

j^{'} = R j

4-

U_{j} (R)

5-

G_{a} = 𝔻_{2} = ℤ_{2} \times ℤ_{2}

6-

U (C_{2}) = i σ_{z}

7-

U (R_{x}) = i σ_{x}

8-

U (C_{2}) U (R_{x}) = - U (R_{x}) U (C_{2})

9-

C_{2} R_{x} = R_{x} C_{2}

10-

ℋ = ℋ^{'} \otimes ℋ_{a}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1506.05041

Formulas:

1-

N_{c} = N_{c}^{iso} = 2 N^{'} - 1

2-

𝒞 (ϕ, γ)

3-

𝒞_{1} (ϕ, γ)

4-

𝒞_{2} (ϕ, γ)

5-

𝒞_{1} (ϕ, γ)

6-

𝒞_{2} (ϕ, γ)

7-

ϕ = A {(γ - γ_{0})}^{2} + ϕ_{0}

8-

σ_{L} / σ_{S} = 1.4

9-

V / (N ϵ)

10-

10^{- 16} > V / (N ϵ) > 0

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: math

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/9701095

Formulas:

1-

{(\dot{M})}^{1 / 3}

2-

\dot{M} = - 2 π r σ u,

3-

\dot{J} = \dot{M} r^{2} Ω + 2 π ν σ r^{3} \frac{d Ω}{d r} .

4-

d Ω / d r < 0

5-

Ω^{2} \sim \frac{1}{r} \frac{d Φ_{σ}}{d r} + \frac{G M_{⋆}}{r^{3}},

6-

Φ_{σ} (r) = - 2 π G \int_{0}^{\infty} K^{(0)} (r, r^{'}) σ (r^{'}) 𝑑 r^{'},

7-

K^{(0)} (r, r^{'}) = (1 / π) \sqrt{r^{'} ζ / r} K (ζ)

8-

ζ \equiv 4 r r^{'} / {(r + r^{'})}^{2}

9-

u (d u / d r)

10-

ν = α c h,

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/1301.7271

Formulas:

1-

i = 1, \dots, n

2-

𝝅_{i} = \frac{\exp (𝑿_{i} 𝜷)}{𝟏_{c}^{'} \exp (𝑿_{i} 𝜷)} .

3-

j = 0, \dots, c - 1

4-

𝒒_{j} = \frac{\exp ({𝑮 𝜽}_{j})}{𝟏_{r}^{'} \exp ({𝑮 𝜽}_{j})},

5-

ℓ (𝜷, 𝜽; 𝒚_{i}, 𝑿_{i})

6-

𝒚_{i}^{'} \log (𝒑_{i})

7-

𝒔_{𝜷} = \sum_{i} 𝑿_{i}^{'} 𝛀_{𝝅_{i}} 𝑸^{'} diag {(𝒑_{i})}^{- 1} 𝒚_{i}

8-

diag (𝝅_{i}) - 𝝅_{i} 𝝅_{i}^{'}

9-

\sum_{j} π_{i j} 𝒒_{j}

10-

𝒔_{j} = \sum_{i} π_{i j} 𝑮^{'} 𝛀_{j} diag {(𝒑_{i})}^{- 1} 𝒚_{i},

Formulas (html):

Correct Categorie: stat

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/0912.2906

Formulas:

1-

\sim < 20 M_{⊙}

2-

χ_{ν}^{2} = 3512 / 3461

3-

N_{H} = (1.04 \pm 0.02) \times 10^{21}

4-

Δ χ^{2} \sim < 7

5-

χ_{ν}^{2} = 3512 / 3461

6-

χ_{ν}^{2} = 3562 / 3475

7-

y = 4 τ^{2} θ =

8-

θ = k T_{e} / m_{e} c^{2}

9-

{\dot{M}}_{E d d}

10-

\dot{M} / {\dot{M}}_{E d d}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: math

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/0603631

Formulas:

1-

(ω_{a}, ω_{r}) = 2 π \times (16, 76) s^{- 1}

2-

B_{z} = 0.87 G

3-

\pm 1 s t

4-

\sqrt{ρ_{0} (z)} \exp (- \frac{i}{ℏ} \int U (z, t) d t)

5-

\sqrt{ρ_{0} (z)} \exp (- i S \cos (k z + ϕ)) .

6-

U (z, t) = u (t) \cdot \cos (k z + ϕ)

7-

k = 2 π / a

8-

E_{r} τ ≪ ℏ / S

9-

E_{r} = {(ℏ k)}^{2} / 2 m

10-

τ < 0.2 m s

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: math

Result: incorrect

Paper: https://arxiv.org/abs/1511.08598

Formulas:

1-

𝒪 (\log \log n)

2-

(s^{α}, s^{1 - δ})

3-

(𝐟_{𝟏}, 𝐟_{𝟐})

4-

\begin{matrix} \exists β \forall c_{1}, c_{2}, c_{3} a \leq c_{1} < c_{2} < c_{3} \leq b \forall s \in ℕ \\ \underset{X \sim μ}{\Pr} [X \in ⟨ c_{2} - \frac{c_{3} - c_{1}}{f_{1} (s)}, c_{2} ⟩ | X \in ⟨ c_{1}, c_{3} ⟩] \leq \frac{β f_{2} (s)}{s} \end{matrix}

5-

⟨ c_{1}, c_{3} ⟩

6-

f_{1} (s)

7-

⟨ c_{1}, c_{3} ⟩

8-

𝒪 (f_{2} (s))

9-

(s^{α}, s^{1 - δ})

10-

\begin{matrix} \exists β \forall c_{1}, c_{2}, c_{3} a \leq c_{1} < c_{2} < c_{3} \leq b \forall s \in ℕ \\ \Pr [X \in ⟨ c_{2} - \frac{c_{3} - c_{1}}{s^{α}}, c_{2} ⟩ | X \in ⟨ c_{1}, c_{3} ⟩] \leq \frac{β s^{1 - δ}}{s} = β s^{- δ} . \end{matrix}

Formulas (html):

Correct Categorie: cs

Guessed Categorie: hep-ph

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/0312596

Formulas:

1-

H = \sum_{j} [U n_{j}^{2} - v_{j} n_{j} - T / 2 \sum_{k \sim j} (a_{j}^{+} a_{k} + a_{k} a_{j}^{+})]

2-

n_{j} = a_{j}^{+} a_{j}

3-

z_{j} = \sqrt{ρ_{j}} ⅇ^{ⅈ ϕ_{j}}

4-

ℋ = \sum_{j} [U {| z_{j} |}^{4} - v_{j} {| z_{j} |}^{2} - T / 2 \sum_{k \sim j} (z_{j}^{*} z_{k} + z_{j} z_{k}^{*})]

5-

{z_{j}, z_{k}^{*}} = δ_{j k}

6-

n = \sum_{j} n_{j}

7-

ρ = \sum_{j} ρ_{j}

8-

{z_{j}, ℋ - μ ρ} = 0

9-

z_{j} = \sqrt{ρ} x_{j}

10-

\sum_{j} x_{j}^{2} = 1

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/1012.3689

Formulas:

1-

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

2-

e^{+} e^{-} \to π^{+} π^{-} (γ)

3-

e^{+} e^{-} \to μ^{+} μ^{-} γ (γ)

4-

(514.1 \pm 2.2 (stat) \pm 3.1 (syst)) \times 10^{- 10}

5-

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

6-

a_{μ}^{h a d}

7-

e^{+} e^{-} \to π^{+} π^{-} (γ)

8-

a_{μ}^{h a d}

9-

e^{+} e^{-} \to X γ_{I S R}

10-

e^{+} e^{-} \to π π (γ_{F S R})

Formulas (html):

Correct Categorie: hep-ex

Guessed Categorie: math

Result: incorrect

Paper: https://arxiv.org/abs/hep-th/9803033

Formulas:

1-

S U (N_{c})

2-

N_{f} \leq 3 N_{c}

3-

N_{f} > 3 N_{c}

4-

S U (N_{c})

5-

S U {(N_{f})}_{L} \times S U {(N_{f})}_{R}

6-

S U (N_{f})

7-

S U (N_{c})

8-

S U (N_{c})

9-

S U (N_{c})

10-

N_{f} \leq 3 N_{c}

Formulas (html):

Correct Categorie: hep-th

Guessed Categorie: hep-th

Result: correct

Paper: https://arxiv.org/abs/1204.2156

Formulas:

1-

G C A_{2}

2-

G C A_{2}

3-

A d S_{3}

4-

G C A_{2}

5-

A d S_{3}

6-

L^{n} = - (n + 1) t^{n} x_{i} \partial_{i} - t^{n + 1} \partial_{t}

7-

M_{i}^{n} = t^{n + 1} \partial_{i}

8-

J_{i j}^{n} = - t^{n} (x_{i} \partial_{j} - x_{j} \partial_{i})

9-

J_{i j}^{0}, L^{\pm 1}, L^{0}, M_{i}^{\pm 1}, M_{i}^{0}

10-

t \to t, x_{i} \to ϵ x_{i}, ϵ \to 0, v_{i} \sim ϵ

Formulas (html):

Correct Categorie: hep-th

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/1307.1377

Formulas:

1-

A B C A B C

2-

R \bar{3} m

3-

- 2 J \sum_{i j} 𝐒_{i} \cdot 𝐒_{j}

4-

- J \sum_{i j} 𝐒_{i} \cdot 𝐒_{j}

5-

A (t) = A_{rel} e^{- {(λ t)}^{β}} + A_{bg},

6-

λ \propto Δ^{2} τ

7-

T_{0} / \ln 10

8-

T ≪ 2 π ρ_{s}

9-

λ = G_{CSS} {(\frac{N_{0} A_{0}}{ℏ})}^{2} \frac{ℏ}{ρ_{s}} {(\frac{T}{T_{0}})}^{3} \exp (T_{0} / T),

10-

T_{0} = 4 π ρ_{s}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1703.04749

Formulas:

1-

L (X, Y)

2-

X {\hat{\otimes}}_{π} Y

3-

S (C, f, α) := {x \in C : f (x) > 1 - α}

4-

\sum_{i = 1}^{n} λ_{i} S_{i},

5-

λ_{1}, \dots, λ_{n} \in [0, 1]

6-

\sum_{i = 1}^{n} λ_{i} = 1

7-

∥ x ∥ > 1 - ε

8-

C := \sum_{i = 1}^{n} S (B_{X}, f_{i}, α)

9-

D := \frac{1}{2} (\sum_{i = 1}^{n} λ_{i} S (B_{X}, f_{i}, α) + \sum_{i = 1}^{n} λ_{i} S (B_{X}, - f_{i}, α))

10-

x = \frac{1}{2} (\sum_{i = 1}^{n} λ_{i} x_{i} + \sum_{i = 1}^{n} λ_{i} y_{i}) \in D

Formulas (html):

Correct Categorie: math

Guessed Categorie: gr-qc

Result: incorrect

Paper: https://arxiv.org/abs/1609.03474

Formulas:

1-

τ_{s} = l / \bar{v} = l / v_{-} - l / v_{+} \approx 70 - 80

2-

\bar{v} \approx 5 \times 10^{4}

3-

n_{s} = 1.9 \times 10^{15}

4-

μ = 2.4 \times 10^{6}

5-

{cm}^{2} . V^{- 1} . s^{- 1}

6-

l = 3.2 \pm 0.4 μ

7-

Δ q (τ)

8-

Δ q (τ)

9-

Δ q (τ) \geq 1

10-

| τ | \approx τ_{s}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: hep-ph

Result: incorrect

Paper: https://arxiv.org/abs/1708.02179

Formulas:

1-

Δ_{t} = t - t_{0}

2-

Δ_{t} \in τ^{-} = [τ_{m i n}^{-}, τ_{m a x}^{-}] \cup [- τ_{m a x}^{-}, - τ_{m i n}^{-}]

3-

τ_{m i n}^{-}, τ_{m a x}^{-}

4-

y_{S} (I_{b}, I_{r}) = {\begin{matrix} 1, & if I o U (I_{b}, I_{r}) \in [σ_{m i n}^{+}, σ_{m a x}^{+}] \\ 0, & if I o U (I_{b}, I_{r}) \in [σ_{m i n}^{-}, σ_{m a x}^{-}] \end{matrix}

5-

I o U (\cdot, \cdot)

6-

[σ_{m i n}^{+}, σ_{m a x}^{+}]

7-

[σ_{m i n}^{-}, σ_{m a x}^{-}]

8-

τ^{-} = [8, 16]

9-

σ^{+} = [0.65, 0.95]

10-

σ^{-} = [0.25, 0.55]

Formulas (html):

Correct Categorie: cs

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/math/0204047

Formulas:

1-

E_{T} = f^{*} E

2-

φ : R^{q} \to R^{p}

3-

R^{q} \overset{φ}{\to} R^{p} \to E \to 0

4-

E / 𝔪^{n} E

5-

R^{m} \oplus {(R / I)}^{n}

6-

R^{q} \overset{φ}{\to} R^{p} \to E \to 0

7-

p = {dim}_{R / 𝔪} (E / 𝔪 E)

8-

φ : R^{q} \to R^{p}

9-

φ : R^{q} \to R^{p}

10-

(\begin{matrix} 1_{m \times m} & 0_{m \times (q - m)} \\ 0_{(p - m) \times m} & 0_{(p - m) \times (q - m)} \end{matrix})

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/1211.2206

Formulas:

1-

0.01 \sim 10 M_{⊙} s^{- 1}

2-

T_{90} > 2 s

3-

T_{90} < 2 s

4-

ψ = - G M / r

5-

\partial / \partial t = \partial / \partial ϕ = 0

6-

\frac{1}{2} v_{r}^{2} + \frac{5}{2} c_{s}^{2} + v_{ϕ}^{2} - r^{2} Ω_{K}^{2} = 0,

7-

\frac{1}{ρ} \frac{d p}{d θ} = v_{ϕ}^{2} \cot θ,

8-

v_{r} = - \frac{3}{2} \frac{α c_{s}^{2}}{r Ω_{K}},

9-

c_{s}^{2} = p / ρ

10-

Ω_{K} = {(G M / r^{3})}^{1 / 2}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/0712.0718

Formulas:

1-

R_{*} ≃ 2 R_{⊙}

2-

15 R_{*} \leq H \leq 26 R_{*}

3-

α_{J 2000.0} = 04^{h} 03^{m} 05 .^{s} 586056

4-

δ_{J 2000.0} = 26^{\circ} 00^{'} 01 .^{''} 50288

5-

α_{J 2000.0} = 04^{h} 14^{m} 12 .^{s} 919833

6-

δ_{J 2000.0} = 28^{\circ} 12^{'} 12 .^{''} 19953

7-

𝒜 ℐ 𝒫 𝒮

8-

15 R_{*} \leq H \leq 26 R_{*}

9-

θ > \arcsin {(B_{s} / B_{H})}^{1 / 2}

10-

R_{*} / c ≃ 85

Formulas (html):

<math><mrow id="S1.p1.6.m6.1.1" xref="S1.p1.6.m6.1.1.cmml"><msub id="S1.p1.6.m6.1.1.2" xref="S1.p1.6.m6.1.1.2.cmml"><mi id="S1.p1.6.m6.1.1.2.2" xref="S1.p1.6.m6.1.1.2.2.cmml">R</mi><mo id="S1.p1.6.m6.1.1.2.3" xref="S1.p1.6.m6.1.1.2.3.cmml">*</mo></msub><mo id="S1.p1.6.m6.1.1.1" xref="S1.p1.6.m6.1.1.1.cmml">≃</mo><mrow id="S1.p1.6.m6.1.1.3" xref="S1.p1.6.m6.1.1.3.cmml"><mn id="S1.p1.6.m6.1.1.3.2" xref="S1.p1.6.m6.1.1.3.2.cmml">2</mn><mo id="S1.p1.6.m6.1.1.3.1" xref="S1.p1.6.m6.1.1.3.1.cmml">⁢</mo><msub id="S1.p1.6.m6.1.1.3.3" xref="S1.p1.6.m6.1.1.3.3.cmml"><mi id="S1.p1.6.m6.1.1.3.3.2" xref="S1.p1.6.m6.1.1.3.3.2.cmml">R</mi><mo id="S1.p1.6.m6.1.1.3.3.3" xref="S1.p1.6.m6.1.1.3.3.3.cmml">⊙</mo></msub></mrow></mrow></math>, <math><mrow id="S1.p1.7.m7.1.1" xref="S1.p1.7.m7.1.1.cmml"><mrow id="S1.p1.7.m7.1.1.2" xref="S1.p1.7.m7.1.1.2.cmml"><mn id="S1.p1.7.m7.1.1.2.2" xref="S1.p1.7.m7.1.1.2.2.cmml">15</mn><mo id="S1.p1.7.m7.1.1.2.1" xref="S1.p1.7.m7.1.1.2.1.cmml">⁢</mo><msub id="S1.p1.7.m7.1.1.2.3" xref="S1.p1.7.m7.1.1.2.3.cmml"><mi id="S1.p1.7.m7.1.1.2.3.2" xref="S1.p1.7.m7.1.1.2.3.2.cmml">R</mi><mo id="S1.p1.7.m7.1.1.2.3.3" xref="S1.p1.7.m7.1.1.2.3.3.cmml">*</mo></msub></mrow><mo id="S1.p1.7.m7.1.1.3" xref="S1.p1.7.m7.1.1.3.cmml">≤</mo><mi id="S1.p1.7.m7.1.1.4" xref="S1.p1.7.m7.1.1.4.cmml">H</mi><mo id="S1.p1.7.m7.1.1.5" xref="S1.p1.7.m7.1.1.5.cmml">≤</mo><mrow id="S1.p1.7.m7.1.1.6" xref="S1.p1.7.m7.1.1.6.cmml"><mn id="S1.p1.7.m7.1.1.6.2" xref="S1.p1.7.m7.1.1.6.2.cmml">26</mn><mo id="S1.p1.7.m7.1.1.6.1" xref="S1.p1.7.m7.1.1.6.1.cmml">⁢</mo><msub id="S1.p1.7.m7.1.1.6.3" xref="S1.p1.7.m7.1.1.6.3.cmml"><mi id="S1.p1.7.m7.1.1.6.3.2" xref="S1.p1.7.m7.1.1.6.3.2.cmml">R</mi><mo id="S1.p1.7.m7.1.1.6.3.3" xref="S1.p1.7.m7.1.1.6.3.3.cmml">*</mo></msub></mrow></mrow></math>, <math><mrow id="S2.p3.1.m1.1.1" xref="S2.p3.1.m1.1.1.cmml"><msub id="S2.p3.1.m1.1.1.2" xref="S2.p3.1.m1.1.1.2.cmml"><mi id="S2.p3.1.m1.1.1.2.2" xref="S2.p3.1.m1.1.1.2.2.cmml">α</mi><mrow id="S2.p3.1.m1.1.1.2.3" xref="S2.p3.1.m1.1.1.2.3.cmml"><mi id="S2.p3.1.m1.1.1.2.3.2" xref="S2.p3.1.m1.1.1.2.3.2.cmml">J</mi><mo id="S2.p3.1.m1.1.1.2.3.1" xref="S2.p3.1.m1.1.1.2.3.1.cmml">⁢</mo><mn id="S2.p3.1.m1.1.1.2.3.3" xref="S2.p3.1.m1.1.1.2.3.3.cmml">2000.0</mn></mrow></msub><mo id="S2.p3.1.m1.1.1.1" xref="S2.p3.1.m1.1.1.1.cmml">=</mo><mrow id="S2.p3.1.m1.1.1.3" xref="S2.p3.1.m1.1.1.3.cmml"><msup id="S2.p3.1.m1.1.1.3.2" xref="S2.p3.1.m1.1.1.3.2.cmml"><mn id="S2.p3.1.m1.1.1.3.2.2" xref="S2.p3.1.m1.1.1.3.2.2.cmml">04</mn><mi mathvariant="normal" id="S2.p3.1.m1.1.1.3.2.3" xref="S2.p3.1.m1.1.1.3.2.3.cmml">h</mi></msup><mo id="S2.p3.1.m1.1.1.3.1" xref="S2.p3.1.m1.1.1.3.1.cmml">⁢</mo><msup id="S2.p3.1.m1.1.1.3.3" xref="S2.p3.1.m1.1.1.3.3.cmml"><mn id="S2.p3.1.m1.1.1.3.3.2" xref="S2.p3.1.m1.1.1.3.3.2.cmml">03</mn><mi mathvariant="normal" id="S2.p3.1.m1.1.1.3.3.3" xref="S2.p3.1.m1.1.1.3.3.3.cmml">m</mi></msup><mo id="S2.p3.1.m1.1.1.3.1a" xref="S2.p3.1.m1.1.1.3.1.cmml">⁢</mo><mn id="S2.p3.1.m1.1.1.3.4" xref="S2.p3.1.m1.1.1.3.4.cmml">05</mn><mo id="S2.p3.1.m1.1.1.3.1b" xref="S2.p3.1.m1.1.1.3.1.cmml">⁢</mo><msup id="S2.p3.1.m1.1.1.3.5" xref="S2.p3.1.m1.1.1.3.5.cmml"><mpadded width="0.0pt" id="S2.p3.1.m1.1.1.3.5.2" xref="S2.p3.1.m1.1.1.3.5.2b.cmml"><mtext mathvariant="bold-sans-serif" id="S2.p3.1.m1.1.1.3.5.2a" xref="S2.p3.1.m1.1.1.3.5.2b.cmml">.</mtext></mpadded><mi mathvariant="normal" id="S2.p3.1.m1.1.1.3.5.3" xref="S2.p3.1.m1.1.1.3.5.3.cmml">s</mi></msup><mo id="S2.p3.1.m1.1.1.3.1c" xref="S2.p3.1.m1.1.1.3.1.cmml">⁢</mo><mn id="S2.p3.1.m1.1.1.3.6" xref="S2.p3.1.m1.1.1.3.6.cmml">586056</mn></mrow></mrow></math>, <math><mrow id="S2.p3.2.m2.1.1" xref="S2.p3.2.m2.1.1.cmml"><msub id="S2.p3.2.m2.1.1.2" xref="S2.p3.2.m2.1.1.2.cmml"><mi id="S2.p3.2.m2.1.1.2.2" xref="S2.p3.2.m2.1.1.2.2.cmml">δ</mi><mrow id="S2.p3.2.m2.1.1.2.3" xref="S2.p3.2.m2.1.1.2.3.cmml"><mi id="S2.p3.2.m2.1.1.2.3.2" xref="S2.p3.2.m2.1.1.2.3.2.cmml">J</mi><mo id="S2.p3.2.m2.1.1.2.3.1" xref="S2.p3.2.m2.1.1.2.3.1.cmml">⁢</mo><mn id="S2.p3.2.m2.1.1.2.3.3" xref="S2.p3.2.m2.1.1.2.3.3.cmml">2000.0</mn></mrow></msub><mo id="S2.p3.2.m2.1.1.1" xref="S2.p3.2.m2.1.1.1.cmml">=</mo><mrow id="S2.p3.2.m2.1.1.3" xref="S2.p3.2.m2.1.1.3.cmml"><msup id="S2.p3.2.m2.1.1.3.2" xref="S2.p3.2.m2.1.1.3.2.cmml"><mn id="S2.p3.2.m2.1.1.3.2.2" xref="S2.p3.2.m2.1.1.3.2.2.cmml">26</mn><mo id="S2.p3.2.m2.1.1.3.2.3" xref="S2.p3.2.m2.1.1.3.2.3.cmml">∘</mo></msup><mo id="S2.p3.2.m2.1.1.3.1" xref="S2.p3.2.m2.1.1.3.1.cmml">⁢</mo><msup id="S2.p3.2.m2.1.1.3.3" xref="S2.p3.2.m2.1.1.3.3.cmml"><mn id="S2.p3.2.m2.1.1.3.3.2" xref="S2.p3.2.m2.1.1.3.3.2.cmml">00</mn><mo id="S2.p3.2.m2.1.1.3.3.3" xref="S2.p3.2.m2.1.1.3.3.3.cmml">′</mo></msup><mo id="S2.p3.2.m2.1.1.3.1a" xref="S2.p3.2.m2.1.1.3.1.cmml">⁢</mo><mn id="S2.p3.2.m2.1.1.3.4" xref="S2.p3.2.m2.1.1.3.4.cmml">01</mn><mo id="S2.p3.2.m2.1.1.3.1b" xref="S2.p3.2.m2.1.1.3.1.cmml">⁢</mo><msup id="S2.p3.2.m2.1.1.3.5" xref="S2.p3.2.m2.1.1.3.5.cmml"><mpadded width="0.0pt" id="S2.p3.2.m2.1.1.3.5.2" xref="S2.p3.2.m2.1.1.3.5.2b.cmml"><mtext mathvariant="bold-sans-serif" id="S2.p3.2.m2.1.1.3.5.2a" xref="S2.p3.2.m2.1.1.3.5.2b.cmml">.</mtext></mpadded><mo id="S2.p3.2.m2.1.1.3.5.3" xref="S2.p3.2.m2.1.1.3.5.3.cmml">′′</mo></msup><mo id="S2.p3.2.m2.1.1.3.1c" xref="S2.p3.2.m2.1.1.3.1.cmml">⁢</mo><mn id="S2.p3.2.m2.1.1.3.6" xref="S2.p3.2.m2.1.1.3.6.cmml">50288</mn></mrow></mrow></math>, <math><mrow id="S2.p3.3.m3.1.1" xref="S2.p3.3.m3.1.1.cmml"><msub id="S2.p3.3.m3.1.1.2" xref="S2.p3.3.m3.1.1.2.cmml"><mi id="S2.p3.3.m3.1.1.2.2" xref="S2.p3.3.m3.1.1.2.2.cmml">α</mi><mrow id="S2.p3.3.m3.1.1.2.3" xref="S2.p3.3.m3.1.1.2.3.cmml"><mi id="S2.p3.3.m3.1.1.2.3.2" xref="S2.p3.3.m3.1.1.2.3.2.cmml">J</mi><mo id="S2.p3.3.m3.1.1.2.3.1" xref="S2.p3.3.m3.1.1.2.3.1.cmml">⁢</mo><mn id="S2.p3.3.m3.1.1.2.3.3" xref="S2.p3.3.m3.1.1.2.3.3.cmml">2000.0</mn></mrow></msub><mo id="S2.p3.3.m3.1.1.1" xref="S2.p3.3.m3.1.1.1.cmml">=</mo><mrow id="S2.p3.3.m3.1.1.3" xref="S2.p3.3.m3.1.1.3.cmml"><msup id="S2.p3.3.m3.1.1.3.2" xref="S2.p3.3.m3.1.1.3.2.cmml"><mn id="S2.p3.3.m3.1.1.3.2.2" xref="S2.p3.3.m3.1.1.3.2.2.cmml">04</mn><mi mathvariant="normal" id="S2.p3.3.m3.1.1.3.2.3" xref="S2.p3.3.m3.1.1.3.2.3.cmml">h</mi></msup><mo id="S2.p3.3.m3.1.1.3.1" xref="S2.p3.3.m3.1.1.3.1.cmml">⁢</mo><msup id="S2.p3.3.m3.1.1.3.3" xref="S2.p3.3.m3.1.1.3.3.cmml"><mn id="S2.p3.3.m3.1.1.3.3.2" xref="S2.p3.3.m3.1.1.3.3.2.cmml">14</mn><mi mathvariant="normal" id="S2.p3.3.m3.1.1.3.3.3" xref="S2.p3.3.m3.1.1.3.3.3.cmml">m</mi></msup><mo id="S2.p3.3.m3.1.1.3.1a" xref="S2.p3.3.m3.1.1.3.1.cmml">⁢</mo><mn id="S2.p3.3.m3.1.1.3.4" xref="S2.p3.3.m3.1.1.3.4.cmml">12</mn><mo id="S2.p3.3.m3.1.1.3.1b" xref="S2.p3.3.m3.1.1.3.1.cmml">⁢</mo><msup id="S2.p3.3.m3.1.1.3.5" xref="S2.p3.3.m3.1.1.3.5.cmml"><mpadded width="0.0pt" id="S2.p3.3.m3.1.1.3.5.2" xref="S2.p3.3.m3.1.1.3.5.2b.cmml"><mtext mathvariant="bold-sans-serif" id="S2.p3.3.m3.1.1.3.5.2a" xref="S2.p3.3.m3.1.1.3.5.2b.cmml">.</mtext></mpadded><mi mathvariant="normal" id="S2.p3.3.m3.1.1.3.5.3" xref="S2.p3.3.m3.1.1.3.5.3.cmml">s</mi></msup><mo id="S2.p3.3.m3.1.1.3.1c" xref="S2.p3.3.m3.1.1.3.1.cmml">⁢</mo><mn id="S2.p3.3.m3.1.1.3.6" xref="S2.p3.3.m3.1.1.3.6.cmml">919833</mn></mrow></mrow></math>, <math><mrow id="S2.p3.4.m4.1.1" xref="S2.p3.4.m4.1.1.cmml"><msub id="S2.p3.4.m4.1.1.2" xref="S2.p3.4.m4.1.1.2.cmml"><mi id="S2.p3.4.m4.1.1.2.2" xref="S2.p3.4.m4.1.1.2.2.cmml">δ</mi><mrow id="S2.p3.4.m4.1.1.2.3" xref="S2.p3.4.m4.1.1.2.3.cmml"><mi id="S2.p3.4.m4.1.1.2.3.2" xref="S2.p3.4.m4.1.1.2.3.2.cmml">J</mi><mo id="S2.p3.4.m4.1.1.2.3.1" xref="S2.p3.4.m4.1.1.2.3.1.cmml">⁢</mo><mn id="S2.p3.4.m4.1.1.2.3.3" xref="S2.p3.4.m4.1.1.2.3.3.cmml">2000.0</mn></mrow></msub><mo id="S2.p3.4.m4.1.1.1" xref="S2.p3.4.m4.1.1.1.cmml">=</mo><mrow id="S2.p3.4.m4.1.1.3" xref="S2.p3.4.m4.1.1.3.cmml"><msup id="S2.p3.4.m4.1.1.3.2" xref="S2.p3.4.m4.1.1.3.2.cmml"><mn id="S2.p3.4.m4.1.1.3.2.2" xref="S2.p3.4.m4.1.1.3.2.2.cmml">28</mn><mo id="S2.p3.4.m4.1.1.3.2.3" xref="S2.p3.4.m4.1.1.3.2.3.cmml">∘</mo></msup><mo id="S2.p3.4.m4.1.1.3.1" xref="S2.p3.4.m4.1.1.3.1.cmml">⁢</mo><msup id="S2.p3.4.m4.1.1.3.3" xref="S2.p3.4.m4.1.1.3.3.cmml"><mn id="S2.p3.4.m4.1.1.3.3.2" xref="S2.p3.4.m4.1.1.3.3.2.cmml">12</mn><mo id="S2.p3.4.m4.1.1.3.3.3" xref="S2.p3.4.m4.1.1.3.3.3.cmml">′</mo></msup><mo id="S2.p3.4.m4.1.1.3.1a" xref="S2.p3.4.m4.1.1.3.1.cmml">⁢</mo><mn id="S2.p3.4.m4.1.1.3.4" xref="S2.p3.4.m4.1.1.3.4.cmml">12</mn><mo id="S2.p3.4.m4.1.1.3.1b" xref="S2.p3.4.m4.1.1.3.1.cmml">⁢</mo><msup id="S2.p3.4.m4.1.1.3.5" xref="S2.p3.4.m4.1.1.3.5.cmml"><mpadded width="0.0pt" id="S2.p3.4.m4.1.1.3.5.2" xref="S2.p3.4.m4.1.1.3.5.2b.cmml"><mtext mathvariant="bold-sans-serif" id="S2.p3.4.m4.1.1.3.5.2a" xref="S2.p3.4.m4.1.1.3.5.2b.cmml">.</mtext></mpadded><mo id="S2.p3.4.m4.1.1.3.5.3" xref="S2.p3.4.m4.1.1.3.5.3.cmml">′′</mo></msup><mo id="S2.p3.4.m4.1.1.3.1c" xref="S2.p3.4.m4.1.1.3.1.cmml">⁢</mo><mn id="S2.p3.4.m4.1.1.3.6" xref="S2.p3.4.m4.1.1.3.6.cmml">19953</mn></mrow></mrow></math>, <math><mrow id="S2.p4.1.m1.1.1" xref="S2.p4.1.m1.1.1.cmml"><mi class="ltx_font_mathcaligraphic" id="S2.p4.1.m1.1.1.2" xref="S2.p4.1.m1.1.1.2.cmml">𝒜</mi><mo id="S2.p4.1.m1.1.1.1" xref="S2.p4.1.m1.1.1.1.cmml">⁢</mo><mi class="ltx_font_mathcaligraphic" id="S2.p4.1.m1.1.1.3" xref="S2.p4.1.m1.1.1.3.cmml">ℐ</mi><mo id="S2.p4.1.m1.1.1.1a" xref="S2.p4.1.m1.1.1.1.cmml">⁢</mo><mi class="ltx_font_mathcaligraphic" id="S2.p4.1.m1.1.1.4" xref="S2.p4.1.m1.1.1.4.cmml">𝒫</mi><mo id="S2.p4.1.m1.1.1.1b" xref="S2.p4.1.m1.1.1.1.cmml">⁢</mo><mi class="ltx_font_mathcaligraphic" id="S2.p4.1.m1.1.1.5" xref="S2.p4.1.m1.1.1.5.cmml">𝒮</mi></mrow></math>, <math><mrow id="S3.SS2.p1.3.m3.1.1" xref="S3.SS2.p1.3.m3.1.1.cmml"><mrow id="S3.SS2.p1.3.m3.1.1.2" xref="S3.SS2.p1.3.m3.1.1.2.cmml"><mn id="S3.SS2.p1.3.m3.1.1.2.2" xref="S3.SS2.p1.3.m3.1.1.2.2.cmml">15</mn><mo id="S3.SS2.p1.3.m3.1.1.2.1" xref="S3.SS2.p1.3.m3.1.1.2.1.cmml">⁢</mo><msub id="S3.SS2.p1.3.m3.1.1.2.3" xref="S3.SS2.p1.3.m3.1.1.2.3.cmml"><mi id="S3.SS2.p1.3.m3.1.1.2.3.2" xref="S3.SS2.p1.3.m3.1.1.2.3.2.cmml">R</mi><mo id="S3.SS2.p1.3.m3.1.1.2.3.3" xref="S3.SS2.p1.3.m3.1.1.2.3.3.cmml">*</mo></msub></mrow><mo id="S3.SS2.p1.3.m3.1.1.3" xref="S3.SS2.p1.3.m3.1.1.3.cmml">≤</mo><mi id="S3.SS2.p1.3.m3.1.1.4" xref="S3.SS2.p1.3.m3.1.1.4.cmml">H</mi><mo id="S3.SS2.p1.3.m3.1.1.5" xref="S3.SS2.p1.3.m3.1.1.5.cmml">≤</mo><mrow id="S3.SS2.p1.3.m3.1.1.6" xref="S3.SS2.p1.3.m3.1.1.6.cmml"><mn id="S3.SS2.p1.3.m3.1.1.6.2" xref="S3.SS2.p1.3.m3.1.1.6.2.cmml">26</mn><mo id="S3.SS2.p1.3.m3.1.1.6.1" xref="S3.SS2.p1.3.m3.1.1.6.1.cmml">⁢</mo><msub id="S3.SS2.p1.3.m3.1.1.6.3" xref="S3.SS2.p1.3.m3.1.1.6.3.cmml"><mi id="S3.SS2.p1.3.m3.1.1.6.3.2" xref="S3.SS2.p1.3.m3.1.1.6.3.2.cmml">R</mi><mo id="S3.SS2.p1.3.m3.1.1.6.3.3" xref="S3.SS2.p1.3.m3.1.1.6.3.3.cmml">*</mo></msub></mrow></mrow></math>, <math><mrow id="S3.SS2.p4.4.m4.1.1" xref="S3.SS2.p4.4.m4.1.1.cmml"><mi id="S3.SS2.p4.4.m4.1.1.3" xref="S3.SS2.p4.4.m4.1.1.3.cmml">θ</mi><mo id="S3.SS2.p4.4.m4.1.1.2" xref="S3.SS2.p4.4.m4.1.1.2.cmml">></mo><mrow id="S3.SS2.p4.4.m4.1.1.1" xref="S3.SS2.p4.4.m4.1.1.1.cmml"><mi id="S3.SS2.p4.4.m4.1.1.1.3" xref="S3.SS2.p4.4.m4.1.1.1.3.cmml">arcsin</mi><mo id="S3.SS2.p4.4.m4.1.1.1.2" xref="S3.SS2.p4.4.m4.1.1.1.2.cmml">⁢</mo><msup id="S3.SS2.p4.4.m4.1.1.1.1" xref="S3.SS2.p4.4.m4.1.1.1.1.cmml"><mrow id="S3.SS2.p4.4.m4.1.1.1.1.1.1" xref="S3.SS2.p4.4.m4.1.1.1.1.1.1.1.cmml"><mo id="S3.SS2.p4.4.m4.1.1.1.1.1.1.2" xref="S3.SS2.p4.4.m4.1.1.1.1.1.1.1.cmml">(</mo><mrow id="S3.SS2.p4.4.m4.1.1.1.1.1.1.1" xref="S3.SS2.p4.4.m4.1.1.1.1.1.1.1.cmml"><msub id="S3.SS2.p4.4.m4.1.1.1.1.1.1.1.2" xref="S3.SS2.p4.4.m4.1.1.1.1.1.1.1.2.cmml"><mi id="S3.SS2.p4.4.m4.1.1.1.1.1.1.1.2.2" xref="S3.SS2.p4.4.m4.1.1.1.1.1.1.1.2.2.cmml">B</mi><mi id="S3.SS2.p4.4.m4.1.1.1.1.1.1.1.2.3" xref="S3.SS2.p4.4.m4.1.1.1.1.1.1.1.2.3.cmml">s</mi></msub><mo id="S3.SS2.p4.4.m4.1.1.1.1.1.1.1.1" xref="S3.SS2.p4.4.m4.1.1.1.1.1.1.1.1.cmml">/</mo><msub id="S3.SS2.p4.4.m4.1.1.1.1.1.1.1.3" xref="S3.SS2.p4.4.m4.1.1.1.1.1.1.1.3.cmml"><mi id="S3.SS2.p4.4.m4.1.1.1.1.1.1.1.3.2" xref="S3.SS2.p4.4.m4.1.1.1.1.1.1.1.3.2.cmml">B</mi><mi id="S3.SS2.p4.4.m4.1.1.1.1.1.1.1.3.3" xref="S3.SS2.p4.4.m4.1.1.1.1.1.1.1.3.3.cmml">H</mi></msub></mrow><mo id="S3.SS2.p4.4.m4.1.1.1.1.1.1.3" xref="S3.SS2.p4.4.m4.1.1.1.1.1.1.1.cmml">)</mo></mrow><mrow id="S3.SS2.p4.4.m4.1.1.1.1.3" xref="S3.SS2.p4.4.m4.1.1.1.1.3.cmml"><mn id="S3.SS2.p4.4.m4.1.1.1.1.3.2" xref="S3.SS2.p4.4.m4.1.1.1.1.3.2.cmml">1</mn><mo id="S3.SS2.p4.4.m4.1.1.1.1.3.1" xref="S3.SS2.p4.4.m4.1.1.1.1.3.1.cmml">/</mo><mn id="S3.SS2.p4.4.m4.1.1.1.1.3.3" xref="S3.SS2.p4.4.m4.1.1.1.1.3.3.cmml">2</mn></mrow></msup></mrow></mrow></math>, <math><mrow id="S3.SS2.p4.7.m7.1.1" xref="S3.SS2.p4.7.m7.1.1.cmml"><mrow id="S3.SS2.p4.7.m7.1.1.2" xref="S3.SS2.p4.7.m7.1.1.2.cmml"><msub id="S3.SS2.p4.7.m7.1.1.2.2" xref="S3.SS2.p4.7.m7.1.1.2.2.cmml"><mi id="S3.SS2.p4.7.m7.1.1.2.2.2" xref="S3.SS2.p4.7.m7.1.1.2.2.2.cmml">R</mi><mo id="S3.SS2.p4.7.m7.1.1.2.2.3" xref="S3.SS2.p4.7.m7.1.1.2.2.3.cmml">*</mo></msub><mo id="S3.SS2.p4.7.m7.1.1.2.1" xref="S3.SS2.p4.7.m7.1.1.2.1.cmml">/</mo><mi mathvariant="normal" id="S3.SS2.p4.7.m7.1.1.2.3" xref="S3.SS2.p4.7.m7.1.1.2.3.cmml">c</mi></mrow><mo id="S3.SS2.p4.7.m7.1.1.1" xref="S3.SS2.p4.7.m7.1.1.1.cmml">≃</mo><mn id="S3.SS2.p4.7.m7.1.1.3" xref="S3.SS2.p4.7.m7.1.1.3.cmml">85</mn></mrow></math>

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1703.06360

Formulas:

1-

β = p_{kin} / p_{B}

2-

H_{β - p h} \approx 1

3-

H_{c h r} \approx 2.5

4-

n = 2, 3, 4, 6, 7, 9

5-

{\bar{B}}_{α} = \frac{1}{n^{3}} \sum_{i = 1}^{n^{3}} B_{α} [i], α = x, y, or z,

6-

δ B_{α}^{2} = \frac{1}{n^{3} - 1} \sum_{i = 1}^{n^{3}} {(B_{α} [i] - {\bar{B}}_{α})}^{2}, α = x, y, or z .

7-

θ = a r c s i n (\frac{\sum_{i}^{N} σ_{i}}{N}), θ_{j} = a r c s i n (\frac{\sum_{i}^{N} {| 𝒋 |}_{i} σ_{i}}{\sum_{i}^{N} {| 𝒋 |}_{i}}),

8-

σ_{i} = \frac{{| 𝒋 \times 𝑩 |}_{i}}{{| 𝒋 |}_{i} {| 𝑩 |}_{i}},

9-

f = \frac{1}{N} \sum_{i}^{N} \frac{{| \nabla 𝑩 |}_{i}}{6 {| 𝑩 |}_{i}} d x,

10-

E_{pix} = \frac{N_{err}}{N},

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: hep-th

Result: incorrect

Paper: https://arxiv.org/abs/1304.0532

Formulas:

1-

\sum_{a} P (a b \dots | x y \dots) = P (b \dots | y \dots) \forall x,

2-

P (b c | y z, a d x w) = \sum_{λ} q (λ) P (b | y, a d x w, λ) P (c | z, a d x w, λ) .

3-

P (a b c d | x y z w)

4-

P (a b c d | x y z w)

5-

t_{A} = - 2 ϵ

6-

t_{B} = t_{C} = 0

7-

2 ϵ c (d - ϵ c) / (d - 4 ϵ c)

8-

t_{A} = t_{D} = - \sqrt{3} v d / (2 c^{2})

9-

t_{B} = t_{C} = 0

10-

\frac{d v (4 \sqrt{3} c - 3 v)}{4 c (c - \sqrt{3} v)}

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: math

Result: incorrect

Paper: https://arxiv.org/abs/1302.4396

Formulas:

1-

f (x) : ℝ^{n} \to ℝ

2-

f (x^{'}, x_{n}) = f (x^{'}, - x_{n})

3-

x = (x^{'}, x_{n}) \in ℝ^{n - 1} \times ℝ

4-

u \in ℝ^{n - 1}

5-

c_{1} = (u_{1} + t, u_{2}, \dots, u_{n - 1}, 0) and c_{2} = (u_{1} - t, u_{2}, \dots, u_{n - 1}, 0)

6-

x \in E_{u, t}

7-

\frac{{(x_{1} - u_{1})}^{2}}{λ^{2}} + \frac{{(x_{2} - u_{2})}^{2}}{λ^{2} - 1} + \dots + \frac{x_{n}^{2}}{λ^{2} - 1} \leq t^{2} .

8-

ν := \sqrt{λ^{2} - 1} .

9-

u \in ℝ^{n - 1}

10-

\begin{matrix} R_{E} f (u, t) = \int_{E_{u, t}} f (x) 𝑑 x . \end{matrix}

Formulas (html):

Correct Categorie: math

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0309288

Formulas:

1-

Δ ν = 274 \pm 11

2-

ν_{b u r s t}

3-

ν_{b u r s t}

4-

ν_{b u r s t} / 2

5-

ν_{l} = 308 \pm 5

6-

ν_{u} = 582 \pm 10

7-

Δ ν = 274 \pm 11

8-

ν_{l} = 385 \pm 9

9-

ν_{u} = 616 \pm 19

10-

Δ ν = 231 \pm 21

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/1903.09753

Formulas:

1-

γ \in ω \cup {ℵ_{0}}

2-

R (i_{0}, \dots, i_{n - 1})

3-

i_{0}, \dots, i_{n - 1} \in ω

4-

ϕ \in ℒ_{ℵ_{1}, ℵ_{0}} (τ)

5-

ℒ_{ℵ_{1}, ℵ_{0}} (τ)

6-

{SP}_{α} (M)

7-

{SP}_{α + 1} (M) = {SP}_{α + 1} (N)

8-

ℒ_{ℵ_{1}, ℵ_{0}} (τ)

9-

{SP}_{α} (𝒜)

10-

| {SP}_{α} (𝒜) | \leq | α |

Formulas (html):

Correct Categorie: math

Guessed Categorie: hep-lat

Result: incorrect

Paper: https://arxiv.org/abs/1512.02460

Formulas:

1-

i = 1, 2, \dots, n

2-

𝐱 = (x_{1}, x_{2}, \dots, x_{n})

3-

{\begin{matrix} {\dot{x}}_{i} & = (ϕ_{i} (𝐱) - \bar{ϕ} (𝐱)) x_{i}, \\ \bar{ϕ} (𝐱) & = \sum_{k = 1}^{n} x_{k} ϕ_{k} (𝐱), \end{matrix}

4-

ϕ_{i} (𝐱)

5-

\bar{ϕ} (𝐱)

6-

\dot{𝐱} = 𝐟 (𝐱)

7-

𝐟 (𝐱^{*}) = 0

8-

S_{n - 1} = {𝐱 \in 𝐑^{n} | x_{i} \geq 0, \sum_{i = 1}^{n} x_{i} = 1},

9-

J (𝐱^{*}) = {[{\frac{\partial f_{i} (𝐱)}{\partial x_{j}} |}_{𝐱 = 𝐱^{*}}]}_{i, j} .

10-

x_{i} (0) > 0

Formulas (html):

Correct Categorie: q-bio

Guessed Categorie: hep-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0306474

Formulas:

1-

Δ \ln M / L_{B} = - 0.14 \pm 0.13

2-

Δ \ln M / L_{B}

3-

r_{e} μ_{e}^{0.8}

4-

r_{e} \propto σ^{1.20} I_{e}^{- 0.80}

5-

M / L \propto σ^{0.50} r_{e}^{0.25} \propto M^{0.25},

6-

Δ M / L_{B} \propto σ^{1.50} r_{e}^{- 1.25} I_{e}^{- 1}

7-

Δ \ln M / L_{B}

8-

Δ \ln M / L_{B} \propto (- 1.25 \pm 0.15) z

9-

Δ \ln M / L_{B} \propto (- 1.12 \pm 0.11) z

10-

\ln M / L_{B}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/0807.0561

Formulas:

1-

n_{s} / m^{*} \propto T_{c}

2-

n_{s} / m^{*} \propto T_{c}

3-

B_{c 1} < B < B_{c 2}

4-

ω_{μ} = γ_{μ} B

5-

= 2 π \times 135.5

6-

P_{x} (t)

7-

P_{x} (t) = \int_{0}^{\infty} p (B) \cos (γ_{μ} B t + ϕ) d B,

8-

B_{VL} (0)

9-

B_{rms}^{2} (T) = B_{VL}^{2} (0) {[1 - {(T / T_{c})}^{r}]}^{2} + B_{bg}^{2}

10-

B_{VL} (0)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/9810346

Formulas:

1-

𝒜^{\frac{1}{2}} 𝒟^{- \frac{1}{2}} \frac{\partial Σ}{\partial t} = 𝒟^{\frac{1}{2}} \frac{1}{r} \frac{\partial}{\partial r} [\frac{𝒟^{- \frac{1}{2}}}{(\partial ℓ / \partial r)} \frac{\partial}{\partial r} (ℬ 𝒞^{- 1} 𝒟 r^{2} W)],

2-

𝒜 \equiv 1 + \frac{A^{2}}{{\tilde{r}}^{2}} + \frac{2 A^{2}}{{\tilde{r}}^{3}}, ℬ \equiv 1 + \frac{A}{{\tilde{r}}^{3 / 2}}, 𝒞 \equiv 1 - \frac{3}{\tilde{r}} + \frac{2 A}{{\tilde{r}}^{3 / 2}}, 𝒟 \equiv 1 - \frac{2}{\tilde{r}} + \frac{A^{2}}{{\tilde{r}}^{2}} .

3-

A \equiv c J / G M^{2}

4-

\tilde{r} \equiv r c^{2} / G M

5-

Σ_{R P D} = (\frac{16 c^{2}}{9 α κ_{e s}^{2}}) W^{- 1} 𝒞 𝒦 𝒟^{- 2},

6-

Σ_{G P D} = {(\frac{m_{p}}{k α})}^{4 / 5} {(\frac{b c}{18 κ_{e s}})}^{1 / 5} {(\frac{r^{3}}{G M})}^{1 / 10} W^{3 / 5} 𝒞^{1 / 5} 𝒟^{- 1 / 5},

7-

𝒦 \equiv 1 - \frac{4 A}{{\tilde{r}}^{3 / 2}} + \frac{3 A^{2}}{{\tilde{r}}^{2}}

8-

Σ_{G P D}

9-

Σ_{R P D}

10-

\partial W / \partial Σ

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/1808.09253

Formulas:

1-

\approx 10^{- 4} - 2

2-

Δ m = 2 - 5

3-

45^{\circ} \leq i \leq 56^{\circ}

4-

\dot{M} \sim 3 \times 10^{15} g s^{- 1}

5-

α = 21^{h} 42^{m} {27.1695}^{s}

6-

δ = + 43^{\circ} 33^{'} {44.601}^{''}

7-

x_{u, i} (t)

8-

x_{r, i} (t)

9-

X_{u, i} (f)

10-

X_{r, i} (f)

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: physics

Result: incorrect

Run 16330494 (TestAgent)