Run 11329966

Paper: https://arxiv.org/abs/1408.3796

Formulas:

1-

t o r s i o n f r e e

2-

s e m i d u a l i z i n g

3-

m o d u l e

4-

t o r s i o n f r e e

5-

R \to {Hom}_{R} (C, C)

6-

{Ext}_{R}^{i} (C, C) = 0

7-

{(-)}^{†} = {Hom}_{R} (-, C)

8-

\dots \to P_{1} \overset{\partial}{\to} P_{0} \to M \to 0

9-

P_{0}^{†} \overset{\partial^{†}}{\to} P_{1}^{†}

10-

{Ext}_{R}^{i} ({Tr}_{C} M, C) = 0

Formulas (html):

Correct Categorie: math

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1011.4244

Formulas:

1-

λ_{S} = λ_{0} Re \sqrt{\frac{ε_{m} + ε_{d}}{ε_{m} ε_{d}}},

2-

L_{O B J}

3-

L_{O B J}

4-

ϕ (𝐫_{n})

5-

A (𝐫_{n}) = 1

6-

E (𝐫_{0}, {ϕ (𝐫_{n})}) = \sum_{n}^{N} g (𝐫_{0}, 𝐫_{n}) \exp [i ϕ (𝐫_{n})],

7-

g (𝐫_{0}, 𝐫_{n})

8-

\tilde{ϕ} (𝐫_{n}, 𝐫_{0}) = - \arg [g (𝐫_{0}, 𝐫_{n})]

9-

C (𝐫_{n}, 𝐫_{0}) = | g (𝐫_{0}, 𝐫_{n}) |

10-

g (𝐫_{n}, 𝐫_{0}) = C (𝐫_{n}, 𝐫_{0}) \exp [i \tilde{ϕ} (𝐫_{n}, 𝐫_{0})] .

Formulas (html):

Correct Categorie: physics

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/hep-ex/0611040

Formulas:

1-

p \bar{p} \to p + e^{+} e^{-} + \bar{p}

2-

{1.6}_{- 0.3}^{+ 0.5} (stat) \pm 0.3 (syst)

3-

γ γ \to ℓ^{+} ℓ^{-}

4-

p \bar{p} \to p + e^{+} e^{-} + \bar{p}

5-

γ γ \to e^{+} e^{-}

6-

1.1 < | η | < 3.6

7-

σ (E) / \sqrt{E} = 13.5 % \oplus 1.5 %

8-

σ (E) / \sqrt{E} = 16 % \oplus 1 %

9-

3.6 < | η | < 5.2

10-

5.4 < | η | < 7.4

Formulas (html):

Correct Categorie: hep-ex

Guessed Categorie: hep-ph

Result: incorrect

Paper: https://arxiv.org/abs/1206.5350

Formulas:

1-

m_{3} (n)

2-

m_{3} (n) \geq n + 1

3-

m_{3} (n)

4-

m_{3} (n)

5-

m_{3} (n)

6-

n \in {17, 18}

7-

f = f (x_{1}, \dots, x_{n})

8-

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

9-

\sum_{i = 1}^{n} t_{i}

10-

\prod_{i = 1}^{n} x_{i}^{t_{i}}

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0206168

Formulas:

1-

< z_{s p e} - z_{p h o t} > = 0.01

2-

V R I J K

3-

U B V R I H

4-

K_{s} < 21 - 23

5-

ℳ_{s t a r s}

6-

\sim 0.1 L_{K}^{*}

7-

\sim 0.4 L_{K}^{*}

8-

ℳ_{s t a r s} / L_{K}

9-

ℳ_{s t a r s} / L_{K}

10-

ℳ_{s t a r s}^{*}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1508.05780

Formulas:

1-

a_{sym}^{*} (A, I)

2-

a_{sym}^{(4)} = 8.33

3-

e_{sym} = a_{sym} I^{2}

4-

I = (N - Z) / A

5-

a_{sym} (A, I) = J - a_{ss} / A^{1 / 3} + a_{sym}^{(4)} I^{2}

6-

a_{sym} (A)

7-

e_{n} (A, I) = e (A, I) - e_{c} (A, I)

8-

e_{n} (A, I)

9-

a_{sym} (A, I)

10-

e (A, I)

Formulas (html):

Correct Categorie: nucl-th

Guessed Categorie: nucl-ex

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0206063

Formulas:

1-

γ = E / m c^{2} = 10^{5}

2-

\vec{x} = \vec{β} c t

3-

γ \sim 10^{3} - 10^{4}

4-

\frac{d^{2} S_{o}}{d Ω d ω} = \frac{1}{c} {(\frac{Z e ω β \sin θ}{2 π})}^{2} {| \int_{- \infty}^{\infty} ϵ^{1 / 4} e^{i ω t (1 - ϵ^{1 / 2} β \cos θ)} 𝑑 t |}^{2} .

5-

d^{2} S_{o} / d Ω d ω

6-

ϵ_{1, 2} = 1 - ω_{1, 2}^{2} / ω^{2}

7-

τ_{1, 2} \leq \frac{1}{ω (1 - ϵ_{1, 2}^{1 / 2} β \cos θ)}

8-

β c τ_{1, 2} = \frac{Z_{1, 2}}{2} = \frac{2 β c}{ω} {(\frac{1}{γ^{2}} + \frac{ω_{1, 2}^{2}}{ω^{2}} + θ^{2})}^{- 1} .

9-

ω_{1, 2} ≪ ω

10-

ω ≲ γ ω_{1}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/1508.00107

Formulas:

1-

x z / y z

2-

x z / y z

3-

x z \pm i y z

4-

x z \pm i y z

5-

x z \pm i y z

6-

j_{e f f}

7-

x z \pm i y z

8-

x z / y z

9-

x z / y z

10-

Λ_{S O C} = t

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/0911.5633

Formulas:

1-

g (t) = \pm g_{0} \cos (2 π t / T_{B})

2-

Ψ (x, t)

3-

V (x) = V_{0} \cos^{2} (π x / b)

4-

Ψ_{n} (t)

5-

i ℏ {\dot{Ψ}}_{n} = - J (Ψ_{n + 1} + Ψ_{n - 1}) + F b n Ψ_{n} + g (t) {| Ψ_{n} |}^{2} Ψ_{n}

6-

\sum_{i} {| Ψ_{i} |}^{2} = 1

7-

J / E \approx 4 {(V_{0} / E)}^{3 / 4} \exp (- 2 \sqrt{V_{0} / E}) / \sqrt{π}

8-

E = ℏ^{2} π^{2} / 2 m b^{2}

9-

g = \sqrt{2 ω_{x} ω_{y} ω_{z} ℏ m / π} N a / J

10-

ϵ (p) = - 2 J \cos (p b / ℏ)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/cond-mat/0301536

Formulas:

1-

d_{x z, y z}

2-

d_{x z, y z}

3-

d_{x z, y z}

4-

W_{x z, y z} < U < W_{x y}

5-

d_{x z, y z}

6-

E_{v H s} > E_{F}

7-

E_{v H s} < E_{F}

8-

W_{x z, y z} \approx 1.3

9-

W_{x y} \approx 3.5

10-

d_{x z, y z}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1712.03533

Formulas:

1-

\sum m_{ν} = 0.711 - 0.335 \cdot δ h + 0.050 \cdot δ b \pm 0.063 eV,

2-

δ h \equiv (h - 0.678) / 0.009

3-

δ b \equiv (Ω_{b} h^{2} - 0.02226) / 0.00023

4-

δ h = \pm 1

5-

δ b = \pm 1

6-

H_{0} \equiv 100 h

7-

\sum m_{ν} = 3 m_{ν}

8-

T_{ν} = m_{ν} / 3.15

9-

T = m_{ν} {(11 / 4)}^{1 / 3} / 3.15

10-

a_{ν} = T_{0} / T = 5.28 \times 10^{- 4} (1 e V / m_{ν})

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/9906311

Formulas:

1-

τ_{SFR} (z)

2-

{(1 + z)}^{γ}

3-

H_{0} = 100 h

4-

N_{PS} (M, z) = \frac{\bar{ρ}}{\sqrt{π}} \frac{γ}{M^{2}} {(\frac{M}{M^{*}})}^{γ / 2} \exp [- {(\frac{M}{M^{*}})}^{γ}],

5-

γ = (3 + n) / 3

6-

M^{*} (z)

7-

M^{*} (z) = M^{*} (0) {[\frac{δ (z)}{δ (0)}]}^{2 / γ} .

8-

\ddot{δ} + 2 \frac{\dot{R}}{R} \dot{δ} - \frac{4 π G \bar{ρ}}{R^{3}} δ = 0,

9-

δ \propto {(1 + z)}^{- 1}

10-

M^{*} (0)

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/0911.1233

Formulas:

1-

V_{c} \approx G D / Δ T_{o}

2-

(V - V_{c}) / V_{c} ≪ 1

3-

(V - V_{c}) / V_{c} ≫ 1

4-

β = \partial (δ T_{k}) / \partial V

5-

δ T_{k} \propto V^{n}

6-

G \approx 5.6 {Kmm}^{- 1}

7-

G = 5.6 {Kmm}^{- 1}

8-

V_{c} = 4.5 \pm 1.5

9-

θ_{a} = - 6^{o}

10-

Λ_{x} = 220 μ m \pm 20 μ m

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1404.3440

Formulas:

1-

I_{1} (x) = \frac{I_{0}}{N^{2}} {[\frac{\sin (π x δ / λ)}{π x δ / λ} \frac{\sin (N π x d / λ)}{\sin (π x d / λ)}]}^{2}

2-

x d / λ = m

3-

Δ x_{1} = \frac{λ}{d} .

4-

ϵ = d - δ ≪ d

5-

{(ϵ / d)}^{2}

6-

\sin^{2} (π x δ / λ) = \sin^{2} (π m - π x ϵ / λ) \approx {(π x ϵ / λ)}^{2}

7-

{(ϵ / d)}^{2}

8-

I (x, y) = \frac{I_{1} (x) I_{1} (y)}{I_{0}} .

9-

{(ϵ / d)}^{4}

10-

Δ x_{2} \approx \frac{1}{N d} = \frac{1}{D}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/1505.04509

Formulas:

1-

[X_{i}, P_{j}] = i δ_{i j}

2-

{i; j} = {1; 2; A; B}

3-

P_{1} - G_{1} P_{A},

4-

X_{A} + G_{1} X_{1},

5-

X_{2} + G_{2} X_{B},

6-

P_{B} - G_{2} P_{2} .

7-

\sqrt{T_{1}} X_{1} - \sqrt{1 - T_{1}} X_{B},

8-

\sqrt{T_{1}} (P_{1} - G_{1} P_{A}) - \sqrt{1 - T_{1}} (P_{B} - G_{2} P_{2}),

9-

\sqrt{T_{1}} X_{B} + \sqrt{1 - T_{1}} X_{1},

10-

\sqrt{T_{1}} (P_{B} - G_{2} P_{2}) + \sqrt{1 - T_{1}} (P_{1} - G_{1} P_{A}),

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: gr-qc

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0303490

Formulas:

1-

α - e l e m e n t s

2-

d [F e / H] / d R_{G} \approx - 0.13 \pm 0.03 d e x k p c^{- 1}

3-

\approx - 0.02 \pm 0.01 d e x k p c^{- 1}

4-

\approx - 0.06 \pm 0.01 d e x k p c^{- 1}

5-

P L Z_{K}

6-

- 2.2 \leq [F e / H] \leq 0

7-

{(M / L)}_{V} \sim 5

8-

M_{V} v s [F e / H]

9-

P L Z_{K}

10-

< P_{a b} > \approx 0.539

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1012.4634

Formulas:

1-

\sum_{v \in V (G)} \max {0, d^{+} (v) - d^{-} (v)}

2-

d^{+} (v)

3-

d^{-} (v)

4-

V (G) \times V (H)

5-

b d \in E (H)

6-

a b \in E (G)

7-

1 = b (P_{m}) \leq b (G) \leq b (K_{m}) = ⌊ \frac{m^{2}}{4} ⌋,

8-

b (P_{m} \times H) \leq b (G \times H) \leq b (K_{m} \times H) .

9-

w_{0} (v)

10-

α = (α_{1}, α_{2}, \dots, α_{n})

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/0909.4458

Formulas:

1-

6.2 \pm 2.2 \times 10^{- 4}

2-

Δ χ^{2} / d o f = 3.1 / 2

3-

χ^{2} / d o f = 40.7 / 16

4-

χ^{2} / d o f = 14.4 / 21

5-

χ^{2} / d o f = 55.4 / 21

6-

\sim 8.2 \times 10^{- 2}

7-

L \sim 8.1 \times 10^{40}

8-

\sim 8.3 \times 10^{- 2}

9-

L \sim 5.0 \times 10^{40}

10-

\sim 3.1 \times 10^{- 2}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1010.4348

Formulas:

1-

H = - \frac{J}{2} \sum_{i} [(σ_{i}^{x} σ_{i + 1}^{x} + σ {}_{i}^{y}σ_{i + 1}^{y}) + Δ σ_{i}^{z} σ_{i + 1}^{z}] - \frac{1}{2} \sum_{i} B_{i} σ_{i}^{z},

2-

(α = x, y, z)

3-

C (t) = \bar{⟨ σ_{j}^{x} (t) σ_{j}^{x} (0) ⟩}

4-

Φ (ω) = \int_{- \infty}^{+ \infty} e^{i ω t} C (t) 𝑑 t,

5-

Φ (ω) = lim_{ε \to 0} [Re \int_{0}^{\infty} 𝑑 t C (t) e^{- z t}],

6-

z = ε + i ω,

7-

σ_{j}^{x} (t)

8-

σ_{j}^{x} (t) = \sum_{ν = 0}^{\infty} a_{ν} (t) f_{ν},

9-

a_{ν} (t)

10-

f_{ν + 1} = i L f_{ν} + Δ_{ν} f_{ν - 1}, ν \geq 0,

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/astro-ph/9608112

Formulas:

1-

\sim 2 - 3 σ

2-

\sim 50 - 100 h^{- 1}

3-

r < 20 h^{- 1}

4-

H_{0} = 100 h

5-

\sim 100 - 150 h^{- 1}

6-

50 - 100 h^{- 1}

7-

< 100 h^{- 1}

8-

\sim 20 - 40 h^{- 1}

9-

\sim 100 h^{- 1}

10-

\sim 30 - 50 h^{- 1}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1911.02017

Formulas:

1-

{ε (𝒌)}

2-

E (V) = 2.21 e V

3-

E (A) = 0.72 e V

4-

E (A) = E^{'} (A) - [E + μ_{T e}]

5-

E (V) = E^{'} (V) - [E - μ_{T e}]

6-

E^{'} (A / V)

7-

{E | \frac{1}{5} 00}

8-

{E | 0 \frac{1}{3} 0}

9-

𝒜 (𝒌, ω) = \sum_{n} P_{n 𝑲} (𝒌) δ (ω - ε_{n} (𝒌))

10-

P_{n 𝑲} (𝒌) = \sum_{m} {| ⟨ m 𝑲 | n 𝒌 ⟩ |}^{2}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/hep-ph/9912427

Formulas:

1-

Δ m_{sun}^{2} \sim 10^{- 6} - 10^{- 4} {eV}^{2} (MSW),

2-

Δ m_{sun}^{2} \sim 10^{- 11} - 10^{- 10} {eV}^{2} (VO),

3-

Δ m_{atm}^{2} \sim 10^{- 3} - 10^{- 2} {eV}^{2} .

4-

\underset{Δ m_{atm}^{2}}{\underset{⏟}{\overset{Δ m_{sun}^{2}}{\overset{⏞}{m_{1} ≪ m_{2}}} ≪ m_{3}}} .

5-

β β_{0 ν}

6-

| ⟨ m ⟩ | = | \sum_{k} U_{e k}^{2} m_{k} |,

7-

k = 1, 2, 3

8-

| ⟨ m ⟩ | ≃ \max_{k} {| ⟨ m ⟩ |}_{k},

9-

{| ⟨ m ⟩ |}_{k}

10-

{| ⟨ m ⟩ |}_{k} \equiv {| U_{e k} |}^{2} m_{k} .

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: hep-ph

Result: correct

Paper: https://arxiv.org/abs/hep-lat/9709128

Formulas:

1-

S U (3)

2-

(16^{3} 48)

3-

(24^{3} 48)

4-

U_{n e w} = c (U_{m i n} + α U_{o l d})

5-

U_{m i n}

6-

U_{o l d}

7-

n_{I} - n_{\bar{I}}

8-

δ = < | Q - (n_{I} - n_{\bar{I}}) | >

9-

D (ρ) \propto ρ^{- α}

10-

< \frac{Q}{| Q |} \frac{q (ρ)}{n (ρ)} >

Formulas (html):

Correct Categorie: hep-lat

Guessed Categorie: hep-lat

Result: correct

Paper: https://arxiv.org/abs/2005.02080

Formulas:

1-

\tilde{x} (t)

2-

\tilde{E} (t) = \frac{1}{\sqrt{2 π}} \int_{Δ ω} E (ω^{'}) e^{- i ω^{'} t} 𝑑 ω^{'},

3-

\ddot{\tilde{x}} + 2 γ \dot{\tilde{x}} + ω_{0}^{2} \tilde{x} + a {\tilde{x}}^{2} = - e \tilde{E} (t) / m,

4-

a \tilde{x} ≪ ω_{0}^{2}

5-

\tilde{x} (t) = {\tilde{x}}_{1} (t) + {\tilde{x}}_{2} (t) + {\tilde{x}}_{3} (t) + \dots + {\tilde{x}}_{n} (t),

6-

\tilde{E} (t)

7-

{\ddot{\tilde{x}}}_{1} + 2 γ {\dot{\tilde{x}}}_{1} + ω_{0}^{2} {\tilde{x}}_{1} =

8-

- e \tilde{E} (t) / m,

9-

{\ddot{\tilde{x}}}_{2} + 2 γ {\dot{\tilde{x}}}_{2} + ω_{0}^{2} {\tilde{x}}_{2} =

10-

- a {\tilde{x}}_{1}^{2},

Formulas (html):

Correct Categorie: physics

Guessed Categorie: physics

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0502045

Formulas:

1-

- α, δ, γ, κ

2-

P_{i} / P_{g a s}

3-

3.3 \leq \log T \leq 4.3

4-

- 8 \leq \log R \leq 3

5-

\frac{1}{κ_{R}} \equiv \frac{\int_{0}^{\infty} \frac{1}{κ_{λ}} \frac{\partial B_{λ}}{\partial T} 𝑑 λ}{\int_{0}^{\infty} \frac{\partial B_{λ}}{\partial T} 𝑑 λ}

6-

\partial B_{λ} / \partial T

7-

κ_{λ} ρ = π \sum_{i} \int_{a} n_{i} (a) Q_{ext} (a, i, λ) a^{2} 𝑑 a

8-

n_{i} (a)

9-

Q_{ext} (a, i, λ)

10-

n_{i} (a)

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/math/0501146

Formulas:

1-

m = 3 d - 1

2-

m = 3 d - 1

3-

N_{d} = \sum_{a + b = d} N_{a} N_{b} (a^{2} b^{2} (\binom{3 d - 4}{3 a - 2}) - a^{3} b (\binom{3 d - 4}{3 a - 1})) .

4-

N () - N () = 8 .

5-

N () + N () \leq 12

6-

σ (C) \in {\pm 1}

7-

| \sum σ (C) |,

8-

T (x, y) = \max_{(i, j) \in Δ} {x \cdot i + y \cdot j + c_{i, j}},

9-

c_{i, j} \in ℝ

10-

T (x, y)

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/1910.03462

Formulas:

1-

- [\frac{{(r^{2} + a^{2})}^{2}}{Δ} - a^{2} \sin^{2} θ] \partial_{t t} Ψ - \frac{4 M a r}{Δ} \partial_{t ϕ} Ψ

2-

- 2 s [r - \frac{M (r^{2} - a^{2})}{Δ} + i a \cos θ] \partial_{t} Ψ

3-

+ Δ^{- s} \partial_{r} (Δ^{s + 1} \partial_{r} Ψ) + \frac{1}{\sin θ} \partial_{θ} (\sin θ \partial_{θ} Ψ) +

4-

[\frac{1}{\sin^{2} θ} - \frac{a^{2}}{Δ}] \partial_{ϕ ϕ} Ψ + 2 s [\frac{a (r - M)}{Δ} + \frac{i \cos θ}{\sin^{2} θ}] \partial_{ϕ} Ψ

5-

- (s^{2} \cot^{2} θ - s) Ψ = - 4 π (r^{2} + a^{2} \cos^{2} θ) T,

6-

Δ = r^{2} - 2 M r + a^{2}

7-

Ψ = {(r - i a \cos θ)}^{4} ψ_{4}

8-

(a / M, p / M, e) = (0.999 99, 2.918, 0.807)

9-

(p / M, e) = (2.250 054 2, 0.96)

10-

a / M = 0.995, 0.999 9, 0.999 95, 0.999 99

Formulas (html):

Correct Categorie: gr-qc

Guessed Categorie: gr-qc

Result: correct

Paper: https://arxiv.org/abs/1212.3460

Formulas:

1-

𝐱 = x^{1}, \dots, x^{r}

2-

𝐲 = y^{1}, \dots, y^{s}

3-

X_{dk} (𝐱, 𝐲)

4-

d σ / d 𝐱 d 𝐲

5-

X_{dk} (𝐱, 𝐲)

6-

W_{max} (X)

7-

X_{dk} (𝐱, 𝐲)

8-

\frac{d σ}{d 𝐱 d 𝐲} (X_{dk} (𝐱, 𝐲)) > r W_{max} (X)

9-

X_{dk} (𝐱, 𝐲)

10-

W_{max} (X)

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: cs

Result: incorrect

Paper: https://arxiv.org/abs/1507.04049

Formulas:

1-

G i n g a

2-

S w i f t

3-

N u c l e a r

4-

S p e c t r o s c o p i c

5-

T e l e s c o p e

6-

A r r a y

7-

0 \overset{\circ}{.} 28

8-

0 \overset{''}{.} 15

9-

0 \overset{''}{.} 76

10-

L P = \sqrt{Q^{2} + U^{2}}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/cond-mat/0312281

Formulas:

1-

3 p \leftarrow 3 s

2-

3 p \leftarrow 3 s

3-

10^{- 2} ρ_{0}

4-

10^{- 3} ρ_{0}

5-

10^{- 4} ρ_{0}

6-

V_{H e - N a}

7-

ρ \sim ρ_{0} / 2

8-

ρ \sim ρ_{0} / 2

9-

S_{N a} = E (Na @ {He}_{N}) - E ({He}_{N})

10-

S_{N a} (N) = S_{0} + \frac{S_{1}}{N^{1 / 3}} + \frac{S_{2}}{N^{2 / 3}}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1611.05396

Formulas:

1-

𝐛 = {[x_{1}, y_{1}, x_{2}, y_{2}]}^{T}

2-

𝐬 = {[x_{1}, y_{1}, \dots, x_{L}, y_{L}]}^{T}

3-

Φ = {ϕ (1), ϕ (2), \dots, ϕ (N)}

4-

ϕ = {𝐀, 𝐞}

5-

ϕ : δ 𝐬 = 𝐀 \cdot f (𝐈, 𝐬^{'}) + 𝐞,

6-

𝐀 \in ℝ^{2 L \times N_{f}}

7-

f (𝐈, 𝐬^{'})

8-

𝐞 \in ℝ^{2 L}

9-

𝐬^{'} \leftarrow 𝐬^{'} + δ 𝐬 .

10-

T = {𝐈_{i}, 𝐛_{i}, 𝐬_{i}^{*}}_{i = 1}^{I}

Formulas (html):

Correct Categorie: cs

Guessed Categorie: cs

Result: correct

Paper: https://arxiv.org/abs/quant-ph/9911112

Formulas:

1-

| 1 ⟩ \leftrightarrow | 3 ⟩

2-

| 2 ⟩ \leftrightarrow | 3 ⟩

3-

\frac{\partial \hat{ρ}}{\partial t} = - \frac{i}{ℏ} [{\hat{ℋ}}_{eff}, \hat{ρ}] + \sum_{i, j, k = 1, 2} \frac{γ_{k 3}^{(i j)}}{2} (2 {\hat{σ}}_{3 k}^{(i)} \hat{ρ} {\hat{σ}}_{k 3}^{(j)} - \hat{ρ} {\hat{σ}}_{3 k}^{(i)} {\hat{σ}}_{k 3}^{(j)} - {\hat{σ}}_{3 k}^{(i)} {\hat{σ}}_{k 3}^{(j)} \hat{ρ}),

4-

σ_{k l}^{(i)}

5-

γ_{k 3} = γ_{k 3}^{(11)} = γ_{k 3}^{(22)}

6-

γ_{k 3}^{(12)} = γ_{k 3}^{(21)}

7-

{\hat{ℋ}}_{eff} = ℏ \sum_{i, k = 1, 2} (δ_{k 3} {\hat{n}}_{k}^{(i)} + \frac{Ω_{k 3}^{(i)}}{2} {\hat{σ}}_{k 3}^{(i)} + χ_{k 3} {\hat{σ}}_{k 3}^{(1)} {\hat{σ}}_{3 k}^{(2)} + H. c.),

8-

{\hat{n}}_{k}^{(i)}

9-

| k ⟩ \leftrightarrow | 3 ⟩

10-

Ω_{k 3}^{(i)}

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: quant-ph

Result: correct

Paper: https://arxiv.org/abs/1108.1149

Formulas:

1-

β_{1} = v_{1} / c = 1.13 \times 10^{- 6}

2-

β_{2} = v_{2} / c = 1 \times 10^{- 4}

3-

β_{3} = v_{3} / c = 1.3 \times 10^{- 3}

4-

v_{m} = c β_{m}

5-

β_{g} = \frac{1 / n_{g} + β_{m}}{1 + β_{m} / n_{g}}

6-

Δ ϕ = \frac{ω}{c} n L

7-

ω = 2 π ν

8-

\frac{d Δ ϕ}{d ω} = \frac{d}{d ω} (\frac{ω n L}{c}) = \frac{L}{c} (n + ω \frac{d n}{d ω}) = \frac{L n_{g}}{c}

9-

Δ ϕ = ω t = ω \frac{L}{v_{g}}

10-

\frac{d Δ ϕ}{d v_{g}} = - ω \frac{L}{v_{g}^{2}} or \frac{1}{2 π} Δ ϕ = - \frac{L}{λ} \frac{1}{β_{g}} \frac{d v_{g}}{v_{g}}

Formulas (html):

Correct Categorie: physics

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/1803.04079

Formulas:

1-

U (g) ρ U^{†} (g) = ρ

2-

ℰ [U (g) ρ U^{†} (g)] = U (g) ℰ (ρ) U^{†} (g)

3-

𝒰_{g} (ρ) := U (g) ρ U^{†} (g) \neq ρ

4-

𝒜_{ℛ} (ρ) = \min_{τ \in 𝒟 (ℋ)} {s \geq 0 | \frac{ρ + s τ}{1 + s} \in 𝒮},

5-

U (g) ρ U^{†} (g)

6-

P_{s} (ρ)

7-

P_{s} (ρ) = \frac{1 + 𝒜_{ℛ} (ρ)}{| G |},

8-

U (g) ρ U^{†} (g)

9-

P_{s} (ρ)

10-

P_{s} (ρ)

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: hep-lat

Result: incorrect

Paper: https://arxiv.org/abs/1604.04817

Formulas:

1-

F_{ν} \propto t^{- 1} - t^{- 2}

2-

F_{ν} \propto ν^{- 0.9 \pm 0.5}

3-

L_{w} \propto t^{- 4 / 5}

4-

F_{ν} \propto ν^{- β} t^{- α}

5-

Q_{x} = Q / 10^{x}

6-

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

7-

E_{p} = 55 \pm 4

8-

α = - 0.61 \pm 0.06

9-

β = - 2.3 \pm 0.3

10-

(7.6 \pm 0.2) \times 10^{- 6}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/quant-ph/0006089

Formulas:

1-

{| ψ_{n} ⟩}

2-

p_{n} = {| c_{n} |}^{2}

3-

| ψ (t) ⟩ = U (t) | ψ (0) ⟩ = \sum_{n} c_{n} (t) | ψ_{n} ⟩

4-

{p_{1}, p_{2}, \dots p_{n}}

5-

S (t) = - \sum_{n} p_{n} (t) \log p_{n} (t)

6-

c_{n} (t) = ⟨ ψ_{n} | e^{- i H t / ℏ} | ψ_{n} ⟩ = \sum_{m} e^{- i E_{m} t / ℏ} P_{n m}

7-

P_{n m} = {| ⟨ ψ_{n} | ϕ_{m} ⟩ |}^{2}

8-

{| ϕ_{m} ⟩}

9-

\sum_{n} P_{n m} = I = \sum_{m} P_{n m}

10-

p_{n} (t) = \sum_{m k} e^{- i (E_{m} - E_{k}) t / ℏ} P_{n m} P_{n k} .

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: quant-ph

Result: correct

Paper: https://arxiv.org/abs/cond-mat/0310133

Formulas:

1-

ξ = 2 d / (d + 3)

2-

ξ = 2 d / (d + 2)

3-

n (t) \sim t^{- ξ}, ξ = \frac{2 d}{d + 2}

4-

d n / d t = - n / τ

5-

n V τ R^{d - 1} \sim 1

6-

R \sim n^{- 1 / d}

7-

\frac{d n}{d t} = - n^{2} V R^{d - 1} = - n^{1 + 1 / d} V .

8-

p \sim m^{1 / 2}, V = p / m \sim n^{1 / 2} .

9-

ξ = 2 d / (d + 2)

10-

ξ_{d} = 2 d / (d + 2)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/2005.04739

Formulas:

1-

Q = ω τ_{p}

2-

R_{0} / r_{0} = 30

3-

V_{a} \cos ω t

4-

\frac{\partial u}{\partial t} + u \frac{\partial u}{\partial r} + \frac{u}{τ} = \frac{e}{m} \frac{\partial φ}{\partial r},

5-

\frac{\partial n_{s}}{\partial t} + \frac{1}{r} \frac{\partial}{\partial r} (r u n_{s}) = 0 .

6-

C (V_{g} - φ) = e n_{s},

7-

C = ε / 4 π d

8-

φ (r_{0}, t) = V_{g} (t) \equiv V_{0} + V_{a} \cos (ω t),

9-

n u_{s} (R_{0}, t) = 0 .

10-

φ_{ω} (r) = - V_{a} \frac{Y_{1} (k R_{0}) J_{0} (k r) - J_{1} (k R_{0}) Y_{0} (k r)}{Y_{0} (k r_{0}) J_{1} (k R_{0}) - Y_{1} (k R_{0}) J_{0} (k r_{0})},

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/1601.04324

Formulas:

1-

O (n^{- 2})

2-

Δ_{qp} = E_{I} - E_{A} = E_{+} + E_{-} - 2 E_{0},

3-

E_{A} = E_{0} - E_{+}

4-

E_{I} = E_{-} - E_{0}

5-

Δ_{exc} = E_{pr} - E_{0},

6-

E (n) = E (\infty) + A n^{- 2},

7-

Δ (n) = Δ (\infty) + B n^{- 1}

8-

ℏ = m_{e} = | e | = 4 π ϵ_{0} = 1

9-

v_{M} = [- 0.2319 - 2 l o g (a n)] / (a n)

10-

R_{\infty}^{*} = μ / 2

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/1310.0351

Formulas:

1-

Γ_{C} \propto \exp (- e / e_{f})

2-

\partial_{t} σ + \nabla \cdot (σ \vec{v})

3-

\partial_{t} (σ \vec{v}) + \nabla \cdot [σ \vec{v} \vec{v}]

4-

= - \nabla P - σ \nabla Φ

5-

\partial_{t} e + \nabla \cdot (e \vec{v})

6-

= - P \nabla \cdot \vec{v} + 𝒬 - Λ

7-

P = (γ - 1) e

8-

σ = σ_{0} r^{- α}

9-

T = T_{0} r^{- β}

10-

σ_{0} = 1.35 \times 10^{- 3}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/0903.3748

Formulas:

1-

μ Φ_{0} / \sqrt{Hz}

2-

Φ_{S Q U I D}

3-

ϕ_{1}^{(n)} + i ϕ_{2}^{(n)} \equiv Φ^{(n)} / I_{FC}

4-

ϕ_{1, 2} \equiv ϕ_{1, 2}^{(1)}

5-

- 3.4 \cdot 10^{- 5}

6-

χ (ω) \equiv χ_{1} + i χ_{2}

7-

𝐁 = μ_{0} χ d \partial \tilde{𝐇} / \partial z

8-

χ_{1, 2} d

9-

Φ_{0} \cdot ϕ_{1, 2}

10-

χ_{1} T = 3 \cdot 10^{- 5}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/0806.1136

Formulas:

1-

G \approx 3 G_{0}

2-

G \approx 1 G_{0}

3-

G_{0} = 2 e / h^{2}

4-

G \approx 1 G_{0}

5-

- 3 \leq E - E_{F} \leq 5

6-

G_{0} = 2 e^{2} / h

7-

G \approx 1 G_{0}

8-

G \approx 1 G_{0}

9-

G \approx 1 G_{0}

10-

G \approx 1 G_{0}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1512.02460

Formulas:

1-

i = 1, 2, \dots, n

2-

𝐱 = (x_{1}, x_{2}, \dots, x_{n})

3-

{\begin{matrix} {\dot{x}}_{i} & = (ϕ_{i} (𝐱) - \bar{ϕ} (𝐱)) x_{i}, \\ \bar{ϕ} (𝐱) & = \sum_{k = 1}^{n} x_{k} ϕ_{k} (𝐱), \end{matrix}

4-

ϕ_{i} (𝐱)

5-

\bar{ϕ} (𝐱)

6-

\dot{𝐱} = 𝐟 (𝐱)

7-

𝐟 (𝐱^{*}) = 0

8-

S_{n - 1} = {𝐱 \in 𝐑^{n} | x_{i} \geq 0, \sum_{i = 1}^{n} x_{i} = 1},

9-

J (𝐱^{*}) = {[{\frac{\partial f_{i} (𝐱)}{\partial x_{j}} |}_{𝐱 = 𝐱^{*}}]}_{i, j} .

10-

x_{i} (0) > 0

Formulas (html):

Correct Categorie: q-bio

Guessed Categorie: cs

Result: incorrect

Paper: https://arxiv.org/abs/1510.04942

Formulas:

1-

S (g, m_{g}) = \int d^{4} x {\frac{1}{4} (F_{μ ν}^{a} F_{μ ν}^{a}) + \frac{1}{2} {\bar{λ}}_{a} (γ^{μ} D_{μ}^{a b} + m) λ_{b} - \frac{Θ}{16 π} ϵ_{μ ν ρ σ} F^{μ ν} F^{ρ σ}} .

2-

A_{μ} (x)

3-

{Q_{α}, Q_{β}} = {(γ^{μ} C)}_{α, β} P_{μ} .

4-

A_{μ} (x)

5-

A_{μ} (x) - 2 i \bar{λ} (x) γ_{μ} ϵ

6-

λ^{a} (x)

7-

λ^{a} (x) - σ_{μ ν} F_{μ ν}^{a} (x) ϵ,

8-

m_{a– π}^{2} \propto m_{g}

9-

\hat{d} = d / a

10-

a = d / \hat{d}

Formulas (html):

Correct Categorie: hep-lat

Guessed Categorie: hep-ph

Result: incorrect

Paper: https://arxiv.org/abs/0909.2875

Formulas:

1-

Q_{U} < 3.9 \times 10^{4}

2-

1.2 \times 10^{4} < Q_{N} < 3.3 \times 10^{5}

3-

T_{eff} = 3500 K

4-

T_{eff} = 3300 K

5-

2 γ_{1} + γ_{2}

6-

2 γ_{2} - γ_{1}

7-

R_{p} / R_{⋆} = 0.08142 \pm 0.00085

8-

R_{⋆} / a = 0.0707 \pm 0.0025

9-

M_{⋆} = 0.452 \pm 0.013

10-

R_{⋆} = 0.437 \pm 0.016 R_{⊙}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1004.1070

Formulas:

1-

E = - J \sum_{< i, j >} σ_{i} σ_{j}

2-

x, y and z

3-

w_{i} = {⟨ σ_{- 1 i} σ_{0} + σ_{0} σ_{1 i} ⟩}_{N}, where i \in [x, y, z]

4-

f_{I I I}

5-

N_{s u b}

6-

(f_{I}, f_{I I}, f_{I I I})

7-

N_{s u b}

8-

N_{s u b}

9-

(f_{I}, f_{I I}, f_{I I I})

10-

T_{x y z}

Formulas (html):

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id="S2.Ex1.m1.4.5.3.2.3.2.3.3" xref="S2.Ex1.m1.4.5.3.2.3.2.3.3.cmml">j</mi></msub></mrow></mrow></mrow></mrow></mrow></math>, <math><mrow id="S2.SS1.p2.1.m1.2.2.1" xref="S2.SS1.p2.1.m1.2.2.2.cmml"><mi id="S2.SS1.p2.1.m1.1.1" xref="S2.SS1.p2.1.m1.1.1.cmml">x</mi><mo rspace="5.3pt" id="S2.SS1.p2.1.m1.2.2.1.2" xref="S2.SS1.p2.1.m1.2.2.2.cmml">,</mo><mrow id="S2.SS1.p2.1.m1.2.2.1.1" xref="S2.SS1.p2.1.m1.2.2.1.1.cmml"><mpadded width="+2.8pt" id="S2.SS1.p2.1.m1.2.2.1.1.2" xref="S2.SS1.p2.1.m1.2.2.1.1.2.cmml"><mi id="S2.SS1.p2.1.m1.2.2.1.1.2a" xref="S2.SS1.p2.1.m1.2.2.1.1.2.cmml">y</mi></mpadded><mo id="S2.SS1.p2.1.m1.2.2.1.1.1" xref="S2.SS1.p2.1.m1.2.2.1.1.1.cmml">⁢</mo><mpadded width="+2.8pt" id="S2.SS1.p2.1.m1.2.2.1.1.3" xref="S2.SS1.p2.1.m1.2.2.1.1.3b.cmml"><mtext id="S2.SS1.p2.1.m1.2.2.1.1.3a" xref="S2.SS1.p2.1.m1.2.2.1.1.3b.cmml">and</mtext></mpadded><mo id="S2.SS1.p2.1.m1.2.2.1.1.1a" xref="S2.SS1.p2.1.m1.2.2.1.1.1.cmml">⁢</mo><mi id="S2.SS1.p2.1.m1.2.2.1.1.4" 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xref="S2.T2.1.1.1.m1.1.1.3.1.cmml">⁢</mo><mi id="S2.T2.1.1.1.m1.1.1.3.4" xref="S2.T2.1.1.1.m1.1.1.3.4.cmml">b</mi></mrow></msub></math>, <math><msub id="S2.T2.16.m2.1.1" xref="S2.T2.16.m2.1.1.cmml"><mi id="S2.T2.16.m2.1.1.2" xref="S2.T2.16.m2.1.1.2.cmml">N</mi><mrow id="S2.T2.16.m2.1.1.3" xref="S2.T2.16.m2.1.1.3.cmml"><mi id="S2.T2.16.m2.1.1.3.2" xref="S2.T2.16.m2.1.1.3.2.cmml">s</mi><mo id="S2.T2.16.m2.1.1.3.1" xref="S2.T2.16.m2.1.1.3.1.cmml">⁢</mo><mi id="S2.T2.16.m2.1.1.3.3" xref="S2.T2.16.m2.1.1.3.3.cmml">u</mi><mo id="S2.T2.16.m2.1.1.3.1b" xref="S2.T2.16.m2.1.1.3.1.cmml">⁢</mo><mi id="S2.T2.16.m2.1.1.3.4" xref="S2.T2.16.m2.1.1.3.4.cmml">b</mi></mrow></msub></math>, <math><mrow id="S2.T2.20.m6.3.3.3" xref="S2.T2.20.m6.3.3.4.cmml"><mo stretchy="false" id="S2.T2.20.m6.3.3.3.4" xref="S2.T2.20.m6.3.3.4.cmml">(</mo><msub id="S2.T2.20.m6.1.1.1.1" xref="S2.T2.20.m6.1.1.1.1.cmml"><mi id="S2.T2.20.m6.1.1.1.1.2" xref="S2.T2.20.m6.1.1.1.1.2.cmml">f</mi><mi id="S2.T2.20.m6.1.1.1.1.3" xref="S2.T2.20.m6.1.1.1.1.3.cmml">I</mi></msub><mo id="S2.T2.20.m6.3.3.3.5" xref="S2.T2.20.m6.3.3.4.cmml">,</mo><msub id="S2.T2.20.m6.2.2.2.2" xref="S2.T2.20.m6.2.2.2.2.cmml"><mi id="S2.T2.20.m6.2.2.2.2.2" xref="S2.T2.20.m6.2.2.2.2.2.cmml">f</mi><mrow id="S2.T2.20.m6.2.2.2.2.3" xref="S2.T2.20.m6.2.2.2.2.3.cmml"><mi id="S2.T2.20.m6.2.2.2.2.3.2" xref="S2.T2.20.m6.2.2.2.2.3.2.cmml">I</mi><mo id="S2.T2.20.m6.2.2.2.2.3.1" xref="S2.T2.20.m6.2.2.2.2.3.1.cmml">⁢</mo><mi id="S2.T2.20.m6.2.2.2.2.3.3" xref="S2.T2.20.m6.2.2.2.2.3.3.cmml">I</mi></mrow></msub><mo id="S2.T2.20.m6.3.3.3.6" xref="S2.T2.20.m6.3.3.4.cmml">,</mo><msub id="S2.T2.20.m6.3.3.3.3" xref="S2.T2.20.m6.3.3.3.3.cmml"><mi id="S2.T2.20.m6.3.3.3.3.2" xref="S2.T2.20.m6.3.3.3.3.2.cmml">f</mi><mrow id="S2.T2.20.m6.3.3.3.3.3" xref="S2.T2.20.m6.3.3.3.3.3.cmml"><mi id="S2.T2.20.m6.3.3.3.3.3.2" xref="S2.T2.20.m6.3.3.3.3.3.2.cmml">I</mi><mo id="S2.T2.20.m6.3.3.3.3.3.1" xref="S2.T2.20.m6.3.3.3.3.3.1.cmml">⁢</mo><mi id="S2.T2.20.m6.3.3.3.3.3.3" xref="S2.T2.20.m6.3.3.3.3.3.3.cmml">I</mi><mo id="S2.T2.20.m6.3.3.3.3.3.1b" xref="S2.T2.20.m6.3.3.3.3.3.1.cmml">⁢</mo><mi id="S2.T2.20.m6.3.3.3.3.3.4" xref="S2.T2.20.m6.3.3.3.3.3.4.cmml">I</mi></mrow></msub><mo stretchy="false" id="S2.T2.20.m6.3.3.3.7" xref="S2.T2.20.m6.3.3.4.cmml">)</mo></mrow></math>, <math><msub id="S2.SS2.p3.3.m3.1.1" xref="S2.SS2.p3.3.m3.1.1.cmml"><mi id="S2.SS2.p3.3.m3.1.1.2" xref="S2.SS2.p3.3.m3.1.1.2.cmml">T</mi><mrow id="S2.SS2.p3.3.m3.1.1.3" xref="S2.SS2.p3.3.m3.1.1.3.cmml"><mi id="S2.SS2.p3.3.m3.1.1.3.2" xref="S2.SS2.p3.3.m3.1.1.3.2.cmml">x</mi><mo id="S2.SS2.p3.3.m3.1.1.3.1" xref="S2.SS2.p3.3.m3.1.1.3.1.cmml">⁢</mo><mi id="S2.SS2.p3.3.m3.1.1.3.3" xref="S2.SS2.p3.3.m3.1.1.3.3.cmml">y</mi><mo id="S2.SS2.p3.3.m3.1.1.3.1a" xref="S2.SS2.p3.3.m3.1.1.3.1.cmml">⁢</mo><mi id="S2.SS2.p3.3.m3.1.1.3.4" xref="S2.SS2.p3.3.m3.1.1.3.4.cmml">z</mi></mrow></msub></math>

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/hep-lat/0208036

Formulas:

1-

O (a^{2})

2-

O (a^{2})

3-

O (a^{2})

4-

δ_{ν, μ} D_{μ} (k) + (1 - δ_{ν, μ}) G_{ν, μ} (k)

5-

D_{μ} (k)

6-

1 - d_{1} \sum_{ν \neq μ} {\bar{s}}_{ν}^{2} + d_{2} \sum_{\binom{ν < ρ}{ν, ρ \neq μ}} {\bar{s}}_{ν}^{2} {\bar{s}}_{ρ}^{2}

7-

- d_{3} {\bar{s}}_{ν}^{2} {\bar{s}}_{ρ}^{2} {\bar{s}}_{σ}^{2} - d_{4} \sum_{ν \neq μ} {\bar{s}}_{ν}^{4},

8-

{\bar{s}}_{ν} = \sin (k_{ν} / 2)

9-

G_{ν, μ} (k)

10-

{\bar{s}}_{μ} {\bar{s}}_{ν} {\tilde{G}}_{ν, μ} (k)

Formulas (html):

Correct Categorie: hep-lat

Guessed Categorie: hep-lat

Result: correct

Paper: https://arxiv.org/abs/1804.06820

Formulas:

1-

J < J_{D A F} \approx 0.6 J_{D}

2-

J > J_{P A F} \approx 1.1 J_{D}

3-

H = J \sum_{⟨ i, j ⟩} 𝐒_{i} \cdot 𝐒_{j} + J_{D} \sum_{{⟨ i, j ⟩}_{D}} 𝐒_{i} \cdot 𝐒_{j},

4-

T = 1 / (2 L)

5-

J = 0.52337 (3)

6-

⟨ S_{i}^{z} S_{j}^{z} ⟩

7-

C_{∥} (r)

8-

C_{⟂} (r)

9-

C_{∥} (r)

10-

C_{∥} (r)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1409.7039

Formulas:

1-

{\hat{E}}^{(+)} (t, z) = \frac{i}{\sqrt{4 π A}} \int 𝑑 ω \sqrt{ω} \hat{a} (ω) e^{- i ω (t - z)},

2-

\hat{a} (ω)

3-

{\hat{a}}^{†} (ω)

4-

{\hat{E}}^{(-)} (t, z) = {\hat{E}}^{(+)} {(t, z)}^{†} .

5-

\hat{I} (t, z)

6-

\hat{I} (t, z) = 2 A {\hat{E}}^{(-)} (t, z) {\hat{E}}^{(+)} (t, z) .

7-

⟨ {\hat{a}}^{†} (ω) \hat{a} (ω^{'}) ⟩ = n (ω) δ (ω - ω^{'}),

8-

\bar{I} \equiv ⟨ \hat{I} (t, z) ⟩ = \int \frac{d ω}{2 π} ω n (ω),

9-

n (ω) = \sqrt{2 π} n_{0} e^{- {(ω - ω_{0})}^{2} τ^{2} / 2},

10-

τ = \frac{1}{δ ω} = \frac{1}{2 π δ ν},

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1507.01643

Formulas:

1-

Ω_{P} = Ω - κ / n

2-

Q = \frac{σ_{R} κ}{3.36 G Σ},

3-

X = \frac{k_{crit} R}{m} = \frac{κ^{2} R}{2 π G Σ m},

4-

k_{crit} = κ^{2} / (2 π G Σ)

5-

M_{*} = 1.9 \times 10^{10} M_{⊙}

6-

M_{*} = 9.5 \times 10^{9} M_{⊙}

7-

M_{*} [M_{⊙}]

8-

m [M_{⊙}]

9-

ϵ_{grav} [pc]

10-

ρ_{*} (R, z) = \frac{M_{*}}{4 π z_{0} R_{S}^{2}} {sech}^{2} (\frac{z}{z_{0}}) \exp (- \frac{R}{R_{S}}),

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Run 11329966 (Agent787)