Run 11274850

Paper: https://arxiv.org/abs/0707.3080

Formulas:

1-

| 𝐁_{ext} | = h f_{ac} / g μ_{B}

2-

| g | = 0.39 \pm 0.01

3-

𝐁_{eff} (t)

4-

f_{ac} = g μ_{B} | 𝐁_{ext} | / h

5-

H_{SO} = α (p_{x} σ_{y} - p_{y} σ_{x}) + β (- p_{x} σ_{x} + p_{y} σ_{y})

6-

𝐁_{eff} (x, y) = 𝐧 \otimes 𝐁_{ext}; n_{x} = \frac{2 m^{*}}{ℏ} (- α y - β x); n_{y} = \frac{2 m^{*}}{ℏ} (α x + β y); n_{z} = 0

7-

𝐱 (t) = (e l_{dot}^{2} / Δ) 𝐄 (t)

8-

𝐁_{eff} (t) ⟂ 𝐁_{ext}

9-

[1 \bar{1} 0]

10-

| 𝐁_{eff} (t) | = 2 | 𝐁_{ext} | \frac{l_{dot}}{l_{SO}} \frac{e | 𝐄 (t) | l_{dot}}{Δ},

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1107.4163

Formulas:

1-

N (t) = λ

2-

c a n d i d a t e_{1}

3-

c a n d i d a t e_{2}

4-

c a n d i d a t e_{1}

5-

c a n d i d a t e_{2}

6-

p_{n} = p_{s} = p_{e} = p_{w} = \frac{1}{4} (1 - β)

7-

p a r e n t_{1}

8-

p a r e n t_{2}

9-

c h i l d_{1}

10-

c h i l d_{2}

Formulas (html):

Correct Categorie: cs

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/0711.2538

Formulas:

1-

1 μ m^{3}

2-

4 π a c_{r} D

3-

c_{r} \propto R^{- 3}

4-

D \sim D_{0} p

5-

p = (1 - c)

6-

a (1 - N b^{3} R^{- 3}) / R^{3}

7-

\bar{τ} = \frac{1}{V} \int_{V} τ (\vec{x}) d^{d} \vec{x}

8-

τ (\vec{x})

9-

D \nabla^{2} τ (\vec{x}) = - 1 .

10-

\frac{1}{2 D (c) (R^{2} - a^{2})} (R^{4} \ln (\frac{R}{a}) - \frac{3 R^{4}}{4} + R^{2} a^{2} - \frac{a^{4}}{4})

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/0910.2789

Formulas:

1-

G_{i j} (t)

2-

= (\sum_{\vec{x}} {Tr}_{sp} {Γ_{\pm} ⟨ Ω | χ_{i} (x) {\bar{χ}}_{j} (0) | Ω ⟩}),

3-

= \sum_{α} λ_{i}^{α} {\bar{λ}}_{j}^{α} e^{- m_{α} t},

4-

{\bar{χ}}_{j} u_{j}^{α}

5-

G_{i j} (t + △ t) u_{j}^{α}

6-

= e^{- m_{α} △ t} G_{i j} (t) u_{j}^{α},

7-

{[G_{i j} (t)]}^{- 1}

8-

{[{(G (t))}^{- 1} G (t + △ t)]}_{i j} u_{j}^{α}

9-

= c^{α} u_{i}^{α},

10-

c^{α} = e^{- m_{α} △ t}

Formulas (html):

Correct Categorie: hep-lat

Guessed Categorie: hep-lat

Result: correct

Paper: https://arxiv.org/abs/1812.06149

Formulas:

1-

\hat{q} = {\hat{q}}_{S} + {\hat{q}}_{H} + {\hat{q}}_{NP},

2-

{\hat{q}}_{H} = \frac{1}{2 E} \int \frac{d p^{', 3}}{{(2 π)}^{3} 2 E^{'}} f_{0} (p^{'}) 2 (s - M^{2}) \int_{- {(s - M^{2})}^{2} / s}^{- Q_{cut}^{2}} q^{2} \frac{d σ_{el}}{d t} 𝑑 t .

3-

{\hat{q}}_{S} = C_{A} T \int_{0}^{Q_{{cut}^{2}}} α_{s} (q^{2}) \frac{m_{D}^{2} d q^{2}}{q^{2} + m_{D}^{2}}

4-

α_{s} (Q) = α_{s} (\max {Q, μ π T})

5-

τ_{f} \sim ω / k_{⟂}^{2}

6-

τ_{f} < t - t_{0}

7-

P = \tilde{λ} / τ_{f}

8-

\tilde{λ} \sim m_{D}^{2} / \hat{q}

9-

\tilde{λ} \propto m_{D}^{2} / \hat{q}

10-

2 π T ≲ ω < E

Formulas (html):

Correct Categorie: nucl-th

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/9810270

Formulas:

1-

220 \pm 30 μ s

2-

400 \pm 100 μ s

3-

Δ E / E = 18 %

4-

\sim 66 k m

5-

\sim 15 m s

6-

\sim 4500 k m

7-

2025 c m^{2}

8-

τ_{r i s e}

9-

τ_{r i s e}

10-

190 \pm 40 μ s

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/physics/0401141

Formulas:

1-

Q_{0} \geq 5 \times 10^{9}

2-

2 Nb + 5 {SO}_{4}^{- -} + 5 H_{2} O

3-

{Nb}_{2} O_{5} + 10 H^{+} + 5 {SO}_{4}^{- -} + 10 e^{-}

4-

{Nb}_{2} O_{5} + 6 HF

5-

H_{2} {NbOF}_{5} + {NbOF}_{2} \cdot 0.5 H_{2} O + 1.5 H_{2} O

6-

{NbOF}_{2} \cdot 0.5 H_{2} O + 4 HF

7-

H_{2} {NbF}_{5} + 1.5 H_{2} O

8-

Q_{e x t}

9-

τ = \frac{Q_{L}}{ω_{0}} with Q_{L} = {(\frac{1}{Q_{0}} + \frac{1}{Q_{e x t}})}^{- 1} \approx \frac{Q_{0}}{2} .

10-

Q_{0} (E_{a c c})

Formulas (html):

Correct Categorie: physics

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/0712.1160

Formulas:

1-

4 - 7 M_{⊙}

2-

1.1 \times 10^{5} yr

3-

1.8 \times 10^{5} yr

4-

2.9 \times 10^{5} yr

5-

1.2 \times 10^{6} yr

6-

4.7 \times 10^{- 7} M_{⊙} {yr}^{- 1}

7-

2.0 \times 10^{- 6} M_{⊙} {yr}^{- 1}

8-

T = 10^{8} K

9-

T = 2 \times 10^{8} K

10-

5.08 \times 10^{- 2} M_{⊙}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1609.02424

Formulas:

1-

Z_{η} = \sqrt{\frac{3}{8}} Z_{χ} - \sqrt{\frac{5}{8}} Z_{ψ}

2-

S O (10)

3-

ℒ \supset \tilde{g} \sum_{f} \bar{f} γ^{μ} (ϵ_{L}^{f} P_{L} + ϵ_{R}^{f} P_{R}) f Z_{μ}^{'} + g_{χ} \bar{χ} γ^{μ} (ϵ_{L}^{χ} P_{L} + ϵ_{R}^{χ} P_{R}) χ Z_{μ}^{'}

4-

ℒ \supset \tilde{g} (\sum_{f} \bar{f} γ^{μ} (V_{f} - A_{f} γ^{5}) f Z_{μ}^{'} + \bar{χ} γ^{μ} (V_{χ} - A_{χ} γ^{5}) χ Z_{μ}^{'})

5-

\tilde{g} V_{f} = \frac{\tilde{g}}{2 D} (ϵ_{L}^{f} + ϵ_{R}^{f}), \tilde{g} A_{f} = \frac{\tilde{g}}{2 D} (ϵ_{L}^{f} - ϵ_{R}^{f})

6-

\tilde{g} V_{χ} = \frac{g_{χ}}{2 D} (ϵ_{L}^{χ} + ϵ_{R}^{χ}), \tilde{g} A_{χ} = \frac{g_{χ}}{2 D} (ϵ_{L}^{χ} - ϵ_{R}^{χ})

7-

\tilde{g} = g \approx 0.65

8-

\tilde{g} = g_{χ} = \sqrt{\frac{5}{3}} g \tan θ_{W} \approx 0.46

9-

U {(1)}_{Y}

10-

\frac{1}{2} - \frac{2}{3} \sin^{2} (θ_{W})

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: hep-ph

Result: correct

Paper: https://arxiv.org/abs/1706.05460

Formulas:

1-

A_{x y} = 1

2-

A_{x y} = 0

3-

(v, k, λ, μ)

4-

A^{2} = (λ - μ) A + (k - μ) I + μ J

5-

- D = {- d ∣ d \in D}

6-

Cay (G, D)

7-

Cay (G, D)

8-

Γ = Cay (G, D)

9-

χ (D) := \sum_{d \in D} χ (d)

10-

(v, k, λ, μ)

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/hep-ph/0106070

Formulas:

1-

\bar{a} = a + δ a

2-

D (Q^{2})

3-

D (Q^{2}) = \int_{0}^{\infty} \frac{d k^{2}}{k^{2}} \bar{a} (k^{2}) Φ (\frac{k^{2}}{Q^{2}})

4-

Φ (k^{2} / Q^{2})

5-

D (Q^{2}) ≃ c_{n} \frac{λ_{n} (μ_{I})}{Q^{2 n}} + \int_{μ_{I}^{2}}^{\infty} \frac{d k^{2}}{k^{2}} a (k^{2}) Φ (\frac{k^{2}}{Q^{2}})

6-

λ_{n} (μ_{I}) = \int_{0}^{μ_{I}^{2}} \frac{d k^{2}}{k^{2}} \bar{a} (k^{2}) k^{2 n}

7-

Φ (k^{2} / Q^{2}) ≃ c_{n} {(k^{2} / Q^{2})}^{n}

8-

N_{f}^{*} < N_{f} < 16.5

9-

D (Q^{2}) = D_{\bar{P T}} (Q^{2})

10-

D_{\bar{P T}} (Q^{2}) \equiv \int_{0}^{\infty} \frac{d k^{2}}{k^{2}} a (k^{2}) Φ (\frac{k^{2}}{Q^{2}})

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: hep-ph

Result: correct

Paper: https://arxiv.org/abs/2004.08223

Formulas:

1-

N_{B} = N - N_{A}

2-

N_{A} = N_{A}^{0}

3-

\underline{N_{A}} = (N_{A}^{0}, N_{A}^{1}, \dots, N_{A}^{T}),

4-

N_{A}^{i} = N_{A}^{i - 1} \pm 1

5-

Prob (\underline{N_{A}}) = \prod_{i = 1}^{T} (δ (N_{A}^{i} - N_{A}^{i - 1}, 1) \frac{N - N_{A}^{i - 1}}{N} + δ (N_{A}^{i} - N_{A}^{i - 1}, - 1) \frac{N_{A}^{i - 1}}{N}) .

6-

w (\underline{N_{A}})

7-

{Prob}_{\mod} (\underline{N_{A}}) = C w (\underline{N_{A}}) Prob (\underline{N_{A}}),

8-

\sum_{\underline{N_{A}}} {Prob}_{\mod} (\underline{N_{A}}) = 1 .

9-

w (\underline{N_{A}}) = δ (N_{A}^{10}, 5) δ (N_{A}^{20}, 5) .

10-

N_{A} = N_{B} = 5

Formulas (html):

Correct Categorie: gr-qc

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/0302137

Formulas:

1-

p (i, j)

2-

\sum_{j} p (i, j) = 1

3-

p (i, j)

4-

p (i, j) = p_{0} (j)

5-

p (l, j)

6-

α^{- p_{a} (l)}

7-

p_{a} (l) = p (l, j) - p_{0} (j)

8-

P (l) = \frac{α^{- p_{a} (l)}}{\sum_{m} α^{- p_{a} (m)}},

9-

H P P H

10-

H P P H

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/0303517

Formulas:

1-

1 / 3 < ν < 2 / 5

2-

R_{H} = h / f e^{2}

3-

f = \frac{n}{2 p n \pm 1}

4-

ν^{*} = n + \frac{m}{2 p^{'} m \pm 1}

5-

ν = \frac{ν^{*}}{2 p ν^{*} \pm 1}

6-

ν = \frac{n}{2 p n \pm 1}

7-

ν = \frac{n + 1}{2 p (n + 1) \pm 1}

8-

2 / 5 > ν > 1 / 3

9-

ν^{*} = 1 + 1 / 3

10-

ν^{*} = 1 + 2 / 3

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/1408.2526

Formulas:

1-

\sim 10^{53} erg s^{- 1}

2-

θ_{jet} = 0.1 °

3-

12 + \log (O / H) > 8.7

4-

< 10^{8} M_{⊙}

5-

12 + \log (O / H) > 8.7

6-

10^{53} erg s^{- 1}

7-

3 < j / 10^{16} {cm}^{2} s^{- 1} < 20

8-

Z < 0.5 Z_{⊙}

9-

n_{H} = 10 {cm}^{- 3}

10-

Z_{crit} = 10^{- 4}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/cond-mat/0702339

Formulas:

1-

ϕ = V_{g} / V_{t o t}

2-

V_{t o t}

3-

v_{s} (t)

4-

v_{s} (z_{s})

5-

z_{s} (t)

6-

z_{s} (t)

7-

v_{s} = d z_{s} / d t

8-

F_{d} = F_{C} + c {| v_{s} |}^{β}

9-

F_{C} = c o n s t

10-

F_{C} = κ | z_{s} |

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1207.2716

Formulas:

1-

\bar{S (E)}

2-

\bar{S (E)}

3-

\bar{S^{m} (E)} = {\bar{S (E)}}^{m} .

4-

\tilde{S} (E)

5-

\tilde{S} (E)

6-

\tilde{S} (E) = S (E \pm i V_{0}),

7-

\bar{{\tilde{S}}^{m} (E)} = {\bar{\tilde{S} (E)}}^{m} .

8-

\tilde{S} = \sqrt{R} e^{i θ},

9-

d P (\tilde{S}) = p (R, θ) d R d θ,

10-

{\tilde{S}}^{'} = \sqrt{R^{'}} e^{i θ^{'}}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: hep-th

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/9703052

Formulas:

1-

F (ν) \sim ν^{- α}

2-

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

3-

x_{g} = 2 G M / c^{2}

4-

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

5-

M = v_{x} / a_{s}

6-

T_{Q P O} \propto M_{B H}

7-

l << l_{m s}

8-

x_{K} \sim 10 x_{g}

9-

x_{s} \sim 10 x_{g}

10-

{\dot{m}}_{d} \sim 0.1 - 0.3

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1805.06070

Formulas:

1-

P (s_{1}, s_{2}, \dots | C) = P (s_{1} | C) P (s_{2} | s_{1}, C) \dots

2-

O (n * m^{2})

3-

y (x) = \sum_{1}^{N} w_{i} ϕ_{σ_{i}} (x - μ_{i})

4-

ϕ_{σ_{i}} (x) = \exp (- σ_{i}^{- 2} {∥ x ∥}^{2})

5-

w_{i}, σ_{i}, μ_{i}

6-

𝒪 (v^{2} d^{2})

7-

𝒪 (v d^{2})

8-

𝒪 (d L^{3})

9-

𝒪 (d (L + T))

10-

𝒪 (d L^{3})

Formulas (html):

Correct Categorie: cs

Guessed Categorie: cs

Result: correct

Paper: https://arxiv.org/abs/1611.04785

Formulas:

1-

𝒪 (α α_{S}^{2})

2-

𝒪 (α_{S}^{2}) \approx 𝒪 (α)

3-

𝒪 (α^{2} α_{S}^{n})

4-

P_{l q} \neq P_{q l}

5-

Δ P_{f F}^{S} \equiv 0

6-

P_{i j} = \sum_{k, l} a_{S}^{k} a^{l} P_{i j}^{(k, l)}

7-

α \equiv 2 π a

8-

α_{S} \equiv 2 π a_{S}

9-

\frac{d q_{v_{i}}}{d t} = P_{q_{i}}^{-} \otimes q_{v_{i}}, \frac{d l_{v_{i}}}{d t} = P_{l}^{-} \otimes l_{v_{i}}, \frac{d {Δ_{2}^{l}, Δ_{3}^{l}}}{d t} = P_{l}^{+} \otimes {Δ_{2}^{l}, Δ_{3}^{l}},

10-

\frac{d {Δ_{u c}, Δ_{c t}}}{d t} = P_{u}^{+} \otimes {Δ_{u c}, Δ_{c t}}, \frac{d {Δ_{d s}, Δ_{s b}}}{d t} = P_{d}^{+} \otimes {Δ_{d s}, Δ_{s b}},

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: hep-ph

Result: correct

Paper: https://arxiv.org/abs/1901.03465

Formulas:

1-

({(x, y)}_{I}, {(x^{'}, y^{'})}_{I})

2-

I (x, y)

3-

D (x, y)

4-

({(x, y)}_{D}, {(x^{'}, y^{'})}_{D})

5-

X = {(x, x^{'})}_{D}

6-

Y = {(y, y^{'})}_{D}

7-

D (X, Y)

8-

m = mode (D (X, Y))

9-

D (x, y) = {\begin{matrix} D (x, y), & if x \in X, y \in Y, \\ and ∥ D (x, y) - m ∥ < t \\ 0, & otherwise \end{matrix} .

10-

D (X, Y)

Formulas (html):

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xref="S3.SS2.p1.1.m1.4.4.2.2.2.3.cmml"><mo stretchy="false" id="S3.SS2.p1.1.m1.4.4.2.2.2.2.3" xref="S3.SS2.p1.1.m1.4.4.2.2.2.3.cmml">(</mo><msup id="S3.SS2.p1.1.m1.4.4.2.2.1.1.1" xref="S3.SS2.p1.1.m1.4.4.2.2.1.1.1.cmml"><mi id="S3.SS2.p1.1.m1.4.4.2.2.1.1.1.2" xref="S3.SS2.p1.1.m1.4.4.2.2.1.1.1.2.cmml">x</mi><mo id="S3.SS2.p1.1.m1.4.4.2.2.1.1.1.3" xref="S3.SS2.p1.1.m1.4.4.2.2.1.1.1.3.cmml">′</mo></msup><mo id="S3.SS2.p1.1.m1.4.4.2.2.2.2.4" xref="S3.SS2.p1.1.m1.4.4.2.2.2.3.cmml">,</mo><msup id="S3.SS2.p1.1.m1.4.4.2.2.2.2.2" xref="S3.SS2.p1.1.m1.4.4.2.2.2.2.2.cmml"><mi id="S3.SS2.p1.1.m1.4.4.2.2.2.2.2.2" xref="S3.SS2.p1.1.m1.4.4.2.2.2.2.2.2.cmml">y</mi><mo id="S3.SS2.p1.1.m1.4.4.2.2.2.2.2.3" xref="S3.SS2.p1.1.m1.4.4.2.2.2.2.2.3.cmml">′</mo></msup><mo stretchy="false" id="S3.SS2.p1.1.m1.4.4.2.2.2.2.5" xref="S3.SS2.p1.1.m1.4.4.2.2.2.3.cmml">)</mo></mrow><mi id="S3.SS2.p1.1.m1.4.4.2.2.4" xref="S3.SS2.p1.1.m1.4.4.2.2.4.cmml">I</mi></msub><mo stretchy="false" id="S3.SS2.p1.1.m1.4.4.2.5" xref="S3.SS2.p1.1.m1.4.4.3.cmml">)</mo></mrow></math>, <math><mrow id="S3.SS2.p1.2.m2.2.3" xref="S3.SS2.p1.2.m2.2.3.cmml"><mi id="S3.SS2.p1.2.m2.2.3.2" xref="S3.SS2.p1.2.m2.2.3.2.cmml">I</mi><mo id="S3.SS2.p1.2.m2.2.3.1" xref="S3.SS2.p1.2.m2.2.3.1.cmml">⁢</mo><mrow id="S3.SS2.p1.2.m2.2.3.3.2" xref="S3.SS2.p1.2.m2.2.3.3.1.cmml"><mo stretchy="false" id="S3.SS2.p1.2.m2.2.3.3.2.1" xref="S3.SS2.p1.2.m2.2.3.3.1.cmml">(</mo><mi id="S3.SS2.p1.2.m2.1.1" xref="S3.SS2.p1.2.m2.1.1.cmml">x</mi><mo id="S3.SS2.p1.2.m2.2.3.3.2.2" xref="S3.SS2.p1.2.m2.2.3.3.1.cmml">,</mo><mi id="S3.SS2.p1.2.m2.2.2" xref="S3.SS2.p1.2.m2.2.2.cmml">y</mi><mo stretchy="false" id="S3.SS2.p1.2.m2.2.3.3.2.3" xref="S3.SS2.p1.2.m2.2.3.3.1.cmml">)</mo></mrow></mrow></math>, <math><mrow id="S3.SS2.p1.3.m3.2.3" xref="S3.SS2.p1.3.m3.2.3.cmml"><mi id="S3.SS2.p1.3.m3.2.3.2" xref="S3.SS2.p1.3.m3.2.3.2.cmml">D</mi><mo id="S3.SS2.p1.3.m3.2.3.1" xref="S3.SS2.p1.3.m3.2.3.1.cmml">⁢</mo><mrow id="S3.SS2.p1.3.m3.2.3.3.2" xref="S3.SS2.p1.3.m3.2.3.3.1.cmml"><mo stretchy="false" id="S3.SS2.p1.3.m3.2.3.3.2.1" xref="S3.SS2.p1.3.m3.2.3.3.1.cmml">(</mo><mi id="S3.SS2.p1.3.m3.1.1" xref="S3.SS2.p1.3.m3.1.1.cmml">x</mi><mo id="S3.SS2.p1.3.m3.2.3.3.2.2" xref="S3.SS2.p1.3.m3.2.3.3.1.cmml">,</mo><mi id="S3.SS2.p1.3.m3.2.2" xref="S3.SS2.p1.3.m3.2.2.cmml">y</mi><mo stretchy="false" id="S3.SS2.p1.3.m3.2.3.3.2.3" xref="S3.SS2.p1.3.m3.2.3.3.1.cmml">)</mo></mrow></mrow></math>, <math><mrow id="S3.SS2.p1.4.m4.4.4.2" xref="S3.SS2.p1.4.m4.4.4.3.cmml"><mo stretchy="false" id="S3.SS2.p1.4.m4.4.4.2.3" xref="S3.SS2.p1.4.m4.4.4.3.cmml">(</mo><msub id="S3.SS2.p1.4.m4.3.3.1.1" xref="S3.SS2.p1.4.m4.3.3.1.1.cmml"><mrow id="S3.SS2.p1.4.m4.3.3.1.1.2.2" xref="S3.SS2.p1.4.m4.3.3.1.1.2.1.cmml"><mo stretchy="false" id="S3.SS2.p1.4.m4.3.3.1.1.2.2.1" xref="S3.SS2.p1.4.m4.3.3.1.1.2.1.cmml">(</mo><mi id="S3.SS2.p1.4.m4.1.1" xref="S3.SS2.p1.4.m4.1.1.cmml">x</mi><mo id="S3.SS2.p1.4.m4.3.3.1.1.2.2.2" xref="S3.SS2.p1.4.m4.3.3.1.1.2.1.cmml">,</mo><mi id="S3.SS2.p1.4.m4.2.2" xref="S3.SS2.p1.4.m4.2.2.cmml">y</mi><mo stretchy="false" id="S3.SS2.p1.4.m4.3.3.1.1.2.2.3" xref="S3.SS2.p1.4.m4.3.3.1.1.2.1.cmml">)</mo></mrow><mi id="S3.SS2.p1.4.m4.3.3.1.1.3" xref="S3.SS2.p1.4.m4.3.3.1.1.3.cmml">D</mi></msub><mo id="S3.SS2.p1.4.m4.4.4.2.4" xref="S3.SS2.p1.4.m4.4.4.3.cmml">,</mo><msub id="S3.SS2.p1.4.m4.4.4.2.2" xref="S3.SS2.p1.4.m4.4.4.2.2.cmml"><mrow id="S3.SS2.p1.4.m4.4.4.2.2.2.2" xref="S3.SS2.p1.4.m4.4.4.2.2.2.3.cmml"><mo stretchy="false" id="S3.SS2.p1.4.m4.4.4.2.2.2.2.3" xref="S3.SS2.p1.4.m4.4.4.2.2.2.3.cmml">(</mo><msup id="S3.SS2.p1.4.m4.4.4.2.2.1.1.1" xref="S3.SS2.p1.4.m4.4.4.2.2.1.1.1.cmml"><mi id="S3.SS2.p1.4.m4.4.4.2.2.1.1.1.2" xref="S3.SS2.p1.4.m4.4.4.2.2.1.1.1.2.cmml">x</mi><mo id="S3.SS2.p1.4.m4.4.4.2.2.1.1.1.3" xref="S3.SS2.p1.4.m4.4.4.2.2.1.1.1.3.cmml">′</mo></msup><mo id="S3.SS2.p1.4.m4.4.4.2.2.2.2.4" xref="S3.SS2.p1.4.m4.4.4.2.2.2.3.cmml">,</mo><msup 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id="S3.SS2.p1.5.m5.1.1" xref="S3.SS2.p1.5.m5.1.1.cmml">x</mi><mo id="S3.SS2.p1.5.m5.2.2.1.1.1.3" xref="S3.SS2.p1.5.m5.2.2.1.1.2.cmml">,</mo><msup id="S3.SS2.p1.5.m5.2.2.1.1.1.1" xref="S3.SS2.p1.5.m5.2.2.1.1.1.1.cmml"><mi id="S3.SS2.p1.5.m5.2.2.1.1.1.1.2" xref="S3.SS2.p1.5.m5.2.2.1.1.1.1.2.cmml">x</mi><mo id="S3.SS2.p1.5.m5.2.2.1.1.1.1.3" xref="S3.SS2.p1.5.m5.2.2.1.1.1.1.3.cmml">′</mo></msup><mo stretchy="false" id="S3.SS2.p1.5.m5.2.2.1.1.1.4" xref="S3.SS2.p1.5.m5.2.2.1.1.2.cmml">)</mo></mrow><mi id="S3.SS2.p1.5.m5.2.2.1.3" xref="S3.SS2.p1.5.m5.2.2.1.3.cmml">D</mi></msub></mrow></math>, <math><mrow id="S3.SS2.p1.6.m6.2.2" xref="S3.SS2.p1.6.m6.2.2.cmml"><mi id="S3.SS2.p1.6.m6.2.2.3" xref="S3.SS2.p1.6.m6.2.2.3.cmml">Y</mi><mo id="S3.SS2.p1.6.m6.2.2.2" xref="S3.SS2.p1.6.m6.2.2.2.cmml">=</mo><msub id="S3.SS2.p1.6.m6.2.2.1" xref="S3.SS2.p1.6.m6.2.2.1.cmml"><mrow id="S3.SS2.p1.6.m6.2.2.1.1.1" xref="S3.SS2.p1.6.m6.2.2.1.1.2.cmml"><mo stretchy="false" id="S3.SS2.p1.6.m6.2.2.1.1.1.2" xref="S3.SS2.p1.6.m6.2.2.1.1.2.cmml">(</mo><mi id="S3.SS2.p1.6.m6.1.1" xref="S3.SS2.p1.6.m6.1.1.cmml">y</mi><mo id="S3.SS2.p1.6.m6.2.2.1.1.1.3" xref="S3.SS2.p1.6.m6.2.2.1.1.2.cmml">,</mo><msup id="S3.SS2.p1.6.m6.2.2.1.1.1.1" xref="S3.SS2.p1.6.m6.2.2.1.1.1.1.cmml"><mi id="S3.SS2.p1.6.m6.2.2.1.1.1.1.2" xref="S3.SS2.p1.6.m6.2.2.1.1.1.1.2.cmml">y</mi><mo id="S3.SS2.p1.6.m6.2.2.1.1.1.1.3" xref="S3.SS2.p1.6.m6.2.2.1.1.1.1.3.cmml">′</mo></msup><mo stretchy="false" id="S3.SS2.p1.6.m6.2.2.1.1.1.4" xref="S3.SS2.p1.6.m6.2.2.1.1.2.cmml">)</mo></mrow><mi id="S3.SS2.p1.6.m6.2.2.1.3" xref="S3.SS2.p1.6.m6.2.2.1.3.cmml">D</mi></msub></mrow></math>, <math><mrow id="S3.SS2.p1.7.m7.2.3" xref="S3.SS2.p1.7.m7.2.3.cmml"><mi id="S3.SS2.p1.7.m7.2.3.2" xref="S3.SS2.p1.7.m7.2.3.2.cmml">D</mi><mo id="S3.SS2.p1.7.m7.2.3.1" xref="S3.SS2.p1.7.m7.2.3.1.cmml">⁢</mo><mrow id="S3.SS2.p1.7.m7.2.3.3.2" xref="S3.SS2.p1.7.m7.2.3.3.1.cmml"><mo stretchy="false" id="S3.SS2.p1.7.m7.2.3.3.2.1" 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xref="S3.SS2.p1.8.m8.3.3.1.1.1.1.cmml"><mi id="S3.SS2.p1.8.m8.3.3.1.1.1.1.2" xref="S3.SS2.p1.8.m8.3.3.1.1.1.1.2.cmml">D</mi><mo id="S3.SS2.p1.8.m8.3.3.1.1.1.1.1" xref="S3.SS2.p1.8.m8.3.3.1.1.1.1.1.cmml">⁢</mo><mrow id="S3.SS2.p1.8.m8.3.3.1.1.1.1.3.2" xref="S3.SS2.p1.8.m8.3.3.1.1.1.1.3.1.cmml"><mo stretchy="false" id="S3.SS2.p1.8.m8.3.3.1.1.1.1.3.2.1" xref="S3.SS2.p1.8.m8.3.3.1.1.1.1.3.1.cmml">(</mo><mi id="S3.SS2.p1.8.m8.1.1" xref="S3.SS2.p1.8.m8.1.1.cmml">X</mi><mo id="S3.SS2.p1.8.m8.3.3.1.1.1.1.3.2.2" xref="S3.SS2.p1.8.m8.3.3.1.1.1.1.3.1.cmml">,</mo><mi id="S3.SS2.p1.8.m8.2.2" xref="S3.SS2.p1.8.m8.2.2.cmml">Y</mi><mo stretchy="false" id="S3.SS2.p1.8.m8.3.3.1.1.1.1.3.2.3" xref="S3.SS2.p1.8.m8.3.3.1.1.1.1.3.1.cmml">)</mo></mrow></mrow><mo stretchy="false" id="S3.SS2.p1.8.m8.3.3.1.1.1.3" xref="S3.SS2.p1.8.m8.3.3.1.1.1.1.cmml">)</mo></mrow></mrow></mrow></math>, <math><mrow id="S3.E1.m1.9.9.1" xref="S3.E1.m1.9.9.1.1.cmml"><mrow id="S3.E1.m1.9.9.1.1" xref="S3.E1.m1.9.9.1.1.cmml"><mrow 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id="S3.E1.m1.5.5.5.5.1.1.3.1" xref="S3.E1.m1.9.9.1.1.3.1.cmml">,</mo></mrow></mtd><mtd columnalign="left" id="S3.E1.m1.6.6.6i" xref="S3.E1.m1.9.9.1.1.3.1.cmml"><mtext id="S3.E1.m1.6.6.6.6.2.1" xref="S3.E1.m1.6.6.6.6.2.1a.cmml">otherwise</mtext></mtd></mtr></mtable></mrow></mrow><mo id="S3.E1.m1.9.9.1.2" xref="S3.E1.m1.9.9.1.1.cmml">.</mo></mrow></math>, <math><mrow id="S3.SS2.p2.1.m1.2.3" xref="S3.SS2.p2.1.m1.2.3.cmml"><mi id="S3.SS2.p2.1.m1.2.3.2" xref="S3.SS2.p2.1.m1.2.3.2.cmml">D</mi><mo id="S3.SS2.p2.1.m1.2.3.1" xref="S3.SS2.p2.1.m1.2.3.1.cmml">⁢</mo><mrow id="S3.SS2.p2.1.m1.2.3.3.2" xref="S3.SS2.p2.1.m1.2.3.3.1.cmml"><mo stretchy="false" id="S3.SS2.p2.1.m1.2.3.3.2.1" xref="S3.SS2.p2.1.m1.2.3.3.1.cmml">(</mo><mi id="S3.SS2.p2.1.m1.1.1" xref="S3.SS2.p2.1.m1.1.1.cmml">X</mi><mo id="S3.SS2.p2.1.m1.2.3.3.2.2" xref="S3.SS2.p2.1.m1.2.3.3.1.cmml">,</mo><mi id="S3.SS2.p2.1.m1.2.2" xref="S3.SS2.p2.1.m1.2.2.cmml">Y</mi><mo stretchy="false" id="S3.SS2.p2.1.m1.2.3.3.2.3" xref="S3.SS2.p2.1.m1.2.3.3.1.cmml">)</mo></mrow></mrow></math>

Correct Categorie: cs

Guessed Categorie: cs

Result: correct

Paper: https://arxiv.org/abs/physics/9706023

Formulas:

1-

\dot{v} (t) = f (t) - τ^{- 1} v (t),

2-

f (t) = f \equiv c o n s t a n t

3-

v (0) = 0

4-

f (t) \leq f

5-

d = \int_{0}^{T} 𝑑 t v (t) .

6-

f (t) = f = c o n s t . \forall t

7-

f (t) = f - c t

8-

\dot{v} (t) = - τ^{- 1} v (t) + \sqrt{{(f - c t)}^{2} - λ^{2} \frac{v {(t)}^{4}}{R^{2}}},

9-

d = d_{c} + d_{s}

10-

\int_{0}^{t_{1}} 𝑑 t v_{c} (t),

Formulas (html):

Correct Categorie: physics

Guessed Categorie: gr-qc

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/9509037

Formulas:

1-

L = η \dot{M} c^{2},

2-

η = \frac{1}{4} \frac{r - 2}{{(r - 1)}^{2}}, r = \frac{r_{i n}}{r_{G}},

3-

r_{G} = 2 G M / c^{2}

4-

L_{E} = \frac{4 π c G M}{κ} = \frac{2.5 \cdot 10^{38}}{1 + X} \frac{M}{M_{⊙}} erg / s,

5-

{\dot{M}}_{C} = \frac{L_{E}}{{(η)}_{m a x} c^{2}} .

6-

\dot{M} / {\dot{M}}_{C} = L / L_{E}

7-

{(η)}_{m a x}

8-

r_{m s} = 3 r_{G}

9-

{\dot{M}}_{C} = \frac{64 π G M}{κ c} = \frac{4.45 \cdot 10^{18}}{1 + X} \frac{M}{M_{⊙}} g / s .

10-

η_{m a x} = 1

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1705.07024

Formulas:

1-

(Ω, 𝒦, P)

2-

M (u (X))

3-

f : [0, 1] \to 𝐑

4-

\int_{0}^{1} f (γ) 𝑑 γ = 1

5-

{[A]}^{γ} = [a_{1} (γ), a_{2} (γ)]

6-

γ \in [0, 1]

7-

E_{f} (u (A))

8-

E_{f} (u (A)) = \frac{1}{2} \int_{0}^{1} [u (a_{1} (γ)) + u (a_{2} (γ))] f (γ) 𝑑 γ

9-

E_{f} (u (A))

10-

E_{f} (A) = \frac{1}{2} \int_{0}^{1} [a_{1} (γ) + a_{2} (γ)] f (γ) 𝑑 γ

Formulas (html):

Correct Categorie: cs

Guessed Categorie: math

Result: incorrect

Paper: https://arxiv.org/abs/1204.5264

Formulas:

1-

ν_{H B O}

2-

ν_{H B O}

3-

ν_{H B O}

4-

ν_{H B O}

5-

ν_{H B O}

6-

ν_{H B O}

7-

ν_{H B O}

8-

k T_{i n}

9-

N_{d i s k}

10-

k T_{b b}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/cond-mat/0407367

Formulas:

1-

B = [4 / (4 j + 1)] B_{f}

2-

B_{f} = 2 π 𝑓 m^{*} / e

3-

(4 / 5) B_{f}

4-

(4 / 9) B_{f}

5-

2 π f m^{*} / e

6-

[4 / (4 j + 1)] B_{f}

7-

(4 / 5) B_{f}

8-

(R_{x y})

9-

(4 / 5) B_{f}

10-

B_{m i n}^{- 1} / δ

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1811.10696

Formulas:

1-

B = {b_{1}, \dots, b_{n}}, b_{i} \in ℝ^{4}

2-

O = {o_{1}, \dots, o_{n}}, o_{i} \in C

3-

R = {r_{1}, \dots, r_{m}}

4-

(b_{i}, o_{i}) \in B \times O

5-

l_{i j} \in ℝ

6-

(b_{j}, o_{j}) \in B \times O

7-

P r (G | I) = P r (B | I) P r (O | B, I) P r (R | B, O, I) .

8-

P r (B | I)

9-

P r (O | B, I)

10-

P r (R | B, O, I)

Formulas (html):

Correct Categorie: cs

Guessed Categorie: cs

Result: correct

Paper: https://arxiv.org/abs/1707.00055

Formulas:

1-

(P, Q, R, S)

2-

[\begin{matrix} P & R \\ S & Q \end{matrix}]

3-

R^{2} = S^{2} = 0

4-

P + Q + R + S

5-

A A^{d} = A^{d} A, A^{d} A A^{d} = A^{d}, A^{k} = A^{k + 1} A^{d},

6-

rank (A^{k}) = rank (A^{k + 1})

7-

ind (A) = 1

8-

N \in ℂ^{n \times n}

9-

P, Q, R, S \in ℂ^{n \times n}

10-

N = P + Q + R + S

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/hep-ph/0210030

Formulas:

1-

q (\bar{q}) g

2-

p + p \to l^{+} + l^{-} +^{'} X^{'},

3-

\frac{d^{3} Δ σ^{p p}}{d Q d p_{T} d y} =

4-

\sum_{a, b = q, g} Δ f_{a}^{p} (μ^{2}) \otimes Δ f_{b}^{p} (μ^{2}) \otimes \frac{d^{3} Δ σ_{a b} (μ^{2})}{d Q d p_{T} d y} .

5-

Δ σ_{a b}

6-

Δ f_{a} (μ^{2})

7-

q + \bar{q} \to g + γ^{*},

8-

g + q (\bar{q}) \to q (\bar{q}) + γ^{*} .

9-

q + \bar{q} \to g + g + γ^{*},

10-

g + q (\bar{q}) \to g + q (\bar{q}) + γ^{*},

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: hep-ph

Result: correct

Paper: https://arxiv.org/abs/cond-mat/9705135

Formulas:

1-

R (t) \sim t^{β}

2-

φ (\vec{x}, t)

3-

C (\vec{r}, t) \equiv < φ (\vec{x}, t) φ (\vec{x} + \vec{r}, t) >

4-

C (\vec{r}, t) = f (r / R (t))

5-

- β H = J_{1} \sum_{< i j >} s_{i} s_{j} + J_{2} \sum_{<< i j, >>} s_{i} s_{j} + J_{3} \sum_{[i, j, k, l]} s_{i} s_{j} s_{k} s_{l},

6-

J_{2} < 0, | J_{1} | < 2 | J_{2} |

7-

R (t) \sim t^{β}

8-

L \sim t^{- 1 / 3}

9-

\begin{matrix} C_{ℓ} (r, t) & = & < s (i, j) s (i + ϵ (i, j) r, j + (1 - ϵ (i, j)) r) > \\ C_{t} (r, t) & = & < {(- 1)}^{r} s (i, j) s (i + (1 - ϵ (i, j)) r, j + ϵ (i, j) r) > \end{matrix}

10-

ϵ (i, j)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/hep-ph/0011156

Formulas:

1-

S \approx M_{s}^{2} \approx 1 / α^{^{'}}

2-

\sqrt{s} \geq \sqrt{S} \approx M_{s}

3-

π^{0} \to γ γ

4-

b = R_{\oplus} + h

5-

σ_{ν} = σ_{p} / 2

6-

N_{m a x} \approx 3 \times 10^{10}

7-

X_{m a x}

8-

X_{m a x}

9-

X_{m a x}

10-

X_{m a x}

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: hep-ph

Result: correct

Paper: https://arxiv.org/abs/nucl-th/0403053

Formulas:

1-

η \propto T / σ_{0}

2-

σ_{0} \sim Λ_{Q C D}^{- 2}

3-

v_{2} (p_{T}) \equiv {⟨ \cos (2 ϕ) ⟩}_{p_{T}}

4-

p_{T} \sim 1.5 GeV

5-

ℓ_{m f p}

6-

ℓ_{m f p} / L

7-

ℓ_{m f p} / L \sim 1 / 5

8-

v_{2} (p_{T})

9-

v_{2} (p_{T})

10-

Λ_{Q C D}^{2}

Formulas (html):

Correct Categorie: nucl-th

Guessed Categorie: hep-ph

Result: incorrect

Paper: https://arxiv.org/abs/0708.2637

Formulas:

1-

\sim 60 ° \pm 20 °

2-

\sim 60 ° - 108 °

3-

λ = 2.2 μ m

4-

f (x) = \frac{s}{s^{2} + {(x - t)}^{2}}, s > 0, - \infty < t < \infty .

5-

60 ° \pm 20 °

6-

80 ° \pm 10 °

7-

80 ° \pm 25 °

8-

\sim 60 ° - 108 °

9-

Δ χ^{2} \approx 5

10-

\sim 60 ° - 108 °

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/cond-mat/0307582

Formulas:

1-

(1 \bar{1} 0)

2-

(1 \bar{1} 0)

3-

(1 \bar{1} 0)

4-

(1 \bar{1} 0)

5-

[1 \bar{1} 0]

6-

(1 \bar{1} 0)

7-

(1 \bar{1} 0)

8-

(1 \bar{1} 0)

9-

(1 \bar{1} 0)

10-

(1 \bar{1} 0)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1908.10093

Formulas:

1-

P m \bar{3} m

2-

P m \bar{3} m

3-

P 4 / m b m

4-

P m b n

5-

P m \bar{3} m

6-

𝐐_{X} = (2, \frac{1}{2}, 0)

7-

𝐐_{M} = (\frac{3}{2}, \frac{1}{2}, 0)

8-

𝐐_{R} = (\frac{1}{2}, \frac{1}{2}, \frac{3}{2})

9-

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

10-

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

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1005.0122

Formulas:

1-

(a, b, σ_{i n t})

2-

w_{a} = - w_{0}

3-

u = \sqrt{σ_{L_{X}}^{2} + σ_{T_{a}}^{2}}

4-

(L_{X}, T_{a})

5-

(Ω_{M}, h) = (0.278, 0.699)

6-

\log L_{X} = a \log [T_{a} / (1 + z)] + b

7-

\log L_{X} = - 1.00 \log (\frac{T_{a}}{1 + z}) + 49.26

8-

σ_{i n t} = 0.66

9-

\log L_{X} = - 1.04 \log (\frac{T_{a}}{1 + z}) + 50.22

10-

σ_{i n t} = 0.23

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/cond-mat/0411487

Formulas:

1-

n = 1.5 \times 10^{11}

2-

N_{m o l} = N_{m a x} (1 - e^{- β / \dot{B}}),

3-

N_{m a x}

4-

δ_{l z} = α n Δ a_{b g} / \dot{B} .

5-

n / {\dot{B}}_{1 / e}

6-

δ_{l z} = 1

7-

N_{m o l} / N_{m a x} = 63 %

8-

n / {\dot{B}}_{1 / e}

9-

n / {\dot{B}}_{1 / e}

10-

4.5 (4) \times 10^{- 7}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1110.6341

Formulas:

1-

A G I L E

2-

F e r m i

3-

A G I L E

4-

S w i f t

5-

S w i f t

6-

S w i f t

7-

A G I L E

8-

A G I L E

9-

S w i f t

10-

F e r m i

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/hep-th/9910212

Formulas:

1-

Z = M \times ℙ^{1}

2-

ω = (ω_{2} + i ω_{3}) + 2 ζ ω_{1} - ζ^{2} (ω_{2} - i ω_{3})

3-

Z \to 𝒪 (2 n_{j}) \to ℙ^{1}

4-

j = 1 \dots k

5-

α^{j} (ζ)

6-

α^{j} (ζ)

7-

α^{j} = \sum_{a = 1}^{2 j} w_{a}^{j} ζ^{a},

8-

α^{j} (ζ) = {(- 1)}^{j} ζ^{2 j} \bar{α^{j} (- 1 / \bar{ζ})} .

9-

\tilde{ζ} = 1 / ζ

10-

\tilde{ω} = \frac{1}{ζ^{2}} ω

Formulas (html):

Correct Categorie: hep-th

Guessed Categorie: hep-th

Result: correct

Paper: https://arxiv.org/abs/cond-mat/0409609

Formulas:

1-

P (N) \sim 10^{- 0.38 N}

2-

P_{c} (M)

3-

P_{c} (M)

4-

P_{c} (M) = 0.150 + {0.857 10}^{- 0.042 M}

5-

P_{c} (M) = {0.410 10}^{- 0.010 M}

6-

P_{c} (G)

7-

P_{c} (G)

8-

P_{c} (G)

9-

P_{c} (G) = - 0.259 + 1.256 G^{- 0.500}

10-

P_{c} (G) = - 0.004 + 4.454 G^{- 1.440}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/9702053

Formulas:

1-

\sim (4 \pm 1) \times 10^{- 6} ph {cm}^{- 2} s^{- 1}

2-

Φ = (3.3 \pm 0.7) \cdot 10^{- 6} ph {cm}^{- 2} s^{- 1}

3-

(4.0 \pm 1.1) \cdot 10^{- 6} ph {cm}^{- 2} s^{- 1}

4-

L_{γ} ≃ 7.2 \times 10^{34} d_{k p c}^{2} erg s^{- 1}

5-

d_{k p c}

6-

\sim 4 \cdot 10^{- 6} ph {cm}^{- 2} s^{- 1}

7-

F (E) = k {(E / E_{o})}^{- α}

8-

k = (3.2 \pm 0.6) \times 10^{- 9} ph {cm}^{- 2} s^{- 1} {MeV}^{- 1}

9-

3.5 \times 10^{- 5} ph {cm}^{- 2} s^{- 1}

10-

3.2 \times 10^{- 4} ph {cm}^{- 2} s^{- 1}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/cond-mat/0512561

Formulas:

1-

χ^{o r b}

2-

χ^{o r b}

3-

T_{1}^{- 1} (T)

4-

T_{1}^{- 1} (T)

5-

π / 2 - τ - π

6-

μ_{0} H = 4.001

7-

- 1 / 2 \leftrightarrow + 1 / 2

8-

\pm 1 / 2 \leftrightarrow \pm 3 / 2

9-

\pm 3 / 2 \leftrightarrow \pm 5 / 2

10-

\pm 5 / 2 \leftrightarrow \pm 7 / 2

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1001.2627

Formulas:

1-

S p i t z e r

2-

S p i t z e r

3-

S p i t z e r S p a c e T e l e s c o p e

4-

S p i t z e r

5-

S p i t z e r

6-

S p i t z e r

7-

S p i t z e r

8-

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

9-

S p i t z e r

10-

S p i t z e r

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1809.04392

Formulas:

1-

{ω_{i j}^{(l)}}

2-

{θ_{i}^{(l)}}

3-

g (x, Q_{0}) = A_{g} x^{- α_{g}} {(1 - x)}^{β_{g}} ξ_{1}^{(L)} (x),

4-

x^{- α_{g}} {(1 - x)}^{β_{g}}

5-

\frac{\partial χ^{2}}{\partial w_{i j}^{(l)}}, \frac{\partial χ^{2}}{\partial θ_{i}^{(l)}} .

6-

σ^{(th)} ({ω, θ}) = {\hat{σ}}_{i j} (Q^{2}) \otimes Γ_{i j, k l} (Q^{2}, Q_{0}^{2}) \otimes q_{k} (Q_{0}, {ω, θ}) \otimes q_{l} (Q_{0}, {ω, θ})

7-

Γ_{i j, k l}

8-

σ^{(th)} ({ω, θ}) = \sum_{i, j = 1}^{n_{f}} \sum_{a, b = 1}^{n_{x}} {𝙵𝙺}_{k, i j, a b} \cdot q_{i} (x_{a}, Q_{0}, {ω, θ}) \cdot q_{j} (x_{b}, Q_{0}, {ω, θ}),

9-

{𝙵𝙺}_{k, i j, a b}

10-

{ω_{i j}^{(l)}, θ_{i}^{(l)}}

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: cs

Result: incorrect

Paper: https://arxiv.org/abs/quant-ph/0507274

Formulas:

1-

| ψ_{A B}^{+} ⟩ = \frac{1}{\sqrt{2}} [{| + 1 ⟩}_{A} {| - 1 ⟩}_{B} + {| - 1 ⟩}_{A} {| + 1 ⟩}_{B}],

2-

{- 1, 0, + 1}

3-

{- 1, 0, + 1}

4-

n \in [1, N]

5-

n \in [1, N]

6-

{S_{β}^{α} (n)}

7-

[S_{α}^{β} (m), S_{σ}^{ρ} (n)] = δ_{n}^{m} {δ_{α}^{ρ} S_{σ}^{β} (n) - δ_{σ}^{β} S_{α}^{ρ} (n)} .

8-

S_{β}^{α} (n)

9-

H = J \sum_{⟨ m, n ⟩} Π_{m, n},

10-

Π_{m, n} = \sum_{α, β} S_{α}^{β} (m) S_{β}^{α} (n)

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/0011235

Formulas:

1-

0 \leq T \leq 0.3 J

2-

T_{c} \sim 0.23 J

3-

P_{L} (q)

4-

P_{L} (q) = \frac{L^{η / 2}}{{(1 + c / L^{ω})}^{2}} \bar{P} (\frac{q L^{η / 2}}{1 + c / L^{ω}}) a t T = T_{c}

5-

\bar{P} (x)

6-

P_{L} (q) = L^{η / 2} (1 + d / L^{ω}) \bar{P} (q L^{η / 2} {(1 + d / L^{ω})}^{1 / 2}) a t T = T_{c}

7-

P_{L} (q)

8-

T_{c} = 0.23 J

9-

T_{c} \sim 0.23 J

10-

P_{L} (q)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/0906.4435

Formulas:

1-

T_{c} \sim δ^{z / (d + z - 2)}

2-

H_{μ} = H - (μ - 4 t^{'}) N

3-

H = - \sum_{i j σ} t_{i j} c_{i σ}^{†} c_{j σ} + U \sum_{i} n_{i ↑} n_{i ↓},

4-

t_{i j} = t

5-

t_{i j} = - t^{'}

6-

t, t^{'} > 0

7-

V (𝐤_{1}, 𝐤_{2}, 𝐤_{3}, 𝐤_{4})

8-

\frac{d V_{T}}{d T} = - V_{T} \circ \frac{d L_{pp}}{d T} \circ V_{T} + V_{T} \circ \frac{d L_{ph}}{d T} \circ V_{T},

9-

𝐤_{1} + 𝐤_{2} = 𝐤_{3} + 𝐤_{4},

10-

L_{ph,pp} (𝐤, 𝐤^{'}) = \frac{f_{T} (ε_{𝐤}) - f_{T} (\pm ε_{𝐤^{'}})}{ε_{𝐤} \mp ε_{𝐤^{'}}},

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/0801.0299

Formulas:

1-

e^{- x / L_{0}}

2-

U = \sum_{n} \sum_{m} \frac{K_{m}}{2} {[q (n a) - q ([n + m] a)]}^{2}

3-

` n a^{'}

4-

M \ddot{q} (n a) = \sum_{m > 0} K_{m} [q ([n + m] a) + q ([n - m] a) - 2 q (n a)],

5-

q (n a) \propto e^{i (k n a - w t)}

6-

ω = 2 \sqrt{\frac{\sum_{m > 0} K_{m} s i n^{2} (m k a / 2)}{M}}

7-

ω = a \sqrt{\frac{\sum_{m > 0} K_{m} m^{2}}{M}} | k |,

8-

\sum_{m > 0} m^{2} K_{m}

9-

K_{m} = \frac{1}{m^{α}}

10-

ω \sim k^{(α - 1) / 2} .

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1406.5626

Formulas:

1-

ℋ = - J \sum_{⟨ i, j ⟩} s_{i} s_{j} - h \sum_{i} s_{i},

2-

s_{i} = \pm 1 / 2

3-

g (M, E)

4-

𝐬_{GS} = {s_{1}, \dots, s_{N}}

5-

𝐬_{GS} = \underset{𝐬}{\arg \min} ℋ (𝐬) .

6-

M_{j} = \sum_{i = 1}^{N} 𝐬_{GS}

7-

j = 1, \dots, W

8-

m = \sum_{j = 1}^{W} M_{j} / (W N)

9-

S / N = \ln W / N

10-

g (M, E)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/2007.03471

Formulas:

1-

ℋ = - J_{1} \sum_{⟨ i, j ⟩} \cos (ϕ_{i} - ϕ_{j}) - J_{q} \sum_{⟨ i, j ⟩} \cos [q (ϕ_{i} - ϕ_{j})],

2-

ϕ_{i} \in [0, 2 π]

3-

ϕ \to ϕ + 2 π

4-

J_{3} = Δ - 1

5-

Δ \in [0, 1]

6-

6 \times 10^{5} - 2.5 \times 10^{6}

7-

e = \frac{⟨ ℋ ⟩}{L^{2}},

8-

c = \frac{⟨ ℋ^{2} ⟩ - {⟨ ℋ ⟩}^{2}}{T^{2} L^{2}},

9-

m_{k} = \frac{⟨ M_{k} ⟩}{L^{2}} = \frac{1}{L^{2}} ⟨ \sqrt{3 \sum_{α = 1}^{3} 𝐌_{k α}^{2}} ⟩, k = 1, 3; α = 1, 2, 3;

10-

𝐌_{k α} = (\sum_{i \in α} \cos (k ϕ_{α i}), \sum_{i \in α} \sin (k ϕ_{α i})),

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Run 11274850 (Agent925)