Run 11339405

Paper: https://arxiv.org/abs/cond-mat/9903117

Formulas:

1-

ρ_{s} (0)

2-

ρ_{s} (T) / ρ_{s} (0)

3-

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

4-

Δ_{k} = Δ_{0} c o s (2 ϕ)

5-

ϕ = a r c t a n (k_{y} / k_{x})

6-

\sim 5 μ m

7-

λ_{a b}^{- 2} (T)

8-

λ_{a b} (0)

9-

λ_{a b} (0)

10-

λ_{a b} (0)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1511.02063

Formulas:

1-

25 c m s

2-

V_{a} = 400 v o l t s

3-

V_{a} = 350 v o l t s

4-

I_{p} \sim 2 m A

5-

n_{i} \approx 1 \times 10^{14} m^{- 3}

6-

T_{e} \approx 5 e V

7-

T_{i} \approx 0.03 e V

8-

n_{d} \approx 1 \times 10^{9} m^{- 3}

9-

m_{d} \approx 1.7 \times 10^{- 13} k g

10-

Q_{d} \approx 4.5 \times 10^{4} e

Formulas (html):

Correct Categorie: physics

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/1007.4106

Formulas:

1-

V (t) = {u_{i}}

2-

E (t) = {e_{i j}}

3-

e_{i j} (t)

4-

D_{i} (t) = ∥ {u_{j} ∣ \exists e_{i j} (t)} ∥

5-

B C_{i} (t) = \sum_{j \neq k} \frac{s p_{j, k} (u_{i}, t)}{s p_{j k} (t)}

6-

s p_{j k}

7-

s p_{j, k} (u_{i}, t)

8-

B C_{14} = 0.668

9-

L_{i} (t)

10-

D_{i} (t)

Formulas (html):

Correct Categorie: cs

Guessed Categorie: cs

Result: correct

Paper: https://arxiv.org/abs/cond-mat/0110644

Formulas:

1-

α = 2 (5 / 2)

2-

α = 2 (5 / 2)

3-

N = 1024 (512)

4-

2 D (3 D)

5-

v_{a b} (r) = (ϵ / α) {(1 - r / σ_{a b})}^{α}

6-

r < σ_{a b}

7-

v_{a b} (r) = 0

8-

r > σ_{a b}

9-

σ_{a b} = (σ_{a} + σ_{b}) / 2

10-

δ ϕ \leq 10^{- 4}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/0812.3339

Formulas:

1-

Δ t = Δ t_{C F L} \min (1, {(τ_{c} / Δ t_{C F L})}^{p}),

2-

T_{0} = 8 \times 10^{3}

3-

β_{r a m}

4-

β_{r a m} \approx 1

5-

β_{r a m} > 1

6-

A_{x} (x, y, z) = \sum_{i, j, k = 1}^{m a x} {| k |}^{- p} \sin (k_{x} x + k_{y} y + k_{z} z + ϕ_{i, j, k}^{x}),

7-

| k | \equiv k_{x}^{2} + k_{y}^{2} + k_{z}^{2}

8-

k_{x} \equiv 2 π i / L_{x}

9-

k_{x, y, z}

10-

1 \leq | k | \leq 4

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/gr-qc/0203024

Formulas:

1-

| ω_{2} - ω_{1} | = Ω

2-

δ ℓ / ℓ \approx 10^{- 20}

3-

\vec{\nabla} \cdot \vec{E} = 0

4-

\vec{\nabla} \cdot \vec{H} = 0

5-

\vec{\nabla} \land \vec{E} + μ_{0} \frac{\partial \vec{H}}{\partial t} = 0

6-

\vec{\nabla} \land \vec{H} - ϵ_{0} \frac{\partial \vec{E}}{\partial t} = 0

7-

\nabla^{2} \vec{E} - \frac{1}{c^{2}} \frac{\partial^{2} \vec{E}}{\partial t^{2}} = 0

8-

\nabla^{2} \vec{H} - \frac{1}{c^{2}} \frac{\partial^{2} \vec{H}}{\partial t^{2}} = 0

9-

c = {(μ_{0} ϵ_{0})}^{- 1 / 2}

10-

\vec{E} (\vec{r}, t) = \sum_{n = 0}^{\infty} ℰ_{n} (t) {\vec{E}}_{n} (\vec{r})

Formulas (html):

Correct Categorie: gr-qc

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/1712.03482

Formulas:

1-

{∥ f ∥}_{𝔢} = sup_{z \in 𝔢} | f (z) |

2-

t_{n} = {∥ T_{n} ∥}_{𝔢}

3-

t_{n} \geq C {(𝔢)}^{n}

4-

t_{n} \geq 2 C {(𝔢)}^{n}

5-

t_{n} = 2 C {(𝔢)}^{n}

6-

𝔢 = P^{- 1} ([- 2, 2])

7-

P (z) \in [- 2, 2]

8-

P (𝔢) = [- 2, 2]

9-

t_{1} = 2 C (𝔢)

10-

{lim}_{n \to \infty} {∥ T_{n} ∥}_{𝔢} / C {(𝔢)}^{n} = 2

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/1404.5450

Formulas:

1-

A (V) = \frac{I (V) + I (- V)}{I (V) - I (- V)},

2-

ℋ_{V} = V / 2 (\sum_{x}^{left lead} {\hat{n}}_{x} - \sum_{x}^{right lead} {\hat{n}}_{x})

3-

- I (- V)

4-

J_{1} = 0.3 J

5-

J_{2} = 0.09 J

6-

w_{1} = 0.3 J

7-

w_{2} = - 0.3 J

8-

w_{3} = 1.5 J

9-

J_{1} = 0.3 J

10-

J_{2} = 0.09 J

Formulas (html):

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id="S2.F1.9.m1.1.1.1.1.1.1.2" xref="S2.F1.9.m1.1.1.1.1.1.1.2.cmml">V</mi></mrow><mo stretchy="false" id="S2.F1.9.m1.1.1.1.1.1.3" xref="S2.F1.9.m1.1.1.1.1.1.1.cmml">)</mo></mrow></mrow></mrow></math>, <math><mrow id="S2.F1.10.m2.1.1" xref="S2.F1.10.m2.1.1.cmml"><msub id="S2.F1.10.m2.1.1.2" xref="S2.F1.10.m2.1.1.2.cmml"><mi id="S2.F1.10.m2.1.1.2.2" xref="S2.F1.10.m2.1.1.2.2.cmml">J</mi><mn id="S2.F1.10.m2.1.1.2.3" xref="S2.F1.10.m2.1.1.2.3.cmml">1</mn></msub><mo id="S2.F1.10.m2.1.1.1" xref="S2.F1.10.m2.1.1.1.cmml">=</mo><mrow id="S2.F1.10.m2.1.1.3" xref="S2.F1.10.m2.1.1.3.cmml"><mn id="S2.F1.10.m2.1.1.3.2" xref="S2.F1.10.m2.1.1.3.2.cmml">0.3</mn><mo id="S2.F1.10.m2.1.1.3.1" xref="S2.F1.10.m2.1.1.3.1.cmml">⁢</mo><mi id="S2.F1.10.m2.1.1.3.3" xref="S2.F1.10.m2.1.1.3.3.cmml">J</mi></mrow></mrow></math>, <math><mrow id="S2.F1.11.m3.1.1" xref="S2.F1.11.m3.1.1.cmml"><msub id="S2.F1.11.m3.1.1.2" xref="S2.F1.11.m3.1.1.2.cmml"><mi id="S2.F1.11.m3.1.1.2.2" xref="S2.F1.11.m3.1.1.2.2.cmml">J</mi><mn id="S2.F1.11.m3.1.1.2.3" xref="S2.F1.11.m3.1.1.2.3.cmml">2</mn></msub><mo id="S2.F1.11.m3.1.1.1" xref="S2.F1.11.m3.1.1.1.cmml">=</mo><mrow id="S2.F1.11.m3.1.1.3" xref="S2.F1.11.m3.1.1.3.cmml"><mn id="S2.F1.11.m3.1.1.3.2" xref="S2.F1.11.m3.1.1.3.2.cmml">0.09</mn><mo id="S2.F1.11.m3.1.1.3.1" xref="S2.F1.11.m3.1.1.3.1.cmml">⁢</mo><mi id="S2.F1.11.m3.1.1.3.3" xref="S2.F1.11.m3.1.1.3.3.cmml">J</mi></mrow></mrow></math>, <math><mrow id="S2.F1.13.m5.1.1" xref="S2.F1.13.m5.1.1.cmml"><msub id="S2.F1.13.m5.1.1.2" xref="S2.F1.13.m5.1.1.2.cmml"><mi mathvariant="normal" id="S2.F1.13.m5.1.1.2.2" xref="S2.F1.13.m5.1.1.2.2.cmml">w</mi><mn id="S2.F1.13.m5.1.1.2.3" xref="S2.F1.13.m5.1.1.2.3.cmml">1</mn></msub><mo id="S2.F1.13.m5.1.1.1" xref="S2.F1.13.m5.1.1.1.cmml">=</mo><mrow id="S2.F1.13.m5.1.1.3" xref="S2.F1.13.m5.1.1.3.cmml"><mn id="S2.F1.13.m5.1.1.3.2" xref="S2.F1.13.m5.1.1.3.2.cmml">0.3</mn><mo id="S2.F1.13.m5.1.1.3.1" xref="S2.F1.13.m5.1.1.3.1.cmml">⁢</mo><mi id="S2.F1.13.m5.1.1.3.3" xref="S2.F1.13.m5.1.1.3.3.cmml">J</mi></mrow></mrow></math>, <math><mrow id="S2.F1.14.m6.1.1" xref="S2.F1.14.m6.1.1.cmml"><msub id="S2.F1.14.m6.1.1.2" xref="S2.F1.14.m6.1.1.2.cmml"><mi mathvariant="normal" id="S2.F1.14.m6.1.1.2.2" xref="S2.F1.14.m6.1.1.2.2.cmml">w</mi><mn id="S2.F1.14.m6.1.1.2.3" xref="S2.F1.14.m6.1.1.2.3.cmml">2</mn></msub><mo id="S2.F1.14.m6.1.1.1" xref="S2.F1.14.m6.1.1.1.cmml">=</mo><mrow id="S2.F1.14.m6.1.1.3" xref="S2.F1.14.m6.1.1.3.cmml"><mo id="S2.F1.14.m6.1.1.3.1" xref="S2.F1.14.m6.1.1.3.1.cmml">-</mo><mrow id="S2.F1.14.m6.1.1.3.2" xref="S2.F1.14.m6.1.1.3.2.cmml"><mn id="S2.F1.14.m6.1.1.3.2.2" xref="S2.F1.14.m6.1.1.3.2.2.cmml">0.3</mn><mo id="S2.F1.14.m6.1.1.3.2.1" xref="S2.F1.14.m6.1.1.3.2.1.cmml">⁢</mo><mi id="S2.F1.14.m6.1.1.3.2.3" xref="S2.F1.14.m6.1.1.3.2.3.cmml">J</mi></mrow></mrow></mrow></math>, <math><mrow id="S2.F1.15.m7.1.1" xref="S2.F1.15.m7.1.1.cmml"><msub id="S2.F1.15.m7.1.1.2" xref="S2.F1.15.m7.1.1.2.cmml"><mi mathvariant="normal" id="S2.F1.15.m7.1.1.2.2" xref="S2.F1.15.m7.1.1.2.2.cmml">w</mi><mn id="S2.F1.15.m7.1.1.2.3" xref="S2.F1.15.m7.1.1.2.3.cmml">3</mn></msub><mo id="S2.F1.15.m7.1.1.1" xref="S2.F1.15.m7.1.1.1.cmml">=</mo><mrow id="S2.F1.15.m7.1.1.3" xref="S2.F1.15.m7.1.1.3.cmml"><mn id="S2.F1.15.m7.1.1.3.2" xref="S2.F1.15.m7.1.1.3.2.cmml">1.5</mn><mo id="S2.F1.15.m7.1.1.3.1" xref="S2.F1.15.m7.1.1.3.1.cmml">⁢</mo><mi id="S2.F1.15.m7.1.1.3.3" xref="S2.F1.15.m7.1.1.3.3.cmml">J</mi></mrow></mrow></math>, <math><mrow id="S2.F2.9.m1.1.1" xref="S2.F2.9.m1.1.1.cmml"><msub id="S2.F2.9.m1.1.1.2" xref="S2.F2.9.m1.1.1.2.cmml"><mi id="S2.F2.9.m1.1.1.2.2" xref="S2.F2.9.m1.1.1.2.2.cmml">J</mi><mn id="S2.F2.9.m1.1.1.2.3" xref="S2.F2.9.m1.1.1.2.3.cmml">1</mn></msub><mo id="S2.F2.9.m1.1.1.1" xref="S2.F2.9.m1.1.1.1.cmml">=</mo><mrow id="S2.F2.9.m1.1.1.3" xref="S2.F2.9.m1.1.1.3.cmml"><mn id="S2.F2.9.m1.1.1.3.2" xref="S2.F2.9.m1.1.1.3.2.cmml">0.3</mn><mo id="S2.F2.9.m1.1.1.3.1" xref="S2.F2.9.m1.1.1.3.1.cmml">⁢</mo><mi id="S2.F2.9.m1.1.1.3.3" xref="S2.F2.9.m1.1.1.3.3.cmml">J</mi></mrow></mrow></math>, <math><mrow id="S2.F2.10.m2.1.1" xref="S2.F2.10.m2.1.1.cmml"><msub id="S2.F2.10.m2.1.1.2" xref="S2.F2.10.m2.1.1.2.cmml"><mi id="S2.F2.10.m2.1.1.2.2" xref="S2.F2.10.m2.1.1.2.2.cmml">J</mi><mn id="S2.F2.10.m2.1.1.2.3" xref="S2.F2.10.m2.1.1.2.3.cmml">2</mn></msub><mo id="S2.F2.10.m2.1.1.1" xref="S2.F2.10.m2.1.1.1.cmml">=</mo><mrow id="S2.F2.10.m2.1.1.3" xref="S2.F2.10.m2.1.1.3.cmml"><mn id="S2.F2.10.m2.1.1.3.2" xref="S2.F2.10.m2.1.1.3.2.cmml">0.09</mn><mo id="S2.F2.10.m2.1.1.3.1" xref="S2.F2.10.m2.1.1.3.1.cmml">⁢</mo><mi id="S2.F2.10.m2.1.1.3.3" xref="S2.F2.10.m2.1.1.3.3.cmml">J</mi></mrow></mrow></math>

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1512.06740

Formulas:

1-

E_{j} (\bar{𝐫}, t) = F_{j} (x, y) A_{j} (z, t) e^{i (k_{j} z - ω_{j} t)}

2-

A_{j} (z, t)

3-

ω_{j} = ω_{0} \mp j Ω_{B}

4-

A_{+} (z, t)

5-

A_{-} (z, t)

6-

Ω_{B} / 2 π \approx

7-

ω_{0} / 2 π \approx

8-

E_{+} (\bar{𝐫}, t)

9-

= F_{p} (x, y) A_{+} (z, t) e^{i (k_{0} z - ω_{0} t)} + c . c .

10-

E_{-} (\bar{𝐫}, t)

Formulas (html):

Correct Categorie: physics

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0610474

Formulas:

1-

χ \equiv \frac{ρ_{c}}{ρ_{a}}, η \equiv \frac{ρ_{b}}{ρ_{a}} .

2-

ρ_{b} h_{b} Γ_{b}^{', 2} v_{b}^{', 2} = ρ_{a} h_{a} Γ_{a}^{', 2} v_{a}^{', 2}

3-

v_{b}^{'} = (v_{b} - v_{a}) / (1 - v_{b} v_{a})

4-

Γ_{b}^{'} = Γ_{b} Γ_{a} (1 - v_{b} v_{a})

5-

v_{a}^{'} = - v_{a}

6-

Γ_{a}^{'} = Γ_{a}

7-

ρ_{b} h_{b} Γ_{b}^{2} {(v_{b} - v_{a})}^{2} = ρ_{a} h_{a} v_{a}^{2} .

8-

v_{a} = \frac{v_{b}}{\sqrt{1 / η^{*}} + 1},

9-

η^{*} = Γ_{b}^{2} \frac{ρ_{b} h_{b}}{ρ_{a} h_{a}} .

10-

v_{a} = v_{b} / (\sqrt{1 / η} + 1)

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0402402

Formulas:

1-

P_{tune} = (Δ n d) / (n Λ)

2-

\frac{m λ}{n_{i}} = Λ_{g} (\sin α_{i} + \sin β_{i})

3-

β_{i} = - α_{i}

4-

α_{2 b} = α_{2}

5-

Λ_{g} = \frac{Λ}{\cos ϕ}

6-

β_{2} + ϕ = α_{2} - ϕ

7-

\frac{m λ}{n_{2}} = 2 Λ \sin α_{2 b}

8-

α_{2 b} = α_{2} - ϕ

9-

n_{2} \sin α_{2 b} = n_{i} \sin α_{i}

10-

\frac{m λ}{n_{i}} = 2 Λ_{g} \sin α_{i} .

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/1206.2479

Formulas:

1-

β^{- 1} \ln 2

2-

β^{- 1} \ln 2

3-

k = 1, 2, \dots

4-

P_{F}^{i} [x]

5-

P_{F}^{f} [x^{'}]

6-

σ := Δ s - \sum_{k} β_{k} Q_{k},

7-

Δ s := (- \ln P_{F}^{f} [x^{'}]) - (- \ln P_{F}^{i} [x])

8-

- β_{k} Q_{k}

9-

P_{F} [X_{F} | x, y]

10-

P_{F}^{i} [x, y]

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1111.1895

Formulas:

1-

i = 1, 2, 3, 4

2-

C m c a

3-

i = 1, 2, 3, 4

4-

E^{AMF} = - \frac{U_{eff}}{2} \sum_{σ} T r {(𝐧_{σ} - {\bar{n}}_{σ} 𝐈)}^{2} .

5-

U_{eff} = U - J

6-

{\bar{n}}_{σ} = T r (𝐧_{σ}) / (2 ℓ + 1)

7-

𝐧_{σ} = 𝝀_{σ} 𝐧_{σ}^{mt}

8-

𝝀_{σ} = 𝐧_{σ} {(𝐧_{σ}^{mt})}^{- 1}

9-

T r 𝝀_{σ} / (2 l + 1) = 2.67

10-

𝐕_{σ}^{AMF, mt} = - U_{eff} 𝝀_{σ} (𝐧_{σ} - {\bar{n}}_{σ} 𝐈) .

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/cond-mat/9609263

Formulas:

1-

⟨ Φ (r) ⟩

2-

{⟨ Φ (l) ⟩}_{a b} = L^{- x_{Φ}} F_{a b} (l / L),

3-

F_{a b} (l / L) = A [1 + B_{a b} {(\frac{l}{L})}^{d} + \dots] \frac{l}{L} ≪ 1 .

4-

A_{a b} L^{- d + 1}

5-

{⟨ Φ (l) ⟩}_{a a} = L^{- x_{Φ}} f_{a a} (l / L)

6-

f_{a a} (v) = f_{a a} (1 - v)

7-

{lim}_{v \to 0} f_{a a} (v) \sim v^{- x_{Φ}}

8-

{[f_{a a} (v)]}^{- 1 / x_{Φ}}

9-

{⟨ Φ (l) ⟩}_{a a} = L^{- x_{Φ}} {[\sum_{k = 1}^{\infty} A_{k} \sin \frac{k π l}{L}]}^{- x_{Φ}}

10-

{⟨ Φ (l) ⟩}_{a a} = A {[\frac{L}{π} \sin π \frac{l}{L}]}^{- x_{Φ}}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/2004.10937

Formulas:

1-

A (x, t)

2-

\frac{1}{ρ} \frac{D ρ}{D t}

3-

= - \frac{\partial u}{\partial x} - {\dot{σ}}_{A}

4-

ρ \frac{D u}{D t}

5-

= - \frac{\partial p}{\partial x}

6-

\frac{D p}{D t}

7-

= c^{2} \frac{D ρ}{D t} + ρ c^{2} \dot{σ}

8-

D / D t = \partial / \partial t + u \partial / \partial x

9-

{\dot{σ}}_{A} = \frac{D \ln A}{D t}

10-

\dot{σ} = - \frac{ρ}{c_{p}} {(\frac{\partial v}{\partial T})}_{p, Y_{i}} \sum_{i = 1}^{N} {(\frac{\partial h}{\partial Y_{i}})}_{p, ρ, Y_{j, j \neq i}} \frac{D Y_{i}}{D t}

Formulas (html):

Correct Categorie: physics

Guessed Categorie: nlin

Result: incorrect

Paper: https://arxiv.org/abs/1204.6368

Formulas:

1-

u (r) = 4 ϵ [{(σ / r)}^{12} - {(σ / r)}^{6}],

2-

ϵ_{T} = \sqrt{ϵ_{C} ϵ}

3-

σ_{T} = (σ_{C} + σ) / 2

4-

Σ_{S} = ℓ^{- 2}

5-

λ, θ (x)

6-

𝐮 = 𝐫_{i}^{'} - 𝐫_{i} < a_{0}

7-

𝐀 = \frac{2 β ℏ}{3 a_{0} e} (u_{x x} - u_{y y}, - 2 u_{x y}),

8-

B = \partial_{y} A_{x} - \partial_{x} A_{y} .

9-

h_{S} (x, y) = h_{0} θ (x),

10-

h_{S} (x, y) = h_{0} θ (x^{2} - d^{2}),

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1901.04251

Formulas:

1-

n - 3, n - 2

2-

\frac{\partial 𝐁}{\partial t} = \nabla \times (𝐯 \times 𝐁) - \nabla \times (η \nabla \times 𝐁),

3-

𝐕 = V_{r} \vec{e_{r}} + V_{θ} \vec{e_{θ}} + r \sin θ Ω \vec{e_{ϕ}} + \vec{V_{b}},

4-

(V_{r}, V_{θ})

5-

[0.65, 1.0] R_{⊙}

6-

Ω (r, θ)

7-

Ω_{c} + \frac{1}{2} [1 + e r f (\frac{r - r_{c}}{d_{1}})] (1 - Ω_{c} - c_{2} \cos^{2} θ),

8-

Ω_{c} = 0.92, c_{2} = 0.2, r_{c} = 0.7 R_{⊙}

9-

d_{1} = 0.15 R_{⊙}

10-

ρ (r) = {[(R_{⊙} / r) - 0.95]}^{m}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/hep-ph/0607306

Formulas:

1-

μ_{0} = 2 m_{Q}

2-

Z \to b \bar{b}

3-

c, b \to X_{c}

4-

μ_{0} = 2 m_{Q}

5-

D_{Q} (x, μ^{2})

6-

D_{c} (x, μ_{0}^{2})

7-

N \frac{x {(1 - x)}^{2}}{{[{(1 - x)}^{2} + ϵ x]}^{2}},

8-

D_{b} (x, μ_{0}^{2})

9-

N x^{α} {(1 - x)}^{β},

10-

χ^{2} / d . o . f .

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: hep-ph

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0007427

Formulas:

1-

m_{v} = 18.97 \pm 0.15

2-

T_{eff} \approx 100, 000 K

3-

L \approx 10 - 1000 L_{⊙}

4-

d = 1047_{- 500}^{+ 1000}

5-

= 80, 000 \pm 10, 000

6-

(M_{V}, V - I)

7-

M_{V} = 10.01 \pm 0.68

8-

M_{V} = 9.68 \pm 0.1

9-

M_{V} = 10.01 \pm 0.68

10-

T_{eff} = 3500 K

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1410.4786

Formulas:

1-

𝒫 \cup (- 𝒫)

2-

𝒪 {(P)}^{\pm}

3-

A = [𝐚_{1}, \dots, 𝐚_{n}] \in ℤ_{\geq 0}^{d \times n}

4-

B = [𝐛_{1}, \dots, 𝐛_{m}] \in ℤ_{\geq 0}^{d \times m}

5-

[𝟎, - B, A] \in ℤ^{d \times (n + m)}

6-

{- 𝐛_{1}, \dots, - 𝐛_{m}, 𝐚_{1}, \dots, 𝐚_{n}}

7-

𝒫 \cap ℤ^{d} = {𝟎, - 𝐛_{1}, \dots, - 𝐛_{m}, 𝐚_{1}, \dots, 𝐚_{n}}

8-

[- B, A]

9-

det (A^{'}) = \pm 1

10-

[d] = {1, \dots, d}

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/cond-mat/9804268

Formulas:

1-

u \sim \exp (- C / f)

2-

ℋ = γ \int d^{D} x [\frac{1}{2} {(\nabla z)}^{2} + V_{L} (z (𝐱)) + V_{R} (z (𝐱), 𝐱)] .

3-

V_{L} (z) = - v a^{2} \cos (2 π z / a)

4-

V_{R} (z (𝐱), 𝐱)

5-

\bar{V_{R} (z, 𝐱)} = 0

6-

\bar{V_{R} (z, 𝐱) V_{R} (z^{'}, 𝐱^{'})} = R (z - z^{'}) δ (𝐱 - 𝐱^{'}) .

7-

R (z) \sim - Δ_{0} | z |

8-

Δ_{0} ξ_{0}^{2}

9-

E_{step} ≃ γ \sqrt{v} L^{D - 1}

10-

w_{step} ≃ v^{- 1 / 2}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/0801.0420

Formulas:

1-

V (x, t) = \frac{V_{0} (t)}{\cosh^{2} [(x - x_{c} (t)) / L]},

2-

V_{0} (t) = A_{0} [1 + κ \sin (ω t + Δ)],

3-

x_{c} (t) = x_{0} \sin (ω t) .

4-

v_{c} (t) \equiv {\dot{x}}_{c} (t) = ω x_{0} \cos (ω t) .

5-

L = x_{0} / 2

6-

r (k_{F}, V_{0}) = \frac{Γ (1 + ν - i k_{F} L) Γ (- ν - i k_{F} L) Γ (i k_{F} L)}{Γ (1 + ν) Γ (- ν) Γ (- i k_{F} L)},

7-

t (k_{F}, V_{0}) = \frac{Γ (1 + ν - i k_{F} L) Γ (- ν - i k_{F} L)}{Γ (1 - i k_{F} L) Γ (- i k_{F} L)},

8-

ν = \frac{1}{2} [- 1 + \sqrt{1 - 8 V_{0} L^{2}}] .

9-

x_{c} (t)

10-

k = \pm k_{F} - v_{c}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/0710.0288

Formulas:

1-

\frac{d E_{i o n}}{d x} (E) = \frac{d E_{i o n - n}}{d x} (E) + \frac{d E_{i o n - e}}{d x} (E)

2-

\frac{d E_{i o n - n}}{d x}

3-

\frac{d E_{i o n - e}}{d x} (E)

4-

\frac{d L_{e}}{d x}

5-

\frac{d L_{i o n}}{d x}

6-

\frac{d L_{e}}{d x}

7-

α \frac{d E_{e - e}}{d x} for electrons

8-

\frac{d L_{i o n}}{d x}

9-

α \frac{d E_{i o n - e}}{d x} (E) = α \times \frac{d E_{i o n}}{d x} \times q^{'} (E) for ions (recoils)

10-

\frac{d E_{e - e}}{d x}

Formulas (html):

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xref="S2.p3.1.m1.1.1.2.cmml"><mi id="S2.p3.1.m1.1.1.2.2" xref="S2.p3.1.m1.1.1.2.2.cmml">d</mi><mo id="S2.p3.1.m1.1.1.2.1" xref="S2.p3.1.m1.1.1.2.1.cmml">⁢</mo><msub id="S2.p3.1.m1.1.1.2.3" xref="S2.p3.1.m1.1.1.2.3.cmml"><mi id="S2.p3.1.m1.1.1.2.3.2" xref="S2.p3.1.m1.1.1.2.3.2.cmml">L</mi><mi id="S2.p3.1.m1.1.1.2.3.3" xref="S2.p3.1.m1.1.1.2.3.3.cmml">e</mi></msub></mrow><mrow id="S2.p3.1.m1.1.1.3" xref="S2.p3.1.m1.1.1.3.cmml"><mi id="S2.p3.1.m1.1.1.3.2" xref="S2.p3.1.m1.1.1.3.2.cmml">d</mi><mo id="S2.p3.1.m1.1.1.3.1" xref="S2.p3.1.m1.1.1.3.1.cmml">⁢</mo><mi id="S2.p3.1.m1.1.1.3.3" xref="S2.p3.1.m1.1.1.3.3.cmml">x</mi></mrow></mfrac></math>, <math><mfrac id="S2.p3.2.m2.1.1" xref="S2.p3.2.m2.1.1.cmml"><mrow id="S2.p3.2.m2.1.1.2" xref="S2.p3.2.m2.1.1.2.cmml"><mi id="S2.p3.2.m2.1.1.2.2" xref="S2.p3.2.m2.1.1.2.2.cmml">d</mi><mo id="S2.p3.2.m2.1.1.2.1" xref="S2.p3.2.m2.1.1.2.1.cmml">⁢</mo><msub id="S2.p3.2.m2.1.1.2.3" xref="S2.p3.2.m2.1.1.2.3.cmml"><mi id="S2.p3.2.m2.1.1.2.3.2" xref="S2.p3.2.m2.1.1.2.3.2.cmml">L</mi><mrow id="S2.p3.2.m2.1.1.2.3.3" xref="S2.p3.2.m2.1.1.2.3.3.cmml"><mi id="S2.p3.2.m2.1.1.2.3.3.2" xref="S2.p3.2.m2.1.1.2.3.3.2.cmml">i</mi><mo id="S2.p3.2.m2.1.1.2.3.3.1" xref="S2.p3.2.m2.1.1.2.3.3.1.cmml">⁢</mo><mi id="S2.p3.2.m2.1.1.2.3.3.3" xref="S2.p3.2.m2.1.1.2.3.3.3.cmml">o</mi><mo id="S2.p3.2.m2.1.1.2.3.3.1a" xref="S2.p3.2.m2.1.1.2.3.3.1.cmml">⁢</mo><mi id="S2.p3.2.m2.1.1.2.3.3.4" xref="S2.p3.2.m2.1.1.2.3.3.4.cmml">n</mi></mrow></msub></mrow><mrow id="S2.p3.2.m2.1.1.3" xref="S2.p3.2.m2.1.1.3.cmml"><mi id="S2.p3.2.m2.1.1.3.2" xref="S2.p3.2.m2.1.1.3.2.cmml">d</mi><mo id="S2.p3.2.m2.1.1.3.1" xref="S2.p3.2.m2.1.1.3.1.cmml">⁢</mo><mi id="S2.p3.2.m2.1.1.3.3" xref="S2.p3.2.m2.1.1.3.3.cmml">x</mi></mrow></mfrac></math>, <math><mstyle displaystyle="true" id="S2.Ex1.m1.1.1" xref="S2.Ex1.m1.1.1.cmml"><mfrac id="S2.Ex1.m1.1.1a" xref="S2.Ex1.m1.1.1.cmml"><mrow id="S2.Ex1.m1.1.1.2" xref="S2.Ex1.m1.1.1.2.cmml"><mi id="S2.Ex1.m1.1.1.2.2" xref="S2.Ex1.m1.1.1.2.2.cmml">d</mi><mo id="S2.Ex1.m1.1.1.2.1" xref="S2.Ex1.m1.1.1.2.1.cmml">⁢</mo><msub id="S2.Ex1.m1.1.1.2.3" xref="S2.Ex1.m1.1.1.2.3.cmml"><mi id="S2.Ex1.m1.1.1.2.3.2" xref="S2.Ex1.m1.1.1.2.3.2.cmml">L</mi><mi id="S2.Ex1.m1.1.1.2.3.3" xref="S2.Ex1.m1.1.1.2.3.3.cmml">e</mi></msub></mrow><mrow id="S2.Ex1.m1.1.1.3" xref="S2.Ex1.m1.1.1.3.cmml"><mi id="S2.Ex1.m1.1.1.3.2" xref="S2.Ex1.m1.1.1.3.2.cmml">d</mi><mo id="S2.Ex1.m1.1.1.3.1" xref="S2.Ex1.m1.1.1.3.1.cmml">⁢</mo><mi id="S2.Ex1.m1.1.1.3.3" xref="S2.Ex1.m1.1.1.3.3.cmml">x</mi></mrow></mfrac></mstyle></math>, <math><mrow id="S2.Ex1.m3.1.1" xref="S2.Ex1.m3.1.1.cmml"><mi id="S2.Ex1.m3.1.1.2" xref="S2.Ex1.m3.1.1.2.cmml">α</mi><mo id="S2.Ex1.m3.1.1.1" xref="S2.Ex1.m3.1.1.1.cmml">⁢</mo><mstyle displaystyle="true" id="S2.Ex1.m3.1.1.3" xref="S2.Ex1.m3.1.1.3.cmml"><mfrac id="S2.Ex1.m3.1.1.3a" xref="S2.Ex1.m3.1.1.3.cmml"><mrow id="S2.Ex1.m3.1.1.3.2" xref="S2.Ex1.m3.1.1.3.2.cmml"><mi id="S2.Ex1.m3.1.1.3.2.2" xref="S2.Ex1.m3.1.1.3.2.2.cmml">d</mi><mo id="S2.Ex1.m3.1.1.3.2.1" xref="S2.Ex1.m3.1.1.3.2.1.cmml">⁢</mo><msub id="S2.Ex1.m3.1.1.3.2.3" xref="S2.Ex1.m3.1.1.3.2.3.cmml"><mi id="S2.Ex1.m3.1.1.3.2.3.2" xref="S2.Ex1.m3.1.1.3.2.3.2.cmml">E</mi><mrow id="S2.Ex1.m3.1.1.3.2.3.3" xref="S2.Ex1.m3.1.1.3.2.3.3.cmml"><mi id="S2.Ex1.m3.1.1.3.2.3.3.2" xref="S2.Ex1.m3.1.1.3.2.3.3.2.cmml">e</mi><mo id="S2.Ex1.m3.1.1.3.2.3.3.1" xref="S2.Ex1.m3.1.1.3.2.3.3.1.cmml">-</mo><mi id="S2.Ex1.m3.1.1.3.2.3.3.3" xref="S2.Ex1.m3.1.1.3.2.3.3.3.cmml">e</mi></mrow></msub></mrow><mrow id="S2.Ex1.m3.1.1.3.3" xref="S2.Ex1.m3.1.1.3.3.cmml"><mi id="S2.Ex1.m3.1.1.3.3.2" xref="S2.Ex1.m3.1.1.3.3.2.cmml">d</mi><mo id="S2.Ex1.m3.1.1.3.3.1" xref="S2.Ex1.m3.1.1.3.3.1.cmml">⁢</mo><mi id="S2.Ex1.m3.1.1.3.3.3" xref="S2.Ex1.m3.1.1.3.3.3.cmml">x</mi></mrow></mfrac></mstyle><mo id="S2.Ex1.m3.1.1.1a" xref="S2.Ex1.m3.1.1.1.cmml">⁢</mo><mtext id="S2.Ex1.m3.1.1.4" xref="S2.Ex1.m3.1.1.4a.cmml"> for electrons</mtext></mrow></math>, <math><mstyle displaystyle="true" id="S2.E2.m1.1.1" xref="S2.E2.m1.1.1.cmml"><mfrac id="S2.E2.m1.1.1a" xref="S2.E2.m1.1.1.cmml"><mrow id="S2.E2.m1.1.1.2" xref="S2.E2.m1.1.1.2.cmml"><mi id="S2.E2.m1.1.1.2.2" xref="S2.E2.m1.1.1.2.2.cmml">d</mi><mo id="S2.E2.m1.1.1.2.1" xref="S2.E2.m1.1.1.2.1.cmml">⁢</mo><msub id="S2.E2.m1.1.1.2.3" xref="S2.E2.m1.1.1.2.3.cmml"><mi id="S2.E2.m1.1.1.2.3.2" xref="S2.E2.m1.1.1.2.3.2.cmml">L</mi><mrow id="S2.E2.m1.1.1.2.3.3" xref="S2.E2.m1.1.1.2.3.3.cmml"><mi id="S2.E2.m1.1.1.2.3.3.2" xref="S2.E2.m1.1.1.2.3.3.2.cmml">i</mi><mo id="S2.E2.m1.1.1.2.3.3.1" xref="S2.E2.m1.1.1.2.3.3.1.cmml">⁢</mo><mi id="S2.E2.m1.1.1.2.3.3.3" xref="S2.E2.m1.1.1.2.3.3.3.cmml">o</mi><mo id="S2.E2.m1.1.1.2.3.3.1a" xref="S2.E2.m1.1.1.2.3.3.1.cmml">⁢</mo><mi id="S2.E2.m1.1.1.2.3.3.4" xref="S2.E2.m1.1.1.2.3.3.4.cmml">n</mi></mrow></msub></mrow><mrow id="S2.E2.m1.1.1.3" xref="S2.E2.m1.1.1.3.cmml"><mi id="S2.E2.m1.1.1.3.2" xref="S2.E2.m1.1.1.3.2.cmml">d</mi><mo id="S2.E2.m1.1.1.3.1" xref="S2.E2.m1.1.1.3.1.cmml">⁢</mo><mi id="S2.E2.m1.1.1.3.3" xref="S2.E2.m1.1.1.3.3.cmml">x</mi></mrow></mfrac></mstyle></math>, <math><mrow id="S2.E2.m3.2.3" xref="S2.E2.m3.2.3.cmml"><mrow id="S2.E2.m3.2.3.2" xref="S2.E2.m3.2.3.2.cmml"><mi id="S2.E2.m3.2.3.2.2" xref="S2.E2.m3.2.3.2.2.cmml">α</mi><mo id="S2.E2.m3.2.3.2.1" xref="S2.E2.m3.2.3.2.1.cmml">⁢</mo><mstyle displaystyle="true" id="S2.E2.m3.2.3.2.3" xref="S2.E2.m3.2.3.2.3.cmml"><mfrac id="S2.E2.m3.2.3.2.3a" xref="S2.E2.m3.2.3.2.3.cmml"><mrow id="S2.E2.m3.2.3.2.3.2" xref="S2.E2.m3.2.3.2.3.2.cmml"><mi id="S2.E2.m3.2.3.2.3.2.2" xref="S2.E2.m3.2.3.2.3.2.2.cmml">d</mi><mo id="S2.E2.m3.2.3.2.3.2.1" xref="S2.E2.m3.2.3.2.3.2.1.cmml">⁢</mo><msub id="S2.E2.m3.2.3.2.3.2.3" xref="S2.E2.m3.2.3.2.3.2.3.cmml"><mi id="S2.E2.m3.2.3.2.3.2.3.2" xref="S2.E2.m3.2.3.2.3.2.3.2.cmml">E</mi><mrow id="S2.E2.m3.2.3.2.3.2.3.3" xref="S2.E2.m3.2.3.2.3.2.3.3.cmml"><mrow id="S2.E2.m3.2.3.2.3.2.3.3.2" xref="S2.E2.m3.2.3.2.3.2.3.3.2.cmml"><mi id="S2.E2.m3.2.3.2.3.2.3.3.2.2" xref="S2.E2.m3.2.3.2.3.2.3.3.2.2.cmml">i</mi><mo id="S2.E2.m3.2.3.2.3.2.3.3.2.1" xref="S2.E2.m3.2.3.2.3.2.3.3.2.1.cmml">⁢</mo><mi id="S2.E2.m3.2.3.2.3.2.3.3.2.3" xref="S2.E2.m3.2.3.2.3.2.3.3.2.3.cmml">o</mi><mo id="S2.E2.m3.2.3.2.3.2.3.3.2.1a" xref="S2.E2.m3.2.3.2.3.2.3.3.2.1.cmml">⁢</mo><mi id="S2.E2.m3.2.3.2.3.2.3.3.2.4" xref="S2.E2.m3.2.3.2.3.2.3.3.2.4.cmml">n</mi></mrow><mo id="S2.E2.m3.2.3.2.3.2.3.3.1" xref="S2.E2.m3.2.3.2.3.2.3.3.1.cmml">-</mo><mi id="S2.E2.m3.2.3.2.3.2.3.3.3" xref="S2.E2.m3.2.3.2.3.2.3.3.3.cmml">e</mi></mrow></msub></mrow><mrow id="S2.E2.m3.2.3.2.3.3" xref="S2.E2.m3.2.3.2.3.3.cmml"><mi id="S2.E2.m3.2.3.2.3.3.2" xref="S2.E2.m3.2.3.2.3.3.2.cmml">d</mi><mo id="S2.E2.m3.2.3.2.3.3.1" xref="S2.E2.m3.2.3.2.3.3.1.cmml">⁢</mo><mi id="S2.E2.m3.2.3.2.3.3.3" xref="S2.E2.m3.2.3.2.3.3.3.cmml">x</mi></mrow></mfrac></mstyle><mo id="S2.E2.m3.2.3.2.1a" xref="S2.E2.m3.2.3.2.1.cmml">⁢</mo><mrow id="S2.E2.m3.2.3.2.4.2" xref="S2.E2.m3.2.3.2.cmml"><mo stretchy="false" id="S2.E2.m3.2.3.2.4.2.1" xref="S2.E2.m3.2.3.2.cmml">(</mo><mi id="S2.E2.m3.1.1" xref="S2.E2.m3.1.1.cmml">E</mi><mo stretchy="false" id="S2.E2.m3.2.3.2.4.2.2" xref="S2.E2.m3.2.3.2.cmml">)</mo></mrow></mrow><mo id="S2.E2.m3.2.3.1" xref="S2.E2.m3.2.3.1.cmml">=</mo><mrow id="S2.E2.m3.2.3.3" xref="S2.E2.m3.2.3.3.cmml"><mrow id="S2.E2.m3.2.3.3.2" xref="S2.E2.m3.2.3.3.2.cmml"><mi id="S2.E2.m3.2.3.3.2.2" xref="S2.E2.m3.2.3.3.2.2.cmml">α</mi><mo id="S2.E2.m3.2.3.3.2.1" xref="S2.E2.m3.2.3.3.2.1.cmml">×</mo><mstyle displaystyle="true" id="S2.E2.m3.2.3.3.2.3" xref="S2.E2.m3.2.3.3.2.3.cmml"><mfrac id="S2.E2.m3.2.3.3.2.3a" xref="S2.E2.m3.2.3.3.2.3.cmml"><mrow id="S2.E2.m3.2.3.3.2.3.2" xref="S2.E2.m3.2.3.3.2.3.2.cmml"><mi id="S2.E2.m3.2.3.3.2.3.2.2" xref="S2.E2.m3.2.3.3.2.3.2.2.cmml">d</mi><mo id="S2.E2.m3.2.3.3.2.3.2.1" xref="S2.E2.m3.2.3.3.2.3.2.1.cmml">⁢</mo><msub id="S2.E2.m3.2.3.3.2.3.2.3" xref="S2.E2.m3.2.3.3.2.3.2.3.cmml"><mi id="S2.E2.m3.2.3.3.2.3.2.3.2" xref="S2.E2.m3.2.3.3.2.3.2.3.2.cmml">E</mi><mrow id="S2.E2.m3.2.3.3.2.3.2.3.3" xref="S2.E2.m3.2.3.3.2.3.2.3.3.cmml"><mi id="S2.E2.m3.2.3.3.2.3.2.3.3.2" xref="S2.E2.m3.2.3.3.2.3.2.3.3.2.cmml">i</mi><mo id="S2.E2.m3.2.3.3.2.3.2.3.3.1" xref="S2.E2.m3.2.3.3.2.3.2.3.3.1.cmml">⁢</mo><mi id="S2.E2.m3.2.3.3.2.3.2.3.3.3" xref="S2.E2.m3.2.3.3.2.3.2.3.3.3.cmml">o</mi><mo id="S2.E2.m3.2.3.3.2.3.2.3.3.1a" xref="S2.E2.m3.2.3.3.2.3.2.3.3.1.cmml">⁢</mo><mi id="S2.E2.m3.2.3.3.2.3.2.3.3.4" xref="S2.E2.m3.2.3.3.2.3.2.3.3.4.cmml">n</mi></mrow></msub></mrow><mrow id="S2.E2.m3.2.3.3.2.3.3" xref="S2.E2.m3.2.3.3.2.3.3.cmml"><mi id="S2.E2.m3.2.3.3.2.3.3.2" xref="S2.E2.m3.2.3.3.2.3.3.2.cmml">d</mi><mo id="S2.E2.m3.2.3.3.2.3.3.1" xref="S2.E2.m3.2.3.3.2.3.3.1.cmml">⁢</mo><mi id="S2.E2.m3.2.3.3.2.3.3.3" xref="S2.E2.m3.2.3.3.2.3.3.3.cmml">x</mi></mrow></mfrac></mstyle><mo id="S2.E2.m3.2.3.3.2.1a" xref="S2.E2.m3.2.3.3.2.1.cmml">×</mo><msup id="S2.E2.m3.2.3.3.2.4" xref="S2.E2.m3.2.3.3.2.4.cmml"><mi id="S2.E2.m3.2.3.3.2.4.2" xref="S2.E2.m3.2.3.3.2.4.2.cmml">q</mi><mo id="S2.E2.m3.2.3.3.2.4.3" xref="S2.E2.m3.2.3.3.2.4.3.cmml">′</mo></msup></mrow><mo id="S2.E2.m3.2.3.3.1" xref="S2.E2.m3.2.3.3.1.cmml">⁢</mo><mrow id="S2.E2.m3.2.3.3.3.2" xref="S2.E2.m3.2.3.3.cmml"><mo stretchy="false" id="S2.E2.m3.2.3.3.3.2.1" xref="S2.E2.m3.2.3.3.cmml">(</mo><mi id="S2.E2.m3.2.2" xref="S2.E2.m3.2.2.cmml">E</mi><mo stretchy="false" id="S2.E2.m3.2.3.3.3.2.2" xref="S2.E2.m3.2.3.3.cmml">)</mo></mrow><mo id="S2.E2.m3.2.3.3.1a" xref="S2.E2.m3.2.3.3.1.cmml">⁢</mo><mtext id="S2.E2.m3.2.3.3.4" xref="S2.E2.m3.2.3.3.4a.cmml"> for ions (recoils)</mtext></mrow></mrow></math>, <math><mfrac id="S2.p3.4.m2.1.1" xref="S2.p3.4.m2.1.1.cmml"><mrow id="S2.p3.4.m2.1.1.2" xref="S2.p3.4.m2.1.1.2.cmml"><mi id="S2.p3.4.m2.1.1.2.2" xref="S2.p3.4.m2.1.1.2.2.cmml">d</mi><mo id="S2.p3.4.m2.1.1.2.1" xref="S2.p3.4.m2.1.1.2.1.cmml">⁢</mo><msub id="S2.p3.4.m2.1.1.2.3" xref="S2.p3.4.m2.1.1.2.3.cmml"><mi id="S2.p3.4.m2.1.1.2.3.2" xref="S2.p3.4.m2.1.1.2.3.2.cmml">E</mi><mrow id="S2.p3.4.m2.1.1.2.3.3" xref="S2.p3.4.m2.1.1.2.3.3.cmml"><mi id="S2.p3.4.m2.1.1.2.3.3.2" xref="S2.p3.4.m2.1.1.2.3.3.2.cmml">e</mi><mo id="S2.p3.4.m2.1.1.2.3.3.1" xref="S2.p3.4.m2.1.1.2.3.3.1.cmml">-</mo><mi id="S2.p3.4.m2.1.1.2.3.3.3" xref="S2.p3.4.m2.1.1.2.3.3.3.cmml">e</mi></mrow></msub></mrow><mrow id="S2.p3.4.m2.1.1.3" xref="S2.p3.4.m2.1.1.3.cmml"><mi id="S2.p3.4.m2.1.1.3.2" xref="S2.p3.4.m2.1.1.3.2.cmml">d</mi><mo id="S2.p3.4.m2.1.1.3.1" xref="S2.p3.4.m2.1.1.3.1.cmml">⁢</mo><mi id="S2.p3.4.m2.1.1.3.3" xref="S2.p3.4.m2.1.1.3.3.cmml">x</mi></mrow></mfrac></math>

Correct Categorie: astro-ph

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/2003.05655

Formulas:

1-

ℰ_{L A B}

2-

ℰ_{L A B}

3-

ℰ_{L A B}

4-

ℰ_{L A B}

5-

\exp (i Θ)

6-

Ψ (x, t)

7-

Φ (x - u t, t)

8-

Θ = - \frac{ϕ}{2} + \frac{m u x}{ℏ} + \frac{a_{1} N}{ℏ} \int^{x} 𝑑 s {| Φ (x - u t, t) |}^{2} .

9-

(\sqrt{R} Φ \to φ)

10-

Θ (θ, τ) = - \frac{q θ}{2} + \frac{u θ}{2} + a \int^{θ} 𝑑 θ^{'} {| φ (θ^{'}, τ) |}^{2} .

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1709.03982

Formulas:

1-

E (B - V)

2-

v_{rad} = 17.84 \pm 0.07

3-

N (H I)

4-

N_{H} = 1.82 \times 10^{13} \int T (v) 𝑑 v atoms {cm}^{- 2},

5-

\log [N (H I)] = 21.1

6-

σ_{EW} = σ_{flux} \times \frac{Δ λ}{N_{pix}}

7-

\log [N (H I)] = 21.1

8-

\log [\frac{N (H I)}{{cm}^{- 2}}] = 19.05 + 0.92 \times \log [\frac{W 5780}{m Å}]

9-

\log [N (H I)] = 21.16

10-

\log [N (H I)] = 19.9

Formulas (html):

<math><mrow id="S1.p2.1.m1.1.1" xref="S1.p2.1.m1.1.1.cmml"><mi id="S1.p2.1.m1.1.1.3" xref="S1.p2.1.m1.1.1.3.cmml">E</mi><mo id="S1.p2.1.m1.1.1.2" xref="S1.p2.1.m1.1.1.2.cmml">⁢</mo><mrow id="S1.p2.1.m1.1.1.1.1" xref="S1.p2.1.m1.1.1.1.1.1.cmml"><mo stretchy="false" id="S1.p2.1.m1.1.1.1.1.2" xref="S1.p2.1.m1.1.1.1.1.1.cmml">(</mo><mrow id="S1.p2.1.m1.1.1.1.1.1" xref="S1.p2.1.m1.1.1.1.1.1.cmml"><mi id="S1.p2.1.m1.1.1.1.1.1.2" xref="S1.p2.1.m1.1.1.1.1.1.2.cmml">B</mi><mo id="S1.p2.1.m1.1.1.1.1.1.1" xref="S1.p2.1.m1.1.1.1.1.1.1.cmml">-</mo><mi id="S1.p2.1.m1.1.1.1.1.1.3" xref="S1.p2.1.m1.1.1.1.1.1.3.cmml">V</mi></mrow><mo stretchy="false" id="S1.p2.1.m1.1.1.1.1.3" xref="S1.p2.1.m1.1.1.1.1.1.cmml">)</mo></mrow></mrow></math>, <math><mrow id="S2.p1.3.m3.1.1" xref="S2.p1.3.m3.1.1.cmml"><msub id="S2.p1.3.m3.1.1.2" xref="S2.p1.3.m3.1.1.2.cmml"><mi id="S2.p1.3.m3.1.1.2.2" xref="S2.p1.3.m3.1.1.2.2.cmml">v</mi><mi id="S2.p1.3.m3.1.1.2.3" xref="S2.p1.3.m3.1.1.2.3.cmml">rad</mi></msub><mo id="S2.p1.3.m3.1.1.1" xref="S2.p1.3.m3.1.1.1.cmml">=</mo><mrow id="S2.p1.3.m3.1.1.3" xref="S2.p1.3.m3.1.1.3.cmml"><mn id="S2.p1.3.m3.1.1.3.2" xref="S2.p1.3.m3.1.1.3.2.cmml">17.84</mn><mo id="S2.p1.3.m3.1.1.3.1" xref="S2.p1.3.m3.1.1.3.1.cmml">±</mo><mn id="S2.p1.3.m3.1.1.3.3" xref="S2.p1.3.m3.1.1.3.3.cmml">0.07</mn></mrow></mrow></math>, <math><mrow id="S2.SS2.SSS2.p1.7.m7.1.1" xref="S2.SS2.SSS2.p1.7.m7.1.1.cmml"><mi id="S2.SS2.SSS2.p1.7.m7.1.1.3" xref="S2.SS2.SSS2.p1.7.m7.1.1.3.cmml">N</mi><mo id="S2.SS2.SSS2.p1.7.m7.1.1.2" xref="S2.SS2.SSS2.p1.7.m7.1.1.2.cmml">⁢</mo><mrow id="S2.SS2.SSS2.p1.7.m7.1.1.1.1" xref="S2.SS2.SSS2.p1.7.m7.1.1.1.1.1.cmml"><mo stretchy="false" id="S2.SS2.SSS2.p1.7.m7.1.1.1.1.2" xref="S2.SS2.SSS2.p1.7.m7.1.1.1.1.1.cmml">(</mo><mrow id="S2.SS2.SSS2.p1.7.m7.1.1.1.1.1" xref="S2.SS2.SSS2.p1.7.m7.1.1.1.1.1.cmml"><mpadded width="+1.7pt" id="S2.SS2.SSS2.p1.7.m7.1.1.1.1.1.2" xref="S2.SS2.SSS2.p1.7.m7.1.1.1.1.1.2.cmml"><mi mathvariant="normal" 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id="S2.E1.m1.2.2.1.1.3" xref="S2.E1.m1.2.2.1.1.3.cmml"><mrow id="S2.E1.m1.2.2.1.1.3.2" xref="S2.E1.m1.2.2.1.1.3.2.cmml"><mn id="S2.E1.m1.2.2.1.1.3.2.2" xref="S2.E1.m1.2.2.1.1.3.2.2.cmml">1.82</mn><mo id="S2.E1.m1.2.2.1.1.3.2.1" xref="S2.E1.m1.2.2.1.1.3.2.1.cmml">×</mo><msup id="S2.E1.m1.2.2.1.1.3.2.3" xref="S2.E1.m1.2.2.1.1.3.2.3.cmml"><mn id="S2.E1.m1.2.2.1.1.3.2.3.2" xref="S2.E1.m1.2.2.1.1.3.2.3.2.cmml">10</mn><mn id="S2.E1.m1.2.2.1.1.3.2.3.3" xref="S2.E1.m1.2.2.1.1.3.2.3.3.cmml">13</mn></msup></mrow><mo id="S2.E1.m1.2.2.1.1.3.1" xref="S2.E1.m1.2.2.1.1.3.1.cmml">⁢</mo><mrow id="S2.E1.m1.2.2.1.1.3.3" xref="S2.E1.m1.2.2.1.1.3.3.cmml"><mo largeop="true" symmetric="true" id="S2.E1.m1.2.2.1.1.3.3.1" xref="S2.E1.m1.2.2.1.1.3.3.1.cmml">∫</mo><mrow id="S2.E1.m1.2.2.1.1.3.3.2" xref="S2.E1.m1.2.2.1.1.3.3.2.cmml"><mi id="S2.E1.m1.2.2.1.1.3.3.2.2" xref="S2.E1.m1.2.2.1.1.3.3.2.2.cmml">T</mi><mo id="S2.E1.m1.2.2.1.1.3.3.2.1" xref="S2.E1.m1.2.2.1.1.3.3.2.1.cmml">⁢</mo><mrow id="S2.E1.m1.2.2.1.1.3.3.2.3.2" xref="S2.E1.m1.2.2.1.1.3.3.2.cmml"><mo stretchy="false" id="S2.E1.m1.2.2.1.1.3.3.2.3.2.1" xref="S2.E1.m1.2.2.1.1.3.3.2.cmml">(</mo><mi id="S2.E1.m1.1.1" xref="S2.E1.m1.1.1.cmml">v</mi><mo rspace="4.2pt" stretchy="false" id="S2.E1.m1.2.2.1.1.3.3.2.3.2.2" xref="S2.E1.m1.2.2.1.1.3.3.2.cmml">)</mo></mrow><mo id="S2.E1.m1.2.2.1.1.3.3.2.1a" xref="S2.E1.m1.2.2.1.1.3.3.2.1.cmml">⁢</mo><mrow id="S2.E1.m1.2.2.1.1.3.3.2.4" xref="S2.E1.m1.2.2.1.1.3.3.2.4.cmml"><mo rspace="0pt" id="S2.E1.m1.2.2.1.1.3.3.2.4.1" xref="S2.E1.m1.2.2.1.1.3.3.2.4.1.cmml">𝑑</mo><mpadded width="+5pt" id="S2.E1.m1.2.2.1.1.3.3.2.4.2" xref="S2.E1.m1.2.2.1.1.3.3.2.4.2.cmml"><mi id="S2.E1.m1.2.2.1.1.3.3.2.4.2a" xref="S2.E1.m1.2.2.1.1.3.3.2.4.2.cmml">v</mi></mpadded></mrow><mo id="S2.E1.m1.2.2.1.1.3.3.2.1b" xref="S2.E1.m1.2.2.1.1.3.3.2.1.cmml">⁢</mo><mpadded width="+1.7pt" id="S2.E1.m1.2.2.1.1.3.3.2.5" xref="S2.E1.m1.2.2.1.1.3.3.2.5.cmml"><mi id="S2.E1.m1.2.2.1.1.3.3.2.5a" xref="S2.E1.m1.2.2.1.1.3.3.2.5.cmml">atoms</mi></mpadded><mo id="S2.E1.m1.2.2.1.1.3.3.2.1c" xref="S2.E1.m1.2.2.1.1.3.3.2.1.cmml">⁢</mo><msup id="S2.E1.m1.2.2.1.1.3.3.2.6" xref="S2.E1.m1.2.2.1.1.3.3.2.6.cmml"><mi id="S2.E1.m1.2.2.1.1.3.3.2.6.2" xref="S2.E1.m1.2.2.1.1.3.3.2.6.2.cmml">cm</mi><mrow id="S2.E1.m1.2.2.1.1.3.3.2.6.3" xref="S2.E1.m1.2.2.1.1.3.3.2.6.3.cmml"><mo id="S2.E1.m1.2.2.1.1.3.3.2.6.3.1" xref="S2.E1.m1.2.2.1.1.3.3.2.6.3.1.cmml">-</mo><mn id="S2.E1.m1.2.2.1.1.3.3.2.6.3.2" xref="S2.E1.m1.2.2.1.1.3.3.2.6.3.2.cmml">2</mn></mrow></msup></mrow></mrow></mrow></mrow><mo id="S2.E1.m1.2.2.1.2" xref="S2.E1.m1.2.2.1.1.cmml">,</mo></mrow></math>, <math><mrow id="S2.SS2.SSS2.p2.3.m1.2.2" xref="S2.SS2.SSS2.p2.3.m1.2.2.cmml"><mrow id="S2.SS2.SSS2.p2.3.m1.2.2.1.1" xref="S2.SS2.SSS2.p2.3.m1.2.2.1.2.cmml"><mi id="S2.SS2.SSS2.p2.3.m1.1.1" xref="S2.SS2.SSS2.p2.3.m1.1.1.cmml">log</mi><mo id="S2.SS2.SSS2.p2.3.m1.2.2.1.1a" xref="S2.SS2.SSS2.p2.3.m1.2.2.1.2.cmml">⁡</mo><mrow id="S2.SS2.SSS2.p2.3.m1.2.2.1.1.1" xref="S2.SS2.SSS2.p2.3.m1.2.2.1.2.cmml"><mo stretchy="false" id="S2.SS2.SSS2.p2.3.m1.2.2.1.1.1.2" xref="S2.SS2.SSS2.p2.3.m1.2.2.1.2.cmml">[</mo><mrow id="S2.SS2.SSS2.p2.3.m1.2.2.1.1.1.1" xref="S2.SS2.SSS2.p2.3.m1.2.2.1.1.1.1.cmml"><mi id="S2.SS2.SSS2.p2.3.m1.2.2.1.1.1.1.3" xref="S2.SS2.SSS2.p2.3.m1.2.2.1.1.1.1.3.cmml">N</mi><mo id="S2.SS2.SSS2.p2.3.m1.2.2.1.1.1.1.2" xref="S2.SS2.SSS2.p2.3.m1.2.2.1.1.1.1.2.cmml">⁢</mo><mrow id="S2.SS2.SSS2.p2.3.m1.2.2.1.1.1.1.1.1" xref="S2.SS2.SSS2.p2.3.m1.2.2.1.1.1.1.1.1.1.cmml"><mo stretchy="false" id="S2.SS2.SSS2.p2.3.m1.2.2.1.1.1.1.1.1.2" xref="S2.SS2.SSS2.p2.3.m1.2.2.1.1.1.1.1.1.1.cmml">(</mo><mrow id="S2.SS2.SSS2.p2.3.m1.2.2.1.1.1.1.1.1.1" xref="S2.SS2.SSS2.p2.3.m1.2.2.1.1.1.1.1.1.1.cmml"><mpadded width="+1.7pt" id="S2.SS2.SSS2.p2.3.m1.2.2.1.1.1.1.1.1.1.2" xref="S2.SS2.SSS2.p2.3.m1.2.2.1.1.1.1.1.1.1.2.cmml"><mi mathvariant="normal" id="S2.SS2.SSS2.p2.3.m1.2.2.1.1.1.1.1.1.1.2a" xref="S2.SS2.SSS2.p2.3.m1.2.2.1.1.1.1.1.1.1.2.cmml">H</mi></mpadded><mo id="S2.SS2.SSS2.p2.3.m1.2.2.1.1.1.1.1.1.1.1" xref="S2.SS2.SSS2.p2.3.m1.2.2.1.1.1.1.1.1.1.1.cmml">⁢</mo><mpadded width="+1.7pt" id="S2.SS2.SSS2.p2.3.m1.2.2.1.1.1.1.1.1.1.3" xref="S2.SS2.SSS2.p2.3.m1.2.2.1.1.1.1.1.1.1.3.cmml"><mi mathsize="70%" mathvariant="normal" id="S2.SS2.SSS2.p2.3.m1.2.2.1.1.1.1.1.1.1.3a" xref="S2.SS2.SSS2.p2.3.m1.2.2.1.1.1.1.1.1.1.3.cmml">I</mi></mpadded></mrow><mo stretchy="false" id="S2.SS2.SSS2.p2.3.m1.2.2.1.1.1.1.1.1.3" xref="S2.SS2.SSS2.p2.3.m1.2.2.1.1.1.1.1.1.1.cmml">)</mo></mrow></mrow><mo stretchy="false" id="S2.SS2.SSS2.p2.3.m1.2.2.1.1.1.3" xref="S2.SS2.SSS2.p2.3.m1.2.2.1.2.cmml">]</mo></mrow></mrow><mo id="S2.SS2.SSS2.p2.3.m1.2.2.2" xref="S2.SS2.SSS2.p2.3.m1.2.2.2.cmml">=</mo><mn id="S2.SS2.SSS2.p2.3.m1.2.2.3" xref="S2.SS2.SSS2.p2.3.m1.2.2.3.cmml">21.1</mn></mrow></math>, <math><mrow id="S4.SS1.p3.2.m2.1.1" xref="S4.SS1.p3.2.m2.1.1.cmml"><msub id="S4.SS1.p3.2.m2.1.1.2" xref="S4.SS1.p3.2.m2.1.1.2.cmml"><mi id="S4.SS1.p3.2.m2.1.1.2.2" xref="S4.SS1.p3.2.m2.1.1.2.2.cmml">σ</mi><mi id="S4.SS1.p3.2.m2.1.1.2.3" xref="S4.SS1.p3.2.m2.1.1.2.3.cmml">EW</mi></msub><mo id="S4.SS1.p3.2.m2.1.1.1" xref="S4.SS1.p3.2.m2.1.1.1.cmml">=</mo><mrow id="S4.SS1.p3.2.m2.1.1.3" xref="S4.SS1.p3.2.m2.1.1.3.cmml"><msub id="S4.SS1.p3.2.m2.1.1.3.2" xref="S4.SS1.p3.2.m2.1.1.3.2.cmml"><mi id="S4.SS1.p3.2.m2.1.1.3.2.2" xref="S4.SS1.p3.2.m2.1.1.3.2.2.cmml">σ</mi><mi id="S4.SS1.p3.2.m2.1.1.3.2.3" xref="S4.SS1.p3.2.m2.1.1.3.2.3.cmml">flux</mi></msub><mo id="S4.SS1.p3.2.m2.1.1.3.1" xref="S4.SS1.p3.2.m2.1.1.3.1.cmml">×</mo><mfrac id="S4.SS1.p3.2.m2.1.1.3.3" xref="S4.SS1.p3.2.m2.1.1.3.3.cmml"><mrow id="S4.SS1.p3.2.m2.1.1.3.3.2" xref="S4.SS1.p3.2.m2.1.1.3.3.2.cmml"><mi mathvariant="normal" id="S4.SS1.p3.2.m2.1.1.3.3.2.2" xref="S4.SS1.p3.2.m2.1.1.3.3.2.2.cmml">Δ</mi><mo id="S4.SS1.p3.2.m2.1.1.3.3.2.1" xref="S4.SS1.p3.2.m2.1.1.3.3.2.1.cmml">⁢</mo><mi id="S4.SS1.p3.2.m2.1.1.3.3.2.3" xref="S4.SS1.p3.2.m2.1.1.3.3.2.3.cmml">λ</mi></mrow><msub id="S4.SS1.p3.2.m2.1.1.3.3.3" xref="S4.SS1.p3.2.m2.1.1.3.3.3.cmml"><mi id="S4.SS1.p3.2.m2.1.1.3.3.3.2" xref="S4.SS1.p3.2.m2.1.1.3.3.3.2.cmml">N</mi><mi id="S4.SS1.p3.2.m2.1.1.3.3.3.3" xref="S4.SS1.p3.2.m2.1.1.3.3.3.3.cmml">pix</mi></msub></mfrac></mrow></mrow></math>, <math><mrow id="S4.SS1.p6.3.m3.2.2" xref="S4.SS1.p6.3.m3.2.2.cmml"><mrow id="S4.SS1.p6.3.m3.2.2.1.1" xref="S4.SS1.p6.3.m3.2.2.1.2.cmml"><mi id="S4.SS1.p6.3.m3.1.1" xref="S4.SS1.p6.3.m3.1.1.cmml">log</mi><mo id="S4.SS1.p6.3.m3.2.2.1.1a" xref="S4.SS1.p6.3.m3.2.2.1.2.cmml">⁡</mo><mrow id="S4.SS1.p6.3.m3.2.2.1.1.1" xref="S4.SS1.p6.3.m3.2.2.1.2.cmml"><mo stretchy="false" id="S4.SS1.p6.3.m3.2.2.1.1.1.2" xref="S4.SS1.p6.3.m3.2.2.1.2.cmml">[</mo><mrow id="S4.SS1.p6.3.m3.2.2.1.1.1.1" xref="S4.SS1.p6.3.m3.2.2.1.1.1.1.cmml"><mi id="S4.SS1.p6.3.m3.2.2.1.1.1.1.3" xref="S4.SS1.p6.3.m3.2.2.1.1.1.1.3.cmml">N</mi><mo id="S4.SS1.p6.3.m3.2.2.1.1.1.1.2" xref="S4.SS1.p6.3.m3.2.2.1.1.1.1.2.cmml">⁢</mo><mrow id="S4.SS1.p6.3.m3.2.2.1.1.1.1.1.1" xref="S4.SS1.p6.3.m3.2.2.1.1.1.1.1.1.1.cmml"><mo stretchy="false" id="S4.SS1.p6.3.m3.2.2.1.1.1.1.1.1.2" xref="S4.SS1.p6.3.m3.2.2.1.1.1.1.1.1.1.cmml">(</mo><mrow id="S4.SS1.p6.3.m3.2.2.1.1.1.1.1.1.1" xref="S4.SS1.p6.3.m3.2.2.1.1.1.1.1.1.1.cmml"><mpadded width="+1.7pt" id="S4.SS1.p6.3.m3.2.2.1.1.1.1.1.1.1.2" xref="S4.SS1.p6.3.m3.2.2.1.1.1.1.1.1.1.2.cmml"><mi mathvariant="normal" id="S4.SS1.p6.3.m3.2.2.1.1.1.1.1.1.1.2a" xref="S4.SS1.p6.3.m3.2.2.1.1.1.1.1.1.1.2.cmml">H</mi></mpadded><mo id="S4.SS1.p6.3.m3.2.2.1.1.1.1.1.1.1.1" xref="S4.SS1.p6.3.m3.2.2.1.1.1.1.1.1.1.1.cmml">⁢</mo><mpadded width="+1.7pt" id="S4.SS1.p6.3.m3.2.2.1.1.1.1.1.1.1.3" xref="S4.SS1.p6.3.m3.2.2.1.1.1.1.1.1.1.3.cmml"><mi mathsize="70%" mathvariant="normal" id="S4.SS1.p6.3.m3.2.2.1.1.1.1.1.1.1.3a" xref="S4.SS1.p6.3.m3.2.2.1.1.1.1.1.1.1.3.cmml">I</mi></mpadded></mrow><mo stretchy="false" id="S4.SS1.p6.3.m3.2.2.1.1.1.1.1.1.3" xref="S4.SS1.p6.3.m3.2.2.1.1.1.1.1.1.1.cmml">)</mo></mrow></mrow><mo stretchy="false" id="S4.SS1.p6.3.m3.2.2.1.1.1.3" xref="S4.SS1.p6.3.m3.2.2.1.2.cmml">]</mo></mrow></mrow><mo id="S4.SS1.p6.3.m3.2.2.2" xref="S4.SS1.p6.3.m3.2.2.2.cmml">=</mo><mn id="S4.SS1.p6.3.m3.2.2.3" xref="S4.SS1.p6.3.m3.2.2.3.cmml">21.1</mn></mrow></math>, <math><mrow id="S4.SS1.p7.1.m1.4.5" xref="S4.SS1.p7.1.m1.4.5.cmml"><mrow id="S4.SS1.p7.1.m1.4.5.2.2" xref="S4.SS1.p7.1.m1.4.5.2.1.cmml"><mi id="S4.SS1.p7.1.m1.2.2" xref="S4.SS1.p7.1.m1.2.2.cmml">log</mi><mo id="S4.SS1.p7.1.m1.4.5.2.2a" xref="S4.SS1.p7.1.m1.4.5.2.1.cmml">⁡</mo><mrow id="S4.SS1.p7.1.m1.4.5.2.2.1" xref="S4.SS1.p7.1.m1.4.5.2.1.cmml"><mo stretchy="false" id="S4.SS1.p7.1.m1.4.5.2.2.1.1" xref="S4.SS1.p7.1.m1.4.5.2.1.cmml">[</mo><mfrac id="S4.SS1.p7.1.m1.1.1" xref="S4.SS1.p7.1.m1.1.1.cmml"><mrow id="S4.SS1.p7.1.m1.1.1.1" xref="S4.SS1.p7.1.m1.1.1.1.cmml"><mi id="S4.SS1.p7.1.m1.1.1.1.3" xref="S4.SS1.p7.1.m1.1.1.1.3.cmml">N</mi><mo id="S4.SS1.p7.1.m1.1.1.1.2" xref="S4.SS1.p7.1.m1.1.1.1.2.cmml">⁢</mo><mrow id="S4.SS1.p7.1.m1.1.1.1.1.1" xref="S4.SS1.p7.1.m1.1.1.1.1.1.1.cmml"><mo stretchy="false" id="S4.SS1.p7.1.m1.1.1.1.1.1.2" xref="S4.SS1.p7.1.m1.1.1.1.1.1.1.cmml">(</mo><mrow id="S4.SS1.p7.1.m1.1.1.1.1.1.1" xref="S4.SS1.p7.1.m1.1.1.1.1.1.1.cmml"><mpadded width="+1.7pt" id="S4.SS1.p7.1.m1.1.1.1.1.1.1.2" xref="S4.SS1.p7.1.m1.1.1.1.1.1.1.2.cmml"><mi mathvariant="normal" id="S4.SS1.p7.1.m1.1.1.1.1.1.1.2a" xref="S4.SS1.p7.1.m1.1.1.1.1.1.1.2.cmml">H</mi></mpadded><mo id="S4.SS1.p7.1.m1.1.1.1.1.1.1.1" xref="S4.SS1.p7.1.m1.1.1.1.1.1.1.1.cmml">⁢</mo><mpadded width="+1.7pt" id="S4.SS1.p7.1.m1.1.1.1.1.1.1.3" xref="S4.SS1.p7.1.m1.1.1.1.1.1.1.3.cmml"><mi mathvariant="normal" id="S4.SS1.p7.1.m1.1.1.1.1.1.1.3a" xref="S4.SS1.p7.1.m1.1.1.1.1.1.1.3.cmml">I</mi></mpadded></mrow><mo stretchy="false" id="S4.SS1.p7.1.m1.1.1.1.1.1.3" xref="S4.SS1.p7.1.m1.1.1.1.1.1.1.cmml">)</mo></mrow></mrow><msup id="S4.SS1.p7.1.m1.1.1.3" xref="S4.SS1.p7.1.m1.1.1.3.cmml"><mi id="S4.SS1.p7.1.m1.1.1.3.2" xref="S4.SS1.p7.1.m1.1.1.3.2.cmml">cm</mi><mrow id="S4.SS1.p7.1.m1.1.1.3.3" xref="S4.SS1.p7.1.m1.1.1.3.3.cmml"><mo id="S4.SS1.p7.1.m1.1.1.3.3.1" xref="S4.SS1.p7.1.m1.1.1.3.3.1.cmml">-</mo><mn id="S4.SS1.p7.1.m1.1.1.3.3.2" xref="S4.SS1.p7.1.m1.1.1.3.3.2.cmml">2</mn></mrow></msup></mfrac><mo stretchy="false" id="S4.SS1.p7.1.m1.4.5.2.2.1.2" xref="S4.SS1.p7.1.m1.4.5.2.1.cmml">]</mo></mrow></mrow><mo id="S4.SS1.p7.1.m1.4.5.1" xref="S4.SS1.p7.1.m1.4.5.1.cmml">=</mo><mrow id="S4.SS1.p7.1.m1.4.5.3" xref="S4.SS1.p7.1.m1.4.5.3.cmml"><mn id="S4.SS1.p7.1.m1.4.5.3.2" xref="S4.SS1.p7.1.m1.4.5.3.2.cmml">19.05</mn><mo id="S4.SS1.p7.1.m1.4.5.3.1" xref="S4.SS1.p7.1.m1.4.5.3.1.cmml">+</mo><mrow id="S4.SS1.p7.1.m1.4.5.3.3" xref="S4.SS1.p7.1.m1.4.5.3.3.cmml"><mn id="S4.SS1.p7.1.m1.4.5.3.3.2" xref="S4.SS1.p7.1.m1.4.5.3.3.2.cmml">0.92</mn><mo id="S4.SS1.p7.1.m1.4.5.3.3.1" xref="S4.SS1.p7.1.m1.4.5.3.3.1.cmml">×</mo><mrow id="S4.SS1.p7.1.m1.4.5.3.3.3.2" xref="S4.SS1.p7.1.m1.4.5.3.3.3.1.cmml"><mi id="S4.SS1.p7.1.m1.3.3" xref="S4.SS1.p7.1.m1.3.3.cmml">log</mi><mo id="S4.SS1.p7.1.m1.4.5.3.3.3.2a" xref="S4.SS1.p7.1.m1.4.5.3.3.3.1.cmml">⁡</mo><mrow id="S4.SS1.p7.1.m1.4.5.3.3.3.2.1" xref="S4.SS1.p7.1.m1.4.5.3.3.3.1.cmml"><mo stretchy="false" id="S4.SS1.p7.1.m1.4.5.3.3.3.2.1.1" xref="S4.SS1.p7.1.m1.4.5.3.3.3.1.cmml">[</mo><mfrac id="S4.SS1.p7.1.m1.4.4" xref="S4.SS1.p7.1.m1.4.4.cmml"><mrow id="S4.SS1.p7.1.m1.4.4.2" xref="S4.SS1.p7.1.m1.4.4.2.cmml"><mi id="S4.SS1.p7.1.m1.4.4.2.2" xref="S4.SS1.p7.1.m1.4.4.2.2.cmml">W</mi><mo id="S4.SS1.p7.1.m1.4.4.2.1" xref="S4.SS1.p7.1.m1.4.4.2.1.cmml">⁢</mo><mn id="S4.SS1.p7.1.m1.4.4.2.3" xref="S4.SS1.p7.1.m1.4.4.2.3.cmml">5780</mn></mrow><mrow id="S4.SS1.p7.1.m1.4.4.3" xref="S4.SS1.p7.1.m1.4.4.3.cmml"><mi mathvariant="normal" id="S4.SS1.p7.1.m1.4.4.3.2" xref="S4.SS1.p7.1.m1.4.4.3.2.cmml">m</mi><mo id="S4.SS1.p7.1.m1.4.4.3.1" xref="S4.SS1.p7.1.m1.4.4.3.1.cmml">⁢</mo><mi mathvariant="normal" id="S4.SS1.p7.1.m1.4.4.3.3" xref="S4.SS1.p7.1.m1.4.4.3.3.cmml">Å</mi></mrow></mfrac><mo stretchy="false" id="S4.SS1.p7.1.m1.4.5.3.3.3.2.1.2" xref="S4.SS1.p7.1.m1.4.5.3.3.3.1.cmml">]</mo></mrow></mrow></mrow></mrow></mrow></math>, <math><mrow id="S4.SS1.p7.2.m2.2.2" xref="S4.SS1.p7.2.m2.2.2.cmml"><mrow id="S4.SS1.p7.2.m2.2.2.1.1" xref="S4.SS1.p7.2.m2.2.2.1.2.cmml"><mi id="S4.SS1.p7.2.m2.1.1" xref="S4.SS1.p7.2.m2.1.1.cmml">log</mi><mo id="S4.SS1.p7.2.m2.2.2.1.1a" xref="S4.SS1.p7.2.m2.2.2.1.2.cmml">⁡</mo><mrow id="S4.SS1.p7.2.m2.2.2.1.1.1" xref="S4.SS1.p7.2.m2.2.2.1.2.cmml"><mo stretchy="false" id="S4.SS1.p7.2.m2.2.2.1.1.1.2" xref="S4.SS1.p7.2.m2.2.2.1.2.cmml">[</mo><mrow id="S4.SS1.p7.2.m2.2.2.1.1.1.1" xref="S4.SS1.p7.2.m2.2.2.1.1.1.1.cmml"><mi id="S4.SS1.p7.2.m2.2.2.1.1.1.1.3" xref="S4.SS1.p7.2.m2.2.2.1.1.1.1.3.cmml">N</mi><mo id="S4.SS1.p7.2.m2.2.2.1.1.1.1.2" xref="S4.SS1.p7.2.m2.2.2.1.1.1.1.2.cmml">⁢</mo><mrow id="S4.SS1.p7.2.m2.2.2.1.1.1.1.1.1" 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id="S4.SS1.p7.2.m2.2.2.1.1.1.3" xref="S4.SS1.p7.2.m2.2.2.1.2.cmml">]</mo></mrow></mrow><mo id="S4.SS1.p7.2.m2.2.2.2" xref="S4.SS1.p7.2.m2.2.2.2.cmml">=</mo><mn id="S4.SS1.p7.2.m2.2.2.3" xref="S4.SS1.p7.2.m2.2.2.3.cmml">21.16</mn></mrow></math>, <math><mrow id="S4.SS1.p7.5.m5.2.2" xref="S4.SS1.p7.5.m5.2.2.cmml"><mrow id="S4.SS1.p7.5.m5.2.2.1.1" xref="S4.SS1.p7.5.m5.2.2.1.2.cmml"><mi id="S4.SS1.p7.5.m5.1.1" xref="S4.SS1.p7.5.m5.1.1.cmml">log</mi><mo id="S4.SS1.p7.5.m5.2.2.1.1a" xref="S4.SS1.p7.5.m5.2.2.1.2.cmml">⁡</mo><mrow id="S4.SS1.p7.5.m5.2.2.1.1.1" xref="S4.SS1.p7.5.m5.2.2.1.2.cmml"><mo stretchy="false" id="S4.SS1.p7.5.m5.2.2.1.1.1.2" xref="S4.SS1.p7.5.m5.2.2.1.2.cmml">[</mo><mrow id="S4.SS1.p7.5.m5.2.2.1.1.1.1" xref="S4.SS1.p7.5.m5.2.2.1.1.1.1.cmml"><mi id="S4.SS1.p7.5.m5.2.2.1.1.1.1.3" xref="S4.SS1.p7.5.m5.2.2.1.1.1.1.3.cmml">N</mi><mo id="S4.SS1.p7.5.m5.2.2.1.1.1.1.2" xref="S4.SS1.p7.5.m5.2.2.1.1.1.1.2.cmml">⁢</mo><mrow id="S4.SS1.p7.5.m5.2.2.1.1.1.1.1.1" 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id="S4.SS1.p7.5.m5.2.2.1.1.1.3" xref="S4.SS1.p7.5.m5.2.2.1.2.cmml">]</mo></mrow></mrow><mo id="S4.SS1.p7.5.m5.2.2.2" xref="S4.SS1.p7.5.m5.2.2.2.cmml">=</mo><mn id="S4.SS1.p7.5.m5.2.2.3" xref="S4.SS1.p7.5.m5.2.2.3.cmml">19.9</mn></mrow></math>

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/hep-ph/9610285

Formulas:

1-

V (q_{1}, q_{2}) = \int d^{4} l \int d^{4} k \frac{1}{P_{1} P_{2} P_{3} P_{4} P_{5} P_{6}},

2-

q = q_{1} + q_{2}

3-

i = 1 \dots 6

4-

(e_{1} + e_{2}, 0, 0, 0)

5-

(e_{1}, q_{z}, 0, 0)

6-

(e_{2}, - q_{z}, 0, 0)

7-

(l_{0}, l_{1}, {\vec{l}}_{⟂})

8-

(k_{0}, k_{1}, {\vec{k}}_{⟂})

9-

{(l + k - q_{1})}^{2} - m_{1}^{2} + i η

10-

{(l + k + q_{2})}^{2} - m_{2}^{2} + i η

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: hep-ph

Result: correct

Paper: https://arxiv.org/abs/2008.05471

Formulas:

1-

Ω / 2 π \approx 40

2-

V (x, y) \approx - V_{0} {| \cos (k x) + e^{i θ} \cos (k y) |}^{2}

3-

k = 2 π / λ

4-

Δ V \equiv - 4 V_{0} \cos (θ)

5-

\frac{n_{-} - n_{+}}{n_{-} + n_{+}}

6-

Δ V_{f} = 0.725 \times V_{0, f}

7-

| F = 2, m_{F} = 2 ⟩

8-

Δ V_{i} = - 1.23 V_{0, i}

9-

V_{0, i} = 4.3 E_{rec}

10-

E_{rec} \equiv ℏ^{2} k^{2} / (2 m)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1308.0369

Formulas:

1-

B - V = + 0.1

2-

Ψ ((t^{'} - t) / s)

3-

W_{n} (s) = \sum_{n^{'} = 0}^{N - 1} x_{n^{'}} Ψ^{⋆} [\frac{(n^{'} - n) δ t}{s}]

4-

Ψ (t / s) = π^{- \frac{1}{4}} \exp (i ω \frac{t}{s}) \exp (- \frac{1}{2} \frac{t^{2}}{s^{2}})

5-

s_{j} = s_{0} 2^{j δ j}, j = 0, 1, \dots, J .

6-

f_{4} = 2 f_{2}

7-

f_{1} = f_{3} - f_{2}

8-

λ λ 4026, 4471

9-

λ λ 5876, 6678, 7065

10-

F_{2} / F_{1} = 0.04 \pm 0.01

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/quant-ph/9709013

Formulas:

1-

\hat{H} = \frac{1}{2} (\hat{a} {\hat{a}}^{†} + {\hat{a}}^{†} \hat{a}) + \frac{1}{2} (\hat{b} {\hat{b}}^{†} + {\hat{b}}^{†} \hat{b}),

2-

\hat{a} (t) = \hat{a} e^{- i t}; \hat{b} (t) = \hat{b} e^{- i t} .

3-

\hat{Ψ} (t) = [\hat{a} (t) e^{- i k_{1} x} + \hat{b} (t) e^{- i k_{2} x}] + h . c .,

4-

I (x, t) = ⟨ {\hat{Ψ}}^{(-)} (t) {\hat{Ψ}}^{(+)} (t) ⟩ = ⟨ [{\hat{a}}^{†} (t) e^{i k_{1} x} + {\hat{b}}^{†} (t) e^{i k_{2} x}] [\hat{a} (t) e^{- i k_{1} x} + \hat{b} (t) e^{- i k_{2} x}] ⟩ .

5-

{| α ⟩}_{a} \otimes {| β ⟩}_{b},

6-

I (x, t) = 2 {| α |}^{2} {1 + \cos [ϕ (x) - ϕ]},

7-

β = α e^{- i ϕ}

8-

ϕ (x) = (k_{1} - k_{2}) x

9-

𝒱 = \frac{I {(x, t)}_{\max} - I {(x, t)}_{\min}}{I {(x, t)}_{\max} + I {(x, t)}_{\min}},

10-

\hat{ℋ} = \frac{1}{2} (\hat{A} {\hat{A}}^{†} + {\hat{A}}^{†} \hat{A}) + \frac{1}{2} (\hat{B} {\hat{B}}^{†} + {\hat{B}}^{†} \hat{B}),

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: quant-ph

Result: correct

Paper: https://arxiv.org/abs/1901.09573

Formulas:

1-

E_{r} = η K

2-

v_{imp} = {13.8}_{- 7.3}^{+ 4.3}

3-

G = Z + k_{R} \log C_{R} + k_{G} \log C_{G} + k_{B} \log C_{B}

4-

G^{'} = 11.61 \pm 0.04

5-

m_{t 2} = m_{t 1} - 2.5 \log (t_{1} / t_{2})

6-

E_{r} = b_{G} 10^{(- G + G_{0}) / 2.5} Δ t Δ λ_{G} f π R^{2}

7-

R = 3.57745 \times 10^{8}

8-

b_{G} = 2.5 \times 10^{- 11}

9-

Δ λ_{G} = 420.360

10-

\log (\frac{E_{r}}{J}) = 6.6 \pm 0.04

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/0810.0976

Formulas:

1-

α_{N} = ⌈ \sqrt{12 N - 3} ⌉,

2-

β_{N} = ⌈ 2 \sqrt{N} ⌉,

3-

6 - 2 α_{N} / N

4-

N = 3 n^{2} + 3 n + 1, n = 1, 2, \dots

5-

α_{\infty} = 2 \sqrt{3 N}

6-

N = M (n) = 3 n^{2} - 3 n + 1, n = 1, 2, \dots

7-

n = 2, 3, \dots

8-

6 (n - 2)

9-

6 \times 3 + (6 n - 12) \times 2 = 2 (9 + 6 n - 12) = 12 n - 6 \equiv 2 α_{M (n)}

10-

n = 1, 2, 3

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

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

Formulas:

1-

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

2-

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

3-

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

4-

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

5-

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

6-

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

7-

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

8-

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

9-

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

10-

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

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: hep-ph

Result: correct

Paper: https://arxiv.org/abs/1112.1246

Formulas:

1-

α_{1} = 1.0, α_{2} = 1.0, α_{3} = 0.5 .

2-

E_{stat} \sim \frac{1}{a} e^{(1)} g_{0}^{2} + \dots

3-

V_{n} (r)

4-

W (r, T)

5-

⟨ W (r, T) ⟩

6-

\sum_{n} c_{n} c_{n}^{*} e^{- V_{n} (r) (T - 2 a)} (with N_{t} \to \infty time-slices) .

7-

⟨ W (r, t) ⟩

8-

C_{l m} (r, T)

9-

l = 1, 2, 3

10-

r_{0} M_{PS} \approx 0.62 \dots 0.64

Formulas (html):

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xref="S2.E2.m3.3.3.2.2.1.1.1.3.1.cmml">⁢</mo><mi id="S2.E2.m3.3.3.2.2.1.1.1.3.3" xref="S2.E2.m3.3.3.2.2.1.1.1.3.3.cmml">a</mi></mrow></mrow><mo stretchy="false" id="S2.E2.m3.3.3.2.2.1.1.3" xref="S2.E2.m3.3.3.2.2.1.1.1.cmml">)</mo></mrow></mrow></mrow></msup></mrow></mrow><mo mathvariant="italic" separator="true" id="S2.E2.m3.4.4.1.1.1.2" xref="S2.E2.m3.4.4.1.1.2.cmml"> </mo><mpadded width="+1.7pt" id="S2.E2.m3.1.1.1a" xref="S2.E2.m3.1.1.1ad.cmml"><mrow id="S2.E2.m3.1.1.1aa" xref="S2.E2.m3.1.1.1ad.cmml"><mtext id="S2.E2.m3.1.1.1ab" xref="S2.E2.m3.1.1.1ad.cmml">(with </mtext><mrow id="S2.E2.m3.1.1.1.m1.1.1" xref="S2.E2.m3.1.1.1.m1.1.1.cmml"><msub id="S2.E2.m3.1.1.1.m1.1.1.2" xref="S2.E2.m3.1.1.1.m1.1.1.2.cmml"><mi id="S2.E2.m3.1.1.1.m1.1.1.2.2" xref="S2.E2.m3.1.1.1.m1.1.1.2.2.cmml">N</mi><mi id="S2.E2.m3.1.1.1.m1.1.1.2.3" xref="S2.E2.m3.1.1.1.m1.1.1.2.3.cmml">t</mi></msub><mo id="S2.E2.m3.1.1.1.m1.1.1.1" xref="S2.E2.m3.1.1.1.m1.1.1.1.cmml">→</mo><mi mathvariant="normal" id="S2.E2.m3.1.1.1.m1.1.1.3" xref="S2.E2.m3.1.1.1.m1.1.1.3.cmml">∞</mi></mrow><mtext id="S2.E2.m3.1.1.1ac" xref="S2.E2.m3.1.1.1ad.cmml"> time-slices)</mtext></mrow></mpadded></mrow><mo id="S2.E2.m3.4.4.1.2">.</mo></mrow></math>, <math><mrow id="S2.E3.m1.3.3.1" xref="S2.E3.m1.3.3.2.cmml"><mo id="S2.E3.m1.3.3.1.2" xref="S2.E3.m1.3.3.2.1.cmml">⟨</mo><mrow id="S2.E3.m1.3.3.1.1" xref="S2.E3.m1.3.3.1.1.cmml"><mi id="S2.E3.m1.3.3.1.1.2" xref="S2.E3.m1.3.3.1.1.2.cmml">W</mi><mo id="S2.E3.m1.3.3.1.1.1" xref="S2.E3.m1.3.3.1.1.1.cmml">⁢</mo><mrow id="S2.E3.m1.3.3.1.1.3.2" xref="S2.E3.m1.3.3.1.1.3.1.cmml"><mo stretchy="false" id="S2.E3.m1.3.3.1.1.3.2.1" xref="S2.E3.m1.3.3.1.1.3.1.cmml">(</mo><mi id="S2.E3.m1.1.1" xref="S2.E3.m1.1.1.cmml">r</mi><mo id="S2.E3.m1.3.3.1.1.3.2.2" xref="S2.E3.m1.3.3.1.1.3.1.cmml">,</mo><mi id="S2.E3.m1.2.2" xref="S2.E3.m1.2.2.cmml">t</mi><mo stretchy="false" id="S2.E3.m1.3.3.1.1.3.2.3" xref="S2.E3.m1.3.3.1.1.3.1.cmml">)</mo></mrow></mrow><mo id="S2.E3.m1.3.3.1.3" xref="S2.E3.m1.3.3.2.1.cmml">⟩</mo></mrow></math>, <math><mrow id="S2.E3.m3.2.3" xref="S2.E3.m3.2.3.cmml"><msub id="S2.E3.m3.2.3.2" xref="S2.E3.m3.2.3.2.cmml"><mi id="S2.E3.m3.2.3.2.2" xref="S2.E3.m3.2.3.2.2.cmml">C</mi><mrow id="S2.E3.m3.2.3.2.3" xref="S2.E3.m3.2.3.2.3.cmml"><mi id="S2.E3.m3.2.3.2.3.2" xref="S2.E3.m3.2.3.2.3.2.cmml">l</mi><mo id="S2.E3.m3.2.3.2.3.1" xref="S2.E3.m3.2.3.2.3.1.cmml">⁢</mo><mi id="S2.E3.m3.2.3.2.3.3" xref="S2.E3.m3.2.3.2.3.3.cmml">m</mi></mrow></msub><mo id="S2.E3.m3.2.3.1" xref="S2.E3.m3.2.3.1.cmml">⁢</mo><mrow id="S2.E3.m3.2.3.3.2" xref="S2.E3.m3.2.3.3.1.cmml"><mo stretchy="false" id="S2.E3.m3.2.3.3.2.1" xref="S2.E3.m3.2.3.3.1.cmml">(</mo><mi id="S2.E3.m3.1.1" xref="S2.E3.m3.1.1.cmml">r</mi><mo id="S2.E3.m3.2.3.3.2.2" xref="S2.E3.m3.2.3.3.1.cmml">,</mo><mi id="S2.E3.m3.2.2" xref="S2.E3.m3.2.2.cmml">T</mi><mo stretchy="false" id="S2.E3.m3.2.3.3.2.3" xref="S2.E3.m3.2.3.3.1.cmml">)</mo></mrow></mrow></math>, <math><mrow id="S2.p1.10.m1.3.4" xref="S2.p1.10.m1.3.4.cmml"><mi id="S2.p1.10.m1.3.4.2" xref="S2.p1.10.m1.3.4.2.cmml">l</mi><mo id="S2.p1.10.m1.3.4.1" xref="S2.p1.10.m1.3.4.1.cmml">=</mo><mrow id="S2.p1.10.m1.3.4.3.2" xref="S2.p1.10.m1.3.4.3.1.cmml"><mn id="S2.p1.10.m1.1.1" xref="S2.p1.10.m1.1.1.cmml">1</mn><mo id="S2.p1.10.m1.3.4.3.2.1" xref="S2.p1.10.m1.3.4.3.1.cmml">,</mo><mn id="S2.p1.10.m1.2.2" xref="S2.p1.10.m1.2.2.cmml">2</mn><mo id="S2.p1.10.m1.3.4.3.2.2" xref="S2.p1.10.m1.3.4.3.1.cmml">,</mo><mn id="S2.p1.10.m1.3.3" xref="S2.p1.10.m1.3.3.cmml">3</mn></mrow></mrow></math>, <math><mrow id="S2.p2.1.m1.1.1" xref="S2.p2.1.m1.1.1.cmml"><mrow id="S2.p2.1.m1.1.1.2" xref="S2.p2.1.m1.1.1.2.cmml"><msub id="S2.p2.1.m1.1.1.2.2" xref="S2.p2.1.m1.1.1.2.2.cmml"><mi id="S2.p2.1.m1.1.1.2.2.2" xref="S2.p2.1.m1.1.1.2.2.2.cmml">r</mi><mn id="S2.p2.1.m1.1.1.2.2.3" xref="S2.p2.1.m1.1.1.2.2.3.cmml">0</mn></msub><mo id="S2.p2.1.m1.1.1.2.1" xref="S2.p2.1.m1.1.1.2.1.cmml">⁢</mo><msub id="S2.p2.1.m1.1.1.2.3" xref="S2.p2.1.m1.1.1.2.3.cmml"><mi id="S2.p2.1.m1.1.1.2.3.2" xref="S2.p2.1.m1.1.1.2.3.2.cmml">M</mi><mi id="S2.p2.1.m1.1.1.2.3.3" xref="S2.p2.1.m1.1.1.2.3.3.cmml">PS</mi></msub></mrow><mo id="S2.p2.1.m1.1.1.1" xref="S2.p2.1.m1.1.1.1.cmml">≈</mo><mrow id="S2.p2.1.m1.1.1.3" xref="S2.p2.1.m1.1.1.3.cmml"><mn id="S2.p2.1.m1.1.1.3.2" xref="S2.p2.1.m1.1.1.3.2.cmml">0.62</mn><mo id="S2.p2.1.m1.1.1.3.1" xref="S2.p2.1.m1.1.1.3.1.cmml">⁢</mo><mi mathvariant="normal" id="S2.p2.1.m1.1.1.3.3" xref="S2.p2.1.m1.1.1.3.3.cmml">…</mi><mo id="S2.p2.1.m1.1.1.3.1a" xref="S2.p2.1.m1.1.1.3.1.cmml">⁢</mo><mn id="S2.p2.1.m1.1.1.3.4" xref="S2.p2.1.m1.1.1.3.4.cmml">0.64</mn></mrow></mrow></math>

Correct Categorie: hep-lat

Guessed Categorie: hep-ph

Result: incorrect

Paper: https://arxiv.org/abs/1712.04626

Formulas:

1-

M_{Z}^{2} ≃ - 2 μ^{2} (M_{Z}) - 2 m_{H_{u}}^{2} (M_{Z})

2-

M_{Z}^{2} ≃ - 1.9 μ^{2} + 5.9 M_{3}^{2} - 1.2 m_{H_{u}}^{2} + 1.5 m_{\tilde{t}}^{2} - 0.8 A_{t} M_{3} + 0.2 A_{t}^{2} + \dots,

3-

m_{\tilde{t}}^{2} \equiv (m_{{\tilde{t}}_{L}}^{2} + m_{{\tilde{t}}_{R}}^{2}) / 2

4-

m_{{\tilde{t}}_{L}} ≃ m_{{\tilde{t}}_{R}}

5-

\ln (M_{G} / M_{Z})

6-

X_{t} / m_{\tilde{t}} = 0

7-

X_{t} / m_{\tilde{t}} ≃ - 1

8-

X_{t} / m_{\tilde{t}} ≃ - 2

9-

X_{t} / m_{\tilde{t}}

10-

f (λ_{t}, α_{3}, Λ)

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: hep-ph

Result: correct

Paper: https://arxiv.org/abs/1105.5739

Formulas:

1-

\frac{\partial 𝐁}{\partial t} = \nabla \times (𝐯 \times 𝐁),

2-

\frac{\partial ρ}{\partial t} + \nabla \cdot (ρ 𝐯) = 0,

3-

ρ \frac{\partial 𝐯}{\partial t} + ρ (𝐯 \cdot \nabla) 𝐯 = - \nabla P - \frac{1}{4 π} 𝐁 \times (\nabla \times 𝐁) - ρ \nabla ϕ,

4-

\nabla^{2} ϕ = 4 π G ρ,

5-

L_{J} = c_{s} {(\frac{π}{G ρ})}^{1 / 2}

6-

ρ_{t h} = \frac{5 π c_{s}^{2}}{3 G {(8 Δ x)}^{2}}

7-

M_{m e r g}

8-

l_{m e r g}

9-

M_{m e r g} = 0.01 M_{⊙}

10-

l_{m e r g} = 10^{15} c m \approx 8 Δ x \approx 70 A U

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1810.01777

Formulas:

1-

t \in [0.624, 2.176]

2-

\ddot{p} = c^{2} \nabla^{2} p

3-

𝜿 = (κ_{1}, κ_{2}, κ_{3})

4-

f \sim (f_{X} / \sqrt{2}) \sqrt{3 - \cos (a κ_{1}) - \cos (a κ_{2}) - \cos (a κ_{3})} .

5-

Γ X M R

6-

Γ X^{'} M^{'} R^{'}

7-

(Γ X^{'} M^{'} R^{'})

8-

𝐓 \nabla^{2} P - (f^{2} - f_{I}^{2}) P = 0,

9-

T_{11}, T_{22}, T_{33}

10-

T_{11} = T_{22} = - 8.6

Formulas (html):

Correct Categorie: physics

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/0905.2711

Formulas:

1-

C \equiv (c_{i j}), i, j = 1, \dots, s

2-

c_{i j} = 1

3-

c_{i i} = 0

4-

{\dot{y}}_{i} = \sum_{j = 1}^{s} C_{i j} y_{j} - ϕ y_{i} .

5-

x_{i} = y_{i} / \sum_{k} y_{k}

6-

{\dot{x}}_{i} = \sum_{j = 1}^{s} c_{i j} x_{j} - x_{i} \sum_{k, j = 1}^{s} c_{k j} x_{j},

7-

\frac{k_{j} m}{\sum_{j = 1}^{s} k_{j}},

8-

s = 40, 60, 80

9-

0.02 (9) \pm 0.02

10-

0.7 (9) \pm 0.09

Formulas (html):

Correct Categorie: nlin

Guessed Categorie: nlin

Result: correct

Paper: https://arxiv.org/abs/1101.0932

Formulas:

1-

τ (E_{0}) ≫ 1

2-

τ (E_{0}) ≫ 1

3-

θ_{j e t} > 0

4-

θ_{o b s}

5-

θ_{PSF} \approx {1.7}^{\circ} {(E_{γ, GeV})}^{- 0.74} {[1 + {(\frac{E_{γ, GeV}}{15})}^{2}]}^{0.37},

6-

θ_{o b s} \pm {0.1}^{\circ}

7-

θ_{jet} ≃ Γ_{jet}^{- 1}

8-

\frac{d N_{γ}}{d E_{γ}} \propto E_{γ}^{- Γ} \exp (- \frac{E_{γ}}{E_{cut}}),

9-

B \sim λ_{B}^{- 1 / 2}

10-

{(λ_{B} / 1 Mpc)}^{- 1 / 2}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/0709.2376

Formulas:

1-

V_{m a x} = 20.7

2-

α = 09^{h} 57^{m} 37 \overset{s}{.} 14

3-

δ = + 69^{\circ} 02^{'} 11^{''}

4-

E (B - V) = 0.08

5-

0 \overset{''}{.} 7 - 2 \overset{''}{.} 0

6-

1 \overset{''}{.} 4

7-

1 \overset{''}{.} 0 - 3 \overset{''}{.} 3

8-

1 \overset{''}{.} 9

9-

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

10-

FWHM \sim 0 \overset{''}{.} 1

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1308.3360

Formulas:

1-

α_{C O} / 0.8

2-

M_{d y n}

3-

ν_{r e s t}

4-

α_{C O} / 0.8

5-

R_{m a j}

6-

R_{m a j}

7-

R_{m a j}

8-

R_{m i n}

9-

L_{C O}^{'} = 3.25 \times 10^{7} I_{C O} ν_{o b s}^{- 2} D_{L}^{2} {(1 + z)}^{- 3}

10-

ν_{o b s}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1211.7287

Formulas:

1-

{Co}_{0.0625} {Zn}_{0.9375} O

2-

Δ E = E_{[100]} - E_{[001]}

3-

M_{L}^{[100]} - M_{L}^{[001]}

4-

δ N = - 1

5-

δ N = - 1

6-

δ N = - 1

7-

C_{0} + C_{1} \cos^{2} θ

8-

δ N = - 1

9-

δ N = - 1

10-

δ N = - 1

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1602.04690

Formulas:

1-

\sim e^{Δ η^{F} (α_{ℙ} (0) - 1)}

2-

α_{ℙ} (0)

3-

\sim e^{- Δ η^{F}}

4-

\frac{d^{2} σ^{S D}}{d M^{2} d t} = \frac{1}{16 π^{2} s} {| g_{ℙ} (t) |}^{2} g_{ℙ} (0) g_{ℙ ℙ ℙ} (0) {(\frac{s}{M^{2}})}^{2 α_{ℙ} (t) - 1} {(M^{2})}^{α_{ℙ} (0) - 1},

5-

\frac{d^{3} σ^{D D}}{d M_{1}^{2} d M_{2}^{2} d t} = \frac{1}{16 π^{3} s} g_{ℙ}^{2} (0) g_{ℙ ℙ ℙ}^{2} (0) {(\frac{s}{M_{1}^{2} M_{2}^{2}})}^{2 α_{ℙ} (t) - 1} {(M_{1}^{2})}^{α_{ℙ} (0) - 1} {(M_{2}^{2})}^{α_{ℙ} (0) - 1},

6-

α_{ℙ} (t) = α_{ℙ} (0) + α^{'} t

7-

α_{ℙ} (0)

8-

g_{ℙ} = g_{p ℙ}

9-

p p \to p^{*} p

10-

p p \to p p^{*}

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: hep-ph

Result: correct

Paper: https://arxiv.org/abs/0712.4301

Formulas:

1-

d S^{2} = γ_{A B} d x^{A} d x^{B} = γ_{μ ν} (x^{ρ}, y) d x^{μ} d x^{ν} + ϵ d y^{2},

2-

n_{A} = δ_{A}^{4},

3-

n_{A} n^{A} = ϵ

4-

R_{μ ν} - ϵ (K_{μ ν}^{'} - 2 K_{μ ρ} K_{ν}^{ρ} + K K_{μ ν}),

5-

- K^{'} - K_{α β} K^{α β},

6-

K_{μ; ν}^{ν} - \frac{\partial K}{\partial x^{μ}} .

7-

K_{μ ν} = g_{μ ν}^{'} / 2

8-

Σ : y = y_{0}

9-

K^{μ ν} = - \frac{1}{2} {(g^{μ ν})}^{'}, K = g_{μ ν} K^{μ ν} = g^{λ ρ} K_{λ ρ}, K^{'} = g^{μ ν} K_{μ ν}^{'} - 2 K_{μ ν} K^{μ ν} .

10-

γ_{μ ν} (x^{ρ}, y) = Ω (x^{ρ}, y) σ_{μ ν} (x^{λ}) .

Formulas (html):

Correct Categorie: gr-qc

Guessed Categorie: gr-qc

Result: correct

Paper: https://arxiv.org/abs/1506.04214

Formulas:

1-

𝒳 \in 𝐑^{P \times M \times N}

2-

{\hat{𝒳}}_{1}, {\hat{𝒳}}_{2}, \dots, {\hat{𝒳}}_{t}

3-

{\tilde{𝒳}}_{t + 1}, \dots, {\tilde{𝒳}}_{t + K} = \underset{𝒳_{t + 1}, \dots, 𝒳_{t + K}}{\arg \max} p (𝒳_{t + 1}, \dots, 𝒳_{t + K} ∣ {\hat{𝒳}}_{t - J + 1}, {\hat{𝒳}}_{t - J + 2}, \dots, {\hat{𝒳}}_{t})

4-

O (M^{K} N^{K} P^{K})

5-

= σ (W_{x i} x_{t} + W_{h i} h_{t - 1} + W_{c i} c_{t - 1} + b_{i})

6-

= σ (W_{x f} x_{t} + W_{h f} h_{t - 1} + W_{c f} c_{t - 1} + b_{f})

7-

= f_{t} \circ c_{t - 1} + i_{t} \circ \tanh (W_{x c} x_{t} + W_{h c} h_{t - 1} + b_{c})

8-

= σ (W_{x o} x_{t} + W_{h o} h_{t - 1} + W_{c o} \circ c_{t} + b_{o})

9-

= o_{t} \circ \tanh (c_{t})

10-

𝒳_{1}, \dots, 𝒳_{t}

Formulas (html):

Correct Categorie: cs

Guessed Categorie: q-bio

Result: incorrect

Paper: https://arxiv.org/abs/2002.00584

Formulas:

1-

a = F / T_{s}

2-

= - F / T_{s}

3-

U_{0} (t)

4-

F_{U 0} (t)

5-

U_{0} (t) = e^{j π (a t) t} for 0 \leq t \leq T_{s} .

6-

F_{U 0} (t) = (a t) for 0 \leq t \leq T_{s} .

7-

D_{0} (t)

8-

F_{D 0} (t)

9-

D_{0} (t) = e^{j π (F - a t) t} for 0 \leq t \leq T_{s} .

10-

F_{D 0} (t) = (F - a t) for 0 \leq t \leq T_{s} .

Formulas (html):

Correct Categorie: eess

Guessed Categorie: eess

Result: correct

Paper: https://arxiv.org/abs/nucl-th/0503045

Formulas:

1-

α_{E} = \frac{2 α}{3} \sum_{N \neq 0} \frac{{| ⟨ N | \vec{D} | 0 ⟩ |}^{2}}{E_{N} - E_{0}},

2-

\log (2 \bar{E} / m_{e}) α_{E} = \frac{2 α}{3} \sum_{N \neq 0} \frac{{| ⟨ N | \vec{D} | 0 ⟩ |}^{2}}{E_{N} - E_{0}} \log [2 (E_{N} - E_{0}) / m_{e}] .

3-

\vec{σ} = - i \frac{2 α}{3} \sum_{N \neq 0} ⟨ 0 | \vec{D} | N ⟩ \times ⟨ N | \vec{D} | 0 ⟩ \equiv - i \frac{2 α}{3} ⟨ 0 | \vec{D} \times \vec{D} | 0 ⟩,

4-

\log (2 \bar{E} / m_{e}) \vec{σ} = - i \frac{2 α}{3} \sum_{N \neq 0} ⟨ 0 | \vec{D} | N ⟩ \times ⟨ N | \vec{D} | 0 ⟩ \log [2 (E_{N} - E_{0}) / m_{e}] .

5-

α_{E}^{β α} = \frac{2 α}{3} \sum_{N \neq 0} \frac{⟨ 0 | D^{β} | N ⟩ ⟨ N | D^{α} | 0 ⟩}{E_{N} - E_{0}},

6-

\log [2 (E_{N} - E_{0}) / m_{e}]

7-

(E_{N} - E_{0})

8-

D^{β α} = \frac{2 α}{3} ⟨ 0 | D^{β} D^{α} | 0 ⟩,

9-

α_{E}^{β α} = \frac{2 α}{3} ⟨ 0 | D^{β} | Δ Ψ^{α} ⟩,

10-

(H - E_{0}) | Δ Ψ^{α} ⟩ = D^{α} | 0 ⟩

Formulas (html):

Correct Categorie: nucl-th

Guessed Categorie: hep-ph

Result: incorrect

Paper: https://arxiv.org/abs/hep-ph/0610319

Formulas:

1-

x ≪ x_{A} = \frac{1}{m_{N} R_{A}} = 0.15 A^{- 1 / 3},

2-

ξ = \log \frac{x_{0}}{x} \sim < \frac{1}{Δ_{e f f}},

3-

Δ_{e f f} ≃ 0.1 - 0.2

4-

F_{2 p} \propto x^{- Δ_{e f f}}

5-

R_{S n / C}

6-

q \bar{q} g

7-

q \bar{q}, q \bar{q} g, \dots

8-

| γ^{*} ⟩ = \sqrt{Z_{g}} Ψ_{q \bar{q}} | q \bar{q} ⟩ + Φ_{q \bar{q} g} | q \bar{q} g ⟩,

9-

Φ_{q \bar{q} g}

10-

q \bar{q} g

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/0906.0083

Formulas:

1-

| ↓ ⟩ = | 5 S_{1 / 2}, F_{1} = 1, m_{F_{1}} = 0 ⟩

2-

| ↑ ⟩ = | 5 S_{1 / 2}, F_{2} = 2, m_{F_{2}} = 0 ⟩

3-

E (r, t)

4-

I (r, t)

5-

E (r, t) = E_{H} + \frac{π c^{2} Γ}{2 ω_{0}^{3}} (\frac{1}{Δ_{F_{2}}^{^{'}}} - \frac{1}{Δ_{F_{1}}^{^{'}}}) I (r, t),

6-

1 / Δ_{F}^{^{'}} = (2 + α g_{F} m_{F}) / Δ_{2, F} + (1 - α g_{F} m_{F}) / Δ_{1, F}

7-

α = {1, 0, - 1}

8-

{5 S_{1 / 2}, F} \to 5 P_{3 / 2}

9-

5 P_{1 / 2}

10-

I (t) = I_{0} [1 + β (t)]

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/quant-ph/0703002

Formulas:

1-

[- i ℏ \frac{\partial}{\partial t} + \hat{H}] Φ_{0} = 0,

2-

\hat{H} = - \sum_{1 \leq i \leq N} \frac{ℏ^{2}}{2 m_{i}} \nabla_{i}^{2} + \sum_{1 \leq i < j \leq N} \frac{q_{i} q_{j}}{| 𝐫_{i} - 𝐫_{j} |} .

3-

Φ = φ (𝐫) Ψ (𝐑) .

4-

φ (𝐫, t) = φ (𝐫_{1}, \dots, 𝐫_{m}, t), Ψ (𝐑, t) = Ψ (𝐫_{m + 1}, \dots, 𝐫_{N}, t) .

5-

\hat{H} = {\hat{h}}_{φ} (𝐫) + {\hat{h}}_{i n t} + {\hat{h}}_{Ψ} (𝐑),

6-

{\hat{h}}_{φ} (𝐫) = - \sum_{1 \leq i \leq m} \frac{ℏ^{2}}{2 m_{i}} \nabla_{i}^{2} + \sum_{1 \leq i < j \leq m} \frac{q_{i} q_{j}}{| 𝐫_{i} - 𝐫_{j} |},

7-

{\hat{h}}_{i n t} = \sum_{1 \leq i \leq m < j \leq N} \frac{q_{i} q_{j}}{| 𝐫_{i} - 𝐫_{j} |} .

8-

\int 𝑑 𝐑 {| Ψ |}^{2} = 1,

9-

d 𝐑 = d 𝐫_{m + 1} \dots d 𝐫_{N} .

10-

[- i ℏ \frac{\partial}{\partial t} + \hat{h} - λ (t)] φ = 0,

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/1202.0860

Formulas:

1-

d s^{2} = - (1 - \frac{2 m}{r}) d t^{2} + \frac{d r^{2}}{1 - \frac{2 m}{r}} + r^{2} d Ω_{2}^{2},

2-

\frac{d r}{d t} = \pm (1 - \frac{2 m}{r}) .

3-

r = 2 m (ℒ (Ψ) + 1)

4-

r = 2 m (ℒ (Φ) + 1) .

5-

ℒ (x) \exp (ℒ (x)) = x

6-

Ψ^{2} \equiv {(\frac{u^{2}}{e})}^{2} \exp (\frac{t}{m}),

7-

Φ^{2} \equiv {(\frac{v^{2}}{e})}^{2} \exp (- \frac{t}{m}),

8-

\exp (\frac{t}{m}) = {(\frac{v}{u})}^{2}

9-

Ψ^{2} = Φ^{2} = {(\frac{u v}{e})}^{2} .

10-

ℒ (- 1 / e) = - 1

Formulas (html):

Correct Categorie: gr-qc

Guessed Categorie: gr-qc

Result: correct

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