Run 11312198

Paper: https://arxiv.org/abs/1305.3713

Formulas:

1-

A d S_{5} \times S^{5}

2-

S U (N_{c})

3-

λ = g_{Y M}^{2} N_{c}

4-

S U (N_{c})

5-

U (N_{f})

6-

U (N_{f})

7-

U {(1)}_{B}

8-

\frac{\partial J}{\partial E}

9-

\begin{matrix} t & x & y & w & z & S^{3} & θ & ψ \\ D 3 & \times & \times & \times & \times \\ D 7 & \times & \times & \times & \times & \times & \times \end{matrix}

10-

S U (N_{c})

Formulas (html):

Correct Categorie: hep-th

Guessed Categorie: hep-th

Result: correct

Paper: https://arxiv.org/abs/1412.2516

Formulas:

1-

S = (s_{1}, \dots s_{m})

2-

\underset{D_{U}}{\Pr} [S] = \frac{{| Per (U_{[n], S}) |}^{2}}{s_{1}! \dots s_{m}!},

3-

U_{[n], S}

4-

N = ((\binom{m}{n}))

5-

o (1 / n)

6-

{∥ 𝒟_{\tilde{U}} - 𝒟_{U} ∥}_{1} \leq n {∥ \tilde{U} - U ∥}_{op}

7-

o (\frac{1}{n})

8-

{∥ 𝒟_{\tilde{U}} - 𝒟_{U} ∥}_{1} = o (1)

9-

{∥ \tilde{U} - U ∥}_{op} = o (\frac{1}{n})

10-

O (n \log m)

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: cs

Result: incorrect

Paper: https://arxiv.org/abs/quant-ph/0504206

Formulas:

1-

w \sim \exp (- A)

2-

A = 2 I m S / ℏ

3-

\exp (- A)

4-

m ω_{c}^{2} {(x - x_{0})}^{2} / 2

5-

ω_{c} = e H / m c

6-

m ω_{c}^{2} b^{2} / 2

7-

(t = i τ)

8-

y = i η (τ)

9-

m ω_{c} \partial η / \partial τ

10-

U (x, y)

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/1104.2151

Formulas:

1-

({\tilde{f}}_{L}, {\tilde{f}}_{R})

2-

ℳ_{\tilde{f}}^{2} = (\begin{matrix} m_{{\tilde{f}}_{L}}^{2} & a_{f}^{*} m_{f} \\ a_{f} m_{f} & m_{{\tilde{f}}_{R}}^{2} \end{matrix})

3-

M_{\tilde{Q}, \tilde{L}}^{2} + (I_{f}^{3 L} - e_{f} s_{W}^{2}) \cos 2 β M_{Z}^{2} + m_{f}^{2}

4-

M_{\tilde{U}, \tilde{D}, \tilde{E}}^{2} + e_{f} s_{W}^{2} \cos 2 β m_{Z}^{2} + m_{f}^{2}

5-

A_{f} - μ^{*} {(\tan β)}^{- 2 I_{f}^{3 L}}

6-

R^{\tilde{f}} = (\cos θ_{\tilde{f}}, \sin θ_{\tilde{f}}; - \sin θ_{\tilde{f}}, \cos θ_{\tilde{f}})

7-

diag (m_{{\tilde{f}}_{1}}^{2}, m_{{\tilde{f}}_{2}}^{2}) = R^{\tilde{f}} ℳ_{\tilde{f}}^{2} {(R^{\tilde{f}})}^{†}

8-

m_{{\tilde{f}}_{1, 2}}^{2}

9-

\frac{1}{2} (m_{{\tilde{f}}_{L}}^{2} + m_{{\tilde{f}}_{R}}^{2} \mp \sqrt{{(m_{{\tilde{f}}_{L}}^{2} - m_{{\tilde{f}}_{R}}^{2})}^{2} + 4 {| a_{f} |}^{2} m_{f}^{2}})

10-

\frac{- a_{f} m_{f}}{\sqrt{{(m_{{\tilde{f}}_{L}}^{2} - m_{{\tilde{f}}_{1}}^{2})}^{2}} + {| a_{f} |}^{2} m_{f}^{2}}

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: hep-ph

Result: correct

Paper: https://arxiv.org/abs/1301.3055

Formulas:

1-

V_{LSR} = + 65.4 \pm 0.5

2-

\log (Q) \geq 50

3-

\log (Q) \sim 48.5

4-

b = - 0 \overset{\circ}{.} 4

5-

l = 19 \overset{\circ}{.} 025, b = - 0 \overset{\circ}{.} 38

6-

V_{LSR} = 65.4 \pm 0.5

7-

l = 18 \overset{\circ}{.} 95, b = - 0 \overset{\circ}{.} 01

8-

0 \leq V_{LSR} \leq + 130

9-

V_{LSR} = 65.4 \pm 0.5

10-

F_{1420} = 40 \pm 0.6

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1604.01879

Formulas:

1-

O (T N^{3})

2-

𝒳 = {x_{1}, x_{2}, \dots, x_{N}}

3-

𝒱 (x_{q}) = {q_{1}, q_{2}, \dots, q_{N_{v}}}

4-

𝒱 (x_{p}) = {p_{1}, p_{2}, \dots, p_{N_{v}}}

5-

D (x_{q}, x_{p}) = \max_{q_{i} \in 𝒱 (x_{q})} \min_{p_{j} \in 𝒱 (x_{p})} d (q_{i}, p_{j}),

6-

D (x_{q}, x_{p}) = \frac{1}{N_{v}} \sum_{q_{i} \in 𝒱 (x_{q})} \min_{p_{j} \in 𝒱 (x_{p})} d (q_{i}, p_{j}) .

7-

S (x_{q}, x_{p}) = \frac{1}{N_{v}} \sum_{q_{i} \in 𝒱 (x_{q})} \max_{p_{j} \in 𝒱 (x_{p})} s (q_{i}, p_{j}),

8-

O (N \times N_{v}^{2})

9-

s^{*} (q_{i}) = \max_{1 \leq j \leq N_{v}} s (q_{i}, p_{j})

10-

s (q_{i}, p_{j})

Formulas (html):

Correct Categorie: cs

Guessed Categorie: cs

Result: correct

Paper: https://arxiv.org/abs/1612.02559

Formulas:

1-

γ : 𝒳 \to ℝ_{+}

2-

γ (\hat{𝐱}) = \hat{t}

3-

𝐱 \in 𝒳 \subset ℝ^{D}

4-

γ : 𝒳 \to ℝ_{+}

5-

[l_{i}, h_{i}]

6-

{t_{1}, \dots, t_{T}}

7-

ϕ : 𝒳 \times ℝ_{+} \to 𝒳, (𝐱, t) \mapsto \hat{𝐱}, s.t. γ (\hat{𝐱}) \approx t .

8-

[l_{i}, h_{i}]

9-

[l, h] = [1, 2]

10-

γ (𝐱) = \hat{t}

Formulas (html):

Correct Categorie: cs

Guessed Categorie: math

Result: incorrect

Paper: https://arxiv.org/abs/1904.00098

Formulas:

1-

H = - \sum_{⟨ 𝑹, 𝑹^{'} ⟩, σ} t_{𝑹 - 𝑹^{'}} c_{𝑹 σ}^{†} c_{𝑹^{'} σ} + U \sum_{𝑹} n_{𝑹, ↑} n_{𝑹, ↓},

2-

σ \in {↑, ↓}

3-

ϵ_{𝒌} (t) = ϵ_{0} (𝒌 - 𝑨 (t))

4-

ϵ_{0} (𝒌) = - 2 t_{hop} [\cos (k_{x} a) + \cos (k_{y} a)]

5-

𝑬 (t) = - \partial_{t} 𝑨 (t)

6-

G_{𝑹 - 𝑹^{'}} (t, t^{'}) = - i ⟨ T_{𝒞} c_{𝑹} (t) c_{𝑹^{'}}^{†} (t^{'}) ⟩

7-

χ_{𝑹 - 𝑹^{'}}^{α} (t, t^{'}) = - i ⟨ T_{𝒞} {\hat{X}}_{𝑹}^{α} (t) {\hat{X}}_{𝑹^{'}}^{α} (t^{'}) ⟩

8-

S_{𝑹} = \sum_{σ σ^{'}} c_{𝑹 σ}^{†} τ_{σ σ^{'}} c_{𝑹 σ^{'}}

9-

X_{𝑹}^{α} = \sum_{σ} n_{𝑹 σ}

10-

f_{𝑹} = \frac{1}{L^{2}} \sum_{𝒒} e^{i 𝒒 𝑹} f_{𝒒}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/math/0611455

Formulas:

1-

f : H (L) \to H (L)

2-

H = H (L)

3-

δ_{p} (q) = {\begin{matrix} 1 & if p = q \\ 0 & otherwise \end{matrix}

4-

(f \cdot g) (q) = f (q) \cdot g (q)

5-

𝐈 = \sum_{p \in L} δ_{p}

6-

ζ (p, q) = {\begin{matrix} 1 & if p \leq q \\ 0 & otherwise \end{matrix}

7-

α q \leq α_{p}

8-

α (δ_{p}) := δ_{α p}

9-

α ζ = ζ^{T} α

10-

ζ α δ_{p} \cdot ζ δ_{p} = δ_{0}

Formulas (html):

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id="S1.p3.3.m3.4.4.1.2" xref="S1.p3.3.m3.4.4.1.2.cmml">⁢</mo><mrow id="S1.p3.3.m3.4.4.1.3.2" xref="S1.p3.3.m3.4.4.1.cmml"><mo stretchy="false" id="S1.p3.3.m3.4.4.1.3.2.1" xref="S1.p3.3.m3.4.4.1.cmml">(</mo><mi id="S1.p3.3.m3.1.1" xref="S1.p3.3.m3.1.1.cmml">q</mi><mo stretchy="false" id="S1.p3.3.m3.4.4.1.3.2.2" xref="S1.p3.3.m3.4.4.1.cmml">)</mo></mrow></mrow><mo id="S1.p3.3.m3.4.4.2" xref="S1.p3.3.m3.4.4.2.cmml">=</mo><mrow id="S1.p3.3.m3.4.4.3" xref="S1.p3.3.m3.4.4.3.cmml"><mrow id="S1.p3.3.m3.4.4.3.2" xref="S1.p3.3.m3.4.4.3.2.cmml"><mrow id="S1.p3.3.m3.4.4.3.2.2" xref="S1.p3.3.m3.4.4.3.2.2.cmml"><mi id="S1.p3.3.m3.4.4.3.2.2.2" xref="S1.p3.3.m3.4.4.3.2.2.2.cmml">f</mi><mo id="S1.p3.3.m3.4.4.3.2.2.1" xref="S1.p3.3.m3.4.4.3.2.2.1.cmml">⁢</mo><mrow id="S1.p3.3.m3.4.4.3.2.2.3.2" xref="S1.p3.3.m3.4.4.3.2.2.cmml"><mo stretchy="false" id="S1.p3.3.m3.4.4.3.2.2.3.2.1" xref="S1.p3.3.m3.4.4.3.2.2.cmml">(</mo><mi id="S1.p3.3.m3.2.2" xref="S1.p3.3.m3.2.2.cmml">q</mi><mo stretchy="false" id="S1.p3.3.m3.4.4.3.2.2.3.2.2" xref="S1.p3.3.m3.4.4.3.2.2.cmml">)</mo></mrow></mrow><mo id="S1.p3.3.m3.4.4.3.2.1" xref="S1.p3.3.m3.4.4.3.2.1.cmml">⋅</mo><mi id="S1.p3.3.m3.4.4.3.2.3" xref="S1.p3.3.m3.4.4.3.2.3.cmml">g</mi></mrow><mo id="S1.p3.3.m3.4.4.3.1" xref="S1.p3.3.m3.4.4.3.1.cmml">⁢</mo><mrow id="S1.p3.3.m3.4.4.3.3.2" xref="S1.p3.3.m3.4.4.3.cmml"><mo stretchy="false" id="S1.p3.3.m3.4.4.3.3.2.1" xref="S1.p3.3.m3.4.4.3.cmml">(</mo><mi id="S1.p3.3.m3.3.3" xref="S1.p3.3.m3.3.3.cmml">q</mi><mo stretchy="false" id="S1.p3.3.m3.4.4.3.3.2.2" xref="S1.p3.3.m3.4.4.3.cmml">)</mo></mrow></mrow></mrow></math>, <math><mrow id="S1.p3.6.m6.1.1" xref="S1.p3.6.m6.1.1.cmml"><mpadded lspace="1.7pt" width="+1.7pt" id="S1.p3.6.m6.1.1.2" xref="S1.p3.6.m6.1.1.2.cmml"><mi id="S1.p3.6.m6.1.1.2a" xref="S1.p3.6.m6.1.1.2.cmml">𝐈</mi></mpadded><mo id="S1.p3.6.m6.1.1.1" xref="S1.p3.6.m6.1.1.1.cmml">=</mo><mrow id="S1.p3.6.m6.1.1.3" xref="S1.p3.6.m6.1.1.3.cmml"><msub id="S1.p3.6.m6.1.1.3.1" xref="S1.p3.6.m6.1.1.3.1.cmml"><mo largeop="true" symmetric="true" id="S1.p3.6.m6.1.1.3.1.2" xref="S1.p3.6.m6.1.1.3.1.2.cmml">∑</mo><mrow id="S1.p3.6.m6.1.1.3.1.3" xref="S1.p3.6.m6.1.1.3.1.3.cmml"><mi id="S1.p3.6.m6.1.1.3.1.3.2" xref="S1.p3.6.m6.1.1.3.1.3.2.cmml">p</mi><mo id="S1.p3.6.m6.1.1.3.1.3.1" xref="S1.p3.6.m6.1.1.3.1.3.1.cmml">∈</mo><mi id="S1.p3.6.m6.1.1.3.1.3.3" xref="S1.p3.6.m6.1.1.3.1.3.3.cmml">L</mi></mrow></msub><msub id="S1.p3.6.m6.1.1.3.2" xref="S1.p3.6.m6.1.1.3.2.cmml"><mi id="S1.p3.6.m6.1.1.3.2.2" xref="S1.p3.6.m6.1.1.3.2.2.cmml">δ</mi><mi id="S1.p3.6.m6.1.1.3.2.3" xref="S1.p3.6.m6.1.1.3.2.3.cmml">p</mi></msub></mrow></mrow></math>, <math><mrow id="S1.Ex2.m1.3.4" xref="S1.Ex2.m1.3.4.cmml"><mrow id="S1.Ex2.m1.3.4.2" xref="S1.Ex2.m1.3.4.2.cmml"><mi id="S1.Ex2.m1.3.4.2.2" xref="S1.Ex2.m1.3.4.2.2.cmml">ζ</mi><mo id="S1.Ex2.m1.3.4.2.1" xref="S1.Ex2.m1.3.4.2.1.cmml">⁢</mo><mrow id="S1.Ex2.m1.3.4.2.3.2" xref="S1.Ex2.m1.3.4.2.3.1.cmml"><mo stretchy="false" id="S1.Ex2.m1.3.4.2.3.2.1" xref="S1.Ex2.m1.3.4.2.3.1.cmml">(</mo><mi id="S1.Ex2.m1.1.1" xref="S1.Ex2.m1.1.1.cmml">p</mi><mo id="S1.Ex2.m1.3.4.2.3.2.2" xref="S1.Ex2.m1.3.4.2.3.1.cmml">,</mo><mi id="S1.Ex2.m1.2.2" xref="S1.Ex2.m1.2.2.cmml">q</mi><mo stretchy="false" id="S1.Ex2.m1.3.4.2.3.2.3" xref="S1.Ex2.m1.3.4.2.3.1.cmml">)</mo></mrow></mrow><mo id="S1.Ex2.m1.3.4.1" xref="S1.Ex2.m1.3.4.1.cmml">=</mo><mrow id="S1.Ex2.m1.3.4.3.2" xref="S1.Ex2.m1.3.4.3.1.cmml"><mo id="S1.Ex2.m1.3.4.3.2.1" xref="S1.Ex2.m1.3.4.3.1.1.cmml">{</mo><mtable columnspacing="5pt" displaystyle="true" rowspacing="0pt" id="S1.Ex2.m1.3.3" xref="S1.Ex2.m1.3.3.cmml"><mtr id="S1.Ex2.m1.3.3a" xref="S1.Ex2.m1.3.3.cmml"><mtd columnalign="center" id="S1.Ex2.m1.3.3b" xref="S1.Ex2.m1.3.3.cmml"><mn id="S1.Ex2.m1.3.3.1.1.1" xref="S1.Ex2.m1.3.3.1.1.1.cmml">1</mn></mtd><mtd columnalign="center" id="S1.Ex2.m1.3.3c" xref="S1.Ex2.m1.3.3.cmml"><mrow id="S1.Ex2.m1.3.3.1.2.1" xref="S1.Ex2.m1.3.3.1.2.1.cmml"><mrow id="S1.Ex2.m1.3.3.1.2.1.2" xref="S1.Ex2.m1.3.3.1.2.1.2.cmml"><mtext id="S1.Ex2.m1.3.3.1.2.1.2.2" xref="S1.Ex2.m1.3.3.1.2.1.2.2a.cmml">if </mtext><mo id="S1.Ex2.m1.3.3.1.2.1.2.1" xref="S1.Ex2.m1.3.3.1.2.1.2.1.cmml">⁢</mo><mi id="S1.Ex2.m1.3.3.1.2.1.2.3" xref="S1.Ex2.m1.3.3.1.2.1.2.3.cmml">p</mi></mrow><mo id="S1.Ex2.m1.3.3.1.2.1.1" xref="S1.Ex2.m1.3.3.1.2.1.1.cmml">≤</mo><mi id="S1.Ex2.m1.3.3.1.2.1.3" xref="S1.Ex2.m1.3.3.1.2.1.3.cmml">q</mi></mrow></mtd></mtr><mtr id="S1.Ex2.m1.3.3d" xref="S1.Ex2.m1.3.3.cmml"><mtd columnalign="center" id="S1.Ex2.m1.3.3e" xref="S1.Ex2.m1.3.3.cmml"><mn id="S1.Ex2.m1.3.3.2.1.1" xref="S1.Ex2.m1.3.3.2.1.1.cmml">0</mn></mtd><mtd columnalign="center" id="S1.Ex2.m1.3.3f" xref="S1.Ex2.m1.3.3.cmml"><mtext id="S1.Ex2.m1.3.3.2.2.1" xref="S1.Ex2.m1.3.3.2.2.1a.cmml">otherwise</mtext></mtd></mtr></mtable><mi id="S1.Ex2.m1.3.4.3.2.2" xref="S1.Ex2.m1.3.4.3.1.1.cmml"/></mrow></mrow></math>, <math><mrow id="S2.I1.i1.p1.2.m2.1.1" xref="S2.I1.i1.p1.2.m2.1.1.cmml"><mrow id="S2.I1.i1.p1.2.m2.1.1.2" xref="S2.I1.i1.p1.2.m2.1.1.2.cmml"><mi id="S2.I1.i1.p1.2.m2.1.1.2.2" xref="S2.I1.i1.p1.2.m2.1.1.2.2.cmml">α</mi><mo id="S2.I1.i1.p1.2.m2.1.1.2.1" xref="S2.I1.i1.p1.2.m2.1.1.2.1.cmml">⁢</mo><mpadded width="+1.7pt" id="S2.I1.i1.p1.2.m2.1.1.2.3" xref="S2.I1.i1.p1.2.m2.1.1.2.3.cmml"><mi id="S2.I1.i1.p1.2.m2.1.1.2.3a" xref="S2.I1.i1.p1.2.m2.1.1.2.3.cmml">q</mi></mpadded></mrow><mo rspace="4.2pt" id="S2.I1.i1.p1.2.m2.1.1.1" xref="S2.I1.i1.p1.2.m2.1.1.1.cmml">≤</mo><msub id="S2.I1.i1.p1.2.m2.1.1.3" xref="S2.I1.i1.p1.2.m2.1.1.3.cmml"><mi id="S2.I1.i1.p1.2.m2.1.1.3.2" xref="S2.I1.i1.p1.2.m2.1.1.3.2.cmml">α</mi><mi id="S2.I1.i1.p1.2.m2.1.1.3.3" xref="S2.I1.i1.p1.2.m2.1.1.3.3.cmml">p</mi></msub></mrow></math>, <math><mrow id="S2.p2.4.m4.1.1" xref="S2.p2.4.m4.1.1.cmml"><mrow id="S2.p2.4.m4.1.1.1" xref="S2.p2.4.m4.1.1.1.cmml"><mi id="S2.p2.4.m4.1.1.1.3" xref="S2.p2.4.m4.1.1.1.3.cmml">α</mi><mo id="S2.p2.4.m4.1.1.1.2" xref="S2.p2.4.m4.1.1.1.2.cmml">⁢</mo><mrow id="S2.p2.4.m4.1.1.1.1.1" xref="S2.p2.4.m4.1.1.1.1.1.1.cmml"><mo stretchy="false" id="S2.p2.4.m4.1.1.1.1.1.2" xref="S2.p2.4.m4.1.1.1.1.1.1.cmml">(</mo><msub id="S2.p2.4.m4.1.1.1.1.1.1" xref="S2.p2.4.m4.1.1.1.1.1.1.cmml"><mi id="S2.p2.4.m4.1.1.1.1.1.1.2" xref="S2.p2.4.m4.1.1.1.1.1.1.2.cmml">δ</mi><mi id="S2.p2.4.m4.1.1.1.1.1.1.3" xref="S2.p2.4.m4.1.1.1.1.1.1.3.cmml">p</mi></msub><mo stretchy="false" id="S2.p2.4.m4.1.1.1.1.1.3" xref="S2.p2.4.m4.1.1.1.1.1.1.cmml">)</mo></mrow></mrow><mo id="S2.p2.4.m4.1.1.2" xref="S2.p2.4.m4.1.1.2.cmml">:=</mo><msub id="S2.p2.4.m4.1.1.3" xref="S2.p2.4.m4.1.1.3.cmml"><mi id="S2.p2.4.m4.1.1.3.2" xref="S2.p2.4.m4.1.1.3.2.cmml">δ</mi><mrow id="S2.p2.4.m4.1.1.3.3" xref="S2.p2.4.m4.1.1.3.3.cmml"><mi id="S2.p2.4.m4.1.1.3.3.2" xref="S2.p2.4.m4.1.1.3.3.2.cmml">α</mi><mo id="S2.p2.4.m4.1.1.3.3.1" xref="S2.p2.4.m4.1.1.3.3.1.cmml">⁢</mo><mi id="S2.p2.4.m4.1.1.3.3.3" xref="S2.p2.4.m4.1.1.3.3.3.cmml">p</mi></mrow></msub></mrow></math>, <math><mrow id="S2.Ex3.m1.1.1" xref="S2.Ex3.m1.1.1.cmml"><mrow id="S2.Ex3.m1.1.1.2" xref="S2.Ex3.m1.1.1.2.cmml"><mi id="S2.Ex3.m1.1.1.2.2" xref="S2.Ex3.m1.1.1.2.2.cmml">α</mi><mo id="S2.Ex3.m1.1.1.2.1" xref="S2.Ex3.m1.1.1.2.1.cmml">⁢</mo><mi id="S2.Ex3.m1.1.1.2.3" xref="S2.Ex3.m1.1.1.2.3.cmml">ζ</mi></mrow><mo id="S2.Ex3.m1.1.1.1" xref="S2.Ex3.m1.1.1.1.cmml">=</mo><mrow id="S2.Ex3.m1.1.1.3" xref="S2.Ex3.m1.1.1.3.cmml"><msup id="S2.Ex3.m1.1.1.3.2" xref="S2.Ex3.m1.1.1.3.2.cmml"><mi id="S2.Ex3.m1.1.1.3.2.2" xref="S2.Ex3.m1.1.1.3.2.2.cmml">ζ</mi><mi id="S2.Ex3.m1.1.1.3.2.3" xref="S2.Ex3.m1.1.1.3.2.3.cmml">T</mi></msup><mo id="S2.Ex3.m1.1.1.3.1" xref="S2.Ex3.m1.1.1.3.1.cmml">⁢</mo><mi id="S2.Ex3.m1.1.1.3.3" xref="S2.Ex3.m1.1.1.3.3.cmml">α</mi></mrow></mrow></math>, <math><mrow id="S2.p3.7.m6.1.1" xref="S2.p3.7.m6.1.1.cmml"><mrow id="S2.p3.7.m6.1.1.2" xref="S2.p3.7.m6.1.1.2.cmml"><mrow id="S2.p3.7.m6.1.1.2.2" xref="S2.p3.7.m6.1.1.2.2.cmml"><mrow id="S2.p3.7.m6.1.1.2.2.2" xref="S2.p3.7.m6.1.1.2.2.2.cmml"><mi id="S2.p3.7.m6.1.1.2.2.2.2" xref="S2.p3.7.m6.1.1.2.2.2.2.cmml">ζ</mi><mo id="S2.p3.7.m6.1.1.2.2.2.1" xref="S2.p3.7.m6.1.1.2.2.2.1.cmml">⁢</mo><mi id="S2.p3.7.m6.1.1.2.2.2.3" xref="S2.p3.7.m6.1.1.2.2.2.3.cmml">α</mi><mo id="S2.p3.7.m6.1.1.2.2.2.1a" xref="S2.p3.7.m6.1.1.2.2.2.1.cmml">⁢</mo><msub id="S2.p3.7.m6.1.1.2.2.2.4" xref="S2.p3.7.m6.1.1.2.2.2.4.cmml"><mi id="S2.p3.7.m6.1.1.2.2.2.4.2" xref="S2.p3.7.m6.1.1.2.2.2.4.2.cmml">δ</mi><mi id="S2.p3.7.m6.1.1.2.2.2.4.3" xref="S2.p3.7.m6.1.1.2.2.2.4.3.cmml">p</mi></msub></mrow><mo id="S2.p3.7.m6.1.1.2.2.1" xref="S2.p3.7.m6.1.1.2.2.1.cmml">⋅</mo><mi id="S2.p3.7.m6.1.1.2.2.3" xref="S2.p3.7.m6.1.1.2.2.3.cmml">ζ</mi></mrow><mo id="S2.p3.7.m6.1.1.2.1" xref="S2.p3.7.m6.1.1.2.1.cmml">⁢</mo><msub id="S2.p3.7.m6.1.1.2.3" xref="S2.p3.7.m6.1.1.2.3.cmml"><mi id="S2.p3.7.m6.1.1.2.3.2" xref="S2.p3.7.m6.1.1.2.3.2.cmml">δ</mi><mi id="S2.p3.7.m6.1.1.2.3.3" xref="S2.p3.7.m6.1.1.2.3.3.cmml">p</mi></msub></mrow><mo id="S2.p3.7.m6.1.1.1" xref="S2.p3.7.m6.1.1.1.cmml">=</mo><msub id="S2.p3.7.m6.1.1.3" xref="S2.p3.7.m6.1.1.3.cmml"><mi id="S2.p3.7.m6.1.1.3.2" xref="S2.p3.7.m6.1.1.3.2.cmml">δ</mi><mn id="S2.p3.7.m6.1.1.3.3" xref="S2.p3.7.m6.1.1.3.3.cmml">0</mn></msub></mrow></math>

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/1703.05316

Formulas:

1-

\sqrt{F_{μ ν} F^{μ ν}}

2-

E R = E P R

3-

F_{r θ} \neq 0,

4-

d s^{2} = - e^{2 Φ (r)} d t^{2} + \frac{d r^{2}}{1 - \frac{b (r)}{r}} + r^{2} d θ^{2},

5-

b (r_{0}) = r_{0}

6-

b^{'} (r) < \frac{b (r)}{r},

7-

{lim}_{r \to \infty} Φ = 0

8-

{lim}_{r \to \infty} \frac{b (r)}{r} = 0

9-

G_{t}^{t} = T_{t}^{t}

10-

8 π G = c = 1

Formulas (html):

Correct Categorie: gr-qc

Guessed Categorie: gr-qc

Result: correct

Paper: https://arxiv.org/abs/0910.2375

Formulas:

1-

(x_{0}, y_{0})

2-

(x_{0}, y_{0})

3-

I (x, y) = a + b x + c y + d x^{2} + e x y + f y^{2}

4-

(x_{s}, y_{s})

5-

(x_{s}, y_{s}) = (\frac{c e - b f}{2 d f - 2 e^{2}}, \frac{b e - c d}{2 d f - 2 e^{2}})

6-

\sqrt{{(x_{s} - x_{0})}^{2} + {(y_{s} - y_{0})}^{2}}

7-

S = A \times 2 π σ^{2}

8-

A e^{\frac{- {(x - x_{s})}^{2} - {(y - y_{s})}^{2}}{2 σ^{2}}} + μ_{s k y}

9-

μ_{s k y}

10-

(x_{0}, y_{0})

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/quant-ph/0606038

Formulas:

1-

lim_{T \to \infty} \frac{1}{T} \int_{0}^{T} f_{t} (v_{o}) 𝑑 t

2-

always exists—or lim_{T \to \infty} \frac{1}{T} \sum_{t = 0}^{T - 1} f_{v_{0}} (t),

3-

V \times N \times {0, 1}

4-

π_{1} (x) = π_{1} (y)

5-

π_{2} (x) = π_{2} (y)

6-

π_{3} (x) = π_{3} (y)

7-

f_{v_{0}} : N \to {0, 1}

8-

f_{v_{0}}^{1}, f_{w_{0}}^{2}

9-

g_{v_{0}, w_{0}}

10-

g_{v_{0}, w_{0}} (n) = f_{v_{0}}^{1} (n) & f_{w_{0}}^{2} (n)

Formulas (html):

<math><mrow id="id1.1.1.1.1" xref="id1.1.1.1.1.cmml"><munder id="id1.1.1.1.1.2" xref="id1.1.1.1.1.2.cmml"><mo movablelimits="false" id="id1.1.1.1.1.2.2" xref="id1.1.1.1.1.2.2.cmml">lim</mo><mrow id="id1.1.1.1.1.2.3" xref="id1.1.1.1.1.2.3.cmml"><mi id="id1.1.1.1.1.2.3.2" xref="id1.1.1.1.1.2.3.2.cmml">T</mi><mo id="id1.1.1.1.1.2.3.1" xref="id1.1.1.1.1.2.3.1.cmml">→</mo><mi mathvariant="normal" id="id1.1.1.1.1.2.3.3" xref="id1.1.1.1.1.2.3.3.cmml">∞</mi></mrow></munder><mo id="id1.1.1.1.1a" xref="id1.1.1.1.1.cmml">⁡</mo><mrow id="id1.1.1.1.1.1" xref="id1.1.1.1.1.1.cmml"><mfrac id="id1.1.1.1.1.1.3" xref="id1.1.1.1.1.1.3.cmml"><mn id="id1.1.1.1.1.1.3.2" xref="id1.1.1.1.1.1.3.2.cmml">1</mn><mi id="id1.1.1.1.1.1.3.3" xref="id1.1.1.1.1.1.3.3.cmml">T</mi></mfrac><mo id="id1.1.1.1.1.1.2" xref="id1.1.1.1.1.1.2.cmml">⁢</mo><mrow id="id1.1.1.1.1.1.1" xref="id1.1.1.1.1.1.1.cmml"><msubsup id="id1.1.1.1.1.1.1.2" xref="id1.1.1.1.1.1.1.2.cmml"><mo largeop="true" symmetric="true" 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id="id3.3.2.2.1.1.id1.3.1.3.2" xref="id3.3.2.2.1.1.id1.3.1.3.2.cmml">T</mi><mo id="id3.3.2.2.1.1.id1.3.1.3.1" xref="id3.3.2.2.1.1.id1.3.1.3.1.cmml">→</mo><mi mathvariant="normal" id="id3.3.2.2.1.1.id1.3.1.3.3" xref="id3.3.2.2.1.1.id1.3.1.3.3.cmml">∞</mi></mrow></munder><mo id="id3.3.2.2.1.1.id1.3a" xref="id3.3.2.2.1.1.id1.3.cmml">⁡</mo><mrow id="id3.3.2.2.1.1.id1.3.2" xref="id3.3.2.2.1.1.id1.3.2.cmml"><mfrac id="id3.3.2.2.1.1.id1.3.2.2" xref="id3.3.2.2.1.1.id1.3.2.2.cmml"><mn id="id3.3.2.2.1.1.id1.3.2.2.2" xref="id3.3.2.2.1.1.id1.3.2.2.2.cmml">1</mn><mi id="id3.3.2.2.1.1.id1.3.2.2.3" xref="id3.3.2.2.1.1.id1.3.2.2.3.cmml">T</mi></mfrac><mo id="id3.3.2.2.1.1.id1.3.2.1" xref="id3.3.2.2.1.1.id1.3.2.1.cmml">⁢</mo><mrow id="id3.3.2.2.1.1.id1.3.2.3" xref="id3.3.2.2.1.1.id1.3.2.3.cmml"><munderover id="id3.3.2.2.1.1.id1.3.2.3.1" xref="id3.3.2.2.1.1.id1.3.2.3.1.cmml"><mo largeop="true" movablelimits="false" symmetric="true" id="id3.3.2.2.1.1.id1.3.2.3.1.2.2" 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xref="id5.2.2.2.1.1.cmml">×</mo><mi id="id5.2.2.2.1.3" xref="id5.2.2.2.1.3.cmml">N</mi><mo id="id5.2.2.2.1.1a" xref="id5.2.2.2.1.1.cmml">×</mo><mrow id="id5.2.2.2.1.4.2" xref="id5.2.2.2.1.4.1.cmml"><mo stretchy="false" id="id5.2.2.2.1.4.2.1" xref="id5.2.2.2.1.4.1.cmml">{</mo><mn id="id4.1.1.1.id1" xref="id4.1.1.1.id1.cmml">0</mn><mo id="id5.2.2.2.1.4.2.2" xref="id5.2.2.2.1.4.1.cmml">,</mo><mn id="id5.2.2.2.id2" xref="id5.2.2.2.id2.cmml">1</mn><mo stretchy="false" id="id5.2.2.2.1.4.2.3" xref="id5.2.2.2.1.4.1.cmml">}</mo></mrow></mrow></math>, <math><mrow id="id7.4.4.2.1" xref="id7.4.4.2.1.cmml"><mrow id="id7.4.4.2.1.2" xref="id7.4.4.2.1.2.cmml"><msub id="id7.4.4.2.1.2.2" xref="id7.4.4.2.1.2.2.cmml"><mi id="id7.4.4.2.1.2.2.2" xref="id7.4.4.2.1.2.2.2.cmml">π</mi><mn id="id7.4.4.2.1.2.2.3" xref="id7.4.4.2.1.2.2.3.cmml">1</mn></msub><mo id="id7.4.4.2.1.2.1" xref="id7.4.4.2.1.2.1.cmml">⁢</mo><mrow id="id7.4.4.2.1.2.3.2" xref="id7.4.4.2.1.2.cmml"><mo stretchy="false" id="id7.4.4.2.1.2.3.2.1" 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id="id9.6.6.2.1.2.2.2" xref="id9.6.6.2.1.2.2.2.cmml">π</mi><mn id="id9.6.6.2.1.2.2.3" xref="id9.6.6.2.1.2.2.3.cmml">2</mn></msub><mo id="id9.6.6.2.1.2.1" xref="id9.6.6.2.1.2.1.cmml">⁢</mo><mrow id="id9.6.6.2.1.2.3.2" xref="id9.6.6.2.1.2.cmml"><mo stretchy="false" id="id9.6.6.2.1.2.3.2.1" xref="id9.6.6.2.1.2.cmml">(</mo><mi id="id8.5.5.1.id1" xref="id8.5.5.1.id1.cmml">x</mi><mo stretchy="false" id="id9.6.6.2.1.2.3.2.2" xref="id9.6.6.2.1.2.cmml">)</mo></mrow></mrow><mo id="id9.6.6.2.1.1" xref="id9.6.6.2.1.1.cmml">=</mo><mrow id="id9.6.6.2.1.3" xref="id9.6.6.2.1.3.cmml"><msub id="id9.6.6.2.1.3.2" xref="id9.6.6.2.1.3.2.cmml"><mi id="id9.6.6.2.1.3.2.2" xref="id9.6.6.2.1.3.2.2.cmml">π</mi><mn id="id9.6.6.2.1.3.2.3" xref="id9.6.6.2.1.3.2.3.cmml">2</mn></msub><mo id="id9.6.6.2.1.3.1" xref="id9.6.6.2.1.3.1.cmml">⁢</mo><mrow id="id9.6.6.2.1.3.3.2" xref="id9.6.6.2.1.3.cmml"><mo stretchy="false" id="id9.6.6.2.1.3.3.2.1" xref="id9.6.6.2.1.3.cmml">(</mo><mi id="id9.6.6.2.id2" xref="id9.6.6.2.id2.cmml">y</mi><mo stretchy="false" id="id9.6.6.2.1.3.3.2.2" xref="id9.6.6.2.1.3.cmml">)</mo></mrow></mrow></mrow></math>, <math><mrow id="id11.8.8.2.1" xref="id11.8.8.2.1.cmml"><mrow id="id11.8.8.2.1.2" xref="id11.8.8.2.1.2.cmml"><msub id="id11.8.8.2.1.2.2" xref="id11.8.8.2.1.2.2.cmml"><mi id="id11.8.8.2.1.2.2.2" xref="id11.8.8.2.1.2.2.2.cmml">π</mi><mn id="id11.8.8.2.1.2.2.3" xref="id11.8.8.2.1.2.2.3.cmml">3</mn></msub><mo id="id11.8.8.2.1.2.1" xref="id11.8.8.2.1.2.1.cmml">⁢</mo><mrow id="id11.8.8.2.1.2.3.2" xref="id11.8.8.2.1.2.cmml"><mo stretchy="false" id="id11.8.8.2.1.2.3.2.1" xref="id11.8.8.2.1.2.cmml">(</mo><mi id="id10.7.7.1.id1" xref="id10.7.7.1.id1.cmml">x</mi><mo stretchy="false" id="id11.8.8.2.1.2.3.2.2" xref="id11.8.8.2.1.2.cmml">)</mo></mrow></mrow><mo id="id11.8.8.2.1.1" xref="id11.8.8.2.1.1.cmml">=</mo><mrow id="id11.8.8.2.1.3" xref="id11.8.8.2.1.3.cmml"><msub id="id11.8.8.2.1.3.2" xref="id11.8.8.2.1.3.2.cmml"><mi id="id11.8.8.2.1.3.2.2" xref="id11.8.8.2.1.3.2.2.cmml">π</mi><mn id="id11.8.8.2.1.3.2.3" xref="id11.8.8.2.1.3.2.3.cmml">3</mn></msub><mo id="id11.8.8.2.1.3.1" xref="id11.8.8.2.1.3.1.cmml">⁢</mo><mrow id="id11.8.8.2.1.3.3.2" xref="id11.8.8.2.1.3.cmml"><mo stretchy="false" id="id11.8.8.2.1.3.3.2.1" xref="id11.8.8.2.1.3.cmml">(</mo><mi id="id11.8.8.2.id2" xref="id11.8.8.2.id2.cmml">y</mi><mo stretchy="false" id="id11.8.8.2.1.3.3.2.2" xref="id11.8.8.2.1.3.cmml">)</mo></mrow></mrow></mrow></math>, <math><mrow id="id13.2.2.2.1" xref="id13.2.2.2.1.cmml"><msub id="id13.2.2.2.1.2" xref="id13.2.2.2.1.2.cmml"><mi id="id13.2.2.2.1.2.2" xref="id13.2.2.2.1.2.2.cmml">f</mi><msub id="id13.2.2.2.1.2.3" xref="id13.2.2.2.1.2.3.cmml"><mi id="id13.2.2.2.1.2.3.2" xref="id13.2.2.2.1.2.3.2.cmml">v</mi><mn id="id13.2.2.2.1.2.3.3" xref="id13.2.2.2.1.2.3.3.cmml">0</mn></msub></msub><mo id="id13.2.2.2.1.1" xref="id13.2.2.2.1.1.cmml">:</mo><mrow id="id13.2.2.2.1.3" xref="id13.2.2.2.1.3.cmml"><mi id="id13.2.2.2.1.3.2" xref="id13.2.2.2.1.3.2.cmml">N</mi><mo id="id13.2.2.2.1.3.1" xref="id13.2.2.2.1.3.1.cmml">→</mo><mrow id="id13.2.2.2.1.3.3.2" xref="id13.2.2.2.1.3.3.1.cmml"><mo stretchy="false" id="id13.2.2.2.1.3.3.2.1" xref="id13.2.2.2.1.3.3.1.cmml">{</mo><mn id="id12.1.1.1.id1" xref="id12.1.1.1.id1.cmml">0</mn><mo id="id13.2.2.2.1.3.3.2.2" xref="id13.2.2.2.1.3.3.1.cmml">,</mo><mn id="id13.2.2.2.id2" xref="id13.2.2.2.id2.cmml">1</mn><mo stretchy="false" id="id13.2.2.2.1.3.3.2.3" xref="id13.2.2.2.1.3.3.1.cmml">}</mo></mrow></mrow></mrow></math>, <math><mrow id="id15.2.2.2.2.2" xref="id15.2.2.2.2.3.cmml"><msubsup id="id14.1.1.1.1.1.id1" xref="id14.1.1.1.1.1.id1.cmml"><mi id="id14.1.1.1.1.1.id1.2.2" xref="id14.1.1.1.1.1.id1.2.2.cmml">f</mi><msub id="id14.1.1.1.1.1.id1.2.3" xref="id14.1.1.1.1.1.id1.2.3.cmml"><mi id="id14.1.1.1.1.1.id1.2.3.2" xref="id14.1.1.1.1.1.id1.2.3.2.cmml">v</mi><mn id="id14.1.1.1.1.1.id1.2.3.3" xref="id14.1.1.1.1.1.id1.2.3.3.cmml">0</mn></msub><mn id="id14.1.1.1.1.1.id1.3" xref="id14.1.1.1.1.1.id1.3.cmml">1</mn></msubsup><mo id="id15.2.2.2.2.2.1" xref="id15.2.2.2.2.3.cmml">,</mo><msubsup id="id15.2.2.2.2.2.id2" xref="id15.2.2.2.2.2.id2.cmml"><mi id="id15.2.2.2.2.2.id2.2.2" xref="id15.2.2.2.2.2.id2.2.2.cmml">f</mi><msub id="id15.2.2.2.2.2.id2.2.3" xref="id15.2.2.2.2.2.id2.2.3.cmml"><mi id="id15.2.2.2.2.2.id2.2.3.2" xref="id15.2.2.2.2.2.id2.2.3.2.cmml">w</mi><mn id="id15.2.2.2.2.2.id2.2.3.3" xref="id15.2.2.2.2.2.id2.2.3.3.cmml">0</mn></msub><mn id="id15.2.2.2.2.2.id2.3" xref="id15.2.2.2.2.2.id2.3.cmml">2</mn></msubsup></mrow></math>, <math><msub id="id17.4.4.2.3" xref="id17.4.4.2.3.cmml"><mi id="id17.4.4.2.3.2" xref="id17.4.4.2.3.2.cmml">g</mi><mrow id="id17.4.4.2.2.2.2" xref="id17.4.4.2.2.2.3.cmml"><msub id="id16.3.3.1.1.1.1.id1" xref="id16.3.3.1.1.1.1.id1.cmml"><mi id="id16.3.3.1.1.1.1.id1.2" xref="id16.3.3.1.1.1.1.id1.2.cmml">v</mi><mn id="id16.3.3.1.1.1.1.id1.3" xref="id16.3.3.1.1.1.1.id1.3.cmml">0</mn></msub><mo id="id17.4.4.2.2.2.2.1" xref="id17.4.4.2.2.2.3.cmml">,</mo><msub id="id17.4.4.2.2.2.2.id2" xref="id17.4.4.2.2.2.2.id2.cmml"><mi id="id17.4.4.2.2.2.2.id2.2" xref="id17.4.4.2.2.2.2.id2.2.cmml">w</mi><mn id="id17.4.4.2.2.2.2.id2.3" xref="id17.4.4.2.2.2.2.id2.3.cmml">0</mn></msub></mrow></msub></math>, <math><mrow id="id22.9.9.5.3" xref="id22.9.9.5.3.cmml"><mrow id="id22.9.9.5.3.2" xref="id22.9.9.5.3.2.cmml"><msub id="id22.9.9.5.3.2.2" xref="id22.9.9.5.3.2.2.cmml"><mi id="id22.9.9.5.3.2.2.2" xref="id22.9.9.5.3.2.2.2.cmml">g</mi><mrow id="id19.6.6.2.2.2.2" xref="id19.6.6.2.2.2.3.cmml"><msub id="id18.5.5.1.1.1.1.id1" xref="id18.5.5.1.1.1.1.id1.cmml"><mi id="id18.5.5.1.1.1.1.id1.2" xref="id18.5.5.1.1.1.1.id1.2.cmml">v</mi><mn id="id18.5.5.1.1.1.1.id1.3" xref="id18.5.5.1.1.1.1.id1.3.cmml">0</mn></msub><mo id="id19.6.6.2.2.2.2.1" xref="id19.6.6.2.2.2.3.cmml">,</mo><msub id="id19.6.6.2.2.2.2.id2" xref="id19.6.6.2.2.2.2.id2.cmml"><mi id="id19.6.6.2.2.2.2.id2.2" xref="id19.6.6.2.2.2.2.id2.2.cmml">w</mi><mn id="id19.6.6.2.2.2.2.id2.3" xref="id19.6.6.2.2.2.2.id2.3.cmml">0</mn></msub></mrow></msub><mo id="id22.9.9.5.3.2.1" xref="id22.9.9.5.3.2.1.cmml">⁢</mo><mrow id="id22.9.9.5.3.2.3.2" xref="id22.9.9.5.3.2.cmml"><mo stretchy="false" id="id22.9.9.5.3.2.3.2.1" xref="id22.9.9.5.3.2.cmml">(</mo><mi id="id20.7.7.3.id1" xref="id20.7.7.3.id1.cmml">n</mi><mo stretchy="false" id="id22.9.9.5.3.2.3.2.2" xref="id22.9.9.5.3.2.cmml">)</mo></mrow></mrow><mo id="id22.9.9.5.3.1" xref="id22.9.9.5.3.1.cmml">=</mo><mrow id="id22.9.9.5.3.3" xref="id22.9.9.5.3.3.cmml"><mrow id="id22.9.9.5.3.3.2" xref="id22.9.9.5.3.3.2.cmml"><msubsup id="id22.9.9.5.3.3.2.2" xref="id22.9.9.5.3.3.2.2.cmml"><mi id="id22.9.9.5.3.3.2.2.2.2" xref="id22.9.9.5.3.3.2.2.2.2.cmml">f</mi><msub id="id22.9.9.5.3.3.2.2.2.3" xref="id22.9.9.5.3.3.2.2.2.3.cmml"><mi id="id22.9.9.5.3.3.2.2.2.3.2" xref="id22.9.9.5.3.3.2.2.2.3.2.cmml">v</mi><mn id="id22.9.9.5.3.3.2.2.2.3.3" xref="id22.9.9.5.3.3.2.2.2.3.3.cmml">0</mn></msub><mn id="id22.9.9.5.3.3.2.2.3" xref="id22.9.9.5.3.3.2.2.3.cmml">1</mn></msubsup><mo id="id22.9.9.5.3.3.2.1" xref="id22.9.9.5.3.3.2.1.cmml">⁢</mo><mrow id="id22.9.9.5.3.3.2.3.2" xref="id22.9.9.5.3.3.2.cmml"><mo stretchy="false" id="id22.9.9.5.3.3.2.3.2.1" xref="id22.9.9.5.3.3.2.cmml">(</mo><mi id="id21.8.8.4.id2" xref="id21.8.8.4.id2.cmml">n</mi><mo stretchy="false" id="id22.9.9.5.3.3.2.3.2.2" xref="id22.9.9.5.3.3.2.cmml">)</mo></mrow></mrow><mo id="id22.9.9.5.3.3.1" xref="id22.9.9.5.3.3.1.cmml">&</mo><mrow id="id22.9.9.5.3.3.3" xref="id22.9.9.5.3.3.3.cmml"><msubsup id="id22.9.9.5.3.3.3.2" xref="id22.9.9.5.3.3.3.2.cmml"><mi id="id22.9.9.5.3.3.3.2.2.2" xref="id22.9.9.5.3.3.3.2.2.2.cmml">f</mi><msub id="id22.9.9.5.3.3.3.2.2.3" xref="id22.9.9.5.3.3.3.2.2.3.cmml"><mi id="id22.9.9.5.3.3.3.2.2.3.2" xref="id22.9.9.5.3.3.3.2.2.3.2.cmml">w</mi><mn id="id22.9.9.5.3.3.3.2.2.3.3" xref="id22.9.9.5.3.3.3.2.2.3.3.cmml">0</mn></msub><mn id="id22.9.9.5.3.3.3.2.3" xref="id22.9.9.5.3.3.3.2.3.cmml">2</mn></msubsup><mo id="id22.9.9.5.3.3.3.1" xref="id22.9.9.5.3.3.3.1.cmml">⁢</mo><mrow id="id22.9.9.5.3.3.3.3.2" xref="id22.9.9.5.3.3.3.cmml"><mo stretchy="false" id="id22.9.9.5.3.3.3.3.2.1" xref="id22.9.9.5.3.3.3.cmml">(</mo><mi id="id22.9.9.5.id3" xref="id22.9.9.5.id3.cmml">n</mi><mo stretchy="false" id="id22.9.9.5.3.3.3.3.2.2" xref="id22.9.9.5.3.3.3.cmml">)</mo></mrow></mrow></mrow></mrow></math>

Correct Categorie: quant-ph

Guessed Categorie: cs

Result: incorrect

Paper: https://arxiv.org/abs/1511.06365

Formulas:

1-

- 90 ° \leq P \leq 90 °

2-

P^{'} = P \pm 90 °

3-

- 90 ° \leq P^{'} \leq 90 °

4-

r = e^{b θ}

5-

P = \tan^{- 1} (- b)

6-

S = | R \frac{\sqrt{1 + b^{2}}}{b} |

7-

r = e^{b [θ - θ_{0}]}

8-

0 \leq θ_{0} < 2 π

9-

V_{m e d}

10-

V_{m e d}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/0808.1150

Formulas:

1-

\sim 1^{'} (2^{'})

2-

\sim 20^{'} (40^{'})

3-

\sim 0.2 (0.1)

4-

\sim 0.9 (0.45)

5-

B_{l o s}

6-

d I / d ν

7-

B_{l o s}

8-

B_{l o s}

9-

B_{l o s}

10-

3 / \sqrt{10 - 1} = 1

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0411327

Formulas:

1-

M [r] < - 22

2-

d o t s

3-

c r o s s e s

4-

(Ω, Λ, H_{0}) = (0.3, 0.7, 70)

5-

σ_{R M S} = 0.05

6-

c r o s s e s

7-

c i r c l e s

8-

c i r c l e s

9-

F (N U V) / F (r) < 0.08

10-

F (F U V) / F (r) < 0.08

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1710.09054

Formulas:

1-

S = \frac{1}{16 π} \int d^{D} x \sqrt{- g} (R - 2 Λ - \frac{1}{4} F_{μ ν} F^{μ ν} - \frac{1}{2} \sum_{I = 1}^{D - 2} {(\partial ψ_{I})}^{2}),

2-

Λ = - \frac{(D - 1) (D - 2)}{2 L^{2}} .

3-

ψ_{I} = β δ_{I a} x^{a}

4-

ψ_{I} = β_{I a} x^{a}

5-

β^{2} \equiv \frac{1}{D - 2} (\sum_{a = 1}^{D - 2} \sum_{I = 1}^{D - 2} β_{I a} β_{I a})

6-

\sum_{I = 1}^{D - 2} β_{I a} β_{I b} = β^{2} δ_{a b}

7-

β_{I a} = β δ_{I a}

8-

d s^{2} = - f (r) d t^{2} + \frac{1}{f (r)} d r^{2} + r^{2} d x^{a} d x^{a}, A = A_{t} (r) d t, with

9-

f (r) = \frac{r^{2}}{L^{2}} - \frac{β^{2}}{2 (D - 3)} - \frac{m}{r^{D - 3}} + \frac{q^{2}}{r^{2 (D - 3)}}, A_{t} = \sqrt{\frac{2 (D - 2)}{D - 3}} (1 - \frac{r_{h}^{D - 3}}{r^{D - 3}}) \frac{q}{r_{h}^{D - 3}}

10-

a = 1, 2 \dots D - 2

Formulas (html):

Correct Categorie: hep-th

Guessed Categorie: hep-th

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0605577

Formulas:

1-

q \equiv M_{2} / M_{1} \approx 1

2-

\sim 1 \overset{''}{.} 5

3-

M_{V e g a}

4-

S p T = 7.26 - 3.44 (F 110 W - F 170 M)

5-

J_{M K O} - F 110 W

6-

- 1.15 + 0.025 (F 110 W - F 170 M)

7-

+ 0.035 {(F 110 W - F 170 M)}^{2}

8-

H_{M K O} - F 170 M

9-

- 0.75 + 0.89 (F 110 W - F 170 M)

10-

- 0.27 {(F 110 W - F 170 M)}^{2}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0511780

Formulas:

1-

S = k \lg N

2-

S / k = - I

3-

y = f (x) + u

4-

P (y; x)

5-

P (y; x)

6-

- I (T)

7-

- I (D | T)

8-

I (D | T) = \sum_{i = 1}^{N} \lg P {(y_{i}; x_{i})}^{- 1}

9-

p (T) = e^{- I (D, T)}

10-

I (D, T) = I (D | T) + I (T)

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: cs

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0507152

Formulas:

1-

L_{E d d} < \sim L < \sim 1 L_{E d d}

2-

L_{E d d}

3-

M_{m a x}

4-

M_{B H} = 10^{8} M_{⊙}

5-

L_{D} > 0.3 L_{E d d}

6-

L_{D} < \sim 0.3 L_{E d d}

7-

M_{m a x}

8-

L_{D} / L_{E d d}

9-

M_{BH} > \sim 10^{7} M_{⊙}

10-

M_{BH} < \sim 10^{7} M_{⊙}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1903.03123

Formulas:

1-

ℳ = 4 π r_{0}^{3} γ {(\frac{{\bar{ρ}}_{0}}{μ_{0}})}^{1 / 2} {(F D)}^{1 / 3}

2-

{\bar{ρ}}_{0} = 11000 \pm 1100 kg m^{- 3}

3-

μ_{0} = 4 π \times 10^{- 7} H / m

4-

\frac{r_{0}}{R_{p}} = \sqrt{\frac{1}{0.21} [1.07 - (\frac{R_{p}}{R_{\oplus}}) / {(\frac{M_{p}}{M_{\oplus}})}^{0.27}]}

5-

\frac{F}{F_{\oplus}} = {(\frac{R_{O_{l}}}{R_{O_{l \oplus}}})}^{2} {(\frac{D}{D_{\oplus}})}^{2 / 3} {(\frac{Ω}{Ω_{\oplus}})}^{7 / 3}

6-

D = 0.65 r_{0}

7-

D = 0.65 r_{0}

8-

D_{\oplus} = 0.65 r_{0_{\oplus}}

9-

ℳ_{m a x}

10-

τ_{s y n c} \approx \frac{4}{9} α Q_{p}^{'} (\frac{R_{p}^{3}}{G M_{p}}) (Ω_{i} - Ω_{f}) {(\frac{M_{p}}{M_{*}})}^{2} {(\frac{d}{R_{p}})}^{6}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1410.5857

Formulas:

1-

\tilde{T} : K \to K

2-

\tilde{T} : K \to K

3-

M_{T} (X)

4-

F_{f} : M_{T} (X) \to ℝ

5-

F_{f} (μ) = \int_{X} f 𝑑 μ .

6-

E n d (K)

7-

D (T, \tilde{T}) = \max_{x \in K} d (T (x), \tilde{T} (x))

8-

H o m (K)

9-

T \in E n d (K)

10-

\tilde{T} \in E n d (K)

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/cond-mat/0701213

Formulas:

1-

ρ (T) χ (T) = c o n s t

2-

ρ (T) χ (T) = c o n s t

3-

ρ (T) = ρ_{0} + A \exp (Δ / k_{B} T)

4-

10^{2} μ Ω

5-

χ (T) = χ_{0} + n C / (T - Θ)

6-

χ_{0} = 5.6 \cdot 10^{- 4}

7-

C = 1.86 \cdot 10^{- 3}

8-

\sim k_{B} T ρ (ϵ_{F})

9-

ρ (ϵ_{F})

10-

10^{- 4} - 10^{- 3}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1404.6919

Formulas:

1-

H = ℏ ω (a^{†} a + \frac{1}{2}) = \frac{ℏ ω}{2} (a^{†} a + a a^{†})

2-

H = ℏ ω a^{†} a .

3-

F_{3 D} = \frac{π^{2} ℏ c}{240} \frac{A}{L^{4}} .

4-

(\begin{matrix} b^{+} \\ a^{-} \end{matrix}) = 𝖲 (\begin{matrix} a^{+} \\ b^{-} \end{matrix}) .

5-

𝖲 = (\begin{matrix} t & \bar{r} \\ r & \bar{t} \end{matrix}),

6-

(a^{-}, b^{+})

7-

𝖲^{†} 𝖲 = 𝟣 .

8-

{| t |}^{2} + {| r |}^{2} = {| \bar{t} |}^{2} + {| \bar{r} |}^{2}

9-

r {\bar{t}}^{*} + t {\bar{r}}^{*}

10-

det (𝖲) = - \frac{r}{{\bar{r}}^{*}} = - \frac{\bar{r}}{r^{*}} .

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: quant-ph

Result: correct

Paper: https://arxiv.org/abs/0704.1453

Formulas:

1-

S (q, ω)

2-

S_{i} (q, ω)

3-

τ = \frac{1}{2} (\sqrt{5} + 1)

4-

{L, S} \mapsto {L S, L}

5-

L S L L S L S L

6-

ℋ = \sum_{j = 1}^{N} \frac{p_{j}^{2}}{2} + V (x_{j} - x_{j + 1} - a_{j}),

7-

a_{j} \equiv a_{0} = τ^{3}

8-

V (x) = x^{4} - 2 x^{2}

9-

L = a_{0} + 1

10-

S = a_{0} - 1

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1506.05257

Formulas:

1-

0.0107 d e g / m

2-

0.009 d e g / m

3-

m_{p q} = \sum_{x, y} x^{p} y^{q} I (x, y),

4-

p, q^{t h}

5-

C = (\frac{m_{10}}{m_{00}}, \frac{m_{01}}{m_{00}}) .

6-

θ = a t a n 2 (m_{10}, m_{01}) .

7-

\sum_{i = 1}^{N} {∥ x_{i}^{(l)} - π^{(l)} ((X_{i}); 𝐫, 𝐭) ∥}^{2} + {∥ x_{i}^{(r)} - π^{(r)} ((X_{i}); 𝐫, 𝐭) ∥}^{2}

8-

𝐦^{', T} 𝐅 𝐦 = 0,

9-

{(x_{l} - π_{l})}^{2} + {(x_{r} - π_{r})}^{2} < θ,

10-

⟨ x_{l}, x_{r}, π_{l}, π_{r} ⟩

Formulas (html):

Correct Categorie: cs

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/nucl-th/9511040

Formulas:

1-

S_{1} \leftrightarrow S_{2} and N \leftrightarrow - D

2-

{| N |}^{2} + {| S_{1} |}^{2} + {| S_{2} |}^{2} + {| D |}^{2}

3-

(S_{1}^{*} S_{2} - N D^{*})

4-

(S_{1} N^{*} - S_{2} D^{*})

5-

(S_{2} N^{*} - S_{1} D^{*})

6-

(S_{1} S_{2}^{*} + N D^{*})

7-

(S_{1} D^{*} + S_{2} N^{*})

8-

{| S_{2} |}^{2} - {| S_{1} |}^{2} - {| D |}^{2} + {| N |}^{2}

9-

(S_{2} D^{*} + S_{1} N^{*})

10-

(S_{2} D^{*} + S_{1} N^{*})

Formulas (html):

Correct Categorie: nucl-th

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0011425

Formulas:

1-

{⟨ B ⟩}_{x} = ⟨ B ⟩ \cos θ

2-

{⟨ B ⟩}_{y} = 0

3-

{⟨ B ⟩}_{z} = ⟨ B ⟩ \sin θ

4-

⟨ B ⟩ / δ B ≪ 1

5-

δ B_{x} = δ B \cos φ

6-

δ B_{y} = δ B \sin φ \cos ψ

7-

δ B_{z} = δ B \sin φ \sin ψ

8-

[- 1, 1]

9-

[0, 2 π)

10-

𝐁 = 𝜹 𝐁 + ⟨ 𝐁 ⟩

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/0808.2075

Formulas:

1-

R \bar{3} c

2-

t_{2 g}^{6} e_{g}^{0}

3-

t_{2 g}^{5} e_{g}^{1}

4-

t_{2 g}^{4} e_{g}^{2}

5-

U_{eff} = U - J

6-

d_{x^{2} - y^{2}}

7-

\frac{1}{\sqrt{3}} (d_{x y} + d_{y z} + d_{x z})

8-

\frac{1}{\sqrt{2}} (d_{z^{2}} + d_{x^{2} - y^{2}})

9-

a^{-} a^{-} a^{-}

10-

U_{eff} = 3.5 e V

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1708.01496

Formulas:

1-

ϕ < ϕ_{J - f r i c t i o n l e s s}

2-

h \times l \times w = 177 \times 138 \times 15

3-

d_{m a x}

4-

a_{m a x}

5-

v_{m i n}

6-

v_{w a v e}

7-

v_{w a v e}

8-

a / a_{m a x}

9-

a_{m a x} = 360

10-

v_{w a v e} / v_{w a v e_{m a x}}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1809.06543

Formulas:

1-

x_{1}, \dots, x_{n}

2-

O ({|| f ||}^{t})

3-

t = t (m, ℓ)

4-

O (n^{m (ℓ - 1)})

5-

x_{1}, \dots, x_{n}

6-

{x_{1}, \dots, x_{n}} \cup R

7-

R [x_{1}, \dots, x_{n}]

8-

f \in R [x_{1}, \dots, x_{n}]

9-

𝐜 = (c_{1}, \dots, c_{n}) \in R^{n}

10-

(a x) b, a (x b), - (a x) (- b) \in R [x]

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/0811.3974

Formulas:

1-

P_{orb} = 44.5 \pm 0.1

2-

(u - g, g - r)

3-

(u - g, g - r)

4-

(g - r, r - i)

5-

M_{g} \approx 10 - 13

6-

A (g) = 0.2

7-

u - g < \min [0.14, 1.35 (g - r) + 0.32] - σ_{u - g}

8-

- 0.42 + σ_{g - r} < g - r < 0.02 - σ_{g - r}

9-

- 0.33 + σ_{r - i} < r - i < 0.03 - σ_{r - i}

10-

σ_{u - g} = \sqrt{σ_{u}^{2} + σ_{g}^{2} + σ_{E (u - g)}^{2}}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1007.4207

Formulas:

1-

T (W) = r_{p} \frac{Γ_{p} / 2}{M_{p} - W - i Γ_{p} / 2} + b_{p},

2-

σ \approx {| T |}^{2} / q^{2}

3-

{| T (W) |}^{2} = T_{\infty}^{2} \frac{{(W - M_{z})}^{2} + Γ_{z}^{2} / 4}{{(W - M_{p})}^{2} + Γ_{p}^{2} / 4},

4-

D (W) = M_{b} - W - i Γ (W) / 2,

5-

Γ (W) / 2

6-

= Γ_{b} / 2 + \tan θ (W - M_{b}),

7-

Γ (M_{b})

8-

M_{p} - i Γ_{p} / 2

9-

D (W) = 0

10-

= M_{b} + \sin θ \cos θ Γ_{b} / 2,

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/1907.13185

Formulas:

1-

𝒔_{d} = {[x_{d}, y_{d}]}^{⊤}

2-

𝒔_{u} = {[x_{u}, y_{u}]}^{⊤} = f (𝒔_{d}; 𝜽) 𝒔_{d}

3-

f (𝒔_{d}; 𝜽)

4-

f (𝒔_{d}; 𝜽)

5-

f (𝒔_{d}; λ) = \frac{1}{1 + λ r^{2}}

6-

f (𝒔_{d}; λ) = 1 + λ r^{2}

7-

r = \sqrt{x_{d}^{2} + y_{d}^{2}}

8-

f (𝒔_{d}; 𝜽)

9-

𝑺_{1} = {[X_{1}, Y_{1}, Z_{1}]}^{⊤}

10-

𝑺_{2} = {[X_{2}, Y_{2}, Z_{2}]}^{⊤}

Formulas (html):

Correct Categorie: cs

Guessed Categorie: cs

Result: correct

Paper: https://arxiv.org/abs/cond-mat/0503321

Formulas:

1-

N d_{1.85} C e_{0.15} C u O_{4 - y}

2-

L a_{1.89} S r_{0.11} C u O_{4}

3-

N d_{1.85} C e_{0.15} C u O_{4 - y}

4-

L a_{1.89} S r_{0.11} C u O_{4}

5-

Δ / k_{B} T_{c} = 1.66

6-

N d_{1.85} C e_{0.15} C u O_{4 - y}

7-

L a_{1.89} S r_{0.11} C u O_{4}

8-

d_{x^{2} - y^{2}}

9-

d V / d I

10-

R_{20 m V}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/cond-mat/9812260

Formulas:

1-

ρ (𝐫, 𝐫^{'}) \equiv ⟨ \hat{ψ} {(𝐫^{'})}^{†} \hat{ψ} (𝐫) ⟩

2-

ϕ_{i} (𝐫)

3-

b_{i} \equiv \int 𝑑 𝐫 ϕ_{i} (𝐫) \hat{ψ} (𝐫)

4-

\hat{ψ} (𝐫)

5-

{[{\hat{ρ}}_{0}]}_{i j} = ⟨ 0 | b_{j}^{†} b_{i} | 0 ⟩ = N_{i} δ_{i j},

6-

q = 0, \pm 1, \pm 2, \dots

7-

B^{†} \equiv \frac{b_{2}^{†} b_{1}}{\sqrt{N_{2} N_{1}}}

8-

{(B^{†})}^{q} | 0 ⟩ q \geq 0

9-

{(B)}^{| q |} | 0 ⟩ q < 0

10-

\sum q | q ⟩ ⟨ q |

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1706.05569

Formulas:

1-

vec (𝒙, 𝒚)

2-

𝒙_{t} \in SE (3)

3-

𝑹_{t} \in SO (3)

4-

{\dot{𝒑}}_{t} \in ℝ^{3}

5-

ℒ ≜ {𝒍^{[j]} \in ℝ^{3} | j = 1 : n_{l}}

6-

𝒵_{t} \subset ℝ_{\geq 0}

7-

p (z_{t} | 𝒙_{t}, 𝒍)

8-

p (𝐱_{t} | 𝐱_{t - 1}, 𝐮_{t - 1})

9-

z_{1 : t} ≜ {z_{1}, \dots, z_{t}}

10-

p (𝐱_{0})

Formulas (html):

Correct Categorie: cs

Guessed Categorie: math

Result: incorrect

Paper: https://arxiv.org/abs/nucl-ex/0403050

Formulas:

1-

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

2-

d N / d y

3-

- 0.1 < y < 3.5

4-

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

5-

- 0.1 < y < 3.5

6-

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

7-

d N / d y

8-

p = 4.5 GeV / c

9-

m_{T} = \sqrt{p_{T}^{2} + m_{0}^{2}}

10-

(y, p_{T})

Formulas (html):

Correct Categorie: nucl-ex

Guessed Categorie: nucl-ex

Result: correct

Paper: https://arxiv.org/abs/1312.4509

Formulas:

1-

Γ = {τ_{1}, τ_{2}, \dots, τ_{n}}

2-

τ_{i} = (P_{i}, C_{i})

3-

| I_{k} | = t_{k + 1} - t_{k}

4-

\sum_{i \in J_{k}} w_{i, k} \leq M, \forall k

5-

0 \leq w_{i, k} \leq 1, \forall k, \forall i .

6-

\sum_{k \in E i} w_{i, k} \times | I_{k} | = C_{i}, \forall i .

7-

W S S_{i}

8-

x_{i j k}

9-

I_{k}, k \in {1, \dots, T}

10-

\sum_{i = 1}^{n} W W S_{i} \times x_{i j k} \leq C_{L_{1}}, \forall j, \forall k .

Formulas (html):

Correct Categorie: cs

Guessed Categorie: cs

Result: correct

Paper: https://arxiv.org/abs/1712.03099

Formulas:

1-

- a \leq y \leq a

2-

\sum_{α} n_{0 α} = n_{0 i}

3-

\sum_{α} n_{0 α} v_{0 α x} = 0

4-

{[f_{2} E_{1 x}^{'}]}^{'} - g_{2} E_{1 x} = 0

5-

1 + \frac{S_{4}}{ω^{2}} - \frac{S_{3}^{2}}{ω^{2} (S_{1} - ω^{2})}

6-

\sum_{α} \frac{n_{0 α}}{n_{0} γ_{0 α}};

7-

\sum_{α} \frac{n_{0 α}}{n_{0} γ_{0 α}^{3}};

8-

\sum_{α} \frac{n_{0 α} v_{0 x α}}{n_{0} γ_{0 α}};

9-

\sum_{α} \frac{n_{0 α} v_{0 x α}^{2}}{n_{0} γ_{0 α}};

10-

ω^{2} = - γ^{2}

Formulas (html):

Correct Categorie: physics

Guessed Categorie: hep-th

Result: incorrect

Paper: https://arxiv.org/abs/quant-ph/0607209

Formulas:

1-

f_{r e a l} (μ)

2-

f_{c o m p l e x} (μ)

3-

μ = \sqrt{\frac{ρ_{11} ρ_{44}}{ρ_{22} ρ_{33}}}

4-

i = 1, \dots 4

5-

V_{s e p / r e a l} = 2 \int_{0}^{1} j a c_{r e a l} (μ) f_{r e a l} (μ) 𝑑 μ

6-

V_{c o m p l e x / r e a l} = 2 \int_{0}^{1} j a c_{c o m p l e x} (μ) f_{c o m p l e x} (μ) 𝑑 μ

7-

d = (n^{2} - 1)

8-

d = \frac{(n - 1) (n + 2)}{2}

9-

n = 4 = 2 \times 2

10-

2^{- 15} (\frac{\sqrt{2} - 1}{3}) \approx 4.2136 \cdot 10^{- 6}

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1604.03643

Formulas:

1-

κ_{q} (s)

2-

x^{''} + κ_{q} (s) x = 0,

3-

x (s) = A_{x} w \cos [ϕ (s) + ϕ_{0}]

4-

ϕ = \int_{0}^{s} 𝑑 s^{'} / w^{2} (s^{'})

5-

w^{''} + κ_{q} (s) w = w^{- 3} .

6-

(\begin{matrix} x \\ x^{'} \end{matrix}) = (\begin{matrix} w & 0 \\ w^{'} & w^{- 1} \end{matrix}) P^{- 1} {(\begin{matrix} w^{- 1} & 0 \\ - w^{'} & w \end{matrix})}_{0} {(\begin{matrix} x \\ x^{'} \end{matrix})}_{0},

7-

P^{'} = P (\begin{matrix} 0 & - w^{- 2} \\ w^{- 2} & 0 \end{matrix}) .

8-

P = (\begin{matrix} \cos ϕ & - \sin ϕ \\ \sin ϕ & \cos ϕ \end{matrix}) .

9-

H = \frac{1}{2} p_{x}^{2} + \frac{1}{2} κ_{q} (s) x^{2},

10-

H = \frac{1}{2} (\begin{matrix} x, & p_{x} \end{matrix}) (\begin{matrix} κ_{q} & 0 \\ 0 & 1 \end{matrix}) (\begin{matrix} x \\ p_{x} \end{matrix}) .

Formulas (html):

Correct Categorie: physics

Guessed Categorie: hep-ph

Result: incorrect

Paper: https://arxiv.org/abs/0904.3127

Formulas:

1-

π_{abs} = 7.2 \pm 1.1

2-

d = 149 (+ 26, - 20)

3-

K_{2} = 92 \pm 3

4-

I = 14 \overset{m}{.} 14

5-

| b | > 30 °

6-

U B V I

7-

[- 31, - 50]

8-

(R - I) > 1.2

9-

V - I \sim + 1.3

10-

I = 14 \overset{m}{.} 15

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/0911.4008

Formulas:

1-

V_{1}, V_{2}, \dots, V_{r}

2-

E (H) \subseteq V_{1} \times V_{2} \times \dots \times V_{r}

3-

| V_{i} | = n

4-

n / 2 + \sqrt{2 n \log n}

5-

⋃_{i \leq r} A_{i}

6-

d (f) = \frac{n}{2}

7-

⋃_{i \leq r} A_{i}

8-

| ⋃_{i \leq r} A_{i} |

9-

| | A_{i} | - \frac{n}{2} | \leq 1

10-

d (f) \geq \frac{n}{2} - 1

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/2008.04428

Formulas:

1-

g_{1} \dots g_{N}

2-

A_{1} \dots A_{256}

3-

f_{k x}, f_{k y}

4-

p_{1} \dots p_{256}

5-

{\vec{f}}_{k} = [\begin{matrix} f_{k x} \\ f_{k y} \\ f_{k a} \end{matrix}] = \sum_{y = 1}^{H = 8} \sum_{x = 1}^{W = 8} p_{k} (x, y) [\begin{matrix} (x - 4.5) / 4 \\ (y - 4.5) / 4 \\ A_{k} (x, y) \end{matrix}]

6-

(f_{k x}, f_{k y})

7-

(f_{k x}, f_{k y})

8-

{\vec{s}}_{1} \dots {\vec{s}}_{N}

9-

{\hat{𝐱}}_{t + 1} = {\hat{𝐱}}_{t} + {\bar{𝐱}}_{t}

10-

\hat{𝐱} \sim 𝒩 (\vec{μ}, \vec{σ})

Formulas (html):

Correct Categorie: cs

Guessed Categorie: cs

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0609713

Formulas:

1-

ρ (r) = \frac{4 ρ_{s}}{(r / r_{s}) {(1 + r / r_{s})}^{2}},

2-

k = 2 π / L

3-

k_{ny} = 2 π / L \times N^{1 / 3} / 2

4-

80 h^{- 1} Mpc

5-

m_{p} = 3.16 \times 10^{8} h^{- 1} M_{⊙}

6-

2.4 h^{- 1} kpc

7-

80 h^{- 1} Mpc

8-

5.0 \times 10^{6} h^{- 1} M_{⊙}

9-

0.6 h^{- 1} kpc

10-

0.1 h^{- 1} Mpc

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/physics/0005025

Formulas:

1-

L = I ω_{c}

2-

m g l \sin θ

3-

L \sin θ ω_{z} Δ t

4-

ω_{z} = m g l / I ω_{c}

5-

ω_{z} = \frac{I ω_{c} \pm \sqrt{I^{2} ω_{c}^{2} + 4 (I - I_{n}) m g l \cos θ}}{2 (I_{n} - I) \cos θ},

6-

I^{2} ω_{c}^{2} + 4 (I - I_{n}) m g l \cos θ > 0

7-

ω_{c} = (2 / I) \sqrt{(I_{n} - I) m g l \cos θ}

8-

\sqrt{1 + x} = 1 + x / 2

9-

x = 4 (I - I_{n}) m g l \cos θ / I^{2} ω_{c}^{2}

10-

ω_{z} = \frac{I ω_{c}}{2 (I_{n} - I) \cos θ} \pm (\frac{I ω_{c}}{2 (I_{n} - I) \cos θ} - \frac{m g l}{I ω_{c}}) .

Formulas (html):

Correct Categorie: physics

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/9911315

Formulas:

1-

- 27 ≲ M_{B_{J}} ≲ - 20

2-

M_{B_{J}} ≃ - 20

3-

\sim 5 ° \times 5 °

4-

M_{B_{J}} = B_{J} + 5 - 5 \log d_{L} (z) + A + K (z)

5-

d_{L} (z)

6-

H_{0} = 50 km s^{- 1} {Mpc}^{- 1}

7-

\log (1 + z)

8-

{(1 + z)}^{4}

9-

γ_{1} (z)

10-

Δ \log (1 + z) = 0.05

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/0907.5037

Formulas:

1-

\sum_{ξ = 1}^{N} {| ⟨ a | ξ ⟩ |}^{2} = 1

2-

P^{a a} = N \sum_{ξ = 1}^{N} {| ⟨ a | ξ ⟩ |}^{4} = N lim_{T \to \infty} \frac{1}{2 T} \int_{- T}^{T} 𝑑 t {| ⟨ a | a (t) ⟩ |}^{2},

3-

P^{a a} = 1

4-

P^{a a} = N

5-

P^{a b} = N \sum_{ξ = 1}^{N} {| ⟨ a | ξ ⟩ |}^{2} {| ⟨ b | ξ ⟩ |}^{2} = N lim_{T \to \infty} \frac{1}{2 T} \int_{- T}^{T} 𝑑 t {| ⟨ a | b (t) ⟩ |}^{2} .

6-

| a ⟩ ⟨ a |

7-

Tr \hat{α} = 1

8-

P^{α β} = N \sum_{ξ = 1}^{N} ⟨ ξ | \hat{α} | ξ ⟩ ⟨ ξ | \hat{β} | ξ ⟩ = N lim_{T \to \infty} \frac{1}{2 T} \int_{- T}^{T} 𝑑 t Tr \hat{α} \hat{β} (t),

9-

\bar{P^{a b}} \approx \bar{\sum_{- τ}^{τ} P^{a b} (t)},

10-

P^{a b} (t) = {| ⟨ a | b (t) ⟩ |}^{2} + ⟨ a | a (t) ⟩ ⟨ b (t) | b ⟩,

Formulas (html):

Correct Categorie: nlin

Guessed Categorie: hep-lat

Result: incorrect

Paper: https://arxiv.org/abs/1510.07870

Formulas:

1-

λ_{o v} H_{p}

2-

1.8 - 1.9 M_{⊙}

3-

M = 1.80 M_{⊙}

4-

M = 1.89 M_{⊙}

5-

Δ M \sim 0.01 M_{⊙}

6-

\log (L / L_{⊙}) \approx 2.142

7-

\sim 10^{6} M_{⊙}

8-

2 - 3 \times 10^{7}

9-

\sim 10^{6} M_{⊙}

10-

\sim 5 \times 10^{5} M_{⊙}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1605.00351

Formulas:

1-

h (x) \in 𝔽_{q} [x]

2-

W \subseteq [0, n] := {0, 1, \dots, n}

3-

S_{W} (h) = \sum_{w \in W} [x^{w}] h (x)

4-

W \subseteq [0, n]

5-

S_{W} (P) = c

6-

W \subseteq [0, n]

7-

S_{W} (P) \neq c

8-

r \leq [(1 / 4 - ϵ) n]

9-

n / 4 + o (n)

10-

𝔽_{q} [x]

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Run 11312198 (Agent336)