Run 11332263

Paper: https://arxiv.org/abs/1912.03455

Formulas:

1-

𝐏^{i} = [P_{x}^{i}, P_{y}^{i}, P_{z}^{i}]

2-

𝐃 \in ℝ^{| 𝐏 | \times 9}

3-

(𝐃_{1}, \dots, 𝐃_{N})

4-

(r, θ_{1}, \dots, θ_{m_{1}})

5-

𝐔 [0.6, 1.3]

6-

𝐔 [0, π / 2]

7-

(a_{1}, a_{2}, \dots, a_{m})

8-

\sum_{i = 1}^{m} a_{i} 𝐃_{i}

9-

[- 15^{^{\circ}}, + 15^{^{\circ}}]

10-

{𝐁_{1}, 𝐁_{2}, \dots, 𝐁_{M}}

Formulas (html):

Correct Categorie: cs

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1401.3313

Formulas:

1-

𝒢_{d} (n, r)

2-

{[0, 1]}^{d}

3-

r^{3 d - 1} > c_{d} \frac{\log n}{n}

4-

O (1 / r^{2})

5-

c (G) \leq 3

6-

c (n) = O (\sqrt{n})

7-

O (n \log \log n / \log n)

8-

c (n) = O (n / \log n)

9-

n 2^{- (1 + o (1)) \sqrt{\log_{2} n}}

10-

n^{1 - o (1)}

Formulas (html):

Correct Categorie: math

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/9803233

Formulas:

1-

{(m - M)}_{o}

2-

{(m - M)}_{o}

3-

{(m - M)}_{o}

4-

E (B - V)

5-

{(m - M)}_{o}

6-

E (B - V)

7-

E (B - V)

8-

E (B - V)

9-

E (B - V)

10-

E {(V - I)}_{C o u s i n s}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/physics/0407129

Formulas:

1-

\overset{\leftrightarrow}{L} = (\begin{matrix} L_{x} & 0 & 0 \\ 0 & L_{y} & 0 \\ 0 & 0 & L_{z} \end{matrix}) .

2-

L_{x} + L_{y} + L_{z} = 1

3-

{\overset{\leftrightarrow}{σ}}_{1} = (\begin{matrix} σ_{11} & 0 & 0 \\ 0 & σ_{22} & 0 \\ 0 & 0 & σ_{33} \end{matrix}) .

4-

{\tilde{\overset{\leftrightarrow}{σ}}}_{1} = \overset{\leftrightarrow}{ν} {\overset{\leftrightarrow}{σ}}_{1} {\overset{\leftrightarrow}{ν}}^{T}

5-

p ⟨ 𝐄_{1} ⟩ + (1 - p) ⟨ 𝐄_{L} ⟩ = ⟨ 𝐄 ⟩,

6-

p ⟨ 𝐄_{1} ⟩ + (1 - p) ⟨ 𝐄_{L} ⟩ = 𝐄_{0},

7-

\nabla^{2} Φ_{1} = 0

8-

⟨ 𝐄_{1} ⟩ = ⟨ \tilde{\overset{\leftrightarrow}{ρ}} ⟩ ⟨ 𝐄_{L} ⟩

9-

⟨ \tilde{\overset{\leftrightarrow}{ρ}} ⟩ = ⟨ \overset{\leftrightarrow}{ν} \overset{\leftrightarrow}{ρ} {\overset{\leftrightarrow}{ν}}^{T} ⟩ .

10-

\overset{\leftrightarrow}{ρ} = (\begin{matrix} \frac{σ_{2}}{L_{x} σ_{11} + (1 - L_{x}) σ_{2}} & 0 & 0 \\ 0 & \frac{σ_{2}}{L_{y} σ_{22} + (1 - L_{y}) σ_{2}} & 0 \\ 0 & 0 & \frac{σ_{2}}{L_{z} σ_{33} + (1 - L_{z}) σ_{2}} \end{matrix}) .

Formulas (html):

Correct Categorie: physics

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1702.06349

Formulas:

1-

(\hat{H} (𝐫, t) - ı \frac{\partial}{\partial t}) ψ (𝐫, t) = 0,

2-

ψ (𝐫, t) = e^{- ı ϵ_{α} t} ϕ (𝐫, t)

3-

ϕ (𝐫, t)

4-

{\hat{H}}^{F} \equiv \hat{H} - ı \frac{\partial}{\partial t}

5-

{\hat{H}}^{F} ϕ_{α} (𝐫, t) = ϵ_{α} ϕ_{α} (𝐫, t) .

6-

\hat{H} (𝐫, t)

7-

\hat{H} (𝐫, t) = {\hat{H}}_{0} (𝐫) + \hat{V} (𝐫, t)

8-

H_{0} (𝐫)

9-

V (𝐫, t)

10-

ϕ_{α} (𝐫, t)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/nucl-ex/0510037

Formulas:

1-

𝐪 = \frac{(𝐩_{𝟏} - 𝐩_{𝟐})}{2}

2-

C (𝐪) = \sum_{l} \sum_{α_{1} \dots α_{l}} C_{α_{1} \dots α_{l}}^{l} (q) A_{α_{1} \dots α_{l}}^{l} (Ω_{𝐪})

3-

l = 0, 1, 2, \dots

4-

α_{i} = x, y or z

5-

A_{α_{1} \dots α_{l}}^{l} (Ω_{𝐪})

6-

C_{α_{1} \dots α_{l}}^{l} (q)

7-

C_{α_{1} \dots α_{l}}^{l} (q) = \frac{(2 l + 1)!!}{l!} \int \frac{d Ω_{𝐪}}{4 π} A_{α_{1} \dots α_{l}}^{l} (Ω_{𝐪}) C (𝐪)

8-

0.20 < k_{T} < 0.36

9-

k_{T} = \frac{(𝐩_{𝟏 𝐓} + 𝐩_{𝟐 𝐓})}{2}

10-

0.20 < k_{T} < 0.36

Formulas (html):

Correct Categorie: nucl-ex

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1411.6480

Formulas:

1-

715 \pm 100 R_{☉}

2-

(5.25 \pm 0.6) \times 10^{50}

3-

13.1 \pm 0.7 M_{☉}

4-

0.012 \pm 0.002 M_{☉}

5-

15 \pm 1 M_{☉}

6-

U B V R I J H K

7-

E (B - V) = {0.037}_{+ 0.008}^{- 0.006}

8-

m - M = 29.96 \pm 0.15

9-

χ = ρ_{c} / ρ

10-

f = μ χ^{- 1}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/2009.11358

Formulas:

1-

M_{BH} = {2.34}_{- 0.43}^{+ 0.43} \times 10^{7}

2-

M_{BH} = 10^{6} - 10^{10}

3-

26 \overset{'}{.} 5 \times 26 \overset{'}{.} 5

4-

4' \times 4'

5-

F_{5007} = (10.05 \pm 0.68) \times 10^{- 13}

6-

T_{m e d}

7-

⟨ σ_{F} / F ⟩

8-

F_{v a r}

9-

R_{m a x}

10-

5100 \times (1 + z)

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1906.09577

Formulas:

1-

q_{c} = 0.0102 Å^{- 1}

2-

Δ ρ = q_{c}^{2} / 16 π = 2.07 \times 10^{10} {cm}^{- 2}

3-

q_{c} = 1.03 \times 0.0102 Å^{- 1}

4-

Δ ρ = 2.20 \times 10^{10} {cm}^{- 2}

5-

{(σ_{q} / q)}^{2} ≃ {(σ_{θ} / θ)}^{2} + {(σ_{λ} / λ)}^{2}

6-

σ_{θ} / θ = σ_{λ} / λ

7-

x (4) - x (3)

8-

x (3) - x (2)

9-

x (2) - x (1)

10-

φ_{o} (i)

Formulas (html):

Correct Categorie: physics

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/gr-qc/0607113

Formulas:

1-

g^{μ ν} \nabla_{μ} \nabla_{ν} ϕ - \frac{m^{2} c^{2}}{ℏ^{2}} ϕ - ζ ℛ ϕ - \frac{λ}{ℏ^{2} c^{2}} {| ϕ |}^{2} ϕ = 0

2-

\nabla_{μ} V^{ν} \equiv \partial_{μ} V^{ν} + Γ_{μ α}^{ν} V^{α} - i \frac{q_{ϕ}}{ℏ c} A_{μ} V^{ν}

3-

V_{μ} = \nabla_{μ} ϕ \equiv \partial_{μ} ϕ

4-

g_{μ ν} (x)

5-

- [1 - 2 \frac{U}{c^{2}} + 2 β {(\frac{U}{c^{2}})}^{2}]

6-

[1 + 2 γ \frac{U}{c^{2}}] δ_{i j}

7-

g_{0 i} = 0

8-

i, j = 1, 2, 3

9-

U (\vec{x}, t) = G_{N} \int d^{3} {\vec{x}}^{'} \frac{ρ_{m} ({\vec{x}}^{'}, t)}{| \vec{x} - {\vec{x}}^{'} |}

10-

ρ_{m} ({\vec{x}}^{'}, t)

Formulas (html):

Correct Categorie: gr-qc

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/0812.4464

Formulas:

1-

𝒓 = 𝜶^{'} / ϵ

2-

α_{I P} (0) = 1 + ϵ_{I P}

3-

α_{I P} (t) = α_{I P} (0) + α_{I P}^{'} t

4-

α_{I P} (0) \approx 1.08

5-

α_{I P}^{'} \approx 0.25

6-

σ^{t o t} (s) = β_{I P p p}^{2} (0) {(\frac{s}{s_{\circ}})}^{α_{I P} (0) - 1} \Rightarrow σ_{\circ} {(\frac{s}{s_{\circ}})}^{ϵ_{I P}},

7-

\frac{d σ^{e l} (s, t)}{d t} = \frac{β_{I P p p}^{4} (t)}{16 π} {(\frac{s}{s_{\circ}})}^{2 [α_{I P} (t) - 1]},

8-

\frac{d^{2} σ_{s d} (s, ξ, t)}{d ξ d t} = \underset{f_{I P / p} (ξ, t)}{\underset{⏟}{\frac{β_{I P p p}^{2} (t)}{16 π} ξ^{1 - 2 α_{I P} (t)}}} \underset{σ^{I P p} (s^{'}, t)}{\underset{⏟}{β_{I P p p} (0) g (t) {(\frac{s^{'}}{s_{\circ}})}^{α_{I P} (0) - 1}}} .

9-

σ^{I P p} (s^{'}, t)

10-

f_{I P / p} (ξ, t)

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/9701064

Formulas:

1-

\log \dot{M} - \log Σ

2-

\log \dot{M} - \log Σ

3-

v_{r} = v_{r} (r, t)

4-

v_{φ} = v_{φ} (r, t)

5-

Φ = - \frac{G M}{\sqrt{r^{2} + z^{2}} - r_{_{G}}} .

6-

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

7-

\frac{D Σ}{D t} = - \frac{Σ}{r} \frac{\partial}{\partial r} (r v_{r})

8-

\frac{D}{D t} = \frac{\partial}{\partial t} + v_{r} \frac{\partial}{\partial r},

9-

Σ = Σ (r, t)

10-

Σ = 2 \int_{0}^{H} ρ 𝑑 z

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/0912.5293

Formulas:

1-

| ψ (0) ⟩

2-

{| ⟨ ψ (0) | ψ (T_{rev}) ⟩ |}^{2}

3-

H = ℏ (χ a^{†} {}^{2}a^{2} + χ^{'} a^{†} {}^{3}a^{3}),

4-

[a, a^{†}] = 1

5-

a^{†} {}^{2}a^{2} = a^{†} a (a^{†} a - 1)

6-

a^{†} {}^{3}a^{3} = a^{†} a (a^{†} a - 1) (a^{†} a - 2)

7-

t = π / (k χ)

8-

U (t) = \exp (- i H t / ℏ)

9-

\exp [- i π n (n - 1) / k]

10-

U (π / k χ)

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: quant-ph

Result: correct

Paper: https://arxiv.org/abs/1401.7764

Formulas:

1-

x^{2} y^{''} (x) + x y^{'} (x) - (x^{2} + ν^{2}) y (x) = 0 .

2-

I_{ν} (x) = \sum_{n \geq 0} \frac{{(\frac{x}{2})}^{2 n + ν}}{n! Γ (ν + n + 1)} = \frac{{(\frac{x}{2})}^{ν}}{Γ (ν + 1)} \cdot {}_{0}F_{1} (ν + 1, \frac{x^{2}}{4})

3-

ν \neq - 1, - 2, \dots

4-

x \mapsto {}_{0}F_{1} (ν + 1, \frac{x^{2}}{4})

5-

ℐ_{ν} : ℝ \to [1, \infty),

6-

ℐ_{ν} (x) = {}_{0}F_{1} (ν + 1, \frac{x^{2}}{4}) = 2^{ν} Γ (ν + 1) x^{- ν} I_{ν} (x) = \sum_{n \geq 0} \frac{{(\frac{1}{4})}^{n}}{{(ν + 1)}_{n} n!} \cdot x^{2 n},

7-

ν \neq - 1, - 2, \dots,

8-

{(a)}_{n} = a (a + 1) (a + 2) \dots (a + n - 1),

9-

{(a)}_{0} = 1

10-

ν > - \frac{1}{2} .

Formulas (html):

Correct Categorie: math

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/physics/0509095

Formulas:

1-

[1, N - 1]

2-

a_{v i} (t + 1) = θ (q_{v} + α a_{v i} (t) + β \sum_{j \in N_{v}, j \neq i} (2 a_{i j} (t) - 1) - c_{i})

3-

θ (x_{i})

4-

2 a_{i j} - 1

5-

⟨ a ⟩ (t) = \frac{2}{N (N - 1)} \sum_{i < j} a_{i j} (t)

6-

c_{i} \equiv c = 0.25

7-

a_{i j} = 0

8-

\frac{d a_{k} (t)}{d t} = W_{0 \to 1} - W_{1 \to 0}

9-

a_{k} (t)

10-

⟨ a ⟩ (t)

Formulas (html):

Correct Categorie: physics

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1609.07314

Formulas:

1-

C_{a b} (j) = \sum_{i = 1}^{N - j} a (i) b (i + j),

2-

C_{c d} (j) = \sum_{i = 1}^{N - j} c (i) d (i + j),

3-

C_{a b c d} (m) = \sum_{j = - M}^{M} C_{a b} (j) C_{c d} (j + m),

4-

\hat{f} (t) = f (t) + i ℋ [f (t)],

5-

\hat{f} (t)

6-

Δ T = T / K

7-

{}_{k}{\hat{C}}_{a b} (j) = \sum_{i = k Δ T + 1}^{(k + 1) Δ T} \hat{a} (i) {\hat{b}}^{*} (i + j)

8-

{}_{k}{\hat{C}}_{a c} (j) = \sum_{i = k Δ T + 1}^{(k + 1) Δ T} \hat{a} (i) {\hat{c}}^{*} (i + j),

9-

{\hat{C}}_{a b c} (m) = \sum_{k = 0}^{K - 1} {}_{k}{\hat{C}}_{a b} (i) {}_{k}{\hat{C}}_{a c}^{*} (j + m),

10-

{\hat{C}}_{a b c}

Formulas (html):

Correct Categorie: physics

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/9910065

Formulas:

1-

𝐇 = 𝐇_{a} - N 𝐌 .

2-

M (H_{a})

3-

χ^{'} (T)

4-

χ^{''} (T)

5-

χ^{'} (T)

6-

M (H_{a})

7-

𝐇_{𝐚} = H_{a} \hat{𝐳}

8-

(ρ, φ, z)

9-

i = 2 n + m - 1

10-

Φ_{i}^{a} = μ_{0} π ρ_{i}^{2} H_{a},

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1010.6077

Formulas:

1-

= (π / 4)

2-

[Δ Ω / (4 π)] = 1 - \cos θ_{obs}

3-

[Δ Ω / (4 π)] = (a / c)

4-

3 \times 10^{22} {cm}^{- 2}

5-

10^{25} {cm}^{- 2}

6-

D [(a / c), N_{H}, E] d E

7-

F_{absorbed} (E)

8-

F_{C} (E)

9-

F_{L} (E)

10-

D [(a / c), N_{H}, E]

Formulas (html):

<math><mrow id="S2.p1.4.m4.1.1" xref="S2.p1.4.m4.1.1.cmml"><mi id="S2.p1.4.m4.1.1.3" xref="S2.p1.4.m4.1.1.3.cmml"/><mo id="S2.p1.4.m4.1.1.2" xref="S2.p1.4.m4.1.1.2.cmml">=</mo><mrow id="S2.p1.4.m4.1.1.1.1" xref="S2.p1.4.m4.1.1.1.1.1.cmml"><mo stretchy="false" id="S2.p1.4.m4.1.1.1.1.2" xref="S2.p1.4.m4.1.1.1.1.1.cmml">(</mo><mrow id="S2.p1.4.m4.1.1.1.1.1" xref="S2.p1.4.m4.1.1.1.1.1.cmml"><mi id="S2.p1.4.m4.1.1.1.1.1.2" xref="S2.p1.4.m4.1.1.1.1.1.2.cmml">π</mi><mo id="S2.p1.4.m4.1.1.1.1.1.1" xref="S2.p1.4.m4.1.1.1.1.1.1.cmml">/</mo><mn id="S2.p1.4.m4.1.1.1.1.1.3" xref="S2.p1.4.m4.1.1.1.1.1.3.cmml">4</mn></mrow><mo stretchy="false" id="S2.p1.4.m4.1.1.1.1.3" xref="S2.p1.4.m4.1.1.1.1.1.cmml">)</mo></mrow></mrow></math>, <math><mrow id="S2.p2.2.m2.1.1" xref="S2.p2.2.m2.1.1.cmml"><mrow id="S2.p2.2.m2.1.1.1.1" xref="S2.p2.2.m2.1.1.1.2.cmml"><mo stretchy="false" id="S2.p2.2.m2.1.1.1.1.2" xref="S2.p2.2.m2.1.1.1.2.1.cmml">[</mo><mrow id="S2.p2.2.m2.1.1.1.1.1" xref="S2.p2.2.m2.1.1.1.1.1.cmml"><mrow id="S2.p2.2.m2.1.1.1.1.1.3" xref="S2.p2.2.m2.1.1.1.1.1.3.cmml"><mi mathvariant="normal" id="S2.p2.2.m2.1.1.1.1.1.3.2" xref="S2.p2.2.m2.1.1.1.1.1.3.2.cmml">Δ</mi><mo id="S2.p2.2.m2.1.1.1.1.1.3.1" xref="S2.p2.2.m2.1.1.1.1.1.3.1.cmml">⁢</mo><mi mathvariant="normal" id="S2.p2.2.m2.1.1.1.1.1.3.3" xref="S2.p2.2.m2.1.1.1.1.1.3.3.cmml">Ω</mi></mrow><mo id="S2.p2.2.m2.1.1.1.1.1.2" xref="S2.p2.2.m2.1.1.1.1.1.2.cmml">/</mo><mrow id="S2.p2.2.m2.1.1.1.1.1.1.1" xref="S2.p2.2.m2.1.1.1.1.1.1.1.1.cmml"><mo stretchy="false" id="S2.p2.2.m2.1.1.1.1.1.1.1.2" xref="S2.p2.2.m2.1.1.1.1.1.1.1.1.cmml">(</mo><mrow id="S2.p2.2.m2.1.1.1.1.1.1.1.1" xref="S2.p2.2.m2.1.1.1.1.1.1.1.1.cmml"><mn id="S2.p2.2.m2.1.1.1.1.1.1.1.1.2" xref="S2.p2.2.m2.1.1.1.1.1.1.1.1.2.cmml">4</mn><mo id="S2.p2.2.m2.1.1.1.1.1.1.1.1.1" xref="S2.p2.2.m2.1.1.1.1.1.1.1.1.1.cmml">⁢</mo><mi id="S2.p2.2.m2.1.1.1.1.1.1.1.1.3" xref="S2.p2.2.m2.1.1.1.1.1.1.1.1.3.cmml">π</mi></mrow><mo stretchy="false" id="S2.p2.2.m2.1.1.1.1.1.1.1.3" xref="S2.p2.2.m2.1.1.1.1.1.1.1.1.cmml">)</mo></mrow></mrow><mo stretchy="false" id="S2.p2.2.m2.1.1.1.1.3" xref="S2.p2.2.m2.1.1.1.2.1.cmml">]</mo></mrow><mo id="S2.p2.2.m2.1.1.2" xref="S2.p2.2.m2.1.1.2.cmml">=</mo><mrow id="S2.p2.2.m2.1.1.3" xref="S2.p2.2.m2.1.1.3.cmml"><mn id="S2.p2.2.m2.1.1.3.2" xref="S2.p2.2.m2.1.1.3.2.cmml">1</mn><mo id="S2.p2.2.m2.1.1.3.1" xref="S2.p2.2.m2.1.1.3.1.cmml">-</mo><mrow id="S2.p2.2.m2.1.1.3.3" xref="S2.p2.2.m2.1.1.3.3.cmml"><mi id="S2.p2.2.m2.1.1.3.3.1" xref="S2.p2.2.m2.1.1.3.3.1.cmml">cos</mi><mo id="S2.p2.2.m2.1.1.3.3a" xref="S2.p2.2.m2.1.1.3.3.cmml">⁡</mo><msub id="S2.p2.2.m2.1.1.3.3.2" xref="S2.p2.2.m2.1.1.3.3.2.cmml"><mi id="S2.p2.2.m2.1.1.3.3.2.2" xref="S2.p2.2.m2.1.1.3.3.2.2.cmml">θ</mi><mi id="S2.p2.2.m2.1.1.3.3.2.3" xref="S2.p2.2.m2.1.1.3.3.2.3.cmml">obs</mi></msub></mrow></mrow></mrow></math>, <math><mrow id="S2.p2.8.m8.2.2" xref="S2.p2.8.m8.2.2.cmml"><mrow id="S2.p2.8.m8.1.1.1.1" xref="S2.p2.8.m8.1.1.1.2.cmml"><mo stretchy="false" id="S2.p2.8.m8.1.1.1.1.2" xref="S2.p2.8.m8.1.1.1.2.1.cmml">[</mo><mrow id="S2.p2.8.m8.1.1.1.1.1" xref="S2.p2.8.m8.1.1.1.1.1.cmml"><mrow id="S2.p2.8.m8.1.1.1.1.1.3" xref="S2.p2.8.m8.1.1.1.1.1.3.cmml"><mi mathvariant="normal" id="S2.p2.8.m8.1.1.1.1.1.3.2" xref="S2.p2.8.m8.1.1.1.1.1.3.2.cmml">Δ</mi><mo id="S2.p2.8.m8.1.1.1.1.1.3.1" xref="S2.p2.8.m8.1.1.1.1.1.3.1.cmml">⁢</mo><mi mathvariant="normal" id="S2.p2.8.m8.1.1.1.1.1.3.3" xref="S2.p2.8.m8.1.1.1.1.1.3.3.cmml">Ω</mi></mrow><mo id="S2.p2.8.m8.1.1.1.1.1.2" xref="S2.p2.8.m8.1.1.1.1.1.2.cmml">/</mo><mrow id="S2.p2.8.m8.1.1.1.1.1.1.1" xref="S2.p2.8.m8.1.1.1.1.1.1.1.1.cmml"><mo stretchy="false" id="S2.p2.8.m8.1.1.1.1.1.1.1.2" xref="S2.p2.8.m8.1.1.1.1.1.1.1.1.cmml">(</mo><mrow id="S2.p2.8.m8.1.1.1.1.1.1.1.1" xref="S2.p2.8.m8.1.1.1.1.1.1.1.1.cmml"><mn id="S2.p2.8.m8.1.1.1.1.1.1.1.1.2" xref="S2.p2.8.m8.1.1.1.1.1.1.1.1.2.cmml">4</mn><mo id="S2.p2.8.m8.1.1.1.1.1.1.1.1.1" xref="S2.p2.8.m8.1.1.1.1.1.1.1.1.1.cmml">⁢</mo><mi id="S2.p2.8.m8.1.1.1.1.1.1.1.1.3" xref="S2.p2.8.m8.1.1.1.1.1.1.1.1.3.cmml">π</mi></mrow><mo stretchy="false" id="S2.p2.8.m8.1.1.1.1.1.1.1.3" xref="S2.p2.8.m8.1.1.1.1.1.1.1.1.cmml">)</mo></mrow></mrow><mo stretchy="false" id="S2.p2.8.m8.1.1.1.1.3" xref="S2.p2.8.m8.1.1.1.2.1.cmml">]</mo></mrow><mo id="S2.p2.8.m8.2.2.3" xref="S2.p2.8.m8.2.2.3.cmml">=</mo><mrow id="S2.p2.8.m8.2.2.2.1" xref="S2.p2.8.m8.2.2.2.1.1.cmml"><mo stretchy="false" id="S2.p2.8.m8.2.2.2.1.2" xref="S2.p2.8.m8.2.2.2.1.1.cmml">(</mo><mrow id="S2.p2.8.m8.2.2.2.1.1" xref="S2.p2.8.m8.2.2.2.1.1.cmml"><mi id="S2.p2.8.m8.2.2.2.1.1.2" xref="S2.p2.8.m8.2.2.2.1.1.2.cmml">a</mi><mo id="S2.p2.8.m8.2.2.2.1.1.1" xref="S2.p2.8.m8.2.2.2.1.1.1.cmml">/</mo><mi id="S2.p2.8.m8.2.2.2.1.1.3" xref="S2.p2.8.m8.2.2.2.1.1.3.cmml">c</mi></mrow><mo stretchy="false" id="S2.p2.8.m8.2.2.2.1.3" xref="S2.p2.8.m8.2.2.2.1.1.cmml">)</mo></mrow></mrow></math>, <math><mrow id="S2.p2.14.m14.1.1" xref="S2.p2.14.m14.1.1.cmml"><mrow id="S2.p2.14.m14.1.1.2" xref="S2.p2.14.m14.1.1.2.cmml"><mn id="S2.p2.14.m14.1.1.2.2" xref="S2.p2.14.m14.1.1.2.2.cmml">3</mn><mo id="S2.p2.14.m14.1.1.2.1" xref="S2.p2.14.m14.1.1.2.1.cmml">×</mo><mpadded width="+5pt" id="S2.p2.14.m14.1.1.2.3" xref="S2.p2.14.m14.1.1.2.3.cmml"><msup id="S2.p2.14.m14.1.1.2.3a" xref="S2.p2.14.m14.1.1.2.3.cmml"><mn id="S2.p2.14.m14.1.1.2.3.2" xref="S2.p2.14.m14.1.1.2.3.2.cmml">10</mn><mn id="S2.p2.14.m14.1.1.2.3.3" xref="S2.p2.14.m14.1.1.2.3.3.cmml">22</mn></msup></mpadded></mrow><mo id="S2.p2.14.m14.1.1.1" xref="S2.p2.14.m14.1.1.1.cmml">⁢</mo><msup id="S2.p2.14.m14.1.1.3" xref="S2.p2.14.m14.1.1.3.cmml"><mi id="S2.p2.14.m14.1.1.3.2" xref="S2.p2.14.m14.1.1.3.2.cmml">cm</mi><mrow id="S2.p2.14.m14.1.1.3.3" xref="S2.p2.14.m14.1.1.3.3.cmml"><mo id="S2.p2.14.m14.1.1.3.3.1" xref="S2.p2.14.m14.1.1.3.3.1.cmml">-</mo><mn id="S2.p2.14.m14.1.1.3.3.2" xref="S2.p2.14.m14.1.1.3.3.2.cmml">2</mn></mrow></msup></mrow></math>, <math><mrow id="S2.p2.15.m15.1.1" xref="S2.p2.15.m15.1.1.cmml"><mpadded width="+5pt" id="S2.p2.15.m15.1.1.2" xref="S2.p2.15.m15.1.1.2.cmml"><msup id="S2.p2.15.m15.1.1.2a" xref="S2.p2.15.m15.1.1.2.cmml"><mn id="S2.p2.15.m15.1.1.2.2" xref="S2.p2.15.m15.1.1.2.2.cmml">10</mn><mn id="S2.p2.15.m15.1.1.2.3" xref="S2.p2.15.m15.1.1.2.3.cmml">25</mn></msup></mpadded><mo id="S2.p2.15.m15.1.1.1" xref="S2.p2.15.m15.1.1.1.cmml">⁢</mo><msup id="S2.p2.15.m15.1.1.3" xref="S2.p2.15.m15.1.1.3.cmml"><mi id="S2.p2.15.m15.1.1.3.2" xref="S2.p2.15.m15.1.1.3.2.cmml">cm</mi><mrow id="S2.p2.15.m15.1.1.3.3" xref="S2.p2.15.m15.1.1.3.3.cmml"><mo id="S2.p2.15.m15.1.1.3.3.1" xref="S2.p2.15.m15.1.1.3.3.1.cmml">-</mo><mn id="S2.p2.15.m15.1.1.3.3.2" xref="S2.p2.15.m15.1.1.3.3.2.cmml">2</mn></mrow></msup></mrow></math>, <math><mrow id="S3.p1.3.m3.3.3" xref="S3.p1.3.m3.3.3.cmml"><mi id="S3.p1.3.m3.3.3.4" xref="S3.p1.3.m3.3.3.4.cmml">D</mi><mo id="S3.p1.3.m3.3.3.3" xref="S3.p1.3.m3.3.3.3.cmml">⁢</mo><mrow id="S3.p1.3.m3.3.3.2.2" xref="S3.p1.3.m3.3.3.2.3.cmml"><mo stretchy="false" id="S3.p1.3.m3.3.3.2.2.3" xref="S3.p1.3.m3.3.3.2.3.cmml">[</mo><mrow id="S3.p1.3.m3.2.2.1.1.1.1" xref="S3.p1.3.m3.2.2.1.1.1.1.1.cmml"><mo stretchy="false" id="S3.p1.3.m3.2.2.1.1.1.1.2" xref="S3.p1.3.m3.2.2.1.1.1.1.1.cmml">(</mo><mrow id="S3.p1.3.m3.2.2.1.1.1.1.1" xref="S3.p1.3.m3.2.2.1.1.1.1.1.cmml"><mi id="S3.p1.3.m3.2.2.1.1.1.1.1.2" xref="S3.p1.3.m3.2.2.1.1.1.1.1.2.cmml">a</mi><mo id="S3.p1.3.m3.2.2.1.1.1.1.1.1" xref="S3.p1.3.m3.2.2.1.1.1.1.1.1.cmml">/</mo><mi id="S3.p1.3.m3.2.2.1.1.1.1.1.3" xref="S3.p1.3.m3.2.2.1.1.1.1.1.3.cmml">c</mi></mrow><mo stretchy="false" id="S3.p1.3.m3.2.2.1.1.1.1.3" xref="S3.p1.3.m3.2.2.1.1.1.1.1.cmml">)</mo></mrow><mo id="S3.p1.3.m3.3.3.2.2.4" xref="S3.p1.3.m3.3.3.2.3.cmml">,</mo><msub id="S3.p1.3.m3.3.3.2.2.2" xref="S3.p1.3.m3.3.3.2.2.2.cmml"><mi id="S3.p1.3.m3.3.3.2.2.2.2" xref="S3.p1.3.m3.3.3.2.2.2.2.cmml">N</mi><mi id="S3.p1.3.m3.3.3.2.2.2.3" xref="S3.p1.3.m3.3.3.2.2.2.3.cmml">H</mi></msub><mo id="S3.p1.3.m3.3.3.2.2.5" xref="S3.p1.3.m3.3.3.2.3.cmml">,</mo><mi id="S3.p1.3.m3.1.1" xref="S3.p1.3.m3.1.1.cmml">E</mi><mo stretchy="false" id="S3.p1.3.m3.3.3.2.2.6" xref="S3.p1.3.m3.3.3.2.3.cmml">]</mo></mrow><mo id="S3.p1.3.m3.3.3.3a" xref="S3.p1.3.m3.3.3.3.cmml">⁢</mo><mi id="S3.p1.3.m3.3.3.5" xref="S3.p1.3.m3.3.3.5.cmml">d</mi><mo id="S3.p1.3.m3.3.3.3b" xref="S3.p1.3.m3.3.3.3.cmml">⁢</mo><mi id="S3.p1.3.m3.3.3.6" xref="S3.p1.3.m3.3.3.6.cmml">E</mi></mrow></math>, <math><mrow id="S3.p1.4.m4.1.2" xref="S3.p1.4.m4.1.2.cmml"><msub id="S3.p1.4.m4.1.2.2" xref="S3.p1.4.m4.1.2.2.cmml"><mi id="S3.p1.4.m4.1.2.2.2" xref="S3.p1.4.m4.1.2.2.2.cmml">F</mi><mi id="S3.p1.4.m4.1.2.2.3" xref="S3.p1.4.m4.1.2.2.3.cmml">absorbed</mi></msub><mo id="S3.p1.4.m4.1.2.1" xref="S3.p1.4.m4.1.2.1.cmml">⁢</mo><mrow id="S3.p1.4.m4.1.2.3.2" xref="S3.p1.4.m4.1.2.cmml"><mo stretchy="false" id="S3.p1.4.m4.1.2.3.2.1" xref="S3.p1.4.m4.1.2.cmml">(</mo><mi id="S3.p1.4.m4.1.1" xref="S3.p1.4.m4.1.1.cmml">E</mi><mo stretchy="false" id="S3.p1.4.m4.1.2.3.2.2" xref="S3.p1.4.m4.1.2.cmml">)</mo></mrow></mrow></math>, <math><mrow id="S3.p1.5.m5.1.2" xref="S3.p1.5.m5.1.2.cmml"><msub id="S3.p1.5.m5.1.2.2" xref="S3.p1.5.m5.1.2.2.cmml"><mi id="S3.p1.5.m5.1.2.2.2" xref="S3.p1.5.m5.1.2.2.2.cmml">F</mi><mi mathvariant="normal" id="S3.p1.5.m5.1.2.2.3" xref="S3.p1.5.m5.1.2.2.3.cmml">C</mi></msub><mo id="S3.p1.5.m5.1.2.1" xref="S3.p1.5.m5.1.2.1.cmml">⁢</mo><mrow id="S3.p1.5.m5.1.2.3.2" xref="S3.p1.5.m5.1.2.cmml"><mo stretchy="false" id="S3.p1.5.m5.1.2.3.2.1" xref="S3.p1.5.m5.1.2.cmml">(</mo><mi id="S3.p1.5.m5.1.1" xref="S3.p1.5.m5.1.1.cmml">E</mi><mo stretchy="false" id="S3.p1.5.m5.1.2.3.2.2" xref="S3.p1.5.m5.1.2.cmml">)</mo></mrow></mrow></math>, <math><mrow id="S3.p1.12.m12.1.2" xref="S3.p1.12.m12.1.2.cmml"><msub id="S3.p1.12.m12.1.2.2" xref="S3.p1.12.m12.1.2.2.cmml"><mi id="S3.p1.12.m12.1.2.2.2" xref="S3.p1.12.m12.1.2.2.2.cmml">F</mi><mi id="S3.p1.12.m12.1.2.2.3" xref="S3.p1.12.m12.1.2.2.3.cmml">L</mi></msub><mo id="S3.p1.12.m12.1.2.1" xref="S3.p1.12.m12.1.2.1.cmml">⁢</mo><mrow id="S3.p1.12.m12.1.2.3.2" xref="S3.p1.12.m12.1.2.cmml"><mo stretchy="false" id="S3.p1.12.m12.1.2.3.2.1" xref="S3.p1.12.m12.1.2.cmml">(</mo><mi id="S3.p1.12.m12.1.1" xref="S3.p1.12.m12.1.1.cmml">E</mi><mo stretchy="false" id="S3.p1.12.m12.1.2.3.2.2" xref="S3.p1.12.m12.1.2.cmml">)</mo></mrow></mrow></math>, <math><mrow id="S3.E1.m1.3.3" xref="S3.E1.m1.3.3.cmml"><mi id="S3.E1.m1.3.3.4" xref="S3.E1.m1.3.3.4.cmml">D</mi><mo id="S3.E1.m1.3.3.3" xref="S3.E1.m1.3.3.3.cmml">⁢</mo><mrow id="S3.E1.m1.3.3.2.2" xref="S3.E1.m1.3.3.2.3.cmml"><mo stretchy="false" id="S3.E1.m1.3.3.2.2.3" xref="S3.E1.m1.3.3.2.3.cmml">[</mo><mrow id="S3.E1.m1.2.2.1.1.1.1" xref="S3.E1.m1.2.2.1.1.1.1.1.cmml"><mo stretchy="false" id="S3.E1.m1.2.2.1.1.1.1.2" xref="S3.E1.m1.2.2.1.1.1.1.1.cmml">(</mo><mrow id="S3.E1.m1.2.2.1.1.1.1.1" xref="S3.E1.m1.2.2.1.1.1.1.1.cmml"><mi id="S3.E1.m1.2.2.1.1.1.1.1.2" xref="S3.E1.m1.2.2.1.1.1.1.1.2.cmml">a</mi><mo id="S3.E1.m1.2.2.1.1.1.1.1.1" xref="S3.E1.m1.2.2.1.1.1.1.1.1.cmml">/</mo><mi id="S3.E1.m1.2.2.1.1.1.1.1.3" xref="S3.E1.m1.2.2.1.1.1.1.1.3.cmml">c</mi></mrow><mo stretchy="false" id="S3.E1.m1.2.2.1.1.1.1.3" xref="S3.E1.m1.2.2.1.1.1.1.1.cmml">)</mo></mrow><mo id="S3.E1.m1.3.3.2.2.4" xref="S3.E1.m1.3.3.2.3.cmml">,</mo><msub id="S3.E1.m1.3.3.2.2.2" xref="S3.E1.m1.3.3.2.2.2.cmml"><mi id="S3.E1.m1.3.3.2.2.2.2" xref="S3.E1.m1.3.3.2.2.2.2.cmml">N</mi><mi id="S3.E1.m1.3.3.2.2.2.3" xref="S3.E1.m1.3.3.2.2.2.3.cmml">H</mi></msub><mo id="S3.E1.m1.3.3.2.2.5" xref="S3.E1.m1.3.3.2.3.cmml">,</mo><mi id="S3.E1.m1.1.1" xref="S3.E1.m1.1.1.cmml">E</mi><mo stretchy="false" id="S3.E1.m1.3.3.2.2.6" xref="S3.E1.m1.3.3.2.3.cmml">]</mo></mrow></mrow></math>

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1109.0477

Formulas:

1-

SL (2, ℝ)

2-

f^{n} (x) = {(f (x))}^{n}

3-

n = 0, 1, \dots

4-

SL (2, ℝ)

5-

C_{c} (X)

6-

C_{0} (X)

7-

L^{p} (X)

8-

C_{0} (X)

9-

λ, λ_{1}, λ_{2} \in ℝ

10-

A_{λ} = {x ∣ f (x) \geq λ}

Formulas (html):

Correct Categorie: math

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0610300

Formulas:

1-

L_{H α} \leq 10^{41} erg \cdot s^{- 1}

2-

R_{B L R s} - L_{H α}

3-

\dot{m_{H α}} > 10^{- 5.5}

4-

\dot{m_{H α}} = L_{H α} / L_{E d d}

5-

R_{B L R s} - L_{H α}

6-

R_{B L R s} - L_{5100 Å}^{α}

7-

M_{B H} - σ

8-

10^{4} - 10^{6} M_{⊙}

9-

R_{B L R s} - L_{H α}^{α}

10-

L_{H α} < 10^{41} erg \cdot s^{- 1}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

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

Formulas:

1-

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

2-

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

3-

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

4-

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

5-

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

6-

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

7-

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

8-

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

9-

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

10-

h < 1 k m

Formulas (html):

Correct Categorie: physics

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/hep-ph/9812331

Formulas:

1-

{(M^{2} / Q^{2})}^{j}

2-

g_{1}^{\pm} (x)

3-

x \frac{d}{d x} x \frac{d}{d x} [\frac{x}{{(1 + 4 M^{2} x^{2} / Q^{2})}^{1 / 2}} \frac{G_{1}^{\pm} (ξ)}{ξ}],

4-

g_{2}^{\pm} (x)

5-

- x \frac{d^{2}}{d x^{2}} x [\frac{x}{{(1 + 4 M^{2} x^{2} / Q^{2})}^{1 / 2}} \frac{G_{1}^{\pm} (ξ)}{ξ}],

6-

g_{3}^{\pm} (x)

7-

2 x^{2} \frac{d^{2}}{d x^{2}} [\frac{x^{2}}{{(1 + 4 M^{2} x^{2} / Q^{2})}^{1 / 2}} \frac{G_{2}^{\pm} (ξ)}{ξ^{2}}],

8-

g_{4}^{\pm} (x)

9-

- x^{2} \frac{d}{d x} x \frac{d^{2}}{d x^{2}} [\frac{x^{2}}{{(1 + 4 M^{2} x^{2} / Q^{2})}^{1 / 2}} \frac{G_{2}^{\pm} (ξ)}{ξ^{2}}],

10-

g_{5}^{\pm} (x)

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/nlin/0303003

Formulas:

1-

E_{1, 2} (x, z)

2-

i \partial_{z} E_{1} + d_{1} \partial_{x}^{2} E_{1} + E_{1}^{*} E_{2} \exp (- i β z) = 0,

3-

i \partial_{z} E_{2} + d_{2} \partial_{x}^{2} E_{2} + E_{1}^{2} \exp (i β z) = 0 .

4-

\partial_{x}^{2} E_{j}

5-

\partial_{x}^{2} E_{j}

6-

e_{2} \exp (i β z)

7-

e_{2} (x, z)

8-

i \partial_{z} E_{1} + d_{1} \partial_{x}^{2} E_{1} + β^{- 1} {| E_{1} |}^{2} E_{1} = 0

9-

\partial_{x}^{2} E_{2}

10-

e_{2} (x, z)

Formulas (html):

Correct Categorie: nlin

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1203.2868

Formulas:

1-

\min {c, | e |}

2-

\min {c, | e |}

3-

χ (G, c)

4-

χ (t, c)

5-

χ (t, c)

6-

χ (t, c)

7-

χ (t, c)

8-

t = c - 1 = 1

9-

χ (1, 2)

10-

χ (c - 1, c)

Formulas (html):

Correct Categorie: math

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/0706.2737

Formulas:

1-

d z / d t

2-

d z / d t

3-

r_{c} = \frac{M_{Pl}}{2 M_{5}^{3}},

4-

H^{2} = {[\sqrt{\frac{ρ}{3 M_{Pl}^{2}} + \frac{1}{4 r_{c}^{2}}} + \frac{1}{2 r_{c}}]}^{2} - \frac{k}{a {(t)}^{2}},

5-

k = 0, \pm 1

6-

Ω_{r_{c}} = \frac{1}{4 r_{c}^{2} H_{0}^{2}},

7-

H {(z)}^{2} / H_{0}^{2} = Ω_{k} {(1 + z)}^{2} + {[\sqrt{Ω_{r_{c}}} + \sqrt{Ω_{r_{c}} + Ω_{m} {(1 + z)}^{3}}]}^{2},

8-

H_{0} = 100 h

9-

Ω_{k} + {[\sqrt{Ω_{r_{c}}} + \sqrt{Ω_{r_{c}} + Ω_{m}}]}^{2} = 1 .

10-

q = - \ddot{a} / a H^{2}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1412.7736

Formulas:

1-

p (a ∣ b)

2-

p (a, b)

3-

p (A B) = p (A, B) p (B)

4-

p (A, B) = \frac{p (A B)}{p (B)}

5-

a_{n} = (1 - 1 / n^{2})

6-

P (q p_{1}, H)

7-

P (q, p_{1} H) = \frac{P (q, H) P (p_{1}, q H)}{P (p_{1}, H)}

8-

P (p_{1}, q H) = 1

9-

P (q, p_{1} H) = \frac{P (q, H)}{P (p_{1}, H)} .

10-

p_{2}, p_{3}, \dots, p_{n}

Formulas (html):

Correct Categorie: physics

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1008.4506

Formulas:

1-

40 M_{J u p}

2-

v s i n (i) = 70

3-

N (L i) = 3.9

4-

[U, V, W] = [- 10.6, - 15.4, - 7.9]

5-

M_{M o o n}

6-

N D I T

7-

D I T = 0.347

8-

Δ K_{s} > 5

9-

Δ K_{s} > 5

10-

s e p_{b g}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/0301245

Formulas:

1-

β = \exp [u]

2-

P (a) = \frac{1}{2 π s} \int_{0}^{\infty} 𝑑 β β^{- 1 / 2} \exp [- \frac{{(\ln \frac{β}{m})}^{2}}{2 s^{2}}] e^{- \frac{1}{2} β a^{2}},

3-

m = \exp [s^{2}]

4-

[- 60, 60] ∋ a

5-

a \in [- 20, 20]

6-

a \in [- 150, 150]

7-

P (a) = \frac{C \exp [- a^{2} / a_{c}^{2}]}{{(1 + \frac{1}{2} V_{0} (q - 1) a^{2})}^{1 / (q - 1)}},

8-

P (a) = \int_{0}^{\infty} 𝑑 β P (a | β) f (β),

9-

P (a | β)

10-

\partial_{t} a = γ F (a) + σ L (t) .

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/2004.13723

Formulas:

1-

ψ \otimes ψ = 𝟙 σ \otimes σ = 𝟙 \oplus ψ ψ \otimes σ = σ,

2-

p_{x} + i p_{y}

3-

p_{x} - i p_{y}

4-

- p_{x} + i p_{y}

5-

C_{2} (\hat{𝒃})

6-

[\bar{1} 10]

7-

C_{2} (\hat{𝒃}) = e^{- i π \hat{𝒃} \cdot 𝑺}

8-

\begin{matrix} C_{2} (\hat{𝒃}) S_{j}^{x} C_{2}^{†} (\hat{𝒃}) & = - S_{C_{2} (\hat{𝒃}) j}^{y} \\ C_{2} (\hat{𝒃}) S_{j}^{y} C_{2}^{†} (\hat{𝒃}) & = - S_{C_{2} (\hat{𝒃}) j}^{x} \\ C_{2} (\hat{𝒃}) S_{j}^{z} C_{2}^{†} (\hat{𝒃}) & = - S_{C_{2} (\hat{𝒃}) j}^{z}, \end{matrix}

9-

C_{2} (\hat{𝒃})

10-

C_{2} (\hat{𝒃})

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/9907238

Formulas:

1-

k_{0} = 2 π / λ_{0} = 0.05

2-

Δ z \approx 0.22 \pm 0.02

3-

120 {(1 + z)}^{- 1}

4-

Ω_{m} = 1 - Ω_{Λ} \approx 0.4 \pm 0.1

5-

- 100 \leq X \leq 200

6-

- 350 \leq Y \leq - 50

7-

k (d) = \frac{2}{N (N + 1)} \frac{V (d)}{V_{ε}} \sum_{i = 1}^{N} \sum_{j = i + 1}^{N} v (f_{i}, f_{j}) .

8-

v (f_{i}, f_{j})

9-

v_{i j} = 1

10-

v_{i j} = 0

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1809.04183

Formulas:

1-

T_{eff} \approx 30 000 K

2-

\log (g) \approx 4.6

3-

T_{eff} \approx 20 000 - 40 000

4-

5.4 \leq \log (g) \leq 6.0

5-

28 000 \leq T_{eff} / K \leq 35 000

6-

\dot{M} = 10^{- 3} M_{⊙} {yr}^{- 1}

7-

\sim 3 \times 10^{- 3} M_{⊙}

8-

\log L / L_{⊙} < - 2

9-

y (t) = A \exp [- i ω t] .

10-

l = 0, k = 0

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/0704.3714

Formulas:

1-

F ≃ F_{n} + a (T) {| ϕ |}^{2} + \frac{λ}{4} {| ϕ |}^{4} .

2-

a (T) ≃ \dot{a} (T_{C}) (T - T_{C})

3-

ℒ = {(D_{μ} ϕ)}^{†} (D^{μ} ϕ) + m^{2} ϕ^{†} ϕ - \frac{λ}{4} {(ϕ^{†} ϕ)}^{2} - \frac{1}{4} F_{μ ν} F^{μ ν},

4-

F_{μ ν} \equiv \partial_{μ} A_{ν} - \partial_{ν} A_{μ}

5-

D_{μ} \equiv \partial_{μ} + 2 i e A_{μ}

6-

ϕ \equiv \frac{1}{\sqrt{2}} (η_{0} + η) e^{i θ / η_{0}},

7-

F_{I} = F_{n} + \frac{1}{2} a_{I} (T) η_{0}^{2} + \frac{λ}{16} η_{0}^{4}

8-

a_{I} = - m^{2} + \frac{λ + 4 e^{2}}{16} T^{2} .

9-

T_{1} = 2 \sqrt{\frac{4 m^{2}}{λ + 4 e^{2}}} .

10-

η_{0}^{2} (T) = - \frac{4 a_{I} (T)}{λ} .

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/hep-ph/9910502

Formulas:

1-

ℒ_{E} = χ^{*} [m^{2} - \partial^{2} + g ϕ] χ + \frac{1}{2} ϕ (μ^{2} - \partial^{2}) ϕ .

2-

Φ_{i} = χ^{*} (x) χ (\bar{x})

3-

Φ_{f} = χ^{*} (y) χ (\bar{y})

4-

G (y, \bar{y} | x, \bar{x}) = N \int 𝒟 χ^{*} \int 𝒟 χ \int 𝒟 ϕ Φ_{f}^{*} Φ_{i} e^{- S_{E}} .

5-

G = - \int_{0}^{\infty} 𝑑 s \int_{0}^{\infty} 𝑑 \bar{s} \int {(𝒟 z)}_{x y} \int {(𝒟 \bar{z})}_{\bar{x} \bar{y}} e^{- S [Z]},

6-

S [Z] \equiv - i K [z, s] - i K [\bar{z}, \bar{s}] + V_{0} [z, s] + 2 V_{12} [z, \bar{z}, s, \bar{s}] + V_{0} [\bar{z}, \bar{s}] .

7-

K [z, s]

8-

(m^{2} + i ϵ) s - \frac{1}{4 s} \int_{0}^{1} 𝑑 τ \frac{d z_{μ} (τ)}{d τ} \frac{d z^{μ} (τ)}{d τ},

9-

V_{0} [z, s]

10-

\frac{g^{2}}{2} s^{2} \int_{0}^{1} 𝑑 τ \int_{0}^{1} 𝑑 τ^{'} Δ (z (τ) - z (τ^{'}), μ),

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1806.06099

Formulas:

1-

^{14, 15, 16, 8, 17}

2-

= {1.39}_{- 0.06}^{+ 0.05}

3-

M_{P} = {1.42}_{- 0.32}^{+ 0.31}

4-

R_{P} = {1.552}_{- 0.057}^{+ 0.048}

5-

M_{P} = 0.223 \pm 0.031

6-

R_{P} = {0.850}_{- 0.022}^{+ 0.026}

7-

= 04^{h} 51^{m} 11^{s}

8-

= + 20^{\circ} 47^{'} 11^{''}

9-

= 10^{h} 42^{m} 44^{s}

10-

= + 06^{\circ} 51^{'} 06^{''}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/gr-qc/0405020

Formulas:

1-

ρ_{p h} = - \frac{1}{2} {\dot{ϕ}}^{2} + V (ϕ),

2-

p_{p h} = - \frac{1}{2} {\dot{ϕ}}^{2} - V (ϕ),

3-

3 H^{2} = - \frac{1}{2} {\dot{ϕ}}^{2} + V (ϕ),

4-

\ddot{ϕ} + 3 H \dot{ϕ} - \frac{d V}{d ϕ} = 0 .

5-

V = \frac{2 (6 + A^{2})}{A^{4}} e^{- A ϕ},

6-

ϕ = \frac{2}{A} \ln t,

7-

a = {(- t)}^{- 2 / A^{2}},

8-

ρ + p = - {\dot{ϕ}}^{2} < 0

9-

γ_{p h} = - \frac{{\dot{ϕ}}^{2}}{ρ_{p h}} = - \frac{A^{2}}{3},

10-

ρ_{p h} = \frac{12}{A^{4} t^{2}}

Formulas (html):

Correct Categorie: gr-qc

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/nucl-th/9806007

Formulas:

1-

ρ (E, N)

2-

ρ (E, N)

3-

ρ (E, N) \exp {- (E - μ N) / T}

4-

ρ (E, N)

5-

ρ (E, N)

6-

ρ (E, N) \exp {- (E - μ N) / T}

7-

ρ (E, N)

8-

| Q (t) ⟩ = \sum_{a l l P} s i g n (P) | q_{P (1)} (t) ⟩ \otimes \dots \otimes | q_{P (A)} (t) ⟩

9-

⟨ \vec{x} | q (t) ⟩

10-

\exp {- \frac{{(\vec{x} - \vec{b} (t))}^{2}}{2 a (t)}} \otimes | m_{s} ⟩ \otimes | m_{t} ⟩,

Formulas (html):

Correct Categorie: nucl-th

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/quant-ph/9907063

Formulas:

1-

H_{iso} / h = \sum_{i}^{N} ν_{i} I_{z i} + \sum_{i < j}^{N} J_{i j} (I_{x i} I_{x j} + I_{y i} I_{y j} + I_{z i} I_{z j})

2-

| ν_{A} - ν_{B} | >> | J |

3-

H_{i s o}^{\circ} / h = ν_{A} I_{z A} + ν_{B} I_{z B} + J I_{z A} I_{z B} .

4-

H_{l i q}^{\circ}

5-

f_{c l o c k}

6-

H_{lc} / h = \sum_{i}^{N} ν_{i}^{'} I_{z i} + \sum_{i < j}^{N} J_{i j} (I_{x i} I_{x j} + I_{y i} I_{y j} + I_{z i} I_{z j}) + \sum_{i < j}^{N} D_{i j} {2 I_{z i} I_{z j} - \frac{1}{2} (I_{x i} I_{x j} + I_{y i} I_{y j})} .

7-

H_{lc}^{\circ} / h = ν_{A}^{'} I_{z A} + ν_{B}^{'} I_{z B} + (J + 2 D) I_{z A} I_{z B} .

8-

f_{c l o c k} = 2 | (J + 2 D) |

9-

T_{2} f_{c l o c k} = 2 T_{2} J

10-

T_{2}^{l c} f_{c l o c k}^{l c} \approx 5 T_{2}^{i s o} f_{c l o c k}^{i s o}

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: quant-ph

Result: correct

Paper: https://arxiv.org/abs/0712.2593

Formulas:

1-

d x^{0} / c

2-

S = \int d^{n + 1} x \sqrt{- g} (e^{α ψ} (ℛ - 2 Λ (ψ) - κ \nabla_{μ} ψ \nabla^{μ} ψ) + e^{β ψ} ℒ_{m} (ϕ_{i}, \partial_{μ} ϕ_{i}))

3-

ψ = \log (c / c_{0})

4-

16 π G / c_{0}^{4}

5-

d x^{0} / c

6-

ℒ = a^{n} e^{α ψ} [- n (n - 1) {(\frac{\dot{a}}{a})}^{2} - 2 α n \dot{ψ} (\frac{\dot{a}}{a}) + n (n - 1) \frac{k}{a^{2}} - κ {\dot{ψ}}^{2} - 2 Λ (ψ)] + a^{n} e^{β ψ} ℒ_{m} (ϕ_{i}, \partial_{μ} ϕ_{i}) .

7-

k = + 1, - 1, 0

8-

ψ = \ln (b), \dot{ψ} = \frac{\dot{b}}{b}

9-

ℒ = - b^{α} [n (n - 1) {\dot{a}}^{2} a^{n - 2} - 2 α n \frac{\dot{b}}{b} \dot{a} a^{n - 1} + κ {(\frac{\dot{b}}{b})}^{2} a^{n} + 2 a^{n} Λ (b)] .

10-

A a^{α^{'}} b^{β^{'}},

Formulas (html):

Correct Categorie: gr-qc

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1901.09569

Formulas:

1-

m_{i} \frac{d}{d t} {\vec{v}}_{i} = {\vec{F}}_{i} and {\underline{𝐈}}_{i} \frac{d}{d t} 𝝎_{i} = {\vec{T}}_{i},

2-

{\vec{V}}_{j} = {\vec{V}}_{j}^{0} (1 + α_{p} Δ T_{t_{0}}^{t}), \forall j \in N_{i}^{V},

3-

Δ T_{t_{0}}^{t}

4-

g = \max (1, p^{gap}) g

5-

α_{c} / α_{p} = 10

6-

α_{c} / α_{p} = 10

7-

α_{c} / α_{p} = 10

8-

α_{c} / α_{p} = 10

9-

α_{c} / α_{p} = 10

10-

α_{c} / α_{p} = 10

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1805.04664

Formulas:

1-

10^{- 6} - 10^{7}

2-

Φ_{ℓ} (t) = ⟨ P_{ℓ} (\cos θ (t)) ⟩,

3-

τ^{(1)} / τ^{(2)} = 3

4-

g_{1} (t)

5-

g_{1} (t) = ⟨ E_{s}^{*} (0) E_{s} (t) ⟩ / ⟨ {| E_{s} |}^{2} ⟩

6-

g_{2} (t) = ⟨ I (t) I (0) ⟩ / {⟨ I ⟩}^{2}

7-

g_{2} (t) = 1 + Λ C^{2} {| g_{1} (t) |}^{2} + 2 Λ C (1 - C) | g_{1} (t) |,

8-

g_{1} (t)

9-

1 - g_{1} (t_{0}) \approx 0.2

10-

g_{1} (t)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0101494

Formulas:

1-

^{3, 4, 5, 6}

2-

\approx 1.3 \times 10^{- 16}

3-

\approx 6.5 \times 10^{- 16}

4-

\overset{<}{\sim} 3 \times 10^{- 16}

5-

ℛ - K_{s} > 5.0

6-

\approx 1.9 \times 10^{- 17}

7-

\approx 17^{'} \times 19^{'}

8-

\approx 1.3 \times 10^{- 16}

9-

\approx 6.5 \times 10^{- 16}

10-

(1.6 \pm 0.4) \times 10^{20}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/gr-qc/9808027

Formulas:

1-

T_{B H} = m_{p l}^{2} / 8 π m

2-

e^{G P_{R} / R} = \frac{1}{2 \sqrt{F_{i n} F_{o u t}}} (F_{i n} + F_{o u t} - \frac{M^{2} G^{2}}{R^{2}} \pm \frac{2 M G}{R} 𝒵)

3-

𝒵 = \sqrt{{(F_{o u t} - F_{i n})}^{2} \frac{R^{2}}{4 M^{2} G^{2}} - \frac{1}{2} (F_{o u t} + F_{i n}) + \frac{M^{2} G^{2}}{4 R^{2}}}

4-

F_{i n, o u t} = 1 - 2 G m_{i n, o u t} / R

5-

m_{i n, o u t}

6-

P_{R} (R)

7-

P_{R} \to - P_{R}

8-

F_{i n} + F_{o u t} - G^{2} M^{2} R^{- 2} - \sqrt{F_{i n} F_{o u t}} ch (G P_{R} / R) = 0

9-

Ψ (m, μ, S + i ζ) + Ψ (m, μ, S - i ζ) =

10-

{(F_{i n} F_{o u t})}^{- 1 / 2} (F_{i n} + F_{o u t} - M^{2} / 4 m^{2} S) Ψ (m, μ, S)

Formulas (html):

Correct Categorie: gr-qc

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/0609083

Formulas:

1-

Δ μ_{i} (T, p_{i})

2-

T, p_{O_{2}}, p_{CO}

3-

(\sqrt{5} \times \sqrt{5}) R 27^{\circ}

4-

T, p_{O_{2}}, p_{CO}

5-

(Δ μ_{O}, Δ μ_{CO})

6-

p (2 \times 2)

7-

(Δ μ_{O}, Δ μ_{CO})

8-

(T, p_{i})

9-

(T, p_{O_{2}}, p_{CO})

10-

T = 300, 400, 600

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/9807351

Formulas:

1-

G_{N S} = \frac{4 e^{2}}{h} \sum_{n} \frac{T_{n}^{2}}{{(2 - T_{n})}^{2}},

2-

G_{N S} = \frac{4 e^{2}}{h} \frac{T_{Q D}^{2}}{{(2 - T_{Q D})}^{2}} .

3-

G_{N} = \frac{2 e^{2}}{h} T_{Q D} .

4-

U \sim e^{2} / C

5-

Im Σ (ε_{F}) = - Γ / 2,

6-

Γ = Γ_{L} + Γ_{R}

7-

⟨ n ⟩ = \frac{2}{π} Im [\log G^{r} (ε_{F})] .

8-

T_{Q D} = Γ_{L} Γ_{R} {| G^{r} (ε_{F}) |}^{2},

9-

T_{Q D} = \frac{4 Γ_{L} Γ_{R}}{Γ^{2}} \sin^{2} φ

10-

φ = π ⟨ n ⟩ / 2

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/0811.3077

Formulas:

1-

H = - \sum_{i, j} t_{i j} \sum_{σ = ↑, ↓} b_{i, σ}^{†} b_{j, σ} + α \sum_{k} n_{k, ↑} n_{k, ↓}

2-

t_{i j} = δ_{i, j + 1} + δ_{i, j - 1}

3-

M_{0} = \sum_{k} n_{k, ↑} n_{k, ↓} .

4-

[[[H, M_{i}], M_{i}], M_{i}] = [H, M_{i}]

5-

i = 0, 1, 2

6-

H = H_{ref, i} + R_{i} + R_{i}^{†}

7-

[H_{ref, i}, M_{i}]

8-

[R_{i}, M_{i}]

9-

H_{ref} \equiv H_{ref, 1} = H_{ref, 2}

10-

μ_{m} = ν_{n} + m

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1601.05629

Formulas:

1-

f (q) = a_{r} q^{r} + \dots + a_{s} q^{s}

2-

a_{r + i} = a_{s - i}

3-

𝒫_{n} (q)

4-

ℝ {(q)}_{n + 1}

5-

⌊ n / 2 ⌋ + 1

6-

{q^{j} (1 + q + \dots + q^{n - 2 j})}, {q^{j} {(1 + q)}^{n - 2 j}}

7-

{q^{j} (1 + q^{n - 2 j})}

8-

𝒫_{n} (q)

9-

a_{0}, a_{1}, \dots, a_{n}

10-

a_{i} = a_{n - i}

Formulas (html):

Correct Categorie: math

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/0710.4598

Formulas:

1-

d s^{2} = η_{μ ν} d x^{μ} d x^{ν} + d r^{2} + r^{2} d θ^{2},

2-

0 \leq θ < 2 π α

3-

D (x^{a}, x^{', a})

4-

r □_{x}^{(6 d)} D (x^{a}, x^{', a}) = i δ^{(6)} (a^{a} - x^{', a})

5-

D_{k} (0, 0) = - \int_{0}^{Λ} \frac{d q q}{2 π α} \frac{i}{k^{2} + q^{2}} = \frac{- i}{2 π α} \log \frac{Λ}{k},

6-

S = - \int d^{4} x d θ d r r (\frac{1}{2} {(\partial_{a} ϕ)}^{2} + δ^{2} (y) [\frac{1}{2} {(\partial_{μ} χ)}^{2} + \frac{m^{2}}{2} χ^{2} + λ χ ϕ]) .

7-

G_{k}^{χ χ} = - i {(k^{2} + m^{2})}^{- 1}

8-

G_{k}^{χ χ} = - \frac{i}{(k^{2} + m^{2}) - i λ^{2} D_{k} (0, 0)} .

9-

D_{k} (0, 0)

10-

D_{k} (0, 0) = - i / 2 π α \log Λ / k

Formulas (html):

Correct Categorie: hep-th

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0701356

Formulas:

1-

R_{p} = 1.01 \pm 0.06 R_{J}

2-

M_{p} = 0.53 M_{J}

3-

ρ_{p} = 0.6 \pm 0.2 g / c m^{3}

4-

R A (2000) = 10 : 53 : 17.91

5-

D E C (2000) = - 61 : 24 : 20.3

6-

M_{P} = 0.53 M_{J}

7-

R_{p} = 1.0 R_{J}

8-

a = 0.047 A U

9-

T_{e f f} = 4650 \pm 95

10-

E (B - V) = 0.16

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/9903406

Formulas:

1-

H = (1 / R_{1} + 1 / R_{2}) / 2

2-

K = 1 / R_{1} R_{2} = - 1 / R_{1}^{2}

3-

\cos x + \cos y + \cos z = 0

4-

Φ (𝐫) = ρ_{O} (𝐫) - ρ_{W} (𝐫)

5-

ρ_{O} (𝐫) + ρ_{W} (𝐫) = 1

6-

Φ (α 𝐫) = - Φ (𝐫)

7-

𝒢 / ℋ ≅ ℤ_{2} ≅ {1, α}

8-

\cos x + \cos y + \cos z = 0

9-

ℋ = P m \bar{3} m

10-

𝒢 = I m \bar{3} m

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/gr-qc/9703023

Formulas:

1-

{(\partial / \partial t)}^{a}

2-

T_{0} = 1 / β_{0} = κ / 2 π

3-

G_{T} (τ, \vec{x}; τ^{'}, {\vec{x}}^{'})

4-

G_{T} (τ, \vec{x}; τ^{'}, {\vec{x}}^{'}) = i tr [e^{- β H} 𝒯 (ϕ (τ, \vec{x}) ϕ (τ^{'}, {\vec{x}}^{'}))] / tr (e^{- β H})

5-

G_{T} (τ, \vec{x}; τ^{'}, {\vec{x}}^{'}) = G_{T} (τ + α, \vec{x}; τ^{'}, {\vec{x}}^{'})

6-

\sum_{m n} (e^{(α - β) E_{m} - α E_{n}} - e^{- β E_{n}}) {| ⟨ m | ϕ (τ, \vec{x}) | n ⟩ |}^{2} = 0

7-

H | m ⟩ = E_{m} | m ⟩

8-

⟨ m | n ⟩ = δ_{m n}

9-

{\vec{x}}^{'} \to \vec{x}

10-

τ \to τ + β_{0}

Formulas (html):

Correct Categorie: gr-qc

Guessed Categorie: quant-ph

Result: incorrect

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