Run 11369302

Paper: https://arxiv.org/abs/2010.14372

Formulas:

1-

M_{⋆} > 10^{10} M_{⊙}

2-

r = 5 r_{e}

3-

f_{5} = f_{D M} (5 r_{e})

4-

\bar{f_{5}} ≃ 0.8 - 0.9

5-

Δ f_{5} ≃ 0.1

6-

M_{⋆} \sim 10^{11} M_{⊙}

7-

f_{D M} (r) = 1 - \frac{M_{b a r y} (r)}{M_{t o t} (r)}

8-

M_{b a r y}

9-

M_{t o t}

10-

r ≲ 2 r_{e}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/hep-ph/0112330

Formulas:

1-

1^{2 S + 1} P_{J}

2-

G e V^{2}

3-

Ψ_{q \bar{q}} (x, y | A) = {\bar{Ψ}}_{\bar{q}} (x) Φ (x, y) Ψ_{q} (y),

4-

G_{q \bar{q}} = {⟨ Ψ_{q \bar{q}}^{+} (\bar{x}, \bar{y} | A) Ψ_{q \bar{q}} (x, y | A) ⟩}_{q \bar{q} A},

5-

{⟨ T r P \exp (i g \oint_{C} 𝑑 z_{μ} A_{μ}) ⟩}_{A} \sim \exp (- σ S_{\min}),

6-

S_{\min} = \int_{0}^{T} 𝑑 t \int_{0}^{1} 𝑑 β \sqrt{{(\dot{w} w^{'})}^{2} - {\dot{w}}^{2} w^{', 2}},

7-

w_{μ} (t, β) = β x_{1 μ} (t) + (1 - β) x_{2 μ} (t),

8-

H = H_{0} + V_{s t r} + V_{s d},

9-

H_{0} = \sum_{i = 1}^{2} (\frac{{\vec{p}}^{2} + m_{i}^{2}}{2 μ_{i}} + \frac{μ_{i}}{2}) + σ r - \frac{κ}{r} - C_{0},

10-

V_{s t r} \approx - \frac{σ (μ_{1}^{2} + μ_{2}^{2} - μ_{1} μ_{2})}{6 μ_{1}^{2} μ_{2}^{2}} \frac{{\vec{L}}^{2}}{r} + \frac{σ^{2} (μ_{1} + μ_{2}) (4 μ_{1}^{2} - 7 μ_{1} μ_{2} + 4 μ_{2}^{2})}{72 μ_{1}^{3} μ_{2}^{3}} {\vec{L}}^{2},

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: hep-ph

Result: correct

Paper: https://arxiv.org/abs/0910.5336

Formulas:

1-

E_{M} = \int (x B_{x} + y B_{y}) B_{z} 𝑑 x 𝑑 y

2-

B_{T} = \sqrt{B_{x}^{2} + B_{y}^{2}} \approx 0

3-

\approx 8 M m

4-

\approx 70 M m

5-

v_{x} = Δ x / Δ t

6-

v_{y} = Δ y / Δ t

7-

E = \dot{E} t

8-

\dot{E} = \int P 𝑑 x 𝑑 y

9-

P = - \frac{1}{4 π} (v_{h} \cdot B_{h}) B_{z}

10-

\sim 1.45 \times 10^{30} e r g s

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1603.05764

Formulas:

1-

Γ (0, 0)

2-

X (π, 0)

3-

M (π, π)

4-

Γ (0, 0)

5-

Γ (0, 0)

6-

X (π, 0)

7-

M (π, π)

8-

Γ (0, 0)

9-

χ_{0}^{p r; s t} (k, ω)

10-

- \frac{1}{N} \sum_{k, μ ν} \frac{a_{μ}^{s} (k) a_{μ}^{p, *} (k) a_{ν}^{r} (k + q) a_{ν}^{t, *} (k + q)}{ω + E_{ν} (k + q) - E_{μ} (k) + i 0^{+}}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1011.4024

Formulas:

1-

p (ξ) = A ξ^{3 μ / 2} Θ (ξ)

2-

ξ = r - r_{0}

3-

A = {[4 π r_{0}^{\frac{3 μ}{2} + 3}, B (3, \frac{3 μ}{2} + 1)]}^{- 1}

4-

p (ξ) \sim {(ξ / r_{0})}^{D - D_{T}} r_{0}^{- 3} = {(ξ / r_{0})}^{D_{A}} r_{0}^{- 3}

5-

p (λ ξ) \sim λ^{D_{A}} p (ξ)

6-

p (η) \sim λ^{D_{A}} p (η / λ)

7-

p (η) \sim η^{D_{A}}

8-

m_{t} > 1 G e v / c^{2}

9-

c {(m_{t} / Λ)}^{- a}

10-

\sqrt{m^{2} + p_{t}^{2}}

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: hep-ph

Result: correct

Paper: https://arxiv.org/abs/1407.3228

Formulas:

1-

P_{j} = \frac{λ^{j}}{j!} \frac{1}{ℰ_{k} (λ)} .

2-

(i, j) \to (i - 1, j + 1)

3-

i P_{i} P_{j}

4-

(i - 1, j + 1) \to (i, j)

5-

(j + 1) P_{i - 1} P_{j + 1}

6-

i P_{i} P_{j} = (j + 1) P_{i - 1} P_{j + 1}

7-

ℰ_{k} (λ)

8-

\sum_{0 \leq j \leq k} P_{j} = 1

9-

ℰ_{k} (λ) = \sum_{j = 0}^{k} \frac{λ^{j}}{j!} .

10-

ρ = \sum_{j = 0}^{k} j P_{j} = λ \frac{ℰ_{k - 1} (λ)}{ℰ_{k} (λ)} .

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: math

Result: incorrect

Paper: https://arxiv.org/abs/1501.03196

Formulas:

1-

Δ s = t_{2, 2}^{s} - t_{1, 1}^{s}, Δ s \in R,

2-

Δ r = t_{2, 2}^{r} - t_{1, 1}^{r}, Δ r \in R .

3-

Δ T = c l k_{S} - c l k_{T},

4-

Δ T \in R .

5-

T_{1, 1} = t_{1, 1}^{r} - t_{1, 1}^{s} + Δ T .

6-

T_{2, 2} = t_{2, 2}^{r} - t_{2, 2}^{s} + Δ T .

7-

Δ_{P_{1}, P_{2}}

8-

= T_{1, 1} - T_{2, 2}

9-

= t_{1, 1}^{r} - t_{1, 1}^{s} + Δ T - t_{2, 2}^{r} + t_{2, 2}^{s} - Δ T

10-

= t_{2, 2}^{s} - t_{1, 1}^{s} - t_{2, 2}^{r} + t_{1, 1}^{r}

Formulas (html):

Correct Categorie: cs

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/2002.07452

Formulas:

1-

f_{k} (𝐱_{k, u})

2-

f_{k} (𝐱_{k, u}) = {\begin{matrix} \frac{1}{π {(R_{k})}^{2}}, & if ∥ 𝐱_{k, u} ∥ \leq R_{k}, \\ 0, & otherwise, \end{matrix}

3-

𝐡_{u} = \sqrt{M} \frac{α_{u, 0} 𝐚 (θ_{u, 0})}{(1 + d_{u}^{η_{u, L O S}})} + \sum_{l = 1}^{L} \sqrt{M} \frac{α_{u, l} 𝐚 (θ_{u, l})}{(1 + d_{u}^{η_{u, N L O S}})},

4-

𝐚 (θ_{u, l})

5-

𝐚 (θ_{u, l}) = \frac{1}{\sqrt{M}} {[\begin{matrix} 1, e^{- j π θ_{u, l}}, \dots, e^{- j π (M - 1) θ_{u, l}} \end{matrix}]}^{T} .

6-

θ_{u, l} = 2 \frac{D}{λ} \sin (ϕ_{u, l})

7-

ϕ_{u, l} \in [0, 2 π]

8-

α_{u, l} \sim 𝒞 𝒩 (0, σ_{u, l}^{2})

9-

η_{u, L O S}

10-

η_{u, N L O S}

Formulas (html):

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xref="S2.Ex2.m1.5.5.5.8.cmml">𝐚</mi><mo id="S2.Ex2.m1.5.5.5.6a" xref="S2.Ex2.m1.5.5.5.6.cmml">⁢</mo><mrow id="S2.Ex2.m1.5.5.5.5.1" xref="S2.Ex2.m1.5.5.5.5.1.1.cmml"><mo stretchy="false" id="S2.Ex2.m1.5.5.5.5.1.2" xref="S2.Ex2.m1.5.5.5.5.1.1.cmml">(</mo><msub id="S2.Ex2.m1.5.5.5.5.1.1" xref="S2.Ex2.m1.5.5.5.5.1.1.cmml"><mi id="S2.Ex2.m1.5.5.5.5.1.1.2" xref="S2.Ex2.m1.5.5.5.5.1.1.2.cmml">θ</mi><mrow id="S2.Ex2.m1.4.4.4.4.2.4" xref="S2.Ex2.m1.4.4.4.4.2.3.cmml"><mi id="S2.Ex2.m1.3.3.3.3.1.1" xref="S2.Ex2.m1.3.3.3.3.1.1.cmml">u</mi><mo id="S2.Ex2.m1.4.4.4.4.2.4.1" xref="S2.Ex2.m1.4.4.4.4.2.3.cmml">,</mo><mn id="S2.Ex2.m1.4.4.4.4.2.2" xref="S2.Ex2.m1.4.4.4.4.2.2.cmml">0</mn></mrow></msub><mo stretchy="false" id="S2.Ex2.m1.5.5.5.5.1.3" xref="S2.Ex2.m1.5.5.5.5.1.1.cmml">)</mo></mrow></mrow><mrow id="S2.Ex2.m1.8.8.8.3" xref="S2.Ex2.m1.8.8.8.3.1.cmml"><mo stretchy="false" id="S2.Ex2.m1.8.8.8.3.2" xref="S2.Ex2.m1.8.8.8.3.1.cmml">(</mo><mrow id="S2.Ex2.m1.8.8.8.3.1" 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xref="S2.Ex2.m1.7.7.7.2.2.2.2.2.1.1.cmml">⁢</mo><mi id="S2.Ex2.m1.7.7.7.2.2.2.2.2.1.3" xref="S2.Ex2.m1.7.7.7.2.2.2.2.2.1.3.cmml">O</mi><mo id="S2.Ex2.m1.7.7.7.2.2.2.2.2.1.1a" xref="S2.Ex2.m1.7.7.7.2.2.2.2.2.1.1.cmml">⁢</mo><mi id="S2.Ex2.m1.7.7.7.2.2.2.2.2.1.4" xref="S2.Ex2.m1.7.7.7.2.2.2.2.2.1.4.cmml">S</mi></mrow></mrow></msub></msubsup></mrow><mo stretchy="false" id="S2.Ex2.m1.8.8.8.3.3" xref="S2.Ex2.m1.8.8.8.3.1.cmml">)</mo></mrow></mfrac></mrow><mo id="S2.Ex2.m1.17.17.1.1.3.1" xref="S2.Ex2.m1.17.17.1.1.3.1.cmml">+</mo><mrow id="S2.Ex2.m1.17.17.1.1.3.3" xref="S2.Ex2.m1.17.17.1.1.3.3.cmml"><munderover id="S2.Ex2.m1.17.17.1.1.3.3.1" xref="S2.Ex2.m1.17.17.1.1.3.3.1.cmml"><mo largeop="true" movablelimits="false" symmetric="true" id="S2.Ex2.m1.17.17.1.1.3.3.1.2.2" xref="S2.Ex2.m1.17.17.1.1.3.3.1.2.2.cmml">∑</mo><mrow id="S2.Ex2.m1.17.17.1.1.3.3.1.2.3" xref="S2.Ex2.m1.17.17.1.1.3.3.1.2.3.cmml"><mi id="S2.Ex2.m1.17.17.1.1.3.3.1.2.3.2" xref="S2.Ex2.m1.17.17.1.1.3.3.1.2.3.2.cmml">l</mi><mo id="S2.Ex2.m1.17.17.1.1.3.3.1.2.3.1" xref="S2.Ex2.m1.17.17.1.1.3.3.1.2.3.1.cmml">=</mo><mn id="S2.Ex2.m1.17.17.1.1.3.3.1.2.3.3" xref="S2.Ex2.m1.17.17.1.1.3.3.1.2.3.3.cmml">1</mn></mrow><mi id="S2.Ex2.m1.17.17.1.1.3.3.1.3" xref="S2.Ex2.m1.17.17.1.1.3.3.1.3.cmml">L</mi></munderover><mrow id="S2.Ex2.m1.17.17.1.1.3.3.2" xref="S2.Ex2.m1.17.17.1.1.3.3.2.cmml"><msqrt id="S2.Ex2.m1.17.17.1.1.3.3.2.2" xref="S2.Ex2.m1.17.17.1.1.3.3.2.2.cmml"><mi id="S2.Ex2.m1.17.17.1.1.3.3.2.2.2" xref="S2.Ex2.m1.17.17.1.1.3.3.2.2.2.cmml">M</mi></msqrt><mo id="S2.Ex2.m1.17.17.1.1.3.3.2.1" xref="S2.Ex2.m1.17.17.1.1.3.3.2.1.cmml">⁢</mo><mfrac id="S2.Ex2.m1.16.16" xref="S2.Ex2.m1.16.16.cmml"><mrow id="S2.Ex2.m1.13.13.5" xref="S2.Ex2.m1.13.13.5.cmml"><msub id="S2.Ex2.m1.13.13.5.7" xref="S2.Ex2.m1.13.13.5.7.cmml"><mi id="S2.Ex2.m1.13.13.5.7.2" xref="S2.Ex2.m1.13.13.5.7.2.cmml">α</mi><mrow id="S2.Ex2.m1.10.10.2.2.2.4" xref="S2.Ex2.m1.10.10.2.2.2.3.cmml"><mi id="S2.Ex2.m1.9.9.1.1.1.1" 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stretchy="false" id="S2.SS2.p3.2.m2.3.3.1.1.3" xref="S2.SS2.p3.2.m2.3.3.1.1.1.cmml">)</mo></mrow></mrow></math>, <math><mrow id="S2.Ex3.m1.4.4.1" xref="S2.Ex3.m1.4.4.1.1.cmml"><mrow id="S2.Ex3.m1.4.4.1.1" xref="S2.Ex3.m1.4.4.1.1.cmml"><mrow id="S2.Ex3.m1.4.4.1.1.1" xref="S2.Ex3.m1.4.4.1.1.1.cmml"><mi id="S2.Ex3.m1.4.4.1.1.1.3" xref="S2.Ex3.m1.4.4.1.1.1.3.cmml">𝐚</mi><mo id="S2.Ex3.m1.4.4.1.1.1.2" xref="S2.Ex3.m1.4.4.1.1.1.2.cmml">⁢</mo><mrow id="S2.Ex3.m1.4.4.1.1.1.1.1" xref="S2.Ex3.m1.4.4.1.1.1.1.1.1.cmml"><mo stretchy="false" id="S2.Ex3.m1.4.4.1.1.1.1.1.2" xref="S2.Ex3.m1.4.4.1.1.1.1.1.1.cmml">(</mo><msub id="S2.Ex3.m1.4.4.1.1.1.1.1.1" xref="S2.Ex3.m1.4.4.1.1.1.1.1.1.cmml"><mi id="S2.Ex3.m1.4.4.1.1.1.1.1.1.2" xref="S2.Ex3.m1.4.4.1.1.1.1.1.1.2.cmml">θ</mi><mrow id="S2.Ex3.m1.3.3.2.4" xref="S2.Ex3.m1.3.3.2.3.cmml"><mi id="S2.Ex3.m1.2.2.1.1" xref="S2.Ex3.m1.2.2.1.1.cmml">u</mi><mo id="S2.Ex3.m1.3.3.2.4.1" xref="S2.Ex3.m1.3.3.2.3.cmml">,</mo><mi id="S2.Ex3.m1.3.3.2.2" xref="S2.Ex3.m1.3.3.2.2.cmml">l</mi></mrow></msub><mo stretchy="false" id="S2.Ex3.m1.4.4.1.1.1.1.1.3" xref="S2.Ex3.m1.4.4.1.1.1.1.1.1.cmml">)</mo></mrow></mrow><mo id="S2.Ex3.m1.4.4.1.1.2" xref="S2.Ex3.m1.4.4.1.1.2.cmml">=</mo><mrow id="S2.Ex3.m1.4.4.1.1.3" xref="S2.Ex3.m1.4.4.1.1.3.cmml"><mstyle displaystyle="true" id="S2.Ex3.m1.4.4.1.1.3.2" xref="S2.Ex3.m1.4.4.1.1.3.2.cmml"><mfrac id="S2.Ex3.m1.4.4.1.1.3.2a" xref="S2.Ex3.m1.4.4.1.1.3.2.cmml"><mn id="S2.Ex3.m1.4.4.1.1.3.2.2" xref="S2.Ex3.m1.4.4.1.1.3.2.2.cmml">1</mn><msqrt id="S2.Ex3.m1.4.4.1.1.3.2.3" xref="S2.Ex3.m1.4.4.1.1.3.2.3.cmml"><mi id="S2.Ex3.m1.4.4.1.1.3.2.3.2" xref="S2.Ex3.m1.4.4.1.1.3.2.3.2.cmml">M</mi></msqrt></mfrac></mstyle><mo id="S2.Ex3.m1.4.4.1.1.3.1" xref="S2.Ex3.m1.4.4.1.1.3.1.cmml">⁢</mo><msup id="S2.Ex3.m1.4.4.1.1.3.3" xref="S2.Ex3.m1.4.4.1.1.3.3.cmml"><mrow id="S2.Ex3.m1.1.1a.3" xref="S2.Ex3.m1.1.1a.2.cmml"><mo id="S2.Ex3.m1.1.1a.3.1" xref="S2.Ex3.m1.1.1a.2.1.cmml">[</mo><mtable id="S2.Ex3.m1.1.1.1.1" xref="S2.Ex3.m1.1.1.1.1.cmml"><mtr id="S2.Ex3.m1.1.1.1.1a" xref="S2.Ex3.m1.1.1.1.1.cmml"><mtd columnalign="center" id="S2.Ex3.m1.1.1.1.1b" xref="S2.Ex3.m1.1.1.1.1.cmml"><mrow id="S2.Ex3.m1.1.1.1.1.9.9.9.9.9" xref="S2.Ex3.m1.1.1.1.1.9.9.9.9.10.cmml"><mn id="S2.Ex3.m1.1.1.1.1.6.6.6.6.6" xref="S2.Ex3.m1.1.1.1.1.6.6.6.6.6.cmml">1</mn><mo id="S2.Ex3.m1.1.1.1.1.9.9.9.9.9.3" xref="S2.Ex3.m1.1.1.1.1.9.9.9.9.10.cmml">,</mo><msup id="S2.Ex3.m1.1.1.1.1.8.8.8.8.8.1" xref="S2.Ex3.m1.1.1.1.1.8.8.8.8.8.1.cmml"><mi id="S2.Ex3.m1.1.1.1.1.8.8.8.8.8.1.2" xref="S2.Ex3.m1.1.1.1.1.8.8.8.8.8.1.2.cmml">e</mi><mrow id="S2.Ex3.m1.1.1.1.1.2.2.2.2.2.2" xref="S2.Ex3.m1.1.1.1.1.2.2.2.2.2.2.cmml"><mo id="S2.Ex3.m1.1.1.1.1.2.2.2.2.2.2.3" xref="S2.Ex3.m1.1.1.1.1.2.2.2.2.2.2.3.cmml">-</mo><mrow id="S2.Ex3.m1.1.1.1.1.2.2.2.2.2.2.4" xref="S2.Ex3.m1.1.1.1.1.2.2.2.2.2.2.4.cmml"><mi id="S2.Ex3.m1.1.1.1.1.2.2.2.2.2.2.4.2" xref="S2.Ex3.m1.1.1.1.1.2.2.2.2.2.2.4.2.cmml">j</mi><mo id="S2.Ex3.m1.1.1.1.1.2.2.2.2.2.2.4.1" xref="S2.Ex3.m1.1.1.1.1.2.2.2.2.2.2.4.1.cmml">⁢</mo><mi id="S2.Ex3.m1.1.1.1.1.2.2.2.2.2.2.4.3" xref="S2.Ex3.m1.1.1.1.1.2.2.2.2.2.2.4.3.cmml">π</mi><mo id="S2.Ex3.m1.1.1.1.1.2.2.2.2.2.2.4.1a" xref="S2.Ex3.m1.1.1.1.1.2.2.2.2.2.2.4.1.cmml">⁢</mo><msub id="S2.Ex3.m1.1.1.1.1.2.2.2.2.2.2.4.4" xref="S2.Ex3.m1.1.1.1.1.2.2.2.2.2.2.4.4.cmml"><mi id="S2.Ex3.m1.1.1.1.1.2.2.2.2.2.2.4.4.2" xref="S2.Ex3.m1.1.1.1.1.2.2.2.2.2.2.4.4.2.cmml">θ</mi><mrow id="S2.Ex3.m1.1.1.1.1.2.2.2.2.2.2.2.2.4" xref="S2.Ex3.m1.1.1.1.1.2.2.2.2.2.2.2.2.3.cmml"><mi id="S2.Ex3.m1.1.1.1.1.1.1.1.1.1.1.1.1.1" xref="S2.Ex3.m1.1.1.1.1.1.1.1.1.1.1.1.1.1.cmml">u</mi><mo id="S2.Ex3.m1.1.1.1.1.2.2.2.2.2.2.2.2.4.1" xref="S2.Ex3.m1.1.1.1.1.2.2.2.2.2.2.2.2.3.cmml">,</mo><mi id="S2.Ex3.m1.1.1.1.1.2.2.2.2.2.2.2.2.2" xref="S2.Ex3.m1.1.1.1.1.2.2.2.2.2.2.2.2.2.cmml">l</mi></mrow></msub></mrow></mrow></msup><mo id="S2.Ex3.m1.1.1.1.1.9.9.9.9.9.4" xref="S2.Ex3.m1.1.1.1.1.9.9.9.9.10.cmml">,</mo><mi mathvariant="normal" id="S2.Ex3.m1.1.1.1.1.7.7.7.7.7" xref="S2.Ex3.m1.1.1.1.1.7.7.7.7.7.cmml">⋯</mi><mo id="S2.Ex3.m1.1.1.1.1.9.9.9.9.9.5" xref="S2.Ex3.m1.1.1.1.1.9.9.9.9.10.cmml">,</mo><msup id="S2.Ex3.m1.1.1.1.1.9.9.9.9.9.2" xref="S2.Ex3.m1.1.1.1.1.9.9.9.9.9.2.cmml"><mi id="S2.Ex3.m1.1.1.1.1.9.9.9.9.9.2.2" xref="S2.Ex3.m1.1.1.1.1.9.9.9.9.9.2.2.cmml">e</mi><mrow id="S2.Ex3.m1.1.1.1.1.5.5.5.5.5.3" xref="S2.Ex3.m1.1.1.1.1.5.5.5.5.5.3.cmml"><mo id="S2.Ex3.m1.1.1.1.1.5.5.5.5.5.3.4" xref="S2.Ex3.m1.1.1.1.1.5.5.5.5.5.3.4.cmml">-</mo><mrow id="S2.Ex3.m1.1.1.1.1.5.5.5.5.5.3.3" xref="S2.Ex3.m1.1.1.1.1.5.5.5.5.5.3.3.cmml"><mi id="S2.Ex3.m1.1.1.1.1.5.5.5.5.5.3.3.3" xref="S2.Ex3.m1.1.1.1.1.5.5.5.5.5.3.3.3.cmml">j</mi><mo id="S2.Ex3.m1.1.1.1.1.5.5.5.5.5.3.3.2" xref="S2.Ex3.m1.1.1.1.1.5.5.5.5.5.3.3.2.cmml">⁢</mo><mi id="S2.Ex3.m1.1.1.1.1.5.5.5.5.5.3.3.4" xref="S2.Ex3.m1.1.1.1.1.5.5.5.5.5.3.3.4.cmml">π</mi><mo id="S2.Ex3.m1.1.1.1.1.5.5.5.5.5.3.3.2a" xref="S2.Ex3.m1.1.1.1.1.5.5.5.5.5.3.3.2.cmml">⁢</mo><mrow id="S2.Ex3.m1.1.1.1.1.5.5.5.5.5.3.3.1.1" xref="S2.Ex3.m1.1.1.1.1.5.5.5.5.5.3.3.1.1.1.cmml"><mo stretchy="false" id="S2.Ex3.m1.1.1.1.1.5.5.5.5.5.3.3.1.1.2" xref="S2.Ex3.m1.1.1.1.1.5.5.5.5.5.3.3.1.1.1.cmml">(</mo><mrow id="S2.Ex3.m1.1.1.1.1.5.5.5.5.5.3.3.1.1.1" xref="S2.Ex3.m1.1.1.1.1.5.5.5.5.5.3.3.1.1.1.cmml"><mi id="S2.Ex3.m1.1.1.1.1.5.5.5.5.5.3.3.1.1.1.2" xref="S2.Ex3.m1.1.1.1.1.5.5.5.5.5.3.3.1.1.1.2.cmml">M</mi><mo id="S2.Ex3.m1.1.1.1.1.5.5.5.5.5.3.3.1.1.1.1" xref="S2.Ex3.m1.1.1.1.1.5.5.5.5.5.3.3.1.1.1.1.cmml">-</mo><mn id="S2.Ex3.m1.1.1.1.1.5.5.5.5.5.3.3.1.1.1.3" xref="S2.Ex3.m1.1.1.1.1.5.5.5.5.5.3.3.1.1.1.3.cmml">1</mn></mrow><mo stretchy="false" id="S2.Ex3.m1.1.1.1.1.5.5.5.5.5.3.3.1.1.3" xref="S2.Ex3.m1.1.1.1.1.5.5.5.5.5.3.3.1.1.1.cmml">)</mo></mrow><mo id="S2.Ex3.m1.1.1.1.1.5.5.5.5.5.3.3.2b" xref="S2.Ex3.m1.1.1.1.1.5.5.5.5.5.3.3.2.cmml">⁢</mo><msub id="S2.Ex3.m1.1.1.1.1.5.5.5.5.5.3.3.5" xref="S2.Ex3.m1.1.1.1.1.5.5.5.5.5.3.3.5.cmml"><mi id="S2.Ex3.m1.1.1.1.1.5.5.5.5.5.3.3.5.2" xref="S2.Ex3.m1.1.1.1.1.5.5.5.5.5.3.3.5.2.cmml">θ</mi><mrow id="S2.Ex3.m1.1.1.1.1.4.4.4.4.4.2.2.2.4" xref="S2.Ex3.m1.1.1.1.1.4.4.4.4.4.2.2.2.3.cmml"><mi id="S2.Ex3.m1.1.1.1.1.3.3.3.3.3.1.1.1.1" xref="S2.Ex3.m1.1.1.1.1.3.3.3.3.3.1.1.1.1.cmml">u</mi><mo id="S2.Ex3.m1.1.1.1.1.4.4.4.4.4.2.2.2.4.1" xref="S2.Ex3.m1.1.1.1.1.4.4.4.4.4.2.2.2.3.cmml">,</mo><mi id="S2.Ex3.m1.1.1.1.1.4.4.4.4.4.2.2.2.2" xref="S2.Ex3.m1.1.1.1.1.4.4.4.4.4.2.2.2.2.cmml">l</mi></mrow></msub></mrow></mrow></msup></mrow></mtd></mtr></mtable><mo id="S2.Ex3.m1.1.1a.3.2" xref="S2.Ex3.m1.1.1a.2.1.cmml">]</mo></mrow><mi id="S2.Ex3.m1.4.4.1.1.3.3.2" xref="S2.Ex3.m1.4.4.1.1.3.3.2.cmml">T</mi></msup></mrow></mrow><mo id="S2.Ex3.m1.4.4.1.2" xref="S2.Ex3.m1.4.4.1.1.cmml">.</mo></mrow></math>, <math><mrow id="S2.SS2.p4.1.m1.6.6" xref="S2.SS2.p4.1.m1.6.6.cmml"><msub id="S2.SS2.p4.1.m1.6.6.3" xref="S2.SS2.p4.1.m1.6.6.3.cmml"><mi id="S2.SS2.p4.1.m1.6.6.3.2" xref="S2.SS2.p4.1.m1.6.6.3.2.cmml">θ</mi><mrow id="S2.SS2.p4.1.m1.2.2.2.4" xref="S2.SS2.p4.1.m1.2.2.2.3.cmml"><mi id="S2.SS2.p4.1.m1.1.1.1.1" xref="S2.SS2.p4.1.m1.1.1.1.1.cmml">u</mi><mo id="S2.SS2.p4.1.m1.2.2.2.4.1" xref="S2.SS2.p4.1.m1.2.2.2.3.cmml">,</mo><mi id="S2.SS2.p4.1.m1.2.2.2.2" xref="S2.SS2.p4.1.m1.2.2.2.2.cmml">l</mi></mrow></msub><mo id="S2.SS2.p4.1.m1.6.6.2" xref="S2.SS2.p4.1.m1.6.6.2.cmml">=</mo><mrow id="S2.SS2.p4.1.m1.6.6.1" xref="S2.SS2.p4.1.m1.6.6.1.cmml"><mn id="S2.SS2.p4.1.m1.6.6.1.3" xref="S2.SS2.p4.1.m1.6.6.1.3.cmml">2</mn><mo id="S2.SS2.p4.1.m1.6.6.1.2" xref="S2.SS2.p4.1.m1.6.6.1.2.cmml">⁢</mo><mfrac id="S2.SS2.p4.1.m1.6.6.1.4" xref="S2.SS2.p4.1.m1.6.6.1.4.cmml"><mi id="S2.SS2.p4.1.m1.6.6.1.4.2" xref="S2.SS2.p4.1.m1.6.6.1.4.2.cmml">D</mi><mi id="S2.SS2.p4.1.m1.6.6.1.4.3" xref="S2.SS2.p4.1.m1.6.6.1.4.3.cmml">λ</mi></mfrac><mo id="S2.SS2.p4.1.m1.6.6.1.2a" xref="S2.SS2.p4.1.m1.6.6.1.2.cmml">⁢</mo><mrow id="S2.SS2.p4.1.m1.6.6.1.1.1" xref="S2.SS2.p4.1.m1.6.6.1.1.2.cmml"><mi id="S2.SS2.p4.1.m1.5.5" xref="S2.SS2.p4.1.m1.5.5.cmml">sin</mi><mo id="S2.SS2.p4.1.m1.6.6.1.1.1a" xref="S2.SS2.p4.1.m1.6.6.1.1.2.cmml">⁡</mo><mrow id="S2.SS2.p4.1.m1.6.6.1.1.1.1" xref="S2.SS2.p4.1.m1.6.6.1.1.2.cmml"><mo stretchy="false" id="S2.SS2.p4.1.m1.6.6.1.1.1.1.2" xref="S2.SS2.p4.1.m1.6.6.1.1.2.cmml">(</mo><msub id="S2.SS2.p4.1.m1.6.6.1.1.1.1.1" xref="S2.SS2.p4.1.m1.6.6.1.1.1.1.1.cmml"><mi id="S2.SS2.p4.1.m1.6.6.1.1.1.1.1.2" xref="S2.SS2.p4.1.m1.6.6.1.1.1.1.1.2.cmml">ϕ</mi><mrow id="S2.SS2.p4.1.m1.4.4.2.4" xref="S2.SS2.p4.1.m1.4.4.2.3.cmml"><mi id="S2.SS2.p4.1.m1.3.3.1.1" xref="S2.SS2.p4.1.m1.3.3.1.1.cmml">u</mi><mo id="S2.SS2.p4.1.m1.4.4.2.4.1" xref="S2.SS2.p4.1.m1.4.4.2.3.cmml">,</mo><mi id="S2.SS2.p4.1.m1.4.4.2.2" xref="S2.SS2.p4.1.m1.4.4.2.2.cmml">l</mi></mrow></msub><mo stretchy="false" id="S2.SS2.p4.1.m1.6.6.1.1.1.1.3" xref="S2.SS2.p4.1.m1.6.6.1.1.2.cmml">)</mo></mrow></mrow></mrow></mrow></math>, <math><mrow id="S2.SS2.p4.4.m4.4.4" xref="S2.SS2.p4.4.m4.4.4.cmml"><msub id="S2.SS2.p4.4.m4.4.4.3" xref="S2.SS2.p4.4.m4.4.4.3.cmml"><mi id="S2.SS2.p4.4.m4.4.4.3.2" xref="S2.SS2.p4.4.m4.4.4.3.2.cmml">ϕ</mi><mrow id="S2.SS2.p4.4.m4.2.2.2.4" xref="S2.SS2.p4.4.m4.2.2.2.3.cmml"><mi id="S2.SS2.p4.4.m4.1.1.1.1" xref="S2.SS2.p4.4.m4.1.1.1.1.cmml">u</mi><mo id="S2.SS2.p4.4.m4.2.2.2.4.1" xref="S2.SS2.p4.4.m4.2.2.2.3.cmml">,</mo><mi id="S2.SS2.p4.4.m4.2.2.2.2" xref="S2.SS2.p4.4.m4.2.2.2.2.cmml">l</mi></mrow></msub><mo id="S2.SS2.p4.4.m4.4.4.2" xref="S2.SS2.p4.4.m4.4.4.2.cmml">∈</mo><mrow id="S2.SS2.p4.4.m4.4.4.1.1" xref="S2.SS2.p4.4.m4.4.4.1.2.cmml"><mo stretchy="false" id="S2.SS2.p4.4.m4.4.4.1.1.2" xref="S2.SS2.p4.4.m4.4.4.1.2.cmml">[</mo><mn id="S2.SS2.p4.4.m4.3.3" xref="S2.SS2.p4.4.m4.3.3.cmml">0</mn><mo id="S2.SS2.p4.4.m4.4.4.1.1.3" xref="S2.SS2.p4.4.m4.4.4.1.2.cmml">,</mo><mrow id="S2.SS2.p4.4.m4.4.4.1.1.1" xref="S2.SS2.p4.4.m4.4.4.1.1.1.cmml"><mn id="S2.SS2.p4.4.m4.4.4.1.1.1.2" xref="S2.SS2.p4.4.m4.4.4.1.1.1.2.cmml">2</mn><mo id="S2.SS2.p4.4.m4.4.4.1.1.1.1" xref="S2.SS2.p4.4.m4.4.4.1.1.1.1.cmml">⁢</mo><mi id="S2.SS2.p4.4.m4.4.4.1.1.1.3" xref="S2.SS2.p4.4.m4.4.4.1.1.1.3.cmml">π</mi></mrow><mo stretchy="false" id="S2.SS2.p4.4.m4.4.4.1.1.4" xref="S2.SS2.p4.4.m4.4.4.1.2.cmml">]</mo></mrow></mrow></math>, <math><mrow id="S2.SS2.p4.6.m6.6.6" xref="S2.SS2.p4.6.m6.6.6.cmml"><msub id="S2.SS2.p4.6.m6.6.6.3" xref="S2.SS2.p4.6.m6.6.6.3.cmml"><mi id="S2.SS2.p4.6.m6.6.6.3.2" xref="S2.SS2.p4.6.m6.6.6.3.2.cmml">α</mi><mrow id="S2.SS2.p4.6.m6.2.2.2.4" xref="S2.SS2.p4.6.m6.2.2.2.3.cmml"><mi id="S2.SS2.p4.6.m6.1.1.1.1" xref="S2.SS2.p4.6.m6.1.1.1.1.cmml">u</mi><mo id="S2.SS2.p4.6.m6.2.2.2.4.1" xref="S2.SS2.p4.6.m6.2.2.2.3.cmml">,</mo><mi id="S2.SS2.p4.6.m6.2.2.2.2" xref="S2.SS2.p4.6.m6.2.2.2.2.cmml">l</mi></mrow></msub><mo id="S2.SS2.p4.6.m6.6.6.2" xref="S2.SS2.p4.6.m6.6.6.2.cmml">∼</mo><mrow id="S2.SS2.p4.6.m6.6.6.1" xref="S2.SS2.p4.6.m6.6.6.1.cmml"><mi class="ltx_font_mathcaligraphic" id="S2.SS2.p4.6.m6.6.6.1.3" xref="S2.SS2.p4.6.m6.6.6.1.3.cmml">𝒞</mi><mo id="S2.SS2.p4.6.m6.6.6.1.2" xref="S2.SS2.p4.6.m6.6.6.1.2.cmml">⁢</mo><mi class="ltx_font_mathcaligraphic" id="S2.SS2.p4.6.m6.6.6.1.4" xref="S2.SS2.p4.6.m6.6.6.1.4.cmml">𝒩</mi><mo id="S2.SS2.p4.6.m6.6.6.1.2a" xref="S2.SS2.p4.6.m6.6.6.1.2.cmml">⁢</mo><mrow id="S2.SS2.p4.6.m6.6.6.1.1.1" xref="S2.SS2.p4.6.m6.6.6.1.1.2.cmml"><mo stretchy="false" id="S2.SS2.p4.6.m6.6.6.1.1.1.2" xref="S2.SS2.p4.6.m6.6.6.1.1.2.cmml">(</mo><mn id="S2.SS2.p4.6.m6.5.5" xref="S2.SS2.p4.6.m6.5.5.cmml">0</mn><mo id="S2.SS2.p4.6.m6.6.6.1.1.1.3" xref="S2.SS2.p4.6.m6.6.6.1.1.2.cmml">,</mo><msubsup id="S2.SS2.p4.6.m6.6.6.1.1.1.1" xref="S2.SS2.p4.6.m6.6.6.1.1.1.1.cmml"><mi id="S2.SS2.p4.6.m6.6.6.1.1.1.1.2.2" xref="S2.SS2.p4.6.m6.6.6.1.1.1.1.2.2.cmml">σ</mi><mrow id="S2.SS2.p4.6.m6.4.4.2.4" xref="S2.SS2.p4.6.m6.4.4.2.3.cmml"><mi id="S2.SS2.p4.6.m6.3.3.1.1" xref="S2.SS2.p4.6.m6.3.3.1.1.cmml">u</mi><mo id="S2.SS2.p4.6.m6.4.4.2.4.1" xref="S2.SS2.p4.6.m6.4.4.2.3.cmml">,</mo><mi id="S2.SS2.p4.6.m6.4.4.2.2" xref="S2.SS2.p4.6.m6.4.4.2.2.cmml">l</mi></mrow><mn id="S2.SS2.p4.6.m6.6.6.1.1.1.1.2.3" xref="S2.SS2.p4.6.m6.6.6.1.1.1.1.2.3.cmml">2</mn></msubsup><mo stretchy="false" id="S2.SS2.p4.6.m6.6.6.1.1.1.4" xref="S2.SS2.p4.6.m6.6.6.1.1.2.cmml">)</mo></mrow></mrow></mrow></math>, <math><msub id="S2.SS2.p5.3.m3.2.3" xref="S2.SS2.p5.3.m3.2.3.cmml"><mi id="S2.SS2.p5.3.m3.2.3.2" xref="S2.SS2.p5.3.m3.2.3.2.cmml">η</mi><mrow id="S2.SS2.p5.3.m3.2.2.2.2" xref="S2.SS2.p5.3.m3.2.2.2.3.cmml"><mi id="S2.SS2.p5.3.m3.1.1.1.1" xref="S2.SS2.p5.3.m3.1.1.1.1.cmml">u</mi><mo id="S2.SS2.p5.3.m3.2.2.2.2.2" xref="S2.SS2.p5.3.m3.2.2.2.3.cmml">,</mo><mrow id="S2.SS2.p5.3.m3.2.2.2.2.1" xref="S2.SS2.p5.3.m3.2.2.2.2.1.cmml"><mi id="S2.SS2.p5.3.m3.2.2.2.2.1.2" xref="S2.SS2.p5.3.m3.2.2.2.2.1.2.cmml">L</mi><mo id="S2.SS2.p5.3.m3.2.2.2.2.1.1" xref="S2.SS2.p5.3.m3.2.2.2.2.1.1.cmml">⁢</mo><mi id="S2.SS2.p5.3.m3.2.2.2.2.1.3" xref="S2.SS2.p5.3.m3.2.2.2.2.1.3.cmml">O</mi><mo id="S2.SS2.p5.3.m3.2.2.2.2.1.1a" xref="S2.SS2.p5.3.m3.2.2.2.2.1.1.cmml">⁢</mo><mi id="S2.SS2.p5.3.m3.2.2.2.2.1.4" xref="S2.SS2.p5.3.m3.2.2.2.2.1.4.cmml">S</mi></mrow></mrow></msub></math>, <math><msub id="S2.SS2.p5.4.m4.2.3" xref="S2.SS2.p5.4.m4.2.3.cmml"><mi id="S2.SS2.p5.4.m4.2.3.2" xref="S2.SS2.p5.4.m4.2.3.2.cmml">η</mi><mrow id="S2.SS2.p5.4.m4.2.2.2.2" xref="S2.SS2.p5.4.m4.2.2.2.3.cmml"><mi id="S2.SS2.p5.4.m4.1.1.1.1" xref="S2.SS2.p5.4.m4.1.1.1.1.cmml">u</mi><mo id="S2.SS2.p5.4.m4.2.2.2.2.2" xref="S2.SS2.p5.4.m4.2.2.2.3.cmml">,</mo><mrow id="S2.SS2.p5.4.m4.2.2.2.2.1" xref="S2.SS2.p5.4.m4.2.2.2.2.1.cmml"><mi id="S2.SS2.p5.4.m4.2.2.2.2.1.2" xref="S2.SS2.p5.4.m4.2.2.2.2.1.2.cmml">N</mi><mo id="S2.SS2.p5.4.m4.2.2.2.2.1.1" xref="S2.SS2.p5.4.m4.2.2.2.2.1.1.cmml">⁢</mo><mi id="S2.SS2.p5.4.m4.2.2.2.2.1.3" xref="S2.SS2.p5.4.m4.2.2.2.2.1.3.cmml">L</mi><mo id="S2.SS2.p5.4.m4.2.2.2.2.1.1a" xref="S2.SS2.p5.4.m4.2.2.2.2.1.1.cmml">⁢</mo><mi id="S2.SS2.p5.4.m4.2.2.2.2.1.4" xref="S2.SS2.p5.4.m4.2.2.2.2.1.4.cmml">O</mi><mo id="S2.SS2.p5.4.m4.2.2.2.2.1.1b" xref="S2.SS2.p5.4.m4.2.2.2.2.1.1.cmml">⁢</mo><mi id="S2.SS2.p5.4.m4.2.2.2.2.1.5" xref="S2.SS2.p5.4.m4.2.2.2.2.1.5.cmml">S</mi></mrow></mrow></msub></math>

Correct Categorie: eess

Guessed Categorie: cs

Result: incorrect

Paper: https://arxiv.org/abs/1705.10644

Formulas:

1-

ψ_{α} (k_{VBM})

2-

ξ_{X ϕ} = {char}_{X ϕ} [ψ_{α} (Γ)] \times \frac{1}{2},

3-

{char}_{X ϕ} [ψ (k)]

4-

ζ_{X ϕ} = {char}_{X ϕ} [ψ_{β} (Γ)] \times \frac{1}{2} .

5-

\sum_{X ϕ} ξ_{X ϕ} = \sum_{X ϕ} ζ_{X ϕ} = \frac{1}{2} .

6-

V_{S, α}^{X ϕ}

7-

= V_{X} (f_{0}) - V_{X} (f_{0} - ξ_{X ϕ})

8-

V_{S, β}^{X ϕ}

9-

= - [V_{X} (f_{0}) - V_{X} (f_{0} - ζ_{X ϕ})],

10-

V_{X} (f)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/nucl-th/0609038

Formulas:

1-

1 < p_{T} (assoc) < 2.5

2-

2.5 < p_{T} < 4.0

3-

1 < p_{T} < 2.5

4-

< p_{T} (assoc) < 2.5

5-

G (α, σ) = \frac{1}{\sqrt{2 π} σ} \exp (- α^{2} / 2 σ^{2}),

6-

σ_{i} = σ_{s} \frac{ρ_{i} / ρ_{1}}{E_{i} / E_{s}},

7-

i = 2, 3, \dots

8-

Δ_{i} = Δ_{s} e^{ρ_{1} - ρ_{i}} \sqrt{E_{i} / E_{s}},

9-

\frac{d E}{d x} \propto - \sqrt{E},

10-

d \sqrt{E} / d x

Formulas (html):

<math><mrow id="id4.4.m4.1.2" xref="id4.4.m4.1.2.cmml"><mn id="id4.4.m4.1.2.2" xref="id4.4.m4.1.2.2.cmml">1</mn><mo id="id4.4.m4.1.2.3" xref="id4.4.m4.1.2.3.cmml"><</mo><mrow id="id4.4.m4.1.2.4" xref="id4.4.m4.1.2.4.cmml"><msub id="id4.4.m4.1.2.4.2" xref="id4.4.m4.1.2.4.2.cmml"><mi id="id4.4.m4.1.2.4.2.2" xref="id4.4.m4.1.2.4.2.2.cmml">p</mi><mi id="id4.4.m4.1.2.4.2.3" xref="id4.4.m4.1.2.4.2.3.cmml">T</mi></msub><mo id="id4.4.m4.1.2.4.1" xref="id4.4.m4.1.2.4.1.cmml">⁢</mo><mrow id="id4.4.m4.1.2.4.3.2" xref="id4.4.m4.1.2.4.cmml"><mo stretchy="false" id="id4.4.m4.1.2.4.3.2.1" xref="id4.4.m4.1.2.4.cmml">(</mo><mi id="id4.4.m4.1.1" xref="id4.4.m4.1.1.cmml">assoc</mi><mo stretchy="false" id="id4.4.m4.1.2.4.3.2.2" xref="id4.4.m4.1.2.4.cmml">)</mo></mrow></mrow><mo id="id4.4.m4.1.2.5" xref="id4.4.m4.1.2.5.cmml"><</mo><mn id="id4.4.m4.1.2.6" xref="id4.4.m4.1.2.6.cmml">2.5</mn></mrow></math>, <math><mrow id="S1.p2.2.m2.1.1" xref="S1.p2.2.m2.1.1.cmml"><mn id="S1.p2.2.m2.1.1.2" xref="S1.p2.2.m2.1.1.2.cmml">2.5</mn><mo id="S1.p2.2.m2.1.1.3" xref="S1.p2.2.m2.1.1.3.cmml"><</mo><msub id="S1.p2.2.m2.1.1.4" xref="S1.p2.2.m2.1.1.4.cmml"><mi id="S1.p2.2.m2.1.1.4.2" xref="S1.p2.2.m2.1.1.4.2.cmml">p</mi><mi id="S1.p2.2.m2.1.1.4.3" xref="S1.p2.2.m2.1.1.4.3.cmml">T</mi></msub><mo id="S1.p2.2.m2.1.1.5" xref="S1.p2.2.m2.1.1.5.cmml"><</mo><mn id="S1.p2.2.m2.1.1.6" xref="S1.p2.2.m2.1.1.6.cmml">4.0</mn></mrow></math>, <math><mrow id="S1.p2.3.m3.1.1" xref="S1.p2.3.m3.1.1.cmml"><mn id="S1.p2.3.m3.1.1.2" xref="S1.p2.3.m3.1.1.2.cmml">1</mn><mo id="S1.p2.3.m3.1.1.3" xref="S1.p2.3.m3.1.1.3.cmml"><</mo><msub id="S1.p2.3.m3.1.1.4" xref="S1.p2.3.m3.1.1.4.cmml"><mi id="S1.p2.3.m3.1.1.4.2" xref="S1.p2.3.m3.1.1.4.2.cmml">p</mi><mi id="S1.p2.3.m3.1.1.4.3" xref="S1.p2.3.m3.1.1.4.3.cmml">T</mi></msub><mo id="S1.p2.3.m3.1.1.5" xref="S1.p2.3.m3.1.1.5.cmml"><</mo><mn id="S1.p2.3.m3.1.1.6" xref="S1.p2.3.m3.1.1.6.cmml">2.5</mn></mrow></math>, <math><mrow id="S2.p1.2.m2.1.2" xref="S2.p1.2.m2.1.2.cmml"><mi id="S2.p1.2.m2.1.2.2" xref="S2.p1.2.m2.1.2.2.cmml"/><mo id="S2.p1.2.m2.1.2.3" xref="S2.p1.2.m2.1.2.3.cmml"><</mo><mrow id="S2.p1.2.m2.1.2.4" xref="S2.p1.2.m2.1.2.4.cmml"><msub id="S2.p1.2.m2.1.2.4.2" xref="S2.p1.2.m2.1.2.4.2.cmml"><mi id="S2.p1.2.m2.1.2.4.2.2" xref="S2.p1.2.m2.1.2.4.2.2.cmml">p</mi><mi id="S2.p1.2.m2.1.2.4.2.3" xref="S2.p1.2.m2.1.2.4.2.3.cmml">T</mi></msub><mo id="S2.p1.2.m2.1.2.4.1" xref="S2.p1.2.m2.1.2.4.1.cmml">⁢</mo><mrow id="S2.p1.2.m2.1.2.4.3.2" xref="S2.p1.2.m2.1.2.4.cmml"><mo stretchy="false" id="S2.p1.2.m2.1.2.4.3.2.1" xref="S2.p1.2.m2.1.2.4.cmml">(</mo><mi id="S2.p1.2.m2.1.1" xref="S2.p1.2.m2.1.1.cmml">assoc</mi><mo stretchy="false" id="S2.p1.2.m2.1.2.4.3.2.2" xref="S2.p1.2.m2.1.2.4.cmml">)</mo></mrow></mrow><mo id="S2.p1.2.m2.1.2.5" xref="S2.p1.2.m2.1.2.5.cmml"><</mo><mn id="S2.p1.2.m2.1.2.6" xref="S2.p1.2.m2.1.2.6.cmml">2.5</mn></mrow></math>, <math><mrow id="S2.E1.m1.4.4.1" xref="S2.E1.m1.4.4.1.1.cmml"><mrow id="S2.E1.m1.4.4.1.1" xref="S2.E1.m1.4.4.1.1.cmml"><mrow id="S2.E1.m1.4.4.1.1.3" xref="S2.E1.m1.4.4.1.1.3.cmml"><mi id="S2.E1.m1.4.4.1.1.3.2" xref="S2.E1.m1.4.4.1.1.3.2.cmml">G</mi><mo id="S2.E1.m1.4.4.1.1.3.1" xref="S2.E1.m1.4.4.1.1.3.1.cmml">⁢</mo><mrow id="S2.E1.m1.4.4.1.1.3.3.2" xref="S2.E1.m1.4.4.1.1.3.3.1.cmml"><mo stretchy="false" id="S2.E1.m1.4.4.1.1.3.3.2.1" xref="S2.E1.m1.4.4.1.1.3.3.1.cmml">(</mo><mi id="S2.E1.m1.1.1" xref="S2.E1.m1.1.1.cmml">α</mi><mo id="S2.E1.m1.4.4.1.1.3.3.2.2" xref="S2.E1.m1.4.4.1.1.3.3.1.cmml">,</mo><mi id="S2.E1.m1.2.2" xref="S2.E1.m1.2.2.cmml">σ</mi><mo stretchy="false" id="S2.E1.m1.4.4.1.1.3.3.2.3" xref="S2.E1.m1.4.4.1.1.3.3.1.cmml">)</mo></mrow></mrow><mo id="S2.E1.m1.4.4.1.1.2" xref="S2.E1.m1.4.4.1.1.2.cmml">=</mo><mrow id="S2.E1.m1.4.4.1.1.1" xref="S2.E1.m1.4.4.1.1.1.cmml"><mstyle displaystyle="true" id="S2.E1.m1.4.4.1.1.1.3" xref="S2.E1.m1.4.4.1.1.1.3.cmml"><mfrac id="S2.E1.m1.4.4.1.1.1.3a" xref="S2.E1.m1.4.4.1.1.1.3.cmml"><mn id="S2.E1.m1.4.4.1.1.1.3.2" xref="S2.E1.m1.4.4.1.1.1.3.2.cmml">1</mn><mrow id="S2.E1.m1.4.4.1.1.1.3.3" xref="S2.E1.m1.4.4.1.1.1.3.3.cmml"><msqrt id="S2.E1.m1.4.4.1.1.1.3.3.2" xref="S2.E1.m1.4.4.1.1.1.3.3.2.cmml"><mrow id="S2.E1.m1.4.4.1.1.1.3.3.2.2" xref="S2.E1.m1.4.4.1.1.1.3.3.2.2.cmml"><mn id="S2.E1.m1.4.4.1.1.1.3.3.2.2.2" xref="S2.E1.m1.4.4.1.1.1.3.3.2.2.2.cmml">2</mn><mo id="S2.E1.m1.4.4.1.1.1.3.3.2.2.1" xref="S2.E1.m1.4.4.1.1.1.3.3.2.2.1.cmml">⁢</mo><mi id="S2.E1.m1.4.4.1.1.1.3.3.2.2.3" xref="S2.E1.m1.4.4.1.1.1.3.3.2.2.3.cmml">π</mi></mrow></msqrt><mo id="S2.E1.m1.4.4.1.1.1.3.3.1" xref="S2.E1.m1.4.4.1.1.1.3.3.1.cmml">⁢</mo><mi id="S2.E1.m1.4.4.1.1.1.3.3.3" xref="S2.E1.m1.4.4.1.1.1.3.3.3.cmml">σ</mi></mrow></mfrac></mstyle><mo id="S2.E1.m1.4.4.1.1.1.2" xref="S2.E1.m1.4.4.1.1.1.2.cmml">⁢</mo><mrow id="S2.E1.m1.4.4.1.1.1.1.1" xref="S2.E1.m1.4.4.1.1.1.1.2.cmml"><mi id="S2.E1.m1.3.3" xref="S2.E1.m1.3.3.cmml">exp</mi><mo id="S2.E1.m1.4.4.1.1.1.1.1a" xref="S2.E1.m1.4.4.1.1.1.1.2.cmml">⁡</mo><mrow id="S2.E1.m1.4.4.1.1.1.1.1.1" xref="S2.E1.m1.4.4.1.1.1.1.2.cmml"><mo stretchy="false" id="S2.E1.m1.4.4.1.1.1.1.1.1.2" xref="S2.E1.m1.4.4.1.1.1.1.2.cmml">(</mo><mrow id="S2.E1.m1.4.4.1.1.1.1.1.1.1" xref="S2.E1.m1.4.4.1.1.1.1.1.1.1.cmml"><mo id="S2.E1.m1.4.4.1.1.1.1.1.1.1.1" xref="S2.E1.m1.4.4.1.1.1.1.1.1.1.1.cmml">-</mo><mrow id="S2.E1.m1.4.4.1.1.1.1.1.1.1.2" xref="S2.E1.m1.4.4.1.1.1.1.1.1.1.2.cmml"><mrow id="S2.E1.m1.4.4.1.1.1.1.1.1.1.2.2" xref="S2.E1.m1.4.4.1.1.1.1.1.1.1.2.2.cmml"><msup id="S2.E1.m1.4.4.1.1.1.1.1.1.1.2.2.2" xref="S2.E1.m1.4.4.1.1.1.1.1.1.1.2.2.2.cmml"><mi id="S2.E1.m1.4.4.1.1.1.1.1.1.1.2.2.2.2" xref="S2.E1.m1.4.4.1.1.1.1.1.1.1.2.2.2.2.cmml">α</mi><mn id="S2.E1.m1.4.4.1.1.1.1.1.1.1.2.2.2.3" xref="S2.E1.m1.4.4.1.1.1.1.1.1.1.2.2.2.3.cmml">2</mn></msup><mo id="S2.E1.m1.4.4.1.1.1.1.1.1.1.2.2.1" xref="S2.E1.m1.4.4.1.1.1.1.1.1.1.2.2.1.cmml">/</mo><mn id="S2.E1.m1.4.4.1.1.1.1.1.1.1.2.2.3" xref="S2.E1.m1.4.4.1.1.1.1.1.1.1.2.2.3.cmml">2</mn></mrow><mo id="S2.E1.m1.4.4.1.1.1.1.1.1.1.2.1" xref="S2.E1.m1.4.4.1.1.1.1.1.1.1.2.1.cmml">⁢</mo><msup id="S2.E1.m1.4.4.1.1.1.1.1.1.1.2.3" xref="S2.E1.m1.4.4.1.1.1.1.1.1.1.2.3.cmml"><mi id="S2.E1.m1.4.4.1.1.1.1.1.1.1.2.3.2" xref="S2.E1.m1.4.4.1.1.1.1.1.1.1.2.3.2.cmml">σ</mi><mn id="S2.E1.m1.4.4.1.1.1.1.1.1.1.2.3.3" xref="S2.E1.m1.4.4.1.1.1.1.1.1.1.2.3.3.cmml">2</mn></msup></mrow></mrow><mo stretchy="false" id="S2.E1.m1.4.4.1.1.1.1.1.1.3" xref="S2.E1.m1.4.4.1.1.1.1.2.cmml">)</mo></mrow></mrow></mrow></mrow><mo id="S2.E1.m1.4.4.1.2" xref="S2.E1.m1.4.4.1.1.cmml">,</mo></mrow></math>, <math><mrow id="S2.E2.m1.1.1.1" xref="S2.E2.m1.1.1.1.1.cmml"><mrow id="S2.E2.m1.1.1.1.1" xref="S2.E2.m1.1.1.1.1.cmml"><msub id="S2.E2.m1.1.1.1.1.2" xref="S2.E2.m1.1.1.1.1.2.cmml"><mi id="S2.E2.m1.1.1.1.1.2.2" xref="S2.E2.m1.1.1.1.1.2.2.cmml">σ</mi><mi id="S2.E2.m1.1.1.1.1.2.3" xref="S2.E2.m1.1.1.1.1.2.3.cmml">i</mi></msub><mo id="S2.E2.m1.1.1.1.1.1" xref="S2.E2.m1.1.1.1.1.1.cmml">=</mo><mrow id="S2.E2.m1.1.1.1.1.3" xref="S2.E2.m1.1.1.1.1.3.cmml"><msub id="S2.E2.m1.1.1.1.1.3.2" xref="S2.E2.m1.1.1.1.1.3.2.cmml"><mi id="S2.E2.m1.1.1.1.1.3.2.2" xref="S2.E2.m1.1.1.1.1.3.2.2.cmml">σ</mi><mi id="S2.E2.m1.1.1.1.1.3.2.3" xref="S2.E2.m1.1.1.1.1.3.2.3.cmml">s</mi></msub><mo id="S2.E2.m1.1.1.1.1.3.1" xref="S2.E2.m1.1.1.1.1.3.1.cmml">⁢</mo><mpadded width="+5pt" id="S2.E2.m1.1.1.1.1.3.3" xref="S2.E2.m1.1.1.1.1.3.3.cmml"><mstyle displaystyle="true" id="S2.E2.m1.1.1.1.1.3.3a" xref="S2.E2.m1.1.1.1.1.3.3.cmml"><mfrac id="S2.E2.m1.1.1.1.1.3.3b" xref="S2.E2.m1.1.1.1.1.3.3.cmml"><mrow id="S2.E2.m1.1.1.1.1.3.3.2" xref="S2.E2.m1.1.1.1.1.3.3.2.cmml"><msub id="S2.E2.m1.1.1.1.1.3.3.2.2" xref="S2.E2.m1.1.1.1.1.3.3.2.2.cmml"><mi id="S2.E2.m1.1.1.1.1.3.3.2.2.2" xref="S2.E2.m1.1.1.1.1.3.3.2.2.2.cmml">ρ</mi><mi id="S2.E2.m1.1.1.1.1.3.3.2.2.3" xref="S2.E2.m1.1.1.1.1.3.3.2.2.3.cmml">i</mi></msub><mo id="S2.E2.m1.1.1.1.1.3.3.2.1" xref="S2.E2.m1.1.1.1.1.3.3.2.1.cmml">/</mo><msub id="S2.E2.m1.1.1.1.1.3.3.2.3" xref="S2.E2.m1.1.1.1.1.3.3.2.3.cmml"><mi id="S2.E2.m1.1.1.1.1.3.3.2.3.2" xref="S2.E2.m1.1.1.1.1.3.3.2.3.2.cmml">ρ</mi><mn id="S2.E2.m1.1.1.1.1.3.3.2.3.3" xref="S2.E2.m1.1.1.1.1.3.3.2.3.3.cmml">1</mn></msub></mrow><mrow id="S2.E2.m1.1.1.1.1.3.3.3" xref="S2.E2.m1.1.1.1.1.3.3.3.cmml"><msub id="S2.E2.m1.1.1.1.1.3.3.3.2" xref="S2.E2.m1.1.1.1.1.3.3.3.2.cmml"><mi id="S2.E2.m1.1.1.1.1.3.3.3.2.2" xref="S2.E2.m1.1.1.1.1.3.3.3.2.2.cmml">E</mi><mi id="S2.E2.m1.1.1.1.1.3.3.3.2.3" xref="S2.E2.m1.1.1.1.1.3.3.3.2.3.cmml">i</mi></msub><mo id="S2.E2.m1.1.1.1.1.3.3.3.1" xref="S2.E2.m1.1.1.1.1.3.3.3.1.cmml">/</mo><msub id="S2.E2.m1.1.1.1.1.3.3.3.3" xref="S2.E2.m1.1.1.1.1.3.3.3.3.cmml"><mi id="S2.E2.m1.1.1.1.1.3.3.3.3.2" xref="S2.E2.m1.1.1.1.1.3.3.3.3.2.cmml">E</mi><mi id="S2.E2.m1.1.1.1.1.3.3.3.3.3" xref="S2.E2.m1.1.1.1.1.3.3.3.3.3.cmml">s</mi></msub></mrow></mfrac></mstyle></mpadded></mrow></mrow><mo id="S2.E2.m1.1.1.1.2" xref="S2.E2.m1.1.1.1.1.cmml">,</mo></mrow></math>, <math><mrow id="S2.p5.11.m9.3.4" xref="S2.p5.11.m9.3.4.cmml"><mi id="S2.p5.11.m9.3.4.2" xref="S2.p5.11.m9.3.4.2.cmml">i</mi><mo id="S2.p5.11.m9.3.4.1" xref="S2.p5.11.m9.3.4.1.cmml">=</mo><mrow id="S2.p5.11.m9.3.4.3.2" xref="S2.p5.11.m9.3.4.3.1.cmml"><mn id="S2.p5.11.m9.1.1" xref="S2.p5.11.m9.1.1.cmml">2</mn><mo id="S2.p5.11.m9.3.4.3.2.1" xref="S2.p5.11.m9.3.4.3.1.cmml">,</mo><mn id="S2.p5.11.m9.2.2" xref="S2.p5.11.m9.2.2.cmml">3</mn><mo id="S2.p5.11.m9.3.4.3.2.2" xref="S2.p5.11.m9.3.4.3.1.cmml">,</mo><mi mathvariant="normal" id="S2.p5.11.m9.3.3" xref="S2.p5.11.m9.3.3.cmml">⋯</mi></mrow></mrow></math>, <math><mrow id="S2.E3.m1.1.1.1" xref="S2.E3.m1.1.1.1.1.cmml"><mrow id="S2.E3.m1.1.1.1.1" xref="S2.E3.m1.1.1.1.1.cmml"><msub id="S2.E3.m1.1.1.1.1.2" xref="S2.E3.m1.1.1.1.1.2.cmml"><mi mathvariant="normal" id="S2.E3.m1.1.1.1.1.2.2" xref="S2.E3.m1.1.1.1.1.2.2.cmml">Δ</mi><mi id="S2.E3.m1.1.1.1.1.2.3" 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Correct Categorie: nucl-th

Guessed Categorie: nucl-ex

Result: incorrect

Paper: https://arxiv.org/abs/1612.08729

Formulas:

1-

n = 6.3 \times 10^{11}

2-

n = 6.1 \times 10^{11}

3-

n = 5.5 \times 10^{12}

4-

n_{p} = n_{0} + C e^{- b / T}

5-

σ (n) = A {(n - n_{p})}^{p}

6-

n_{p} = n_{0} + C e^{- b / T}

7-

n_{p} = 0.83 + 1.46 e^{- 2.25 / T}

8-

n_{p} = 0.95 + 0.88 e^{- 3.00 / T}

9-

V_{t h} = 0.14

10-

n_{c o n f}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/astro-ph/9801079

Formulas:

1-

\dot{M} > \sim 0.1 {\dot{M}}_{E d d i n g t o n}

2-

{\dot{M}}_{i n} \sim 1000 {\dot{M}}_{E}

3-

10^{- 5} L_{E d d}

4-

10^{- 14} M_{⊙}

5-

10^{- 9} M_{⊙}

6-

n_{e} / n_{γ} \propto r^{1 / 2}

7-

F_{r} = \int_{R_{s}}^{r} D 𝑑 r

8-

D = D_{0} e^{- α {(r / r_{p} - 1)}^{2}}

9-

\dot{M} > \sim 0.3 {\dot{M}}_{E d d}

10-

{\dot{M}}_{i n} = Θ_{i n} ρ ϑ r^{2} .

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1703.07701

Formulas:

1-

\frac{σ_{⟂}}{σ_{∥}} = \frac{1}{2} (1 + \frac{E_{F}}{2 E_{0}}) \frac{m_{∥}}{m_{⟂}},

2-

H_{0} = \frac{ℏ^{2} k_{⟂}^{2} σ_{0}}{2 m_{⟂}} + \frac{ℏ^{2} k_{z}^{2} σ_{0}}{2 m_{∥}} + ℏ α (\hat{z} \times 𝐤) \cdot 𝝈,

3-

𝐤 = (k_{x}, k_{y}, k_{z})

4-

𝜶 = α \hat{z}

5-

k_{⟂} = \sqrt{k_{x}^{2} + k_{y}^{2}}

6-

E_{𝐤 s} = \frac{ℏ^{2}}{2 m_{⟂}} {(k_{⟂} + s k_{0})}^{2} + \frac{ℏ^{2} k_{z}^{2}}{2 m_{∥}},

7-

k_{0} = m_{⟂} α / ℏ

8-

E_{0} = ℏ^{2} k_{0}^{2} / 2 m_{⟂}

9-

N (E_{F}) = a \sqrt{E_{F} - E_{0}} ℱ (\sqrt{E_{0} / (E_{F} - E_{0})})

10-

a = \sqrt{2 m_{∥}} m_{⟂} / (π^{2} ℏ^{3})

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0603301

Formulas:

1-

N \propto B \propto z^{- 3}

2-

L_{b} \sim \frac{c}{ω Δ n}

3-

Δ n = \frac{2 ω_{p}^{2}}{γ^{3} ω^{2} θ^{2}},

4-

ω_{p} \equiv \sqrt{\frac{4 π N e^{2}}{m}}

5-

\frac{2 ω_{p}^{2} (r_{p}) r_{p}}{γ^{3} c ω θ^{2} (r_{p})} = 1 .

6-

\frac{r_{p}}{r_{L}} = 0.18 P^{- 3 / 2} γ_{1.5}^{- 3 / 2} κ_{2}^{1 / 2} B_{⋆ 12}^{1 / 2} ν_{9}^{- 1 / 2} θ_{- 1}^{- 1} .

7-

κ_{2} \equiv \frac{κ}{10^{2}}

8-

B_{⋆_{12}} \equiv \frac{B_{⋆}}{10^{12} G}

9-

ν_{9} \equiv \frac{ν}{10^{9} Hz}

10-

γ_{1.5} \equiv \frac{γ}{10^{1.5}}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/0812.2363

Formulas:

1-

Min I = 2 436 860.3311 + 1.9403494 \times E

2-

Min I = T_{0} + E P_{s} - \frac{e P_{a}}{π} \cos ω_{E} + \frac{3}{8} \frac{e^{2} P_{a}}{π} \sin 2 ω_{E} + \dots

3-

Min II = T_{0} + E P_{s} - \frac{P_{a}}{2} + \frac{e P_{a}}{π} \cos ω_{E} + \frac{3}{8} \frac{e^{2} P_{a}}{π} \sin 2 ω_{E} - \dots

4-

P_{s} \approx P_{a} (1 - ω^{'} / 2 π)

5-

ω_{E} = ω_{0} + ω^{'} E

6-

ω^{'} = 2 π P / U

7-

U / P = 68700 \pm 500

8-

T_{0} = 51063.6537 \pm 0.0001 (H J D)

9-

ω_{0} = 150^{\circ} \pm 5^{\circ}

10-

ω = {154.7}^{\circ} \pm {3.9}^{\circ}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/quant-ph/0703058

Formulas:

1-

a = \sqrt{ℏ / m ω}

2-

ξ = R^{2} / 2 a^{2} ≪ 1

3-

U (r) = {\begin{matrix} - U_{0}, r < R \\ 0, r > R \end{matrix}

4-

A_{ϕ} = \frac{H ρ}{2}, A_{ρ} = A_{z} = 0 .

5-

i ℏ \frac{\partial}{\partial t} ψ (t, 𝐫) = \hat{H} ψ (t, 𝐫),

6-

\hat{H} = - \frac{ℏ^{2}}{2 m} [\frac{\partial}{ρ \partial ρ} (\frac{ρ \partial}{\partial ρ}) + \frac{\partial^{2}}{\partial z^{2}} + \frac{\partial^{2}}{ρ^{2} \partial ϕ^{2}}] - \frac{i ℏ ω}{2} \frac{\partial}{\partial ϕ} + \frac{m ω^{2}}{8} ρ^{2} + U (\sqrt{ρ^{2} + z^{2}}) + μ σ_{3} H,

7-

ω = \frac{| e | m}{H c}, μ = \frac{| e | ℏ}{2 m c}, σ_{3} = (\begin{matrix} 1 0 \\ 0 1 \end{matrix}) .

8-

ψ (t, 𝐫) = e^{\frac{- i E t}{ℏ}} ψ_{E} (𝐫) .

9-

ψ_{E} (𝐫) = \int_{- \infty}^{+ \infty} 𝑑 p_{z} \sum_{l = - \infty}^{+ \infty} \sum_{n_{ρ} = 0}^{\infty} C_{E n_{ρ} l p_{z}} ψ_{n_{ρ} l p_{z}} (𝐫) .

10-

ψ_{n_{ρ} l p_{z}} (𝐫) = \frac{1}{2} \frac{e^{i p_{z} z / ℏ}}{\sqrt{2 π ℏ}} \frac{e^{i l ϕ}}{\sqrt{2 π}} \frac{1}{a} I_{n_{ρ} l} (ρ^{2} / 2 a^{2}) (\begin{matrix} 1 + s \\ 1 - s \end{matrix}) .

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/1607.02204

Formulas:

1-

{H S}_{p}, {R G B}_{p}, {L a b}_{p}, {H O G}_{p}, {L B P}_{p}

2-

𝐅_{a} (c)

3-

𝐟_{a} (c)

4-

𝐅_{b} (c)

5-

𝐟_{b} (c)

6-

𝐅_{a} (c) = [𝐅_{a}^{T} (c) | 𝐅_{a}^{G} (c)]

7-

𝐅_{b} (c) = [𝐅_{b}^{T} (c) | 𝐅_{b}^{P} (c)]

8-

𝐅_{a}^{T} (c)

9-

𝐅_{b}^{T} (c)

10-

𝐅_{a}^{G} (c)

Formulas (html):

Correct Categorie: cs

Guessed Categorie: cs

Result: correct

Paper: https://arxiv.org/abs/0910.1907

Formulas:

1-

- e 𝐄 \times 𝛀

2-

s p d s^{⋆}

3-

s p s^{⋆}

4-

[00 \bar{1}]

5-

σ_{x y} = - \frac{e^{2}}{V ℏ} ⟨ Ω_{z} ⟩,

6-

⟨ Ω_{z} ⟩ = \sum_{𝐤, n} Ω_{z} (n, 𝐤) f_{n, 𝐤}

7-

Ω_{z} (n, 𝐤) = 2 Im ⟨ \partial_{k_{y}} u_{n, 𝐤} | \partial_{k_{x}} u_{n, 𝐤} ⟩,

8-

Ω_{z} (n, 𝐤) = 2 Im \sum_{n^{'} \neq n} \frac{c_{n n^{'}}^{y} c_{n^{'} n}^{x}}{{(ϵ_{n, 𝐤} - ϵ_{n^{'}, 𝐤})}^{2}},

9-

𝐜_{n n^{'}} = ⟨ u_{n, 𝐤} | \partial_{𝐤} {\hat{H}}_{𝐤} | u_{n^{'}, 𝐤} ⟩

10-

s p d s^{⋆}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/cond-mat/9806045

Formulas:

1-

D_{1} = E_{1} + 4 π P_{1} (E_{1}) = E_{2} + 4 π P_{2} (E_{2}) = D_{2} .

2-

P_{i} (E) = P_{i}^{(0)} + χ_{i} E_{i},

3-

4 π (P_{2}^{(0)} - P_{1}^{(0)}) = ε_{1}^{\infty} E_{1} - ε_{2}^{\infty} E_{2},

4-

ε_{1}^{\infty} E_{1} = ε_{2}^{\infty} E_{2} .

5-

E \equiv E_{1} = - E_{2}, Δ E \equiv E_{1} - E_{2} = 2 E,

6-

4 π (P_{2}^{(0)} - P_{1}^{(0)}) = \frac{1}{2} (ε_{1}^{\infty} + ε_{2}^{\infty}) Δ E .

7-

s_{int} = \pm Δ E / 4 π

8-

\pm 2 (P_{2}^{(0)} - P_{1}^{(0)}) / (ε_{1}^{\infty} + ε_{2}^{\infty})

9-

\pm 2 Δ P^{(0)} / (ε_{1}^{\infty} + ε_{2}^{\infty}) .

10-

{\bar{ε}}^{\infty} = (ε_{1}^{\infty} + ε_{2}^{\infty})

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0408328

Formulas:

1-

{\tilde{M}}_{P} = M_{P} \sin i

2-

< 0.06 A U

3-

10^{- 3} M_{☉}^{\frac{1}{2}} R_{☉}^{5}

4-

10^{- 3} M_{☉}^{\frac{1}{2}} R_{☉}^{5}

5-

P_{*} < 3 d a y s

6-

\frac{d Ω_{*}}{d t}

7-

- sign (Ω_{*} - n) \frac{3 k_{2, *}}{2 C_{*} Q_{*}} (\frac{{\tilde{M}}_{P}^{2}}{M_{*}}) (\frac{R_{*}^{5}}{a^{3}}) \frac{G M_{*}}{a^{3}}

8-

\frac{d a}{d t}

9-

sign (Ω_{*} - n) \frac{3 k_{2, *}}{Q_{*}} (\frac{{\tilde{M}}_{P}}{M_{*}}) {(\frac{R_{*}}{a})}^{5} a \sqrt{\frac{G M_{*}}{a^{3}}}

10-

C_{*} = I_{*} M_{*} R_{*}^{2}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1111.0997

Formulas:

1-

T_{N} = T_{T O}

2-

T_{N} \leq T_{T O}

3-

ρ_{b} / ρ_{a} = 1.2, 1.4, 1.5

4-

ϵ = \frac{(a_{O} - b_{O})}{(a_{O} + b_{O})}

5-

ϵ \equiv \frac{(a_{O} - b_{O})}{(a_{O} + b_{O})}

6-

ρ_{b}^{*} \equiv 2 ρ_{t} - ρ_{a}

7-

ρ_{b}^{*} = 2 * ρ_{t} - ρ_{a}

8-

T_{N} \leq T_{T O}

9-

ϵ = \frac{(a_{O} - b_{O})}{(a_{O} + b_{O})}

10-

ϵ = \frac{a_{O} - b_{O}}{a_{O} + b_{O}}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: nucl-th

Result: incorrect

Paper: https://arxiv.org/abs/1710.09493

Formulas:

1-

a (S) = k / n

2-

a (S) = 1

3-

a (S) \geq \frac{k - 1}{m - 1}

4-

m - 1 = (k - 1) q + r

5-

a (S) \geq ⌈ \frac{n - r}{q} ⌉ / n

6-

\frac{k - 1}{m - 1 - r}

7-

S = (X, E)

8-

S = (X, E)

9-

a (S) := \frac{Δ (S)}{| E |} .

10-

H = (V, E)

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0508491

Formulas:

1-

P = - A (a) / ρ

2-

A (a) = A_{0} a^{- n}

3-

[- 1.3, 2.6]

4-

(Λ C D M)

5-

P = - A / ρ

6-

P_{c h} = - \frac{A}{ρ_{c h}^{α}}

7-

ρ_{c h} = {(A + \frac{B}{a^{3 (1 + α)}})}^{\frac{1}{1 + α}}

8-

8 π G A^{1 / (1 + α)}

9-

P_{c h} = - \frac{A (a)}{ρ_{c h}}

10-

A (a) = A_{0} a^{- n}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1709.01458

Formulas:

1-

(\frac{d E}{d X}) (X)

2-

(\frac{d E}{d X}) (X)

3-

(\frac{d E}{d X}) (X)

4-

N_{ch} (X)

5-

α (X) = \frac{1}{N_{ch} (X)} (\frac{d E}{d X}) (X) .

6-

s (X) = \frac{3}{1 + 2 X_{\max} / X},

7-

α (s) = \frac{c_{1}}{{(c_{2} + s)}^{c_{3}}} + c_{4} + c_{5} \cdot s,

8-

c_{1} = 3.90883 MeV g^{- 1} {cm}^{2}

9-

MeV g^{- 1} {cm}^{2}

10-

c_{5} = 0.13180 MeV g^{- 1} {cm}^{2}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1206.4101

Formulas:

1-

ℱ = U - T S

2-

Δ U = U_{12} - (U_{11} + U_{22}) / 2

3-

Δ ℱ = - A σ \propto R^{2}

4-

Δ ℱ = V Δ U \propto R^{3}

5-

𝒫 (ε) = \frac{1}{\bar{ε} - ε_{0}} \exp [- \frac{ε - ε_{0}}{\bar{ε} - ε_{0}}]

6-

\vec{v} = (u, v)

7-

ξ (x, y, t)

8-

ξ = 1 (0)

9-

\frac{\partial}{\partial t} [ξ] + \frac{\partial}{\partial x} [ξ u] + \frac{\partial}{\partial y} [ξ v] - \frac{\partial}{\partial y} [ξ v_{s} (ξ)] = 0,

10-

\vec{v} = (u, v)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/math/0211183

Formulas:

1-

v_{1}, \dots, v_{n}

2-

{G |}_{v_{1}, \dots, v_{k}}

3-

x_{1}, x_{2}, \dots

4-

a, a^{'} \in A

5-

b, b^{'} \in B

6-

\bar{a^{'} b^{'}}

7-

(a, b, b^{'})

8-

(b^{'}, a, a^{'})

9-

ϕ : [0, 1] \to B

10-

\bar{a ϕ (t)}

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/1401.1527

Formulas:

1-

J_{2} > J_{1} / 2

2-

K (𝐒_{i} \cdot 𝐒_{j})

3-

J_{1 a} = J_{1 b}

4-

J_{1 a} = J_{1 b}

5-

K \sim J_{1}, J_{2}

6-

z_{Li, Na, La}

7-

{E (0) |}_{M (90)} - {E (0) |}_{M (0)}

8-

J_{1} - J_{2} - K

9-

\begin{matrix} H = J_{1} \sum_{n n} 𝐒_{i} \cdot 𝐒_{j} + J_{2} \sum_{n n n} 𝐒_{i} \cdot 𝐒_{j} \\ - K \sum_{n n} {(𝐒_{i} \cdot 𝐒_{j})}^{2} . \end{matrix}

10-

𝐪 = (1, 0)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/cond-mat/0412381

Formulas:

1-

i U_{z} + \frac{1}{2 k_{0} n_{e}} U_{x x} - \frac{1}{2} k_{0} n_{e}^{2} r_{33} \frac{E_{0}}{1 + I_{0} (x) + {| U |}^{2}} U = 0 .

2-

I_{0} (x)

3-

2 k_{0} n_{e}

4-

1 / (k_{0}^{2} n_{e}^{4} r_{33})

5-

i U_{z} + U_{x x} - \frac{E_{0}}{1 + I_{0} (x) + {| U |}^{2}} U = 0 .

6-

U (x, z) = u (x) \exp (i μ z)

7-

u_{x x} - \frac{E_{0}}{1 + I_{0} (x) + {| u |}^{2}} u = μ u .

8-

I_{0} (x) = V_{0} [\exp (- \frac{{(x - a)}^{2}}{2 ϵ^{2}}) + \exp (- \frac{{(x + a)}^{2}}{2 ϵ^{2}})],

9-

I_{0} (x)

10-

{λ, (a, b)}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/1302.3899

Formulas:

1-

\frac{\partial Φ}{\partial \bar{z}} = μ (z) \frac{\partial Φ}{\partial z}, a.e. z \in ℂ

2-

{∥ μ ∥}_{\infty} < 1

3-

{∥ μ ∥}_{\infty} = 1

4-

μ = \sum_{j = 1}^{n} μ_{j} χ_{Ω_{j}}

5-

{∥ μ_{j} ∥}_{\infty} < 1

6-

j = 1, \dots N

7-

z + O (1 / z)

8-

| μ (x) - μ (y) | \leq C {| x - y |}^{ε}

9-

A (0, r_{1}, r_{2}) := {z : 0 \leq r_{1} < | z | < r_{2} \leq \infty}

10-

M (A) = \log \frac{r_{2}}{r_{1}}

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/0811.2165

Formulas:

1-

J_{z} = \pm 3 / 2

2-

S_{z} = - 5 / 2

3-

S_{z} = 5 / 2

4-

S_{z} = - 5 / 2

5-

τ_{X - M n}

6-

D_{0} S_{z}^{2}

7-

D_{0} = 7 μ

8-

ρ_{+ 5 / 2} (t)

9-

ρ_{+ 5 / 2} (0) = 1

10-

⟨ ρ_{+ 5 / 2} (t) ⟩

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1304.4117

Formulas:

1-

l^{1} (𝔾)

2-

c_{0} (𝔾)

3-

f_{n} (K) = sup {μ^{n} (K x^{- 1}) : x \in G}

4-

μ \in l^{1} (G)

5-

c_{0} (𝔾)

6-

(l^{\infty} (𝔾), Γ, φ, ψ)

7-

Γ : l^{\infty} (𝔾) \to l^{\infty} (𝔾) \bar{\otimes} l^{\infty} (𝔾)

8-

l^{\infty} (𝔾)

9-

l^{\infty} (𝔾)

10-

l^{1} (𝔾) := l^{\infty} {(𝔾)}_{*}

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/1611.05248

Formulas:

1-

G = (V, E)

2-

O (n_{𝑜𝑓𝑓}^{2} \cdot S)

3-

O (n_{𝑜𝑓𝑓}^{2} \cdot t_{p})

4-

O (d^{2} \cdot \max {t_{u}, t_{q}})

5-

O (d \cdot t_{q})

6-

G = (V, E)

7-

S = O (d^{1 - 2 / c} m n^{1 / c - 1 / (c \log (2 d))} \log^{2} n)

8-

\tilde{O} (S)

9-

O (d^{2 c + 4} \log^{2} n \log \log n)

10-

o (m n^{1 / c})

Formulas (html):

Correct Categorie: cs

Guessed Categorie: cs

Result: correct

Paper: https://arxiv.org/abs/0710.2068

Formulas:

1-

μ = i μ_{I}

2-

0 \leq μ_{I} / T < π / 3

3-

(β, {\hat{μ}}_{I}, {\hat{μ}}_{R})

4-

μ = i μ_{I}

5-

θ \equiv μ_{I} / T

6-

θ = 2 π (k + 1 / 2) / N

7-

k = 0, 1, 2, \dots

8-

0 \leq θ < π / N

9-

(β, {\hat{μ}}_{I})

10-

β = 2 N / g^{2}

Formulas (html):

Correct Categorie: hep-lat

Guessed Categorie: hep-lat

Result: correct

Paper: https://arxiv.org/abs/cond-mat/0403539

Formulas:

1-

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

2-

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

3-

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

4-

I = I_{c1} \sin (ϕ) + I_{c2} \sin (2 ϕ) + \dots,

5-

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

6-

Φ_{i} = Φ_{x} + I L,

7-

ϕ + \frac{2 π Φ_{i}}{Φ_{0}} = 2 n π

8-

I = - I_{c1} \sin (\frac{2 π Φ_{i}}{Φ_{0}}) - I_{c2} \sin (\frac{4 π Φ_{i}}{Φ_{0}}) - \dots .

9-

Φ_{x} = Φ_{i} + I_{c1} L \sin (\frac{2 π Φ_{i}}{Φ_{0}}) + I_{c2} L \sin (\frac{4 π Φ_{i}}{Φ_{0}}) .

10-

U (Φ_{i}, Φ_{x}) = \frac{{(Φ_{i} - Φ_{x})}^{2}}{2 L} + \int_{0}^{ϕ} I d ϕ,

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/0909.2167

Formulas:

1-

\log P_{i}, M_{2}^{i}

2-

\log P_{i}, M_{2}^{i}

3-

q_{c} = [1.67 - x + 2 {(\frac{M_{c1}^{P}}{M_{1}^{P}})}^{5}] / 2.13,

4-

x = d \ln R_{1}^{P} / d \ln M_{1}^{p}

5-

α_{CE} Δ E_{orb} \geq | E_{bind} |,

6-

\log P^{i}, M_{2}^{i}

7-

M_{WD}^{i}, M_{2}^{i}, \log P^{i}

8-

M_{1}^{p} = \frac{0.19 X}{{(1 - X)}^{0.75} + 0.032 {(1 - X)}^{0.25}},

9-

n (q) = 1, 0 < q \leq 1,

10-

q = M_{2}^{p} / M_{1}^{p}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0303053

Formulas:

1-

3 h^{- 1} Mpc

2-

R_{s} = 8 h^{- 1} Mpc

3-

R_{s} = 12 h^{- 1} Mpc

4-

v_{12} (r)

5-

σ_{12} (r)

6-

β \equiv Ω_{0}^{0.6} / b

7-

σ_{12} = 580 \pm 80 km s^{- 1}

8-

r_{p} = 1 h^{- 1} Mpc

9-

\sim 400 km s^{- 1}

10-

r_{p} = 2 h^{- 1} Mpc

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/2003.08075

Formulas:

1-

153 ″ \times 153 ″

2-

V_{f i t, i} = a v_{i} + b

3-

g_{S u n}

4-

g_{S u n}

5-

Δ B = (B_{f i t, N} - B_{f i t, 1}) / {\bar{B}}_{f i t}

6-

B_{f i t, i} = a b_{i} + b

7-

Δ v_{e n d} = \frac{v_{e n d} - V_{f i t, e n d}}{V_{f i t, e n d}}, Δ b_{e n d} = \frac{b_{e n d} - B_{f i t, e n d}}{B_{f i t, e n d}}

8-

Δ v_{e n d}

9-

Δ b_{e n d}

10-

Δ v_{e n d}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1310.1398

Formulas:

1-

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

2-

C h a n d r a

3-

N e w t o n

4-

M_{Δ} = (4 π / 3) Δ ρ_{c} R_{Δ}^{3}

5-

M_{⋆} = 10^{10.3} M_{⊙}

6-

M_{⋆} > 10^{10.3} M_{⊙}

7-

Δ v = 3000 km s^{- 1}

8-

σ_{v} \sim 300 - 500

9-

M_{cut} (z)

10-

M_{⋆} / M_{⊙} = 10^{9}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/0902.4425

Formulas:

1-

γ n \to K^{+} K^{-} n

2-

U χ P T

3-

J^{P} = 1 / 2^{+}

4-

N^{*} (1710)

5-

ϕ K \bar{K}

6-

t^{1} g^{12} t^{2} + t^{1} [G^{121} T_{R}^{21} + G^{123} T_{R}^{23}]

7-

t^{1} g^{13} t^{3} + t^{1} [G^{131} T_{R}^{31} + G^{132} T_{R}^{32}]

8-

t^{2} g^{21} t^{1} + t^{2} [G^{212} T_{R}^{12} + G^{213} T_{R}^{13}]

9-

t^{2} g^{23} t^{3} + t^{2} [G^{231} T_{R}^{31} + G^{232} T_{R}^{32}]

10-

t^{3} g^{31} t^{1} + t^{3} [G^{312} T_{R}^{12} + G^{313} T_{R}^{13}]

Formulas (html):

Correct Categorie: nucl-th

Guessed Categorie: hep-ph

Result: incorrect

Paper: https://arxiv.org/abs/1511.06108

Formulas:

1-

k = 1.8 \cdot 10^{6}

2-

\sqrt{s_{N N}} = 2.76

3-

ρ (r \pm δ r) = C \frac{1}{2 δ r} \sum_{i, r_{i} \in [r - δ r, r + δ r]} \frac{p_{T, i}}{p_{T, jet}}

4-

r = \sqrt{Δ η^{2} + Δ ϕ^{2}}

5-

100 < p_{T, jet} < 120

6-

ξ = - \log p_{T} / p_{T, jet}

7-

ξ = - \log (p_{T} / p_{T, jet})

8-

g = \sum_{i} \frac{p_{T, i}}{p_{T, jet}} r_{i} and p_{T, D} = \frac{\sqrt{\sum_{i} p_{T, i}^{2}}}{p_{T, jet}} .

9-

60 < p_{T, jet}^{ch} < 80

10-

\sqrt{s_{N N}} = 2.76

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: hep-ex

Result: incorrect

Paper: https://arxiv.org/abs/1805.09532

Formulas:

1-

s p^{3} d^{5}

2-

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

3-

d_{3 z 2 - r^{2}}

4-

| Φ_{σ} ⟩ = {(d_{3 z^{2} - r^{2}, σ}, d_{x^{2} - y^{2}, σ}, d_{x y, σ}, p_{x, σ}^{+}, p_{y, σ}^{+}, p_{z, σ}^{-})}^{T}

5-

p_{i}^{ν} = (p_{i}^{t} + ν p_{i}^{b}) / \sqrt{2}

6-

i = x, y, z

7-

H = H_{S K} \otimes 1 + H_{S O},

8-

H_{S K} = \sum_{i, j} \sum_{α, β} (ϵ_{i α} δ_{i j} δ_{α β} + t_{i α, j β}) b_{i α}^{†} b_{j β},

9-

H_{S O} = \sum_{i} \sum_{σ, σ^{'}} \frac{λ_{i}}{2 ℏ} 𝐋_{i} \cdot 𝝉_{σ σ^{'}},

10-

b_{i α}^{†} (b_{i α})

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1003.5360

Formulas:

1-

t \to b + W^{+}

2-

{\bar{B}}_{c} (Υ)

3-

t \to b \bar{c} (\bar{b}) + c (b) + W^{+}

4-

p_{4} = p_{\bar{c}}

5-

p_{6} = p_{W^{+}}

6-

p_{0} = p_{3} + p_{4}

7-

p_{3} = \frac{m_{b}}{m_{c}} p_{4}

8-

t (p_{1}) \to {\bar{B}}_{c} / {\bar{B}}_{c}^{*} (p_{0}) + c (p_{5}) + W^{+} (p_{6}),

9-

v (p_{4}) \bar{u} (p_{3})

10-

\frac{1}{2 \sqrt{2}} i γ_{5} (p_{0} + m_{b} + m_{c}) \times (\frac{1}{\sqrt{\frac{m_{b} + m_{c}}{2}}} ψ_{{\bar{B}}_{c}} (0)) \otimes (\frac{𝟏_{c}}{\sqrt{N_{c}}})

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: hep-ph

Result: correct

Paper: https://arxiv.org/abs/quant-ph/9707010

Formulas:

1-

| ψ_{0} ⟩ \in ℋ

2-

{| ψ_{g} ⟩}

3-

| ψ_{g} ⟩ = T (g) | ψ_{0} ⟩, g \in G .

4-

T (h) | ψ_{0} ⟩ = e^{i ϕ (h)} | ψ_{0} ⟩, | e^{i ϕ (h)} | = 1, h \in H .

5-

g = Ω h, g \in G, h \in H, Ω \in X .

6-

| ψ_{g} ⟩ = e^{i δ} | ψ_{g^{'}} ⟩

7-

δ = ϕ (h) - ϕ (h^{'})

8-

| Ω ⟩ \equiv | ψ_{Ω} ⟩

9-

Ω = Ω (g)

10-

\int_{X} 𝑑 μ (Ω) | Ω ⟩ ⟨ Ω | = I,

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: quant-ph

Result: correct

Paper: https://arxiv.org/abs/2012.00553

Formulas:

1-

x (n; t)

2-

a (t) = t - c

3-

\tilde{a} (t) = t - \tilde{c}

4-

\tilde{a} (t) = a (t) + η

5-

η = c - \tilde{c}

6-

𝐟 (x (n; t)) \in ℝ^{p}

7-

\hat{a} (t) = G [\tilde{a} (t), {𝐟 (x (n; t_{k}))}_{k = 1}^{L}]

8-

\hat{a} (t)

9-

k = 1, \dots, L

10-

\tilde{a} (t)

Formulas (html):

Correct Categorie: eess

Guessed Categorie: nlin

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/0105433

Formulas:

1-

- {(ρ^{'})}^{2} / ρ

2-

n (x) = (2 N + 1) / 2 L - \sin [2 π (2 N + 1) x / L] / [2 L \sin (2 π x / L)]

3-

n_{a p p r o x} (x) = (2 N / L) {[3 \coth^{2} (k_{F} x) - 1]}^{- 1}

4-

k_{F} = 2 π N / L

5-

2 i \partial_{τ} f = - \partial_{y}^{2} f + [{| f |}^{4} + w^{2} y^{2}] f

6-

f = A e^{i θ}

7-

A = ρ {(τ)}^{- 1 / 2} h (y / ρ (τ)), θ = θ_{0} (τ) + \frac{1}{2} \frac{d \ln ρ}{d τ} y^{2},

8-

\frac{d^{2} ρ}{d τ^{2}}

9-

- w^{2} ρ + \frac{γ}{ρ^{3}}

10-

\frac{d^{2} h}{d v^{2}}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/cond-mat/0105307

Formulas:

1-

F (r) = 4 π σ (r) r^{2} - \frac{4 π}{3} r^{3} T {\tilde{s}}_{c}

2-

σ (r) \equiv σ_{0} a^{1 / 2} r^{3 / 2}

3-

N \equiv \frac{4 π}{3} {(r / a)}^{3}

4-

F (N) = γ \sqrt{N} - T s_{c} N

5-

γ \equiv 2 \sqrt{3 π} σ_{0} a^{2}

6-

s_{c} (T)

7-

γ = \frac{3}{2} \sqrt{3 π} k_{B} T \ln (α_{L} a^{2} / π e)

8-

α_{L} a^{2} \sim 10^{2}

9-

F^{‡} \equiv γ^{2} / 4 T s_{c}

10-

N_{0} = {(γ / 2 T s_{c})}^{2}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0503368

Formulas:

1-

ρ (r) = \frac{1}{r}

2-

r \geq 20 U A

3-

a = 8.74 \pm 1.33 \times 10^{- 8} \frac{cm}{s^{2}},

4-

Λ = 3 Ω_{D E} {(\frac{H_{0}}{c})}^{2}

5-

Ω_{D E} = 0.7

6-

Λ = 1.2 h \times 10^{- 56} {cm}^{- 2}

7-

a_{Λ} = c^{2} \sqrt{Λ} = 9.79 \times 10^{- 8} \frac{cm}{s^{2}}

8-

ρ (r) \propto \frac{1}{r}

9-

ρ (\vec{r})

10-

\vec{\nabla} \cdot \vec{a} = - 4 π G ρ (\vec{r}),

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1507.00147

Formulas:

1-

𝒯_{n, r} (u, v, w)

2-

𝒯_{n, r} (u, v, w),

3-

r = 0, 1, \dots, n;

4-

T_{n, r} (u, v, w)

5-

T_{n, r} (u, v, w)

6-

T_{n, s} (u, v, w)

7-

W (u, v, w) = 1

8-

P_{n, r} (u, v, w)

9-

P_{n, s} (u, v, w),

10-

𝒯_{n, r} (u, v, w)

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/quant-ph/0303092

Formulas:

1-

(A_{1} e^{i φ_{1}}, A_{2} e^{i φ_{2}}, \dots, A_{N} e^{i φ_{N}})

2-

(A_{1}, A_{2}, \dots, A_{N})

3-

(e^{i φ_{1}}, e^{i φ_{2}}, \dots, e^{i φ_{N}})

4-

A \leftrightarrow e^{i φ}

5-

𝐉 = \sum_{k = 1}^{P} {\vec{v}}^{k} \otimes {\vec{v}}^{k}

6-

{\vec{v}}^{o u t p u t} = 𝐉 {\vec{v}}^{i n p u t}

7-

k = 1, \dots, P

8-

{\vec{v}}^{k} = ψ^{k}

9-

{\vec{v}}^{k} = A^{k}

10-

j, h = 1, \dots, N

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: quant-ph

Result: correct

Paper: https://arxiv.org/abs/1108.1124

Formulas:

1-

π = (x_{1}, x_{2}, \dots, x_{n})

2-

x_{i} ≺ x_{i + 1}

3-

(x_{1}, x_{2}, \dots, x_{i - 1}, x_{i + 1}, x_{i}, x_{i + 2}, \dots, x_{n})

4-

π = (x_{1}, x_{2}, \dots, x_{n})

5-

(x_{1}, x_{2}, \dots, x_{i - 1}, x_{i + 1}, x_{i}, x_{i + 2}, \dots, x_{n})

6-

x_{i} ≺ x_{i + 1}

7-

x = z_{1}, z_{2}, \dots z_{k} = y

8-

z_{α} ∥ z_{α + 1}

9-

α \in [k - 1]

10-

x ≺ z \Rightarrow y ≺ z

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

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